Reduction Operations

Reduce an input, e.g. compute sum or mean over elements.

ReduceSum (z, axis=None)
ReduceLogSum (z, axis=None)
ReduceMean (z, axis=None)
ReduceMin (z, axis=None)
ReduceMax (z, axis=None)

Parameters

• z: data to reduce
• axis (default: None): if specified, perform reduction along this axis only

Return value

Reduced value

Description

These functions compute aggregates (sum, mean, etc.) over all values of an input vector or tensor. Available aggregations are:

• ReduceSum(): the sum over the elements
• ReduceLogSum(): the sum over elements in log representations (logC = log (exp (logA) + exp (logB)))
• ReduceMean(): the mean over the elements
• ReduceSum(): the maximum value of the elements
• ReduceSum(): the minimum value

By default, aggregation is done over all elements. In case of a tensor with rank>1, the optional axis parameter specifies a single axis that the reduction is performed over. For example, axis=2 applied to a [M x N]-dimensional matrix would aggregate over all columns, yielding a [M x 1] result.

Reducing over sequences

If the input is a sequence, reduction is performed separately for every sequence item. These operations do not support reduction over sequences. Instead, you can achieve this with a recurrence. For example, to sum up all elements of a sequence x, you can say:

sum = x + PastValue (0, sum, initialHiddenActivation=0)

Examples