Dmitry Krotov (@DimaKrotov) / X

Dmitry Krotov

390 posts

Dmitry Krotov

@DimaKrotov

Physics, Associative Memory, Generative AI. Formerly: @MITIBMLab, @IBMResearch, @the_IAS, @Princeton

Cambridge, MA

Joined December 2011

Pinned
Dmitry Krotov
@DimaKrotov
May 19, 2023
Recent advances in Hopfield networks of associative memory may be the guiding theoretical principle for designing novel large scale neural architectures. I explain my enthusiasm about these ideas in the article ⬇️⬇️⬇️. Please let me know what you think.
A new frontier for Hopfield networks
From nature.com
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Dmitry Krotov
@DimaKrotov
Sep 10, 2021
Replying to @hardmaru
I wish they had also created a diverse dataset of rugs so that it didn’t confuse black stripes with cliffs and I could finally get my entire house cleaned 😂
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Dmitry Krotov
@DimaKrotov
Jul 10, 2025
In physics there is an elegant method for computing the correlation functions called generating function. The idea is simple - instead of computing correlators one by one - you define a function of a parameter and compute the average of that new function. Individual correlators
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Dmitry Krotov
@DimaKrotov
Jul 11, 2025
Lagrangians are often used in physics for deriving the energy of mechanical systems. But are they useful for neural networks and AI? It turns out they are extremely helpful for working with energy-based models and energy-based Associative Memories. You need to specify a
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Dmitry Krotov
@DimaKrotov
Oct 8, 2024
Given today’s great news from the #NobelPrize2024, I want to share a couple of personal thoughts on Hopfield Networks. This idea had an enormous impact on at least three large disciplines: Statistical Physics, Computer Science and AI, and Neuroscience.
209K
Dmitry Krotov
@DimaKrotov
Aug 15, 2023
What could be the computational function of astrocytes in the brain? We hypothesize that they may be the biological cells that could implement the Transformer's attention operation commonly used in AI. Much improved compared to an earlier preprint:
pnas.org
Building transformers from neurons and astrocytes | PNAS
Glial cells account for between 50% and 90% of all human brain cells, and serve a variety of important developmental, structural, and metabolic fun...
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Dmitry Krotov
@DimaKrotov
Oct 6, 2022
Are you a PhD student who wants to work on Transformers, Hopfield Networks, NeuroAI? Apply to our summer internship program @IBMResearch. Great opportunity to do cutting edge research and spend an awesome summer at the @MITIBMLab. DM or send me an email. careers.ibm.com/job/16615779/m…
Dmitry Krotov
@DimaKrotov
Jul 15, 2021
One of the great features of deep learning is that we can easily stack multiple layers (e.g. dense, conv, attention) with arbitrary activation functions to build a useful feedforward network. Wouldn’t it be cool if we could do the same for Modern Hopfield Networks with feedback?
Dmitry Krotov
@DimaKrotov
Jul 10, 2025
Replying to @DimaKrotov
Well, it turns out you can use this generating function to count the number of local minima in energy-based models. This number, in turn, allows you to compute the information storage capacity of Associative Memory. Want to learn more? Check out Chapter 2 of our #ICML2025
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Dmitry Krotov
@DimaKrotov
Jul 12, 2025
I am frequently asked about the difference between binary and continuous Hopfield networks. Binary networks operate on discrete spins that are flipped in random order, continuous ones are described by differential equations and continuous state vectors. What is the right way to
17K
Dmitry Krotov
@DimaKrotov
Oct 8, 2024
Huge congratulations to John Hopfield for the 2024 Physics Nobel Prize! #NobelPrize2024 @HopfieldJohn
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Dmitry Krotov
@DimaKrotov
Oct 2, 2023
Two papers about Diffusion Models and Dense Associative Memories appeared on arXiv today: 1. arxiv.org/abs/2309.17290 2. arxiv.org/abs/2309.16750 While certainly more work is needed to establish the detailed relationship between the two models, high-level analogies are clear.
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Dmitry Krotov
@DimaKrotov
Aug 18, 2020
New microscopic theory of Dense Associative Memory aka modern Hopfield network can be reduced to the model proposed in “Hopfield Networks is All You Need’’ paper, which is equivalent to self-attention mechanism of Transformers. Work with @HopfieldJohn arxiv.org/abs/2008.06996
Dmitry Krotov
@DimaKrotov
Jul 9, 2025
What is Associative Memory and how can it be used in modern AI? 🔷 If I show you an image of a strawberry, can you remember what it smells like or tastes like? 🔷 Can you name a movie by seeing the emojis below? 🔷 Can you name the gentlemen in the picture without seeing
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