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sketched_kernels.py
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sketched_kernels.py
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# Copyright 2020 Amazon.com, Inc. or its affiliates. All Rights Reserved.
#
# Licensed under the Apache License, Version 2.0 (the "License").
# You may not use this file except in compliance with the License.
# A copy of the License is located at
#
# http://www.apache.org/licenses/LICENSE-2.0
#
# or in the "license" file accompanying this file. This file is distributed
# on an "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either
# express or implied. See the License for the specific language governing
# permissions and limitations under the License.
# ==============================================================================
import torch
import torch.nn as nn
import numpy as np
from abc import ABC
class SketchedKernels(ABC):
r"""
Compute kernel matrices of individual residual blocks given the sketched feature matrices
and the sketched gradient matrices.
"""
def __init__(self, model, loader, imgsize, device, M, T, freq_print, beta=0.5):
r"""
Initialise variables
"""
self.model = model
self.loader = loader
self.imgsize = imgsize
self.device = device
self.M = M
self.T = T
self.freq_print = freq_print
self.beta = beta
self.n_samples = 0 # number of data samples in the given dataset
self.sketched_matrices = {}
self.kernel_matrices = {}
# allocate CPU memory for storing sketched feature matrices
# and sketched gradient matrices
self.allocate_memory()
def allocate_memory(self):
r"""
Forward a random input to the given neural network to compute the size of the output at each residual block,
and allocate memory for storing sketched feature matrices and sketched gradient matrices.
Parameters
--------
None
Returns
--------
None
"""
# create a random input with the same size of the data samples
# for ImageNet models in PyTorch, the input size is 3 x 224 x 224
rand_inputs = torch.randn(1, 3, self.imgsize, self.imgsize).to(self.device)
rand_inputs.requires_grad = True
_, rand_feats = self.forward_with_gradient_hooks(rand_inputs)
# allocate CPU memory for the sketched feature matrix and the gradient matrix for each layer
# the size of the required memory for each layer is 2 x n_buckets x d_output,
# since each of the sketched feature and gradient matrix requires n_buckets x d_output
for i in range(len(rand_feats)):
layer_sizes = np.prod(rand_feats[i].size())
self.sketched_matrices[i] = torch.zeros(2, self.M, layer_sizes)
rand_feats[i].data.zero_()
# remove random features produced from the generated random input
del rand_feats
torch.cuda.empty_cache()
def forward_with_gradient_hooks(self, input_features):
r"""
Compute feature vectors by forwarding the data x into a given neural network model,
also register feature vectors to retain the gradient vectors w.r.t. individual ones.
The function is adapted from the model definition file provided by PyTorch:
https://pytorch.org/docs/stable/_modules/torchvision/models/resnet.html
Parameters
---------
model : PyTorch model instance
the given neural network model
input_features : (n_samples, n_channels, height, width) PyTorch tensor
the input data
Returns
--------
out : (n_samples, d_output) PyTorch tensor
the output of the top layer
feats : (n_ResBlocks) list
a dictionary that contains the feature vectors produced from individual Residual Blocks
"""
feats = [input_features]
out = self.model.conv1(input_features)
feats.append(out)
out = self.model.bn1(out)
out = self.model.relu(out)
out = self.model.maxpool(out)
feats.append(out)
# The residual blocks in a ResNet model are grouped into four stages
for layer in [self.model.layer1, self.model.layer2, self.model.layer3, self.model.layer4]:
for mod in layer:
out = mod(out)
feats.append(out)
out = out.mean(dim=(2,3))
feats.append(out)
out = self.model.fc(out)
for feat in feats:
feat.retain_grad()
return out, feats
def cwt_matrix(self, n_rows, n_cols, T):
r"""
Generate a matrix S which represents a Clarkson-Woodruff transform in PyTorch according the following reference.
Clarkson, Kenneth L., and David P. Woodruff. "Low-rank approximation and regression in input sparsity time." Journal of the ACM (JACM) 63.6 (2017): 1-45.
Parameters
--------
n_rows : int
Number of rows of S
n_cols : int
Number of columns of S
T : int
Number of nonzeros elements per column
Returns
--------
S : (n_rows, n_cols) PyTorch sparse matrix
The returned matrix has ``n_cols x T'' nonzeros entries.
Notes
--------
The current version only generates the sparse matrix S with the CPU backend.
"""
all_rows = []
all_cols = []
all_signs = []
for t in range(T):
chunk = int(n_rows / T)
shift = int(t * chunk)
rows = torch.randint(shift, shift+chunk, (1, n_cols))
cols = torch.arange(n_cols).view(1,-1)
signs = torch.randn(n_cols).sign().float()
all_rows.append(rows)
all_cols.append(cols)
all_signs.append(signs)
rows = torch.cat(all_rows, dim=1)
cols = torch.cat(all_cols, dim=1)
pos = torch.cat([rows.long(), cols.long()], dim=0)
signs = torch.cat(all_signs, dim=0)
cwt = torch.sparse.FloatTensor(pos, signs, torch.Size([n_rows, n_cols]))
return cwt
def cwt_sketching(self, X, S):
r"""
Sketch the input matrix X with the sparse random matrix S
Parameters
--------
X : (n_samples, n_dim) dense matrix
matrix to be sketched
S : (n_sketches, n_samples) PyTorch sparse matrix
sparse random matrix
Returns
--------
sketched : (n_sketches, n_dim) dense matrix
The returned matrix is the sketched matrix which is a summary of the input matrix X
Notes
--------
The current version is only with the CPU backend.
"""
sketched = torch.sparse.mm(S, X)
return sketched
def compute_sketched_mat(self):
r"""
Given a PreActResNet model and a dataset, the module computes the sketched matrices
for feature and gradient vectors respectively generated from individual residual blocks.
Parameters
--------
model : PyTorch model
A PreActResNet model
loader : DataLoader
A iterable DataLoader instance in PyTorch
Returns
--------
No returns
Notes
--------
The module runs efficiently with GPU backend, also runs with CPU backend.
"""
self.model.eval()
total = 0
# Iterate through the data loader in batches:
for batch_idx, (data, target) in enumerate(self.loader):
# load a batch of data samples
data, target = data.to(self.device), target.to(self.device)
data.requires_grad = True
output, feats = self.forward_with_gradient_hooks(data)
# calculate the log-likelihood and the predicted distribution over labels
logp = torch.log_softmax(output, dim=-1)
prob = torch.softmax(output, dim=-1)
# calculate the q distribution which is a smoothed predicted distribution
q_dist = (prob ** self.beta) / (prob ** self.beta).sum(dim=-1, keepdim=True)
# zero gradients in the models and calculate the gradients w.r.t. feature maps
self.model.zero_grad()
torch.autograd.backward(logp, grad_tensors=q_dist)
batchsize = data.size(dim=0)
self.n_samples += batchsize
with torch.no_grad():
# generate a CWT matrix
s = self.cwt_matrix(self.M, batchsize, self.T).to(self.device)
# calculate the sketched feature vectors and gradient vectors for individual layers
for layer_id in range(len(feats)):
# number of data points x dimension
batched_feats = feats[layer_id].data.view(batchsize, -1)
batched_grads = feats[layer_id].grad.data.view(batchsize, -1)
# sketch the feature vectors into buckets
# accumulate buckets on CPU backend
sketched_feats = self.cwt_sketching(batched_feats, s) / (self.T ** 0.5)
self.sketched_matrices[layer_id][0] += sketched_feats.cpu()
# delete intermediate variables to create memory for the following matrix multiplication
del batched_feats
torch.cuda.empty_cache()
# sketch the gradient vectors into buckets
sketched_grads = self.cwt_sketching(batched_grads, s) / (self.T ** 0.5)
self.sketched_matrices[layer_id][1] += sketched_grads.cpu()
# delete intermediate variables to create memory for the following matrix multiplication
del batched_grads
torch.cuda.empty_cache()
feats[layer_id].data.zero_()
feats[layer_id].grad.data.zero_()
if batch_idx % self.freq_print == 0:
print("finished {:d}/{:d}".format(batch_idx, len(self.loader)))
def compute_sketched_kernels(self):
r"""
Compute the sketched feature matrices and sketched gradient matrices first,
and then calculate the kernel matrices for individual layers.
Parameters
--------
None
Returns
--------
No returns
"""
self.compute_sketched_mat()
for layer_id in range(len(self.sketched_matrices)):
temp = torch.bmm(self.sketched_matrices[layer_id], self.sketched_matrices[layer_id].transpose(1,2))
self.kernel_matrices[layer_id] = (temp[0] * temp[1]).numpy()
del self.sketched_matrices[layer_id]
torch.cuda.empty_cache()