PIDformer: Transformer Meets Control Theory

• URL: http://arxiv.org/abs/2402.15989v1
• Date: Sun, 25 Feb 2024 05:04:51 GMT
• Title: PIDformer: Transformer Meets Control Theory
• Authors: Tam Nguyen, C\'esar A. Uribe, Tan M. Nguyen, Richard G. Baraniuk
• Abstract summary: We unveil self-attention as an autonomous state-space model that inherently promotes smoothness in its solutions. 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. Motivated by this control framework, we derive a novel class of transformers, PID-controlled Transformer (PIDformer)
• Score: 28.10913642120948
• License: http://creativecommons.org/licenses/by/4.0/
• 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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