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OPTIMAL ROBUST MEMORIZATION WITH RELU NEURAL NETWORKS
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Studies the minimal ReLU network size needed to robustly memorize a finite classification dataset, proving NP-hardness of computing the optimal size and giving matching-order constructions.
Problem
Robust memorization with neural networks: determining the expressive power needed for ReLU networks to interpolate a finite labeled dataset while remaining robust to input perturbations, a problem that has not been thoroughly studied.
Approach
Theoretical analysis of robust memorization: proves NP-hardness of computing the optimal ReLU network size for robust memorization and establishes optimal (tight) bounds on the network size needed for robust interpolation of finite classification datasets.
Key results
- Proves that computing the optimal ReLU neural network size for robust memorization is NP-hard.
Limitations
- Full text unavailable; results drawn only from the truncated abstract.
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