# An Adaptive Tangent Feature Perspective of Neural Networks

arXiv: https://arxiv.org/abs/2308.15478 · HTML: https://mlsanity.com/paper/2308.15478/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 23 of its 42 references that are in the map.
- First posted on arXiv 29 Aug 2023.

## Builds on (most cited first, 23 of 23)

- [LoRA: Low-Rank Adaptation of Large Language Models](https://mlsanity.com/paper/2106.09685/) (2021)
- [Sequence to Sequence Learning with Neural Networks](https://mlsanity.com/paper/1409.3215/) (2014)
- [Neural Tangent Kernel: Convergence and Generalization in Neural Networks](https://mlsanity.com/paper/1806.07572/) (2018)
- [Sparks of Artificial General Intelligence: Early experiments with GPT-4](https://mlsanity.com/paper/2303.12712/) (2023)
- [Understanding deep learning requires rethinking generalization](https://mlsanity.com/paper/1611.03530/) (2016)
- [Wide Neural Networks of Any Depth Evolve as Linear Models Under Gradient Descent](https://mlsanity.com/paper/1902.06720/) (2019)
- [On Lazy Training in Differentiable Programming](https://mlsanity.com/paper/1812.07956/) (2018)
- [Benign Overfitting in Linear Regression](https://mlsanity.com/paper/1906.11300/) (2019)
- [Surprises in High-Dimensional Ridgeless Least Squares Interpolation](https://mlsanity.com/paper/1903.08560/) (2019)
- [Measuring the Intrinsic Dimension of Objective Landscapes](https://mlsanity.com/paper/1804.08838/) (2018)
- [Just Interpolate: Kernel "Ridgeless" Regression Can Generalize](https://mlsanity.com/paper/1808.00387/) (2018)
- [To understand deep learning we need to understand kernel learning](https://mlsanity.com/paper/1802.01396/) (2018)
- [Tensor Programs II: Neural Tangent Kernel for Any Architecture](https://mlsanity.com/paper/2006.14548/) (2020)
- [Neural Networks as Kernel Learners: The Silent Alignment Effect](https://mlsanity.com/paper/2111.00034/) (2021)
- [On the Optimal Weighted ℓ2 Regularization in Overparameterized Linear Regression](https://mlsanity.com/paper/2006.05800/) (2020)
- [The Recurrent Neural Tangent Kernel](https://mlsanity.com/paper/2006.10246/) (2020)
- [The Global Landscape of Neural Networks: An Overview](https://mlsanity.com/paper/2007.01429/) (2020)
- [A Farewell to the Bias-Variance Tradeoff? An Overview of the Theory of Overparameterized Machine Learning](https://mlsanity.com/paper/2109.02355/) (2021)
- [Analyzing Finite Neural Networks: Can We Trust Neural Tangent Kernel Theory?](https://mlsanity.com/paper/2012.04477/) (2020)
- [Neural Tangent Kernel Beyond the Infinite-Width Limit: Effects of Depth and Initialization](https://mlsanity.com/paper/2202.00553/) (2022)
- [Fast Rates for Noisy Interpolation Require Rethinking the Effects of Inductive Bias](https://mlsanity.com/paper/2203.03597/) (2022)
- [Neural (Tangent Kernel) Collapse](https://mlsanity.com/paper/2305.16427/) (2023)
- [The Flip Side of the Reweighted Coin: Duality of Adaptive Dropout and Regularization](https://mlsanity.com/paper/2106.07769/) (2021)

## Built on by (most cited first, 1 of 1)

- [Improving Adaptivity via Over-Parameterization in Sequence Models](https://mlsanity.com/paper/2409.00894/) (2024)

## Abstract (arXiv)

In order to better understand feature learning in neural networks, we propose a framework for understanding linear models in tangent feature space where the features are allowed to be transformed during training. We consider linear transformations of features, resulting in a joint optimization over parameters and transformations with a bilinear interpolation constraint. We show that this optimization problem has an equivalent linearly constrained optimization with structured regularization that encourages approximately low rank solutions. Specializing to neural network structure, we gain insights into how the features and thus the kernel function change, providing additional nuance to the phenomenon of kernel alignment when the target function is poorly represented using tangent features. We verify our theoretical observations in the kernel alignment of real neural networks.