Interactive Visualization

Energy-Based
Reasoning Models

Explore the fundamentals of EBMs through interactive visualizations. Learn how energy functions power modern AI reasoning.

Energy Landscape

Energy-Based Models define a scalar energy function E(x) over configurations. Lower energy = more likely. The surface shows valleys (low energy) representing "good" configurations.

p(x) ∝ exp(-E(x))

Low Energy (Likely)

High Energy (Unlikely)

Langevin Dynamics Sampling

To sample from an EBM, particles follow the energy gradient downhill while random noise enables exploration. Watch particles converge to low-energy regions.

x_t+1 = x_t − ε∇E(x_t) + √(2ε) · noise

Step Size (ε) 0.10

Noise Scale 0.10

0.00

Avg Energy

Steps

Particles

Contrastive Learning

Training shapes the energy landscape: push positive examples to lower energy, negative examples to higher energy.

L = max(0, E(x⁺) − E(x⁻) + margin)

Positive (correct)

Negative (flawed)

0.50

E(positive)

0.50

E(negative)

Step

1.00

Loss

Best-of-N Selection

Generate N candidate reasoning chains, select the one with lowest energy. More candidates → better results.

Inference-time scaling: Improve accuracy without retraining by generating more candidates and selecting the best one according to the energy function.

N (candidates) 4

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Selected Energy

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Correct?

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Accuracy

Reasoning Chain Verification

EBMs verify multi-step reasoning by assigning energy to each step. High energy steps indicate potential errors in the reasoning chain.