AntisymmetricRNN: A Dynamical System View on Recurrent Neural Networks (1902.09689v1)

Abstract: Recurrent neural networks have gained widespread use in modeling sequential data. Learning long-term dependencies using these models remains difficult though, due to exploding or vanishing gradients. In this paper, we draw connections between recurrent networks and ordinary differential equations. A special form of recurrent networks called the AntisymmetricRNN is proposed under this theoretical framework, which is able to capture long-term dependencies thanks to the stability property of its underlying differential equation. Existing approaches to improving RNN trainability often incur significant computation overhead. In comparison, AntisymmetricRNN achieves the same goal by design. We showcase the advantage of this new architecture through extensive simulations and experiments. AntisymmetricRNN exhibits much more predictable dynamics. It outperforms regular LSTM models on tasks requiring long-term memory and matches the performance on tasks where short-term dependencies dominate despite being much simpler.

• The paper introduces the AntisymmetricRNN architecture that improves RNN trainability by discretizing stable ODEs to mitigate gradient issues.
• It leverages stability properties from ordinary differential equations to enhance the modeling of long-term dependencies while preserving short-term performance.
• Empirical evaluations demonstrate that AntisymmetricRNN outperforms LSTMs in long-term memory tasks with a simpler and computationally efficient design.

AntisymmetricRNN: A Dynamical System View on Recurrent Neural Networks

This paper presents a novel approach to improving the trainability and performance of Recurrent Neural Networks (RNNs) by drawing parallels with ordinary differential equations (ODEs) and introducing the AntisymmetricRNN architecture. Traditional RNNs often struggle with long-term dependencies due to the challenges associated with exploding and vanishing gradients. These issues complicate efficient learning of sequential data, a limitation that the proposed framework addresses through a mathematically grounded perspective.

The authors leverage the stability properties inherent in specific ordinary differential equations to enhance the modeling capabilities of RNNs, particularly in scenarios demanding long-term memory retention. The AntisymmetricRNN architecture is derived by discretizing ODEs that exhibit desired stability characteristics, which in turn helps to overcome gradient-related issues without incurring additional computational costs. This design philosophy contrasts with existing methods that tend to require substantial computational resources for improving RNN performance.

Through rigorous simulations and empirical evaluations, the AntisymmetricRNN demonstrates a marked improvement over conventional architectures, particularly in tasks that require handling extended dependencies. The architecture not only outperforms Long Short-Term Memory (LSTM) networks on long-term memory tasks but also consistently matches their performance on tasks dominated by short-term dependencies. Notably, it achieves these results with a simpler configuration.

The implications of this research are significant, offering a new lens through which RNN trainability can be enhanced by applying concepts from dynamical systems theory. This interdisciplinary approach opens avenues for further exploration of stable ODEs and numeric discretization techniques that could yield more robust recurrent architectures. The ability to merge insights from ODEs with neural network design has the potential to inspire innovations in both artificial intelligence and mathematical modeling domains. This synergy could lead to architectures that embody improved predictability and stability, facilitating a deeper understanding and novel applications in sequential data modeling. Future investigations may focus on identifying additional stable ODE frameworks that contribute to the development of well-conditioned RNN structures.