Discovering a Zeta Map Algorithm on Dyck Paths via Mechanistic Interpretability
Machine learning is increasingly used in mathematical discovery, but in mathematics the desired output is often not a prediction itself, but an explicit construction that can be checked independently. We study this setting through the zeta map on Dyck paths, a classical bijection in the combinatorics of the q,t-Catalan numbers. We train a deliberately small one-layer, one-head encoder-decoder transformer on this map and analyze its learned computation using mechanistic interpretability tools, including decoder cross-attention analysis, linear probing, and causal intervention. The analysis reveals a level-based mechanism: encoder representations make path levels linearly accessible, while ...
| Authors | Xiaoyu Huang, Blake Jackson, Kyu-Hwan Lee |
|---|---|
| Primary category | cs.LG |
| Published | 28 May 2026 |
| Last updated at source | 28 May 2026 |
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