Single neurons possess the capacity to extract ranks of items in a linear order using a simple local rule for synaptic plasticity, according to research published in Nature Communications. Researchers Yukun Yang and Wolfgang Maass from the Institute of Machine Learning and Neural Computation at Graz University of Technology presented the mathematical theory to show how biological circuits handle relational learning.
The model addresses a long-standing question in neuroscience, as the exact mechanisms by which brains extract relations between objects and concepts to build cognitive maps for decision-making had remained unclear. The team showed that their model explains human brain data on how cognitive maps emerge from linear orders while accounting for the terminal item effect in transitive inference. It also enables internal representations to reconfigure rapidly whenever new evidence appears. Additionally, Yang and Maass formulated a theoretical explanation for why two-dimensional projections of neural representations of linear orders appear curved rather than linear inside the brain.
Because the theoretical framework requires only local synaptic plasticity within shallow networks, it can execute relational learning and rapid inference on low-energy edge hardware. To test this capability, the researchers successfully implemented and demonstrated the model on the Loihi 2 neuromorphic chip. Hardware support and implementation advice for the chip demonstration were provided by Philipp Plank.
The study acknowledges feedback from Christopher Summerfield, Giovanni Pezzulo, Guozhang Chen, Alice Dauphin, and Hui Lin, alongside an anonymous reviewer who noted an alternative proof of the Rank Convergence Theorem for δ=0 through the Perceptron Convergence Theorem. Funding was provided in part by the U.S. National Science Foundation under EFRI BRAID project 2318152 and the Austrian Science Fund through its Excellence Cluster on Bilateral AI. Nature Communications received the manuscript on 22 July 2025, accepted it on 20 July 2026, and published the final open-access paper on 05 August 2026.
