Lectures on Neural Dynamics
Content
Chapter 1: Neural circuit models based on firing rates and Hopfield networks: their dynamics, interconnections, and local Hebbian adaptation rules
Chapter 2: Stability in dynamic neural networks using Lyapunov methods, multistability, and energy functions
Chapter 3: Optimization in neural networks through biologically inspired gradient dynamics and sparse representations.
Chapter 4: Unsupervised learning via neural dynamics, linking Hebbian rules to tasks like PCA, clustering, and similarity-based representation learning.
Download and copyright information
Version dated Jun 15, 2025
Complete book in upright format [PDF file]
Complete book in slide/landscape format [PDF]
@Book{lectures-neural-dynamics,
author = {F. Bullo},
title = {Lectures on Neural Dynamics},
year = 2025,
url = {https://fbullo.github.io/lnd}
}
Copyright information
These lecture notes are intended for personal non-commercial use only: you may not use this material for commercial purposes and you may not copy and redistribute this material in any medium or format.
Why I decided to self-publish a print-on-demand book
There are several reasons why I decided to self-publish this book via the print-on-demand service by Kindle Direct Publishing (former Amazon CreateSpace). I appreciate the ability to:
retain the full copyrights of all the material,
make the document freely available online in multiple versions (see above),
retain direct anytime control over the paperback publication costs, retain a majority of the royalties after low fix costs, and set a low price,
update the book revision at any time (simply re-upload the PDF file, minimal turn-around time, no need for any permission, and never out-of-print), and
make available a high-quality paperback book through a broad distribution network.
As a combination of this flexibility, I typically polish and enrich the book every time I teach the course.
Similar arguments are presented in the write-up Why I Self-Publish My Mathematics Texts With Amazon by Robert Ghrist
History
Spring 2022: first time I taught the course
Winter 2025: second time I taught the course and first book draft
May 8, 2025: first edition online
May 27, 2025: small update with improvements to similarity matching, downloadable python code, and more
Jun 15, 2025: small update with improvements to softmax treatment, preface, exercises, and more
Jul 2, 2025: small update with improvements to the stability proof of Hopfield models and the removal of python code
Jul 16, 2025: substantial revision of stability statements and proofs for the Hopfield and firing rate model + miscellaneous typos
Feedback
I am thankful for any feedback information, including suggestions, evaluations, error descriptions, or comments about teaching or research uses. Please email bullo at ucsb.edu