Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Kernel Mode Decomposition and programmable/interpretable regression
  networks   Mode decomposition is a prototypical pattern recognition problem that can be
addressed from the (a priori distinct) perspectives of numerical approximation,
statistical inference and deep learning. Could its analysis through these
combined perspectives be used as a Rosetta stone for deciphering mechanisms at
play in deep learning? Motivated by this question we introduce programmable and
interpretable regression networks for pattern recognition and address mode
decomposition as a prototypical problem. The programming of these networks is
achieved by assembling elementary modules decomposing and recomposing kernels
and data. These elementary steps are repeated across levels of abstraction and
interpreted from the equivalent perspectives of optimal recovery, game theory
and Gaussian process regression (GPR). The prototypical mode/kernel
decomposition module produces an optimal approximation $(w_1,w_2,\cdots,w_m)$
of an element $(v_1,v_2,\ldots,v_m)$ of a product of Hilbert subspaces of a
common Hilbert space from the observation of the sum $v:=v_1+\cdots+v_m$. The
prototypical mode/kernel recomposition module performs partial sums of the
recovered modes $w_i$ based on the alignment between each recovered mode $w_i$
and the data $v$. We illustrate the proposed framework by programming
regression networks approximating the modes $v_i=
a_i(t)y_i\big(\theta_i(t)\big)$ of a (possibly noisy) signal $\sum_i v_i$ when
the amplitudes $a_i$, instantaneous phases $\theta_i$ and periodic waveforms
$y_i$ may all be unknown and show near machine precision recovery under
regularity and separation assumptions on the instantaneous amplitudes $a_i$ and
frequencies $\dot{\theta}_i$. The structure of some of these networks share
intriguing similarities with convolutional neural networks while being
interpretable, programmable and amenable to theoretical analysis.

37
The categories of this paper are: supr-con
0
The categories of this paper are: hep-ph
15
The categories of this paper are: nucl-ex
35
The categories of this paper are: mtrl-th
6
The categories of this paper are: astro-ph
12
The categories of this paper are: nucl-th
9
The categories of this paper are: nlin
18
The categories of this paper are: econ
13
The categories of this paper are: quant-ph
36
The categories of this paper are: cmp-lg
21
The categories of this paper are: adap-org
11
The categories of this paper are: hep-lat
25
The categories of this paper are: patt-sol
29
The categories of this paper are: funct-an
26
The categories of this paper are: bayes-an
8
The categories of this paper are: hep-ex