arXiv:2605.17767v2 Announce Type: replace-cross Abstract: We study feature learning in two-layer neural networks within the linear-width regime, where the number of hidden neurons, sample size, and input dimension scale proportionally. While recent work has analyzed feature learning via a single step of gradient descent on the first layer weights in this regime, such one-step update schemes are fundamentally limited: the update to the weights is approximately rank-one, captures only a single direction, and requires the target function to have an information exponent of one. In this paper, we g
The paper addresses a current limitation in understanding feature learning within neural networks, building on recent work in the linear-width regime.
Improved theoretical understanding of neural network training mechanisms could lead to more efficient and robust AI models, impacting a wide range of applications.
This research refines our understanding of how feature learning occurs in specific neural network architectures, highlighting the benefits of multi-step gradient descent over single-step approaches.
- · AI researchers
- · Deep learning practitioners
- · AI software developers
- · Inefficient AI training methods
More accurate and stable neural network training algorithms could be developed based on these theoretical insights.
Enhanced training efficiency might reduce computational resource requirements for certain AI tasks, potentially impacting compute infrastructure demands.
Advances in foundational AI algorithms could accelerate progress in various AI applications, including autonomous systems and agentic AI.
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