Your network · 2 inputs → 2 ReLU units → 1 sigmoid output

Four training rows and two different held-out rows. Only training rows supply gradients. This is a deterministic teaching network, not a trained production model.

1. Forward
2. Loss
3. Backward
4. Update

Next: Forward · Epoch 0 · Updates 0 · Changed parameters: 0 of 9 · Next training rows: A1, A2.

Forward computes this batch's predictions; weights stay fixed.

Batch size

Changing batch size restarts this run. All means four rows averaged before one update.

Learning rate

Step multiplier. An edit discards pending batch arithmetic and keeps the parameters. Use arrow keys on the slider. Press Enter or leave the number field to apply an exact edit.

Training loss

Mean over all four training rows at current parameters.

0.589058

mean BCE(training)

The update itself uses only its current batch.

Validation loss

Mean over two held-out rows; not fitted.

0.573756

mean BCE(held-out)

A decrease is not guaranteed or evidence about all future data.

Model parameters · Initial → Current

Hidden rows: h1=ReLU(w11x1+w12x2+b1), h2=ReLU(w21x1+w22x2+b2); score=v1h1+v2h2+bOutput.
Parameter	Initial	Current
w11	0.600000	0.600000
w12	-0.200000	-0.200000
w21	-0.300000	-0.300000
w22	0.800000	0.800000
b1	0.100000	0.100000
b2	0.100000	0.100000
v1	0.500000	0.500000
v2	-0.400000	-0.400000
bOutput	0.000000	0.000000

Loss history after each update

Solid indigo: full Training loss. Dashed orange: Validation loss. No fabricated history at update zero; exact current losses are above.

Exact examples

Row	x1	x2	Label	Split
A1	-1	-1	0	Training
A2	-1	1	0	Training
A3	1	-1	1	Training
A4	1	1	1	Training
H1	-0.5	0.5	0	Held-out
H2	0.5	-0.5	1	Held-out

Exact batch arithmetic

BCE=max(z,0)−label×z+ln(1+exp(−|z|)). Its score derivative is p−label. ReLU's derivative is zero at zero. Row gradients are averaged before Update; no batch accumulation across updates.

Execute Forward to populate a batch trace.

Exact loss history

Update	Training	Validation

Scope and sources

Fixed row order, no shuffling, momentum, regularization or early stopping. Batch size edits restart parameters. Run one epoch finishes the remaining batches if already partway through an epoch. The tiny held-out set is validation evidence, not a final-test score or a guarantee. Display rounds to six decimals; all computations use full precision.

Deep Learning · Batch and minibatch optimization
PyTorch · Stable binary cross entropy

Open AI Grounds on a desktop

The Training Loop