This is the first post in a planned series about mean field theory that we am writing together with Lauren Greenspan (this post was generated by Dmitry with lots of input from Lauren, and was split into two parts, the second of which is written jointly). These posts are a combination of an explainer and some original research/ experiments.

The goal of these posts is to explain an approach to understanding and interpreting model internals which we informally denote "mean field theory" or MFT. In the literature, the closest matching term is "adaptive mean field theory". We will use the term loosely to denote a rich emerging literature that applies many-body thermodynamic methods to neural net interpretability. It includes work on both Bayesian learning and dynamics (SGD), and work in wider "NNFT" (neural net field theory) contexts. Dmitry's recent post on learning sparse denoising also heuristically fits into this picture (or more precisely, a small extension of it).

Our team at Principles of Intelligence (formerly PIBBSS) believes that this point of view on interpretability remains highly neglected, and should be better understood and these ideas should be used much more in interpretability thinking and tools.

We [...]

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Outline:

(01:42) What do we mean by mean field theory

(02:38) Why MFT

(04:25) Brief FAQ section

(11:34) Introduction to the theory

(11:38) The background (and the foreground)

(12:34) Self-consistency

(18:01) Neural nets and mean field

(19:00) The mean-field background and foreground for a neural net

(20:29) Experimental setting and pretty picture

The original text contained 4 footnotes which were omitted from this narration.

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First published:
April 4th, 2026

Source:
https://www.lesswrong.com/posts/rduzFkTKx5pGKWKcL/mean-field-sequence-an-introduction

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Narrated by TYPE III AUDIO.

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Images from the article:

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“Mean field sequence: an introduction” by Dmitry Vaintrob, Lauren Greenspan

LessWrong (30+ Karma)

“Mean field sequence: an introduction” by Dmitry Vaintrob, Lauren Greenspan