Solving math word problems with process- and outcome-based feedback
read the original abstract
Recent work has shown that asking language models to generate reasoning steps improves performance on many reasoning tasks. When moving beyond prompting, this raises the question of how we should supervise such models: outcome-based approaches which supervise the final result, or process-based approaches which supervise the reasoning process itself? Differences between these approaches might naturally be expected not just in final-answer errors but also in reasoning errors, which can be difficult to detect and are problematic in many real-world domains such as education. We run the first comprehensive comparison between process- and outcome-based approaches trained on a natural language task, GSM8K. We find that pure outcome-based supervision produces similar final-answer error rates with less label supervision. However, for correct reasoning steps we find it necessary to use process-based supervision or supervision from learned reward models that emulate process-based feedback. In total, we improve the previous best results from 16.8% $\to$ 12.7% final-answer error and 14.0% $\to$ 3.4% reasoning error among final-answer-correct solutions.
This paper has not been read by Pith yet.
Forward citations
Cited by 60 Pith papers
-
MedPRMBench: A Fine-grained Benchmark for Process Reward Models in Medical Reasoning
MedPRMBench is the first fine-grained benchmark for process reward models in medical reasoning, featuring 6500 questions, 13000 chains, 113910 step labels, and a baseline that improves downstream QA accuracy by 3.2-6....
-
AgentLens: Revealing The Lucky Pass Problem in SWE-Agent Evaluation
10.7% of passing SWE-agent trajectories are Lucky Passes with chaotic behaviors, and a quality score based on process references changes model rankings across eight backends.
-
Unmasking On-Policy Distillation: Where It Helps, Where It Hurts, and Why
Distillation signals align better with ideal updates on incorrect student rollouts than correct ones, with optimal teacher context depending on student capacity and task.
-
The Last Word Often Wins: A Format Confound in Chain-of-Thought Corruption Studies
Corruption studies on CoT chains detect the position of explicit answer statements rather than computational steps, as evidenced by format ablations collapsing suffix sensitivity 19x and models following conflicting a...
-
Unsupervised Process Reward Models
Unsupervised PRMs derived from LLM probabilities achieve up to 15% better error detection than LLM judges and match supervised PRMs in verification and RL tasks.
-
Distributional Process Reward Models: Calibrated Prediction of Future Rewards via Conditional Optimal Transport
Conditional optimal transport calibrates PRMs by learning monotonic conditional quantile functions over success probabilities conditioned on hidden states, yielding improved calibration and downstream Best-of-N perfor...
-
Post Reasoning: Improving the Performance of Non-Thinking Models at No Cost
Post-Reasoning boosts LLM accuracy by reversing the usual answer-after-reasoning order, delivering mean relative gains of 17.37% across 117 model-benchmark pairs with zero extra cost.
-
Logic-Regularized Verifier Elicits Reasoning from LLMs
LOVER creates an unsupervised logic-regularized verifier that reaches 95% of supervised verifier performance on reasoning tasks across 10 datasets.
-
Maximizing Rollout Informativeness under a Fixed Budget: A Submodular View of Tree Search for Tool-Use Agentic Reinforcement Learning
InfoTree casts intermediate state selection in tree search as monotone submodular maximization under fixed rollout budgets, yielding closed-form UUCB terms and lifting mixed-outcome ratios while outperforming flat GRP...
-
Correct Is Not Enough: Training Reasoning Planners with Executor-Grounded Rewards
TraceLift trains reasoning planners with executor-grounded rewards that multiply a rubric-based reasoning quality score by measured uplift on a frozen executor, outperforming execution-only training on math and code b...
-
Generalized Distributional Alignment Games for Unbiased Answer-Level Fine-Tuning
Generalized Bregman alignment games plus U-statistics and optimal minimax polynomial estimators remove Jensen bias and achieve optimal statistical rates for unbiased answer-level fine-tuning.
-
Decoding-Time Debiasing via Process Reward Models: From Controlled Fill-in to Open-Ended Generation
Decoding-time use of process reward models for bias mitigation raises fairness scores by up to 0.40 on a bilingual benchmark while preserving fluency across four LLMs and extends to open-ended generation with low overhead.
-
AgentEval: DAG-Structured Step-Level Evaluation for Agentic Workflows with Error Propagation Tracking
AgentEval evaluates agentic workflows via DAGs with step metrics, a 21-category failure taxonomy, and error propagation tracking, yielding 2.17x higher failure recall than end-to-end methods and strong human agreement.
-
Fine-Tuning Small Reasoning Models for Quantum Field Theory
Small 7B reasoning models were fine-tuned on synthetic and curated QFT problems using RL and SFT, yielding performance gains, error analysis, and public release of data and traces.
-
Navigating the Conceptual Multiverse
The conceptual multiverse system with a verification framework for decision structures helps users in philosophy, AI alignment, and poetry build clearer working maps of open-ended problems by making implicit LLM choic...
-
Does RL Expand the Capability Boundary of LLM Agents? A PASS@(k,T) Analysis
RL expands the capability boundary of LLM agents on compositional tool-use tasks, shown by non-converging pass curves at large k with increasing T, while SFT regresses it and the effect is absent on simpler tasks.
-
AI Achieves a Perfect LSAT Score
Language models achieve a perfect LSAT score, with experiments showing that internal thinking phases and a fine-tuned process reward model are key to high performance on logical reasoning questions.
-
Structural Evaluation Metrics for SVG Generation via Leave-One-Out Analysis
Element-level leave-one-out analysis yields per-element quality scores and four structural metrics (purity, coverage, compactness, locality) that quantify SVG modularity and enable artifact detection.
-
Generate, Filter, Control, Replay: A Comprehensive Survey of Rollout Strategies for LLM Reinforcement Learning
This survey introduces the Generate-Filter-Control-Replay (GFCR) taxonomy to structure rollout pipelines for RL-based post-training of reasoning LLMs.
-
Sampling for Quality: Training-Free Reward-Guided LLM Decoding via Sequential Monte Carlo
Sequential Monte Carlo sampling from a reward-augmented sequence distribution improves LLM performance on HumanEval by up to 54.9% and MATH500 by up to 8.8%, outperforming standard sampling and GRPO.
-
WMF-AM: Probing LLM Working Memory via Depth-Parameterized Cumulative State Tracking
WMF-AM is a depth-parameterized benchmark that measures LLMs' cumulative state tracking ability without scratchpads, validated on 28 models across arithmetic and non-arithmetic tasks with ablations confirming the construct.
-
ToolPRM: Fine-Grained Inference Scaling of Structured Outputs for Function Calling
ToolPRM provides fine-grained intra-call process supervision via a new dataset and reward model, outperforming outcome and coarse-grained alternatives on function-calling benchmarks.
-
Seg-Zero: Reasoning-Chain Guided Segmentation via Cognitive Reinforcement
Seg-Zero uses cognitive reinforcement learning on a decoupled reasoning-plus-segmentation architecture to produce explicit reasoning chains and reach 57.5 zero-shot accuracy on ReasonSeg, beating prior supervised LISA...
-
Do NOT Think That Much for 2+3=? On the Overthinking of o1-Like LLMs
o1-like models overthink easy tasks; self-training reduces compute use without accuracy loss on GSM8K, MATH500, GPQA, and AIME.
-
GSM-Symbolic: Understanding the Limitations of Mathematical Reasoning in Large Language Models
LLMs display high variance and major accuracy drops on GSM-Symbolic variants of grade-school math problems, indicating they replicate training patterns rather than execute logical reasoning.
-
Let's Verify Step by Step
Process supervision significantly outperforms outcome supervision for training models on the MATH dataset, achieving 78% accuracy on a representative test subset with active learning and a released 800k step-label dataset.
-
Learning from Failures: Correction-Oriented Policy Optimization with Verifiable Rewards
CIPO jointly optimizes standard RLVR rewards with correction samples derived from the model's own failed attempts, yielding better reasoning and self-correction on math and code benchmarks.
-
LLMs Know When They Know, but Do Not Act on It: A Metacognitive Harness for Test-time Scaling
A metacognitive harness uses LLMs' pre- and post-solution self-monitoring signals to control test-time reasoning, raising pooled accuracy from 48.3% to 56.9% on text, code, and multimodal benchmarks.
-
Distribution Corrected Offline Data Distillation for Large Language Models
A distribution-correction framework for offline LLM reasoning distillation improves accuracy on math benchmarks by adaptively aligning teacher supervision with the student's inference-time distribution.
-
When Reasoning Traces Become Performative: Step-Level Evidence that Chain-of-Thought Is an Imperfect Oversight Channel
CoT traces align with internal answer commitment in only 61.9% of steps on average, dominated by confabulated continuations after commitment has stabilized.
-
Verifiable Process Rewards for Agentic Reasoning
Verifiable Process Rewards (VPR) converts symbolic oracles into dense turn-level supervision for reinforcement learning in agentic reasoning, outperforming outcome-only rewards and transferring to general benchmarks.
-
Rubric-Grounded RL: Structured Judge Rewards for Generalizable Reasoning
Rubric-grounded RL with LLM judges on document-derived criteria raises Llama-3.1-8B normalized reward to 71.7% on held-out rubrics and improves performance on GSM8K, MATH, and GPQA benchmarks.
-
Distributional Process Reward Models: Calibrated Prediction of Future Rewards via Conditional Optimal Transport
Conditional optimal transport is used to turn raw PRM outputs into monotonic quantile functions that improve calibration and downstream Best-of-N performance on MATH-500 and AIME.
-
RLearner-LLM: Balancing Logical Grounding and Fluency in Large Language Models via Hybrid Direct Preference Optimization
RLearner-LLM achieves up to 6x gains in NLI entailment over standard fine-tuning by using an automated hybrid DPO pipeline that balances logic and fluency across multiple model sizes and domains.
-
RLearner-LLM: Balancing Logical Grounding and Fluency in Large Language Models via Hybrid Direct Preference Optimization
RLearner-LLM's Hybrid-DPO fuses DeBERTa NLI and LLM verifier scores to deliver up to 6x higher NLI entailment than standard SFT while preserving answer coverage across academic domains.
-
Correct Is Not Enough: Training Reasoning Planners with Executor-Grounded Rewards
TraceLift trains reasoning planners using rewards that credit traces for both rubric quality and actual performance gains on a frozen executor, outperforming final-answer-only training on math and code tasks.
-
DGPO: Distribution Guided Policy Optimization for Fine Grained Credit Assignment
DGPO is a critic-free RL framework that uses bounded Hellinger distance and entropy-gated advantage redistribution to enable fine-grained token-level credit assignment in long CoT generations for LLM alignment, report...
-
DGPO: Distribution Guided Policy Optimization for Fine Grained Credit Assignment
DGPO reinterprets distribution deviation as a guiding signal in a critic-free policy optimization framework to enable fine-grained credit assignment for LLM chain-of-thought reasoning.
-
Controllable and Verifiable Process Data Synthesis for Process Reward Models
A controllable synthesis method creates prefix-invalid yet trajectory-consistent process supervision data for training and evaluating process reward models by injecting verifiable errors into symbolic reasoning chains.
-
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.
-
Adaptive Test-Time Compute Allocation with Evolving In-Context Demonstrations
An adaptive test-time framework uses a warm-up phase on the test set to build evolving in-context examples, then concentrates compute on unresolved queries to outperform static baselines on math, coding, and reasoning...
-
TPS-CalcBench: A Benchmark and Diagnostic Evaluation Framework for LLM Analytical Calculation Competence in Hypersonic Thermal Protection System Engineering
TPS-CalcBench is a new benchmark and evaluation framework that tests LLMs on analytical calculations in hypersonic aerodynamics and gas dynamics, using dual-track scoring and interventions to detect physically invalid...
-
Process Reward Models Meet Planning: Generating Precise and Scalable Datasets for Step-Level Rewards
PDDL planning problems are used to generate about one million precise reasoning steps for training Process Reward Models, and adding this data to existing datasets improves LLM performance on both mathematical and non...
-
Adaptive Test-Time Compute Allocation for Reasoning LLMs via Constrained Policy Optimization
A Lagrangian-relaxation plus imitation-learning pipeline adaptively allocates test-time compute to LLMs, outperforming uniform baselines by up to 12.8% relative accuracy on MATH while staying within a fixed average budget.
-
The Past Is Not Past: Memory-Enhanced Dynamic Reward Shaping
MEDS improves LLM RL performance by up to 4.13 pass@1 and 4.37 pass@128 points by dynamically penalizing rollouts matching prevalent historical error clusters identified via memory-stored representations and density c...
-
PRISM-MCTS: Learning from Reasoning Trajectories with Metacognitive Reflection
PRISM-MCTS improves MCTS-based reasoning efficiency by maintaining a shared memory of heuristics and fallacies reinforced by a process reward model, halving required trajectories on GPQA while outperforming prior methods.
-
Relative Density Ratio Optimization for Stable and Statistically Consistent Model Alignment
Relative density ratio optimization stabilizes direct density ratio estimation for language model alignment while preserving statistical consistency without assuming a Bradley-Terry preference model.
-
Towards Safer Large Reasoning Models by Promoting Safety Decision-Making before Chain-of-Thought Generation
Safety degradation in large reasoning models occurs only after chain-of-thought is enabled; adding pre-CoT safety signals from a BERT classifier on safe models improves safety while preserving reasoning ability.
-
AgentXRay: White-Boxing Agentic Systems via Workflow Reconstruction
AgentXRay formulates workflow reconstruction as combinatorial optimization and uses Monte Carlo Tree Search with Red-Black Pruning to approximate black-box agent behaviors via output-based proxy metrics.
-
Learning Decentralized LLM Collaboration with Multi-Agent Actor Critic
Multi-agent actor-critic methods with a centralized critic improve decentralized LLM collaboration over Monte Carlo baselines in long-horizon and sparse-reward settings.
-
Process Reinforcement through Implicit Rewards
PRIME enables online process reward model updates in LLM RL using implicit rewards from rollouts and outcome labels, yielding 15.1% average gains on reasoning benchmarks and surpassing a stronger instruct model with 1...
-
The Lessons of Developing Process Reward Models in Mathematical Reasoning
Monte Carlo data synthesis for PRMs underperforms LLM-judge and human methods, Best-of-N evaluations suffer from process-outcome misalignment and score inflation, and consensus filtering yields better PRMs with higher...
-
Training Language Models to Self-Correct via Reinforcement Learning
SCoRe uses multi-turn online RL with regularization on self-generated traces to improve LLM self-correction, achieving 15.6% and 9.1% gains on MATH and HumanEval for Gemini models.
-
Inference Scaling Laws: An Empirical Analysis of Compute-Optimal Inference for Problem-Solving with Language Models
Empirical analysis shows scaling inference compute via strategies like tree search can be more efficient than scaling model parameters, with 7B models plus novel search outperforming 34B models.
-
Improve Mathematical Reasoning in Language Models by Automated Process Supervision
OmegaPRM automates collection of 1.5 million process supervision labels via binary-search MCTS, raising Gemini Pro math accuracy from 51% to 69.4% on MATH500 and Gemma2 27B from 42.3% to 58.2%.
-
LiveCodeBench: Holistic and Contamination Free Evaluation of Large Language Models for Code
LiveCodeBench collects 400 recent contest problems to create a contamination-free benchmark evaluating LLMs on code generation and related capabilities like self-repair and execution.
-
Math-Shepherd: Verify and Reinforce LLMs Step-by-step without Human Annotations
Math-Shepherd is an automatically trained process reward model that scores solution steps to verify and reinforce LLMs, lifting Mistral-7B from 77.9% to 89.1% on GSM8K and 28.6% to 43.5% on MATH.
-
Reinforced Self-Training (ReST) for Language Modeling
ReST improves LLM translation quality on benchmarks via offline RL on self-generated data, achieving gains in a compute-efficient way compared to typical RLHF.
-
RLearner-LLM: Balancing Logical Grounding and Fluency in Large Language Models via Hybrid Direct Preference Optimization
Hybrid-DPO combining NLI and verifier scores delivers up to 6x NLI improvement over SFT baselines across multiple LLMs and domains while preserving answer coverage and inference speed.
-
SCPRM: A Schema-aware Cumulative Process Reward Model for Knowledge Graph Question Answering
SCPRM adds prefix conditioning and schema distance to process reward models so that Monte Carlo Tree Search can explore knowledge-graph reasoning paths with both cumulative and future guidance, yielding a 1.18% averag...
discussion (0)
Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.