Recursive architectures such as Tiny Recursive Models (TRMs) perform implicit reasoning through iterative latent computation, yet the geometric structure of these reasoning trajectories remains poorly understood. We investigate the activation manifold of TRMs during recursive unrolling and find that activations occupy an effectively linear, low-dimensional subspace whose principal directions can be tracked dynamically with cheap power iterations. This suggests that weight-sharing concentrates iterative computation along a small number of dominant eigendirections, and we find that this concentration varies sharply across computational sites. We exploit this structure through LASER (Low-Rank Activation SVD for Efficient Recursion), a dynamic compression framework that maintains an evolving low-rank basis via matrix-free subspace tracking with a fidelity-triggered reset mechanism, achieving ${\sim}60\%$ activation memory savings with no statistically significant accuracy degradation. Our analysis raises questions about how recursive architectures allocate representational capacity during implicit reasoning, and whether this concentration can be exploited to improve the efficiency and stability of latent computation.

翻译：诸如小递归模型（TRMs）等递归架构通过迭代式隐式计算实现隐式推理，然而这些推理轨迹的几何结构仍鲜为人知。我们研究了TRM在递归展开过程中的激活流形，发现激活值占据了一个有效线性且低维的子空间，其主方向可通过廉价幂迭代法动态追踪。这表明权重共享将迭代计算集中到少数主导特征方向上，且我们发现这种集中在不同计算位置间存在显著差异。我们通过LASER（面向高效递归的低秩激活奇异值分解）利用这一结构——该动态压缩框架通过无矩阵子空间跟踪及保真度触发的重置机制维护一个演进中的低秩基，在无统计显著精度损失的情况下实现了约60%的激活内存节省。我们的分析引发了关于递归架构如何在隐式推理中分配表征能力、以及这种集中特性能否用于提升隐式计算的效率与稳定性等问题。