用简单分类器挖掘大模型内在推理能力，提升数学题解题效果

Pre-trained large language models (LLMs) have been demonstrated to possess intrinsic reasoning capabilities that can emerge naturally when expanding the response space. However, the neural representation mechanisms underlying these intrinsic capabilities and approaches for their optimal utilization remain inadequately understood. In this work, we make the key discovery that a simple linear classifier can effectively detect intrinsic reasoning capabilities in LLMs' activation space, particularly within specific representation types and network layers. Based on this finding, we propose a classifier-guided search framework that strategically explore a tree-structured response space. In each node expansion, the classifier serves as a scoring and ranking mechanism that efficiently allocates computational resources by identifying and prioritizing more thoughtful reasoning directions for continuation. After completing the tree expansion, we collect answers from all branches to form a candidate answer pool. We propose a branch-aggregation selection method that marginalizes over all supporting branches by aggregating their thoughtfulness scores, thereby identifying the optimal answer from the pool. Experimental results show that our framework's comprehensive exploration not only covers valid reasoning chains but also effectively identifies them, achieving significant improvements across multiple arithmetic reasoning benchmarks.