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Enrico @enricocaprioglio.bsky.social · 18/09/2025

Is there any reason to believe that this intuition works for other complex systems? And does it work using real data (our proofs do require the correlation matrices to have a spectral radius < 2)? Surprisingly, yeah it works!

(LEFT) Antibalanced interaction motifs characterize synergy-dominated complex systems with pairwise coupling. Plots show Ω versus the number of antibalanced triangles in the pairwise coupling matrix. (a) For the Ising model we compute Ω exactly for each possible coupling configuration (β = 0.25). (b) For the SL network of oscillators we report the mean Ω (circle) over 100 initial conditions and the minimum Ω (star) found (lower bound) across configurations with a specific no. of antibalanced triangles.

The curves in both (a) and (b) are similar to the one for the OU process. With no antibalanced triangles, the system is displaying the highest redundancy. While for the largest number of antibalanced triangles, the system show the lowest Ω(X) (most synergistic)

(RIGHT) Structural balance-energy predicts synergy: the most synergistic N-plets maximise U and positive U guarantees synergy-dominance. (a) N-plets from a multivariate time-series of 9 foreign-exchange (FX) rate logarithmic returns. (b) N-plets from resting-state fMRI functional-connectivity matrices (229 brain regions).
Here we see that Ω(X) and a measure of balanced U behave very similarly (strongly anticorrelated). Near zero however, interesting stuff happens.

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Enrico @enricocaprioglio.bsky.social · 18/09/2025

Some final thoughts/questions: 1 - Interesting things happen at the pairwise level, which need to be taken into account. Negative/inhibitory interactions are very important in many biological systems (and maybe in social systems as well? idk)

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Enrico @enricocaprioglio.bsky.social · 18/09/2025

2 - synergy from low-order interactions does seem less mysterious now! But, how do these antibalanced interaction motifs came to be? 3 - SBT and multivariate IT thus seem very similar (especially when you assume Gaussianity). What can we learn from combining these two lines of work?

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