Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Estimating the Unique Information of Continuous Variables   The integration and transfer of information from multiple sources to multiple
targets is a core motive of neural systems. The emerging field of partial
information decomposition (PID) provides a novel information-theoretic lens
into these mechanisms by identifying synergistic, redundant, and unique
contributions to the mutual information between one and several variables.
While many works have studied aspects of PID for Gaussian and discrete
distributions, the case of general continuous distributions is still uncharted
territory. In this work we present a method for estimating the unique
information in continuous distributions, for the case of one versus two
variables. Our method solves the associated optimization problem over the space
of distributions with fixed bivariate marginals by combining copula
decompositions and techniques developed to optimize variational autoencoders.
We obtain excellent agreement with known analytic results for Gaussians, and
illustrate the power of our new approach in several brain-inspired neural
models. Our method is capable of recovering the effective connectivity of a
chaotic network of rate neurons, and uncovers a complex trade-off between
redundancy, synergy and unique information in recurrent networks trained to
solve a generalized XOR task.

31
The categories of this paper are: ao-sci
21
The categories of this paper are: adap-org
0
The categories of this paper are: hep-ph
13
The categories of this paper are: quant-ph
26
The categories of this paper are: bayes-an
25
The categories of this paper are: patt-sol
14
The categories of this paper are: math-ph
22
The categories of this paper are: chao-dyn
34
The categories of this paper are: chem-ph
9
The categories of this paper are: nlin
33
The categories of this paper are: plasm-ph
3
The categories of this paper are: physics
17
The categories of this paper are: q-fin
5
The categories of this paper are: gr-qc
6
The categories of this paper are: astro-ph
36
The categories of this paper are: cmp-lg