Solving Every Step Is Not Enough: Milestone Oracles Reveal a Composition Gap in LLM Math Reasoning

arXiv:2609.32235 · cs.CL · Submitted 2026-09-26 · Read on arXiv

cs.CL

Submitted: 2026-09-26

Updated: 2026-09-26

Code: https://github.com/slark-prime/OracleLadder

Terminology

• Verifier — 59× in this paper · explained in 2 episodes
• Accuracy — 28× in this paper · explained in 1 episode
• Benchmark — 13× in this paper · explained in 2 episodes
• Verification — 7× in this paper · explained in 2 episodes
• LLM judge — 6× in this paper · explained in 2 episodes
• Reinforcement Learning — 6× in this paper · explained in 4 episodes
• GRPO — 4× in this paper · explained in 6 episodes
• Trace — 4× in this paper · explained in 2 episodes
• Ablation — 3× in this paper · explained in 1 episode
• Adam — 3× in this paper · explained in 2 episodes
• Robustness — 3× in this paper · explained in 5 episodes
• Chain-of-Thought Prompting — 2× in this paper · explained in 2 episodes
• Large Language Models (LLMs) — 2× in this paper · explained in 6 episodes
• Accountability — 1× in this paper · explained in 2 episodes
• AdamW Optimizer — 1× in this paper · explained in 1 episode
• Adaptation — 1× in this paper · explained in 1 episode
• Alignment — 1× in this paper · explained in 1 episode
• Benchmarking — 1× in this paper · explained in 3 episodes
• Decoupling — 1× in this paper · explained in 2 episodes
• Degeneracy — 1× in this paper · explained in 3 episodes
• Distillation — 1× in this paper · explained in 2 episodes
• LLM-as-a-Judge — 1× in this paper · explained in 3 episodes
• Massachusetts Institute of Technology — 1× in this paper
• Provenance — 1× in this paper · explained in 4 episodes
• Verifiable Rewards — 1× in this paper · explained in 2 episodes

Sources

• Have LLMs Advanced Enough? A Challenging Problem Solving Benchmark For Large Language Models
• Large Language Monkeys: Scaling Inference Compute with Repeated Sampling
• TheoremQA: A Theorem-driven Question Answering dataset
• DeepSeek-V3 Technical Report
• DeepSeek-R1: Incentivizing Reasoning Capability in LLMs via Reinforcement Learning
• Omni-MATH: A Universal Olympiad Level Mathematic Benchmark For Large Language Models
• FrontierMath: A Benchmark for Evaluating Advanced Mathematical Reasoning in AI
• rStar-Math: Small LLMs Can Master Math Reasoning with Self-Evolved Deep Thinking
• OlympiadBench: A Challenging Benchmark for Promoting AGI with Olympiad-Level Bilingual Multimodal Scientific Problems
• Measuring Massive Multitask Language Understanding
• Measuring Mathematical Problem Solving With the MATH Dataset
• Not All LLM Reasoners Are Created Equal
• LoRA: Low-Rank Adaptation of Large Language Models
• OlympicArena: Benchmarking Multi-discipline Cognitive Reasoning for Superintelligent AI
• Decomposed Prompting: A Modular Approach for Solving Complex Tasks
• Measuring Faithfulness in Chain-of-Thought Reasoning
• GSM-Plus: A Comprehensive Benchmark for Evaluating the Robustness of LLMs as Mathematical Problem Solvers
• Holistic Evaluation of Language Models
• Let's Verify Step by Step
• Improve Mathematical Reasoning in Language Models by Automated Process Supervision

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