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UnweightedAggregationFactory
for fast Walsh-Hadamard transform.
Inherits From: UnweightedAggregationFactory
tff.aggregators.HadamardTransformFactory(
inner_agg_factory: Optional[tff.aggregators.UnweightedAggregationFactory
] = None,
num_repeats: int = 1
)
The created tff.templates.AggregationProcess
takes an input structure
and applies the randomized fast Walsh-Hadamard transform to each tensor in the
structure, reshaped to a rank-1 tensor in O(d*log(d))
time, where d
is the
number of elements of the tensor.
See https://en.wikipedia.org/wiki/Fast_Walsh%E2%80%93Hadamard_transform
Specifically, for each tensor, the following operations are first performed at
tff.CLIENTS
:
- Flattens the tensor into a rank-1 tensor.
- Pads the tensor to
d_2
dimensions with zeros, whered_2
is the smallest power of 2 larger than or equal tod
. - Multiplies the padded tensor with random
+1/-1
values (i.e. flipping the signs). This is equivalent to multiplication by a diagonal matrix with Rademacher random varaibles on diagonal. - Applies the fast Walsh-Hadamard transform.
Steps 3 and 4 are repeated multiple times with independent randomness, if
num_repeats > 1
.
The resulting tensors are passed to the inner_agg_factory
. After
aggregation, at tff.SEREVR
, inverses of these steps are applied in reverse
order.
The allowed input dtypes are integers and floats. However, the dtype passed to
the inner_agg_factory
will always be a float.
Methods
create
create(
value_type: factory.ValueType
) -> tff.templates.AggregationProcess
Creates a tff.aggregators.AggregationProcess
without weights.
The provided value_type
is a non-federated tff.Type
, that is, not a
tff.FederatedType
.
The returned tff.aggregators.AggregationProcess
will be created for
aggregation of values matching value_type
placed at tff.CLIENTS
.
That is, its next
method will expect type
<S@SERVER, {value_type}@CLIENTS>
, where S
is the unplaced return type of
its initialize
method.
Args | |
---|---|
value_type
|
A non-federated tff.Type .
|
Returns | |
---|---|
A tff.templates.AggregationProcess .
|