  The inductive biases of trained neural networks are difficult to understand
and, consequently, to adapt to new settings. We study the inductive biases of
linearizations of neural networks, which we show to be surprisingly good
summaries of the full network functions. Inspired by this finding, we propose a
technique for embedding these inductive biases into Gaussian processes through
a kernel designed from the Jacobian of the network. In this setting, domain
adaptation takes the form of interpretable posterior inference, with
accompanying uncertainty estimation. This inference is analytic and free of
local optima issues found in standard techniques such as fine-tuning neural
network weights to a new task. We develop significant computational speed-ups
based on matrix multiplies, including a novel implementation for scalable
Fisher vector products. Our experiments on both image classification and
regression demonstrate the promise and convenience of this framework for
transfer learning, compared to neural network fine-tuning. Code is available at
https://github.com/amzn/xfer/tree/master/finite_ntk.
