mlsanityData to 14 Oct 2026

The role of parameter Jacobians in the stability of network outputs

arXiv 2608.27748 ↗First posted 27 Aug 2026math.FA stat.MLcited by 0

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Abstract (arXiv)

In the framework of network dynamics, learning models, and neural tangent kernels (NTK), we show that the corresponding linearized dynamics leads naturally to a semigroup formulation. More precisely, in our analysis of input/output models, the time-dynamics is presented via special semigroups of linear operators on Hilbert spaces, together with an associated class of semigroup perturbations. In this context, we then present new and explicit a priori perturbation-bound results: for the fixed-kernel linearization constructions arising in the NTK setting, we prove norm-bounds on the corresponding semigroup perturbations, in the form of explicit finite-time perturbation estimates. We further present refinements on prescribed task spaces, Ces`aro-averaged (ergodic) comparisons estimates, and versions in which the lower spectral edge assumption is replaced by a spectral-distribution condition. We also extend the comparison to nonautonomous NTK evolutions through piecewise-frozen approximations, record a corresponding discrete Euler specialization, and offer worked examples in order to illustrate our perturbation-bound estimates.

Key facts. No citing papers in the map yet (data through 14 Oct 2026). Builds on 18 of its 50 references that are in the map. First posted on arXiv 27 Aug 2026.

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18 of 50 references.

References · 18

  1. 2018Neural Tangent Kernel: Convergence and Generalization in Neural Networkscited by 2,621
  2. 2019Wide Neural Networks of Any Depth Evolve as Linear Models Under Gradient Descentcited by 738
  3. 2018On Lazy Training in Differentiable Programmingcited by 675
  4. 2020Intrinsic Dimensionality Explains the Effectiveness of Language Model Fine-Tuningcited by 671
  5. 2021Neural Networks as Kernel Learners: The Silent Alignment Effectcited by 106
  6. 2019Dynamics of Deep Neural Networks and Neural Tangent Hierarchycited by 96
  7. 2022Limitations of the NTK for Understanding Generalization in Deep Learningcited by 35
  8. 2020Analyzing Finite Neural Networks: Can We Trust Neural Tangent Kernel Theory?cited by 33
  9. 2021Spectral Analysis of the Neural Tangent Kernel for Deep Residual Networkscited by 21
  10. 2022Evolution of Neural Tangent Kernels under Benign and Adversarial Trainingcited by 14
  11. 2022Binary Iterative Hard Thresholding Converges with Optimal Number of Measurements for 1-Bit Compressed Sensingcited by 9
  12. 2023An Exact Kernel Equivalence for Finite Classification Modelscited by 5
6 more
  1. 2023Robust 1-bit Compressed Sensing with Iterative Hard Thresholdingcited by 4
  2. 2024On the Convergence Analysis of Over-Parameterized Variational Autoencoders: A Neural Tangent Kernel Perspectivecited by 3
  3. 2023Operator theory, kernels, and Feedforward Neural Networkscited by 2
  4. 2025Infinite-Dimensional Operator/Block Kaczmarz Algorithms: Regret Bounds and λ-Effectivenesscited by 2
  5. 2023Tight conditions for when the NTK approximation is validcited by 1
  6. 2026Use of operator defect identities in multi-channel signal plus residual-analysis via iterated products and telescoping energy-residuals: Applications to kernels in machine learningcited by 1

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