Gradient descent on wide shallow models with bounded nonlinearities converges globally in the mean-field limit as non-global critical points are unstable under the dynamics.
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Dynamic Mode Decomposition shows that short contiguous spans of Vision Transformer blocks can be approximated by a low-rank linear operator K with high predictive fidelity for p<=4 steps, but this approximation fails to outperform an identity baseline when propagated to the final layer.
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On the global convergence of gradient descent for wide shallow models with bounded nonlinearities
Gradient descent on wide shallow models with bounded nonlinearities converges globally in the mean-field limit as non-global critical points are unstable under the dynamics.
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Dynamic Mode Decomposition along Depth in Vision Transformers
Dynamic Mode Decomposition shows that short contiguous spans of Vision Transformer blocks can be approximated by a low-rank linear operator K with high predictive fidelity for p<=4 steps, but this approximation fails to outperform an identity baseline when propagated to the final layer.