Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Statistical Mechanics of Deep Linear Neural Networks: The
  Back-Propagating Kernel Renormalization   The success of deep learning in many real-world tasks has triggered an
intense effort to understand the power and limitations of deep learning in the
training and generalization of complex tasks, so far with limited progress. In
this work, we study the statistical mechanics of learning in Deep Linear Neural
Networks (DLNNs) in which the input-output function of an individual unit is
linear. Despite the linearity of the units, learning in DLNNs is nonlinear,
hence studying its properties reveals some of the features of nonlinear Deep
Neural Networks (DNNs). Importantly, we solve exactly the network properties
following supervised learning using an equilibrium Gibbs distribution in the
weight space. To do this, we introduce the Back-Propagating Kernel
Renormalization (BPKR), which allows for the incremental integration of the
network weights starting from the network output layer and progressing backward
until the first layer's weights are integrated out. This procedure allows us to
evaluate important network properties, such as its generalization error, the
role of network width and depth, the impact of the size of the training set,
and the effects of weight regularization and learning stochasticity. BPKR does
not assume specific statistics of the input or the task's output. Furthermore,
by performing partial integration of the layers, the BPKR allows us to compute
the properties of the neural representations across the different hidden
layers. We have proposed an extension of the BPKR to nonlinear DNNs with ReLU.
Surprisingly, our numerical simulations reveal that despite the nonlinearity,
the predictions of our theory are largely shared by ReLU networks in a wide
regime of parameters. Our work is the first exact statistical mechanical study
of learning in a family of DNNs, and the first successful theory of learning
through successive integration of DoFs in the learned weight space.

13
The categories of this paper are: quant-ph
7
The categories of this paper are: hep-th
2
The categories of this paper are: math
32
The categories of this paper are: atom-ph
5
The categories of this paper are: gr-qc
4
The categories of this paper are: cond-mat
36
The categories of this paper are: cmp-lg
33
The categories of this paper are: plasm-ph
21
The categories of this paper are: adap-org
18
The categories of this paper are: econ
9
The categories of this paper are: nlin
22
The categories of this paper are: chao-dyn
31
The categories of this paper are: ao-sci
29
The categories of this paper are: funct-an
10
The categories of this paper are: q-bio
24
The categories of this paper are: dg-ga