Goldstone Modes: How Physics Unlocks Deep Network Trainability

Paper: Spontaneous symmetry breaking and Goldstone modes for deep information propagation (2605.14685)
Published: 14 May 2026.

Learn more on Emergent Mind: https://www.emergentmind.com/papers/2605.14685
arXiv: https://arxiv.org/abs/2605.14685
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This presentation explores how spontaneous symmetry breaking in neural networks creates Goldstone-like excitations that enable robust information propagation across depth and time. Drawing from equilibrium statistical mechanics, the work demonstrates that internal layer equivariance under continuous symmetry groups such as U(1) and O(k) provides a protected channel for signal transmission, independent of task symmetries. Through rigorous mean-field analysis and experiments on feedforward, recurrent, and convolutional architectures, the authors show how symmetry-protected modes improve trainability in very deep networks and long-sequence tasks without normalization or skip connections.

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