Results and interactive plots
Data preview and detected points
Landscape data preview
Critical points
Formula used
The calculator treats the selected surface as a scalar loss function over two parameter directions. It estimates gradients with central differences. Curvature is estimated from a local Hessian matrix.
L = f(θ₁, θ₂)
∇L = [∂L/∂θ₁, ∂L/∂θ₂]
H = [[∂²L/∂θ₁², ∂²L/∂θ₁∂θ₂],
[∂²L/∂θ₂∂θ₁, ∂²L/∂θ₂²]]
Sharpness ≈ max(L in neighborhood) − Lminimum
Flatness ≈ 1 / (1 + |largest Hessian eigenvalue|)
Path length = Σ √((xᵢ − xᵢ₋₁)² + (yᵢ − yᵢ₋₁)²)
Numerical values are educational approximations. They are not substitutes for exact model-level Hessian calculations.
How to use
Select a synthetic landscape or provide matrix data. Configure parameter ranges, transformation rules, and optimizer settings. Then calculate and inspect every interactive result.
Use surface, contour, heatmap, or wireframe views. Compare regularized or validation landscapes. Export plots and metrics for further analysis.
Example data
| X | Y | Loss | Interpretation |
|---|---|---|---|
| -2.0 | -2.0 | 4.42 | High-loss basin edge |
| -1.0 | 0.5 | 1.18 | Local descent region |
| 0.3 | -0.2 | 0.14 | Approximate minimum |
| 1.4 | 1.2 | 2.06 | Sharp ridge region |
Frequently asked questions
What is a loss landscape?
It maps model loss across selected parameter directions. Valleys indicate lower-loss regions. Ridges show sensitive parameter combinations.
Does this calculate a complete neural-network landscape?
No browser tool can scan every parameter directly. This calculator explores two selected directions. It provides practical visual approximations.
What indicates a sharp minimum?
Loss rises quickly around a sharp minimum. Large curvature estimates support that interpretation. Wider basins usually appear flatter.
How are saddle points detected?
The tool checks small gradients and opposing Hessian eigenvalue signs. Grid resolution affects detection quality. Increase resolution for detailed analysis.
Why normalize loss values?
Normalization improves visual comparison across different scales. Minimum shifting preserves relative differences. Min-max scaling compresses values uniformly.
Can I import training history?
Yes, enter path coordinates manually or upload compatible data. The path overlays parameter movement. Final-distance metrics update automatically.
Which optimizer simulation is most realistic?
Adam and Momentum show common adaptive movement patterns. Results remain simplified numerical demonstrations. Real models may behave differently.
What grid resolution should I use?
Start between forty and sixty points per axis. Higher resolutions improve detail. They also require more browser processing.
Can I compare two landscapes?
Yes, select a comparison mode and strength. The calculator shows differences or overlays. Similarity metrics appear in exported results.