High-rank connectivity scaffolds support precision and generalisation in recurrent neural networks
Abstract
A major challenge in neuroscience and machine learning is to connect single-neuron influence, population dynamics, and circuit connectivity in a causal account of computation. Much previous work has shown that low-rank connectivity can generate low-dimensional dynamics in trained artificial neural networks, but this leaves unclear the functional relevance of the higher-rank structure of biological neural circuits and many artificial neuronal networks. Here we analyse recurrent neural networks trained to locate rewards by integrating continuously varying speed inputs in one- and two-dimensional spatial tasks. We find that dominant low-dimensional dynamics encode task locations, and can be causally manipulated to instruct behavioural outcomes. However, after decomposing the underlying circuitry we found that while low-rank connectivity accounts for the low-dimensional dynamics, accurate performance and generalisation to novel speed distributions requires high-rank connectivity. We demonstrate that this is achieved through distributed signalling that corrects errors in low-dimensional location representations. Thus, combined perturbation-, representation-, and circuit-level analyses demonstrate a novel mechanism for robust spatial computation and show how high-rank connectivity in neural circuits can provide a scaffold that supports precision and generalisation.
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BibTeX
@misc{hawes2026highrank,
title = {{High-rank connectivity scaffolds support precision and generalisation in recurrent neural networks}},
author = {Ian Hawes and Matt Nolan},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.35207},
eprint = {2609.35207},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.35207},
}
RIS
TY - UNPB
TI - High-rank connectivity scaffolds support precision and generalisation in recurrent neural networks
AU - Ian Hawes
AU - Matt Nolan
PY - 2026
DA - 2026/09/28
PB - arXiv
DO - 10.48550/arxiv.2609.35207
UR - https://arxiv.org/abs/2609.35207
AB - A major challenge in neuroscience and machine learning is to connect single-neuron influence, population dynamics, and circuit connectivity in a causal account of computation. Much previous work has shown that low-rank connectivity can generate low-dimensional dynamics in trained artificial neural networks, but this leaves unclear the functional relevance of the higher-rank structure of biological neural circuits and many artificial neuronal networks. Here we analyse recurrent neural networks trained to locate rewards by integrating continuously varying speed inputs in one- and two-dimensional spatial tasks. We find that dominant low-dimensional dynamics encode task locations, and can be causally manipulated to instruct behavioural outcomes. However, after decomposing the underlying circuitry we found that while low-rank connectivity accounts for the low-dimensional dynamics, accurate performance and generalisation to novel speed distributions requires high-rank connectivity. We demonstrate that this is achieved through distributed signalling that corrects errors in low-dimensional location representations. Thus, combined perturbation-, representation-, and circuit-level analyses demonstrate a novel mechanism for robust spatial computation and show how high-rank connectivity in neural circuits can provide a scaffold that supports precision and generalisation.
ER -