Before you can read the parent note, you must be fluent in the alphabet it speaks. This page introduces every symbol and idea it assumes, from absolute zero, in the order they build on each other. Read top to bottom; nothing later uses anything not yet defined.
Look at the figure. A photo is a grid: rows and columns of these little squares. Zoom in far enough and the "cat" dissolves into a spreadsheet of numbers.
Figure 1 — Left: a picture as your eye sees it. Right: the very same picture as the computer stores it, one integer per pixel (0–255). The figure exists to hammer home the single most important mental model on this page: an image is literally a grid of numbers.
A colour image is not one grid but three stacked grids: one for Red, one for Green, one for Blue (RGB). Each grid has the same shape.
Figure 2 — A colour image is three grids stacked into a box: one grid per channel (R, G, B). The box is H tall, W wide, and 3 deep. This figure defines what the symbol RH×W×3 looks like as a physical shape, so the notation below is a picture you already know.
So X∈R224×224×3 just means "a colour image that is 224 pixels tall, 224 pixels wide". It is the picture in figure 2, written in symbols.
The parent note leans on three Greek symbols. Here is each in plain words.
Figure 3 — Six pixel values shown as dots on a number line. The amber vertical line is the mean μ (the balance point); the white double-arrow shows the spread, roughly one standard deviation σ on each side. The figure turns the abstract words "average" and "spread" into two visible distances.
This is the single most important symbol in the whole parent note, and it looks scary only until you unpack it.
Every big formula in the parent — the convolution sum, the softmax denominator, the cross-entropy loss — is just one or two of these loops nested. Learn to read ∑ and half the notation is already yours. (Later, once we introduce the number of classes C in §9, you will see the upper limit written as C instead of the generic n — same symbol, just a specific value for how many items to add.)
Now the whole network can be written as one nested onion:
y^=softmax(f(L)(⋯f(2)(f(1)(X))⋯))
Data flows left-in, right-out — that flow is what "forward pass" means. You already know every symbol here except softmax, which §9 builds from scratch.
Figure 4 — The curve y=ex. It never touches or crosses zero (always positive, even for negative x), and it climbs steadily left to right (order-preserving). These are exactly the two properties that make it the right tool for turning logits into probabilities.
Everything upstream (numbers, grids, sums, Greek letters, ex, log) feeds the three big machines of the parent note: normalization, softmax, and cross-entropy loss. With these foundations you can also step sideways into Transfer learning, ResNet architecture, Multi-label classification and Object detection, all built on the very same alphabet. Return to the parent pipeline note when this checklist is green.
Cover the right side and test yourself (the ::: separates the prompt from the hidden answer). If any answer surprises you, reread that section.
What does a pixel value of 255 mean?
Maximum brightness for that channel (white / full light).
How does an integer pixel become an entry of the real-valued tensor X?
Divide it by 255 (and optionally normalize), turning e.g. 180 into the real number 0.706.
What does X∈R224×224×3 describe?
A colour image, 224 tall, 224 wide, 3 channels (RGB), of real numbers.
Is the superscript in RH×W×3 a power?
No — it is a shape tag saying how many slots the box has and how they are arranged.
Is yi,c a multiplication?
No — it is a single number at address (row i, class c).
Do indices on this page start at 0 or 1?
At 1 (maths convention); most code starts at 0.
What is xraw?
A single entry of the image before normalization; xnorm is that same entry after subtracting μ and dividing by σ.
What do μ and σ measure?
μ = the average (balance point); σ = the spread around it.
Unroll ∑j=13aj.
a1+a2+a3.
Is h(2) "h squared"?
No — it is the output of layer 2; the superscript in parentheses is a label.
What is the difference between y and y^?
y is the true (one-hot) label; y^ is the model's predicted probabilities.
What does the hat in y^ signify?
An estimate / the model's guess, as opposed to the true value y.
What is a logit zi?
The raw, unnormalized score the last layer gives to class i — any real number, not yet a probability.
What does C stand for?
The number of possible classes (labels) in the task.
Write the softmax of z at position i.
y^i=ezi/∑j=1Cezj.
Name two properties of ex softmax relies on.
It is always positive and always increasing.
Which base does log use here?
Natural log, base e≈2.718 (sometimes written ln).
What does y^true mean?
The predicted probability the model gave to the correct class (the entry where y has its 1).
Why does the cross-entropy penalty use −log?
A correct confident guess (y^true≈1) gives near-zero penalty; a confident wrong guess gives a large positive penalty, and the minus makes the cost positive.
What does argmaxcy^c return?
The position (class index) of the largest probability, not the value.
Recall Self-check: read this line from the parent aloud
y^i=∑j=1Cezjezi — can you say what every symbol means?
Answer ::: "The predicted probability y^i for class i equals e raised to that class's logit zi, divided by the sum of ezj over all C classes." Here z is the raw-score (logit) vector from §7, e keeps things positive, and the ∑ normalizes so probabilities add to 1.
