Daily Papers

Verifiable formal languages like Lean have profoundly impacted mathematical reasoning, particularly through the use of large language models (LLMs) for automated reasoning. A significant challenge in training LLMs for these formal languages is the lack of parallel datasets that align natural language with formal language proofs. To address this challenge, this paper introduces a novel framework for translating the Mathlib4 corpus (a unified library of mathematics in formal language Lean 4) into natural language. Building upon this, we employ a dual augmentation strategy that combines tactic-based and informal-based approaches, leveraging the Lean-jixia system, a Lean 4 analyzer. We present the results of this pipeline on Mathlib4 as Herald (Hierarchy and Retrieval-based Translated Lean Dataset). We also propose the Herald Translator, which is fine-tuned on Herald. Herald translator achieves a 93.2% accuracy (Pass@128) on formalizing statements in the miniF2F-test and a 22.5% accuracy on our internal graduate-level textbook dataset, outperforming InternLM2-Math-Plus-7B (74.0% and 7.5%) and TheoremLlama (50.1% and 4.0%). Furthermore, we propose a section-level translation framework for real-world applications. As a direct application of Herald translator, we have successfully translated a template section in the Stack project, marking a notable progress in the automatic formalization of graduate-level mathematical literature. Our model, along with the datasets, will be open-sourced to the public soon.

We introduce our Leanabell-Prover-V2, a 7B large language models (LLMs) that can produce formal theorem proofs in Lean 4, with verifier-integrated Long Chain-of-Thoughts (CoT). Following our previous work Leanabell-Prover-V1, we continual to choose to posttrain existing strong prover models for further performance improvement. In our V2 version, we mainly upgrade the Reinforcement Learning (RL) with feedback provided by the Lean 4 verifier. Crucially, verifier feedback, such as indicating success or detailing specific errors, allows the LLM to become ``self-aware'' of the correctness of its own reasoning process and learn to reflexively correct errors. Leanabell-Prover-V2 directly optimizes LLM reasoning trajectories with multi-turn verifier interactions, together with feedback token masking for stable RL training and a simple reward strategy. Experiments show that Leanabell-Prover-V2 improves performance by 3.2% (pass@128) with Kimina-Prover-Preview-Distill-7B and 2.0% (pass@128) with DeepSeek-Prover-V2-7B on the MiniF2F test set. The source codes, curated data and models are available at: https://github.com/Leanabell-LM/Leanabell-Prover-V2.

Recent reinforcement learning (RL) techniques have yielded impressive reasoning improvements in language models, yet it remains unclear whether post-training truly extends a model's reasoning ability beyond what it acquires during pre-training. A central challenge is the lack of control in modern training pipelines: large-scale pre-training corpora are opaque, mid-training is often underexamined, and RL objectives interact with unknown prior knowledge in complex ways. To resolve this ambiguity, we develop a fully controlled experimental framework that isolates the causal contributions of pre-training, mid-training, and RL-based post-training. Our approach employs synthetic reasoning tasks with explicit atomic operations, parseable step-by-step reasoning traces, and systematic manipulation of training distributions. We evaluate models along two axes: extrapolative generalization to more complex compositions and contextual generalization across surface contexts. Using this framework, we reconcile competing views on RL's effectiveness. We show that: 1) RL produces true capability gains (pass@128) only when pre-training leaves sufficient headroom and when RL data target the model's edge of competence, tasks at the boundary that are difficult but not yet out of reach. 2) Contextual generalization requires minimal yet sufficient pre-training exposure, after which RL can reliably transfer. 3) Mid-training significantly enhances performance under fixed compute compared with RL only, demonstrating its central but underexplored role in training pipelines. 4) Process-level rewards reduce reward hacking and improve reasoning fidelity. Together, these results clarify the interplay between pre-training, mid-training, and RL, offering a foundation for understanding and improving reasoning LM training strategies.

The common paradigm of reinforcement learning with verifiable rewards (RLVR) is to let agents make multiple attempts at a task, and optimize towards the successful ones. This becomes problematic in the realms of self-improvement, where tasks are so difficult that the agent has a low or even no chance of success, and where there are no teacher models or example solutions to distill from. In this paper, we introduce RLTLDR. After each failed attempt, we show the policy the verifier outputs and let it write its own feedback, in the form of a single TL;DR insight. The next rollout is conditioned on all previous insights, and we sequentially sample rollouts until a solution is found. Moreover, we enable backpropagation on the in-context insights to internalize a direct task to insight mapping. On challenging tool-calling and coding datasets (filtered to Pass@128=0), standard GRPO training of a Qwen 3.5 9B Thinking policy stays flat at a Pass@1 of 0% to 1%. RLTLDR breaks through this learning barrier, achieving a Pass@1 of 14-31% with insights in context during training and, crucially, 12-13% when no insight is in context at eval time. We identify that the key is the task to insight internalization. To study this further, we reduce our approach to SFTLDR, training only on (task, insight) tuples, without showing or backpropagating on any rollouts. Training on only 4k of these tuples recovers almost the full performance of RLTLDR and classical SFT on full rollouts. This demonstrates a promising compacted training paradigm of the form "on this sort of task, keep this sort of thing in mind", which we hope to inspire future research on.

Reinforcement learning has become a common post-training technique to improve the accuracy of LLMs on verifiable tasks. However, such training can narrow the set of solutions the model can produce. Several approaches have attempted to address this behavior-sharpening effect, but they often optimize metrics that do not reflect the diversity of correct solutions. Ideally, we want a model that can produce multiple good solutions, not only a single reliable one. We propose EliteReplay, a post-training recipe that pairs GRPO with an "elite" archive built by quality-diversity search. Before training, we use the frozen base model to collect solutions that span distinct approaches; during training, GRPO is combined with a replay loss on this archive. The result is a post-trained model that improves accuracy while preserving more of the base model's solution diversity. On multiple text-to-SQL tasks, EliteReplay achieves a higher pass@128 than all baselines, producing up to 77% more distinct correct strategies than the strongest baselines. It preserves most of the base model's correct strategies, outperforming existing methods in strategy retention. This diversity translates into practical benefits on ambiguous questions, where EliteReplay covers both interpretations nearly twice as often as the strongest baseline on AmbiQT.

Reinforcement Learning with Verifiable Rewards (RLVR) enhances reasoning of Large Language Models (LLMs) but usually exhibits limited generation diversity due to the over-incentivization of positive rewards. Although methods like Negative Sample Reinforcement (NSR) mitigate this issue by upweighting penalty from negative samples, they may suppress the semantic distributions shared between positive and negative responses. To boost reasoning ability without losing diversity, this paper proposes negative sample projection Residual Reinforcement Learning (ResRL) that decouples similar semantic distributions among positive and negative responses. We theoretically link Lazy Likelihood Displacement (LLD) to negative-positive head-gradient interference and derive a single-forward proxy that upper-bounds representation alignment to guide conservative advantage reweighting. ResRL then projects negative-token hidden representations onto an SVD-based low-rank positive subspace and uses projection residuals to modulate negative gradients, improving reasoning while preserving diversity and outperforming strong baselines on average across twelve benchmarks spanning Mathematics, Code, Agent Tasks, and Function Calling. Notably, ResRL surpasses NSR on mathematical reasoning by 9.4\% in Avg@16 and 7.0\% in Pass@128. Code is available at https://github.com/1229095296/ResRL.git.

Despite the success of reinforcement learning for large language models, a common failure mode is reduced sampling diversity, where the policy repeatedly generates similar erroneous behaviors. Classical entropy regularization encourages randomness under the current policy, but does not explicitly discourage recurrent failure patterns across rollouts. We propose MEDS, a Memory-Enhanced Dynamic reward Shaping framework that incorporates historical behavioral signals into reward design. By storing and leveraging intermediate model representations, we capture features of past rollouts and use density-based clustering to identify frequently recurring error patterns. Rollouts assigned to more prevalent error clusters are penalized more heavily, encouraging broader exploration while reducing repeated mistakes. Across five datasets and three base models, MEDS consistently improves average performance over existing baselines, achieving gains of up to 4.13 pass@1 points and 4.37 pass@128 points. Additional analyses using both LLM-based annotations and quantitative diversity metrics show that MEDS increases behavioral diversity during sampling.

Speculative decoding accelerates large language model inference by drafting future tokens cheaply and verifying them with the target model in parallel. Block drafters score a whole block of future tokens in one forward pass, yet standard decoding verifies only the top-scoring chain and discards the other candidates. Because these candidates are already scored, verifying more of them adds target computation but no extra drafting. We introduce CAST (Cost-Aware Speculative Trees), which packs these candidates into a tree and verifies it in a single target pass, leaving the target model, drafter weights, and decoding rule untouched. To decide how wide the tree should be, CAST adds candidates while the expected gain from the next one outweighs the verification time it adds. The width therefore adapts to each deployment from a latency measurement, without sweeping over widths. We evaluate CAST across five domains on three GPU generations and two model families. At its predicted width, CAST is faster than the standard chain in all eight settings, by up to 43%. We also find that the best width depends strongly on the deployment. Where verification cost jumps at a kernel boundary, a 128-token tree is only 2% faster than the standard chain, whereas the tree at the predicted width is 20% faster. Furthermore, we prove that CAST leaves the target output distribution unchanged under both greedy and sampled decoding. Code is available at https://github.com/js-lee-AI/CAST.

A multi-agent system can reduce latency on complex tasks by executing work concurrently. Several pioneering harness frameworks support multi-agent systems. However, the scalability of current multi-agent harnesses is often constrained by a central orchestrator's capacity to allocate tasks and coordinate workers. To address this limitation, we introduce Agensh, a scalable self-organized multi-agent harness without a central orchestrator: concurrent workers execute a multi-agent cooperation loop, continuously gathering context, claiming and self-assigning sub-tasks, taking action and sharing findings, verifying results, and merging progress in an asynchronous manner. The loop is supported by the agentic organization infrastructure comprising three components: a shared workspace holds proposed, ongoing, and completed work; a message interface lets workers communicate; and shared context retains reusable findings and work intentions. To test the scalability of Agensh, we evaluate it on the five hardest ProgramBench tasks with GPT-5.6-sol (high). Scaling from 1 to 128 agents raises the mean final test-pass rate from 19.31% to 28.78%, an approximately 49% relative improvement. Larger organizations reach comparable test-pass rates earlier. On pandoc, scaling from 1 to 1,024 agents raises the final test-pass rate from 33.89% to 55.06%. Worker trajectories further show that different forms of self-organized cooperation gradually emerges and standardizes as the organization grows. These results reveal the number of agents as a new scaling dimension for multi-agent organizations to expand the frontier of general intelligence, offering a practical solution for complex tasks under hard latency constraints or time budgets.

Reinforcement Learning with Verifiable Rewards (RLVR) has shown remarkable success in improving the mathematical reasoning of large language models. Yet problems beyond the model's current capability, where rollouts uniformly fail and no learning signal is produced, are structurally wasted despite marking the most informative training frontier. We show that these otherwise-inert problems can be unlocked via teacher-guided curriculum learning: partial reasoning traces from a stronger model create a graded difficulty landscape, and a backward-chaining curriculum progressively withdraws guidance until the model solves problems unaided. Training on only 128 unsolvable problems matches or exceeds GRPO trained on a full 2,000-problem corpus (~16x data efficiency) on the nine-benchmark average for both base models, while substantially expanding the reasoning boundary measured by pass@k at large k. Furthermore, we identify a distribution-shift cost that is particularly acute in the unsolvable-only regime and propose Monotone Frontier Curriculum (MFC), a method that monotonically drives training toward unguided solving, consistently outperforming existing curriculum methods.

Fully continuous diffusion language models (dLMs) denoise continuous representations without intermediate discretization, then decode all response tokens in parallel at the final step. Their performance on challenging reasoning tasks remains less established than that of autoregressive (AR) LLMs and masked dLMs. We scale Embedded Language Flows (ELF) to mathematical reasoning and code generation on GSM8K, MATH-500, HumanEval, and MBPP. We introduce ELF-REG, which improves learning with representation alignment and entanglement (REPA+REG), where a frozen AR teacher supervises intermediate denoiser features and supplies a global representation that is jointly denoised with the response. ELF-REG-L achieves 55.96% pass@1 on GSM8K at 64 network function evaluations (NFE), and 13.39% on MATH-500 and 22.56% on HumanEval at 128 NFE. It outperforms the evaluated comparable-scale dLMs in pass@1 on GSM8K and code, and improves MATH-500 pass@1 from 10.55% for the ELF-L baseline to 13.39% with ELF-REG-L. Without few-step training, the same task-specific checkpoints support strong low-NFE performance through early-stop, which decodes an intermediate clean prediction without completing the denoising trajectory. At 16 NFE, ELF-REG-L reaches 41.21% HumanEval pass@10, outperforming recent continuous dLMs of comparable scale.

Reinforcement learning with verifiable rewards (RLVR) has become the standard method for training language models to reason. However, RLVR typically relies solely on outcome correctness, which does not guarantee that the CoT causally contributes to the final answer. Without this connection, outcome rewards may fail to reinforce high-quality reasoning. Existing causality metrics assess CoT causality by perturbing the CoT, such as deleting reasoning steps or injecting errors, and measuring changes in the final answer. However, these perturbations inevitably alter information in each step. Consequently, high causality scores may reflect sensitivity to information changes introduced by perturbation rather than true causality. Such confounding effects further induce undesirable reasoning behaviors when these metrics are used as training rewards, including generating less informative CoTs and reducing exploration and self-correction. To address this problem, we propose CRoS (Causality Reward on Scrambled CoTs), a novel CoT causality metric that perturbs the order of reasoning steps without altering content, thereby preserving information within each step. On Reasoning Gym with Gemma-3-4B, CRoS outperforms existing causality and outcome rewards in out-of-domain accuracy, CoT quality, and CoT faithfulness. Specifically, CRoS achieves 46.8% accuracy on five unseen logic and games datasets, outperforming the strongest baseline (43.8%). It also achieves better CoT quality, consistently outperforming baselines in CoT-Pass@K from K=1 to 128, averaging 43.4% vs. 41.4%. For CoT faithfulness, CRoS achieves a hint acknowledgment score of 34.0% vs. 20.2%.

We present context parallelism for long-context large language model inference, which achieves near-linear scaling for long-context prefill latency with up to 128 H100 GPUs across 16 nodes. Particularly, our method achieves 1M context prefill with Llama3 405B model in 77s (93% parallelization efficiency, 63% FLOPS utilization) and 128K context prefill in 3.8s. We develop two lossless exact ring attention variants: pass-KV and pass-Q to cover a wide range of use cases with the state-of-the-art performance: full prefill, persistent KV prefill and decode. Benchmarks on H100 GPU hosts inter-connected with RDMA and TCP both show similar scalability for long-context prefill, demonstrating that our method scales well using common commercial data center with medium-to-low inter-host bandwidth.

Continuous diffusion generates complete reasoning solutions through iterative refinement in latent space. We introduce Latent Flow Reasoning Models (LFRMs), an ELF-based training and inference recipe. Our experiments show that accurate decoding alone does not ensure strong reasoning performance. We therefore learn compact representations from multiple layers of a strong autoregressive teacher. Their decomposition also enables asynchronous denoising at different rates. We show that prompt encodings need only preserve the information required for the correct text-conditional score, rather than exactly match teacher features, and use a staged curriculum to learn a compact prompt encoder that replaces the teacher Transformer at inference. We adapt DiffusionNFT to learned self-conditioning guidance and incorporate gold-solution endpoints to supplement sparse rewards. Our supervised models outperform reported results from recent continuous-diffusion baselines at comparable backbone scales on mathematical reasoning and HumanEval code generation. With a 638M-parameter denoising backbone and learned prompt conditioning, post-NFT LFRM-L achieves 63.74% pass@1 on GSM8K and 24.6% on MATH500 at 64 denoising steps, and 32.85% on HumanEval and 30.18% on HumanEval+ at 128 denoising steps. Code will be available at: https://github.com/chengxiang/LFRM

Relative-position attention mechanisms offer compelling alternatives to RoPE across various transformer architectures, delivering superior performance in domains such as audio. These mechanisms typically modify attention scores by adding content-position or bias-position terms. Unlike RoPE, which encodes position via per-token rotations directly on the queries and keys, relative-position terms generally require pairwise offset-dependent computation or lookups, complicating their integration into fused attention kernels and introducing severe memory, bandwidth, and compute overheads as sequences scale. To address this bottleneck, we propose an exact attention algorithm that incorporates additive relative-position terms into FlashAttention-style tiled computation. Our method (1) uses offset-aware tiling to avoid redundant indexing and memory accesses, (2) computes only the necessary key/query-relation products and reuses them across token pairs in both forward and backward passes, and (3) uses offset-based gradient sharding and aggregation, eliminating atomic contention. We provide a unified, efficient Triton implementation across diverse relative-position attention mechanisms and evaluate it against naive and specialized implementations. For 8K-token sequences, our method speeds up the forward (backward) pass by 1.8-6.4times (2.0-21times) and reduces peak memory up to 2.9-128times (1.4-54times) over the strongest baseline for each mechanism, enabling long-context end-to-end transcription that is 1.8times faster and uses 2.4times less memory. Our method thus provides a drop-in, hardware-efficient solution for scaling relative-position attention transformers.