1,245 research outputs found

    Learning with Algebraic Invariances, and the Invariant Kernel Trick

    Get PDF
    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

    Get PDF
    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

    Get PDF
    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

    Get PDF
    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
    • …
    corecore