"PIDformer: Transformer Meets Control Theory"

Control theory meets transformers to create more stable and robust models

https://arxiv.org/abs/2402.15989

🔍 Original Problem:

Transformer architectures face two critical issues: vulnerability to input corruptions (like noise/blur) and rank collapse in deep layers where token embeddings become increasingly similar, limiting representation capacity.

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🛠️ Solution in this Paper:

PIDformer introduces a Proportional-Integral-Derivative (PID) control system into transformers. It treats self-attention as a state-space model and adds closed-loop feedback control to preserve high-frequency details while improving stability. The PID controller helps maintain detailed information that would otherwise be lost during processing, making the model more resilient to perturbations.

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💡 Key Insights:

→ Self-attention operates as an autonomous state-space model that minimizes nonlocal total variation

→ This smoothness property leads to rank collapse and diminished representation capacity

→ PID control framework can effectively counteract information loss while maintaining stability

→ The controlled state-space model proves theoretically robust against input perturbations

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📊 Results:

→ Enhanced robustness against adversarial attacks on ImageNet classification

→ Superior performance on ADE20K image segmentation tasks

→ Improved language modeling results on WikiText-103 benchmark