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publications
Scale-Invariant Dynamics in a Purely Deterministic Game of Life Model
ArXiv, 2025-June
Abstract: Scale invariance is a key feature that characterizes criticality in complex dynamical systems, which often organize into structures exhibiting no typical size and/or lifespan. While random external inputs or tunable stochastic interactions are typically required for showcasing such criticality, the question of whether scale-invariant dynamics can emerge from purely deterministic interactions remains unclear. In this work, we discover highly affirmative signatures of critical dynamics in equal-state clusters that emerge in the \(\textit{logistic}\) Game of life (LGOL): an extension of Conway’s GOL into a Cantor set state space that is nevertheless deterministic. We uncover at least three types of asymptotic behavior, i.e. phases, that are separated by two fundamentally distinct critical points. The first critical point — associated with a peculiar form of self-organized criticality — defines the non-analytic boundary between a sparse-static and a sparse-dynamic asymptotic phase. Meanwhile, the second point marks an enigmatic deterministic percolation transition between the sparse-dynamic and a third, dense-dynamic phase. Moreover, we identify distinct power-law distributions of cluster sizes with unconventional critical exponents that challenge the current paradigms for critical behavior. Overall, our work concretely paves the way for studying emergent scale invariance in purely deterministic systems.
HSG-12M: A Large-Scale Spatial Multigraph Dataset
ArXiv, 2025-June
Abstract: Existing graph benchmarks assume non-spatial, simple edges, collapsing physically distinct paths into a single link. We introduce HSG-12M, the first large-scale dataset of \(\textbf{spatial multigraphs}\) — graphs embedded in a metric space where multiple geometrically distinct trajectories between two nodes are retained as separate edges. HSG-12M contains 11.6 million static and 5.1 million dynamic \(\textit{Hamiltonian spectral graphs}\) across 1401 characteristic-polynomial classes, derived from 177 TB of spectral potential data. Each graph encodes the full geometry of a 1-D crystal’s energy spectrum on the complex plane, producing diverse, physics-grounded topologies that transcend conventional node-coordinate datasets. To enable future extensions, we release \(\href{https://github.com/sarinstein-yan/Poly2Graph}{\texttt{Poly2Graph}}\): a high-performance, open-source pipeline that maps arbitrary 1-D crystal Hamiltonians to spectral graphs. Benchmarks with popular GNNs expose new challenges in learning from multi-edge geometry at scale. Beyond its practical utility, we show that spectral graphs serve as universal topological fingerprints of polynomials, vectors, and matrices, forging a new algebra-to-graph link. HSG-12M lays the groundwork for geometry-aware graph learning and new opportunities of data-driven scientific discovery in condensed matter physics and beyond.
Precise Identification of Topological Phase Transitions with Eigensystem-Based Clustering
AI4X 2025 International Conference, 2025-July
Abstract: Recent advances in machine learning have spurred new ways to explore and classify quantum phases of matter. We propose an Eigensystem-based representation, combined with a Gaussian Mixture Model (GMM), to unsupervisedly cluster Hamiltonians into distinct topological phases with minimal feature engineering. The method identifies different topological phases without any prior knowledge, pinpoints phase boundaries with remarkable precision \(\sim\mathcal{O}(10^{-5})\), remains robust under moderate noise, and scales efficiently via a simple dimensionality-reduction step. The success of GMM offers a novel physical insight — each phase forms a well-separated multivariate Gaussian in a high-dimensional “Eigensystem space.” We illustrate the approach on several 1D lattice models, all achieving near 100% accuracies.
Automated Metric Discovery: Navigating Quantum Geometry with Symbolic Regression
AI4X 2025 International Conference, 2025-July
Abstract: I demonstrated how symbolic regression can \(\textit{automatically learn}\) quantum geometric metrics from numerical data, recovering known formulas (e.g. Fubini-Study and Bures) in a transparent, closed-form fashion. Beyond these canonical examples, the same approach opens the door to exploring \(\textit{customized}\) quantum metrics that maximize a problem-specific objective.
Classifying the Graph Topology of Non-Hermitian Energy Spectra with Graph Transformer.
AAAI 2026 XAI4Science Workshop, 2025-November
Abstract: Classifying non-Hermitian energy spectra under open boundary conditions is an open challenge in physics.
This classification is a critical prerequisite for the rational inverse design of systems exhibiting desired dynamics and topological responses. While graph topology has emerged as a promising approach for characterizing these spectra, systematic methods for distilling non-Hermitian spectra into their corresponding graph representations have been lacking. Moreover, the resulting graphs often exhibit complexities that defy manual classification, necessitating machine learning approaches.
In this work, we introduce a two-step framework for classifying non-Hermitian spectra based on their graph topologies. The first step employs Poly2Graph, an automated, high-performance pipeline that distills non-Hermitian spectra into spectral graphs suitable for graph neural networks (GNNs). The second step involves generating a large dataset of these spectral graphs and training a GNN for classification. We propose GnLTransformer, a novel architecture featuring dual channels that leverage line graphs to explicitly capture higher-order topological features. GnLTransformer achieves over 99% classification accuracy on our dataset, outperforming standard baselines by 32%. Notably, beyond conventional GNNs, GnLTransformer offers inherent explainability regarding higher-order topology. As a further contribution, we release a new multi-graph dataset comprising over 117K spectral graphs.