Nonlinear Dynamics In Optimization Landscape of Shallow Neural Networks with Tunable Leaky ReLU
Read the original on arXiv Machine Learning →The Flow has not summarised this story yet — read it at arXiv Machine Learning.
The Flow has not summarised this story yet — read it at arXiv Machine Learning.
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The paper investigates how gradient descent behaves near codimension‑one bifurcations in recurrent neural networks by analyzing the global empirical Neural Tangent Kernel (GeNTK). Under local center‑manifold conditions, the parameter‑to‑state Jacobian is approximated by a low‑rank normal‑form operator, causing the GeNTK and Fisher information matrix to become strongly amplified and anisotropic, concentrating on a rank‑one or rank‑two channel depending on the bifurcation type. Experiments on high‑dimensional RNNs confirm that this low‑rank concentration coincides with abrupt loss changes, subtask interference, and aligns with changes in memory dynamics in a 15‑task LeakyRNN.