Core Concepts
The orthogonal component of a neural network's weights stabilizes early in the training process, enabling efficient low-rank training methods that maintain accuracy while significantly reducing the number of trainable parameters.
Abstract
This study explores the learning dynamics of neural networks by analyzing the singular value decomposition (SVD) of their weights throughout training. The investigation reveals that an orthogonal basis within each multidimensional weight's SVD representation stabilizes during training.
Building on this finding, the authors introduce Orthogonality-Informed Adaptive Low-Rank (OIALR) training, a novel training method that exploits the intrinsic orthogonality of neural networks. OIALR seamlessly integrates into existing training workflows with minimal accuracy loss, as demonstrated by benchmarking on various datasets and well-established network architectures. With appropriate hyperparameter tuning, OIALR can surpass conventional training setups, including those of state-of-the-art models.
The key steps of OIALR are:
- Start training in a traditional full-rank scheme.
- After a number of iterations, transition the network's multidimensional weights to their UΣV^T representation via SVD.
- No longer train the orthogonal bases U and V^T with backpropagation, but train only the square matrix Σ.
- After a specified number of training steps, update the bases U and V^T by extracting the new bases from the trained Σ matrix using an SVD of Σ.
- Remove singular values whose absolute magnitude is less than a fraction of the largest singular value.
- Repeat steps 3-5 until the end of training.
This process allows for a significant reduction in the number of trainable parameters while maintaining or enhancing network performance and training time.
Stats
The study reports the following key metrics:
Top-1 validation accuracy
Percentage of trainable parameters relative to the full-rank model
Average network Stability, which measures the alignment of the orthogonal bases between training steps
Quotes
"Our investigation reveals that an orthogonal basis within each multidimensional weight's SVD representation stabilizes during training."
"OIALR seamlessly integrates into existing training workflows with minimal accuracy loss, as demonstrated by benchmarking on various datasets and well-established network architectures."
"With appropriate hyperparameter tuning, OIALR can surpass conventional training setups, including those of state-of-the-art models."