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

arXiv: https://arxiv.org/abs/2607.10296 · HTML: https://mlsanity.com/paper/2607.10296/

## 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 30 of its 45 references that are in the map.
- First posted on arXiv 11 Jul 2026.

## Placed in

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

## Builds on (most cited first, 30 of 30)

- [The Llama 3 Herd of Models](https://mlsanity.com/paper/2407.21783/) (2024)
- [Training Verifiers to Solve Math Word Problems](https://mlsanity.com/paper/2110.14168/) (2021)
- [Qwen3 Technical Report](https://mlsanity.com/paper/2505.09388/) (2025)
- [ReAct: Synergizing Reasoning and Acting in Language Models](https://mlsanity.com/paper/2210.03629/) (2022)
- [Explaining and Harnessing Adversarial Examples](https://mlsanity.com/paper/1412.6572/) (2014)
- [DeepSeek-R1: Incentivizing Reasoning Capability in LLMs via Reinforcement Learning](https://mlsanity.com/paper/2501.12948/) (2025)
- [Measuring Mathematical Problem Solving With the MATH Dataset](https://mlsanity.com/paper/2103.03874/) (2021)
- [Emergent Abilities of Large Language Models](https://mlsanity.com/paper/2206.07682/) (2022)
- [Least-to-Most Prompting Enables Complex Reasoning in Large Language Models](https://mlsanity.com/paper/2205.10625/) (2022)
- [Representation Engineering: A Top-Down Approach to AI Transparency](https://mlsanity.com/paper/2310.01405/) (2023)
- [Train Short, Test Long: Attention with Linear Biases Enables Input Length Extrapolation](https://mlsanity.com/paper/2108.12409/) (2021)
- [Steering Language Models With Activation Engineering](https://mlsanity.com/paper/2308.10248/) (2023)
- [Plug and Play Language Models: A Simple Approach to Controlled Text Generation](https://mlsanity.com/paper/1912.02164/) (2019)
- [Eliciting Latent Predictions from Transformers with the Tuned Lens](https://mlsanity.com/paper/2303.08112/) (2023)
- [Patchscopes: A Unifying Framework for Inspecting Hidden Representations of Language Models](https://mlsanity.com/paper/2401.06102/) (2024)
- [Sensitivity and Generalization in Neural Networks: an Empirical Study](https://mlsanity.com/paper/1802.08760/) (2018)
- [Holistic Evaluation of Language Models](https://mlsanity.com/paper/2211.09110/) (2022)
- [The CLRS-Text Algorithmic Reasoning Language Benchmark](https://mlsanity.com/paper/2406.04229/) (2024)
- [Chain-of-Thought Compression Should Not Be Blind: V-Skip for Efficient Multimodal Reasoning via Dual-Path Anchoring](https://mlsanity.com/paper/2601.13879/) (2026)
- [PointCoT: A Multi-modal Benchmark for Explicit 3D Geometric Reasoning](https://mlsanity.com/paper/2602.23945/) (2026)
- [Not All Queries Need Deep Thought: CoFiCot for Adaptive Coarse-to-fine Stateful Refinement](https://mlsanity.com/paper/2603.08251/) (2026)
- [Not All Errors Are Created Equal: ASCoT Addresses Late-Stage Fragility in Efficient LLM Reasoning](https://mlsanity.com/paper/2508.05282/) (2025)
- [PointRFT: Explicit Reinforcement Fine-tuning for Point Cloud Few-shot Learning](https://mlsanity.com/paper/2603.23957/) (2026)
- [Mitigating Hallucinations via Inter-Layer Consistency Aggregation in Large Vision-Language Models](https://mlsanity.com/paper/2505.12343/) (2025)
- [Intern-Atlas: A Methodological Evolution Graph as Research Infrastructure for AI Scientists](https://mlsanity.com/paper/2604.28158/) (2026)
- [Tri-Efficient Transfer Learning for Point Cloud Videos](https://mlsanity.com/paper/2606.24175/) (2026)
- [NanoResearch: Co-Evolving Skills, Memory, and Policy for Personalized Research Automation](https://mlsanity.com/paper/2605.10813/) (2026)
- [FADE: Mitigating Hallucinations by Reducing Language-Prior Dominance in Large Vision-Language Models](https://mlsanity.com/paper/2606.29431/) (2026)
- [CFMS: A Coarse-to-Fine Multimodal Synthesis Framework for Enhanced Tabular Reasoning](https://mlsanity.com/paper/2604.10973/) (2026)
- [SeeMe: Mitigating Hallucinations in Large Vision-Language Models through Effective Visual Token Engineering](https://mlsanity.com/paper/2607.04163/) (2026)

## Abstract (arXiv)

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.