Assessing Criticality as an Evolutionary Setpoint across the Visual Hierarchy

Applicant: Sean McCracken, Ph.D.

Postdoctoral Research fellow, University of Virginia. Cang Lab.

Host Laboratory: Dr. Jianhua (JC) Cang, University of Virginia

Total Budget Requested: $10,000 USD (in RSC)

Timeline: ~6 Months

1. Overview

A central challenge for any neural circuit is maintaining a balance between stability and sensitivity, i.e. homeostasis. If a network is too stable (sub-critical), it cannot efficiently propagate signals ; if it is too excitable (super-critical), it risks runaway activity and noise saturation. The "Criticality Hypothesis" posits that the healthy brain operates at or near a universal optimum (between order and chaos) to maximize information capacity and dynamic range. While studies suggest criticality as a universal homeostatic setpoint in the visual cortex (V1) (Ma et al., 2025; Hengen et al., 2013; Shew et al., 2015), it remains unknown the relationship with critical dynamics and subcortical visual hubs (i.e. Superior Colliculus (SC) or Lateral Geniculate Nucleus (LGN)), which face different computational constraints and functions.

This project will re-analyze five high-density electrophysiological datasets across mice (LGN: Zhao et al., 2013); V1: Fu et a., 2023; SC: Li et al., 2025; LGN and SC: Elsayed et al., 2026) and the Tree Shrew (SC = Li et al., 2026) all collected within the Cang lab at UVA. By applying a standardized "temporal coarse graining" analysis, we can determine the deviation from criticality coefficient (DCC) over time and across visual stimulation conditions. These analysis and others will determine how criticality is related to visual perception and homeostasis across the visual system heirarchy. We will determine if subcortical structures remain "pinned" to criticality regardless of visual stimulation, contrast this with cortical state-shifting, and develop a cross-species model of subcortical homeostasis

2. Introduction

2.1. Criticality as the computational setpoint of the nervous system

Criticality is a state where neuronal population dynamics exhibit scale invariance and marginal stability near a boundary. There are two necessary and sufficient conditions that constitute the general definition of criticality in neural systems: (1) scale-invariant population dynamics (Stanley, 1999) and (2) existence near a boundary in parameter space. Because it is incredibly difficult to experimentally determine the parameter boundary in neuronal dynamics without manipulating circuits to cause seizures, scale invariance serves as the key feature extracted from data to support the criticality hypothesis.

Recently, a meta-analysis of over 46 studies utilizing single-neuron resolution in awake animals demonstrated that in-vivo recordings display critical dynamics only when data is binned with larger time windows, indicating that robust scale invariance emerges at larger timescales (Shew and Hengen, 2025). The two seminal approaches for evaluating this scale invariance are neuronal avalanche analysis and long-range temporal correlations (LRTC) (Linkenkaer-Hansen, 2001; Beggs and Plenz, 2003). This proposal plans to assess if neuronal dynamics across the visual hierarchy are scale-invariant by evaluating LRTCs, avalanche distributions, and the distance from criticality coefficient. Given the recent evidence for criticality as a fundamental computational principle in awake animals (Hengen and Shrew, 2025) and the visual system (Ma et al., 2025), evaluating awake recordings of mice across the visual system would allow for analytical determination of criticality as a unifying homeostatic principle across a neural system.

2.2. Hierarchical Processing and the Unifying Principle

The visual system processes information through a sophisticated hierarchy, where neural codes become increasingly decorrelated and abstract as information ascends. While current models focus on the mechanical differences between regions—such as the spatial decorrelation in V1 (Elsayed et al., 2025) versus the stable vector summation in the SC (Li et al., 2025)—this project explores a more fundamental question: Is criticality the manifestation of a unifying principle that underlies the nervous system?

We hypothesize that criticality is not merely a local circuit trick, but the enactment of an underlying, mathematically "perfect" state of organization. In this view, the diverse architectures of the visual hierarchy are different structural attempts to achieve the same ideal state of balance. If the cortex constantly shifts its dynamic regime to process complex binocular integration, we must ask if this is a "departure" from perfection or a sophisticated way of maintaining it across multiple scales. By contrast, we will investigate whether the subcortex remains the "anchor" of this state—locked at or near criticality, with little deviations, to ensure that the organism’s most vital, reflexive interactions with reality are guided by this optimized dynamic order.

Beyond a local circuit property, criticality may represent a universal "Goldilocks" state for the nervous system—a metaphysical unifying point where information transmission is maximized across disperse neural systems and ecological environments. If the "Criticality Hypothesis" holds, it suggests that despite the vast differences in morphology between a mouse and a human, the underlying computational state required for complex life is identical in similar subsystems. This project suggests that criticality may be a biological constant, and explores directly how different species tune their hardware to this specific frequency of operation.

2.3. The Evolutionary Gradient: From Mouse to Tree Shrew

We propose that the precision of these setpoints correlates with evolutionary complexity and behavioral demands.

The Mouse (Sub-critical/Noisy): As a nocturnal prey species, the mouse visual system may operate in a slightly sub-critical, noisier regime. In this state, the network is "safer" and less prone to runaway excitation, but it pays a price in information capacity and signal interpretability.
The Tree Shrew (The Evolutionary Bridge): As a diurnal species with a fovea and advanced visually-guided behaviors (e.g., high-speed arboreal jumping), the tree shrew represents a middle point between rodents and humans. Such complex, high-stakes motor control likely requires an optimum for criticality to process orientation-invariant signals at reflexive speeds.
The Tuning Hypothesis: We hypothesize that advanced neural systems are defined not just by being critical, but by the strength of their "homeostatic pull"—the ability to suffer massive deviations (learning, arousal) and return precisely to the critical setpoint. The Tree Shrew SC, therefore, should show a much tighter adherence to criticality than the mouse.

3. Specific Aims

Aim 1: Determine if subcortical structures (SC and dLGN) operate at criticality and if this state is invariant to visual stimulation or arousal.

We will test if the "setpoint" of criticality is more rigidly maintained in the subcortex than the cortex. Cortical circuits in V1 are known to undergo dramatic state changes during locomotion or heightened arousal to facilitate spatial decorrelation (REF). We hypothesize that subcortical structures, tasked with stable threat detection and stable motor output, will exhibit scale-invariant dynamics (power-law distributions) that are significantly more robust to fluctuations than V1. We may then also hypothesize that the SC would be more robust, and have fewer fluctuations from criticality, than the LGN due to the LGN <—> V1 connectivity.

Aim 2: Compare criticality across animal species and develop a model for homeostatic connectivity in the SC.

Using data from both the mouse (nocturnal, prey) and the tree shrew (diurnal, evolutionarily closer to primates), we will assess if the "critical" state of the SC is an evolutionarily conserved feature of vertebrate vision. We will then develop a computational branching-process model to determine if the SC naturally drives toward a critical state in each aninmal, how deviations occur during visual stimulation, and compare these dynamics to mouse cortex. Together, these analyses will prove an evolutionary relationship across organisms in regards to criticality and neural system dynamics.

3. Methods

To avoid the "contradictory findings" identified in early criticality research (Figure 1), we will implement the following criteria in our analyses, with a specific focus on the vital role of temporal coarse graining ($\Delta T$).

Figure 1, from Hengen and Shrew, 2025 (Posted with their permission). A full list and spectrum for the evidence for criticality, with many studies prior to 2014 showing negative evidence for criticality.

3.1. Temporal Coarse Graining and Scale Invariance

A meta-analysis of 140 avalanche distributions revealed that early spike-based reports often failed to find evidence for criticality due to insufficient temporal coarse graining (Hengen and Shrew, 2025). Specifically, studies using small time bins ($\Delta T < 10\text{ ms}$) consistently failed to capture fluctuations spanning more than 1.5 decades of scale-invariant range. Because neuronal spiking is a point process, capturing slow, multi-timescale dynamics requires a $\Delta T$ large enough that the observation of multiple spikes is likely. In this study, we will move beyond fixed, small windows and adopt a systematic variation of $\Delta T$. We will vary $\Delta T$ from 10-1000 ms to represent the intrinsic timescale of information transmission across neural networks.

We will evaluate avalanche distributions across a wide range of $\Delta T$ and evaluate the propper binning to maximize critical dynamics. We expect to observe a strong correlation between $\Delta T$ and the scale-invariant range. By identifying the "critical" bin size where signatures like parabolic avalanche shapes and power-law scaling emerge, we can reconcile our findings with recent high-resolution studies that report robust evidence for criticality.

3.2. Avalanche Definition and the Deviation from Criticality Coefficient (DCC)

Neural data will be discretized into bins of size $\Delta T$. An "avalanche" is defined as the integrated network activity between threshold crossings (size $S$) and the time elapsed between crossings (duration $D$). A hallmark of a system at criticality is a specific scaling relationship between average avalanche size and duration: $\langle S \rangle \sim D^\beta$. We will extract the empirically fitted exponent ($\beta_{fit}$) and compare it to the predicted exponent derived from the probability distributions:

$\beta_{pred}$ = $\frac{\alpha - 1}{\tau - 1}$

The Deviation from Criticality Coefficient (DCC) is defined as:

$DCC $= $|\beta_{fit} - \beta_{pred}|$

The DCC serves as a highly sensitive, single-number metric representing how far the network state has drifted from true criticality.

3.3. Goodness-of-Fit and Meta-Comparison

We will employ rigorous inclusion criteria and the "WebPlotDigitizer" methodology to benchmark our data against established scale-invariant ranges. We will strictly analyze Probability Density Functions (PDF) rather than Complementary Cumulative Distribution Functions (CCDF) to avoid masking deviations in the distribution tails. We require fit lines to stay within a defined error band for at least 0.99 of their length across at least two decades of scale.

3.4. Complementary Metrics: Branching Ratio, Shape Collapse, and Long-Range Temporal Correlations

To corroborate DCC and avalanche findings, we will employ three additional metrics to fully characterize the network state:

Branching Ratio ($m$): Based on the methods of Wilting and Priesemann (2018), we will examine the ratio of the number of neurons spiking at time $t+1$ relative to time $t$. Because networks suffer from subsampling bias, we will examine different time lags ($k$) to obtain an exponential curve, extracting an accurate $m$ that is robust to missing data. Critical networks maintain a branching ratio of $m \approx 1.0$, meaning activity sustains itself without exploding or dying out.
Shape Collapse: We will verify if avalanche profiles of varying durations can be scaled into a universal, scale-invariant shape $F(t/D)$.
Detrended Fluctuation Analysis (DFA): We will start all analyses by applying a 300 Hz High-Pass filter to isolate multi-unit activity and single action potentials. However, we will also run analyses across different frequencies depending on the changes and optimizations of $\Delta T$. We will be especially interested in evaluating spiking and fluctuations at lower frequencies (<100Hz), similar to Local field potentials, that may be also tuning to criticality.

3.5. Table 1: Definition of quantifiable metrics and their relationship to criticality.

Metric	Processing Requirement	Critical Value	Interpretation
DFA Exponent ($\alpha$)	Requires a "continuous" signal (e.g., firing rate or LFP envelope).	$\alpha \approx 2.0$	Measures long-range "memory." High values mean current activity is influenced by activity from 10+ seconds ago.
Avalanche Power Law ($\kappa$)	Requires "binarized" spike trains (0s and 1s) after filtering.	$\kappa \approx 1.0$	Measures the "transfer of energy." Indicates if activity can cascade through the network without dying out or exploding.
Branching Ratio ($m$)	Requires counting spikes in successive time bins ($t$ vs $t+1$).	$m \approx 1.0$	Measures "sustainability." At 1.0, one spike triggers exactly one other spike on average.
Deviation from Criticality Coefficient (DCC)	Calculated by comparing the slopes of size and duration distributions.	$< 0.2$	The ultimate "check." If the physical scaling of the network matches the theoretical prediction, the system is critical.

4. Expected Results

4.1. Aim 1: Subcortical Invariance vs. Cortical State-Shifting

V1 Prediction: We expect V1 to exhibit "criticality-adjacent" dynamics that fluctuate based on behavioral state. During quiet wakefulness, V1 should remain near criticality (DCC < 0.2). However, during intense visual processing (e.g., binocular disparity integration) or heightened arousal, we expect a transient shift toward sub-criticality (DCC > 0.2), reflecting a temporary sacrifice of scale-invariance to facilitate spatial decorrelation.
SC/dLGN Prediction: Unlike the cortex, subcortical regions are expected to remain "pinned" to the critical setpoint. We predict these regions will maintain a robust power-law distribution with a size slope ($\tau$) near -1.5 and a duration slope ($\alpha$) near -2.0. Crucially, the DCC should remain consistently near 0, and the Kappa ($\kappa$) metric should remain stable regardless of visual stimulus complexity or arousal levels. The shifts in criticality with and without stimulus, as determined by delta DCC, will likely be much smaller in the subcortex as compared to the visual cortex.

4.2. Aim 2: Cross-Species Convergence

Predictive Gradient: We expect to see a clear gradient of "critical precision" across the visual hierarchy: Mouse SC < Tree Shrew SC < Human (Theoretical). * Tree Shrew SC: Because tree shrews rely on high-fidelity visual perception for survival, we predict their SC will display significantly more "parabolic" avalanche shapes and a DCC closer to zero than the mouse.

Metaphysical Implication: If the Tree Shrew SC is more "critical" than the mouse, it suggests that the evolution of the fovea and advanced perception is fundamentally tied to the network's ability to minimize its Deviation from Criticality Coefficient. This would frame the DCC not just as a metric of metaphysical phenomenon, but as a metric of evolutionary "fitness."

4.3. Table 2: Expected values of different criticality metrics

Metric	Sub-Critical (Stable/Random)	Critical (The "Sweet Spot")	Super-Critical (Unstable/Seizure)	Physical Meaning
DCC (Criticality Metric)	< 0.2	< 0.1	> 0.2	Measures the departure of avalanche scaling from theoretical predictions.
DFA Exponent (a=alpha)	a ~.5	a ~2	a > 1.0$	Measures the "memory" of the system. Does a neuron firing now make it more likely to fire 10 seconds from now?

(Long-Range Temporal Correlations)	Signal is random (white noise). No memory of the past.	Signal has "1/f" or Pink Noise structure. Long-term memory exists; the past influences the future across all time scales.	Signal is highly correlated (Brownian noise). System is too rigid and potentially "locked in."
Avalanche Power Law (k=kappa)	K<1Exponential Cutoff	K ~ 1	K > 1 (~1.5)	Measures the "transfer of energy". If one neuron spikes, how many others does it trigger in a cascade?

(Cluster Size Distribution)	Distributions curve downward quickly. Large bursts of activity are impossible.	Straight line on a log-log plot (Power Law). Avalanches of all sizes are possible, even massive ones.	Excess of huge events. The system runs away into giant, synchrony-driven bursts (like a seizure).
Branching Ratio (s)	s < 1.0	S ~~ 1	S > 1.0$	Measures "sustainability". Does a spark of activity fade away, sustain itself perfectly, or turn into a wildfire?

(Stability Parameter)	Activity dies out quickly. The network is dampened (strong inhibition).	Activity is sustained but does not explode. One spike triggers, on average, exactly one other spike.	Activity explodes. One spike triggers two, which trigger four... (Runaway excitation).

5. Future Directions

5.1. Expanded Feature Analysis & Arousal

While initial work will focus on general population dynamics, future phases will correlate criticality metrics with specific visual features (e.g., spatial frequency, motion direction) or arousal states (locomotion, saccade/attending). We will utilize existing Cang Lab data that includes pupil tracking and treadmill speed to perform a fine-grained analysis of how "distance from the critical point" correlates with the animal's instantaneous arousal level and its ability to detect low-contrast visual features. These analyses are outside of the initial scope of the 6-month time frame but could be interesting and feasible in a relatively short time.

5.2. Spatial Criticality and High-Resolution Imaging

While temporal avalanches provide a robust measure of network state, criticality also predicts specific spatial scaling properties. To build upon the proposed electrophysiological temporal assessments, we will expa nd our analysis to include existing and future high-resolution Ca2+ imaging datasets from the Cang Lab (Liu et al., 2023; Savier et al., 2019) to corroborate criticality in the time domain and ask if critical dynamics exist spatially.

We will assess if the spatial correlation length of neural activity scales with the size of the observed field, a hallmark of systems existing at a phase transition. By applying "spatial coarse-graining" to in-vivo imaging data, we will determine if the visual network maintains scale-invariant activity patterns across different cortical and subcortical topographies. I am highly motivated to eventually pair these spatial dynamic assessments with spatial transcriptomic techniques (MERFISH or XENIUM) to identify the molecular markers of local neural hubs driving these states.

5.3. De Novo Experimental Design: Longitudinal Free Movement

The ultimate goal is to design an experiment specifically for criticality assessment after obtaining preliminary data and funding from this proposal. This will allow for more well defined and manipulatable paradigms that assess criticality and shifts in homeostasis directly. These data will be critical for high impact publications and funding in the future. Mice implanted with high-density Neuropixels probes in different regions of the brain or head-mounted mini-2p scopes will be mounted, all allowing for in-vivo recordings in freely moving animals. A "naturalistic" home-cage environment where mice are tracked 24/7 for weeks would be ideal, with different visual stimulation and visual behavior tasks to perform. This will allow us to observe how criticality recovers how and if criticality is a fundamental feature of homeostasis over large time scales.

5.4. Retinal Input and RGC Homeostasis

A critical gap in the current literature of hierarchical visual processing is whether the "critical" state observed in the brain is inherited from the sensory periphery or computed de novo within central circuits.

We will test if the retina—the first stage of the visual nervous system—already operates at a setpoint of criticality, or if it remains sub-critical to ensure high-fidelity "raw data" transmission. By comparing mouse and tree shrew RGCs, we can ask if the evolutionary drive toward criticality begins at the very first synapse of the visual system or emerges as a result of central circuit integration.

Leveraging my doctoral expertise in Retinal Ganglion Cell (RGC) in vivo imaging (McCracken et al., 2023), we will perform targeted retina recordings and imaging, building directly upon paradigms established in multiple Cang Lab publications (e.g., Zhao et al., 2013; Li et al., 2025). We will test the hypothesis that RGCs operate in a sub-critical, high-fidelity regime to ensure noise-free signal transmission to the brain, and that the "tuning" to criticality only emerges at the first major subcortical synapses in the dLGN or SC. This directly supports the overarching goal of understanding how neural circuit architecture constraints homeostatic setpoints across the visual hierarchy.

5.5. Summary

In total, this proposal, especially with these future directions considered, will provide a strong foundation for an F99 to assess the mechanism and purpose of criticality across the visual hierarchy. I am most excited long-term to assess this spatially, using in-vivo imaging of Ca2+ recordings across the brain and spatial transcriptomic techniques, as well as assess the role of inhibition and neuromodulation (either with biosensors or manipulations of those specific neurons). These ideas on top of the strong foundation built from completion of this proposal I believe will make for a high quality F99/K00 proposal to allow me to transition to an independent professorship.

6. Timeline and Budget

6.1. Timeline

To assess the evolutionary role of criticality in visual perception, the proposed six-month timeline is structured into three distinct phases that transition from data standardization to high-level evolutionary modeling. The first two months focus on the "Rosetta Stone" period, where diverse electrophysiological datasets from the mouse LGN, SC, and V1, as well as the tree shrew SC, are converted into a unified NWB format. During this phase, we will implement a dynamic temporal coarse-graining loop to map the "Scaling Surface" across species, identifying the precise temporal windows where power-law scaling and scale-invariance emerge. This foundational work ensures that all subsequent comparisons of the Deviation from Criticality Coefficient (DCC) are grounded in a mathematically consistent framework across the visual hierarchy.

The middle and final stages of the roadmap focus on testing the "Subcortical Anchor" hypothesis and the "Evolutionary Pull" of neural complexity. By month four, we will contrast the state-shifting dynamics of the visual cortex with the hypothesized stability of subcortical hubs, utilizing Detrended Fluctuation Analysis (DFA) to quantify long-range temporal correlations. The project concludes in months five and six with a cross-species synthesis, determining if the diurnal tree shrew maintains a tighter adherence to criticality than the nocturnal mouse. This final phase will result in a publication to ResearchHub Journal and presentation of all data/code obtained. Together this will provide me with substantial experience and a fundamental scientific foundation a successful F99/K00 proposal and transition to an independent professorship

6.2. Budget:

Personnel Stipend ($8,000): Support for the junior researcher (postdoc/student) to dedicate significant time for data re-analysis and modeling code development.
Compute/Cloud Costs ($500): AWS or Google Colab credits for running computationally intensive shuffling statistics for power-law fitting.
Publication/Dissemination ($1,500): Costs associated with open-access publication fees, including publishing in ResearchHub Journal, and conference travel to present these preliminary findings (SfN or ARVO)

7. Open-Source Commitment

Preregistration: The study hypothesis (SC is invariant to arousal-driven criticality shifts) will be preregistered in ResearchHub Journal immediately upon funding and ideas/feedback will be taken accordingly.
Code: All analysis scripts (Python/MATLAB) for calculating criticality metrics from calcium data will be open-sourced via GitHub.
Data: The derived datasets (spike-inferred raster plots) will be uploaded to a public repository (e.g., DANDI or Zenodo) to facilitate further community analysis.

8. References

Ma, Z., Turrigiano, G. G., Wessel, R. & Hengen, K. B. Cortical Circuit Dynamics Are Homeostatically Tuned to Criticality In Vivo. Neuron 104, 655-664.e4 (2019).
Hengen, K. B. & Shew, W. L. Is criticality a unified setpoint of brain function? Neuron. Volume 113, Issue 16 p 2582-2598.e2 2025
Hengen, K. B., Lambo, M. E., Van Hooser, S. D., Katz, D. B. & Turrigiano, G. G. Firing Rate Homeostasis in Visual Cortex of Freely Behaving Rodents. Neuron 80, 335–342 (2013).
Shew, W. L. et al. Adaptation to sensory input tunes visual cortex to criticality. Nature Physics 11, 659–663 (2015).
Zhao, X., Chen, H., Liu, X. & Cang, J. Orientation-selective Responses in the Mouse Lateral Geniculate Nucleus. J Neurosci 33, 12751–12763 (2013).
Fu, J., Tanabe, S. & Cang, J. Widespread and Multifaceted Binocular Integration in the Mouse Primary Visual Cortex. J. Neurosci. 43, 6495–6507 (2023).
Li, C., DePiero, V. J., Chen, H., Tanabe, S. & Cang, J. Probabilistically constrained vector summation of motion direction in the mouse superior colliculus. Current Biology 35, 723-733.e3 (2025).
Elsayed, A., Skyberg, R., Cang, J. & Meliza, C. D. Synergistic Geniculate and Cortical Dynamics Facilitate a Decorrelated Spatial Frequency Code in the Early Visual System. J Neurosci. 46 (1) e1070252025 (2026).
Li, C., Savier, E. L., Chen, H. & Cang, J. Visual Motion Processing in The Tree Shrew Superior Colliculus. J Neurosci. 46 (3) e1511252025. (2026)
Stanley, H. E. Scaling, universality, and renormalization: Three pillars of modern critical phenomena. Rev. Mod. Phys. 71, S358–S366 (1999).
Linkenkaer-Hansen, K., Nikouline, V. V., Palva, J. M. & Ilmoniemi, R. J. Long-Range Temporal Correlations and Scaling Behavior in Human Brain Oscillations. J. Neurosci. 21, 1370–1377 (2001).
Beggs, J. M. & Plenz, D. Neuronal Avalanches in Neocortical Circuits. J. Neurosci. 23, 11167–11177 (2003).
Ma, Z., Turrigiano, G. G., Wessel, R. & Hengen, K. B. Cortical circuit dynamics are homeostatically tuned to criticality in vivo. Neuron 104, 655-664.e4 (2019).
Savier, E. L., Chen, H. & Cang, J. Effects of Locomotion on Visual Responses in the Mouse Superior Colliculus. J. Neurosci. 39, 9360–9368 (2019).
Liu, Y. et al. Mapping Visual Functions onto Molecular Cell Types in the Mouse Superior Colliculus. Neuron 111, 1876-1886.e5 (2023).
McCracken, S. et al. Diversity in homeostatic calcium set points predicts retinal ganglion cell survival following optic nerve injury in vivo. Cell Rep 42, 113165 (2023).
Wilting, J. & Priesemann, V. Inferring collective dynamical states from widely unobserved systems. Nature Communications 9, 2325 (2018).

Assessing Criticality as an Evolutionary Setpoint across the Visual Hierarchy

Proposal

Proposal

Proposal

Proposal

Assessing Criticality as an Evolutionary Setpoint across the Visual Hierarchy

Proposal

Proposal

Funding Progress

Nonprofit Recipient

Topics

DOI

Funding Progress

Nonprofit Recipient

Topics

DOI