Training Sparse Neural Network by Constraining Synaptic Weight on Unit Lp Sphere
This work addresses the need for efficient and generalizable sparse neural networks, offering a novel optimization method with theoretical guarantees, though it is incremental in building on existing sparsity techniques.
The authors tackled the problem of training sparse neural networks by constraining synaptic weights on a unit Lp-sphere, which allows flexible control of sparsity via parameter p and improves generalization, as validated on benchmark datasets across domains.
Sparse deep neural networks have shown their advantages over dense models with fewer parameters and higher computational efficiency. Here we demonstrate constraining the synaptic weights on unit Lp-sphere enables the flexibly control of the sparsity with p and improves the generalization ability of neural networks. Firstly, to optimize the synaptic weights constrained on unit Lp-sphere, the parameter optimization algorithm, Lp-spherical gradient descent (LpSGD) is derived from the augmented Empirical Risk Minimization condition, which is theoretically proved to be convergent. To understand the mechanism of how p affects Hoyer's sparsity, the expectation of Hoyer's sparsity under the hypothesis of gamma distribution is given and the predictions are verified at various p under different conditions. In addition, the "semi-pruning" and threshold adaptation are designed for topology evolution to effectively screen out important connections and lead the neural networks converge from the initial sparsity to the expected sparsity. Our approach is validated by experiments on benchmark datasets covering a wide range of domains. And the theoretical analysis pave the way to future works on training sparse neural networks with constrained optimization.