Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Understanding Approximate Fisher Information for Fast Convergence of
  Natural Gradient Descent in Wide Neural Networks   Natural Gradient Descent (NGD) helps to accelerate the convergence of
gradient descent dynamics, but it requires approximations in large-scale deep
neural networks because of its high computational cost. Empirical studies have
confirmed that some NGD methods with approximate Fisher information converge
sufficiently fast in practice. Nevertheless, it remains unclear from the
theoretical perspective why and under what conditions such heuristic
approximations work well. In this work, we reveal that, under specific
conditions, NGD with approximate Fisher information achieves the same fast
convergence to global minima as exact NGD. We consider deep neural networks in
the infinite-width limit, and analyze the asymptotic training dynamics of NGD
in function space via the neural tangent kernel. In the function space, the
training dynamics with the approximate Fisher information are identical to
those with the exact Fisher information, and they converge quickly. The fast
convergence holds in layer-wise approximations; for instance, in block diagonal
approximation where each block corresponds to a layer as well as in block
tri-diagonal and K-FAC approximations. We also find that a unit-wise
approximation achieves the same fast convergence under some assumptions. All of
these different approximations have an isotropic gradient in the function
space, and this plays a fundamental role in achieving the same convergence
properties in training. Thus, the current study gives a novel and unified
theoretical foundation with which to understand NGD methods in deep learning.

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The categories of this paper are: chem-ph
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The categories of this paper are: physics
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The categories of this paper are: alg-geom
8
The categories of this paper are: hep-ex
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The categories of this paper are: astro-ph
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The categories of this paper are: funct-an
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The categories of this paper are: atom-ph
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The categories of this paper are: cmp-lg
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The categories of this paper are: quant-ph
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The categories of this paper are: hep-th
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The categories of this paper are: acc-phys
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The categories of this paper are: supr-con
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The categories of this paper are: solv-int
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The categories of this paper are: ao-sci
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The categories of this paper are: comp-gas
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The categories of this paper are: chao-dyn