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Selecting a Neural Network Transfer Function: Classic vs. Current

Selecting a Neural Network Transfer Function: Classic vs. Current

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Neural Network Transfer Functions: Sigmoid, Tanh, and ReLU   Making it or breaking it with neural networks: how to make smart choices.     Why We Weren’t Getting Convergence   This last week, in working with a very simple and straightforward XOR neural network, a lot of my students were having convergence problems. The most likely reason? Very likely, it’s been my choice for the transfer function. I had given them a very simple network. (Lots of them are still…

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Notational Frenzy

Notational Frenzy

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When the Subtle Art of Mathematical Notation Defeats You (and How to Fight Back)   A couple of years ago, I was teaching Time Series and Forecasting for the first time. I didn’t know the subject – at all – but that didn’t bother me. Hey, it was mathematics, right? Anything that’s mathematical, I can eat for lunch, and then want some dessert-equations afterwards. First week, introducing the subject. That went fine. Second week, Simple Exponential Smoothing (SES). That’s simple….

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

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

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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

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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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Labor Day Reading and Academic Year Kick-Off

Labor Day Reading and Academic Year Kick-Off

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Deep Learning / Machine Learning Reading and Study Guide:   Several of you have been asking for guided reading lists. This makes sense.   Your Starting Point for Neural Networks, Deep Learning, and Machine Learning   Your study program (reading and code) depends on where you are. Starting out (High-grass country; St. Louis to Alcove Springs): Basic neural networks and deep learning; architecture for common networks, such as CNNs (convolutional neural networks); learning rules and architecture design. Well on the…

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The Statistical Mechanics Underpinnings of Machine Learning

The Statistical Mechanics Underpinnings of Machine Learning

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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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2025 and Beyond

2025 and Beyond

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Artificial Intelligence and Jobs by the Year 2025: One of my biggest take-aways from the recent (May, 2017) NVIDIA GTC (GPU Technology Conference) was less about the technology, and more about the near-term jobs impact of artificial intelligence (AI) and robotics. Making smart education and career decisions is crucial, as the emerging combination of AI and robotics will have a huge impact on jobs. Those of you studying artificial intelligence, deep learning, and neural networks will have a stronger career…

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Seven Statistical Mechanics / Bayesian Equations That You Need to Know

Seven Statistical Mechanics / Bayesian Equations That You Need to Know

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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)

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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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Deep Learning: The Fast Evolution of Artificial Intelligence

Deep Learning: The Fast Evolution of Artificial Intelligence

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Just one of the slides from a presentation that I’m working up for an upcoming online presentation at Northwestern University, but it tells the story. Just one more thought: here’s the rapid pace of evolution within just the image analysis realm of AI, largely due to multiple layers (sometimes, many, many, MANY multiple layers) of networks, a good fraction of which are Convolutional Neural Networks, or CNNs. Error rates have dropped from over 15% to about 3% within just four…

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