Learning distributed representations with efficient SoftMax normalization

• URL: http://arxiv.org/abs/2303.17475v4
• Date: Sun, 01 Jun 2025 14:02:31 GMT
• Title: Learning distributed representations with efficient SoftMax normalization
• Authors: Lorenzo Dall'Amico, Enrico Maria Belliardo,
• Abstract summary: We propose a linear-time approximation to compute the normalization constants of $rm SoftMax(XYT)$ for embedding vectors with bounded norms.<n>We show on some pre-trained embedding datasets that the proposed estimation method achieves higher or comparable accuracy with competing methods.<n>The proposed algorithm is interpretable and easily adapted to arbitrary embedding problems.
• Score: 3.8673630752805437
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: 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.

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