Gary Shiu

Jacky H. T. Yip, Adam Rouhiainen, Gary Shiu

The topology of the large-scale structure of the universe contains valuable information on the underlying cosmological parameters. While persistent homology can extract this topological information, the optimal method for parameter estimation from the tool remains an open question. To address this, we propose a neural network model to map persistence images to cosmological parameters. Through a parameter recovery test, we demonstrate that our model makes accurate and precise estimates, considerably outperforming conventional Bayesian inference approaches.

Haotian Cao, Garrett Merz, Kyle Cranmer et al.

We study the use of transformers to reconstruct the compositions of tensor products of two-dimensional rational conformal field theories (RCFTs) based on their low-energy spectra. The task is challenging due to its combinatorial nature. The constituent theories are characterized by their central charges and affine Lie algebra labels. We achieve 98% accuracy in recovering the constituents of tensor products theories constructed from Wess-Zumino-Witten models. We further demonstrate that our method generalizes to CFTs with larger central charge and unseen classes of RCFTs by adding a small number of out-of-domain examples. Our results show that transformers are effective at this task and point towards a new tool for bulk reconstruction in AdS/CFT.

Charles Arnal, Jacky H. T. Yip, François Charton et al.

Triangulations, i.e., well-structured decompositions of geometric objects into triangle-like pieces, are central objects in many domains of mathematics and physics. In particular, fine, regular, and star triangulations (FRSTs) of 4D reflexive polytopes give rise to smooth Calabi-Yau threefolds, which are of significant interest in string theory. However, the high dimensionality and combinatorial complexity of triangulations make them particularly challenging to model with classical numerical methods or machine learning. In this work, we show that transformers, equipped with an appropriate encoding scheme, can be effectively trained to representatively generate new FRSTs across a range of polytope sizes. Moreover, these models can also self-improve through retraining on their own output. This opens the door to both concrete applications to the classification of Calabi-Yau manifolds and further research in physics, combinatorics and algebraic geometry.

Jacky H. T. Yip, Charles Arnal, François Charton et al.

Fine, regular, and star triangulations (FRSTs) of four-dimensional reflexive polytopes give rise to toric varieties, within which generic anticanonical hypersurfaces yield smooth Calabi-Yau threefolds. We introduce CYTransformer, a deep learning model based on the transformer architecture, to automate the generation of FRSTs. We demonstrate that CYTransformer efficiently and unbiasedly samples FRSTs for polytopes across a range of sizes, and can self-improve through retraining on its own output. These results lay the foundation for AICY: a community-driven platform designed to combine self-improving machine learning models with a continuously expanding database to explore and catalog the Calabi-Yau landscape.

Juan Calles, Jacky H. T. Yip, Gabriella Contardo et al.

Building upon [2308.02636], we investigate the constraining power of persistent homology on cosmological parameters and primordial non-Gaussianity in a likelihood-free inference pipeline utilizing machine learning. We evaluate the ability of Persistence Images (PIs) to infer parameters, comparing them to the combined Power Spectrum and Bispectrum (PS/BS). We also compare two classes of models: neural-based and tree-based. PIs consistently lead to better predictions compared to the combined PS/BS for parameters that can be constrained, i.e., for $\{Ω_{\rm m}, σ_8, n_{\rm s}, f_{\rm NL}^{\rm loc}\}$. PIs perform particularly well for $f_{\rm NL}^{\rm loc}$, highlighting the potential of persistent homology for constraining primordial non-Gaussianity. Our results indicate that combining PIs with PS/BS provides only marginal gains, indicating that the PS/BS contains little additional or complementary information to the PIs. Finally, we provide a visualization of the most important topological features for $f_{\rm NL}^{\rm loc}$ and for $Ω_{\rm m}$. This reveals that clusters and voids (0-cycles and 2-cycles) are most informative for $Ω_{\rm m}$, while $f_{\rm NL}^{\rm loc}$ is additionally informed by filaments (1-cycles).

Gregory J. Loges, Gary Shiu

Intersecting branes provide a useful mechanism to construct particle physics models from string theory with a wide variety of desirable characteristics. The landscape of such models can be enormous, and navigating towards regions which are most phenomenologically interesting is potentially challenging. Machine learning techniques can be used to efficiently construct large numbers of consistent and phenomenologically desirable models. In this work we phrase the problem of finding consistent intersecting D-brane models in terms of genetic algorithms, which mimic natural selection to evolve a population collectively towards optimal solutions. For a four-dimensional ${\cal N}=1$ supersymmetric type IIA orientifold with intersecting D6-branes, we demonstrate that $\mathcal{O}(10^6)$ unique, fully consistent models can be easily constructed, and, by a judicious choice of search environment and hyper-parameters, $\mathcal{O}(30\%)$ of the found models contain the desired Standard Model gauge group factor. Having a sizable sample allows us to draw some preliminary landscape statistics of intersecting brane models both with and without the restriction of having the Standard Model gauge factor.

Alex Cole, Matteo Biagetti, Gary Shiu

We present a pipeline for characterizing and constraining initial conditions in cosmology via persistent homology. The cosmological observable of interest is the cosmic web of large scale structure, and the initial conditions in question are non-Gaussianities (NG) of primordial density perturbations. We compute persistence diagrams and derived statistics for simulations of dark matter halos with Gaussian and non-Gaussian initial conditions. For computational reasons and to make contact with experimental observations, our pipeline computes persistence in sub-boxes of full simulations and simulations are subsampled to uniform halo number. We use simulations with large NG ($f_{\rm NL}^{\rm loc}=250$) as templates for identifying data with mild NG ($f_{\rm NL}^{\rm loc}=10$), and running the pipeline on several cubic volumes of size $40~(\textrm{Gpc/h})^{3}$, we detect $f_{\rm NL}^{\rm loc}=10$ at $97.5\%$ confidence on $\sim 85\%$ of the volumes for our best single statistic. Throughout we benefit from the interpretability of topological features as input for statistical inference, which allows us to make contact with previous first-principles calculations and make new predictions.

Alex Cole, Gregory J. Loges, Gary Shiu

We apply persistent homology to the task of discovering and characterizing phase transitions, using lattice spin models from statistical physics for working examples. Persistence images provide a useful representation of the homological data for conducting statistical tasks. To identify the phase transitions, a simple logistic regression on these images is sufficient for the models we consider, and interpretable order parameters are then read from the weights of the regression. Magnetization, frustration and vortex-antivortex structure are identified as relevant features for characterizing phase transitions.