Related papers: Spectral Geometry for Deep Learning: Compression a…
This thesis addresses two persistent and closely related challenges in modern deep learning, reliability and efficiency, through a unified framework grounded in Spectral Geometry and Random Matrix Theory (RMT). As deep networks and large…
Large language models (LLMs) offer broad utility but remain prone to hallucination and out-of-distribution (OOD) errors. We propose EigenTrack, an interpretable real-time detector that uses the spectral geometry of hidden activations, a…
Large language models achieve impressive results but distinguishing factual reasoning from hallucinations remains challenging. We propose a spectral analysis framework that models transformer layers as dynamic graphs induced by attention,…
Training loss and throughput can hide distinct internal representation in language-model training. To examine these hidden mechanics, we use spectral measurements as practical and operational diagnostics. Using a controlled family of…
Large deep learning models such as BERT and ResNet achieve state-of-the-art performance but are costly to deploy at the edge due to their size and compute demands. We present RMT-KD, a compression method that leverages Random Matrix Theory…
Detecting hallucinations in large language models (LLMs) remains a fundamental challenge for their trustworthy deployment. Going beyond basic uncertainty-driven hallucination detection frameworks, we propose a simple yet powerful method…
Large Language Models (LLMs) often produce fluent yet factually incorrect statements-a phenomenon known as hallucination-posing serious risks in high-stakes domains. We present Layer-wise Semantic Dynamics (LSD), a geometric framework for…
Diagrammatic techniques to compute perturbatively the spectral properties of Euclidean Random Matrices in the high-density regime are introduced and discussed in detail. Such techniques are developed in two alternative and very different…
The representations of neural networks are often compared to those of biological systems by performing regression between the neural network responses and those measured from biological systems. Many different state-of-the-art deep neural…
We consider increasingly complex models of matrix denoising and dictionary learning in the Bayes-optimal setting, in the challenging regime where the matrices to infer have a rank growing linearly with the system size. This is in contrast…
Modern Machine Learning (ML) and Deep Neural Networks (DNNs) often operate on high-dimensional data and rely on overparameterized models, where classical low-dimensional intuitions break down. In particular, the proportional regime where…
We present an approach for analyzing grouping information contained within a neural network's activations, permitting extraction of spatial layout and semantic segmentation from the behavior of large pre-trained vision models. Unlike prior…
The goal of this thesis is to improve our understanding of the internal mechanisms by which deep artificial neural networks create meaningful representations and are able to generalize. We focus on the challenge of characterizing the…
Large language models (LLMs) have demonstrated remarkable capabilities across various domains, although their susceptibility to hallucination poses significant challenges for their deployment in critical areas such as healthcare. To address…
Hidden Markov models (HMMs) are widely used statistical models for modeling sequential data. The parameter estimation for HMMs from time series data is an important learning problem. The predominant methods for parameter estimation are…
Inverse Tone Mapping (ITM) methods attempt to reconstruct High Dynamic Range (HDR) information from Low Dynamic Range (LDR) image content. The dynamic range of well-exposed areas must be expanded and any missing information due to…
Deep neural networks have exhibited remarkable performance in image super-resolution (SR) tasks by learning a mapping from low-resolution (LR) images to high-resolution (HR) images. However, the SR problem is typically an ill-posed problem…
Compression techniques for deep neural network models are becoming very important for the efficient execution of high-performance deep learning systems on edge-computing devices. The concept of model compression is also important for…
Deep neural networks have achieved strong performance in image classification tasks due to their ability to learn complex patterns from high-dimensional data. However, their large computational and memory requirements often limit deployment…
In this paper, we focus on fraud detection on a signed graph with only a small set of labeled training data. We propose a novel framework that combines deep neural networks and spectral graph analysis. In particular, we use the node…