SPARK is introduced, which uses hidden-state response to diagnose whether a model internally enters an effective reasoning state and to guide lightweight test-time steering, and suggests that susceptibility can serve not only as a diagnostic signal for reasoning failures, but also as a practical guide for targeted test-time intervention.
Abstract
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.
This work treats each reasoning trace as a sequence of latent states rather than an unstructured texts, and investigates whether inference time interventions can provide fine-grained control over the self-looping reasoning process.
Experimental results show that CritICL consistently outperforms standard in-context learning and achieves performance competitive with or superior to test-time scaling methods, while requiring significantly fewer generations and lower token cost.
Yu-Fan Wu, Yinghui He, Zhengyi Hu et al.· 1 citation
This work presents a theoretical framework that reveals how reasoning steps can amplify error through three failure modes: incorrect sub-task decomposition, incorrect sub-task solving, and incorrect final answer summarization, and introduces structured interventions that adapt CoT generation according to the identified failure types.
Haibo Jin, Peiyan Zhang, Man Luo et al.· Neural Information Processin...· 1 citation
A graded, multi-family, failure-aware framework for stress-testing reasoning models that exposes structure that an aggregate score hides and exposes consistent weaknesses across all models.
Identical language-model answers can arise from hidden states that support different future computations, so current-answer probes do not establish a reusable internal interface. We introduce forked futures: future operations are sampled only after a prefix state has formed, and states are compared through the response distributions induced by those operations. This yields an empirical causal quotient over hidden states without requiring researcher-specified latent labels. Shared, Local, Mixture, and Distributed interfaces then compete under prequential causal description length subject to future-signature fidelity and matched capacity constraints. In the two detailed model evaluations, Shared has the lowest held-out description length, with gains of 0.216 nats on Qwen2.5-1.5B and 0.294 nats on Llama-3-8B, while maintaining tightly clustered mean future-signature distortion; a five-backbone sweep preserves the positive direction of Sharedness Gain. The figure-aligned transplantation analysis gives Shared the strongest joint target-correctness, locality, copy-preservation, and composite profile, and API-aligned paths mediate 0.749 of the target effect versus 0.150 for matched null paths. In the blind four-class model-organism test, 14/16 architectures are recovered, with one observed non-Shared to Shared error among 12 non-Shared organisms. These results support an economical reusable causal interface within the tested operation banks, while keeping the claim explicitly conditional on the candidate architectures, interventions, and held-out futures.
Siyuan Ma, Yiqin Luo, Zhangji et al.· arXiv.org· 4 citations
When a large language model fails a reasoning task, it is often assumed to lack the underlying capability. However, this conflates a genuine absence of reasoning with a late-stage output bottleneck. We observe a consistent readout gap across diverse reasoning benchmarks: hidden-state probes successfully decode correct answers even when native sequence scoring completely collapses due to structural biases. To test whether instance-specific logic survives this collapse, we introduce a diagnostic protocol using a minimal, target-label-free additive correction. Fitting just two parameters on as few as 25 unlabeled examples recovers 9--34 accuracy points for Qwen3.5 models, transferring successfully to OLMo-2-1B and Llama-3.1-8B. Crucially, these recovered decisions persist on hard instances unresolved by simple lexical overlap and significantly exceed count-preserving permutation baselines. Our results show that many apparent zero-shot reasoning deficits are expression failures masking intact internal logic, urging a narrower interpretation of benchmark evaluations.
