Daily Papers

Fine-grained robotic evaluation matters for understanding embodied models, going beyond binary success rates and rule-based process scores. We present PRM-as-a-Judge 1.5, a toolkit for robot process assessment that turns rollout videos into dense progress curves and derives multiple fine metrics. PRM-as-a-Judge 1.5 introduces three metrics, building on version 1.0, that characterize failure-side progress, post-drawdown recovery, and success-side execution quality, helping users understand embodied model capability. Based on the rollout videos from benchmarks, we perform a comprehensive assessment of the embodied models, providing some fine-grained metric results and key findings. We further introduce RoboPulse++ to evaluate the reliability of process reward models (PRM), providing evaluators with a more accurate testing platform. Moreover, we release a user-friendly assessment suite, including the benchmark, metric implementation, and visualization tools, to support reproducible manipulation process evaluation. We call on the community to rethink how robots are evaluated and establish transparent, procedural, and reproducible assessment as a foundation for the next generation of embodied intelligence.

In an unbounded plane, straight lines are used extensively for mathematical analysis. They are tools of convenience. However, those with high slope values become unbounded at a faster rate than the independent variable. So, straight lines, in this work, are made to be bounded by introducing a parametric nonlinear term that is positive. The straight lines are transformed into bounded nonlinear curves that become unbounded at a much slower rate than the independent variable. This transforming equation can be expressed as a continued fraction of straight lines. The continued fraction is real-valued and converges to the solutions of the transforming equation. Following Euler's method, the continued fraction has been reduced into an infinite series. The usefulness of the bounding nature of continued fraction is demonstrated by solving the problem of image classification. Parameters estimated on the Fashion-MNIST dataset of greyscale images using continued fraction of regression lines have less variance, converge quickly and are more accurate than the linear counterpart. Moreover, this multi-dimensional parametric estimation problem can be expressed on xy- plane using the parameters of the continued fraction and patterns emerge on planar plots.

This research enhances linear regression models by integrating a Kalman filter and analysing curve areas to minimize loss. The goal is to develop an optimal linear regression equation using stochastic gradient descent (SGD) for weight updating. Our approach involves a stepwise process, starting with user-defined parameters. The linear regression model is trained using SGD, tracking weights and loss separately and zipping them finally. A Kalman filter is then trained based on weight and loss arrays to predict the next consolidated weights. Predictions result from multiplying input averages with weights, evaluated for loss to form a weight-versus-loss curve. The curve's equation is derived using the two-point formula, and area under the curve is calculated via integration. The linear regression equation with minimum area becomes the optimal curve for prediction. Benefits include avoiding constant weight updates via gradient descent and working with partial datasets, unlike methods needing the entire set. However, computational complexity should be considered. The Kalman filter's accuracy might diminish beyond a certain prediction range.

Robotic learning takes place in dynamic environments with large behavior spaces. A terminal success signal only tells the robot whether the task is completed. It does not explain whether the current behavior is making progress, remaining unchanged, or undoing earlier progress. For this reason, recent studies have increasingly explored progress rewards that provide feedback during task execution. However, the current literature lacks a shared framework. Existing methods use different observations, goal specifications, output signals, supervision sources, and evaluation protocols. This makes it difficult to compare them and understand what their results actually validate. In this survey, we provide a unified view of progress reward modeling for robotic learning. We organize the field in three connected steps. We first study the interface of a progress model. This defines the problem from the outside by asking what information the model receives and what form of progress signal it produces. We then move inside the model and study the methods used to construct this signal. This reveals the different assumptions and mechanisms behind progress estimation and reward generation. Finally, we examine the data and benchmarks that support these methods. This shows how progress supervision is obtained and what different evaluations actually measure. Together, these three perspectives connect what a progress model is, how it is built, and how its quality is validated. We further summarize the main limitations of current approaches and discuss future research directions.

LLM-based (Large Language Model) GUI (Graphical User Interface) agents can potentially reshape our daily lives significantly. However, current LLM-based GUI agents suffer from the scarcity of high-quality training data owing to the difficulties of trajectory collection and reward annotation. Existing works have been exploring LLMs to collect trajectories for imitation learning or to offer reward signals for online RL training. However, the Outcome Reward Model (ORM) used in existing works cannot provide finegrained feedback and can over-penalize the valuable steps in finally failed trajectories. To this end, we propose Progress Reward Model (ProgRM) to provide dense informative intermediate rewards by predicting a task completion progress for each step in online training. To handle the challenge of progress reward label annotation, we further design an efficient LCS-based (Longest Common Subsequence) self-annotation algorithm to discover the key steps in trajectories and assign progress labels accordingly. ProgRM is evaluated with extensive experiments and analyses. Actors trained with ProgRM outperform leading proprietary LLMs and ORM-trained actors, illustrating the effectiveness of ProgRM. The codes for experiments will be made publicly available upon acceptance.

In traditional financial markets, yield curves are widely available for countries (and, by extension, currencies), financial institutions, and large corporates. These curves are used to calibrate stochastic interest rate models, discount future cash flows, and price financial products. Yield curves, however, can be readily computed only because of the current size and structure of bond markets. In cryptocurrency markets, where fixed-rate lending and bonds are almost nonexistent as of early 2025, the yield curve associated with each currency must be estimated by other means. In this paper, we show how mathematical tools can be used to construct yield curves for cryptocurrencies by leveraging data from the highly developed markets for cryptocurrency derivatives.

A longitudinal web crawl is a sequence of partial samples of an evolving URL population. Pairwise containment between two crawls is the standard probe; under a simple urn model of the crawl -- each round samples a fraction of the URLs and replaces a fraction -- it recovers two interpretable rates, per-round survival α and coverage c, but treats the population as uniform and consumes one pair at a time. In this work, we define a formal language for talking about a crawl. We extend this analysis with the discovery curve U(s, T), the cumulative URL footprint over a sliding window of T crawls starting at s, which under the same urn model is also a closed-form function of (α, c). Containment and the discovery curve are then two projections of one process: independent fits agree on (α, c) when the urn is homogeneous, so any disagreement is itself a measurement. Applied to Common Crawl (2020--2025, domain granularity) and to the German Academic Web (GAW, URL granularity), the two projections disagree on both archives, and a two-component urn with a persistent core fraction κ alongside shell parameters (α_partial, c_partial) reconciles the disagreement. A residual on c_partial remains, signaling that the shell itself is not homogeneous; κ is recorded as the scalar entry point to a rank-resolved generalization, which is left to follow-up work. web archive \and crawl coverage \and discovery curve \and urn model \and two-component model \and URL lifetime

Straight line equation y=mx with slope m, when singularly perturbed as ay^3+y=mx with a positive parameter a, results in S-shaped curves or S-curves on a real plane. As arightarrow 0, we get back y=mx which is a cumulative distribution function of a continuous uniform distribution that describes the occurrence of every event in an interval to be equally probable. As arightarrowinfty, the derivative of y has finite support only at y=0 resembling a degenerate distribution. Based on these arguments, in this work, we propose that these S-curves can represent maximum entropy uniform distribution to a zero entropy single value. We also argue that these S-curves are superposable as they are only parametrically nonlinear but fundamentally linear. So far, the superposed forms have been used to capture the patterns of natural systems such as nonlinear dynamics of biological growth and kinetics of enzyme reactions. Here, we attempt to use the S-curve and its superposed form as statistical models. We fit the models on a classical dataset containing flower measurements of iris plants and analyze their usefulness in pattern recognition. Based on these models, we claim that any non-uniform pattern can be represented as a singular perturbation to uniform distribution. However, our parametric estimation procedure have some limitations such as sensitivity to initial conditions depending on the data at hand.

A common expectation is that career productivity peaks rather early and then gradually declines with seniority. But whether this holds true is still an open question. Here we investigate the productivity trajectories of almost 8,500 scientists from over fifty disciplines using methods from time series analysis, dimensionality reduction, and network science, showing that there exist six universal productivity patterns in research. Based on clusters of productivity trajectories and network representations where researchers with similar productivity patterns are connected, we identify constant, u-shaped, decreasing, periodic-like, increasing, and canonical productivity patterns, with the latter two describing almost three-fourths of researchers. In fact, we find that canonical curves are the most prevalent, but contrary to expectations, productivity peaks occur much more frequently around mid-career rather than early. These results outline the boundaries of possible career paths in science and caution against the adoption of stereotypes in tenure and funding decisions.

Long-horizon robotic manipulation requires dense feedback that reflects how a task advances through its procedural stages, not merely whether the final outcome is successful. Existing reward models often rely on trajectory-level success labels or time-based interpolation, which can conflate elapsed time with true task progress and therefore fail to capture unfinished steps, stagnation, and failure states. We present ProcVLM, a progress-aware vision-language model that learns procedure-grounded progress as a dense reward signal for manipulation. Rather than deriving progress from terminal outcomes or temporal proxies, ProcVLM grounds progress estimation in procedural structure and intra-stage visual change, and further adopts a reasoning-before-estimation paradigm that infers the remaining atomic actions before estimating task progress. Specifically, we construct this supervision by synthesizing frame-level subtask-semantic annotations, assigning progress budgets according to subtask structure, and distributing each budget based on intra-subtask visual change. To train ProcVLM at scale, we build a standardized procedural supervision synthesis pipeline and construct ProcCorpus-60M from 30 embodied datasets with 60M annotated frames, from which we derive ProcVQA for procedure-aware pretraining, with progress estimation as the central task alongside action segmentation and future planning. Experiments on ProcVQA and reward-model benchmarks show that ProcVLM improves embodied procedural reasoning and yields more discriminative trajectory-internal progress estimates than representative baselines, supporting its use as a dense reward model for downstream reward-guided policy optimization. Project page: https://procvlm.github.io/

Trajectory planning is commonly used as part of a local planner in autonomous driving. This paper considers the problem of planning a continuous-curvature-rate trajectory between fixed start and goal states that minimizes a tunable trade-off between passenger comfort and travel time. The problem is an instance of infinite dimensional optimization over two continuous functions: a path, and a velocity profile. We propose a simplification of this problem that facilitates the discretization of both functions. This paper also proposes a method to quickly generate minimal-length paths between start and goal states based on a single tuning parameter: the second derivative of curvature. Furthermore, we discretize the set of velocity profiles along a given path into a selection of acceleration way-points along the path. Gradient-descent is then employed to minimize cost over feasible choices of the second derivative of curvature, and acceleration way-points, resulting in a method that repeatedly solves the path and velocity profiles in an iterative fashion. Numerical examples are provided to illustrate the benefits of the proposed methods.

Disease progression simulation is a crucial area of research that has significant implications for clinical diagnosis, prognosis, and treatment. One major challenge in this field is the lack of continuous medical imaging monitoring of individual patients over time. To address this issue, we develop a novel framework termed Progressive Image Editing (PIE) that enables controlled manipulation of disease-related image features, facilitating precise and realistic disease progression simulation. Specifically, we leverage recent advancements in text-to-image generative models to simulate disease progression accurately and personalize it for each patient. We theoretically analyze the iterative refining process in our framework as a gradient descent with an exponentially decayed learning rate. To validate our framework, we conduct experiments in three medical imaging domains. Our results demonstrate the superiority of PIE over existing methods such as Stable Diffusion Walk and Style-Based Manifold Extrapolation based on CLIP score (Realism) and Disease Classification Confidence (Alignment). Our user study collected feedback from 35 veteran physicians to assess the generated progressions. Remarkably, 76.2% of the feedback agrees with the fidelity of the generated progressions. To our best knowledge, PIE is the first of its kind to generate disease progression images meeting real-world standards. It is a promising tool for medical research and clinical practice, potentially allowing healthcare providers to model disease trajectories over time, predict future treatment responses, and improve patient outcomes.

We introduce a new method of generating Computer Aided Design (CAD) profiles via a sequence of simple geometric constructions including curve offsetting, rotations and intersections. These sequences start with geometry provided by a designer and build up the points and curves of the final profile step by step. We demonstrate that adding construction steps between the designer's input geometry and the final profile improves generation quality in a similar way to the introduction of a chain of thought in language models. Similar to the constraints in a parametric CAD model, the construction sequences reduce the degrees of freedom in the modeled shape to a small set of parameter values which can be adjusted by the designer, allowing parametric editing with the constructed geometry evaluated to floating point precision. In addition we show that applying reinforcement learning to the construction sequences gives further improvements over a wide range of metrics, including some which were not explicitly optimized.

Estimating task progress requires reasoning over long-horizon dynamics rather than recognizing static visual content. While modern Vision-Language Models (VLMs) excel at describing what is visible, it remains unclear whether they can infer how far a task has progressed from partial observations. To this end, we introduce Progress-Bench, a benchmark for systematically evaluating progress reasoning in VLMs. Beyond benchmarking, we further explore a human-inspired two-stage progress reasoning paradigm through both training-free prompting and training-based approach based on curated dataset ProgressLM-45K. Experiments on 14 VLMs show that most models are not yet ready for task progress estimation, exhibiting sensitivity to demonstration modality and viewpoint changes, as well as poor handling of unanswerable cases. While training-free prompting that enforces structured progress reasoning yields limited and model-dependent gains, the training-based ProgressLM-3B achieves consistent improvements even at a small model scale, despite being trained on a task set fully disjoint from the evaluation tasks. Further analyses reveal characteristic error patterns and clarify when and why progress reasoning succeeds or fails.

Mathematical reasoning remains a significant challenge for Large Language Models (LLMs) due to hallucinations. When combined with formal proof assistants like Lean, these hallucinations can be eliminated through rigorous verification, making theorem proving reliable. However, even with formal verification, LLMs still struggle with long proofs and complex mathematical formalizations. While Lean with LLMs offers valuable assistance with retrieving lemmas, generating tactics, or even complete proofs, it lacks a crucial capability: providing a sense of proof progress. This limitation particularly impacts the overall development efficiency in large formalization projects. We introduce LeanProgress, a method that predicts the progress in the proof. Training and evaluating our models made on a large corpus of Lean proofs from Lean Workbook Plus and Mathlib4 and how many steps remain to complete it, we employ data preprocessing and balancing techniques to handle the skewed distribution of proof lengths. Our experiments show that LeanProgress achieves an overall prediction accuracy of 75.1\% in predicting the amount of progress and, hence, the remaining number of steps. When integrated into a best-first search framework using Reprover, our method shows a 3.8\% improvement on Mathlib4 compared to baseline performances of 41.2\%, particularly for longer proofs. These results demonstrate how proof progress prediction can enhance both automated and interactive theorem proving, enabling users to make more informed decisions about proof strategies.

Daily progress notes are common types in the electronic health record (EHR) where healthcare providers document the patient's daily progress and treatment plans. The EHR is designed to document all the care provided to patients, but it also enables note bloat with extraneous information that distracts from the diagnoses and treatment plans. Applications of natural language processing (NLP) in the EHR is a growing field with the majority of methods in information extraction. Few tasks use NLP methods for downstream diagnostic decision support. We introduced the 2022 National NLP Clinical Challenge (N2C2) Track 3: Progress Note Understanding - Assessment and Plan Reasoning as one step towards a new suite of tasks. The Assessment and Plan Reasoning task focuses on the most critical components of progress notes, Assessment and Plan subsections where health problems and diagnoses are contained. The goal of the task was to develop and evaluate NLP systems that automatically predict causal relations between the overall status of the patient contained in the Assessment section and its relation to each component of the Plan section which contains the diagnoses and treatment plans. The goal of the task was to identify and prioritize diagnoses as the first steps in diagnostic decision support to find the most relevant information in long documents like daily progress notes. We present the results of 2022 n2c2 Track 3 and provide a description of the data, evaluation, participation and system performance.