Author Archives: rojefferson

Variational autoencoders

As part of one of my current research projects, I’ve been looking into variational autoencoders (VAEs) for the purpose of identifying and analyzing attractor solutions within higher-dimensional phase spaces. Of course, I couldn’t resist diving into the deeper mathematical theory … Continue reading

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Black hole entropy: the heat kernel method

As part of my ongoing love affair with black holes, I’ve been digging more deeply into what it means for them to have entropy, which of course necessitates investigating how this is assigned in the first place. This is a … Continue reading

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Restricted Boltzmann machines

As a theoretical physicist making their first foray into machine learning, one is immediately captivated by the fascinating parallel between deep learning and the renormalization group. In essence, both are concerned with the extraction of relevant features via a process … Continue reading

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What is entropy?

You should call it entropy, for two reasons. In the first place your uncertainty function has been used in statistical mechanics under that name, so it already has a name. In the second place, and more important, no one really … Continue reading

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Boltzmann machines

I alluded previously that information geometry had many interesting applications, among them machine learning and computational neuroscience more generally. A classic example is the original paper by Amari, Kurata, and Nagaoka, Information Geometry of Boltzmann Machines [1]. This paper has … Continue reading

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Information geometry (part 3/3)

Insofar as quantum mechanics can be regarded as an extension of (classical) probability theory, most of the concepts developed in the previous two parts of this sequence can be extended to quantum information theory as well, thus giving rise to … Continue reading

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Boundary conditions in AdS/CFT

The issue of boundary conditions in AdS/CFT has confused me for years; not because it’s intrinsically complicated, but because most of the literature simply regurgitates a superficial explanation for the standard prescription which collapses at the first inquiry. Typically, the … Continue reading

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Tomita-Takesaki in Rindler space

Rindler space provides a convenient example to elucidate some basic properties of AQFT — specifically Tomita-Takesaki theory — in what is arguably the case of greatest interest to high-energy theorists. We shall begin by introducing a few fundamental objects in … Continue reading

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Information geometry (part 2/3)

In the previous post, we introduced the -connection, and alluded to a dualistic structure between and . In particular, the cases are intimately related to two important families of statistical models, the exponential or e-family with affine connection , and … Continue reading

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Information geometry (part 1/3)

Information geometry is a rather interesting fusion of statistics and differential geometry, in which a statistical model is endowed with the structure of a Riemannian manifold. Each point on the manifold corresponds to a probability distribution function, and the metric … Continue reading

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