This paper generalizes the connection between graph theory, association schemes, and coding theory to the space of tensors over a finite field, and derives the spectrum of the corresponding graph.

The paper introduces Automatically Differentiable Nonlinear Tensor Networks (ADNTNs) to achieve massive, structured compression of deep neural networks, demonstrating compression ratios up to 77,000x…

This paper presents a method for identifying probabilistic structures from empirical probability tensors using algebraic statistics and Kronecker-stack class of configuration matrices.

This paper connects a generalized notion of tensor rank with multiplicative complexity, enabling control of arithmetic complexity in any constant degree of multilinearity and applications to fine-grai…

This paper introduces and studies the block tensor rank of sum-rank metric codes, showing its additive decomposition and deriving lower bounds.

The paper presents a solution to enable multiple double arithmetic on NVIDIA A100 tensor cores, which are unsuited for branching operations caused by renormalization.

This paper provides explicit error bounds for the infinite-width Gaussian-process limit of random neural networks using tensor programs and quantitative convergence theory in Wasserstein distance.

This paper introduces a robust OR polynomial framework to derive certificates for positive semidefinite matrices across OR constraints, and applies it to acute-free families and multicolor Ramsey numb…

This paper introduces a new way to represent finite posets as subwords of finite words in categories, and characterizes the monic categories that admit this representation.

The paper introduces TN-SHAP-G, a novel framework that uses graph-structured tensor networks to efficiently approximate and compute Shapley values and interaction indices for black-box models, overcom…

The paper investigates applying Riemannian optimization techniques to low-rank matrix parameters for deep learning, but finds that the proposed methods do not conclusively outperform the AdamW baselin…

The paper analyzes low-degree estimation thresholds for recovering hidden signals in planted hypergraphs and tensor PCA, establishing sharp phase transitions and providing polynomial-time recovery alg…

This paper proves that single-vector embeddings require a larger representation size than multi-vector embeddings to approximate certain similarities.

This paper introduces the Distributed Truncated Spectral Transform (DTST) for Fourier Neural Operators (FNOs), achieving significant speedups in distributed computing.

This paper investigates the closeness of singularity for $n imes n$ unimodular matrices, specifically for $(2k+1)$-ary and $(k+1)$-ary cases of $4 imes 4$ nonnegative unimodular matrices.

This paper studies the expressivity of shallow polynomial neural networks with monomial activation functions over finite fields, quantifying it by the cardinality of the neuromanifold and deriving low…