Gauge Freedom and Metric Dependence in Neural Representation Spaces
Neural network representations are often analyzed as vectors in a fixed Euclidean space. However, their coordinates are not uniquely defined. If a hidden representation is transformed by an invertible linear map, the network function can be preserved by applying the inverse transformation to downstream weights. Representations are therefore defined only up to invertible linear transformations. We study neural representation spaces from this geometric viewpoint and treat them as vector spaces with a gauge freedom under the general linear group. Within this framework, commonly used similarity measures such as cosine similarity become metric-dependent quantities whose values can change under...
| Authors | Jericho Cain |
|---|---|
| Primary category | cs.LG |
| Published | 6 March 2026 |
| Last updated at source | 6 March 2026 |
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