Position: A Theory of Deep Learning Must Include Compositional Sparsity

Overparametrized Deep Neural Networks (DNNs) have demonstrated remarkable success in a wide variety of domains too high-dimensional for classical shallow networks subject to the curse of dimensionality. However, open questions about fundamental principles, that govern the learning dynamics of DNNs, remain. In this position paper we argue that it is the ability of DNNs to exploit the compositionally sparse structure of the target function driving their success. As such, DNNs can leverage the property that most practically relevant functions can be composed from a small set of constituent functions, each of which relies only on a low-dimensional subset of all inputs. We show that this property is shared by all efficiently Turing-computable functions and is therefore highly likely present in all current learning problems. While some promising theoretical insights on questions concerned with approximation and generalization exist in the setting of compositionally sparse functions, several important questions on the learnability and optimization of DNNs remain. Completing the picture of the role of compositional sparsity in deep learning is essential to a comprehensive theory of artificial, and even general, intelligence.

Inducing Semi-Structured Sparsity by Masking for Efficient Model Inference in Convolutional Networks

The crucial role of convolutional models, both as standalone vision models and backbones in foundation models, necessitates effective acceleration techniques. This paper proposes a novel method to learn semi-structured sparsity patterns for convolution kernels in the form of maskings enabling the utilization of readily available hardware accelerations. The approach accelerates convolutional models more than two-fold during inference without decreasing model performance. At the same time, the original model weights and structure remain unchanged keeping the model thus easily updatable. Beyond the immediate practical use, the effect of maskings on prediction is easily quantifiable. Therefore, guarantees on model predictions under maskings are derived showing stability bounds for learned maskings even after updating the original underlying model.