Talks

As progress in AI hurtles forward at a speed seldom seen in the history of science, theorists who wish to gain a first-principles understanding of AI can be overwhelmed by the enormous number of papers, notational choices, and assumptions in the literature. I will make a pitch for developing a “Theoretical Minimum” for theoretical physicists aiming to study AI, with the goal of getting members of our community up to speed as quickly as possible with a suite of standard results whose validity can be checked by numerical experiments requiring only modest compute. In particular, this will require close collaboration between statistical physics, condensed matter physics, and high-energy physics, three communities that all have important perspectives to bring to the table but whose notation must be harmonized in order to be accessible to new researchers. I will focus my discussion on (a) the various approaches to the infinite-width limit, which seems like the best entry point for theoretical physicists who first encounter neural networks, and (b) the need for benchmark datasets from physics complex enough to capture aspects of natural-language data but which are nonetheless “calculable” from first-principles using tools of theoretical physics.

Diffusion models have shown remarkable success in generating high-dimensional data such as images and language – a feat only possible if data has strong underlying structure. Understanding deep generative models thus requires understanding the structure of the data they learn from. In particular, natural data is often composed of features organized hierarchically. In this talk, we will model this structure using probabilistic context-free grammars – tree-like generative models from linguistics. I will present a theory of denoising diffusion on this data, predicting a phase transition that governs the reconstruction of features at various hierarchical levels. I will show empirical evidence for it in both image and language diffusion models. I will then discuss how diffusion models learn these grammars, revealing a quantitative relationship between data correlations and the training set size needed to learn how to hierarchically compose new data. In particular, we predict a polynomial scaling of sample complexity with data dimension, providing a mechanism by which diffusion models avoid the curse of dimensionality. Additionally, this theory predicts that models trained on limited data generate outputs that are locally coherent but lack global consistency, an effect empirically confirmed across modalities. These results offer a new perspective on how generative models learn to become creative and compose novel data by progressively uncovering the latent hierarchical structure.

Can the effectiveness of a medical treatment be determined without the expense of a randomized controlled trial? Can the impact of a new policy be disentangled from other factors that happen to vary at the same time? Questions such as these are the purview of the field of causal inference, a general-purpose science of cause and effect, applicable in domains ranging from epidemiology to economics. Researchers in this field seek in particular to find techniques for extracting causal conclusions from statistical data. Meanwhile, one of the most significant results in the foundations of quantum theory—Bell's theorem—can also be understood as an attempt to disentangle correlation and causation. Recently, it has been recognized that Bell's result is an early foray into the field of causal inference and that the insights derived from 60 years of research on his theorem can supplement and improve upon state-of-the-art causal inference techniques. In the other direction, the conceptual framework developed by causal inference researchers provides a fruitful new perspective on what could possibly count as a satisfactory causal explanation of the quantum correlations observed in Bell experiments. Efforts to elaborate upon these connections have led to an exciting flow of techniques and insights across the disciplinary divide. This talk will highlight some of what is happening at the intersection of these two fields.

In this talk, I will discuss how physics can help improve our understanding of deep learning systems and guide improvements to their scaling strategies. I will first discuss mathematical results based on mean-field techniques from statistical physics to analyze the feature learning dynamics of neural networks as well as posteriors of large Bayesian neural networks. This theory will provide insights to develop initialization and optimization schemes for neural networks that admit well defined infinite width and depth limits and behave consistently across model scales, providing practical advantages. These limits also enable a theoretical characterization of the types of learned solutions reached by deep networks, and provide a starting point to characterize generalization and neural scaling laws (see Cengiz Pehlevan's talk).

Galaxy clusters and superclusters are among the youngest structures forming in the Universe. The intra-cluster medium (ICM) and inter-galactic medium (IGM) are both unique plasmas that host magnetic fields and cosmic rays. Radio band observations provide the probes to these, so-called non thermal components, via the detectable synchrotron radiation. The particle acceleration mechanisms involve the role of shocks and turbulence in the magnetized plasma that can be probed with radio band continuum and polarization observations. I will present our work on studying turbulence and shocks in the high redshift, massive galaxy cluster El Gordo and the Saraswati supercluster with the precursors and pathfinders of the SKA. I will discuss our findings on the evolution of radio galaxies in superclusters and the properties of intra-cluster turbulence using radio and X-ray observations and provide a perspective on the exciting possibilities with the SKA.

With the increased sensitivity and field of view of SKA pathfinders, dynamic radio imaging (imaging the time axis) is becoming a burgeoning field, yielding rich new discoveries of transients and variable sources. MeerKAT is capable of reaching sub-150 uJy image rms in an 8s integration, which opens up studies of variability on much shorter timescales than was possible with previous radio interferometers. This also has important implications for interferometric SETI, since any potential technosignatures would be a subset of such transient events.

At the same time, imaging at such short timescales introduces its own substantial challenges. Instrumental effects that tend to average out in a traditional long synthesis observation can become limiting for dynamic imaging if not addressed correctly. I will discuss these challenges and present MeerKAT dynamic imaging of Jupiter’s radiation belts, which have led to the serendipitous discovery of a pulsar-class object named the PARROT (pulsar with abnormal refraction recurring on odd timescales).

This work has led to the development of (and given the name to) a more general dynamic imaging pipeline, developed in collaboration with the Breakthrough Listen initiative. The PARROT pipeline is capable of detecting short-duration transients in imaging data, and yielding light curves and dynamic spectra for thousands of field sources en masse. We are already starting to use it to “mine” existing archival MeerKAT data, yielding a couple of new discoveries. The longer-term plan is to develop the PARROT pipeline to a state where it can be run in real-time, commensally with any MeerKAT imaging observation. This would open the door to transient event triggers -- something that has never been done with a radio interferometer before.    

Dark matter plays a major role in the equilibrium of galaxy disks, especially the outer disks of galaxies where the stellar disk surface density declines. The hydrostatic equilibrium of the HI disk in these regions can be used to probe the dark matter distribution within the disk. In this presentation we show that the disk dark matter in nearly face-on galaxies can be probed with sensitive HI velocity dispersion observations. Alternatively, the HI disk thickness in edge-on galaxies can be used to estimate the disk dark matter. We show that both methods have assumptions and advantages/disadvantages. Assuming a form of the halo potential, we show that the disk dark matter can be used to probe the halo shape. We apply our methods to nearby galaxies and show that smaller dwarf galaxies appear to be more dark matter dominated and their halo shapes appear to be oblate, whereas massive galaxies have more spherical halos. We also discuss how HI velocity dispersion can explore the dark matter distribution of very close, low luminosity satellites such as Leo-T. The halo shape can affect galaxy disk properties, such as the stellar velocity dispersion and disk surface density, which in turn affects bar formation, gas kinematics and star formation in galaxy disks, all of which are important for galaxy evolution. Our study thus demonstrates the importance of SKA HI surveys to probe the dark matter distribution in galaxies. We discuss how the SKA sensitivity will allow us to probe HI and dark matter at much larger distances compared to present studies.