NP-Hardness of Minimizing Neurons in Two-Hidden-Layer ReLU Neural Networks
A fundamental question in neural network architecture optimization is whether the minimum hidden-neuron count required to approximate a target function within a prescribed tolerance can be computed efficiently. This paper resolves this question for two-hidden-layer ReLU networks under an $L^p(\mathbb{R}^d,\mathbb{R}^m)$ approximation constraint. For every fixed $d \ge 1$, $m \ge 1$, and $1 \le p < \infty$, we prove that computing the optimum exactly is NP-hard. The result holds even when the target is represented by a rational ReLU network whose realization is nonzero, componentwise nonnegative, compactly supported, globally Lipschitz, and continuous piecewise affine. The polynomial-time ...
| Authors | Sangrock Lee |
|---|---|
| Primary category | cs.LG |
| Published | 8 October 2026 |
| Last updated at source | 8 October 2026 |
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