The Gradient Does Not See Rank: Rank-Indifference in Matrix-CODI on ProsQA
Continuous chain-of-thought models compress reasoning into latent tokens. Matrix-valued variants, which route each latent token through a d x d matrix bottleneck, introduce rank as a single-sample structural observable on the latent matrix Z. If matrix latents carry parallel reasoning paths via superposition, rank should track them, and truncating Z to low rank should hurt accuracy on tasks whose solutions plausibly require multiple components. Across four training regimes of a matrix-CODI model (three on ProsQA, one on GSM8K-Aug below the learning threshold), the rank-k projection ablation curve is flat to within 0.6 percentage points. A three-seed replication yields 81.0 +/- 2.0 percent...
| Authors | Samuel Larson |
|---|---|
| Primary category | cs.LG |
| Published | 2 September 2026 |
| Last updated at source | 2 September 2026 |
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