Related papers: Learning with the $p$-adics
Geometric algebra is an optimal frame work for calculating with vectors. The geometric algebra of a space includes elements that represent all the its subspaces (lines, planes, volumes, ...). Conformal geometric algebra expands this…
Learning expressive probabilistic models correctly describing the data is a ubiquitous problem in machine learning. A popular approach for solving it is mapping the observations into a representation space with a simple joint distribution,…
System identification has greatly benefited from deep learning techniques, particularly for modeling complex, nonlinear dynamical systems with partially unknown physics where traditional approaches may not be feasible. However, deep…
Based on the property that solving the system of linear matrix equations via the column space and the row space projections boils down to an approximation in the least squares error sense, a formulation for learning the weight matrices of…
While neural networks are good at learning unspecified functions from training samples, they cannot be directly implemented in hardware and are often not interpretable or formally verifiable. On the other hand, logic circuits are…
We introduce the Abductive Rule Learner with Context-awareness (ARLC), a model that solves abstract reasoning tasks based on Learn-VRF. ARLC features a novel and more broadly applicable training objective for abductive reasoning, resulting…
We introduce Residue Hyperdimensional Computing, a computing framework that unifies residue number systems with an algebra defined over random, high-dimensional vectors. We show how residue numbers can be represented as high-dimensional…
Deep learning models are often considered black boxes due to their complex hierarchical transformations. Identifying suitable architectures is crucial for maximizing predictive performance with limited data. Understanding the geometric…
Parametrized Quantum Circuits (PQCs) enable a novel method for machine learning (ML). However, from a computational point of view they present a challenge to existing eXplainable AI (xAI) methods. On the one hand, measurements on quantum…
We propose a novel probabilistic dimensionality reduction framework that can naturally integrate the generative model and the locality information of data. Based on this framework, we present a new model, which is able to learn a smooth…
In most real-world applications of artificial intelligence, the distributions of the data and the goals of the learners tend to change over time. The Probably Approximately Correct (PAC) learning framework, which underpins most machine…
This paper is concerned with a covering problem of Euclidean space by a particular arrangement of cones that are not necessarily full and are allowed to overlap. The problem provides an equivalent geometric reformulation of the solvability…
Deep learning has achieved great success in modeling dynamical systems, providing data-driven simulators to predict complex phenomena, even without known governing equations. However, existing models have two major limitations: their narrow…
We describe an essential improvement of our recent algorithm for computing cohomology of Lie (super)algebra based on partition of the whole cochain complex into minimal subcomplexes. We replace the arithmetic of rational numbers or integers…
Quantum computers hold great promise to enhance machine learning, but their current qubit counts restrict the realisation of this promise. In an attempt to placate this limitation techniques can be applied for evaluating a quantum circuit…
We propose a geometric framework for learning meta-embeddings of words from different embedding sources. Our framework transforms the embeddings into a common latent space, where, for example, simple averaging of different embeddings (of a…
In this paper, we present a new algorithm for semi-supervised representation learning. In this algorithm, we first find a vector representation for the labels of the data points based on their local positions in the space. Then, we map the…
Non-Euclidean constraints are inherent in many kinds of data in computer vision and machine learning, typically as a result of specific invariance requirements that need to be respected during high-level inference. Often, these geometric…
Neural Radiance Fields (NeRFs) have emerged as a groundbreaking paradigm for representing 3D objects and scenes by encoding shape and appearance information into the weights of a neural network. Recent studies have demonstrated that these…
In this paper, we investigate abstract homomorphism from the special linear group over complete discrete valuation rings with finite residue field, such as the ring of p-adic integers, into the general linear group over the reals. We find…