# Can Computation from Earlier Problems Help LLMs Solve New Ones?

arXiv: https://arxiv.org/abs/2609.39394 · HTML: https://mlsanity.com/paper/2609.39394/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 25 of its 35 references that are in the map.
- First posted on arXiv 30 Sep 2026.

## Builds on (most cited first, 25 of 25)

- [Qwen3 Technical Report](https://mlsanity.com/paper/2505.09388/) (2025)
- [Measuring Mathematical Problem Solving With the MATH Dataset](https://mlsanity.com/paper/2103.03874/) (2021)
- [RoFormer: Enhanced Transformer with Rotary Position Embedding](https://mlsanity.com/paper/2104.09864/) (2021)
- [Prefix-Tuning: Optimizing Continuous Prompts for Generation](https://mlsanity.com/paper/2101.00190/) (2021)
- [The Power of Scale for Parameter-Efficient Prompt Tuning](https://mlsanity.com/paper/2104.08691/) (2021)
- [Let's Verify Step by Step](https://mlsanity.com/paper/2305.20050/) (2023)
- [GPQA: A Graduate-Level Google-Proof Q&A Benchmark](https://mlsanity.com/paper/2311.12022/) (2023)
- [DAPO: An Open-Source LLM Reinforcement Learning System at Scale](https://mlsanity.com/paper/2503.14476/) (2025)
- [FlashAttention-2: Faster Attention with Better Parallelism and Work Partitioning](https://mlsanity.com/paper/2307.08691/) (2023)
- [Efficient Streaming Language Models with Attention Sinks](https://mlsanity.com/paper/2309.17453/) (2023)
- [Transformer-XL: Attentive Language Models Beyond a Fixed-Length Context](https://mlsanity.com/paper/1901.02860/) (2019)
- [GQA: Training Generalized Multi-Query Transformer Models from Multi-Head Checkpoints](https://mlsanity.com/paper/2305.13245/) (2023)
- [SGLang: Efficient Execution of Structured Language Model Programs](https://mlsanity.com/paper/2312.07104/) (2023)
- [Training Large Language Models to Reason in a Continuous Latent Space](https://mlsanity.com/paper/2412.06769/) (2024)
- [Gated Delta Networks: Improving Mamba2 with Delta Rule](https://mlsanity.com/paper/2412.06464/) (2024)
- [LLMs Get Lost In Multi-Turn Conversation](https://mlsanity.com/paper/2505.06120/) (2025)
- [Prompt Cache: Modular Attention Reuse for Low-Latency Inference](https://mlsanity.com/paper/2311.04934/) (2023)
- [Think before you speak: Training Language Models With Pause Tokens](https://mlsanity.com/paper/2310.02226/) (2023)
- [CacheBlend: Fast Large Language Model Serving for RAG with Cached Knowledge Fusion](https://mlsanity.com/paper/2405.16444/) (2024)
- [Recurrent Memory Transformer](https://mlsanity.com/paper/2207.06881/) (2022)
- [Think Silently, Think Fast: Dynamic Latent Compression of LLM Reasoning Chains](https://mlsanity.com/paper/2505.16552/) (2025)
- [Deliberation in Latent Space via Differentiable Cache Augmentation](https://mlsanity.com/paper/2412.17747/) (2024)
- [Restoring Exploration after Post-Training: Latent Exploration Decoding for Large Reasoning Models](https://mlsanity.com/paper/2602.01698/) (2026)
- [Beyond Speedup -- Utilizing KV Cache for Sampling and Reasoning](https://mlsanity.com/paper/2601.20326/) (2026)
- [Pair-In, Pair-Out: Latent Multi-Token Prediction for Efficient LLMs](https://mlsanity.com/paper/2605.27255/) (2026)

## Abstract (arXiv)

Large language models often solve independent problems in the same conversation. Can computation from earlier problems help them solve new ones? To answer this question, we first conduct preliminary experiments showing that retained history can raise or lower later-turn accuracy, even within the same domain. To understand these effects, we use controlled replay to isolate internal state changes specific to each problem-history pairing. Across different histories, these changes preserve similar relationships among current problems. To improve reasoning under retained history, we introduce STAIR (Stale-Token Attention for Inter-query Reuse). STAIR captures keys and values from earlier response generation in a fixed bank. It learns to redirect current queries when they read this bank during prompt processing. The base model remains frozen; only 12,288 parameters are trained. Across three Qwen models and four benchmarks, STAIR improves average later-turn accuracy by up to 11.67 percentage points over the unmodified model with history.