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blocksparse.py
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blocksparse.py
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from typing import List
import numpy as np
import aesara
from aesara.gradient import grad_undefined
from aesara.graph.basic import Apply
from aesara.graph.op import Op
from aesara.tensor.type import discrete_dtypes
class SparseBlockGemv(Op):
"""
This op computes the dot product of specified pieces of vectors
and matrices, returning pieces of vectors::
for b in range(batch_size):
for j in range(o.shape[1]):
for i in range(h.shape[1]):
o[b, j, :] += numpy.dot(h[b, i], W[iIdx[b, i], oIdx[b, j]])
where b, h, W, o iIdx, oIdx are defined in the docstring of make_node.
.. image:: ../../../images/blocksparse.png
:scale: 50 %
"""
__props__ = ("inplace",)
registered_opts: List = []
def __init__(self, inplace=False):
self.inplace = inplace
if self.inplace:
self.destroy_map = {0: [0]}
def make_node(self, o, W, h, inputIdx, outputIdx):
"""
Compute the dot product of the specified pieces of vectors
and matrices.
The parameter types are actually their expected shapes
relative to each other.
Parameters
----------
o : batch, oWin, oSize
output vector
W : iBlocks, oBlocks, iSize, oSize
weight matrix
h : batch, iWin, iSize
input from lower layer (sparse)
inputIdx : batch, iWin
indexes of the input blocks
outputIdx : batch, oWin
indexes of the output blocks
Returns
-------
(batch, oWin, oSize)
dot(W[i, j], h[i]) + o[j]
Notes
-----
- `batch` is the number of examples in a minibatch (batch size).
- `iBlocks` is the total number of blocks in the input (from lower
layer).
- `iSize` is the size of each of these input blocks.
- `iWin` is the number of blocks that will be used as inputs. Which
blocks will be used is specified in `inputIdx`.
- `oBlocks` is the number or possible output blocks.
- `oSize` is the size of each of these output blocks.
- `oWin` is the number of output blocks that will actually be computed.
Which blocks will be computed is specified in `outputIdx`.
"""
o = aesara.tensor.as_tensor_variable(o)
W = aesara.tensor.as_tensor_variable(W)
h = aesara.tensor.as_tensor_variable(h)
inputIdx = aesara.tensor.as_tensor_variable(inputIdx)
outputIdx = aesara.tensor.as_tensor_variable(outputIdx)
if o.ndim != 3:
raise TypeError("The output o must be a 2D tensor")
if W.ndim != 4:
raise TypeError("The weight matrix W must be a 4D tensor")
if h.ndim != 3:
raise TypeError("The input h must be a 3D tensor")
if inputIdx.ndim != 2:
raise TypeError("The input indices inputIdx must be a 2D tensor")
if outputIdx.ndim != 2:
raise TypeError("The output indices outputIdx must be a 2D tensor")
assert inputIdx.type.dtype in discrete_dtypes
assert outputIdx.type.dtype in discrete_dtypes
return Apply(self, [o, W, h, inputIdx, outputIdx], [o.type()])
def perform(self, node, inp, out_):
o, W, h, iIdx, oIdx = inp[:5]
if not self.inplace:
o = o.copy()
for b in range(o.shape[0]):
for j in range(o.shape[1]):
outputIdx = oIdx[b, j]
for i in range(h.shape[1]):
inputIdx = iIdx[b, i]
w = W[inputIdx, outputIdx]
o[b, j, :] += np.dot(h[b, i], w)
out_[0][0] = o
def infer_shape(self, fgraph, node, input_shapes):
return [input_shapes[0]]
def grad(self, inputs, grads):
o, W, h, inputIdx, outputIdx = inputs
go = grads[0]
outer_fun = SparseBlockOuter(self.inplace)
gemv_fun = SparseBlockGemv(self.inplace)
Wgrad = outer_fun(W.zeros_like(), h, go, inputIdx, outputIdx)
hgrad = gemv_fun(
h.zeros_like(), W.dimshuffle((1, 0, 3, 2)), go, outputIdx, inputIdx
)
return [
go,
Wgrad,
hgrad,
grad_undefined(self, 3, inputIdx, "grad of inputIdx makes no sense"),
grad_undefined(self, 4, outputIdx, "grad of outputIdx makes no sense"),
]
class SparseBlockOuter(Op):
"""
This computes the outer product of two sets of pieces of vectors
updating a full matrix with the results::
for b in range(batch_size):
o[xIdx[b, i], yIdx[b, j]] += (alpha * outer(x[b, i], y[b, j]))
This op is involved in the gradient of SparseBlockGemv.
"""
__props__ = ("inplace",)
registered_opts: List = []
def __init__(self, inplace=False):
self.inplace = inplace
if self.inplace:
self.destroy_map = {0: [0]}
def make_node(self, o, x, y, xIdx, yIdx, alpha=None):
"""
Compute the dot product of the specified pieces of vectors
and matrices.
The parameter types are actually their expected shapes
relative to each other.
Parameters
----------
o : xBlocks, yBlocks, xSize, ySize
x : batch, xWin, xSize
y : batch, yWin, ySize
xIdx : batch, iWin
indexes of the x blocks
yIdx : batch, oWin
indexes of the y blocks
Returns
-------
(xBlocks, yBlocks, xSize, ySize)
outer(x[i], y[j]) + o[i, j]
Notes
-----
- `batch` is the number of examples in a minibatch (batch size).
- `xBlocks` is the total number of blocks in x.
- `xSize` is the size of each of these x blocks.
- `xWin` is the number of blocks that will be used as x. Which blocks
will be used is specified in `xIdx`.
- `yBlocks` is the number or possible y blocks.
- `ySize` is the size of each of these y blocks.
- `yWin` is the number of y blocks that will actually be computed.
Which blocks will be computed is specified in `yIdx`.
"""
one = aesara.tensor.constant(np.asarray(1.0, dtype="float32"))
o = aesara.tensor.as_tensor_variable(o)
x = aesara.tensor.as_tensor_variable(x)
y = aesara.tensor.as_tensor_variable(y)
if alpha is None:
alpha = one
return Apply(self, [o, x, y, xIdx, yIdx, alpha], [o.type()])
def infer_shape(self, fgraph, node, input_shapes):
return [input_shapes[0]]
def perform(self, node, inp, out_):
o, x, y, xIdx, yIdx, alpha = inp[:6]
if not self.inplace:
o = o.copy()
for b in range(x.shape[0]):
for i in range(xIdx.shape[1]):
for j in range(yIdx.shape[1]):
o[xIdx[b, i], yIdx[b, j]] += np.outer(x[b, i], y[b, j, :])
out_[0][0] = o
sparse_block_gemv = SparseBlockGemv(False)
sparse_block_gemv_inplace = SparseBlockGemv(True)
sparse_block_outer = SparseBlockOuter(False)
sparse_block_outer_inplace = SparseBlockOuter(True)
def sparse_block_dot(W, h, inputIdx, b, outputIdx):
"""
Compute the dot product (plus bias) of the specified pieces of vectors
and matrices. See SparseBlockGemv to get more information.
The parameter types are actually their expected shapes relative to
each other.
Parameters
----------
W : iBlocks, oBlocks, iSize, oSize
weight matrix
h : batch, iWin, iSize
input from lower layer (sparse)
inputIdx : batch, iWin
indexes of the input blocks
b : oBlocks, oSize
bias vector
outputIdx : batch, oWin
indexes of the output blocks
Returns
-------
(batch, oWin, oSize)
dot(W[i, j], h[i]) + b[j] but b[j] is only added once
Notes
-----
- `batch` is the number of examples in a minibatch (batch size).
- `iBlocks` is the total number of blocks in the input (from lower layer).
- `iSize` is the size of each of these input blocks.
- `iWin` is the number of blocks that will be used as inputs. Which blocks
will be used is specified in `inputIdx`.
- `oBlocks` is the number or possible output blocks.
- `oSize` is the size of each of these output blocks.
- `oWin` is the number of output blocks that will actually be computed.
Which blocks will be computed is specified in `outputIdx`.
"""
assert inputIdx.ndim == h.ndim - 1
assert outputIdx.ndim == inputIdx.ndim
if h.ndim == 2:
h = h.dimshuffle("x", 0, 1)
inputIdx = inputIdx.dimshuffle("x", 0)
outputIdx = outputIdx.dimshuffle("x", 0)
return SparseBlockGemv()(b.take(outputIdx, axis=0), W, h, inputIdx, outputIdx)