A Tropical Geometry View of Forgetting: A Per-Unit Projector for Knowledge-Preserving Fine-Tuning

Excerpt

arXiv:2610.04670v1 Announce Type: new Abstract: 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