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arXiv · 2402.15989

PIDformer: Transformer Meets Control Theory

Tam Nguyen·César A. Uribe·Tan M. Nguyen·Richard G. Baraniuk
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Abstract

In this work, we address two main shortcomings of transformer architectures: input corruption and rank collapse in their output representation. We unveil self-attention as an autonomous state-space model that inherently promotes smoothness in its solutions, leading to lower-rank outputs and diminished representation capacity. Moreover, the steady-state solution of the model is sensitive to input perturbations. We incorporate a Proportional-Integral-Derivative (PID) closed-loop feedback control system with a reference point into the model to improve robustness and representation capacity. This integration aims to preserve high-frequency details while bolstering model stability, rendering it more noise-resilient. The resulting controlled state-space model is theoretically proven robust and adept at addressing the rank collapse. Motivated by this control framework, we derive a novel class of transformers, PID-controlled Transformer (PIDformer), aimed at improving robustness and mitigating the rank-collapse issue inherent in softmax transformers. We empirically evaluate the model for advantages and robustness against baseline transformers across various practical tasks, including object classification, image segmentation, and language modeling.

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Tam Nguyen, César A. Uribe, Tan M. Nguyen, Richard G. Baraniuk. 2024-02-25. PIDformer: Transformer Meets Control Theory. https://arxiv.org/abs/2402.15989

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