A recurrent neural network can appear to keep track of location with just two broad activity patterns, yet still need a much larger set of hidden connections to behave accurately when movement speeds change. That is the central finding of a study that examined simulated networks on linear-track and two-dimensional spatial tasks.
The result points to a split between a compact internal map and a more detailed connectivity scaffold. The first part makes the network’s estimate of location easy to read; the second was associated with precision and recovery after speed-related errors. Because the evidence came from simulated recurrent networks, the study does not directly test biological circuits.
The map was simple. The behaviour was not.
The researchers analysed a representative agent and evaluated results across 162 models with varying architectures. The networks made a stop-or-go choice at each timestep. They were tested not only at the speed distribution used during training, but also after speed was rescaled to half or twice the standard level.
When the activity was reduced to broad patterns, the first two principal components formed a looping shape that mapped onto track location. That shape remained similar across cue conditions and speed distributions, and location could be decoded accurately from it.
But a readable location map did not guarantee full task performance. The first four principal components tracked location while impairing behaviour when the rest of the activity was removed. On standard trials, the reported threshold for more than 99% reward was the first 15 components; on novel-speed trials, more than 35 were associated with that level of reward. The sixth component explained only 4.1% of the variance, yet clamping it was associated with a 93% reduction in uncued performance.
The extra structure carried information about speed
The recurrent weight matrices were full rank, meaning they contained many independent connectivity modes rather than only a small set. A standard decomposition showed a sharply uneven strength profile: the first two mode-strength values averaged 5.2 times the mean of the remaining values. The leading modes were associated mainly with location, while modes ranked above two carried less location information and more information about speed.
This pattern led the authors to describe the network as having a core and a scaffold. The leading, low-rank modes supported the dominant location manifold, while later modes were associated with distributed corrections. In the simulations, a single-step speed perturbation moved the location-related modes away from their expected values. Full-rank networks returned modes one and two toward those values on the next timestep, whereas a rank-two version did not. More than 224 modes were associated with performance comparable to the full network.
Rank here refers to how many connectivity modes are retained when the recurrent matrix is simplified. At the training speed distribution, retaining five modes produced more than 75% reward and a location-decoding score above 0.65, but the reported threshold for more than 99% reward was at least 224 modes. The gap widened when the networks faced unfamiliar speeds: at half speed, networks retaining fewer than 128 modes obtained no uncued rewards, while at twice speed, rank above 128 was associated with first-stop accuracy comparable to the full-rank network.
Where the correction signals mattered
The perturbation tests suggested that the modes did not all play interchangeable roles. Removing self-recurrence within either of the first two modes, or removing inputs from later modes onto those leading modes, was associated with 0% uncued reward. Removing self-recurrence from modes four onward had no reported effect, while removing inputs onto later modes left uncued reward above 99%.
The same broad pattern appeared in a two-dimensional task, although the compact representation was less complete. The first two principal components accounted for 66% of activity variance. Cued reward was maximized at rank 16, and both cued and uncued reward were maximal by rank 64, but location decoding at rank 64 remained below 0.7. After a speed perturbation, the reported error was below 0.2 activity units in full-rank networks and above 1.0 activity units at rank two.
Some neuron-level tests also connected targeted changes with behaviour. Manipulating a population smaller than 2% of the neurons, when selected by its behavioural effect, was associated with a predictable shift in stopping location. Larger populations were needed when neurons were selected using principal-component loading alone.
A result about models, not brains
The authors interpret the findings as evidence that higher-rank structure is functional rather than leftover complexity. The work used trained artificial recurrent networks and model manipulations, so it is not direct evidence that humans, animals or biological circuits use an equivalent scaffold. It also does not establish that the pattern extends beyond the tested spatial tasks and speed distributions.
Approximately half of the trained networks exceeded 95% final mean reward and were retained for analysis, so selection of successful models may affect how broadly the results apply. Some of the central demonstrations focused on a representative 512-neuron network. Those choices leave open how consistently the same pattern would appear across other models and tasks.
The authors state that all data will be made available through the Nolan Lab repository on the University of Edinburgh DataShare site and that the analysis code will be made available from the Nolan Lab GitHub page. The work was supported by the Simons Initiative for the Developing Brain, Wellcome Trust funding, the Wellcome Translational Neuroscience PhD programme, UKRI BBSRC funding and Edinburgh Compute and Data Facility resources. The authors declare no competing interest.
Paper data and sources
Original title: High-rank connectivity scaffolds support precision and generalisation in recurrent neural networks
Authors: Ian Hawes, Matt Nolan
Journal/Repository: arXiv
Status: Preprint, not yet peer-reviewed
First online: 2026-09-28
DOI: Not available
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