New Paradigm for Learning Stability: PID-Transformer
To address gradient instability and oscillatory behavior during the training of large-scale neural architectures like Transformers, we propose a novel architecture that directly incorporates PID (Proportional-Integral-Derivative) principles from control engineering. Explore its principles and remarkable effects through this interactive report.
Problem: The Path of Unstable Training
Existing Transformer models tend to exhibit inefficient and unstable changes in their internal representations (Hidden States) during training. This hinders learning speed and degrades performance. The visualization below clearly demonstrates this issue.
Latent Space Trajectory Comparison (PCA)
The Baseline model without a controller shows an unstable path, taking a long detour to reach the target point (🔴).
In contrast, the Hero Model with the PID controller learns efficiently by taking a very smooth and direct path from the starting point (🟢) to the target.
Solution: Embedded Intelligent Controller
We have integrated a learnable 'Geometric PID Controller' directly into the Transformer. This controller actively stabilizes the model's internal signals in real-time, optimizing the training process. Key components include:
Geometric PID Controller
A controller designed to operate in high-dimensional vector spaces. Based on the current error ($e_t$), it generates an optimal control signal ($u_t$) by combining three terms: Proportional (P), Integral (I), and Derivative (D).
P (Proportional) - Proportional Control
Reacts immediately proportional to the current error. Guides the system quickly to the target value.
I (Integral) - Integral Control
Accumulates all past errors to eliminate steady-state error.
D (Derivative) - Derivative Control
Measures the rate of change of the error to suppress overshoot and enhance system stability.
Performance Comparison Dashboard
Compare how our proposed 'Hero Model' outperforms the 'Baseline Model'. Click the buttons below to visualize data for each model.
Training Loss Curve
PID Controller Term Norms
Gradient Spectrum Analysis (GSA)
Conclusion & Future Work
Key Achievements
This research presents a principled methodology for bridging control theory and deep learning, making the training process of complex neural network models more stable, efficient, and interpretable. Our proposed AdaptiveDim+Gating PID-Transformer significantly outperforms existing models in terms of performance, control efficiency, fundamental stability, and intelligent representation learning.
Future Directions
This work opens new possibilities for control theory-based deep learning stabilization. Future research can explore applying dynamic reference signals, deeper analysis of control strategies, and extending the control module to other architectures.