# Stabilizing RNN Gradients through Pre-training

arXiv: https://arxiv.org/abs/2308.12075 · HTML: https://mlsanity.com/paper/2308.12075/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 35 of its 88 references that are in the map.
- First posted on arXiv 23 Aug 2023.

## Builds on (most cited first, 30 of 35)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Language Models are Few-Shot Learners](https://mlsanity.com/paper/2005.14165/) (2020)
- [Layer Normalization](https://mlsanity.com/paper/1607.06450/) (2016)
- [Delving Deep into Rectifiers: Surpassing Human-Level Performance on ImageNet Classification](https://mlsanity.com/paper/1502.01852/) (2015)
- [Gaussian Error Linear Units (GELUs)](https://mlsanity.com/paper/1606.08415/) (2016)
- [Efficiently Modeling Long Sequences with Structured State Spaces](https://mlsanity.com/paper/2111.00396/) (2021)
- [Implicit Neural Representations with Periodic Activation Functions](https://mlsanity.com/paper/2006.09661/) (2020)
- [Transformers are RNNs: Fast Autoregressive Transformers with Linear Attention](https://mlsanity.com/paper/2006.16236/) (2020)
- [Transformer-XL: Attentive Language Models Beyond a Fixed-Length Context](https://mlsanity.com/paper/1901.02860/) (2019)
- [Averaging Weights Leads to Wider Optima and Better Generalization](https://mlsanity.com/paper/1803.05407/) (2018)
- [RWKV: Reinventing RNNs for the Transformer Era](https://mlsanity.com/paper/2305.13048/) (2023)
- [Simplified State Space Layers for Sequence Modeling](https://mlsanity.com/paper/2208.04933/) (2022)
- [Exact solutions to the nonlinear dynamics of learning in deep linear neural networks](https://mlsanity.com/paper/1312.6120/) (2013)
- [Language Modeling with Gated Convolutional Networks](https://mlsanity.com/paper/1612.08083/) (2016)
- [Resurrecting Recurrent Neural Networks for Long Sequences](https://mlsanity.com/paper/2303.06349/) (2023)
- [Hyena Hierarchy: Towards Larger Convolutional Language Models](https://mlsanity.com/paper/2302.10866/) (2023)
- [Lookahead Optimizer: k steps forward, 1 step back](https://mlsanity.com/paper/1907.08610/) (2019)
- [Unitary Evolution Recurrent Neural Networks](https://mlsanity.com/paper/1511.06464/) (2015)
- [AdaBelief Optimizer: Adapting Stepsizes by the Belief in Observed Gradients](https://mlsanity.com/paper/2010.07468/) (2020)
- [Towards the Systematic Reporting of the Energy and Carbon Footprints of Machine Learning](https://mlsanity.com/paper/2002.05651/) (2020)
- [SuperSpike: Supervised learning in multi-layer spiking neural networks](https://mlsanity.com/paper/1705.11146/) (2017)
- [Long short-term memory and learning-to-learn in networks of spiking neurons](https://mlsanity.com/paper/1803.09574/) (2018)
- [The Principles of Deep Learning Theory](https://mlsanity.com/paper/2106.10165/) (2021)
- [Independently Recurrent Neural Network (IndRNN): Building A Longer and Deeper RNN](https://mlsanity.com/paper/1803.04831/) (2018)
- [The Heidelberg spiking datasets for the systematic evaluation of spiking neural networks](https://mlsanity.com/paper/1910.07407/) (2019)
- [A Simple Way to Initialize Recurrent Networks of Rectified Linear Units](https://mlsanity.com/paper/1504.00941/) (2015)
- [Accurate and efficient time-domain classification with adaptive spiking recurrent neural networks](https://mlsanity.com/paper/2103.12593/) (2021)
- [Gradients are Not All You Need](https://mlsanity.com/paper/2111.05803/) (2021)
- [Orthogonal Deep Neural Networks](https://mlsanity.com/paper/1905.05929/) (2019)
- [Convolutional Networks for Fast, Energy-Efficient Neuromorphic Computing](https://mlsanity.com/paper/1603.08270/) (2016)

## Abstract (arXiv)

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.