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MILES: Modular Instruction Memory with Learnable Selection for Self-Improving LLM Reasoning

NeurIPS 2026 · Large language models › Reasoning and chain of thought · approach: Routing, pruning and distillation for reasoning · 0 citations (OpenAlex)

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Proposes MILES, a frozen-LLM test-time framework that builds modular (sub-goal, sub-instruction) memory from confident samples and learns per-unit selection heads to compose step-level memory for uncertain samples.

Problem

Test-time reasoning with frozen LLMs over sequential problem streams: existing memory methods store whole solutions or select memory units heuristically (similarity or prompting) rather than optimizing selection for final-answer correctness, and learned selection usually needs fixed action spaces, l

Approach

Stores step-level memory as asymmetric (sub-goal embedding, sub-instruction text) pairs, with a per-unit one-vs-rest selection head trained by BCE on MCTS rollout correctness from confident samples (pseudo-labeled by self-consistency), combined with similarity retrieval in a coarse-to-fine two-layer selection used with memory-guided tree search on uncertain samples.

Key results

• On AIME 2024 with GPT-4.1-mini, MILES reaches 66.67% vs 56.67% for self-consistency and 63.33% for Dynamic CheatSheet.
• MILES achieves 92.60% on MATH-500 with GPT-4.1-mini vs 89.40% for self-consistency.
• Ablation on AIME 2024 shows both layers together give 66.67% vs 60.00% with neither; LLM-prompt reranking gives no gain (60.00%).

Surprising findings

• Dynamic CheatSheet performs poorly with Qwen3-30B-Instruct on AIME 2024 (23.33%) and GPT-OSS-20B on AIME 2024 (43.33%), below zero-shot CoT.
• LLM-prompt reranking fails to improve over the no-reranker baseline.

Limitations

• Relies on the instruction-following capability of the underlying LLM.
• Requires rollout-based MCTS data collection, adding computational overhead.
• Evaluated on small uncertain subsets in offline experiments (13 and 31 samples).

Experimental setup

Datasets: MATH-500 AIME 2024 AIME 2025 GPQA-Diamond MMLU-Pro Physics MMLU-Pro Engineering AIME 2020-2024 GPQA non-Diamond

Benchmarks: MATH-500 AIME 2024 AIME 2025 GPQA-Diamond MMLU-Pro Physics MMLU-Pro Engineering

Metrics: final-answer accuracy response-token cost correct-answer proportion sub-instruction accuracy

Baselines: Zero-shot CoT Self-Consistency Dynamic CheatSheet Buffer-of-Thoughts Tree-of-Thoughts rStar DORA

Builds on: Buffer-of-Thoughts Dynamic CheatSheet Tree-of-Thoughts advantage-weighted regression direct preference optimization EXIT

Closest papers by meaning

• Light-IF: Endowing LLMs with Generalizable Reasoning via Preview and Self-Checking for Complex Instruction Following (AAAI 2026 · similarity 0.91)
• Incentivizing Reasoning for Advanced Instruction-Following of Large Language Models (NeurIPS 2025 · similarity 0.90)
• Beyond Test-Time Memory: State-Space Optimal Control for LLM Reasoning (ICML 2026 · similarity 0.90)
• REASONING COMPILER: LLM-Guided Optimizations for Efficient Model Serving (NeurIPS 2025 · similarity 0.90)
• MAmmoTH2: Scaling Instructions from the Web (NeurIPS 2024 · similarity 0.89)
• DOTS: Learning to Reason Dynamically in LLMs via Optimal Reasoning Trajectories Search (ICLR 2025 · similarity 0.89)