# The Neural Tangent Kernel for Classification

arXiv: https://arxiv.org/abs/2605.17606 · HTML: https://mlsanity.com/paper/2605.17606/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 28 of its 30 references that are in the map.
- First posted on arXiv 17 May 2026.

## Builds on (most cited first, 28 of 28)

- [Rethinking the Inception Architecture for Computer Vision](https://mlsanity.com/paper/1512.00567/) (2015)
- [Neural Tangent Kernel: Convergence and Generalization in Neural Networks](https://mlsanity.com/paper/1806.07572/) (2018)
- [When Does Label Smoothing Help?](https://mlsanity.com/paper/1906.02629/) (2019)
- [Wide Neural Networks of Any Depth Evolve as Linear Models Under Gradient Descent](https://mlsanity.com/paper/1902.06720/) (2019)
- [Prevalence of Neural Collapse during the terminal phase of deep learning training](https://mlsanity.com/paper/2008.08186/) (2020)
- [The Implicit Bias of Gradient Descent on Separable Data](https://mlsanity.com/paper/1710.10345/) (2017)
- [Deep Neural Networks as Gaussian Processes](https://mlsanity.com/paper/1711.00165/) (2017)
- [Gradient Descent Finds Global Minima of Deep Neural Networks](https://mlsanity.com/paper/1811.03804/) (2018)
- [On Exact Computation with an Infinitely Wide Neural Net](https://mlsanity.com/paper/1904.11955/) (2019)
- [A Mean Field View of the Landscape of Two-Layers Neural Networks](https://mlsanity.com/paper/1804.06561/) (2018)
- [Gradient Descent Maximizes the Margin of Homogeneous Neural Networks](https://mlsanity.com/paper/1906.05890/) (2019)
- [Gaussian Process Behaviour in Wide Deep Neural Networks](https://mlsanity.com/paper/1804.11271/) (2018)
- [Loss landscapes and optimization in over-parameterized non-linear systems and neural networks](https://mlsanity.com/paper/2003.00307/) (2020)
- [Generalization Bounds of Stochastic Gradient Descent for Wide and Deep Neural Networks](https://mlsanity.com/paper/1905.13210/) (2019)
- [Directional convergence and alignment in deep learning](https://mlsanity.com/paper/2006.06657/) (2020)
- [A* Sampling](https://mlsanity.com/paper/1411.0030/) (2014)
- [Tensor Programs II: Neural Tangent Kernel for Any Architecture](https://mlsanity.com/paper/2006.14548/) (2020)
- [On the linearity of large non-linear models: when and why the tangent kernel is constant](https://mlsanity.com/paper/2010.01092/) (2020)
- [Bayesian Deep Ensembles via the Neural Tangent Kernel](https://mlsanity.com/paper/2007.05864/) (2020)
- [Overparameterized Nonlinear Learning: Gradient Descent Takes the Shortest Path?](https://mlsanity.com/paper/1812.10004/) (2018)
- [An Unconstrained Layer-Peeled Perspective on Neural Collapse](https://mlsanity.com/paper/2110.02796/) (2021)
- [Imbalance Trouble: Revisiting Neural-Collapse Geometry](https://mlsanity.com/paper/2208.05512/) (2022)
- [On the training dynamics of deep networks with L2 regularization](https://mlsanity.com/paper/2006.08643/) (2020)
- [On the Eigenvalue Decay Rates of a Class of Neural-Network Related Kernel Functions Defined on General Domains](https://mlsanity.com/paper/2305.02657/) (2023)
- [The Positivity of the Neural Tangent Kernel](https://mlsanity.com/paper/2404.12928/) (2024)
- [A Gaussian Process View on Observation Noise and Initialization in Wide Neural Networks](https://mlsanity.com/paper/2502.01556/) (2025)
- [Richer Bayesian Last Layers with Subsampled NTK Features](https://mlsanity.com/paper/2602.01279/) (2026)
- [Diagonalizing the Softmax: Hadamard Initialization for Tractable Cross-Entropy Dynamics](https://mlsanity.com/paper/2512.04006/) (2025)

## Abstract (arXiv)

In wide neural networks, the Neural Tangent Kernel (NTK) remains approximately constant during training, providing a powerful theoretical tool for studying training dynamics, generalization, and connections to kernel methods. However, this theory is largely restricted to regression losses. It was previously thought that training on a classification loss, or more generally losses involving nonlinear output transformations, breaks this property, leading to divergent logits and a breakdown of the linearization. In this paper, we extend NTK theory to classification by identifying conditions under which wide neural networks remain in the lazy training regime. We show that parameter-space regularization ensures a constant NTK during training for cross-entropy loss, while in the absence of regularization the regime is recovered when targets are non-degenerate, i.e. when all classes have strictly positive probability. Under these conditions, training is well-approximated by the linearized model, yielding an explicit characterization of the solution in terms of the NTK. We further analyze the distribution of trained predictors induced by random initialization and relate this notion of model uncertainty to Bayesian methods.