Stabilizing RNN Gradients through Pre-training

• URL: http://arxiv.org/abs/2308.12075v2
• Date: Fri, 5 Jan 2024 00:56:41 GMT
• Title: Stabilizing RNN Gradients through Pre-training
• Authors: Luca Herranz-Celotti, Jean Rouat
• Abstract summary: Theory of learning proposes to prevent the gradient from exponential growth with depth or time, to stabilize and improve training. We extend known stability theories to encompass a broader family of deep recurrent networks, requiring minimal assumptions on data and parameter distribution. We propose a new approach to mitigate this issue, that consists on giving a weight of a half to the time and depth contributions to the gradient.
• Score: 3.335932527835653
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Numerous theories of learning propose to prevent the gradient from exponential growth with depth or time, to stabilize and improve training. Typically, these analyses are conducted on feed-forward fully-connected neural networks or simple single-layer recurrent neural networks, given their mathematical tractability. In contrast, this study demonstrates that pre-training the network to local stability can be effective whenever the architectures are too complex for an analytical initialization. Furthermore, we extend known stability theories to encompass a broader family of deep recurrent networks, requiring minimal assumptions on data and parameter distribution, a theory we call the Local Stability Condition (LSC). Our investigation reveals that the classical Glorot, He, and Orthogonal initialization schemes satisfy the LSC when applied to feed-forward fully-connected neural networks. However, analysing deep recurrent networks, we identify a new additive source of exponential explosion that emerges from counting gradient paths in a rectangular grid in depth and time. We propose a new approach to mitigate this issue, that consists on giving a weight of a half to the time and depth contributions to the gradient, instead of the classical weight of one. Our empirical results confirm that pre-training both feed-forward and recurrent networks, for differentiable, neuromorphic and state-space models to fulfill the LSC, often results in improved final performance. This study contributes to the field by providing a means to stabilize networks of any complexity. Our approach can be implemented as an additional step before pre-training on large augmented datasets, and as an alternative to finding stable initializations analytically.

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