Scientific Series

We develop a general approach to "interpret" what a network has learned by introducing strong inductive biases. In particular, we focus on Graph Neural Networks. 

The technique works as follows: we first encourage sparse latent representations when we train a GNN in a supervised setting, then we apply symbolic regression to components of the learned model to extract explicit physical relations. The symbolic expressions extracted from the GNN using our technique also generalized to out-of-distribution data better than the GNN itself. Our approach offers alternative directions for interpreting neural networks and discovering novel physical principles from the representations they learn.

In particular, we will show examples of recovery of newton's law and masses of solar system bodies with real ephemeris data and recovery of navier-stokes equations with turbulence dataset.  We will speculate what one can do with this new tool.
 

We introduce a viewpoint that the Standard Model (SM) is a low-energy quantum vacuum arising from various neighbor Grand Unification (GUT) like vacua competition in an immense quantum phase diagram. In general, we find the SM arises near the gapless quantum critical regions between the competing neighbor vacua. Alternatively, we can also phrase this viewpoint in terms of the deformation class of quantum field theory (QFT), specified by its symmetry G and its anomaly (i.e., cobordism invariant). Seemly different QFTs of the same deformation class can be deformed to each other via quantum phase transitions. We show that GUT such as Georgi-Glashow su(5), Pati-Salam su(4)×su(2)×su(2), Barr’s flipped u(5), and familiar or modified so(n) models of Spin(n) gauge group, e.g., with n = 10, 18 can all reside in an appropriate SM deformation class, labeled by Z_{16} and Z_2 nonperturbative global anomaly index. We show that Ultra Unification, which replaces some of sterile neutrinos with new exotic gapped/gapless sectors (e.g., topological or conformal field theory) or gravitational sectors with topological origins via cobordism constraints, also resides in an SM deformation class. Neighbor quantum phases near SM or their phase transitions, and neighbor gauge enhanced gapless quantum criticality naturally exhibit beyond SM phenomena. We give a new proposal on the neutrino mass origin. The talk is mainly based on: arxiv 1910.14668, 2006.16996, 2008.06499, 2012.15860, 2106.16248, 2111.10369, 2112.14765. Some of these works are in collaboration with Zheyan Wan and Yi-Zhuang You. 

Zoom Link: https://pitp.zoom.us/j/94634619703?pwd=VWlWZHNIMm1sS2owWnlhSmhZTTNvUT09

There is an extremely rich history of interaction between physics and moduli spaces, for instance cohomological Hall algebras/algebras of BPS states, or vertex/chiral algebras. In this talk, I will explain a link between Joyce vertex algebras and one dimensional CoHAs, based on my paper 2110.14356, where quantum vertex algebras play a central role. The main technical tool is a ``bivariant" Euler class which makes torus localisation work in this context. I will also talk about ongoing work, in this area as well as in closely related projects.

Zoom Link: https://pitp.zoom.us/j/93045858347?pwd=N25FNVVjNEFFN09sdmFUV2M2YlZ5QT09

TTbar and JTbar - deformed CFTs provide an interesting example of non-local, yet UV-complete two-dimensional QFTs that are entirely solvable. I will start by showing that both classes of theories possess Virasoro x Virasoro or Virasoro- Kac- Moody x Virasoro - Kac- Moody symmetry. For the case of JTbar, I will discuss the classical realization of these symmetries in terms of field-dependent coordinate transformations and show how the associated generators can be used to define an analogue of "primary" operators in this non-local theory, whose correlation functions are entirely fixed in terms of those of the undeformed CFT. In particular, two and three-point functions are simply given by the corresponding momentum-space correlator in the undeformed CFT, with all dimensions replaced by particular momentum-dependent conformal dimensions. Interestingly, scattering amplitudes off the near-horizon of extremal black holes are known to take a strikingly similar form.

We present a model of quantum gravity in which dimension, topology and geometry of spacetime are collective dynamical variables that describe the pattern of entanglement of underlying quantum matter. As spacetimes with arbitrary dimensions can emerge, the gauge symmetry is generalized to a group that includes diffeomorphisms in general dimensions. The gauge symmetry obeys a first-class constraint operator algebra, and is reduced to a generalized hypersurface deformation algebra in states that exhibit classical spacetimes. In the semi-classical limit, we find a saddle-point solution that describes a series of (3+1)-dimensional de Sitter-like spacetimes with the Lorentzian signature bridged by Euclidean spaces in between.

Black hole spectroscopy is a powerful tool to probe the Kerr nature of astrophysical compact objects and their environment. The observation of multiple ringdown modes in gravitational waveforms could soon lead to high-precision gravitational spectroscopy, thus it is critical to understand if the quasinormal mode spectrum itself is stable against perturbations. In this talk, I will review the pseudospectrum, a mathematical tool which can shed light on the spectral stability of quasinormal modes, and discuss its novel applications in black holes and exotic compact objects. Furthermore, I will demonstrate that quasinormal spectra generically suffer from spectral instabilities and will argue how such
behavior may affect black hole spectroscopy.

Zoom Link: https://pitp.zoom.us/j/99111452809?pwd=bVp6TVdYQkJzU0Mvd2MxY2piclMzUT09

The Quantum Bayesian, or QBist, interpretation regards the quantum formalism to be a tool that a single agent may adopt to help manage their expectations for the consequences of their actions. In other words, quantum theory is an addition to decision theory, and its shape, we hope, can teach us something about the nature of reality. Beyond simple consistency, an interpretation is judged by its capacity to point the way forward. In the first half of the talk, I will highlight several ways in which my collaborators and I have applied QBist intuitions to pose and solve technical questions regarding the informational structure and conceptual function of quantum theory. At the root of many of these developments is the notion of a reference measurement, the key to a probabilistic representation of quantum theory. In this setting, we can explore the boundary of the quantum reasoning structure from a uniquely QBist angle. Working with such representations grants a new perspective and inspires questions which wouldn't have occurred otherwise; as examples, we will meet downstream results concerning quantum channels, discrete quasiprobability representations, and a variant of the information-disturbance tradeoff. Most recently, I have pursued ways in which QBism could be applied to the construction of new tools and strategies for existing problems in quantum information and computation. In the second half of the talk, we will encounter the first of these, an agent-based modeling proposal where multiple, suitably interacting, QBist decision-makers might collectively work out the solution to a task of interest in the right circumstances. I will describe some initial explorations of modeling agent belief dynamics in two contexts: first, an expectation sampling interaction with an eye to agential agreement, and, second, a setting where agents are players of quantum games. In the future, we imagine it is possible that a sufficiently mature development of the agent-based program we have begun could suggest new approaches to quantum algorithm design.

Zoom Link: https://pitp.zoom.us/j/95668668835?pwd=MUJtRGMxbEFzSEdVVmZ3TkR3dVVVZz09

Several puzzles and issues in quantum gravity are related to the question of what type of high-energy information is actually available to low-energy observers. In this talk I will try to argue that the best description available to a low-energy observer is probably of a statistical nature. Such a statistical description naturally connects to e.g. the eigenstate thermalization hypothesis, and wormholes and the apparent lack of factorization. I will describe this statistical picture and the evidence we have for it, and what we could possibly learn from it. Partially based on work in progress.

Zoom Link: https://pitp.zoom.us/j/96646337719?pwd=UVRKN3Y4Q05xNXk1VExOenYwSFZvZz09

In the fuzzy dark matter model, dark matter consists of “axion-like” ultra-light scalar particles of mass around 10⁻²² eV. This candidate behaves similarly to cold dark matter on large scales, but exhibits different properties on smaller (galactic) scales due to macroscopic wave effects arising from the extremely light particles’ large de Broglie wavelengths. It has both particle physics motivations and a rich astrophysical phenomenology, giving rise to notable differences in the structures on highly non-linear scales due to the manifestation of wave effects, which can impact a number of contentious small-scale tensions in the standard cosmological model, ΛCDM. Some of the unique features include transient wave interference patterns and granules, the presence flat-density cores (solitons) at the centers of dark matter halos, and the formation of quantized vortices. I will present large numerical simulations of cosmic structure formation with this dark matter model – including the full non-linear wave dynamics – using a pseudo-spectral method to numerically solve the Schrödinger–Poisson equations, and the significant computational challenges associated with these equations. I will discuss several observables, such as the evolution of the matter power spectrum, the fuzzy dark matter halo mass function, dark matter halo density profiles, and the question of a fuzzy dark matter core–halo mass relation, using results obtained from these simulations, and contrast them with corresponding results for the cold dark matter model.

Aside from quantum mechanics, other areas in physics constrain information processing. From relativity, we know information cannot move faster than the speed of light. In quantum gravity, we expect but don't fully understand additional constraints, for instance on how densely information can be stored. Can we develop an understanding of information processing in the context of quantum gravity? Towards doing so, we consider quantum information within ``holographic'' spacetimes, which have an alternative, non-gravitational, description. In that context questions about information processing in the presence of gravity can be translated to different questions about quantum information without gravity. As a specific example, we study constraints on computation within a gravitating region, and use the holographic description to argue that gravity constrains the complexity of operations that can happen inside the region. Along the way, we are led to new connections relating quantum gravity, position-based cryptography, quantum secret sharing and complexity theory.