Aggregations & the axis argument

The mental model that fixes it

An aggregation (sum, mean, max, std, …) takes many numbers and reduces them to fewer. The axis argument says which dimension to reduce along — and the trick is that the axis you name is the one that disappears.

Picture a 2-D array as a grid with axis=0 running vertically (down the rows) and axis=1 running horizontally (across the columns) — the same order as .shape = (rows, cols). So:

• axis=0 → travel down each column, combining all the rows → the row dimension collapses → you get one number per column (a column-wise result).
• axis=1 → travel across each row, combining all the columns → the column dimension collapses → you get one number per row (a row-wise result).
• no axis → collapse everything to a single scalar.

The size rule makes it concrete: aggregating a (3, 4) array over axis=0 leaves shape (4,) (rows gone); over axis=1 leaves (3,) (columns gone). Pick an axis and operation below — the highlighted arrows show what's being combined, and the result appears along the axis that survives:

axis=0 vs axis=1, decoded

The exam asks for np.sum([[1, 2], [3, 4]], axis=1) and axis=0 on the array [[1, 2], [3, 4]] (click Load above to see it live):

• axis=1 sums across each row → [1+2, 3+4] = [3, 7].
• axis=0 sums down each column → [1+3, 2+4] = [4, 6].
• No axis → 1+2+3+4 = 10.

If you ever blank on it mid-problem, fall back to the shape rule: a (2, 2) array summed over axis=1 must come out shape (2,) — one number per row — so it has to be the row sums.

Why you'll use this constantly

Reductions over an axis are the bread and butter of data work and ML preprocessing:

• Per-feature statistics: with data shaped (samples, features), X.mean(axis=0) gives the mean of each feature — exactly what you subtract to center data before standardizing (then broadcasting it back).
• Per-sample reductions: X.sum(axis=1) totals each row — e.g. summing a one-hot or a probability row.
• Softmax & normalization divide by a sum taken over a specific axis — get the axis wrong and the numbers are silently meaningless.
• Higher dimensions: for an image batch (N, H, W, C), axis=(1, 2) averages over height & width to get a per-image, per-channel value. Same rule: the named axes vanish.

Tip: pass keepdims=True when you want the collapsed axis to stay as size 1 (e.g. (3, 1) instead of (3,)) so the result broadcasts cleanly back against the original — the usual move in a softmax.