Convergent Evolution: How Different Language Models Learn Similar Number Representations
Language models trained on natural text learn to represent numbers using periodic features with dominant periods at $T=2, 5, 10$. In this paper, we identify a two-tiered hierarchy of these features: while Transformers, Linear RNNs, LSTMs, and classical word embeddings trained in different ways all learn features that have period-$T$ spikes in the Fourier domain, only some learn geometrically separable features that can be used to linearly classify a number mod-$T$. To explain this incongruity, we prove that Fourier domain sparsity is necessary but not sufficient for mod-$T$ geometric separability. Empirically, we investigate when model training yields geometrically separable features, fin...
| Authors | Deqing Fu, Tianyi Zhou, Mikhail Belkin et al. |
|---|---|
| Primary category | cs.CL |
| Published | 22 April 2026 |
| Last updated at source | 17 August 2026 |
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