Lesson 4 of 7
The rule is behind you. This is where you find out whether you have it: pair after pair of shapes, one verdict each, and no partial credit.
You know the rule -- line the shapes up from the right, pad the shorter one with ones, and every aligned pair must match or contain a one. Knowing it and being able to run it in your head on a pair you have never seen are different skills, and only the second one is any use at the moment a training run dies.
So this lesson is almost all challenge. Six rounds that escalate: shapes that already line up, shapes that need padding, shapes that fail -- where the question is which axis stopped them -- shapes that succeed and hand you something you did not want, the expressions this actually turns up in, and three operands at once. Every board is decided by the rule rather than by an answer someone typed, and a wrong answer draws the alignment you should have drawn.
Pairs of shapes, one after another. Say what comes out, or which axis stops them. Nothing runs — every board is decided by the rule itself, and every answer draws the alignment underneath it, so a wrong one shows you the rule you missed rather than the shape you missed.
Challenge
1 of 5
Two shapes, the same number of axes. Say what comes out.
Nothing to pad here -- the axes already line up one for one. Each pair either matches, has a one to stretch, or does not meet at all. Type the shape that comes out, or say it breaks.
Challenge
1 of 5
Different ranks. Pad the short one before you compare anything.
Now the two shapes have different numbers of axes, so the padding rule is what is being tested. Line them up from the right in your head first; the answers are obvious afterwards and impossible before.
1 of 1
The line that raised is where two shapes met. It is almost never where the wrong one was made.
Finding the axis is the part you can do on paper. In a running program there is a second half, and it is the half that costs the afternoon: the shapes are a symptom, and the line in the traceback is where the symptom showed, not where the disease is. Here is one as it actually arrives:
Traceback (most recent call last):
File "/work/train.py", line 62, in <module>
scaled = features * weights
~~~~~~~~~^~~~~~~~~
ValueError: operands could not be broadcast together with shapes (60000,784) (785,)Three parts of that pull their weight, and it is worth knowing which:
Then comes the step people skip. One of those two shapes is the one you meant and the other is not, and the multiply is innocent of both. Above, 784 columns against 785 weights is an off-by-one in how the weights were built -- perhaps a bias column that was concatenated twice, perhaps one that was never dropped. Editing the line that raised can only ever hide it.
So: pick the shape you did not expect, find where that array was last assigned, and fix it there. A reduction that dropped an axis, a model whose predictions come back as a column, a df[["y"]] where you wanted df["y"] -- the origin is usually a long way above the crash.
Two related messages are worth recognizing on sight, because they mean the destination got involved rather than the inputs:
ValueError: non-broadcastable output operand with shape (3,1)
doesn't match the broadcast shape (3,3)
ValueError: could not broadcast input array from shape (3,) into shape (4,)The first is an in-place operation, a += b. Broadcasting is allowed to stretch the operands it reads; it is not allowed to grow the array it writes into, so an a that would have to become bigger raises instead. The second is an assignment into a slice, a[...] = b, where the right-hand side has to fit the destination it is being poured into. Both are about where the answer is going, which is why neither reads like the message you were expecting.
Before any of that, one line settles it. Put print(a.shape, b.shape) immediately above the statement that raised and run it again -- you are then reading two facts rather than reconstructing them, and you will usually recognize the wrong one on sight.
Challenge
1 of 5
Every pair here fails. Name the axis that stops it.
This is the question the error message refuses to answer, and the one you will be asked by a traceback at some point this month. Pad, walk from the right, and stop at the first pair that is neither equal nor a one.
Challenge
1 of 4
These all succeed. Say what you actually get.
Nothing here raises, which is what makes it expensive. Each pair holds the same numbers you expected and arranges them into something you did not ask for. Predict the shape, then read what it would have cost.
Challenge
1 of 6
Lines you will write. Same question.
Every board here is an expression out of ordinary model code, with the shapes it meets on the day. Two of them are the same normalization written twice, once carelessly.
Challenge
1 of 3
Three operands, folded left to right.
NumPy takes them two at a time, so the second comparison is against a shape that appears nowhere in the expression. Work it out in order rather than all at once.