A Tropical Geometry View of Forgetting: A Per-Unit Projector for Knowledge-Preserving Fine-Tuning
Fine-tuning a language model on new text degrades what it already does. Replay-free projectors such as Adam-NSCL and GPM forbid one shared subspace of a layer's inputs in every row of the update. The tropical geometry of a ReLU layer shows why this is too coarse. In data space, the units' walls are tropical hypersurfaces whose cells are dual to the upper vertices of a zonotope; in weight space, each old token is a hyperplane, and the tokens cut out a polyhedron, the closure of the weights that keep every token on its side. An exact identity joins the two pictures: the squared change of the layer's output under any weight change splits into in-cell, open-to-closed and closed-to-open terms,...
| Authors | Yuyang Zhang, Xiaoyin Chen, Chunlin Ren et al. |
|---|---|
| Primary category | cs.AI |
| Published | 3 October 2026 |
| Last updated at source | 3 October 2026 |
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