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Many problems across computer vision and the natural sciences require the analysis of spherical data, for which representations may be learned efficiently by encoding equivariance to rotational symmetries. We present a generalized spherical…

The research described in this note aims at solving the constructive membership problem for the class of quasisimple classical groups. Our algorithms are developed in the black-box group model; that is, they do not require specific…

Post-Quantum Cryptography (PQC) attempts to find cryptographic protocols resistant to attacks using Shor polynomial time algorithm for numerical field problems or Grover search algorithm. A mostly overlooked but valuable line of solutions…

The study of representations invariant to common transformations of the data is important to learning. Most techniques have focused on local approximate invariance implemented within expensive optimization frameworks lacking explicit…

The central discovery of $2d$ conformal theory was holomorphic factorization, which expressed correlation functions through bilinear combinations of conformal blocks, which are easily cut and joined without a need to sum over the entire…

Many scientific and geometric problems exhibit general linear symmetries, yet most equivariant neural networks are built for compact groups or simple vector features, limiting their reuse on matrix-valued data such as covariances, inertias,…

Graph augmentation has received great attention in recent years for graph contrastive learning (GCL) to learn well-generalized node/graph representations. However, mainstream GCL methods often favor randomly disrupting graphs for…

Cylindrical algebraic decompositions (CADs) are a key tool for solving problems in real algebraic geometry and beyond. We recently presented a new CAD algorithm combining two advances: truth-table invariance, making the CAD invariant with…

Recent studies have shown that Graph Convolutional Networks (GCNs) are vulnerable to adversarial attacks on the graph structure. Although multiple works have been proposed to improve their robustness against such structural adversarial…

Block encoding is a successful technique used in several powerful quantum algorithms. In this work we provide an explicit quantum circuit for block encoding a sparse matrix with a periodic diagonal structure. The proposed methodology is…

Graph contrastive learning (GCL), learning the node representation by contrasting two augmented graphs in a self-supervised way, has attracted considerable attention. GCL is usually believed to learn the invariant representation. However,…

Recent years have seen an increasing involvement of Deep Learning in the cryptanalysis of various ciphers. The present study is inspired by past works on differential distinguishers, to develop a Deep Neural Network-based differential…

At SAC 2013, Berger et al. first proposed the Extended Generalized Feistel Networks (EGFN) structure for the design of block ciphers with efficient diffusion. Later, based on the Type-2 EGFN, they instantiated a new lightweight block cipher…

Graph Contrastive Learning (GCL) has emerged as a powerful paradigm for training Graph Neural Networks (GNNs) in the absence of task-specific labels. However, its scalability on large-scale graphs is hindered by the intensive message…

Analysis of the topology of a graph, regular or bipartite one, can be done by clustering for regular ones or co-clustering for bipartite ones. The Stochastic Block Model and the Latent Block Model are two models, which are very similar for…

Substitution boxes with thorough cryptographic strengths are essential for the development of strong encryption systems. They are the only portions capable of inducing nonlinearity in symmetric encryption systems. Bijective substitution…

We study the statistical-computational trade-offs for learning with exact invariances (or symmetries) using kernel regression. Traditional methods, such as data augmentation, group averaging, canonicalization, and frame-averaging, either…

We consider the ring I_n of polynomial invariants over weighted graphs on n vertices. Our primary interest is the use of this ring to define and explore algebraic versions of isomorphism problems of graphs, such as Ulam's reconstruction…

The graph contrastive learning (GCL) framework has gained remarkable achievements in graph representation learning. However, similar to graph neural networks (GNNs), GCL models are susceptible to graph structural attacks. As an unsupervised…

Sharding is the prevalent approach to breaking the trilemma of simultaneously achieving decentralization, security, and scalability in traditional blockchain systems, which are implemented as replicated state machines relying on atomic…