Related papers: Euclidean, Projective, Conformal: Choosing a Geome…

With the growth of machine learning algorithms with geometry primitives, a high-efficiency library with differentiable geometric operators are desired. We present an optimized Differentiable Geometry Algorithm Library (DGAL) loaded with…

Transformer models have recently gained popularity in graph representation learning as they have the potential to learn complex relationships beyond the ones captured by regular graph neural networks. The main research question is how to…

We propose models of quantum neural networks through Clifford algebras, which are capable of capturing geometric features of systems and to produce entanglement. Due to their representations in terms of Pauli matrices, the Clifford algebras…

As transformers are equivariant to the permutation of input tokens, encoding the positional information of tokens is necessary for many tasks. However, since existing positional encoding schemes have been initially designed for NLP tasks,…

We introduce the Graded Transformer framework, a new class of sequence models that embeds algebraic inductive biases through grading transformations on vector spaces. Extending Graded Neural Networks (GNNs), we propose two architectures:…

We introduce randomized algorithms to Clifford's Geometric Algebra, generalizing randomized linear algebra to hypercomplex vector spaces. This novel approach has many implications in machine learning, including training neural networks to…

Can transformers generalize efficiently on problems that require dealing with examples with different levels of difficulty? We introduce a new task tailored to assess generalization over different complexities and present results that…

Graph foundation models represent a transformative paradigm for learning transferable representations across diverse graph domains. Recent methods leverage large language models to unify graph and text modalities into a shared…

This paper concentrates on the homogeneous (conformal) model of Euclidean space (Horosphere) with subspaces that intuitively correspond to Euclidean geometric objects in three dimensions. Mathematical details of the construction and…

Transformers are effective and efficient at modeling complex relationships and learning patterns from structured data in many applications. The main aim of this paper is to propose and design NLAFormer, which is a transformer-based…

Despite the wide variety of input types in machine learning, this diversity is often not fully reflected in their representations or model architectures, leading to inefficiencies throughout a model's lifecycle. This paper introduces an…

Geometric algebra is a mathematical structure that is inherent in any metric vector space, and defined by the requirement that the metric tensor is given by the scalar part of the product of vectors. It provides a natural framework in which…

In this work, we introduce the Geometry-Aware Large Reconstruction Model (GeoLRM), an approach which can predict high-quality assets with 512k Gaussians and 21 input images in only 11 GB GPU memory. Previous works neglect the inherent…

Graph Transformers (GTs) have shown strong empirical performance, yet current architectures vary widely in their use of attention mechanisms, positional embeddings (PEs), and expressivity. Existing expressivity results are often tied to…

We prove that the set of non-degenerate second order maximally superintegrable systems in the complex Euclidean plane carries a natural structure of a projective variety, equipped with a linear isometry group action. This is done by…

Quadratic surfaces gain more and more attention among the Geometric Algebra community and some frameworks were proposed in order to represent, transform, and intersect these quadratic surfaces. As far as the authors know, none of these…

An algebra $\mathcal{A}$ of $n\times n$ complex matrices is said to be \textit{idempotent compressible} if $E\mathcal{A}E$ is an algebra for all idempotents $E\in\mathbb{M}_n(\mathbb{C})$. Analogously, $\mathcal{A}$ is said to be…

Conformal symmetries, i.e.\ coordinate transformations that preserve angles, play a key role in many fields, including physics, mathematics, computer vision and (geometric) machine learning. Here we build a neural network that is…

Transformers have become methods of choice in many applications thanks to their ability to represent complex interactions between elements. However, extending the Transformer architecture to non-sequential data such as molecules and…

We propose a metric learning framework for the construction of invariant geometric functions of planar curves for the Eucledian and Similarity group of transformations. We leverage on the representational power of convolutional neural…