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← Tensor Foundations step 2 of 7
Reshape a Tensor
Reshaping changes how values are grouped into dimensions. It keeps their logical order: reading the input and output in row-major order gives the same sequence. It does not swap rows and columns.
Your task
Implement reshape_tensor(x, shape).
xis a tensor andshapeis a list of target dimensions.- The supplied shape is valid and has the same total number of elements as x.
- Return a tensor with that shape, preserving the values, dtype and device. Leave x unchanged. You do not need to guarantee that the result shares storage.
For x=[[1, 2, 3], [4, 5, 6]], reshaping to [3, 2] produces
[[1, 2], [3, 4], [5, 6]]. Transposing the same input would instead produce
[[1, 4], [2, 5], [3, 6]]. Both results have shape (3, 2), but their values
are arranged differently.
A common use is flattening several feature dimensions into one while retaining
the batch dimension. The total element count must stay the same: a (2, 3)
tensor has six elements, so it cannot be reshaped to (2, 4).
Use x.reshape(shape) in either framework. In PyTorch, reshape can copy data
when needed; this task does not require the stricter storage rules of view.
Explore how the same sequence fits different shapes below.
Loading visualization…
Understand the ideas behind this exercise. The Problem tab contains the exact implementation requirements.
Give each tensor axis a meaning
A tensor's shape tells you how many entries each axis has. It does not tell you
what those entries represent. For example, (batch, features) and
(features, batch) use different axis orders. Name the axes before choosing an
operation.
A reduction combines entries along an axis, for example by summing or
averaging. Averaging the features of a (B, D) tensor gives one number per
example, with shape (B,). Keeping the reduced axis gives shape (B, 1) instead.
For [[2, 4, 6], [1, 3, 5]], the row means with the axis kept are [[4], [3]].
Subtracting them from the input gives [[-2, 0, 2], [-2, 0, 2]]: each row has
been centered using its own mean.
Reshape and transpose do different jobs
A reshape regroups elements using the operation's traversal order. A transpose
changes the axis order. For the usual row-major reshape, [[1, 2, 3], [4, 5, 6]]
reshaped to (3, 2) becomes [[1, 2], [3, 4], [5, 6]]. Transposing the original
instead gives [[1, 4], [2, 5], [3, 6]].
Both results have shape (3, 2), but their entries mean different things. Check
values as well as shapes. Unequal axis sizes make many axis mistakes easier to
spot than square examples do.
Concatenate along an axis or stack on a new one
Concatenation extends an existing axis. Stacking creates a new axis. For two
arrays of shape (2, 3), concatenating on axis zero gives (4, 3). Stacking on
a new leading axis gives (2, 2, 3).
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