arxiv: 2604.17713 · v1 · submitted 2026-04-20 · 💻 cs.LG

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Modeling Higher-Order Brain Interactions via a Multi-View Information Bottleneck Framework for fMRI-based Psychiatric Diagnosis

Kunyu Zhang , Qiang Li , Vince D. Calhoun , Shujian Yu

Authors on Pith no claims yet

Pith reviewed 2026-05-10 04:57 UTC · model grok-4.3

classification 💻 cs.LG

keywords O-informationhigher-order interactionsfMRIpsychiatric diagnosisinformation bottleneckmulti-view learningbrain connectivitysynergy-redundancy

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The pith

A signed measure of higher-order brain interactions improves fMRI psychiatric diagnosis when fused in a multi-view information bottleneck.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper aims to show that resting-state fMRI can yield better psychiatric diagnoses by explicitly modeling higher-order interactions among brain regions, which may be either synergistic or redundant rather than simply additive. It introduces O-information as a signed quantity that distinguishes these informational characters and embeds third- and fourth-order terms into a tri-view information bottleneck architecture that fuses pairwise, triadic, and tetradic connectivities while penalizing redundancy. A reader would care because most existing methods rely on pairwise edges or heuristic hyperedges that leave the synergy-redundancy balance uncharacterized, potentially missing dynamics central to conditions such as depression and autism. The authors also supply Gaussian and randomized Rényi accelerations to make fourth-order computation feasible.

Core claim

The paper claims that O-information supplies a signed characterization of whether higher-order interactions are synergy- or redundancy-dominated, and that integrating third- and fourth-order O-information into a unified multi-view information bottleneck framework captures comprehensive brain connectivity for improved psychiatric diagnosis from fMRI data, outperforming pairwise and hypergraph baselines on multiple datasets while revealing interpretable region-level patterns.

What carries the argument

O-information, the signed information-theoretic measure of higher-order interactions, integrated as the third and fourth views inside the multi-view information bottleneck that fuses connectivity orders while penalizing redundancy.

If this is right

The tri-view architecture yields consistent gains over eleven baselines, including graph neural networks and hypergraph methods, across four independent fMRI cohorts.
The framework identifies region-level synergy-redundancy patterns that conventional hypergraph constructions do not explicitly report.
The two acceleration strategies deliver more than thirty-fold speedup, making fourth-order terms practical for routine analysis.
Explicit redundancy penalization produces more compact and clinically interpretable representations than unpenalized higher-order models.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

If the identified synergy-redundancy maps generalize, they could function as candidate biomarkers for stratifying patients before symptom onset or for tracking treatment response.
The same multi-view fusion logic could be transferred to EEG or MEG recordings to examine how higher-order dynamics evolve over shorter timescales.
The signed character of O-information raises the question of whether healthy brains maintain a different synergy-redundancy balance than disordered ones, a testable hypothesis left open by the current diagnostic focus.
Scalability improvements open the door to population-scale studies that correlate fourth-order patterns with genetic or environmental variables.

Load-bearing premise

The Gaussian analytical approximation and randomized Rényi estimator must preserve the signed synergy-redundancy distinctions in O-information so the resulting patterns remain clinically meaningful rather than estimation artifacts.

What would settle it

A side-by-side run on the same datasets in which exact O-information computation replaces the accelerated estimators and produces materially different diagnostic accuracies or different region-level synergy-redundancy maps.

Figures

Figures reproduced from arXiv: 2604.17713 by Kunyu Zhang, Qiang Li, Shujian Yu, Vince D. Calhoun.

**Figure 2.** Figure 2: Overview of the MvHo-IB++ framework. Raw rs-fMRI data are parcellated using the AAL-116 atlas or the Neuromark 2.2 template to extract ROI/ICN time series, from which three complementary views are constructed: a 2D pairwise mutual-information matrix, a 3D third-order O-information tensor, and a 4D fourth-order O-information tensor. Each view is processed by a specialized encoder (GIN hϕ1 , Brain3DCNN hϕ2 ,… view at source ↗

**Figure 3.** Figure 3: Venn diagram illustration of total correlation (TC) and dual total [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗

**Figure 4.** Figure 4: Architecture of Brain4DCNN with three hierarchical layers. (a) The [PITH_FULL_IMAGE:figures/full_fig_p005_4.png] view at source ↗

**Figure 5.** Figure 5: Hyperparameter sensitivity analysis on the UCLA dataset. Panels [PITH_FULL_IMAGE:figures/full_fig_p008_5.png] view at source ↗

**Figure 6.** Figure 6: Discriminative higher-order interaction patterns in major depressive [PITH_FULL_IMAGE:figures/full_fig_p010_6.png] view at source ↗

read the original abstract

Resting-state functional magnetic resonance imaging (fMRI) has emerged as a cornerstone for psychiatric diagnosis, yet most approaches rely on pairwise brain cortical or sub-cortical connectivities that overlooks higher-order interactions (HOIs) central to complex brain dynamics. While hypergraph methods encode HOIs through predefined hyperedges, their construction typically relies on heuristic similarity metrics and does not explicitly characterize whether interactions are synergy- or redundancy-dominated. In this paper, we introduce $O$-information, a signed measure that characterizes the informational nature of HOIs, and integrate third- and fourth-order $O$-information into a unified multi-view information bottleneck framework for fMRI-based psychiatric diagnosis. To enable scalable $O$-information estimation, we further develop two independent acceleration strategies: a Gaussian analytical approximation and a randomized matrix-based R\'enyi entropy estimator, achieving over a 30-fold computational speedup compared with conventional estimators. Our tri-view architecture systematically fuses pairwise, triadic, and tetradic brain interactions, capturing comprehensive brain connectivity while explicitly penalizing redundancy. Extensive evaluation across four benchmark datasets (REST-meta-MDD, ABIDE, UCLA, ADNI) demonstrates consistent improvements, outperforming 11 baseline methods including state-of-the-art graph neural network (GNN) and hypergraph based approaches. Moreover, our method reveals interpretable region-level synergy-redundancy patterns which are not explicitly characterized by conventional hypergraph formulations.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Desk Editor's Note private letter to a colleague

The tri-view IB with signed third- and fourth-order O-information is a clean modeling step for fMRI HOIs, but the speed-up approximations lack the sign-preservation checks needed to support the interpretability claims.

read the letter

The core move here is embedding signed O-information as three separate views inside an information-bottleneck objective so the model can explicitly favor synergy over redundancy in brain interactions. That is new relative to standard hypergraph or pairwise GNN approaches, and the two acceleration tricks (Gaussian analytical approximation plus randomized matrix-based Rényi estimator) make the higher-order terms feasible at scale, delivering the reported 30-fold speedup. Running the same pipeline on four standard datasets and beating eleven baselines is also solid execution for this kind of work. The interpretability maps of synergy-redundancy patterns follow directly from the signed measure if everything else holds. The soft spots sit in the empirical support. The abstract gives no error bars, no ablation on how much the approximations distort the signed O-information, and no detail on how the three views are weighted inside the bottleneck loss. If the Gaussian or randomized estimators flip or blur the sign of the higher-order terms, the claimed clinical patterns become unreliable even if classification accuracy improves. That assumption is load-bearing for the paper's main selling point. This is aimed at people already working on connectivity-based psychiatric classifiers who want a practical way to move past pairwise graphs without jumping straight to full hypergraph construction. The modeling is coherent and the datasets are appropriate, so it deserves a serious referee who can ask for the missing validation on the estimators and a few targeted ablations. I would bring it to a reading group to walk through the approximation details and see whether the sign preservation actually checks out.

Referee Report

4 major / 2 minor

Summary. The manuscript proposes a multi-view information bottleneck framework for fMRI-based psychiatric diagnosis that incorporates higher-order interactions using third- and fourth-order O-information as signed measures of synergy and redundancy. It introduces Gaussian analytical approximation and randomized matrix-based Rényi entropy estimator for efficient computation, achieving over 30-fold speedup, and evaluates the approach on four benchmark datasets, claiming consistent outperformance over 11 baseline methods including GNN and hypergraph approaches, along with interpretable region-level patterns.

Significance. If the approximations are shown to preserve the signed nature of O-information and the empirical claims are supported by statistical analysis, this could represent a significant advance in modeling complex brain dynamics for diagnosis by explicitly distinguishing synergy-dominated from redundancy-dominated higher-order interactions in a unified framework, going beyond pairwise or heuristic hypergraph methods.

major comments (4)

[Methods (O-information estimation)] The Gaussian analytical approximation and randomized matrix-based Rényi estimator are central to scalability, but the manuscript lacks explicit validation that these approximations preserve the sign of O-information (positive for synergy, negative for redundancy) compared to exact estimators. Without such checks on synthetic or small-scale data, the claimed interpretability of synergy-redundancy patterns may be compromised.
[Experimental Results] The abstract and results claim consistent improvements on four datasets without reporting error bars, standard deviations, or statistical significance tests (e.g., paired t-tests or Wilcoxon tests) against baselines. This omission weakens the support for the central empirical claim of outperformance.
[Multi-view IB Framework] There is no description or ablation on how the three views (pairwise, triadic, tetradic) are balanced or weighted inside the information bottleneck objective, nor on the sensitivity to the trade-off parameters. This is load-bearing for the tri-view fusion claim.
[Ablation Studies] No ablation is provided on the effect of the approximation error on classification accuracy or on the extracted HOI patterns, leaving the contribution of the acceleration strategies to the overall performance unclear.

minor comments (2)

[Abstract] The abstract mentions 'over a 30-fold computational speedup' but does not specify the baseline estimator or the datasets used for timing.
[Notation] Clarify the exact definition of O-information for orders 3 and 4, perhaps with equations in the main text rather than appendix.

Simulated Author's Rebuttal

4 responses · 0 unresolved

We thank the referee for the detailed and constructive review. We address each major comment below and will revise the manuscript to incorporate the requested clarifications, validations, and analyses.

read point-by-point responses

Referee: [Methods (O-information estimation)] The Gaussian analytical approximation and randomized matrix-based Rényi estimator are central to scalability, but the manuscript lacks explicit validation that these approximations preserve the sign of O-information (positive for synergy, negative for redundancy) compared to exact estimators. Without such checks on synthetic or small-scale data, the claimed interpretability of synergy-redundancy patterns may be compromised.

Authors: We agree that explicit sign-preservation validation is necessary to support the interpretability of the extracted patterns. While the approximations are analytically motivated to retain the signed nature of O-information, we did not report direct comparisons in the original submission. We will add a dedicated validation subsection using synthetic multivariate Gaussian data and small discrete systems, comparing the sign and magnitude of O-information from our estimators against exact computations, and include these results in the revised Methods and Experiments sections. revision: yes
Referee: [Experimental Results] The abstract and results claim consistent improvements on four datasets without reporting error bars, standard deviations, or statistical significance tests (e.g., paired t-tests or Wilcoxon tests) against baselines. This omission weakens the support for the central empirical claim of outperformance.

Authors: We acknowledge that the absence of variability measures and statistical tests limits the strength of the empirical claims. In the revision we will report all results as mean ± standard deviation across 10 independent runs (different random seeds and data splits), add error bars to all figures and tables, and include paired statistical significance tests (Wilcoxon signed-rank test with Bonferroni correction) against the 11 baselines. The abstract and results sections will be updated to reflect these additions. revision: yes
Referee: [Multi-view IB Framework] There is no description or ablation on how the three views (pairwise, triadic, tetradic) are balanced or weighted inside the information bottleneck objective, nor on the sensitivity to the trade-off parameters. This is load-bearing for the tri-view fusion claim.

Authors: We agree that the weighting and sensitivity analysis are essential for the tri-view claim. The current objective combines the three views via a weighted sum of their respective IB terms, with weights proportional to the number of interactions per order and a shared trade-off parameter β. We will expand the Methods section with the explicit multi-view objective function, describe the weighting scheme, and add an ablation study varying β across a range of values to demonstrate robustness and the contribution of each view. revision: yes
Referee: [Ablation Studies] No ablation is provided on the effect of the approximation error on classification accuracy or on the extracted HOI patterns, leaving the contribution of the acceleration strategies to the overall performance unclear.

Authors: We concur that quantifying the impact of the approximations on downstream performance and patterns is important. We will add an ablation study that (i) compares classification accuracy using the proposed estimators versus exact estimators on feasible small-scale subsets of the data, and (ii) measures stability of the extracted region-level synergy-redundancy patterns under approximation error. These results will be reported in a new ablation subsection. revision: yes

Circularity Check

0 steps flagged

No significant circularity; derivation is self-contained

full rationale

The paper computes third- and fourth-order O-information directly from fMRI data (via Gaussian approximation and randomized Rényi estimator for speed), then feeds the resulting signed synergy/redundancy values into a standard multi-view information-bottleneck objective whose loss penalizes redundancy. No equation defines the diagnosis label or classification target in terms of itself; no fitted parameter is relabeled as a prediction; the IB objective is the conventional one and does not smuggle an ansatz via self-citation. The reported performance gains are measured on external benchmark datasets, keeping the chain independent of the target variable.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The framework rests on the domain assumption that O-information computed from BOLD time series faithfully reflects synergy versus redundancy in neural populations; no new free parameters or invented entities are declared in the abstract.

axioms (1)

domain assumption O-information estimated from fMRI time series accurately distinguishes synergy-dominated from redundancy-dominated higher-order interactions
Central modeling choice stated in the abstract; no independent validation of the signed measure on fMRI is provided here.

pith-pipeline@v0.9.0 · 5564 in / 1231 out tokens · 32505 ms · 2026-05-10T04:57:36.593454+00:00 · methodology

discussion (0)

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Here, O-information is reduced in SZ (triplet:∆ =−0.096; quadru- plet:∆ =−0.134), the only negative-valued pattern among the top discriminators

and quadruplet (83, 84, 95, 96), links the networks tem- poroparietal (ICA83, ICA84), and default mode (ICA96). Here, O-information is reduced in SZ (triplet:∆ =−0.096; quadru- plet:∆ =−0.134), the only negative-valued pattern among the top discriminators. Together, these findings support the dysconnection hypothe- sis [53], indicating that schizophrenia ...
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Similarly, in MDD, triplet (73, 74, 76) extends to quadruplet (73, 74, 75, 76), and triplet (55, 56, 100) to quadruplet (55, 56, 99, 100)

to quadruplet (83, 84, 95, 96). Similarly, in MDD, triplet (73, 74, 76) extends to quadruplet (73, 74, 75, 76), and triplet (55, 56, 100) to quadruplet (55, 56, 99, 100). In MCI, triplet (3, 7, 23) extends to quadruplet (3, 7, 22, 23), triplet (48, 50, 52) to quadruplet (48, 50, 52, 54), and triplet (92, 100, 102) to quadru- plet (92, 100, 102, 104). This...