Reasoning failures in large language models (LLMs) are usually evaluated from final answers, but a wrong answer does not reveal why the model failed. The same incorrect output may reflect missing capability, an unstable reasoning trajectory, or a failure to activate a reasoning state that is already available in the frozen model. Existing prompting and benchmark-based evaluation methods mostly operate at the output level, while generic activation-steering methods typically apply global directions without diagnosing which examples require intervention. In this paper, we introduce SPARK, which uses hidden-state response to diagnose whether a model internally enters an effective reasoning state and to guide lightweight test-time steering. The key observation is that raw hidden-state susceptibility is strongly confounded by prompt length, especially in programmatic and algorithmic reasoning where harder serialized instances naturally become longer. SPARK therefore uses length-controlled susceptibility to separate input-scale effects from residual reasoning activation, and combines this signal with cross-layer coordination to select reasoning-active anchors and under-activated hard examples. We use FRONTIER-4.5K as a controlled programmatic reasoning suite for latent profiling and difficulty-aware analysis, and evaluate SPARK-Steering on GSM8K and MATH-500 with forward-only benchmark profiling. Our method improves Qwen3 series models consistently; on MATH-500, accuracy rises from 82.0% to 84.6% for Qwen3-4B and from 82.4% to 85.6% for Qwen3-8B. These results suggest that susceptibility can serve not only as a diagnostic signal for reasoning failures, but also as a practical guide for targeted test-time intervention.
Dongxu Zhang, Yiding Sun, Zihao Guo et al.· 0 citations
Large reasoning models often solve problems through long chain-of-thought (CoT) traces, yet much of this computation is spent on redundant derivations, repeated self-verification, and detours that do not improve the final answer. Existing on-policy self-distillation methods reduce this cost by matching a student model to a concise copy of itself on prefixes sampled from the student's own rollouts. We show that this objective has an initialization bottleneck. Since supervision is applied only to visited prefixes, training from a verbose base model places the KL loss on contexts that are often noisy, redundant, or already off track. In such regions, a concise teacher can provide only local corrections, while the student continues to explore trajectories that an efficient reasoner should avoid. In this paper, we propose BIRD(Bootstrapped Iterative Self-Reasoning Distillation), a two-stage self-reasoning distillation method that improves the rollout distribution before on-policy training. BIRD first samples concise solutions from the base model under a brevity instruction, keeps only answer-correct traces, and performs a lightweight prompt-switch SFT step. The traces are generated with the brevity instruction but learned under the original task prompt, turning instruction-induced conciseness into a default reasoning behavior. Starting from this warm model, BIRD then applies on-policy reverse-KL distillation with a concise self-teacher, now on cleaner and more informative prefixes. Across Qwen3 series models, BIRD achieves a stronger accuracy-efficiency trade-off than prompting and cold-start on-policy distillation on MATH-500 and AIME benchmarks. On Qwen3-8B, it improves MATH-500 accuracy from 86.2% to 92.0% while reducing the average response length from 3,099 to 1,115 tokens. These results highlight prefix support as a central factor in efficient reasoning distillation.
Leichao Dong, Dongxu Zhang, Yiding Sun et al.· 0 citations