Flow models reach 99.2% Sudoku accuracy in 7 passes and 96.1% on out-of-distribution Sudoku-Extreme by selecting dynamically stable candidates and training with self-conditioning plus DPO to avoid failed outputs.
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Step-DPO: Step-wise Preference Optimization for Long-chain Reasoning of LLMs
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abstract
Mathematical reasoning presents a significant challenge for Large Language Models (LLMs) due to the extensive and precise chain of reasoning required for accuracy. Ensuring the correctness of each reasoning step is critical. To address this, we aim to enhance the robustness and factuality of LLMs by learning from human feedback. However, Direct Preference Optimization (DPO) has shown limited benefits for long-chain mathematical reasoning, as models employing DPO struggle to identify detailed errors in incorrect answers. This limitation stems from a lack of fine-grained process supervision. We propose a simple, effective, and data-efficient method called Step-DPO, which treats individual reasoning steps as units for preference optimization rather than evaluating answers holistically. Additionally, we have developed a data construction pipeline for Step-DPO, enabling the creation of a high-quality dataset containing 10K step-wise preference pairs. We also observe that in DPO, self-generated data is more effective than data generated by humans or GPT-4, due to the latter's out-of-distribution nature. Our findings demonstrate that as few as 10K preference data pairs and fewer than 500 Step-DPO training steps can yield a nearly 3% gain in accuracy on MATH for models with over 70B parameters. Notably, Step-DPO, when applied to Qwen2-72B-Instruct, achieves scores of 70.8% and 94.0% on the test sets of MATH and GSM8K, respectively, surpassing a series of closed-source models, including GPT-4-1106, Claude-3-Opus, and Gemini-1.5-Pro. Our code, data, and models are available at https://github.com/dvlab-research/Step-DPO.
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representative citing papers
A recurrent-depth architecture enables language models to improve reasoning performance by iterating computation in latent space, achieving gains equivalent to much larger models on benchmarks.
StrucTab achieves SOTA table parsing performance by unifying structural subtasks through sequential reasoning and using decomposed RL rewards in Uni-TabRL, plus a new TableVerse-5K benchmark.
DiARC improves LLM performance on ARC-like benchmarks by constructing and training on preference pairs from three types of negative samples while keeping demonstrations fixed.
The log-probability ratio from RL post-training recovers the optimal advantage function, providing an effective free signal for test-time scaling, uncertainty estimation, and failure attribution in LLM agents.
ReSum's contrastive RL branching on self-summarization points improves LLM math reasoning accuracy by about 4% and shortens rollouts by about 18.6% across tested backbones.
TRACE is a rollout budget allocation framework that models ReAct turns as tree nodes and uses a predictor to allocate samples to informative prefixes, yielding a 2.8-point accuracy gain on Multi-Hop QA at equal cost.
DyCon dynamically controls reasoning depth in LRMs by modeling evolving difficulty from step-level embeddings, reducing redundant steps across multiple benchmarks.
CPT is introduced as a pairwise reasoning-trace comparison stage that improves the reasoning-metacognition trade-off over standard SFT+RL pipelines across model scales.
RACER routes between reasoning and non-reasoning LLM judges via constrained distributionally robust optimization to achieve better accuracy-cost trade-offs under distribution shift.
CoRD uses collaborative multi-teacher step-wise decoding with perplexity-guided beam search to generate higher-quality Long-CoT data that lets smaller models reach near-teacher performance with less supervision.
Offline KL-regularized MABs require sample complexity scaling as O(η S A C^π*/ε) for large regularization and Ω(S A C^π*/ε²) for small regularization, with matching lower bounds across the full range.
PaTaRM converts pairwise preference data into pointwise reward signals via a novel PAR mechanism and task-adaptive rubrics, reporting 8.7% gains on RewardBench/RMBench and 13.6% relative RLHF improvement.
Survey that defines agentic RL for LLMs via POMDPs, introduces a taxonomy of planning/tool-use/memory/reasoning capabilities and domains, and compiles open environments from over 500 papers.
SENTINEL reduces MLLM object hallucinations by over 90% via sentence-level early intervention with detector-bootstrapped preference data and C-DPO loss, outperforming prior SOTA on hallucination and capability benchmarks.
DeFactoX, a curriculum-driven DPO variant with Actuality and Finesse loss weighting, improves automatic and human scores for Hindi news explanation generation over existing preference optimization baselines.
ReTool uses outcome-driven RL to train 32B LLMs to dynamically use code tools during reasoning, reaching 72.5% accuracy on AIME and surpassing o1-preview.
Mixed Preference Optimization with the MMPR dataset boosts multimodal CoT reasoning, lifting InternVL2-8B to 67.0 accuracy on MathVista (+8.7 points) and matching the 76B model.
Agent Q integrates MCTS-guided search, self-critique, and off-policy DPO to train LLM agents that outperform behavior cloning and reinforced fine-tuning baselines in WebShop and achieve up to 95.4% success in real-world booking scenarios.
APPO improves LLM agent training by branching at tokens selected for both uncertainty and future impact, then scaling credit for consequential reasoning procedures.
AI for mathematics is best described as a supervision ladder — final answers, programs, process rewards, proof-assistant kernels — culminating in verified-discovery workflows.
Dynamic-dLLM achieves over 3x average inference speedup on dLLMs like LLaDA-8B via adaptive cache budgets and decoding thresholds while preserving benchmark performance.
YFPO augments standard preference optimization with neuron-level activation margins from math-related features to improve LLM reasoning on math tasks.
Mid-training LLMs on self-generated diverse reasoning paths improves subsequent RL performance on mathematical benchmarks and OOD tasks.
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Flow Reasoning Models: Scaling Reasoning Through Iterative Self-Refinement
Flow models reach 99.2% Sudoku accuracy in 7 passes and 96.1% on out-of-distribution Sudoku-Extreme by selecting dynamically stable candidates and training with self-conditioning plus DPO to avoid failed outputs.
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Scaling up Test-Time Compute with Latent Reasoning: A Recurrent Depth Approach
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StrucTab: A Structured Optimization Framework for Table Parsing
StrucTab achieves SOTA table parsing performance by unifying structural subtasks through sequential reasoning and using decomposed RL rewards in Uni-TabRL, plus a new TableVerse-5K benchmark.
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DiARC: Distinguishing Positive and Negative Samples Helps Improving ARC-like Reasoning Ability of Large Language Models
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The log-probability ratio from RL post-training recovers the optimal advantage function, providing an effective free signal for test-time scaling, uncertainty estimation, and failure attribution in LLM agents.
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ReSum: Synergizing LLM Reasoning and Summarization with Reinforcement Learning
ReSum's contrastive RL branching on self-summarization points improves LLM math reasoning accuracy by about 4% and shortens rollouts by about 18.6% across tested backbones.
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TRACE: A Unified Rollout Budget Allocation Framework for Efficient Agentic Reinforcement Learning
TRACE is a rollout budget allocation framework that models ReAct turns as tree nodes and uses a predictor to allocate samples to informative prefixes, yielding a 2.8-point accuracy gain on Multi-Hop QA at equal cost.
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DyCon: Dynamic Reasoning Control via Evolving Difficulty Modeling
DyCon dynamically controls reasoning depth in LRMs by modeling evolving difficulty from step-level embeddings, reducing redundant steps across multiple benchmarks.
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Enhancing LLM Metacognition via Cognitive Pairwise Training
CPT is introduced as a pairwise reasoning-trace comparison stage that improves the reasoning-metacognition trade-off over standard SFT+RL pipelines across model scales.
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Reasoning Is Not Free: Robust Adaptive Cost-Efficient Routing for LLM-as-a-Judge
RACER routes between reasoning and non-reasoning LLM judges via constrained distributionally robust optimization to achieve better accuracy-cost trade-offs under distribution shift.
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Distilling Long-CoT Reasoning through Collaborative Step-wise Multi-Teacher Decoding
CoRD uses collaborative multi-teacher step-wise decoding with perplexity-guided beam search to generate higher-quality Long-CoT data that lets smaller models reach near-teacher performance with less supervision.
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On the Optimal Sample Complexity of Offline Multi-Armed Bandits with KL Regularization
Offline KL-regularized MABs require sample complexity scaling as O(η S A C^π*/ε) for large regularization and Ω(S A C^π*/ε²) for small regularization, with matching lower bounds across the full range.
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PaTaRM: Bridging Pairwise and Pointwise Signals via Preference-Aware Task-Adaptive Reward Modeling
PaTaRM converts pairwise preference data into pointwise reward signals via a novel PAR mechanism and task-adaptive rubrics, reporting 8.7% gains on RewardBench/RMBench and 13.6% relative RLHF improvement.
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The Landscape of Agentic Reinforcement Learning for LLMs: A Survey
Survey that defines agentic RL for LLMs via POMDPs, introduces a taxonomy of planning/tool-use/memory/reasoning capabilities and domains, and compiles open environments from over 500 papers.
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Mitigating Object Hallucinations via Sentence-Level Early Intervention
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From Fragments to Facts: A Curriculum-Driven DPO Approach for Generating Hindi News Veracity Explanations
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ReTool: Reinforcement Learning for Strategic Tool Use in LLMs
ReTool uses outcome-driven RL to train 32B LLMs to dynamically use code tools during reasoning, reaching 72.5% accuracy on AIME and surpassing o1-preview.
-
Enhancing the Reasoning Ability of Multimodal Large Language Models via Mixed Preference Optimization
Mixed Preference Optimization with the MMPR dataset boosts multimodal CoT reasoning, lifting InternVL2-8B to 67.0 accuracy on MathVista (+8.7 points) and matching the 76B model.
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Agent Q: Advanced Reasoning and Learning for Autonomous AI Agents
Agent Q integrates MCTS-guided search, self-critique, and off-policy DPO to train LLM agents that outperform behavior cloning and reinforced fine-tuning baselines in WebShop and achieve up to 95.4% success in real-world booking scenarios.
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APPO: Agentic Procedural Policy Optimization
APPO improves LLM agent training by branching at tokens selected for both uncertainty and future impact, then scaling credit for consequential reasoning procedures.
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Artificial Intelligence for Mathematical Reasoning: An Integrated Survey of Language Models, Neuro-symbolic Systems, and Verified Discovery
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Dynamic-dLLM: Dynamic Cache-Budget and Adaptive Parallel Decoding for Training-Free Acceleration of Diffusion LLM
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YFPO: A Preliminary Study of Yoked Feature Preference Optimization with Neuron-Guided Rewards for Mathematical Reasoning
YFPO augments standard preference optimization with neuron-level activation margins from math-related features to improve LLM reasoning on math tasks.
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Mid-Training with Self-Generated Data Improves Reinforcement Learning in Language Models
Mid-training LLMs on self-generated diverse reasoning paths improves subsequent RL performance on mathematical benchmarks and OOD tasks.
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Decomposing the Delta: What Do Models Actually Learn from Preference Pairs?
Larger differences in generator capability between chosen and rejected reasoning traces improve out-of-domain performance, while filtering pairs by sample-level quality deltas enables more data-efficient training.
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Hard Negative Sample-Augmented DPO Post-Training for Small Language Models
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SHE: Stepwise Hybrid Examination Reinforcement Learning Framework for E-commerce Search Relevance
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A Comprehensive Survey of Self-Evolving AI Agents: A New Paradigm Bridging Foundation Models and Lifelong Agentic Systems
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Sample-efficient LLM Optimization with Reset Replay
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