automated reasoning teams

Abstract: Reinforcement learning with verifiable rewards (RLVR) enables large language models (LLMs) to continuously self-improve their reasoning capabilities. Compared to RLVR's scalar rewards, recent self-supervised on-policy distillation methods leverage denser supervision signals. However, both paradigms suffer from exploration bottlenecks, struggling to escape local optima when the policy fails to sample valid solutions. Relying on external demonstrations can bypass this issue; however, the off-policy nature hinders genuine self-improvement and the mismatched-distribution reasoning can not be fully exploited. In this work, we propose Self-Evolution Policy Optimization (SEPO), a framework that drives continuous reasoning capability evolution via guided exploration and in-distribution exploitation. Specifically, SEPO utilizes labels to elicit correct reasoning from the policy, unlocking the exploration potential. By treating current policy conditioned on this in-distribution reasoning as a self-teacher, SEPO distills the newly discovered solution back into the policy. Through this iterative cycle of policy-intrinsic exploration and exploitation, SEPO achieves robust and continuous capability evolution. Across scientific, tool-use, and complex logical reasoning domains, SEPO consistently achieves the best performance under identical training time or steps, demonstrating superior efficiency and convergence ceilings. Notably, SEPO maintains stable improvements even in scenarios where baselines severely underperform or fail entirely, such as on complex tasks or with small-scale models. Our code is available at https://github.com/Eric8932/SEPO.

Abstract: Decision models answer typed questions, such as multiple-choice or yes/no questions, with a probability for each option. We add test-time search to frozen decision models, with no training: we show the model a complete proposed answer, read off its probability of saying "Yes" to the proposal's correctness, and search for answers that it rates higher. The search is done either by editing one answer at a time or by joint optimization, which changes several answers at once. Search raises accuracy for every model and test set we tried, and the gains are largest for exact correctness on logic puzzles, where every answer in a task must be right. On 128 such puzzles, it takes Qwen3.8-27B from 2 to 30 exactly correct puzzles ($15\times$) and its per-blank accuracy from 27.8% to 48.5%. On a shared set of 47 puzzles, searching over each model's own Yes/No score raises the per-blank accuracy of StartLux Instant, Perplexity Decider, Clef, and JEV, which we reach only through its public API, by 4.0 to 13.0 percentage points, and raises the number of puzzles they get exactly correct, out of 47 and averaged over three search seeds, from 10 to 35, 9 to 26, 2 to 11, and 9 to 31.7 respectively.

Abstract: Self-evolving tool-integrated agents learn from tasks and feedback generated within their own training loop. A Curriculum Agent generates tasks, while an Executor Agent learns from self-consistency signals through reinforcement learning. However, relying solely on the current Executor for feedback has two limitations: group-relative advantages vanish under full consensus, while uncertainty-based curriculum rewards favor disagreement without showing whether the generated tasks support further learning. These limitations motivate an additional reference beyond the current Executor. We propose \textit{AnchorLoop}, which introduces a frozen copy of the previous iteration's Executor as a historical reference and reuses it on both sides of the training loop. For the Executor, the anchor provides a cross-reference advantage that evaluates current outputs against both current and historical majority answers. For the Curriculum, it provides an agreement-based reference based on differences in sampled majority agreement. Since the Executor and anchor have identical parameters during Curriculum training, this comparison serves as a proxy for task selection rather than evidence of inter-version improvement or correctness. Across 13 reasoning benchmarks, AnchorLoop improves over Agent0 by 2.5\% on mathematical reasoning and 2.8\% on general reasoning tasks. It also maintains higher effective-advantage variance and continues improving in later iterations as the unanchored baseline shows diminishing gains. These results demonstrate the benefit of introducing a lightweight historical reference into self-evolving tool-integrated agents without external task or answer supervision.

Abstract: In this paper, we investigate connections between dependence logics, viewed as a subclass of relating logics, and three-valued logics. More specifically, we identify common features of Epstein's subject-matter semantics and the variable-inclusion conditions characteristic of some infectious many-valued logics. Inspired by Del Cerro and Lugardon's sequent calculi for dependence logics, in which classical connectives are combined with connectives satisfying Epstein-style conditions, we introduce two three-valued dependence-like logics that combine classical conjunction and disjunction with infectious negation and implication. We also provide sound, complete, and cut-free bisequent calculi for these logics.

Abstract: While modern large language models (LLMs) have been trained to reason through verbalized chains-of-thought, the generation cost grows substantially due to suboptimal paths to reach the final answer. Furthermore, as new insights are discovered while observing various input queries (e.g. through self-reflection), limited mechanisms exist for carrying forward these findings to be applied to subsequent problems. One can view the list of such strategies or behaviors as a growing cheatsheet, with elements retrieved from this memory module at inference-time. In this work, we consider structured cheatsheets, with learned clusters of behaviors. We introduce a Hierarchical Dirichlet Process Gaussian Mixture Model (HDP-GMM) over behavior embeddings, which shares components across domains while allowing domain-specific mixing weights, and uses the posterior predictive to retrieve relevant behaviors for a query; we call this a $\textit{Bayesian Cheatsheet}$. This mechanism allows for cheap adaptation in an online test-time training (TTT) setting, softly updating the mixture's sufficient statistics following each sample and enabling the creation of new components when the synthesized behaviors are sufficiently novel. We demonstrate that Bayesian Cheatsheet achieves clear performance gains relative to existing memory modules across reasoning benchmarks such as AIME'25, Omni-MATH, and PhysReason, even in the cold-start setting. We show that the Bayesian Cheatsheet is an adaptively reorganizing memory module, as behaviors can be re-assigned to components through a single step of collapsed Gibbs sampling. Our findings highlight the value of Bayesian-inspired memory modules for effective test-time adaptation and the role of structure in metacognitive reasoning.

Abstract: Humans can often acquire and synthesize complex, recursive concepts from minimal experience. Leveraging cognitive insights, we propose the Minimalist Machine, a framework for inductive program synthesis designed to model such conceptual learning. The system uses a compact relational subset of Prolog: Programs are searched within a fixed schema of body-free facts and two-body conjunctive Horn clauses. Recursion is not defined by a dedicated metarule. Instead, it emerges when a target predicate is reused inside the body of a learned clause. Inspired by a primary school curriculum, the model is taught through a human-curated, sequential introduction of new concepts in arithmetic. Starting from initially empty knowledge base, it first acquires simple structural predicates, then successor-based state transformations, and finally recursive programs for addition, subtraction, multiplication, and division. Ultimately, this approach yields the fully transparent, inductive reasoning trace necessary for human-like conceptual learning.

Abstract: Reinforcement learning from verifiable rewards (RLVR) usually optimizes answer correctness, yet useful language-model behavior also requires high-quality reasoning and concise responses. Existing multi-reward post-training methods typically scalarize rewards or combine specialists without explicitly protecting a reward priority order. This is problematic when trade-offs are asymmetric: conciseness, for example, should not improve at the cost of correctness. We introduce Lexicographic Multi-Objective On-Policy Distillation (LMOPD), a multi-teacher method for integrating reward-specialized policies under explicit priorities. For each student rollout, LMOPD selects the specialist for the first objective whose gate detects a deficiency, then locally projects its centered log-policy correction to remove components that oppose higher-priority specialists. We evaluate 30B-A3B mixture-of-experts transformer models in two- and four-expert settings on three math benchmarks, measuring retained specialist gains. With two experts, LMOPD's point estimates fully retain the accuracy and reasoning-quality gains while acquiring $46.9\%$ of the conciseness gain. With four experts, it retains $\approx90\%$ of both the accuracy gain and reasoning-correctness gain, compared to only $\approx57\%$ by the next best evaluated baseline. Matched four-expertablations show that lexicographic routing outperforms random routing and that projection further strengthens both top-priority capabilities. Across both scales, LMOPD preserves the highest-priority capabilities more effectively than the existing baselines we evaluate, demonstrating the value of explicit priorities for specialist integration.

Abstract: Skill evolution offers a promising way to improve large language model agents without updating their parameters, but its use in formal theorem proving remains underexplored. Existing methods mainly target natural-language reasoning, improving skills by analyzing successful and failed trajectories and incrementally revising solving strategies. Although the Lean verifier provides reliable execution feedback, when all sampled trajectories fail, existing skill evolution methods lack successful trajectories from which to infer effective update directions. Furthermore, these methods also focus mainly on the root instruction file, thus underexploring the evolution of reference knowledge including mathematical concepts and proving techniques. To address these limitations, we propose a mutation-enhanced skill self-evolution framework for building skill-augmented Lean provers. The framework jointly evolves a high-level solving policy and its reference knowledge through progressive and mutation-based updates. Progressive evolution derives local improvements from successful and failed trajectories, while mutation is triggered when no complete proof can be generated, sampling mathematical concepts to produce and select new skill candidates under verifier feedback. We evaluate our method on MiniF2F, PutnamBench, the 2025 International Mathematical Olympiad (IMO 2025), and the 2026 USA Mathematical Olympiad (USAMO 2026). Under the same backbone model, trajectorysampling budget, and test-time compute, our method achieves proof success rates of 100.0%, 90.6%, 4/6, and 4/6, respectively, with GPT-5.5, outperforming the baseline methods. Further analysis shows that concept-guided mutation outperforms random-text-guided mutation by 6.9 and 8.2 percentage points on MiniF2F and PutnamBench, respectively, while solving one additional problem on both IMO 2025 and USAMO 2026.

Abstract: Abductive learning combines neural perception with symbolic reasoning, using explanations generated by abduction to supervise the perception model. Multiple valid explanations of the same symbolic target can assign conflicting labels to the same inputs. Common policies select a single candidate as a pseudo-label, which may reinforce mistaken assignments, or weight all candidates, which may spread supervision across competing labels. These risks motivate selecting a retained subset to balance supervision sharpness and model-mass coverage. To guide this choice, we bound the coordinate-level supervision error using retained uncertainty, discarded model mass, and model mismatch. For a fixed model and training pair, only the first two terms depend on the retained set. We propose Abductive Candidate Retention (ACR), which uses these terms to guide greedy additions, accepting a candidate when its recovered mass exceeds the increase in retained uncertainty. Experiments show that ACR improves concept accuracy over single-candidate baselines and A3BL in most evaluated aggregated mod-addition settings. Objective ablations support the joint use of uncertainty and posterior mass.

Abstract: Multi-reward policy optimization requires a joint update that reflects both the learning signals and the intended relationships among objectives. We introduce Objective-wise Reconciled Policy Gradient (ORPG), which constructs a separate clipped policy objective for each reward and reconciles the resulting gradients into one policy update. For compatible gradients, a cosine-dependent interpolation coordinates their contributions through a partially normalized reference while preserving the norm of their sum. We characterize this update as the unique solution of a spherical directional compromise. For conflicting gradients, projection follows the task's priorities. We evaluate the same compatible rule in helpfulness--safety alignment and correctness--cost optimization for mathematical reasoning. ORPG substantially improves average Useful and Harmless scores over the strongest external baseline on each axis. In mathematics, it achieves the highest average full-budget accuracy and three-budget hypervolume among the compared methods, with more accurate and shorter responses than the initial policy. Component comparisons and training dynamics show the larger contribution of compatible coordination and a complementary benefit from conflict handling. These results support gradient reconciliation for objectives with equal standing and for objectives with an explicit priority.

Abstract: Long-term memory supports the self-evolution of LLM agents by retaining experience and skills across tasks and enabling their retrieval, reuse, and revision in subsequent long-horizon decision-making. Yet existing memory management approaches remain limited to discriminative retrieval and to address the sparse, hierarchical, and highly redundant structure of reusable experience: only a small, task-dependent subset of trajectories and memories warrants retention, retrieval, or revision. Learning these operations is further complicated by sparse, delayed, and indirect task-level feedback, with weak supervision across the memory lifecycle. Moreover, continual memory evolution introduces an architectural tension as addressing invariance: stored experience is perpetually revised, yet the addressing interface consumed by learned retrieval policies must remain stable. To address, we present GenMem, which reformulates memory management as generative symbolic addressing. Its core mechanism is the Symbolic Identifier (SID), a multi-level discrete token tuple drawn from a Cartesian-product address space that factorizes a million-scale sparse memory space using fewer than one hundred discrete symbols. Instead of generating ever-changing raw content, the memory agent learns to generate SIDs, while memory evolution rewrites the payload at a fixed address without shifting the address itself. Architecturally, GenMem couples a MemRetriever and a MemEvolver within a multi-agent harness, trained via GRPO with dense process and outcome rewards with two-channels optimization. Under offline memory evolution, experiments spanning ALFWorld, WebShop, multi-hop QA, medical reasoning, and deep research evaluate GenMem against strong memory-augmented baselines...

Abstract: Imperfect verifiers can assign a harmful update direction even when clipping and regularization bound its magnitude. We introduce Audit-First VAPO, which separates discrete directional admission from continuous magnitude control. An observation-only accept-appeal-abstain policy uses a finite secondary-verification budget; its action trace is frozen before clean labels are joined. Simultaneous finite-sample bounds then certify selected harmful risk, coverage, and verifier-call rate over a predeclared policy family. Conditional Hoeffding-Azuma bounds account for the dependence induced by shared budgets, and rollout or verifier changes initiate a new certification stage. After admission, a bounded trust-clip-KL actuator controls magnitude. We evaluate two models on two reasoning benchmarks against static RLVR, matched-random selection, confidence thresholding, noise correction, and verifier augmentation. On Qwen3.5-0.8B and GSM8K at target risk $ρ=0.08$, RC-VAPO achieves 74.1% accuracy, selected harmful risk 0.0697, coverage 0.4125, and relative verifier cost $1.16\times$. At matched coverage and update magnitude, its selected-risk difference from matched random is -0.0260 with paired 95% interval $[-0.0364,-0.0157]$. Across asymmetric, confidence-dependent, and correlated-verifier noise, the certificate is satisfied on 57 of 60 independent runs. These comparisons isolate informative directional selection from proposal suppression, update shrinkage, and additional verifier computation.

Abstract: Humans and machines often solve harder problems by spending more time on computation. In deep learning, looped models implement this idea during inference by recurrently updating a hidden state. In practice, however, their training backpropagates through only one or a few updates, making it hard to train early updates to support future ones. We propose looped flows, an approach that sidesteps this issue by training the recurrence with local denoising objectives. By imposing temporal association across denoising objectives through progressively decreasing noise levels and shared noise, the model is incentivized to learn recurrent states that transfer useful computation over time, even when gradients cover only a few updates. We then formulate inference as integrating the velocity of a probability flow parameterized by the learned denoiser, coupled with recurrent states. This allows solving harder problems by spending more computation through a finer temporal grid and enables multiple valid predictions from different initial noise samples. Across six reasoning benchmarks including two multi-solution benchmarks, looped flows outperform prior state-of-the-art looped models overall, achieving 58.8% test accuracy on ARC-AGI-1 and 12.2% on ARC-AGI-2.