Theory + AI Workshop: Theoretical Physics for AI

Apr 9, 2025, 8:00 a.m. → Apr 11, 2025, 5:00 p.m. America/Toronto

PI/4-400 - Space Room (Perimeter Institute for Theoretical Physics)

 

This 5-day program will explore the intersection of AI and fundamental theoretical physics. The event will feature two components, a symposium and a workshop, centered around two complementary themes: AI for theoretical physics and theoretical physics for AI.

The program will begin on April 7 and 8 with a large symposium with speakers and panel discussions focusing on the promise of AI to accelerate progress in theoretical physics. These talks will address the possibilities and challenges associated with AI ‘doing science.’ The event will bring together physicists, engineers, AI researchers, and entrepreneurs to collect different perspectives on what the future of theoretical physics will look like, the engineering challenges we should expect along the way, what tools and collaborations will be needed to help get us there, and what exciting steps are already underway.

Registration for the symposium is available on the symposium website. 

The symposium will be followed by a workshop on April 9, 10, 11 focusing on developing a theoretical framework for AI enabling the development of reliable, robust, and interpretable AI models for physics. Recent advances in theoretical foundations of AI, inspired by techniques from string theory, quantum field theory (QFT), and statistical physics, have uncovered parallels between AI systems and physical theories, utilizing methods like renormalization group (RG) flows, Feynman path integrals etc. to deepen understanding of deep neural networks (DNNs), generative AI (e.g., LLMs and diffusion models), and scaling laws. Key topics include physics-informed optimization and learning, the role of RG and QFT for DNNs and generative AI, and the application of physics to AI interpretability. Through interdisciplinary dialogue, the event aims to foster collaborations, advance the theoretical foundations of AI, and explore its potential in areas like theoretical physics and mathematics.

 

Speakers:

 

• David Berman (Queen Mary University of London)
• Blake Bordelon (Harvard University)
• Jordan Cotler (Harvard University)
• Hugo Cui (Harvard University)
• Alessandro Favero (EPFL)
• Ro Jefferson (Utrecht University)
• Yonatan Kahn (University of Toronto)
• Dmitry Krotov (IBM)
• Bruno Loureiro (École Normale Supérieure in Paris)
• Luisa Lucie-Smith (The University of Hamburg)
• Cengiz Pehlevan (Harvard University)
• Rob Spekkens (Perimeter Institute)

 

Scientific Organizers:

• Anindita Maiti (Perimeter Institute)
• Matt Johnson (Perimeter Institute)
• Sabrina Pasterski (Perimeter Institute)

 

Advisory Committee:

• Achim Kempf (University of Waterloo)
• Cengiz Pehlevan (Harvard University)
• Hiranya Peiris (University of Cambridge)
• Roger Melko (University of Waterloo)

 

 

Wed, April 9

9:00 a.m. Registration

1 Opening Remarks

2 Scaling Limits for Learning: Dynamics and Statics

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).

Speaker: Blake Bordelon (Harvard University)

10:30 a.m. Break - Coffee Station

3 Causal Inference Meets Quantum Physics

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.

Speaker: Robert Spekkens (Perimeter Institute)

4 Discussion

12:30 p.m. Lunch - Upper Bistro Dining Room (2nd Floor)

5 Creativity by Compositionality in Generative Diffusion Models

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.

Speaker: Alessandro Favero (École Polytechnique Fédérale de Lausanne)

6 Towards a “Theoretical Minimum” for Physicists in AI

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.

Speaker: Yonatan Kahn (University of Toronto)

3:00 p.m. Break - Coffee Station

7 Discussion

6:00 p.m. Banquet

Thu, April 10

8 Solvable models of scaling and emergence in deep learning

Speaker: Cengiz Pehlevan (Harvard University)

9 Architectural bias in a transport-based generative model : an asymptotic perspective

We consider the problem of learning a generative model parametrized by a two-layer auto-encoder, and trained with online stochastic gradient descent, to sample from a high-dimensional data distribution with an underlying low-dimensional structure. We provide a tight asymptotic characterization of low-dimensional projections of the resulting generated density, and evidence how mode(l) collapse can arise. On the other hand, we discuss how in a case where the architectural bias is suited to the target density, these simple models can efficiently learn to sample from a binary Gaussian mixture target distribution.

Speaker: Hugo Cui (Harvard University)

10:30 a.m. Break - Coffee Station

10 Statistical physics of learning with two-layer neural networks

Feature learning - or the capacity of neural networks to adapt to the data during training - is often quoted as one of the fundamental reasons behind their unreasonable effectiveness. Yet, making mathematical sense of this seemingly clear intuition is still a largely open question. In this talk, I will discuss a simple setting where we can precisely characterise how features are learned by a two-layer neural network during the very first few steps of training, and how these features are essential for the network to efficiently generalise under limited availability of data.

Speaker: Bruno Loureiro (École Normale Supérieure - PSL)

11 Discussion

12:30 p.m. Lunch - Upper Bistro Dining Room (2nd Floor)

12 Renormalization Group Flows: from Optimal Transport to Diffusion Models

We show that Polchinski’s equation for exact renormalization group flow is equivalent to the optimal transport gradient flow of a field-theoretic relative entropy. This gives a surprising information-theoretic formulation of the exact renormalization group, expressed in the language of optimal transport. We will provide reviews of both the exact renormalization group, as well as the theory of optimal transportation. Our techniques generalize to other RG flow equations beyond Polchinski's. Moreover, we establish a connection between this more general class of RG flows and stochastic Langevin PDEs, enabling us to construct ML-based adaptive bridge samplers for lattice field theories. Finally, we will discuss forthcoming work on related methods to variationally approximate ground states of quantum field theories.

Speaker: Jordan Cotler (Harvard University)

13 Aspects of RG flows and Bayesian Updating

We will examine the idea of Bayesian updating as an inverse diffusion like process and its relation to the exact renormalisation group. In particular we will look at the role of Fisher Information, its metric and possible physical interpretations.

Speaker: David Berman (Queen Mary University of London)

3:00 p.m. Break - Coffee Station

14 Discussion

Fri, April 11

15 NN/QFT correspondence

As we've seen at this workshop, exciting progress has recently been made in the study of neural networks by applying ideas and techniques from theoretical physics. In this talk, I will discuss a precise relation between quantum field theory and deep neural networks, the NN/QFT correspondence. In particular, I will go beyond the level of analogy by explicitly constructing the QFT corresponding to a class of networks encompassing both vanilla feedforward and recurrent architectures. The resulting theory closely resembles the well-studied O(N) vector model, in which the variance of the weight initializations plays the role of the 't Hooft coupling. In this framework, the Gaussian process approximation used in machine learning corresponds to a free field theory, and finite-width effects can be computed perturbatively in the ratio of depth to width, T/N. These provide corrections to the correlation length that controls the depth to which information can propagate through the network, and thereby sets the scale at which such networks are trainable by gradient descent. This analysis provides a non-perturbative description of networks at initialization, and opens several interesting avenues to the study of criticality in these models.

Speaker: Ro Jefferson (Utrecht University)

16 Explainable AI in (Astro)physics

Machine learning has significantly improved the way scientists model and interpret large datasets across a broad range of the physical sciences; yet, its "black box" nature often limits our ability to trust and understand its results. Interpretable and explainable AI is ultimately required to realize the potential of machine-assisted scientific discovery. I will review efforts toward explainable AI focusing in particular in applications within the field of Astrophysics. I will present an explainable deep learning framework which combines model compression and information theory to achieve explainability. I will demonstrate its relevance to cosmological large-scale structures, such as dark matter halos and galaxies, as well as the cosmic microwave background, revealing new physical insights derived from these explainable AI models.

Speaker: Luisa Lucie-Smith (The University of Hamburg)

10:30 a.m. Break - Coffee Station

17 Discussion

18 Closing Remarks

12:30 p.m. Lunch - Upper Bistro Dining Room (2nd Floor)

4:00 p.m. Friday Social