ICML 2026 论文列表

International Conference on Machine Learning

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Awakening Visual Reasoning: Mitigating Post-Training Failure in Vision-Text Compression

Xing Xi, Liyao Li, Hao Chen, NINGTAO WANG, Peixian Chen, Peilin Tong, Xing Fu, Yu Cheng, Haobo Wang, Gang Chen, Junbo Zhao, Ronghua Luo

展开摘要

Vision-Text Compression (VTC) offers a scalable path for long-context multimodal modeling by rendering textual data into dense visual tokens. While recent Vision-Language Models (VLMs) demonstrate high decoding fidelity (OCR) on such inputs, they exhibit a severe reasoning gap: models that reason robustly on native text often fail on visually compressed equivalents, particularly in long-range retrieval and multi-step deduction. We identify a phenomenon of post-training transfer failure, where standard supervised fine-tuning and reinforcement learning on visual prompts yield marginal gains compared to their textual counterparts. To address this, we propose CoRe (Coordinated Reasoning), a training framework that enforces lockstep consistency between the reasoning processes of textual and visual modalities. By treating the text-conditioned policy as a dynamic anchor, CoRe aligns the visual-conditioned policy via step-wise distribution matching, seamlessly integrating into both SFT and RL pipelines. Extensive evaluations across mathematical reasoning, long-context memory, and tabular retrieval benchmarks show that CoRe significantly outperforms standard visual post-training, recovering up to 70% of the performance gap relative to the textual upper bound and effectively activating latent reasoning capabilities in the compressed visual modality.

Poster
Better, Faster: Harnessing Self-Improvement in Large Reasoning Models

Qihuang Zhong, Liang Ding, Juhua Liu, Bo Du, Leszek Rutkowski, Dacheng Tao

展开摘要

Self-improvement training enables the large reasoning models (LRMs) to improve themselves by self-generating reasoning trajectories as training data without external supervision. However, we find that this method often falls short in complex reasoning tasks and even leads to model collapse. Through a series of preliminary analyses, we reveal two problems: (1) data imbalance, where most training samples are simple, but the challenging yet crucial samples are scarce; (2) overthinking, where many undesired samples with redundant reasoning steps are used for self-training. To this end, we propose HSIR, which effectively Harnesses Self-Improvement in large Reasoning models via two simple-yet-effective approaches. Specifically, HSIR introduces a verify-then-exit sampling strategy to mitigate data imbalance by efficiently collecting more accurate solutions for difficult queries, and designs an Intrinsic Diversity score to quantify overthinking and filter out the undesired solutions. We apply HSIR to various post-training paradigms, among which we further propose H-GRPO, an enhanced GRPO algorithm that leverages the intrinsic diversity as an external reward to encourage concise and diverse reasoning via reinforcement learning. Extensive results show that HSIR not only effectively enhances the reasoning performance, i.e., bringing up to +10.9% average performance gains, but also significantly improves the reasoning efficiency by reducing up to 42.4% relative inference overhead.

Poster
Test-Time Training with KV Binding Is Secretly Linear Attention

Junchen Liu, Sven Elflein, Or Litany, Zan Gojcic, Ruilong Li

展开摘要

Test-time training (TTT) with KV binding as sequence modeling layer is commonly interpreted as a form of online meta-learning that memorizes a key–value mapping at test time. However, our analysis reveals multiple phenomena that contradict this memorization-based interpretation. Motivated by these findings, we revisit the formulation of TTT and show that a broad class of TTT architectures can be expressed as a form of learned linear attention operator. Beyond explaining previously puzzling model behaviors, this perspective yields multiple practical benefits: it enables principled architectural simplifications, admits fully parallel formulations that preserve performance while improving efficiency, and provides a systematic reduction of diverse TTT variants to a standard linear attention form. Overall, our results reframe TTT not as test-time memorization, but as learned linear attention with enhanced representational capacity. Project page: https://research.nvidia.com/labs/sil/projects/tttla/.

Poster
From Historical Patches to Repair Plans: Outcome-Conditioned Reasoning for Repository-Level Program Repair

Chenglin Li, Yisen Xu, Zehao Wang, Shin Hwei Tan, Tse-Hsun Chen

展开摘要

Repository-level automated program repair (APR) requires long-horizon reasoning over interdependent decisions. However, most LLM-based approaches reconstruct repair reasoning independently for each issue, failing to reuse successful patterns from prior repairs, even though real-world repositories contain many related issues with shared structure or constraints. Existing methods typically rely on forward exploration, which operates under outcome uncertainty, incurs substantial inference-time overhead, and can drift from the final correct patch. We propose Conditional Reasoning Distillation (ConRAD), which leverages in-repository resolved issues by reconstructing repair reasoning backward from verified patches and distilling outcome-consistent, stage-wise repair reasoning plans. Injected at inference time, these plans guide fault localization and patch generation, replacing open-ended exploration with constrained inference without fine-tuning or search. On SWE-Bench Lite, ConRAD improves Pass@1 by 10.4\% (GPT-4o), 8.6\% (DeepSeek-V3), and 10.3\% (GPT-5), demonstrating a scalable inference-time alternative to forward exploration for long-horizon APR.

Poster
Blending Supervised and Reinforcement Fine-Tuning with Prefix Sampling

Zeyu Huang, Tianhao Cheng, Zihan Qiu, Zili Wang, Xu Yinghui, Edoardo Ponti, Ivan Titov

展开摘要

Existing LLMs-post-training techniques are broadly categorized into supervised fine-tuning (SFT) and reinforcement fine-tuning (RFT). Each paradigm presents a distinct trade-off: (1) SFT excels at mimicking demonstration data, but can lead to problematic generalization as a form of behavior cloning. (2) Conversely, RFT can significantly enhance a model's performance but is prone to learning unexpected behaviors, and its performance is sensitive to the initial policy. In this paper, we propose a unified view of these methods and introduce Prefix-RFT, a hybrid approach that synergizes learning from both demonstration and exploration. Using mathematical reasoning problems as a test bed, we empirically demonstrate that Prefix-RFT is simple yet effective. Not only does it surpass the performance of standalone SFT and RFT, but it also outperforms parallel mixed-policy RFT methods. Our analysis highlights the complementary nature of SFT and RFT, validating that Prefix-RFT effectively harmonizes them. Further ablation studies confirm the method's robustness to variations in the quality and quantity of demonstration data.

Poster
MECAT: A Multi-Experts Constructed Benchmark for Fine-Grained Audio Understanding Tasks

Yadong Niu, TIANZI WANG, Heinrich Dinkel, Xingwei Sun, Jiahao Zhou, Gang Li, Jizhong Liu, Xunying Liu, Jian Luan

展开摘要

While large audio-language models have advanced open-ended audio understanding, they still fall short of nuanced human-level comprehension. This gap persists largely because current benchmarks, limited by data annotations and evaluation metrics, fail to reliably distinguish between generic and highly detailed model outputs. To this end, this work introduces MECAT, a Multi-Expert Constructed Benchmark for Fine-Grained Audio Understanding Tasks. Generated via a pipeline that integrates analysis from specialized expert models with Chain-of-Thought large language model reasoning, MECAT provides multi-perspective, fine-grained captions and open-set question-answering pairs. The benchmark is complemented by a novel metric: DATE (Discriminative-Enhanced Audio Text Evaluation). This metric penalizes generic terms and rewards detailed descriptions by combining single-sample semantic similarity with cross-sample discriminability. A comprehensive evaluation of state-of-the-art audio models is also presented, providing new insights into their current capabilities and limitations. The code and data are publicly available at https://github.com/xiaomi-research/mecat.

Poster
Advantage Collapse in Group Relative Policy Optimization: Diagnosis and Mitigation

Xixiang He, QiYao Sun, Ao Cheng, Xingming Li, Xuanyu Ji, Hailun Lu, Runke Huang, Qingyong Hu

展开摘要

Group Relative Policy Optimization (GRPO), a prominent algorithm within the Reinforcement Learning from Verifiable Rewards (RLVR) framework, has achieved strong results in improving the reasoning capabilities of large language models (LLMs). However, GRPO is prone to advantage collapse, a failure mode where homogeneous rewards within a group (e.g., all correct or all incorrect answers) yield near-zero advantages and vanishing gradients. To address this, we introduce the Advantage Collapse Rate (ACR), the first diagnostic metric quantifying the proportion of training batches with ineffective gradients. Across models from 0.5B to 14B parameters on mathematical reasoning benchmarks, we show that ACR strongly predicts training stagnation and final performance. We then propose Adaptive Virtual Sample Policy Optimization (AVSPO), a lightweight extension of GRPO that injects virtual reward samples, guided by real-time ACR monitoring, to enable learning from homogeneous groups without additional model rollouts. AVSPO reduces advantage collapse by 58–63% relative to GRPO and yields consistent accuracy gains of 4–6 percentage points across all model scales, while maintaining generalization on the evaluated out-of-domain task. Code and datasets are available at https://github.com/hexixiang/Advantage-Collapse-Rate.

Poster
R$^3$L: Reasoning 3D Layouts from Relative Spatial Relations

Zhifeng Gu, Yuqi Wang, Bing Wang

展开摘要

Relative spatial relations provide a compact representation of spatial structure and are fundamental to relative spatial reasoning in 3D layout generation. Recent works leverage Multimodal Large Language Models (MLLMs) to infer such relations, but the inferred relations are often unreliable and are typically handled with post-hoc heuristics. In this paper, we propose R$^3$L, a general framework that improves the reliability and consistency of relative spatial reasoning for 3D layout generation. Our key motivation is that multi-hop reasoning requires repeated reference-frame transformations, which accumulate errors in inferred relations and lead to semantic and metric drift. To mitigate this, we propose invariant spatial decomposition to break coupled relation chains, and consistent spatial imagination to promote self-consistency through an imagine-and-revise loop. We further introduce supportive spatial optimization to ease pose optimization via global-to-local coordinate re-parameterization. Extensive experiments across diverse scene types and instructions demonstrate that R$^3$L produces more physically feasible and semantically consistent layouts. Notably, our analysis shows that resolving frame-induced inconsistencies is crucial for reliable multi-hop relative spatial reasoning. The code is available at https://github.com/Neal2020GitHub/R3L.

Poster
On the Limits of Test-Time Compute: Sequential Reward Filtering for Better Inference

Yue Yu, Qiwei Di, Quanquan Gu, Dongruo Zhou

展开摘要

Test-time compute (TTC) has become an increasingly prominent paradigm for enhancing large language models (LLMs). Despite the empirical success of methods such as best-of-$n$ (BoN) sampling and sequential revision, their fundamental limits remain unclear. We address this gap by analyzing a mixture-of-reference policy model and proving that standard BoN is inherently suboptimal. To move closer to the optimal frontier, we study reward-filtered sequential inference, a simple procedure that selectively incorporates only high-reward generations into the context. This mechanism concentrates computation on superior policy candidates and suppresses inferior ones. On the theoretical side, we show that reward-filtered sequential inference yields strictly stronger guarantees than standard TTC paradigms. On the empirical side, we evaluate such an inference strategy across diverse benchmarks and observe consistent improvements over widely used approaches, demonstrating the practical effectiveness of our framework.

Poster
DC-W2S: Dual-Consensus Weak-to-Strong Training for Reliable Process Reward Modeling in Biological Reasoning

Chi-Min Chan, Ehsan Hajiramezanali, Xiner Li, Edward De Brouwer, Carl Edwards, Wei Xue, Sirui Han, Yike Guo, Gabriele Scalia

展开摘要

In scientific reasoning tasks, the veracity of the reasoning process is as critical as the final outcome. While Process Reward Models (PRMs) offer a solution to the coarse-grained supervision problems inherent in Outcome Reward Models (ORMs), their deployment is hindered by the prohibitive cost of obtaining expert-verified step-wise labels. This paper addresses the challenge of training reliable PRMs using abundant but noisy "weak" supervision. We argue that existing Weak-to-Strong Generalization (W2SG) theories lack prescriptive guidelines for selecting high-quality training signals from noisy data. To bridge this gap, we introduce the Dual-Consensus Weak-to-Strong (DC-W2S) framework. By intersecting Self-Consensus (SC) metrics among weak supervisors with Neighborhood-Consensus (NC) metrics in the embedding space, we stratify supervision signals into distinct reliability regimes. We then employ a curriculum of instance-level balanced sampling and label-level reliability-aware masking to guide the training process. We demonstrate that DC-W2S enables the training of robust PRMs for complex reasoning without exhaustive expert annotation, proving that strategic data curation is more effective than indiscriminate training on large-scale noisy datasets.

Poster
Thinking in Scales: Accelerating Gigapixel Pathology Image Analysis via Adaptive Continuous Reasoning

Jiusong Ge, Yingkang Zhan, Wenjie Zhao, Di Zhang, Ke Wang, Jiashuai Liu, Chunze Yang, Chengzu Li, Jian Zhang, Yuxin Dong, Ni Zhang, Qidong Liu, Mireia Crispin-Ortuzar, Mireia Crispin-Ortuzar, Huazhu Fu, Chen Li, Zeyu Gao

展开摘要

Traditional whole slide image (WSI) analysis methods typically rely on the multiple instance learning (MIL) paradigm, which extracts patch-level features at high magnification and aggregates them for slide-level prediction. However, such exhaustive patch-level processing is computationally expensive, severely limiting the efficiency and scalability of WSI analysis. To address this challenge, we propose PathCTM (a Pathology-oriented Continuous Thought Model) that enables token-efficient scale-space continuous reasoning for gigapixel WSIs. PathCTM formulates diagnostic inference as a dynamic sequential information pursuit. It progressively transitions from low-magnification global to high-magnification local inspection, and adaptively terminates inference when sufficient evidence is gathered to effectively bound decision uncertainty. Specifically, it uses conditional computation for dynamic scale switching with attention-guided region pruning, coupled with confidence-aware early stopping. Extensive experiments demonstrate that, compared with standard MIL-based methods, PathCTM reduces the number of required image patches by 95.95\% and shortens inference time by approximately 95.62\%, while maintaining AUC without degradation. Code is available at https://github.com/JSGe-AI/PathCTM.

Poster
Shrinking the Variance: Shrinkage Baselines for Reinforcement Learning with Verifiable Rewards

Guanning Zeng, Zhaoyi Zhou, Daman Arora, Andrea Zanette

展开摘要

Reinforcement Learning with Verifiable Rewards (RLVR) has emerged as a powerful paradigm for post-training large reasoning models (LRMs) using policy-gradient methods such as GRPO. To stabilize training, these methods typically center trajectory rewards by subtracting the empirical mean for each prompt. Statistically, this centering acts as a control variate (or baseline), reducing the variance of the policy-gradient estimator. Typically, the mean reward is estimated using per-prompt empirical averages for each prompt in a batch. Drawing inspiration from Stein's paradox, we propose using shrinkage estimators that combine per-prompt and cross-prompt means to improve the overall per-prompt mean estimation accuracy, particularly in the low-generation regime typical of RLVR. Theoretically, we construct a shrinkage-based baseline that provably yields lower-variance policy-gradient estimators across algorithms. This baseline serves as a drop-in replacement for existing per-prompt mean baselines, requiring no additional hyperparameters or computation. Empirically, shrinkage baselines consistently outperform standard empirical-mean baselines, leading to lower-variance gradient updates and improved training stability.

Poster
Thoughtbubbles: an Unsupervised Method for Parallel Thinking in Latent Space

Houjun Liu, Shikhar Murty, Christopher D Manning, Róbert Csordás

展开摘要

Current approaches for scaling inference-time compute in transformers train them to emit explicit chain-of-thought tokens before producing an answer. While these methods are powerful, they are limited because they cannot be applied during pretraining and rely solely on serially-generated, natural-language verbalization. In this work, we propose Thoughtbubbles, a transformer variant that natively performs parallel adaptive computation in latent space by learning to fork or delete residual streams. Thus, tokens requiring more computation can form a "bubble" of cloned residuals in the middle of the network. Crucially, this behavior is learned during pretraining with only language modeling loss. Using half of the training budget, Thoughtbubbles outperforms the perplexity and zero-shot evals of both standard decoder LMs and those using non-adaptive parallel computation approaches. These results hold across model sizes from 150M to 1.9B. Thoughtbubbles achieves competitive GSM8K results using half of the baseline's token budget. The implicit nature of our method enables models to begin learning adaptive computation at pretraining time, paving the way to unified train-time and test-time scaling behaviors.

Poster
Seeing is Solving: Unlocking Efficient Multimodal RL via View Alignment

Qinsi Wang, Jing Shi, Kun Wan, Handong Zhao, Hancheng Ye, Zishan Shao, Jinghan Ke, Yudong Liu, Daniel Miranda, Purvak Lapsiya, Yiran Chen, Wentian Zhao

展开摘要

Although Reinforcement Learning Fine-Tuning (RLFT) applied to Vision-Language Models (VLMs) substantially enhances multimodal reasoning capabilities, their prohibitive training cost limits broad adoption. Surprisingly, most existing methods simply port Large Language Model (LLM) RLFT techniques to VLMs, while ignoring a intrinsic property of multimodal models: their dynamic text–vision alignment. We ask a new question: Can this intrinsic alignment be turned into a training signal that makes VLM RLFT more efficient? We analyze how a VLM plans to attend, actually attends, and ideally should attend during reasoning, and derive two lightweight metrics from these patterns. Predictive View Accuracy (PVA) estimates sample difficulty, and Reasoning View Accuracy (RVA) reflects the quality of chain-of-thought (CoT) reasoning. These alignment signals enable automated data curriculum and dense reasoning supervision. We introduce FOCUS-RL, a plug-and-play framework that can be seamlessly integrated into any VLM and dramatically boosts RLFT training efficiency. FOCUS-RL achieves 2.5 x – 4 x faster convergence over vanilla GRPO and consistent accuracy gains (+4.4 on average) across six different benchmarks and multiple VLM families.

Poster
Deep Scientific Reasoning under Physical Constraints: Structure-Aware Spectrum Prediction

Yingheng Wang, Tao Yu, Shufeng Kong, Francesco Ricci, John M Gregoire, Carla P Gomes

展开摘要

Structured scientific spectra encode rich physical information while obeying hard constraints, such as conservation laws and characteristic spectral geometry. Accurate prediction of these spectra is central to materials discovery, yet existing methods often treat them as unconstrained sequences and therefore fail to enforce the underlying physical structure. Taking electronic density of states (eDOS) as the prototypical example, we introduce \textbf{DeepSciReasoner}, a general paradigm for predicting scientific spectra under physical constraints. The framework combines structure-aware spectrum decoding with constraint-preserving physical reasoning, allowing predictions to capture rich spectral structure while respecting the underlying physics. We evaluate DeepSciReasoner on eDOS, phonon density of states (phDOS), X-ray absorption near-edge structure (XANES), and Raman spectra, where it substantially improves prediction accuracy while maintaining physical consistency. These results establish DeepSciReasoner as a reusable blueprint for structured scientific spectrum prediction under hard physical constraints.

Poster
GIFT: Bootstrapping Image-to-CAD Program Synthesis via Geometric Feedback

Giorgio Giannone, Anna C. Doris, Amin Heyrani Nobari, Kai Xu, Akash Srivastava, Faez Ahmed

展开摘要

Generating executable CAD programs from images requires alignment between visual geometry and symbolic program representations, a capability that current methods fail to learn reliably as design complexity increases. Existing fine-tuning approaches rely on either limited supervised datasets or expensive post-training pipelines, resulting in brittle systems that restrict progress in generative CAD design. We argue that the primary bottleneck lies not in model or algorithmic capacity, but in the scarcity of diverse training examples that align visual geometry with program syntax. This limitation is especially acute because the collection of diverse and verified engineering datasets is both expensive and difficult to scale, constraining the development of robust generative CAD models. We introduce Geometric Inference Feedback Tuning (GIFT), a data augmentation framework that leverages geometric feedback to turn test-time compute into a bootstrapped set of high-quality training samples. GIFT combines two mechanisms: Soft-Rejection Sampling (GIFT-REJECT), which retains diverse high-fidelity programs beyond exact ground-truth matches, and Failure-Driven Augmentation (GIFT-FAIL), which converts near-miss predictions into synthetic training examples that improve robustness on challenging geometries. By amortizing inference-time search into the model parameters, GIFT captures the benefits of test-time scaling while reducing inference compute by 80%. It improves mean IoU by 12% over a strong supervised baseline and remains competitive with more complex multimodal systems, without requiring additional human annotation or specialized architectures.

Poster
VR-Thinker: Boosting Multimodal Reward Models through Think with Image Reasoning

Qunzhong Wang, Jie Liu, Jiajun Liang, Yuanxing Zhang, Yilei JIANG, Yaozhi ZHENG, Xintao Wang, Pengfei Wan, Xiangyu Yue, Jiaheng Liu

展开摘要

Recent advancements in multimodal reward models (RMs) have substantially improved post-training for visual generative models. However, current RMs face inherent limitations: **(1)** visual inputs consume large context budgets, forcing fewer frames and causing a loss of details; and **(2)** all visual information is packed into the initial prompt, exacerbating forgetting during chain-of-thought reasoning. To overcome these issues, we introduce **VR-Thinker**, a thinking-with-image RM equipped with visual reasoning operation and a configurable visual memory window. This allows the RM to actively acquire visual evidence, improving reasoning fidelity and reliability. We activate visual reasoning via a reinforcement fine-tuning pipeline: **(i)** **Cold Start** with curated visual chain-of-thought data to distill basic operation formatting; **(ii)** select samples with correct judgments, then conduct **Rejection sampling Fine-Tuning** on these high-quality traces to further enhance reasoning; and **(iii)** apply **Group Relative Policy Optimization** (GRPO) to strengthen reasoning. Our approach delivers state-of-the-art accuracy among open-source models on video preference benchmarks: a 7B **VR-Thinker** achieves 80.5\% on VideoGen Reward, 82.3\% on GenAI-Bench, and 75.6\% on MJ-Bench-Video.

Poster
PETS: A Principled Framework Towards Optimal Trajectory Allocation for Efficient Test-Time Self-Consistency

Zhangyi Liu, Huaizhi Qu, Xiaowei Yin, He Sun, Yanjun Han, Tianlong Chen, Zhun Deng

展开摘要

Test-time scaling can improve model performance by aggregating stochastic reasoning trajectories. However, achieving sample-efficient test-time self-consistency under a limited budget remains an open challenge. We introduce PETS (**P**rincipled and **E**fficient **T**est-Time **S**elf-Consistency), which initiates a principled study of trajectory allocation through an optimization framework. Central to our approach is the *self-consistency rate*}, a new measure defined as agreement with the infinite-budget majority vote. This formulation makes sample-efficient test-time allocation theoretically grounded and amenable to rigorous analysis. We study both offline and online settings. In the offline regime, where all questions are known in advance, we connect trajectory allocation to crowdsourcing, a classic and well-developed area, by modeling reasoning traces as workers. This perspective allows us to leverage rich existing theory, yielding theoretical guarantees and an efficient majority-voting-based allocation algorithm. In the online streaming regime, where questions arrive sequentially and allocations must be made on the fly, we propose a novel method inspired by the offline framework. Our approach adapts budgets to question difficulty while preserving strong theoretical guarantees and computational efficiency. Experiments show that PETS consistently outperforms uniform allocation. On GPQA, PETS achieves perfect self-consistency in both settings while reducing the sampling budget by up to $75\\%$ (offline) and $55\\%$ (online) relative to uniform allocation.

Poster
Less Diverse, Less Safe: The Indirect But Pervasive Risk of Test-Time Scaling in Large Language Models

Shahriar Kabir Nahin, Hadi Askari, Muhao Chen, Anshuman Chhabra

展开摘要

Test-Time Scaling (TTS) improves LLM reasoning by exploring multiple candidate responses and then operating over this set to find the best output. A tacit premise behind TTS is that sufficiently diverse candidate pools enhance reliability. In this work, we show that this assumption in TTS introduces a previously unrecognized failure mode. When candidate diversity is curtailed, even by a modest amount, TTS becomes much more likely to produce unsafe outputs. We present a reference-guided diversity reduction protocol (RefDiv) that serves as a diagnostic attack to stress test TTS pipelines. Through extensive experiments across open-source models (e.g. Qwen3, Mistral, Llama3.1, Gemma3) and two widely used TTS strategies (Monte Carlo Tree Search and Best-of-N), constraining diversity consistently signifies the rate at which TTS produces unsafe results. The effect is often stronger than that produced by prompts directly with high adversarial intent scores. This observed phenomenon also transfers across TTS strategies and to closed-source models (e.g. OpenAI o3-mini and Gemini-2.5-Pro), thus indicating that this is a general and extant property of TTS rather than a model-specific artifact. Additionally, we find that numerous widely used safety guardrail classifiers (e.g. Llama-Guard), are unable to flag the adversarial input prompts generated by RefDiv, demonstrating that existing defenses offer limited protection against this diversity-driven failure mode.

Poster
On the Emergence of Implicit Curriculum in RLVR Learning Dynamics

Yu Huang, Zixin Wen, Yuejie Chi, Yuting Wei, Aarti Singh, Yingbin Liang, Yuxin Chen

展开摘要

Reinforcement learning with verifiable rewards (RLVR) has been a main driver of recent breakthroughs in large reasoning models. Yet it remains a mystery how rewards based solely on final outcomes can help overcome the long-horizon barrier to extended reasoning. To understand this, we develop a theory of the training dynamics of RLVR for transformers on compositional reasoning tasks. Our theory shows that mixed-difficulty training naturally induces an **implicit curriculum**: without any explicit schedule, easier problems become learnable first and shape the frontier for harder ones, creating a learning progression from easy to hard during optimization. The effectiveness of this curriculum is governed by the smoothness of the difficulty spectrum. When the spectrum is smooth, training dynamics enter a well-behaved *relay* regime, in which persistent gradient signals on easier problems make slightly harder ones tractable and keep training at the edge of competence. When the spectrum contains abrupt discontinuities, training undergoes grokking-type phase transitions with prolonged plateaus before progress recurs. As a technical contribution, our analysis develops and adapts techniques from Fourier analysis on finite groups to our setting. We validate the predicted mechanisms empirically via synthetic experiments.

Poster