The lab

Learn how models learn

Train a line, build a classifier, and explore decisions with synthetic data.

How a model learns

Fit completion time from task complexity through actual gradient updates.

Try this Train one step to see the prediction line move toward the observations.

Step 0 · MSE 1222.450 → 1222.450Zero weights and bias. Train to make the first update.

24 synthetic task observations · Green line = predicted time

Dots = observations · dashed verticals = residuals (prediction errors). The initial dashed green prediction is zero and overlaps the bottom axis.

Learning rate

MSE versus training step

Initial 1222.450 · Current 1222.450. Zero-based scale expands only if loss exceeds the previous high; a falling curve alone does not establish convergence.

Inspect example

TASK-1 · Observed 8.038 minutes

Features0.000
Weighted score z0.000
Predicted minutes0.000

Inspect the mathematics

Standardized features: -1.661. Scaling uses the 24 synthetic training observations.

z = w · x + b; w = [0.000], b = 0.000. The weighted score is 0.000.

Residual = observed − predicted = 8.038 minutes. Slope in original units = 0.000; intercept = 0.000.

MSE = mean((prediction − observation)²); gradient = 2 mean((prediction − observation)x). The bias gradient omits x. Each step subtracts learning rate × gradient; parameter bounds remain ±100.

Explore parameters manually

Manual edits pause training and begin a new trace at step zero. They are not learned updates.

Weight 1Bias

Independently synthetic records; training runs locally in your browser. No confidential agency data. Lower training loss does not establish generalization or real-world performance. Training pauses on lesson changes; no motion starts automatically.

JavaScript is disabled. Linear regression fits a line by reducing mean squared error. Logistic regression transforms a weighted feature score with sigmoid and learns using log loss. Evaluation compares model-generated predictions with labels on held-out records. Enable JavaScript to train these synthetic models locally; no real records or operational performance are represented.