Polynomial Learning of Positive ReLU Networks under Gaussian Inputs
We study positive, bias-free, one-hidden-layer ReLU networks under standard Gaussian inputs. We obtain algorithms with polynomial sample and real-arithmetic complexity, without separation or conditioning assumptions on the hidden directions. When the conditional label mean is a width-$k$ network with total output weight at most one, the learner achieves squared prediction error $\varepsilon$ with output width at most $k+\min\{k,d\}$ and complexity linear in one plus the residual second moment. For arbitrary labels with bounded second moment, we obtain a positive ReLU network of width $O(k\log(2/\varepsilon))$. Its risk is bounded by the irreducible noise variance plus $Ck^3\log^{9/2}(2k/\...
| Authors | Zhijie Zheng |
|---|---|
| Primary category | cs.LG |
| Published | 18 October 2026 |
| Last updated at source | 20 October 2026 |
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- 21 Oct 2026 Description: We study bias-free, one-hidden-layer ReLU networks with nonnegative output weights under standard Gaussian inputs. Hidden directions may be arbitrarily close or linearly dependent. The labels have the target as their conditional mean, and o → We study positive, bias-free, one-hidden-layer ReLU networks under standard Gaussian inputs. We obtain algorithms with polynomial sample and real-arithmetic complexity, without separation or conditioning assumptions on the hidden directions
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