Saved in:
Bibliographic Details
Main Authors: Dall'Amico, Lorenzo, Belliardo, Enrico Maria
Format: Preprint
Published: 2023
Subjects:
Online Access:https://arxiv.org/abs/2303.17475
Tags: Add Tag
No Tags, Be the first to tag this record!
_version_ 1866908388126883840
author Dall'Amico, Lorenzo
Belliardo, Enrico Maria
author_facet Dall'Amico, Lorenzo
Belliardo, Enrico Maria
contents Learning distributed representations, or embeddings, that encode the relational similarity patterns among objects is a relevant task in machine learning. A popular method to learn the embedding matrices $X, Y$ is optimizing a loss function of the term ${\rm SoftMax}(XY^T)$. The complexity required to calculate this term, however, runs quadratically with the problem size, making it a computationally heavy solution. In this article, we propose a linear-time heuristic approximation to compute the normalization constants of ${\rm SoftMax}(XY^T)$ for embedding vectors with bounded norms. We show on some pre-trained embedding datasets that the proposed estimation method achieves higher or comparable accuracy with competing methods. From this result, we design an efficient and task-agnostic algorithm that learns the embeddings by optimizing the cross entropy between the softmax and a set of probability distributions given as inputs. The proposed algorithm is interpretable and easily adapted to arbitrary embedding problems. We consider a few use cases and observe similar or higher performances and a lower computational time than similar ``2Vec'' algorithms.
format Preprint
id arxiv_https___arxiv_org_abs_2303_17475
institution arXiv
publishDate 2023
record_format arxiv
spellingShingle Learning distributed representations with efficient SoftMax normalization
Dall'Amico, Lorenzo
Belliardo, Enrico Maria
Machine Learning
Computation and Language
Learning distributed representations, or embeddings, that encode the relational similarity patterns among objects is a relevant task in machine learning. A popular method to learn the embedding matrices $X, Y$ is optimizing a loss function of the term ${\rm SoftMax}(XY^T)$. The complexity required to calculate this term, however, runs quadratically with the problem size, making it a computationally heavy solution. In this article, we propose a linear-time heuristic approximation to compute the normalization constants of ${\rm SoftMax}(XY^T)$ for embedding vectors with bounded norms. We show on some pre-trained embedding datasets that the proposed estimation method achieves higher or comparable accuracy with competing methods. From this result, we design an efficient and task-agnostic algorithm that learns the embeddings by optimizing the cross entropy between the softmax and a set of probability distributions given as inputs. The proposed algorithm is interpretable and easily adapted to arbitrary embedding problems. We consider a few use cases and observe similar or higher performances and a lower computational time than similar ``2Vec'' algorithms.
title Learning distributed representations with efficient SoftMax normalization
topic Machine Learning
Computation and Language
url https://arxiv.org/abs/2303.17475