The Geometric Alignment Tax: Tokenization vs. Continuous Geometry in Scientific Foundation Models
Foundation models for biology and physics optimize predictive accuracy, but their internal representations systematically fail to preserve the continuous geometry of the systems they model. We identify the root cause: the Geometric Alignment Tax, an intrinsic cost of forcing continuous manifolds through discrete categorical bottlenecks. Controlled ablations on synthetic dynamical systems demonstrate that replacing cross-entropy with a continuous head on an identical encoder reduces geometric distortion by up to 8.5x, while learned codebooks exhibit a non-monotonic double bind where finer quantization worsens geometry despite improving reconstruction. Under continuous objectives, three arc...
| Authors | Prashant C. Raju |
|---|---|
| Primary category | cs.LG |
| Published | 5 April 2026 |
| Last updated at source | 5 April 2026 |
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