Shared Priors Collapse Communication Complexity

Shared Model ON: Alice sends a quantized seed (up to 16 bits); Bob regenerates the exact curve using the same generator function
Shared Model OFF: Alice sends evenly-spaced y-samples (8 bits each); Bob interpolates linearly between them
Curve Generation: Perlin noise combined with sinusoidal harmonics, parameterized by a random seed
Error Metric: Mean absolute error between truth and reconstruction

An interactive demonstration of how shared knowledge dramatically reduces communication costs. The left panel shows a complex curve held by Alice. The right panel shows what Bob can reconstruct from a limited message. When both share the same generator (a prior), Alice can transmit just a tiny seed to reproduce rich structure. Without shared priors, Alice must send sampled values—more bits mean better reconstruction.

How to use: Press S to toggle shared model on/off. Press +/- to increase/decrease the bit budget. Press R to generate a new random curve. Observe how shared priors allow near-perfect reconstruction with minimal bits, while no shared prior requires many more bits to approximate the curve.