# Credit Assignment via Neural Manifold Noise Correlation

arXiv: https://arxiv.org/abs/2601.02636 · HTML: https://mlsanity.com/paper/2601.02636/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 14 of its 48 references that are in the map.
- First posted on arXiv 6 Jan 2026.

## Builds on (most cited first, 14 of 14)

- [Optuna: A Next-generation Hyperparameter Optimization Framework](https://mlsanity.com/paper/1907.10902/) (2019)
- [Estimating the intrinsic dimension of datasets by a minimal neighborhood information](https://mlsanity.com/paper/1803.06992/) (2018)
- [Direct Feedback Alignment Provides Learning in Deep Neural Networks](https://mlsanity.com/paper/1609.01596/) (2016)
- [Assessing the Scalability of Biologically-Motivated Deep Learning Algorithms and Architectures](https://mlsanity.com/paper/1807.04587/) (2018)
- [Deep Learning without Weight Transport](https://mlsanity.com/paper/1904.05391/) (2019)
- [Scaling Forward Gradient With Local Losses](https://mlsanity.com/paper/2210.03310/) (2022)
- [Biologically-plausible learning algorithms can scale to large datasets](https://mlsanity.com/paper/1811.03567/) (2018)
- [Credit Assignment in Neural Networks through Deep Feedback Control](https://mlsanity.com/paper/2106.07887/) (2021)
- [A Hebbian/Anti-Hebbian Neural Network for Linear Subspace Learning: A Derivation from Multidimensional Scaling of Streaming Data](https://mlsanity.com/paper/1503.00669/) (2015)
- [Two Routes to Scalable Credit Assignment without Weight Symmetry](https://mlsanity.com/paper/2003.01513/) (2020)
- [The least-control principle for local learning at equilibrium](https://mlsanity.com/paper/2207.01332/) (2022)
- [Minimizing Control for Credit Assignment with Strong Feedback](https://mlsanity.com/paper/2204.07249/) (2022)
- [How to guess a gradient](https://mlsanity.com/paper/2312.04709/) (2023)
- [Biologically Plausible Online Principal Component Analysis Without Recurrent Neural Dynamics](https://mlsanity.com/paper/1810.06966/) (2018)

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

- [Conditioned Direct Feedback Alignment via Activity and Error Geometry](https://mlsanity.com/paper/2607.18574/) (2026)

## Abstract (arXiv)

Credit assignment--how changes in individual neurons and synapses affect a network's output--is central to learning in brains and machines. Noise correlation, which estimates gradients by correlating perturbations of activity with changes in output, provides a biologically plausible solution to credit assignment but scales poorly as accurately estimating the Jacobian requires that the number of perturbations scale with network size. Moreover, isotropic noise conflicts with neurobiological observations that neural activity lies on a low-dimensional manifold. To address these drawbacks, we propose neural manifold noise correlation (NMNC), which performs credit assignment using perturbations restricted to the neural manifold. We show theoretically and empirically that the Jacobian row space aligns with the neural manifold in trained networks, and that manifold dimensionality scales slowly with network size. NMNC substantially improves performance and sample efficiency over vanilla noise correlation in convolutional networks trained on CIFAR-10, ImageNet-scale models, and recurrent networks. NMNC also yields representations more similar to the primate visual system than vanilla noise correlation. These findings offer a mechanistic hypothesis for how biological circuits could support credit assignment, and suggest that biologically inspired constraints may enable, rather than limit, effective learning at scale.