Backpropagation Demystified: How Neural Networks Learn

Learn the fundamentals of neural network training: forward propagation, loss functions, gradient descent, the chain rule, and activation functions like ReLU.

#neural-networks#backpropagation#machine-learning#artificial-intelligence#deep-learning#gradient-descent#data-science

Watch
Pitch

Neural Networks / Backpropagation

What is Backpropagation?

            Slide 1 of 8
        

A neural network is an optimization problem — find the best weights and biases to minimize error.

Backpropagation tells us which direction to adjust each parameter.

The network is one big nested function — calculus lets us trace how any weight affects the final loss.

Instinct version: drag a weight slider, watch loss go up → move it the other way. Backprop is the math of that instinct.

Made by

NEURAL NETWORKS / BACKPROPAGATION

Forward Propagation

The Network Makes a Prediction

Before we can go backward, we go forward.

Each neuron: multiply input by weight, add bias → output

neuron(x) = wx + b

Each layer's output becomes the next layer's input — a chain of functions.

Example: x = 2.1, w = 1, b = 0 → ŷ = (1)(2.1) + 0 = 2.1

The forward pass gives us: a prediction + all intermediate values needed for backprop.

Made by

NEURAL NETWORKS / BACKPROPAGATION

Measuring Mistakes

            The Loss Function
        

We need a score for how wrong the network is — that's the loss.

Mean Squared Error (MSE):

                    Loss = (1/n) Σ (ŷᵢ − yᵢ)²
                

For each example: (predicted − true)² then average across all.

Squaring: negatives don't cancel, and big mistakes are penalized harder.

No loss = no signal. The loss is the score we minimize.

                Example: (2.1 − 4)² = (−1.9)² = 3.61
            

Made by

NEURAL NETWORKS / BACKPROPAGATION

Which Way is Down?

            Gradient Descent
        

The gradient = direction of steepest ascent (loss increases fastest).

To lower loss: go the opposite direction — steepest descent.

Learning rate controls step size: too large = overshoot, too small = very slow.

Start at random weights
Compute gradient (steepest ascent)
Flip it → steepest descent
Take a small step
Repeat until minimum

Made by

NEURAL NETWORKS / BACKPROPAGATION

The Chain Rule

            Connecting the Dots Backward
        

The network is a nested function: loss depends on neuron output, which depends on weights.

Chain rule: to find ∂loss/∂w, multiply upstream × local gradient.

                    ∂loss/∂w = (∂loss/∂ŷ) × (∂ŷ/∂w)
                

                    ∂loss/∂b = (∂loss/∂ŷ) × (∂ŷ/∂b)
                

Upstream gradient: how loss reacts to the layer's output.

Local gradient: how the layer's output reacts to its own parameter.

Key benefit: intermediate values from the forward pass get reused — no redundant computation.

Made by

NEURAL NETWORKS / BACKPROPAGATION

Backward Propagation

            Computing the Gradient
        

                x = 2.1, w = 1, b = 0  →  ŷ = 2.1, y = 4, loss = 3.61
            

∂loss/∂w = −7.98
∂loss/∂b = −3.8

lr = 0.01
w := 1 − (0.01)(−7.98) = 1.0798
b := 0 − (0.01)(−3.8) = 0.038

New loss = 2.87 ↓ (was 3.61) — saved 0.74 in one step!

💡

Negative gradient = loss drops when we increase the parameter → so we increase it.

Made by

NEURAL NETWORKS / BACKPROPAGATION

Why We Need More Than a Line

            Activation Functions
        

A single linear neuron can only produce straight lines — stacking more doesn't help.

Real data: curves, patterns, images, language. Needs non-linearity.

Three ways to add complexity: more neurons, more layers, activation functions.

f(x) = max(0, x)

input < 0: output 0 (off)
input > 0: pass through

Still differentiable — chain rule still works. Backprop still runs.

Linear — Poor Fit

ReLU — Great Fit

ReLU Shape

Made by

NEURAL NETWORKS / BACKPROPAGATION

Why Backpropagation Makes Learning Possible

The Full Picture

Doesn't change whether you have 1 neuron or 175 billion.

Deeper networks = more derivatives to chain. The logic is identical.

Allows any neural network — spam filter to language model — to learn from data.

"As far as neural networks reach, backpropagation will follow."

Made by

DESIGNER-MADE
PRESENTATION,
GENERATED FROM
YOUR PROMPT

Create your own professional slide deck with real images, data charts, and unique design in under a minute.

Generate For Free

DESIGNER-MADE PRESENTATION, GENERATED FROM YOUR PROMPT

Backpropagation Demystified: How Neural Networks Learn

DESIGNER-MADE
PRESENTATION,
GENERATED FROM
YOUR PROMPT