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New principle establishes stability threshold for residual neural network architectures

By PulseAugur Editorial · [2 sources] ·

Researchers have introduced the 'sublinear-growth principle' for deep residual architectures, establishing a sharp stability threshold for the velocity field's input-magnitude exponent. This principle, supported by ODE theory and optimal-control analysis, posits that an exponent of q=1 is necessary and sufficient for stable training and inference. Experiments demonstrate that modifying Mamba blocks to adhere to this q<=1 criterion, even without layer normalization, results in stable training, suggesting the exponent is a more critical factor than normalization layers. AI

IMPACT This research could lead to more stable and reliable neural network training and inference, potentially impacting the design of future AI models.

RANK_REASON The cluster contains two arXiv preprints detailing a new theoretical principle for neural network stability.

Read on arXiv cs.LG →

AI-generated summary · Google Gemini · from 2 sources. How we write summaries →

New principle establishes stability threshold for residual neural network architectures

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COVERAGE [2]

  1. arXiv cs.LG TIER_1 English(EN) · Markos A. Katsoulakis ·

    Sharp Stability Threshold and Certification for Designing Stable Residual Architectures

    We propose \emph{the sublinear-growth principle} for deep residual architectures -- a sharp stability threshold on the input-magnitude exponent of every residual block's velocity field: $$\|v(x, t)\| \leq c\,\|x\|^q + b, \qquad q \in [0, 1].$$ The threshold $q = 1$ is established…

  2. arXiv stat.ML TIER_1 English(EN) · Hyemin Gu, Michael Tyrrell, Tuhin Sahai, Markos A. Katsoulakis ·

    Sharp Stability Threshold and Certification for Designing Stable Residual Architectures

    arXiv:2607.14576v1 Announce Type: cross Abstract: We propose \emph{the sublinear-growth principle} for deep residual architectures -- a sharp stability threshold on the input-magnitude exponent of every residual block's velocity field: $$\|v(x, t)\| \leq c\,\|x\|^q + b, \qquad q …

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