Related papers: Lie Algebra Canonicalization: Equivariant Neural O…
Left invariant affine structures in a Lie group $G$ are in one-to-one correspondence with left-symmetric algebras over its Lie algebra $\mathfrak g=T_eG$ (``over'' means that the commutator $[x,y]=xy-yx$ coincides with the Lie bracket;…
Large language models with billions of parameters are often over-provisioned: many layers contribute little unique information yet dominate the memory and energy footprint during inference. We present LieQ Layer-wise information…
This article explores the convergence of connectionist and symbolic artificial intelligence (AI), from historical debates to contemporary advancements. Traditionally considered distinct paradigms, connectionist AI focuses on neural…
Equivariant neural networks are designed to respect symmetries through their architecture, boosting generalization and sample efficiency when those symmetries are present in the data distribution. Real-world data, however, often departs…
Conventional and deep learning-based methods have shown great potential in the medical imaging domain, as means for deriving diagnostic, prognostic, and predictive biomarkers, and by contributing to precision medicine. However, these…
Entity alignment (EA) aims at identifying equivalent entity pairs across different knowledge graphs (KGs) that refer to the same real-world identity. To circumvent the shortage of seed alignments provided for training, recent EA models…
Kernel canonical correlation analysis (KCCA) is a nonlinear multi-view representation learning technique with broad applicability in statistics and machine learning. Although there is a closed-form solution for the KCCA objective, it…
Recent advancements in neural network quantisation have yielded remarkable outcomes, with three-bit networks reaching state-of-the-art full-precision accuracy in complex tasks. These achievements present valuable opportunities for…
This paper considers the problem of canonical-correlation analysis (CCA) (Hotelling, 1936) and, more broadly, the generalized eigenvector problem for a pair of symmetric matrices. These are two fundamental problems in data analysis and…
Variational quantum machine learning is an extensively studied application of near-term quantum computers. The success of variational quantum learning models crucially depends on finding a suitable parametrization of the model that encodes…
Let g be a Lie bialgebra and let V be a finite-dimensional g-module. We study deformations of the symmetric algebra of V which are equivariant with respect to an action of the quantized enveloping algebra of g. In particular we investigate…
Solving systems of ordinary differential equations (ODEs) is essential when it comes to understanding the behavior of dynamical systems. Yet, automated solving remains challenging, in particular for nonlinear systems. Computer algebra…
We study the problem of matrix Lie algebra conjugacy. Lie algebras arise centrally in areas as diverse as differential equations, particle physics, group theory, and the Mulmuley--Sohoni Geometric Complexity Theory program. A matrix Lie…
Low-precision quantization is recognized for its efficacy in neural network optimization. Our analysis reveals that non-quantized elementwise operations which are prevalent in layers such as parameterized activation functions, batch…
We present a method for associating labeled directed graphs to finite-dimensional Lie algebras, thereby enabling rapid identification of key structural algebraic features. To formalize this approach, we introduce the concept of…
Canonical Correlation Analysis (CCA) models are powerful for studying the associations between two sets of variables. The canonically correlated representations, termed \textit{canonical variates} are widely used in unsupervised learning to…
The Lie linearizability criteria are extended to complex functions for complex ordinary differential equations. The linearizability of complex ordinary differential equations is used to study the linearizability of corresponding systems of…
As a crucial step toward real-world learning scenarios with changing environments, dataset shift theory and invariant representation learning algorithm have been extensively studied to relax the identical distribution assumption in…
In this paper we address the problem of matching sets of vectors embedded in the same input space. We propose an approach which is motivated by canonical correlation analysis (CCA), a statistical technique which has proven successful in a…
Learned image compression (LIC) methods often employ symmetrical encoder and decoder architectures, evitably increasing decoding time. However, practical scenarios demand an asymmetric design, where the decoder requires low complexity to…