Conference

Cosmological data is consistent with a positive cosmological constant. In this talk I discuss an approach pioneered by Smolin that uses a non-perturbative exact quantization of gavity with a cosmological constant in the Ashtekar formalism. I discuss follow up work by the Author and his collaborators that address some conceptual and potential physical predictions of this approach. I end with a discussion of Smolin's cosmic natural selection as a predictive mechanism which also had consequences in particular Anthrophic landscape realizations in string theory.

I will tell stories. About Lee's physics. About his insights that have shaped many of the ideas that we take for granted today. From the birth of Loop Quantum Gravity to the discreteness of physical space.

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.

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.

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.

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.

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.