# Quantifying the Benefit of Using Differentiable Learning over Tangent Kernels

We study the relative power of learning with gradient descent on differentiable models, such as neural networks, versus using the corresponding tangent kernels. We show that under certain conditions, gradient descent achieves small error only if a related tangent kernel method achieves a non-trivial advantage over random guessing (a.k.a. weak learning), though this advantage might be very small even when gradient descent can achieve arbitrarily high accuracy. Complementing this, we show that without these conditions, gradient descent can in fact learn with small error even when no kernel method, in particular using the tangent kernel, can achieve a non-trivial advantage over random guessing.

## Authors

• 14 publications
• 8 publications
• 30 publications
• 86 publications
09/26/2019

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Recent work has revealed that overparameterized networks trained by grad...
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In this paper we first identify a basic limitation in gradient descent-b...
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Deep learning's successes are often attributed to its ability to automat...
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### Benchmarking Approximate Inference Methods for Neural Structured Prediction

Exact structured inference with neural network scoring functions is comp...
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