Deep Learning: Forward Pass & Backpropagation

Neural Network Training

Learning rate 0.60

Training speed 1.0×

Loss

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Accuracy

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Epoch

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Phase

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How it works

This is a real 4-layer network (2 → 5 → 5 → 1 neurons) learning to classify whether a random 2D point falls inside a circle — no canned animation. Every training cycle, a green pulse carries the input forward through each weighted connection, layer by layer, until the output neuron produces a prediction (forward pass). The network then compares that prediction to the correct label and sends a magenta pulse backward through the same edges, carrying the error gradient from output to input (backpropagation). Each edge's color encodes its current weight sign (blue = positive, orange = negative) and its thickness the weight's magnitude; after every backward pass those edges actually update.

forward:  a[l+1] = f( W[l]·a[l] + b[l] )
loss:     L = -[y·log(ŷ) + (1-y)·log(1-ŷ)]
backward: δ[l]   = (Wᵀ·δ[l+1]) ⊙ f'(z[l])
update:   W[l]  -= lr · δ[l+1]·a[l]ᵀ

Learning rate — the step size in the weight-update rule above; too high and the loss oscillates or diverges, too low and training crawls.
Training speed — how fast the forward/backward cycle repeats, i.e. how many gradient-descent steps run per second.
Activation — the nonlinearity f applied at each hidden neuron (tanh or ReLU); it is what lets stacked linear layers learn a curved decision boundary at all.
Reset weights — reinitializes every weight to a small random value and restarts training from epoch 0, useful for comparing runs.

Real-world relevance: this same forward-pass-then-backpropagate loop, run millions of times over massive layer stacks, is exactly how today's deep learning systems — image classifiers, language models, recommendation engines — learn from data and improve their predictions.

Positive weight Negative weight Forward signal Backward gradient

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