Exponential Approximation Rates and Parameter Efficiency of Learnable Bernstein Activations

arXiv:2602.04264v2 Announce Type: replace-cross Abstract: The choice of activation function fundamentally shapes the representational capacity and parameter efficiency of deep neural networks, yet most widely used activations lack rigorous theoretical guarantees on these properties. We provide a theoretical analysis of DeepBern-Nets (DBNs) -- networks employing learnable Bernstein polynomial activations -- showing that their approximation error decays with the network depth $L$ and the polynomia