The paper introduces COMET, a novel PLS-SVD framework, to analyze the audio-text modality gap in CLAP models, showing that shared concepts are captured by a small subset of axes, and proposes a spectr…

This paper proves an inverse-polynomial spectral-gap bound for the lazy swap chain on binary matrices with prescribed row and column sums, which is a standard sampler for fixed-margin null models.

Low-Pass Flow Matching introduces a spectral bias into the flow matching process, allowing it to better model natural data by transitioning from a standard source spectrum to a frequency-decaying bias…

The paper introduces a Jacobian-based spectral audit to evaluate neural operators, demonstrating that standard prediction error metrics fail to capture crucial local dynamical structures and operator…

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

This paper derives the gradient of the Wolkowicz-Styan upper bound on the maximum eigenvalue of the cross-entropy loss Hessian in three-layer NNs to characterize directions leading to flat minima and…

This paper proposes a method for handling overparameterized linear regression using early-stopped negative-shifted gradient descent, which allows for smooth filters and mixed-sign capabilities.

This paper develops a unified spectral analysis framework to explain how knowledge transfer (KT) works across different machine learning regimes, such as Knowledge Distillation and Weak-to-Strong gene…

This paper presents two quantum algorithms for solving linear systems with normalized solution $|x angle$ to accuracy $ε$, independent of the condition number $κ$.

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 provides bounds on the difference between the annihilation number and independence number of a finite simple graph, and proves these bounds for various types of graphs.

This paper derives a method to predict and mitigate intruder dimensions caused by LoRA fine-tuning in deep learning models, improving performance and reducing forgetting.

This paper introduces a structural theorem for the sparsifiability of real-valued codes, which generalizes both combinatorial and continuous notions of sparsification.

The paper analyzes the algorithmic complexity of finding collisions in single-layer binary neural networks, establishing that the collision resistance depends critically on the activation function's t…