1,245 research outputs found
Learning with Algebraic Invariances, and the Invariant Kernel Trick
When solving data analysis problems it is important to integrate prior
knowledge and/or structural invariances. This paper contributes by a novel
framework for incorporating algebraic invariance structure into kernels. In
particular, we show that algebraic properties such as sign symmetries in data,
phase independence, scaling etc. can be included easily by essentially
performing the kernel trick twice. We demonstrate the usefulness of our theory
in simulations on selected applications such as sign-invariant spectral
clustering and underdetermined ICA
Neural networks, surrogate models and black box algorithms: theory and applications
In this Ph. D. Thesis we will analyze some of the most used surrogate models,
together with a particular type of line search black box strategy. After introducing
these powerful tools, we will present the Canonical Duality Theory, the potentiality
it has to improve these tools, and some of their applications.
The principal contributes of this Thesis are the reformulation of the Radial Basis
Neural Network problem in its canonical dual form in Section 2.2 and the application
of the surrogate models and black box algorithms presented in this Thesis on various
real world problems reported in Chapter 3
Neural networks, surrogate models and black box algorithms: theory and applications
In this Ph. D. Thesis we will analyze some of the most used surrogate models,
together with a particular type of line search black box strategy. After introducing
these powerful tools, we will present the Canonical Duality Theory, the potentiality
it has to improve these tools, and some of their applications.
The principal contributes of this Thesis are the reformulation of the Radial Basis
Neural Network problem in its canonical dual form in Section 2.2 and the application
of the surrogate models and black box algorithms presented in this Thesis on various
real world problems reported in Chapter 3
Information geometry in quantum field theory: lessons from simple examples
Motivated by the increasing connections between information theory and
high-energy physics, particularly in the context of the AdS/CFT correspondence,
we explore the information geometry associated to a variety of simple systems.
By studying their Fisher metrics, we derive some general lessons that may have
important implications for the application of information geometry in
holography. We begin by demonstrating that the symmetries of the physical
theory under study play a strong role in the resulting geometry, and that the
appearance of an AdS metric is a relatively general feature. We then
investigate what information the Fisher metric retains about the physics of the
underlying theory by studying the geometry for both the classical 2d Ising
model and the corresponding 1d free fermion theory, and find that the curvature
diverges precisely at the phase transition on both sides. We discuss the
differences that result from placing a metric on the space of theories vs.
states, using the example of coherent free fermion states. We compare the
latter to the metric on the space of coherent free boson states and show that
in both cases the metric is determined by the symmetries of the corresponding
density matrix. We also clarify some misconceptions in the literature
pertaining to different notions of flatness associated to metric and non-metric
connections, with implications for how one interprets the curvature of the
geometry. Our results indicate that in general, caution is needed when
connecting the AdS geometry arising from certain models with the AdS/CFT
correspondence, and seek to provide a useful collection of guidelines for
future progress in this exciting area.Comment: 36 pages, 2 figures; added new section and appendix, miscellaneous
improvement
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