arXiv:2605.23087v1 Announce Type: new Abstract: Neural collapse (NC) describes the structured geometry that emerges in the features and weights of trained classifiers. Recent theory suggests NC can be suboptimal in deep architectures, attributing this to an explicit low-rank bias from L2 regularization. We study the deep unconstrained feature model (UFM)-equivalent to a deep linear network with orthogonal inputs-trained without regularization, to isolate how gradient descent and depth alone shape NC. We show that depth induces an implicit low-rank bias: low-rank matrices propagate norm more ef
This research is part of the ongoing advancement in understanding the fundamental mechanisms of deep learning, particularly how architectural choices like depth influence model behavior in unregularized settings.
A strategic reader should care because deeper understanding of implicit biases in neural networks can lead to more efficient, robust, and explainable AI systems, impacting development and deployment strategies.
This research changes our understanding of how depth alone, without explicit regularization, introduces a low-rank bias in neural networks, potentially informing future model design and training methodologies.
- · AI researchers
- · Deep learning framework developers
- · Companies investing in explainable AI
- · Developers relying solely on explicit regularization
- · Systems with unoptimized deep architectures
The immediate effect is a refined theoretical understanding of how architectural depth contributes to neural network behavior.
This understanding could lead to the development of new deep learning architectures that inherently mitigate or leverage this implicit bias more effectively.
Improved fundamental understanding of AI could accelerate progress in various applications, making AI systems more reliable and efficient across industries.
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Read at arXiv cs.LG