Model optimizer behavior with advanced controls easily. See convergence, loss, and parameter movement across iterations. Export results, compare methods, and tune smarter every session.
This tool compares optimizer paths on a one-parameter objective. The overall page is single column, while the form uses a responsive 3, 2, and 1 column grid.
These sample settings show how the calculator can be used to compare optimizer behavior under the same target and starting point.
| Optimizer | Initial Parameter | Target | Learning Rate | Steps | Weight Decay | Gradient Clip | Expected Behavior |
|---|---|---|---|---|---|---|---|
| SGD | 10 | 0 | 0.08 | 25 | 0.01 | 5 | Simple descent with steady shrinking updates. |
| Momentum | 10 | 0 | 0.05 | 25 | 0.01 | 5 | Faster progress, with possible overshoot near target. |
| RMSProp | 10 | 0 | 0.03 | 25 | 0.01 | 5 | Adaptive scaling often stabilizes noisy gradients. |
| Adam | 10 | 0 | 0.10 | 25 | 0.01 | 5 | Balanced speed and stability for many cases. |
The calculator uses a regularized quadratic objective:
L(θ) = 0.5(θ - target)² + 0.5λθ²
The gradient is:
g = (θ - target) + λθ
If clipping is active, the gradient becomes:
g_clipped = min(max(g, -clip), clip)
The decayed learning rate is:
lr_t = lr / (1 + decay × (t - 1))
update = lr_t × g, then θ = θ - updatev = momentum × v + lr_t × g, then θ = θ - vs = β2 × s + (1 - β2) × g², then update = lr_t × g / (sqrt(s) + ε)m and second moment v are updated, bias corrected, then used in update = lr_t × m̂ / (sqrt(v̂) + ε)This setup is intentionally controlled, so you can compare optimizer mechanics without the noise of a full training pipeline.
It simulates how one parameter moves toward a target minimum under a chosen optimizer. The loss is quadratic, so you can compare convergence speed, update size, and stability without training a full model.
A scalar parameter isolates optimizer behavior. You can clearly see how learning rate, momentum, beta values, clipping, and decay shape updates before applying similar tuning ideas to larger machine learning problems.
Adam is often a practical starting point. SGD is simpler, Momentum can accelerate progress, and RMSProp adapts step size using recent squared gradients. The chart helps compare their behavior with the same inputs.
Weight decay penalizes large parameter values. In this calculator it affects both the loss and gradient, which can improve stability and pull the solution toward smaller magnitudes.
Clipping limits very large gradients. That can prevent unstable jumps, especially when learning rates are aggressive or the starting value is far from the target.
Decay lowers the effective learning rate over time. Early steps stay larger, later steps become smaller, and the path often settles with less oscillation near the target.
No. It is a controlled optimizer simulation for intuition and comparison. It helps study update mechanics, not benchmark a specific dataset, architecture, or production model.
CSV supports spreadsheet analysis and extra charting. PDF is useful for reports, client notes, or saving a clean summary of settings, results, and iteration history.
Important Note: All the Calculators listed in this site are for educational purpose only and we do not guarentee the accuracy of results. Please do consult with other sources as well.