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Neural networks have demonstrated a wide range of successes, but their ``black box" nature raises concerns about transparency and reliability. Previous research on ReLU networks has sought to unwrap these networks into linear models based…

We introduce a novel generative framework for functions by integrating Implicit Neural Representations (INRs) and Transformer-based hypernetworks into latent variable models. Unlike prior approaches that rely on MLP-based hypernetworks with…

With the rapid discovery of emergent phenomena in deep learning and large language models, understanding their cause has become an urgent need. Here, we propose a rigorous entropic-force theory for understanding the learning dynamics of…

Learning representations of data is an important problem in statistics and machine learning. While the origin of learning representations can be traced back to factor analysis and multidimensional scaling in statistics, it has become a…

Within the last decade, neural network based predictors have demonstrated impressive - and at times super-human - capabilities. This performance is often paid for with an intransparent prediction process and thus has sparked numerous…

Why does Deep Learning work? What representations does it capture? How do higher-order representations emerge? We study these questions from the perspective of group theory, thereby opening a new approach towards a theory of Deep learning.…

Recently, continuous representation methods emerge as novel paradigms that characterize the intrinsic structures of real-world data through function representations that map positional coordinates to their corresponding values in the…

Electromagnetic inverse scattering problems (ISPs) aim to retrieve permittivities of dielectric scatterers from the scattering measurement. It is often highly nonlinear, caus-ing the problem to be very difficult to solve. To alleviate the…

Graph Neural Networks (GNNs) are a popular approach for predicting graph structured data. As GNNs tightly entangle the input graph into the neural network structure, common explainable AI approaches are not applicable. To a large extent,…

Growing concerns over the lack of transparency in AI, particularly in high-stakes fields like healthcare and finance, drive the need for explainable and trustworthy systems. While Large Language Models (LLMs) perform exceptionally well in…

In this work we revisit the most fundamental building block in deep learning, the multi-layer perceptron (MLP), and study the limits of its performance on vision tasks. Empirical insights into MLPs are important for multiple reasons. (1)…

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…

Linear Programs (LPs) have been one of the building blocks in machine learning and have championed recent strides in differentiable optimizers for learning systems. While there exist solvers for even high-dimensional LPs, understanding said…

The transparent formulation of explanation methods is essential for elucidating the predictions of neural networks, which are typically black-box models. Layer-wise Relevance Propagation (LRP) is a well-established method that transparently…

We propose a new class of deep reinforcement learning (RL) algorithms that model latent representations in hyperbolic space. Sequential decision-making requires reasoning about the possible future consequences of current behavior.…

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…

Deep learning has revolutionized artificial intelligence (AI), achieving remarkable progress in fields such as computer vision, speech recognition, and natural language processing. Moreover, the recent success of large language models…

Real-world information networks are increasingly occurring across various disciplines including online social networks and citation networks. These network data are generally characterized by sparseness, nonlinearity and heterogeneity…

Recent techniques that integrate \emph{solver layers} into Deep Neural Networks (DNNs) have shown promise in bridging a long-standing gap between inductive learning and symbolic reasoning techniques. In this paper we present a set of…

To accelerate materials discovery using self-driving labs (SDLs), we present a machine learning pipeline that predicts the electrical conductivity of doped conjugated polymers using rapid, non-destructive optical spectroscopy. Our approach…