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arXiv · 2305.08001

Structured and Fast Optimization: The Kronecker SGD Algorithm

Zhao Song·Song Yue
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Abstract

Stochastic gradient descent (SGD) now acts as a fundamental part of optimization in current machine learning. Meanwhile, deep learning architectures have shown outstanding performance in a wide range of fields, such as natural language processing, bioinformatics, and computer vision. Nevertheless, as the parameter size $d$ increases, these models encounter serious efficiency challenges. Previous studies show that the per step calculation expense scales linearly with the input size $d$. To mitigate this, our paper explores inherent patterns, such as Kronecker products within the training examples. We consider input data points that can be represented as tensor products of lower-dimensional vectors. We introduce a novel stochastic optimization method where the computational load for every update scales sublinearly with $d$, assuming moderate structural properties of the inputs. We believe our research is the first work achieving this result, representing a significant step forward for efficient deep learning optimization. Our theoretical findings are supported by a formal theorem, demonstrating that the proposed algorithm can train a two-layer fully connected neural network with a per-iteration cost independent of $d$.

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Zhao Song, Song Yue. 2023-05-13. Structured and Fast Optimization: The Kronecker SGD Algorithm. https://arxiv.org/abs/2305.08001

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