# Task-Driven Kernel Flows: Label Rank Compression and Laplacian Spectral Filtering

arXiv: https://arxiv.org/abs/2601.00276 · HTML: https://mlsanity.com/paper/2601.00276/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 9 of its 13 references that are in the map.
- First posted on arXiv 1 Jan 2026.

## Builds on (most cited first, 9 of 9)

- [A Simple Framework for Contrastive Learning of Visual Representations](https://mlsanity.com/paper/2002.05709/) (2020)
- [Neural Tangent Kernel: Convergence and Generalization in Neural Networks](https://mlsanity.com/paper/1806.07572/) (2018)
- [Barlow Twins: Self-Supervised Learning via Redundancy Reduction](https://mlsanity.com/paper/2103.03230/) (2021)
- [On the Spectral Bias of Neural Networks](https://mlsanity.com/paper/1806.08734/) (2018)
- [Prevalence of Neural Collapse during the terminal phase of deep learning training](https://mlsanity.com/paper/2008.08186/) (2020)
- [On Lazy Training in Differentiable Programming](https://mlsanity.com/paper/1812.07956/) (2018)
- [On Exact Computation with an Infinitely Wide Neural Net](https://mlsanity.com/paper/1904.11955/) (2019)
- [Understanding Dimensional Collapse in Contrastive Self-supervised Learning](https://mlsanity.com/paper/2110.09348/) (2021)
- [Neural Collapse Under MSE Loss: Proximity to and Dynamics on the Central Path](https://mlsanity.com/paper/2106.02073/) (2021)

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

- [Uncovering the Latent Potential of Deep Intermediate Representations](https://mlsanity.com/paper/2605.23033/) (2026)

## Abstract (arXiv)

We present a theory of feature learning in wide L2-regularized networks showing that supervised learning is inherently compressive. We derive a kernel ODE that predicts a "water-filling" spectral evolution and prove that for any stable steady state, the kernel rank is bounded by the number of classes (C). We further demonstrate that SGD noise is similarly low-rank (O(C)), confining dynamics to the task-relevant subspace. This framework unifies the deterministic and stochastic views of alignment and contrasts the low-rank nature of supervised learning with the high-rank, expansive representations of self-supervision.