Module 02: Energy-Based Models (EBMs)

JEPA is an Energy-Based Model. Instead of probabilities, it calculates compatibility.

The Mathematical Foundation

JEPA assigns a scalar "Energy" to pairs of inputs. Low energy signifies compatibility (the prediction matches the context), while high energy signifies a lack of physical or semantic relationship.

E(x, y, z) = ||Sy - P(Sx, z)||2

Where Sx is the Context Encoder, P is the Predictor, and z is a Latent Variable.

Interactive Simulation: "The Energy Landscape"

CURRENT ENERGY LEVEL
0.42
Ball Position = Prediction (y)
Terrain Height = Energy E(x,y)

Interpretation Guide

The 3D landscape represents the model's internal understanding of the world.

• Valleys (Low Energy): High-compatibility states. These are "physically possible" futures that match the context.
• Peaks (High Energy): Low-compatibility states. These represent semantic contradictions or physical impossibilities.
• The Ball: Represents a candidate prediction. Drag the mouse to test different states and observe how the energy (cost) spikes as you move toward the peaks.

Escaping the Partition Function

Standard probabilistic models require calculating a Partition Function to normalize probabilities. EBMs avoid this entirely, making them more efficient for complex, high-dimensional spaces like video or 3D environments.

The biggest challenge in EBMs is preventing Representation Collapse, where the model assigns zero energy to everything.

References: [3] JEPA Overview (DataOps Labs), [12] Yann LeCun - A Path Towards Autonomous Machine Intelligence.