Compute the mean of every row of a matrix:

Compute the mean of every column of a matrix:

Define an array of rank 3:

Compute the standard deviation over the second dimension:

The resulting array is of rank 2, and the second axis has been removed:

Visualize the input and output arrays:

Define an array of rank 5:

Reduce the dimensions of the array by computing the total over dimensions 2 and 4:

Take an array of dimensions 2×3×4:

Apply head h along the first level, obtaining a result of dimensions 3×4:

Apply head h along the second level, obtaining a result of dimensions 2×4:

Apply head h along the third level, obtaining a result of dimensions 2×3:

Take an array of five levels:

Reduce several consecutive levels of the array:

This is equivalent to listing explicitly the reduced levels:

The order of the given levels is irrelevant:

Take an array organized by years, trimesters and months in its three levels:

Reduce along the third level (months), obtaining a matrix with dimensions two years by four trimesters:

Reduce along the second level (trimesters):

Reduce along the first level (years):

Reduce simultaneously two levels, in three different possible ways, with results always being vectors:

Reduce all levels at once, with a scalar result:

ArrayReduce[f,array,n] is equivalent to ArrayReduce[f,array,{n}] for a positive integer n:

ArrayReduce[Total,array,n] is equivalent to Total[array,{n}]:

ArrayReduce[Total,array,1;;n] is equivalent to Total[array,n]:

For an array a of depth k, ArrayReduce[f,a,{1,…,k}] is equivalent to f[Flatten[a]]:

For an array a of depth k, ArrayReduce[f,a,{}] is equivalent to Map[f,a,{k}]:

For an array a of depth k and a list ν={n₁,n₂,…,n_s} of distinct levels n_i≤k, ArrayReduce[f,a,ν] is equivalent to Map[f,Flatten[a,{{m₁},…,{m_r},ν}],{r}] with {m₁,...,m_r}=Complement[Range[k],ν]:

For an array a of depth k and levels n₁≤n₂≤k, ArrayReduce[f,a,n₁;;n₂] is equivalent to ArrayReduce[f,a,Range[n₁,n₂]]:

For an array a, ArrayReduce[f,a,{{n₁,…,n_s}}] is equivalent to ArrayReduce[f,a,{n₁,…,n_s}]:

For a rectangular array a, TensorContract[a,{{i₁,i₂},{j₁,j₂},…}] is equivalent to ArrayReduce[Tr,a,{{i₁,j₁,…},{i₂,j₂,…}}]:

AggregationLayer[f,levels][array] can also be expressed as ArrayReduce[f,array,levels]: