Seeing the Brain Predict in Real-Time: An Animated Python Journey

In our previous post, we explored the core idea of the Free Energy Principle – the brain as a prediction machine striving to minimize the difference between its expectations and sensory reality. We even built a simple Python program to demonstrate this.

Now, let's take it a step further and visualize this predictive process as it unfolds. We've enhanced our Python code to create a dynamic animation, giving us a glimpse into how an "internal belief" (our brain's model) continuously adapts to incoming "sensory input."

Animating the Prediction: Our Updated Python Code

Python

import numpy as np
import matplotlib.pyplot as plt
import matplotlib.animation as animation

def generate_world_state(time_step):
    """A simple, changing "world" state."""
    return np.sin(0.1 * time_step) + np.random.normal(0, 0.1)

def generate_sensory_input(world_state):
    """Sensory input with some noise."""
    return world_state + np.random.normal(0, 0.2)

def predictive_coding(internal_belief, sensory_input, learning_rate):
    """Updates the internal belief based on prediction error."""
    prediction_error = sensory_input - internal_belief
    updated_belief = internal_belief + learning_rate * prediction_error
    return updated_belief, prediction_error

# Simulation parameters
time_steps = 200
learning_rate = 0.1
initial_belief = 0.0

# Initialize lists and setup the animation figure
fig, (ax1, ax2) = plt.subplots(2, 1, figsize=(12, 8))
line_world, = ax1.plot([], [], label='True World State', linestyle='--')
line_sensory, = ax1.plot([], [], label='Sensory Input', alpha=0.7)
line_belief, = ax1.plot([], [], label='Internal Belief', color='red')
# ... (rest of the plotting and animation setup as in the previous post) ...

The key addition here is the use of matplotlib.animation. Instead of plotting everything at the end, the animate(i) function is called repeatedly. In each frame of the animation:

1. A new state of the "world" is generated.
2. Noisy "sensory input" is produced.
3. Our simulated "brain's" internal_belief is updated based on the prediction error (the difference between the sensory input and the current belief).
4. The plots are updated to show the current state of the world, the sensory input, the internal belief, and the prediction error.

Seeing Prediction Unfold

When you run this program, you'll see two plots evolving in real-time:

• Top Plot: Shows the true underlying state of the world (dashed blue), the noisy sensory input (light blue), and the "brain's" internal belief (red line). Watch how the red line continuously adjusts, trying to track the underlying pattern despite the noisy sensory information. This represents the ongoing predictive analysis – the brain constantly refining its model of what's happening.
• Bottom Plot: Displays the prediction error (purple line). Notice how the updates in the internal belief in the top plot correspond to changes in the prediction error. The system is always trying to minimize this error.

What Does This Mean?

This animation offers a more dynamic way to understand predictive coding, a cornerstone of Friston's Free Energy Principle. The continuously moving red line (internal belief) visually represents the brain's ongoing attempt to predict what's coming next. When the sensory input deviates from the prediction, the internal belief is adjusted to reduce this mismatch.

Think of it like driving a car on a winding road. Your brain constantly predicts the upcoming curves. When your visual input (the road ahead) doesn't match your prediction, you adjust the steering wheel (update your internal model/belief about the road) to minimize the "prediction error" and stay on track.

While our simulation is incredibly simplified, it captures the essence of this continuous, error-driven process that the Free Energy Principle suggests underlies much of how living systems interact with their environment.

What do you observe in the animation? Does it give you a better feel for the "continuous" nature of predictive analysis? Share your thoughts in the comments!