Hierarchical organization of critical brain dynamics

Abstract: The hierarchical organization of the brain is a fundamental structural principle, while brain criticality is a leading hypothesis for its collective dynamics. However, the connection between structure and signatures of criticality remains an open question. Here, we address this issue by applying phenomenological renormalization group approaches to large-scale neuronal spiking activity from the mouse visual cortex and hippocampus. We find that signatures of criticality are not uniform, but instead vary systematically along the known anatomical hierarchy in both brain systems. Strikingly, the direction along this gradient is inconsistent across different criticality exponents, revealing a nontrivial, measure-dependent organization: exponents based on static properties point to a gradient in one direction, while the exponent based on dynamic properties points in the opposite direction. Moreover, the signatures across the visual system are strongly modulated by the engagement in a visual task. We show that the correlations among criticality markers of different brain regions during active engagement are sufficient to reconstruct the anatomical hierarchy from the dynamics. Scaling exponents closely follow a theoretically predicted scaling relation among them, and covary with the hierarchical position. Our findings provide a direct link between the collective dynamics of neurons and the macroscopic architecture of the brain.

• The paper shows that signatures of critical brain dynamics vary systematically across anatomical hierarchies, particularly in visual and hippocampal regions.
• The study employs PRG and community detection methods to reveal contrasting static and dynamic scaling exponents along neural hierarchies.
• Findings suggest that behavioral context modulates these critical signatures, indicating dynamic tuning of brain computation near phase transitions.

Hierarchical Structure in Critical Brain Dynamics

Introduction

The concept of criticality in neural systems posits that brain dynamics operate near phase transitions, theoretically optimizing computational performance, information capacity, and sensitivity to inputs. Yet, the spatial organization of critical signatures across the brain, and their potential alignment with anatomical hierarchies, remains unclear and contested. The study "Hierarchical organization of critical brain dynamics" (2604.21832) rigorously investigates this issue using large-scale spiking data from mouse visual cortex and hippocampus, leveraging both phenomenological renormalization group (PRG) analyses and community detection methods.

Methodological Framework and Data Acquisition

The study employs PRG techniques—including momentum-space and real-space approaches—to mass neuronal spiking recordings in mice performing visual tasks. Coarse-graining procedures and statistical distances (notably the Jensen-Shannon distance, $D_{JS}$) quantify deviations from Gaussianity in progressively aggregated activity, offering multi-scale estimates of proximity to criticality.

Figure 1: Anatomical localization and visual hierarchy of mouse brain regions subjected to PRG analysis.

Selection criteria required >128 simultaneously recorded units per region to ensure statistical stability, with regional analysis spanning the full depth of the visual hierarchy and hippocampus. Experimental phases included active, passive, and non-natural image (NNI) presentations.

Non-Gaussianity and Regional Gradients in Critical Signatures

A central finding is the observation that the distribution of $D_{JS}$—which indexes distance from a trivial fixed point corresponding to Gaussian dynamics—varies systematically across the anatomical hierarchy. Visual areas display diverse, region-specific $D_{JS}$ distributions, with the primary visual cortex (VISp) exhibiting the largest deviations from Gaussianity, particularly during task engagement. In contrast, more integrative regions (e.g., VISam) demonstrate reduced $D_{JS}$, closer to triviality.

Figure 2: Distributions of Jensen-Shannon distance $D_{JS}$ for visual and hippocampal regions, illustrating region- and context-dependence.

The hippocampus presents a similar but less contextually modulated gradient, with the dentate gyrus (DG) manifesting pronounced critical deviations, unlike the more intermediate Cornu Ammonis areas.

Figure 3: Median and quartile statistics of $D_{JS}$ across hierarchical axes for visual and hippocampal systems, with pronounced active task modulation in the visual hierarchy.

Extraction and Alignment of Functional and Anatomical Hierarchies

Temporal correlations in $D_{JS}$ across regions reveal modular community structure corresponding to established anatomical divisions. Functional connectivity derived from these criticality signatures robustly maps onto known hierarchies in both the visual system and hippocampus across behavioral contexts; functional integration is highest during natural image processing.

Figure 4: Inter-regional correlation matrices of $D_{JS}$ during various phases, with dendrograms depicting inferred functional hierarchies.

Community detection on these correlation matrices recapitulates the partition between visual cortical and hippocampal systems, and further refines the hierarchical gradient within each system based solely on dynamic critical signatures.

Scaling Exponents and Conflicting Criticality Gradients

The real-space PRG approach provides static scaling exponents ($\alpha$ from variance scaling, $\beta$ from silence probability) and a dynamical exponent ($D_{JS}$0 from autocorrelation scaling). The key findings are:

• Static exponents ($D_{JS}$1, $D_{JS}$2) exhibit decreasing trends along the anatomical hierarchy, i.e., regions closer to sensory input (VISp or DG) possess more pronounced critical scaling, with higher $D_{JS}$3 and lower $D_{JS}$4 values.
• In contrast, the dynamical exponent $D_{JS}$5 increases along the hierarchy, indicating longer temporal correlations (critical slowing down) at higher integrative levels (e.g., VISam), directly conflicting with the static scaling trend.

  Figure 5: Region- and context-wise distributions of $D_{JS}$6, $D_{JS}$7, and $D_{JS}$8 exponents, showing opposing gradients for static and dynamic measures across hierarchies.

The measured static exponents closely follow the theoretical scaling relation $D_{JS}$9, indicating broad consistency of PRG theory across spatially disparate neural populations.

Figure 6: Interrelation of scaling exponents, showing the collapse of empirical static exponents along the theoretical scaling law for both visual cortex and hippocampus.

Discussion and Theoretical Implications

This work unambiguously demonstrates that signatures of critical brain dynamics are not spatially uniform but closely track anatomical hierarchies. The divergence in gradient direction between static and dynamic criticality markers challenges over-simplifications in the interpretation of brain criticality and indicates a measure-dependent organization. This has theoretical implications for understanding the optimization hypothesis—whether computation in the brain is maximized at a putative critical point and, crucially, whether different computational goals may select for distinct operational points along critical manifolds.

The functional connection matrices inferred from critical signatures outperform traditional approaches based on firing rates or naive correlation in recapitulating brain architecture. This advances methods for connectomics and offers new paradigms for the identification of mesoscale networks purely from collective dynamics and scaling deviations, potentially applicable to other neural recording modalities.

Prospects for Future Research in Systems Neuroscience and AI

The finding that criticality signatures reflecting different aspects of collective neural dynamics (static vs. dynamical) follow opposing anatomical gradients necessitates more nuanced models of how criticality interfaces with information processing and behavioral modulation. Specifically, the context-dependent gain in criticality signatures during task engagement suggests dynamic tuning of operational regimes, with implications for models of attention, consciousness, and state-dependent computation. The methodological toolkit—especially robust, distributional measures of non-Gaussianity under coarse-graining—can also enhance the study of emergent computation in artificial systems, toward building neuromorphic or brain-inspired AI architectures that leverage critical dynamics for flexible, efficient information processing.

Conclusion

This study rigorously links large-scale critical dynamics to the hierarchical architecture of the brain, with distinct, measure-dependent gradients revealed by PRG analyses. The ability to reconstruct anatomical hierarchies from dynamics alone, the divergence between static and dynamical critical scaling, and the modulation of criticality by behavioral context collectively challenge monolithic interpretations of brain criticality and advance both theoretical and practical methodologies for understanding collective computation in neural systems.