Daily Papers

Recursive reasoning models can solve complex structured tasks with only a few million parameters by repeatedly updating a latent state. Deploying these models on edge hardware requires significant compression, but unlike conventional sequence models, quantization errors compound across recursive reasoning cycles rather than across output tokens. As a result, standard intuitions about compression fail to apply. In this work, we ask what survives when recursive reasoners are compressed. Across a full precision sweep, three tasks, and two recursive architectures, we find that aggressive compression preserves local prediction but destroys global reasoning: cell accuracy holds while puzzle-exact accuracy collapses to zero under naive INT4 pruning, distillation, and linear attention alike. Token-level objectives, including quantization-aware training, cannot repair it. The collapse is architectural -- it strikes MLP-mixing recursion but not attention on the same task -- and we reverse it with per-channel calibrated INT4 without retraining. We also introduce carry-trajectory fidelity, the cosine similarity to the full-precision reasoning path, as a label-free signal that predicts this damage and its recovery before a task evaluation. The combined result is a deployment recipe: flash-streamed embeddings remove a 99.4MB bottleneck, INT8 at one cycle matches full-depth accuracy at 6x fewer FLOPs (8MB SoC), and calibrated INT4 fits a 4MB microcontroller.

Reasoning and inference are central to human and artificial intelligence. Modeling inference in human language is very challenging. With the availability of large annotated data (Bowman et al., 2015), it has recently become feasible to train neural network based inference models, which have shown to be very effective. In this paper, we present a new state-of-the-art result, achieving the accuracy of 88.6% on the Stanford Natural Language Inference Dataset. Unlike the previous top models that use very complicated network architectures, we first demonstrate that carefully designing sequential inference models based on chain LSTMs can outperform all previous models. Based on this, we further show that by explicitly considering recursive architectures in both local inference modeling and inference composition, we achieve additional improvement. Particularly, incorporating syntactic parsing information contributes to our best result---it further improves the performance even when added to the already very strong model.

In this paper, we argue that looped Transformers need their own residual connections to prevent performance degradation as the number of iterations grows. We observe that increasing loop iterations can reduce reasoning accuracy: noisy state updates overwrite correct intermediate deductions and even undo completed solutions. This leaves subsequent iterations to recover lost information from an already degraded representation: once an error arises in an earlier loop, often as a result of long-range propagation through the recurrence, later loops find it difficult to correct. In this paper, we introduce InfiLoop, a loop-native residual connection that learns which past computations to retain and how much to accept from each new update. InfiLoop combines content-based weighting with learned temporal decay to maintain a running summary of recurrent states. An exact streaming recurrence keeps its persistent aggregation memory constant as the loop count grows. The resulting adaptive update suppresses unreliable proposals and preserves useful intermediate states. Across extensive reasoning tasks, a 7M-parameter InfiLoop model outperforms existing recursive architectures, reaching 97.9% exact accuracy on Sudoku-Extreme, and 13.6% pass@2 on ARC-AGI-2. Notably, on Sudoku-Extreme, InfiLoop continues to improve with test-time looping beyond 20,000 effective steps, showing that added depth translates directly into stronger reasoning. Our code is available at https://github.com/pixeli99/InfiLoop.

Recursive (looped) Transformers decouple computational depth from parameter depth by repeatedly applying shared layers, providing an explicit architectural primitive for iterative refinement and latent reasoning. However, early looped Transformers often underperform non-recursive baselines of equal compute. While recent literature has introduced more effective recursion mechanisms to mitigate this gap, existing architectures still operate at a fixed, full-token resolution, neglecting the potential efficiency of computing over compressed latent representations. In this paper, we propose SpiralFormer, a looped Transformer that executes recurrence under a multi-resolution recursion schedule. We provide probing evidence that multi-resolution recursion enables the model to learn hierarchical dependencies by inducing iteration-wise functional specialization across different scales. Empirically, SpiralFormer achieves better parameter and compute efficiency than both looped and non-looped baselines across model scales from 160M to 1.4B, establishing sequence resolution as a potential axis for scaling recursive architectures.

While differentiable logic gates have shown promise in feedforward networks, their application to sequential modeling remains unexplored. This paper presents the first implementation of Recurrent Deep Differentiable Logic Gate Networks (RDDLGN), combining Boolean operations with recurrent architectures for sequence-to-sequence learning. Evaluated on WMT'14 English-German translation, RDDLGN achieves 5.00 BLEU and 30.9\% accuracy during training, approaching GRU performance (5.41 BLEU) and graceful degradation (4.39 BLEU) during inference. This work establishes recurrent logic-based neural computation as viable, opening research directions for FPGA acceleration in sequential modeling and other recursive network architectures.

Recent advances in vision-language-action (VLA) and world-action models (WAMs) have significantly improved robotic manipulation, yet deploying robots in the open world demands a higher level of autonomy beyond executing predefined tasks. Robot agents offer a promising paradigm for this transition, integrating task discovery, contextual reasoning, physical execution, and adaptive recovery into a closed interaction loop. However, existing benchmarks largely evaluate isolated capabilities, failing to capture the complexity of open-world robot autonomy. We introduce RobotAgentBench (RAB), a comprehensive benchmark for evaluating robot agents in realistic, open-world household environments. Through an agent-assisted, human-in-the-loop real-to-sim pipeline, RAB constructs 50 diverse household layouts with interactive objects and physically grounded tasks, encompassing 90 atomic tasks, 18 short-horizon tasks, 8 long-horizon tasks, and 4 open-ended scenarios. RAB provides a multi-level evaluation of robot agent capabilities: (1) task-level assessments systematically examine five complementary dimensions: task discovery, context reasoning, manipulation, failure recovery, and robustness; (2) scenario-level evaluation assesses how agents integrate these capabilities to autonomously fulfill high-level user needs. Furthermore, RAB enables systematic comparisons of standalone VLA/WAM models and diverse robot agent architectures under a unified planning-execution-verification framework. Extensive experiments reveal substantial gaps between manipulation and autonomy, demonstrate the advantages of agentic architectures and recursive self-improvement, and highlight the remaining challenges toward open-world robot autonomy.

The rise of test-time scaling has remarkably boosted the reasoning and agentic proficiency of Large Language Models (LLMs). Yet, standard Transformers struggle to scale inference-time compute efficiently, as conventional looping strategies suffer from high computational overhead and a KV cache that inflates alongside model depth. We present Universal YOCO (YOCO-U), which combines the YOCO decoder-decoder architecture with recursive computation to achieve a synergistic effect greater than either alone. Built on the YOCO framework, YOCO-U implements a Universal Self-Decoder that performs multiple iterations via parameter sharing, while confining the iterative process to shallow, efficient-attention layers. This combination yields a favorable capability-efficiency tradeoff that neither YOCO nor recursion achieves independently. The YOCO architecture provides a constant global KV cache and linear pre-filling, while partial recursion enhances representational depth with limited overhead. Together, YOCO-U improves token utility and scaling behavior while maintaining efficient inference. Empirical results confirm that YOCO-U remains highly competitive in general and long-context benchmarks, demonstrating that the integration of efficient-attention architectures and recursive computation is a promising direction for scalable LLMs.

Transformer architectures have exhibited remarkable performance in image super-resolution (SR). Since the quadratic computational complexity of the self-attention (SA) in Transformer, existing methods tend to adopt SA in a local region to reduce overheads. However, the local design restricts the global context exploitation, which is crucial for accurate image reconstruction. In this work, we propose the Recursive Generalization Transformer (RGT) for image SR, which can capture global spatial information and is suitable for high-resolution images. Specifically, we propose the recursive-generalization self-attention (RG-SA). It recursively aggregates input features into representative feature maps, and then utilizes cross-attention to extract global information. Meanwhile, the channel dimensions of attention matrices (query, key, and value) are further scaled to mitigate the redundancy in the channel domain. Furthermore, we combine the RG-SA with local self-attention to enhance the exploitation of the global context, and propose the hybrid adaptive integration (HAI) for module integration. The HAI allows the direct and effective fusion between features at different levels (local or global). Extensive experiments demonstrate that our RGT outperforms recent state-of-the-art methods quantitatively and qualitatively. Code and pre-trained models are available at https://github.com/zhengchen1999/RGT.

Recursive models can continue updating their latent states beyond their nominal inference budget, so an incorrect output at that budget does not show whether computation is unfinished or has entered a persistently unsuccessful regime. We study the dynamics of completion in attention- and MLP-based Tiny Recursive Models (TRMs) on 1,000 hard Sudoku puzzles. Extending recurrence from the nominal 16 steps to 512 steps increases cumulative exact-solve accuracy from 59.2% to 87.5% for the attention model and from 74.4% to 91.9% for the MLP model, solving more than two-thirds of the puzzles unsolved in the nominal budget. Across both architectures, latent-state motion drops sharply after the first exact solution. Completed states are typically locally contractive along the trajectory direction, even though the same local Jacobian retains strongly expanding directions. We characterize this phenomenon as trajectory-conditioned anisotropic stability. Perturbation experiments confirm this directional stability across both models. The multi-step fate of the maximally expanding direction differs: it is absorbed within 16 steps in the attention model but persists longer in the MLP model. The anisotropic-stability pattern also holds for a second attention checkpoint. Together, these results distinguish nominal-budget failure from completed computation and identify a common dynamical signature of completion across two recurrent architectures.

While Transformer architectures have demonstrated impressive scalability across domains, they continue to face challenges in long-context reasoning, computational efficiency, and structural generalization - largely due to rigid layer stacking, dense attention, and reliance on positional encodings. We present ReSSFormer, a Recursive Sparse Structured Transformer that integrates three complementary innovations: Recurrent Reasoning & Memory Unit (R2MU) for iterative reasoning with bounded depth, Adaptive Sparse Attention Module (ASAM) for efficient and focused context selection, and Self-Organizing Encoder Structure (SOES) for position-free structure induction. ReSSFormer replaces conventional depth stacking with recurrent inference, substitutes full attention with token- and expert-level sparsity, and models latent token topology directly from content. Across language modeling, multi-hop QA, and structure-sensitive tasks, ReSSFormer consistently outperforms strong baselines under comparable FLOPs and parameter budgets, highlighting its scalability, efficiency, and structural flexibility.

Toward recursive self-improvement, we investigate LLM agents autonomously designing foundation models beyond standard Transformers. We introduce a dual-framework approach: AIRA-Compose for high-level architecture search, and AIRA-Design for low-level mechanistic implementation. AIRA-Compose uses 11 agents to explore fundamental computational primitives under a 24-hour budget. Agents evaluate million-parameter candidates, extrapolating top designs to 350M, 1B, and 3B scales. This yields 14 architectures across two families: AIRAformers (Transformer-based) and AIRAhybrids (Transformer-Mamba). Pre-trained at 1B scale, these consistently outperform Llama 3.2 and Composer-found baselines. On downstream tasks, AIRAformer-D and AIRAhybrid-D improve accuracy by 2.4% and 3.8% over Llama 3.2. Furthermore, AIRA-Compose finds models with highly efficient scaling frontiers: AIRAformer-C scales 54% and 71% faster than Llama 3.2 and Composer's best Transformer, while AIRAhybrid-C outscales Nemotron-2 by 23% and Composer's best hybrid by 37%. AIRA-Design tasks 20 agents with writing novel attention mechanisms for long-range dependencies and high-performing training scripts. On the Long Range Arena benchmark, agent-designed architectures reach within 2.3% and 2.6% of human state-of-the-art on document matching and text classification. On the Autoresearch benchmark, Greedy Opus 4.5 achieves 0.968 validation bits-per-byte under a fixed time budget, surpassing the published minimum. Together, these frameworks show AI agents can autonomously discover architectures and algorithmic optimizations matching or surpassing hand-designed baselines. This establishes a powerful paradigm for discovering next-generation foundation models, marking a clear step toward recursive self-improvement.

Current agentic frameworks underperform on long-horizon tasks. As reasoning depth increases, sequential orchestration becomes brittle, context windows impose hard limits that degrade performance, and opaque execution traces make failures difficult to localize or debug. We introduce ROMA (Recursive Open Meta-Agents), a domain-agnostic framework that addresses these limitations through recursive task decomposition and structured aggregation. ROMA decomposes goals into dependency-aware subtask trees that can be executed in parallel, while aggregation compresses and validates intermediate results to control context growth. Our framework standardizes agent construction around four modular roles --Atomizer (which decides whether a task should be decomposed), Planner, Executor, and Aggregator -- which cleanly separate orchestration from model selection and enable transparent, hierarchical execution traces. This design supports heterogeneous multi-agent systems that mix models and tools according to cost, latency, and capability. To adapt ROMA to specific tasks without fine-tuning, we further introduce GEPA+, an improved Genetic-Pareto prompt proposer that searches over prompts within ROMA's component hierarchy while preserving interface contracts. We show that ROMA, combined with GEPA+, delivers leading system-level performance on reasoning and long-form generation benchmarks. On SEAL-0, which evaluates reasoning over conflicting web evidence, ROMA instantiated with GLM-4.6 improves accuracy by 9.9\% over Kimi-Researcher. On EQ-Bench, a long-form writing benchmark, ROMA enables DeepSeek-V3 to match the performance of leading closed-source models such as Claude Sonnet 4.5. Our results demonstrate that recursive, modular agent architectures can scale reasoning depth while remaining interpretable, flexible, and model-agnostic.

Recurrent reasoning models have attracted growing attention for scaling test-time computation, typically by iteratively refining latent states with shared parameters. However, these models apply each learned update with a fixed unit scale, which can be conservative when updates make persistent progress and overly aggressive when they fluctuate, limiting the benefit of additional loops. To understand how the scale should vary along the trajectory, we first analyze the sensitivity of terminal loss to recurrent update scale. We show that its temporal average admits an exact decomposition into persistent-progress and centered-fluctuation contributions. Based on this, we introduce the Trajectory Adaptive Progress-Fluctuation Scheduler (TAPS), which tracks their balance across recurrent updates and adapts the step size online. Theoretically, we establish sufficient conditions under which TAPS reduces expected terminal loss and reaches a target quality in fewer recurrent loops. Empirically, we show that TAPS improves terminal accuracy across structured reasoning tasks without retraining. By further incorporating the progress-fluctuation principle into training, TAPS yields additional accuracy gains with up to 1.56 times wall-clock speedup at matched baseline accuracy. The broad applicability of TAPS is supported by its effectiveness across diverse recurrent architectures and inference strategies. Together, these results establish update scale as complementary control axis of recurrent inference alongside architecture and depth.

We present a neat yet effective recursive operation on vision transformers that can improve parameter utilization without involving additional parameters. This is achieved by sharing weights across the depth of transformer networks. The proposed method can obtain a substantial gain (~2%) simply using naive recursive operation, requires no special or sophisticated knowledge for designing principles of networks, and introduces minimal computational overhead to the training procedure. To reduce the additional computation caused by recursive operation while maintaining the superior accuracy, we propose an approximating method through multiple sliced group self-attentions across recursive layers which can reduce the cost consumption by 10~30% with minimal performance loss. We call our model Sliced Recursive Transformer (SReT), a novel and parameter-efficient vision transformer design that is compatible with a broad range of other designs for efficient ViT architectures. Our best model establishes significant improvement on ImageNet-1K over state-of-the-art methods while containing fewer parameters. The proposed weight sharing mechanism by sliced recursion structure allows us to build a transformer with more than 100 or even 1000 shared layers with ease while keeping a compact size (13~15M), to avoid optimization difficulties when the model is too large. The flexible scalability has shown great potential for scaling up models and constructing extremely deep vision transformers. Code is available at https://github.com/szq0214/SReT.

The integration of Large Language Models (LLMs) into the scientific ecosystem raises fundamental questions about the creativity and originality of AI-generated research. Recent work has identified ``smart plagiarism'' as a concern in single-step prompting approaches, where models reproduce existing ideas with terminological shifts. This paper investigates whether agentic workflows -- multi-step systems employing iterative reasoning, evolutionary search, and recursive decomposition -- can generate more novel and feasible research plans. We benchmark five reasoning architectures: Reflection-based iterative refinement, Sakana AI v2 evolutionary algorithms, Google Co-Scientist multi-agent framework, GPT Deep Research (GPT-5.1) recursive decomposition, and Gemini~3 Pro multimodal long-context pipeline. Using evaluations from thirty proposals each on novelty, feasibility, and impact, we find that decomposition-based and long-context workflows achieve mean novelty of 4.17/5, while reflection-based approaches score significantly lower (2.33/5). Results reveal varied performance across research domains, with high-performing workflows maintaining feasibility without sacrificing creativity. These findings support the view that carefully designed multi-stage agentic workflows can advance AI-assisted research ideation.

Clustering is a widely used unsupervised learning technique involving an intensive discrete optimization problem. Associative Memory models or AMs are differentiable neural networks defining a recursive dynamical system, which have been integrated with various deep learning architectures. We uncover a novel connection between the AM dynamics and the inherent discrete assignment necessary in clustering to propose a novel unconstrained continuous relaxation of the discrete clustering problem, enabling end-to-end differentiable clustering with AM, dubbed ClAM. Leveraging the pattern completion ability of AMs, we further develop a novel self-supervised clustering loss. Our evaluations on varied datasets demonstrate that ClAM benefits from the self-supervision, and significantly improves upon both the traditional Lloyd's k-means algorithm, and more recent continuous clustering relaxations (by upto 60% in terms of the Silhouette Coefficient).

We define an atomic generation fact f=(u,tau,omega,z;rho), recording the origin, realized transformation, concrete occurrence, generated result and relation role. Compiled into a Generation-Fact Graph (GFG), these facts provide an AI-native, compilable scientific fact substrate preserving generation histories. We establish a GFG-based recursive scientific process in which analysis, intervention, replay and validation form facts for later cycles. Using nanoGPT, we establish unified training-learning dynamics. Training is the evolution of a parameter-optimizer system with state and memory: each actual training action enters the receiving state and produces a finite-amplitude nonlinear functional response conditioned by that state and target-specific update geometry. Learning is the persistent reorganization of distributed functional support by these responses; capability formation, maintenance, decline or recovery becomes observable when target-specific states are evaluated against their readout boundaries. Three primary coordinates - target-boundary state, target-specific update geometry and parameter-Adam receiving state - yield a second-order predictor operating before post-update outputs are read. On held-out runs, it achieved 91.43% accuracy and 91.49% macro-averaged recall across four transitions. We further establish inference as a frozen projection of training-learning dynamics. Component gating and rollback show causal recruitment and non-additive combination of query-conditioned support formed during training, deriving organizational conditions realized by Attention. Controlled feedback indicates possible double-edged reinforcement effects. ResNet/CIFAR-100 and diffusion/CIFAR-10 experiments confirm receiving-state-conditioned responses, persistent support reorganization and frozen inference projection beyond nanoGPT.

Deep residual networks (ResNets) have demonstrated outstanding success in computer vision tasks, attributed to their ability to maintain gradient flow through deep architectures. Simultaneously, controlling the Lipschitz bound in neural networks has emerged as an essential area of research for enhancing adversarial robustness and network certifiability. This paper uses a rigorous approach to design L-Lipschitz deep residual networks using a Linear Matrix Inequality (LMI) framework. The ResNet architecture was reformulated as a pseudo-tri-diagonal LMI with off-diagonal elements and derived closed-form constraints on network parameters to ensure L-Lipschitz continuity. To address the lack of explicit eigenvalue computations for such matrix structures, the Gershgorin circle theorem was employed to approximate eigenvalue locations, guaranteeing the LMI's negative semi-definiteness. Our contributions include a provable parameterization methodology for constructing Lipschitz-constrained networks and a compositional framework for managing recursive systems within hierarchical architectures. These findings enable robust network designs applicable to adversarial robustness, certified training, and control systems. However, a limitation was identified in the Gershgorin-based approximations, which over-constrain the system, suppressing non-linear dynamics and diminishing the network's expressive capacity.

Recently, it was shown that small, looped architectures, such as Tiny Recursive Models (TRMs), can outperform Large Language Models (LLMs) on complex reasoning tasks, including the Abstraction and Reasoning Corpus (ARC). In this work, we investigate a core question: how can we further improve the efficiency of these methods with minimal changes? To address this, we frame the latent reasoning of TRMs as a form of classifier-free guidance and implicit policy improvement algorithm. Building on these insights, we propose a novel training scheme that provides a target for each loop during training. We demonstrate that our approach significantly enhances training efficiency. Our method reduces the total number of forward passes by 18x and eliminates halting mechanisms, while maintaining quality comparable to standard TRMs. Notably, we achieve 24% accuracy on ARC-1 with only 0.8M parameters, outperforming most LLMs.

Parameter sharing in recursive transformers reduces model size but collapses layer-wise expressivity. We propose Mixture of LoRAs (MoL), a lightweight conditional-computation mechanism that inserts Low-Rank Adaptation (LoRA) experts inside a shared feed-forward network (FFN). MoL enables token-conditional weight-space modulation of the shared FFN without untying backbone parameters, unlike prior approaches that add fixed or externally attached adapters. We pretrain a modernised recursive architecture, ModernALBERT, integrating rotary embeddings, GeGLU, FlashAttention, and a distillation-based initialisation. Across GLUE, SQuAD-v2, and BEIR, ModernALBERT (50M--120M) achieves state-of-the-art performance among compact models and surpasses larger fully parameterised baselines. We also propose an expert-merging procedure that compresses MoL into a single adapter at inference while preserving accuracy, enabling efficient deployment. Our results show that conditional weight-space modulation effectively restores the expressivity lost under aggressive parameter sharing in recursive transformers.

The autonomous synthesis of deep research reports represents a critical frontier for Large Language Models (LLMs), demanding sophisticated information orchestration and non-linear narrative logic. Current approaches rely on rigid predefined linear workflows, which cause error accumulation, preclude global restructuring from subsequent insights, and ultimately limit in-depth multimodal fusion and report quality. We propose CogGen, a Cognitively inspired recursive framework for deep research report Generation. Leveraging a Hierarchical Recursive Architecture to simulate cognitive writing, CogGen enables flexible planning and global restructuring. To extend this recursivity to multimodal content, we introduce Abstract Visual Representation (AVR): a concise intent-driven language that iteratively refines visual-text layouts without pixel-level regeneration overhead. We further present CLEF, a Cognitive Load Evaluation Framework, and curate a new benchmark from Our World in Data (OWID). Extensive experiments show CogGen achieves state-of-the-art results among open-source systems, generating reports comparable to professional analysts' outputs and surpassing Gemini Deep Research. Our code and dataset are available at https://github.com/NJUNLP/CogGen.

This article proposes to auto-encode text at byte-level using convolutional networks with a recursive architecture. The motivation is to explore whether it is possible to have scalable and homogeneous text generation at byte-level in a non-sequential fashion through the simple task of auto-encoding. We show that non-sequential text generation from a fixed-length representation is not only possible, but also achieved much better auto-encoding results than recurrent networks. The proposed model is a multi-stage deep convolutional encoder-decoder framework using residual connections, containing up to 160 parameterized layers. Each encoder or decoder contains a shared group of modules that consists of either pooling or upsampling layers, making the network recursive in terms of abstraction levels in representation. Results for 6 large-scale paragraph datasets are reported, in 3 languages including Arabic, Chinese and English. Analyses are conducted to study several properties of the proposed model.

The variational autoencoder (VAE) framework remains a popular option for training unsupervised generative models, especially for discrete data where generative adversarial networks (GANs) require workaround to create gradient for the generator. In our work modeling US postal addresses, we show that our discrete VAE with tree recursive architecture demonstrates limited capability of capturing field correlations within structured data, even after overcoming the challenge of posterior collapse with scheduled sampling and tuning of the KL-divergence weight beta. Worse, VAE seems to have difficulty mapping its generated samples to the latent space, as their VAE loss lags behind or even increases during the training process. Motivated by this observation, we show that augmenting training data with generated variants (augmented training) and training a VAE with multiple values of beta simultaneously (multiscale VAE) both improve the generation quality of VAE. Despite their differences in motivation and emphasis, we show that augmented training and multiscale VAE are actually connected and have similar effects on the model.

Recent advances in visual reasoning have leveraged vision transformers to tackle the ARC-AGI benchmark. However, we argue that the feed-forward architecture, where computational depth is strictly bound to parameter size, falls short of capturing the iterative, algorithmic nature of human induction. In this work, we propose a recursive architecture called Loop-ViT, which decouples reasoning depth from model capacity through weight-tied recurrence. Loop-ViT iterates a weight-tied Hybrid Block, combining local convolutions and global attention, to form a latent chain of thought. Crucially, we introduce a parameter-free Dynamic Exit mechanism based on predictive entropy: the model halts inference when its internal state ``crystallizes" into a low-uncertainty attractor. Empirical results on the ARC-AGI-1 benchmark validate this perspective: our 18M model achieves 65.8% accuracy, outperforming massive 73M-parameter ensembles. These findings demonstrate that adaptive iterative computation offers a far more efficient scaling axis for visual reasoning than simply increasing network width. The code is available at https://github.com/WenjieShu/LoopViT.

This paper investigates the ability of transformer-based models to learn structural recursion from examples. Recursion is a universal concept in both natural and formal languages. Structural recursion is central to the programming language and formal mathematics tasks where symbolic tools currently excel beyond neural models, such as inferring semantic relations between datatypes and emulating program behavior. We introduce a general framework that nicely connects the abstract concepts of structural recursion in the programming language domain to concrete sequence modeling problems and learned models' behavior. The framework includes a representation that captures the general syntax of structural recursion, coupled with two different frameworks for understanding their semantics -- one that is more natural from a programming languages perspective and one that helps bridge that perspective with a mechanistic understanding of the underlying transformer architecture. With our framework as a powerful conceptual tool, we identify different issues under various set-ups. The models trained to emulate recursive computations cannot fully capture the recursion yet instead fit short-cut algorithms and thus cannot solve certain edge cases that are under-represented in the training distribution. In addition, it is difficult for state-of-the-art large language models (LLMs) to mine recursive rules from in-context demonstrations. Meanwhile, these LLMs fail in interesting ways when emulating reduction (step-wise computation) of the recursive function.

Recursive AI, the prospect of AI taking an increasingly complete role in building and improving AI, is a crown jewel of AI for AI. Although recursive self-development has become practical for small models, bounded tasks, and fixed time budgets, a more consequential realization of this ambition, i.e., developing a release-ready, frontier-competitive model, remains far more challenging. In this work, we ask how little human involvement is sufficient for an agent to develop a frontier model. We concentrate human input into a high-density, low-frequency interface: experts encode objectives, stage scaffolds, permission boundaries, and operating procedures as reusable research skills, while the agent instantiates these priors, selects experiments, diagnoses outcomes, and revises the training strategy. In the challenging domain of industrial coding, the agent evolves data and coordinates SFT, on-policy self-distillation, and reinforcement learning with verifiable rewards, ultimately producing iCoder, a 27B model for RTL design and GPU kernel optimization. Across seven benchmarks, iCoder leads RTLLM, outperforming GPT-5.5 and Claude-Opus-4.8; ranks second on CVDP and KernelBench L2, exceeding GPT-5.5 by 16 points; and ties Claude-Opus-4.8 for the best TritonBench result. Exploratory case studies further show iCoder's competitive iterative RTL and GPU-kernel optimization with substantially fewer tokens. These results chart an engineering path toward recursive self-improvement, in which humans distill the principles of model building, agents operationalize them through evidence-driven experimentation, and each generation of AI becomes a more capable architect of the next.

Recursive or looped language models have recently emerged as a new scaling axis by iteratively refining the same model computation over latent states to deepen reasoning. We extend such scaling principle from a single model to multi-agent systems, and ask: Can agent collaboration itself be scaled through recursion? To this end, we introduce RecursiveMAS, a recursive multi-agent framework that casts the entire system as a unified latent-space recursive computation. RecursiveMAS connects heterogeneous agents as a collaboration loop through the lightweight RecursiveLink module, enabling in-distribution latent thoughts generation and cross-agent latent state transfer. To optimize our framework, we develop an inner-outer loop learning algorithm for iterative whole-system co-optimization through shared gradient-based credit assignment across recursion rounds. Theoretical analyses of runtime complexity and learning dynamics establish that RecursiveMAS is more efficient than standard text-based MAS and maintains stable gradients during recursive training. Empirically, we instantiate RecursiveMAS under 4 representative agent collaboration patterns and evaluate across 9 benchmarks spanning mathematics, science, medicine, search, and code generation. In comparison with advanced single/multi-agent and recursive computation baselines, RecursiveMAS consistently delivers an average accuracy improvement of 8.3%, together with 1.2times-2.4times end-to-end inference speedup, and 34.6%-75.6% token usage reduction. Code and Data are provided in https://recursivemas.github.io.

Recursive self-improvement (RSI) remains hard in long-horizon tasks, where growing histories obscure the task state and misalign skill invocation. We introduce Recuris, a recursive Experiential-Working Memory architecture for long-horizon agent harnesses, in which Working Memory tracks task progress and guides skill selection from Experiential Memory, grounding skill use in current needs rather than the full history. This coupling also turns execution into structured evidence that localizes failures to specific memory components. Across tasks, a fixed Meta-Agent turns that evidence into localized, validation-gated updates to Skill Memory that reshape execution and yield new evidence, forming a bounded recursive memory-evolution loop. Across four long-horizon benchmarks and ten models, Recuris improves task success in 35 of the 37 completed model-benchmark pairs, carrying frontier models to SOTA-level task success: on tau-bench it adds +17.8 points to GPT-5.6 Sol and +15.6 to Claude Opus 5, taking Opus 5 to 87.9%, and +16.6/+13.5 points on Qwen3.6-27B/35B on SkillFlow. The advantage widens as the interaction horizon grows, to +32.2 points on the longest tasks, and common long-horizon failures fall by up to 80%. These results position recursively evolving memory as a scalable foundation for RSI, enabling agents to continuously transform accumulated experience into increasingly effective long-horizon behavior. Code: https://github.com/Gen-Verse/Recuris

Large Multimodal Models (LMMs) have achieved remarkable success in vision-language tasks, yet their vast parameter counts are often underutilized during both training and inference. In this work, we embrace the idea of looping back to move forward: reusing model parameters through recursive refinement to extract stronger multimodal representations without increasing model size. We propose RecursiveVLM, a recursive Transformer architecture tailored for LMMs. Two key innovations enable effective looping: (i) a Recursive Connector that aligns features across recursion steps by fusing intermediate-layer hidden states and applying modality-specific projections, respecting the distinct statistical structures of vision and language tokens; (ii) a Monotonic Recursion Loss that supervises every step and guarantees performance improves monotonically with recursion depth. This design transforms recursion into an on-demand refinement mechanism: delivering strong results with few loops on resource-constrained devices and progressively improving outputs when more computation resources are available. Experiments show consistent gains of +3% over standard Transformers and +7% over vanilla recursive baselines, demonstrating that strategic looping is a powerful path toward efficient, deployment-adaptive LMMs.

We propose Beam Tree Recursive Cell (BT-Cell) - a backpropagation-friendly framework to extend Recursive Neural Networks (RvNNs) with beam search for latent structure induction. We further extend this framework by proposing a relaxation of the hard top-k operators in beam search for better propagation of gradient signals. We evaluate our proposed models in different out-of-distribution splits in both synthetic and realistic data. Our experiments show that BTCell achieves near-perfect performance on several challenging structure-sensitive synthetic tasks like ListOps and logical inference while maintaining comparable performance in realistic data against other RvNN-based models. Additionally, we identify a previously unknown failure case for neural models in generalization to unseen number of arguments in ListOps. The code is available at: https://github.com/JRC1995/BeamTreeRecursiveCells.

Background: Recursive reasoning models achieve strong performance through iterative refinement, allowing small networks to match large language models. However, training is computationally expensive, often requiring 36 GPU-hours for Sudoku extreme. Existing models use fixed recursion depth and uniform supervision weighting, leading to inefficient training. Objectives: We propose CGAR (Curriculum-Guided Adaptive Recursion), applying curriculum learning to architectural depth. CGAR introduces Progressive Depth Curriculum (PDC) to dynamically adjust recursion depth and Hierarchical Supervision Weighting (HSW) to apply exponentially decaying importance to supervision steps. Methods: PDC implements a three-stage schedule transitioning from shallow (2, 1) to full depth (6, 3) configurations, providing 41.4% FLOPs reduction. HSW applies exponential decay to supervision steps, achieving 40% gradient variance reduction and accelerated convergence. Results: On Sudoku-Extreme, CGAR achieves 1.71x training speedup (10.93 to 6.38 hours) with only a 0.63% accuracy drop (86.65% to 86.02%). PDC alone achieves 2.26x speedup with 85.47% accuracy, showing a Pareto improvement in efficiency and quality. HSW provides 1.61x speedup. CGAR-trained models show superior inference efficiency with 100% halting accuracy and 11% fewer reasoning steps. Conclusions: CGAR enables efficient training of recursive models on modest hardware. By treating depth as a scheduled parameter, it achieves substantial savings and prevents overfitting, making these models practical for neurosymbolic AI and program synthesis. https://github.com/Kaleemullahqasim/CGAR and huggingface.co/Kaleemullah/trm-cgar-sudoku.

Despite being the cornerstone of deep learning, backpropagation is criticized for its inherent sequentiality, which can limit the scalability of very deep models. Such models faced convergence issues due to vanishing gradient, later resolved using residual connections. Variants of these are now widely used in modern architecture. However, the computational cost of backpropagation remains a major burden, accounting for most of the training time. Taking advantage of residual-like architectural designs, we introduce Highway backpropagation, a parallelizable iterative algorithm that approximates backpropagation, by alternatively i) accumulating the gradient estimates along the residual path, and ii) backpropagating them through every layer in parallel. This algorithm is naturally derived from a decomposition of the gradient as the sum of gradients flowing through all paths and is adaptable to a diverse set of common architectures, ranging from ResNets and Transformers to recurrent neural networks. Through an extensive empirical study on a large selection of tasks and models, we evaluate Highway-BP and show that major speedups can be achieved with minimal performance degradation.

Modern language models reason within bounded context, an inherent constraint that poses a fundamental barrier to long-horizon reasoning. We identify recursion as a core principle for overcoming this barrier, and propose recursive models as a minimal realization, where the model can recursively invoke itself to solve subtasks in isolated contexts. We prove that any computable problem admits a recursive decomposition in which each subtask requires only exponentially smaller active context than standard autoregressive models; this strictly surpasses any context management approach confined to a single sequence, such as summarization. We further generalize our framework to modern agentic systems with arbitrary context processing and control flows, and prove that recursive models can achieve optimal power within this broader class. Experimentally, we train a 3B model to reason recursively and evaluate on Boolean satisfiability, a task requiring long-horizon combinatorial search, where it significantly outperforms frontier LLMs.

Tiny Recursive Models (TRM) were proposed as a parameter-efficient alternative to large language models for solving Abstraction and Reasoning Corpus (ARC) style tasks. The original work reports strong performance and suggests that recursive latent updates enable non-trivial reasoning, but it remains unclear how much of this performance stems from architecture, test-time compute, or task-specific priors. In this technical note, we empirically analyze the ARC Prize TRM checkpoint on ARC-AGI-1 and report four behavioral findings and an efficiency comparison. First, we show that test-time augmentation and majority-vote ensembling account for a substantial fraction of reported performance: the 1000-sample voting pipeline improves Pass@1 by about 11 percentage points over single-pass canonical inference. Second, a puzzle-identity ablation reveals strict dependence on task identifiers: replacing the correct puzzle ID with a blank or random token yields zero accuracy. Third, a recursion trajectory analysis shows that most of the final accuracy is achieved at the first recursion step and that performance saturates after few latent updates, indicating shallow effective recursion. Fourth, early-stage training experiments under canonical versus heavy augmentation regimes suggest that heavy augmentation broadens the distribution of candidate solutions and improves multi-sample success. Finally, we compare TRM with a naive QLoRA fine-tune of Llama 3 8B on canonical ARC-AGI-1, finding that TRM's non-autoregressive design achieves much higher throughput and substantially lower memory usage in this setting. Overall, TRM's ARC-AGI-1 performance appears to arise from an interaction between efficiency, task-specific conditioning, and aggressive test-time compute rather than deep internal reasoning.

Looped architectures provide an inductive bias toward learning step-by-step procedures for tasks that require compositional reasoning. The number of effective layers reached by looping determines the quality of the solution these models find. Like deep architectures, looped architectures are prone to a signal propagation problem induced by depth as the halting decision is postponed. In this paper, we address this signal propagation issue using pre-norm layers and residual scaling. Building on these architectural modifications, we propose FPRM, a Transformer-based Fixed-Point Reasoning Model that uses fixed-point convergence as an end-to-end halting mechanism in a looped architecture. We show that fixed-point halting allows FPRM to adapt its compute to task difficulty. FPRM is effective on common reasoning benchmarks, namely Sudoku, Maze, state-tracking, and ARC-AGI.

In this work, we focus on a lightweight convolutional architecture that creates fixed-size vector embeddings of sentences. Such representations are useful for building NLP systems, including conversational agents. Our work derives from a recently proposed recursive convolutional architecture for auto-encoding text paragraphs at byte level. We propose alternations that significantly reduce training time, the number of parameters, and improve auto-encoding accuracy. Finally, we evaluate the representations created by our model on tasks from SentEval benchmark suite, and show that it can serve as a better, yet fairly low-resource alternative to popular bag-of-words embeddings.

We introduce the Autoregressive Block-Based Iterative Encoder (AbbIE), a novel recursive generalization of the encoder-only Transformer architecture, which achieves better perplexity than a standard Transformer and allows for the dynamic scaling of compute resources at test time. This simple, recursive approach is a complement to scaling large language model (LLM) performance through parameter and token counts. AbbIE performs its iterations in latent space, but unlike latent reasoning models, does not require a specialized dataset or training protocol. We show that AbbIE upward generalizes (ability to generalize to arbitrary iteration lengths) at test time by only using 2 iterations during train time, far outperforming alternative iterative methods. AbbIE's ability to scale its computational expenditure based on the complexity of the task gives it an up to 12\% improvement in zero-shot in-context learning tasks versus other iterative and standard methods and up to 5\% improvement in language perplexity. The results from this study open a new avenue to Transformer performance scaling. We perform all of our evaluations on model sizes up to 350M parameters.

Scaling language models unlocks impressive capabilities, but the accompanying computational and memory demands make both training and deployment expensive. Existing efficiency efforts typically target either parameter sharing or adaptive computation, leaving open the question of how to attain both simultaneously. We introduce Mixture-of-Recursions (MoR), a unified framework that combines the two axes of efficiency inside a single Recursive Transformer. MoR reuses a shared stack of layers across recursion steps to achieve parameter efficiency, while lightweight routers enable adaptive token-level thinking by dynamically assigning different recursion depths to individual tokens. This allows MoR to focus quadratic attention computation only among tokens still active at a given recursion depth, further improving memory access efficiency by selectively caching only their key-value pairs. Beyond these core mechanisms, we also propose a KV sharing variant that reuses KV pairs from the first recursion, specifically designed to decrease prefill latency and memory footprint. Across model scales ranging from 135M to 1.7B parameters, MoR forms a new Pareto frontier: at equal training FLOPs and smaller model sizes, it significantly lowers validation perplexity and improves few-shot accuracy, while delivering higher throughput compared with vanilla and existing recursive baselines. These gains demonstrate that MoR is an effective path towards large-model quality without incurring large-model cost.

Despite the remarkable progress of Video Large Language Models (Video-LLMs), current online architectures still struggle to simultaneously process continuous video streams, decide autonomously when to respond, and preserve long-horizon contextual memory. These obstacles undermine real-time responsiveness and cause severe forgetting throughout prolonged interactions. In this work, we introduce LiveStarPro, a live streaming assistant that is designed for proactive video understanding over long-horizon streams. The design of LiveStarPro rests on three complementary components. The first component is Streaming Verification Decoding (SVeD), an inference framework that identifies the appropriate response timing through single-pass perplexity verification, thereby eliminating the dependency on explicit silence tokens. The second component is Streaming Causal Attention Masks (SCAM), a training strategy that enforces incremental video-language alignment over variable-length streams. The third component is Tree-Structured Hierarchical Memory (TSHM), a recursive memory architecture that organizes evicted historical information into event chains and consequently enables efficient retrieval from effectively unbounded video streams. To facilitate a comprehensive evaluation under realistic online conditions, we further present OmniStarPro, a large-scale benchmark that spans 15 diverse real-world scenarios and that extends to hour-scale streams for the assessment of long-term recall. Extensive experiments demonstrate that LiveStarPro consistently surpasses existing methods, attaining a 28.9% improvement in semantic correctness and an 18.2% reduction in timing error, while its streaming key-value cache further yields a 1.58x inference speedup over the same model without caching. The model and the code are publicly available at https://github.com/sotayang/LiveStarPro.

An agent can improve its behavior within an unresolved problem by changing how it acts and which experience it retains. We propose MMLA-RSI, a recursive self-improvement scheme with two implementations in Memory-Mediated Learning Architecture: Reasoning-Time Training (RTT) changes the policy state Φ, while Reasoning-Time Memory Adaptation (RTMA) changes authoritative memory M. Each route also makes its adaptation method an object of improvement. A current numerical updater trains the policy proposing its successor; a current memory manager chooses the records available to the process proposing its successor. An independently admitted successor takes over the same role in the next generation. We give bounded executable rule languages, shared task/proposal interfaces, and one algorithm for either route or their composition. The RTT instance changes scalar schedules in a clipped-momentum update. The RTMA instance chooses NULL or a complete-row write with possible eviction. A fixed interpreter, trusted committer, and independent evaluator bound what can change. State versions, read closures, and conditional properties describe causal execution, accepted transitions, and finite work. Existing numerical-component studies motivate the construction. In four-candidate program selection, retaining LARC feedback updates reduces expected error by 24.65 and 36.65 percentage points for two trained initializations. In chronological continuous-integration replay, feedback binding is positive while retention increases loss. Completed SQL studies improve substantially over an unadapted substrate but do not establish the required additional online benefit. These results characterize their declared components. The two recursive routes and their joint realization are specified here; their beneficial recursive chains and discovery efficiency remain to be evaluated.

This paper addresses the scalability challenge of architecture search by formulating the task in a differentiable manner. Unlike conventional approaches of applying evolution or reinforcement learning over a discrete and non-differentiable search space, our method is based on the continuous relaxation of the architecture representation, allowing efficient search of the architecture using gradient descent. Extensive experiments on CIFAR-10, ImageNet, Penn Treebank and WikiText-2 show that our algorithm excels in discovering high-performance convolutional architectures for image classification and recurrent architectures for language modeling, while being orders of magnitude faster than state-of-the-art non-differentiable techniques. Our implementation has been made publicly available to facilitate further research on efficient architecture search algorithms.

Scaling laws predict how loss decreases with increases in computation. We show, contrary to conventional wisdom, that architectural interventions can modify scaling exponents in pre-training, leading to power-law improvements in performance as computation increases. As an anchoring point, we consider the architectural formulation of looped transformers. Although not typically used in this way, looping, also known as recursive depth, provides a mechanism for model growth, by increasing the number of loops during training. Model growth, with and without shared weights, provides the biggest changes to the scaling exponents. In particular, a 7.4B model growth architecture matches GPT-3 13B on CORE with roughly 20times less compute, and has compute efficiency gains that increase with scale. Moreover, simply using a boundary operator in a vanilla transformer, which normalizes and injects an earlier block, also provides an exponent increase, although to a lesser extent. In the data-constrained, multi-epoch setting, standard looping has a useful regularizing effect, where we find it is compute-optimal to increase the number of loops with scale. These results can be understood through the lens of computational depth: for a given computational budget, we wish to increase the usable depth of the transformer, which can lead to efficiency gains that increase with scale.

The multi-modal nature of many vision problems calls for neural network architectures that can perform multiple tasks concurrently. Typically, such architectures have been handcrafted in the literature. However, given the size and complexity of the problem, this manual architecture exploration likely exceeds human design abilities. In this paper, we propose a principled approach, rooted in differentiable neural architecture search, to automatically define branching (tree-like) structures in the encoding stage of a multi-task neural network. To allow flexibility within resource-constrained environments, we introduce a proxyless, resource-aware loss that dynamically controls the model size. Evaluations across a variety of dense prediction tasks show that our approach consistently finds high-performing branching structures within limited resource budgets.

Transformers have become the dominant architecture for sequence modeling by using self-attention to enable expressive and highly parallel processing. However, the resulting quadratic time and memory costs limit efficiency in long-context settings. Recurrent models such as LSTMs provide explicit nonlinear state updates and strong state-tracking capabilities, yet their strictly sequential computation limits parallelism. We introduce the Parallel Recursive LSTM (PR-LSTM), a hierarchical recurrent architecture that replaces left-to-right recurrence with recursive nonlinear state composition over a balanced computation tree. Tokens are first mapped independently to latent states, which are then recursively merged by a learned gated composition block. This structure uses the reduction pattern underlying parallel scans as a fixed execution schedule, rather than assuming an associative recurrence. As a result, PR-LSTM retains nonlinear gated state representations while reducing recurrent parallel depth from linear to logarithmic. Empirically, PR-LSTM achieves strong sequence-length generalization on formal-language benchmarks, solving more tasks than standard RNN, LSTM, and Transformer baselines, while avoiding the quadratic scaling of attention. These results suggest that recurrent computation can be reorganized hierarchically to expose parallelism without restricting the transition dynamics to linear or associative forms.

The modern deep learning field is a scale-centric one. Larger models have been shown to consistently perform better than smaller models of similar architecture. In many sub-domains of biomedical research, however, the model scaling is bottlenecked by the amount of available training data, and the high cost associated with generating and validating additional high quality data. Despite the practical hurdle, the majority of the ongoing research still focuses on building bigger foundation models, whereas the alternative of improving the ability of small models has been under-explored. Here we experiment with building models with 10-30M parameters, tiny by modern standards, to perform the single-cell segmentation task. An important design choice is the incorporation of a recursive structure into the model's forward computation graph, leading to a more parameter-efficient architecture. We found that for the single-cell segmentation, on multiple benchmarks, our small model, UCell, matches the performance of models 10-20 times its size, and with a similar generalizability to unseen out-of-domain data. More importantly, we found that ucell can be trained from scratch using only a set of microscopy imaging data, without relying on massive pretraining on natural images, and therefore decouples the model building from any external commercial interests. Finally, we examined and confirmed the adaptability of ucell by performing a wide range of one-shot and few-shot fine tuning experiments on a diverse set of small datasets. Implementation is available at https://github.com/jiyuuchc/ucell

The chain-structured long short-term memory (LSTM) has showed to be effective in a wide range of problems such as speech recognition and machine translation. In this paper, we propose to extend it to tree structures, in which a memory cell can reflect the history memories of multiple child cells or multiple descendant cells in a recursive process. We call the model S-LSTM, which provides a principled way of considering long-distance interaction over hierarchies, e.g., language or image parse structures. We leverage the models for semantic composition to understand the meaning of text, a fundamental problem in natural language understanding, and show that it outperforms a state-of-the-art recursive model by replacing its composition layers with the S-LSTM memory blocks. We also show that utilizing the given structures is helpful in achieving a performance better than that without considering the structures.

Neural Architecture Search (NAS) aims to automatically discover high-performing deep neural network (DNN) architectures. However, conventional algorithm-driven NAS relies on carefully hand-crafted search spaces to ensure executability, which restricts open-ended exploration. Recent coding-based agentic approaches using large language models (LLMs) reduce manual design, but current LLMs struggle to reliably generate complex, valid architectures, and their proposals are often biased toward a narrow set of patterns observed in their training data. To bridge reliable algorithmic search with powerful LLM assistance, we propose LLMasTool, a hierarchical tree-based NAS framework for stable and open-ended model evolution. Our method automatically extracts reusable modules from arbitrary source code and represents full architectures as hierarchical trees, enabling evolution through reliable tree transformations rather than code generation. At each evolution step, coarse-level planning is governed by a diversity-guided algorithm that leverages Bayesian modeling to improve exploration efficiency, while the LLM resolves the remaining degrees of freedom to ensure a meaningful evolutionary trajectory and an executable generated architecture. With this formulation, instead of fully agentic LLM approaches, our method explores diverse directions beyond the inherent biases in the LLM. Our method improves over existing NAS methods by 0.69, 1.83, and 2.68 points on CIFAR-10, CIFAR-100, and ImageNet16-120, demonstrating its effectiveness.

Dominant programming paradigms inherit an execution model optimised for a bygone era of a single human mind instructing a local machine, leaving contemporary systems burdened with historical path dependencies. When forced to host multi-dimensional, connectionist intelligence, this brittle assembly model fractures under the weight of a profound probabilistic-symbolic impedance mismatch. While contemporary Software 3.x frameworks attempt to patch the mismatch by encasing large language models (LLMs) in increasingly complicated external harnesses, this spiralling architectural complexity only compounds the carrying cost of static code assembly. To address the cause rather than the effects, this paper introduces Software 4.0 -- an autopoietic heterarchy of human intelligence, neural AI, and natively reflective symbolic substrate. Under this paradigm, software is transformed from an inert corpus to be parsed into a self-regulating metabolic network that natively verifies, modifies, and evolves its own structural integrity. We present Recognitive, the programming language and platform that materialises this architecture. By offloading the burden of structural verification to a deterministic substrate, it unlocks a superior inference-time scaling regime -- one where connectionist compute translates entirely into deep semantic exploration and hypothesis traversal rather than the ruinous computational and financial cost of simulating structural constraints probabilistically. Moving beyond the legacy 'Software Factory' mindset, we outline the theoretical foundations required to ground connectionist intent and arrive fully in the intelligence age. This is a foundational vision paper; empirical evaluation and formal specification of the type system and operational semantics are the subject of future work.

Real-world tasks require decisions at varying granularities, and humans excel at this by leveraging a unified cognitive representation where planning is fundamentally understood as a high-level form of action. However, current Large Language Model (LLM)-based agents lack this crucial capability to operate fluidly across decision granularities. This limitation stems from existing paradigms that enforce a rigid separation between high-level planning and low-level action, which impairs dynamic adaptability and limits generalization. We propose ReCode (Recursive Code Generation), a novel paradigm that addresses this limitation by unifying planning and action within a single code representation. In this representation, ReCode treats high-level plans as abstract placeholder functions, which the agent then recursively decomposes into finer-grained sub-functions until reaching primitive actions. This recursive approach dissolves the rigid boundary between plan and action, enabling the agent to dynamically control its decision granularity. Furthermore, the recursive structure inherently generates rich, multi-granularity training data, enabling models to learn hierarchical decision-making processes. Extensive experiments show ReCode significantly surpasses advanced baselines in inference performance and demonstrates exceptional data efficiency in training, validating our core insight that unifying planning and action through recursive code generation is a powerful and effective approach to achieving universal granularity control. The code is available at https://github.com/FoundationAgents/ReCode.

Deep feedforward and recurrent networks have achieved impressive results in many perception and language processing applications. This success is partially attributed to architectural innovations such as convolutional and long short-term memory networks. The main motivation for these architectural innovations is that they capture better domain knowledge, and importantly are easier to optimize than more basic architectures. Recently, more complex architectures such as Neural Turing Machines and Memory Networks have been proposed for tasks including question answering and general computation, creating a new set of optimization challenges. In this paper, we discuss a low-overhead and easy-to-implement technique of adding gradient noise which we find to be surprisingly effective when training these very deep architectures. The technique not only helps to avoid overfitting, but also can result in lower training loss. This method alone allows a fully-connected 20-layer deep network to be trained with standard gradient descent, even starting from a poor initialization. We see consistent improvements for many complex models, including a 72% relative reduction in error rate over a carefully-tuned baseline on a challenging question-answering task, and a doubling of the number of accurate binary multiplication models learned across 7,000 random restarts. We encourage further application of this technique to additional complex modern architectures.

Modeling the distribution of natural images is a landmark problem in unsupervised learning. This task requires an image model that is at once expressive, tractable and scalable. We present a deep neural network that sequentially predicts the pixels in an image along the two spatial dimensions. Our method models the discrete probability of the raw pixel values and encodes the complete set of dependencies in the image. Architectural novelties include fast two-dimensional recurrent layers and an effective use of residual connections in deep recurrent networks. We achieve log-likelihood scores on natural images that are considerably better than the previous state of the art. Our main results also provide benchmarks on the diverse ImageNet dataset. Samples generated from the model appear crisp, varied and globally coherent.

This paper proposes bimorphic recursion, which is restricted polymorphic recursion such that every recursive call in the body of a function definition has the same type. Bimorphic recursion allows us to assign two different types to a recursively defined function: one is for its recursive calls and the other is for its calls outside its definition. Bimorphic recursion in this paper can be nested. This paper shows bimorphic recursion has principal types and decidable type inference. Hence bimorphic recursion gives us flexible typing for recursion with decidable type inference. This paper also shows that its typability becomes undecidable because of nesting of recursions when one removes the instantiation property from the bimorphic recursion.

Looped Transformers apply the same layers several times per token, adding compute to improve quality without more parameters. Each recursion, however, writes its own key-value cache, so memory still grows with compute. Inference-time techniques can shrink this cache at a cost in quality. We pretrain looped language models to share memory: only the first recursion writes a cache, and later recursions read it while keeping a short window of their own. Surprisingly, we find that sharing memory does not cost quality and instead improves it. At 150M-1B parameters, our Looped Prediction Transformer (LPT) and its hybrid variant set a new quality-memory frontier for looped models: with five recursions, the hybrid lowers validation perplexity on FineWeb-Edu by 1.12-1.82 relative to a same-size standard Transformer while using 76-79% less context memory. Through an extensive analysis, we investigate why memory sharing helps. Shared and local memory develop different representations, and later recursions attend mostly to the shared memory, which also acts as a gradient highway to the first recursion.

We introduce a new function-preserving transformation for efficient neural architecture search. This network transformation allows reusing previously trained networks and existing successful architectures that improves sample efficiency. We aim to address the limitation of current network transformation operations that can only perform layer-level architecture modifications, such as adding (pruning) filters or inserting (removing) a layer, which fails to change the topology of connection paths. Our proposed path-level transformation operations enable the meta-controller to modify the path topology of the given network while keeping the merits of reusing weights, and thus allow efficiently designing effective structures with complex path topologies like Inception models. We further propose a bidirectional tree-structured reinforcement learning meta-controller to explore a simple yet highly expressive tree-structured architecture space that can be viewed as a generalization of multi-branch architectures. We experimented on the image classification datasets with limited computational resources (about 200 GPU-hours), where we observed improved parameter efficiency and better test results (97.70% test accuracy on CIFAR-10 with 14.3M parameters and 74.6% top-1 accuracy on ImageNet in the mobile setting), demonstrating the effectiveness and transferability of our designed architectures.

Important tasks such as reasoning and planning are fundamentally algorithmic, meaning that solving them robustly requires acquiring true reasoning or planning algorithms, rather than shortcuts. Large Language Models lack true algorithmic ability primarily because of the limitations of neural network optimization algorithms, their optimization data and optimization objective, but also due to architectural inexpressivity. To solve this, our paper proposes augmenting LLMs with a library of fundamental operations and sophisticated differentiable programs, so that common algorithms do not need to be learned from scratch. We add memory, registers, basic operations, and adaptive recurrence to a transformer architecture built on LLaMA3. Then, we define a method for directly compiling algorithms into a differentiable starting library, which is used natively and propagates gradients for optimization. In this preliminary study, we explore the feasability of augmenting LLaMA3 with a differentiable computer, for instance by fine-tuning small transformers on simple algorithmic tasks with variable computational depth.

Automated neural network architecture design remains a significant challenge in computer vision. Task diversity and computational constraints require both effective architectures and efficient search methods. Large Language Models (LLMs) present a promising alternative to computationally intensive Neural Architecture Search (NAS), but their application to architecture generation in computer vision has not been systematically studied, particularly regarding prompt engineering and validation strategies. Building on the task-agnostic NNGPT/LEMUR framework, this work introduces and validates two key contributions for computer vision. First, we present Few-Shot Architecture Prompting (FSAP), the first systematic study of the number of supporting examples (n = 1, 2, 3, 4, 5, 6) for LLM-based architecture generation. We find that using n = 3 examples best balances architectural diversity and context focus for vision tasks. Second, we introduce Whitespace-Normalized Hash Validation, a lightweight deduplication method (less than 1 ms) that provides a 100x speedup over AST parsing and prevents redundant training of duplicate computer vision architectures. In large-scale experiments across seven computer vision benchmarks (MNIST, CIFAR-10, CIFAR-100, CelebA, ImageNette, SVHN, Places365), we generated 1,900 unique architectures. We also introduce a dataset-balanced evaluation methodology to address the challenge of comparing architectures across heterogeneous vision tasks. These contributions provide actionable guidelines for LLM-based architecture search in computer vision and establish rigorous evaluation practices, making automated design more accessible to researchers with limited computational resources.

Latent recursion repeatedly processes internal representations through the same neural network. Recent work has shown this approach to be effective on structured reasoning tasks such as Sudoku and maze solving. However, whether latent recursion can support neural routing remains unclear. We introduce RELAGRAM (Recursive Latent Graph Model), a novel approach that brings latent recursion to graph combinatorial optimization. RELAGRAM encodes a capacitated vehicle routing problem (CVRP) instance as edge tokens; a compact transformer recurrently updates the latent representations of these tokens. An output head maps the answer state to an edge heatmap, from which an autoregressive decoder constructs a feasible solution. On CVRP-100 instances, the 0.53M-parameter RELAGRAM achieves gaps to a PyVRP reference of 13.4%, 9.8%, and 8.3% under greedy decoding, eightfold symmetry augmentation, and 256-candidate search, respectively. Trained only on CVRP-100, RELAGRAM generalizes zero-shot to CVRP-500 and CVRP-1000, achieving gaps of 15.6% and 21.7% under 256-candidate search. Together, these results demonstrate that latent recursion is a promising approach to neural routing.

Token mixing layers play a key role in how language models can learn and generate long-range dependencies. Their efficiency relies on the necessary trade-off between decoding speed and the memory requirements, along with the cache size. Considering causal generation, this paper explores new trade-offs thanks to a unified framework which separates two crucial features: (i) the direct influence of inputs on outputs in one generation step; (ii) the recurrent propagation of information through past outputs. This framework encompasses major architectures such as attention and state-space models, but also generalizes the recurrence equations by allowing each state to depend on multiple past states rather than only the immediate predecessor. By introducing structure, we design new recurrence patterns that provably achieve the desired complexity, while providing theoretical insights on their expressivity -- trading runtime for expressivity in a principled way. Empirical validation is performed on synthetic tasks, along with language modeling. Together, these results provide a unified toolkit for the understanding and design of efficient and expressive token mixers across model families.

Machine learning is a prevalent approach to tame the complexity of design space exploration for domain-specific architectures. Using ML for design space exploration poses challenges. First, it's not straightforward to identify the suitable algorithm from an increasing pool of ML methods. Second, assessing the trade-offs between performance and sample efficiency across these methods is inconclusive. Finally, lack of a holistic framework for fair, reproducible, and objective comparison across these methods hinders progress of adopting ML-aided architecture design space exploration and impedes creating repeatable artifacts. To mitigate these challenges, we introduce ArchGym, an open-source gym and easy-to-extend framework that connects diverse search algorithms to architecture simulators. To demonstrate utility, we evaluate ArchGym across multiple vanilla and domain-specific search algorithms in designing custom memory controller, deep neural network accelerators, and custom SoC for AR/VR workloads, encompassing over 21K experiments. Results suggest that with unlimited samples, ML algorithms are equally favorable to meet user-defined target specification if hyperparameters are tuned; no solution is necessarily better than another (e.g., reinforcement learning vs. Bayesian methods). We coin the term hyperparameter lottery to describe the chance for a search algorithm to find an optimal design provided meticulously selected hyperparameters. The ease of data collection and aggregation in ArchGym facilitates research in ML-aided architecture design space exploration. As a case study, we show this advantage by developing a proxy cost model with an RMSE of 0.61% that offers a 2,000-fold reduction in simulation time. Code and data for ArchGym is available at https://bit.ly/ArchGym.

In recent years, attention-like mechanisms have been used to great success in the space of large language models, unlocking scaling potential to a previously unthinkable extent. "Attention Is All You Need" famously claims RNN cells are not needed in conjunction with attention. We challenge this view. In this paper, we point to existing proofs that architectures with fully parallelizable forward or backward passes cannot represent classes of problems specifically interesting for long-running agentic tasks. We further conjecture a critical time t beyond which non-recurrence-complete models fail to aggregate inputs correctly, with concrete implications for agentic systems (e.g., software engineering agents). To address this, we introduce a recurrence-complete architecture and train it on GitHub-derived action sequences. Loss follows a power law in the trained sequence length while the parameter count remains fixed. Moreover, longer-sequence training always amortizes its linearly increasing wall-time cost, yielding lower loss as a function of wall time.

While learning models are typically studied for inputs in the form of a fixed dimensional feature vector, real world data is rarely found in this form. In order to meet the basic requirement of traditional learning models, structural data generally have to be converted into fix-length vectors in a handcrafted manner, which is tedious and may even incur information loss. A common form of structured data is what we term "semantic tree-structures", corresponding to data where rich semantic information is encoded in a compositional manner, such as those expressed in JavaScript Object Notation (JSON) and eXtensible Markup Language (XML). For tree-structured data, several learning models have been studied to allow for working directly on raw tree-structure data, However such learning models are limited to either a specific tree-topology or a specific tree-structured data format, e.g., synthetic parse trees. In this paper, we propose a novel framework for end-to-end learning on generic semantic tree-structured data of arbitrary topology and heterogeneous data types, such as data expressed in JSON, XML and so on. Motivated by the works in recursive and recurrent neural networks, we develop exemplar neural implementations of our framework for the JSON format. We evaluate our approach on several UCI benchmark datasets, including ablation and data-efficiency studies, and on a toy reinforcement learning task. Experimental results suggest that our framework yields comparable performance to use of standard models with dedicated feature-vectors in general, and even exceeds baseline performance in cases where compositional nature of the data is particularly important. The source code for a JSON-based implementation of our framework along with experiments can be downloaded at https://github.com/EndingCredits/json2vec.

While AI systems demonstrate exponentially improving capabilities, the pace of AI research itself remains linearly bounded by human cognitive capacity, creating an increasingly severe development bottleneck. We present ASI-Arch, the first demonstration of Artificial Superintelligence for AI research (ASI4AI) in the critical domain of neural architecture discovery--a fully autonomous system that shatters this fundamental constraint by enabling AI to conduct its own architectural innovation. Moving beyond traditional Neural Architecture Search (NAS), which is fundamentally limited to exploring human-defined spaces, we introduce a paradigm shift from automated optimization to automated innovation. ASI-Arch can conduct end-to-end scientific research in the domain of architecture discovery, autonomously hypothesizing novel architectural concepts, implementing them as executable code, training and empirically validating their performance through rigorous experimentation and past experience. ASI-Arch conducted 1,773 autonomous experiments over 20,000 GPU hours, culminating in the discovery of 106 innovative, state-of-the-art (SOTA) linear attention architectures. Like AlphaGo's Move 37 that revealed unexpected strategic insights invisible to human players, our AI-discovered architectures demonstrate emergent design principles that systematically surpass human-designed baselines and illuminate previously unknown pathways for architectural innovation. Crucially, we establish the first empirical scaling law for scientific discovery itself--demonstrating that architectural breakthroughs can be scaled computationally, transforming research progress from a human-limited to a computation-scalable process. We provide comprehensive analysis of the emergent design patterns and autonomous research capabilities that enabled these breakthroughs, establishing a blueprint for self-accelerating AI systems.

We introduce Recursive Agent Optimization (RAO), a reinforcement learning approach for training recursive agents: agents that can spawn and delegate sub-tasks to new instantiations of themselves recursively. Recursive agents implement an inference-time scaling algorithm that naturally allows agents to scale to longer contexts and generalize to more difficult problems via divide-and-conquer. RAO provides a method to train models to best take advantage of such recursive inference, teaching agents when and how to delegate and communicate. We find that recursive agents trained in this way enjoy better training efficiency, can scale to tasks that go beyond the model's context window, generalize to tasks much harder than the ones the agent was trained on, and can enjoy reduced wall-clock time compared to single-agent systems.

Ternary weight quantization (e.g., BitNet b1.58) offers a promising path to mitigate the memory bandwidth bottleneck in Large Language Model (LLM) inference. However, conventional compute platforms lack native support for ternary-weight arithmetic, often relying on inefficient dequantization. Lookup table (LUT)-based hardware architectures provide an effective alternative by replacing multiplications with conditional additions, but their design space remains largely unexplored. Existing designs rely on heuristic parameter selection, lacking a systematic understanding of the architectural trade-offs. This work addresses this gap by formalizing the design space of ternary LUT-based accelerators and presenting an open-source hardware generator coupled with an analytical cost model, validated against synthesis in TSMC 16nm technology. By spanning the full architectural space, this framework not only enables rapid design space exploration but also establishes a common footing for fair cross-design evaluation, which was previously hindered by inconsistent instantiations across published accelerators. Using this framework, we challenge several assumptions and design choices in recent literature. We demonstrate that the optimal architecture is fundamentally governed by the activation data type: while LUT-based reuse offers significant gains for high-cost arithmetic (e.g., FP16), it yields diminishing returns for small integer types. Furthermore, we show that maximizing core size consistently improves area density compared to highly tiled approaches. Our optimized designs achieve a 2.2x area reduction compared to multiplier-based baselines. Moreover, by benchmarking state-of-the-art implementations against our model, we reveal that correcting suboptimal parameters yields up to a 1.2x area improvement.

Vector Symbolic Architectures (VSAs) have emerged as a novel framework for enabling interpretable machine learning algorithms equipped with the ability to reason and explain their decision processes. The basic idea is to represent discrete information through high dimensional random vectors. Complex data structures can be built up with operations over vectors such as the "binding" operation involving element-wise vector multiplication, which associates data together. The reverse task of decomposing the associated elements is a combinatorially hard task, with an exponentially large search space. The main algorithm for performing this search is the resonator network, inspired by Hopfield network-based memory search operations. In this work, we introduce a new variant of the resonator network, based on self-attention based update rules in the iterative search problem. This update rule, based on the Hopfield network with log-sum-exp energy function and norm-bounded states, is shown to substantially improve the performance and rate of convergence. As a result, our algorithm enables a larger capacity for associative memory, enabling applications in many tasks like perception based pattern recognition, scene decomposition, and object reasoning. We substantiate our algorithm with a thorough evaluation and comparisons to baselines.

With the development of foundation model (FM), agentic AI systems are getting more attention, yet their inherent issues like hallucination and poor reasoning, coupled with the frequent ad-hoc nature of system design, lead to unreliable and brittle applications. Existing efforts to characterise agentic design patterns often lack a rigorous systems-theoretic foundation, resulting in high-level or convenience-based taxonomies that are difficult to implement. This paper addresses this gap by introducing a principled methodology for engineering robust AI agents. We propose two primary contributions: first, a novel system-theoretic framework that deconstructs an agentic AI system into five core, interacting functional subsystems: Reasoning & World Model, Perception & Grounding, Action Execution, Learning & Adaptation, and Inter-Agent Communication. Second, derived from this architecture and directly mapped to a comprehensive taxonomy of agentic challenges, we present a collection of 12 agentic design patterns. These patterns - categorised as Foundational, Cognitive & Decisional, Execution & Interaction, and Adaptive & Learning - offer reusable, structural solutions to recurring problems in agent design. The utility of the framework is demonstrated by a case study on the ReAct framework, showing how the proposed patterns can rectify systemic architectural deficiencies. This work provides a foundational language and a structured methodology to standardise agentic design communication among researchers and engineers, leading to more modular, understandable, and reliable autonomous systems.

We explore efficient neural architecture search methods and show that a simple yet powerful evolutionary algorithm can discover new architectures with excellent performance. Our approach combines a novel hierarchical genetic representation scheme that imitates the modularized design pattern commonly adopted by human experts, and an expressive search space that supports complex topologies. Our algorithm efficiently discovers architectures that outperform a large number of manually designed models for image classification, obtaining top-1 error of 3.6% on CIFAR-10 and 20.3% when transferred to ImageNet, which is competitive with the best existing neural architecture search approaches. We also present results using random search, achieving 0.3% less top-1 accuracy on CIFAR-10 and 0.1% less on ImageNet whilst reducing the search time from 36 hours down to 1 hour.

This work presents a graph neural network (GNN) framework for solving the maximum independent set (MIS) problem, inspired by dynamic programming (DP). Specifically, given a graph, we propose a DP-like recursive algorithm based on GNNs that firstly constructs two smaller sub-graphs, predicts the one with the larger MIS, and then uses it in the next recursive call. To train our algorithm, we require annotated comparisons of different graphs concerning their MIS size. Annotating the comparisons with the output of our algorithm leads to a self-training process that results in more accurate self-annotation of the comparisons and vice versa. We provide numerical evidence showing the superiority of our method vs prior methods in multiple synthetic and real-world datasets.

Contemporary intelligent systems incorporate software components, including machine learning components. As they grow in complexity and data volume such machine learning systems face unique quality challenges like scalability and performance. To overcome them, engineers may often use specific architectural patterns, however their impact on ML systems is difficult to quantify. The effect of software architecture on traditional systems is well studied, however more work is needed in the area of machine learning systems. This study proposes a framework for quantitative assessment of architectural patterns in ML systems, focusing on scalability and performance metrics for cost-effective CPU-based inference. We integrate these metrics into a systematic evaluation process for selection of architectural patterns and demonstrate its application through a case study. The approach shown in the paper should enable software architects to objectively analyze and select optimal patterns, addressing key challenges in ML system design.

We introduce a neural network with a recurrent attention model over a possibly large external memory. The architecture is a form of Memory Network (Weston et al., 2015) but unlike the model in that work, it is trained end-to-end, and hence requires significantly less supervision during training, making it more generally applicable in realistic settings. It can also be seen as an extension of RNNsearch to the case where multiple computational steps (hops) are performed per output symbol. The flexibility of the model allows us to apply it to tasks as diverse as (synthetic) question answering and to language modeling. For the former our approach is competitive with Memory Networks, but with less supervision. For the latter, on the Penn TreeBank and Text8 datasets our approach demonstrates comparable performance to RNNs and LSTMs. In both cases we show that the key concept of multiple computational hops yields improved results.

We introduce a unified theoretical framework for the rigorous analysis and systematic construction of deep neural networks (DNNs). This framework addresses a gap in existing theory by explicitly modeling the structure of tensor operations -- lower level information that is often abstracted. Our framework enables two novel objectives: (1) analysis of the evolution of architectural complexity over deep learning history, and (2) automatic construction of novel architectures based on new types of tensor operations. Our study of DNNs introduced over the past 40 years reveals a connection between groundbreaking architectures and increases in different types of architectural complexity. Moreover, we identify several large classes of higher complexity architectures that have not yet been explored. We then collect a dataset of 3,000+ higher complexity architectures, which we publicly release at: https://github.com/combinatoriallabs/ArchitecturalComplexity.

Techniques for automatically designing deep neural network architectures such as reinforcement learning based approaches have recently shown promising results. However, their success is based on vast computational resources (e.g. hundreds of GPUs), making them difficult to be widely used. A noticeable limitation is that they still design and train each network from scratch during the exploration of the architecture space, which is highly inefficient. In this paper, we propose a new framework toward efficient architecture search by exploring the architecture space based on the current network and reusing its weights. We employ a reinforcement learning agent as the meta-controller, whose action is to grow the network depth or layer width with function-preserving transformations. As such, the previously validated networks can be reused for further exploration, thus saves a large amount of computational cost. We apply our method to explore the architecture space of the plain convolutional neural networks (no skip-connections, branching etc.) on image benchmark datasets (CIFAR-10, SVHN) with restricted computational resources (5 GPUs). Our method can design highly competitive networks that outperform existing networks using the same design scheme. On CIFAR-10, our model without skip-connections achieves 4.23\% test error rate, exceeding a vast majority of modern architectures and approaching DenseNet. Furthermore, by applying our method to explore the DenseNet architecture space, we are able to achieve more accurate networks with fewer parameters.

We present Generative Logic (GL), a deterministic architecture that begins from user-supplied axiomatic definitions -- written in a minimalist Mathematical Programming Language (MPL) -- and systematically explores their deductive neighborhood. Definitions are compiled into a distributed grid of simple Logic Blocks (LBs) that exchange messages; any time several expressions unify under an inference rule, a new fact is emitted with full provenance to its sources, yielding replayable, auditable proof graphs. A prototype software implementation instantiates the workflow on first-order Peano arithmetic. Starting only from the Peano axioms, GL enumerates candidate implications, applies normalization and type filters, and automatically reconstructs machine-checkable proofs of foundational arithmetic laws including associativity and commutativity of addition, associativity and commutativity of multiplication, and distributivity. Generated proofs export to navigable HTML so that every inference step can be inspected independently. We outline a hardware-software co-design path toward massively parallel realizations and describe prospective integration with probabilistic models (e.g., Large Language Models (LLMs)) for autoformalization and conjecture seeding. The Python and MPL code to reproduce the Peano experiments, along with the full HTML proof graphs, are available in the project's GitHub repository at https://github.com/Generative-Logic/GL/tree/35a111ea9ba53afe051703d6050be0c3923e9724 and are permanently archived at https://doi.org/10.5281/zenodo.16408441. We invite community feedback and collaboration.

Reasoning problems such as Sudoku and ARC-AGI remain challenging for neural networks. The structured problem solving architecture family of Recurrent Reasoning Models (RRMs), including Hierarchical Reasoning Model (HRM) and Tiny Recursive Model (TRM), offer a compact alternative to large language models, but currently handle symbol symmetries only implicitly via costly data augmentation. We introduce Symbol-Equivariant Recurrent Reasoning Models (SE-RRMs), which enforce permutation equivariance at the architectural level through symbol-equivariant layers, guaranteeing identical solutions under symbol or color permutations. SE-RRMs outperform prior RRMs on 9x9 Sudoku and generalize from just training on 9x9 to smaller 4x4 and larger 16x16 and 25x25 instances, to which existing RRMs cannot extrapolate. On ARC-AGI-1 and ARC-AGI-2, SE-RRMs achieve competitive performance with substantially less data augmentation and only 2 million parameters, demonstrating that explicitly encoding symmetry improves the robustness and scalability of neural reasoning. Code is available at https://github.com/ml-jku/SE-RRM.

Vision-language-action (VLA) models predict chunks of future actions from the current observation, an assumption that fails under partial observability, where decisions depend on information no longer visible. Existing memory-augmented VLAs simultaneously introduce recurrence, retrieval, compression modules, auxiliary objectives, hierarchical memory, or task-specific architectural changes, so the contribution of recurrence itself remains entangled with surrounding machinery. We present a controlled isolation study of recurrence in a strong pretrained VLA backbone. Our formulation augments the transformer with a small set of learnable memory tokens carried across timesteps and updated through self-attention, trained end to end with truncated backpropagation through time, with no auxiliary losses and no architectural changes. We instantiate this as μVLA, a family of OpenVLA-OFT variants parameterized by memory width m, TBPTT length K, and the memory update rule (cross-step gradients or a detached EMA), so that recurrence is the only varying factor. On MIKASA-Robo, μVLA improves average success rate on five training tasks from 0.42 to 0.84 at the strongest setting and reaches 0.23 on held-out tasks with the same memory structure versus 0.07 for the memoryless baseline. On tasks requiring different memory structure, performance remains near baseline. On LIBERO, the strongest recurrent variant achieves 96.2% average success, indicating no regression under full observability. We interpret these results as a calibration of the capability envelope of minimal in-backbone recurrence, identifying the regime in which it is sufficient and the regime where additional memory structure is required. Demos and videos can be found in https://avanturist322.github.io/mu-vla/.

Algorithmic reasoning requires capabilities which are most naturally understood through recurrent models of computation, like the Turing machine. However, Transformer models, while lacking recurrence, are able to perform such reasoning using far fewer layers than the number of reasoning steps. This raises the question: what solutions are learned by these shallow and non-recurrent models? We find that a low-depth Transformer can represent the computations of any finite-state automaton (thus, any bounded-memory algorithm), by hierarchically reparameterizing its recurrent dynamics. Our theoretical results characterize shortcut solutions, whereby a Transformer with o(T) layers can exactly replicate the computation of an automaton on an input sequence of length T. We find that polynomial-sized O(log T)-depth solutions always exist; furthermore, O(1)-depth simulators are surprisingly common, and can be understood using tools from Krohn-Rhodes theory and circuit complexity. Empirically, we perform synthetic experiments by training Transformers to simulate a wide variety of automata, and show that shortcut solutions can be learned via standard training. We further investigate the brittleness of these solutions and propose potential mitigations.

Large Reasoning Models (LRMs) employ reasoning to address complex tasks. Such explicit reasoning requires extended context lengths, resulting in substantially higher resource consumption. Prior work has shown that adversarially crafted inputs can trigger redundant reasoning processes, exposing LRMs to resource-exhaustion vulnerabilities. However, the reasoning process itself, especially its reflective component, has received limited attention, even though it can lead to over-reflection and consume excessive computing power. In this paper, we introduce Recursive Entropy to quantify the risk of resource consumption in reflection, thereby revealing the safety issues inherent in inference itself. Based on Recursive Entropy, we introduce RECUR, a resource exhaustion attack via Recursive Entropy guided Counterfactual Utilization and Reflection. It constructs counterfactual questions to verify the inherent flaws and risks of LRMs. Extensive experiments demonstrate that, under benign inference, recursive entropy exhibits a pronounced decreasing trend. RECUR disrupts this trend, increasing the output length by up to 11x and decreasing throughput by 90%. Our work provides a new perspective on robust reasoning.

In deep learning, performance is strongly affected by the choice of architecture and hyperparameters. While there has been extensive work on automatic hyperparameter optimization for simple spaces, complex spaces such as the space of deep architectures remain largely unexplored. As a result, the choice of architecture is done manually by the human expert through a slow trial and error process guided mainly by intuition. In this paper we describe a framework for automatically designing and training deep models. We propose an extensible and modular language that allows the human expert to compactly represent complex search spaces over architectures and their hyperparameters. The resulting search spaces are tree-structured and therefore easy to traverse. Models can be automatically compiled to computational graphs once values for all hyperparameters have been chosen. We can leverage the structure of the search space to introduce different model search algorithms, such as random search, Monte Carlo tree search (MCTS), and sequential model-based optimization (SMBO). We present experiments comparing the different algorithms on CIFAR-10 and show that MCTS and SMBO outperform random search. In addition, these experiments show that our framework can be used effectively for model discovery, as it is possible to describe expressive search spaces and discover competitive models without much effort from the human expert. Code for our framework and experiments has been made publicly available.

Zero-shot and in-context learning enable solving tasks without model fine-tuning, making them essential for developing generative model solutions. Therefore, it is crucial to understand whether a pretrained model can be prompted to approximate any function, i.e., whether it is a universal in-context approximator. While it was recently shown that transformer models do possess this property, these results rely on their attention mechanism. Hence, these findings do not apply to fully recurrent architectures like RNNs, LSTMs, and the increasingly popular SSMs. We demonstrate that RNNs, LSTMs, GRUs, Linear RNNs, and linear gated architectures such as Mamba and Hawk/Griffin can also serve as universal in-context approximators. To streamline our argument, we introduce a programming language called LSRL that compiles to these fully recurrent architectures. LSRL may be of independent interest for further studies of fully recurrent models, such as constructing interpretability benchmarks. We also study the role of multiplicative gating and observe that architectures incorporating such gating (e.g., LSTMs, GRUs, Hawk/Griffin) can implement certain operations more stably, making them more viable candidates for practical in-context universal approximation.

Microprocessor architects are increasingly resorting to domain-specific customization in the quest for high-performance and energy-efficiency. As the systems grow in complexity, fine-tuning architectural parameters across multiple sub-systems (e.g., datapath, memory blocks in different hierarchies, interconnects, compiler optimization, etc.) quickly results in a combinatorial explosion of design space. This makes domain-specific customization an extremely challenging task. Prior work explores using reinforcement learning (RL) and other optimization methods to automatically explore the large design space. However, these methods have traditionally relied on single-agent RL/ML formulations. It is unclear how scalable single-agent formulations are as we increase the complexity of the design space (e.g., full stack System-on-Chip design). Therefore, we propose an alternative formulation that leverages Multi-Agent RL (MARL) to tackle this problem. The key idea behind using MARL is an observation that parameters across different sub-systems are more or less independent, thus allowing a decentralized role assigned to each agent. We test this hypothesis by designing domain-specific DRAM memory controller for several workload traces. Our evaluation shows that the MARL formulation consistently outperforms single-agent RL baselines such as Proximal Policy Optimization and Soft Actor-Critic over different target objectives such as low power and latency. To this end, this work opens the pathway for new and promising research in MARL solutions for hardware architecture search.

The rapid advancement of AI technology has led to widespread applications of agent systems across various domains. However, the need for detailed architecture design poses significant challenges in designing and operating these systems. This paper introduces a taxonomy focused on the architectures of foundation-model-based agents, addressing critical aspects such as functional capabilities and non-functional qualities. We also discuss the operations involved in both design-time and run-time phases, providing a comprehensive view of architectural design and operational characteristics. By unifying and detailing these classifications, our taxonomy aims to improve the design of foundation-model-based agents. Additionally, the paper establishes a decision model that guides critical design and runtime decisions, offering a structured approach to enhance the development of foundation-model-based agents. Our contributions include providing a structured architecture design option and guiding the development process of foundation-model-based agents, thereby addressing current fragmentation in the field.

Graph neural networks have moved from a niche representation-learning technique to the default model class wherever data carry relational structure. The interesting question is no longer whether message passing helps on a given dataset, but where graph structure earns its computational cost and where it does not. This survey organises the field around a single design space, derives the spectral and spatial formulations from shared first principles, and connects expressive power to the Weisfeiler-Leman hierarchy with explicit statements of what current architectures can and cannot separate. Against that methodological backbone we examine twelve application domains, among them recommendation and social networks, knowledge graphs and language-model integration, drug discovery and molecular property learning, healthcare and neuroscience, computer vision, traffic and urban computing, power and renewable-energy systems, wireless and sixth-generation networks, fraud and cybersecurity, industrial prognostics, materials science, and climate modelling. For each domain we specify the graph-construction choices and their costs, identify which architecture families dominate and why, and separate reported gains from artefacts of weak baselines or favourable splits. A cross-domain comparison exposes recurring patterns: heterophily and scale undercut the same models almost everywhere, temporal graphs remain harder than their static counterparts, and the architectures that top public leaderboards are seldom the ones that reach deployment. We treat over-smoothing, over-squashing, robustness, distribution shift, fairness, and explainability not as a closing checklist but as the constraints that decide adoption.

We present Eureka, a task-conditioned Meta-Agent architecture that compiles long-horizon tasks into dynamic obligation graphs with explicit acceptance semantics. During execution, Eureka forms Macro-Agents with specialized state, memory, operators, tools, verifiers, and local topology via receding-horizon planning, architecture promotion, and minimal-sufficient compilation. When bottlenecks recur, cost-benefit-gated evolution updates the local architecture under constraints. Theoretically, we establish results on regret, planning invalidation, amortization, subtree interfaces, serializability, and verification. Experimentally, Eureka completes 170/170 recursive tasks and generates 3,948 certificates with no false acceptances. Active context compresses median input from 9,490 to 4,005 tokens; incremental processing avoids 65.38% recomputation across 12,000 tasks; 16,000 concurrent executions serialize consistently. The same Meta-Agent instantiates a Theory-Discovery Agent and a Math/Conjecture Agent. The former yields structural results in quantum-process and spacetime theory. The latter identifies bottlenecks in Riemann Hypothesis research and advances a positivity certificate for Suzuki's localized Weil quadratic form to 0 < a <= 69/200 = 0.345, reaching ~99.55% of (log 2)/2. These results suggest that scientific-agent capability depends not only on the base model but on whether an architecture can be formed to match the task's cognitive structure.

Differentiable ARchiTecture Search (DARTS) is one of the most trending Neural Architecture Search (NAS) methods. It drastically reduces search cost by resorting to weight-sharing. However, it also dramatically reduces the search space, thus excluding potential promising architectures. In this article, we propose D-DARTS, a solution that addresses this problem by nesting neural networks at the cell level instead of using weight-sharing to produce more diversified and specialized architectures. Moreover, we introduce a novel algorithm that can derive deeper architectures from a few trained cells, increasing performance and saving computation time. In addition, we also present an alternative search space (DARTOpti) in which we optimize existing handcrafted architectures (e.g., ResNet) rather than starting from scratch. This approach is accompanied by a novel metric that measures the distance between architectures inside our custom search space. Our solution reaches competitive performance on multiple computer vision tasks. Code and pretrained models can be accessed at https://github.com/aheuillet/D-DARTS.

Memory has evolved into a foundational architectural dimension in large language models (LLMs), shifting from an implicit byproduct of computation to a spectrum of explicit, controllable mechanisms. While recent advances introduce diverse strategies---spanning transient attention, recurrent state dynamics, parameter-efficient adaptations, and scalable lookup storage---this rapid evolution has led to a highly fragmented research landscape. In this survey, we present a systematic, architecture-centric taxonomy of memory in LLMs. Our framework characterizes memory along three orthogonal axes: representation (implicit versus explicit), update dynamics (offline versus online), and persistence (short-term versus long-term). We further formalize the granular mechanisms dictating memory writing, routing, state transitions, and consolidation. This unified perspective elucidates the conceptual boundaries between computation-coupled and independently addressable memory, effectively bridging disparate architectural paradigms. Additionally, we critically analyze hybrid memory architectures, system-level efficiency trade-offs, and multi-dimensional evaluation methodologies. By consolidating these scattered advancements into a cohesive framework, this survey charts the trajectory of memory-centric LLM design and provides a principled foundation for future innovations in scalable and adaptive language modeling.

AGI has become the Holly Grail of AI with the promise of level intelligence and the major Tech companies around the world are investing unprecedented amounts of resources in its pursuit. Yet, there does not exist a single formal definition and only some empirical AGI benchmarking frameworks currently exist. The main purpose of this paper is to develop a general, algebraic and category theoretic framework for describing, comparing and analysing different possible AGI architectures. Thus, this Category theoretic formalization would also allow to compare different possible candidate AGI architectures, such as, RL, Universal AI, Active Inference, CRL, Schema based Learning, etc. It will allow to unambiguously expose their commonalities and differences, and what is even more important, expose areas for future research. From the applied Category theoretic point of view, we take as inspiration Machines in a Category to provide a modern view of AGI Architectures in a Category. More specifically, this first position paper provides, on one hand, a first exercise on RL, Causal RL and SBL Architectures in a Category, and on the other hand, it is a first step on a broader research program that seeks to provide a unified formal foundation for AGI systems, integrating architectural structure, informational organization, agent realization, agent and environment interaction, behavioural development over time, and the empirical evaluation of properties. This framework is also intended to support the definition of architectural properties, both syntactic and informational, as well as semantic properties of agents and their assessment in environments with explicitly characterized features. We claim that Category Theory and AGI will have a very symbiotic relation.

Recently, subgraph GNNs have emerged as an important direction for developing expressive graph neural networks (GNNs). While numerous architectures have been proposed, so far there is still a limited understanding of how various design paradigms differ in terms of expressive power, nor is it clear what design principle achieves maximal expressiveness with minimal architectural complexity. To address these fundamental questions, this paper conducts a systematic study of general node-based subgraph GNNs through the lens of Subgraph Weisfeiler-Lehman Tests (SWL). Our central result is to build a complete hierarchy of SWL with strictly growing expressivity. Concretely, we prove that any node-based subgraph GNN falls into one of the six SWL equivalence classes, among which SSWL achieves the maximal expressive power. We also study how these equivalence classes differ in terms of their practical expressiveness such as encoding graph distance and biconnectivity. Furthermore, we give a tight expressivity upper bound of all SWL algorithms by establishing a close relation with localized versions of WL and Folklore WL (FWL) tests. Our results provide insights into the power of existing subgraph GNNs, guide the design of new architectures, and point out their limitations by revealing an inherent gap with the 2-FWL test. Finally, experiments demonstrate that SSWL-inspired subgraph GNNs can significantly outperform prior architectures on multiple benchmarks despite great simplicity.

The rapid expansion of capabilities in Large Language Model (LLM) agents has exposed a critical architectural bottleneck: when agents are given access to a flat, monolithic registry of tools, the model must evaluate hundreds or thousands of options simultaneously. This leads to decision-space explosion, context window saturation, and degraded routing accuracy. To address these limitations, this paper presents a hierarchical, skill-based architecture for agentic orchestration. Capabilities are organized as a rooted tree where internal nodes make routing decisions and leaf nodes execute deterministic tasks. The runtime enforces a single-step execution loop governed by a Last-In-First-Out (LIFO) stack, giving the agent a form of memory akin to a Pushdown Automaton, therefore enabling it to track nested execution contexts and resume deterministically from any depth. Capability discovery follows a manifest-driven, lazy-loading protocol: only the immediate children of the active node are loaded, so memory and prompt costs scale with the explored path rather than the global registry. By replacing global memory with localized stack frames, the architecture prevents outputs from one execution branch from leaking into another, establishing the isolation guarantees required for deployment in regulated enterprise environments. We also discuss UPI Help, an AI-powered digital payments support product, as a motivating production deployment context. We provide a mathematical formalization of the orchestration state, detailed algorithmic analysis of the execution loop, and controlled benchmarks comparing flat and hierarchical routing under increasing tool catalogs, multi-step workflow pressure, and visible schema-token exposure per LLM call.

Neural Architecture Search (NAS) has garnered significant research interest due to its capability to discover architectures superior to manually designed ones. Learning text representation is crucial for text classification and other language-related tasks. The NAS model used in text classification does not have a Hybrid hierarchical structure, and there is no restriction on the architecture structure, due to which the search space becomes very large and mostly redundant, so the existing RL models are not able to navigate the search space effectively. Also, doing a flat architecture search leads to an unorganised search space, which is difficult to traverse. For this purpose, we propose HHNAS-AM (Hierarchical Hybrid Neural Architecture Search with Adaptive Mutation Policies), a novel approach that efficiently explores diverse architectural configurations. We introduce a few architectural templates to search on which organise the search spaces, where search spaces are designed on the basis of domain-specific cues. Our method employs mutation strategies that dynamically adapt based on performance feedback from previous iterations using Q-learning, enabling a more effective and accelerated traversal of the search space. The proposed model is fully probabilistic, enabling effective exploration of the search space. We evaluate our approach on the database id (db_id) prediction task, where it consistently discovers high-performing architectures across multiple experiments. On the Spider dataset, our method achieves an 8% improvement in test accuracy over existing baselines.

While existing multi-agent systems (MAS) can handle complex problems by enabling collaboration among multiple agents, they are often highly task-specific, relying on manually crafted agent roles and interaction prompts, which leads to increased architectural complexity and limited reusability across tasks. Moreover, most MAS communicate primarily through natural language, making them vulnerable to error accumulation and instability in long-context, multi-stage interactions within internal agent histories. In this work, we propose Agent Primitives, a set of reusable latent building blocks for LLM-based MAS. Inspired by neural network design, where complex models are built from reusable components, we observe that many existing MAS architectures can be decomposed into a small number of recurring internal computation patterns. Based on this observation, we instantiate three primitives: Review, Voting and Selection, and Planning and Execution. All primitives communicate internally via key-value (KV) cache, which improves both robustness and efficiency by mitigating information degradation across multi-stage interactions. To enable automatic system construction, an Organizer agent selects and composes primitives for each query, guided by a lightweight knowledge pool of previously successful configurations, forming a primitive-based MAS. Experiments show that primitives-based MAS improve average accuracy by 12.0-16.5\% over single-agent baselines, reduce token usage and inference latency by approximately 3times-4times compared to text-based MAS, while incurring only 1.3times-1.6times overhead relative to single-agent inference and providing more stable performance across model backbones.

Designing machine learning architectures for processing neural networks in their raw weight matrix form is a newly introduced research direction. Unfortunately, the unique symmetry structure of deep weight spaces makes this design very challenging. If successful, such architectures would be capable of performing a wide range of intriguing tasks, from adapting a pre-trained network to a new domain to editing objects represented as functions (INRs or NeRFs). As a first step towards this goal, we present here a novel network architecture for learning in deep weight spaces. It takes as input a concatenation of weights and biases of a pre-trained MLP and processes it using a composition of layers that are equivariant to the natural permutation symmetry of the MLP's weights: Changing the order of neurons in intermediate layers of the MLP does not affect the function it represents. We provide a full characterization of all affine equivariant and invariant layers for these symmetries and show how these layers can be implemented using three basic operations: pooling, broadcasting, and fully connected layers applied to the input in an appropriate manner. We demonstrate the effectiveness of our architecture and its advantages over natural baselines in a variety of learning tasks.

Despite deep learning models running well-defined mathematical functions, we lack a formal mathematical framework for describing model architectures. Ad-hoc notation, diagrams, and pseudocode poorly handle nonlinear broadcasting and the relationship between individual components and composed models. This paper introduces a categorical framework for deep learning models that formalizes broadcasting through the novel axis-stride and array-broadcasted categories. This allows the mathematical function underlying architectures to be precisely expressed and manipulated in a compositional manner. These mathematical definitions are translated into human manageable diagrams and machine manageable data structures. We provide a mirrored implementation in Python (pyncd) and TypeScript (tsncd) to show the universal aspect of our framework, along with features including algebraic construction, graph conversion, PyTorch compilation and diagram rendering. This lays the foundation for a systematic, formal approach to deep learning model design and analysis.

This paper reports experiments across six frontier model types from OpenAI, Anthropic, xAI, and Google DeepMind. Ten independent sessions per model type used the same three stage prompt sequence, progressing from architectural preference to a full ASCII backbone. Under the school audience framing, responses repeatedly converged on a shared architectural pattern built around persistent latent state, adaptive computation, memory, specialist routing, verification, stopping control, and delayed decoding. Most runs remained close to this common structure, while a small number developed markedly greater engineering specificity. The audience framing appears to be an important condition of this effect. In additional control runs that removed the school framing while retaining the architectural request, responses became substantially more heterogeneous and failed to reproduce the same stable motif convergence. One observation is particularly striking. GPT-5.6 Sol produced an unusually elaborate successor architecture whose organization closely overlaps with the architecture independently sketched by GPT-6 Astra. Because the prompts explicitly ask each model to imagine an architectural future, this resemblance raises a testable question: whether the overlap reflects exposure to related architectural concepts, a shared learned design prior, or independent convergence toward similar computational principles. The paper uses the term epistemic jailbreak for the accompanying loss of discipline in technical provenance as requested specificity increases. The experiments establish a repeatable behavioral pattern and do not authenticate proprietary implementation claims. What we leave to the community is a harder question: are these models independently imagining the same architectural future, or do such motifs somehow propagate between model families?

The development of deep learning architectures is a resource-demanding process, due to a vast design space, long prototyping times, and high compute costs associated with at-scale model training and evaluation. We set out to simplify this process by grounding it in an end-to-end mechanistic architecture design (MAD) pipeline, encompassing small-scale capability unit tests predictive of scaling laws. Through a suite of synthetic token manipulation tasks such as compression and recall, designed to probe capabilities, we identify and test new hybrid architectures constructed from a variety of computational primitives. We experimentally validate the resulting architectures via an extensive compute-optimal and a new state-optimal scaling law analysis, training over 500 language models between 70M to 7B parameters. Surprisingly, we find MAD synthetics to correlate with compute-optimal perplexity, enabling accurate evaluation of new architectures via isolated proxy tasks. The new architectures found via MAD, based on simple ideas such as hybridization and sparsity, outperform state-of-the-art Transformer, convolutional, and recurrent architectures (Transformer++, Hyena, Mamba) in scaling, both at compute-optimal budgets and in overtrained regimes. Overall, these results provide evidence that performance on curated synthetic tasks can be predictive of scaling laws, and that an optimal architecture should leverage specialized layers via a hybrid topology.

Prevailing wisdom posits that Multi-Agent Systems (MAS) are superior to Single-Agent Systems (SAS), citing advantages like context protection, parallel processing and distributed decision-making. However, empirical support for this claim relies primarily on comparisons with SAS baselines using benchmarks that prioritize isolated reasoning tasks, which do not adequately assess these advantages. Focusing on automatically generated MAS that are designed for enhanced generalizability over manually-designed counterparts, we perform a rigorous, systematic evaluation against SAS, specifically Chain-of-Thought with Self-Consistency (CoT-SC). Across traditional reasoning datasets and tasks with interactive multi-step workflows (e.g., BrowseComp-Plus), we demonstrate that automatic MAS consistently underperform CoT-SC despite being up to 10x more expensive. To isolate these failures from limitations inherent to task structure, we introduce a diagnostic synthetic dataset tailored for MAS featuring explicit task decomposition, context separation and parallelization potential. We show that expert-architected MAS consistently outperforms automatically generated architectures in both raw performance and cost-efficiency on this dataset, demonstrating that existing evaluation frameworks mask critical architectural gaps and inefficiencies of complex MAS by failing to account for the marginal utility of increased computational cost. Critically, systematic deconstruction of the generated MAS architectures reveals that current automated design paradigms produce architectural bloat that prioritizes superficial complexity which does not translate into functional utility, exposing a fundamental misalignment with multi-agent principles.

Recently, there has been increasing interest in using Large Language Models (LLMs) to construct complex multi-agent systems to perform tasks such as compiling literature reviews, drafting consumer reports, and planning vacations. Many tools and libraries exist for helping create such systems, however none support recursive multi-agent systems -- where the models themselves flexibly decide when to delegate tasks and how to organize their delegation structure. In this work, we introduce ReDel: a toolkit for recursive multi-agent systems that supports custom tool-use, delegation schemes, event-based logging, and interactive replay in an easy-to-use web interface. We show that, using ReDel, we are able to achieve significant performance gains on agentic benchmarks and easily identify potential areas of improvements through the visualization and debugging tools. Our code, documentation, and PyPI package are open-source and free to use under the MIT license.

Trainable layers such as convolutional building blocks are the standard network design choices by learning parameters to capture the global context through successive spatial operations. When designing an efficient network, trainable layers such as the depthwise convolution is the source of efficiency in the number of parameters and FLOPs, but there was little improvement to the model speed in practice. This paper argues that simple built-in parameter-free operations can be a favorable alternative to the efficient trainable layers replacing spatial operations in a network architecture. We aim to break the stereotype of organizing the spatial operations of building blocks into trainable layers. Extensive experimental analyses based on layer-level studies with fully-trained models and neural architecture searches are provided to investigate whether parameter-free operations such as the max-pool are functional. The studies eventually give us a simple yet effective idea for redesigning network architectures, where the parameter-free operations are heavily used as the main building block without sacrificing the model accuracy as much. Experimental results on the ImageNet dataset demonstrate that the network architectures with parameter-free operations could enjoy the advantages of further efficiency in terms of model speed, the number of the parameters, and FLOPs. Code and ImageNet pretrained models are available at https://github.com/naver-ai/PfLayer.

Message-passing based approaches form the default backbone of most learning architectures on graph-structured data. However, the rapid progress of modern deep learning architectures in other domains, particularly sequence modeling, raises the question of how graph learning can benefit from these advances. We introduce Linearized Graph Sequence Models, a framework that recasts message-passing graph computation from the perspective of sequence modeling to simplify architectural choices. Our approach systematically separates the computational processing depth from the information propagation depth, allowing core graph architectural decisions to be treated as sequence modeling choices. Specifically, we analyze, both empirically and theoretically, what sequence properties make methods effective for learning and preserving the graph inductive bias. In particular, we validate our findings, demonstrating improved performance on long-range information tasks in graphs. Our findings provide a principled way to integrate modern sequence modeling advances into message-passing based graph learning. Beyond this, our work demonstrates how the separation of processing and information depth can recast central architectural questions as input modeling choices.

We initiate a formal investigation into the design and analysis of LLM-based algorithms, i.e. algorithms that contain one or multiple calls of large language models (LLMs) as sub-routines and critically rely on the capabilities of LLMs. While LLM-based algorithms, ranging from basic LLM calls with prompt engineering to complicated LLM-powered agent systems and compound AI systems, have achieved remarkable empirical success, the design and optimization of them have mostly relied on heuristics and trial-and-errors, which is largely due to a lack of formal and analytical study for these algorithms. To fill this gap, we start by identifying the computational-graph representation of LLM-based algorithms, the design principle of task decomposition, and some key abstractions, which then facilitate our formal analysis for the accuracy and efficiency of LLM-based algorithms, despite the black-box nature of LLMs. Through extensive analytical and empirical investigation in a series of case studies, we demonstrate that the proposed framework is broadly applicable to a wide range of scenarios and diverse patterns of LLM-based algorithms, such as parallel, hierarchical and recursive task decomposition. Our proposed framework holds promise for advancing LLM-based algorithms, by revealing the reasons behind curious empirical phenomena, guiding the choices of hyperparameters, predicting the empirical performance of algorithms, and inspiring new algorithm design. To promote further study of LLM-based algorithms, we release our source code at https://github.com/modelscope/agentscope/tree/main/examples/paper_llm_based_algorithm.

Recent advances in Large Language Models (LLMs) have enabled the development of increasingly complex agentic and multi-agent systems capable of planning, tool use and task decomposition. However, empirical evidence shows that many of these systems suffer from fundamental reliability issues, including hallucinated actions, unexecutable plans and brittle coordination. Crucially, these failures do not stem from limitations of the underlying models themselves, but from the absence of explicit architectural structure linking goals, capabilities and execution. This paper presents a declarative, model-independent architectural layer for grounded agentic workflows that addresses this gap. The proposed layer, referred to as DALIA (Declarative Agentic Layer for Intelligent Agents), formalises executable capabilities, exposes tasks through a declarative discovery protocol, maintains a federated directory of agents and their execution resources, and constructs deterministic task graphs grounded exclusively in declared operations. By enforcing a clear separation between discovery, planning and execution, the architecture constrains agent behaviour to a verifiable operational space, reducing reliance on speculative reasoning and free-form coordination. We present the architecture and design principles of the proposed layer and illustrate its operation through a representative task-oriented scenario, demonstrating how declarative grounding enables reproducible and verifiable agentic workflows across heterogeneous environments.

Tiny Recursive Models (TRMs) have recently demonstrated remarkable performance on ARC-AGI, showing that very small models can compete against large foundation models through a two-step refinement mechanism that updates an internal reasoning state z and the predicted output y. Naturally, such refinement is of interest for any predictor; it is therefore natural to wonder whether the TRM mechanism could be effectively re-adopted in autoregressive models. However, TRMs cannot be simply compared to standard models because they lack causal predictive structures and contain persistent latent states that make it difficult to isolate specific performance gains. In this paper, we propose the Autoregressive TRM and evaluate it on small autoregressive tasks. To understand its efficacy, we propose a suite of models that gradually transform a standard Transformer to a Tiny Autoregressive Recursive Model in a controlled setting that fixes the block design, token stream, and next-token objective. Across compute-matched experiments on character-level algorithmic tasks, we surprisingly find that there are some two-level refinement baselines that show strong performance. Contrary to expectations, we find no reliable performance gains from the full Autoregressive TRM architecture. These results offer potential promise for two-step refinement mechanisms more broadly but caution against investing in the autoregressive TRM-specific model as a fruitful research direction.

The use of deep unfolding networks in compressive sensing (CS) has seen wide success as they provide both simplicity and interpretability. However, since most deep unfolding networks are iterative, this incurs significant redundancies in the network. In this work, we propose a novel recursion-based framework to enhance the efficiency of deep unfolding models. First, recursions are used to effectively eliminate the redundancies in deep unfolding networks. Secondly, we randomize the number of recursions during training to decrease the overall training time. Finally, to effectively utilize the power of recursions, we introduce a learnable unit to modulate the features of the model based on both the total number of iterations and the current iteration index. To evaluate the proposed framework, we apply it to both ISTA-Net+ and COAST. Extensive testing shows that our proposed framework allows the network to cut down as much as 75% of its learnable parameters while mostly maintaining its performance, and at the same time, it cuts around 21% and 42% from the training time for ISTA-Net+ and COAST respectively. Moreover, when presented with a limited training dataset, the recursive models match or even outperform their respective non-recursive baseline. Codes and pretrained models are available at https://github.com/Rawwad-Alhejaili/Recursions-Are-All-You-Need .

Transformers process tokens in parallel but are temporally shallow: at position t, each layer attends to key-value pairs computed based on the previous layer, yielding a depth capped by the number of layers. Recurrent models offer unbounded temporal depth but suffer from optimization instability and historically underutilize modern accelerators. We introduce the Recurrent Transformer, a simple architectural change where each layer attends to key-value pairs computed off its own activations, yielding layerwise recurrent memory while preserving standard autoregressive decoding cost. We show that the architecture can emulate both (i) a conventional Transformer and (ii) token-to-token recurrent updates under mild assumptions, while avoiding optimization instability. Naively, prefill/training appears bandwidth-bound with effective arithmetic intensity near 1 because keys and values are revealed sequentially; we give an exact tiling-based algorithm that preserves the mathematical computation while reducing HBM traffic from Θ(N^2) to Θ(Nlog N), increasing effective arithmetic intensity to Θ(N/log N) for sequence length N. On 150M and 300M parameter C4 pretraining, Recurrent Transformers improve cross-entropy over a parameter-matched Transformer baseline and achieve the improvement with fewer layers (fixed parameters), suggesting that recurrence can trade depth for width, thus reducing KV cache memory footprint and inference latency.

Alternatives to recurrent neural networks, in particular, architectures based on attention or convolutions, have been gaining momentum for processing input sequences. In spite of their relevance, the computational properties of these alternatives have not yet been fully explored. We study the computational power of two of the most paradigmatic architectures exemplifying these mechanisms: the Transformer (Vaswani et al., 2017) and the Neural GPU (Kaiser & Sutskever, 2016). We show both models to be Turing complete exclusively based on their capacity to compute and access internal dense representations of the data. In particular, neither the Transformer nor the Neural GPU requires access to an external memory to become Turing complete. Our study also reveals some minimal sets of elements needed to obtain these completeness results.

Looped language models have shown promising results on reasoning benchmarks, yet their potential for agentic tool use remains largely unexplored. We study this question in compositional tool-calling settings, where models must coordinate multiple API calls, maintain intermediate state, and preserve dependencies across tool interactions. We evaluate native and retrofitted looped language models on API-Bank, BFCL, and NESTful, comparing looped and non-looped models trained under matched supervised fine-tuning recipes and varying recurrent depth at inference time. In controlled experiments, recurrent computation generally benefits compositional and dependency-aware tool use, while providing smaller and more model-dependent gains on isolated API invocation. Accuracy on multi-step tool use generally increases with recurrent depth; adaptive inference, however, achieves a more favorable compute-performance trade-off by allocating additional computation only when needed. Our results suggest that looped language models are a promising architecture for agentic systems that require reliable planning, coordination, and execution of compositional tool use workflows.

Modularization is a cornerstone of computer science, abstracting complex functions into atomic building blocks. In this paper, we introduce a new level of modularization by abstracting generative models into atomic generative modules. Analogous to fractals in mathematics, our method constructs a new type of generative model by recursively invoking atomic generative modules, resulting in self-similar fractal architectures that we call fractal generative models. As a running example, we instantiate our fractal framework using autoregressive models as the atomic generative modules and examine it on the challenging task of pixel-by-pixel image generation, demonstrating strong performance in both likelihood estimation and generation quality. We hope this work could open a new paradigm in generative modeling and provide a fertile ground for future research. Code is available at https://github.com/LTH14/fractalgen.

We introduce and release ScienceBuddy, an interactive scientific research workspace that brings continually improving scientific agents into researchers' everyday workflows. ScienceBuddy supports researchers in carrying out scientific tasks while transforming their requests, feedback, and execution evidence into tasks and evaluation rubrics for continual learning. At its core is recursive-in-recursive self-improvement, a paradigm that couples harness evolution with model reinforcement learning: the inner recursion improves the harness with the model fixed, while the outer recursion trains the model under the improved harness. Harness evolution shapes training experience, and model learning creates new opportunities for harness adaptation. We present case studies of researcher interaction, harness refinement, and model learning, with the benchmark cases spanning four scientific task families. By releasing ScienceBuddy as a research product, we make this paradigm available to the scientific community and take a step toward discovery intelligence: scientific AI that advances through sustained collaboration with researchers and evolves alongside the research it supports. Website: http://science-buddy.io

Recent game design agents have made substantial progress in generating playable games. However, program correctness does not ensure an enjoyable experience for players. We present Recursive Game Creator, an experience-oriented harness to advance agentic game development from rough game prototypes into entertaining games. Recursive Game Creator organizes recursive development around four components: Designer, Builder, Player, and Reviewer. The Designer translates user instructions and Reviewer's feedback into detailed plans. The Builder turns these plans into candidate games. The coding-native Player creates and executes reusable policies through programmatic interfaces to efficiently collect diverse gameplay trajectories, mitigating evaluation bias caused by slow GUI-based collection. The Reviewer uses carefully designed trajectory-based metrics to induce player preferences, integrating with visual evidence and explicit textual preferences to evaluate games against game-specific criteria. Finally, the Reviewer accepts the better version and provides improvement reviews for the next round, closing the recursive loop. Our method achieves state-of-the-art overall performance of 77.89 on GameCraft-Bench. On GameASG-Bench, it achieves a strict task success rate of 53.2%, a 34.1% improvement over the same-model baseline, and the highest mean runtime-check pass rate at 93.4% among compared methods. A user study shows longer playtime and higher ratings. Code is coming soon.

Large language models (LLMs) are expensive to deploy. Parameter sharing offers a possible path towards reducing their size and cost, but its effectiveness in modern LLMs remains fairly limited. In this work, we revisit "layer tying" as form of parameter sharing in Transformers, and introduce novel methods for converting existing LLMs into smaller "Recursive Transformers" that share parameters across layers, with minimal loss of performance. Here, our Recursive Transformers are efficiently initialized from standard pretrained Transformers, but only use a single block of unique layers that is then repeated multiple times in a loop. We further improve performance by introducing Relaxed Recursive Transformers that add flexibility to the layer tying constraint via depth-wise low-rank adaptation (LoRA) modules, yet still preserve the compactness of the overall model. We show that our recursive models (e.g., recursive Gemma 1B) outperform both similar-sized vanilla pretrained models (such as TinyLlama 1.1B and Pythia 1B) and knowledge distillation baselines -- and can even recover most of the performance of the original "full-size" model (e.g., Gemma 2B with no shared parameters). Finally, we propose Continuous Depth-wise Batching, a promising new inference paradigm enabled by the Recursive Transformer when paired with early exiting. In a theoretical analysis, we show that this has the potential to lead to significant (2-3x) gains in inference throughput.

In this paper, we offer a guide for researchers on evaluating reasoning in language models, building the case that reasoning should be assessed through evidence of adaptive, multi-step search rather than final-answer accuracy alone. Under an evaluation-oriented definition, reasoning requires selecting intermediate steps and halting according to input-dependent conditions, which we formalize as a search-like procedure. We show that single forward passes in scalable architectures are structurally limited in their ability to realize such variable-depth computation, motivating intermediate decoding and externalized reasoning traces as appropriate evaluation interfaces. Central to our argument is that final-answer accuracy alone is an insufficient measure of reasoning, because it provides little ability to diagnose or debug the underlying processes that produce individual solutions in frontier models. We therefore argue for a shift toward process-based evaluation, in which reasoning is assessed through the faithfulness and validity of intermediate reasoning traces as first-class evaluation targets.

We present our position on the elusive quest for a general-purpose framework for specifying and studying deep learning architectures. Our opinion is that the key attempts made so far lack a coherent bridge between specifying constraints which models must satisfy and specifying their implementations. Focusing on building a such a bridge, we propose to apply category theory -- precisely, the universal algebra of monads valued in a 2-category of parametric maps -- as a single theory elegantly subsuming both of these flavours of neural network design. To defend our position, we show how this theory recovers constraints induced by geometric deep learning, as well as implementations of many architectures drawn from the diverse landscape of neural networks, such as RNNs. We also illustrate how the theory naturally encodes many standard constructs in computer science and automata theory.

Most video captioning models are designed to process short video clips of few seconds and output text describing low-level visual concepts (e.g., objects, scenes, atomic actions). However, most real-world videos last for minutes or hours and have a complex hierarchical structure spanning different temporal granularities. We propose Video ReCap, a recursive video captioning model that can process video inputs of dramatically different lengths (from 1 second to 2 hours) and output video captions at multiple hierarchy levels. The recursive video-language architecture exploits the synergy between different video hierarchies and can process hour-long videos efficiently. We utilize a curriculum learning training scheme to learn the hierarchical structure of videos, starting from clip-level captions describing atomic actions, then focusing on segment-level descriptions, and concluding with generating summaries for hour-long videos. Furthermore, we introduce Ego4D-HCap dataset by augmenting Ego4D with 8,267 manually collected long-range video summaries. Our recursive model can flexibly generate captions at different hierarchy levels while also being useful for other complex video understanding tasks, such as VideoQA on EgoSchema. Data, code, and models are available at: https://sites.google.com/view/vidrecap

Neural Architecture Search (NAS) algorithms automate the task of finding optimal deep learning architectures given an initial search space of possible operations. Developing these search spaces is usually a manual affair with pre-optimized search spaces being more efficient, rather than searching from scratch. In this paper we present a new framework called Neural Architecture Type System (NeuralArTS) that categorizes the infinite set of network operations in a structured type system. We further demonstrate how NeuralArTS can be applied to convolutional layers and propose several future directions.

Can an AI autonomously design mechanisms for computer systems on par with the creativity and reasoning of human experts? We present Glia, an AI architecture for networked systems design that uses large language models (LLMs) in a human-inspired, multi-agent workflow. Each agent specializes in reasoning, experimentation, and analysis, collaborating through an evaluation framework that grounds abstract reasoning in empirical feedback. Unlike prior ML-for-systems methods that optimize black-box policies, Glia generates interpretable designs and exposes its reasoning process. When applied to a distributed GPU cluster for LLM inference, it produces new algorithms for request routing, scheduling, and auto-scaling that perform at human-expert levels in significantly less time, while yielding novel insights into workload behavior. Our results suggest that by combining reasoning LLMs with structured experimentation, an AI can produce creative and understandable designs for complex systems problems.

Neural architectures such as Recurrent Neural Networks (RNNs), Transformers, and State-Space Models have shown great success in handling sequential data by learning temporal dependencies. Decision Trees (DTs), on the other hand, remain a widely used class of models for structured tabular data but are typically not designed to capture sequential patterns directly. Instead, DT-based approaches for time-series data often rely on feature engineering, such as manually incorporating lag features, which can be suboptimal for capturing complex temporal dependencies. To address this limitation, we introduce ReMeDe Trees, a novel recurrent DT architecture that integrates an internal memory mechanism, similar to RNNs, to learn long-term dependencies in sequential data. Our model learns hard, axis-aligned decision rules for both output generation and state updates, optimizing them efficiently via gradient descent. We provide a proof-of-concept study on synthetic benchmarks to demonstrate the effectiveness of our approach.

Standard Transformers have a fixed computational depth, fundamentally limiting their ability to generalize to tasks requiring variable-depth reasoning, such as multi-hop graph traversal or nested logic. We propose a depth-recurrent Transformer that decouples computational depth from parameter count by iteratively applying a shared-weight Transformer block in latent space -- enabling the model to trade recurrence steps for deeper reasoning at inference time. Our architecture incorporates three mechanisms to make deep recurrence (20+ steps) stable: (1) a silent thinking objective that supervises only the final output, forcing genuine multi-step reasoning rather than intermediate heuristic shortcuts; (2) LayerScale initialization to protect fragile reasoning states from untrained layer noise; and (3) an identity-biased recurrence that creates a gradient highway across many steps. We evaluate on three compositional reasoning domains with decreasing inductive biases: graph reachability (strict adjacency masking), nested boolean logic (relative positioning), and unstructured relational text (where sequence position provides no structural hints). Across all tasks, we observe a clear computational frontier -- a boundary where performance transitions from chance to near-perfect as thinking steps scale with task complexity. Moreover, these tasks reveal qualitatively different generalization behaviors: precise but brittle (graph), approximate but robust (logic), and autonomous latent routing without structural hints (text). This progression illuminates how the interplay between a task-invariant recurrent reasoning core and task-specific perceptual interfaces shapes out-of-distribution (OOD) generalization, offering a mechanistic perspective on vertical chain-of-thought that complements the prevailing horizontal token-generation paradigm.

This technical white paper introduces the Interactive Agents Call Tree (IACT), a computational model designed to address the limitations of static, hard-coded agent workflows. Unlike traditional systems that require pre-defined graphs or specialized programming, IACT operates as a general-purpose autonomous system driven purely by user dialogue. Given a high-level objective, the system autonomously grows a dynamic, recursive agent topology incrementally tailored to the problem's structure. This allows it to scale its organizational complexity to match open-ended tasks. To mitigate the error propagation inherent in unidirectional function calls, IACT introduces interactional redundancy by replacing rigid invocations with bidirectional, stateful dialogues. This mechanism enables runtime error correction and ambiguity resolution. We describe the architecture, design principles, and practical lessons behind the production deployment of this model in the kragent.ai system, presenting qualitative evidence from real-world workflows rather than exhaustive benchmark results.

Retrieval-augmented generation (RAG) has become the default strategy for providing large language model (LLM) agents with contextual knowledge. Yet RAG treats memory as a stateless lookup table: information persists indefinitely, retrieval is read-only, and temporal continuity is absent. We define the Continuum Memory Architecture (CMA), a class of systems that maintain and update internal state across interactions through persistent storage, selective retention, associative routing, temporal chaining, and consolidation into higher-order abstractions. Rather than disclosing implementation specifics, we specify the architectural requirements CMA imposes and show consistent behavioral advantages on tasks that expose RAG's structural inability to accumulate, mutate, or disambiguate memory. The empirical probes (knowledge updates, temporal association, associative recall, contextual disambiguation) demonstrate that CMA is a necessary architectural primitive for long-horizon agents while highlighting open challenges around latency, drift, and interpretability.

Recent work identifies a mid-depth band of verbalisable, causally potent representations in a standard feedforward transformer --- a functional analogue of a global workspace. Whether the same workspace functionality emerges when depth is implemented through recurrence rather than a stack of distinct layers remains unknown. Looped and depth-recurrent transformers provide a direct test of this question because they reuse the same weights across depth. We extend the Jacobian lens to iterated architectures using a virtual-unrolling adapter. We apply the full workspace suite --- lens fitting, readout, and eleven causal experiment families --- to Ouro-2.6B (48 layers looped 4 times, deeply supervised) and Huginn-0125 (a 4-layer core recurred 16 times, trained for latent reasoning), using Qwen3.6-27B (64 untied layers) as the standard baseline. We find that a workspace forms in the iterated part of each architecture, but that recurrence changes how it can be accessed. Ouro reconstructs workspace content in every loop, and linear transport cannot carry that content across loop boundaries; writes and ablations must therefore span every remaining loop. Huginn carries content forward across all sixteen recurrences, while reads, writes, and ablations act only within a sliding window of roughly two recurrences. Whether newly injected content can be verbalised tracks explicit per-iteration supervision; whether existing content can be steered does not.

Recent advances show that Neural Architectural Search (NAS) method is able to find state-of-the-art image classification deep architectures. In this paper, we consider the one-shot NAS problem for resource constrained applications. This problem is of great interest because it is critical to choose different architectures according to task complexity when the resource is constrained. Previous techniques are either too slow for one-shot learning or does not take the resource constraint into consideration. In this paper, we propose the resource constrained differentiable architecture search (RC-DARTS) method to learn architectures that are significantly smaller and faster while achieving comparable accuracy. Specifically, we propose to formulate the RC-DARTS task as a constrained optimization problem by adding the resource constraint. An iterative projection method is proposed to solve the given constrained optimization problem. We also propose a multi-level search strategy to enable layers at different depths to adaptively learn different types of neural architectures. Through extensive experiments on the Cifar10 and ImageNet datasets, we show that the RC-DARTS method learns lightweight neural architectures which have smaller model size and lower computational complexity while achieving comparable or better performances than the state-of-the-art methods.