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Deep Learning


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Deep learning allows computational models that are composed of multiple processing layers to learn representations of data with multiple levels of abstraction. These methods have dramatically improved the state-of-the-art in speech recognition, visual object recognition, object detection and many other domains such as drug discovery and genomics. Deep learning discovers intricate structure in large data sets by using the backpropagation algorithm to indicate how a machine should change its internal parameters that are used to compute the representation in each layer from the representation in the previous layer. Deep convolutional nets have brought about breakthroughs in processing images, video, speech and audio, whereas recurrent nets have shone light on sequential data such as text and speech.
Multilayer neural networks and backpropagation. a, A multi-layer neural network (shown by the connected dots) can distort the input space to make the classes of data (examples of which are on the red and blue lines) linearly separable. Note how a regular grid (shown on the left) in input space is also transformed (shown in the middle panel) by hidden units. This is an illustrative example with only two input units, two hidden units and one output unit, but the networks used for object recognition or natural language processing contain tens or hundreds of thousands of units. Reproduced with permission from C. Olah ( b, The chain rule of derivatives tells us how two small effects (that of a small change of x on y, and that of y on z) are composed. A small change Δx in x gets transformed first into a small change Δy in y by getting multiplied by ∂y/∂x (that is, the definition of partial derivative). Similarly, the change Δy creates a change Δz in z. Substituting one equation into the other gives the chain rule of derivatives — how Δx gets turned into Δz through multiplication by the product of ∂y/∂x and ∂z/∂x. It also works when x, y and z are vectors (and the derivatives are Jacobian matrices). c, The equations used for computing the forward pass in a neural net with two hidden layers and one output layer, each constituting a module through which one can backpropagate gradients. At each layer, we first compute the total input z to each unit, which is a weighted sum of the outputs of the units in the layer below. Then a non-linear function f(.) is applied to z to get the output of the unit. For simplicity, we have omitted bias terms. The non-linear functions used in neural networks include the rectified linear unit (ReLU) f(z) = max(0,z), commonly used in recent years, as well as the more conventional sigmoids, such as the hyberbolic tangent, f(z) = (exp(z) − exp(−z))/(exp(z) + exp(−z)) and logistic function logistic, f(z) = 1/(1 + exp(−z)). d, The equations used for computing the backward pass. At each hidden layer we compute the error derivative with respect to the output of each unit, which is a weighted sum of the error derivatives with respect to the total inputs to the units in the layer above. We then convert the error derivative with respect to the output into the error derivative with respect to the input by multiplying it by the gradient of f(z). At the output layer, the error derivative with respect to the output of a unit is computed by differentiating the cost function. This gives yl − tl if the cost function for unit l is 0.5(yl − tl)2, where tl is the target value. Once the ∂E/∂zk is known, the error-derivative for the weight wjk on the connection from unit j in the layer below is just yj ∂E/∂zk.
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1Facebook AI Research, 770 Broadway, New York, New York 10003 USA. 2New York University, 715 Broadway, New York, New York 10003, USA. 3Department of Computer Science and Operations
Research Université de Montréal, Pavillon André-Aisenstadt, PO Box 6128 Centre-Ville STN Montréal, Quebec H3C 3J7, Canada. 4Google, 1600 Amphitheatre Parkway, Mountain View, California
94043, USA. 5Department of Computer Science, University of Toronto, 6 King’s College Road, Toronto, Ontario M5S 3G4, Canada.
achine-learning technology powers many aspects of modern
society: from web searches to content filtering on social net-
works to recommendations on e-commerce websites, and
it is increasingly present in consumer products such as cameras and
smartphones. Machine-learning systems are used to identify objects
in images, transcribe speech into text, match news items, posts or
products with users’ interests, and select relevant results of search.
Increasingly, these applications make use of a class of techniques called
deep learning.
Conventional machine-learning techniques were limited in their
ability to process natural data in their raw form. For decades, con-
structing a pattern-recognition or machine-learning system required
careful engineering and considerable domain expertise to design a fea-
ture extractor that transformed the raw data (such as the pixel values
of an image) into a suitable internal representation or feature vector
from which the learning subsystem, often a classifier, could detect or
classify patterns in the input.
Representation learning is a set of methods that allows a machine to
be fed with raw data and to automatically discover the representations
needed for detection or classification. Deep-learning methods are
representation-learning methods with multiple levels of representa-
tion, obtained by composing simple but non-linear modules that each
transform the representation at one level (starting with the raw input)
into a representation at a higher, slightly more abstract level. With the
composition of enough such transformations, very complex functions
can be learned. For classification tasks, higher layers of representation
amplify aspects of the input that are important for discrimination and
suppress irrelevant variations. An image, for example, comes in the
form of an array of pixel values, and the learned features in the first
layer of representation typically represent the presence or absence of
edges at particular orientations and locations in the image. The second
layer typically detects motifs by spotting particular arrangements of
edges, regardless of small variations in the edge positions. The third
layer may assemble motifs into larger combinations that correspond
to parts of familiar objects, and subsequent layers would detect objects
as combinations of these parts. The key aspect of deep learning is that
these layers of features are not designed by human engineers: they
are learned from data using a general-purpose learning procedure.
Deep learning is making major advances in solving problems that
have resisted the best attempts of the artificial intelligence commu-
nity for many years. It has turned out to be very good at discovering
intricate structures in high-dimensional data and is therefore applica-
ble to many domains of science, business and government. In addition
to beating records in image recognition
and speech recognition
, it
has beaten other machine-learning techniques at predicting the activ-
ity of potential drug molecules
, analysing particle accelerator data
reconstructing brain circuits11, and predicting the effects of mutations
in non-coding DNA on gene expression and disease12,13. Perhaps more
surprisingly, deep learning has produced extremely promising results
for various tasks in natural language understanding14, particularly
topic classification, sentiment analysis, question answering
and lan-
guage translation16,17.
We think that deep learning will have many more successes in the
near future because it requires very little engineering by hand, so it
can easily take advantage of increases in the amount of available com-
putation and data. New learning algorithms and architectures that are
currently being developed for deep neural networks will only acceler-
ate this progress.
Supervised learning
The most common form of machine learning, deep or not, is super-
vised learning. Imagine that we want to build a system that can classify
images as containing, say, a house, a car, a person or a pet. We first
collect a large data set of images of houses, cars, people and pets, each
labelled with its category. During training, the machine is shown an
image and produces an output in the form of a vector of scores, one
for each category. We want the desired category to have the highest
score of all categories, but this is unlikely to happen before training.
We compute an objective function that measures the error (or dis-
tance) between the output scores and the desired pattern of scores. The
machine then modifies its internal adjustable parameters to reduce
this error. These adjustable parameters, often called weights, are real
numbers that can be seen as ‘knobs’ that define the input–output func-
tion of the machine. In a typical deep-learning system, there may be
hundreds of millions of these adjustable weights, and hundreds of
millions of labelled examples with which to train the machine.
To properly adjust the weight vector, the learning algorithm com-
putes a gradient vector that, for each weight, indicates by what amount
the error would increase or decrease if the weight were increased by a
tiny amount. The weight vector is then adjusted in the opposite direc-
tion to the gradient vector.
The objective function, averaged over all the training examples, can
Deep learning allows computational models that are composed of multiple processing layers to learn representations of
data with multiple levels of abstraction. These methods have dramatically improved the state-of-the-art in speech rec-
ognition, visual object recognition, object detection and many other domains such as drug discovery and genomics. Deep
learning discovers intricate structure in large data sets by using the backpropagation algorithm to indicate how a machine
should change its internal parameters that are used to compute the representation in each layer from the representation in
the previous layer. Deep convolutional nets have brought about breakthroughs in processing images, video, speech and
audio, whereas recurrent nets have shone light on sequential data such as text and speech.
Deep learning
Yann LeCun1,2, Yoshua Bengio3 & Geoffrey Hinton4,5
436 | NATURE | VOL 521 | 28 MAY 2015
REVIEW doi:10.1038/nature14539
© 2015 Macmillan Publishers Limited. All rights reserved
be seen as a kind of hilly landscape in the high-dimensional space of
weight values. The negative gradient vector indicates the direction
of steepest descent in this landscape, taking it closer to a minimum,
where the output error is low on average.
In practice, most practitioners use a procedure called stochastic
gradient descent (SGD). This consists of showing the input vector
for a few examples, computing the outputs and the errors, computing
the average gradient for those examples, and adjusting the weights
accordingly. The process is repeated for many small sets of examples
from the training set until the average of the objective function stops
decreasing. It is called stochastic because each small set of examples
gives a noisy estimate of the average gradient over all examples. This
simple procedure usually finds a good set of weights surprisingly
quickly when compared with far more elaborate optimization tech-
. After training, the performance of the system is measured
on a different set of examples called a test set. This serves to test the
generalization ability of the machine — its ability to produce sensible
answers on new inputs that it has never seen during training.
Many of the current practical applications of machine learning use
linear classifiers on top of hand-engineered features. A two-class linear
classifier computes a weighted sum of the feature vector components.
If the weighted sum is above a threshold, the input is classified as
belonging to a particular category.
Since the 1960s we have known that linear classifiers can only carve
their input space into very simple regions, namely half-spaces sepa
rated by a hyperplane
. But problems such as image and speech recog-
nition require the input–output function to be insensitive to irrelevant
variations of the input, such as variations in position, orientation or
illumination of an object, or variations in the pitch or accent of speech,
while being very sensitive to particular minute variations (for example,
the difference between a white wolf and a breed of wolf-like white
dog called a Samoyed). At the pixel level, images of two Samoyeds in
different poses and in different environments may be very different
from each other, whereas two images of a Samoyed and a wolf in the
same position and on similar backgrounds may be very similar to each
other. A linear classifier, or any other ‘shallow’ classifier operating on
Figure 1 | Multilayer neural networks and backpropagation. a, A multi-
layer neural network (shown by the connected dots) can distort the input
space to make the classes of data (examples of which are on the red and
blue lines) linearly separable. Note how a regular grid (shown on the left)
in input space is also transformed (shown in the middle panel) by hidden
units. This is an illustrative example with only two input units, two hidden
units and one output unit, but the networks used for object recognition
or natural language processing contain tens or hundreds of thousands of
units. Reproduced with permission from C. Olah (
b, The chain rule of derivatives tells us how two small effects (that of a small
change of x on y, and that of y on z) are composed. A small change Δx in
x gets transformed first into a small change Δy in y by getting multiplied
by ∂y/x (that is, the definition of partial derivative). Similarly, the change
Δy creates a change Δz in z. Substituting one equation into the other
gives the chain rule of derivatives — how Δx gets turned into Δz through
multiplication by the product of ∂y/∂x and ∂z/∂x. It also works when x,
y and z are vectors (and the derivatives are Jacobian matrices). c, The
equations used for computing the forward pass in a neural net with two
hidden layers and one output layer, each constituting a module through
which one can backpropagate gradients. At each layer, we first compute
the total input z to each unit, which is a weighted sum of the outputs of
the units in the layer below. Then a non-linear function f(.) is applied to
z to get the output of the unit. For simplicity, we have omitted bias terms.
The non-linear functions used in neural networks include the rectified
linear unit (ReLU) f(z) = max(0,z), commonly used in recent years, as
well as the more conventional sigmoids, such as the hyberbolic tangent,
f(z) = (exp(z) − exp(−z))/(exp(z) + exp(−z)) and logistic function logistic,
f(z) = 1/(1 + exp(−z)). d, The equations used for computing the backward
pass. At each hidden layer we compute the error derivative with respect to
the output of each unit, which is a weighted sum of the error derivatives
with respect to the total inputs to the units in the layer above. We then
convert the error derivative with respect to the output into the error
derivative with respect to the input by multiplying it by the gradient of f(z).
At the output layer, the error derivative with respect to the output of a unit
is computed by differentiating the cost function. This gives yltl if the cost
function for unit l is 0.5(yltl)2, where tl is the target value. Once the ∂E/∂zk
is known, the error-derivative for the weight wjk on the connection from
unit j in the layer below is just yjE/∂zk.
(1 sigmoid)
(2 sigmoid)
Compare outputs with correct
answer to get error derivatives
zj=wij xi
zk=wjk yj
Output units
Input units
Hidden units H2
Hidden units H1
28 MAY 2015 | VOL 521 | NATURE | 437
© 2015 Macmillan Publishers Limited. All rights reserved
raw pixels could not possibly distinguish the latter two, while putting
the former two in the same category. This is why shallow classifiers
require a good feature extractor that solves the selectivity–invariance
dilemma — one that produces representations that are selective to
the aspects of the image that are important for discrimination, but
that are invariant to irrelevant aspects such as the pose of the animal.
To make classifiers more powerful, one can use generic non-linear
features, as with kernel methods
, but generic features such as those
arising with the Gaussian kernel do not allow the learner to general-
ize well far from the training examples
. The conventional option is
to hand design good feature extractors, which requires a consider-
able amount of engineering skill and domain expertise. But this can
all be avoided if good features can be learned automatically using a
general-purpose learning procedure. This is the key advantage of
deep learning.
A deep-learning architecture is a multilayer stack of simple mod-
ules, all (or most) of which are subject to learning, and many of which
compute non-linear input–output mappings. Each module in the
stack transforms its input to increase both the selectivity and the
invariance of the representation. With multiple non-linear layers, say
a depth of 5 to 20, a system can implement extremely intricate func-
tions of its inputs that are simultaneously sensitive to minute details
— distinguishing Samoyeds from white wolves — and insensitive to
large irrelevant variations such as the background, pose, lighting and
surrounding objects.
Backpropagation to train multilayer architectures
From the earliest days of pattern recognition22,23, the aim of research-
ers has been to replace hand-engineered features with trainable
multilayer networks, but despite its simplicity, the solution was not
widely understood until the mid 1980s. As it turns out, multilayer
architectures can be trained by simple stochastic gradient descent.
As long as the modules are relatively smooth functions of their inputs
and of their internal weights, one can compute gradients using the
backpropagation procedure. The idea that this could be done, and
that it worked, was discovered independently by several different
groups during the 1970s and 1980s24–27.
The backpropagation procedure to compute the gradient of an
objective function with respect to the weights of a multilayer stack
of modules is nothing more than a practical application of the chain
rule for derivatives. The key insight is that the derivative (or gradi-
ent) of the objective with respect to the input of a module can be
computed by working backwards from the gradient with respect to
the output of that module (or the input of the subsequent module)
(Fig.1). The backpropagation equation can be applied repeatedly to
propagate gradients through all modules, starting from the output
at the top (where the network produces its prediction) all the way to
the bottom (where the external input is fed). Once these gradients
have been computed, it is straightforward to compute the gradients
with respect to the weights of each module.
Many applications of deep learning use feedforward neural net-
work architectures (Fig. 1), which learn to map a fixed-size input
(for example, an image) to a fixed-size output (for example, a prob-
ability for each of several categories). To go from one layer to the
next, a set of units compute a weighted sum of their inputs from the
previous layer and pass the result through a non-linear function. At
present, the most popular non-linear function is the rectified linear
unit (ReLU), which is simply the half-wave rectifier f(z) = max(z, 0).
In past decades, neural nets used smoother non-linearities, such as
tanh(z) or 1/(1 + exp(−z)), but the ReLU typically learns much faster
in networks with many layers, allowing training of a deep supervised
network without unsupervised pre-training28. Units that are not in
the input or output layer are conventionally called hidden units. The
hidden layers can be seen as distorting the input in a non-linear way
so that categories become linearly separable by the last layer (Fig.1).
In the late 1990s, neural nets and backpropagation were largely
forsaken by the machine-learning community and ignored by the
computer-vision and speech-recognition communities. It was widely
thought that learning useful, multistage, feature extractors with lit-
tle prior knowledge was infeasible. In particular, it was commonly
thought that simple gradient descent would get trapped in poor local
minima — weight configurations for which no small change would
reduce the average error.
In practice, poor local minima are rarely a problem with large net-
works. Regardless of the initial conditions, the system nearly always
reaches solutions of very similar quality. Recent theoretical and
empirical results strongly suggest that local minima are not a serious
issue in general. Instead, the landscape is packed with a combinato-
rially large number of saddle points where the gradient is zero, and
the surface curves up in most dimensions and curves down in the
Figure 2 | Inside a convolutional network. The outputs (not the filters)
of each layer (horizontally) of a typical convolutional network architecture
applied to the image of a Samoyed dog (bottom left; and RGB (red, green,
blue) inputs, bottom right). Each rectangular image is a feature map
corresponding to the output for one of the learned features, detected at each
of the image positions. Information flows bottom up, with lower-level features
acting as oriented edge detectors, and a score is computed for each image class
in output. ReLU, rectified linear unit.
Red Green Blue
Samoyed (16); Papillon (5.7); Pomeranian (2.7); Arctic fox (1.0); Eskimo dog (0.6); white wolf (0.4); Siberian husky (0.4)
Convolutions and ReLU
Max pooling
Max pooling
Convolutions and ReLU
Convolutions and ReLU
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. The analysis seems to show that saddle points with
only a few downward curving directions are present in very large
numbers, but almost all of them have very similar values of the objec-
tive function. Hence, it does not much matter which of these saddle
points the algorithm gets stuck at.
Interest in deep feedforward networks was revived around 2006
(refs31–34) by a group of researchers brought together by the Cana-
dian Institute for Advanced Research (CIFAR). The researchers intro-
duced unsupervised learning procedures that could create layers of
feature detectors without requiring labelled data. The objective in
learning each layer of feature detectors was to be able to reconstruct
or model the activities of feature detectors (or raw inputs) in the layer
below. By ‘pre-training’ several layers of progressively more complex
feature detectors using this reconstruction objective, the weights of a
deep network could be initialized to sensible values. A final layer of
output units could then be added to the top of the network and the
whole deep system could be fine-tuned using standard backpropaga-
. This worked remarkably well for recognizing handwritten
digits or for detecting pedestrians, especially when the amount of
labelled data was very limited36.
The first major application of this pre-training approach was in
speech recognition, and it was made possible by the advent of fast
graphics processing units (GPUs) that were convenient to program
and allowed researchers to train networks 10 or 20 times faster. In
2009, the approach was used to map short temporal windows of coef-
ficients extracted from a sound wave to a set of probabilities for the
various fragments of speech that might be represented by the frame
in the centre of the window. It achieved record-breaking results on a
standard speech recognition benchmark that used a small vocabu-
and was quickly developed to give record-breaking results on
a large vocabular y task39. By 2012, versions of the deep net from 2009
were being developed by many of the major speech groups6 and were
already being deployed in Android phones. For smaller data sets,
unsupervised pre-training helps to prevent overfitting
, leading to
significantly better generalization when the number of labelled exam-
ples is small, or in a transfer setting where we have lots of examples
for some ‘source’ tasks but very few for some ‘target’ tasks. Once deep
learning had been rehabilitated, it turned out that the pre-training
stage was only needed for small data sets.
There was, however, one particular type of deep, feedforward net-
work that was much easier to train and generalized much better than
networks with full connectivity between adjacent layers. This was
the convolutional neural network (ConvNet)41,42. It achieved many
practical successes during the period when neural networks were out
of favour and it has recently been widely adopted by the computer-
vision community.
Convolutional neural networks
ConvNets are designed to process data that come in the form of
multiple arrays, for example a colour image composed of three 2D
arrays containing pixel intensities in the three colour channels. Many
data modalities are in the form of multiple arrays: 1D for signals and
sequences, including language; 2D for images or audio spectrograms;
and 3D for video or volumetric images. There are four key ideas
behind ConvNets that take advantage of the properties of natural
signals: local connections, shared weights, pooling and the use of
many layers.
The architecture of a typical ConvNet (Fig. 2) is structured as a
series of stages. The first few stages are composed of two types of
layers: convolutional layers and pooling layers. Units in a convolu-
tional layer are organized in feature maps, within which each unit
is connected to local patches in the feature maps of the previous
layer through a set of weights called a filter bank. The result of this
local weighted sum is then passed through a non-linearity such as a
ReLU. All units in a feature map share the same filter bank. Differ-
ent feature maps in a layer use different filter banks. The reason for
this architecture is twofold. First, in array data such as images, local
groups of values are often highly correlated, forming distinctive local
motifs that are easily detected. Second, the local statistics of images
and other signals are invariant to location. In other words, if a motif
can appear in one part of the image, it could appear anywhere, hence
the idea of units at different locations sharing the same weights and
detecting the same pattern in different parts of the array. Mathemati-
cally, the filtering operation performed by a feature map is a discrete
convolution, hence the name.
Although the role of the convolutional layer is to detect local con-
junctions of features from the previous layer, the role of the pooling
layer is to merge semantically similar features into one. Because the
relative positions of the features forming a motif can vary somewhat,
reliably detecting the motif can be done by coarse-graining the posi-
tion of each feature. A typical pooling unit computes the maximum
of a local patch of units in one feature map (or in a few feature maps).
Neighbouring pooling units take input from patches that are shifted
by more than one row or column, thereby reducing the dimension of
the representation and creating an invariance to small shifts and dis-
tortions. Two or three stages of convolution, non-linearity and pool-
ing are stacked, followed by more convolutional and fully-connected
layers. Backpropagating gradients through a ConvNet is as simple as
through a regular deep network, allowing all the weights in all the
filter banks to be trained.
Deep neural networks exploit the property that many natural sig-
nals are compositional hierarchies, in which higher-level features
are obtained by composing lower-level ones. In images, local combi-
nations of edges form motifs, motifs assemble into parts, and parts
form objects. Similar hierarchies exist in speech and text from sounds
to phones, phonemes, syllables, words and sentences. The pooling
allows representations to vary very little when elements in the previ-
ous layer vary in position and appearance.
The convolutional and pooling layers in ConvNets are directly
inspired by the classic notions of simple cells and complex cells in
visual neuroscience
, and the overall architecture is reminiscent of
the LGN–V1–V2–V4–IT hierarchy in the visual cortex ventral path-
way44. When ConvNet models and monkeys are shown the same pic-
ture, the activations of high-level units in the ConvNet explains half
of the variance of random sets of 160neurons in the monkey’s infer-
otemporal cortex
. ConvNets have their roots in the neocognitron
the architecture of which was somewhat similar, but did not have an
end-to-end supervised-learning algorithm such as backpropagation.
A primitive 1D ConvNet called a time-delay neural net was used for
the recognition of phonemes and simple words47,48.
There have been numerous applications of convolutional net-
works going back to the early 1990s, starting with time-delay neu-
ral networks for speech recognition
and document reading
. The
document reading system used a ConvNet trained jointly with a
probabilistic model that implemented language constraints. By the
late 1990s this system was reading over 10% of all the cheques in the
United States. A number of ConvNet-based optical character recog-
nition and handwriting recognition systems were later deployed by
. ConvNets were also experimented with in the early 1990s
for object detection in natural images, including faces and hands
and for face recognition52.
Image understanding with deep convolutional networks
Since the early 2000s, ConvNets have been applied with great success to
the detection, segmentation and recognition of objects and regions in
images. These were all tasks in which labelled data was relatively abun-
dant, such as traffic sign recognition
, the segmentation of biological
images54 particularly for connectomics55, and the detection of faces,
text, pedestrians and human bodies in natural images
. A major
recent practical success of ConvNets is face recognition59.
Importantly, images can be labelled at the pixel level, which will have
applications in technology, including autonomous mobile robots and
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self-driving cars
. Companies such as Mobileye and NVIDIA are
using such ConvNet-based methods in their upcoming vision sys-
tems for cars. Other applications gaining importance involve natural
language understanding14 and speech recognition7.
Despite these successes, ConvNets were largely forsaken by the
mainstream computer-vision and machine-learning communities
until the ImageNet competition in 2012. When deep convolutional
networks were applied to a data set of about a million images from
the web that contained 1,000 different classes, they achieved spec-
tacular results, almost halving the error rates of the best compet-
ing approaches
. This success came from the efficient use of GPUs,
ReLUs, a new regularization technique called dropout
, and tech-
niques to generate more training examples by deforming the existing
ones. This success has brought about a revolution in computer vision;
ConvNets are now the dominant approach for almost all recognition
and detection tasks
and approach human performance on
some tasks. A recent stunning demonstration combines ConvNets
and recurrent net modules for the generation of image captions
Recent ConvNet architectures have 10 to 20 layers of ReLUs, hun-
dreds of millions of weights, and billions of connections between
units. Whereas training such large networks could have taken weeks
only two years ago, progress in hardware, software and algorithm
parallelization have reduced training times to a few hours.
The performance of ConvNet-based vision systems has caused
most major technology companies, including Google, Facebook,
Microsoft, IBM, Yahoo!, Twitter and Adobe, as well as a quickly
growing number of start-ups to initiate research and development
projects and to deploy ConvNet-based image understanding products
and services.
ConvNets are easily amenable to efficient hardware implemen-
tations in chips or field-programmable gate arrays66,67. A number
of companies such as NVIDIA, Mobileye, Intel, Qualcomm and
Samsung are developing ConvNet chips to enable real-time vision
applications in smartphones, cameras, robots and self-driving cars.
Distributed representations and language processing
Deep-learning theory shows that deep nets have two different expo-
nential advantages over classic learning algorithms that do not use
distributed representations
. Both of these advantages arise from the
power of composition and depend on the underlying data-generating
distribution having an appropriate componential structure
. First,
learning distributed representations enable generalization to new
combinations of the values of learned features beyond those seen
during training (for example, 2n combinations are possible with n
binary features)
. Second, composing layers of representation in
a deep net brings the potential for another exponential advantage
(exponential in the depth).
The hidden layers of a multilayer neural network learn to repre-
sent the network’s inputs in a way that makes it easy to predict the
target outputs. This is nicely demonstrated by training a multilayer
neural network to predict the next word in a sequence from a local
Figure 3 | From image to text. C aptions generated by a recurrent neural
network (RNN) taking, as extra input, the representation extracted by a deep
convolution neural network (CNN) from a test image, with the RNN trained to
‘translate’ high-level representations of images into captions (top). Reproduced
with permission from ref. 102. When the RNN is given the ability to focus its
attention on a different location in the input image (middle and bottom; the
lighter patches were given more attention) as it generates each word (bold), we
found86 that it exploits this to achieve better ‘translation’ of images into captions.
Deep CNN
Generating RNN
A group of people
shopping at an outdoor
There are many
vegetables at the
fruit stand.
A woman is throwing a frisbee in a park.
A little girl sitting on a bed with a teddy bear. A group of people sitting on a boat in the water. A girae standing in a forest with
A dog is standing on a hardwood oor. A stop sign is on a road with a
mountain in the background
440 | NATURE | VOL 521 | 28 MAY 2015
© 2015 Macmillan Publishers Limited. All rights reserved
context of earlier words
. Each word in the context is presented to
the network as a one-of-N vector, that is, one component has a value
of 1 and the rest are0. In the first layer, each word creates a different
pattern of activations, or word vectors (Fig.4). In a language model,
the other layers of the network learn to convert the input word vec-
tors into an output word vector for the predicted next word, which
can be used to predict the probability for any word in the vocabulary
to appear as the next word. The network learns word vectors that
contain many active components each of which can be interpreted
as a separate feature of the word, as was first demonstrated
in the
context of learning distributed representations for symbols. These
semantic features were not explicitly present in the input. They were
discovered by the learning procedure as a good way of factorizing
the structured relationships between the input and output symbols
into multiple ‘micro-rules’. Learning word vectors turned out to also
work very well when the word sequences come from a large corpus
of real text and the individual micro-rules are unreliable71. When
trained to predict the next word in a news story, for example, the
learned word vectors for Tuesday and Wednesday are very similar, as
are the word vectors for Sweden and Norway. Such representations
are called distributed representations because their elements (the
features) are not mutually exclusive and their many configurations
correspond to the variations seen in the observed data. These word
vectors are composed of learned features that were not determined
ahead of time by experts, but automatically discovered by the neural
network. Vector representations of words learned from text are now
very widely used in natural language applications14,17,72–76.
The issue of representation lies at the heart of the debate between
the logic-inspired and the neural-network-inspired paradigms for
cognition. In the logic-inspired paradigm, an instance of a symbol is
something for which the only property is that it is either identical or
non-identical to other symbol instances. It has no internal structure
that is relevant to its use; and to reason with symbols, they must be
bound to the variables in judiciously chosen rules of inference. By
contrast, neural networks just use big activity vectors, big weight
matrices and scalar non-linearities to perform the type of fast ‘intui-
tive’ inference that underpins effortless commonsense reasoning.
Before the introduction of neural language models71, the standard
approach to statistical modelling of language did not exploit distrib-
uted representations: it was based on counting frequencies of occur-
rences of short symbol sequences of length up to N (called N-grams).
The number of possible N-grams is on the order of VN, where V is
the vocabulary size, so taking into account a context of more than a
handful of words would require very large training corpora. N-grams
treat each word as an atomic unit, so they cannot generalize across
semantically related sequences of words, whereas neural language
models can because they associate each word with a vector of real
valued features, and semantically related words end up close to each
other in that vector space (Fig.4).
Recurrent neural networks
When backpropagation was first introduced, its most exciting use was
for training recurrent neural networks (RNNs). For tasks that involve
sequential inputs, such as speech and language, it is often better to
use RNNs (Fig. 5). RNNs process an input sequence one element at a
time, maintaining in their hidden units a ‘state vector’ that implicitly
contains information about the history of all the past elements of
the sequence. When we consider the outputs of the hidden units at
different discrete time steps as if they were the outputs of different
neurons in a deep multilayer network (Fig.5, right), it becomes clear
how we can apply backpropagation to train RNNs.
RNNs are very powerful dynamic systems, but training them has
proved to be problematic because the backpropagated gradients
either grow or shrink at each time step, so over many time steps they
typically explode or vanish77,78.
Thanks to advances in their architecture
and ways of training
, RNNs have been found to be very good at predicting the
next character in the text
or the next word in a sequence
, but they
can also be used for more complex tasks. For example, after reading
an English sentence one word at a time, an English ‘encoder’ network
can be trained so that the final state vector of its hidden units is a good
representation of the thought expressed by the sentence. This thought
vector can then be used as the initial hidden state of (or as extra input
to) a jointly trained French ‘decoder’ network, which outputs a prob-
ability distribution for the first word of the French translation. If a
particular first word is chosen from this distribution and provided
as input to the decoder network it will then output a probability dis-
tribution for the second word of the translation and so on until a
full stop is chosen17,72,76. Overall, this process generates sequences of
French words according to a probability distribution that depends on
the English sentence. This rather naive way of performing machine
translation has quickly become competitive with the state-of-the-art,
and this raises serious doubts about whether understanding a sen-
tence requires anything like the internal symbolic expressions that are
manipulated by using inference rules. It is more compatible with the
view that everyday reasoning involves many simultaneous analogies
Figure 4 | Visualizing the learned word vectors. On the left is an illustration
of word representations learned for modelling language, non-linearly projected
to 2D for visualization using the t-SNE algorithm103. On the right is a 2D
representation of phrases learned by an English-to-French encoder–decoder
recurrent neural network75. One can observe that semantically similar words
or sequences of words are mapped to nearby representations. The distributed
representations of words are obtained by using backpropagation to jointly learn
a representation for each word and a function that predicts a target quantity
such as the next word in a sequence (for language modelling) or a whole
sequence of translated words (for machine translation)18,75.
−37 −36 −35 −34 −33 −32 −31 −30 −29
organizations institutions
society industry
−5.5 −5 −4.5 −4 −3.5 −3 −2.5 −2
over the past few months
that a few days
In the last few days
the past few days
In a few months
in the coming months
a few months ago
" the two groups
of the two groups
over the last few months
dispute between the two
the last two decades
the next six months
two months before being
for nearly two months
over the last two decades
within a few months
28 MAY 2015 | VOL 521 | NATURE | 441
© 2015 Macmillan Publishers Limited. All rights reserved
that each contribute plausibility to a conclusion84,85.
Instead of translating the meaning of a French sentence into an
English sentence, one can learn to ‘translate’ the meaning of an image
into an English sentence (Fig. 3). The encoder here is a deep Con-
vNet that converts the pixels into an activity vector in its last hidden
layer. The decoder is an RNN similar to the ones used for machine
translation and neural language modelling. There has been a surge of
interest in such systems recently (see examples mentioned in ref. 86).
RNNs, once unfolded in time (Fig. 5), can be seen as very deep
feedforward networks in which all the layers share the same weights.
Although their main purpose is to learn long-term dependencies,
theoretical and empirical evidence shows that it is difficult to learn
to store information for very long78.
To correct for that, one idea is to augment the network with an
explicit memory. The first proposal of this kind is the long short-term
memory (LSTM) networks that use special hidden units, the natural
behaviour of which is to remember inputs for a long time
. A special
unit called the memory cell acts like an accumulator or a gated leaky
neuron: it has a connection to itself at the next time step that has a
weight of one, so it copies its own real-valued state and accumulates
the external signal, but this self-connection is multiplicatively gated
by another unit that learns to decide when to clear the content of the
LSTM networks have subsequently proved to be more effective
than conventional RNNs, especially when they have several layers for
each time step
, enabling an entire speech recognition system that
goes all the way from acoustics to the sequence of characters in the
transcription. LSTM networks or related forms of gated units are also
currently used for the encoder and decoder networks that perform
so well at machine translation17,72,76.
Over the past year, several authors have made different proposals to
augment RNNs with a memory module. Proposals include the Neural
Turing Machine in which the network is augmented by a ‘tape-like
memory that the RNN can choose to read from or write to88, and
memory networks, in which a regular network is augmented by a
kind of associative memory
. Memory networks have yielded excel-
lent performance on standard question-answering benchmarks. The
memory is used to remember the story about which the network is
later asked to answer questions.
Beyond simple memorization, neural Turing machines and mem-
ory networks are being used for tasks that would normally require
reasoning and symbol manipulation. Neural Turing machines can
be taught ‘algorithms’. Among other things, they can learn to output
a sorted list of symbols when their input consists of an unsorted
sequence in which each symbol is accompanied by a real value that
indicates its priority in the list
. Memory networks can be trained
to keep track of the state of the world in a setting similar to a text
adventure game and after reading a story, they can answer questions
that require complex inference
. In one test example, the network is
shown a 15-sentence version of the The Lord of the Rings and correctly
answers questions such as “where is Frodo now?”89.
The future of deep learning
Unsupervised learning
had a catalytic effect in reviving interest in
deep learning, but has since been overshadowed by the successes of
purely supervised learning. Although we have not focused on it in this
Review, we expect unsupervised learning to become far more important
in the longer term. Human and animal learning is largely unsupervised:
we discover the structure of the world by observing it, not by being told
the name of every object.
Human vision is an active process that sequentially samples the optic
array in an intelligent, task-specific way using a small, high-resolution
fovea with a large, low-resolution surround. We expect much of the
future progress in vision to come from systems that are trained end-to-
end and combine ConvNets with RNNs that use reinforcement learning
to decide where to look. Systems combining deep learning and rein-
forcement learning are in their infancy, but they already outperform
passive vision systems
at classification tasks and produce impressive
results in learning to play many different video games100.
Natural language understanding is another area in which deep learn-
ing is poised to make a large impact over the next few years. We expect
systems that use RNNs to understand sentences or whole documents
will become much better when they learn strategies for selectively
attending to one part at a time76,86.
Ultimately, major progress in artificial intelligence will come about
through systems that combine representation learning with complex
reasoning. Although deep learning and simple reasoning have been
used for speech and handwriting recognition for a long time, new
paradigms are needed to replace rule-based manipulation of symbolic
expressions by operations on large vectors101.
Received 25 February; accepted 1 May 2015.
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Acknowledgements The authors would like to thank the Natural Sciences and
Engineering Research Council of Canada, the Canadian Institute For Advanced
Research (CIFAR), the National Science Foundation and Office of Naval Research
for support. Y.L. and Y.B. are CIFAR fellows.
Author Information Reprints and permissions information is available at The authors declare no competing financial
interests. Readers are welcome to comment on the online version of this
paper at Correspondence should be addressed to Y.L.
444 | NATURE | VOL 521 | 28 MAY 2015
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... Here, data in the form of (x; y) is used to train a model that predicts y given x as input (Jordan & Mitchell, 2015). Deep learning represents a subfield of ML that uses multiple processing layers for learning (LeCun et al., 2015). Deep learning has caused breakthroughs in many areas, including speech recognition and object detection (Stone et al., 2016). ...
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