Permutation invariant matrix statistics and computational language tasks

• URL: http://arxiv.org/abs/2202.06829v2
• Date: Tue, 26 Sep 2023 17:29:38 GMT
• Title: Permutation invariant matrix statistics and computational language tasks
• Authors: Manuel Accettulli Huber, Adriana Correia, Sanjaye Ramgoolam, Mehrnoosh Sadrzadeh
• Abstract summary: We introduce a geometry of observable vectors for words, defined by exploiting the graph-theoretic basis for the permutation invariants. We describe successful applications of this unified framework to a number of tasks in computational linguistics.
• Score: 0.7373617024876724
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: The Linguistic Matrix Theory programme introduced by Kartsaklis, Ramgoolam and Sadrzadeh is an approach to the statistics of matrices that are generated in type-driven distributional semantics, based on permutation invariant polynomial functions which are regarded as the key observables encoding the significant statistics. In this paper we generalize the previous results on the approximate Gaussianity of matrix distributions arising from compositional distributional semantics. We also introduce a geometry of observable vectors for words, defined by exploiting the graph-theoretic basis for the permutation invariants and the statistical characteristics of the ensemble of matrices associated with the words. We describe successful applications of this unified framework to a number of tasks in computational linguistics, associated with the distinctions between synonyms, antonyms, hypernyms and hyponyms.

Related papers

• Permutation Equivariant Neural Networks for Symmetric Tensors [0.0]
  We present two different characterisations of all linear permutation equivariant functions between symmetric power spaces of $mathbbRn$. We show that these functions are highly efficient compared to standard tensors and have potential to generalise well to symmetrics of different sizes.
  arXiv  Detail & Related papers  (2025-03-14T10:33:13Z)
• Symmetry Discovery for Different Data Types [52.2614860099811]
  Equivariant neural networks incorporate symmetries into their architecture, achieving higher generalization performance. We propose LieSD, a method for discovering symmetries via trained neural networks which approximate the input-output mappings of the tasks. We validate the performance of LieSD on tasks with symmetries such as the two-body problem, the moment of inertia matrix prediction, and top quark tagging.
  arXiv  Detail & Related papers  (2024-10-13T13:39:39Z)
• Understanding Matrix Function Normalizations in Covariance Pooling through the Lens of Riemannian Geometry [63.694184882697435]
  Global Covariance Pooling (GCP) has been demonstrated to improve the performance of Deep Neural Networks (DNNs) by exploiting second-order statistics of high-level representations.
  arXiv  Detail & Related papers  (2024-07-15T07:11:44Z)
• Domain Embeddings for Generating Complex Descriptions of Concepts in Italian Language [65.268245109828]
  We propose a Distributional Semantic resource enriched with linguistic and lexical information extracted from electronic dictionaries. The resource comprises 21 domain-specific matrices, one comprehensive matrix, and a Graphical User Interface. Our model facilitates the generation of reasoned semantic descriptions of concepts by selecting matrices directly associated with concrete conceptual knowledge.
  arXiv  Detail & Related papers  (2024-02-26T15:04:35Z)
• Mathematical Foundations for a Compositional Account of the Bayesian Brain [0.0]
  We use the tools of contemporary applied category theory to supply functorial semantics for approximate inference. We define fibrations of statistical games and classify various problems of statistical inference as corresponding sections. We construct functors which explain the compositional structure of predictive coding neural circuits under the free energy principle.
  arXiv  Detail & Related papers  (2022-12-23T18:58:17Z)
• Learning Graphical Factor Models with Riemannian Optimization [70.13748170371889]
  This paper proposes a flexible algorithmic framework for graph learning under low-rank structural constraints. The problem is expressed as penalized maximum likelihood estimation of an elliptical distribution. We leverage geometries of positive definite matrices and positive semi-definite matrices of fixed rank that are well suited to elliptical models.
  arXiv  Detail & Related papers  (2022-10-21T13:19:45Z)
• Riemannian statistics meets random matrix theory: towards learning from high-dimensional covariance matrices [2.352645870795664]
  This paper shows that there seems to exist no practical method of computing the normalising factors associated with Riemannian Gaussian distributions on spaces of high-dimensional covariance matrices. It is shown that this missing method comes from an unexpected new connection with random matrix theory. Numerical experiments are conducted which demonstrate how this new approximation can unlock the difficulties which have impeded applications to real-world datasets.
  arXiv  Detail & Related papers  (2022-03-01T03:16:50Z)
• Adversarially-Trained Nonnegative Matrix Factorization [77.34726150561087]
  We consider an adversarially-trained version of the nonnegative matrix factorization. In our formulation, an attacker adds an arbitrary matrix of bounded norm to the given data matrix. We design efficient algorithms inspired by adversarial training to optimize for dictionary and coefficient matrices.
  arXiv  Detail & Related papers  (2021-04-10T13:13:17Z)
• Joint Network Topology Inference via Structured Fusion Regularization [70.30364652829164]
  Joint network topology inference represents a canonical problem of learning multiple graph Laplacian matrices from heterogeneous graph signals. We propose a general graph estimator based on a novel structured fusion regularization. We show that the proposed graph estimator enjoys both high computational efficiency and rigorous theoretical guarantee.
  arXiv  Detail & Related papers  (2021-03-05T04:42:32Z)
• The general theory of permutation equivarant neural networks and higher order graph variational encoders [6.117371161379209]
  We derive formulae for general permutation equivariant layers, including the case where the layer acts on matrices by permuting their rows and columns simultaneously. This case arises naturally in graph learning and relation learning applications. We present a second order graph variational encoder, and show that the latent distribution of equivariant generative models must be exchangeable.
  arXiv  Detail & Related papers  (2020-04-08T13:29:56Z)
• Positive maps and trace polynomials from the symmetric group [0.0]
  We develop a method to obtain operator inequalities and identities in several variables. We give connections to concepts in quantum information theory and invariant theory.
  arXiv  Detail & Related papers  (2020-02-28T17:43:37Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.