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Variational autoencoders (VAEs) employ Bayesian inference to interpret sensory inputs, mirroring processes that occur in primate vision across both ventral (Higgins et al., 2021) and dorsal (Vafaii et al., 2023) pathways. Despite their…

In this PhD thesis, we explore and apply methods inspired by the free energy principle to two important areas in machine learning and neuroscience. The free energy principle is a general mathematical theory of the necessary…

Computer-aided engineering techniques are indispensable in modern engineering developments. In particular, partial differential equations are commonly used to simulate the dynamics of physical phenomena, but very large systems are often…

Inference in both brains and machines can be formalized by optimizing a shared objective: maximizing the evidence lower bound (ELBO) in machine learning, or minimizing variational free energy (F) in neuroscience (ELBO = -F). While this…

We introduce an information-theoretic framework that uses variational autoencoders (VAEs) to extract compact, physically interpretable manifolds from high-dimensional flow-field data. To this end, the Kullback--Leibler (KL) divergence in…

The present paper proposes an adaptive biasing potential for the computation of free energy landscapes. It is motivated by statistical learning arguments and unifies the tasks of biasing the molecular dynamics to escape free energy wells…

Arranging many modules within a bounded domain without overlap, central to the Electronic Design Automation (EDA) of very large-scale integrated (VLSI) circuits, represents a broad class of discrete geometric optimization problems with…

We consider $N$ bosons in a box in $\mathbb {R}^d$ with volume $N/\rho$ under the influence of a mutually repellent pair potential. The particle density $\rho\in (0,\infty)$ is kept fixed. Our main result is the identification of the…

This paper investigates how neurons can use metabolic cost to facilitate learning at a population level. Although decision-making by individual neurons has been extensively studied, questions regarding how neurons should behave to cooperate…

We present new intuitions and theoretical assessments of the emergence of disentangled representation in variational autoencoders. Taking a rate-distortion theory perspective, we show the circumstances under which representations aligned…

The Free-Energy-Principle (FEP) is an influential and controversial theory which postulates a deep and powerful connection between the stochastic thermodynamics of self-organization and learning through variational inference. Specifically,…

A new form of variational autoencoder (VAE) is developed, in which the joint distribution of data and codes is considered in two (symmetric) forms: ($i$) from observed data fed through the encoder to yield codes, and ($ii$) from latent…

Although artificial neural networks are often described as brain-inspired, their representations typically rely on continuous activations, such as the continuous latent variables in variational autoencoders (VAEs), which limits their…

Extracting compact, physically interpretable representations from high-dimensional scientific data is a persistent challenge due to the complex, nonlinear structures inherent in physical systems. We propose a Gaussian Mixture Variational…

Lateral predictive coding is a recurrent neural network which creates energy-efficient internal representations by exploiting statistical regularity in sensory inputs. Here we investigate the trade-off between information robustness and…

An approach to implementing variational Bayesian inference in biological systems is considered, under which the thermodynamic free energy of a system directly encodes its variational free energy. In the case of the brain, this assumption…

Sensory observations about the world are invariably ambiguous. Inference about the world's latent variables is thus an important computation for the brain. However, computational constraints limit the performance of these computations.…

Variational quantum algorithms are leading candidates for near-term advantage, yet their scalability is fundamentally limited by the ``Barren Plateau'' phenomenon. While traditionally attributed to geometric concentration of measure, I…

We introduce an optimization framework for variational inference based on the coupled free energy, extending variational inference techniques to account for the curved geometry of the coupled exponential family. This family includes…

The variational autoencoder (VAE) is a simple and efficient generative artificial intelligence method for modeling complex probability distributions of various types of data, such as images and texts. However, it suffers some main…