Physics

Inference

Mathematics

Agronomy

Biology

Statistics

Pruning

Initialization

Machine learning

Engineering

Gaussian

Mathematical analysis

Industrial engineering

Artificial intelligence

Generalization

Programming language

Geometry

Lottery

Work flow

Flow (mathematics)

Computer science

Sparse matrix

Quantum mechanics

Artificial neural network

Early stopping

Sparse Neural Networks (NNs) can match the generalization of dense NNs using a fraction of the compute/storage for inference, and have the potential to enable efficient training. However, naively training unstructured sparse NNs from random initialization results in significantly worse generalization, with the notable exceptions of Lottery Tickets (LTs) and Dynamic Sparse Training (DST). In this work, we attempt to answer: (1) why training unstructured sparse networks from random initialization performs poorly and; (2) what makes LTs and DST the exceptions? We show that sparse NNs have poor gradient flow at initialization and propose a modified initialization for unstructured connectivity. Furthermore, we find that DST methods significantly improve gradient flow during training over traditional sparse training methods. Finally, we show that LTs do not improve gradient flow, rather their success lies in re-learning the pruning solution they are derived from — however, this comes at the cost of learning novel solutions.

Gradient Flow in Sparse Neural Networks and How Lottery Tickets Win