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Trajectory Visualizer

Watch optimizers navigate the loss landscape in real-time

🏆 Winner: Muon

Achieved lowest loss of 0.180 in 10 iterations

Muon's orthogonal updates excel at navigating narrow valleys with sharp curvature

Landscape: Rosenbrock Valley

Expected Winner: Muon

⏯️ Animation Controls

Progress10/10

🗺️ Loss Landscape

🎯 Optimizer Selection

🏆

⚙️ Hyperparameters

0.01
0.90
256.00
10.00
300.00

3D Loss Landscape - Rosenbrock Valley

Iteration: 10

📊 Live Performance Metrics

AdamW

Current Loss:1.500
Convergence:10 iter
Path Length:15.45

Muon

🏆
Current Loss:0.180
Convergence:5 iter
Path Length:18.91

Muon's orthogonal updates excel at navigating narrow valleys with sharp curvature

Falcon

Current Loss:0.950
Convergence:8 iter
Path Length:16.13

🧮 Loss Function Mathematics

Rosenbrock Valley

f(x,y) = (1-x)² + 100(y-x²)²

Narrow curved valley - tests handling of ill-conditioned problems

Global Minimum
(1, 1)
Local Minima
No

📖 About Optimizers

AdamW

Adaptive moment estimation with decoupled weight decay

θ ← θ - α·m̂/(√v̂ + ε) - λθ

Muon

Orthogonal updates via SVD for 2D parameters

g = UΣV^T; Δθ = -η·UV^T

Falcon

Frequency-domain filtering with orthogonal updates

Ĝ = FFTMask(∇L, ρ); Δθ = Muon(Ĝ)

"Each optimizer carves its own path through the manifold of loss—
some swift and direct, others spiraling with geometric grace."