Cost Function Curve Calculator

Calculated Results

Load a preset or enter data, then calculate.

Ready

Formula Used

Select a function to display its formula.

Curve Analysis

Analysis appears after calculation.

Detailed Calculation Table

#	X	Actual	Predicted	Residual	\|Residual\|	Squared	Individual Loss	Weight	Weighted Loss	Parameter	Gradient	Iteration
No calculated rows yet.

Calculator Settings

Choose a preset, then adjust every available setting.

Import CSV

Cost function

Input separator

Decimal precision

Actual values

Predicted values

Used directly, or replaced by model predictions during a sweep.

Feature X values

Sample weights

Validation actual values

Validation X values

Huber delta

Quantile value

Numerical epsilon

Curve generation mode

Parameter name

Model intercept

Minimum parameter

Maximum parameter

Parameter step

Maximum curve points

Initial parameter

Classification threshold

Direct or comparison curve data

Format: Series|x:y,x:y. Use one series per line.

Optimizer

Learning rate

Maximum iterations

Batch size

Convergence tolerance

Early-stopping patience

Regularization

Regularization strength

Elastic Net L1 ratio

Momentum beta

RMSprop beta

Adam beta₂

Enable early stopping

Show separate penalty curve

Show optimization path

Chart type

Curve color

Chart background

Line width

Line style

Curve smoothing

Marker style

Marker size

Legend position

Y-axis scale

Chart width percentage

Chart height

Chart title

X-axis title

Y-axis title

X-axis minimum

X-axis maximum

Y-axis minimum

Y-axis maximum

Show grid

Show legend

Mark minimum cost

Editable Input Table

#	X	Actual	Predicted	Weight

Formula Reference

Cost functions summarize prediction error into one measurable value. Lower values usually indicate better fit. Context still determines the best function.

Function	Formula	Typical use
MSE	J = (1/n) Σ(y − ŷ)²	Regression with stronger outlier penalties.
MAE	J = (1/n) Σ\|y − ŷ\|	Robust regression interpretation.
Binary cross-entropy	J = −(1/n) Σ[y ln(p)+(1−y)ln(1−p)]	Binary probability predictions.
Huber	Quadratic near zero, linear outside delta.	Regression with moderate outliers.
Quantile	J = mean(max(qr,(q−1)r))	Conditional quantile estimation.

How to Use

Choose a cost function and enter matching numeric arrays. Select a curve mode and parameter range. Press calculate to update every result.

Enable optimization to simulate parameter updates across iterations. Compare training and validation behavior when available. Export the finished chart and calculations.

Example Data

X	Actual	Predicted	Weight
1	3	2.8	1
2	5	5.3	1
3	7	6.6	1
4	9	9.4	1

Frequently Asked Questions

What does the minimum point represent?

It represents the lowest tested cost. The related parameter is the best tested value.

Why can validation cost increase?

The model may start fitting training noise. This pattern often suggests overfitting.

Which cost function should I choose?

Match the function to the prediction task. Consider robustness and probability assumptions.

Why does a high learning rate diverge?

Large updates can overshoot the minimum. Repeated overshooting may increase cost rapidly.

What does regularization add?

Regularization adds a parameter penalty. It can discourage overly complex fitted models.

Can I import a CSV file?

Yes. Use columns named x, actual, predicted, and weight.

What is the generalization gap?

It is validation cost minus training cost. Larger positive gaps may indicate overfitting.

How does early stopping work?

It tracks improvement across iterations. Training stops after the selected patience expires.

Can I use a custom expression?

Yes. Use y, p, r, w, numbers, and Math functions.