MatrixFormer: A Foundation Model for Matrix Completion

Dwaipayan Saha, Jacob Feitelberg, Kyuseong Choi, Raaz Dwivedi, Anish Agarwal

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.