Implicit Bias in Matrix Factorization and its Explicit Realization in a New Architecture

A recent study published on arXiv explores the implicit bias present in matrix factorization, specifically focusing on how gradient descent algorithms tend to favor low-rank solutions even when sequences are unbounded. This finding confirms that gradient descent inherently promotes simpler, low-rank structures during optimization. To better capture and understand this behavior, the researchers introduced a new architecture designed to explicitly realize the implicit bias observed. According to the study, factors within this architecture develop low-rank structures while their magnitudes increase, providing a clearer representation of the underlying dynamics. This work builds on existing knowledge about gradient descent's tendencies and offers a novel framework for analyzing matrix factorization processes. The research contributes to the broader field of machine learning by elucidating how optimization methods influence model complexity. These insights may have implications for designing more efficient algorithms that leverage implicit biases for improved performance.