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A Critical Review of Recurrent Neural Networks for Sequence Learning
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A Critical Review of Recurrent Neural Networks
for Sequence Learning
Zachary C. Lipton
University of California, San Diego
zlipton@cs.ucsd.edu
June 5th, 2015
Abstract
Countless learning tasks require dealing with sequential data. Image
captioning, speech synthesis, music generation, and video game playing
all require that a model generate sequences of outputs. In other domains,
such as time series prediction, video analysis, and music information re-
trieval, a model must learn from sequences of inputs. Significantly more
interactive tasks, such as natural language translation, engaging in dia-
logue, and robotic control, often demand both.
Recurrent neural networks (RNNs) are a powerful family of connec-
tionist models that capture time dynamics via cycles in the graph. Unlike
feedforward neural networks, recurrent networks can process examples one
at a time, retaining a state, or memory, that reflects an arbitrarily long
context window. While these networks have long been difficult to train
and often contain millions of parameters, recent advances in network archi-
tectures, optimization techniques, and parallel computation have enabled
large-scale learning with recurrent nets.
Over the past few years, systems based on state of the art long short-
term memory (LSTM) and bidirectional recurrent neural network (BRNN)
architectures have demonstrated record-setting performance on tasks as
varied as image captioning, language translation, and handwriting recog-
nition. In this review of the literature we synthesize the body of research
that over the past three decades has yielded and reduced to practice these
powerful models. When appropriate, we reconcile conflicting notation and
nomenclature. Our goal is to provide a mostly self-contained explication
of state of the art systems, together with a historical perspective and
ample references to the primary research.
1 Introduction
Recurrent neural networks (RNNs) are a superset of feedforward neural net-
works, augmented with the ability to pass information across time steps. They
1

are a rich family of models capable of nearly arbitrary computation. A well-
known result by Siegelman and Sontag from 1991 demonstrated that a finite
sized recurrent neural network with sigmoidal activation functions can simulate
a universal Turing machine [52]. In practice, the ability to model temporal
dependencies makes recurrent neural networks especially suited to tasks where
input and/or output consist of sequences of points that are not independent.
1.1 Why Recurrent Nets?
In this section, we address the fundamental reasons why recurrent neural net-
works warrant serious study for modeling sequential input and output. To be
clear, we are motivated by a desire to achieve empirical results. This warrants
clarification because recurrent nets have roots in both cognitive modeling and
supervised machine learning, and owing to this difference of perspectives, many
of these papers have different aims and priorities. In the foundational papers,
generally published in cognitive science and computational neuroscience jour-
nals ([32], [33], [17]), biologically plausible mechanisms are emphasized. In other
papers ([51], [55], [34]), biological inspiration is downplayed in favor of achiev-
ing empirical results on important tasks and datasets. Given the empirical aim,
we now address three significant questions one might reasonably want answered
before reading further.
Why Model Time Explicitly?
In light of the practical success and economic value of time-agnostic models,
this is a fair question. Support vector machines, logistic regression, and feedfor-
ward networks have proved immensely useful without explicitly modeling time.
Arguably, it is precisely the assumption of independence that has led to much
recent progress in machine learning. Further, many models implicitly capture
time by concatenating each input with some number of its immediate prede-
cessors and successors, presenting the machine learning model with a sliding
window of context about each point of interest. This approach has been used
with deep belief nets for speech modeling in [42].
Unfortunately, despite the usefulness of the independence assumption, it
precludes modeling long-range time-dependencies. For example, a model trained
using a finite-length context window of length 5 could never be trained to answer
the simple question, “what was the data point seen 10 time steps ago?” For
a practical application such as call center automation, such a limited system
might learn to route calls, but could never participate in an extended dialogue.
Since the earliest conception of artificial intelligence, we have sought to build
systems that interact with humans in time. In Alan Turing’s groundbreaking
paper Computing Machinery and Intelligence, he proposes an “Imitation Game”
which judges a machine’s intelligence by its ability to convincingly engage in
dialogue [63]. Besides dialogue systems, modern interactive systems of economic
importance include self-driving cars and robotic surgery, among others. Ignoring
2

an explicit model of time, it seems unlikely that any combination of classifiers
or regressors can be cobbled together to provide this functionality.
Why Neural Networks and Not Markov Models?
Recurrent neural networks are not the first models to capture time dependen-
cies. Markov chains, which model transitions between observed sequences of
states (s(1)
, s(2)
, ... , s(T )
), were first described by mathematician Andrey
Markov in 1906. Hidden Markov models (HMMs), which model observed data
(o(1)
, o(2)
, ..., o(T )
) as probabilistically dependent upon unobserved states, were
described in the 1950s and have been widely studied since the 1960s. However,
traditional Markov model approaches are limited because their states must be
drawn from a modestly sized discrete state space sj ∈ S. The Viterbi algorithm,
which is used to perform efficient inference on hidden Markov models, scales in
time O(|S|2
). Further, the transition table capturing the probability of moving
between any two adjacent states is of size |S|2
. Thus, standard operations are
infeasible with an HMM when the set of possible hidden states is larger than
roughly 106
states. Further, each hidden state s(t)
can depend only on the pre-
vious state s(t−1)
. While it is possible to extend any Markov model to account
for a larger context window by creating a new state-space equal to the cross
product of the possible states at each time in the window, this procedure grows
the state space exponentially with the size of the window, rendering Markov
models computationally impractical for modeling long-range dependencies.
Given the limitations of Markov models, we ought to explain why it is sen-
sible that connectionist models, i.e., artificial neural networks, should fare bet-
ter. First, recurrent neural networks can capture long-range time dependencies,
overcoming the chief limitation of Markov models. This point requires a careful
explanation. As in Markov models, any state in a traditional RNN depends
only on the current input as well as the state of the network at the previous
time step 1
. However, the hidden state at any time step can contain information
from an arbitrarily long context window. This is possible because the number
of distinct states that can be represented in a hidden layer of nodes grows ex-
ponentially with the number of nodes in the layer. Even if each node took only
binary values, the network could represent 2N
states where N is the number of
nodes in the hidden layer. Given real-valued outputs, even assuming the lim-
ited precision of 64 bit numbers, a single hidden layer of nodes can represent
264N
distinct states. While the potential expressive power grows exponentially
with the number of nodes in the hidden representation, the complexity of both
inference and training grows only quadratically.
Second, it is generally desirable to extend neural networks to tackle any
supervised learning problem because they are powerful learning models that
achieve state of the art results in a wide range of supervised learning tasks.
1Bidirectional recurrent neural networks (BRNNs) [51] extend RNNs to model dependence
on both past states and future states. Traditional RNNs only model the dependence of each
event on the past. This extension is especially useful for sequence to sequence learning with
fixed length examples.
3

Over the past several years, storage has become more affordable, datasets have
grown far larger, and the field of parallel computing has advanced considerably.
In the setting of such large high-dimensional datasets, simple linear models
under-fit and often underutilize computing resources. Deep learning methods, in
particular those based on deep belief networks (DNNs), which are greedily built
by stacking restricted Boltzmann machines, and convolutional neural networks,
which exploit the local dependency of visual information, have demonstrated
record-setting results on many important applications. Neural networks are
especially well-suited for machine perception tasks, where the raw underlying
features are not individually informative. This success is attributed to their
ability to learn hierarchical representations, unlike traditional algorithms, which
rely upon hand-engineered features. However, despite their power, feedforward
neural nets have limitations. Most notably, they rely on the assumption of
independence among the data points. Additionally, these networks generally
rely on input consisting of fixed length vectors. Thus it is sensible to extend
these powerful learning tools to model data with temporal structure, especially
in the many domains where neural nets are already the state of the art.
Are RNNs Too Expressive?
As described earlier, finite-sized RNNs with sigmoidal activations are Turing
complete. The capability of RNNs to run arbitrary computation clearly demon-
strates their expressive power, but one could argue that the C programming
language is equally capable of expressing arbitrary programs. And yet there are
no papers claiming that the invention of C represents a panacea for machine
learning. Out of the box, C offers no simple way of efficiently exploring the
space of programs. There is no straightforward way to calculate the gradient
of an arbitrary C program to minimize a chosen loss function. Further, the
biggest problem with treating the set of programs expressible in C as a family
of machine learning models is that this set is far too large. Given any finite sized
dataset, there exist countless programs which can overfit the data, generating
desired output but failing to generalize to test data.
Why then should RNN’s not suffer from similar problems? First, given any
fixed architecture (set of nodes, edges, and activation functions), the recurrent
neural networks described in this paper are fully differentiable end to end. The
derivative of the loss function can always be calculated with respect to each of
the parameters (weights) in the model. Second, while the Turing-completeness
of finite-length RNNs is an impressive property, given any fixed-size RNN and
a specific architecture, it is not actually possible to generate any arbitrary pro-
gram. Further, unlike an arbitrary program composed in C, a recurrent neu-
ral network can be regularized via standard techniques such as weight decay,
dropout, and limiting the degrees of freedom.
4

1.2 Comparison to Prior Work
The literature on recurrent neural networks can seem impenetrable to the unini-
tiated. Shorter papers assume familiarity with a large body of background lit-
erature. Diagrams are frequently underspecified, failing to indicate which edges
span time steps and which don’t. Worse, jargon abounds while notation is fre-
quently inconsistent across papers or overloaded within papers. Readers are
frequently in the unenviable position of having to synthesize conflicting infor-
mation across many papers in order to understand but one. For example, in
many papers subscripts index both nodes and time steps. In others, h simul-
taneously stands for link functions and a layer of hidden nodes. The variable t
simultaneously stands for both time indices and targets, sometimes in the same
equation. Many terrific breakthrough papers have appeared recently, but clear
reviews of recurrent neural network literature are rare.
Among the most useful resources are Alex Graves’ 2012 book on supervised
sequence labelling with recurrent neural networks [23] and Felix Gers’ doctoral
thesis [18]. More recently, [14] covers recurrent neural nets for language mod-
eling. Other resources focus on a specific technical aspect such as [48], which
surveys gradient calculations in recurrent neural networks. In this review pa-
per, we aim to provide a readable, intuitive, and consistently notated review on
recurrent neural networks for sequence learning. We emphasize models, algo-
rithms, and results, but focus equally on distilling the intuitions that have guided
this largely heuristic and empirical field. In addition to concrete modeling de-
tails, we offer qualitative arguments, a historical perspective, and comparisons
to alternative methodology where appropriate.
2 Background
Here we introduce formal notation and provide a brief background on neural
networks.
2.1 Time
To be clear, RNNs are not limited to sequences which index time. They have
been used successfully on non-temporal sequence data, including genetic data
[3]. However, computation proceeds in time, and many important applications
have an explicit or implicit temporal aspect. While we refer to time throughout
this paper, the methods described here are applicable to wider family of tasks.
In this paper, by time, we refer to data points x(t)
that arrive and desired
outputs y(t)
that are generated in a discrete sequence of time steps indexed by
t. We use superscripts with parentheses and not subscripts to obviate confu-
sion between time steps and neurons. Our sequences may be of finite length
or countably infinite. When they are finite, we call the maximum time in-
dex of the sequence T. Thus a sequence of consecutive inputs can be denoted
(x(1)
, x(2)
, ..., x(T )
) and outputs can be notated (y(1)
, y(2)
, ..., y(T )
) These time
5

steps may be equally spaced samples from a continuous real-world process. Ex-
amples would include the still images that comprise the frames of videos or the
discrete amplitudes sampled at fixed intervals to comprise audio recordings. The
time steps may also be ordinal, with no exact correspondence to durations. In
fact, these techniques can be extended to domains including genetic sequences,
where the sequence has a defined order but no real correspondence to time. This
is the case with natural language. In the word sequence “John Coltrane plays
the saxophone”, x(1)
= John, x(2)
= Coltrane, etc.
2.2 Neural Networks
Neural networks are biologically inspired models of computation. Generally,
a neural network consists of a set of artificial neurons, commonly referred to
as nodes or units, and a set of directed edges between them, which intuitively
represent the synapses in a biological neural network. Associated with each
neuron j is an activation function lj, which is sometimes called a link function.
We use the notation “lj” and not “hj” (unlike some other papers) to distinguish
the activation function lj from the values of the hidden nodes in a network, which
is commonly notated h in the RNN literature.
Associated with each edge from node j0
to j is a weight wjj0 . Following
the convention adopted in several foundational recurrent net papers ([31], [18],
[20], [61]), we index neurons with j and j0
, and by wjj0 , we denote the weight
corresponding to the directed edge from node j0
to node j. It is important to
note that in many papers, textbooks, and lecture notes, the indices are flipped
and wj0j 6= wjj0 denotes the weight on the directed edge from the node j0
to the
node j as in [16] and on Wikipedia [67].
The value vj of each neuron j is calculated by applying its activation function
to a weighted sum of its inputs (Figure 1):
vj = lj


X
j0
wjj0 · vj0

 .
For convenience, we term the weighted sum inside the parenthesis the incom-
ing activation and notate it as aj. We represent this entire process in figures
by depicting neurons as circles and edges as arrows connecting them. When
appropriate, we mark the exact activation function with a symbol, e.g., σ for
sigmoid.
Common choices for the activation function include the sigmoid σ(z) =
1/(1 + e−z
) and the tanh function φ(z) = (ez
− e−z
)/(ez
+ e−z
) which has
become common in feedforward neural nets and was applied to recurrent nets
in [61]. Another activation which has become the state of the art in deep learning
research is the rectified linear unit (ReLU) lj(z) = max(0, z). These units have
been demonstrated to improve the performance of many deep neural networks
([42], [46], [71]) on tasks as varied as speech processing and object recognition,
and have been used in recurrent neural networks by [6].
6

Figure 1: An artificial neuron computes a nonlinear function of a weighted sum
of its inputs.
The activation function at the output nodes depends upon the task. For
multi-class classification, we apply a softmax nonlinearity to the layer. The
softmax function calculates
ŷk =
eak
PK
k0=1 eak0
where K is the total number of outputs. The denominator is normalization
consisting of a sum of exponentials over all output nodes, ensuring that the
output sums to 1. For multilabel classification the activation function is simply
a point-wise sigmoid. For regression we may have linear output. Due to the
overwhelming number of current applications involving multi-class classification,
especially for recurrent nets, in this paper, unless otherwise specified, we assume
that softmax is applied at the output.
2.3 Feedforward Neural Networks
With a neural model of computation, one must determine the order in which
computation should proceed. Should nodes be sampled one at a time and up-
dated, or should the value of all nodes be calculated at once and then all updates
applied simultaneously? Feedforward neural networks (Figure 2) are a restricted
class of neural networks which deal with this problem by forbidding cycles in
the graph. Thus all nodes can be arranged into layers. The outputs in each
layer can be calculated given the outputs from the lower layers.
The input x to a feedforward network is presented by setting the values of
the lowest layer. Each higher layer is then successively computed until out-
put is generated at the topmost layer ŷ. These networks are frequently used
for supervised learning tasks such as classification and regression. Learning is
accomplished by iteratively updating each of the weights to minimize a loss
7

Figure 2: A feedforward neural network. An example is presented to the network
by setting the values of the blue nodes. Each layer is calculated successively as
a function of the prior layers until output is produced at the topmost layer.
function, L(ŷ, y), which penalizes the distance between the output ŷ and the
target y. Backpropagation, an algorithm introduced to neural networks in [50],
computes the gradient of the loss with respect to each parameter using the chain
rule. While the optimization surfaces for neural networks are highly non-convex,
and exact optimization is known to be an NP-Hard problem, a large body of
work on heuristic pre-training and optimization techniques has led to impres-
sive empirical success on many supervised learning tasks. Convolutional neural
networks, developed by Yann LeCun, [37] are a variant of feedforward neural
network that, since 2012, hold records in many computer vision tasks, such as
object detection [35].
Feedforward networks, however, are limited. After each example is pro-
cessed, the entire state of the network is lost. If each data point is independently
sampled, this presents no problem. But if data points are related in time, this
is unacceptable. Frames from video, snippets of audio, and words pulled from
sentences, represent settings where the independence assumption fails.
2.4 Training Neural Networks via Backpropagation
The most successful algorithm for training neural networks is backpropagation,
introduced to neural networks by Rumelhart et al. in 1985 [50]. Backpropa-
gation uses the chain rule to calculate the derivative of a loss function L with
respect to each parameter in the network. The weights are then adjusted by
gradient descent. Because the loss surface is non-convex, there is no assurance
that backpropagation will reach a global minimum. However, in practice, net-
works trained with backpropagation and gradient following techniques have been
8

remarkably successful. In practice, most networks are trained with stochastic
gradient descent (SGD) using mini-batches. Here, w.l.o.g. we discuss only the
case with batch size equal to 1. The stochastic gradient update equation is given
by
w ← w − η∇wFi
where η is the learning rate and ∇wFi is the gradient of the objective function
with respect to the parameters w as calculated on a single example (xi, yi).
In practice, many variants of SGD are used to accelerate learning. Some
popular heuristics, such as AdaGrad [15], AdaDelta [70], and RMSprop [1],
adaptively tune the learning rate for each feature. AdaGrad, arguably the most
popular, adapts the learning rate by caching the sum of squared gradients with
respect to each parameter at each time step. The step size for each feature is
scaled to the inverse of this cache. This leads to fast convergence on convex error
surfaces, but because the cached sum is monotonically increasing, AdaGrad has
a monotonically decreasing learning rate. This may be undesirable on highly
non-convex loss surfaces. RMSprop modifies AdaGrad by introducing a decay
factor on the cache, transforming the monotonic growing cache into a moving
average. Momentum methods are another common SGD variant used to train
neural networks. These methods add to each update a decaying sum of the pre-
vious updates. When the momentum parameter is well-tuned and the network
is initialized well, momentum methods can train deep nets and recurrent nets
competitively with more computationally expensive methods like the Hessian
Free optimizer [60].
To calculate the gradient in a feedforward neural network, backpropagation
proceeds as follows. First, an example is forward propagated through the net-
work to produce a value vj at each node and outputs ŷ at the topmost layer.
Then, a loss function L(ŷk, yk) is assessed at each output node k. Subsequently,
for each output node k, we can calculate
δk =
∂L(ŷk, yk)
∂ŷk
· l0
k(ak).
Given these values δk, for each node in the level prior we can calculate
δj = l0
(aj)
X
k
δk · wkj.
This calculation is performed successively for each lower layer to calculate δj for
every node j given the δ values for each node connected by an outgoing edge.
Each value δj represents the derivative ∂L/aj of the total loss function w.r.t.
that node’s incoming activation. Given the values vj calculated on the forward
pass, and the values δj calculated on the backward pass, the derivative of the
loss L with respect a given parameter wjj0 is given by
∂L
∂wjj0
= δjvj0 .
9

Large scale feedforward neural networks trained via backpropagation have set
many large-scale machine learning records, most notably on the computer vision
task of object detection ([38], [35]).
Several other methods have been explored for learning the weights in a neu-
ral network. Early work, including Hopfield nets [32], learned via a Hebbian
principle but did not produce networks useful for discriminative tasks. A num-
ber of papers from the 1990s ([5], [26]) championed the idea of learning neural
networks with genetic algorithms with some even claiming that achieving suc-
cess on real-world problems by applying many small changes to a network’s
weights was impossible. Despite the subsequent success of backpropagation,
interest in genetic algorithms persists. Several recent papers explore genetic
algorithms for neural networks, especially as means of learning the architecture
of neural networks, a problem not addressed by backpropagation ([4], [27]). By
the architecture we mean the number of layers, the number of nodes in each, the
connectivity pattern among the layers, the choice of activation functions, etc.
One open question in neural network research is how to exploit sparsity in
training. In a neural network with sigmoidal or tanh activation functions, the
nodes in each layer never take value exactly 0. Thus, even if the inputs are
sparse, the nodes at each hidden layer are not. However, a rectified linear units
(ReLUs) introduce sparsity to hidden layers [21]. In this setting, a promising
path may be to store the sparsity pattern when computing each layer’s values
and use it to speed up computation of the next layer in the network. A growing
body of recent work ([11], [36], [53], [39]), thus read shows that given sparse
inputs to a linear model with any standard regularizer, sparsity can be fully ex-
ploited even if the gradient is not sparse (owing to regularization). Given sparse
hidden layers, these approaches can be extended to the layer-wise computations
in neural networks.
3 Recurrent Neural Networks
Recurrent neural networks are a strict superset of feedforward neural networks,
augmented by the inclusion of recurrent edges that span adjacent time steps,
introducing a notion of time to the model. While RNNs may not contain cycles
among the conventional edges, recurrent edges may form cycles, including self-
connections. At time t, nodes receiving input along recurrent edges receive input
activation from the current example x(t)
and also from hidden nodes h(t−1)
in
the network’s previous state. The output ŷ(t)
is calculated given the hidden
state h(t)
at that time step. Thus, input x(t−1)
at time t − 1 can influence the
output ŷ(t)
at time t by way of these recurrent connections.
We can show in two equations, all calculations necessary for computation at
each time step on the forward pass in a simple recurrent neural network:
h(t)
= σ(Whxx + Whhh(t−1)
+ bh)
ŷ(t)
= softmax(Wyhh(t)
+ by)
10

Here Whx is the matrix of weights between the input and hidden layers and
Whh is the matrix of recurrent weights between the hidden layers at adjacent
time steps. The vectors bh and by are biases which allow each node to learn an
offset.
Most of the models discussed in this paper consist of networks with recurrent
hidden layers. However, some proposed models, such as Jordan Networks, allow
for connections between the outputs in one state and the hidden layer in the
next. Others, such as Sutskever et al.’s model for sequence to sequence learning
[62], compute the output at each time step and pass a representation of this
information as the input at the following time step.
Figure 3: A simple recurrent network. At each time step t, activation is passed
along solid edges as in a feedforward network. Dashed edges connect the source
node j0
at time t, i.e., j0(t)
to the target node at the following time step j(t+1)
.
A simple recurrent network is depicted in Figure 3. The dynamics of this
network across time steps can be visualized by unfolding the network (Figure
4). Given this picture, the model can be interpreted not as cyclic, but rather
as a deep network with one layer per time step and shared weights across time
steps. It’s then clear that the unfolded network can be trained across many time
steps using backpropagation. This algorithm is called backpropagation through
time (BPTT), and was introduced in 1990 [66].
3.1 Past Approaches
Early foundational work on recurrent networks took in the 1980s. In 1982,
Hopfield introduced a family of recurrent neural networks [32]. We’ll avoid
a prolonged discussion of these networks as they are not currently used for
sequence learning. Hopfield’s nets have some pattern recognition capabilities
but offer no clear method for supervised training. These networks are defined
11

Figure 4: Visualizing the network unfolded across time steps.
by the values of the weights between nodes and the link functions are simple
thresholding at 0. In these nets, a pattern is placed in the network by setting
the values of the nodes. The network then runs for some time according to its
update rules, and eventually a pattern is read out. The networks are useful for
recovering a stored pattern from a corrupted version and are the forerunners of
Boltzmann machines and auto-encoders.
Figure 5: A recurrent neural network as proposed by Jordan (1986).
Jordan networks (Figure 5), introduced by Michael Jordan in 1986, present
an early architecture for supervised learning on sequences ([33]). A Jordan
12

Figure 6: An Elman network as described in Finding Structure in Time (1990)
[17]. Hidden units are connected 1-to-1 to context units across time steps, which
in turn feed back into the corresponding hidden units.
network resembles a feedforward network with a single hidden layer, but is ex-
tended with context units. 2
Outputs are fed into the context units, which then
feed in to the hidden nodes at the following time step. Additionally, context
units have self-connected edges. Intuitively, these self-connected edges gives Jor-
dan networks a means to send information across multiple time steps without
perturbing the output at each intermediary time step. In Jordan’s setup, the
network was used to plan actions and thus these context units allow the network
to remember actions taken (outputs) at the previous time steps. Several modern
architectures utilize some form of direct feedback from output nodes. [62] trans-
lates sentences between natural languages. When generating text sequences, the
word chosen at each time step is fed into the network at the following time step.
Elman networks, introduced in [17], simplify the structure in the Jordan
network. Associated with each unit in the hidden layer is a single context unit.
Each context unit j0
takes as input the state of the corresponding hidden node
j at the previous time step, along an edge of unit weight wj0j = 1. Effectively,
this entire setup is equivalent to a simple RNN in which each hidden node has
a single self-connected recurrent edge. Some of Elman’s ideas, including fixed-
weight edges and the importance of self-connected recurrent edges in hidden
nodes survive in Hochreiter and Schmidhuber’s subsequent work on Long Short-
Term Memory [31].
In the paper, Elman trains the network using backpropagation and demon-
strates that the network can learn long-range time dependencies. The paper
features two sets of experiments. The first extends the logic operation exclusive
2In Jordan’s paper, he calls these “state units”. Elman calls a corresponding structure
“context units”. In this paper we simplify terminology by using only “context units”.
13

OR (XOR) to the time domain by concatenating sequences of three tokens. For
each three-token segment, e.g. “011”, the first two tokens (“01”) are chosen
randomly and the third (“1”) is chosen by performing XOR on them. A com-
pletely random guess should achieve accuracy of 50%. A perfect system should
perform the same as random for the first two tokens, but guess the third token
perfectly, achieving accuracy of 66.6...%. Elman’s simple network does in fact
do get close to this maximum achievable score.
3.2 Training Recurrent Networks
Learning with recurrent neural networks has long been considered to be diffi-
cult. As with all neural networks, the optimization is NP-Hard. But learning
on recurrent networks can be especially hard due to the difficulty of learning
long-range dependencies as described by Bengio et al in 1994 [8] and expanded
upon in [30]. The well known problems of vanishing and exploding gradients
occur when propagating errors across many time steps. As a trivial example,
consider a network with a single input node, a single output node, and a single
recurrent hidden node (Figure 7). Now consider an input passed to the network
at time τ and an error calculated at time t, assuming input of 0 in the inter-
vening time steps. Owing to the weight tying across time steps (the recurrent
edge at hidden node j always has the same weight), the impact of the input
at time τ on the output at time t will either explode exponentially or rapidly
approach zero as t − τ grows large, depending on whether the weight |wjj| > 1
or |wjj| < 1 and also upon the activation function in the hidden node (Figure
8). Given activation function lj = σ, the vanishing gradient problem is more
pressing, but with a rectified linear unit max(0, x), it’s easier to imagine the
exploding gradient, even with this trivial example. In [47], Pascanu et al. give
a thorough mathematical treatment of the vanishing and exploding gradient
problems, characterizing exact conditions under which these problems may oc-
cur. Given these conditions under which the gradient may vanish or explode,
they suggest an approach to training via a regularization term, which forces the
weights to values where the gradient neither vanishes nor explodes.
Truncated backpropagation through time (TBPTT) is one solution to this
problem for continuously running networks [68]. With TBPTT, some maximum
number of time steps is set along which error can be propagated. While TBPTT
with a small cutoff can be used to alleviate the exploding gradient problem, it
requires that one sacrifice the ability to learn long-range dependencies.
The optimization problem represents a more fundamental obstacle that can-
not as easily be dealt with by modifying network architecture. It has been
known since at least 1993 that optimizing even a 3-layer neural network is NP-
Complete [10]. However, recent empirical and theoretical studies suggest that
the problem may not be as hard in practice as once thought. [13] shows that
while many critical points exist on the error surfaces of large neural networks,
the ratio of saddle points to true local minima increases exponentially with the
size of the network
Fast implementations and improved gradient following heuristics have ren-
14

Figure 7: A simple recurrent net with one input unit, one output unit, and one
recurrent hidden unit.
Figure 8: A visualization of the vanishing gradient problem, using the architec-
ture depicted in Figure 7. If the weight along the purple edge is less than one,
the effect of the input at the first time step on the output at the final time step
will rapidly diminish as a function of the size of the interval in between. An
illustration like this appears in [23]
.
15

dered RNN training feasible. For example, implementations of forward and
backward propagation using GPUs, such as Theano ([9]) and Torch ([12]), have
made it easy to implement fast training algorithms. In 1996, prior to the intro-
duction of the LSTM, attempts to train recurrent nets to bridge long time gaps
were shown to perform no better than random guessing [29]. However, success-
fully trained RNNs are now relatively common. Sutskever and Martens reported
success training recurrent neural networks with a Hessian-Free, i.e., truncated
Newton approach [44] and applied it to a network which learns to generate text
one character at a time in [61]. In the paper that described the abundance of
saddle points on the error surfaces of neural networks ([13]), the authors present
a saddle-free version of Newton’s method. Unlike Newton’s method, which is
attracted to critical points, including saddle points, this variant is specially de-
signed to escape from them. Experimental results include a demonstration of
improved performance on recurrent networks. Newton’s method requires com-
puting the Hessian, which is prohibitively expensive for large networks, scaling
quadratically with the number of parameters. While their algorithm only ap-
proximates the Hessian, it is still computationally expensive compared to SGD.
Thus the authors describe a hybrid approach whereby the saddle-free Newton
method is applied in places where SGD appears to be stuck.
3.3 Modern RNNs
The most successful RNN architectures for sequence learning date to two papers
from 1997. The first, Long Short-Term Memory, by Hochreiter and Schmidhu-
ber, introduces the memory cell, a unit of computation that replaces traditional
artificial neurons in the hidden layer of a network. With these memory cells,
networks are able to overcome some difficulties with training encountered in
earlier recurrent nets. The second, Bidirectional Recurrent Neural Networks, by
Schuster and Paliwal, introduces the BRNN architecture in which information
from both the future and the past are used to determine the output at any
time t. This is in contrast to previous systems, in which only past input can
affect the output, and has been used successfully for sequence labeling tasks in
natural language processing, among others. Fortunately, the two innovations
are not mutually exclusive, and have been successfully combined by Graves et
al. for phoneme classification [25] and handwriting recognition [24].
3.3.1 Long Short-Term Memory (LSTM)
In 1997, to overcome the problem of vanishing gradients, Hochreiter and Schmid-
huber introduced the LSTM model. This model resembles a standard neural
network with a recurrent hidden layer, only each ordinary node (Figure 1) in
the hidden layer is replaced with a memory cell (Figure 9). The memory cell
contains a node with a self-connected recurrent edge of weight 1, ensuring that
the gradient can pass across many time steps without vanishing or exploding.
To distinguish that we are referencing a memory cell and not an ordinary node,
we use the index c.
16

Figure 9: LSTM memory cell as initially described in Hochreiter [31]. The
self-connected node is the internal state s. The diagonal line indicates that it
is linear, i.e. no link function is applied there. Nodes marked “Π” output the
product of their inputs. Dashed lines indicate recurrent edges and pink edges
have fixed weight of 1.
17

The term “Long Short-Term Memory” comes from the following intuition.
Simpler recurrent neural networks have long term memory in the form of weights.
The weights change very slowly over time encoding general knowledge about the
data. They also have short term memory in the form of ephemeral activations,
which pass from each node’s output to successive nodes. The LSTM model
introduces an intermediary sort of memory via the memory cell. A memory cell
is a composite of simpler units with the novel addition of multiplicative nodes,
represented in diagrams with Π. All elements of the LSTM cell are enumerated
and described below.
• Internal State: At the heart of each memory cell is a node s with linear
activation, which is referred to in the original paper as the “internal state”
of the cell. We index cells with c and thus the internal state of a cell c is
sc.
• Constant error carousel: The internal state sc has a self-connected (re-
current) edge with weight 1. This edge, called the constant error carousel,
spans adjacent time steps with constant weight, assuring that error can
flow across time steps without vanishing.
• Input Node: This node behaves as an ordinary neuron, taking input
from the rest of the network (at the previous time step) as well as from
the input. In the original paper and most subsequent work the input
node is labeled g. We adhere to this convention but note that it may be
confusing as g does not stand for gate. In the original paper, the gates
are called yin and yout but this is confusing because y generally stands for
output in the machine learning literature. Seeking comprehensibility, we
break with this convention and use i, f, and o to refer to input, forget
and output gates respectively as in [62]. When we use vector notation
we are referring to the values of the nodes in an entire layer of cells. For
example, g is a vector containing the value of g at each memory cell in a
layer. When the subscript c is used, it is to refer to an individual memory
cell.
• Multiplicative Gating: Multiplicative gates are distinctive features of
the LSTM model. Here a sigmoidal unit called a gate is learned given
the input and the incoming recurrent connections from the previous time
step. Some value of interest is then multiplied by this output. If the
gate outputs 0, flow through the gate is cut off. If the gate outputs 1, all
activation is passed through the gate.
– Input gate: The original LSTM contains two gates. The first is an
input gate ic, which is multiplied by the input node gc.
– Output gate: The second gate is termed the output gate, which we
notate as oc. This gate is multiplied by the value of the internal state
sc to produce the value of vc output by the memory cell . This then
feeds into the LSTM hidden layer at the next time step h(t+1)
as well
as the output nodes ŷ(t)
at the current time step.
18

Figure 10: LSTM memory cell with forget gate as described by Felix Gers et
al. in [20].
Since the original LSTM was introduced, several variations have been proposed.
Forget gates, proposed in 2000 by Gers and Schmidhuber [20], add a gate similar
to input and output gates to allow the network to flush information from the
constant error carousel. Also in 2000, Gers and Schmidhuber proposed peephole
connections [19], which pass from the carousel directly to the input and output
gates of that same node without first having to pass through the output gate.
They report that these connections improve performance on timing tasks where
the network must learn to measure precise intervals between events. While peep-
hole connections are not common in modern papers, forget gates have become
a mainstay of LSTM work.
Put formally, computation in the LSTM model proceeds according to the
following calculations which must be evaluated at each time step. This gives
the full algorithm for a modern LSTM with forget gates.
g(t)
= φ(Wgxx(t)
+ Wihh(t−1)
+ bg)
i(t)
= σ(Wixx(t)
+ Wihh(t−1)
+ bi)
f(t)
= σ(Wfxx(t)
+ Wfhh(t−1)
+ bf )
o(t)
= σ(Woxx(t)
+ Wohh(t−1)
+ bo)
s(t)
= g(t)
i(i)
+ s(t−1)
f(t)
h(t)
= s(t)
o(t)
19

where stands for element-wise multiplication. The calculations for the simpler
LSTM without forget gates is given by setting f(t)
= 1 for all t. We use the
tanh function φ for the input node g following the latest state of the art setup of
Zaremba and Sutskever in [69]. However, in the original LSTM paper [31], the
activation function for g is the sigmoid σ. Again, h(t−1)
is a vector containing
the values vc output by each memory cell c in the hidden layer at the previous
time step.
Intuitively, in terms of the forward pass, the LSTM can learn when to let
activation into the internal state. So long as the input gate takes value 0, no
activation can get in. Similarly, the output gate learns when to let the value
out. When both gates are closed, the activation is trapped in the LSTM, neither
growing nor shrinking, nor affecting the output at the intermediary time steps.
In terms of the backwards pass, the constant error carousel enables the gradient
to propagate back across many time steps, neither exploding nor vanishing.
In this sense, the gates are learning when to let error in, and when to let it
out. In practice, the LSTM has shown a superior ability to learn long-range
dependencies as compared to simple RNNs. Consequently, the majority of state
of the art application papers covered in this review use the LSTM model.
3.4 Bidirectional Recurrent Neural Networks (BRNNs)
Along with the LSTM, one of the most used RNN setups is the bidirectional
recurrent neural network (BRNN) (Figure 11) first described in [51]. In this
architecture, there are two layers of hidden nodes. Both hidden layers are con-
nected to input and output. The two hidden layers are differentiated in that the
first has recurrent connections from the past time steps while in the second the
direction of recurrent of connections is flipped, passing activation backwards in
time. Given a fixed length sequence, the BRNN can be learned with ordinary
backpropagation. The following three equations describe a BRNN:
h
(t)
f = σ(Whf xx + Whf hf
h
(t−1)
f + bhf
)
h
(t)
b = σ(Whbxx + Whbhb
hb
(t+1)
+ bhb
)
ŷ(t)
= softmax(Wyhf
hf
(t)
+ Wyhb
hb
(t)
+ by)
Where h
(t)
f and h
(t)
b correspond to the hidden layers in the forwards and back-
wards directions respectively.
One limitation of the BRNN is that cannot run continuously, as it requires
a fixed endpoint in both the future and in the past. Further, it is not an
appropriate machine learning algorithm for the online setting, as it is implausible
to receive information from the future, i.e., sequence elements that have not been
observed. But for sequence prediction over a sequence of fixed length, it is often
sensible to account for both past and future data. Consider the natural language
task of part of speech tagging. Given a word in a sentence, information about
both the words which precede and those which succeed it is useful for predicting
20

Figure 11: Structure of a bidirectional recurrent neural network as described by
Schuster and Paliwal in [51].
that word’s part of speech. Karpathy et al. use such a network for generating
captions for images [34].
The LSTM and BRNN are in fact compatible ideas. The former introduces a
new basic unit from which to compose a hidden layer, while the latter concerns
the wiring of the hidden layers, regardless of what nodes they contain. Such an
approach, termed a BLSTM was used by Graves et al. to achieve state of the
art results on handwriting recognition and phoneme classification [24] [25].
4 Applications of LSTM and BRNN
In the previous sections, we introduced the basic building blocks from which
nearly all state of the art recurrent neural networks are composed. Now, we’ll
look at several application areas where recurrent networks have been employed
successfully. We’ll quickly introduce the representations used for input and
output and the commonly used performance metrics. Then we will survey state
of the art results in machine translation, image captioning, video captioning,
and handwriting recognition.
4.1 Representing Natural Language for Input and Output
Many applications of RNNs involve text processing. Some applications, e.g.
image captioning, involve generating strings of text. Others, such as machine
translation and dialogue systems, require both inputting and outputting text.
21

In this section, we provide the background necessary to understand how text is
represented in most recurrent net models.
When words are output at each time step, generally the output consists of
a softmax vector y(t)
∈ RK
where K is the size of the vocabulary. A softmax
layer is like an element-wise logistic function that is normalized so that all of
its components sum to 1. Intuitively these outputs correspond to probabilities
that each word is the correct output at that time step.
For application where inputs consist of sequences of words, typically the
words are fed to the network one at a time as inputs in consecutive time steps.
In these cases, the simplest way to represent words is a one-hot encoding, using
binary vectors with a length equal to the size of the vocabulary, e.g. “1000” and
“0100” would represent the first and second words in the vocabulary respectively.
Such an encoding is discussed in [17] among others. However, this encoding is
inefficient, requiring as many bits as the vocabulary is large. Further, it offers
no direct way to capture different aspects of similarity between words in the
encoding itself. Thus it is more common to model words with a distributed
representation using a meaning vector. In some cases, these meanings for words
are learned given a large corpus of supervised data, but it is common to initialize
the meaning vectors using an embedding based on word co-occurence statistics.
Freely available code to produce word vectors from co-occurrence stats include
Glove from Pennington Socher and Manning [49], and word2vec [22], which
implements a word embedding algorithm from Mikolov et al. [45].
Such distributed representations for symbolic data were described by Hinton
in 1986 [28], used extensively for natural language by Bengio et al. in 2003 [7],
and more recently brought to wider attention in the deep learning community
by Socher, Manning and Ng in a number of papers describing Recursive Auto-
encoder (RAE) networks ([57], [54], [58], [56]). For clarity we point out that
these recursive networks, which are sometimes referred to as “RNNs” are not
recurrent neural nets. In contrast to RNNs which model arbitrary dependencies
between inputs at different points in the sequence, recursive networks assume a
tree structure where each word in a sentence is a leaf and each sentence can be
represented as a binary tree. In this model, each internal node has a meaning
vector which can be calculated by concatenating the meanings of its children
and multiplying the composite vector by an encoding matrix. Each meaning
vector mj ∈ Rd
and the encoding matrix Ae ∈ R2d×d
. The composite meaning
mp ∈ Rd
given to the parent p of two child nodes l and r in the syntax tree is
mp = σ(Ae[ml; mr]T
)
This method seems restricted to sentences, and incompatible with the online
setting where the full sequence may not be fixed in advance. Additionally,
while it has been successfully used for classification tasks, it offers no generative
model for composing text.
In many experiments with recurrent neural networks ([17], [61], [69]), input
is fed in one character at a time (and output generated one character at a time).
While the output is nearly always a softmax layer, many papers omit details
22

of how they represent single-character inputs. It seems reasonable to infer that
characters are encoded with a one-hot encoding. We know of no cases of paper
using a distributed representation at the single-character level.
4.1.1 Evaluation Methodology
One serious obstacle to training systems to output variable length sequences of
words are the flaws of the available performance metrics. Developed in 2002,
BLEU score, a common evaluation metric for machine translation, is related to
modified unigram precision [?]. It is extended by taking the geometric mean
of the n-gram precisions for all values of n between 1 and some upper limit
N. In practice, 4 is a typical value for N, shown to maximize agreement with
human raters. Because precision can be made high by offering absurdly short
translations, the authors of BLEU introduce a brevity penalty BP. Where q
is the length of the candidate translation and r is the length of the reference
translations the brevity penalty is expressed as
BP =
(
1 if q > r
e(1−r/q)
if q <= r
.
Then the BLEU score can be calculated as
BLEU = BP · exp
N
X
n=1
wn log pn
!
where wn is a uniform weight 1/N and pn is the modified n-gram precision.
BLEU score is commonly used in recent papers to evaluate both translation
and captioning systems. While BLEU score does appear highly correlated with
human judgments, there is no guarantee that any given translation with a higher
BLEU score is superior to another which receives a lower BLEU score. In fact,
while BLEU scores agree with human judgement across large sets of translations,
they are significantly less accurate at the sentence level.
METEOR, introduced in 2005 by Banerjee and Lavie is an alternative met-
ric intended to overcome these weaknesses of the BLEU score [?]. METEOR
is scored based on explicit word to word matches between candidates and ref-
erences. When multiple references exist, the best score is used. Unlike BLEU,
METEOR exploits known synonyms and stemming. First they compute an
F-score
Fα =
P · R
α · P + (1 − α) · R
based on single word matches where P is the precision and R is the recall. Then
they calculate a fragmenting penalty Pen ∝ ch/m where ch is the smallest
number of chunks of consecutive words such that the words are adjacent in
both the candidate and the reference, and m is the total number of matched
unigrams yielding the score:
METEOR = (1 − Pen) · Fα.
23

Empirically, this metric has been found to agree more with human raters than
BLEU score.
However, METEOR is less straight-forward to calculate than BLEU. To
replicate the METEOR score reported by another party, one must exactly repli-
cate their stemming and synonym matching, as well as the calculations. Both
metrics rely upon having the exact same set of candidate translations.
Even in the straightforward case of binary classification, without time de-
pendencies, commonly used performance metrics like F1 give rise to complicated
thresholding strategies which may not accord with any reasonable intuition of
what should constitute good performance [40]. Along the same lines, given these
new performance metrics which are weak proxies for our objectives and which
cannot be optimized directly, it may be difficult to differentiate systems which
are truly stronger and those which most meticulously game the performance
metrics of interest.
4.2 Text Translation
Natural language translation is a fundamental problem in machine learning that
resists solutions with shallow methods. Some tasks, like document classification,
can be performed successfully with representations like bag-of-words, which ig-
nore word order. But word order is essential in translation. The sentences
“Scientist killed by raging virus” and “Virus killed by raging scientist” have
identical bag-of-words representations.
In Sequence to Sequence Learning, published in 2014, Sutskever et al. present
a translation model using two multilayered LSTMs and demonstrate impressive
performance translating from English to French. The first LSTM is used for
encoding an input phrase from the source language and one for decoding the
output phrase in the target language. Their model works according to the
following procedure (Figure 12):
• The source phrase is fed to the encode LSTM, one word at a time. The in-
puts are word vectors. This LSTM does not output anything. In practice,
the authors found that significantly better results were achieved when the
input sentence was fed into the network in reverse order.
• When the end of the phrase is reached, a special input which indicates the
beginning of the sentence is fed to the decoder LSTM. This second LSTM
gets as input the start token, and also the final state of the encoder This
LSTM outputs softmax probabilities over the vocabulary at each time
step.
• A word is chosen and fed to the network at the next step. At this time
step, the network receives activation along all recurrent edges as well as
the word vector of the chosen word.
For training, the true inputs are fed to the encoder, the true translation is
fed to the decoder, and loss is propagated back from the outputs of the decoder.
24

Figure 12: Sequence to sequence LSTM model as described by Sutskever et
al. [62]. The input blocks (blue and purple) all correspond to word vectors,
which are fully connected to the corresponding hidden state. Red nodes are
softmax outputs. The network consists of an encoding model (LSTM1) and
a decoding model (LSTM2). Weights are tied among all encoding steps and
among all decoding time steps.
The network is trained to maximize the likelihood of the correct translation.
At inference time a left to right beam search is used to determine which words
to output. A few among the most likely next words are chosen for expansion
after each time step. The beam search ends when the network outputs an end-
of-sentence (EOS) token. They train the model using only stochastic gradient
descent, without momentum, halving the learning rate every half epoch, after
the first five. Using this approach, they achieve a BLEU score of 34.81, which
outperforms the best previous neural network NLP systems, and is very close to
the best published results, including systems that have explicitly programmed
domain expertise. When their system is used to rerank candidate translations
from another system, they achieved a BLEU score of 36.5
Another RNN approach to language translation is presented by Auli et
al. in Joint Language and Translation Modeling with Recurrent Neural Net-
works. Their RNN model uses the word embeddings of Mikolov [2] and a lattice
representation of the decoder output to facilitate search over the space of possi-
ble translations. In their lattice, each node corresponds to a sequence of words.
They report a BLEU score of 28.5 on French-English translation tasks. Both
papers report results on data from WMT datasets but Sutskever et al. only re-
port results on English to French translation while Auli et al. report French to
English translation. Thus it is impossible to directly compare the performance
of the two models.
4.3 Image Captioning
Recently, recurrent neural networks have been used successfully for image cap-
tioning, [34,43,65]. In this task, a training set consists of input images x and
target captions y. Given a large set of image-caption pairs, a model is trained
25

to predict the appropriate caption for an image.
Vinyals et al. follow up on the success in language to language translation
by considering captioning as a case of image to language translation. Instead of
both encoding and decoding with LSTMs, they introduce the idea of encoding
an image with a convolutional neural network, and then decoding it with an
LSTM. This idea is the core of several papers which address this topic. This
work clearly precedes [34] as it is cited throughout, but [43] claim it as an
independent innovation. With this architecture, they achieve then state of the
art results on the Pascal, Flickr30k, and COCO datasets.
Karpathy et al. similarly use a convolutional neural network to encode im-
ages together with a bidirectional neural network to decode translations, using
word2vec embeddings as word representations [34]. They consider both full-
frame evaluations and a model that captures correspondences between image
regions and text snippets. At inference, their procedure resembles the one de-
scribed for Sutskever et al., where sentences are decoded one word at a time.
The most probable word is chosen and fed to the network at the next time step.
This process is repeated until an EOS token is produced.
4.4 Other Interesting Applications
Handwriting recognition is an application area where bidirectional LSTMs have
been used to achieve state of the art results. In work by Liwicki, Graves et
al. ( [41], [24]), data is collected from a whiteboard using an eBeam interface.
The interface collects the (x, y) coordinates of the pen at regularly sampled time
steps. In the more recent paper, they use a bidirectional LSTM model, outper-
forming an HMM model by achieving 81.5% word-level accuracy, compared to
70.1% for the HMM.
In the last year, a number of papers have emerged, that extend the success
of recurrent networks for translation and image captioning to new domains.
Among the most interesting of these applications are unsupervised video encod-
ing [59], video captioning [64] and program execution [69]. In [64], Venugopalan
et al. demonstrate a sequence to sequence architecture similar to that which
Sutskever uses for natural language translation. However, instead of both en-
coding and decoding words, they encode frames from a video and decode words.
At each time step the input to the encoding LSTM is the topmost hidden layer
of convolutional neural network. At decoding time, the network outputs prob-
abilities over the vocabulary at each time step.
In Learning to Execute ([69]), Zaremba and Sutskever experiment with net-
works which read computer programs one character at a time and predict their
output. They focus on programs which output integers and find that for simple
programs, including adding two nine-digit numbers, their network, which uses
LSTM units, several stacked hidden layers, and makes a single left to right pass
through the program, can predict the output with 99% accuracy.
26

5 Discussion
Over the past thirty-five years, recurrent networks have gone from impractical
models, primarily of interest for cognitive modeling and computational neuro-
science, to powerful and practical tools for large-scale supervised learning. This
progress owes to advances in model architectures, training algorithms, and par-
allel computing. Recurrent nets are especially interesting because they seem
able to overcome many of the extreme restrictions generally placed on data by
traditional machine learning approaches. With recurrent nets, the assumption
of independence between consecutive examples is broken, the assumption of
fixed-dimension input is broken, and yet RNN models perform competitively
with or outperform the state of the art on many tasks.
While LSTMs and BRNNs set records, we find it noteworthy that many
advances come from novel architectures rather than fundamentally novel algo-
rithms. It seems that research exploring the space of possible models, either
via genetic algorithms or a Markov Chain Monte Carlo based approach, should
be promising. Along these lines, we note that neural networks seem to of-
fer a wide range of easily transferable techniques. New activation functions,
training procedures, initializations procedures, etc. are generally transferable
across networks and tasks, often conferring similar benefits. As the number of
such techniques grows, the practicality of testing all combinations diminishes.
However it seems reasonable to infer that as a community, neural network re-
searchers are exploring the space of a model architectures and configurations
much as a genetic algorithm might, mixing and matching techniques, with a
fitness function in the form of evaluation metrics on major datasets of interest.
This suggests two things. First, as stated before, this body of research would
benefit from automated procedures to explore the space of models. Second, as we
build systems designed to perform more complex tasks, we would benefit from
improved fitness functions. BLEU inspires less confidence than the accuracy
reported on a binary classification task. To this end, when possible, it seems
prudent to individually test techniques first with classic feedforward networks
on datasets with established benchmarks before applying them to recurrent
networks in settings with less concrete evaluation criteria.
Lastly, the rapid success of recurrent neural networks on natural language
tasks leads us to believe that extensions of this work to longer form text would
be fruitful. Additionally, we imagine that dialogue systems could be built along
similar principles to the architectures used for translation, encoding prompts and
generating responses, retaining the entirety of conversation history as contextual
information.
Acknowledgements
My research is funded by generous support from the Division of Biomedical In-
formatics at UCSD, via a training grant from the National Library of Medicine.
This review has benefited from insightful comments from Charles Elkan, John
27

Berkowitz, Julian MacAuley, Balakrishnan Narayanaswamy, Stefanos Poulis,
Sharad Vikram.
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