Quotient Geometry, Effective Curvature, and Implicit Bias in Simple Shallow Neural Networks
Overparameterized shallow neural networks admit substantial parameter redundancy: distinct parameter vectors may represent the same predictor due to hidden-unit permutations, rescalings, and related symmetries. As a result, geometric quantities computed directly in the ambient Euclidean parameter space can reflect artifacts of representation rather than intrinsic properties of the predictor. In this paper, we develop a differential-geometric framework for analyzing simple shallow networks through the quotient space obtained by modding out parameter symmetries on a regular set. We first characterize the symmetry and quotient structure of regular shallow-network parameters and show that the...
| Authors | Hang-Cheng Dong, Pengcheng Cheng |
|---|---|
| Primary category | cs.LG |
| Published | 23 March 2026 |
| Last updated at source | 23 March 2026 |
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