MinkowskiRBFLayer Visualization

1. Input Space (2D Euclidean)

Data Points

2. Minkowski Spacetime Projection (1+1D) Y: Time, X: Space

Reference Points

Timelike (Real)

Spacelike (Imag)

3. Layer Output (Complex Magnitude) Select a reference point

Timelike Strength

Spacelike Strength

How it Works

The MinkowskiRBFLayer projects input data into a pseudo-Riemannian manifold (Minkowski spacetime) and computes distances to learned reference points using the Minkowski metric.

ds² = -c²(Δt)² + (Δx)²

Unlike standard Euclidean distance, this metric distinguishes between two fundamental types of relationships:

Timelike (ds² < 0): Events are causally connected. The output is a Real number representing the proper time.
Spacelike (ds² > 0): Events are causally disconnected. The output is an Imaginary number representing the proper distance.

Interaction: Hover over the "Spacetime Projection" canvas. The yellow stars are reference points. The cursor acts as a probe, showing the light cone (white X). Points inside the top/bottom cones are Timelike (Cyan), points outside are Spacelike (Magenta).