Related papers: Geometric Generalization of Neural Operators from …
This is a master's thesis concerning the theoretical ideas of geometric deep learning. Geometric deep learning aims to provide a structured characterization of neural network architectures, specifically focused on the ideas of invariance…
It is by now well-established that modern over-parameterized models seem to elude the bias-variance tradeoff and generalize well despite overfitting noise. Many recent works attempt to analyze this phenomenon in the relatively tractable…
Federated learning over graph-structured data exposes a fundamental mismatch between standard aggregation mechanisms and the operator nature of graph neural networks (GNNs). While federated optimization treats model parameters as elements…
We propose a method for the approximation of high- or even infinite-dimensional feature vectors, which play an important role in supervised learning. The goal is to reduce the size of the training data, resulting in lower storage…
We present a mathematical structure which unifies mathematical structures of general relativity and quantum mechanics. It consists of the noncommutative algebra of compactly supported, complex valued functions ${\mathcal A}$, with…
Neural operators have emerged as promising surrogate models for solving partial differential equations (PDEs), but struggle to generalise beyond training distributions and are often constrained to a fixed temporal discretisation. This work…
Recently, we have witnessed the great success of the generalist model in natural language processing. The generalist model is a general framework trained with massive data and is able to process various downstream tasks simultaneously.…
Random feature approximation is arguably one of the most widely used techniques for kernel methods in large-scale learning algorithms. In this work, we analyze the generalization properties of random feature methods, extending previous…
Kernel methods are versatile tools for function approximation and surrogate modeling. In particular, greedy techniques offer computational efficiency and reliability through inherent sparsity and provable convergence. Inspired by the…
Despite classical statistical theory predicting severe overfitting, modern massively overparameterized neural networks still generalize well. This unexpected property is attributed to the network's so-called implicit bias, which describes…
Teacher-student models provide a framework in which the typical-case performance of high-dimensional supervised learning can be described in closed form. The assumptions of Gaussian i.i.d. input data underlying the canonical teacher-student…
Effectively predicting molecular interactions has the potential to accelerate molecular dynamics by multiple orders of magnitude and thus revolutionize chemical simulations. Graph neural networks (GNNs) have recently shown great successes…
Quantum kernel methods offer significant theoretical benefits by rendering classically inseparable features separable in quantum space. Yet, the practical application of Quantum Machine Learning (QML), currently constrained by the…
Advances in experimental neuroscience have transformed our ability to explore the structure and function of neural circuits. At the same time, advances in machine learning have unleashed the remarkable computational power of artificial…
Gaussian Process (GP) regression is a powerful nonparametric Bayesian framework, but its performance depends critically on the choice of covariance kernel. Selecting an appropriate kernel is therefore central to model quality, yet remains…
Deep sequence models are said to store atomic facts predominantly in the form of associative memory: a brute-force lookup of co-occurring entities. We identify a dramatically different form of storage of atomic facts that we term as…
Bias formation in deep neural networks (DNNs) remains a critical yet poorly understood challenge, influencing both fairness and reliability in artificial intelligence systems. Inspired by the human visual system, which decouples object…
The paper uses statistical and differential geometric motivation to acquire prior information about the learning capability of an artificial neural network on a given dataset. The paper considers a broad class of neural networks with…
Parametric approaches to Learning, such as deep learning (DL), are highly popular in nonlinear regression, in spite of their extremely difficult training with their increasing complexity (e.g. number of layers in DL). In this paper, we…
The correlation matrix is a central representation of functional brain networks in neuroimaging. Traditional analyses often treat pairwise interactions independently in a Euclidean setting, overlooking the intrinsic geometry of correlation…