AI News, Kernels and Quantum Gravity Part 3: CoherentStates
- On Sunday, June 3, 2018
- By Read More
Kernels and Quantum Gravity Part 3: CoherentStates
This would not be a pedagogic machine learning blog if I did not go into some overly abstract formalism…here we introduce the Kernel formalism using the languages of Coherent States: We define a space of labels (that is isomorphic to , or, more generally, just a locally compact space), and an abstract Hilbert space We seek a map between the two: such that
So rather than introduce an expression for , we introduce a operator acting on the Hilbert space that encapsulates the fact that our basis set is non-orthogonal (and perhaps overcomplete?)
The main difference is that in other fields, one (usually) tries to use their prior knowledge of the problem to actually find the solution and does not just guess random Kernels and crossvalidate (although there are important cases where it does seem like this, such as in Quantum Chemical Density Functional Theory).
would accept this recent paper on Reproducing Kernel Banach Spaces with the ℓ1 Norm In Physics, we may think of the labels as the Classical variables of phase space and the Hilbert space as the space of Quantum Mechanical wavefunctions .
More importantly, for understanding machine learning, we will see the mathematical formulation of Frame Quantization and the attempts to capture the mathematics of coherent states under a single mathematical formalism (and how and when this is doable) .
- On Monday, September 23, 2019
Lecture 12.4 — Support Vector Machines | (Kernels-I) — [ Machine Learning | Andrew Ng]
Copyright Disclaimer Under Section 107 of the Copyright Act 1976, allowance is made for "FAIR USE" for purposes such as criticism, comment, news reporting, ...
Seth Lloyd: Quantum Machine Learning
Seth Lloyd visited the Quantum AI Lab at Google LA to give a tech talk on "Quantum Machine Learning." This talk took place on January 29, 2014. Speaker Info: ...
Inside a Neural Network - Computerphile
Just what is happening inside a Convolutional Neural Network? Dr Mike Pound shows us the images in between the input and the result. How Blurs & Filters ...
Linear transformations and matrices | Essence of linear algebra, chapter 3
Matrices can be thought of as transforming space, and understanding how this work is crucial for understanding many other ideas that follow in linear algebra.
Support Vector Machines - The Math of Intelligence (Week 1)
Support Vector Machines are a very popular type of machine learning model used for classification when you have a small dataset. We'll go through when to use ...
10-701 Machine Learning Fall 2014 - Lecture 6
Topics: reproducing kernel Hilbert space, kernel perceptron algorithm and analysis Lecturer: Geoff Gordon ...
9. Perturbative Renormalization Group Part 1
MIT 8.334 Statistical Mechanics II: Statistical Physics of Fields, Spring 2014 View the complete course: Instructor: Mehran Kardar In ..
On Characterizing the Capacity of Neural Networks using Algebraic Topology
The learnability of different neural architectures can be characterized directly by computable measures of data complexity. In this talk, we reframe the problem of ...
Topological Treatment of Neural Activity and the Quantum Question Order Effect
Seth Lloyd - Mechanical Engineering, MIT.
Dr. Yann LeCun, "How Could Machines Learn as Efficiently as Animals and Humans?"
Brown Statistics, NESS Seminar and Charles K. Colver Lectureship Series Deep learning has caused revolutions in computer perception and natural language ...