Quantifying and Optimizing Simplicity via Polynomial Representations
Deep networks often exhibit a preference for "simple" solutions, and such a simplicity bias is widely believed to play a key role in generalization. Yet a broadly applicable, quantitative measure of simplicity remains elusive. We introduce polynomial representations as a distribution-aware, low-dimensional surrogate for neural functions: we approximate a network's predictive behavior along data-dependent interpolation paths using orthogonal polynomial bases, yielding a compact functional representation. We show that the effective degree of this representation serves as a practical simplicity metric that is predictive of generalization across tasks and architectures, and consistently outpe...
| Authors | Tianren Zhang, Xiangxin Li, Minghao Xiao et al. |
|---|---|
| Primary category | cs.AI |
| Published | 28 May 2026 |
| Last updated at source | 8 June 2026 |
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