Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: An induction proof of the backpropagation algorithm in matrix notation   Backpropagation (BP) is a core component of the contemporary deep learning
incarnation of neural networks. Briefly, BP is an algorithm that exploits the
computational architecture of neural networks to efficiently evaluate the
gradient of a cost function during neural network parameter optimization. The
validity of BP rests on the application of a multivariate chain rule to the
computational architecture of neural networks and their associated objective
functions. Introductions to deep learning theory commonly present the
computational architecture of neural networks in matrix form, but eschew a
parallel formulation and justification of BP in the framework of matrix
differential calculus. This entails several drawbacks for the theory and
didactics of deep learning. In this work, we overcome these limitations by
providing a full induction proof of the BP algorithm in matrix notation.
Specifically, we situate the BP algorithm in the framework of matrix
differential calculus, encompass affine-linear potential functions, prove the
validity of the BP algorithm in inductive form, and exemplify the
implementation of the matrix form BP algorithm in computer code.

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The categories of this paper are: hep-ph
29
The categories of this paper are: funct-an
23
The categories of this paper are: solv-int
17
The categories of this paper are: q-fin
26
The categories of this paper are: bayes-an
30
The categories of this paper are: q-alg
34
The categories of this paper are: chem-ph
22
The categories of this paper are: chao-dyn
19
The categories of this paper are: eess
27
The categories of this paper are: comp-gas
33
The categories of this paper are: plasm-ph
37
The categories of this paper are: supr-con
11
The categories of this paper are: hep-lat
18
The categories of this paper are: econ
14
The categories of this paper are: math-ph
9
The categories of this paper are: nlin