arXiv:2606.29176v1 Announce Type: new Abstract: A deep network's loss is invariant to continuous symmetries of its parameters: the logit shift, the ReLU rescaling, the LayerNorm scale, the per-head attention rotation. Adam's per-coordinate preconditioner drifts along each symmetry orbit, which pulls the trajectory off the symmetry quotient where the optimization lives and blurs the singular-learning rate the quotient makes readable. We build DDC, a Dead-Direction Conditioner that lifts a base optimizer into a $G$-equivariant one: it conditions the optimizer's state in the orbit decomposition o
This research addresses a fundamental issue in training deep networks with continuous symmetries, building on recent advances in theoretical understanding of AI optimization landscapes.
Improved optimization techniques can lead to more stable, efficient, and performant AI models, accelerating development and reducing computational cost for complex architectures.
Optimizers can now be designed to be 'gauge-equivariant,' allowing them to navigate the optimization landscape more effectively by respecting inherent symmetries in network parameters.
- · AI researchers and developers
- · Companies with large deep learning models
- · Hardware manufacturers (indirectly, via increased efficiency)
- · Inefficient AI training practices
More robust and faster training of deep neural networks becomes possible.
This could lead to a faster iteration cycle for new AI architectures and capabilities.
Reduced computational overhead for complex AI systems could indirectly impact energy consumption and accessibility of advanced AI.
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Read at arXiv cs.LG