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New Theorem Proves Gradient Trajectory Convergence in Deep Neural Networks

By PulseAugur Editorial · [2 sources] ·

A new paper published on arXiv introduces a theorem that addresses the gradient conjecture at infinity for definable potentials. The research proves that gradient trajectories of such potentials have finite spherical length and converge directionally. This finding has implications for the training of deep neural networks (DNNs), suggesting that the training flow converges when activation and loss functions are definable and continuously differentiable. AI

IMPACT This research suggests a theoretical convergence property in DNN training under specific conditions, potentially impacting optimization strategies.

RANK_REASON The cluster contains a research paper detailing a mathematical theorem with implications for deep neural network training.

Read on Hugging Face Daily Papers →

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

New Theorem Proves Gradient Trajectory Convergence in Deep Neural Networks

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COVERAGE [2]

  1. arXiv cs.LG TIER_1 English(EN) · Thang Do, Arnulf Jentzen, Benno Kuckuck ·

    On the gradient conjecture at infinity: Finite spherical length for gradient trajectories of definable potentials

    arXiv:2610.29211v1 Announce Type: cross Abstract: We prove that for every open $ U \subseteq \mathbb R^n $ the spherical projection of every gradient trajectory $\theta(t)$, $t \geq 0$, of a definable $C^1$-potential $F \colon U \to \mathbb R$ has finite length and, in particular…

  2. Hugging Face Daily Papers TIER_1 English(EN) ·

    On the gradient conjecture at infinity: Finite spherical length for gradient trajectories of definable potentials

    We prove that for every open $ U \subseteq \mathbb R^n $ the spherical projection of every gradient trajectory $θ(t)$, $t \geq 0$, of a definable $C^1$-potential $F \colon U \to \mathbb R$ has finite length and, in particular, converges (directional convergence). In other words, …

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