8 research outputs found
A Gradient Descent Algorithm on the Grassman Manifold for Matrix Completion
We consider the problem of reconstructing a low-rank matrix from a small
subset of its entries. In this paper, we describe the implementation of an
efficient algorithm called OptSpace, based on singular value decomposition
followed by local manifold optimization, for solving the low-rank matrix
completion problem. It has been shown that if the number of revealed entries is
large enough, the output of singular value decomposition gives a good estimate
for the original matrix, so that local optimization reconstructs the correct
matrix with high probability. We present numerical results which show that this
algorithm can reconstruct the low rank matrix exactly from a very small subset
of its entries. We further study the robustness of the algorithm with respect
to noise, and its performance on actual collaborative filtering datasets.Comment: 26 pages, 15 figure
Recommender Systems with Generative Retrieval
Modern recommender systems perform large-scale retrieval by first embedding
queries and item candidates in the same unified space, followed by approximate
nearest neighbor search to select top candidates given a query embedding. In
this paper, we propose a novel generative retrieval approach, where the
retrieval model autoregressively decodes the identifiers of the target
candidates. To that end, we create semantically meaningful tuple of codewords
to serve as a Semantic ID for each item. Given Semantic IDs for items in a user
session, a Transformer-based sequence-to-sequence model is trained to predict
the Semantic ID of the next item that the user will interact with. To the best
of our knowledge, this is the first Semantic ID-based generative model for
recommendation tasks. We show that recommender systems trained with the
proposed paradigm significantly outperform the current SOTA models on various
datasets. In addition, we show that incorporating Semantic IDs into the
sequence-to-sequence model enhances its ability to generalize, as evidenced by
the improved retrieval performance observed for items with no prior interaction
history.Comment: Preprint versio