from e2cnn.gspaces import *
from e2cnn.nn import FieldType
from e2cnn.nn import GeometricTensor
from e2cnn.nn.modules.equivariant_module import EquivariantModule
from e2cnn.nn.modules.utils import indexes_from_labels
import torch
from typing import List, Tuple, Any
from collections import defaultdict
import numpy as np
__all__ = ["InducedNormPool"]
[docs]class InducedNormPool(EquivariantModule):
def __init__(self, in_type: FieldType, **kwargs):
r"""
Module that implements Induced Norm Pooling.
This module requires the input fields to be associated to an induced representation from a representation
which supports 'norm' non-linearities.
First, for each input field, an output one is built by taking the maximum norm of all its sub-fields.
Args:
in_type (FieldType): the input field type
"""
assert isinstance(in_type.gspace, GeneralOnR2)
super(InducedNormPool, self).__init__()
for r in in_type.representations:
assert any(nl.startswith('induced_norm') for nl in r.supported_nonlinearities), \
'Error! Representation "{}" does not support "induced_norm" non-linearity'.format(r.name)
self.space = in_type.gspace
self.in_type = in_type
# build the output representation substituting each input field with a trivial representation
self.out_type = FieldType(self.space, [self.space.trivial_repr] * len(in_type))
# whether each group of fields is contiguous or not
self._contiguous = {}
# group fields by their size and the size of the subfields and
# - check if fields of the same size are contiguous
# - retrieve the indices of the fields
# indices of the channels corresponding to fields belonging to each group in the input representation
_in_indices = defaultdict(lambda: [])
# indices of the channels corresponding to fields belonging to each group in the output representation
_out_indices = defaultdict(lambda: [])
# number of fields of each size
self._nfields = defaultdict(int)
# whether each group of fields is contiguous or not
self._contiguous = {}
position = 0
last_id = None
for i, r in enumerate(self.in_type.representations):
subfield_size = None
for nl in r.supported_nonlinearities:
if nl.startswith('induced_norm'):
assert subfield_size is None, "Error! The representation supports multiple " \
"sub-fields of different sizes"
subfield_size = int(nl.split('_')[-1])
assert r.size % subfield_size == 0
id = (r.size, subfield_size)
if id != last_id:
self._contiguous[id] = not id in self._contiguous
last_id = id
_in_indices[id] += list(range(position, position + r.size))
_out_indices[id] += [i]
self._nfields[id] += 1
position += r.size
for id, contiguous in self._contiguous.items():
if contiguous:
# for contiguous fields, only the first and last indices are kept
_in_indices[id] = torch.LongTensor([min(_in_indices[id]), max(_in_indices[id])+1])
_out_indices[id] = torch.LongTensor([min(_out_indices[id]), max(_out_indices[id])+1])
else:
# otherwise, transform the list of indices into a tensor
_in_indices[id] = torch.LongTensor(_in_indices[id])
_out_indices[id] = torch.LongTensor(_out_indices[id])
# register the indices tensors as parameters of this module
self.register_buffer('in_indices_{}'.format(id), _in_indices[id])
self.register_buffer('out_indices_{}'.format(id), _out_indices[id])
[docs] def forward(self, input: GeometricTensor) -> GeometricTensor:
r"""
Apply the Norm Pooling to the input feature map.
Args:
input (GeometricTensor): the input feature map
Returns:
the resulting feature map
"""
assert input.type == self.in_type
input = input.tensor
b, c, h, w = input.shape
output = torch.empty(self.evaluate_output_shape(input.shape), device=input.device, dtype=torch.float)
for id, contiguous in self._contiguous.items():
size, subfield_size = id
n_subfields = size // subfield_size
in_indices = getattr(self, f"in_indices_{id}")
out_indices = getattr(self, f"out_indices_{id}")
if contiguous:
fm = input[:, in_indices[0]:in_indices[1], ...]
else:
fm = input[:, in_indices, ...]
# split the channel dimension in 2 dimensions, separating fields
fm, _ = fm.view(b, -1, n_subfields, subfield_size, h, w).norm(dim=3).max(dim=2)
if contiguous:
output[:, out_indices[0]:out_indices[1], ...] = fm
else:
output[:, out_indices, ...] = fm
# wrap the result in a GeometricTensor
return GeometricTensor(output, self.out_type)
def evaluate_output_shape(self, input_shape: Tuple[int, int, int, int]) -> Tuple[int, int, int, int]:
assert len(input_shape) == 4
assert input_shape[1] == self.in_type.size
b, c, hi, wi = input_shape
return b, self.out_type.size, hi, wi
def check_equivariance(self, atol: float = 1e-6, rtol: float = 1e-5) -> List[Tuple[Any, float]]:
c = self.in_type.size
x = torch.randn(3, c, 10, 10)
x = GeometricTensor(x, self.in_type)
errors = []
for el in self.space.testing_elements:
out1 = self(x).transform_fibers(el)
out2 = self(x.transform_fibers(el))
errs = (out1.tensor - out2.tensor).detach().numpy()
errs = np.abs(errs).reshape(-1)
print(el, errs.max(), errs.mean(), errs.var())
assert torch.allclose(out1.tensor, out2.tensor, atol=atol, rtol=rtol), \
'The error found during equivariance check with element "{}" is too high: max = {}, mean = {} var ={}' \
.format(el, errs.max(), errs.mean(), errs.var())
errors.append((el, errs.mean()))
return errors