arXiv：cs.LG· Yuto Inui, Takuya Konishi, Yoshinobu Kawahara·· 4 小时前
Invariant-Measure Reasoners：用不变测度实现稳定表征的潜在推理
Invariant-Measure Reasoners: Stable Representations for Latent Reasoning
AI 导读
研究者提出不变测度推理器（ImR），用不变测度作为稳定表征来缓解潜在推理模型随循环深度增加导致的预测不稳定问题。该测度刻画潜在状态在紧致子集上的长期分布，ImR 从预测头输出在该测度下的期望进行预测，可用于微调现有模型的预测头或从头训练。在迷宫和数独任务上，两种方式均降低了预测不稳定性并提升了准确率，部分设置下 ImR 训练的模型更常表现出非不动点行为却仍保持高准确率。
正文
Abstract:Latent reasoning models repeatedly update a latent state using the same recurrent block. As the recurrent depth increases, the sequence of latent states may converge to a compact subset of the state space without necessarily converging to a fixed point. Existing models typically predict by applying a prediction head to a single latent state. However, the latent state can continue to change even after many updates, potentially making predictions unstable across recurrent depths. To address this instability, we introduce invariant-measure reasoners (ImR), a framework that uses an invariant measure as a stable representation. This measure describes the long-run distribution of latent states on the compact subset and is invariant under updates by the recurrent block. ImR predicts from the expectation of the prediction head's output under this measure. We use ImR in two ways: fine-tuning only the prediction head of existing models and training models from scratch. Both approaches reduce prediction instability and improve accuracy in many settings on maze and Sudoku tasks. In some settings, models trained with ImR exhibit non-fixed-point behavior more frequently than existing models yet achieve high accuracy even with such behavior, unlike existing models. These results suggest that ImR can leverage otherwise destabilizing dynamics for latent reasoning.
| Subjects: | Machine Learning (cs.LG) |
| Cite as: | arXiv:2610.10996 [cs.LG] |
| (or arXiv:2610.10996v1 [cs.LG] for this version) | |
| https://doi.org/10.48550/arXiv.2610.10996 arXiv-issued DOI via DataCite (pending registration) |
Submission history
From: Yuto Inui [view email]
[v1]
Wed, 7 Oct 2026 23:33:05 UTC (471 KB)
来源：arXiv：cs.LG · arxiv.org