Recurrent neural networks: vanishing and exploding gradients are not the end of the story

• URL: http://arxiv.org/abs/2405.21064v2
• Date: Tue, 05 Nov 2024 10:28:21 GMT
• Title: Recurrent neural networks: vanishing and exploding gradients are not the end of the story
• Authors: Nicolas Zucchet, Antonio Orvieto,
• Abstract summary: Recurrent neural networks (RNNs) notoriously struggle to learn long-term memories. The recent success of state-space models (SSMs) to overcome such difficulties challenges our theoretical understanding.
• Score: 13.429440202738647
• License:
• Abstract: Recurrent neural networks (RNNs) notoriously struggle to learn long-term memories, primarily due to vanishing and exploding gradients. The recent success of state-space models (SSMs), a subclass of RNNs, to overcome such difficulties challenges our theoretical understanding. In this paper, we delve into the optimization challenges of RNNs and discover that, as the memory of a network increases, changes in its parameters result in increasingly large output variations, making gradient-based learning highly sensitive, even without exploding gradients. Our analysis further reveals the importance of the element-wise recurrence design pattern combined with careful parametrizations in mitigating this effect. This feature is present in SSMs, as well as in other architectures, such as LSTMs. Overall, our insights provide a new explanation for some of the difficulties in gradient-based learning of RNNs and why some architectures perform better than others.

Related papers

• Deeper or Wider: A Perspective from Optimal Generalization Error with Sobolev Loss [2.07180164747172]
  We compare deeper neural networks (DeNNs) with a flexible number of layers and wider neural networks (WeNNs) with limited hidden layers. We find that a higher number of parameters tends to favor WeNNs, while an increased number of sample points and greater regularity in the loss function lean towards the adoption of DeNNs.
  arXiv  Detail & Related papers  (2024-01-31T20:10:10Z)
• Pursing the Sparse Limitation of Spiking Deep Learning Structures [42.334835610250714]
  Spiking Neural Networks (SNNs) are garnering increased attention for their superior computation and energy efficiency. We introduce an innovative algorithm capable of simultaneously identifying both weight and patch-level winning tickets. We demonstrate that our spiking lottery ticket achieves comparable or superior performance even when the model structure is extremely sparse.
  arXiv  Detail & Related papers  (2023-11-18T17:00:40Z)
• Reparameterization through Spatial Gradient Scaling [69.27487006953852]
  Reparameterization aims to improve the generalization of deep neural networks by transforming convolutional layers into equivalent multi-branched structures during training. We present a novel spatial gradient scaling method to redistribute learning focus among weights in convolutional networks.
  arXiv  Detail & Related papers  (2023-03-05T17:57:33Z)
• Knowledge Enhanced Neural Networks for relational domains [83.9217787335878]
  We focus on a specific method, KENN, a Neural-Symbolic architecture that injects prior logical knowledge into a neural network. In this paper, we propose an extension of KENN for relational data.
  arXiv  Detail & Related papers  (2022-05-31T13:00:34Z)
• Deep Architecture Connectivity Matters for Its Convergence: A Fine-Grained Analysis [94.64007376939735]
  We theoretically characterize the impact of connectivity patterns on the convergence of deep neural networks (DNNs) under gradient descent training. We show that by a simple filtration on "unpromising" connectivity patterns, we can trim down the number of models to evaluate.
  arXiv  Detail & Related papers  (2022-05-11T17:43:54Z)
• Training High-Performance Low-Latency Spiking Neural Networks by Differentiation on Spike Representation [70.75043144299168]
  Spiking Neural Network (SNN) is a promising energy-efficient AI model when implemented on neuromorphic hardware. It is a challenge to efficiently train SNNs due to their non-differentiability. We propose the Differentiation on Spike Representation (DSR) method, which could achieve high performance.
  arXiv  Detail & Related papers  (2022-05-01T12:44:49Z)
• Reducing Catastrophic Forgetting in Self Organizing Maps with Internally-Induced Generative Replay [67.50637511633212]
  A lifelong learning agent is able to continually learn from potentially infinite streams of pattern sensory data. One major historic difficulty in building agents that adapt is that neural systems struggle to retain previously-acquired knowledge when learning from new samples. This problem is known as catastrophic forgetting (interference) and remains an unsolved problem in the domain of machine learning to this day.
  arXiv  Detail & Related papers  (2021-12-09T07:11:14Z)
• Wide Neural Networks Forget Less Catastrophically [39.907197907411266]
  We study the impact of "width" of the neural network architecture on catastrophic forgetting. We study the learning dynamics of the network from various perspectives.
  arXiv  Detail & Related papers  (2021-10-21T23:49:23Z)
• UnICORNN: A recurrent model for learning very long time dependencies [0.0]
  We propose a novel RNN architecture based on a structure preserving discretization of a Hamiltonian system of second-order ordinary differential equations. The resulting RNN is fast, invertible (in time), memory efficient and we derive rigorous bounds on the hidden state gradients to prove the mitigation of the exploding and vanishing gradient problem.
  arXiv  Detail & Related papers  (2021-03-09T15:19:59Z)
• Modeling from Features: a Mean-field Framework for Over-parameterized Deep Neural Networks [54.27962244835622]
  This paper proposes a new mean-field framework for over- parameterized deep neural networks (DNNs) In this framework, a DNN is represented by probability measures and functions over its features in the continuous limit. We illustrate the framework via the standard DNN and the Residual Network (Res-Net) architectures.
  arXiv  Detail & Related papers  (2020-07-03T01:37:16Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.