SPARK: Susceptibility-Guided Profiling and Steering of Latent Reasoning States in Large Language Models

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.

QPILOTS: Efficient Test-Time Q-Steering for Flow Policies

Flow-matching and diffusion policies are expressive action generators, but optimizing them with temporal-difference reinforcement learning (RL) remains difficult. Effective policy extraction requires exploiting the critic's action gradient, yet directly backpropagating this signal through a multi-step denoising process can be numerically unstable. Existing methods work around this either by discarding gradient information, distilling the policy into a simpler one-step actor, or repeatedly fine-tuning the denoising policy as the critic improves. We propose QPILOTS, a method that leaves the original policy unmodified and steers the denoising process at inference time. At each denoising step, instead of evaluating the critic on the noisy intermediate action where critic predictions are unreliable, we first project that intermediate state to an estimate of the final clean action and compute the critic gradient there. We introduce two variants: QPILOTS-U uses a fast single-point approximation, while QPILOTS-M draws differentiable posterior samples via a learned auxiliary network. On a standard offline-to-online RL benchmark, QPILOTS achieves the best aggregate performance, reaching an average success rate of 90% across 50 tasks. We also apply QPILOTS to steer a large, frozen, pretrained Vision-Language Action (VLA) foundation model, outperforming or matching prior inference-time approaches across six manipulation tasks in simulation.