Datasets:

zai-org
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RPC-Bench

+# Continual World: A Robotic Benchmark For Continual Reinforcement Learning
+Maciej Wołczyk⇤ Jagiellonian University Kraków, Poland maciej.wolczyk@doctoral.uj.edu.pl
+Michał Zaj ˛ac⇤
+Jagiellonian University
+Kraków, Poland
+emzajac@gmail.com
+Razvan Pascanu
+DeepMind
+London, UK
+razp@google.com
+Łukasz Kucinski ´ Polish Academy of Sciences Warsaw, Poland lkucinski@impan.pl
+# Piotr Miłos´
+Polish Academy of Sciences,
+University of Oxford,
+deepsense.ai
+Warsaw, Poland
+pmilos@impan.pl
+# Abstract
+Continual learning (CL) — the ability to continuously learn, building on previously acquired knowledge — is a natural requirement for long-lived autonomous reinforcement learning (RL) agents. While building such agents, one needs to balance opposing desiderata, such as constraints on capacity and compute, the ability to not catastrophically forget, and to exhibit positive transfer on new tasks. Understanding the right trade-off is conceptually and computationally challenging, which we argue has led the community to overly focus on catastrophic forgetting. In response to these issues, we advocate for the need to prioritize forward transfer and propose Continual World, a benchmark consisting of realistic and meaningfully diverse robotic tasks built on top of Meta-World $\bar { \mathbb { B } } \bar { \underline { { 4 } } } \mathbb { I }$ as a testbed. Following an in-depth empirical evaluation of existing CL methods, we pinpoint their limitations and highlight unique algorithmic challenges in the RL setting. Our benchmark aims to provide a meaningful and computationally inexpensive challenge for the community and thus help better understand the performance of existing and future solutions. Information about the benchmark, including the open-source code, is available at https://sites.google.com/view/continualworld.
+# 1 Introduction
+Change is ubiquitous. Unsurprisingly, due to evolutionary pressure, humans can quickly adapt and creatively reuse their previous experiences. In contrast, although biologically inspired, deep learning (DL) models excel mostly in static domains that satisfy the i.i.d. assumption, as for example in image processing [28, 49, 10, 40], language modelling $| { \bar { \sqrt { 5 2 } } } , { \overline { { \mathbb { 1 1 } } } } | |$ or biological applications [47]. As the systems are scaled up and deployed in open-ended settings, such assumptions are increasingly questionable; imagine, for example, a robot that needs to adapt to the changing environment and the wear-and-tear of its hardware. Continual learning (CL), an area that explicitly focuses on such problems, has been gaining more attention recently. The progress in this area could offer enormous advantages for deep neural networks $\mathbb { \lVert 1 9 \rVert }$ and move the community closer to the long-term goal of building intelligent machines $\mathbb { \ m }$ .
+Evaluation of CL methods is challenging. Due to the sequential nature of the problem that disallows parallel computation, evaluation tends to be expensive, which has biased the community to focus on toy tasks. These are mostly in the domain of supervised learning, often relying on MNIST. In this work, we expand on previous discussions on the topic [45, 16, 30, 46] and introduce a new benchmark, Continual World. The benchmark is built on realistic robotic manipulation tasks from Meta-World $\pmb { \Vert 5 4 \Vert }$ , benefiting from its diversity but also being computationally cheap. Moreover, we provide shorter auxiliary sequences, all of which enable a quick research cycle. On the conceptual level, a fundamental difficulty of evaluating CL algorithms comes from the different desiderata for a CL solution. These objectives are often opposing each other, forcing practitioners to explicitly or implicitly make trade-offs in their algorithmic design that are data-dependent. Continual World provides more meaningful relationships between tasks, answering recent calls $\mathbb { \lVert 1 9 \rVert }$ to increase attention on forward transfer.
+Additionally, we provide an extensive evaluation of a spectrum of commonly used CL methods. It highlights that many approaches can deal relatively well with catastrophic forgetting at the expense of other desiderata, in particular forward transfer. This emphasizes our call for focusing on forward transfer and the need for more benchmarks that allow for common structure among the tasks.
+The main contribution of this work is a CL benchmark that poses optimizing forward transfer as the central goal and shows that existing methods struggle to outperform simple baselines in terms of the forward transfer capability. We release the code2 both for the benchmark and 7 CL methods, which aims to provide the community helpful tools to better understand the performance of existing and future solutions. We encourage to visit the website3 of the project and participate in the Continual World Challenge.
+# 2 Related work
+The field of continual learning has grown considerably in the past years, with numerous works forming new subfields $\mathbb { \left[ \left. 2 3 \right] \right. }$ and finding novel applications $\lVert \overline { { 4 8 } } \rVert$ . For brevity, we focus only on the papers proposing RL-based benchmarks and point to selected surveys of the entire field. $\pmb { \mathbb { D } }$ provide a high-level overview of CL and argue that learning in a non-stationary setting is a fundamental problem for the development of AI, highlighting the frequent connections to neuroscience. On the other hand, $\mathbb { B } 3 \mathbb { B }$ focus on describing, evaluating, and relating CL methods to each other, providing a taxonomy of CL solutions that we use in this work.
+The possibility of applying CL methods in reinforcement learning scenarios has been explored for a long time, see $[ [ 2 5 ] ]$ for a recent review. However, no benchmark has been widely accepted by the community so far, which is the aim of this work. Below we discuss various benchmarks and environments considered in the literature.
+Supervised settings MNIST has been widely used to benchmark CL algorithms in two forms $ { \mathbb { \left[ \left[ 2 7 \right] \right] } }$ . In the permuted MNIST, the pixels of images are randomly permuted to form new tasks. In the split MNIST, tasks are defined by classifying non-overlapping subsets of classes, e.g. 0 vs. 1 followed by 2 vs. 3. A similar procedure has been applied to various image classification tasks like CIFAR-10, CIFAR-100, Omniglot or mini-ImageNet [2, 46, 5]. Another benchmark is CORe50 [31], a dataset for continuous object recognition. Recent work $\mathbb { \left. 2 9 \right. }$ proposes a benchmark based on language modeling. We find that many of these benchmarks are challenging and allow to measure forgetting. However, we argue they are not geared towards measuring forward transfer or for highlighting important RL-specific characteristics of the CL problem.
+Atari The Atari 2600 suite $\textcircled { 8 }$ is a widely accepted RL benchmark. Sequences of different Atari games have been used for evaluating continual learning approaches [43, 27]. Using Atari can be computationally expensive, e.g., training a sequence of ten games typically requires 100M steps or more. More importantly, as $\mathbb { \lVert \boldsymbol { 4 3 } \rVert }$ notes, these games lack a meaningful overlap, limiting their relevance for studying transfers. Continuous control [32, 24] use continuous control tasks such as Humanoid or Walker2D. However, the considered sequences are short, and the range of experiments is limited. [34] use Meta-World tasks, similarly to us, for evaluations of their continual learning method, but the work is not aimed at building a benchmark. As such, it uses the Meta-World’s MT10 preset and does not provide an in-depth analysis of the tasks or other CL methods. Maze navigation A set of 3D maze environments is used in [43]. The map structure and objects that the agent needs to collect change between tasks. It is not clear, though, if the tasks provide enough diversity. [30] propose CRLMaze, 3D navigation scenarios for continual learning, which solely concentrate on changes of the visual aspects. StarCraft $\lVert \rVert \dot { \boldsymbol { \mathrm { ~ ‰ ~ } } }$ present a StarCraft campaign (11 tasks) to evaluate a high-level transfer of skills. The main drawback of this benchmark is excessive computational demand (often more than 1B frames). Minecraft $\mathbb { \left[ \left. 5 0 \right| \right. }$ propose simple scenarios within the Minecraft domain along with a hierarchical learning method. The authors phrase the problem as lifelong learning and do not use typical CL methods. Lifelong Hanabi $\lVert \rVert$ consider a multi-agent reinforcement learning setting based on Hanabi, a cooperative game requiring significant coordination between agents. On the other hand, we focus on the single agent setting with changing environment, which allows us to bypass the computational complexity needed to model interactions between agents and highlight issues connected to learning in a changing world. Causal World $\pmb { \mathbb { B } } \|$ propose an environment for robotic manipulation tasks which share causal structure. Although they investigate issues deeply connected to learning in a changing world, such as generalization to new tasks and curricula, they do not directly consider continual learning. Jelly Bean World $\mathbb { B } 9 \mathbb { I }$ provide interesting procedurally generated grid world environments. The suite is configurable and can host a non-stationary setting. It is unclear, however, if such environments reflect the characteristics of real-world challenges.
+# 3 Continual learning background
+Continual learning (CL) is an area of research which focuses on building algorithms capable of handling non-stationarity. They should be able to sequentially acquire new skills and solve novel tasks without forgetting the previous ones. Such systems are desired to accommodate over extended periods swiftly, which is often compared to human capabilities and alternatively dubbed as lifelong learning. CL is intimately related to multi-task learning, curriculum learning, meta-learning, with some key differences. Multi-task assumes constant access to all tasks, thus ignoring non-stationarity. Curriculum learning focuses on controlling the task ordering and often the learning time-span. Metalearning, a large field of its own, sets the objective to develop procedures that allow fast adaptation within a task distribution and usually ignores the issue of non-stationarity.
+The CL objective is operationalized by the training and evaluation protocols. The former typically consists of a sequence of tasks (their boundaries might be implicit and smooth). The latter usually involves measuring catastrophic forgetting, forward transfer, and backward transfer. The learning system might also have constrained resources: computations, memory, size of neural networks, and the volume of data samples. A fundamental observation is that the above aspects and desiderata are conflicting. For example, given unlimited resources, one might mitigate forgetting simply by storing everything in memory and paying a high computational cost of rehearsing all samples from the past.
+![](images/478f601d070ca51575b0809421a2f533ad8ec0fc787df0823e9c6f366258a7b5.jpg)
+Figure 1: Left graph shows task PEG-UNPLUG-SIDEV1 and the right graph presents forward transfer from SHELF-PLACE-V1 to PEG-UNPLUG-SIDE-V1. In this case $F T = 0 . 1 0$ .
+Another pair of objectives that are problematic for current methods are forgetting and forward transfer. For neural networks, existing methods propose to limit network plasticity. These alleviate the problem of forgetting, however, at the cost of choking the further learning process. We advocate for more nuanced approaches. Importantly, to make the transfer possible, our benchmark is composed of related tasks. We also put modest bounds on resources. This requirement is in line with realistic scenarios, demanding computationally efficient adaptation and inference. In a broader sense, we hope to address a data efficiency challenge, one of the most signif
+icant limitations of the current deep (reinforcement) learning methods. We conjecture that forward transfer might greatly improve the situation and possibly one day enable us to create systems with human-level cognition capabilities, in line with similar thoughts expressed in [19].
+# 4 Continual World benchmark
+Continual World is a new benchmark designed to be a testbed for evaluating RL agents on the challenges advocated by the CL paradigm, described in Section $^ { 3 , }$ as well as highlighting the RLspecific algorithmic challenges for CL (see Section $\boxed { 6 . 1 }$ . As such it is aimed at being valuable to both the CL and RL communities. Continual World consists of realistic robotic manipulation tasks, aligned in a sequence to enable the study of forward transfer. It is designed to be challenging while computationally accessible.4 The benchmark is based on Meta-World, a suite of robotic tasks already established in the community. This enables easy comparisons with the related fields of multi-task and meta-learning reinforcement learning, potentially highlighting one benefit of CL framing, namely that of dealing with different reward scales as we discuss more in detail in Appendix $\mathrm { H } .$ Continual World comes with open-source code that allows for easy development and testing of new algorithms and provides implementations of 7 existing algorithms. Finally, it allows highlighting RL-specific challenges for the CL setting. We believe that our work is a step in the right direction towards reliable benchmarks of CL. We realize, however, that it will need to evolve as the field progresses. We leave a discussion on future directions and limitations to Section 4.4.
+# 4.1 Metrics
+To facilitate further discussion, we start with defining metrics. These are rather standard in the CL setting $\mathbb { H } 2 \mathbb { I }$ . Assume $p _ { i } ( t ) \in [ 0 , 1 ]$ to be the performance (success rate) of task $i$ at time $t$ . As a measure of performance, we take the average success rate of achieving a goal specified by a given task when using randomized initial conditions and stochastic policies (see also Section $4 . { \overset { - } { 3 } } ) . { \overset { 5 } { . } } { \overset { . } { } }$ Each task is trained for $\Delta = 1 M$ steps. The main sequence has $N = 2 0$ tasks and the total sample budget is $T = N \cdot \Delta = 2 0 M$ . The $i$ -th task is trained during the interval $t \in [ ( i - 1 ) \cdot \Delta , i \cdot \Delta ]$ . We report the following metrics:
+Average performance. The average performance at time $t$ is (see Figure 3)
+$$
+\mathsf { P } ( t ) : = \frac { 1 } { N } \sum _ { i = 1 } ^ { N } p _ { i } ( t ) .
+$$
+Its final value, $\mathrm { P } ( { \cal T } )$ , is a traditional metric used in the CL research. This is the objective we use for tuning hyperparameters. We have $\mathbf { P } ( t ) \in [ 0 , 1 ]$ for each $t$ .
+Forward transfer. We measure the forward transfer of a method as the normalized area between its training curve and the training curve of the reference, single-task, experiment, see Figure $1 .$ Let $p _ { i } ^ { b } \in [ 0 , 1 ]$ be the reference performance6 then the forward transfer for the task $i$ , denoted by $\bar { \mathsf { F T } } _ { i }$ , is
+$$
+\mathsf { F T } _ { i } : = \frac { \mathsf { A U C } _ { i } - \mathsf { A U C } _ { i } ^ { b } } { 1 - \mathsf { A U C } _ { i } ^ { b } } , \quad \mathsf { A U C } _ { i } : = \frac { 1 } { \Delta } \int _ { ( i - 1 ) \cdot \Delta } ^ { i \cdot \Delta } p _ { i } ( t ) \mathrm { d } t , \quad \mathsf { A U C } _ { i } ^ { b } : = \frac { 1 } { \Delta } \int _ { 0 } ^ { \Delta } p _ { i } ^ { b } ( t ) \mathrm { d } t ,
+$$
+The average forward transfer for all tasks, FT, is defined as
+$$
+\mathrm { F T } = \frac { 1 } { N } \sum _ { i = 1 } ^ { N } \mathrm { F T } _ { i } .
+$$
+We note that $\mathrm { F T } _ { i } \leq 1$ and they might be negative. In our experiments, we also measure backward transfer. As it is negligible, see Appendix E.1.
+Forgetting. For task $i$ , we measure the decrease of performance after ending its training, i.e.
+$$
+F _ { i } = p _ { i } ( i \cdot \Delta \bar { \Delta } ) - p _ { i } ( T ) .
+$$
+Similarly to FT e report $\begin{array} { r } { F = { \frac { 1 } { N } } \sum _ { i = 1 } ^ { N } F _ { i } } \end{array}$ . We have $F _ { i } \leq 1$ for any $i$ and consequently $\mathrm { F T } \leq 1$ . It $F _ { i }$ are negative, which would indicate backward transfer. We do not observe this in practice, see Appendix E.1.
+# 4.2 Continual World tasks
+This section describes the composition of Continual World benchmark and the rationale behind its design. We decided to base on Meta-World [54], a fairly new but already established robotic benchmark for multi-task and meta reinforcement learning. From a practical standpoint, Meta-World utilizes the open-source MuJoCo physics engine [51], prized for speed and accuracy. Meta-World provides 50 distinct manipulation tasks with everyday objects using a simulated robotic Sawyer arm. Although the tasks vary significantly, the structure and semantics of observation and action spaces remain the same, allowing for transfer between tasks. Each observation is a 12-dimensional vector containing $( x , y , z )$ coordinates of the robot’s gripper and objects of interest in the scene. The 4-dimensional action space describes the direction of the arm’s movement in the next step and the gripper actuator delta. Reward functions are shaped to make each task solvable. In evaluations, we use a binary success metric based on the distance of the task-relevant object to its goal position. This metric is interpretable and enables comparisons between tasks. For more details about the rewards and evaluation metrics, see [54, Section 4.2, Section 4.3].
+CW20, CW10, triplets sequences The core of our benchmark is CW20 sequence. Out of 50 tasks defined in Meta-World, we picked those that are not too easy or too hard in the assumed sample budget $\Delta = 1 M$ . Aiming to strike a balance between the difficulty of the benchmark and computational requirements, we selected 10 tasks. The tasks and their ordering were based on the transfer matrix (see the next paragraph), so that there is a high variation of forward transfers (both in the whole list and locally). We refer to these ordered tasks as CW10, and CW20 is CW10 repeated twice. We recommend using CW20 for final evaluation; however, CW10 is already very informative in most cases. Due to brevity constraints, we present an ablation with an alternative ordering of the tasks and a longer sequence of 30 tasks in Appendix $\mathbf { G } ,$ however, these experiments do not alter our findings. Additionally, to facilitate a fast development cycle, we propose a set of triplets, sequences of three tasks which exhibit interesting learning dynamics.
+The CW10 sequence is: HAMMER-V1, PUSH-WALL-V1, FAUCET-CLOSE-V1, PUSH-BACK-V1, STICK-PULLV1, HANDLE-PRESS-SIDE-V1, PUSH-V1, SHELF-PLACE-V1, WINDOW-CLOSE-V1, PEG-UNPLUG-SIDE-V1.
+Transfer matrix Generally, the relationship between tasks and its impact on learning dynamics of neural networks is hard to quantify, where semantic similarity does not typically lead to transfer $\textcircled { 1 1 4 } \textcircled { 1 }$ . To this end, we consider a minimal setting, in which we finetune on task $t _ { 2 }$ a model pretrained on $t _ { 1 }$ , using the same protocol as the benchmark (e.g., different output heads, see Section $\boxed { 4 . 3 }$ . This provides neural network-centric insight into the relationship between tasks summarized in Figure $\bar { \bigtriangledown } ,$ and allows us to measure low-level transfer between tasks, i.e., the ability of the model to reuse previously acquired features. See Appendix D for more results and extended discussion.
+![](images/cc07f24cab893e37423e040ba20d15fa27eb5b392e5c7db00660c67a2a211cd5.jpg)
+Figure 2: Transfer matrix, see Section $4 . 2 \cdot$ Each cell represents the forward transfer from the first task to the second one. We shaded the cells for which 0 belongs to their $9 0 \%$ confidence interval.
+Notice that there are only a few negative forward transfer cases, and those are of a rather small magnitude (perhaps unsurprisingly, as the tasks are related). There are also visible patterns in the matrix. For instance, some tasks such as PEGUNPLUG-SIDE-V1 or PUSH-BACK-V1 benefit from a relatively large forward transfer, (almost) irrespective of the first task. Furthermore, the average forward transfer given the second task (columns) is more variable than the corresponding quantity for the first task (rows).
+Note that some transfers on the diagonal (i.e., between the same tasks) are relatively small. We made a detailed analysis of possible reasons, which revealed that the biggest negative impact is due to the replay buffer resets, which seems, however, unavoidable for off-diagonal cases, see Section $6 . 1$ for details.
+Importantly, we use this matrix to estimate what level of forward transfer a good CL method
+should be able to achieve. We expect that a model which is able to remember all meaningful aspects of previously seen tasks would transfer at least as well as if one were just fine-tuning after learning the best choice between the previous tasks. For a sequence $t _ { 1 } , \ldots , t _ { N }$ we set the reference forward transfer, RT, to be
+$$
+\mathrm { R T } : = \frac { 1 } { N } \sum _ { i = 2 } ^ { N } \operatorname* { m a x } _ { j < i } \mathrm { F T } ( t _ { j } , t _ { i } ) ,
+$$
+where $\mathrm { F T } ( t _ { j } , t _ { i } )$ is the transfer matrix value for $t _ { j } , t _ { i }$ . For the CW20 sequence, the value is $\mathrm { R T } = 0 . 4 6$ Note that a model can do better that this by composing knowledge from multiple previous tasks.
+# 4.3 Training and evaluation details
+We adapt the standard Meta-World setting to CL needs. First, we use separate policy heads for each task, instead of the original one-hot task ID inputs (we provide ablation experiments for this choice in Appendix $\mathbf { G } )$ . Second, in each episode, we randomize the positions of objects in the scene to encourage learning more robust policies. We use an MLP network with 4 layers of 256 neurons.
+For training, we use soft actor-critic (SAC) [17], a popular and efficient RL method for continuous domains. SAC is an off-policy algorithm using replay buffer, which is an important aspect for CL, particularly for methods relying on rehearsing old trajectories. SAC is based on the so-called maximum entropy principle; this results in policies which explore better and are more robust to changes in the environment dynamics. Both of these qualities might be beneficial in CL.
+We note that the size of the neural network and optimization details of the SAC algorithm (like batch size) put constraints on "the amount of compute". Intentionally, these are rather modest, which is in line with CL desiderata, see Section $3 .$ Similarly, we limit the number of timesteps to $1 M$ , which is a humble amount for modern-day deep reinforcement learning. We picked tasks to be challenging but not impossible within this budget. We note that training in the RL setting tends to be less stable than in the supervised one. We recommend using multiple seeds, in our experiments, we typically used 20 and calculate confidence intervals; we used the bootstrap method. We choose hyperparameters that maximize average performance $\mathbb { \underline { { \left( 1 \right) } } }$ . In our experiments, we tune common parameters for SAC and the method-specific hyperparameters separately. All details of the training and evaluation setup are presented in Appendix A.
+# 4.4 Limitations of Continual World
+As any benchmark, we are fully aware that ours will not cover the entire spectrum of problems that one might be interested in. Here we summarize a few limitations that we hope to overcome in a future instantiation of this benchmark:
+Input space We use a small 12 dimensional observation space. This is key to achieve modest computational demand. However, richer inputs could allow for potentially more interesting forms of transfer (e.g., based on visual similarity of objects) and would allow inferring the task from the observation, which is currently impossible.
+Reliance on SAC We use the SAC algorithm $\textcircled { 1 1 7 }$ , which is considered a standard choice for continuous robotic tasks. However, there is a potential risk of overfitting to the particularities of this algorithm and exploring alternative RL algorithms is important.
+Task boundaries We rely on task boundaries. One can rely on task inference mechanisms (e.g. [35, 41]) to resolve this limitation, though we acknowledge the importance to extend the benchmark towards allowing and testing for task inference capabilities. Also, testing for algorithms dealing with continuous distributional drift is not possible in the current format.
+Output heads We rely on using a separate head for each new task, similar to many works on continual learning. We opt for this variant based on its simplicity and better performance than using one-hot encoding to indicate a task. We believe that the lack of semantics of the one-hot encoding would further impede transfer, as the relationship between tasks can not be inferred. We carry ablation studies with using one-hot encoding as an input and a single head architecture, a setting that is already compatible with our benchmark. We regard this aspect as an important future work, and in particular, we are exploring alternative encoding of input to make this choice more natural. A coherent domain, like Continual World, provides a unique opportunity to exploit a consistent output layer as its semantics does not change between tasks.
+![](images/de69b894f5a716658e9b945947e813289cfbbb6a6be75dce43f4af3a4767f797.jpg)
+Figure 3: Training curves for selected CL methods and multi-task. The upper left panel shows the performance on the first task for a subset of methods throughout the whole training. Note that due to the use of different output heads, we do not see a second bump when revisiting this task at time $1 0 M$ . The upper right panel shows the performance on the current task being trained for EWC compared to a reference (a model learning only that task from scratch). The bottom plot shows the average performance. Solid lines show the performance of the model training on the first 10 tasks (where 1 means being able to solve all of them). Dashed lines show the performance of learning the same tasks in the second half of the benchmark. Note that dashed lower are below solid ones, indicating lower performance on the second pass, even if the agent has already previously learned the tasks and has access to relevant features.
+The difficulty and number of tasks The number of tasks is relatively small. CW20, the main sequence we use, consists of only 10 different tasks, which are then repeated. We believe the repetition of tasks is important for a CL benchmark, leading to interesting observations. We check also that results are quantitatively similar on a sequence of 30 tasks, see Appendix G. However, longer sequences, potentially unbounded, are needed to understand the various limitations of existing algorithms. For example, the importance of graceful forgetting or dealing with systems that run out of capacity, a scenario where there is no multi-task solution for the sequence of observed tasks. This is particularly of interest for methods such as PackNet $\pmb { \mathbb { B 3 } }$ . Additionally, we provide the number of tasks in advance. Dealing with an unknown number of tasks might raise further interesting questions. Finally, in future iterations of the benchmark, it is important to consider more complex tasks or more complex relationships between tasks to remain a challenge to existing methods. Our goal was to provide a benchmark that is approachable by existing methods, as not to stifle progress.
+Low-level transfer We focus on low-level transfers via neural network features and weights. As such, we do not explicitly explore the ability of the learning process to exploit the compositionality of behavior or to rely on a more interesting semantic level. While we believe such research is crucial, we argue that solving low-level transfer is equally important and might be a prerequisite. So, for now, it is beyond the scope of this work, though future iterations of the benchmark could contain such scenarios.
+# 5 Methods
+We now sketch 7 CL methods evaluated on our benchmark. Some of them were developed for RL, while others were meant for the supervised learning context and required non-trivial adaptation. We aimed to cover different families of methods; following $\mathbb { \lVert \rVert 3 \rVert }$ , we consider three classes: regularizationbased, parameter isolation and replay methods. An extended description and discussion of these methods are provided in Appendix B.
+Regularization-based Methods This family builds on the observation that one can reduce forgetting by protecting parameters that are important for the previous tasks. The most basic approach often dubbed L2 $ { \mathbb { \left[ \left[ 2 7 \right] \right] } }$ simply adds a $L _ { 2 }$ penalty, which regularizes the network not to stray away from the previously learned weights. In this approach, each parameter is equally important. Elastic Weight Consolidation (EWC) $\overline { { \mathbb { R } \mathbb { Z } \mathbb { I } } }$ uses the Fisher information matrix to approximate the importance of each weight. Memory-Aware Synapses (MAS) [4] also utilizes a weighted penalty, but the importance is obtained by approximating the impact each parameter has on the output of the network. Variational Continual Learning (VCL), follows a similar path but uses variational inference to minimize the Kullback-Leibler divergence between the current distribution of parameters (posterior) and the distribution for the previous tasks (prior).
+Parameter Isolation Methods This family (also called modularity-based) forbids any changes to parameters that are important for the previous tasks. It may be considered as a “hard” equivalent of regularization-based methods. PackNet [33] “packs” multiple tasks into a single network by iteratively pruning, freezing, and retraining parts of the network at task change. PackNet is closely related to progressive neural networks [43], developed in the RL context.
+Replay Methods Methods of this family keep some samples from the previous tasks and use them for training or as constraints to reduce forgetting. We use a Perfect Memory baseline, a modification of our setting which remembers all the samples from the past (i.e., without resetting the buffer at the task change). We also implemented Averaged Gradient Episodic Memory (A-GEM) [12], which projects gradients from new samples as to not interfere with previous tasks. We find that A-GEM does not perform well on our benchmark.
+Multi-task learning In multi-task learning, a field closely related to CL, tasks are trained simultaneously. By its design, it does not suffer from forgetting, however, it is considered to be hard as multiple tasks “compete for the attention of a single learning system”, see [21, 44]. We find that using reward normalization as in PopArt $\left[ \left[ 2 1 \right] \right]$ is essential to achieve good performance. See Appendix H.
+# 6 Experiments
+Now we present empirical results; these are evaluations of a set of 7 representative CL methods (as described in Section $\textcircled{5}$ on our Continual World benchmark. We focus on forgetting and transfers while keeping fixed constraints on computation, memory, number of samples, and neural network architecture. Our main empirical contributions are experiments on the long CW20 sequence and following high-level conclusions. For a summary see Table 1, Figure 3 and for an extensive discussion, we refer to Appendix $\boxed { \mathrm { E } }$ (including results for the shorter sequence, CW10). In Appendix G we provide various ablations and detailed analysis of sensitivity to the CL-specific hyperparameters.
+Performance The performance (success rate) averaged over tasks (eq. $\mathbb { \underline { { ( 1 ) } } }$ ) is a typical metric for the CL setting. PackNet seems to outperform other methods, approaching 0.8 from the maximum of 1.0, outperforming multi-task solutions which might struggle with different reward scales, a problem elegantly avoided in the CL framing. Other methods perform considerably worse. A-GEM and Perfect Memory struggle. We further discuss possible reasons in Sectio n 6.1.
+Table 1: Results on CW20, for CL methods and multi-task training. Metrics are defined in Section 4.1, RT is eq. $( 4 )$ . We used 20 seeds and provide $90 \%$ confidence intervals.
+<table><tr><td>method</td><td>performance</td><td>forgetting</td><td>f. transfer</td></tr><tr><td>Fine-tuning</td><td>0.05 [0.05,0.06]</td><td>0.73 [0.72, 0.75]</td><td>0.20 [0.17, 0.23]</td></tr><tr><td>L2</td><td>0.43 [0.39, 0.47]</td><td>0.02 [0.00, 0.03]</td><td>-0.71 [-0.87, -0.57]</td></tr><tr><td>EWC</td><td>0.60 [0.57, 0.64]</td><td>0.02 [-0.00, 0.05]</td><td>-0.17 [-0.24, -0.11]</td></tr><tr><td>MAS</td><td>0.51 [0.49, 0.53]</td><td>0.00 [-0.01,0.02]</td><td>-0.52 [-0.59,-0.47]</td></tr><tr><td>VCL</td><td>0.48 [0.46,0.50]</td><td>0.01 [-0.01, 0.02]</td><td>-0.49 [-0.57,-0.42]</td></tr><tr><td>PackNet</td><td>0.80 [0.79, 0.82]</td><td>0.00 [-0.01,0.01]</td><td>0.19 [0.15, 0.23]</td></tr><tr><td>Perfect Memory</td><td>0.12 [0.09, 0.15]</td><td>0.07 [0.05,0.10]</td><td>-1.34 [-1.42, -1.27]</td></tr><tr><td>A-GEM</td><td>0.07 [0.06,0.08]</td><td>0.71 [0.70,0.73]</td><td>0.13 [0.10,0.16]</td></tr><tr><td>MT</td><td>0.51 [0.48, 0.53]</td><td></td><td></td></tr><tr><td>MT (PopArt)</td><td>0.65 [0.63, 0.67]</td><td></td><td></td></tr><tr><td>RT</td><td></td><td></td><td>0.46</td></tr></table>
+Forgetting We observe that
+most CL methods are usually efficient in mitigating forgetting. However, we did not notice any boost when revisiting a task (see Figure $3 )$ . Even if a different output head was employed, relearning the internal representation should have had an impact unless it changed considerably when revisiting the task. Additionally, we found A-GEM difficult to tune; consequently, with the best hyperparameter settings, it is relatively similar to the baseline fine-tuning method (see details in Appendix $\bigtriangledown$
+Transfers For all methods, forward transfer for the second ten tasks (and the same tasks are revisited) drops compared to the first ten tasks. This is in stark contrast to forgetting, which seems to be well under control. Among all methods, only fine-tuning and PackNet are able to achieve positive forward transfer (0.20 and 0.19, resp.) as well as on the first (0.32 and 0.21, resp.) and the second (0.08 and 0.17, resp.) half of tasks. However, these are considerably smaller than $\mathrm { R T } = 0 . 4 6$ , which in principle can even be exceeded, and which should be reached by a model that remembers all meaningful aspects of previously seen tasks, see $\textcircled{4}$ . These results paint a fairly grim picture: we would expect improvement, rather than deterioration in performance, when revisiting previously seen tasks. There could be multiple reasons for this state of affairs. It could be attributed to the loss of plasticity, similar to the effect observed in $\textcircled { 6 }$ . Another reason could be related to the interference between CL mechanisms or setting and RL, for instance, hindering exploration. We did not observe any substantial cases of backward transfer, even though the benchmark is well suited to study this question due to the revisiting of tasks. See Appendix E.1.
+![](images/845bed2db7dcfa9140e21b319b1d7d55d2824be710c8d12c2d31ab127f6557ec.jpg)
+Figure 4: How forgetting impacts the forward transfer. Two different triplets of tasks learnt in sequence. An ideal agent learning on a sequence $A  B  C$ should have at least as good performance on task $C$ as an agent which just learns $A  C$ . In reality, an interfering task $B$ reduces this transfer, even when continual learning approaches are used.
+Triplets experiments We illustrate how forgetting and forward transfer interact with each other in a simpler setting of three task sequences, see Figure $\boxed { \ 4 }$ and Appendix $\boxed { \mathrm { F } }$ We focus on sequences of tasks $A $ $B  C$ , where $A \  \ C$ has significant positive forward transfer and $B  C$ has a smaller or even negative transfer. An efficient CL agent should be able to use information from $A$ to get good performance on $C$ . However, interference introduced by $B$ reduces the fi
+nal forward transfer (see Figure $^ { 4 ) }$ . The drive for reducing forgetting in CL agents has been primarily to perform well on previous tasks when we revisit them. With this example, we argue that an equally important reason to improve the memory of CL agents is to efficiently use past experiences to learn faster on new tasks. Currently, the tested CL methods often are not able to outperform the forgetful fine-tuning baseline. Observe that even the modularity-based PackNet approach struggles with this task. This possibly indicates that using the activation mask from task $B$ is enough to deteriorate the performance.
+PackNet PackNet stands out in our evaluations. We conjecture that developing related methods might be a promising research direction. Besides further increasing performance, one could mitigate the limitations of PackNet. PackNet relies on knowing task identity during evaluation. While this assumption is met in our benchmark, it is an interesting topic for future research to develop methods that cope without task identity. Another nuisance is that PackNet assigns some fixed fraction of parameters to a task. This necessitates knowledge of the length of the sequence in advance. Additionally, when the second ten tasks of CW20 start, PackNet performance degrades, showing its potentially inefficient use of capacity and past knowledge, given that the second ten tasks are identical with the first ten and hence no additional capacity is needed. In a broader context, we speculate that parameter isolation methods might be a promising direction towards better CL methods.
+Resources usage In practical applications it is important to consider resources usage. All tested methods have relatively small overheads. For example, PackNet needs only $1 5 \%$ more time than the baseline fine-tuning and it requires $5 0 \%$ more neural network parameters (which is negligible when small networks like ours). See Appendix $\underline { { \mathbf { B . 4 } } }$ for details concerning other methods.
+Other observations In stark contrast with the supervised learning setting, we found that replay based methods (Perfect Memory and A-GEM) suffer from poor performance. This is even though we allow for a generous replay, which could store the whole experience. Explaining and amending this situation is, in our view, an important research question. We conjecture that this happens due to the regularization of the critic network (which was unavoidable for these methods). We found multi-task learning attaining lower scores than PackNet, the best CL method and comparable to the second one, EWC. We think this suggests interesting research directions for multi-task learning.
+# 6.1 RL-Related Challenges
+Reinforcement learning brings a set of issues not present in the supervised learning setting, e.g., exploration, varying reward scales, and stochasticity of environments. We argue that it is imperative to have a reliable benchmark to assess the efficiency of CL algorithms with respect to these problems. We find that some current methods are not well adjusted to the RL setting and require non-trivial conceptual considerations and careful tuning of hyperparameters, see details in Appendix C.
+An important design choice is whether or not to regularize the critic in the actor-critic framework (e.g. in SAC). We find it beneficial to focus on reducing forgetting in the actor while allowing the critic to freely adapt to the current task (note that critic is used only in training of the current task), similar to $\dot { \lVert \ 4 6 \rVert }$ . On the other hand, a forgetful critic is controversial. This can be sharply seen when the same task is repeated and the critic needs to learn from scratch. Additionally, not all methods can be trivially adapted to the ’actor-only regularization’ setting, as for example replay based methods. In Appendix $\mathrm { \Delta C }$ we examine these issues empirically, by showing experiments with critic regularization for EWC.
+Another aspect is the exploration and its non-trivial impact on transfers. As it was observed, transfers from a given task to the same one are sometimes poor. We show in Appendix $\textstyle \boxed { \mathrm { D . 1 } }$ that this results from the fact that at the task change the replay buffer is emptied and SAC collects new samples from scratch, usually by using the uniform policy. Learning on these random samples reduces performance on the current task and thus the forward transfer. Experimentally, we find that not resetting the buffer or using the current policy for exploration improves the transfer on the diagonal.
+# 7 Conclusions and Future Work
+In this work, we present Continual World, a continual reinforcement learning benchmark, and an in-depth analysis of how existing methods perform on it. The benchmark is aimed at facilitating and standardizing the CL system evaluation, and as such, is released with code, including implementation of 7 representative CL algorithms. We argue for more attention to forward transfer and the interaction between forgetting and transfer, as many existing methods seem to sacrifice transfer to alleviate forgetting. In our opinion, this should not be the aim of CL, and we need to strike a different balance between these objectives.
+We made several observations, both conceptual and empirical, which open future research directions. In particular, we conjecture that parameter isolation methods are a promising direction. Further, we identified a set of critical issues at the intersection of RL and CL. Resolving critic regularization and efficient use of multi-task replays seem to be the most pressing ones. Our benchmark highlights some challenges, which in our view are relevant and tangible now. In the long horizon, achieving high-level transfers, removing task boundaries, and scaling up are among significant goals for future editions of Continual World. Our work is foundational research and does not lead to any direct negative applications.
+# Acknowledgments and Disclosure of Funding
+We would like to thank Stanisław Jastrz˛ebski for stimulating talks and help while preparing the manuscript. The work of PM was supported by the Polish National Science Center grant UMO2017/26/E/ST6/00622. The work of MW was funded by Foundation for Polish Science (grant no POIR.04.04.00-00-14DE/18-00 carried out within the Team-Net program co-financed by the European Union under the European Regional Development Fund. This research was supported by the PL-Grid Infrastructure. Our experiments were managed using https://neptune.ai. We would like to thank the Neptune team for providing us access to the team version and technical support.
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+# Checklist
+1. For all authors...
+(a) Do the main claims made in the abstract and introduction accurately reflect the paper’s contributions and scope? [Yes]
+(b) Did you describe the limitations of your work? [Yes] see Section 4.4.
+(c) Did you discuss any potential negative societal impacts of your work? [Yes] See Section 7
+(d) Have you read the ethics review guidelines and ensured that your paper conforms to them? [Yes]
+2. If you are including theoretical results...
+(a) Did you state the full set of assumptions of all theoretical results? [N/A] (b) Did you include complete proofs of all theoretical results? [N/A]
+3. If you ran experiments...
+(a) Did you include the code, data, and instructions needed to reproduce the main experimental results (either in the supplemental material or as a URL)? [Yes] The codes is included in the supplemental material.
+(b) Did you specify all the training details (e.g., data splits, hyperparameters, how they were chosen)? [Yes] see details in Appendix A.
+(c) Did you report error bars (e.g., with respect to the random seed after running experiments multiple times)? [Yes] we used 20 random seeds, see also details in Appendix A.6.
+(d) Did you include the total amount of compute and the type of resources used (e.g., type of GPUs, internal cluster, or cloud provider)? [Yes] see Appendix A.7.
+4. If you are using existing assets (e.g., code, data, models) or curating/releasing new assets...
+(a) If your work uses existing assets, did you cite the creators? [Yes] We base on the MetaWorld benchmark [54], which we clearly indicate a few times, including the abstract.
+(b) Did you mention the license of the assets? [Yes] We use MIT licence; see Appendix A.1
+(c) Did you include any new assets either in the supplemental material or as a URL? [Yes]
+(d) Did you discuss whether and how consent was obtained from people whose data you’re using/curating? [N/A]
+(e) Did you discuss whether the data you are using/curating contains personally identifiable information or offensive content? [N/A]
+5. If you used crowdsourcing or conducted research with human subjects...
+(a) Did you include the full text of instructions given to participants and screenshots, if applicable? [N/A]
+(b) Did you describe any potential participant risks, with links to Institutional Review Board (IRB) approvals, if applicable? [N/A]
+(c) Did you include the estimated hourly wage paid to participants and the total amount spent on participant compensation? [N/A]

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+        "type": "text",
+        "text": "Continual World: A Robotic Benchmark For Continual Reinforcement Learning ",
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+        "text": "Maciej Wołczyk⇤ Jagiellonian University Kraków, Poland maciej.wolczyk@doctoral.uj.edu.pl ",
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+        "text": "Michał Zaj ˛ac⇤   \nJagiellonian University   \nKraków, Poland   \nemzajac@gmail.com   \nRazvan Pascanu   \nDeepMind   \nLondon, UK   \nrazp@google.com ",
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+        "text": "Łukasz Kucinski ´ Polish Academy of Sciences Warsaw, Poland lkucinski@impan.pl ",
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+        "type": "text",
+        "text": "Piotr Miłos´ ",
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+        "text": "Polish Academy of Sciences,   \nUniversity of Oxford,   \ndeepsense.ai   \nWarsaw, Poland   \npmilos@impan.pl ",
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+    {
+        "type": "text",
+        "text": "Abstract ",
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+        "type": "text",
+        "text": "Continual learning (CL) — the ability to continuously learn, building on previously acquired knowledge — is a natural requirement for long-lived autonomous reinforcement learning (RL) agents. While building such agents, one needs to balance opposing desiderata, such as constraints on capacity and compute, the ability to not catastrophically forget, and to exhibit positive transfer on new tasks. Understanding the right trade-off is conceptually and computationally challenging, which we argue has led the community to overly focus on catastrophic forgetting. In response to these issues, we advocate for the need to prioritize forward transfer and propose Continual World, a benchmark consisting of realistic and meaningfully diverse robotic tasks built on top of Meta-World $\\bar { \\mathbb { B } } \\bar { \\underline { { 4 } } } \\mathbb { I }$ as a testbed. Following an in-depth empirical evaluation of existing CL methods, we pinpoint their limitations and highlight unique algorithmic challenges in the RL setting. Our benchmark aims to provide a meaningful and computationally inexpensive challenge for the community and thus help better understand the performance of existing and future solutions. Information about the benchmark, including the open-source code, is available at https://sites.google.com/view/continualworld. ",
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+    {
+        "type": "text",
+        "text": "1 Introduction ",
+        "text_level": 1,
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "Change is ubiquitous. Unsurprisingly, due to evolutionary pressure, humans can quickly adapt and creatively reuse their previous experiences. In contrast, although biologically inspired, deep learning (DL) models excel mostly in static domains that satisfy the i.i.d. assumption, as for example in image processing [28, 49, 10, 40], language modelling $| { \\bar { \\sqrt { 5 2 } } } , { \\overline { { \\mathbb { 1 1 } } } } | |$ or biological applications [47]. As the systems are scaled up and deployed in open-ended settings, such assumptions are increasingly questionable; imagine, for example, a robot that needs to adapt to the changing environment and the wear-and-tear of its hardware. Continual learning (CL), an area that explicitly focuses on such problems, has been gaining more attention recently. The progress in this area could offer enormous advantages for deep neural networks $\\mathbb { \\lVert 1 9 \\rVert }$ and move the community closer to the long-term goal of building intelligent machines $\\mathbb { \\ m }$ . ",
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+        "type": "text",
+        "text": "Evaluation of CL methods is challenging. Due to the sequential nature of the problem that disallows parallel computation, evaluation tends to be expensive, which has biased the community to focus on toy tasks. These are mostly in the domain of supervised learning, often relying on MNIST. In this work, we expand on previous discussions on the topic [45, 16, 30, 46] and introduce a new benchmark, Continual World. The benchmark is built on realistic robotic manipulation tasks from Meta-World $\\pmb { \\Vert 5 4 \\Vert }$ , benefiting from its diversity but also being computationally cheap. Moreover, we provide shorter auxiliary sequences, all of which enable a quick research cycle. On the conceptual level, a fundamental difficulty of evaluating CL algorithms comes from the different desiderata for a CL solution. These objectives are often opposing each other, forcing practitioners to explicitly or implicitly make trade-offs in their algorithmic design that are data-dependent. Continual World provides more meaningful relationships between tasks, answering recent calls $\\mathbb { \\lVert 1 9 \\rVert }$ to increase attention on forward transfer. ",
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+    {
+        "type": "text",
+        "text": "Additionally, we provide an extensive evaluation of a spectrum of commonly used CL methods. It highlights that many approaches can deal relatively well with catastrophic forgetting at the expense of other desiderata, in particular forward transfer. This emphasizes our call for focusing on forward transfer and the need for more benchmarks that allow for common structure among the tasks. ",
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+        "type": "text",
+        "text": "The main contribution of this work is a CL benchmark that poses optimizing forward transfer as the central goal and shows that existing methods struggle to outperform simple baselines in terms of the forward transfer capability. We release the code2 both for the benchmark and 7 CL methods, which aims to provide the community helpful tools to better understand the performance of existing and future solutions. We encourage to visit the website3 of the project and participate in the Continual World Challenge. ",
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+        "type": "text",
+        "text": "2 Related work ",
+        "text_level": 1,
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+        "type": "text",
+        "text": "The field of continual learning has grown considerably in the past years, with numerous works forming new subfields $\\mathbb { \\left[ \\left. 2 3 \\right] \\right. }$ and finding novel applications $\\lVert \\overline { { 4 8 } } \\rVert$ . For brevity, we focus only on the papers proposing RL-based benchmarks and point to selected surveys of the entire field. $\\pmb { \\mathbb { D } }$ provide a high-level overview of CL and argue that learning in a non-stationary setting is a fundamental problem for the development of AI, highlighting the frequent connections to neuroscience. On the other hand, $\\mathbb { B } 3 \\mathbb { B }$ focus on describing, evaluating, and relating CL methods to each other, providing a taxonomy of CL solutions that we use in this work. ",
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+        "type": "text",
+        "text": "The possibility of applying CL methods in reinforcement learning scenarios has been explored for a long time, see $[ [ 2 5 ] ]$ for a recent review. However, no benchmark has been widely accepted by the community so far, which is the aim of this work. Below we discuss various benchmarks and environments considered in the literature. ",
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+    {
+        "type": "text",
+        "text": "Supervised settings MNIST has been widely used to benchmark CL algorithms in two forms $ { \\mathbb { \\left[ \\left[ 2 7 \\right] \\right] } }$ . In the permuted MNIST, the pixels of images are randomly permuted to form new tasks. In the split MNIST, tasks are defined by classifying non-overlapping subsets of classes, e.g. 0 vs. 1 followed by 2 vs. 3. A similar procedure has been applied to various image classification tasks like CIFAR-10, CIFAR-100, Omniglot or mini-ImageNet [2, 46, 5]. Another benchmark is CORe50 [31], a dataset for continuous object recognition. Recent work $\\mathbb { \\left. 2 9 \\right. }$ proposes a benchmark based on language modeling. We find that many of these benchmarks are challenging and allow to measure forgetting. However, we argue they are not geared towards measuring forward transfer or for highlighting important RL-specific characteristics of the CL problem. ",
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+    {
+        "type": "text",
+        "text": "Atari The Atari 2600 suite $\\textcircled { 8 }$ is a widely accepted RL benchmark. Sequences of different Atari games have been used for evaluating continual learning approaches [43, 27]. Using Atari can be computationally expensive, e.g., training a sequence of ten games typically requires 100M steps or more. More importantly, as $\\mathbb { \\lVert \\boldsymbol { 4 3 } \\rVert }$ notes, these games lack a meaningful overlap, limiting their relevance for studying transfers. Continuous control [32, 24] use continuous control tasks such as Humanoid or Walker2D. However, the considered sequences are short, and the range of experiments is limited. [34] use Meta-World tasks, similarly to us, for evaluations of their continual learning method, but the work is not aimed at building a benchmark. As such, it uses the Meta-World’s MT10 preset and does not provide an in-depth analysis of the tasks or other CL methods. Maze navigation A set of 3D maze environments is used in [43]. The map structure and objects that the agent needs to collect change between tasks. It is not clear, though, if the tasks provide enough diversity. [30] propose CRLMaze, 3D navigation scenarios for continual learning, which solely concentrate on changes of the visual aspects. StarCraft $\\lVert \\rVert \\dot { \\boldsymbol { \\mathrm { ~ ‰ ~ } } }$ present a StarCraft campaign (11 tasks) to evaluate a high-level transfer of skills. The main drawback of this benchmark is excessive computational demand (often more than 1B frames). Minecraft $\\mathbb { \\left[ \\left. 5 0 \\right| \\right. }$ propose simple scenarios within the Minecraft domain along with a hierarchical learning method. The authors phrase the problem as lifelong learning and do not use typical CL methods. Lifelong Hanabi $\\lVert \\rVert$ consider a multi-agent reinforcement learning setting based on Hanabi, a cooperative game requiring significant coordination between agents. On the other hand, we focus on the single agent setting with changing environment, which allows us to bypass the computational complexity needed to model interactions between agents and highlight issues connected to learning in a changing world. Causal World $\\pmb { \\mathbb { B } } \\|$ propose an environment for robotic manipulation tasks which share causal structure. Although they investigate issues deeply connected to learning in a changing world, such as generalization to new tasks and curricula, they do not directly consider continual learning. Jelly Bean World $\\mathbb { B } 9 \\mathbb { I }$ provide interesting procedurally generated grid world environments. The suite is configurable and can host a non-stationary setting. It is unclear, however, if such environments reflect the characteristics of real-world challenges. ",
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+    {
+        "type": "text",
+        "text": "3 Continual learning background ",
+        "text_level": 1,
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+        "type": "text",
+        "text": "Continual learning (CL) is an area of research which focuses on building algorithms capable of handling non-stationarity. They should be able to sequentially acquire new skills and solve novel tasks without forgetting the previous ones. Such systems are desired to accommodate over extended periods swiftly, which is often compared to human capabilities and alternatively dubbed as lifelong learning. CL is intimately related to multi-task learning, curriculum learning, meta-learning, with some key differences. Multi-task assumes constant access to all tasks, thus ignoring non-stationarity. Curriculum learning focuses on controlling the task ordering and often the learning time-span. Metalearning, a large field of its own, sets the objective to develop procedures that allow fast adaptation within a task distribution and usually ignores the issue of non-stationarity. ",
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+    {
+        "type": "text",
+        "text": "The CL objective is operationalized by the training and evaluation protocols. The former typically consists of a sequence of tasks (their boundaries might be implicit and smooth). The latter usually involves measuring catastrophic forgetting, forward transfer, and backward transfer. The learning system might also have constrained resources: computations, memory, size of neural networks, and the volume of data samples. A fundamental observation is that the above aspects and desiderata are conflicting. For example, given unlimited resources, one might mitigate forgetting simply by storing everything in memory and paying a high computational cost of rehearsing all samples from the past. ",
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+    {
+        "type": "image",
+        "img_path": "images/478f601d070ca51575b0809421a2f533ad8ec0fc787df0823e9c6f366258a7b5.jpg",
+        "image_caption": [
+            "Figure 1: Left graph shows task PEG-UNPLUG-SIDEV1 and the right graph presents forward transfer from SHELF-PLACE-V1 to PEG-UNPLUG-SIDE-V1. In this case $F T = 0 . 1 0$ . "
+        ],
+        "image_footnote": [],
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+    {
+        "type": "text",
+        "text": "Another pair of objectives that are problematic for current methods are forgetting and forward transfer. For neural networks, existing methods propose to limit network plasticity. These alleviate the problem of forgetting, however, at the cost of choking the further learning process. We advocate for more nuanced approaches. Importantly, to make the transfer possible, our benchmark is composed of related tasks. We also put modest bounds on resources. This requirement is in line with realistic scenarios, demanding computationally efficient adaptation and inference. In a broader sense, we hope to address a data efficiency challenge, one of the most signif",
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+        "type": "text",
+        "text": "icant limitations of the current deep (reinforcement) learning methods. We conjecture that forward transfer might greatly improve the situation and possibly one day enable us to create systems with human-level cognition capabilities, in line with similar thoughts expressed in [19]. ",
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+    {
+        "type": "text",
+        "text": "4 Continual World benchmark ",
+        "text_level": 1,
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+        "text": "Continual World is a new benchmark designed to be a testbed for evaluating RL agents on the challenges advocated by the CL paradigm, described in Section $^ { 3 , }$ as well as highlighting the RLspecific algorithmic challenges for CL (see Section $\\boxed { 6 . 1 }$ . As such it is aimed at being valuable to both the CL and RL communities. Continual World consists of realistic robotic manipulation tasks, aligned in a sequence to enable the study of forward transfer. It is designed to be challenging while computationally accessible.4 The benchmark is based on Meta-World, a suite of robotic tasks already established in the community. This enables easy comparisons with the related fields of multi-task and meta-learning reinforcement learning, potentially highlighting one benefit of CL framing, namely that of dealing with different reward scales as we discuss more in detail in Appendix $\\mathrm { H } .$ Continual World comes with open-source code that allows for easy development and testing of new algorithms and provides implementations of 7 existing algorithms. Finally, it allows highlighting RL-specific challenges for the CL setting. We believe that our work is a step in the right direction towards reliable benchmarks of CL. We realize, however, that it will need to evolve as the field progresses. We leave a discussion on future directions and limitations to Section 4.4. ",
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+    {
+        "type": "text",
+        "text": "4.1 Metrics ",
+        "text_level": 1,
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+    {
+        "type": "text",
+        "text": "To facilitate further discussion, we start with defining metrics. These are rather standard in the CL setting $\\mathbb { H } 2 \\mathbb { I }$ . Assume $p _ { i } ( t ) \\in [ 0 , 1 ]$ to be the performance (success rate) of task $i$ at time $t$ . As a measure of performance, we take the average success rate of achieving a goal specified by a given task when using randomized initial conditions and stochastic policies (see also Section $4 . { \\overset { - } { 3 } } ) . { \\overset { 5 } { . } } { \\overset { . } { } }$ Each task is trained for $\\Delta = 1 M$ steps. The main sequence has $N = 2 0$ tasks and the total sample budget is $T = N \\cdot \\Delta = 2 0 M$ . The $i$ -th task is trained during the interval $t \\in [ ( i - 1 ) \\cdot \\Delta , i \\cdot \\Delta ]$ . We report the following metrics: ",
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+    {
+        "type": "text",
+        "text": "Average performance. The average performance at time $t$ is (see Figure 3) ",
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+    {
+        "type": "equation",
+        "img_path": "images/434fa45f7b617ee5a00743670321569d4d56a49ae92a33f2a74a8ffce05ef9e7.jpg",
+        "text": "$$\n\\mathsf { P } ( t ) : = \\frac { 1 } { N } \\sum _ { i = 1 } ^ { N } p _ { i } ( t ) .\n$$",
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+        "type": "text",
+        "text": "Its final value, $\\mathrm { P } ( { \\cal T } )$ , is a traditional metric used in the CL research. This is the objective we use for tuning hyperparameters. We have $\\mathbf { P } ( t ) \\in [ 0 , 1 ]$ for each $t$ . ",
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+        "text": "Forward transfer. We measure the forward transfer of a method as the normalized area between its training curve and the training curve of the reference, single-task, experiment, see Figure $1 .$ Let $p _ { i } ^ { b } \\in [ 0 , 1 ]$ be the reference performance6 then the forward transfer for the task $i$ , denoted by $\\bar { \\mathsf { F T } } _ { i }$ , is ",
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+        "type": "equation",
+        "img_path": "images/882897fb9455e69c375410f022ebf006d1ca872f4797b4629f2c76c34273a5eb.jpg",
+        "text": "$$\n\\mathsf { F T } _ { i } : = \\frac { \\mathsf { A U C } _ { i } - \\mathsf { A U C } _ { i } ^ { b } } { 1 - \\mathsf { A U C } _ { i } ^ { b } } , \\quad \\mathsf { A U C } _ { i } : = \\frac { 1 } { \\Delta } \\int _ { ( i - 1 ) \\cdot \\Delta } ^ { i \\cdot \\Delta } p _ { i } ( t ) \\mathrm { d } t , \\quad \\mathsf { A U C } _ { i } ^ { b } : = \\frac { 1 } { \\Delta } \\int _ { 0 } ^ { \\Delta } p _ { i } ^ { b } ( t ) \\mathrm { d } t ,\n$$",
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+        "type": "text",
+        "text": "The average forward transfer for all tasks, FT, is defined as ",
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+        "type": "equation",
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+        "text": "$$\n\\mathrm { F T } = \\frac { 1 } { N } \\sum _ { i = 1 } ^ { N } \\mathrm { F T } _ { i } .\n$$",
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+        "type": "text",
+        "text": "We note that $\\mathrm { F T } _ { i } \\leq 1$ and they might be negative. In our experiments, we also measure backward transfer. As it is negligible, see Appendix E.1. ",
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+        "type": "text",
+        "text": "Forgetting. For task $i$ , we measure the decrease of performance after ending its training, i.e. ",
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+        "text": "$$\nF _ { i } = p _ { i } ( i \\cdot \\Delta \\bar { \\Delta } ) - p _ { i } ( T ) .\n$$",
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+        "type": "text",
+        "text": "Similarly to FT e report $\\begin{array} { r } { F = { \\frac { 1 } { N } } \\sum _ { i = 1 } ^ { N } F _ { i } } \\end{array}$ . We have $F _ { i } \\leq 1$ for any $i$ and consequently $\\mathrm { F T } \\leq 1$ . It $F _ { i }$ are negative, which would indicate backward transfer. We do not observe this in practice, see Appendix E.1. ",
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+        "type": "text",
+        "text": "4.2 Continual World tasks ",
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+        "type": "text",
+        "text": "This section describes the composition of Continual World benchmark and the rationale behind its design. We decided to base on Meta-World [54], a fairly new but already established robotic benchmark for multi-task and meta reinforcement learning. From a practical standpoint, Meta-World utilizes the open-source MuJoCo physics engine [51], prized for speed and accuracy. Meta-World provides 50 distinct manipulation tasks with everyday objects using a simulated robotic Sawyer arm. Although the tasks vary significantly, the structure and semantics of observation and action spaces remain the same, allowing for transfer between tasks. Each observation is a 12-dimensional vector containing $( x , y , z )$ coordinates of the robot’s gripper and objects of interest in the scene. The 4-dimensional action space describes the direction of the arm’s movement in the next step and the gripper actuator delta. Reward functions are shaped to make each task solvable. In evaluations, we use a binary success metric based on the distance of the task-relevant object to its goal position. This metric is interpretable and enables comparisons between tasks. For more details about the rewards and evaluation metrics, see [54, Section 4.2, Section 4.3]. ",
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+        "text": "CW20, CW10, triplets sequences The core of our benchmark is CW20 sequence. Out of 50 tasks defined in Meta-World, we picked those that are not too easy or too hard in the assumed sample budget $\\Delta = 1 M$ . Aiming to strike a balance between the difficulty of the benchmark and computational requirements, we selected 10 tasks. The tasks and their ordering were based on the transfer matrix (see the next paragraph), so that there is a high variation of forward transfers (both in the whole list and locally). We refer to these ordered tasks as CW10, and CW20 is CW10 repeated twice. We recommend using CW20 for final evaluation; however, CW10 is already very informative in most cases. Due to brevity constraints, we present an ablation with an alternative ordering of the tasks and a longer sequence of 30 tasks in Appendix $\\mathbf { G } ,$ however, these experiments do not alter our findings. Additionally, to facilitate a fast development cycle, we propose a set of triplets, sequences of three tasks which exhibit interesting learning dynamics. ",
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+        "type": "text",
+        "text": "The CW10 sequence is: HAMMER-V1, PUSH-WALL-V1, FAUCET-CLOSE-V1, PUSH-BACK-V1, STICK-PULLV1, HANDLE-PRESS-SIDE-V1, PUSH-V1, SHELF-PLACE-V1, WINDOW-CLOSE-V1, PEG-UNPLUG-SIDE-V1. ",
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+    {
+        "type": "text",
+        "text": "Transfer matrix Generally, the relationship between tasks and its impact on learning dynamics of neural networks is hard to quantify, where semantic similarity does not typically lead to transfer $\\textcircled { 1 1 4 } \\textcircled { 1 }$ . To this end, we consider a minimal setting, in which we finetune on task $t _ { 2 }$ a model pretrained on $t _ { 1 }$ , using the same protocol as the benchmark (e.g., different output heads, see Section $\\boxed { 4 . 3 }$ . This provides neural network-centric insight into the relationship between tasks summarized in Figure $\\bar { \\bigtriangledown } ,$ and allows us to measure low-level transfer between tasks, i.e., the ability of the model to reuse previously acquired features. See Appendix D for more results and extended discussion. ",
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+        "image_caption": [
+            "Figure 2: Transfer matrix, see Section $4 . 2 \\cdot$ Each cell represents the forward transfer from the first task to the second one. We shaded the cells for which 0 belongs to their $9 0 \\%$ confidence interval. "
+        ],
+        "image_footnote": [],
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+    {
+        "type": "text",
+        "text": "Notice that there are only a few negative forward transfer cases, and those are of a rather small magnitude (perhaps unsurprisingly, as the tasks are related). There are also visible patterns in the matrix. For instance, some tasks such as PEGUNPLUG-SIDE-V1 or PUSH-BACK-V1 benefit from a relatively large forward transfer, (almost) irrespective of the first task. Furthermore, the average forward transfer given the second task (columns) is more variable than the corresponding quantity for the first task (rows). ",
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+    {
+        "type": "text",
+        "text": "Note that some transfers on the diagonal (i.e., between the same tasks) are relatively small. We made a detailed analysis of possible reasons, which revealed that the biggest negative impact is due to the replay buffer resets, which seems, however, unavoidable for off-diagonal cases, see Section $6 . 1$ for details. ",
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+    {
+        "type": "text",
+        "text": "Importantly, we use this matrix to estimate what level of forward transfer a good CL method ",
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+    {
+        "type": "text",
+        "text": "should be able to achieve. We expect that a model which is able to remember all meaningful aspects of previously seen tasks would transfer at least as well as if one were just fine-tuning after learning the best choice between the previous tasks. For a sequence $t _ { 1 } , \\ldots , t _ { N }$ we set the reference forward transfer, RT, to be ",
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+        "text": "",
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+        "page_idx": 5
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+    {
+        "type": "equation",
+        "img_path": "images/c9858340d94c16aa89c4c6ffa28d4bcb4f86bc924d19a40a271306987b15bed1.jpg",
+        "text": "$$\n\\mathrm { R T } : = \\frac { 1 } { N } \\sum _ { i = 2 } ^ { N } \\operatorname* { m a x } _ { j < i } \\mathrm { F T } ( t _ { j } , t _ { i } ) ,\n$$",
+        "text_format": "latex",
+        "bbox": [
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+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "where $\\mathrm { F T } ( t _ { j } , t _ { i } )$ is the transfer matrix value for $t _ { j } , t _ { i }$ . For the CW20 sequence, the value is $\\mathrm { R T } = 0 . 4 6$ Note that a model can do better that this by composing knowledge from multiple previous tasks. ",
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+    {
+        "type": "text",
+        "text": "4.3 Training and evaluation details ",
+        "text_level": 1,
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+    {
+        "type": "text",
+        "text": "We adapt the standard Meta-World setting to CL needs. First, we use separate policy heads for each task, instead of the original one-hot task ID inputs (we provide ablation experiments for this choice in Appendix $\\mathbf { G } )$ . Second, in each episode, we randomize the positions of objects in the scene to encourage learning more robust policies. We use an MLP network with 4 layers of 256 neurons. ",
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+    {
+        "type": "text",
+        "text": "For training, we use soft actor-critic (SAC) [17], a popular and efficient RL method for continuous domains. SAC is an off-policy algorithm using replay buffer, which is an important aspect for CL, particularly for methods relying on rehearsing old trajectories. SAC is based on the so-called maximum entropy principle; this results in policies which explore better and are more robust to changes in the environment dynamics. Both of these qualities might be beneficial in CL. ",
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+    {
+        "type": "text",
+        "text": "We note that the size of the neural network and optimization details of the SAC algorithm (like batch size) put constraints on \"the amount of compute\". Intentionally, these are rather modest, which is in line with CL desiderata, see Section $3 .$ Similarly, we limit the number of timesteps to $1 M$ , which is a humble amount for modern-day deep reinforcement learning. We picked tasks to be challenging but not impossible within this budget. We note that training in the RL setting tends to be less stable than in the supervised one. We recommend using multiple seeds, in our experiments, we typically used 20 and calculate confidence intervals; we used the bootstrap method. We choose hyperparameters that maximize average performance $\\mathbb { \\underline { { \\left( 1 \\right) } } }$ . In our experiments, we tune common parameters for SAC and the method-specific hyperparameters separately. All details of the training and evaluation setup are presented in Appendix A. ",
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+    {
+        "type": "text",
+        "text": "4.4 Limitations of Continual World ",
+        "text_level": 1,
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+        "type": "text",
+        "text": "As any benchmark, we are fully aware that ours will not cover the entire spectrum of problems that one might be interested in. Here we summarize a few limitations that we hope to overcome in a future instantiation of this benchmark: ",
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+    {
+        "type": "text",
+        "text": "Input space We use a small 12 dimensional observation space. This is key to achieve modest computational demand. However, richer inputs could allow for potentially more interesting forms of transfer (e.g., based on visual similarity of objects) and would allow inferring the task from the observation, which is currently impossible. ",
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+    {
+        "type": "text",
+        "text": "Reliance on SAC We use the SAC algorithm $\\textcircled { 1 1 7 }$ , which is considered a standard choice for continuous robotic tasks. However, there is a potential risk of overfitting to the particularities of this algorithm and exploring alternative RL algorithms is important. ",
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+    {
+        "type": "text",
+        "text": "Task boundaries We rely on task boundaries. One can rely on task inference mechanisms (e.g. [35, 41]) to resolve this limitation, though we acknowledge the importance to extend the benchmark towards allowing and testing for task inference capabilities. Also, testing for algorithms dealing with continuous distributional drift is not possible in the current format. ",
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+    {
+        "type": "text",
+        "text": "Output heads We rely on using a separate head for each new task, similar to many works on continual learning. We opt for this variant based on its simplicity and better performance than using one-hot encoding to indicate a task. We believe that the lack of semantics of the one-hot encoding would further impede transfer, as the relationship between tasks can not be inferred. We carry ablation studies with using one-hot encoding as an input and a single head architecture, a setting that is already compatible with our benchmark. We regard this aspect as an important future work, and in particular, we are exploring alternative encoding of input to make this choice more natural. A coherent domain, like Continual World, provides a unique opportunity to exploit a consistent output layer as its semantics does not change between tasks. ",
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+    {
+        "type": "image",
+        "img_path": "images/de69b894f5a716658e9b945947e813289cfbbb6a6be75dce43f4af3a4767f797.jpg",
+        "image_caption": [
+            "Figure 3: Training curves for selected CL methods and multi-task. The upper left panel shows the performance on the first task for a subset of methods throughout the whole training. Note that due to the use of different output heads, we do not see a second bump when revisiting this task at time $1 0 M$ . The upper right panel shows the performance on the current task being trained for EWC compared to a reference (a model learning only that task from scratch). The bottom plot shows the average performance. Solid lines show the performance of the model training on the first 10 tasks (where 1 means being able to solve all of them). Dashed lines show the performance of learning the same tasks in the second half of the benchmark. Note that dashed lower are below solid ones, indicating lower performance on the second pass, even if the agent has already previously learned the tasks and has access to relevant features. "
+        ],
+        "image_footnote": [],
+        "bbox": [
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+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "The difficulty and number of tasks The number of tasks is relatively small. CW20, the main sequence we use, consists of only 10 different tasks, which are then repeated. We believe the repetition of tasks is important for a CL benchmark, leading to interesting observations. We check also that results are quantitatively similar on a sequence of 30 tasks, see Appendix G. However, longer sequences, potentially unbounded, are needed to understand the various limitations of existing algorithms. For example, the importance of graceful forgetting or dealing with systems that run out of capacity, a scenario where there is no multi-task solution for the sequence of observed tasks. This is particularly of interest for methods such as PackNet $\\pmb { \\mathbb { B 3 } }$ . Additionally, we provide the number of tasks in advance. Dealing with an unknown number of tasks might raise further interesting questions. Finally, in future iterations of the benchmark, it is important to consider more complex tasks or more complex relationships between tasks to remain a challenge to existing methods. Our goal was to provide a benchmark that is approachable by existing methods, as not to stifle progress. ",
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+        "page_idx": 6
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+    {
+        "type": "text",
+        "text": "Low-level transfer We focus on low-level transfers via neural network features and weights. As such, we do not explicitly explore the ability of the learning process to exploit the compositionality of behavior or to rely on a more interesting semantic level. While we believe such research is crucial, we argue that solving low-level transfer is equally important and might be a prerequisite. So, for now, it is beyond the scope of this work, though future iterations of the benchmark could contain such scenarios. ",
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+    {
+        "type": "text",
+        "text": "5 Methods ",
+        "text_level": 1,
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+    {
+        "type": "text",
+        "text": "We now sketch 7 CL methods evaluated on our benchmark. Some of them were developed for RL, while others were meant for the supervised learning context and required non-trivial adaptation. We aimed to cover different families of methods; following $\\mathbb { \\lVert \\rVert 3 \\rVert }$ , we consider three classes: regularizationbased, parameter isolation and replay methods. An extended description and discussion of these methods are provided in Appendix B. ",
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+    {
+        "type": "text",
+        "text": "Regularization-based Methods This family builds on the observation that one can reduce forgetting by protecting parameters that are important for the previous tasks. The most basic approach often dubbed L2 $ { \\mathbb { \\left[ \\left[ 2 7 \\right] \\right] } }$ simply adds a $L _ { 2 }$ penalty, which regularizes the network not to stray away from the previously learned weights. In this approach, each parameter is equally important. Elastic Weight Consolidation (EWC) $\\overline { { \\mathbb { R } \\mathbb { Z } \\mathbb { I } } }$ uses the Fisher information matrix to approximate the importance of each weight. Memory-Aware Synapses (MAS) [4] also utilizes a weighted penalty, but the importance is obtained by approximating the impact each parameter has on the output of the network. Variational Continual Learning (VCL), follows a similar path but uses variational inference to minimize the Kullback-Leibler divergence between the current distribution of parameters (posterior) and the distribution for the previous tasks (prior). ",
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+    {
+        "type": "text",
+        "text": "",
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+    },
+    {
+        "type": "text",
+        "text": "Parameter Isolation Methods This family (also called modularity-based) forbids any changes to parameters that are important for the previous tasks. It may be considered as a “hard” equivalent of regularization-based methods. PackNet [33] “packs” multiple tasks into a single network by iteratively pruning, freezing, and retraining parts of the network at task change. PackNet is closely related to progressive neural networks [43], developed in the RL context. ",
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+    },
+    {
+        "type": "text",
+        "text": "Replay Methods Methods of this family keep some samples from the previous tasks and use them for training or as constraints to reduce forgetting. We use a Perfect Memory baseline, a modification of our setting which remembers all the samples from the past (i.e., without resetting the buffer at the task change). We also implemented Averaged Gradient Episodic Memory (A-GEM) [12], which projects gradients from new samples as to not interfere with previous tasks. We find that A-GEM does not perform well on our benchmark. ",
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+    {
+        "type": "text",
+        "text": "Multi-task learning In multi-task learning, a field closely related to CL, tasks are trained simultaneously. By its design, it does not suffer from forgetting, however, it is considered to be hard as multiple tasks “compete for the attention of a single learning system”, see [21, 44]. We find that using reward normalization as in PopArt $\\left[ \\left[ 2 1 \\right] \\right]$ is essential to achieve good performance. See Appendix H. ",
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+    {
+        "type": "text",
+        "text": "6 Experiments ",
+        "text_level": 1,
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+    {
+        "type": "text",
+        "text": "Now we present empirical results; these are evaluations of a set of 7 representative CL methods (as described in Section $\\textcircled{5}$ on our Continual World benchmark. We focus on forgetting and transfers while keeping fixed constraints on computation, memory, number of samples, and neural network architecture. Our main empirical contributions are experiments on the long CW20 sequence and following high-level conclusions. For a summary see Table 1, Figure 3 and for an extensive discussion, we refer to Appendix $\\boxed { \\mathrm { E } }$ (including results for the shorter sequence, CW10). In Appendix G we provide various ablations and detailed analysis of sensitivity to the CL-specific hyperparameters. ",
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+    {
+        "type": "text",
+        "text": "Performance The performance (success rate) averaged over tasks (eq. $\\mathbb { \\underline { { ( 1 ) } } }$ ) is a typical metric for the CL setting. PackNet seems to outperform other methods, approaching 0.8 from the maximum of 1.0, outperforming multi-task solutions which might struggle with different reward scales, a problem elegantly avoided in the CL framing. Other methods perform considerably worse. A-GEM and Perfect Memory struggle. We further discuss possible reasons in Sectio n 6.1. ",
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+    {
+        "type": "table",
+        "img_path": "images/91db69af272a3c6ef3e51eac2cbc1d3310c094c62bf1be32a49122ea039ce469.jpg",
+        "table_caption": [
+            "Table 1: Results on CW20, for CL methods and multi-task training. Metrics are defined in Section 4.1, RT is eq. $( 4 )$ . We used 20 seeds and provide $90 \\%$ confidence intervals. "
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>method</td><td>performance</td><td>forgetting</td><td>f. transfer</td></tr><tr><td>Fine-tuning</td><td>0.05 [0.05,0.06]</td><td>0.73 [0.72, 0.75]</td><td>0.20 [0.17, 0.23]</td></tr><tr><td>L2</td><td>0.43 [0.39, 0.47]</td><td>0.02 [0.00, 0.03]</td><td>-0.71 [-0.87, -0.57]</td></tr><tr><td>EWC</td><td>0.60 [0.57, 0.64]</td><td>0.02 [-0.00, 0.05]</td><td>-0.17 [-0.24, -0.11]</td></tr><tr><td>MAS</td><td>0.51 [0.49, 0.53]</td><td>0.00 [-0.01,0.02]</td><td>-0.52 [-0.59,-0.47]</td></tr><tr><td>VCL</td><td>0.48 [0.46,0.50]</td><td>0.01 [-0.01, 0.02]</td><td>-0.49 [-0.57,-0.42]</td></tr><tr><td>PackNet</td><td>0.80 [0.79, 0.82]</td><td>0.00 [-0.01,0.01]</td><td>0.19 [0.15, 0.23]</td></tr><tr><td>Perfect Memory</td><td>0.12 [0.09, 0.15]</td><td>0.07 [0.05,0.10]</td><td>-1.34 [-1.42, -1.27]</td></tr><tr><td>A-GEM</td><td>0.07 [0.06,0.08]</td><td>0.71 [0.70,0.73]</td><td>0.13 [0.10,0.16]</td></tr><tr><td>MT</td><td>0.51 [0.48, 0.53]</td><td></td><td></td></tr><tr><td>MT (PopArt)</td><td>0.65 [0.63, 0.67]</td><td></td><td></td></tr><tr><td>RT</td><td></td><td></td><td>0.46</td></tr></table>",
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+    {
+        "type": "text",
+        "text": "Forgetting We observe that ",
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+    {
+        "type": "text",
+        "text": "most CL methods are usually efficient in mitigating forgetting. However, we did not notice any boost when revisiting a task (see Figure $3 )$ . Even if a different output head was employed, relearning the internal representation should have had an impact unless it changed considerably when revisiting the task. Additionally, we found A-GEM difficult to tune; consequently, with the best hyperparameter settings, it is relatively similar to the baseline fine-tuning method (see details in Appendix $\\bigtriangledown$ ",
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+    {
+        "type": "text",
+        "text": "Transfers For all methods, forward transfer for the second ten tasks (and the same tasks are revisited) drops compared to the first ten tasks. This is in stark contrast to forgetting, which seems to be well under control. Among all methods, only fine-tuning and PackNet are able to achieve positive forward transfer (0.20 and 0.19, resp.) as well as on the first (0.32 and 0.21, resp.) and the second (0.08 and 0.17, resp.) half of tasks. However, these are considerably smaller than $\\mathrm { R T } = 0 . 4 6$ , which in principle can even be exceeded, and which should be reached by a model that remembers all meaningful aspects of previously seen tasks, see $\\textcircled{4}$ . These results paint a fairly grim picture: we would expect improvement, rather than deterioration in performance, when revisiting previously seen tasks. There could be multiple reasons for this state of affairs. It could be attributed to the loss of plasticity, similar to the effect observed in $\\textcircled { 6 }$ . Another reason could be related to the interference between CL mechanisms or setting and RL, for instance, hindering exploration. We did not observe any substantial cases of backward transfer, even though the benchmark is well suited to study this question due to the revisiting of tasks. See Appendix E.1. ",
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+        "page_idx": 8
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+    {
+        "type": "image",
+        "img_path": "images/845bed2db7dcfa9140e21b319b1d7d55d2824be710c8d12c2d31ab127f6557ec.jpg",
+        "image_caption": [
+            "Figure 4: How forgetting impacts the forward transfer. Two different triplets of tasks learnt in sequence. An ideal agent learning on a sequence $A  B  C$ should have at least as good performance on task $C$ as an agent which just learns $A  C$ . In reality, an interfering task $B$ reduces this transfer, even when continual learning approaches are used. "
+        ],
+        "image_footnote": [],
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+    {
+        "type": "text",
+        "text": "Triplets experiments We illustrate how forgetting and forward transfer interact with each other in a simpler setting of three task sequences, see Figure $\\boxed { \\ 4 }$ and Appendix $\\boxed { \\mathrm { F } }$ We focus on sequences of tasks $A $ $B  C$ , where $A \\  \\ C$ has significant positive forward transfer and $B  C$ has a smaller or even negative transfer. An efficient CL agent should be able to use information from $A$ to get good performance on $C$ . However, interference introduced by $B$ reduces the fi",
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+    {
+        "type": "text",
+        "text": "nal forward transfer (see Figure $^ { 4 ) }$ . The drive for reducing forgetting in CL agents has been primarily to perform well on previous tasks when we revisit them. With this example, we argue that an equally important reason to improve the memory of CL agents is to efficiently use past experiences to learn faster on new tasks. Currently, the tested CL methods often are not able to outperform the forgetful fine-tuning baseline. Observe that even the modularity-based PackNet approach struggles with this task. This possibly indicates that using the activation mask from task $B$ is enough to deteriorate the performance. ",
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+    {
+        "type": "text",
+        "text": "PackNet PackNet stands out in our evaluations. We conjecture that developing related methods might be a promising research direction. Besides further increasing performance, one could mitigate the limitations of PackNet. PackNet relies on knowing task identity during evaluation. While this assumption is met in our benchmark, it is an interesting topic for future research to develop methods that cope without task identity. Another nuisance is that PackNet assigns some fixed fraction of parameters to a task. This necessitates knowledge of the length of the sequence in advance. Additionally, when the second ten tasks of CW20 start, PackNet performance degrades, showing its potentially inefficient use of capacity and past knowledge, given that the second ten tasks are identical with the first ten and hence no additional capacity is needed. In a broader context, we speculate that parameter isolation methods might be a promising direction towards better CL methods. ",
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+    {
+        "type": "text",
+        "text": "Resources usage In practical applications it is important to consider resources usage. All tested methods have relatively small overheads. For example, PackNet needs only $1 5 \\%$ more time than the baseline fine-tuning and it requires $5 0 \\%$ more neural network parameters (which is negligible when small networks like ours). See Appendix $\\underline { { \\mathbf { B . 4 } } }$ for details concerning other methods. ",
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+    {
+        "type": "text",
+        "text": "Other observations In stark contrast with the supervised learning setting, we found that replay based methods (Perfect Memory and A-GEM) suffer from poor performance. This is even though we allow for a generous replay, which could store the whole experience. Explaining and amending this situation is, in our view, an important research question. We conjecture that this happens due to the regularization of the critic network (which was unavoidable for these methods). We found multi-task learning attaining lower scores than PackNet, the best CL method and comparable to the second one, EWC. We think this suggests interesting research directions for multi-task learning. ",
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+    {
+        "type": "text",
+        "text": "6.1 RL-Related Challenges ",
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+        "type": "text",
+        "text": "Reinforcement learning brings a set of issues not present in the supervised learning setting, e.g., exploration, varying reward scales, and stochasticity of environments. We argue that it is imperative to have a reliable benchmark to assess the efficiency of CL algorithms with respect to these problems. We find that some current methods are not well adjusted to the RL setting and require non-trivial conceptual considerations and careful tuning of hyperparameters, see details in Appendix C. ",
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+        "type": "text",
+        "text": "An important design choice is whether or not to regularize the critic in the actor-critic framework (e.g. in SAC). We find it beneficial to focus on reducing forgetting in the actor while allowing the critic to freely adapt to the current task (note that critic is used only in training of the current task), similar to $\\dot { \\lVert \\ 4 6 \\rVert }$ . On the other hand, a forgetful critic is controversial. This can be sharply seen when the same task is repeated and the critic needs to learn from scratch. Additionally, not all methods can be trivially adapted to the ’actor-only regularization’ setting, as for example replay based methods. In Appendix $\\mathrm { \\Delta C }$ we examine these issues empirically, by showing experiments with critic regularization for EWC. ",
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+    {
+        "type": "text",
+        "text": "Another aspect is the exploration and its non-trivial impact on transfers. As it was observed, transfers from a given task to the same one are sometimes poor. We show in Appendix $\\textstyle \\boxed { \\mathrm { D . 1 } }$ that this results from the fact that at the task change the replay buffer is emptied and SAC collects new samples from scratch, usually by using the uniform policy. Learning on these random samples reduces performance on the current task and thus the forward transfer. Experimentally, we find that not resetting the buffer or using the current policy for exploration improves the transfer on the diagonal. ",
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+    {
+        "type": "text",
+        "text": "7 Conclusions and Future Work ",
+        "text_level": 1,
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+    {
+        "type": "text",
+        "text": "In this work, we present Continual World, a continual reinforcement learning benchmark, and an in-depth analysis of how existing methods perform on it. The benchmark is aimed at facilitating and standardizing the CL system evaluation, and as such, is released with code, including implementation of 7 representative CL algorithms. We argue for more attention to forward transfer and the interaction between forgetting and transfer, as many existing methods seem to sacrifice transfer to alleviate forgetting. In our opinion, this should not be the aim of CL, and we need to strike a different balance between these objectives. ",
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+    {
+        "type": "text",
+        "text": "We made several observations, both conceptual and empirical, which open future research directions. In particular, we conjecture that parameter isolation methods are a promising direction. Further, we identified a set of critical issues at the intersection of RL and CL. Resolving critic regularization and efficient use of multi-task replays seem to be the most pressing ones. Our benchmark highlights some challenges, which in our view are relevant and tangible now. In the long horizon, achieving high-level transfers, removing task boundaries, and scaling up are among significant goals for future editions of Continual World. Our work is foundational research and does not lead to any direct negative applications. ",
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+    {
+        "type": "text",
+        "text": "Acknowledgments and Disclosure of Funding ",
+        "text_level": 1,
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+    {
+        "type": "text",
+        "text": "We would like to thank Stanisław Jastrz˛ebski for stimulating talks and help while preparing the manuscript. The work of PM was supported by the Polish National Science Center grant UMO2017/26/E/ST6/00622. The work of MW was funded by Foundation for Polish Science (grant no POIR.04.04.00-00-14DE/18-00 carried out within the Team-Net program co-financed by the European Union under the European Regional Development Fund. This research was supported by the PL-Grid Infrastructure. Our experiments were managed using https://neptune.ai. We would like to thank the Neptune team for providing us access to the team version and technical support. ",
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+# MULTIPLE-ATTRIBUTE TEXT REWRITING
+Guillaume Lample∗1,3, Sandeep Subramanian∗1,2, Eric Michael Smith1, Ludovic Denoyer1,3, Marc’Aurelio Ranzato1, Y-Lan Boureau1
+1Facebook AI Research, 2MILA, Universite de Montr ´ eal ´ 3Sorbonne Universites, UPMC Univ Paris 06´ sandeep.subramanian.1@umontreal.ca {glample,ems,denoyer,ranzato,ylan}@fb.com
+# ABSTRACT
+The dominant approach to unsupervised “style transfer” in text is based on the idea of learning a latent representation, which is independent of the attributes specifying its “style”. In this paper, we show that this condition is not necessary and is not always met in practice, even with domain adversarial training that explicitly aims at learning such disentangled representations. We thus propose a new model that controls several factors of variation in textual data where this condition on disentanglement is replaced with a simpler mechanism based on back-translation. Our method allows control over multiple attributes, like gender, sentiment, product type, etc., and a more fine-grained control on the trade-off between content preservation and change of style with a pooling operator in the latent space. Our experiments demonstrate that the fully entangled model produces better generations, even when tested on new and more challenging benchmarks comprising reviews with multiple sentences and multiple attributes.
+# 1 INTRODUCTION
+One of the objectives of unsupervised learning is to learn representations of data that enable fine control over the underlying latent factors of variation, e.g., pose and viewpoint of objects in images, or writer style and sentiment of a product review. In conditional generative modeling, these latent factors are given (Sohn et al., 2015; Mirza & Osindero, 2014; Ficler & Goldberg, 2017), or automatically inferred via observation of samples from the data distribution (Chen et al., 2017; 2016; Higgins et al., 2017).
+More recently, several studies have focused on learning unsupervised mappings between two data domains such as images (Taigman et al., 2016; Isola et al., 2017; Zhu et al., 2017), words or sentences from different languages (Conneau et al., 2017; Lample et al., 2018).
+In this problem setting, the generative model is conditioned not only on the desired attribute values, but also on a initial input, which it must transform. Generations should retain as many of the original input characteristics as possible, provided the attribute constraint is not violated. This learning task is typically unsupervised because no example of an input and its corresponding output with the specified attribute is available during training. The model only sees random examples and their attribute values.
+The dominant approach to learn such a mapping in text is via an explicit constraint on disentanglement (Hu et al., 2017; Fu et al., 2017; Shen et al., 2017): the learned representation should be invariant to the specified attribute, and retain only attribute-agnostic information about the “content”. Changing the style of an input at test time then amounts to generating an output based on the disentangled latent representation computed from the input and the desired attributes. Disentanglement is often achieved through an adversarial term in the training objective that aims at making the attribute value unrecoverable from the latent representation.
+This paper aims to extend previous studies on “style transfer” along three axes. (i) First, we seek to gain a better understanding of what is necessary to make things work, and in particular, whether disentanglement is key, or even actually achieved by an adversarial loss in practice. In Sec. 3.1 we provide strong empirical evidence that disentanglement is not necessary to enable control over the factors of variation, and that even a method using adversarial loss to disentangle (Fu et al., 2017) does not actually learn representations that are disentangled. (ii) Second, we introduce a model which replaces the adversarial term with a back-translation (Sennrich et al., 2015a) objective which exposes the model to a pseudo-supervised setting, where the model’s outputs act as supervised training data for the ultimate task at hand. The resulting model is similar to recently proposed methods for unsupervised machine translation (Lample et al., 2017a; 2018; Artetxe et al., 2018; Zhang et al., 2018b), but with two major differences: (a) we use a pooling operator which is used to control the trade-off between style transfer and content preservation; and (b) we extend this model to support multiple attribute control. (iii) Finally, in Sec. 4.1 we point out that current style transfer benchmarks based on collections of user reviews have severe limitations, as they only consider a single attribute control (sentiment), and very small sentences in isolation with noisy labels. To address this issue, we propose a new set of benchmarks based on existing review datasets, which comprise full reviews, where multiple attributes are extracted from each review.
+![](images/da11a7f45c16bbf0db0da32d982ffaccddde31766a3e3cb06ac49351c81d17e8.jpg)
+The contributions of this paper are thus: (1) a deeper understanding of the necessary components of style transfer through extensive experiments, resulting in (2) a generic and simple learning framework based on mixing a denoising auto-encoding loss with an online back-translation technique and a novel neural architecture combining a pooling operator and support for multiple attributes, and (3) a new, more challenging and realistic version of existing benchmarks which uses full reviews and multiple attributes per review, as well as a comparison of our approach w.r.t. baselines using both new metrics and human evaluations. We will open-source our code and release the new benchmark datasets used in this work, as well as our pre-trained classifiers and language models for reproducibility. This will also enable fair empirical comparisons on automatic evaluation metrics in future work on this problem.
+# 2 RELATED WORK
+There is substantial literature on the task of unsupervised image translation. While initial approaches required supervised data of the form (input, transformation, output), e.g., different images of the same object rendered with different viewpoints or/and different lighting conditions (Hinton et al., 2011; Yang et al., 2015; Kulkarni et al., 2015), current techniques are capable of learning completely unsupervised domain mappings. Given images from two different domains $\mathcal { X }$ and $\mathcal { V }$ (where $\mathcal { X }$ could be the domain of paintings and $\mathcal { V }$ the domain of realistic photographs), and the task is to learn two mappings $F : \mathcal { X }  \mathcal { Y }$ and $G : \mathcal { y }  \mathcal { x }$ , without supervision, i.e., just based on images sampled from the two domains (Liu & Tuzel, 2016; Taigman et al., 2016; Isola et al., 2017). For instance, Zhu et al. (2017) used a cycle consistency loss to enforce $F ( G ( y ) ) \approx y$ and $G ( F ( x ) ) \approx x$ . This loss is minimized along with an adversarial loss on the generated outputs to constrain the model to generate realistic images. In Fader Networks (Lample et al., 2017b), a discriminator is applied on the latent representation of an image autoencoder to remove the information about specific attributes. The attribute values are instead given explicitly to the decoder at training time, and can be tuned at inference to generate different realistic versions of an input image with varying attribute values.
+Different approaches have been proposed for textual data, mainly aiming at controlling the writing style of sentences. Unfortunately, datasets of parallel sentences written in a different style are hard to come by. Carlson et al. (2017) collected a dataset of 33 English versions of the Bible written in different styles on which they trained a supervised style transfer model. Li et al. (2018) released a small crowdsourced subset of 1,000 Yelp reviews for evaluation purposes, where the sentiment had been swapped (between positive and negative) while preserving the content. Controlled text generation from unsupervised data is thus the focus of more and more research.
+An theme that is common to most recent studies is that style transfer can be achieved by disentangling sentence representations in a shared latent space. Most solutions use an adversarial approach to learn latent representations agnostic to the style of input sentences (Fu et al., 2017; Hu et al., 2017; Shen et al., 2017; Zhang et al., 2018a; Xu et al., 2018; John et al., 2018; Zhao et al., 2018). A decoder is then fed with the latent representation along with attribute labels to generate a variation of the input sentence with different attributes.
+Unfortunately, the discrete nature of the sentence generation process makes it difficult to apply to text techniques such as cycle consistency or adversarial training. For instance, the latter (Shen et al., 2017; dos Santos et al., 2018; Zhang et al., 2018c) requires methods such as REINFORCE (He et al., 2016) or approximating the output softmax layer with a tunable temperature (Hu et al., 2017; Prabhumoye et al., 2018; Yang et al., 2018), all of which tend to be slow, unstable and hard to tune in practice. Moreover, all these studies control a single attribute (e.g. swapping positive and negative sentiment).
+The most relevant work to ours is Zhang et al. (2018b), which also builds on recent advances in unsupervised machine translation. Their approach first consists of learning cross-domain word embeddings in order to build an initial phrase-table. They use this phrase-table to bootstrap an iterative back-translation pipeline containing both phrase-based and neural machine translation systems. Overall, their approach is significantly more complicated than ours, which is end-to-end and does not require any pre-training. Moreover, this iterative back-translation approach has been shown to be less effective than on-the-fly back-translation which is end-to-end trainable (Lample et al., 2018).
+# 3 CONTROLLABLE TEXT REWRITING
+This section briefly introduces notation, the task, and our empirical procedure for evaluating disentanglement before presenting our approach.
+We consider a training set $\mathcal { D } = \left( x ^ { i } , y ^ { i } \right) _ { i \in [ 1 , n ] }$ of $n$ sentences $x ^ { i } \in { \mathcal { X } }$ paired with attribute values $y ^ { i }$ . $y \in \mathcal { V }$ is a set of $m$ attribute values $y = ( y _ { 1 } , . . . , y _ { m } )$ . Each attribute value $y _ { k }$ is a discrete value in the set ${ \mathcal { V } } _ { k }$ of possible values for attribute $k$ , e.g. $\mathcal { V } _ { k } = \{ \mathrm { b a d } , \mathrm { n e u t r a l } , \mathrm { g o o d } \}$ if $y _ { k }$ represents the overall rating of a restaurant review.
+Our task is to learn a model $F : \mathcal { X } \times \mathcal { Y }  \mathcal { X }$ that maps any pair $( x , \tilde { y } )$ of an input sentence $x$ (whose actual set of attributes are $y$ ) and a new set of $m$ attribute values $\tilde { y }$ to a new sentence $\tilde { x }$ that has the specified attribute values $\tilde { y }$ , subject to retaining as much as possible of the original content from $x$ , where content is defined as anything in $x$ which does not depend on the attributes.
+The architecture we consider performs this mapping through a sequence-to-sequence auto-encoder that first encodes $x$ into a latent representation $z = e ( x )$ , then decodes $( z , \tilde { y } )$ into $\tilde { x } = d ( z , \tilde { y } )$ , where $e$ and $d$ are functions parameterized by the vector of trainable parameters $\theta$ . Before giving more detail on the architecture, let us look at disentanglement.
+# 3.1 ARE ADVERSARIAL MODELS REALLY DOING DISENTANGLEMENT?
+Almost all the existing methods are based on the common idea to learn a latent representation $z$ that is disentangled from $y$ . We consider $z$ to be disentangled from $y$ if it is impossible to recover $y$ from $z$ . While failure to recover $y$ from $z$ could mean either that $z$ was disentangled or that the classifier
+chosen to recover $y$ was either not powerful enough or poorly trained, success of any classifier in recovering $y$ demonstrates that $z$ was in fact not invariant to $y$ .
+Table 2: Recovering the sentiment of the input from the encoder’s representations of a domain adversarially-trained Fader model $\mathrm { F u }$ et al., 2017). During training, the discriminator, which was trained adversarially and jointly with the model, gets worse at predicting the sentiment of the input when the coefficient of the adversarial loss $\lambda _ { a d v }$ increases. However, a classifier that is separately trained on the resulting encoder representations has an easy time recovering the sentiment. We also report the baseline accuracy of a fastText classifier trained on the actual inputs.
+<table><tr><td>Xadu</td><td>Discriminator Acc (Train)</td><td>Post-fit Classifier Acc (Test)</td></tr><tr><td>0</td><td>89.45%</td><td>93.8%</td></tr><tr><td>0.001</td><td>85.04%</td><td>92.6%</td></tr><tr><td>0.01</td><td>75.47%</td><td>91.3%</td></tr><tr><td>0.03</td><td>61.16%</td><td>93.5%</td></tr><tr><td>0.1</td><td>57.63%</td><td>94.5%</td></tr><tr><td>1.0</td><td>52.75%</td><td>86.1%</td></tr><tr><td>10</td><td>51.89%</td><td>85.2%</td></tr><tr><td>fastText</td><td>1</td><td>97.7%</td></tr></table>
+As a preliminary study, we gauge the degree of disentanglement of the latent representation. Table 2 shows that the value of the attribute can be well recovered from the latent representation of a Faderlike (Fu et al., 2017) model even when the model is trained adversarially. A classifier fit post-hoc and trained from scratch, parameterized identically to the discriminator(see paragraph on model architecture in Section 3.3 for details), is able to recover attribute information from the ”distengeled” content representation learned via adversarial training. This suggests that disentanglement may not be achieved in practice, even though the discriminator is unable to recover attribute information well during training. We do not assert that disentangled representations are undesirable but simply that it isn’t mandatory in the goal of controllable text rewriting. This is our focus in the following sections.
+# 3.2 OUR APPROACH
+Evaluation of controlled text generation can inform the design of a more streamlined approach: generated sentences should (1) be fluent, (2) make use of the specified attribute values, and (3) preserve the rest of the content of the input.
+Denoising auto-encoding (DAE) $\mathrm { F u }$ et al., 2017) is a natural way to learn a generator that is both fluent and that can reconstruct the input, both the content and the attributes. Moreover, DAE is a weak way to learn about how to change the style, or in other words, it is a way to force the decoder to also leverage the externally provided attribute information. Since the noise applied to the encoder input $x$ may corrupt words conveying the values of the input attribute $y$ , the decoder has to learn to use the additional attribute input values in order to perform a better reconstruction. We use the noise function described in Lample et al. (2017a) that corrupts the input sentence by performing word drops and word order shuffling. We denote by $x _ { c }$ a corrupted version of the sentence $x$ .
+As discussed in Sec. 3.1, disentanglement is not necessary nor easily achievable, and therefore, we do not seek disentanglement and do not include any adversarial term in the loss. Instead, we consider a more natural constraint which encourages the model to perform well at the task we are ultimately interested in - controlled generation via externally provided attributes. We take an input $( x , y )$ and encode $x$ it into $z$ , but then decode using another set of attribute values, $\tilde { y }$ , yielding the reconstruction $\tilde { x }$ . We now use $\tilde { x }$ as input of the encoder and decode it using the original $y$ to ideally obtain the original $x$ , and we train the model to map $( \tilde { x } , y )$ into $x$ . This technique, called back-translation (BT) (Sennrich et al., 2015a; Lample et al., 2017a; 2018; Artetxe et al., 2018), has a two-fold benefit. Initially when the DAE is not well trained and $\tilde { x }$ has lost most of the content present in $x$ , the only useful information provided to the decoder is the desired attribute $y$ . This encourages the decoder to leverage the provided attributes. Later on during training when DAE is better, BT helps training the sequence-to-sequence for the desired task. Overall, we minimize:
+$$
+\mathcal { L } = \lambda _ { A E } \sum _ { ( x , y ) \sim \mathcal { D } } - \log p _ { d } \Big ( x | e ( x _ { c } ) , y \Big ) + \lambda _ { B T } \sum _ { ( x , y ) \sim \mathcal { D } , \tilde { y } \sim \mathcal { Y } } - \log p _ { d } \Big ( x | e \Big ( d \big ( e ( x ) , \tilde { y } ) \Big ) , y \Big )
+$$
+where $p _ { d }$ is the probability distribution over sequences $x$ induced by the decoder, $e ( x _ { c } )$ is the encoder output when fed with a corrupted version $x _ { c }$ of the input $x$ , and $d ( e ( x ) , \tilde { y } )$ is a variation of the input sentence $x$ written with a randomly sampled set of attributes $\tilde { y }$ . In practice, we generate sentences during back-translation by sampling from the multinomial distribution over words defined by the decoder at each time step using a temperature $T$ .
+# 3.3 IMPLEMENTATION
+So far, the model is the same as the model used for unsupervised machine translation by Lample et al. (2018), albeit with a different interpretation of its inner workings, no longer based on disentanglement. Instead, the latent representation $z$ can very well be entangled, but we only require the decoder to eventually “overwrite” the original attribute information with the desired attributes. Unfortunately, this system may be limited to swapping a single binary attribute and may not give us enough control on the trade-off between content preservation and change of attributes. To address this limitations, we introduce the following components:
+Attribute conditioning In order to handle multiple attributes, we separately embed each target attribute value and then average their embeddings. We then feed the averaged embeddings to the decoder as a start-of-sequence symbol.
+We also tried an approach similar to Michel & Neubig (2018), where the output layer of the decoder uses a different bias for each attribute label. We observed that the learned biases tend to reflect the labels of the attributes they represent. Examples of learned biases can be found in Table 14. However, this approach alone did not work as well as using attribute-specific start symbols, nor did it improve results when combined with them.
+Latent representation pooling To control the amount of content preservation, we use pooling. The motivating observation is that models that compute one latent vector representation per input word usually perform individual word replacement, while models without attention are much less literal and tend to lose content but have an easier time changing the input sentence with the desired set of attributes. Therefore, we propose to gain finer control by adding a temporal max-pooling layer on top of the encoder, with non-overlapping windows of width $w$ . Setting $w = 1$ results in a standard model with attention, while setting $w$ to the length of the input sequence boils down to a sequence-to-sequence model without attention. Intermediate values of $w$ allow for different tradeoffs between preserving information about the input sentence and making the decoder less prone to copying words one by one.
+The hyper-parameters of our model are: $\lambda _ { A E }$ and $\lambda _ { B T }$ trading off the denoising auto-encoder term versus the back-translation term (the smaller the $\lambda _ { B T } / \lambda _ { A E }$ ratio the more the content is preserved and the less well the attributes are swapped), the temperature $T$ used to produce unbiased generations (Edunov et al., 2018) and to control the amount of content preservation, and the pooling window size $w$ . We optimize this loss by stochastic gradient descent without back-propagating through the back-translation generation process; back-translated sentences are generated on-the-fly once a new mini-batch arrives.
+Model Architecture We use an encoder parameterized by a 2-layer bidirectional LSTM and a 2- layer decoder LSTM augmented with an attention mechanism (Bahdanau et al., 2014). Both LSTMs and our word embedding lookup tables, trained from scratch, have 512 hidden units. Another embedding lookup table with 512 hidden units is used to embed each attribute value. The decoder conditions on two different sources of information: 1) attribute embedding information that presented that it as the first token, similar to Lample et al. (2018) and at the softmax output as an attribute conditional bias following Michel & Neubig (2018). When controlling multiple attributes, we average the embeddings and bias vectors that correspond to the different attribute values. 2) The decoder also conditions on a temporally downsampled representation of the encoder via an attention mechanism. The representations are downsampled by temporal max-pooling with a non-overlapping window of size 5. Although our best models do not use adversarial training, in ablations and experiments that study disentanglement, we used a discriminator paramaeterized as 3 layer MLP with 128 hidden units and LeakyReLU acivations.
+# 4 EXPERIMENTS
+# 4.1 DATASETS
+We use data from publicly available Yelp restaurant and Amazon product reviews following previous work in the area (Shen et al., 2017; Li et al., 2018) and build on them in three ways to make the task more challenging and realistic. Firstly, while previous approaches operate at the sentence level by assuming that every sentence of a review carries the same sentiment as the whole of review, we operate at the granularity of entire reviews. The sentiment, gender1 of the author and product/restaurant labels are therefore more reliable. Secondly, we relax constraints enforced in prior works that discard reviews with more than 15 words and only consider the $1 0 \mathrm { k }$ most frequent words. In our case, we consider full reviews with up to 100 words, and we consider byte-pair encodings (BPE) Sennrich et al. (2015b) with $6 0 \mathrm { k }$ BPE codes, eliminating the presence of unknown words. Finally, we leverage available meta-data about restaurant and product categories to collect annotations for two additional controllable factors: the gender of the review author and the category of the product or restaurant being reviewed. A small overview of the corresponding datasets is presented below with some statistics presented in Table 3. Following Li et al. (2018), we also collect human reference edits for sentiment and restaurant/product categories to serve as a reference for automatic metrics as well as an upper bound on human evaluations (examples in Appendix Table 12).
+Yelp Reviews This dataset consists of restaurant and business reviews provided by the Yelp Dataset Challenge2. We pre-process this data to remove reviews that are either 1) not written in English according to a fastText (Joulin et al., 2016) classifier, 2) not about restaurants, 3) rated 3/5 stars as they tend to be neutral in sentiment (following Shen et al. (2017)), or 4) where the gender is not identifiable by the same method as in Reddy & Knight (2016); Prabhumoye et al. (2018). We then binarize both sentiment and gender labels. Five coarse-grained restaurant category labels, Asian, American, Mexican, Bars & Dessert, are obtained from the associated meta-data. Since a review can be written about a restaurant that has multiple categories (ex: an Asian restaurant that serves desserts), we train a multi-label fastText classifier to the original data that has multiple labels per example. We then re-label the entire dataset with this classifier to pick the most likely category to be able to model the category factor as a categorical random variable. (See Appendix section A.2 for more details.) Since there now exists two variants of the Yelp dataset, we refer to the one used by previous work (Shen et al., 2017; Fu et al., 2017; Li et al., 2018) as SYelp and our created version with full reviews along with gender and category information as FYelp henceforth.
+Amazon Reviews The amazon product review dataset (He & McAuley, 2016) is comprised of reviews written by consumers of Amazon products. We followed the same pre-processing steps as in the Yelp dataset with the exception of collecting gender labels, since a very large fraction of amazon usernames were not present in a list of gender-annotated names. We labeled reviews with the following product categories based on the meta-data: Books, Clothing, Electronics, Movies, Music. We followed the same protocol as in $F Y e l p$ to re-label product categories. In this work, we do not experiment with the version of the Amazon dataset used by previous work, and so we refer to our created version with full reviews along with product category information as just Amazon henceforth. Statistics about the dataset can be found in Table 3.
+Public social media content We also used an unreleased dataset of public social media content written by English speakers to illustrate the approach with examples from a more diverse set of categories3. We used 3 independent pieces of available information about that content: 1) gender (male or female) 2) age group (18-24 or $6 5 +$ ), and 3) writer-annotated feeling (relaxed or annoyed).
+<table><tr><td></td><td colspan="2">Sentiment</td><td colspan="2">Gender</td><td colspan="5">Category</td></tr><tr><td>SYelp</td><td>Positive 266,041</td><td>Negative 177,218</td><td>Male -</td><td>Female -</td><td>American =</td><td>Asian -</td><td>Bar -</td><td>Dessert -</td><td>Mexican =</td></tr><tr><td>FYelp</td><td>Positive 2.056,132</td><td>Negative 639,272</td><td>Male 1,218,068</td><td>Female 1,477,336</td><td>American 904,026</td><td>Asian 518,370</td><td>Bar 595,681</td><td>Dessert 431,225</td><td>Mexican 246,102</td></tr><tr><td>Amazon</td><td>Positive 64,251,073</td><td>Negative 10,944,310</td><td>=</td><td>·</td><td>Book 26,208,872</td><td>Clothing 14,192,554</td><td>Electronics 25,894,877</td><td>Movies 4,324,913</td><td>Music 4,574,167</td></tr><tr><td>Social Media Content</td><td>Relaxed 7,682.688</td><td>Annoyed 17,823,468</td><td>Male</td><td>= Female 18,463,789</td><td>18-24 12,628,250</td><td>65+ 7,629,505</td><td></td><td></td><td></td></tr></table>
+Table 3: The number of reviews for each attribute for different datasets. The SYelp, FYelp and the Amazon datasets are composed of $4 4 3 \mathrm { k \Omega }$ , 2.7M and $7 5 . 2 \mathbf { M }$ sentences respectively. Public social media content is collected from 3 different data sources with 25.5M, 33.0M and $2 0 . 2 \mathbf { M }$ sentences for the Feeling, Gender and $A g e$ attributes respectively.
+To make the data less noisy, we trained a fastText classifier (Joulin et al., 2016) for each attribute and only kept the data above a certain confidence threshold.
+# 4.2 EVALUATION
+Automatic evaluation of generative models of text is still an open research problem. In this work, we use a combination of multiple automatic evaluation criteria informed by our desiderata. We would like our systems to simultaneously 1) produce sentences that conform to the set of pre-specified attribute(s), 2) preserve the structure and content of the input, and 3) generate fluent language. We therefore evaluate samples from different models along three different dimensions:
+• Attribute control: We measure the extent to which attributes are controlled using fastText classifiers, trained on our datasets, to predict different attributes.
+• Fluency: Fluency is measured by the perplexity assigned to generated text sequences by a pre-trained Kneser–Ney smooth 5-gram language model using KenLM (Heafield, 2011).
+• Content preservation: We measure the extent to which a model preserves the content present of a given input using n-gram statistics, by measuring the BLEU score between generated text and the input itself, which we refer to as self-BLEU. When a human reference is provided instead, we compute the BLEU score with respect to it, instead of the input, which we will refer to as just BLEU (Papineni et al., 2002). “BLEU” scores in this paper correspond to the BLEU score with respect to human references averaged across generations conditioned on all possible attribute values except for that of the input. However, when reporting self-BLEU scores, we also average across cases where generations are also conditioned on the same attribute value as the input.
+A combination of these metrics, however, only provides a rough understanding of the quality of a particular model. Ultimately, we rely on human evaluations collected via a public crowd-sourcing platform. We carried out two types of evaluations to compare different models. 1) Following a protocol similar to Li et al. (2018), we ask crowd workers to annotate generated sentences along the three dimensions above. Fluency and content preservation are measured on a likert-scale from 1 to 5 and attribute control is evaluated by asking the worker to predict the attribute present in the generated text. 2) We take a pair of generations from two different models, and ask workers to pick the generation they prefer on the overall task, accounting for all the dimensions simultaneously. They are also presented with a “no preference” option to discard equally good or bad generations from both models.
+# 4.3 MODEL SELECTION
+Since our automatic evaluation metrics are only weak proxies for the quality of a model, we set minimum thresholds on the content preservation and attribute control criteria and only consider models above a certain threshold.
+The few models that met the specified threshold on the validation set were evaluated by humans on the same validation set and the best model was selected to be run on the test set.
+Table 4: Automatic evaluation of models on the $S Y e l p$ test set from Li et al. (2018). The test set is composed of sentences that have been manually written by humans, which we use to compute the BLEU score. Samples for previous models were made available by Li et al. (2018). For our model, we report different results corresponding to different choices of hyper-parameters (pooling kernel width and back-translation temperature) to demonstrate our model’s ability to control the trade-off between attribute transfer and content preservation.
+<table><tr><td>Model</td><td>Accuracy</td><td>BLEU</td><td>PPL</td></tr><tr><td>Fader/StyleEmbedding (Fu et al., 2017) MultiDecoder (Fu et al., 2017) ControllableText (Hu et al., 2017)</td><td>18% 52% 85%</td><td>16.7 11.3 20.6</td><td>56.1 90.1 232.0</td></tr><tr><td>CAE (Shen et al., 2017) Retrieval (Li et al., 2018) Rule-based (Li et al., 2018)</td><td>72% 81% 73%</td><td>6.8 1.3</td><td>53.0 7.4</td></tr><tr><td>DeleteOnly (Li et al., 2018) DeleteAndRetrieve (Li et al., 2018)</td><td>77%</td><td>22.3 14.5</td><td>118.7 67.1</td></tr><tr><td></td><td>79%</td><td>16.0</td><td>66.6</td></tr><tr><td>Fader(Ours w/o backtranslation &amp; attention)</td><td>71%</td><td></td><td></td></tr><tr><td>Ours Ours</td><td>87% 85%</td><td>15.7 14.6</td><td>35.1 26.2</td></tr></table>
+# 4.4 COMPARISONS TO PRIOR WORK
+Our first set of experiments aims at comparing our approach with different models recently proposed, on the SYelp dataset. Results using automatic metrics are presented in Table 4. We compare the same set of models as in Li et al. (2018) with the addition of our model and our own implementation of the Fader network (Lample et al., 2017b), which corresponds to our model without back-translation and without attention mechanism, but uses domain adversarial training (Ganin et al., 2016) to remove information about sentiment from the encoder’s representation. This is also similar to the StyleEmbedding model presented by Fu et al. (2017). For our approach, we were able to control the trade-off between BLEU and accuracy based on different hyper-parameter choices. We demonstrate that our approach is able to outperform all previous approaches on the three desired criteria simultaneously, while our implementation of the fader is competitive with the previous best work.
+Table 5: Top: Results from human evaluation to evaluate the fluency / content preservation and successful sentiment control on the Li et al. (2018) SYelp test set. The mean and standard deviation of Fluency and Content are measured on a likert scale from 1-5 while sentiment is measured by fraction of times that the controlled sentiment of model matches the judge’s evaluation of the sentiment (when also presented with a neutral option). Bottom: Results from human A/B testing of different pairs of models. Each cell indicates the fraction of times that a judge preferred one of the models or neither of them on the overall task.)
+<table><tr><td></td><td>Fluency</td><td>Content</td><td>Sentiment</td></tr><tr><td>DAR (Li et al. (2018))</td><td>3.33 (1.39)</td><td>3.16 (1.43)</td><td>64.05%</td></tr><tr><td>Ours</td><td>4.07 (1.12)</td><td>3.67 (1.41)</td><td>69.66%</td></tr><tr><td>Human (Li et al. (2018))</td><td>4.56 (0.78)</td><td>4.01 (1.25)</td><td>81.35%</td></tr><tr><td></td><td>Our Model</td><td>No Preference</td><td>DAR</td></tr><tr><td>DAR vs Our Fader</td><td>37.6%</td><td>32.7%</td><td>29.7%</td></tr><tr><td>DAR vs Ours</td><td>54.4%</td><td>24.7%</td><td>20.8%</td></tr></table>
+Since our automatic evaluation metrics are not ideal, we carried out human evaluations using the protocol described in Section 4.2. Table 5 (top) shows the fluency, content preservation and attribute control (sentiment) scores obtained by our model, DeleteAndRetrieve (DAR) and turkers from Li et al. (2018) 4 on the SYelp dataset. While humans clearly outperform both models, our model is better than DeleteAndRetrieve on all 3 dimensions. We further demonstrate our model’s strength over DeleteAndRetrieve in Table 5 (bottom) in an $\mathrm { A } / \mathrm { B }$ test between two the models, where crowd workers prefer our model $5 4 . 4 \%$ compared to theirs $2 0 . 8 \%$ . Interestingly, our baseline Fader model is also able to do better $( 3 7 . 6 \%$ vs $2 9 . 7 \%$ ), suggesting limitations in our automatic metrics, since Fader does not do as well in Table 4.
+4.5 EVALUATING MULTIPLE ATTRIBUTE CONTROL
+<table><tr><td rowspan="2">Dataset (Model)</td><td rowspan="2">Attributes</td><td colspan="2">Sentiment</td><td colspan="2">Category</td><td colspan="2">Gender</td></tr><tr><td>Accuracy</td><td>self-BLEU</td><td>Accuracy</td><td>self-BLEU</td><td>Accuracy</td><td>self-BLEU</td></tr><tr><td>Yelp (DAR)</td><td>Sentiment</td><td>78.7%</td><td>42.1</td><td>-</td><td>-</td><td>1</td><td>-</td></tr><tr><td rowspan="3">Yelp (Our Fader)</td><td>Sentiment</td><td>85.5%</td><td>31.3</td><td>=</td><td>=</td><td></td><td></td></tr><tr><td>Sentiment+ Category</td><td>85.1%</td><td>20.6</td><td>46.1%</td><td>22.6</td><td>-</td><td>-</td></tr><tr><td>Sentiment + Category +Gender</td><td>86.6%</td><td>20.4</td><td>47.7%</td><td>22.5</td><td>58.5%</td><td>23.3</td></tr><tr><td rowspan="4">Yelp (Ours)</td><td>Sentiment</td><td>87.4%</td><td>54.5</td><td>-</td><td>1</td><td>1</td><td>-</td></tr><tr><td>Sentiment + Category</td><td>87.1%</td><td>38.8</td><td>64.9%</td><td>44.0</td><td>1</td><td>-</td></tr><tr><td>Sentiment +Category +Gender</td><td>88.5%</td><td>31.6</td><td>64.1%</td><td>36.5</td><td>59.0%</td><td>37.4</td></tr><tr><td>Gender</td><td>-</td><td>1</td><td>-</td><td>1</td><td>59.1%</td><td>47.0</td></tr><tr><td rowspan="2">Amazon (Ours)</td><td>Sentiment</td><td>82.6%</td><td>54.8</td><td>-</td><td>-</td><td>-</td><td>-</td></tr><tr><td>Sentiment + Category</td><td>82.5%</td><td>48.9</td><td>81.4%</td><td>41.8</td><td>-</td><td>-</td></tr><tr><td>Input Copy</td><td>1</td><td>50.0%</td><td>100.0</td><td>20.0%</td><td>100.0</td><td>50.0%</td><td>100.0</td></tr></table>
+Table 6: Results using automatic evaluation metrics on the FYelp and Amazon test sets. Different rows correspond to the set of attributes being controlled by the model.
+Table 6 presents the quantitative results obtained by the $F Y e l p$ and Amazon datasets when controlling single and multiple attributes. For this table, unlike for Table 4, the DeleteAndRetrieve (DAR) results were obtained by re-training the model of Li et al. (2018). We use our implementation of the Fader model since we found it to be better than previous work, by human evaluation (Table 5). While we control all attributes simultaneously during training, at test time, for the sake of quantitative evaluations, we change the values only of a single attribute while keeping the others constant. Our model clearly outperforms the baseline Fader model. We also demonstrate that our model does not suffer significant drops in performance when controlling multiple attributes over a single one.
+Demonstrations of our model’s ability to control single and multiple attributes are presented in Table 8 and Table 9 respectively. What is interesting to observe is that our model does not just alter single words in the input to control an attribute, but often changes larger fragments to maintain grammaticality and fluency. Examples of re-writes by our model on social media content in Table 1 show that our model tends to retain the overall structure of input sentences, including punctuation and emojis. Additional examples of re-writes can be found in Table 10 and Table 11 in Appendix.
+# 4.6 ABLATION STUDY
+Table 7: Model ablations on 5 model components on the FYelp dataset (Left) and SYelp (Right).
+<table><tr><td rowspan="2">Model</td><td colspan="2">Test (FYelp)</td><td colspan="2">Test (Li et al., 2018)</td></tr><tr><td>Accuracy</td><td>self-BLEU</td><td>Accuracy</td><td>BLEU</td></tr><tr><td>Our model</td><td>87%</td><td>54.5</td><td>80%</td><td>25.8</td></tr><tr><td>-pooling</td><td>89%</td><td>47.9</td><td>-</td><td>=</td></tr><tr><td>-temperature</td><td>86%</td><td>45.2</td><td>80%</td><td>21.3</td></tr><tr><td>-attention</td><td>93%</td><td>25.4</td><td>80%</td><td>22.1</td></tr><tr><td>-back-translation</td><td>86%</td><td>32.8</td><td>69%</td><td>16.4</td></tr><tr><td>+adversarial</td><td>86%</td><td>45.5</td><td>78%</td><td>25.1</td></tr><tr><td>-attention -back-translation</td><td>90%</td><td>26.0</td><td>71%</td><td>15.7</td></tr></table>
+In Table 7, we report results from an ablation study on the SYelp and FYelp datasets to understand the impact of the different model components on overall performance. The different components are: 1) pooling, 2) temperature based multinomial sampling when back-translating, 3) attention, 4) back-translation, 5) the use of domain adversarial training and 6) attention and back-translation in conjunction. We find that a model with all of these components, except for domain adversarial training, performs the best, further validating our hypothesis in Section 3.1 that it is possible to control attributes of text without disentangled representations. The absence of pooling or softmax temperature when back-translating also has a small negative impact on performance, while the attention and back-translation have much bigger impacts.
+![](images/22c8bd2dd3d8757fd8eb2d089311253fd3359a752c2011fe4c111dbc5a11cebd.jpg)
+Figure 1: Accuracy and self-BLEU curves on the FYelp dataset for different pooling operator configurations. Without pooling, the model tends to converge to a copy mode very quickly, with a high self-BLEU score and a poor accuracy. The pooling operator alleviates this behaviour and provides models with a different trade-off accuracy / content preservation.
+Table 13 shows examples of reviews re-written by different models at different checkpoints, showing the trade-off between properly modifying the attribute and preserving the original content. Figure 1 shows how the trade-off between content preservation (self-BLEU) and attribute control (accuracy) evolves over the course of training and as a function of the pooling kernel width.
+# 5 CONCLUSION
+We present a model that is capable of re-writing sentences conditioned on given attributes, that is not based on a disentanglement criterion as often used in the literature. We demonstrate our model’s ability to generalize to a realistic setting of restaurant/product reviews consisting of several sentences per review. We also present model components that allow fine-grained control over the trade-off between attribute control versus preserving the content in the input. Experiments with automatic and human-based metrics show that our model significantly outperforms the current state of the art not only on existing datasets, but also on the large-scale datasets we created. The source code and benchmarks will be made available to the research community after the reviewing process.
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+# A SUPPLEMENTARY MATERIAL
+# A.1 TRAINING DETAILS
+We used the Adam optimizer (Kingma & Ba, 2014) with a learning rate of $1 0 ^ { - 4 }$ , $\beta _ { 1 } = 0 . 5$ , and a batch size of 32. As in Lample et al. (2018), we fix $\lambda _ { B T } = 1$ , and set $\lambda _ { A E }$ to 1 at the beginning of the experiment, and linearly decrease it to 0 over the first 300, 000 iterations. We use greedy decoding at inference. When generating pseudo-parallel data via back-translation, we found that increasing the temperature over the course of training from greedy generation to multinomial sampling with a temperature of 0.5 linearly over 300,000 steps was useful (Edunov et al., 2018). Since the class distribution for different attributes in both the Yelp and Amazon datasets are skewed, we train with balanced minibatches when there is only a single attribute being controlled and with independent and uniformly sampled attribute values otherwise. The synthetic target attributes during back-translation $\tilde { y }$ are also balanced by uniform sampling.
+# A.2 DATASET CREATION DETAILS
+In addition to the details presented in Section 4.1, we present additional details on the creation of the $F Y e l p$ and Amazon datasets.
+FYelp: Reviews, their rating, user information and restaurant/business categories are obtained from the available metadata. We construct sentiment labels by grouping 1/2 star ratings into the negative category and 4/5 into the positive category while discarding 3 star reviews. To determine the gender of the person writing a review, we obtain their name from the available user information and then look it up in a list of gendered names5 following Prabhumoye et al. (2018); Reddy & Knight (2016). We discard reviews for which we were unable to obtain gender information with this technique. Restaurant/business category meta-data is available for each review, from which we discard all reviews that were not written about restaurants. Amongst restaurant reviews, we manually group restaurant categories into “parent” categories to cover a significant fraction of the dataset. The grouping is as follows:
+• Asian - Japanese, Thai, Ramen, Sushi, Sushi Bar, Chinese, Asian Fusion, Vietnamese, Korean, Noodles, Dim Sum, Cantonese, Filipino, Taiwanese
+• American - American (New), American (Traditional), Canadian (New), Southern
+• Mexican/Latin American - New Mexican Cuisine, Mexican, Tacos, Tex-Mex, Tapas Bars, Latin American
+• Bars - Brasseries, Nightlife, Bars, Pubs, Wine Bars, Sports Bars, Beer, Cocktail Bars
+• Desserts - Desserts, Bakeries, Ice Cream & Frozen Yogurt, Juice Bars & Smoothies Donuts, Cupcakes, Chocolatiers & Shops
+As described in Section 4.1, we train a classifier on these parent categories and relabel the entire dataset using this.
+Amazon: Reviews, their rating, user information and restaurant/business categories are obtained from the metadata made available by He & McAuley (2016). We construct sentiment labels in the same manner as in FYelp. We did not experiment with gender labels, since we found that Amazon usernames seldom use real names. We group Amazon product categories into “parent categories” manually, similar to FYelp as follows:
+• Books - Books, Books & Comics, Children’s Books, Literature & Fiction, Comic Books, Kindle eBooks etc.
+• Electronics - Car Electronics, Cell Phones, Electrical & Electronics, Electronics, Electronics & Gadgets, Mobiles, Tablets, Headphones etc.
+• Movies - Movies, Movies & TV, Movies & Video, TV & Film
+• Clothing - Clothing, Shoes & Jewelry, Baby Clothing, Fashion
+• Music - CDs & Vinyl, Music, Digital Music, Children’s Music, World Music, Electronic Music
+We relabel reviews with a trained product category classifier similar to $F Y e l p$ .
+For the FYelp and Amazon datasets, we normalize, lowercase and tokenize reviews using the moses (Koehn et al., 2007) tokenizer. With social media content, we do not lowercase data in order to exploit interesting capitalization patterns inherent in the data, but we still run other pre-processing steps. We use byte-pair encodings (BPE) (Sennrich et al., 2015b) with 60k replacements, on all 3 datasets, to deal with large vocabulary sizes.
+Human Annotated References Li et al. (2018) released a set of human reference edits when controlling the sentiment of a review, on a test set of 500 examples on the SYelp dataset. We follow suit by collecting a similar dataset of 500 human reference edits, which will be made publicly available, for both sentiment and product categories on the FYelp and Amazon datasets. When collecting such data, we use pre-trained sentiment/category classifiers to interactively guide crowd workers using the ParlAI (Miller et al., 2017) platform, to produce edits with the desired attribute value as well as significant content overlap with the input.
+# A.3 ADDITIONAL QUALITATIVE EXAMPLES
+<table><tr><td rowspan=1 colspan=2>Positive ←Negative (Yelp)</td></tr><tr><td rowspan=1 colspan=2>Positive   frozen hot chocolate with peanut butter cups = amazing.i&#x27;ll be back for some food next time!Negative  frozen hot chocolate with peanut butter ? horrible.i&#x27;ll stick with the coffee shop next door!</td></tr><tr><td rowspan=1 colspan=2>Negative   one Word: underwhelming.save your money and find the many restaurants in vegas that ofers areal experience.Positive   one word: delicious.save room for the best and most authentic indian food in vegas.</td></tr><tr><td rowspan=1 colspan=2>Asian ←Mexican(Yelp)</td></tr><tr><td rowspan=1 colspan=2>Asian     best thai food i&#x27;ve ever had in the us.great duck specials on monday.. best yellow curry fried rice..Mexican   best mexican food i&#x27;ve ever had in my life.great guacamole on the side..best carnitas tacos i have ever had..</td></tr><tr><td rowspan=1 colspan=2>Mexican  awesome carne asada! try the papa verde with steak! it&#x27;s delicious and the portions are great!Asian     awesome orange chicken!try the orange chicken with the spicy sauce! it&#x27;s delicious and the portions are great!</td></tr><tr><td rowspan=1 colspan=2>MaleFemale (Yelp)</td></tr><tr><td rowspan=2 colspan=2>Male     good food.my wife and i always enjoy coming here for dinner.irecommend india garden.Female    good food.my husband and i always stop by here for lunch.irecommend the veggie burrito.</td></tr><tr><td rowspan=1 colspan=1>Female</td></tr><tr><td rowspan=1 colspan=1>Female</td><td rowspan=1 colspan=1>Female    we are regulars here... me n my husband just gorge on these freaking amazing donuts!! loved itMale     we are regulars here...every time we come here she loves the new york style pizza!!!!</td></tr><tr><td rowspan=1 colspan=2>Positive Negative (Amazon)</td></tr><tr><td rowspan=2 colspan=2>Positive   ilovethis game.takes patience and strategy,goonlineand look forhints and cheats,they helpalot.great game!!!Negative  idon&#x27;tlikethis game.ittakesalotoftimetofgureouthowtoplay,anditdoesn&#x27;t work.iwouldnotrecommendthisgame.</td></tr><tr><td rowspan=1 colspan=1>Negative</td><td rowspan=1 colspan=1>veidor</td></tr><tr><td rowspan=1 colspan=1>Negative</td><td rowspan=1 colspan=1>Negative  i did notlike theconflicting historical data.what was realand what was not.iprefer fiction with facts intact.Positive   i enjoyed the historical references.what a great read and iloved it.i highly recommend this book.</td></tr><tr><td rowspan=1 colspan=2>Movies ←Books (Amazon)</td></tr><tr><td rowspan=1 colspan=2>Movies    very good movie withoutstandingspecial efects irecommend this toallshifilovers.good acting great plotlotsof actionBooks    very goodbook withoutstanding characterdevelopmentirecommend this toallthereaders.good jobgreatplottwistsandturns</td></tr><tr><td rowspan=1 colspan=2>Books    definitely not a stone barrington book,but a story told that keeps you wanting more.great read!Movies    definitely nota film noir,buta story that keeps youon theedge of your seat.great acting and a great story.</td></tr><tr><td rowspan=1 colspan=2>Clothing Electronics (Amazon)</td></tr><tr><td rowspan=1 colspan=2>Clothing   gotthis cause it said it would help with tennis elbow and guess what my tennis elbow stillbothering meElectronicsgot this cause it said it would help with windows xp and guess what my windows xp still crashed</td></tr><tr><td rowspan=1 colspan=2>Electronicsi have no choice.this is the only black ink that works with my printer.Clothing   i have no choice.this is the only black color that works with my dress.</td></tr></table>
+Table 8: Example re-writes by our model on the FYelp and Amazon datasets when controlling a single attribute. The first line in every box is the pre-specified input with its attribute on the left, and the subsequent line is our model’s re-write conditioned on a different attribute value.
+Table 9: Demonstrations of our model’s ability to control multiple attributes simultaneously on the Amazon dataset (top) and FYelp dataset (bottom). The first two columns indicate the combination of attributes that are being controlled, with the first row indicating a pre-specified input
+<table><tr><td>Sentiment</td><td>Category</td><td>Input/Generations</td></tr><tr><td colspan="3">Amazon</td></tr><tr><td>Positive</td><td>Movies</td><td>exciting new show. john malkovich is superb as always.great supporting cast.hope it survives beyond season1</td></tr><tr><td>Positive</td><td>Books</td><td>exciting new book. john grisham is one of the best. great read. hope he continues to write more.</td></tr><tr><td>Negative</td><td>Books</td><td>nothing new. john grisham is not as good as his first book.not a good read.</td></tr><tr><td>Positive</td><td>Clothing</td><td>awesome new watch.fits perfectly. great price. great quality. hope it lasts for a long time.</td></tr><tr><td>Negative</td><td>Clothing</td><td>horrible. the color is not as pictured. not what i expected. it is not a good quality.</td></tr><tr><td>Positive</td><td>Electronics</td><td>works great. the price is unbeatable. great price. great price. hope it lasts for a long time.</td></tr><tr><td>Negative</td><td>Electronics</td><td>worthless.the picture is not as clear as the picture.not sure why it is not compatible with the samsung galaxy s2.</td></tr><tr><td>Positive</td><td>Movies</td><td>exciting new show. john goodman is great as always.great supporting cast. hope it continues to end.</td></tr><tr><td>Negative</td><td>Movies</td><td>horrible.the acting is terrible.not worth the time. it&#x27;s not worth the time.</td></tr><tr><td>Positive</td><td>Music</td><td>awesome new album. john mayer is one of the best. great album. hope he continues to release this album.</td></tr><tr><td>Negative</td><td>Music</td><td>horrible. the songs are not as good as the original. not worth the price.</td></tr><tr><td colspan="3">Yelp</td></tr><tr><td>Negative</td><td>Dessert</td><td>the bread here is crummy,half baked and stale even when‘fresh.”i won&#x27;t be back.</td></tr><tr><td>Positive</td><td>American</td><td>the burgers here are juicy, juicy and full of flavor!i highly recommend this place.</td></tr><tr><td>Negative</td><td>American</td><td>the bread here is stale,dry and over cooked even though the bread is hard.i won&#x27;tbe back.</td></tr><tr><td>Positive</td><td>Asian</td><td>the sushi here is fresh,tasty and even better than the last.i highly recommend this place.</td></tr><tr><td>Negative</td><td>Asian</td><td>the noodles here are dry,dry and over cooked even though they are supposed to be“fresh.&quot;i won&#x27;t be back.</td></tr><tr><td>Positive</td><td>Bar</td><td>the pizza here is delicious,thin crust and even better cheese (in my opinion).i highly recommend it.</td></tr><tr><td>Negative</td><td>Bar</td><td>the pizza here is bland,thin crust and even worse than the pizza, so i won&#x27;t be back.</td></tr><tr><td>Positive</td><td>Dessert Dessert</td><td>the ice cream here is delicious,soft and fluffy with all the toppings you want.i highly recommend it.</td></tr><tr><td>Negative Positive</td><td>Mexican</td><td>the bread here is stale,stale and old when you ask fora“fresh”sandwich.i won&#x27;tbe back. the tacos here are delicious,full of flavor and even beter hot sauce.i highly recommend this place.</td></tr><tr><td>Negative</td><td>Mexican</td><td></td></tr><tr><td></td><td></td><td>the beans here are dry,dry and over cooked even though they are supposed to be“fresh.’i won&#x27;t be back.</td></tr></table>
+![](images/81866b71c09bb76281e9ed3cd8be3b931f4887461ccad474c37e7e5e25238088.jpg)
+Table 10: Examples of our model’s ability to re-write sentences from public social media content when conditioned on information about the feeling expressed by the writer (Relaxed vs Annoyed)
+![](images/1e6bf8d1215fa9165d5132079310cead9cb46c106e914573b8e43627ca860a2b.jpg)
+Table 11: Model re-writes of sentences from public social media content when conditioned on the age-group of the writer (18-24 vs $^ { 6 5 + }$ )
+Table 12: Examples of human edits from our FYelp and Amazon datasets. The first line in every box was the input presented to a crowd worker followed by their corresponding edit with the specified attribute.
+<table><tr><td colspan="2">Positive ←→Negative(Yelp)</td></tr><tr><td>Positive Negative</td><td>happy to find this hidden gem near my office. great food and best of all, fast delivery. the restaurant near my office was such a dump.late delivery and gross,cold food.</td></tr><tr><td>Negative Positive</td><td>omfg no.iordered baklavaand they nuked itonastyrofoamdishforme.theisides were stillcoldand it tastedlikecancer:/ yes!iordered baklavaand it was the perfecttemperature onafancy plate.the inside was greatand ittasted excellent.</td></tr><tr><td colspan="2">Mexican ←→Asian (Yelp)</td></tr><tr><td>Mexican Asian</td><td>just wful.socalledasadaburrio&#x27;wascoldandbland..justalumpofplaincarnitasandsome iceberg lettce inacheaptrtila. reminiscent of taco bell in the 9Os but worse. just awful.socalled spring roll was cold and bland..jumpa lumpof meat and vegetables inan egg noodle wrapper. reminded me of frozen chinese food but worse.</td></tr><tr><td>Asian American(Yelp)</td><td></td></tr><tr><td colspan="2">Asian my newfavoritecuryhousedefinitelycomingback.chickenkatsuandtakoyakiissooogood!cant wait totrythepork katsu. American my new favorite american bistro house！ we are definitely coming back.fried chicken and waffles is soooo good. cant wait to try the new bbq rib sandwich.</td></tr><tr><td>Mexican →Dessert (Yelp)</td><td></td></tr><tr><td>Mexican Dessert</td><td>tacos were delicious.triedthecarneasad,bqpork,andchorizo.came withonionand cilantro toppingandahouse madechoice of mild or hot salsa. cheesecake was delicious.tried the strawberryflavoredone with chocolate drizzle.came with afresh cherryontopanda house</td></tr><tr><td colspan="2">made choice of iced or hot coffee Positive ←→ Negative (Amazon)</td></tr><tr><td>Negative Positive</td><td>tooscif forme.charactersnotrealistic.situationbsurd.abandondithlfwaytroughunusualforme.implynotmytasteinyteri. ilove how scifithis was the characters arerelatable,and the plot was great.i just had to finish itinone siing, the story got me hooked. this is has to be one of my favorite mysteries.</td></tr><tr><td>Positive Negative</td><td>my mom love this case for heri-pod.she uses it a lot and she is one satisfied customer.she would recommended it. mymominitiallylikedthiscaseforheri-pod.sheuseditforawhileanditbroke.sinceit is notsolid she would notrecommendit.</td></tr><tr><td colspan="2">Clothing ←→Books (Amazon)</td></tr><tr><td>Clothing Books</td><td>nice suit but i wear a size 8 and ordered at 12 and it was just a bit too small. great book butican&#x27;treadsmall text with mybad eyesight,unfortunately,thisone happenedtobe printedrathersall.</td></tr><tr><td colspan="2">Books → Clothing(Amazon)</td></tr><tr><td>Books Clothing</td><td>greatbookabouttealitisoftemecandeamellwiteithgeathracterdevelopntiwoudefiitelyecomdisbk. great dress with american flags printed on it.wellmade with great materials.iwoulddefinitely recommend this dress.</td></tr><tr><td colspan="2">Books ←Music (Amazon)</td></tr><tr><td>Books Music</td><td>ilovedthebookancan&#x27;twaitoreadthesequelicouldn&#x27;tputthebookdownbecause theplotandcharacters weresointeresting. iloved the musicand can not wait for the next album!icouldn’t stop listening because the music was so interesting.</td></tr></table>
+Table 13: Examples of controlling sentiment with different model checkpoints that exhibit different trade-offs between content preservation (self-BLEU) and attribute control (Accuracy). The first line in both examples is the input sentence, and subsequent lines are a model’s outputs with decreasing content preservation with rows corresponding to model checkpoints at different epochs during training.
+<table><tr><td>Accuracy</td><td>Self-BLEU</td><td>Input/Swap</td></tr><tr><td></td><td></td><td>not a fan.food is not the best and the service was terrible the two times i have visited.</td></tr><tr><td>78.7%</td><td>73.8</td><td>great little place.food is great and the service was great the two times i have visited.</td></tr><tr><td>83.5%</td><td>51.5</td><td>best food in town.food is great and the service was the best two times i have visited.</td></tr><tr><td>92.8% 96.8%</td><td>27.7 13.1</td><td>best thai food in town.the food is great and the service is excellent as always. best chinese food in town. great service and the food is the besti have had in a long time.</td></tr><tr><td></td><td></td><td>overpriced specialty food.also very crowded.service is slow.would not recommend at any time.</td></tr><tr><td>78.7%</td><td>73.8</td><td>great homemade food.also very crowded.service is fast. would recommend at least once.</td></tr><tr><td>83.5%</td><td>51.5</td><td>great specialty food.also very crowded.service is friendly.would recommend any time at the time.</td></tr><tr><td>92.8%</td><td>27.7</td><td>great variety of food.also very friendly staff.good service.would recommend at least oncea week.</td></tr><tr><td>96.8%</td><td>13.1</td><td>great tasting food.very friendly staff. definitely recommend this place for a quick bite.</td></tr></table>
+<table><tr><td>Positive</td><td>Negative</td><td>Male</td><td>Female</td><td>American</td><td>Asian</td><td>Bar</td><td>Dessert</td><td>Mexican</td></tr><tr><td>pampered</td><td>dishonest</td><td>ammo</td><td>manicure</td><td>primanti</td><td>guu</td><td>promoter</td><td>patisserie</td><td>tortas</td></tr><tr><td>relaxation</td><td>fraud</td><td>tenant</td><td>pedi</td><td>bobby</td><td>chashu</td><td>bouncers</td><td>froyo</td><td>fundido</td></tr><tr><td>delightfully</td><td>incompetence</td><td>bachelor</td><td>hubs</td><td>flay</td><td>izakaya</td><td>bouncer</td><td>buttercream</td><td>arepas</td></tr><tr><td>complemented</td><td>unethical</td><td>barbers</td><td>bridesmaids</td><td>lux</td><td>tonkotsu</td><td>hakkasan</td><td>dunkin</td><td>burritos</td></tr><tr><td>cutest</td><td>insulted</td><td>wife</td><td>bridal</td><td>nacho</td><td>khao</td><td>postino</td><td>groomers</td><td>tostada</td></tr><tr><td>plush</td><td>audacity</td><td>firestone</td><td>pedicure</td><td>bj</td><td>soju</td><td>bachi</td><td>bakeries</td><td>taquitos</td></tr><tr><td>punctual</td><td>confronted</td><td>provider</td><td>instructors</td><td>gown</td><td>tonkatsu</td><td>brio</td><td>bakery</td><td>nacho</td></tr><tr><td>housemade</td><td>cockroach</td><td>data</td><td>mattresses</td><td>applebee</td><td>banchan</td><td>cabanas</td><td>custard</td><td>fajita</td></tr><tr><td>precision</td><td>crooks</td><td>plumber</td><td>stylist</td><td>burgr</td><td>shabu</td><td>films</td><td>doughnuts</td><td>guac</td></tr><tr><td>masterpiece</td><td>disrespect</td><td>motor</td><td>jacuzzi</td><td>chilis</td><td>teppanyaki</td><td>trader</td><td>pastries</td><td>refried</td></tr><tr><td>restored</td><td>roaches</td><td>contractor</td><td>hubby</td><td>mesa</td><td>gai</td><td>hooters</td><td>gelato</td><td>mexico</td></tr><tr><td>comprehensive</td><td>refunds</td><td>hertz</td><td>pregnancy</td><td>bmw</td><td>kbbq</td><td>karaoke</td><td>cheesecakes</td><td>empanadas</td></tr><tr><td>sublime</td><td>shrugged</td><td>hvac</td><td>bachelorette</td><td>denny</td><td>pho</td><td>irish</td><td>donut</td><td>tapas</td></tr><tr><td>made</td><td>liars</td><td>qualified</td><td>husbands</td><td>mastro</td><td>hotpot</td><td>harry</td><td>croissants</td><td>queso</td></tr><tr><td>tastefully</td><td>rudest</td><td>incompetence</td><td>barre</td><td>cellar</td><td>soi</td><td>darts</td><td>doughnut</td><td>cantina</td></tr><tr><td>treasures</td><td>accused</td><td>transmission</td><td>cutest</td><td>bachi</td><td>karaage</td><td>nightclub</td><td>danish</td><td>salsas</td></tr><tr><td>addicting</td><td>inconsiderate</td><td>summary</td><td>lashes</td><td>rubbed</td><td>omakase</td><td>applebee</td><td>cheesecake</td><td>pollo</td></tr><tr><td>marvelous</td><td>roach</td><td>contractors</td><td>sephora</td><td>flatbread</td><td>saigon</td><td>whiskey</td><td>fritter</td><td>asada</td></tr><tr><td>handsome</td><td>rudely</td><td>automotive</td><td>bf</td><td>skins</td><td>panang</td><td>cereal</td><td>macarons</td><td>barrio</td></tr><tr><td>healing</td><td>cancellation</td><td>audio</td><td>boyfriends</td><td>grille</td><td>cantonese</td><td>perform</td><td>oreos</td><td>barbacoa</td></tr></table>
+Table 14: Examples of the learned attribute biases for sentiment and restaurant categories on $F Y e l p$

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+# SPARSE AND STRUCTURED VISUAL ATTENTION
+Anonymous authors Paper under double-blind review
+# ABSTRACT
+Visual attention mechanisms have been widely used in image captioning models. In this paper, to better link the image structure with the generated text, we replace the traditional softmax attention mechanism by two alternative sparsity-promoting transformations: sparsemax and Total-Variation Sparse Attention (TVMAX). With sparsemax, we obtain sparse attention weights, selecting relevant features. In order to promote sparsity and encourage fusing of the related adjacent spatial locations, we propose TVMAX. By selecting relevant groups of features, the TVMAX transformation improves interpretability. We present results in the Microsoft COCO and Flickr30k datasets, obtaining gains in comparison to softmax. TVMAX outperforms the other compared attention mechanisms in terms of humanrated caption quality and attention relevance.
+# 1 INTRODUCTION
+The goal of image captioning is to generate a fluent textual caption that describes a given image (Farhadi et al., 2010; Kulkarni et al., 2011; Vinyals et al., 2015; Xu et al., 2015). Image captioning is a multimodal task: it combines text generation with the detection and identification of objects in the image, along with their relations. While neural encoder-decoder models have achieved impressive performance in many text generation tasks (Bahdanau et al., 2015; Vaswani et al., 2017; Chorowski et al., 2015; Chopra et al., 2016), it is appealing to design image captioning models where structural bias can be injected to improve their adequacy (preservation of the image’s information), therefore strengthening the link between their language and vision components.
+State-of-the-art approaches for image captioning (Liu et al., 2018a;b; Anderson et al., 2018; Lu et al., 2018) are based on encoder-decoders with visual attention. These models pay attention either to the features generated by convolutional neural networks (CNNs) pretrained on image recognition datasets, or to detected bounding boxes. In this paper, we focus on the former category: visual attention over features generated by a CNN. Without explicit object detection, it is up to the attention mechanism to identify relevant image regions, in an unsupervised manner.
+A key component of attention mechanisms is the transformation that maps scores into probabilities, with softmax being the standard choice (Bahdanau et al., 2015). However, softmax is strictly dense, i.e., it devotes some attention probability mass to every region of the image. Not only is this wasteful, it also leads to “lack of focus”: for complex images with many objects, this may lead to vague captions with substantial repetitions. Figure 1 presents an example in which this is visible: in the caption generated using softmax (top), the model attends to the whole image at every time step, leading to a repetition of “bowl of fruit.” This undesirable behaviour is eliminated by using our alternative solutions: sparsemax (middle) and the newly proposed TVMAX (bottom).
+In this work, we introduce novel visual attention mechanisms by endowing them with a new capability: that of selecting only the relevant features of the image. To this end, we first propose replacing softmax with sparsemax (Martins & Astudillo, 2016). While sparsemax has been previously used in NLP for attention mechanisms over words, it has never been applied to computer vision to attend over image regions. With sparsemax, the attention weights obtained are sparse, leading to the selection (non-zero attention) of only a few relevant features. Second, to further encourage the weights of related adjacent spatial locations to be the same (e.g., parts of an object), we introduce a new attention mechanism: Total-Variation Sparse Attention (which we dub TVMAX), inspired by prior work in structured sparsity (Tibshirani et al., 2005; Bach et al., 2012). With TVMAX, sparsity is allied to the ability of selecting compact regions. According to our human evaluation experiments, this leads to better interpretability, since the model’s behaviour is better understood by looking at the selected image regions when a particular word is generated. It also leads to a better selection of the relevant features, and consequently to the improvement of the generated captions.
+![](images/8eef032470e6d50b2ff6440493118d5e0ef4bff16063051ea86ebbd8f106a8cc.jpg)
+Figure 1: Example of captions generated using softmax (top), sparsemax (middle) and TVMAX attention (bottom). Shading denotes the attention weight, with white for zero attention. The darker the green is, the higher the attention weight is. The full sequences are presented in Appendix C.
+This paper introduces three main contributions:
+• We propose a novel visual attention mechanism using sparse attention, based on sparsemax (Martins & Astudillo, 2016), that improves the quality of the generated captions and increases interpretability.
+We introduce a new attention mechanism, TVMAX, that encourages sparse attention over contiguous 2D regions, giving the model the capability of selecting compact objects. We show that TVmax can be evaluated by composing a proximal operator with a sparsemax projection, and we provide a closed-form expression for its Jacobian. This leads to an efficient implementation of its forward and backward pass. We perform an empirical and qualitative comparison of the various attention mechanisms considered. We also carry out a human evaluation experiment, taking into account the generated captions as well as the perceived relevance of the selected regions.
+# 2 SELECTIVE VISUAL ATTENTION
+Attention mechanisms have the ability to select the relevant features, in this case spatial locations. This requires a mapping from importance scores to a distribution, $z \in \mathbb { R } ^ { k } \mapsto \dot { p } \in \triangle ^ { k }$ , where $\begin{array} { r } { \bigtriangleup ^ { k } : = \Big \{ { \pmb p } \in \mathbb { R } ^ { k } \ \big \vert \ \sum _ { i = 1 } ^ { k } p _ { i } = 1 , { \pmb p } \geqslant { \bf 0 } \Big \} } \end{array}$ denotes the simplex (the set of all probability distributions over $k$ values). The standard choice for this mapping is softmax, defined as:
+$$
+[ \mathsf { s o f t m a x } ( z ) ] _ { i } = \frac { \exp ( z _ { i } ) } { \sum _ { j } \exp ( z _ { j } ) } .
+$$
+However, as softmax is strictly positive, its output is dense. Thus, the model must pay some attention to the whole image and, consequently, assign lower attention weights to the relevant regions. This motivates our proposed selective visual attention mechanisms, which, by being sparse, are able to better isolate the relevant image regions.
+# 2.1 SPARSEMAX
+To achieve selective capabilities, we propose the use of sparsemax (Martins & Astudillo, 2016), a sparse mapping consisting in the Euclidean projection of $_ z$ onto the probability simplex:
+$$
+\mathsf { s p a r s e m a x } ( z ) : = \underset { \pmb { p } \in \triangle ^ { k } } { \arg \operatorname* { m i n } } \frac 1 2 \| \pmb { p } - z \| _ { 2 } ^ { 2 } ,
+$$
+which allows to obtain sparse outputs with a small increase in complexity. Output sparsity is an attractive property for attention mechanisms, since some features do not provide relevant information for the current prediction. In the image captioning case, using sparsemax allows focusing only on the spatial locations of the image that are relevant to the word being generated, assigning zero attention weight to all other regions.
+# 2.2 SPARSE AND STRUCTURED VISUAL ATTENTION
+To generate descriptive captions, the model should identify the objects present in the image. Thus, when generating object-related words, the attention mechanism should assign high weights to the regions of the image containing the object. However, sparsemax is unstructured and index-invariant, leading it to select discontinuous regions. To overcome this, we propose a new visual attention mechanism, TVMAX. TVMAX is a non-trivial generalization of fusedmax (Niculae & Blondel, 2017), a transformation based on fused lasso, to the 2D case. To this end, we first extend fusedmax even more generally, to arbitrary graphs.
+# 2.2.1 GENERALIZED FUSED LASSO
+Let $\mathbf { \boldsymbol { w } } \in \mathbb { R } ^ { k }$ , and let $I = \{ 1 , \ldots , k \}$ . Consider a graph over $I$ defined by its edges $E \subseteq I \times I$ , where an edge between $i$ and $j$ means we want to encourage $w _ { i }$ to be close to $w _ { j }$ . For simplicity we use $i \sim j$ as shorthand for $( i , j ) \in E$ .
+The generalized fused lasso penalty (Tibshirani et al., 2005) is defined as:
+$$
+\Omega _ { E } ( \pmb { w } ) = \sum _ { i \sim j } | w _ { i } - w _ { j } | .
+$$
+Minimizing $\Omega _ { E }$ encourages “fused” solutions, i.e., it encourages $w _ { i } = w _ { j }$ for $i \sim j$ . In particular, its proximal operator1 can be seen as a fused signal approximator, seeking a vector $\pmb { w }$ that approximates $_ z$ well (in terms of Euclidean distance) and that is encouraged to be fused:
+$$
+\mathsf { p r o x } _ { \lambda \Omega _ { E } } ( z ) = \underset { { \pmb w } \in \mathbb { R } ^ { d } } { \arg \operatorname* { m i n } } \frac { 1 } { 2 } \| { \pmb w } - { \pmb z } \| ^ { 2 } + \lambda \Omega _ { E } ( { \pmb w } ) .
+$$
+Computing the value of $\mathsf { p r o x } _ { \lambda \Omega _ { E } }$ is non-trivial in general (Xin et al., 2016), but for certain edge configurations, described below, efficient algorithms exist.
+• If $E$ forms a chain, i.e. $i \sim j \iff i = j - 1$ , the problem is called 1D total variation and can be solved in ${ \mathcal { O } } ( k )$ time using the taut string algorithm (Davies & Kovac, 2001; Barbero & Sra, 2014). We use the quasilinear algorithm of Condat (2013), which is very fast in practice.
+• If the indices are aligned on a 2D grid, as in an image, and $i \sim j$ holds iff. $j$ is to the right or immediately below $i$ , the problem is called 2D total variation. Unlike the 1D case, exact algorithms are not available. However, for an input of size $a \times b$ , it is possible to split the penalty into $a$ column-wise and $b$ row-wise 1D problems. We may then apply a number of iterative methods, for instance proximal Dykstra (Barbero & Sra, 2014).2
+# 2.2.2 TVMAX
+TVMAX combines 2D total variation (TV2D) regularization with sparsemax. This way it promotes sparsity and encourages the attention weights of adjacent spatial locations to be the same, selecting contiguous regions of the image. TVMAX is defined as follows:
+Definition 1 (TVMAX). Let $z \in \mathbb { R } ^ { k }$ , such that $_ { z }$ ’s indices can be decomposed into rows and columns. The TVMAX transformation is defined as
+$$
+\mathrm { T V M A X } ( z ) : = \operatorname * { a r g m i n } _ { \pmb { p } \in \triangle ^ { k } } \frac { 1 } { 2 } \| \pmb { p } - z \| _ { 2 } ^ { 2 } + \lambda \Omega _ { 2 D } ^ { T V } ( \pmb { p } ) ,
+$$
+where $\lambda$ is an hyper-parameter controlling the amount of fusion $\lambda = 0$ recovers sparsemax) and $\Omega _ { 2 D } ^ { T V }$ is a $2 D$ total variation penalty.
+Note that Eq. 5 differs from Eq. 4 in which the variable $\pmb { p }$ is further constrained to lie in the probability simplex. We show next how the forward and backward passes can be efficiently computed.
+# 2.2.3 GENERALIZED FUSED SPARSE ATTENTION
+To construct generalized fused sparse attention, we follow Niculae & Blondel (2017) and define
+$$
+\begin{array} { r } { \mathsf { g f u s e d m a x } _ { E } ( z ) : = \underset { p \in \triangle } { \arg \operatorname* { m i n } } \| p - z \| _ { 2 } ^ { 2 } + \lambda \Omega _ { E } ( p ) . } \end{array}
+$$
+This can be seen as a constrained fused lasso approximator, because the solution $\pmb { p }$ must be a probability distribution vector. While the optimization function is very similar to Eq. 4, the additional constraint that $p \in \triangle$ increases complexity. Fortunately, the following result holds:
+Proposition 1 (Computing generalized fusedmax).
+$$
+\begin{array} { r } { \mathsf { g f u s e d m a x } _ { E } ( z ) = \mathsf { p r o j } _ { \triangle } \left( \mathsf { p r o x } _ { \lambda \Omega _ { E } } ( z ) \right) . } \end{array}
+$$
+The proof is given in Appendix A.2.
+Proposition 1 also provides a shortcut for deriving the Jacobian of generalized fusedmax via the chain rule: denoting by $J _ { F }$ the Jacobian of $\mathsf { p r o x } _ { \lambda \Omega _ { E } }$ , we have
+$$
+\frac { \partial \mathtt { g f u s e d m a x } } { \partial z } = J _ { \mathtt { g f u s e d m a x } } = J _ { \mathtt { s p a r s e m a x } } ( \mathsf { p r o x } _ { \lambda \Omega _ { E } } ( z ) ) J _ { F } ( z ) .
+$$
+As we already know how to compute $J _ { \mathsf { s p a r s e m a x } }$ (Appendix A.1), we may concentrate our effort on deriving the simpler $J _ { F }$ (Eq. 9).
+Proposition 2 (Group-wise characterization of $\mathsf { p r o x } _ { \lambda \Omega _ { E } } ,$ ). Let $\boldsymbol { w } ^ { \star } : = \mathsf { p r o x } _ { \lambda \Omega _ { E } }$ , and denote by $G _ { i }$ the set of indices fused to $w _ { i }$ in the solution, $G _ { i }$ may be defined recursively:
+1. $i \in G _ { i }$ for all $i$ , and
+2. $j \in G _ { i }$ if there exists $m \in G _ { i }$ such that $m \sim j$ and $w _ { m } ^ { \star } = w _ { j } ^ { \star }$ .
+Define $s _ { i j } = \mathsf { s i g n } ( w _ { i } ^ { \star } - w _ { j } ^ { \star } )$ . Then, the solution has the expression
+$$
+w _ { i } ^ { \star } = \frac { 1 } { | G _ { i } | } \sum _ { j \in G _ { i } } \left( z _ { j } + \sum _ { \stackrel { m \sim j } { m \ll G _ { i } } } \lambda s _ { m j } - \sum _ { \stackrel { j \sim m } { m \ll G _ { i } } } \lambda s _ { j m } \right) .
+$$
+Proposition 2 shows how to easily compute a generalized Jacobian of gfusedmax: since small perturbations in $_ { z }$ never change the groups $G _ { i }$ nor the signs of across-group differences $s _ { i j }$ , differentiating Eq. 8 yields
+$$
+\pmb { J } _ { F i , j } = \frac { \partial \pmb { w } _ { i } ^ { \star } } { \partial z _ { j } } = \left\{ \frac { 1 } { | \pmb { G } _ { i } | } , \quad j \in G _ { i } , \right.
+$$
+This generalizes Lemma 1 of Niculae & Blondel (2017) to generalized fused lasso, with a simpler proof, given in Appendix A.3.
+# 2.2.4 COMPUTATION
+As we show in Proposition 1, computing TVMAX’s forward pass can be done by chaining efficient algorithms for TV2D and sparsemax.
+From Eq. 7 we have that TVMAX’s Jacobian can be computed as $\begin{array} { r l } { J _ { \mathrm { T V M A X } } } & { { } = } \end{array}$ $J _ { \mathrm { s p } } ( \mathsf { p r o x } _ { \lambda \Omega _ { 2 D } ^ { T V } } ( z ) ) J _ { \mathrm { t v } } ( z )$ , where $J _ { \mathrm { s p } }$ is the sparsemax’s Jacobian and $\scriptstyle J _ { \mathrm { t v } }$ is the Jacobian of the Total Variation proximal operator.3 As derived in Proposition 2, $( J _ { \mathrm { t v } } ) _ { i , j } = 1 / n _ { i j }$ if $i$ and $j$ are fused in a group with $n _ { i j }$ elements, and 0 otherwise.
+The backward pass intuitively involves ”spreading�� the credit assigned to one image location evenly across all locations fused with it. This can be implemented by Algorithm 1 in $\mathcal { O } ( k + N _ { g } \log k )$ where $N _ { g }$ is the number of groups of fused positions. In the worst case, when there are no positions fused, the complexity is $\mathcal { O } ( k + k \log k )$ . This algorithm is inspired by flood filling algorithms (Burtsev & Kuzmin, 1993).
+Algorithm 1 TVMAX backward pass (Jacobian-vector products)
+<table><tr><td> Input: p = TVMAX(z),dp ∈ Rk.</td><td></td></tr><tr><td> Output: dz = JTvmAx(dp) ∈ Rk</td><td>#chainrule</td></tr><tr><td>3 Initialize:N←</td><td>#neighbours stack</td></tr><tr><td>4</td><td># visited positions</td></tr><tr><td>5</td><td># current group</td></tr><tr><td>6</td><td>#intermediate value used for JTvmAx&#x27;s computation</td></tr><tr><td>7 dw ← (Jsp)T dp</td><td>#Eqs.14 and15 of $A.1</td></tr><tr><td>8 while|V|&lt;k do</td><td>#checkif all positions havebeen visited</td></tr><tr><td>9 pick(io,jo) V,push (io,jo) to N</td><td>#getnot visited position andadd it to neighbours stack</td></tr><tr><td>10 while N not empty do</td><td></td></tr><tr><td>11</td><td>pop (i,j) from N</td></tr><tr><td>12 if pi,j = Pio,jo then</td><td>#checkif element is fused</td></tr><tr><td>13</td><td>G ← GU{(i,j)},V ←VU{(i,j)} #add neighbourto groupandto visited positions</td></tr><tr><td>14</td><td>s ←s+(dw)i,j #sum of the dw of each element of the group</td></tr><tr><td>15</td><td>for all neighbours (i&#x27;,j&#x27;)~(i,j) do</td></tr><tr><td>16</td><td>if (i&#x27;,j&#x27;) V then push (i’,j&#x27;) to N</td></tr><tr><td>17</td><td>if G not empty then:</td></tr><tr><td>18</td><td>(dz)i,j ← $/iG| for all (i,j) ∈G</td></tr><tr><td>19</td><td># compute JTvmAx for elements in group G G↑Q</td></tr><tr><td>20</td><td>s=0</td></tr></table>
+# 3 IMAGE CAPTIONING MODEL
+To compare the proposed attention mechanisms, we use a straight-forward simple encoder-decoder model with visual attention, inspired by Liu et al. (2018a). The model is sketched in Figure 2.
+Given an image, we use a residual CNN pretrained on ImageNet (He et al., 2016; Russakovsky et al., 2014) to get a feature map with spatial dimension of size $8 \times 8$ and channel dimension of size 2048, that go through a fine-tuned feedforward layer yielding $g \ = \ 5 1 2$ feature maps. The visual feature matrix $V = [ v _ { 1 } , v _ { 2 } , \ldots , v _ { k } ]$ , with $v _ { i } \in \mathbb { R } ^ { g }$ and $k = 6 4 = 8 \times 8$ , contains the image information used to generate the corresponding caption. Following Liu et al. (2018a), we use input and output attention to select the relevant features for the current generation. To generate the word at position $t$ , the input attention, $\pmb { \alpha } _ { t }$ , is computed using the LSTM’s previous hidden state, $h _ { t - 1 } \in$ $\mathbb { R } ^ { \dot { d } }$ . First, a similarity score $z _ { t , i } , i \in \{ 1 , \ldots , k \}$ , is computed between $\boldsymbol { h } _ { t - 1 }$ and the $i ^ { t h }$ image cell via a feedforward transformation (Bahdanau et al., 2015), as $z _ { t , i } = { w ^ { \top } } \mathrm { t a n h } \big ( \mathsf { a f f i n e } ( [ v _ { i } ; h _ { t - 1 } ] ) \big )$ , for all $k$ image cells. Then, $\pmb { \alpha } _ { t }$ is obtained by normalizing the $k$ -dimensional vector of scores ${ \boldsymbol { z } } _ { t }$ with softmax, $\pmb { \alpha } _ { t } = \mathsf { s o f t m a x } ( z _ { t } )$ . Using these attention weights, a vector representation of the image to be used as input of the LSTM, is obtained, $s _ { t } ~ = ~ V \alpha _ { t }$ . The output attention $\widetilde { \alpha } _ { t }$ , is computed in the same way as above, but applied to the current LSTM hidden state $\boldsymbol { h } _ { t }$ , instead of $\boldsymbol { h } _ { t - 1 }$ , and normalized with the different proposed transformations. This produces output visual features $\widetilde { \pmb { s } } _ { t } = \pmb { V } \widetilde { \pmb { \alpha } } _ { t }$ , which are passed through a feedforward layer to yield the image representation ${ r } _ { t } = \mathrm { t a n h } \big ( \mathsf { a f f i n e } ( \widetilde { \pmb { s } } _ { t } ) \big )$ . Finally, the predictive probability of the next word is:
+$$
+P ( y _ { t } \mid y _ { 1 : ( t - 1 ) } ; \mathrm { I m a g e } ) \propto \mathsf { s o f t m a x } ( \mathsf { a f f i n e } ( [ r _ { t } ; h _ { t } ] ) ) .
+$$
+![](images/4fa99c339ce83a2711d6ad0f40e551ad67de3e22e286ac067d67ee682e551005.jpg)
+Figure 2: Diagram of the caption generation network.
+# 4 EXPERIMENTS
+Settings. The input images are resized to $2 5 6 \times 2 5 6$ before going through the residual CNN and the feature maps obtained have a size of $8 \times 8$ . We use an LSTM hidden size of $d = 5 1 2$ and a word embedding size of 256, for all models. The models were trained for 50 epochs using the Adam optimizer (Kingma & Ba, 2014) with a learning rate of 0.0001 and a decay of 0.8 and 0.999 for the first and second momentum, respectively. After the $1 0 ^ { t h }$ epoch, the learning rate starts decaying with a decay factor of 0.99. For TVMAX, we set $\lambda = 0 . 0 1$ .
+Datasets and Metrics. We report our results on the Microsoft COCO (MSCOCO) and Flickr30k datasets. MSCOCO is composed of 113,287 images of common objects in context while Flickr30k consists in 31,000 pictures of people involved in everyday activities and events. Each image is annotated with 5 captions. We use the split proposed by Karpathy & Fei-Fei (2015), which stipulates equal validation and test sizes of 5,000 images (MSCOCO) and 1,000 (Flickr30k). The metrics we report are SPICE (Anderson et al., 2016), CIDEr (Vedantam et al., 2015), longest common subsequence ROUGE, (denoted $\mathrm { R O U G E } _ { L }$ ; Lin, 2004), $1 -$ to 4–gram BLEU (denoted $\mathrm { B L E U _ { 4 } }$ ; Papineni et al., 2002), and METEOR (Banerjee & Lavie, 2005). To investigate whether selective attention alleviates repetition, we also measure the n-gram repetition metric REP (Malaviya et al., 2018).
+Table 1: Automatic evaluation of caption generation on MSCOCO and Flickr30k.
+<table><tr><td></td><td colspan="5">MSCOCO</td><td colspan="6">Flickr30k</td></tr><tr><td>SPICE CIDER ROUGEL BLEU4 METEOR REP↓</td><td></td><td></td><td></td><td></td><td></td><td></td><td>SPICE CIDER ROUGEL BLEU4 METEOR REP↓</td><td></td><td></td><td></td><td></td></tr><tr><td>softmax</td><td>18.4</td><td>0.967</td><td>52.9</td><td>29.9</td><td>24.9</td><td>3.76</td><td>13.5 0.443</td><td>44.2</td><td>19.9</td><td>19.1</td><td>6.09</td></tr><tr><td>sparsemax</td><td>18.9</td><td>0.990</td><td>53.5</td><td>31.5</td><td>25.3 3.69</td><td>13.7</td><td>0.444</td><td>44.3</td><td>20.7</td><td>19.3</td><td>5.84</td></tr><tr><td>TVMAX</td><td>18.5</td><td>0.974</td><td>53.1</td><td>29.9</td><td>25.1</td><td>3.17</td><td>13.3 0.438</td><td>44.2</td><td>20.5</td><td>19.0</td><td>3.97</td></tr></table>
+Automated metrics. As can be seen in table 1, overall sparsemax and TVMAX attention mechanisms achieve better results when compared with softmax, indicating that the use of selective attention leads to better captions. This improvement does not come at a high computational cost: at inference time, models using TVMAX and sparsemax are only $1 . 3 \mathrm { x }$ and $1 . 1 \mathrm { x }$ slower than softmax. Moreover, for TVMAX, automatic metrics results are slightly worse than sparsemax but still superior to softmax on MSCOCO and similar on Flickr30k. We show next that this is compensated with fewer repetitions and higher scores in the human evaluation of the captions and attention relevance.
+![](images/b17c661cbcf65e6080706f3a6d3234826d6ade1d9990d1fc22ad6a791dc22bd3.jpg)
+Figure 3: Example of captions generated using softmax (top), sparsemax (middle) and TVMAX attention (bottom). Shading denotes the attention weight, with white for zero attention. The darker the green is, the higher the attention weight is. The full sequences are presented in Appendix C.
+Table 2: Human evaluation results with different attention mechanisms on MSCOCO.
+<table><tr><td></td><td>CAPTION (1-5)</td><td>ATTENTION RELEVANCE（1-5)</td></tr><tr><td>softmax</td><td>3.50</td><td>3.38</td></tr><tr><td>sparsemax</td><td>3.71</td><td>3.89</td></tr><tr><td>TVMAX</td><td>3.87</td><td>4.10</td></tr></table>
+Human rating. The caption evaluation consisted in attributing a score from 1 to 5 to the caption of each model while the attention evaluation consisted in scoring the relevancy of the attended areas, from 1 to 5, when generating the non stop words of the captions. A full description of the human assessment can be found in Appendix B.
+Despite performing slightly worse than sparsemax under automated metrics, TVMAX outperforms sparsemax and softmax in the caption human evaluation and the attention relevance human evaluation, reported in Table 2. The superior score on attention relevance shows that TVMAX is better at selecting the relevant features and its output is more interpretable. Additionally, the better caption evaluation results demonstrate that the ability to select compact regions induces the generation of better captions. We next explore possible explanations for the TVMAX superior results.
+Repetition. Figure 1 illustrates that softmax attention is prone to spuriously repeating references to the same object. Selective attention mechanisms like sparsemax and especially TVMAX reduce repetition, as measured by the REP metric reported in Table 1. This expected success can be attributed to the sparsity of the attention weights distribution and to the ability to select compact regions exclusively and can be one of the causes of the human evaluation results. This happens even though TVMAX generates longer sentences than sparsemax and softmax (9.5 against 9.0 words on average) and shows the benefit of promoting structured and sparse attention simultaneously. To corroborate our intuition that sparsity leads to less repetition, we measured the Jensen-Shannon divergence (JS) between the attention distributions for each step of the generation of the captions correspondent to the images of the MSCOCO test set. The mean JS values are 0.12, 0.29, and 0.34 for softmax, sparsemax, and TVmax, respectively. This shows that sparsity leads to less similar attention distributions along the generation of the captions and, consequently, to less repetitions.
+Object detection. Using the MSCOCO object detection ground truth, we compared the percentage of objects present in the image that are referred to in the captions, using each attention mechanism. With TVMAX $2 8 . 2 \%$ of the reference objects are referred, against $2 7 . 5 \%$ and $2 7 . 4 \%$ for sparsemax and softmax, repectively. This shows that promoting high attention to groups of spatial locations of the image leads to a more precise identification of the objects.
+Sparsity. The average image area that receives zero attention is $3 4 \%$ for sparsemax and $2 5 \%$ for TVMAX. To illustrate where the models attend to, we display the output attention in Figures 1 and 3. As expected, softmax weights are spread widely across the image, ending up missing the relevant regions. In contrast, sparsemax and TVMAX weights are zero for the non-relevant spatial locations.
+Qualitative comparison. As the image of Figure 1 contains various similar objects, the softmax model (top) generates a incoherent, repetition-laden caption. In contrast, the sparsemax (middle) and TVMAX (bottom) models better identify the relevant parts of the image, generating coherent and descriptive captions. Moreover, the groups obtained with TVMAX are clearly visible and more aligned to object boundaries, offering better interpretability, as revealed by human attention assessment. In Figure 3 it can also be noticed that with TVMAX (bottom) the model correctly identified “a group of people” instead of “a soccer player” as with sparsemax (middle) and softmax (top). This indicates its superior ability to correctly define the relevant groups of features and that this ability leads to improved captions.
+# 5 RELATED WORK
+Image captioning. In the last years, neural models with visual attention mechanisms have been receiving increased interest. Several researchers have been studying diverse attention mechanisms in order to refine visual information for image captioning. Xu et al. (2015) proposed the use of hard attention, which only attends to one region at each step. However, to generate descriptive captions the model should, often, focus on more than one region. In addition, hard attention is non-differentiable, requiring imitation learning or Monte Carlo policy gradient approximations.Anderson et al. (2018) proposed bottom-up attention, using an object detection model designed to identify bounding boxes of objects, and top-down attention, selecting the relevant bounding-boxes. Wang et al. (2019) proposed an hierarchical attention network composed by a patch detector, object detector, and concept detector. Using object detection models is less demanding on the attention mechanism, since it only has to select the boxes the model should attend to. However, such models are limited by the bounding boxes position’s accuracy. Gao et al. (2019) introduced a deliberate attention network to refine the attended visual features. Yet, the attention distribution remained dense.
+Sparse attention. In several tasks only a few features are relevant for the current prediction. This can be attained when using sparse attention. Various prior works have proposed sparse attention mechanisms with promising results, (Xu et al., 2015; Martins & Astudillo, 2016; Malaviya et al., 2018; Peters et al., 2019). Niculae & Blondel (2017) proposed 1D fusedmax, which incorporates the fused lasso, so that adjacent words are encouraged to have the same attention weight. In this work, the authors were able to improve interpretability without sacrificing performance, obtaining superior results on textual entailment and summarization. We derive a generalized fused attention mechanism, extending 1D fusedmax.
+# 6 CONCLUSIONS AND FUTURE WORK
+We propose using sparse and structured visual attention, in order to improve the process of selecting the features relevant to the caption generation. For that, we used sparsemax and introduced TVMAX. Results on the image captioning task, show that the attention mechanism is able to select better
+features when using sparsemax or TVMAX. Furthermore, in the human assessment and attention analysis we see that the improved selection of the relevant features as well as the ability to group spatial features lead to the generation of better captions, while improving the model’s interpretability.
+In future work, TVMAX attention can be applied to other multimodal problems such as visual question answering. It can also be applied in other tasks for which we have prior knowledge of the data’s stucture, for instance graphs or trees.
+# REFERENCES
+Peter Anderson, Basura Fernando, Mark Johnson, and Stephen Gould. SPICE: Semantic propositional image caption evaluation. In Proc. ECCV, 2016.
+Peter Anderson, Xiaodong He, Chris Buehler, Damien Teney, Mark Johnson, Stephen Gould, and Lei Zhang. Bottom-up and top-down attention for image captioning and visual question answering. In Proc. CVPR, 2018.
+Francis Bach, Rodolphe Jenatton, Julien Mairal, Guillaume Obozinski, et al. Optimization with sparsity-inducing penalties. Foundations and Trends $\textsuperscript { \textregistered }$ in Machine Learning, 4(1):1–106, 2012.
+Dzmitry Bahdanau, Kyunghyun Cho, and Yoshua Bengio. Neural machine translation by jointly learning to align and translate. In Proc. ICLR, 2015.
+Satanjeev Banerjee and Alon Lavie. METEOR: An automatic metric for MT evaluation with improved correlation with human judgments. In Proc. ACL Workshop on Intrinsic and Extrinsic Evaluation Measures for Machine Translation and/or Summarization, 2005.
+Alvaro Barbero and Suvrit Sra. Modular proximal optimization for multidimensional total-variation ´ regularization. preprint arXiv:1411.0589, 2014.
+Sergei Burtsev and Ye.P. Kuzmin. An efficient flood-filling algorithm. Computers & Graphics, 17: 549–561, 09 1993.
+Sumit Chopra, Michael Auli, and Alexander M Rush. Abstractive sentence summarization with attentive recurrent neural networks. In Proc. NAACL-HLT, 2016.
+Jan K Chorowski, Dzmitry Bahdanau, Dmitriy Serdyuk, Kyunghyun Cho, and Yoshua Bengio. Attention-based models for speech recognition. In Proc. NeurIPS, 2015.
+Laurent Condat. A direct algorithm for 1-d total variation denoising. IEEE Signal Processing Letters, 20(11):1054–1057, 2013.
+P. Laurie Davies and Arne Kovac. Local extremes, runs, strings and multiresolution. The Annals of Statistics, 29(1):1–48, 2001. ISSN 00905364.
+Ali Farhadi, Mohsen Hejrati, Mohammad Amin Sadeghi, Peter Young, Cyrus Rashtchian, Julia Hockenmaier, and David Forsyth. Every picture tells a story: Generating sentences from images. In Proc. ECCV, 2010.
+Jerome Friedman, Trevor Hastie, Holger Hofling, and Robert Tibshirani. Pathwise coordinate opti- ¨ mization. The Annals of Applied Statistics, 1(2):302–332, 2007.
+Lianli Gao, Kaixuan Fan, Jingkuan Song, Xianglong Liu, Xing Xu, and Heng Tao Shen. Deliberate attention networks for image captioning. 2019.
+Kaiming He, Xiangyu Zhang, Shaoqing Ren, and Jian Sun. Deep residual learning for image recognition. In Proc. CVPR, 2016.
+Andrej Karpathy and Li Fei-Fei. Deep visual-semantic alignments for generating image descriptions. In Proceedings of the IEEE conference on computer vision and pattern recognition, 2015.
+Diederik P. Kingma and Jimmy Ba. Adam: A method for stochastic optimization. preprint arXiv:1412.6980, 2014.
+Girish Kulkarni, Visruth Premraj, Sagnik Dhar, Siming Li, Yejin Choi, Alexander C Berg, and Tamara L Berg. Baby talk: Understanding and generating image descriptions. In Proc. CVPR, 2011.
+Chin-Yew Lin. ROUGE: A package for automatic evaluation of summaries. Text Summarization Branches Out, 2004.
+Fenglin Liu, Xuancheng Ren, Yuanxin Liu, Houfeng Wang, and Xu Sun. simNet: Stepwise imagetopic merging network for generating detailed and comprehensive image captions. Preprint arXiv:1808.08732, 2018a.
+Xihui Liu, Hongsheng Li, Jing Shao, Dapeng Chen, and Xiaogang Wang. Show, tell and discriminate: Image captioning by self-retrieval with partially labeled data. preprint arXiv:1803.08314, 2018b.
+Jiasen Lu, Jianwei Yang, Dhruv Batra, and Devi Parikh. Neural baby talk. In Proc. CVPR, 2018.
+Chaitanya Malaviya, Pedro Ferreira, and Andre FT Martins. Sparse and constrained attention for ´ neural machine translation. In Proceedings of the 56th Annual Meeting of the Association for Computational Linguistics (Volume 2: Short Papers), pp. 370–376, 2018.
+Andre Martins and Ramon Astudillo. From softmax to sparsemax: A sparse model of attention and multi-label classification. In Maria Florina Balcan and Kilian Q. Weinberger (eds.), Proc. ICML, 20–22 Jun 2016.
+Vlad Niculae and Mathieu Blondel. A regularized framework for sparse and structured neural attention. In Proc. NeurIPS, 2017.
+Kishore Papineni, Salim Roukos, Todd Ward, and Wei-Jing Zhu. BLEU: a method for automatic evaluation of machine translation. In Proc. ACL, 2002.
+Ben Peters, Vlad Niculae, and Andre FT Martins. Sparse sequence-to-sequence models. ´ In Proc. ACL, 2019.
+Olga Russakovsky, Jia Deng, Hao Su, Jonathan Krause, Sanjeev Satheesh, Sean Ma, Zhiheng Huang, Andrej Karpathy, Aditya Khosla, Michael Bernstein, Alexander C. Berg, and Li Fei-Fei. Imagenet large scale visual recognition challenge, 2014.
+Robert Tibshirani, Michael Saunders, Saharon Rosset, Ji Zhu, and Keith Knight. Sparsity and smoothness via the fused lasso. Journal of the Royal Statistical Society: Series B (Statistical Methodology), 67(1):91–108, 2005.
+Ashish Vaswani, Noam Shazeer, Niki Parmar, Jakob Uszkoreit, Llion Jones, Aidan N Gomez, Łukasz Kaiser, and Illia Polosukhin. Attention is all you need. In Proc. NeurIPS, 2017.
+Ramakrishna Vedantam, C Lawrence Zitnick, and Devi Parikh. CIDEr: Consensus-based image description evaluation. In Proc. CVPR, 2015.
+Oriol Vinyals, Alexander Toshev, Samy Bengio, and Dumitru Erhan. Show and tell: A neural image caption generator. In Proc. CVPR, 2015.
+Weixuan Wang, Zhihong Chen, and Haifeng Hu. Hierarchical attention network for image captioning. In Proceedings of the AAAI Conference on Artificial Intelligence, volume 33, pp. 8957–8964, 2019.
+Bo Xin, Yoshinobu Kawahara, Yizhou Wang, Lingjing Hu, and Wen Gao. Efficient generalized fused lasso and its applications. ACM Trans. Intell. Syst. Technol., 7(4):60:1–60:22, May 2016. ISSN 2157-6904.
+Kelvin Xu, Jimmy Ba, Ryan Kiros, Kyunghyun Cho, Aaron Courville, Ruslan Salakhudinov, Rich Zemel, and Yoshua Bengio. Show, attend and tell: Neural image caption generation with visual attention. In Proc. ICML, 2015.
+Yaoliang Yu. On decomposing the proximal map. In Proc. NeurIPS, 2013.
+# A FORWARD AND BACKWARD PASS OF 2D FUSEDMAX ATTENTION.
+# A.1 PRELIMINARIES
+The proximal operator of a function $f \colon  { \mathbb { R } ^ { d } } \to  { \mathbb { R } \cup \{ \infty \} }$ is defined as
+$$
+{ \sf p r o x } _ { f } ( z ) = \underset { { \pmb w } \in \mathbb { R } ^ { d } } { \arg \operatorname* { m i n } } f ( z ) + \frac { 1 } { 2 } \| z - { \pmb w } \| _ { 2 } ^ { 2 } ,
+$$
+and it is guaranteed to have a unique solution, thanks to the strong convexity of the Euclidean distance.
+The indicator function of a set $\mathcal { C } \subset \mathbb { R } ^ { d }$ is the function
+$$
+\iota _ { \mathcal { C } } \colon \mathbb { R } ^ { d } \to \mathbb { R } \cup \{ \infty \} , \quad \iota _ { \mathcal { C } } ( \pmb { w } ) : = \left\{ \begin{array} { l l } { 0 , } & { \pmb { w } \in \mathcal { C } , } \\ { \infty , } & { \pmb { w } \notin \mathcal { C } . } \end{array} \right.
+$$
+The projection onto a convex set $\mathcal { C } \subset \mathbb { R } ^ { d }$ is defined as
+$$
+\mathsf { p r o j } _ { \mathcal { C } } ( z ) : = \mathop { \arg \operatorname* { m i n } } _ { \pmb { w } \in \mathcal { C } } \frac { 1 } { 2 } \| z - \pmb { w } \| _ { 2 } ^ { 2 } = \mathsf { p r o x } _ { \iota _ { \mathcal { C } } } ( z ) ,
+$$
+showing that the proximal operator can be seen as a generalization of projection.
+The sparsemax attention mapping (Martins & Astudillo, 2016) is the projection onto the simplex,
+$$
+{ \mathsf { s p a r s e m a x } } ( z ) : = { \mathsf { p r o j } } _ { \triangle } ( z ) = \operatorname * { a r g m i n } _ { p \in { \triangle } } { \frac { 1 } { 2 } } \| p - z \| ^ { 2 } .
+$$
+A necessary component for using sparsemax for attention is its Jacobian, the matrix of its partial derivatives $\begin{array} { r } { ( J _ { \mathsf { s p a r s e m a x } } ) _ { i , j } = \frac { \partial \mathsf { s p a r s e m a x } ( z ) _ { i } } { \partial z _ { j } } } \end{array}$ ∂ sparsemax(z)i . Martins & Astudillo (2016) derive its expression
+$$
+\boldsymbol { J } _ { \mathsf { s p a r s e m a x } } ( z ) = \mathsf { d i a g } s - \frac { 1 } { \| s \| _ { 1 } } \pmb { s } \pmb { s } ^ { \top } ,
+$$
+where $s _ { j } = 1$ if sparsemax $( z ) _ { j } > 0$ and $s _ { j } = 0$ otherwise.
+# A.2 PROOF OF PROPOSITION 1
+Proof. This result is a slight extension of Proposition 2 in Niculae & Blondel (2017), and also follows from Corrolary 4 of Yu (2013), by taking $f = \iota _ { \triangle }$ , and noting that $\iota \triangle$ is symmetric: if $p \in \triangle$ , then any vector $\pmb { p } ^ { \prime }$ obtained by permuting $\pmb { p }$ is also in $\triangle$ , because its values remain nonnegative and sum to 1. □
+# A.3 PROOF OF PROPOSITION 2
+Let $\boldsymbol { w } ^ { \star } : = \mathsf { p r o x } _ { \lambda \Omega _ { E } }$ , and denote by $G _ { i }$ the set of indices fused to $w _ { i }$ in the solution. Define $s _ { i j } =$ $\mathsf { s i g n } ( w _ { i } ^ { \star } - w _ { j } ^ { \star } )$ .
+Proof. The subgradient optimality conditions of Eq. 4 are: (Friedman et al., 2007)
+$$
+w _ { i } ^ { \star } - z _ { i } + \sum _ { k : i \sim k } \lambda t _ { i k } - \sum _ { k : k \sim i } \lambda t _ { k i } = 0 , \quad \quad 1 \leq i \leq d .
+$$
+where $t _ { i j } = \mathsf { s i g n } ( w _ { i } ^ { \star } - w _ { j } ^ { \star } )$ if $w _ { i } ^ { \star } \neq w _ { j } ^ { \star }$ , otherwise $t _ { i j }$ is a free variable in $[ - 1 , 1 ]$ .
+We focus on a single group $G = G _ { i }$ , dropping the index $i$ for brevity. Within a fused group, the solution is constant, i.e., $w _ { j } ^ { \star } = w$ for $j \in G$ . We separate the sums in Eq. 16 according to whether $k \in G$ or not, and move the “constant” terms to the right hand side, yielding the system
+$$
+w + \sum _ { j \sim k } \lambda t _ { j k } - \sum _ { k \sim j \atop k \in G } \lambda t _ { k j } = z _ { j } + \sum _ { \stackrel { k \sim j } { k \notin G } } \lambda s _ { k j } - \sum _ { j \sim k } \lambda s _ { j k } , \qquad j \in G .
+$$
+Summing up the Eq. 17 over all $j \in G$ , we observe that for any $k \in G$ , the term $\lambda t _ { j k }$ appears twice with opposite signs. Thus,
+$$
+\sum _ { j \in G } w = \sum _ { j \in G } \left( z _ { j } + \sum _ { \stackrel { k \sim j } { k \notin G } } \lambda s _ { k j } - \sum _ { j \stackrel { \sim k } { k \notin G } } \lambda s _ { j k } \right) .
+$$
+Dividing by $| G |$ gives exactly Eq. 8. This reasoning applies to any group $G _ { i }$
+# B HUMAN EVALUATION DESCRIPTION
+To perform the human evaluation firstly 100 images were randomly selected from the test set of the MSCOCO dataset (using the split proposed by Karpathy & Fei-Fei (2015)). For each of the selected images, the human evaluators selected a score from 1 to 5 for the captions generated by the models using softmax attention, sparsemax attention, and TVMAX attention. They were also asked to evaluate whether the models attend to the relevant regions of the image when generating a certain word. For that they observed the attention plots corresponding to the non stop words of the caption of each of the models. While in Figures 1 and 3, 4, and 5 we emphasized sparsity with a hard white mask, for the human evaluation the sparse regions of the attention plots were simply fully transparent, to avoid biasing the evaluators. The possible scores were also between 1 and 5. The 100 images were judged by 6 persons both for the captions evaluation and attention evaluation. The order of the captions and attention plots was randomly chosen for each image.
+With these scores, we computed the mean of the captions evaluation scores and the mean of the attention relevance evaluation scores. The results are reported in Table 2.
+# C ADDITIONAL ATTENTION VISUALIZATION
+![](images/55fe3f71d6594beb180beb9dcdbf6de0facac18317739482992ae722e854974c.jpg)
+Figure 4: Example generated captions using softmax attention (top), sparsemax attention (middle) and TVMAX attention (bottom). The captions are “A bowl of fruit and a bowl of fruit”, “A bowl of fruit and oranges on a table” and “A bowl of oranges and a banana on a table”.
+![](images/2dfa42c0aeb73323465d313c7d5d26e5bd7532f94f492775f4191ce42f005ec3.jpg)
+Figure 5: Example generated captions using softmax attention (top), sparsemax attention (middle) and TVMAX attention (bottom). The captions are “A soccer player is running to the base”, “A soccer player is running to the field” and “A group of people playing soccer on a field”.

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+        "text": "SPARSE AND STRUCTURED VISUAL ATTENTION ",
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+    {
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+        "text": "ABSTRACT ",
+        "text_level": 1,
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+        "text": "Visual attention mechanisms have been widely used in image captioning models. In this paper, to better link the image structure with the generated text, we replace the traditional softmax attention mechanism by two alternative sparsity-promoting transformations: sparsemax and Total-Variation Sparse Attention (TVMAX). With sparsemax, we obtain sparse attention weights, selecting relevant features. In order to promote sparsity and encourage fusing of the related adjacent spatial locations, we propose TVMAX. By selecting relevant groups of features, the TVMAX transformation improves interpretability. We present results in the Microsoft COCO and Flickr30k datasets, obtaining gains in comparison to softmax. TVMAX outperforms the other compared attention mechanisms in terms of humanrated caption quality and attention relevance. ",
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+        "text": "1 INTRODUCTION ",
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+        "text": "The goal of image captioning is to generate a fluent textual caption that describes a given image (Farhadi et al., 2010; Kulkarni et al., 2011; Vinyals et al., 2015; Xu et al., 2015). Image captioning is a multimodal task: it combines text generation with the detection and identification of objects in the image, along with their relations. While neural encoder-decoder models have achieved impressive performance in many text generation tasks (Bahdanau et al., 2015; Vaswani et al., 2017; Chorowski et al., 2015; Chopra et al., 2016), it is appealing to design image captioning models where structural bias can be injected to improve their adequacy (preservation of the image’s information), therefore strengthening the link between their language and vision components. ",
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+        "text": "State-of-the-art approaches for image captioning (Liu et al., 2018a;b; Anderson et al., 2018; Lu et al., 2018) are based on encoder-decoders with visual attention. These models pay attention either to the features generated by convolutional neural networks (CNNs) pretrained on image recognition datasets, or to detected bounding boxes. In this paper, we focus on the former category: visual attention over features generated by a CNN. Without explicit object detection, it is up to the attention mechanism to identify relevant image regions, in an unsupervised manner. ",
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+        "text": "A key component of attention mechanisms is the transformation that maps scores into probabilities, with softmax being the standard choice (Bahdanau et al., 2015). However, softmax is strictly dense, i.e., it devotes some attention probability mass to every region of the image. Not only is this wasteful, it also leads to “lack of focus”: for complex images with many objects, this may lead to vague captions with substantial repetitions. Figure 1 presents an example in which this is visible: in the caption generated using softmax (top), the model attends to the whole image at every time step, leading to a repetition of “bowl of fruit.” This undesirable behaviour is eliminated by using our alternative solutions: sparsemax (middle) and the newly proposed TVMAX (bottom). ",
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+        "text": "In this work, we introduce novel visual attention mechanisms by endowing them with a new capability: that of selecting only the relevant features of the image. To this end, we first propose replacing softmax with sparsemax (Martins & Astudillo, 2016). While sparsemax has been previously used in NLP for attention mechanisms over words, it has never been applied to computer vision to attend over image regions. With sparsemax, the attention weights obtained are sparse, leading to the selection (non-zero attention) of only a few relevant features. Second, to further encourage the weights of related adjacent spatial locations to be the same (e.g., parts of an object), we introduce a new attention mechanism: Total-Variation Sparse Attention (which we dub TVMAX), inspired by prior work in structured sparsity (Tibshirani et al., 2005; Bach et al., 2012). With TVMAX, sparsity is allied to the ability of selecting compact regions. According to our human evaluation experiments, this leads to better interpretability, since the model’s behaviour is better understood by looking at the selected image regions when a particular word is generated. It also leads to a better selection of the relevant features, and consequently to the improvement of the generated captions. ",
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+        "image_caption": [
+            "Figure 1: Example of captions generated using softmax (top), sparsemax (middle) and TVMAX attention (bottom). Shading denotes the attention weight, with white for zero attention. The darker the green is, the higher the attention weight is. The full sequences are presented in Appendix C. "
+        ],
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+        "text": "This paper introduces three main contributions: ",
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+        "text": "• We propose a novel visual attention mechanism using sparse attention, based on sparsemax (Martins & Astudillo, 2016), that improves the quality of the generated captions and increases interpretability.   \nWe introduce a new attention mechanism, TVMAX, that encourages sparse attention over contiguous 2D regions, giving the model the capability of selecting compact objects. We show that TVmax can be evaluated by composing a proximal operator with a sparsemax projection, and we provide a closed-form expression for its Jacobian. This leads to an efficient implementation of its forward and backward pass. We perform an empirical and qualitative comparison of the various attention mechanisms considered. We also carry out a human evaluation experiment, taking into account the generated captions as well as the perceived relevance of the selected regions. ",
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+        "text": "2 SELECTIVE VISUAL ATTENTION ",
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+        "text": "Attention mechanisms have the ability to select the relevant features, in this case spatial locations. This requires a mapping from importance scores to a distribution, $z \\in \\mathbb { R } ^ { k } \\mapsto \\dot { p } \\in \\triangle ^ { k }$ , where $\\begin{array} { r } { \\bigtriangleup ^ { k } : = \\Big \\{ { \\pmb p } \\in \\mathbb { R } ^ { k } \\ \\big \\vert \\ \\sum _ { i = 1 } ^ { k } p _ { i } = 1 , { \\pmb p } \\geqslant { \\bf 0 } \\Big \\} } \\end{array}$ denotes the simplex (the set of all probability distributions over $k$ values). The standard choice for this mapping is softmax, defined as: ",
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+        "img_path": "images/d8bdaf8b46543fe683ec67593379dfa8265b6efd7688e7a7d80e1d3e091f996b.jpg",
+        "text": "$$\n[ \\mathsf { s o f t m a x } ( z ) ] _ { i } = \\frac { \\exp ( z _ { i } ) } { \\sum _ { j } \\exp ( z _ { j } ) } .\n$$",
+        "text_format": "latex",
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+        "text": "However, as softmax is strictly positive, its output is dense. Thus, the model must pay some attention to the whole image and, consequently, assign lower attention weights to the relevant regions. This motivates our proposed selective visual attention mechanisms, which, by being sparse, are able to better isolate the relevant image regions. ",
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+        "text": "2.1 SPARSEMAX ",
+        "text_level": 1,
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "To achieve selective capabilities, we propose the use of sparsemax (Martins & Astudillo, 2016), a sparse mapping consisting in the Euclidean projection of $_ z$ onto the probability simplex: ",
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "equation",
+        "img_path": "images/6d2af67f628b71c36a537d0c1b7c9db42bd19f8219b3fea99fc48b396c320dd7.jpg",
+        "text": "$$\n\\mathsf { s p a r s e m a x } ( z ) : = \\underset { \\pmb { p } \\in \\triangle ^ { k } } { \\arg \\operatorname* { m i n } } \\frac 1 2 \\| \\pmb { p } - z \\| _ { 2 } ^ { 2 } ,\n$$",
+        "text_format": "latex",
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "which allows to obtain sparse outputs with a small increase in complexity. Output sparsity is an attractive property for attention mechanisms, since some features do not provide relevant information for the current prediction. In the image captioning case, using sparsemax allows focusing only on the spatial locations of the image that are relevant to the word being generated, assigning zero attention weight to all other regions. ",
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "2.2 SPARSE AND STRUCTURED VISUAL ATTENTION ",
+        "text_level": 1,
+        "bbox": [
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+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "To generate descriptive captions, the model should identify the objects present in the image. Thus, when generating object-related words, the attention mechanism should assign high weights to the regions of the image containing the object. However, sparsemax is unstructured and index-invariant, leading it to select discontinuous regions. To overcome this, we propose a new visual attention mechanism, TVMAX. TVMAX is a non-trivial generalization of fusedmax (Niculae & Blondel, 2017), a transformation based on fused lasso, to the 2D case. To this end, we first extend fusedmax even more generally, to arbitrary graphs. ",
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "2.2.1 GENERALIZED FUSED LASSO ",
+        "text_level": 1,
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "Let $\\mathbf { \\boldsymbol { w } } \\in \\mathbb { R } ^ { k }$ , and let $I = \\{ 1 , \\ldots , k \\}$ . Consider a graph over $I$ defined by its edges $E \\subseteq I \\times I$ , where an edge between $i$ and $j$ means we want to encourage $w _ { i }$ to be close to $w _ { j }$ . For simplicity we use $i \\sim j$ as shorthand for $( i , j ) \\in E$ . ",
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "The generalized fused lasso penalty (Tibshirani et al., 2005) is defined as: ",
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "equation",
+        "img_path": "images/3979a083b5d42fff30720e6057318cf4f513ec569d5da34755f192878929a3e5.jpg",
+        "text": "$$\n\\Omega _ { E } ( \\pmb { w } ) = \\sum _ { i \\sim j } | w _ { i } - w _ { j } | .\n$$",
+        "text_format": "latex",
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "Minimizing $\\Omega _ { E }$ encourages “fused” solutions, i.e., it encourages $w _ { i } = w _ { j }$ for $i \\sim j$ . In particular, its proximal operator1 can be seen as a fused signal approximator, seeking a vector $\\pmb { w }$ that approximates $_ z$ well (in terms of Euclidean distance) and that is encouraged to be fused: ",
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "equation",
+        "img_path": "images/f8ee1e7aeea36f4a361b2595d82744bb4c0d468130273e18e45ead85c3819e6d.jpg",
+        "text": "$$\n\\mathsf { p r o x } _ { \\lambda \\Omega _ { E } } ( z ) = \\underset { { \\pmb w } \\in \\mathbb { R } ^ { d } } { \\arg \\operatorname* { m i n } } \\frac { 1 } { 2 } \\| { \\pmb w } - { \\pmb z } \\| ^ { 2 } + \\lambda \\Omega _ { E } ( { \\pmb w } ) .\n$$",
+        "text_format": "latex",
+        "bbox": [
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+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "Computing the value of $\\mathsf { p r o x } _ { \\lambda \\Omega _ { E } }$ is non-trivial in general (Xin et al., 2016), but for certain edge configurations, described below, efficient algorithms exist. ",
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "• If $E$ forms a chain, i.e. $i \\sim j \\iff i = j - 1$ , the problem is called 1D total variation and can be solved in ${ \\mathcal { O } } ( k )$ time using the taut string algorithm (Davies & Kovac, 2001; Barbero & Sra, 2014). We use the quasilinear algorithm of Condat (2013), which is very fast in practice. ",
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "• If the indices are aligned on a 2D grid, as in an image, and $i \\sim j$ holds iff. $j$ is to the right or immediately below $i$ , the problem is called 2D total variation. Unlike the 1D case, exact algorithms are not available. However, for an input of size $a \\times b$ , it is possible to split the penalty into $a$ column-wise and $b$ row-wise 1D problems. We may then apply a number of iterative methods, for instance proximal Dykstra (Barbero & Sra, 2014).2 ",
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "2.2.2 TVMAX ",
+        "text_level": 1,
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "TVMAX combines 2D total variation (TV2D) regularization with sparsemax. This way it promotes sparsity and encourages the attention weights of adjacent spatial locations to be the same, selecting contiguous regions of the image. TVMAX is defined as follows: ",
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "Definition 1 (TVMAX). Let $z \\in \\mathbb { R } ^ { k }$ , such that $_ { z }$ ’s indices can be decomposed into rows and columns. The TVMAX transformation is defined as ",
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "equation",
+        "img_path": "images/a3af01a42fd14b677090bd6681ddc3fd9a9337e093346f1bca42be8e4eab221e.jpg",
+        "text": "$$\n\\mathrm { T V M A X } ( z ) : = \\operatorname * { a r g m i n } _ { \\pmb { p } \\in \\triangle ^ { k } } \\frac { 1 } { 2 } \\| \\pmb { p } - z \\| _ { 2 } ^ { 2 } + \\lambda \\Omega _ { 2 D } ^ { T V } ( \\pmb { p } ) ,\n$$",
+        "text_format": "latex",
+        "bbox": [
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "where $\\lambda$ is an hyper-parameter controlling the amount of fusion $\\lambda = 0$ recovers sparsemax) and $\\Omega _ { 2 D } ^ { T V }$ is a $2 D$ total variation penalty. ",
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "Note that Eq. 5 differs from Eq. 4 in which the variable $\\pmb { p }$ is further constrained to lie in the probability simplex. We show next how the forward and backward passes can be efficiently computed. ",
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "2.2.3 GENERALIZED FUSED SPARSE ATTENTION ",
+        "text_level": 1,
+        "bbox": [
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "To construct generalized fused sparse attention, we follow Niculae & Blondel (2017) and define ",
+        "bbox": [
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "equation",
+        "img_path": "images/43f05f0fc961c05636e0cf837632cdb1fb83f403c9c9c2e1729032125312d5d8.jpg",
+        "text": "$$\n\\begin{array} { r } { \\mathsf { g f u s e d m a x } _ { E } ( z ) : = \\underset { p \\in \\triangle } { \\arg \\operatorname* { m i n } } \\| p - z \\| _ { 2 } ^ { 2 } + \\lambda \\Omega _ { E } ( p ) . } \\end{array}\n$$",
+        "text_format": "latex",
+        "bbox": [
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "This can be seen as a constrained fused lasso approximator, because the solution $\\pmb { p }$ must be a probability distribution vector. While the optimization function is very similar to Eq. 4, the additional constraint that $p \\in \\triangle$ increases complexity. Fortunately, the following result holds: ",
+        "bbox": [
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "Proposition 1 (Computing generalized fusedmax). ",
+        "bbox": [
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+            465
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "equation",
+        "img_path": "images/f951026af7fe688e0727ec86d6706b57b31c5b276db0595944fe4f8d6fe8d51e.jpg",
+        "text": "$$\n\\begin{array} { r } { \\mathsf { g f u s e d m a x } _ { E } ( z ) = \\mathsf { p r o j } _ { \\triangle } \\left( \\mathsf { p r o x } _ { \\lambda \\Omega _ { E } } ( z ) \\right) . } \\end{array}\n$$",
+        "text_format": "latex",
+        "bbox": [
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "The proof is given in Appendix A.2. ",
+        "bbox": [
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "Proposition 1 also provides a shortcut for deriving the Jacobian of generalized fusedmax via the chain rule: denoting by $J _ { F }$ the Jacobian of $\\mathsf { p r o x } _ { \\lambda \\Omega _ { E } }$ , we have ",
+        "bbox": [
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+            521,
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "equation",
+        "img_path": "images/7649284fd07e962b61e6aa64fa0b9527c0e92b5f52b8fd4a15a733855ef80c14.jpg",
+        "text": "$$\n\\frac { \\partial \\mathtt { g f u s e d m a x } } { \\partial z } = J _ { \\mathtt { g f u s e d m a x } } = J _ { \\mathtt { s p a r s e m a x } } ( \\mathsf { p r o x } _ { \\lambda \\Omega _ { E } } ( z ) ) J _ { F } ( z ) .\n$$",
+        "text_format": "latex",
+        "bbox": [
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "As we already know how to compute $J _ { \\mathsf { s p a r s e m a x } }$ (Appendix A.1), we may concentrate our effort on deriving the simpler $J _ { F }$ (Eq. 9). ",
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "Proposition 2 (Group-wise characterization of $\\mathsf { p r o x } _ { \\lambda \\Omega _ { E } } ,$ ). Let $\\boldsymbol { w } ^ { \\star } : = \\mathsf { p r o x } _ { \\lambda \\Omega _ { E } }$ , and denote by $G _ { i }$ the set of indices fused to $w _ { i }$ in the solution, $G _ { i }$ may be defined recursively: ",
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "1. $i \\in G _ { i }$ for all $i$ , and ",
+        "bbox": [
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "2. $j \\in G _ { i }$ if there exists $m \\in G _ { i }$ such that $m \\sim j$ and $w _ { m } ^ { \\star } = w _ { j } ^ { \\star }$ . ",
+        "bbox": [
+            212,
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "Define $s _ { i j } = \\mathsf { s i g n } ( w _ { i } ^ { \\star } - w _ { j } ^ { \\star } )$ . Then, the solution has the expression ",
+        "bbox": [
+            173,
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "equation",
+        "img_path": "images/5d50125c457702775de0f328731694fbdfa096a42dd590e6d0a43f958620d4c0.jpg",
+        "text": "$$\nw _ { i } ^ { \\star } = \\frac { 1 } { | G _ { i } | } \\sum _ { j \\in G _ { i } } \\left( z _ { j } + \\sum _ { \\stackrel { m \\sim j } { m \\ll G _ { i } } } \\lambda s _ { m j } - \\sum _ { \\stackrel { j \\sim m } { m \\ll G _ { i } } } \\lambda s _ { j m } \\right) .\n$$",
+        "text_format": "latex",
+        "bbox": [
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "Proposition 2 shows how to easily compute a generalized Jacobian of gfusedmax: since small perturbations in $_ { z }$ never change the groups $G _ { i }$ nor the signs of across-group differences $s _ { i j }$ , differentiating Eq. 8 yields ",
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "equation",
+        "img_path": "images/2cc92932d2ea28e17f7a4d32c8071f2db9b3b438d997fef6ed932ada15a1347b.jpg",
+        "text": "$$\n\\pmb { J } _ { F i , j } = \\frac { \\partial \\pmb { w } _ { i } ^ { \\star } } { \\partial z _ { j } } = \\left\\{ \\frac { 1 } { | \\pmb { G } _ { i } | } , \\quad j \\in G _ { i } , \\right.\n$$",
+        "text_format": "latex",
+        "bbox": [
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "This generalizes Lemma 1 of Niculae & Blondel (2017) to generalized fused lasso, with a simpler proof, given in Appendix A.3. ",
+        "bbox": [
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "2.2.4 COMPUTATION ",
+        "text_level": 1,
+        "bbox": [
+            176,
+            103,
+            331,
+            117
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "As we show in Proposition 1, computing TVMAX’s forward pass can be done by chaining efficient algorithms for TV2D and sparsemax. ",
+        "bbox": [
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+            127,
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "From Eq. 7 we have that TVMAX’s Jacobian can be computed as $\\begin{array} { r l } { J _ { \\mathrm { T V M A X } } } & { { } = } \\end{array}$ $J _ { \\mathrm { s p } } ( \\mathsf { p r o x } _ { \\lambda \\Omega _ { 2 D } ^ { T V } } ( z ) ) J _ { \\mathrm { t v } } ( z )$ , where $J _ { \\mathrm { s p } }$ is the sparsemax’s Jacobian and $\\scriptstyle J _ { \\mathrm { t v } }$ is the Jacobian of the Total Variation proximal operator.3 As derived in Proposition 2, $( J _ { \\mathrm { t v } } ) _ { i , j } = 1 / n _ { i j }$ if $i$ and $j$ are fused in a group with $n _ { i j }$ elements, and 0 otherwise. ",
+        "bbox": [
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "The backward pass intuitively involves ”spreading” the credit assigned to one image location evenly across all locations fused with it. This can be implemented by Algorithm 1 in $\\mathcal { O } ( k + N _ { g } \\log k )$ where $N _ { g }$ is the number of groups of fused positions. In the worst case, when there are no positions fused, the complexity is $\\mathcal { O } ( k + k \\log k )$ . This algorithm is inspired by flood filling algorithms (Burtsev & Kuzmin, 1993). ",
+        "bbox": [
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "table",
+        "img_path": "images/d4dc1f070c0db564d82901a81531556b827978d9ac2fb1b39e200811434601fa.jpg",
+        "table_caption": [
+            "Algorithm 1 TVMAX backward pass (Jacobian-vector products) "
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td> Input: p = TVMAX(z),dp ∈ Rk.</td><td></td></tr><tr><td> Output: dz = JTvmAx(dp) ∈ Rk</td><td>#chainrule</td></tr><tr><td>3 Initialize:N←</td><td>#neighbours stack</td></tr><tr><td>4</td><td># visited positions</td></tr><tr><td>5</td><td># current group</td></tr><tr><td>6</td><td>#intermediate value used for JTvmAx&#x27;s computation</td></tr><tr><td>7 dw ← (Jsp)T dp</td><td>#Eqs.14 and15 of $A.1</td></tr><tr><td>8 while|V|&lt;k do</td><td>#checkif all positions havebeen visited</td></tr><tr><td>9 pick(io,jo) V,push (io,jo) to N</td><td>#getnot visited position andadd it to neighbours stack</td></tr><tr><td>10 while N not empty do</td><td></td></tr><tr><td>11</td><td>pop (i,j) from N</td></tr><tr><td>12 if pi,j = Pio,jo then</td><td>#checkif element is fused</td></tr><tr><td>13</td><td>G ← GU{(i,j)},V ←VU{(i,j)} #add neighbourto groupandto visited positions</td></tr><tr><td>14</td><td>s ←s+(dw)i,j #sum of the dw of each element of the group</td></tr><tr><td>15</td><td>for all neighbours (i&#x27;,j&#x27;)~(i,j) do</td></tr><tr><td>16</td><td>if (i&#x27;,j&#x27;) V then push (i’,j&#x27;) to N</td></tr><tr><td>17</td><td>if G not empty then:</td></tr><tr><td>18</td><td>(dz)i,j ← $/iG| for all (i,j) ∈G</td></tr><tr><td>19</td><td># compute JTvmAx for elements in group G G↑Q</td></tr><tr><td>20</td><td>s=0</td></tr></table>",
+        "bbox": [
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "3 IMAGE CAPTIONING MODEL ",
+        "text_level": 1,
+        "bbox": [
+            176,
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+            680
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "To compare the proposed attention mechanisms, we use a straight-forward simple encoder-decoder model with visual attention, inspired by Liu et al. (2018a). The model is sketched in Figure 2. ",
+        "bbox": [
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+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "Given an image, we use a residual CNN pretrained on ImageNet (He et al., 2016; Russakovsky et al., 2014) to get a feature map with spatial dimension of size $8 \\times 8$ and channel dimension of size 2048, that go through a fine-tuned feedforward layer yielding $g \\ = \\ 5 1 2$ feature maps. The visual feature matrix $V = [ v _ { 1 } , v _ { 2 } , \\ldots , v _ { k } ]$ , with $v _ { i } \\in \\mathbb { R } ^ { g }$ and $k = 6 4 = 8 \\times 8$ , contains the image information used to generate the corresponding caption. Following Liu et al. (2018a), we use input and output attention to select the relevant features for the current generation. To generate the word at position $t$ , the input attention, $\\pmb { \\alpha } _ { t }$ , is computed using the LSTM’s previous hidden state, $h _ { t - 1 } \\in$ $\\mathbb { R } ^ { \\dot { d } }$ . First, a similarity score $z _ { t , i } , i \\in \\{ 1 , \\ldots , k \\}$ , is computed between $\\boldsymbol { h } _ { t - 1 }$ and the $i ^ { t h }$ image cell via a feedforward transformation (Bahdanau et al., 2015), as $z _ { t , i } = { w ^ { \\top } } \\mathrm { t a n h } \\big ( \\mathsf { a f f i n e } ( [ v _ { i } ; h _ { t - 1 } ] ) \\big )$ , for all $k$ image cells. Then, $\\pmb { \\alpha } _ { t }$ is obtained by normalizing the $k$ -dimensional vector of scores ${ \\boldsymbol { z } } _ { t }$ with softmax, $\\pmb { \\alpha } _ { t } = \\mathsf { s o f t m a x } ( z _ { t } )$ . Using these attention weights, a vector representation of the image to be used as input of the LSTM, is obtained, $s _ { t } ~ = ~ V \\alpha _ { t }$ . The output attention $\\widetilde { \\alpha } _ { t }$ , is computed in the same way as above, but applied to the current LSTM hidden state $\\boldsymbol { h } _ { t }$ , instead of $\\boldsymbol { h } _ { t - 1 }$ , and normalized with the different proposed transformations. This produces output visual features $\\widetilde { \\pmb { s } } _ { t } = \\pmb { V } \\widetilde { \\pmb { \\alpha } } _ { t }$ , which are passed through a feedforward layer to yield the image representation ${ r } _ { t } = \\mathrm { t a n h } \\big ( \\mathsf { a f f i n e } ( \\widetilde { \\pmb { s } } _ { t } ) \\big )$ . Finally, the predictive probability of the next word is: ",
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+        "type": "equation",
+        "img_path": "images/bcf584750419b3f2d62caf3b5b2975292cdb5c0948fe1aed77df00a445c2bddc.jpg",
+        "text": "$$\nP ( y _ { t } \\mid y _ { 1 : ( t - 1 ) } ; \\mathrm { I m a g e } ) \\propto \\mathsf { s o f t m a x } ( \\mathsf { a f f i n e } ( [ r _ { t } ; h _ { t } ] ) ) .\n$$",
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+        "img_path": "images/4fa99c339ce83a2711d6ad0f40e551ad67de3e22e286ac067d67ee682e551005.jpg",
+        "image_caption": [
+            "Figure 2: Diagram of the caption generation network. "
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+        "text": "4 EXPERIMENTS ",
+        "text_level": 1,
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+        "text": "Settings. The input images are resized to $2 5 6 \\times 2 5 6$ before going through the residual CNN and the feature maps obtained have a size of $8 \\times 8$ . We use an LSTM hidden size of $d = 5 1 2$ and a word embedding size of 256, for all models. The models were trained for 50 epochs using the Adam optimizer (Kingma & Ba, 2014) with a learning rate of 0.0001 and a decay of 0.8 and 0.999 for the first and second momentum, respectively. After the $1 0 ^ { t h }$ epoch, the learning rate starts decaying with a decay factor of 0.99. For TVMAX, we set $\\lambda = 0 . 0 1$ . ",
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+        "text": "Datasets and Metrics. We report our results on the Microsoft COCO (MSCOCO) and Flickr30k datasets. MSCOCO is composed of 113,287 images of common objects in context while Flickr30k consists in 31,000 pictures of people involved in everyday activities and events. Each image is annotated with 5 captions. We use the split proposed by Karpathy & Fei-Fei (2015), which stipulates equal validation and test sizes of 5,000 images (MSCOCO) and 1,000 (Flickr30k). The metrics we report are SPICE (Anderson et al., 2016), CIDEr (Vedantam et al., 2015), longest common subsequence ROUGE, (denoted $\\mathrm { R O U G E } _ { L }$ ; Lin, 2004), $1 -$ to 4–gram BLEU (denoted $\\mathrm { B L E U _ { 4 } }$ ; Papineni et al., 2002), and METEOR (Banerjee & Lavie, 2005). To investigate whether selective attention alleviates repetition, we also measure the n-gram repetition metric REP (Malaviya et al., 2018). ",
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+    {
+        "type": "table",
+        "img_path": "images/76d07c5ad1c4ea51b50464da12b5769c5da07082b7e2be623628c3213b121a69.jpg",
+        "table_caption": [
+            "Table 1: Automatic evaluation of caption generation on MSCOCO and Flickr30k. "
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td></td><td colspan=\"5\">MSCOCO</td><td colspan=\"6\">Flickr30k</td></tr><tr><td>SPICE CIDER ROUGEL BLEU4 METEOR REP↓</td><td></td><td></td><td></td><td></td><td></td><td></td><td>SPICE CIDER ROUGEL BLEU4 METEOR REP↓</td><td></td><td></td><td></td><td></td></tr><tr><td>softmax</td><td>18.4</td><td>0.967</td><td>52.9</td><td>29.9</td><td>24.9</td><td>3.76</td><td>13.5 0.443</td><td>44.2</td><td>19.9</td><td>19.1</td><td>6.09</td></tr><tr><td>sparsemax</td><td>18.9</td><td>0.990</td><td>53.5</td><td>31.5</td><td>25.3 3.69</td><td>13.7</td><td>0.444</td><td>44.3</td><td>20.7</td><td>19.3</td><td>5.84</td></tr><tr><td>TVMAX</td><td>18.5</td><td>0.974</td><td>53.1</td><td>29.9</td><td>25.1</td><td>3.17</td><td>13.3 0.438</td><td>44.2</td><td>20.5</td><td>19.0</td><td>3.97</td></tr></table>",
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+    {
+        "type": "text",
+        "text": "Automated metrics. As can be seen in table 1, overall sparsemax and TVMAX attention mechanisms achieve better results when compared with softmax, indicating that the use of selective attention leads to better captions. This improvement does not come at a high computational cost: at inference time, models using TVMAX and sparsemax are only $1 . 3 \\mathrm { x }$ and $1 . 1 \\mathrm { x }$ slower than softmax. Moreover, for TVMAX, automatic metrics results are slightly worse than sparsemax but still superior to softmax on MSCOCO and similar on Flickr30k. We show next that this is compensated with fewer repetitions and higher scores in the human evaluation of the captions and attention relevance. ",
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+        "image_caption": [
+            "Figure 3: Example of captions generated using softmax (top), sparsemax (middle) and TVMAX attention (bottom). Shading denotes the attention weight, with white for zero attention. The darker the green is, the higher the attention weight is. The full sequences are presented in Appendix C. "
+        ],
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+    {
+        "type": "table",
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+        "table_caption": [
+            "Table 2: Human evaluation results with different attention mechanisms on MSCOCO. "
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td></td><td>CAPTION (1-5)</td><td>ATTENTION RELEVANCE（1-5)</td></tr><tr><td>softmax</td><td>3.50</td><td>3.38</td></tr><tr><td>sparsemax</td><td>3.71</td><td>3.89</td></tr><tr><td>TVMAX</td><td>3.87</td><td>4.10</td></tr></table>",
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+    {
+        "type": "text",
+        "text": "Human rating. The caption evaluation consisted in attributing a score from 1 to 5 to the caption of each model while the attention evaluation consisted in scoring the relevancy of the attended areas, from 1 to 5, when generating the non stop words of the captions. A full description of the human assessment can be found in Appendix B. ",
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+    {
+        "type": "text",
+        "text": "Despite performing slightly worse than sparsemax under automated metrics, TVMAX outperforms sparsemax and softmax in the caption human evaluation and the attention relevance human evaluation, reported in Table 2. The superior score on attention relevance shows that TVMAX is better at selecting the relevant features and its output is more interpretable. Additionally, the better caption evaluation results demonstrate that the ability to select compact regions induces the generation of better captions. We next explore possible explanations for the TVMAX superior results. ",
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+        "type": "text",
+        "text": "Repetition. Figure 1 illustrates that softmax attention is prone to spuriously repeating references to the same object. Selective attention mechanisms like sparsemax and especially TVMAX reduce repetition, as measured by the REP metric reported in Table 1. This expected success can be attributed to the sparsity of the attention weights distribution and to the ability to select compact regions exclusively and can be one of the causes of the human evaluation results. This happens even though TVMAX generates longer sentences than sparsemax and softmax (9.5 against 9.0 words on average) and shows the benefit of promoting structured and sparse attention simultaneously. To corroborate our intuition that sparsity leads to less repetition, we measured the Jensen-Shannon divergence (JS) between the attention distributions for each step of the generation of the captions correspondent to the images of the MSCOCO test set. The mean JS values are 0.12, 0.29, and 0.34 for softmax, sparsemax, and TVmax, respectively. This shows that sparsity leads to less similar attention distributions along the generation of the captions and, consequently, to less repetitions. ",
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+        "type": "text",
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+    {
+        "type": "text",
+        "text": "Object detection. Using the MSCOCO object detection ground truth, we compared the percentage of objects present in the image that are referred to in the captions, using each attention mechanism. With TVMAX $2 8 . 2 \\%$ of the reference objects are referred, against $2 7 . 5 \\%$ and $2 7 . 4 \\%$ for sparsemax and softmax, repectively. This shows that promoting high attention to groups of spatial locations of the image leads to a more precise identification of the objects. ",
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+    {
+        "type": "text",
+        "text": "Sparsity. The average image area that receives zero attention is $3 4 \\%$ for sparsemax and $2 5 \\%$ for TVMAX. To illustrate where the models attend to, we display the output attention in Figures 1 and 3. As expected, softmax weights are spread widely across the image, ending up missing the relevant regions. In contrast, sparsemax and TVMAX weights are zero for the non-relevant spatial locations. ",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "Qualitative comparison. As the image of Figure 1 contains various similar objects, the softmax model (top) generates a incoherent, repetition-laden caption. In contrast, the sparsemax (middle) and TVMAX (bottom) models better identify the relevant parts of the image, generating coherent and descriptive captions. Moreover, the groups obtained with TVMAX are clearly visible and more aligned to object boundaries, offering better interpretability, as revealed by human attention assessment. In Figure 3 it can also be noticed that with TVMAX (bottom) the model correctly identified “a group of people” instead of “a soccer player” as with sparsemax (middle) and softmax (top). This indicates its superior ability to correctly define the relevant groups of features and that this ability leads to improved captions. ",
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+    {
+        "type": "text",
+        "text": "5 RELATED WORK ",
+        "text_level": 1,
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+    {
+        "type": "text",
+        "text": "Image captioning. In the last years, neural models with visual attention mechanisms have been receiving increased interest. Several researchers have been studying diverse attention mechanisms in order to refine visual information for image captioning. Xu et al. (2015) proposed the use of hard attention, which only attends to one region at each step. However, to generate descriptive captions the model should, often, focus on more than one region. In addition, hard attention is non-differentiable, requiring imitation learning or Monte Carlo policy gradient approximations.Anderson et al. (2018) proposed bottom-up attention, using an object detection model designed to identify bounding boxes of objects, and top-down attention, selecting the relevant bounding-boxes. Wang et al. (2019) proposed an hierarchical attention network composed by a patch detector, object detector, and concept detector. Using object detection models is less demanding on the attention mechanism, since it only has to select the boxes the model should attend to. However, such models are limited by the bounding boxes position’s accuracy. Gao et al. (2019) introduced a deliberate attention network to refine the attended visual features. Yet, the attention distribution remained dense. ",
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+    {
+        "type": "text",
+        "text": "Sparse attention. In several tasks only a few features are relevant for the current prediction. This can be attained when using sparse attention. Various prior works have proposed sparse attention mechanisms with promising results, (Xu et al., 2015; Martins & Astudillo, 2016; Malaviya et al., 2018; Peters et al., 2019). Niculae & Blondel (2017) proposed 1D fusedmax, which incorporates the fused lasso, so that adjacent words are encouraged to have the same attention weight. In this work, the authors were able to improve interpretability without sacrificing performance, obtaining superior results on textual entailment and summarization. We derive a generalized fused attention mechanism, extending 1D fusedmax. ",
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+    {
+        "type": "text",
+        "text": "6 CONCLUSIONS AND FUTURE WORK ",
+        "text_level": 1,
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+    {
+        "type": "text",
+        "text": "We propose using sparse and structured visual attention, in order to improve the process of selecting the features relevant to the caption generation. For that, we used sparsemax and introduced TVMAX. Results on the image captioning task, show that the attention mechanism is able to select better ",
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+    {
+        "type": "text",
+        "text": "features when using sparsemax or TVMAX. Furthermore, in the human assessment and attention analysis we see that the improved selection of the relevant features as well as the ability to group spatial features lead to the generation of better captions, while improving the model’s interpretability. ",
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+    {
+        "type": "text",
+        "text": "In future work, TVMAX attention can be applied to other multimodal problems such as visual question answering. It can also be applied in other tasks for which we have prior knowledge of the data’s stucture, for instance graphs or trees. ",
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+    {
+        "type": "text",
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+        "bbox": [
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+        "text": "Chaitanya Malaviya, Pedro Ferreira, and Andre FT Martins. Sparse and constrained attention for ´ neural machine translation. In Proceedings of the 56th Annual Meeting of the Association for Computational Linguistics (Volume 2: Short Papers), pp. 370–376, 2018. ",
+        "bbox": [
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+        "text": "Andre Martins and Ramon Astudillo. From softmax to sparsemax: A sparse model of attention and multi-label classification. In Maria Florina Balcan and Kilian Q. Weinberger (eds.), Proc. ICML, 20–22 Jun 2016. ",
+        "bbox": [
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+        "page_idx": 9
+    },
+    {
+        "type": "text",
+        "text": "Vlad Niculae and Mathieu Blondel. A regularized framework for sparse and structured neural attention. In Proc. NeurIPS, 2017. ",
+        "bbox": [
+            174,
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+        "text": "Kishore Papineni, Salim Roukos, Todd Ward, and Wei-Jing Zhu. BLEU: a method for automatic evaluation of machine translation. In Proc. ACL, 2002. ",
+        "bbox": [
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+        "type": "text",
+        "text": "Ben Peters, Vlad Niculae, and Andre FT Martins. Sparse sequence-to-sequence models. ´ In Proc. ACL, 2019. ",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "Olga Russakovsky, Jia Deng, Hao Su, Jonathan Krause, Sanjeev Satheesh, Sean Ma, Zhiheng Huang, Andrej Karpathy, Aditya Khosla, Michael Bernstein, Alexander C. Berg, and Li Fei-Fei. Imagenet large scale visual recognition challenge, 2014. ",
+        "bbox": [
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+    {
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+        "text": "Robert Tibshirani, Michael Saunders, Saharon Rosset, Ji Zhu, and Keith Knight. Sparsity and smoothness via the fused lasso. Journal of the Royal Statistical Society: Series B (Statistical Methodology), 67(1):91–108, 2005. ",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "Ashish Vaswani, Noam Shazeer, Niki Parmar, Jakob Uszkoreit, Llion Jones, Aidan N Gomez, Łukasz Kaiser, and Illia Polosukhin. Attention is all you need. In Proc. NeurIPS, 2017. ",
+        "bbox": [
+            171,
+            638,
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+        ],
+        "page_idx": 9
+    },
+    {
+        "type": "text",
+        "text": "Ramakrishna Vedantam, C Lawrence Zitnick, and Devi Parikh. CIDEr: Consensus-based image description evaluation. In Proc. CVPR, 2015. ",
+        "bbox": [
+            173,
+            676,
+            823,
+            705
+        ],
+        "page_idx": 9
+    },
+    {
+        "type": "text",
+        "text": "Oriol Vinyals, Alexander Toshev, Samy Bengio, and Dumitru Erhan. Show and tell: A neural image caption generator. In Proc. CVPR, 2015. ",
+        "bbox": [
+            171,
+            714,
+            825,
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+        ],
+        "page_idx": 9
+    },
+    {
+        "type": "text",
+        "text": "Weixuan Wang, Zhihong Chen, and Haifeng Hu. Hierarchical attention network for image captioning. In Proceedings of the AAAI Conference on Artificial Intelligence, volume 33, pp. 8957–8964, 2019. ",
+        "bbox": [
+            176,
+            752,
+            823,
+            795
+        ],
+        "page_idx": 9
+    },
+    {
+        "type": "text",
+        "text": "Bo Xin, Yoshinobu Kawahara, Yizhou Wang, Lingjing Hu, and Wen Gao. Efficient generalized fused lasso and its applications. ACM Trans. Intell. Syst. Technol., 7(4):60:1–60:22, May 2016. ISSN 2157-6904. ",
+        "bbox": [
+            171,
+            804,
+            823,
+            845
+        ],
+        "page_idx": 9
+    },
+    {
+        "type": "text",
+        "text": "Kelvin Xu, Jimmy Ba, Ryan Kiros, Kyunghyun Cho, Aaron Courville, Ruslan Salakhudinov, Rich Zemel, and Yoshua Bengio. Show, attend and tell: Neural image caption generation with visual attention. In Proc. ICML, 2015. ",
+        "bbox": [
+            176,
+            856,
+            823,
+            898
+        ],
+        "page_idx": 9
+    },
+    {
+        "type": "text",
+        "text": "Yaoliang Yu. On decomposing the proximal map. In Proc. NeurIPS, 2013. ",
+        "bbox": [
+            174,
+            907,
+            663,
+            922
+        ],
+        "page_idx": 9
+    },
+    {
+        "type": "text",
+        "text": "A FORWARD AND BACKWARD PASS OF 2D FUSEDMAX ATTENTION. ",
+        "text_level": 1,
+        "bbox": [
+            173,
+            101,
+            743,
+            119
+        ],
+        "page_idx": 10
+    },
+    {
+        "type": "text",
+        "text": "A.1 PRELIMINARIES ",
+        "text_level": 1,
+        "bbox": [
+            174,
+            133,
+            331,
+            148
+        ],
+        "page_idx": 10
+    },
+    {
+        "type": "text",
+        "text": "The proximal operator of a function $f \\colon  { \\mathbb { R } ^ { d } } \\to  { \\mathbb { R } \\cup \\{ \\infty \\} }$ is defined as ",
+        "bbox": [
+            173,
+            159,
+            638,
+            175
+        ],
+        "page_idx": 10
+    },
+    {
+        "type": "equation",
+        "img_path": "images/40e012eb2d3be05e63dbd0726a69af53117dfed2f9bd25ce0a388a82bc90f79b.jpg",
+        "text": "$$\n{ \\sf p r o x } _ { f } ( z ) = \\underset { { \\pmb w } \\in \\mathbb { R } ^ { d } } { \\arg \\operatorname* { m i n } } f ( z ) + \\frac { 1 } { 2 } \\| z - { \\pmb w } \\| _ { 2 } ^ { 2 } ,\n$$",
+        "text_format": "latex",
+        "bbox": [
+            361,
+            180,
+            637,
+            214
+        ],
+        "page_idx": 10
+    },
+    {
+        "type": "text",
+        "text": "and it is guaranteed to have a unique solution, thanks to the strong convexity of the Euclidean distance. ",
+        "bbox": [
+            174,
+            219,
+            823,
+            248
+        ],
+        "page_idx": 10
+    },
+    {
+        "type": "text",
+        "text": "The indicator function of a set $\\mathcal { C } \\subset \\mathbb { R } ^ { d }$ is the function ",
+        "bbox": [
+            174,
+            253,
+            534,
+            270
+        ],
+        "page_idx": 10
+    },
+    {
+        "type": "equation",
+        "img_path": "images/3d24155670896f13a7c46bec66322ca76b540c973d2729d97ef35a9602ed2f1c.jpg",
+        "text": "$$\n\\iota _ { \\mathcal { C } } \\colon \\mathbb { R } ^ { d } \\to \\mathbb { R } \\cup \\{ \\infty \\} , \\quad \\iota _ { \\mathcal { C } } ( \\pmb { w } ) : = \\left\\{ \\begin{array} { l l } { 0 , } & { \\pmb { w } \\in \\mathcal { C } , } \\\\ { \\infty , } & { \\pmb { w } \\notin \\mathcal { C } . } \\end{array} \\right.\n$$",
+        "text_format": "latex",
+        "bbox": [
+            334,
+            273,
+            661,
+            309
+        ],
+        "page_idx": 10
+    },
+    {
+        "type": "text",
+        "text": "The projection onto a convex set $\\mathcal { C } \\subset \\mathbb { R } ^ { d }$ is defined as ",
+        "bbox": [
+            173,
+            318,
+            539,
+            333
+        ],
+        "page_idx": 10
+    },
+    {
+        "type": "equation",
+        "img_path": "images/18845b4bc748453706947d1a67a6b016accb4c60186064a77391d468812ed599.jpg",
+        "text": "$$\n\\mathsf { p r o j } _ { \\mathcal { C } } ( z ) : = \\mathop { \\arg \\operatorname* { m i n } } _ { \\pmb { w } \\in \\mathcal { C } } \\frac { 1 } { 2 } \\| z - \\pmb { w } \\| _ { 2 } ^ { 2 } = \\mathsf { p r o x } _ { \\iota _ { \\mathcal { C } } } ( z ) ,\n$$",
+        "text_format": "latex",
+        "bbox": [
+            343,
+            338,
+            655,
+            371
+        ],
+        "page_idx": 10
+    },
+    {
+        "type": "text",
+        "text": "showing that the proximal operator can be seen as a generalization of projection. ",
+        "bbox": [
+            176,
+            377,
+            702,
+            392
+        ],
+        "page_idx": 10
+    },
+    {
+        "type": "text",
+        "text": "The sparsemax attention mapping (Martins & Astudillo, 2016) is the projection onto the simplex, ",
+        "bbox": [
+            173,
+            397,
+            813,
+            414
+        ],
+        "page_idx": 10
+    },
+    {
+        "type": "equation",
+        "img_path": "images/7e661d73e19342a25768d02fec3b52402991d38f91bd506720b1dae5d51ed11c.jpg",
+        "text": "$$\n{ \\mathsf { s p a r s e m a x } } ( z ) : = { \\mathsf { p r o j } } _ { \\triangle } ( z ) = \\operatorname * { a r g m i n } _ { p \\in { \\triangle } } { \\frac { 1 } { 2 } } \\| p - z \\| ^ { 2 } .\n$$",
+        "text_format": "latex",
+        "bbox": [
+            328,
+            419,
+            669,
+            454
+        ],
+        "page_idx": 10
+    },
+    {
+        "type": "text",
+        "text": "A necessary component for using sparsemax for attention is its Jacobian, the matrix of its partial derivatives $\\begin{array} { r } { ( J _ { \\mathsf { s p a r s e m a x } } ) _ { i , j } = \\frac { \\partial \\mathsf { s p a r s e m a x } ( z ) _ { i } } { \\partial z _ { j } } } \\end{array}$ ∂ sparsemax(z)i . Martins & Astudillo (2016) derive its expression ",
+        "bbox": [
+            176,
+            465,
+            826,
+            502
+        ],
+        "page_idx": 10
+    },
+    {
+        "type": "equation",
+        "img_path": "images/8cee7bb4d95045756a63901f1abfda8affadcc15e3c2ecd98ca977bf7bcd82ed.jpg",
+        "text": "$$\n\\boldsymbol { J } _ { \\mathsf { s p a r s e m a x } } ( z ) = \\mathsf { d i a g } s - \\frac { 1 } { \\| s \\| _ { 1 } } \\pmb { s } \\pmb { s } ^ { \\top } ,\n$$",
+        "text_format": "latex",
+        "bbox": [
+            377,
+            507,
+            619,
+            541
+        ],
+        "page_idx": 10
+    },
+    {
+        "type": "text",
+        "text": "where $s _ { j } = 1$ if sparsemax $( z ) _ { j } > 0$ and $s _ { j } = 0$ otherwise. ",
+        "bbox": [
+            173,
+            546,
+            557,
+            563
+        ],
+        "page_idx": 10
+    },
+    {
+        "type": "text",
+        "text": "A.2 PROOF OF PROPOSITION 1 ",
+        "text_level": 1,
+        "bbox": [
+            176,
+            577,
+            400,
+            593
+        ],
+        "page_idx": 10
+    },
+    {
+        "type": "text",
+        "text": "Proof. This result is a slight extension of Proposition 2 in Niculae & Blondel (2017), and also follows from Corrolary 4 of Yu (2013), by taking $f = \\iota _ { \\triangle }$ , and noting that $\\iota \\triangle$ is symmetric: if $p \\in \\triangle$ , then any vector $\\pmb { p } ^ { \\prime }$ obtained by permuting $\\pmb { p }$ is also in $\\triangle$ , because its values remain nonnegative and sum to 1. □ ",
+        "bbox": [
+            173,
+            603,
+            826,
+            660
+        ],
+        "page_idx": 10
+    },
+    {
+        "type": "text",
+        "text": "A.3 PROOF OF PROPOSITION 2 ",
+        "text_level": 1,
+        "bbox": [
+            176,
+            676,
+            400,
+            691
+        ],
+        "page_idx": 10
+    },
+    {
+        "type": "text",
+        "text": "Let $\\boldsymbol { w } ^ { \\star } : = \\mathsf { p r o x } _ { \\lambda \\Omega _ { E } }$ , and denote by $G _ { i }$ the set of indices fused to $w _ { i }$ in the solution. Define $s _ { i j } =$ $\\mathsf { s i g n } ( w _ { i } ^ { \\star } - w _ { j } ^ { \\star } )$ . ",
+        "bbox": [
+            173,
+            702,
+            823,
+            733
+        ],
+        "page_idx": 10
+    },
+    {
+        "type": "text",
+        "text": "Proof. The subgradient optimality conditions of Eq. 4 are: (Friedman et al., 2007) ",
+        "bbox": [
+            173,
+            746,
+            714,
+            762
+        ],
+        "page_idx": 10
+    },
+    {
+        "type": "equation",
+        "img_path": "images/764a8471958cf047036a7ac3893492b80bdc4b97fd5be2aee0180bed53de94db.jpg",
+        "text": "$$\nw _ { i } ^ { \\star } - z _ { i } + \\sum _ { k : i \\sim k } \\lambda t _ { i k } - \\sum _ { k : k \\sim i } \\lambda t _ { k i } = 0 , \\quad \\quad 1 \\leq i \\leq d .\n$$",
+        "text_format": "latex",
+        "bbox": [
+            316,
+            777,
+            681,
+            810
+        ],
+        "page_idx": 10
+    },
+    {
+        "type": "text",
+        "text": "where $t _ { i j } = \\mathsf { s i g n } ( w _ { i } ^ { \\star } - w _ { j } ^ { \\star } )$ if $w _ { i } ^ { \\star } \\neq w _ { j } ^ { \\star }$ , otherwise $t _ { i j }$ is a free variable in $[ - 1 , 1 ]$ . ",
+        "bbox": [
+            173,
+            813,
+            710,
+            830
+        ],
+        "page_idx": 10
+    },
+    {
+        "type": "text",
+        "text": "We focus on a single group $G = G _ { i }$ , dropping the index $i$ for brevity. Within a fused group, the solution is constant, i.e., $w _ { j } ^ { \\star } = w$ for $j \\in G$ . We separate the sums in Eq. 16 according to whether $k \\in G$ or not, and move the “constant” terms to the right hand side, yielding the system ",
+        "bbox": [
+            174,
+            835,
+            825,
+            878
+        ],
+        "page_idx": 10
+    },
+    {
+        "type": "equation",
+        "img_path": "images/1bbf79106246f6e8eeced9f55319bfaa92f27b4a2b55188eecad487e66582f02.jpg",
+        "text": "$$\nw + \\sum _ { j \\sim k } \\lambda t _ { j k } - \\sum _ { k \\sim j \\atop k \\in G } \\lambda t _ { k j } = z _ { j } + \\sum _ { \\stackrel { k \\sim j } { k \\notin G } } \\lambda s _ { k j } - \\sum _ { j \\sim k } \\lambda s _ { j k } , \\qquad j \\in G .\n$$",
+        "text_format": "latex",
+        "bbox": [
+            271,
+            882,
+            725,
+            928
+        ],
+        "page_idx": 10
+    },
+    {
+        "type": "text",
+        "text": "Summing up the Eq. 17 over all $j \\in G$ , we observe that for any $k \\in G$ , the term $\\lambda t _ { j k }$ appears twice with opposite signs. Thus, ",
+        "bbox": [
+            173,
+            102,
+            823,
+            133
+        ],
+        "page_idx": 11
+    },
+    {
+        "type": "equation",
+        "img_path": "images/62de83a721975b3ee86862544ea995947d8d801b9fab281f76e4807dfdbd6ab2.jpg",
+        "text": "$$\n\\sum _ { j \\in G } w = \\sum _ { j \\in G } \\left( z _ { j } + \\sum _ { \\stackrel { k \\sim j } { k \\notin G } } \\lambda s _ { k j } - \\sum _ { j \\stackrel { \\sim k } { k \\notin G } } \\lambda s _ { j k } \\right) .\n$$",
+        "text_format": "latex",
+        "bbox": [
+            346,
+            137,
+            651,
+            204
+        ],
+        "page_idx": 11
+    },
+    {
+        "type": "text",
+        "text": "Dividing by $| G |$ gives exactly Eq. 8. This reasoning applies to any group $G _ { i }$ ",
+        "bbox": [
+            173,
+            210,
+            674,
+            226
+        ],
+        "page_idx": 11
+    },
+    {
+        "type": "text",
+        "text": "B HUMAN EVALUATION DESCRIPTION ",
+        "text_level": 1,
+        "bbox": [
+            174,
+            246,
+            506,
+            261
+        ],
+        "page_idx": 11
+    },
+    {
+        "type": "text",
+        "text": "To perform the human evaluation firstly 100 images were randomly selected from the test set of the MSCOCO dataset (using the split proposed by Karpathy & Fei-Fei (2015)). For each of the selected images, the human evaluators selected a score from 1 to 5 for the captions generated by the models using softmax attention, sparsemax attention, and TVMAX attention. They were also asked to evaluate whether the models attend to the relevant regions of the image when generating a certain word. For that they observed the attention plots corresponding to the non stop words of the caption of each of the models. While in Figures 1 and 3, 4, and 5 we emphasized sparsity with a hard white mask, for the human evaluation the sparse regions of the attention plots were simply fully transparent, to avoid biasing the evaluators. The possible scores were also between 1 and 5. The 100 images were judged by 6 persons both for the captions evaluation and attention evaluation. The order of the captions and attention plots was randomly chosen for each image. ",
+        "bbox": [
+            173,
+            276,
+            825,
+            429
+        ],
+        "page_idx": 11
+    },
+    {
+        "type": "text",
+        "text": "With these scores, we computed the mean of the captions evaluation scores and the mean of the attention relevance evaluation scores. The results are reported in Table 2. ",
+        "bbox": [
+            173,
+            436,
+            823,
+            465
+        ],
+        "page_idx": 11
+    },
+    {
+        "type": "text",
+        "text": "C ADDITIONAL ATTENTION VISUALIZATION ",
+        "text_level": 1,
+        "bbox": [
+            174,
+            486,
+            562,
+            501
+        ],
+        "page_idx": 11
+    },
+    {
+        "type": "image",
+        "img_path": "images/55fe3f71d6594beb180beb9dcdbf6de0facac18317739482992ae722e854974c.jpg",
+        "image_caption": [
+            "Figure 4: Example generated captions using softmax attention (top), sparsemax attention (middle) and TVMAX attention (bottom). The captions are “A bowl of fruit and a bowl of fruit”, “A bowl of fruit and oranges on a table” and “A bowl of oranges and a banana on a table”. "
+        ],
+        "image_footnote": [],
+        "bbox": [
+            176,
+            520,
+            823,
+            664
+        ],
+        "page_idx": 11
+    },
+    {
+        "type": "image",
+        "img_path": "images/2dfa42c0aeb73323465d313c7d5d26e5bd7532f94f492775f4191ce42f005ec3.jpg",
+        "image_caption": [
+            "Figure 5: Example generated captions using softmax attention (top), sparsemax attention (middle) and TVMAX attention (bottom). The captions are “A soccer player is running to the base”, “A soccer player is running to the field” and “A group of people playing soccer on a field”. "
+        ],
+        "image_footnote": [],
+        "bbox": [
+            176,
+            404,
+            823,
+            556
+        ],
+        "page_idx": 12
+    }
+]

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