MatrixFormer: A Foundation Model for Matrix Completion

Abstract:Matrix completion underlies problems from tabular imputation to causal inference, yet existing tabular foundation models treat it as entry-by-entry prediction, repeating context for every target and discarding the matrix's two-dimensional structure. We introduce MatrixFormer, a pre-trained matrix-native transformer that predicts a full distribution for every missing entry in a single forward pass. MatrixFormer is trained entirely on synthetic low-rank and latent-factor matrices under diverse missingness patterns. Applied zero-shot and with the same model weights, MatrixFormer achieves competitive performance on causal inference panel-data tasks, language-model benchmark-score completion, tabular imputation, and recommendation systems matrix completion. These results position MatrixFormer as a general-purpose foundation model for matrix completion.

Machine Learning (cs.LG); Artificial Intelligence (cs.AI)

arXiv:2610.06751 [cs.LG]

(or arXiv:2610.06751v1 [cs.LG] for this version)

https://doi.org/10.48550/arXiv.2610.06751 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

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