Implicit Regularization in Perturbed Deep Matrix Factorization: Spectral Conditions and Stability
arXiv:2605.28613v1 Announce Type: cross Abstract: This paper studies the stability of low-rank implicit regularization in perturbed deep matrix factorization, where the target matrix is corrupted by a noise matrix. We first derive sufficient spectral conditions under which gradient descent exhibits a low-rank phase in the noiseless setting. These conditions show how the target spectrum, initialization, and step size jointly determine the existence of a nonempty low-rank interval. We then analyze the perturbed gradient descent dynamics, proving convergence guarantees and quantifying how the per
The paper provides theoretical advances in understanding implicit regularization in deep matrix factorization, especially under perturbed conditions, which is crucial for robust AI model development.
Improved theoretical understanding of deep learning models contributes to more stable, reliable, and interpretable AI systems, influencing design choices and performance guarantees.
This research provides specific spectral conditions and stability analysis, offering clearer guidelines for optimizing deep matrix factorization models in noisy environments.
- · AI researchers
- · Machine learning engineers
- · Deep learning practitioners
- · AI systems lacking theoretical rigor
It will lead to more robust and higher-performing low-rank models in various AI applications.
This foundational work could enhance the trustworthiness and deployment of AI in critical sectors requiring high stability through better understanding of model robustness.
These theoretical insights may accelerate the development of explainable AI by shedding light on intrinsic properties of deep learning architectures allowing more efficient applications.
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