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Category: Statistical Mechanics

Third Stage Boost – Part 2: Implications of Neuromorphic Computing

Third Stage Boost – Part 2: Implications of Neuromorphic Computing

Neuromorphic Computing: Statistical Mechanics & Criticality   Last week, I suggested that we were on the verge of something new, and referenced an article by von Bubnoff: A brain built from atomic switches [that] can learn, together with the follow-on article Brain Built on Switches. The key innovation described in this article was a silver mesh, as shown in the following figure. This mesh is a “network of microscopically thin intersecting silver wires,” grown via a combination of electrochemical and…

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Third Stage Boost: Statistical Mechanics and Neuromorphic Computing – Part 1

Third Stage Boost: Statistical Mechanics and Neuromorphic Computing – Part 1

Next-Generation Neural Network Architectures: More Brain-Like   Three generations of artificial intelligence.. The third generation is emerging … right about … now. That’s what is shown in this figure, presented in log-time scale. Brief history of AI in log-time scale The first generation of AI, symbolic AI, began conceptually around 1954, and lasted until 1986; 32 years. On the log-time scale shown in the figure above, this entire era takes place under the first curve; the black bell-shaped curve on…

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Machine Learning: Multistage Boost Process

Machine Learning: Multistage Boost Process

Three Stages to Orbital Altitude in Machine Learning Several years ago, Regina Dugan (then Director of DARPA) gave a talk in which she showed a clip of epic NASA launch fails. Not just one, but many fails. The theme was that we had to risk failure in order to succeed with innovation. This YouTube vid of rocket launch failures isn’t the exact clip that she showed (the “action” doesn’t kick in for about a minute), but it’s pretty close. For…

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Neg-Log-Sum-Exponent-Neg-Energy – That’s the Easy Part!

Neg-Log-Sum-Exponent-Neg-Energy – That’s the Easy Part!

The Surprising (Hidden) “Gotcha” in This Energy Equation: A couple of days ago, I was doing one of my regular weekly online “Synch” sessions with my Deep Learning students. In a sort of “Beware, here there be dragons!” moment, I showed them this energy equation from the Hinton et al. (2012) Nature review paper on acoustic speech modeling: One of my students pointed out, “That equation looks kind of simple.” Well, he’s right. And I kind of bungled the answer,…

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Seven Essential Machine Learning Equations: A Cribsheet (Really, the Précis)

Seven Essential Machine Learning Equations: A Cribsheet (Really, the Précis)

Making Machine Learning As Simple As Possible Albert Einstein is credited with saying, Everything should be made as simple as possible, but not simpler. Machine learning is not simple. In fact, once you get beyond the simple “building blocks” approach of stacking things higher and deeper (sometimes made all too easy with advanced deep learning packages), you are in the midst of some complex stuff. However, it does not need to be more complex than it has to be.  …

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A Tale of Two Probabilities

A Tale of Two Probabilities

Probabilities: Statistical Mechanics and Bayesian:   Machine learning fuses several different lines of thought, including statistical mechanics, Bayesian probability theory, and neural networks. There are two different ways of thinking about probability in machine learning; one comes from statistical mechanics, and the other from Bayesian logic. Both are important. They are also very different. While these two different ways of thinking about probability are usually very separate, they come together in some of the more advanced machine learning topics, such…

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The Statistical Mechanics Underpinnings of Machine Learning

The Statistical Mechanics Underpinnings of Machine Learning

Machine Learning Is Different Now:   Actually, machine learning is a continuation of what it always has been, which is deeply rooted in statistical physics (statistical mechanics). It’s just that there’s a culmination of insights that are now a very substantive body of work, with more theoretical rigor behind them than most of us know.     A Lesson from Mom: It takes a lot of time to learn a new discipline. This is something that I learned from my…

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Seven Statistical Mechanics / Bayesian Equations That You Need to Know

Seven Statistical Mechanics / Bayesian Equations That You Need to Know

Essential Statistical Mechanics for Deep Learning   If you’re self-studying machine learning, and feel that statistical mechanics is suddenly showing up more than it used to, you’re not alone. Within the past couple of years, statistical mechanics (statistical thermodynamics) has become a more integral topic, along with the Kullback-Leibler divergence measure and several inference methods for machine learning, including the expectation maximization (EM) algorithm along with variational Bayes.     Statistical mechanics has always played a strong role in machine…

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How to Read Karl Friston (in the Original Greek)

How to Read Karl Friston (in the Original Greek)

Karl Friston, whom we all admire, has written some lovely papers that are both enticing and obscure. Cutting to the chase, what we really want to understand is this equation: In a Research Digest article, Peter Freed writes: … And today, Karl Friston is not explaining [the free energy principle] in a way that makes it usable to your average psychiatrist/psychotherapist on the street – which is frustrating. I am not alone in my confusion, and if you read the…

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Approximate Bayesian Inference

Approximate Bayesian Inference

Variational Free Energy I spent some time trying to figure out the derivation for the variational free energy, as expressed in some of Friston’s papers (see citations below). While I made an intuitive justification, I just found this derivation (Kokkinos; see the reference and link below): Other discussions about variational free energy: Whereas maximum a posteriori methods optimize a point estimate of the parameters, in ensemble learning an ensemble is optimized, so that it approximates the entire posterior probability distribution…

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