Related papers: Spectral Geometry for Deep Learning: Compression a…

Random Matrix Theory (RMT) is capable of making predictions for the spectral fluctuations of a physical system only after removing the influence of the level density by unfolding the spectra. When the level density is known, unfolding is…

Neural models learn representations of high-dimensional data on low-dimensional manifolds. Multiple factors, including stochasticities in the training process, model architectures, and additional inductive biases, may induce different…

Hyperspectral images are crucial for many research works. Spectral super-resolution (SSR) is a method used to obtain high spatial resolution (HR) hyperspectral images from HR multispectral images. Traditional SSR methods include…

Large Language Models (LLMs) frequently generate plausible but non-factual content, a phenomenon known as hallucination. While existing detection methods typically rely on computationally expensive sampling-based consistency checks or…

One of the fundamental problems within the field of machine learning is dimensionality reduction. Dimensionality reduction methods make it possible to combat the so-called curse of dimensionality, visualize high-dimensional data and, in…

Spectral dimensionality reduction algorithms are widely used in numerous domains, including for recognition, segmentation, tracking and visualization. However, despite their popularity, these algorithms suffer from a major limitation known…

There is a large variety of machine learning methodologies that are based on the extraction of spectral geometric information from data. However, the implementations of many of these methods often depend on traditional eigensolvers, which…

Deep Neural Networks are powerful tools for understanding complex patterns and making decisions. However, their black-box nature impedes a complete understanding of their inner workings. Saliency-Guided Training (SGT) methods try to…

Large Language Models (LLMs) are increasingly deployed in high-stakes financial domains, yet they suffer from specific, reproducible hallucinations when performing arithmetic operations. Current mitigation strategies often treat the model…

Retrieval-Augmented Generation (RAG) models are designed to incorporate external knowledge, reducing hallucinations caused by insufficient parametric (internal) knowledge. However, even with accurate and relevant retrieved content, RAG…

Retrieval-Augmented Generation (RAG) models frequently encounter hallucination phenomena when integrating external information with internal parametric knowledge. Empirical studies demonstrate that the disequilibrium between external…

Large Reasoning Models (LRMs) have shown impressive capabilities in multi-step reasoning tasks. However, alongside these successes, a more deceptive form of model error has emerged--Reasoning Hallucination--where logically coherent but…

In this paper, we propose a spectral framework that embeds 1D and 2D quasiperiodic Helmholtz eigenvalue problems into higher-dimensional (2D and 4D) periodic spaces via the projection method \cite{jiang2014numerical, jiang2024numerical}. To…

Retrieval-augmented generation (RAG) aims to mitigate the hallucination of Large Language Models (LLMs) by retrieving and incorporating relevant external knowledge into the generation process. However, the external knowledge may contain…

Anomaly detection in massive networks has numerous theoretical and computational challenges, especially as the behavior to be detected becomes small in comparison to the larger network. This presentation focuses on recent results in three…

Supervised topic models simultaneously model the latent topic structure of large collections of documents and a response variable associated with each document. Existing inference methods are based on variational approximation or Monte…

This research work delves into the manifestation of hallucination within Large Language Models (LLMs) and its consequential impacts on applications within the domain of mental health. The primary objective is to discern effective strategies…

We demonstrate the use of deep learning for fast spectral deconstruction of speckle patterns. The artificial neural network can be effectively trained using numerically constructed multispectral datasets taken from a measured spectral…

Spectral methods are popular in detecting global structures in the given data that can be represented as a matrix. However when the data matrix is sparse or noisy, classic spectral methods usually fail to work, due to localization of…

Self-supervised learning (SSL) as an effective paradigm of representation learning has achieved tremendous success on various curated datasets in diverse scenarios. Nevertheless, when facing the long-tailed distribution in real-world…