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) - λθMuon
Orthogonal updates via SVD for 2D parameters
g = UΣV^T; Δθ = -η·UV^TFalcon
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."