# Offline Guidance, Online Reasoning: Reusing LLM Feedback for Small Language Models

arXiv: https://arxiv.org/abs/2609.39346 · HTML: https://mlsanity.com/paper/2609.39346/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in Reasoning benchmarks and evaluation, one of 17 directions in LLM reasoning.
- Builds on 12 of its 48 references that are in the map.
- First posted on arXiv 30 Sep 2026.

## Placed in

- LLM reasoning / [Reasoning benchmarks and evaluation](https://mlsanity.com/lr/reasoning-benchmarks-and-evaluation/)

## Builds on (most cited first, 12 of 12)

- [GPT-4 Technical Report](https://mlsanity.com/paper/2303.08774/) (2023)
- [Training Verifiers to Solve Math Word Problems](https://mlsanity.com/paper/2110.14168/) (2021)
- [Qwen3 Technical Report](https://mlsanity.com/paper/2505.09388/) (2025)
- [Let's Verify Step by Step](https://mlsanity.com/paper/2305.20050/) (2023)
- [Qwen2.5-Math Technical Report: Toward Mathematical Expert Model via Self-Improvement](https://mlsanity.com/paper/2409.12122/) (2024)
- [Steering Language Models With Activation Engineering](https://mlsanity.com/paper/2308.10248/) (2023)
- [Guiding Reasoning in Small Language Models with LLM Assistance](https://mlsanity.com/paper/2504.09923/) (2025)
- [Prototype-Based Dynamic Steering for Large Language Models](https://mlsanity.com/paper/2510.05498/) (2025)
- [RISER: Orchestrating Latent Reasoning Skills for Adaptive Activation Steering](https://mlsanity.com/paper/2601.09269/) (2026)
- [Efficient Reasoning with Balanced Thinking](https://mlsanity.com/paper/2603.12372/) (2026)
- [MentorCollab: Large-to-Small Inference-Time Mentorship for Concise Reasoning in Language Models](https://mlsanity.com/paper/2602.05307/) (2026)
- [PyroDash: Cost-Efficient Token-Level Small-Large Language Model Collaborative Inference](https://mlsanity.com/paper/2607.20327/) (2026)

## Abstract (arXiv)

Large language models (LLMs) offer strong reasoning capabilities but are often costly to access through commercial APIs, while small language models (SLMs) are easier to deploy locally yet remain weaker in reasoning. This capability-deployment gap has motivated LLM-SLM collaboration, which aims to improve SLM reasoning using LLM capabilities while preserving the deployment advantages of SLMs. Existing approaches mainly follow two paradigms. Knowledge distillation uses LLM-generated answers and reasoning trajectories to train SLMs offline, but requires parameter updates and additional training. Alternatively, online collaboration routes difficult problems to an LLM or leverages LLM-generated guidance and corrections when an SLM encounters difficulties. Although effective, online collaboration requires repeated LLM access. Moreover, the guidance produced for a particular problem is discarded after inference and cannot benefit subsequent problems involving similar reasoning states. In the paper, we focus on a more constrained setting in which the LLM is accessed only offline, the SLM parameters remain fixed, and online inference is performed solely by the SLM. To this end, we propose Reusable Latent Correction (RLC), which converts one-off natural-language guidance from a black-box LLM into persistent corrective experiences in the hidden space of an SLM. RLC stores these experiences in an external bank and retrieves them according to the SLM's current reasoning state, enabling the SLM to reuse LLM-derived corrections during inference without any online LLM calls. Experiments across multiple reasoning benchmarks and SLM scales show that RLC consistently improves SLM reasoning without parameter updates or online LLM calls. Code is available at https://github.com/ZBH031/reusable-latent-correction.