Credit Assignment via Neural Manifold Noise Correlation

Byungwoo Kang, Maceo Richards, Bernardo L. Sabatini
Proceedings of the 43rd International Conference on Machine Learning, PMLR 306:55700-55722, 2026.

Abstract

Credit assignment, the process of determining how changes in individual neurons and synapses influence a network’s output, is central to learning in brains and machines. Noise correlation-based methods, which estimate gradients by correlating perturbations of activity with changes in output, provide 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.

Cite this Paper

BibTeX
@InProceedings{pmlr-v306-kang26n, title = {Credit Assignment via Neural Manifold Noise Correlation}, author = {Kang, Byungwoo and Richards, Maceo and Sabatini, Bernardo L.}, booktitle = {Proceedings of the 43rd International Conference on Machine Learning}, pages = {55700--55722}, year = {2026}, editor = {Zhang, Tong and Dudik, Miroslav and Jaggi, Martin and Agarwal, Alekh and Li, Sharon and Schuurmans, Dale and Zhu, Jerry and Berkenkamp, Felix and Dong, Hanze and Bietti, Alberto}, volume = {306}, series = {Proceedings of Machine Learning Research}, month = {06--11 Jul}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v306/main/assets/kang26n/kang26n.pdf}, url = {https://proceedings.mlr.press/v306/kang26n.html}, abstract = {Credit assignment, the process of determining how changes in individual neurons and synapses influence a network’s output, is central to learning in brains and machines. Noise correlation-based methods, which estimate gradients by correlating perturbations of activity with changes in output, provide 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.} }
Endnote
%0 Conference Paper %T Credit Assignment via Neural Manifold Noise Correlation %A Byungwoo Kang %A Maceo Richards %A Bernardo L. Sabatini %B Proceedings of the 43rd International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2026 %E Tong Zhang %E Miroslav Dudik %E Martin Jaggi %E Alekh Agarwal %E Sharon Li %E Dale Schuurmans %E Jerry Zhu %E Felix Berkenkamp %E Hanze Dong %E Alberto Bietti %F pmlr-v306-kang26n %I PMLR %P 55700--55722 %U https://proceedings.mlr.press/v306/kang26n.html %V 306 %X Credit assignment, the process of determining how changes in individual neurons and synapses influence a network’s output, is central to learning in brains and machines. Noise correlation-based methods, which estimate gradients by correlating perturbations of activity with changes in output, provide 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.
APA
Kang, B., Richards, M. & Sabatini, B.L.. (2026). Credit Assignment via Neural Manifold Noise Correlation. Proceedings of the 43rd International Conference on Machine Learning, in Proceedings of Machine Learning Research 306:55700-55722 Available from https://proceedings.mlr.press/v306/kang26n.html.

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