# Blog Posts

### Surgeries and Anyon Condensation

Here I will provide some geometric intuition for the discussions in a recent preprint with Y L Liu. (The title of this blog post is the unused title of an older draft and was proposed by Leon.)

### Some Thoughts on MDPI and the Business of Open Access

It’s not a secret that I support open access publishing. If I’ve met you before you’ve probably heard my opinions on this matter (if not, avail yourself here). A couple of weeks ago, the arXiv—mainstay of academic research in mathematics, physics, computer science, and more—ran a forum on accessibility...

### The Sparse Coupling Conjecture: New Results

In a recent paper of mine, arXiv:2207.07620, I give a set of proofs that resolve (to the best extent which is likely possible, anyway) an open question in the study of complex systems and random dynamics. Here I’ll discuss the conjecture (including relevant background), and my results, at a...

### Classical Physics for the Bayesian Mechanic (Bayesian Mechanics III)

Here I’ll briefly summarise some of the coarser points of a recent preprint of mine, arXiv:2206.12996, and in doing so, summarise the state of the art of Bayesian mechanics. The introduction of the paper frames this summary quite well. I’ll get to talk about supersymmetry too, which will be...

### A Working Definition of Bayesian Mechanics (Bayesian Mechanics II)

In a previous blog post, I discussed a paper of mine about the maths behind Bayesian mechanics (cited here as [Sak22]) and mentioned that an additional lengthy paper was on its way about the physics behind Bayesian mechanics (the free energy principle, in particular). That paper, joint with...

### Agent/Environment Symmetry and Entropy/Free Energy Duality (Bayesian Mechanics I)

Here I discuss a lengthy new paper of mine entitled

*Towards a Geometry and Analysis for Bayesian Mechanics*(preprint arXiv:2204.11900, cited here as [Sak22]). I’ll give a broad overview of the paper, contextualising the results and walking through the thought process. A future post will be devoted to an...### High Energy Physics and Energy-Based Learning

Last week, I released a set of results proving some identities from gauge theory in the context of maximum entropy (preprint arXiv:2203.08119). In a more detailed sketch than the linked tweet, but staying less formal than the linked paper, I’ll comment a little on the ‘hidden stuff’ in that...

### More About What Mean Field Theory Actually Means

Wherein I discuss at length what puts the ‘mean’ in mean field theory, and why we minimise free energy to calculate it. Some more general comments on free energy are given, because I can’t help myself. The proofs (about the effective field in the middle, and about variational inference at...

### Making and Breaking Symmetries in Mind and Life

Adam Safron, Michael Levin, Adeel Razi, Zahra Sheikhbahaee, Magnus Bein, and I, have been thinking deeply about some issues at the intersection of symmetry, morphogenesis, self-organisation, and inference. We are so interested in these problems that we want to organise a special issue at the

*Royal Society Interface*devoted...### Activation Functions and Models of Magnets

As stated on the home page of this website, I’m going to start writing the occasional blog post about my work. At the time of writing, I had resisted the temptation for a while, but I think it would be nice to post about specific things (e.g. papers) every once...

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