arXiv subjects

Simon Zhang

Publications and source records attributed to Simon Zhang.

8 recordsLinked to original sources

arXiv2026

An End-to-End Differentiable Forward Model for High-Energy Diffraction Microscopy

High-Energy Diffraction Microscopy (HEDM) recovers crystallographic orientation, strain, and grain position from rotating-crystal X-ray diffraction patterns. Existing forward models in far-field (FF), near-field (NF), and point-focused (pf) HEDM are not differentiable, which forecloses gradient-based joint parameter refinement, physics-informed regularisation, and Bayesian uncertainty quantification. We present the first end-to-end differentiable HEDM forward model covering all three geometries, implemented in PyTorch with pixel-exact agreement against the established MIDAS reference simulators (162/162 FF, 2304/2304 NF including a non-zero detector-tilt sweep, and 1088/1096 pf-HEDM spots matched). Three demonstrations validate the framework: joint orientation-strain-position recovery in NF-HEDM at ~6 nm precision; round-trip refinement on a real 214-grain alpha-Ti FF-HEDM dataset reaching 100% grain recovery from a 1.5 degree initial perturbation with residuals matching the production fit to 0.3%; and joint refinement of all per-detector geometry parameters and per-grain state on a synthetic four-panel FF-HEDM setup, recovering panel rotations about the beam axis to ~10 mu-rad and a global rotation-axis wedge to ~26 mu-rad. The framework is released as the open-source midas-diffract package (pip install midas-diffract).

cond-mat.mtrl-sci↗

arXiv2026

Adversarial Label Invariant Graph Data Augmentations for Out-of-Distribution Generalization

Out-of-distribution (OoD) generalization occurs when representation learning encounters a distribution shift. This occurs frequently in practice when training and testing data come from different environments. Covariate shift is a type of distribution shift that occurs only in the input data, while the concept distribution stays invariant. We propose RIA - Regularization for Invariance with Adversarial training, a new method for OoD generalization under convariate shift. Motivated by an analogy to $Q$-learning, it performs an adversarial exploration for counterfactual data environments. These new environments are induced by adversarial label invariant data augmentations that prevent a collapse to an in-distribution trained learner. It works with many existing OoD generalization methods for covariate shift that can be formulated as constrained optimization problems. We develop an alternating gradient descent-ascent algorithm to solve the problem in the context of causally generated graph data, and perform extensive experiments on OoD graph classification for various kinds of synthetic and natural distribution shifts. We demonstrate that our method can achieve high accuracy compared with OoD baselines.

cs.LG↗

arXiv2025

Compression of Voxelized Vector Field Data by Boxes is Hard

Voxelized vector field data consists of a vector field over a high dimensional lattice. The lattice consists of integer coordinates called voxels. The voxelized vector field assigns a vector at each voxel. This data type encompasses images, tensors, and voxel data. Assume there is a nice energy function on the vector field. We consider the problem of lossy compression of voxelized vector field data in Shannon's rate-distortion framework. This means the data is compressed and then decompressed up to an error bound on the energy distortion at each voxel. Our first result is that under general conditions, lossy compression of voxelized vector fields is undecidable to compute. This is caused by having an infinite number of Euclidean vectors. We formulate this problem instead in terms of clustering the finite number of indices of a voxelized vector field by boxes. We call this problem the $(k,D)$-RectLossyVVFCompression problem. We show four main results about the $(k,D)$-RectLossyVVFCompression problem. The first is that it is decidable. The second is that decompression for this problem is polynomial time tractable. This means that the only obstruction to a tractable solution of the $(k,D)$-RectLossyVVFCompression problem lies in the compression stage. This is shown by the two hardness results about the compression stage. We show that the compression stage is NP-Hard to compute exactly and that it is even APX-Hard to approximate for $k,D\geq 2$. Assuming $P\neq NP$, this shows that when $k,D \geq 2$ there can be no exact polynomial time algorithm nor can there even be a PTAS approximation algorithm for the $(k,D)$-RectLossyVVFCompression problem.

cs.CC↗

arXiv2025

Computing and Learning on Combinatorial Data

The twenty-first century is a data-driven era where human activities and behavior, physical phenomena, scientific discoveries, technology advancements, and almost everything that happens in the world resulting in massive generation, collection, and utilization of data. Connectivity in data is a crucial property. A straightforward example is the World Wide Web, where every webpage is connected to other web pages through hyperlinks, providing a form of directed connectivity. Combinatorial data refers to combinations of data items based on certain connectivity rules. Other forms of combinatorial data include social networks, meshes, community clusters, set systems, and molecules. This Ph.D. dissertation focuses on learning and computing with combinatorial data. We study and examine topological and connectivity features within and across connected data to improve the performance of learning and achieve high algorithmic efficiency.

cs.AI↗

arXiv2024

GEFL: Extended Filtration Learning for Graph Classification

Extended persistence is a technique from topological data analysis to obtain global multiscale topological information from a graph. This includes information about connected components and cycles that are captured by the so-called persistence barcodes. We introduce extended persistence into a supervised learning framework for graph classification. Global topological information, in the form of a barcode with four different types of bars and their explicit cycle representatives, is combined into the model by the readout function which is computed by extended persistence. The entire model is end-to-end differentiable. We use a link-cut tree data structure and parallelism to lower the complexity of computing extended persistence, obtaining a speedup of more than 60x over the state-of-the-art for extended persistence computation. This makes extended persistence feasible for machine learning. We show that, under certain conditions, extended persistence surpasses both the WL[1] graph isomorphism test and 0-dimensional barcodes in terms of expressivity because it adds more global (topological) information. In particular, arbitrarily long cycles can be represented, which is difficult for finite receptive field message passing graph neural networks. Furthermore, we show the effectiveness of our method on real world datasets compared to many existing recent graph representation learning methods.

cs.LG↗

arXiv2024

Expressive Higher-Order Link Prediction through Hypergraph Symmetry Breaking

A hypergraph consists of a set of nodes along with a collection of subsets of the nodes called hyperedges. Higher-order link prediction is the task of predicting the existence of a missing hyperedge in a hypergraph. A hyperedge representation learned for higher order link prediction is fully expressive when it does not lose distinguishing power up to an isomorphism. Many existing hypergraph representation learners, are bounded in expressive power by the Generalized Weisfeiler Lehman-1 (GWL-1) algorithm, a generalization of the Weisfeiler Lehman-1 algorithm. However, GWL-1 has limited expressive power. In fact, induced subhypergraphs with identical GWL-1 valued nodes are indistinguishable. Furthermore, message passing on hypergraphs can already be computationally expensive, especially on GPU memory. To address these limitations, we devise a preprocessing algorithm that can identify certain regular subhypergraphs exhibiting symmetry. Our preprocessing algorithm runs once with complexity the size of the input hypergraph. During training, we randomly replace subhypergraphs identified by the algorithm with covering hyperedges to break symmetry. We show that our method improves the expressivity of GWL-1. Our extensive experiments also demonstrate the effectiveness of our approach for higher-order link prediction on both graph and hypergraph datasets with negligible change in computation.

cs.LG↗

arXiv2021

Approximating 1-Wasserstein Distance between Persistence Diagrams by Graph Sparsification

Persistence diagrams (PD)s play a central role in topological data analysis. This analysis requires computing distances among such diagrams such as the $1$-Wasserstein distance. Accurate computation of these PD distances for large data sets that render large diagrams may not scale appropriately with the existing methods. The main source of difficulty ensues from the size of the bipartite graph on which a matching needs to be computed for determining these PD distances. We address this problem by making several algorithmic and computational observations in order to obtain, in theory, a near-linear fully polynomial-time approximation scheme. This is theoretically optimal assuming the $(1+\epsilon)$-approximate EMD conjecture in constant dimension, which is that the EMD problem on the plane cannot be approximated by a PTAS in time $O(\frac{1}{\epsilon^2}n)$ up to polylog factors. In our implementation, first, taking advantage of the distribution of PD points, we \emph{condense} them thereby decreasing the number of nodes in the graph for computation. The increase in point multiplicities is addressed by reducing the matching problem to a min-cost flow problem on a transshipment network. Second, we use Well Separated Pair Decomposition to sparsify the graph to a size that is linear in the number of points. Both node and arc sparsifications contribute to the approximation factor where we leverage a lower bound given by the Relaxed Word Mover's distance. Third, we eliminate bottlenecks during the sparsification procedure by introducing parallelism. Fourth, we develop an open source software called PDoptFlow based on our algorithm, exploiting parallelism by GPU and multicore. We perform extensive experiments and show that the actual empirical error is very low. We also show that we can achieve high performance at low guaranteed relative errors, improving upon the state of the arts.

cs.CG↗

arXiv2020

GPU-Accelerated Computation of Vietoris-Rips Persistence Barcodes

The computation of Vietoris-Rips persistence barcodes is both execution-intensive and memory-intensive. In this paper, we study its computational structure and identify several unique mathematical properties and algorithmic opportunities with connections to the GPU. Mathematically and empirically, we look into the properties of apparent pairs, which are independently identifiable persistence pairs comprising up to 99\% of persistence pairs. We prove tight upper and lower bounds of the apparent pair rate and some probabilistic lower bounds. We also design massively parallel algorithms to take advantage of the very large number of simplices that can be processed independently of each other. Having identified these opportunities, we develop a GPU-accelerated software for computing Vietoris-Rips persistence barcodes, called Ripser++. Under nice sampling conditions, we show that the expected work complexity of our algorithm is near linear in the number of simplices. The expected depth complexity is dependent only on the computation of the expected number of $p$-dimensional homological cycles. The software achieves up to 30x speedup over the total execution time of the original Ripser and also reduces CPU-memory usage by up to 2.0x. We believe our GPU-acceleration based efforts open a new chapter for the advancement of topological data analysis in the post-Moore's Law era.

cs.CG↗