N-ODE Transformer: A Depth-Adaptive Variant of the Transformer Using Neural Ordinary Differential Equations

• URL: http://arxiv.org/abs/2010.11358v1
• Date: Thu, 22 Oct 2020 00:48:24 GMT
• Title: N-ODE Transformer: A Depth-Adaptive Variant of the Transformer Using Neural Ordinary Differential Equations
• Authors: Aaron Baier-Reinio and Hans De Sterck
• Abstract summary: We use neural ordinary differential equations to formulate a variant of the Transformer that is depth-adaptive in the sense that an input-dependent number of time steps is taken by the ordinary differential equation solver. We consider the simple problem of determining the parity of a binary sequence, for which the standard Transformer has known limitations. We find, however, that the depth-adaptivity of the N-ODE Transformer does not provide a remedy for the inherently nonlocal nature of the parity problem.
• Score: 1.2183405753834562
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We use neural ordinary differential equations to formulate a variant of the Transformer that is depth-adaptive in the sense that an input-dependent number of time steps is taken by the ordinary differential equation solver. Our goal in proposing the N-ODE Transformer is to investigate whether its depth-adaptivity may aid in overcoming some specific known theoretical limitations of the Transformer in handling nonlocal effects. Specifically, we consider the simple problem of determining the parity of a binary sequence, for which the standard Transformer has known limitations that can only be overcome by using a sufficiently large number of layers or attention heads. We find, however, that the depth-adaptivity of the N-ODE Transformer does not provide a remedy for the inherently nonlocal nature of the parity problem, and provide explanations for why this is so. Next, we pursue regularization of the N-ODE Transformer by penalizing the arclength of the ODE trajectories, but find that this fails to improve the accuracy or efficiency of the N-ODE Transformer on the challenging parity problem. We suggest future avenues of research for modifications and extensions of the N-ODE Transformer that may lead to improved accuracy and efficiency for sequence modelling tasks such as neural machine translation.

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