Riding the Fixed-Point Curve: Image Classification in the Continuous Thought Machine
The Continuous Thought Machine (CTM) is a recurrent network that attends to inputs and makes predictions based on the synchronization between its neurons. On tasks spanning many domains, it displays emergent thought processes that have not been explained. We report a number of findings about how the CTM classifies images, focusing on ImageNet. Each thinking step is an attracting but strongly non-normal map exhibiting balanced amplification (Murphy and Miller, 2009); while attraction is already present at CTM initialization, training highly promotes non-normality. By Banach's theorem, the neural state has a locally unique attracting fixed point, which moves at every step, and the thought t...
| Authors | Thomas Hannagan |
|---|---|
| Primary category | cs.LG |
| Published | 13 October 2026 |
| Last updated at source | 13 October 2026 |
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