Select to Think: Unlocking SLM Potential with Local Sufficiency

Large Language Models (LLMs) solve many reasoning tasks via chain-of-thought (CoT) prompting, but smaller models (about 7 to 8B parameters) still struggle with multi-step reasoning under tight compute and token budgets. Existing test time reasoning methods such as self consistency (sampling multiple rationales and voting), Tree-of-Thoughts (search over intermediate thoughts), and critique revise loops improve performance, but often at high token cost and without fine-grained step-level control. This project1 aims to address that gap: can Small Language Models (SLMs) reason reliably using the same or fewer tokens? This question is both scientific and practical. Scientifically, it probes whether process supervision and simple test-time controls (such as token budgets and rejection of redundant steps) can substitute for model scale or large sampling counts. Practically, many deployments (on-device, low-latency, or cost-constrained settings) cannot afford huge models or dozens of sampled rationales per query. A method that improves SLM reasoning at fixed cost would therefore be directly useful.

Token-level collaboration allows a large language model (LLM) to assist a small language model (SLM) when their predictions diverge. Existing methods either use LLM-generated intervention tokens or rank candidates with the LLM's next-token probabilities. Both rely on the LLM's local preference, even though an LLM-selected token may be difficult for the SLM to build on. We present FutureBridge, which ranks joint LLM-SLM token candidates according to how well they support the SLM's subsequent reasoning. During training, an answer-verified LLM trajectory supplies a fixed shared future, and a frozen SLM evaluates every candidate under this common context. The resulting counterfactual scores supervise a lightweight token reranker that observes only the current state and candidate token. At inference, FutureBridge uses the LLM only to expand the candidate pool, selects one token, and returns generation to the SLM without generating or appending a future suffix. Across five mathematical reasoning benchmarks, FutureBridge improves the Qwen3-1.7B SLM's Math Avg. by 35.1% relative to greedy SLM decoding. These results indicate that token selection benefits from modeling whether the receiving SLM can use each candidate to continue reasoning, rather than relying on the LLM's local preference alone.

Recently, language models have made rapid progress across various domains and applications. However, their capability for self-improvement, i.e., whether they are adept at recognising and correcting flaws in their own reasoning, remains dubious. In this study, we address this question by constructing a sufficiency test to rigorously examine the self-correction capabilities of small language models (SLMs). We propose a minimal three-step self-correction pipeline that collects initial SLM answers, prompts the same model to generate hints for its incorrect responses given the ground truth, and feeds the model the same question with its own feedback to refine the initial answer. We evaluate a variety of instruction-tuned and reasoning SLMs in this experimental setup on arithmetic and logical reasoning benchmarks. Our findings show that SLMs with injected hint sentences yield only a 4.4 percent gain over initial question-answering accuracy. Even though the correct answer was provided alongside the model's incorrect reasoning, the evaluated SLMs fail to understand what was missing in their reasoning and show minimal semantic difference between hints that lead to corrections and ones that do not. Furthermore, our experiments show that longer hints are positively correlated with incorrect final answers, suggesting that longer deliberation on problems can hinder the reasoning process, meaning that SLMs do not necessarily scale in performance with a larger compute budget.