Bypass Exponential Time Preprocessing: Fast Neural Network Training via Weight-Data Correlation Preprocessing

Josh Alman · 杰昊 梁 · Zhao Song · Ruizhe Zhang · Danyang Zhuo

Great Hall & Hall B1+B2 (level 1) #521
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Wed 13 Dec 3 p.m. PST — 5 p.m. PST

Abstract: Over the last decade, deep neural networks have transformed our society, and they are already widely applied in various machine learning applications. State-of-the-art deep neural networks are becoming larger in size every year to deliver increasing model accuracy, and as a result, model training consumes substantial computing resources and will only consume more in the future.Using current training methods, in each iteration, to process a data point $x \in \mathbb{R}^d$ in a layer, we need to spend $\Theta(md)$ time to evaluate all the $m$ neurons in the layer. This means processing the entire layer takes $\Theta(nmd)$ time for $n$ data points. Recent work [Song, Yang and Zhang, NeurIPS 2021] reduces this time per iteration to $o(nmd)$, but requires exponential time to preprocess either the data or the neural network weights, making it unlikely to have practical usage. In this work, we present a new preprocessing method that simply stores the weight-data correlation in a tree data structure in order to quickly and dynamically detect which neurons fire at each iteration. Our method requires only $O(nmd)$ time in preprocessing and still achieves $o(nmd)$ time per iteration. We complement our new algorithm with a lower bound, proving that assuming a popular conjecture from complexity theory, one could not substantially speed up our algorithm for dynamic detection of firing neurons.

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