Huge thanks for this fun collaboration to past and present members of the NPLab — Matteo Neri, @poetz.bsky.social, Davide Orsenigo, Matteo Diano, @marilyngatica.bsky.social, @lordgrilo.bsky.social 🙌🧠

14/ This work takes an important step toward a unified roadmap for navigating the complex, fragmented landscape of higher-order brain connectivity.

13/ In short:

✅ HOIs provide richer, biologically grounded insights into brain function
✅ The research landscape is now organized — synergy, redundancy, topology
✅ HOIs better capture traits; FC better captures states
✅ Tools are available for broader use (HOI toolbox, TDA code, etc.)

12/ One standout: topological scaffolds. They act as integrators — capturing synergy in nodes, and structure-function coupling at edges. They're central in linking connectivity patterns to behavior.

11/ Even dopamine levels relate: lower dopamine -> more flexible task-related reconfiguration.

10/ HOIs also help explain how the brain reconfigures during different tasks. Social/emotional tasks show more synergy, while sensorimotor ones lean on redundancy.

9/ This shows a key trade-off:

🔍 If you want to understand who a person is (trait-level): use HOIs
⚡ If you want to know what they're doing (state-level): FC is often enough

8/🧠 For task decoding, though, classic FC is still one of the top methods.

7/ When it comes to applications, HOIs show their power:

🎯 For brain fingerprinting (ID'ing individuals), HOI metrics outperform classical functional connectivity (FC)

6/ But there's more.

These metrics also reflect the brain’s neurochemistry:
• Redundant metrics correlate with metabolic maps
• Synergistic & topological metrics align with receptor distributions

5/ Despite different math, rank differences of all HOI metrics align with the brain's core hierarchy: from sensory (unimodal) to associative (transmodal) cortex.

This "HOI axis" reflects fundamental computational principles embedded in the brain’s layout. 🧭

4/ First big insight: HOI metrics fall into 3 categories:

🔴 Redundant: capture overlapping info (e.g., within sensory networks)
🔵 Synergistic: capture integrative info (e.g., across systems)
🟣 Topological: bridge the two, identifying mesoscale structures

3/ Yet with all these new tools — PhiID, O-information, PED, persistent homology, triangles, scaffolds — no one knew how they compared, what they captured, or when to use which.

This paper tackles this directly with a comprehensive comparison across 10 HOI metrics.

2/ Brain models often focus on pairs of regions, but real interactions might involve groups acting together

HOI methods aim to capture this, from detecting synergy and redundancy using different information-theoretic approaches to mapping topological cycles in brain networks.

🧵 1/ Over the past years, brain connectivity research has moved beyond simple pairwise interactions. A wide range of higher-order interaction (HOI) methods — from information theory to topological data analysis — have emerged.

But the field is quite fragmented. Let's dive in. 🧠