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Our book on Generative AI and Stochastic Thermodynamics is out this month. @wellingmax, @sirui_lu97 and I have been posting about some interesting topics it covers.

Today we have my favourite animations yet, and some groundwork for the coming days: five related Markov kernels.
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Lars Holdijk retweeted
Finally getting around to sharing our Riemannian Metric Matching paper! We presented it as an oral at ICML this summer, and it also received the Best Short Paper Award at the ICLR GRAM workshop 🎉
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Lars Holdijk retweeted
Finally got my hands on a copy.
My new book written with @sirui_lu97 and @HoldijkLars is ready to be ordered!

Major societal and economic shifts have always been anchored in foundational physics.
During the 1st Industrial Revolution, thermodynamics showed us how to harness energy to power steam engines.
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Great new paper from Sandeep Cranganore, Sebastian Lehner, @jo_brandstetter and @wellingmax!

Very nice perspective on escorting fields for finite-time driving! Sandeep shows that you can just read them off the FP generator's spectrum, at any speed!

arxiv.org/abs/2607.24393
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Lars Holdijk retweeted
Replying to @wellingmax
@wellingmax @sirui_lu97 Just adding that all royalties will go to AIMS (@AIMSacza), where the lecture series the book grew out of was first given.

More about AIMS and its mission can be found here: aims.ac.za
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Lars Holdijk retweeted
My new book written with @sirui_lu97 and @HoldijkLars is ready to be ordered!

Major societal and economic shifts have always been anchored in foundational physics.
During the 1st Industrial Revolution, thermodynamics showed us how to harness energy to power steam engines.
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Lars Holdijk retweeted
CN101 - A Digital Thermodynamic Computer for Generative AI is now live on arXiv.

Conventional chips spend energy suppressing noise to compute deterministically; CN101 is a noisy system engineered so its settling behavior is the computation, implemented in digital CMOS and evaluated on generative AI workloads from image generation across six chips to molecular free-energy estimation.

In a companion post, @ColesThermoAI, our Chief Scientist, shares reflections on the journey and why AI inference needs hardware built for its physics.

Paper: arxiv.org/abs/2608.00754

Patrick's post: normalcomputing.com/blog/ai-infere…

Quanta article: quantamagazine.org/thermodynamic-…
#ThermodynamicComputing #AIHardware
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Replying to @HoldijkLars
Let's relate them all together. F and A share the stationary distribution; R and D share the hatted one (with momenta flipped); B stands alone here as it is built from the marginals, not the stationary distributions.

Why do we need these five kernels? That we will see tomorrow.
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Replying to @HoldijkLars
Find the book with 20% off using code GEAST26 at cambridge.org/9781009709033 (valid to 31 July 2027). All royalties go to AIMS (@AIMSacza), where @wellingmax and I gave the lecture series the book grew out of.

Read more about AIMS and its mission: aims.ac.za
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Sirui takes over for day 3: normalizing flows.

Yesterday the ELBO appeared as a free energy with a gap. Today the gap closes, not by better inference but by construction: invertible maps leave nothing unobserved.

Exact likelihoods, for the price of invertibility.
Our book "Generative AI and Stochastic Thermodynamics: A Tale of Free Energies" is out this month. With @HoldijkLars and @wellingmax we're posting about topics it covers. Yesterday: the ELBO as a free energy.

Today: normalizing flows. Remove the noise, and the bound becomes exact.
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Lars Holdijk retweeted
Our book "Generative AI and Stochastic Thermodynamics: A Tale of Free Energies" is out this month. With @HoldijkLars and @wellingmax we're posting about topics it covers. Yesterday: the ELBO as a free energy.

Today: normalizing flows. Remove the noise, and the bound becomes exact.
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Our book "Generative AI and Stochastic Thermodynamics: A Tale of Free Energies" is out this month. Over the coming weeks @sirui_lu97, @wellingmax and I will post about some of the topics it covers.

Starting it off: heat and work in latent variable models and variational EM.
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Replying to @HoldijkLars
Up next: Variational Free Energy and the ELBO.

The book is currently 20% off with code GEAST26 at cambridge.org/9781009709033. All royalties go to AIMS (@AIMSacza), where @wellingmax and I gave the lecture series the book grew out of.
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Replying to @HoldijkLars
@AIMSacza @wellingmax Connection No. 2 is up: the variational free energy, and why the ELBO is one 👇

x.com/HoldijkLars/st…
Our book "Generative AI and Stochastic Thermodynamics: A Tale of Free Energies" is out this month. With @sirui_lu97 and @wellingmax I'm posting about topics it covers. Yesterday: heat and work in variational EM.

Today: the variational free energy, and why the ELBO is one.
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Our book "Generative AI and Stochastic Thermodynamics: A Tale of Free Energies" is out this month. With @sirui_lu97 and @wellingmax I'm posting about topics it covers. Yesterday: heat and work in variational EM.

Today: the variational free energy, and why the ELBO is one.
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Replying to @HoldijkLars
One obstacle left: a separate φ per datapoint. Inference solved from scratch, every time.

The VAE amortizes: one shared encoder q(z|x, φ) predicts the outcome of inference, with z = μ(x) + σ(x)·ε keeping gradients alive.

Encoder and decoder descend the same free energy.
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Replying to @HoldijkLars
Find the book with 20% off using code GEAST26 at cambridge.org/9781009709033 (valid to 31 July 2027). All royalties go to AIMS (@AIMSacza), where @wellingmax and I gave the lecture series the book grew out of.

Read more about AIMS and its mission: aims.ac.za
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