A quick look at the gist of the backpropagation idea to calculate the gradients of neural networks, which go into the stochastic gradient descent algorithm. Check it out! Video. Notes.
Author Archives: joaquindrut
Machine learning and stochastic gradient descent
I very briefly describe gradient descent (GD) and how it is used in the context of machine learning: the stochastic gradient descent algorithm (SGD). The idea is simple: divide your data into randomly chosen mini-batches and use a mini-batch to estimate the gradient of your cost function. Use that to do GD iterations at fixed …
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Machine learning and linear algebra
A first look at how linear algebra shows up in elementary machine learning. If you are new to linear algebra, you may find this interesting! Check it out! Video. Notes.
Toward QMC: Generating field configurations.
I review the basics of the Metropolis algorithm and comment on the infamous “sign problem” affecting most areas of physics. Video. Notes.
Toward QMC: Calculating thermal expectation values
I show the first notions of how to go about calculating thermal expectation values in quantum Monte Carlo. I work out an example for the particle number operator and show expressions for the one-body density matrix. I assume that the field configurations are given. More on how to obtain those samples next time! Video. Notes.
Toward QMC: Spacetime determinant identities
I show how to rewrite the fermionic and bosonic determinants of previous videos in a blown-up spacetime formulation, where the matrices now become sparse and the connections to QFT and entanglement become much more interesting and useful! Check it out. Video. Notes.
Toward QMC: Trace-determinant identities. Part 2.
This is the fourth episode of the “Toward QMC” series. In the previous episode, I started to show how a crucial identity is proven in the case of fermions. Here I give more details on how to carry out that proof for products of multiple operators and explain what happens in the bosonic case. Check …
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Toward QMC: Trace-determinant identities. Part 1.
This is the third episode of the “Toward QMC” series. In the previous episode, I brought up a trace-determinant identity without proof. Here I take a big first step to show how that identity is proven in the case of fermions. More on this (including bosons!) in part 2! Video. Notes.
Toward QMC: Hubbard-Stratonovich transformation
This is the second episode of the Toward-QMC series. I discuss how interactions enter the thermodynamics of quantum systems from an operational standpoint. The Hubbard-Stratonovich transformation allows us to take a step forward by decomposing the interaction factor as an integral over external fields. Check it out! More details on the algebra next time.Video. Notes.
Toward QMC: Trotter-Suzuki factorization
Here’s a first installment of an introductory series dedicated to quantum Monte Carlo at finite temperature. First step: a brief technical note on the Trotter-Suzuki factorization. Video. Notes.