A new diagnostic reveals that L=2 equivariant force field backbones preserve frequencies up to l=4 but collapse at l=5 on aspirin, consistent with a finite-degree span theorem and controls.
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Regularized Newton's method for neural networks converges exponentially to zero loss with uniform spectral rates in the infinite-width limit via a derived Newton neural tangent kernel.
Neural ODE flow maps composed with embedding and projection yield shallow networks with universal approximation in C^0, preserved under separate Lipschitz or norm constraints but with quantified loss when both are imposed.
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Diagnosing Spectral Ceilings in Equivariant Neural Force Fields
A new diagnostic reveals that L=2 equivariant force field backbones preserve frequencies up to l=4 but collapse at l=5 on aspirin, consistent with a finite-degree span theorem and controls.
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Convergence Analysis of Newton's Method for Neural Networks in the Overparameterized Limit
Regularized Newton's method for neural networks converges exponentially to zero loss with uniform spectral rates in the infinite-width limit via a derived Newton neural tangent kernel.
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Approximation properties of neural ODEs
Neural ODE flow maps composed with embedding and projection yield shallow networks with universal approximation in C^0, preserved under separate Lipschitz or norm constraints but with quantified loss when both are imposed.