The receptive field in Convolutional Neural Networks (CNN) is the region of the input space that affects a particular unit of the network. Note that this input region can be not only the input of the network but also output from other units in the network, therefore this receptive field can be calculated relative to the input that we consider and also relative the unit that we are taking into consideration as the “receiver” of this input region. Usually, when the receptive field term is mentioned, it is taking into consideration the final output unit of the network (i.e. a single unit on a binary classification task) in relation to the network input (i.e. input image of the network).
It is easy to see that on a CNN, the receptive field can be increased using different methods such as: stacking more layers (depth), subsampling (pooling, striding), filter dilation (dilated convolutions), etc. In theory, when you stack more layers you can increase your receptive field linearly, however, in practice, things aren’t simple as we thought, as shown by Luo, Wenjie et al. article. In the article, they introduce the concept of the “Effective Receptive Field”, or ERF; the intuition behind the concept is that not all pixels in the receptive field contribute equally to the output unit’s response. When doing the forward pass, we can see that the central receptive field pixels can propagate their information to the output using many different paths, as they are part of multiple output unit’s calculations.
In the figure below, we can see in left the input pixels, after that we have a feature map calculated from the input pixels using a 3×3 convolution filter and then finally the output after another 3×3 filtering. The numbers inside the pixels on the left image represent how many times this pixel was part of a convolution step (each sliding step of the filter). As we can see, some pixels like the central ones will have their information propagated through many different paths in the network, while the pixels on the borders are propagated along a single path.
Receptive Field across 3 different layers using 3×3 filters.
By looking at the image above, it isn’t that surprising that the effective receptive field impact on the final output computation will look more like a Gaussian distribution instead of a uniform distribution. What is actually more even interesting is that this receptive field is dynamic and changes during the training. The impact of this on the backpropagation is that the central pixels will have a larger gradient magnitude when compared to the border pixels.
In the article written by Luo, Wenjie et al., they devised a way to quantify the effect on each input pixel of the network by calculating the quantity that represents how much each pixel contributes to the output .
In the paper, they did experimentations to visualize the effective receptive field using multiple different architectures, activations, etc. I replicate here the ones that I found most interesting:
Figure 1 from the paper “Understanding the Effective Receptive Field in Deep Convolutional Neural Networks”, by Luo, Wenjie et al.
As we can see from the Figure 1 of the paper, where they compare the effect of the number of layers, initialization schemes, and different activations, the results are amazing. We can clearly see the Gaussian and also the sparsity added by the ReLU activations.
There are also some comparisons on Figure 3 of the paper, where CIFAR-10 and CamVid datasets were used to train the network.
Figure 3 of the paper “Understanding the Effective Receptive Field in Deep Convolutional Neural Networks”, by Luo, Wenjie et al.
As we can see, the size of the effective receptive field is very dynamic and it is increased by a large margin after the training, which implies, as stated by authors of the paper, that better initialization schemes can be employed to increase the receptive field in the beginning of the training. They actually developed a different initialization scheme and were able to get 30% training speed-up, however, these results weren’t consistent.
Foveal vision on reading activity. Image from http://www.learning-systems.ch.
What is also very interesting, is that the effective receptive field has a very close relationship with the foveal vision of the human eye, which produces the sharp central vision, effect of the high-density region of cone cells (as shown in the image below) present in the eye fundus.
Fovea region on the human eye. Image from http://eyetracking.me.
Our central sharp vision also decays rapidly like the effective receptive field that is very similar to a Gaussian. It is amazing that this effect is also naturally present on the CNN networks.
PS: Just for the sake of curiosity, some birds that do complex aerial movements such as the hummingbird, have two foveas instead of a single one, which means that they have a sharp accurate vision not only on the central region but also on the sides.
One of the most amazing components of the TensorFlow architecture is the computation graph that can be serialized using Protocol Buffers. This computation graph follows a well-defined format (click here for the proto files) and describes the computation that you specify (it can be a Deep Learning model like a CNN, a simple Logistic Regression or even any computation you want). For instance, here is an example of a very simple TensorFlow computation graph that we will use in this tutorial (using TensorFlow Python API):
As you can see, this is a very simple computation graph. First, we define the placeholder that will hold the input tensor and after that we specify the computation that should happen using this input tensor as input data. Here we can also see that we’re defining two important nodes of this graph, one is called “input” (the aforementioned placeholder) and the other is called “output“, that will hold the result of the final computation. This graph is the same as the following formula for a scalar: , where I intentionally added redundant operations to see LLVM constant propagation later.
In the last line of the code, we’re persisting this computation graph (including the constant values) into a serialized protobuf file. The final True parameter is to output a textual representation instead of binary, so it will produce the following human-readable output protobuf file (I omitted a part of it for brevity):
This is a very simple graph, and TensorFlow graphs are actually never that simple, because TensorFlow models can easily contain more than 300 nodes depending on the model you’re specifying, specially for Deep Learning models.
We’ll use the above graph to show how we can JIT native code for this simple graph using LLVM framework.
The LLVM Frontend, IR and Backend
The LLVM framework is a really nice, modular and complete ecosystem for building compilers and toolchains. A very nice description of the LLVM architecture that is important for us is shown in the picture below:
LLVM Compiler Architecture (AOSA/LLVM, Chris Lattner)
(The picture above is just a small part of the LLVM architecture, for a comprehensive description of it, please see the nice article from the AOSA book written by Chris Lattner)
Looking in the image above, we can see that LLVM provides a lot of core functionality, in the left side you see that many languages can write code for their respective language frontends, after that it doesn’t matter in which language you wrote your code, everything is transformed into a very powerful language called LLVM IR (LLVM Intermediate Representation) which is as you can imagine, a intermediate representation of the code just before the assembly code itself. In my opinion, the IR is the key component of what makes LLVM so amazing, because it doesn’t matter in which language you wrote your code (or even if it was a JIT’ed IR), everything ends in the same representation, and then here is where the magic happens, because the IR can take advantage of the LLVM optimizations (also known as transform and analysis passes).
After this IR generation, you can feed it into any LLVM backend to generate native code for any architecture supported by LLVM (such as x86, ARM, PPC, etc) and then you can finally execute your code with the native performance and also after LLVM optimization passes.
In order to JIT code using LLVM, all you need is to build the IR programmatically, create a execution engine to convert (during execution-time) the IR into native code, get a pointer for the function you have JIT’ed and then finally execute it. I’ll use here a Python binding for LLVM called llvmlite, which is very Pythonic and easy to use.
JIT’ing TensorFlow Graph using Python and LLVM
Let’s now use the LLVM and Python to JIT the TensorFlow computational graph. This is by no means a comprehensive implementation, it is very simplistic approach, a oversimplification that assumes some things: a integer closure type, just some TensorFlow operations and also a single scalar support instead of high rank tensors.
So, let’s start building our JIT code; first of all, let’s import the required packages, initialize some LLVM sub-systems and also define the LLVM respective type for the TensorFlow integer type:
from ctypes import CFUNCTYPE, c_int
import tensorflow as tf
from google.protobuf import text_format
from tensorflow.core.framework import graph_pb2
from tensorflow.core.framework import types_pb2
from tensorflow.python.framework import ops
import llvmlite.ir as ll
import llvmlite.binding as llvm
llvm.initialize()
llvm.initialize_native_target()
llvm.initialize_native_asmprinter()
TYPE_TF_LLVM = {
types_pb2.DT_INT32: ll.IntType(32),
}
After that, let’s define a class to open the TensorFlow exported graph and also declare a method to get a node of the graph by name:
class TFGraph(object):
def __init__(self, filename="graph.pb", binary=False):
self.graph_def = graph_pb2.GraphDef()
with open("graph.pb", "rb") as f:
if binary:
self.graph_def.ParseFromString(f.read())
else:
text_format.Merge(f.read(), self.graph_def)
def get_node(self, name):
for node in self.graph_def.node:
if node.name == name:
return node
And let’s start by defining our main function that will be the starting point of the code:
As you can see in the code above, we open the serialized protobuf graph and then get the input and output nodes of this graph. After that we also map the type of the both graph nodes (input/output) to the LLVM type (from TensorFlow integer to LLVM integer). We start then by defining a LLVM Module, which is the top level container for all IR objects. One module in LLVM can contain many different functions, here we will create just one function that will represent the graph, this function will receive as input argument the input data of the same type of the input node and then it will return a value with the same type of the output node.
After that we start by creating the entry block of the function and using this block we instantiate our IR Builder, which is a object that will provide us the building blocks for JIT’ing operations of TensorFlow graph.
Let’s now define the function that will do the real work of converting TensorFlow nodes into LLVM IR:
def build_graph(ir_builder, graph, node):
if node.op == "Add":
left_op_node = graph.get_node(node.input[0])
right_op_node = graph.get_node(node.input[1])
left_op = build_graph(ir_builder, graph, left_op_node)
right_op = build_graph(ir_builder, graph, right_op_node)
return ir_builder.add(left_op, right_op)
if node.op == "Sub":
left_op_node = graph.get_node(node.input[0])
right_op_node = graph.get_node(node.input[1])
left_op = build_graph(ir_builder, graph, left_op_node)
right_op = build_graph(ir_builder, graph, right_op_node)
return ir_builder.sub(left_op, right_op)
if node.op == "Placeholder":
function_args = ir_builder.function.args
for arg in function_args:
if arg.name == node.name:
return arg
raise RuntimeError("Input [{}] not found !".format(node.name))
if node.op == "Const":
llvm_const_type = TYPE_TF_LLVM[node.attr["dtype"].type]
const_value = node.attr["value"].tensor.int_val[0]
llvm_const_value = llvm_const_type(const_value)
return llvm_const_value
In this function, we receive by parameters the IR Builder, the graph class that we created earlier and the output node. This function will then recursively build the LLVM IR by means of the IR Builder. Here you can see that I only implemented the Add/Sub/Placeholder and Const operations from the TensorFlow graph, just to be able to support the graph that we defined earlier.
After that, we just need to define a function that will take a LLVM Module and then create a execution engine that will execute the LLVM optimization over the LLVM IR before doing the hard-work of converting the IR into native x86 code:
In the code above, you can see that we first get the CPU features (SSE, etc) into a list, after that we parse the LLVM IR from the module and then we create a engine using maximum optimization level (opt=3, roughly equivalent to the GCC -O3 parameter), we’re also printing the assembly code (in my case, the x86 assembly built by LLVM).
And here we just finish our run_main() function:
ret = build_graph(ir_builder, graph, output_node)
ir_builder.ret(ret)
with open("output.ir", "w") as f:
f.write(str(module))
engine = create_engine(module)
func_ptr = engine.get_function_address("tensorflow_graph")
cfunc = CFUNCTYPE(c_int, c_int)(func_ptr)
ret = cfunc(10)
print "Execution output: {}".format(ret)
As you can see in the code above, we just call the build_graph() method and then use the IR Builder to add the “ret” LLVM IR instruction (ret = return) to return the output of the IR function we just created based on the TensorFlow graph. We’re also here writing the IR output to a external file, I’ll use this LLVM IR file later to create native assembly for other different architectures such as ARM architecture. And finally, just get the native code function address, create a Python wrapper for this function and then call it with the argument “10”, which will be input data and then output the resulting output value.
And that is it, of course that this is just a oversimplification, but now we understand the advantages of having a JIT for our TensorFlow models.
The output LLVM IR, the advantage of optimizations and multiple architectures (ARM, PPC, x86, etc)
For instance, lets create the LLVM IR (using the code I shown above) of the following TensorFlow graph:
As you can see, the LLVM IR looks a lot like an assembly code, but this is not the final assembly code, this is just a non-optimized IR yet. Just before generating the x86 assembly code, LLVM runs a lot of optimization passes over the LLVM IR, and it will do things such as dead code elimination, constant propagation, etc. And here is the final native x86 assembly code that LLVM generates for the above LLVM IR of the TensorFlow graph:
As you can see, the optimized code removed a lot of redundant operations, and ended up just doing a add operation of 103, which is the correct simplification of the computation that we defined in the graph. For large graphs, you can see that these optimizations can be really powerful, because we are reusing the compiler optimizations that were developed for years in our Machine Learning model computation.
You can also use a LLVM tool called “llc”, that can take an LLVM IR file and the generate assembly for any other platform you want, for instance, the command-line below will generate native code for ARM architecture:
As you can see above, the ARM assembly code is also just a “add” assembly instruction followed by a return instruction.
This is really nice because we can take natural advantage of the LLVM framework. For instance, today ARM just announced the ARMv8-A with Scalable Vector Extensions (SVE) that will support 2048-bit vectors, and they are already working on patches for LLVM. In future, a really nice addition to LLVM would be the development of LLVM Passes for analysis and transformation that would take into consideration the nature of Machine Learning models.
And that’s it, I hope you liked the post ! Is really awesome what you can do with a few lines of Python, LLVM and TensorFlow.
Update 22 Aug 2016: TensorFlow team is actually working on a JIT (I don’t know if they are using LLVM, but it seems the most reasonable way to go in my opinion). In their paper, there is also a very important statement regarding Future Work that I cite here:
“We also have a number of concrete directions to improve the performance of TensorFlow. One such direction is our initial work on a just-in-time compiler that can take a subgraph of a TensorFlow execution, perhaps with some runtime profiling information about the typical sizes and shapes of tensors, and can generate an optimized routine for this subgraph. This compiler will understand the semantics of perform a number of optimizations such as loop fusion, blocking and tiling for locality, specialization for particular shapes and sizes, etc.” – TensorFlow White Paper
Full code
from ctypes import CFUNCTYPE, c_int
import tensorflow as tf
from google.protobuf import text_format
from tensorflow.core.framework import graph_pb2
from tensorflow.core.framework import types_pb2
from tensorflow.python.framework import ops
import llvmlite.ir as ll
import llvmlite.binding as llvm
llvm.initialize()
llvm.initialize_native_target()
llvm.initialize_native_asmprinter()
TYPE_TF_LLVM = {
types_pb2.DT_INT32: ll.IntType(32),
}
class TFGraph(object):
def __init__(self, filename="graph.pb", binary=False):
self.graph_def = graph_pb2.GraphDef()
with open("graph.pb", "rb") as f:
if binary:
self.graph_def.ParseFromString(f.read())
else:
text_format.Merge(f.read(), self.graph_def)
def get_node(self, name):
for node in self.graph_def.node:
if node.name == name:
return node
def build_graph(ir_builder, graph, node):
if node.op == "Add":
left_op_node = graph.get_node(node.input[0])
right_op_node = graph.get_node(node.input[1])
left_op = build_graph(ir_builder, graph, left_op_node)
right_op = build_graph(ir_builder, graph, right_op_node)
return ir_builder.add(left_op, right_op)
if node.op == "Sub":
left_op_node = graph.get_node(node.input[0])
right_op_node = graph.get_node(node.input[1])
left_op = build_graph(ir_builder, graph, left_op_node)
right_op = build_graph(ir_builder, graph, right_op_node)
return ir_builder.sub(left_op, right_op)
if node.op == "Placeholder":
function_args = ir_builder.function.args
for arg in function_args:
if arg.name == node.name:
return arg
raise RuntimeError("Input [{}] not found !".format(node.name))
if node.op == "Const":
llvm_const_type = TYPE_TF_LLVM[node.attr["dtype"].type]
const_value = node.attr["value"].tensor.int_val[0]
llvm_const_value = llvm_const_type(const_value)
return llvm_const_value
def create_engine(module):
features = llvm.get_host_cpu_features().flatten()
llvm_module = llvm.parse_assembly(str(module))
target = llvm.Target.from_default_triple()
target_machine = target.create_target_machine(opt=3, features=features)
engine = llvm.create_mcjit_compiler(llvm_module, target_machine)
engine.finalize_object()
print target_machine.emit_assembly(llvm_module)
return engine
def run_main():
graph = TFGraph("graph.pb", False)
input_node = graph.get_node("input")
output_node = graph.get_node("output")
input_type = TYPE_TF_LLVM[input_node.attr["dtype"].type]
output_type = TYPE_TF_LLVM[output_node.attr["T"].type]
module = ll.Module()
func_type = ll.FunctionType(output_type, [input_type])
func = ll.Function(module, func_type, name='tensorflow_graph')
func.args[0].name = 'input'
bb_entry = func.append_basic_block('entry')
ir_builder = ll.IRBuilder(bb_entry)
ret = build_graph(ir_builder, graph, output_node)
ir_builder.ret(ret)
with open("output.ir", "w") as f:
f.write(str(module))
engine = create_engine(module)
func_ptr = engine.get_function_address("tensorflow_graph")
cfunc = CFUNCTYPE(c_int, c_int)(func_ptr)
ret = cfunc(10)
print "Execution output: {}".format(ret)
if __name__ == "__main__":
run_main()
Presentation about an “Achitectural Zoo” of different applications and architectures of CNNs. Presented at Machine Learning Meetup in Porto Alegre yesterday.
The Voynich Manuscript is a hand-written codex written in an unknown system and carbon-dated to the early 15th century (1404–1438). Although the manuscript has been studied by some famous cryptographers of the World War I and II, nobody has deciphered it yet. The manuscript is known to be written in two different languages (Language A and Language B) and it is also known to be written by a group of people. The manuscript itself is always subject of a lot of different hypothesis, including the one that I like the most which is the “culture extinction” hypothesis, supported in 2014 by Stephen Bax. This hypothesis states that the codex isn’t ciphered, it states that the codex was just written in an unknown language that disappeared due to a culture extinction. In 2014, Stephen Bax proposed a provisional, partial decoding of the manuscript, the video of his presentation is very interesting and I really recommend you to watch if you like this codex. There is also a transcription of the manuscript done thanks to the hard-work of many folks working on it since many moons ago.
Word vectors
My idea when I heard about the work of Stephen Bax was to try to capture the patterns of the text using word2vec. Word embeddings are created by using a shallow neural network architecture. It is a unsupervised technique that uses supervided learning tasks to learn the linguistic context of the words. Here is a visualization of this architecture from the TensorFlow site:
These word vectors, after trained, carry with them a lot of semantic meaning. For instance:
We can see that those vectors can be used in vector operations to extract information about the regularities of the captured linguistic semantics. These vectors also approximates same-meaning words together, allowing similarity queries like in the example below:
Word vectors can also be used (surprise) for translation, and this is the feature of the word vectors that I think that its most important when used to understand text where we know some of the words translations. I pretend to try to use the words found by Stephen Bax in the future to check if it is possible to capture some transformation that could lead to find similar structures with other languages. A nice visualization of this feature is the one below from the paper “Exploiting Similarities among Languages for Machine Translation“:
This visualization was made using gradient descent to optimize a linear transformation between the source and destination language word vectors. As you can see, the structure in Spanish is really close to the structure in English.
EVA Transcription
To train this model, I had to parse and extract the transcription from the EVA (European Voynich Alphabet) to be able to feed the Voynich sentences into the word2vec model. This EVA transcription has the following format:
The first data between “<” and “>” has information about the folio (page), line and author of the transcription. The transcription block above is the transcription for the first two lines of the first folio of the manuscript below:
Part of the “f1r”
As you can see, the EVA contains some code characters, like for instance “!”, “*” and they all have some meaning, like to inform that the author doing that translation is not sure about the character in that position, etc. EVA also contains transcription from different authors for the same line of the folio.
To convert this transcription to sentences I used only lines where the authors were sure about the entire line and I used the first line where the line satisfied this condition. I also did some cleaning on the transcription to remove the drawings names from the text, like: “text.text.text-{plant}text” -> “text text texttext”.
After this conversion from the EVA transcript to sentences compatible with the word2vec model, I trained the model to provide 100-dimensional word vectors for the words of the manuscript.
Vector space visualizations using t-SNE
After training word vectors, I created a visualization of the 100-dimensional vectors into a 2D embedding space using t-SNE algorithm:
As you can see there are a lot of small clusters and there visually two big clusters, probably accounting for the two different languages used in the Codex (I still need to confirm this regarding the two languages aspect). After clustering it with DBSCAN (using the original word vectors, not the t-SNE transformed vectors), we can clearly see the two major clusters:
Now comes the really interesting and useful part of the word vectors, if use a star name from the folio below (it’s pretty obvious why it is know that this is probably a star name):
I get really interesting similar words, like for instance the ocphy and other close star names:
It also returns the word “qoekaiin” from the folio 48, that precedes the same star name:
As you can see, word vectors are really useful to find some linguistic structures, we can also create another plot, showing how close are the star names in the 2D embedding space visualization created using t-SNE:
As you can see, we zoomed the major cluster of stars and we can see that they are really all grouped together in the vector space. These representations can be used for instance to infer plat names from the herbal section, etc.
My idea was to show how useful word vectors are to analyze unknown codex texts, I hope you liked and I hope that this could be somehow useful for other people how are also interested in this amazing manuscript.
If you are following some Machine Learning news, you certainly saw the work done by Ryan Dahl on Automatic Colorization (Hacker News comments, Reddit comments). This amazing work uses pixel hypercolumn information extracted from the VGG-16 network in order to colorize images. Samim also used the network to process Black & White video frames and produced the amazing video below:
Colorizing Black&White Movies with Neural Networks (video by Samim, network by Ryan)
But how does this hypercolumns works ? How to extract them to use on such variety of pixel classification problems ? The main idea of this post is to use the VGG-16 pre-trained network together with Keras and Scikit-Learn in order to extract the pixel hypercolumns and take a superficial look at the information present on it. I’m writing this because I haven’t found anything in Python to do that and this may be really useful for others working on pixel classification, segmentation, etc.
Hypercolumns
Many algorithms using features from CNNs (Convolutional Neural Networks) usually use the last FC (fully-connected) layer features in order to extract information about certain input. However, the information in the last FC layer may be too coarse spatially to allow precise localization (due to sequences of maxpooling, etc.), on the other side, the first layers may be spatially precise but will lack semantic information. To get the best of both worlds, the authors of the hypercolumn paper define the hypercolumn of a pixel as the vector of activations of all CNN units “above” that pixel.
Hypercolumn Extraction (by Hypercolumns for Object Segmentation and Fine-grained Localization)
The first step on the extraction of the hypercolumns is to feed the image into the CNN (Convolutional Neural Network) and extract the feature map activations for each location of the image. The tricky part is when the feature maps are smaller than the input image, for instance after a pooling operation, the authors of the paper then do a bilinear upsampling of the feature map in order to keep the feature maps on the same size of the input. There are also the issue with the FC (fully-connected) layers, because you can’t isolate units semantically tied only to one pixel of the image, so the FC activations are seen as 1×1 feature maps, which means that all locations shares the same information regarding the FC part of the hypercolumn. All these activations are then concatenated to create the hypercolumn. For instance, if we take the VGG-16 architecture to use only the first 2 convolutional layers after the max pooling operations, we will have a hypercolumn with the size of:
64 filters (first conv layer before pooling)
+
128 filters (second conv layer before pooling ) = 192 features
This means that each pixel of the image will have a 192-dimension hypercolumn vector. This hypercolumn is really interesting because it will contain information about the first layers (where we have a lot of spatial information but little semantic) and also information about the final layers (with little spatial information and lots of semantics). Thus this hypercolumn will certainly help in a lot of pixel classification tasks such as the one mentioned earlier of automatic colorization, because each location hypercolumn carries the information about what this pixel semantically and spatially represents. This is also very helpful on segmentation tasks (you can see more about that on the original paper introducing the hypercolumn concept).
Everything sounds cool, but how do we extract hypercolumns in practice ?
VGG-16
Before being able to extract the hypercolumns, we’ll setup the VGG-16 pre-trained network, because you know, the price of a good GPU (I can’t even imagine many of them) here in Brazil is very expensive and I don’t want to sell my kidney to buy a GPU.
VGG16 Network Architecture (by Zhicheng Yan et al.)
To setup a pretrained VGG-16 network on Keras, you’ll need to download the weights file from here (vgg16_weights.h5 file with approximately 500MB) and then setup the architecture and load the downloaded weights using Keras (more information about the weights file and architecture here):
from matplotlib import pyplot as plt
import theano
import cv2
import numpy as np
import scipy as sp
from keras.models import Sequential
from keras.layers.core import Flatten, Dense, Dropout
from keras.layers.convolutional import Convolution2D, MaxPooling2D
from keras.layers.convolutional import ZeroPadding2D
from keras.optimizers import SGD
from sklearn.manifold import TSNE
from sklearn import manifold
from sklearn import cluster
from sklearn.preprocessing import StandardScaler
def VGG_16(weights_path=None):
model = Sequential()
model.add(ZeroPadding2D((1,1),input_shape=(3,224,224)))
model.add(Convolution2D(64, 3, 3, activation='relu'))
model.add(ZeroPadding2D((1,1)))
model.add(Convolution2D(64, 3, 3, activation='relu'))
model.add(MaxPooling2D((2,2), stride=(2,2)))
model.add(ZeroPadding2D((1,1)))
model.add(Convolution2D(128, 3, 3, activation='relu'))
model.add(ZeroPadding2D((1,1)))
model.add(Convolution2D(128, 3, 3, activation='relu'))
model.add(MaxPooling2D((2,2), stride=(2,2)))
model.add(ZeroPadding2D((1,1)))
model.add(Convolution2D(256, 3, 3, activation='relu'))
model.add(ZeroPadding2D((1,1)))
model.add(Convolution2D(256, 3, 3, activation='relu'))
model.add(ZeroPadding2D((1,1)))
model.add(Convolution2D(256, 3, 3, activation='relu'))
model.add(MaxPooling2D((2,2), stride=(2,2)))
model.add(ZeroPadding2D((1,1)))
model.add(Convolution2D(512, 3, 3, activation='relu'))
model.add(ZeroPadding2D((1,1)))
model.add(Convolution2D(512, 3, 3, activation='relu'))
model.add(ZeroPadding2D((1,1)))
model.add(Convolution2D(512, 3, 3, activation='relu'))
model.add(MaxPooling2D((2,2), stride=(2,2)))
model.add(ZeroPadding2D((1,1)))
model.add(Convolution2D(512, 3, 3, activation='relu'))
model.add(ZeroPadding2D((1,1)))
model.add(Convolution2D(512, 3, 3, activation='relu'))
model.add(ZeroPadding2D((1,1)))
model.add(Convolution2D(512, 3, 3, activation='relu'))
model.add(MaxPooling2D((2,2), stride=(2,2)))
model.add(Flatten())
model.add(Dense(4096, activation='relu'))
model.add(Dropout(0.5))
model.add(Dense(4096, activation='relu'))
model.add(Dropout(0.5))
model.add(Dense(1000, activation='softmax'))
if weights_path:
model.load_weights(weights_path)
return model
As you can see, this is a very simple code to declare the VGG16 architecture and load the pre-trained weights (together with Python imports for the required packages). After that we’ll compile the Keras model:
im_original = cv2.resize(cv2.imread('madruga.jpg'), (224, 224))
im = im_original.transpose((2,0,1))
im = np.expand_dims(im, axis=0)
im_converted = cv2.cvtColor(im_original, cv2.COLOR_BGR2RGB)
plt.imshow(im_converted)
Image used
As we can see, we loaded the image, fixed the axes and then we can now feed the image into the VGG-16 to get the predictions:
out = model.predict(im)
plt.plot(out.ravel())
Predictions
As you can see, these are the final activations of the softmax layer, the class with the “jersey, T-shirt, tee shirt” category.
Extracting arbitrary feature maps
Now, to extract the feature map activations, we’ll have to being able to extract feature maps from arbitrary convolutional layers of the network. We can do that by compiling a Theano function using the get_output() method of Keras, like in the example below:
In the example above, I’m compiling a Theano function to get the 3 layer (a convolutional layer) feature map and then showing only the 3rd feature map. Here we can see the intensity of the activations. If we get feature maps of the activations from the final layers, we can see that the extracted features are more abstract, like eyes, etc. Look at this example below from the 15th convolutional layer:
As you can see, this second feature map is extracting more abstract features. And you can also note that the image seems to be more stretched when compared with the feature we saw earlier, that is because the the first feature maps has 224×224 size and this one has 56×56 due to the downscaling operations of the layers before the convolutional layer, and that is why we lose a lot of spatial information.
Extracting hypercolumns
Now finally let’s extract the hypercolumns of arbitrary set of layers. To do that, we will define a function to extract these hypercolumns:
def extract_hypercolumn(model, layer_indexes, instance):
layers = [model.layers[li].get_output(train=False) for li in layer_indexes]
get_feature = theano.function([model.layers[0].input], layers,
allow_input_downcast=False)
feature_maps = get_feature(instance)
hypercolumns = []
for convmap in feature_maps:
for fmap in convmap[0]:
upscaled = sp.misc.imresize(fmap, size=(224, 224),
mode="F", interp='bilinear')
hypercolumns.append(upscaled)
return np.asarray(hypercolumns)
As we can see, this function will expect three parameters: the model itself, an list of layer indexes that will be used to extract the hypercolumn features and an image instance that will be used to extract the hypercolumns. Let’s now test the hypercolumn extraction for the first 2 convolutional layers:
layers_extract = [3, 8]
hc = extract_hypercolumn(model, layers_extract, im)
That’s it, we extracted the hypercolumn vectors for each pixel. The shape of this “hc” variable is: (192L, 224L, 224L), which means that we have a 192-dimensional hypercolumn for each one of the 224×224 pixel (a total of 50176 pixels with 192 hypercolumn feature each).
Let’s plot the average of the hypercolumns activations for each pixel:
Ad you can see, those first hypercolumn activations are all looking like edge detectors, let’s see how these hypercolumns looks like for the layers 22 and 29:
As we can see now, the features are really more abstract and semantically interesting but with spatial information a little fuzzy.
Remember that you can extract the hypercolumns using all the initial layers and also the final layers, including the FC layers. Here I’m extracting them separately to show how they differ in the visualization plots.
Simple hypercolumn pixel clustering
Now, you can do a lot of things, you can use these hypercolumns to classify pixels for some task, to do automatic pixel colorization, segmentation, etc. What I’m going to do here just as an experiment, is to use the hypercolumns (from the VGG-16 layers 3, 8, 15, 22, 29) and then cluster it using KMeans with 2 clusters:
Now you can imagine how useful hypercolumns can be to tasks like keypoints extraction, segmentation, etc. It’s a very elegant, simple and useful concept.
Convolutional neural networks (or ConvNets) are biologically-inspired variants of MLPs, they have different kinds of layers and each different layer works different than the usual MLP layers. If you are interested in learning more about ConvNets, a good course is the CS231n – Convolutional Neural Newtorks for Visual Recognition. The architecture of the CNNs are shown in the images below:
As you can see, the ConvNets works with 3D volumes and transformations of these 3D volumes. I won’t repeat in this post the entire CS231n tutorial, so if you’re really interested, please take time to read before continuing.
Lasagne and nolearn
One of the Python packages for deep learning that I really like to work with is Lasagne and nolearn. Lasagne is based on Theano so the GPU speedups will really make a great difference, and their declarative approach for the neural networks creation are really helpful. The nolearn libary is a collection of utilities around neural networks packages (including Lasagne) that can help us a lot during the creation of the neural network architecture, inspection of the layers, etc.
What I’m going to show in this post, is how to build a simple ConvNet architecture with some convolutional and pooling layers. I’m also going to show how you can use a ConvNet to train a feature extractor and then use it to extract features before feeding them into different models like SVM, Logistic Regression, etc. Many people use pre-trained ConvNet models and then remove the last output layer to extract the features from ConvNets that were trained on ImageNet datasets. This is usually called transfer learning because you can use layers from other ConvNets as feature extractors for different problems, since the first layer filters of the ConvNets works as edge detectors, they can be used as general feature detectors for other problems.
Loading the MNIST dataset
The MNIST dataset is one of the most traditional datasets for digits classification. We will use a pickled version of it for Python, but first, lets import the packages that we will need to use:
import matplotlib
import matplotlib.pyplot as plt
import matplotlib.cm as cm
from urllib import urlretrieve
import cPickle as pickle
import os
import gzip
import numpy as np
import theano
import lasagne
from lasagne import layers
from lasagne.updates import nesterov_momentum
from nolearn.lasagne import NeuralNet
from nolearn.lasagne import visualize
from sklearn.metrics import classification_report
from sklearn.metrics import confusion_matrix
As you can see, we are importing matplotlib for plotting some images, some native Python modules to download the MNIST dataset, numpy, theano, lasagne, nolearn and some scikit-learn functions for model evaluation.
After that, we define our MNIST loading function (this is pretty the same function used in the Lasagne tutorial):
As you can see, we are downloading the MNIST pickled dataset and then unpacking it into the three different datasets: train, validation and test. After that we reshape the image contents to prepare them to input into the Lasagne input layer later and we also convert the numpy array types to uint8 due to the GPU/theano datatype restrictions.
After that, we’re ready to load the MNIST dataset and inspect it:
As you can see, in the parameter layers we’re defining a dictionary of tuples with the layer names/types and then we define the parameters for these layers. Our architecture here is using two convolutional layers with poolings and then a fully connected layer (dense layer) and the output layer. There are also dropouts between some layers, the dropout layer is a regularizer that randomly sets input values to zero to avoid overfitting (see the image below).
Dropout layer effect (from CS231n website).
After calling the train method, the nolearn package will show status of the learning process, in my machine with my humble GPU I got the results below:
The code above will plot the following filters below:
The first layer 5x5x32 filters.
As you can see, the nolearn plot_conv_weights plots all the filters present in the layer we specified.
Theano layer functions and Feature Extraction
Now it is time to create theano-compiled functions that will feed-forward the input data into the architecture up to the layer you’re interested. I’m going to get the functions for the output layer and also for the dense layer before the output layer:
As you can see, we have now two theano functions called f_output and f_dense (for the output and dense layers). Please note that in order to get the layers here we are using a extra parameter called “deterministic“, this is to avoid the dropout layers affecting our feed-forward pass.
We can now convert an example instance to the input format and then feed it into the theano function for the output layer:
instance = X_test[0][None, :, :]
%timeit -n 500 f_output(instance)
500 loops, best of 3: 858 µs per loop
As you can see, the f_output function takes an average of 858 µs. We can also plot the output layer activations for the instance:
pred = f_output(instance)
N = pred.shape[1]
plt.bar(range(N), pred.ravel())
The code above will create the following plot:
Output layer activations.
As you can see, the digit was recognized as the digit 7. The fact that you can create theano functions for any layer of the network is very useful because you can create a function (like we did before) to get the activations for the dense layer (the one before the output layer) and you can use these activations as features and use your neural network not as classifier but as a feature extractor. Let’s plot now the 256 unit activations for the dense layer:
pred = f_dense(instance)
N = pred.shape[1]
plt.bar(range(N), pred.ravel())
The code above will create the following plot below:
Dense layer activations.
You can now use the output of the these 256 activations as features on a linear classifier like Logistic Regression or SVM.
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, where I intentionally added redundant operations to see LLVM constant propagation later.
