Efficient Algorithms for Learning Depth-2 Neural Networks with General ReLU Activations
This addresses a key limitation in neural network theory for researchers, as prior methods assumed zero bias, making it an incremental but important extension.
The paper tackles the problem of learning depth-2 neural networks with general ReLU activations, including bias terms, by developing polynomial-time algorithms that achieve sample efficiency under mild assumptions, establishing identifiability of parameters.
We present polynomial time and sample efficient algorithms for learning an unknown depth-2 feedforward neural network with general ReLU activations, under mild non-degeneracy assumptions. In particular, we consider learning an unknown network of the form $f(x) = {a}^{\mathsf{T}}σ({W}^\mathsf{T}x+b)$, where $x$ is drawn from the Gaussian distribution, and $σ(t) := \max(t,0)$ is the ReLU activation. Prior works for learning networks with ReLU activations assume that the bias $b$ is zero. In order to deal with the presence of the bias terms, our proposed algorithm consists of robustly decomposing multiple higher order tensors arising from the Hermite expansion of the function $f(x)$. Using these ideas we also establish identifiability of the network parameters under minimal assumptions.