481 research outputs found
Bayesian inference with finitely wide neural networks
The analytic inference, e.g. predictive distribution being in closed form,
may be an appealing benefit for machine learning practitioners when they treat
wide neural networks as Gaussian process in Bayesian setting. The realistic
widths, however, are finite and cause weak deviation from the Gaussianity under
which partial marginalization of random variables in a model is
straightforward. On the basis of multivariate Edgeworth expansion, we propose a
non-Gaussian distribution in differential form to model a finite set of outputs
from a random neural network, and derive the corresponding marginal and
conditional properties. Thus, we are able to derive the non-Gaussian posterior
distribution in Bayesian regression task. In addition, in the bottlenecked deep
neural networks, a weight space representation of deep Gaussian process, the
non-Gaussianity is investigated through the marginal kernel.Comment: v2: added relevant references, example of simple non-Gaussian
bivariate distribution and corresponding inferenc
Antilinear spectral symmetry and the vortex zero-modes in topological insulators and graphene
We construct the general extension of the four-dimensional Jackiw-Rossi-Dirac
Hamiltonian that preserves the antilinear reflection symmetry between the
positive and negative energy eigenstates. Among other systems, the resulting
Hamiltonian describes the s-wave superconducting vortex at the surface of the
topological insulator, at a finite chemical potential, and in the presence of
both Zeeman and orbital couplings to the external magnetic field. Here we find
that the bound zero-mode exists only when the Zeeman term is below a critical
value. Other physical realizations pertaining to graphene are considered, and
some novel zero-energy wave functions are analytically computed.Comment: 6 revtex pages; typos corrected, published versio
Zero modes and charged Skyrmions in graphene bilayer
We show that the electric charge of the Skyrmion in the vector order
parameters that characterize the quantum anomalous spin Hall state and the
layer-antiferromagnet in a graphene bilayer is four and zero, respectively. The
result is based on the demonstration that a vortex configuration in two broken
symmetry states in bilayer graphene with the quadratic band crossing has the
number of zero modes doubled relative to the single layer. The doubling can be
understood as a result of Kramers' theorem implied by the "pseudo time
reversal" symmetry of the vortex Hamiltonian. Disordering the quantum anomalous
spin Hall state by Skyrmion condensation should produce a superconductor of an
elementary charge 4e.Comment: 4+ pages, one table, one figure; (v2) improved pedagogy, new
expression for the Pontryagin index derived, additional explanations; (v3)
new and updated references, minor typos corrected, published versio
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