Mechanisms of Width Scaling in Normalized Residual Networks: The Effective Alignment Dimension
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arXiv:2607.24887v1 Announce Type: new Abstract: Existing theories of neural-network width characterize asymptotic limits, but provide limited guidance on whether an expansion direction identified from finite training data remains beneficial on unseen data. We study this problem for function-preserving residual expansion and introduce the effective alignment dimension, a measurable quantity describing the signal-noise geometry of activation gradients. By deriving the exact mean and variance of…
1Key Takeaways
- arXiv:2607.24887v1 Announce Type: new Abstract: Existing theories of neural-network width characterize asymptotic limits, but provide limited guidance on whether an expansion direction identified from finite training data remains beneficial on unseen data.
- We study this problem for function-preserving residual expansion and introduce the effective alignment dimension, a measurable quantity describing the signal-noise geometry of activation gradients.
- By deriving the exact mean and variance of….
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3Why it matters
Research breakthroughs often arrive in products months later—early signals matter for strategy. arXiv ML reports that arXiv:2607.24887v1 Announce Type: new Abstract: Existing theories of neural-network width characterize asymptotic limits, but provide limited guidance on whether an expansion direction identified from finite training data remains beneficial on unseen data.
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