The Brain as a Jazz Trio: Why Three-Way Connections Matter More Than Pairs ✛

Original: "High-Order Triadic Functional Connectivity in the Brain and Beyond"
arXiv:2609.03987v1 · 2026-09-03 · CC BY 4.0 · 2 min
Scientists have found a way to see how three brain regions work together, and it changes the picture.

A jazz trio plays in a club: pianist, bassist, and drummer. If you listen to only two of them, you can understand how the pianist adapts to the bass or the bass to the drums. But the real music emerges when all three play together: one phrase changes the playing of the others. The brain at work resembles such a trio: several regions act in concert, and this collective interplay cannot be reduced to individual pairs.

Previously, scientists measured brain connections only in pairs: they took the signal from one region, the signal from another, and looked at how well they agreed. But this missed situations where three regions coordinate together. The new method assesses exactly these triple interactions. The researchers used fMRI data from 600 people at rest and 66 people watching a movie. For each triple among 105 brain regions, they computed a measure of joint dependence that indicates how strongly these regions are linked.

Triple connections turned out to be 34 times more numerous than pairwise ones: 187 460 versus 5 460. But instead of chaos, they form organized groups that reflect the brain's real functioning.

It turned out that triple connections carry more information than pairwise ones, and that during task performance the brain uses more complex collective interactions. This is like jazz: when musicians play together, the music is richer than the sum of individual duets. The new method allows us to see this collective play and understand what happens when the ensemble falls apart in disease.

The number of unique triples from 105 networks (187,460) is roughly equal to the number of words in the novel "War and Peace" (about 188,000). If we tried to enumerate all triples for 1,000 regions, the number would exceed the number of atoms in the observable universe.

The idea that the brain processes information not pairwise but as whole ensembles echoes the concept of collective intelligence in Stanisław Lem's "Solaris," where the ocean exhibits intelligent behavior only as a whole, not through individual elements.

TC(X_1,...,X_n) = \sum_{i=1}^{n} H(X_i) - H(X_1,...,X_n)
A measure of the overall dependence among several variables; it is zero if the variables are independent.
H_\alpha(X) = \frac{1}{1-\alpha} \log \operatorname{tr}(A^\alpha)
Allows computing entropy from the Gram matrix without explicitly estimating the probability density.
Concepts
brain connectivity neural network neural network memory architecture working memory parietal region brain information storage learning hippocampus synapse functional analysis visual cortex transfer learning complex systems weight frame transformers magnetic superconductivity coupling order pattern recognition