Related papers: Discovering Sparse Representations of Lie Groups w…

A study is made of real Lie algebras admitting a hypersymplectic structure, and we provide a method to construct such hypersymplectic Lie algebras. We use this method in order to obtain the classification of all hypersymplectic structures…

We present a new interpretation for reduced density matrices of secondary variables in relativistic systems via an analysis of Wigner's method to construct the irreducible unitary representations of the Poincar\'e group. We argue that the…

Interpretable entity representations (IERs) are sparse embeddings that are "human-readable" in that dimensions correspond to fine-grained entity types and values are predicted probabilities that a given entity is of the corresponding type.…

When the system is linear, why should learning be nonlinear? Linear dynamical systems, the analytical backbone of control theory, signal processing and circuit analysis, have exact closed-form solutions via the state transition matrix. Yet…

Because of the importance of unitarity in quantum physics, work on the representations of the de Sitter group has focussed on the unitary case, which necessarily means infinite dimensional matrices for this non-compact group. Here we…

We show that irreducible unitary representations of nilpotent super Lie groups can be obtained by induction from a distinguished class of sub super Lie groups. These sub super Lie groups are natural analogues of polarizing subgroups that…

Disentangled representation learning aims to uncover latent variables underlying the observed data, and generally speaking, rather strong assumptions are needed to ensure identifiability. Some approaches rely on sufficient changes on the…

We describe a systematic method to construct arbitrary highest-weight modules, including arbitrary finite-dimensional representations, for any finite dimensional simple Lie algebra $\mathfrak{g}$. The Lie algebra generators are represented…

We use character theory of finite groups of Lie type to establish new results on representation varieties of Fuchsian groups, and also on probabilistic generation of groups of Lie type.

Transformers can learn to perform numerical computations from examples only. I study nine problems of linear algebra, from basic matrix operations to eigenvalue decomposition and inversion, and introduce and discuss four encoding schemes to…

Deep learning models have significantly improved the visual quality and accuracy on compressive sensing recovery. In this paper, we propose an algorithm for signal reconstruction from compressed measurements with image priors captured by a…

We describe a method for fast approximation of sparse coding. The input space is subdivided by a binary decision tree, and we simultaneously learn a dictionary and assignment of allowed dictionary elements for each leaf of the tree. We…

We propose the fundamental and two dimensional representation of the Lorentz groups on a (3+1)-dimensional hypercubic lattice, from which representations of higher dimensions can be constructed. For the unitary representation of the…

This paper explores a fully unsupervised deep learning approach for computing distance-preserving maps that generate low-dimensional embeddings for a certain class of manifolds. We use the Siamese configuration to train a neural network to…

Sparse modelling or model selection with categorical data is challenging even for a moderate number of variables, because one parameter is roughly needed to encode one category or level. The Group Lasso is a well known efficient algorithm…

This paper introduces the Reed Muller Sieve, a deterministic measurement matrix for compressed sensing. The columns of this matrix are obtained by exponentiating codewords in the quaternary second order Reed Muller code of length $N$. For…

Employing equivariance in neural networks leads to greater parameter efficiency and improved generalization performance through the encoding of domain knowledge in the architecture; however, the majority of existing approaches require an a…

Understanding the internal representations of large language models (LLMs) remains a central challenge for interpretability research. Sparse autoencoders (SAEs) offer a promising solution by decomposing activations into interpretable…

Symbolic regression is a machine learning technique that can learn the governing formulas of data and thus has the potential to transform scientific discovery. However, symbolic regression is still limited in the complexity and…

Algebraic characterization of logic programs has received increasing attention in recent years. Researchers attempt to exploit connections between linear algebraic computation and symbolic computation in order to perform logical inference…