Colloquium

Over the last half decade, the capabilities of large language models (LLMs) have leapt from preschooler to graduate student and beyond. This talk reviews recent progress in teaching LLMs to do science and reasoning, and speculates as to what it will mean for the future of theoretical physics if these trends continue.

For decades, we have known that most of the matter in the Universe is invisible. This unseen component—dark matter—accounts for roughly 85% of all matter and plays a central role in shaping cosmic structure. Yet, despite decades of experimental effort and remarkable ingenuity, its fundamental nature remains unknown. Dark matter provides compelling evidence for physics beyond the Standard Model, motivating a broad landscape of candidates ranging from weakly interacting massive particles to ultralight axions. Astrophysical observations offer a complementary avenue to laboratory experiments for testing dark matter models across a broad range of masses and interaction strengths. In this talk, I will present novel observational strategies designed to uncover signatures of new physics and highlight the opportunities opened by current and next-generation observatories. In particular, I will demonstrate how modern astrophysical observatories can be repurposed as laboratories for fundamental physics, using JWST infrared observations to search for axion dark matter and radio observations of cosmic filaments to test WIMP scenarios.

Deep generative models are emerging as powerful tools for solving physics problems, enabling new approaches to inference, sampling, anomaly detection, and signal reconstruction. In the first part of the talk, I will discuss how generative models, designed with physical principles such as symmetry and multi-scale structure, can be used to construct likelihood functions for cosmological inference at the field level, extracting 3–5× the information from weak gravitational lensing compared to traditional two-point statistics. This framework also enables anomaly detection of model misspecification and enhances interpretability through sample generation. I will also show that these physics-informed generative models apply beyond cosmology, including sampling lattice models in statistical physics and anomaly detection in collider physics. In the second part, I will discuss how generative models can be used to construct physically informed priors for inverse problems. This framework enables image reconstruction from intensity interferometry, opening a path to imaging supermassive black hole accretion disks. If time permits, I will also talk about how the same ideas apply to the gravitational wave background analysis from pulsar timing arrays, reconciling an apparent inconsistency with astrophysical predictions.

The stunning capabilities of modern AI systems give rise to many questions regarding how they work and how much more capable they can possibly get. One way to gain additional insight is via synthetic models of data with tunable complexity, which can capture the basic relevant structures of real data. In recent work we have focused on sequences obtained from random walks on graphs, hypergraphs, and hierarchical graphical structures. I will present some recent empirical results regarding how transformers learn sequences arising from random walks on graphs. The focus will be on neural scaling laws, unexpected temperature-dependent effects, and sample complexity. If there is time, I will also discuss the effect of parameterization strategies on hyperparameter scaling laws, where we see the critical importance of appropriately scaling the embedding layer learning rate.

Quantum computers promise to simulate quantum systems and answer open questions across science from condensed matter and quantum chemistry to particle physics and quantum gravity. Two problems stand in the way: how to build them, and how to use them. Each brings hard optimisation, inference, and compilation problems — naturally suited to AI.  Along the first direction, I present a new paradigm for designing quantum error-correcting codes tailored to specific algorithms, yielding order-of-magnitude improvements on targeted tasks. Machine learning, paired with SAT and tensor-network environments, extends this approach beyond analytic and brute-force design. Along the second direction, I present an experimentally realised scheme for a universal fault-tolerant gate set, and show how machine learning optimises its key bottlenecks. Looking ahead, I discuss the open question of how to integrate large-scale quantum computers with AI to tackle more difficult problems.

Optimal transport (OT) theory, first conceived to solve problems of moving dirt, has since evolved into a powerful mathematical framework with far-reaching applications across machine learning, probability and statistics, and theoretical physics. In particle physics, OT underpins many modern machine learning algorithms and data-analysis methods. It also offers rigorous numerical strategies for non-perturbative field theory calculations and provides a framework for strengthening the connection between field theories and neural networks. In this talk, I will motivate how OT provides a unifying language for connecting ensembles of neural networks, statistical field theories, and exact renormalization group flows. I will highlight how viewing field theories as probability distributions (over an infinite dimensional function space) makes OT a natural tool, offering both numerical strategies and analytic insights. Additionally, OT and the renormalization group can be used to better understand feature learning and training dynamics in ensembles of asymptotically wide neural networks. The goal is not only to showcase the wide and wonderful reach of OT in physics, but also to illustrate how it opens new perspectives for tackling non-perturbative problems and for deepening the dialogue between physics and machine learning.

Axions are some of the best-motivated beyond the Standard Model particle candidates at present. These ultralight particles may account for the cosmological dark matter and explain other outstanding problems in nature, such as the strong-CP problem; they also are now known to emerge generically in string theory.  Axions are expected to couple ultra-weakly with ordinary matter, which complicates their detection. However, thanks to recent theoretical, experimental, and observational progress these particles may be discovered or ruled out within the near future. I will review some of the recent ideas that may soon play a role in axion discovery, including computing the evolution of axions in the early universe using supercomputers and novel observational signatures of axions that emerge in extreme astrophysical environments such as supernovae.

I will describe new ideas relating quantum chaos to the complexity of time evolution.  One approach treats physical time evolution as a quantum computation, and bounds the smallest quantum circuit that can simulate this evolution.  The second approach quantifies how ergodically and rapidly a quantum state explores the accessible part of the system's Hilbert space.  I will illustrate how these measures separate integrable and chaotic quantum systems by considering examples including spin chains, quantum billiards, quantum many body systems, and Random Matrix Theory.  I will end by describing an application of these methods to a conjecture that geometrizes complexity in quantum gravity, and will comment on the relevance of these ideas for the break down of effective field theory near spacelike singularities.