Related papers: Geometric Algebra Transformer
Geometric number systems, obtained by extending the real number system to include new anticommuting square roots of +1 and -1, provide a royal road to higher mathematics by largely sidestepping the tedious languages of tensor analysis and…
Artificial intelligence for scientific discovery has recently generated significant interest within the machine learning and scientific communities, particularly in the domains of chemistry, biology, and material discovery. For these…
We introduce Graphical Algebraic Geometry (GAG), a family of diagrammatic languages extending the Graphical Linear Algebra programme. We construct several languages within this family and prove that they are universal and complete for the…
Recent feed-forward networks have achieved remarkable progress in sparse-view 3D reconstruction by predicting dense point maps directly from RGB images. However, they often suffer from geometric inconsistencies and limited fine-grained…
Neural representations of 3D data have been widely adopted across various applications, particularly in recent work leveraging coordinate-based networks to model scalar or vector fields. However, these approaches face inherent challenges,…
We study the problem of extracting accurate correspondences for point cloud registration. Recent keypoint-free methods have shown great potential through bypassing the detection of repeatable keypoints which is difficult to do especially in…
Classical phasor analysis is fundamentally limited to sinusoidal single-frequency conditions, which poses challenges when working in the presence of harmonics. Furthermore, the conventional solution, which consists of decomposing signals…
Exploiting symmetries and invariance in data is a powerful, yet not fully exploited, way to achieve better generalisation with more efficiency. In this paper, we introduce two graph network architectures that are equivariant to several…
This study introduces geometric algebra to decompose credit system relationships into their projective (correlation-like) and rotational (feedback-spiral) components. We represent economic states as multi-vectors in Clifford algebra, where…
Modeling geospatial tabular data with deep learning has become a promising alternative to traditional statistical and machine learning approaches. However, existing deep learning models often face challenges related to scalability and…
We study the problem of extracting accurate correspondences for point cloud registration. Recent keypoint-free methods bypass the detection of repeatable keypoints which is difficult in low-overlap scenarios, showing great potential in…
While widespread, Transformers lack inductive biases for geometric symmetries common in science and computer vision. Existing equivariant methods often sacrifice the efficiency and flexibility that make Transformers so effective through…
This paper presents a transformative framework for artificial neural networks over graded vector spaces, tailored to model hierarchical and structured data in fields like algebraic geometry and physics. By exploiting the algebraic…
3D GAN inversion aims to achieve high reconstruction fidelity and reasonable 3D geometry simultaneously from a single image input. However, existing 3D GAN inversion methods rely on time-consuming optimization for each individual case. In…
We study the 8 natural GL equivariant geometric realization questions for the space of generalized algebraic curvature tensors. All but one of them is solvable; a non-zero projectively flat Ricci antisymmetric generalized algebraic…
Knowledge graph (KG) embedding aims at embedding entities and relations in a KG into a lowdimensional latent representation space. Existing KG embedding approaches model entities andrelations in a KG by utilizing real-valued ,…
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…
Despite their empirical success, pushing Transformer architectures to extreme depth often leads to a paradoxical failure: representations become increasingly redundant, lose rank, and ultimately collapse. Existing explanations largely…
Geometry problem solving presents a formidable challenge within the NLP community. Existing approaches often rely on models designed for solving math word problems, neglecting the unique characteristics of geometry math problems.…
Graph Transformers (GTs) have demonstrated a strong capability in modeling graph structures by addressing the intrinsic limitations of graph neural networks (GNNs), such as over-smoothing and over-squashing. Recent studies have proposed…