arXiv:2603.06737v1 Announce Type: cross Abstract: We describe an experiment in large-scale autoformalization of algebraic topology in an Interactive Theorem Proving (ITP) environment, where the workload is distributed among multiple LLM-based coding agents. Rather than relying on static central planning, we implement a simulated bounty-based marketplace in which agents dynamically propose new lemmas (formal statements), attach bounties to them, and compete to discharge these proof obligations and claim the bounties. The agents interact directly with the interactive proof system: they can invoke tactics, inspect proof states and goals, analyze tactic successes and failures, and iteratively refine their proof scripts. In addition to constructing proofs, agents may introduce new formal definitions and intermediate lemmas to structure the development. All accepted proofs are ultimately checked and verified by the underlying proof assistant. This setting explores collaborative, decentralized proof search and theory building, and the use of market-inspired mechanisms to scale autoformalization in ITP.

arXiv:2602.18843v2 Announce Type: replace Abstract: We introduce ABD, a benchmark for default-exception abduction over finite first-order worlds. Given a background theory with an abnormality predicate and a set of relational structures, a model must output a first-order formula that defines exceptions, restoring satisfiability while keeping exceptions sparse. We formalize three observation regimes (closed-world, existential completion, universal completion) with exact SMT verification. Evaluating ten frontier LLMs on 600 instances, the best models achieve high validity but parsimony gaps remain, and holdout evaluation reveals distinct generalization failure modes across regimes.

arXiv:2603.03346v1 Announce Type: cross Abstract: Modeling the unsaturated behavior of porous materials with multimodal pore size distributions presents significant challenges, as standard hydraulic models often fail to capture their complex, multi-scale characteristics. A common workaround involves superposing unimodal retention functions, each tailored to a specific pore size range; however, this approach requires separate parameter identification for each mode, which limits interpretability and generalizability, especially in data-sparse scenarios. In this work, we introduce a fundamentally different approach: a physics-constrained machine learning framework designed for meta-modeling, enabling the automatic discovery of closed-form mathematical expressions for multimodal water retention curves directly from experimental data. Mathematical expressions are represented as binary trees and evolved via genetic programming, while physical constraints are embedded into the loss function to guide the symbolic regressor toward solutions that are physically consistent and mathematically robust. Our results demonstrate that the proposed framework can discover closed-form equations that effectively represent the water retention characteristics of porous materials with varying pore structures. To support third-party validation, application, and extension, we make the full implementation publicly available in an open-source repository.

arXiv:2505.21668v3 Announce Type: replace Abstract: Practical guidance on training Large Language Models (LLMs) to leverage Code Interpreter across diverse tasks remains lacking. We present R1-Code-Interpreter, an extension of a text-only LLM trained via multi-turn supervised fine-tuning (SFT) and reinforcement learning (RL) to autonomously generate multiple code queries during step-by-step reasoning. Unlike prior RL + tool-use efforts focused on narrow domains such as math or retrieval, we curate 144 diverse reasoning and planning tasks and show that training a general-purpose Code Interpreter across them presents significant challenges due to task heterogeneity and scarcity of effective samples. To address this, we introduce a multi-stage curriculum learning approach that partitions training samples by measured improvement potential. The RL training prioritizes samples with higher potential and gradually shifts to lower-potential ones, increasing the average RL gains from merely +3.4% to +9.3% across Qwen-2.5 models (3/7/14B). Our final model, R1-CI-14B, improves average accuracy on the 37 test tasks from 44.1% to 72.4%, outperforming text-only GPT-4o (58.6%) and GPT-4o with Code Interpreter (70.9%). Notably, R1-CI-14B also exhibits emergent self-checking behavior through code generation. Datasets, Codes, and Models are available at https://github.com/yongchao98/R1-Code-Interpreter and https://huggingface.co/yongchao98.

arXiv:2602.18916v1 Announce Type: cross Abstract: Legal reasoning requires not only high accuracy but also the ability to justify decisions through verifiable and contestable arguments. However, existing Large Language Model (LLM) approaches, such as Chain-of-Thought (CoT) and Retrieval-Augmented Generation (RAG), often produce unstructured explanations that lack a formal mechanism for verification or user intervention. To address this limitation, we propose Adaptive Collaboration of Argumentative LLMs (ACAL), a neuro-symbolic framework that integrates adaptive multi-agent collaboration with an Arena-based Quantitative Bipolar Argumentation Framework (A-QBAF). ACAL dynamically deploys expert agent teams to construct arguments, employs a clash resolution mechanism to adjudicate conflicting claims, and utilizes uncertainty-aware escalation for borderline cases. Crucially, our framework supports a Human-in-the-Loop (HITL) contestability workflow, enabling users to directly audit and modify the underlying reasoning graph to influence the final judgment. Empirical evaluations on the LegalBench benchmark demonstrate that ACAL outperforms strong baselines across Gemini-2.5-Flash-Lite and Gemini-2.5-Flash architectures, effectively balancing efficient predictive performance with structured transparency and contestability. Our implementation is available at: https://github.com/loc110504/ACAL.

arXiv:2506.07751v4 Announce Type: replace-cross Abstract: Recent studies have shown that large language models (LLMs), especially smaller ones, often lack robustness in grade school math (GSM) reasoning. In particular, they tend to experience performance drops when faced with distribution shifts, such as changes to numerical or nominal variables, or insertions of distracting clauses. A possible strategy to address this involves generating synthetic data to further "instantiate" reasoning problems on potential variations. In this work, we instead focus on the strategy of "abstracting" reasoning problems. This not only helps counteract distribution shifts but also facilitates the connection to symbolic tools for deriving solutions. Focusing on GSM, we find that this abstraction process is better acquired through reinforcement learning (RL) than just supervised fine-tuning, which often fails to produce faithful abstractions. Our method, AbstRaL -- which promotes abstract reasoning in LLMs using RL on granular abstraction data -- significantly mitigates performance degradation on recent GSM perturbation benchmarks. Besides, improving GSM robustness via AbstRaL is shown to also implicitly benefit LLMs' capabilities on OOD mathematical and general reasoning tasks, indicating that abstract thinking broadly enables better generalizability.

arXiv:2602.08885v4 Announce Type: replace-cross Abstract: Symbolic regression (SR) aims to discover interpretable analytical expressions that accurately describe observed data. Amortized SR promises to be much more efficient than the predominant genetic programming SR methods, but currently struggles to scale to realistic scientific complexity. We find that a key obstacle is the lack of a fast reduction of equivalent expressions to a concise normalized form. Amortized SR has addressed this by general-purpose Computer Algebra Systems (CAS) like SymPy, but the high computational cost severely limits training and inference speed. We propose SimpliPy, a rule-based simplification engine achieving a 100-fold speed-up over SymPy at comparable quality. This enables substantial improvements in amortized SR, including scalability to much larger training sets, more efficient use of the per-expression token budget, and systematic training set decontamination with respect to equivalent test expressions. We demonstrate these advantages in our Flash-ANSR framework, which achieves much better accuracy than amortized baselines (NeSymReS, E2E) on the FastSRB benchmark. Moreover, it performs on par with state-of-the-art direct optimization (PySR) while recovering more concise instead of more complex expressions with increasing inference budget.

arXiv:2602.07672v2 Announce Type: replace-cross Abstract: Code World Models (CWMs) are language models trained to simulate program execution by predicting explicit runtime state after every executed command. This execution-based world modeling enables internal verification within the model, offering an alternative to natural language chain-of-thought reasoning. However, the sources of errors and the nature of CWMs' limitations remain poorly understood. We study CWMs from two complementary perspectives: local semantic execution and long-horizon state tracking. On real-code benchmarks, we identify two dominant failure regimes. First, dense runtime state reveals produce token-intensive execution traces, leading to token-budget exhaustion on programs with long execution histories. Second, failures disproportionately concentrate in string-valued state, which we attribute to limitations of subword tokenization rather than program structure. To study long-horizon behavior, we use a controlled permutation-tracking benchmark that isolates state propagation under action execution. We show that long-horizon degradation is driven primarily by incorrect action generation: when actions are replaced with ground-truth commands, a Transformer-based CWM propagates state accurately over long horizons, despite known limitations of Transformers in long-horizon state tracking. These findings suggest directions for more efficient supervision and state representations in CWMs that are better aligned with program execution and data types.