Related papers: Versor: A Geometric Sequence Architecture
To accommodate structured approaches of neural computation, we propose a class of recurrent neural networks for indexing and storing sequences of symbols or analog data vectors. These networks with randomized input weights and orthogonal…
Modern computer vision architectures, from CNNs to Transformers, predominantly rely on the stacking of heuristic modules: spatial mixers (Attention/Conv) followed by channel mixers (FFNs). In this work, we challenge this paradigm by…
Embedding a web-scale information network into a low-dimensional vector space facilitates tasks such as link prediction, classification, and visualization. Past research has addressed the problem of extracting such embeddings by adopting…
We propose two tiers of modifications to FPGA logic cell architecture to deliver a variety of performance and utilization benefits with only minor area overheads. In the irst tier, we augment existing commercial logic cell datapaths with a…
This is an introduction to geometric algebra, an alternative to traditional vector algebra that expands on it in two ways: 1. In addition to scalars and vectors, it defines new objects representing subspaces of any dimension. 2. It defines…
Making accurate predictions of chaotic time series is a complex challenge. Reservoir computing, a neuromorphic-inspired approach, has emerged as a powerful tool for this task. It exploits the memory and nonlinearity of dynamical systems…
Vector-symbolic architectures (VSAs) provide methods for computing which are highly flexible and carry unique advantages. Concepts in VSAs are represented by 'symbols,' long vectors of values which utilize properties of high-dimensional…
Geometrical interpretations of deep learning models offer insightful perspectives into their underlying mathematical structures. In this work, we introduce a novel approach that leverages differential geometry, particularly concepts from…
There is often variation in the shape and size of input data used for deep learning. In many cases, such data can be represented using tensors with non-uniform shapes, or ragged tensors. Due to limited and non-portable support for efficient…
Recent advances in feature learning have shown that self-supervised vision foundation models can capture semantic correspondences but often lack awareness of underlying 3D geometry. GECO addresses this gap by producing geometrically…
These are lecture notes for a course on the theory of Clifford algebras, with special emphasis on their wide range of applications in mathematics and physics. Clifford algebra is introduced both through a conventional tensor algebra…
Vector algebra is a powerful and needful tool for Physics but unfortunately, due to lack of mathematical skills, it becomes misleading for first undergraduate courses of science and engineering studies. Standard vector identities are…
Statistical learning methods show great promise in providing an accurate prediction of materials and molecular properties, while minimizing the need for computationally demanding electronic structure calculations. The accuracy and…
This paper describes a novel algorithmic framework to minimize a finite-sum of functions available over a network of nodes. The proposed framework, that we call~\GTVR, is stochastic and decentralized, and thus is particularly suitable for…
Many quantities we are interested in predicting are geometric tensors; we refer to this class of problems as geometric prediction. Attempts to perform geometric prediction in real-world scenarios have been limited to approximating them…
Since context modeling is critical for estimating depth from a single image, researchers put tremendous effort into obtaining global context. Many global manipulations are designed for traditional CNN-based architectures to overcome the…
While the Clifford (geometric) algebra Fourier Transform (CFT) is global, we introduce here the local Clifford (geometric) algebra (GA) wavelet concept. We show how for $n=2,3 (\mod 4)$ continuous $Cl_n$-valued admissible wavelets can be…
Word embedding is a useful approach to capture co-occurrence structures in large text corpora. However, in addition to the text data itself, we often have additional covariates associated with individual corpus documents---e.g. the…
Vector space models for symbolic processing that encode symbols by random vectors have been proposed in cognitive science and connectionist communities under the names Vector Symbolic Architecture (VSA), and, synonymously, Hyperdimensional…
Hyperdimensional computing (HDC), also known as vector symbolic architectures (VSA), is a computing framework used within artificial intelligence and cognitive computing that operates with distributed vector representations of large fixed…