#01Nov 10, 2026
cs.LG
TorchCurves: Differentiable Parametric Curves
Alex Shtoff
We present TorchCurves, a PyTorch library that treats vector-valued parametric curves as learnable primitives. Its central operation maps batches of scalar inputs to points on curves represented in B-spline or Legendre polynomial bases, with differentiation through both inputs and coefficients. Curve coefficients can be optimized jointly with the surrounding model or produced by another network. The library provides trainable modules, reusable basis modules, and a functional interface, supporting applications ranging from continuous feature embeddings to Kolmogorov-Arnold networks and functional regression. Its implementation combines classical evaluation algorithms with vectorized PyTorch operations, emphasizing readability and maintainability without custom hardware kernels. Timing experiments compare curve evaluation against NumPy and SciPy and KAN training against EfficientKAN across a range of problem sizes. The results illustrate where this generality remains computationally practical and where overhead is substantial. Library is available on GitHub at https://github.com/alexshtf/torchcurves.
#02Nov 10, 2026
cs.LG
AutoScaffold: AI-Guided Scaffolding for Reinforcement Learning of Language Models
Zijian Zhang, Rizhen Hu, Jiangweizhi Peng and 4 more
Reinforcement learning with verifiable rewards (RLVR) produces rich training experience, yet outcome rewards reduce each attempt to a single number and leave most of this information unused. Training-time scaffolds, such as strategies or hints added to the prompt during training, offer a natural way to turn this information into guidance, but their design and adaptation are largely left to humans and tailored to specific domains. We introduce AutoScaffold, a unified AI-for-AI framework that turns a student's training experience into adaptive scaffolds, with minimal domain-specific information and no human intervention during training. A frozen teacher periodically examines this experience, diagnoses bottlenecks, and designs scaffolds in two forms: (i) strategies shared across a class of tasks and (ii) hints for individual hard tasks, adjusting the content and amount of support as the student learns. The scaffolds are removed at evaluation. We apply the same framework to ALFWorld, search-based QA, mathematical reasoning, and GPU kernel generation. When evaluated without scaffolds, students trained with AutoScaffold outperform those trained with the corresponding RL baselines in all four domains, with gains of 7.2 points in ALFWorld success and 4.0 points in average QA exact match. On GPU kernel generation, AutoScaffold increases the fraction of tasks with a correct kernel that runs faster than the PyTorch reference by up to 5.0 points. On math, our student surpasses QuestA's reported accuracy using approximately one-third as many student training steps. Analyses show that the teacher identifies a different failure in each task class and shifts its scaffolds from step-by-step workflows to targeted fixes as the student improves, and that its revised scaffolds help the student learn more than keeping the previous scaffold or using no scaffold.
#03Nov 10, 2026
cs.AI
Evaluating LLM-Generated World Models for Neuro-Symbolic Reasoning
Souhaila Djaffal, Amna Jamal, Gagana Madhugiri Devaraja and 2 more
Formal world models can support planning, verification, and safety reasoning, but constructing them from open-ended natural-language situations is difficult, particularly in multi-agent settings where several formalizations may be plausible. We study whether five LLMs can generate such world models as partially observable stochastic games and whether mechanical validity is sufficient to establish that the resulting model faithfully represents the intended decision problem. We introduce a benchmark of 44 scenarios spanning game, situational, and cultural settings and evaluate generated world models along three dimensions: mechanical validity, reference-relative structural agreement, and semantic criteria. Across three empirical tracks, we analyze 410 first-pass generations. In the reference-backed game track, 134/135 generated world models pass a strict mechanical audit, yet mean permutation-invariant structural F1 is only 0.366, with just 28/134 mechanically valid models exactly matching the authored reference. In the cultural track, explicitly naming the country changes the generated structural representation for most LLMs while producing only small changes in automated semantic scores. These results show that executability is a necessary but insufficient criterion for LLM-generated world models: models that are mechanically valid can still differ substantially in the structure used by downstream neuro-symbolic reasoning and planning.
#04Nov 10, 2026
cs.LG
Continual-ARC: Measuring Skill Acquisition over a Working Lifetime
Daniel Lenton
Agent harnesses have emerged as a promising mechanism for continual learning, alongside test-time parametric learning. However, the current benchmarks have several limitations: they generally focus on a single applied domain, serve each instance only once, and assume a single family of learner, so memory-based and weight-based systems are rarely compared on the same scale. We propose Continual-ARC, a lifelong stream built from the three ARC-AGI editions, whose tasks need no domain knowledge. The same tasks return after dormant gaps with fresh instances, while new tasks keep arriving. On each instance, the learner may pay for demonstrations, submit answers, or act inside the harness, with retries permitted on incorrect submissions, which are paid for. Each instance is scored based on the share of this feedback budget consumed. Since a learner may keep anything between instances, memory-based and weight-based systems are scored on the same scale. After the stream, the learner is frozen and tested on fresh instances of the tasks it met, which measures memorization, and on unseen tasks, which measures generalization. We run an agent harness with frozen weights, with and without persistence, on Qwen3.5-9B and GLM-5.3 Flash, comparing them with two prompting floors, a program-induction method and Qwen3.5-9B's weights trained to imitate GLM-5.3 Flash. Persistence in the harness generally does not improve memorization unless provided with explicit expert guidance. Most harness-based methods still learn less than a floor that simply caches each task's demonstrations, across all models we tested. No harness-based method gains on unseen tasks, whereas weight-based learning shows substantial gains. This opens the door to future weight-based continual learning that could teach models to drive harnesses in new domains.
#05Nov 10, 2026
math.ST
Nonparametric Maximum Likelihood Estimation for Mixtures of Logistic Regressions
Muheng Li, Peize Zhang, Xin Bing
Mixtures of logistic regressions provide a flexible framework for modeling binary responses, extending standard logistic regression to accommodate unobserved heterogeneity while retaining an interpretable regression structure. In this paper, we study such models with an unspecified mixing distribution. We analyze a sieve nonparametric maximum likelihood estimator (NPMLE) and derive nonasymptotic bounds on the estimation error of the resulting mixture regression function under both fixed and random designs. Our results reveal an explicit tradeoff between statistical estimation error and the approximation error induced by the sieve radius, from which we derive convergence rates under several tail conditions on the mixing distribution. For computation, we propose a finite-particle algorithm that approximates the sieve NPMLE by optimizing the locations and weights of a finitely supported mixing distribution. The method offers numerical advantages over existing algorithms and comes with rigorous convergence guarantees. For any fixed dataset, we establish global convergence of the likelihood to the restricted NPMLE value when the number of particles exceeds a finite threshold. When the true mixing distribution is finitely supported, we further establish uniform global convergence guarantees and derive error bounds that separate algorithmic and statistical errors. Our analysis also yields a denoising bound for the mixing distribution and an identifiability result that complements existing results in the literature.