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First Principles: Criticality

Imagine building a brain from scratch... you have billions of knobs to turn --- one for everything that controls how neurons work, individually and as a group. Your goal is to make the smartest machine possible. But the sheer number of possible combinations is effectively infinite --- you could spend eternity searching. You'll quickly find a serious problem (the heart of the matter, really): most settings are dead ends. They either lead to boring, rigid dynamics that can't learn anything new, or explosive, chaotic activity that destroys any meaningful computation. Every once in a while, you'd stumble upon a boundary in this vast parameter space where the behavior suddenly jumps from stable to explosive. This is a tipping point called criticality. Here, something magical happens: your brain exhibits scale-invariant dynamics: it generates patterns of all shapes and sizes that last from milliseconds to minutes. Your brain becomes marginally stable, making it exquisitely sensitive to inputs (like other thoughts and the outside world) while remaining controllable. It's like a fighter jet (marginally stable, easy to spin and flip) versus a 747 (pure stability, very hard to turn around). At criticality, your brain is maximally tunable, so small knob twists can reconfigure the entire system for new tasks. And perhaps most importantly, it develops a generative capacity —the ability to create complex, internally-driven dynamics that aren't just reflections of external stimuli. Unless we've been wrong about the brain this whole time, that's what your internal world is. It's a reasonable hypothesis to suggest that this tipping point is the final target of all the set-points throughout the brain. Because if you want a brain that can learn anything, adapt to anything, and generate the rich internal dynamics necessary for behavior and healthy cognition, criticality starts to sound like it might not just be optimal, but almost inevitable. Our data and many other groups' suggest that evolution, development, and homeostasis all converge on this mathematical principle. Because it's the only place in parameter space where flexible, general-purpose computation is actually possible.

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How to Explore Criticality

Goal: Manipulate network parameters and see if you can get rich activity that spans multiple spatial and temporal scales. Just as your cognition is defined by acute, rapid calculations as well as long lasting, multi-modal processes, an effective model of the brain should sit near some "sweet spot" where flurries of neuronal activity (avalanches) are diverse in size/duration but don't explode into seizure-like activity.

Getting Started:

  • Click anywhere in the simulation to seed a set of neural avalanches.
  • Adjust excitatory drive to control how easily neurons activate each other.
  • Balance the network with inhibition to prevent runaway activity.

What to Look For:

  • Power Law Distribution: A straight line in the log-log plot is a signature of critical dynamics.
  • Diverse Avalanche Sizes: Small, medium, and large cascades should all occur
  • System Phase Indicator: Try to keep the marker in the "Critical" zone
  • Complexity Score: Higher scores indicate more interesting, variable dynamics

Visual Cues: Cyan = active excitatory neurons, Red = active inhibitory neurons, Dark colors = refractory (temporarily inactive)

Neural Circuit
1.00
Excitatory Drive: Controls how likely neurons are to activate their neighbors. Higher values make avalanches more likely to spread. This is the fundamental "gain" of the network - too low and nothing happens, too high and everything explodes.
0.20
🛡️ Real inhibitory neurons suppress activity
Inhibitory Strength: 20% of neurons are inhibitory (red). When they activate, they create suppression zones around themselves, making nearby excitatory neurons less likely to fire. This prevents runaway activity and is crucial for maintaining stable dynamics.
0.010
Long-Range Connections: Probability that neurons have distant connections (shown as purple lines). These allow avalanches to "jump" across the network, creating more complex propagation patterns and larger cascades.
3
Refractory Period: After firing, neurons can't fire again for this many timesteps (shown as dark colors). This prevents neurons from firing continuously and makes the dynamics more biologically realistic.
0.0
⚠️ Strengthens connections between correlated neurons
Hebbian Plasticity: "Neurons that fire together, wire together." This gradually strengthens connections between neurons that are frequently co-active, creating preferred pathways for avalanche propagation. Can push the system away from criticality over time.
System Phase
Subcritical Critical Supercritical
System Phase: Estimates where the system currently sits based on avalanche characteristics. This measurement is significantly lagged - it takes time to collect enough data after you change parameters. Subcritical = small avalanches die out quickly. Critical = diverse avalanche sizes with power-law distribution. Supercritical = large system-spanning avalanches.
Live Analytics
Complexity Score
0
Complexity Score: Measures how variable and interesting the activity patterns are. Higher scores indicate the system is generating diverse, unpredictable dynamics - a hallmark of critical systems. Based on the coefficient of variation of activity levels.
Avalanche Size Distribution (log-log)
Power Law Distribution: In critical systems, avalanche sizes follow a power law - many small avalanches, fewer large ones. This appears as a straight line on a log-log plot. The slope tells you how "critical" the system is.
Population Activity Trace
Activity Trace: Shows the total number of active neurons over time. Critical systems show bursts of activity of varying sizes, creating an irregular, bursty pattern rather than constant activity.
Active Neurons 0
Active Neurons: Current number of excitatory neurons firing (shown in cyan). This fluctuates as avalanches propagate through the network.
Inhibitory Active 0
Inhibitory Active: Current number of inhibitory neurons firing (shown in red). These create suppression zones that help control avalanche spread.
Active Avalanches 0
Active Avalanches: Number of avalanche cascades currently propagating through the network. Each seed can start its own avalanche tree.
Recent Completion --
Recent Completion: Size of the most recently completed avalanche. Shows individual avalanche sizes as they finish propagating.
Largest Avalanche 0
Largest Avalanche: The biggest cascade of neuron activations recorded so far. In critical systems, this can be quite large but shouldn't dominate. If this number keeps growing, you might be supercritical.
Power Law Slope --
Power Law Slope: The slope of the avalanche size distribution in log-log space. Critical systems typically have slopes around -1.5 to -2.0. Steeper slopes indicate more subcritical dynamics.
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