# A Blueprint for Equilibrium-Based Differentiable Continuous-Variable Thermodynamic Computing

arXiv: https://arxiv.org/abs/2607.16183 · HTML: https://mlsanity.com/paper/2607.16183/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 77 of its 229 references that are in the map.
- First posted on arXiv 17 Jul 2026.

## Builds on (most cited first, 30 of 77)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [The Llama 3 Herd of Models](https://mlsanity.com/paper/2407.21783/) (2024)
- [Score-Based Generative Modeling through Stochastic Differential Equations](https://mlsanity.com/paper/2011.13456/) (2020)
- [Layer Normalization](https://mlsanity.com/paper/1607.06450/) (2016)
- [Dropout as a Bayesian Approximation: Representing Model Uncertainty in Deep Learning](https://mlsanity.com/paper/1506.02142/) (2015)
- [Outrageously Large Neural Networks: The Sparsely-Gated Mixture-of-Experts Layer](https://mlsanity.com/paper/1701.06538/) (2017)
- [Switch Transformers: Scaling to Trillion Parameter Models with Simple and Efficient Sparsity](https://mlsanity.com/paper/2101.03961/) (2021)
- [On Layer Normalization in the Transformer Architecture](https://mlsanity.com/paper/2002.04745/) (2020)
- [Automatic differentiation in machine learning: a survey](https://mlsanity.com/paper/1502.05767/) (2015)
- [Compositional Visual Generation with Composable Diffusion Models](https://mlsanity.com/paper/2206.01714/) (2022)
- [Variational Dropout and the Local Reparameterization Trick](https://mlsanity.com/paper/1506.02557/) (2015)
- [How to Train Your Energy-Based Models](https://mlsanity.com/paper/2101.03288/) (2021)
- [On Neural Differential Equations](https://mlsanity.com/paper/2202.02435/) (2022)
- [Noisy Networks for Exploration](https://mlsanity.com/paper/1706.10295/) (2017)
- [Variational Dropout Sparsifies Deep Neural Networks](https://mlsanity.com/paper/1701.05369/) (2017)
- [Equilibrium Propagation: Bridging the Gap Between Energy-Based Models and Backpropagation](https://mlsanity.com/paper/1602.05179/) (2016)
- [Concrete Dropout](https://mlsanity.com/paper/1705.07832/) (2017)
- [SARATHI: Efficient LLM Inference by Piggybacking Decodes with Chunked Prefills](https://mlsanity.com/paper/2308.16369/) (2023)
- [Power Hungry Processing: Watts Driving the Cost of AI Deployment?](https://mlsanity.com/paper/2311.16863/) (2023)
- [Parameter Space Noise for Exploration](https://mlsanity.com/paper/1706.01905/) (2017)
- [The Hardware Lottery](https://mlsanity.com/paper/2009.06489/) (2020)
- [LLM Inference Unveiled: Survey and Roofline Model Insights](https://mlsanity.com/paper/2402.16363/) (2024)
- [Equinox: neural networks in JAX via callable PyTrees and filtered transformations](https://mlsanity.com/paper/2111.00254/) (2021)
- [Underdamped Langevin MCMC: A non-asymptotic analysis](https://mlsanity.com/paper/1707.03663/) (2017)
- [Deep Structured Energy Based Models for Anomaly Detection](https://mlsanity.com/paper/1605.07717/) (2016)
- [Transformer for Graphs: An Overview from Architecture Perspective](https://mlsanity.com/paper/2202.08455/) (2022)
- [Convergence of Langevin MCMC in KL-divergence](https://mlsanity.com/paper/1705.09048/) (2017)
- [Training End-to-End Analog Neural Networks with Equilibrium Propagation](https://mlsanity.com/paper/2006.01981/) (2020)
- [Neural Enhanced Belief Propagation on Factor Graphs](https://mlsanity.com/paper/2003.01998/) (2020)

## Built on by (most cited first, 2 of 2)

- [Thermalizing Stochastic Programs](https://mlsanity.com/paper/2608.01615/) (2026)
- [Analog-Friendly Predictive Coding without Activation Derivatives](https://mlsanity.com/paper/2609.32350/) (2026)

## Abstract (arXiv)

To help address the escalating energy and latency demands of machine-learning workloads, we introduce a blueprint for an energy-efficient and fast thermodynamic computing stack that leverages stochastic analog processes in physical hardware. In this work, we focus on energy-based thermodynamic computing where the stochastic process is well described by Langevin dynamics with tunable energy potentials. The implementation of such potentials in physical hardware enables us to generate and sample from basic parameterized energy-based models. We demonstrate how to construct and train popular classes of machine learning models based on these hardware-native energy-based models, using the framework of probabilistic graphical models. We analyze the runtime and energy consumption of different models in this thermodynamic paradigm based on theoretical considerations and numerical studies. As a preliminary experimental realization of such hardware, we present our stochastic analog superconducting circuits driven by thermal noise. Together, these results outline a path toward energy-efficient thermodynamic hardware for probabilistic machine learning.