Related papers: Designing Universal Causal Deep Learning Models: T…

The challenge of approximating functions in infinite-dimensional spaces from finite samples is widely regarded as formidable. We delve into the challenging problem of the numerical approximation of Sobolev-smooth functions defined on…

We propose a manifold matching approach to generative models which includes a distribution generator (or data generator) and a metric generator. In our framework, we view the real data set as some manifold embedded in a high-dimensional…

Geometry-aware optimizers such as Newton and natural gradient can improve conditioning in deep learning, but scalable variants such as K-FAC, Shampoo, and related preconditioners usually impose structural approximations early, often…

We consider conceptual issues of deep learning (DL) for metric detectors using test particle geodesics in curved spacetimes. Advantages of DL metric detectors are emphasized from a view point of general coordinate transformations. Two given…

Most design methods contain a forward framework, asking for primary specifications of a building to generate an output or assess its performance. However, architects urge for specific objectives though uncertain of the proper design…

Many geometric optimization problems can be reduced to finding points in space (centers) minimizing an objective function which continuously depends on the distances from the centers to given input points. Examples are $k$-Means, Geometric…

Deep Neural Networks achieve state-of-the-art results in many different problem settings by exploiting vast amounts of training data. However, collecting, storing and - in the case of supervised learning - labelling the data is expensive…

Deep learning (DL) creates impactful advances following a virtuous recipe: model architecture search, creating large training data sets, and scaling computation. It is widely believed that growing training sets and models should improve…

In comparison to classical shallow representation learning techniques, deep neural networks have achieved superior performance in nearly every application benchmark. But despite their clear empirical advantages, it is still not well…

Structure-based drug design uses three-dimensional geometric information of macromolecules, such as proteins or nucleic acids, to identify suitable ligands. Geometric deep learning, an emerging concept of neural-network-based machine…

The generalization mystery in deep learning is the following: Why do over-parameterized neural networks trained with gradient descent (GD) generalize well on real datasets even though they are capable of fitting random datasets of…

Current continuous generative models (e.g., Diffusion Models, Flow Matching) implicitly assume that locally consistent causal mechanisms naturally yield globally coherent counterfactuals. In this paper, we prove that this assumption fails…

We present PyTorch Geometric Temporal a deep learning framework combining state-of-the-art machine learning algorithms for neural spatiotemporal signal processing. The main goal of the library is to make temporal geometric deep learning…

Regression with non-Euclidean responses -- e.g., probability distributions, networks, symmetric positive-definite matrices, and compositions -- has become increasingly important in modern applications. In this paper, we propose deep…

Why do deep neural networks (DNNs) benefit from very high dimensional parameter spaces? Their huge parameter complexities vs stunning performance in practice is all the more intriguing and not explainable using the standard theory of model…

Deep learning (DL) research yields accuracy and product improvements from both model architecture changes and scale: larger data sets and models, and more computation. For hardware design, it is difficult to predict DL model changes.…

Deep kernel learning (DKL) and related techniques aim to combine the representational power of neural networks with the reliable uncertainty estimates of Gaussian processes. One crucial aspect of these models is an expectation that, because…

This paper investigates the foundations of deep learning through insight of geometry, algebra and differential calculus. At is core, artificial intelligence relies on assumption that data and its intrinsic structure can be embedded into…

Depth is widely viewed as a central contributor to the success of deep neural networks, whereas standard neural network approximation theory typically provides guarantees only for the final output and leaves the role of intermediate layers…

Deep learning (DL) shows its prosperity in a wide variety of fields. The development of a DL model is a time-consuming and resource-intensive procedure. Hence, dedicated GPU accelerators have been collectively constructed into a GPU…