Related papers: Versor: A Geometric Sequence Architecture

Intrinsic graph convolution operators with differentiable kernel functions play a crucial role in analyzing 3D shape meshes. In this paper, we present a fast and efficient intrinsic mesh convolution operator that does not rely on the…

Transformer models are computationally costly on long sequences since regular attention has quadratic $O(n^2)$ time complexity. We introduce Wavelet-Enhanced Random Spectral Attention (WERSA), a novel mechanism of linear $O(n)$ time…

Tensor completion is a natural higher-order generalization of matrix completion where the goal is to recover a low-rank tensor from sparse observations of its entries. Existing algorithms are either heuristic without provable guarantees,…

There has been recent interest in novel Clifford geometric invariants of linear transformations. This motivates the investigation of such invariants for a certain type of geometric transformation of interest in the context of root systems,…

Geometric algebra was initiated by W.K. Clifford over 130 years ago. It unifies all branches of physics, and has found rich applications in robotics, signal processing, ray tracing, virtual reality, computer vision, vector field processing,…

The success of building a high-resolution velocity model using machine learning is hampered by generalization limitations that often limit the success of the approach on field data. This is especially true when relying on neural operators…

Vector Symbolic Architectures (VSAs) are a powerful framework for representing compositional reasoning. They lend themselves to neural-network implementations, allowing us to create neural networks that can perform cognitive functions, like…

The precise simulation of particle transport through detectors remains a key element for the successful interpretation of high energy physics results. However, Monte Carlo based simulation is extremely demanding in terms of computing…

Clifford algebras have broad applications in science and engineering. The use of Clifford algebras can be further promoted in these fields by availability of computational tools that automate tedious routine calculations. We offer an…

We introduce SCORES, a recursive neural network for shape composition. Our network takes as input sets of parts from two or more source 3D shapes and a rough initial placement of the parts. It outputs an optimized part structure for the…

Convolutional Neural Networks (CNNs) are widely used in deep learning applications, e.g. visual systems, robotics etc. However, existing software solutions are not efficient. Therefore, many hardware accelerators have been proposed…

Graph Neural Networks (GNNs) are de facto solutions to structural data learning. However, it is susceptible to low-quality and unreliable structure, which has been a norm rather than an exception in real-world graphs. Existing graph…

Historically, there have been many attempts to produce an appropriate mathematical formalism for modeling the nature of physical space, such as Euclid's geometry, Descartes' system of Cartesian coordinates, the Argand plane, Hamilton's…

Tensor algebra is widely used in many applications, such as scientific computing, machine learning, and data analytics. The tensors represented real-world data are usually large and sparse. There are tens of storage formats designed for…

3D visual grounding aims to identify the target object within a 3D point cloud scene referred to by a natural language description. Previous works usually require significant data relating to point color and their descriptions to exploit…

Vector Symbolic Architectures (VSAs) are high-dimensional vector representations of objects (eg., words, image parts), relations (eg., sentence structures), and sequences for use with machine learning algorithms. They consist of a vector…

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…

Sequential Recommendation is a widely studied paradigm for learning users' dynamic interests from historical interactions for predicting the next potential item. Although lots of research work has achieved remarkable progress, they are…

Use of generative models and deep learning for physics-based systems is currently dominated by the task of emulation. However, the remarkable flexibility offered by data-driven architectures would suggest to extend this representation to…

Temporal Graph Neural Networks (TGNNs) are powerful models to capture temporal, structural, and contextual information on temporal graphs. The generated temporal node embeddings outperform other methods in many downstream tasks. Real-world…