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+# Collaborating with Humans without Human Data
+
+DJ Strouse⇤, Kevin R. McKee, Matt Botvinick, Edward Hughes, Richard Everett⇤ DeepMind {strouse, kevinrmckee, botvinick, edwardhughes, reverett}@deepmind.com
+
+# Abstract
+
+Collaborating with humans requires rapidly adapting to their individual strengths, weaknesses, and preferences. Unfortunately, most standard multi-agent reinforcement learning techniques, such as self-play (SP) or population play (PP), produce agents that overfit to their training partners and do not generalize well to humans. Alternatively, researchers can collect human data, train a human model using behavioral cloning, and then use that model to train “human-aware” agents (“behavioral cloning play”, or BCP). While such an approach can improve the generalization of agents to new human co-players, it involves the onerous and expensive step of collecting large amounts of human data first. Here, we study the problem of how to train agents that collaborate well with human partners without using human data. We argue that the crux of the problem is to produce a diverse set of training partners. Drawing inspiration from successful multi-agent approaches in competitive domains, we find that a surprisingly simple approach is highly effective. We train our agent partner as the best response to a population of self-play agents and their past checkpoints taken throughout training, a method we call Fictitious Co-Play (FCP). Our experiments focus on a two-player collaborative cooking simulator that has recently been proposed as a challenge problem for coordination with humans. We find that FCP agents score significantly higher than SP, PP, and BCP when paired with novel agent and human partners. Furthermore, humans also report a strong subjective preference to partnering with FCP agents over all baselines.
+
+# 1 Introduction
+
+Generating agents which collaborate with novel partners is a longstanding challenge for Artificial Intelligence (AI) [4, 16, 37, 52]. Achieving ad-hoc, zero-shot coordination [31, $\boxed { 6 6 }$ is especially important in situations where an AI must generalize to novel human partners [6, 61]. Many successful approaches have employed human models, either constructed explicitly [14, 35, 53] or learnt implicitly [12, 60]. By contrast, recent work in competitive domains has shown that it is possible to reach humanlevel using model-free reinforcement learning (RL) without human data, via self-play [8, 9, 63, 64]. This begs the question: Can model-free RL without human data generate agents that can collaborate with novel humans?
+
+We seek an answer to this question in the space of common-payoff games, where all agents work towards a shared goal and receive the same reward. Self-play (SP), in which an agent learns from repeated games played against copies of itself, does not produce agents that generalize well to novel co-players [10, 11, 21, 44]. Intuitively, this is because agents trained in self-play only ever need to coordinate with themselves, and so make for brittle and stubborn collaborators with new partners who act differently. Population play (PP) trains a population of agents, all of whom interact with each other $\pmb { \| 3 9 \| }$ . While PP can generate agents capable of cooperation with humans in competitive team games $\pmb { \Vert 3 4 \Vert }$ , it still fails to produce robust partners for novel humans in pure common-payoff settings [12]. PP in common-payoff settings naturally encourages agents to play the same way, reducing strategic diversity and producing agents not so different from self-play $\dot { \lVert 2 4 \rVert }$ .
+
+![](images/70b2b8c1e9478aed36abef766805e05c03561ba29533d4a7de7ad061fa2d261f.jpg)  
+Figure 1: In this work, we evaluate a variety of agent training methods (Section 2) in zero-shot coordination with agents (Section 4). We then run a human-agent collaborative study designed to elicit human preferences over agents (Section 5)
+
+Our approach starts with the intuition that the key to producing robust agent collaborators is exposure to diverse training partners. We find that a surprisingly simple strategy is effective in generating sufficient diversity. We train $N$ self-play agents varying only their random seed for neural network initialization. Periodically during training, we save agent “checkpoints” representing their strategy at that point in time. Then, we train an agent partner as the best-response to both the fully-trained agents and their past checkpoints. The different checkpoints simulate different skill levels, and the different random seeds simulate breaking symmetries in different ways. We refer to this agent training procedure as Fictitious $\mathbf { C o }$ -Play (FCP) for its relationship to fictitious self-play [7, 27, 28, 69].
+
+We evaluate FCP in a fully-observable two-player common-payoff collaborative cooking simulator. Based on the game Overcooked $\mathbb { \left. \boldsymbol { \ 2 5 } \right. }$ , it has recently been proposed as a coordination challenge for AI [12, 50, 70]. State-of-the-art performance in producing agents capable of generalization to novel humans was achieved in $[ \mathbb { 1 2 } ]$ via behavioral cloning (BC) of human data. More precisely, BC was used to produce models that can stand in as human proxies during training in simulation, a method we call behavioral cloning play (BCP). We demonstrate that FCP outperforms BCP in generalizing to both novel agent and human partners, and that humans express a significant preference for partnering with FCP over BCP. Our method avoids the cost and potential privacy concerns of collecting human data for training, while achieving better outcomes for humans at test time.
+
+We summarize the novel contributions of this paper as follows:
+
+1. We propose Fictitious Co-Play (FCP) to train agents capable of zero-shot coordination with humans (Section 2.1).   
+2. We demonstrate that FCP agents generalize better than SP, PP, and BCP in zero-shot coordination with a variety of held-out agents (Section 4.2).   
+3. We propose a rigorous human-agent interaction study with behavioral analysis and participant feedback (Section $5 . 1 )$ .   
+4. We demonstrate that FCP significantly outperforms the BCP state-of-the-art, both in task score and in human partner preference (Section $\underline { { \overline { { 5 . 2 } } } } )$ .
+
+# 2 Methods
+
+# 2.1 Fictitious Co-Play (FCP)
+
+Diverse training conditions have been shown to make agents more robust, from environmental variations (i.e. domain randomization $\textcircled { 1 5 4 } , \textcircled { 5 6 } , \textcircled { 6 7 } \textcircled { 1 }$ to heterogeneity in training partners $\mathbb { \left. \boldsymbol { \mathfrak { G } } \boldsymbol { \mathfrak { g } } \right. }$ . We seek to train agents that are robust partners for humans in common-payoff games, and so extend this line of work to that setting.
+
+One important challenge in collaborating with novel partners is dealing with symmetries $\pmb { \mathbb { B } } \mathbf { \mathbb { 1 } }$ . For example, two agents A and B facing each other may move past each other by A going left and B going right, or vice versa. Both are valid solutions, but a good agent partner will adaptively switch between these conventions if a human clearly prefers one over the other. A second important challenge is dealing with variations in skill level. Good agent partners should be able to assist both highly-skilled partners, as well as partners who are still learning.
+
+![](images/2372b76b2e16cbfb2db5439982c244e9b3e60b30aff99699aa5043d431598f6f.jpg)  
+Figure 2: The four agent training methods we evaluate in this work. Self-play (SP) where an agent learns with itself, population-play (PP) where a population of agents are co-trained together, and behavioral cloning play (BCP) where data from human games is used to create a behaviorally cloned agent with which an RL agent is then trained. In our method, Fictitious Co-Play (FCP), $N$ self-play agents are trained independently and checkpointed throughout training. An agent is then trained to best respond to the entire population of SP agents and their checkpoints.
+
+Fictitious co-play (FCP) is a simple two-stage approach for training agents that overcomes both of these challenges (Figure $2 ,$ right). In the first stage, we train a diverse pool of partners. To allow the pool to represent different symmetry breaking conventions, we train $N$ partner agents in self-play. Since these partners are trained independently, they can arrive at different arbitrary conventions for breaking symmetries. To allow the pool to represent different skill levels, we use multiple checkpoints of each self-play partner throughout training. The final checkpoint represents a fully-trained “skillful” partner, while earlier checkpoints represent less skilled partners. Notably, by using multiple checkpoints per partner, this additional diversity in skill incurs no extra training cost.
+
+In the second stage, we train an FCP agent as the best response to the pool of diverse partners created in the first stage. Importantly, the partner parameters are frozen and thus FCP must learn to adapt to partners, rather than expect partners to adapt to it. In this way, FCP agents are prepared to follow the lead of human partners, and learn a general policy across a range of strategies and skills. We call our method “fictitious” co-play for its relationship to fictitious self-play in which competitive agents are trained with past checkpoints (in that case, to avoid strategy cycling) [7, 27, 28, 39, 69].
+
+# 2.2 Baselines and ablations
+
+We compare FCP agents to the three baseline training methods listed below, each varying only in their set of training partners, with the RL algorithm and architecture consistent across all agents:
+
+1. Self-play (SP), where agents learn solely through interaction with themselves.   
+2. Population-play (PP), where a population of agents are co-trained through random pairings.   
+3. Behavioral cloning play (BCP), where an agent is trained with a BC model of a human [12].
+
+We also evaluate three variations on FCP to better understand the conditions for its success:
+
+1. To test the importance of including past checkpoints in training, we evaluate an ablation of FCP in which agents are trained only with the converged checkpoints of their partners $\mathrm { F C P } _ { - T }$ for “FCP minus time”). 2. To test whether FCP would benefit from additional diversity in its partner population, we evaluate an augmentation of FCP in which the population of SP partners varies not just in random seed, but also in architecture $\operatorname { F C P } _ { + A }$ for “FCP plus architectural variation”). 3. To test whether architectural variation can serve as a full replacement for playing with past checkpoints, we evaluate the combination of both modifications $( \mathrm { F C P } _ { - T , + A } )$ .
+
+# 2.3 Environment
+
+Following prior work on zero-shot coordination in human-agent interaction, we study the Overcooked environment (see Figure 3) [12, 13, 38, 50, 70]. We draw particular inspiration from the environment in Carroll et al. [12]. For full details, see Appendix A.
+
+In this environment, players are placed into a gridworld kitchen as chefs and tasked with delivering as many cooked dishes of tomato soup as possible within an episode. This involves a series of sequential high-level actions to which both players can contribute: collecting tomatoes, depositing them into cooking pots, letting the tomatoes cook into soup, collecting a dish, getting the soup, and delivering it. Upon a successful delivery, both players are rewarded equally.
+
+To effectively complete the task, players must learn to navigate the kitchen and interact with objects in the correct order, all while maintaining awareness of their partner’s behavior to coordinate with them. This environment therefore presents the challenges of both movement and strategic coordination.
+
+Each player observes an egocentric RGB view of the world, and at every step can perform one of six actions: stand still, move {up, down, left, right}, interact. The behavior ofLÈ¡áyҏįŘįºµò‹µÒ¡y® interact varies based on the cell which the player is facing (e.g. place tomato on counter).
+
+![](images/48e8af75423e0fa5e5c23e2088c49716c4c6044ee3579f26cdd9911dbb4b4925.jpg)  
+Figure 3: The Overcooked environment: a two-player common-payoff game in which players must coordinate to cook and deliver soup.
+
+![](images/2b3253fcaac0677dbb15cc1ed5aa0663e561ff52605ba15bd61605f96c716872.jpg)  
+Figure 4: Layouts: the kitchens which agents and humans play in, each emphasizing different coordination strategies. Highlighted in bold are the terms used to refer to each in the rest of this paper.
+
+# 2.4 Implementation details
+
+Here we highlight several key implementation details for our training methods. For full details, including the architectures, hyperparameters, and compute used, please see Appendix B.
+
+For our reinforcement learning agents, we use the V-MPO $\boldsymbol { \left[ \left[ 6 5 \right] \right] }$ algorithm along with a ResNet [26] plus LSTM $\mathbb { \left| \bigstar \bigstar \right\| }$ architecture which we found led to optimal behavior across all layouts. Agents are trained using a distributed set of environments running in parallel $\textcircled { 1 1 7 }$ , each sampling two agents from the training population to play together every episode.
+
+Both PP and FCP are trained with a population size of $N = 3 2$ agents which are sampled uniformly. For FCP, we use 3 checkpoints for each agent, therefore incurring no additional training burden: (1) at initialization (i.e. a low-skilled agent), (2) at the end of training (i.e. a fully-trained expert agent), and (3) at the middle of training, defined as when the agent reaches $50 \%$ of its final reward (i.e. an average-skilled agent). When varying architecture for the training partners of the $\operatorname { F C P } _ { + A }$ and $\mathrm { F C P } _ { - T , + A }$ variants, we vary whether the partners use memory (i.e. LSTM vs not) and the width of their policy and value networks (i.e. 16 vs 256). In total, we train 8 agents for each of the 4 combinations, leaving the total population size of $N = 3 2$ unchanged, ensuring a fair comparison.
+
+To train agents via behavioral cloning $\left[ \left[ 5 8 \right] \right]$ , we use the open-source Acme $\pmb { \mathbb { B } } 0 \|$ to learn a policy from human gameplay data. Specifically, we collected 5 human-human trajectories of length 1200 time steps for each of the 5 layouts, resulting in 60k total environment steps. We divide this data in half and train two BC agents: (1) a partner for training a BCP agent, and (2) a “human proxy” partner for agent-agent evaluation. Following Carroll et al. $\bar { \lVert 1 2 \rVert }$ , we use a set of feature-based observations for the agents (as opposed to RGB) and generate comparable results: performance is higher on 3 layouts (asymmetric, cramped, and ring) but poorer on the other 2 (circuit and forced).
+
+# 3 Related work
+
+Ad-hoc team play There is a large and diverse body of literature on ad-hoc team-play $ { \mathbb { B } } ,  { \mathbb { G } } 6  { \mathbb { I } }$ , also known as zero-shot coordination $\bar { \mathbb { B } } \mathbb { I }$ . Prior work based in game-theoretic settings has suggested the benefits of planning $\pmb { \mathbb { Z } 1 }$ , online learning $\mathbb { \left| \left. \sum \right. { ] } \right| }$ , and novel solution concepts $\bar { \mathbb { D } }$ , to name a few examples. More recently, multi-agent deep reinforcement learning has provided the tools to scale to more complex gridworld or continuous control settings, leading to work on hierarchical social planning $\widehat { \left\| 3 6 \right\| }$ , adapting to existing social conventions $\checkmark$ , trajectory diversity $\lVert \rVert \dot { \boldsymbol { \mathrm { E } } } \rVert$ , and theory of mind [14]. Ad-hoc team-play among novel agent partners is also an object of active study in the emergent communication literature [10, 11, 43]. This prior work has tended to focus on generalization to held-out agent partners as a proxy for human co-players.
+
+Collaborative play with novel humans has been evaluated more actively in the context of training agent assistants; see for instance [57, 68]. To our knowledge, our FCP agents represent the stateof-the-art in coordinating with novel human partners on an equal footing of capabilities in a rich gridworld environment, as measured by the challenge tasks in Carroll et al. [12].
+
+Diversity in multi-agent reinforcement learning In multi-agent reinforcement learning, agents that train with behaviorally diverse populations of game partners tend to demonstrate stronger performance than their self-play counterparts. For example, across a range of multi-agent games, generalization to held-out populations can be improved by training larger and more diverse populations [13, 42, 50]. In mixed-motive settings, cooperation among agents can be encouraged through social diversity, such as in player preferences and rewards [3, 47, 49]. Similarly, competitiveness can be optimized through selective matchmaking between increasingly diverse agents $[ \overbrace { 2 4 } , \overbrace { 3 9 } , \overbrace { 6 9 } ]$ .
+
+Despite the increased focus on improving multi-agent performance, evaluation has typically been constrained to agent-agent settings. High-performing agents have infrequently been evaluated with humans, particularly in non-competitive domains $\bar { \lVert 1 6 rVert }$ . We add to this growing literature, showing that training with diversity is a powerful approach for effective human-agent collaboration.
+
+Human-agent interaction In recent years, increased attention has been directed toward designing machine learning agents capable of collaborating with humans [41, 57, 68, 72] (see also $\boxed { \boxed { 1 6 } }$ for a broader review on Cooperative AI). Tylkin et al. $\lVert \rVert$ is particularly notable in also demonstrating that partially trained agents can be useful learning targets for human helpers, although in a different domain (cooperative Atari). Our method, FCP, can be seen as extending theirs by training with multiple “skill levels” and random seeds, rather than just one, which we demonstrate to be crucial to our agents’ performance (Tables 1 and 2 and Figure 7b).
+
+A key preceding entry in this research area is Carroll et al. $\pmb { \mathbb { I } }$ , who similarly investigated humanagent coordination in Overcooked. We use their method (BCP) as a baseline throughout our experiments (Section $\boxed { 2 . 2 }$ . Relative to BCP, our approach removes the need for the expensive step of human data collection for agent training. Furthermore, through our novel human-agent experimental design, we go beyond objective performance metrics to compare the subjective preferences that agents generate. For a detailed comparison of methods and results, see Appendix E.
+
+# 4 Zero-shot coordination with agents
+
+In this section, we evaluate our FCP agent, its ablations, and the baselines with held-out agents.
+
+# 4.1 Evaluation method: collaborative evaluation with agent partners
+
+Our primary concern in this work is generalization to novel human partners (as investigated in Section $\textcircled{5}$ . However, just as collecting human-human data for behavioral cloning is expensive, so too is evaluating agents with humans. Consequently, we instead use generalization to held-out agent partners as a cheap proxy of performance with humans. This is then used to guide our model selection process, allowing us to be more targeted with the agents we select for our human-agent evaluations.
+
+We evaluate with three held-out populations:
+
+1. A BC model trained on human data, $H _ { \mathrm { p r o x y } }$ , intended as a proxy of generalization to humans, as done by Carroll et al. $[ \overbrace { | 1 2 | }$ . 2. A set of self-play agents varying in seed, architecture, and training time (specifically, heldout seeds of the $N = 3 2$ partners trained for the $\mathrm { F C P } _ { + A }$ agent; see Section 2.4). These are intended to test generalization to a diverse yet still skillful population. 3. Randomly initialized agents intended to test generalization to low-skill partners.
+
+For all results, we report the average number of deliveries made by both players within an episode, aggregated across the 5 different layouts from Figure $^ 4$ (with the per-layout results reported in Appendix $\underline { { \overline { { ( \mathrm { C . 2 } ) } } } }$ . We estimate mean and standard deviation across 5 random seeds. For each seed, we evaluate the agent with all members of the held-out population for 10 episodes per agent-partner pair.
+
+# 4.2 Results
+
+# Finding 1: FCP significantly outperforms all baselines
+
+To begin, we compare our FCP agent and the baselines when partnered with the three held-out populations introduced above. As can be seen in Figure $\boxed { 5 }$ FCP significantly outperforms all baselines when partnered with all three held-out populations. Notably, it performs better than BCP with $H _ { \mathrm { p r o x y } }$ even though BCP trains with such a model and FCP does not. Similar to Carroll et al. $\mathbb { \lVert 1 2 \rVert }$ , we find that BCP significantly outscores SP.
+
+When paired with a randomly initialized partner which behaves suboptimally, we see an even greater difference between FCP and the baselines. Given that FCP is trained with non-held-out versions of such agents, it may not be surprising that it does so well with partners that behave poorly. However, what is surprising is how brittle the other training methods are. This suggests that they may not perform well with humans who are not highly skilled players, which we will see in Section 5.
+
+![](images/8083dcac415b6ef9624e1aa4f428a0a33c3e9d47ce8903df3798f3e80ef0427c.jpg)  
+Figure 5: Agent-agent collaborative evaluation: Performance of each agent when partnered with each of the held-out populations (Section $4 . 1 )$ in episodes of length $T = 5 4 0$ . Importantly, FCP scores higher than all baselines with a variety of test partners. Error bars represent standard deviation over five random training seeds. Plots aggregate data across kitchen layouts; results calculated by individual layout can be found in Appendix C.2.
+
+Finding 2: Training with past checkpoints is the most beneficial variation for performance Next, we investigate how the different training partner variations influence FCP’s performance. In particular, we separately ablate the past checkpoints $( T )$ and architecture $( A )$ variations, evaluating them with the same partners as in Figure 5. The results of this evaluation are presented in Table 1. Comparing the FCP and $\mathrm { F C P } _ { - T }$ columns, we see that removing past checkpoints from training significantly reduces performance. Comparing the FCP and $\operatorname { F C P } _ { + A }$ columns, we see that adding architectural variation to the training population offers no improvement over training with past
+
+<table><tr><td>Partner</td><td>FCP</td><td>FCP-T</td><td>FCP+A</td><td>FCP-T,+A</td></tr><tr><td>Hproxy</td><td>10.6± 0.5</td><td>4.7± 0.4</td><td>9.9±0.6</td><td>7.0±0.8</td></tr><tr><td>Diverse SP</td><td>11.2 ± 0.1</td><td>6.9 ± 0.1</td><td>11.1 ± 0.4</td><td>8.6 ± 0.4</td></tr><tr><td>Random</td><td>8.6± 0.2</td><td>1.0 ± 0.1</td><td>8.4±0.4</td><td>3.2 ± 0.5</td></tr></table>
+
+Table 1: Ablation results: Performance of each variation of FCP – training with past partner checkpoints $T$ for time) and adding partner variation in architecture $( A )$ . Scores are mean deliveries with standard deviation over 5 random seeds. Notably, we find that the inclusion of past checkpoints is essential for strong performance $( \mathrm { F C P } > \mathrm { F C P } _ { - T }$ ), and additionally including architectural variation does not improve performance $( \mathrm { F C P } \approx \mathrm { F C P } _ { + A . }$ ). However, architectural variation is better than no variation, improving performance when past checkpoints are not available $( \mathrm { F C P } _ { - T , + A } > \mathrm { F C P } _ { - T , }$ ).
+
+checkpoints. However, comparing the $\mathrm { F C P } _ { - T }$ and $\mathrm { F C P } _ { - T , + A }$ columns, we see that without training with past checkpoints, architectural variation in the population does improve performance.
+
+# 5 Zero-shot coordination with humans
+
+Ultimately, our goal is to develop agents capable of coordinating with novel human partners. In this section, we run an online study to evaluate our FCP agent and the baseline agents in collaborative play with human partners.
+
+![](images/5856cbdd90eeef2a7a6093668472063862a759746c339aa0324e78efb5d67b22.jpg)  
+Figure 6: Human-agent collaborative study: For our human-agent collaboration study, we recruited participants online to play games with FCP and baseline agents. Participants played a randomized sequence of episodes with different agent partners and kitchen layouts. After every two episodes, participants reported the direction and strength of their preference between their last two partners.
+
+# 5.1 Evaluation method: collaborative evaluation with human participants
+
+To test how effectively FCP’s performance generalizes to human partners, we recruited participants from Prolific $\mathbb { 1 1 8 } , \lvert 5 5 \rvert$ for an online collaboration study $N = 1 1 4$ ; $3 7 . 7 \%$ female, $5 9 . 6 \%$ male, $1 . 8 \%$ nonbinary; median age between 25–34 years). We used a within-participant design for the study: each participant played with a full cohort of agents (i.e. generated through every training method). This design allowed us to evaluate both objective performance as well as subjective preferences.
+
+Participants first read game instructions and played a short tutorial episode guiding them through the dish preparation sequence (see Appendix $\dot { \mathrm { \bf D } } . 1 . 1$ for instruction text and study screenshots). Participants then played 20 episodes with a randomized sequence of agent partners and kitchen layouts. Episodes lasted $T = 3 0 0$ steps (1 minute) each. After every two episodes, participants reported their preference over the agent partners from those episodes on a five-point Likert-type scale. After playing all 20 episodes, participants completed a debrief questionnaire collecting standard demographic information and open-ended feedback on the study. Our statistical analysis below primarily relies upon the repeated-measures analysis of variance (ANOVA) method. See Appendix D for additional details of our study design and analysis, including independent ethical review.
+
+# 5.2 Results
+
+Finding 1: FCP coordinates best with humans, achieving the highest score across maps To begin, we compare the objective team performance supported by our FCP and baseline agents. The strong FCP performance observed in agent-agent play generalizes to human-agent collaboration:
+
+the FCP-human teams significantly outperform all other agent-human teams, achieving the highest average scores across maps, every $p < 0 . 0 0 1$ (Figure $\mathrm { 7 a ) }$ , while performing as well as or better than the other teams on each individual map (see Appendix $\mathbf { D } . 3 )$ . Echoing the results from our agent-agent ablation experiments (Table $\perp )$ , the inclusion of past checkpoints in training proves critical to FCP’s strong performance, $p < 0 . 0 { \overline { { 0 1 } } }$ (Figure $\textcircled { 7 6 }$ . Similar to Carroll et al. $[ \left[ 1 2 \right] ]$ , we find that BCP outscores SP when collaborating with human players, $p < 0 . 0 0 1$ .
+
+# Finding 2: Participants prefer FCP over all baselines
+
+FCP’s strong collaborative performance carries over to our participants’ subjective partner preferences. Participants expressed a significant preference for FCP partners over all other agents, including BCP, with every $p < 0 . 0 5$ (Figure $\dot { \bigtriangledown } \dot { \mathbf { c } } { \big \rVert }$ . Notably, while human-BCP and human-PP teams did not significantly differ in their completed deliveries, participants reported significantly preferring BCP over PP, $p = 0 . 0 0 3$ , highlighting the informativeness of our subjective analysis.
+
+![](images/14e048153d10325b3617f94b393393ed3ab6cf3e38198f8791acf0fc83b051df.jpg)  
+Figure 7: Human-agent collaborative evaluation: Evaluation and preference metrics from humanagent play in episodes of length $T = 3 0 0$ . Error bars represents $9 5 \%$ confidence intervals, calculated over episodes. Plots aggregate data across kitchen layouts; results calculated by individual layout can be found in Appendix D.3.
+
+# 5.3 Exploratory behavioral analysis
+
+To better understand how the human-agent scores and preferences may have arisen, here we analyze the resulting action trajectories of each human and agent player in our experiment.
+
+![](images/65959c0ab23a18c0f8de72bc451d199e7d9d9cc2698e7ca2ac4f320e26dac829.jpg)
+
+Figure 8: Behavioral analysis: (a) FCP is able to move most frequently $3 5 \%$ of the time), corresponding to the best movement coordination with human partners. (b) FCP exhibits the most equal preferences over cooking pots (0.11 difference), aligning with human preferences. Values are calculated as the absolute difference in preferences between the two pots; 1 indicates that the player only uses one of the two available pots, while 0 indicates that the player uses both pots equally.
+
+# Finding 1: FCP exhibits the best movement coordination with humans
+
+First, we investigate how much each player moves in an episode (Figure $\textcircled { 8 \mathrm { a } }$ , where moving in a higher fraction of timesteps may suggest fewer collisions and thus better coordination with a partner. Notably, we observe two results: (1) humans rarely move, a behavior which is out-of-distribution for typical training methods (e.g. SP, PP) but is seen in the training distribution for BCP and FCP.
+
+(2) FCP moves the most on all layouts other than Forced, suggesting it is better at coordinating its movement strategy with its partner. This result was also reported by human participants, for example: “I noticed that some of my partners seemed to know they needed to move around me, while others seemed to get ‘stuck’ until I moved out of their way” (see Appendix D for more examples).
+
+# Finding 2: FCP’s preferences over cooking pots aligns best with that of humans
+
+Next, we investigate whether there was a preference for a specific cooking pot in the layouts which included two cooking pots (Figure $\textcircled { 8 6 }$ . To do this, we calculate the difference in the number of times each pot was used by each player, where a high value indicates a strong preference for one pot and a low value indicates more equal preference for the two pots.
+
+As can be seen in the FCP column, our agent typically has the most aligned preferences with that of humans (0.11 for FCP to 0.14 for humans). Behaviorally speaking, this means that our agent prefers one cooking pot over the other $5 5 . 5 \%$ of the time (i.e. a 0.11 point difference). In contrast, all other agents have a strong preference for a single pot. This is a non-adaptive strategy which generalizes poorly to typical human behavior of using both pots, leading to worse performance.
+
+# 6 Discussion
+
+Summary In this work, we investigated the challenging problem of zero-shot collaboration with humans without using human data in the training pipeline. To accomplish this, we introduced Fictitious Co-Play (FCP) – a surprisingly simple yet effective method based on creating a diverse set of training partners. We found that FCP agents scored significantly higher than all baselines when partnered with both novel agent and human partners. Furthermore, through a rigorous human-agent experimental design, we also found that humans reported a strong subjective preference to partnering with FCP agents over all baselines.
+
+Limitations and future work Our method currently relies on the manual process of initially training and selecting a diverse set of partners. This is not only time consuming, but also prone to researcher biases that may negatively influence the behavior of the created agents. Additionally, while we found FCP with a partner population size of $N = 3 2$ sufficient here, for more complex games, FCP may require an unrealistically large partner population size to represent sufficiently diverse strategies. To address these concerns, methods for automatically generating partner diversity for common-payoff games may be important. Possibilities include adaptive population matchmaking as been used in competitive zero-sum games $\mathbb { \lVert 6 9 \rVert }$ , as well as auxiliary objectives that explicitly encourage behavioral diversity [19, 45, 46].
+
+Our method requires a known and fixed reward function. We also focus on one domain in order to compare with prior work which has argued that human-in-the-loop training is necessary. Consequently, the resulting agents are only designed to adaptively collaborate on a single task, and not to infer human preferences in general $\textcircled { 1 1 } \textcircled { 3 3 } \textcircled { 5 9 }$ . Moreover, if a task’s reward function is poorly aligned with how humans approach the task, our method may well produce subpar partners, as would any method without access to human data. Thus, additional domains and tasks should be studied to better understand how our method generalizes. Targeted experiments to test specific forms of generalization may be especially helpful in this regard $\overline { { [ 3 8 ] } }$ , as could approaches that procedurally generate environment layouts requiring diverse solutions $\pmb { \mathbb { Z } } 2 \mathbf { l }$
+
+Finally, it may be possible to produce even stronger agent assistants by combining the strengths of FCP (i.e. diversity) and BCP (i.e. human-like play). Indeed, Knott et al. $\textcircled { \lvert 3 8 \rvert }$ recently demonstrated that modifying BCP to train with multiple BC partners produces more robust collaboration with held-out agents, a finding that would be interesting to test with human partners.
+
+Societal impact A challenge for this line of work is ensuring agent behavior is aligned with human values (i.e. the AI value alignment problem [23, 59]). Our method has no guarantees that the resulting policy aligns with the preferences, intentions, or welfare of its potential partners. It likewise does not exclude the possibility that the target being optimized for is harmful (e.g. if the agent’s partner expresses preferences or intentions to harm others). This could therefore produce negative societal effects either if training leads to poor alignment or if agents are optimized for harmful metrics.
+
+One potential strategy for mitigating these risks is the use of human preference data [15]. Such data could be used to fine-tune and filter trained agents before deployment, encouraging better alignment with human values. A key question in this line of research is how human preference data should be aggregated—or selected, in the case of expert preferences—when our aim is to create socially aligned agents (i.e. agents that are sufficiently aligned for everyone). Relatedly, targeted research on human beliefs and perceptions of AI $\lVert \overline { { 4 8 } } \rVert$ , and how they steer human-agent interaction, would help inform agent design for positive societal impact. For instance, developers could incorporate specific priors into agents to reinforce tendencies for fair outcomes $\pm \mathbb { Z } 0 . \pm \mathbb { B } 2 \mathbb { I }$ .
+
+Conclusion We proposed a method which is both effective at collaborating with humans and simple to implement. We also presented a rigorous and general methodology for evaluating with humans and eliciting their preferences. Together, these establish a strong foundation for future research on the important challenge of human-agent collaboration for benefiting society.
+
+# Acknowledgements
+
+The authors would like to thank Mary Cassin for creating the game sprite art; Rohin Shah, Thore Graepel, and Iason Gabriel for feedback on the draft; Lucy Campbell-Gillingham, Tina Zhu, and Saffron Huang for support in evaluating agents with humans; and Max Kleiman-Weiner, Natasha Jaques, Marc Lanctot, Mike Bowling, and Dan Roberts for useful discussions.
+
+# Funding disclosure
+
+This work was funded solely by DeepMind. The authors declare no competing interests.
+
+# References
+
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+    {
+        "type": "text",
+        "text": "Collaborating with Humans without Human Data ",
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+        "type": "text",
+        "text": "DJ Strouse⇤, Kevin R. McKee, Matt Botvinick, Edward Hughes, Richard Everett⇤ DeepMind {strouse, kevinrmckee, botvinick, edwardhughes, reverett}@deepmind.com ",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "Abstract ",
+        "text_level": 1,
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+        "type": "text",
+        "text": "Collaborating with humans requires rapidly adapting to their individual strengths, weaknesses, and preferences. Unfortunately, most standard multi-agent reinforcement learning techniques, such as self-play (SP) or population play (PP), produce agents that overfit to their training partners and do not generalize well to humans. Alternatively, researchers can collect human data, train a human model using behavioral cloning, and then use that model to train “human-aware” agents (“behavioral cloning play”, or BCP). While such an approach can improve the generalization of agents to new human co-players, it involves the onerous and expensive step of collecting large amounts of human data first. Here, we study the problem of how to train agents that collaborate well with human partners without using human data. We argue that the crux of the problem is to produce a diverse set of training partners. Drawing inspiration from successful multi-agent approaches in competitive domains, we find that a surprisingly simple approach is highly effective. We train our agent partner as the best response to a population of self-play agents and their past checkpoints taken throughout training, a method we call Fictitious Co-Play (FCP). Our experiments focus on a two-player collaborative cooking simulator that has recently been proposed as a challenge problem for coordination with humans. We find that FCP agents score significantly higher than SP, PP, and BCP when paired with novel agent and human partners. Furthermore, humans also report a strong subjective preference to partnering with FCP agents over all baselines. ",
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+    {
+        "type": "text",
+        "text": "1 Introduction ",
+        "text_level": 1,
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+    },
+    {
+        "type": "text",
+        "text": "Generating agents which collaborate with novel partners is a longstanding challenge for Artificial Intelligence (AI) [4, 16, 37, 52]. Achieving ad-hoc, zero-shot coordination [31, $\\boxed { 6 6 }$ is especially important in situations where an AI must generalize to novel human partners [6, 61]. Many successful approaches have employed human models, either constructed explicitly [14, 35, 53] or learnt implicitly [12, 60]. By contrast, recent work in competitive domains has shown that it is possible to reach humanlevel using model-free reinforcement learning (RL) without human data, via self-play [8, 9, 63, 64]. This begs the question: Can model-free RL without human data generate agents that can collaborate with novel humans? ",
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+    {
+        "type": "text",
+        "text": "We seek an answer to this question in the space of common-payoff games, where all agents work towards a shared goal and receive the same reward. Self-play (SP), in which an agent learns from repeated games played against copies of itself, does not produce agents that generalize well to novel co-players [10, 11, 21, 44]. Intuitively, this is because agents trained in self-play only ever need to coordinate with themselves, and so make for brittle and stubborn collaborators with new partners who act differently. Population play (PP) trains a population of agents, all of whom interact with each other $\\pmb { \\| 3 9 \\| }$ . While PP can generate agents capable of cooperation with humans in competitive team games $\\pmb { \\Vert 3 4 \\Vert }$ , it still fails to produce robust partners for novel humans in pure common-payoff settings [12]. PP in common-payoff settings naturally encourages agents to play the same way, reducing strategic diversity and producing agents not so different from self-play $\\dot { \\lVert 2 4 \\rVert }$ . ",
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+        "image_caption": [
+            "Figure 1: In this work, we evaluate a variety of agent training methods (Section 2) in zero-shot coordination with agents (Section 4). We then run a human-agent collaborative study designed to elicit human preferences over agents (Section 5) "
+        ],
+        "image_footnote": [],
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+        "text": "Our approach starts with the intuition that the key to producing robust agent collaborators is exposure to diverse training partners. We find that a surprisingly simple strategy is effective in generating sufficient diversity. We train $N$ self-play agents varying only their random seed for neural network initialization. Periodically during training, we save agent “checkpoints” representing their strategy at that point in time. Then, we train an agent partner as the best-response to both the fully-trained agents and their past checkpoints. The different checkpoints simulate different skill levels, and the different random seeds simulate breaking symmetries in different ways. We refer to this agent training procedure as Fictitious $\\mathbf { C o }$ -Play (FCP) for its relationship to fictitious self-play [7, 27, 28, 69]. ",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "We evaluate FCP in a fully-observable two-player common-payoff collaborative cooking simulator. Based on the game Overcooked $\\mathbb { \\left. \\boldsymbol { \\ 2 5 } \\right. }$ , it has recently been proposed as a coordination challenge for AI [12, 50, 70]. State-of-the-art performance in producing agents capable of generalization to novel humans was achieved in $[ \\mathbb { 1 2 } ]$ via behavioral cloning (BC) of human data. More precisely, BC was used to produce models that can stand in as human proxies during training in simulation, a method we call behavioral cloning play (BCP). We demonstrate that FCP outperforms BCP in generalizing to both novel agent and human partners, and that humans express a significant preference for partnering with FCP over BCP. Our method avoids the cost and potential privacy concerns of collecting human data for training, while achieving better outcomes for humans at test time. ",
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+    {
+        "type": "text",
+        "text": "We summarize the novel contributions of this paper as follows: ",
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+    {
+        "type": "text",
+        "text": "1. We propose Fictitious Co-Play (FCP) to train agents capable of zero-shot coordination with humans (Section 2.1).   \n2. We demonstrate that FCP agents generalize better than SP, PP, and BCP in zero-shot coordination with a variety of held-out agents (Section 4.2).   \n3. We propose a rigorous human-agent interaction study with behavioral analysis and participant feedback (Section $5 . 1 )$ .   \n4. We demonstrate that FCP significantly outperforms the BCP state-of-the-art, both in task score and in human partner preference (Section $\\underline { { \\overline { { 5 . 2 } } } } )$ . ",
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+        "type": "text",
+        "text": "2 Methods ",
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+        "type": "text",
+        "text": "2.1 Fictitious Co-Play (FCP) ",
+        "text_level": 1,
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+        "type": "text",
+        "text": "Diverse training conditions have been shown to make agents more robust, from environmental variations (i.e. domain randomization $\\textcircled { 1 5 4 } , \\textcircled { 5 6 } , \\textcircled { 6 7 } \\textcircled { 1 }$ to heterogeneity in training partners $\\mathbb { \\left. \\boldsymbol { \\mathfrak { G } } \\boldsymbol { \\mathfrak { g } } \\right. }$ . We seek to train agents that are robust partners for humans in common-payoff games, and so extend this line of work to that setting. ",
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+    {
+        "type": "text",
+        "text": "One important challenge in collaborating with novel partners is dealing with symmetries $\\pmb { \\mathbb { B } } \\mathbf { \\mathbb { 1 } }$ . For example, two agents A and B facing each other may move past each other by A going left and B going right, or vice versa. Both are valid solutions, but a good agent partner will adaptively switch between these conventions if a human clearly prefers one over the other. A second important challenge is dealing with variations in skill level. Good agent partners should be able to assist both highly-skilled partners, as well as partners who are still learning. ",
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+        "image_caption": [
+            "Figure 2: The four agent training methods we evaluate in this work. Self-play (SP) where an agent learns with itself, population-play (PP) where a population of agents are co-trained together, and behavioral cloning play (BCP) where data from human games is used to create a behaviorally cloned agent with which an RL agent is then trained. In our method, Fictitious Co-Play (FCP), $N$ self-play agents are trained independently and checkpointed throughout training. An agent is then trained to best respond to the entire population of SP agents and their checkpoints. "
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+        "text": "Fictitious co-play (FCP) is a simple two-stage approach for training agents that overcomes both of these challenges (Figure $2 ,$ right). In the first stage, we train a diverse pool of partners. To allow the pool to represent different symmetry breaking conventions, we train $N$ partner agents in self-play. Since these partners are trained independently, they can arrive at different arbitrary conventions for breaking symmetries. To allow the pool to represent different skill levels, we use multiple checkpoints of each self-play partner throughout training. The final checkpoint represents a fully-trained “skillful” partner, while earlier checkpoints represent less skilled partners. Notably, by using multiple checkpoints per partner, this additional diversity in skill incurs no extra training cost. ",
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+        "type": "text",
+        "text": "In the second stage, we train an FCP agent as the best response to the pool of diverse partners created in the first stage. Importantly, the partner parameters are frozen and thus FCP must learn to adapt to partners, rather than expect partners to adapt to it. In this way, FCP agents are prepared to follow the lead of human partners, and learn a general policy across a range of strategies and skills. We call our method “fictitious” co-play for its relationship to fictitious self-play in which competitive agents are trained with past checkpoints (in that case, to avoid strategy cycling) [7, 27, 28, 39, 69]. ",
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+        "text": "2.2 Baselines and ablations ",
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+        "type": "text",
+        "text": "We compare FCP agents to the three baseline training methods listed below, each varying only in their set of training partners, with the RL algorithm and architecture consistent across all agents: ",
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+        "type": "text",
+        "text": "1. Self-play (SP), where agents learn solely through interaction with themselves.   \n2. Population-play (PP), where a population of agents are co-trained through random pairings.   \n3. Behavioral cloning play (BCP), where an agent is trained with a BC model of a human [12]. ",
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+        "type": "text",
+        "text": "We also evaluate three variations on FCP to better understand the conditions for its success: ",
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+        "text": "1. To test the importance of including past checkpoints in training, we evaluate an ablation of FCP in which agents are trained only with the converged checkpoints of their partners $\\mathrm { F C P } _ { - T }$ for “FCP minus time”). 2. To test whether FCP would benefit from additional diversity in its partner population, we evaluate an augmentation of FCP in which the population of SP partners varies not just in random seed, but also in architecture $\\operatorname { F C P } _ { + A }$ for “FCP plus architectural variation”). 3. To test whether architectural variation can serve as a full replacement for playing with past checkpoints, we evaluate the combination of both modifications $( \\mathrm { F C P } _ { - T , + A } )$ . ",
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+        "type": "text",
+        "text": "2.3 Environment ",
+        "text_level": 1,
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+        "type": "text",
+        "text": "Following prior work on zero-shot coordination in human-agent interaction, we study the Overcooked environment (see Figure 3) [12, 13, 38, 50, 70]. We draw particular inspiration from the environment in Carroll et al. [12]. For full details, see Appendix A. ",
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+    {
+        "type": "text",
+        "text": "In this environment, players are placed into a gridworld kitchen as chefs and tasked with delivering as many cooked dishes of tomato soup as possible within an episode. This involves a series of sequential high-level actions to which both players can contribute: collecting tomatoes, depositing them into cooking pots, letting the tomatoes cook into soup, collecting a dish, getting the soup, and delivering it. Upon a successful delivery, both players are rewarded equally. ",
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+        "type": "text",
+        "text": "To effectively complete the task, players must learn to navigate the kitchen and interact with objects in the correct order, all while maintaining awareness of their partner’s behavior to coordinate with them. This environment therefore presents the challenges of both movement and strategic coordination. ",
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+    {
+        "type": "text",
+        "text": "Each player observes an egocentric RGB view of the world, and at every step can perform one of six actions: stand still, move {up, down, left, right}, interact. The behavior ofLÈ¡áyҏįŘį\u000eºµò‹µÒ¡y® interact varies based on the cell which the player is facing (e.g. place tomato on counter). ",
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+    {
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+        "img_path": "images/48e8af75423e0fa5e5c23e2088c49716c4c6044ee3579f26cdd9911dbb4b4925.jpg",
+        "image_caption": [
+            "Figure 3: The Overcooked environment: a two-player common-payoff game in which players must coordinate to cook and deliver soup. "
+        ],
+        "image_footnote": [],
+        "bbox": [
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+    {
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+        "img_path": "images/2b3253fcaac0677dbb15cc1ed5aa0663e561ff52605ba15bd61605f96c716872.jpg",
+        "image_caption": [
+            "Figure 4: Layouts: the kitchens which agents and humans play in, each emphasizing different coordination strategies. Highlighted in bold are the terms used to refer to each in the rest of this paper. "
+        ],
+        "image_footnote": [],
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+    {
+        "type": "text",
+        "text": "2.4 Implementation details ",
+        "text_level": 1,
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+    {
+        "type": "text",
+        "text": "Here we highlight several key implementation details for our training methods. For full details, including the architectures, hyperparameters, and compute used, please see Appendix B. ",
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+        "type": "text",
+        "text": "For our reinforcement learning agents, we use the V-MPO $\\boldsymbol { \\left[ \\left[ 6 5 \\right] \\right] }$ algorithm along with a ResNet [26] plus LSTM $\\mathbb { \\left| \\bigstar \\bigstar \\right\\| }$ architecture which we found led to optimal behavior across all layouts. Agents are trained using a distributed set of environments running in parallel $\\textcircled { 1 1 7 }$ , each sampling two agents from the training population to play together every episode. ",
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+        "type": "text",
+        "text": "Both PP and FCP are trained with a population size of $N = 3 2$ agents which are sampled uniformly. For FCP, we use 3 checkpoints for each agent, therefore incurring no additional training burden: (1) at initialization (i.e. a low-skilled agent), (2) at the end of training (i.e. a fully-trained expert agent), and (3) at the middle of training, defined as when the agent reaches $50 \\%$ of its final reward (i.e. an average-skilled agent). When varying architecture for the training partners of the $\\operatorname { F C P } _ { + A }$ and $\\mathrm { F C P } _ { - T , + A }$ variants, we vary whether the partners use memory (i.e. LSTM vs not) and the width of their policy and value networks (i.e. 16 vs 256). In total, we train 8 agents for each of the 4 combinations, leaving the total population size of $N = 3 2$ unchanged, ensuring a fair comparison. ",
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+        "type": "text",
+        "text": "",
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+    {
+        "type": "text",
+        "text": "To train agents via behavioral cloning $\\left[ \\left[ 5 8 \\right] \\right]$ , we use the open-source Acme $\\pmb { \\mathbb { B } } 0 \\|$ to learn a policy from human gameplay data. Specifically, we collected 5 human-human trajectories of length 1200 time steps for each of the 5 layouts, resulting in 60k total environment steps. We divide this data in half and train two BC agents: (1) a partner for training a BCP agent, and (2) a “human proxy” partner for agent-agent evaluation. Following Carroll et al. $\\bar { \\lVert 1 2 \\rVert }$ , we use a set of feature-based observations for the agents (as opposed to RGB) and generate comparable results: performance is higher on 3 layouts (asymmetric, cramped, and ring) but poorer on the other 2 (circuit and forced). ",
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+    {
+        "type": "text",
+        "text": "3 Related work ",
+        "text_level": 1,
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+    {
+        "type": "text",
+        "text": "Ad-hoc team play There is a large and diverse body of literature on ad-hoc team-play $ { \\mathbb { B } } ,  { \\mathbb { G } } 6  { \\mathbb { I } }$ , also known as zero-shot coordination $\\bar { \\mathbb { B } } \\mathbb { I }$ . Prior work based in game-theoretic settings has suggested the benefits of planning $\\pmb { \\mathbb { Z } 1 }$ , online learning $\\mathbb { \\left| \\left. \\sum \\right. { ] } \\right| }$ , and novel solution concepts $\\bar { \\mathbb { D } }$ , to name a few examples. More recently, multi-agent deep reinforcement learning has provided the tools to scale to more complex gridworld or continuous control settings, leading to work on hierarchical social planning $\\widehat { \\left\\| 3 6 \\right\\| }$ , adapting to existing social conventions $\\checkmark$ , trajectory diversity $\\lVert \\rVert \\dot { \\boldsymbol { \\mathrm { E } } } \\rVert$ , and theory of mind [14]. Ad-hoc team-play among novel agent partners is also an object of active study in the emergent communication literature [10, 11, 43]. This prior work has tended to focus on generalization to held-out agent partners as a proxy for human co-players. ",
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+    {
+        "type": "text",
+        "text": "Collaborative play with novel humans has been evaluated more actively in the context of training agent assistants; see for instance [57, 68]. To our knowledge, our FCP agents represent the stateof-the-art in coordinating with novel human partners on an equal footing of capabilities in a rich gridworld environment, as measured by the challenge tasks in Carroll et al. [12]. ",
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+    {
+        "type": "text",
+        "text": "Diversity in multi-agent reinforcement learning In multi-agent reinforcement learning, agents that train with behaviorally diverse populations of game partners tend to demonstrate stronger performance than their self-play counterparts. For example, across a range of multi-agent games, generalization to held-out populations can be improved by training larger and more diverse populations [13, 42, 50]. In mixed-motive settings, cooperation among agents can be encouraged through social diversity, such as in player preferences and rewards [3, 47, 49]. Similarly, competitiveness can be optimized through selective matchmaking between increasingly diverse agents $[ \\overbrace { 2 4 } , \\overbrace { 3 9 } , \\overbrace { 6 9 } ]$ . ",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "Despite the increased focus on improving multi-agent performance, evaluation has typically been constrained to agent-agent settings. High-performing agents have infrequently been evaluated with humans, particularly in non-competitive domains $\\bar { \\lVert 1 6 rVert }$ . We add to this growing literature, showing that training with diversity is a powerful approach for effective human-agent collaboration. ",
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+    {
+        "type": "text",
+        "text": "Human-agent interaction In recent years, increased attention has been directed toward designing machine learning agents capable of collaborating with humans [41, 57, 68, 72] (see also $\\boxed { \\boxed { 1 6 } }$ for a broader review on Cooperative AI). Tylkin et al. $\\lVert \\rVert$ is particularly notable in also demonstrating that partially trained agents can be useful learning targets for human helpers, although in a different domain (cooperative Atari). Our method, FCP, can be seen as extending theirs by training with multiple “skill levels” and random seeds, rather than just one, which we demonstrate to be crucial to our agents’ performance (Tables 1 and 2 and Figure 7b). ",
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+        "type": "text",
+        "text": "A key preceding entry in this research area is Carroll et al. $\\pmb { \\mathbb { I } }$ , who similarly investigated humanagent coordination in Overcooked. We use their method (BCP) as a baseline throughout our experiments (Section $\\boxed { 2 . 2 }$ . Relative to BCP, our approach removes the need for the expensive step of human data collection for agent training. Furthermore, through our novel human-agent experimental design, we go beyond objective performance metrics to compare the subjective preferences that agents generate. For a detailed comparison of methods and results, see Appendix E. ",
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+    {
+        "type": "text",
+        "text": "4 Zero-shot coordination with agents ",
+        "text_level": 1,
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+        "type": "text",
+        "text": "In this section, we evaluate our FCP agent, its ablations, and the baselines with held-out agents. ",
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+    {
+        "type": "text",
+        "text": "4.1 Evaluation method: collaborative evaluation with agent partners ",
+        "text_level": 1,
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+    {
+        "type": "text",
+        "text": "Our primary concern in this work is generalization to novel human partners (as investigated in Section $\\textcircled{5}$ . However, just as collecting human-human data for behavioral cloning is expensive, so too is evaluating agents with humans. Consequently, we instead use generalization to held-out agent partners as a cheap proxy of performance with humans. This is then used to guide our model selection process, allowing us to be more targeted with the agents we select for our human-agent evaluations. ",
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+    {
+        "type": "text",
+        "text": "We evaluate with three held-out populations: ",
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+    {
+        "type": "text",
+        "text": "1. A BC model trained on human data, $H _ { \\mathrm { p r o x y } }$ , intended as a proxy of generalization to humans, as done by Carroll et al. $[ \\overbrace { | 1 2 | }$ . 2. A set of self-play agents varying in seed, architecture, and training time (specifically, heldout seeds of the $N = 3 2$ partners trained for the $\\mathrm { F C P } _ { + A }$ agent; see Section 2.4). These are intended to test generalization to a diverse yet still skillful population. 3. Randomly initialized agents intended to test generalization to low-skill partners. ",
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+        "type": "text",
+        "text": "For all results, we report the average number of deliveries made by both players within an episode, aggregated across the 5 different layouts from Figure $^ 4$ (with the per-layout results reported in Appendix $\\underline { { \\overline { { ( \\mathrm { C . 2 } ) } } } }$ . We estimate mean and standard deviation across 5 random seeds. For each seed, we evaluate the agent with all members of the held-out population for 10 episodes per agent-partner pair. ",
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+    {
+        "type": "text",
+        "text": "4.2 Results ",
+        "text_level": 1,
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+    {
+        "type": "text",
+        "text": "Finding 1: FCP significantly outperforms all baselines ",
+        "text_level": 1,
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+    {
+        "type": "text",
+        "text": "To begin, we compare our FCP agent and the baselines when partnered with the three held-out populations introduced above. As can be seen in Figure $\\boxed { 5 }$ FCP significantly outperforms all baselines when partnered with all three held-out populations. Notably, it performs better than BCP with $H _ { \\mathrm { p r o x y } }$ even though BCP trains with such a model and FCP does not. Similar to Carroll et al. $\\mathbb { \\lVert 1 2 \\rVert }$ , we find that BCP significantly outscores SP. ",
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+    {
+        "type": "text",
+        "text": "When paired with a randomly initialized partner which behaves suboptimally, we see an even greater difference between FCP and the baselines. Given that FCP is trained with non-held-out versions of such agents, it may not be surprising that it does so well with partners that behave poorly. However, what is surprising is how brittle the other training methods are. This suggests that they may not perform well with humans who are not highly skilled players, which we will see in Section 5. ",
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+    {
+        "type": "image",
+        "img_path": "images/8083dcac415b6ef9624e1aa4f428a0a33c3e9d47ce8903df3798f3e80ef0427c.jpg",
+        "image_caption": [
+            "Figure 5: Agent-agent collaborative evaluation: Performance of each agent when partnered with each of the held-out populations (Section $4 . 1 )$ in episodes of length $T = 5 4 0$ . Importantly, FCP scores higher than all baselines with a variety of test partners. Error bars represent standard deviation over five random training seeds. Plots aggregate data across kitchen layouts; results calculated by individual layout can be found in Appendix C.2. "
+        ],
+        "image_footnote": [],
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "Finding 2: Training with past checkpoints is the most beneficial variation for performance Next, we investigate how the different training partner variations influence FCP’s performance. In particular, we separately ablate the past checkpoints $( T )$ and architecture $( A )$ variations, evaluating them with the same partners as in Figure 5. The results of this evaluation are presented in Table 1. Comparing the FCP and $\\mathrm { F C P } _ { - T }$ columns, we see that removing past checkpoints from training significantly reduces performance. Comparing the FCP and $\\operatorname { F C P } _ { + A }$ columns, we see that adding architectural variation to the training population offers no improvement over training with past ",
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+    {
+        "type": "table",
+        "img_path": "images/56b2734b6d3a9e5266ca9b0dd8d3ba9f6d27df29190a11ac23347bb9e9fb3c37.jpg",
+        "table_caption": [],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>Partner</td><td>FCP</td><td>FCP-T</td><td>FCP+A</td><td>FCP-T,+A</td></tr><tr><td>Hproxy</td><td>10.6± 0.5</td><td>4.7± 0.4</td><td>9.9±0.6</td><td>7.0±0.8</td></tr><tr><td>Diverse SP</td><td>11.2 ± 0.1</td><td>6.9 ± 0.1</td><td>11.1 ± 0.4</td><td>8.6 ± 0.4</td></tr><tr><td>Random</td><td>8.6± 0.2</td><td>1.0 ± 0.1</td><td>8.4±0.4</td><td>3.2 ± 0.5</td></tr></table>",
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+        "type": "text",
+        "text": "Table 1: Ablation results: Performance of each variation of FCP – training with past partner checkpoints $T$ for time) and adding partner variation in architecture $( A )$ . Scores are mean deliveries with standard deviation over 5 random seeds. Notably, we find that the inclusion of past checkpoints is essential for strong performance $( \\mathrm { F C P } > \\mathrm { F C P } _ { - T }$ ), and additionally including architectural variation does not improve performance $( \\mathrm { F C P } \\approx \\mathrm { F C P } _ { + A . }$ ). However, architectural variation is better than no variation, improving performance when past checkpoints are not available $( \\mathrm { F C P } _ { - T , + A } > \\mathrm { F C P } _ { - T , }$ ). ",
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+        "type": "text",
+        "text": "checkpoints. However, comparing the $\\mathrm { F C P } _ { - T }$ and $\\mathrm { F C P } _ { - T , + A }$ columns, we see that without training with past checkpoints, architectural variation in the population does improve performance. ",
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+        "type": "text",
+        "text": "5 Zero-shot coordination with humans ",
+        "text_level": 1,
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+        "text": "Ultimately, our goal is to develop agents capable of coordinating with novel human partners. In this section, we run an online study to evaluate our FCP agent and the baseline agents in collaborative play with human partners. ",
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+            "Figure 6: Human-agent collaborative study: For our human-agent collaboration study, we recruited participants online to play games with FCP and baseline agents. Participants played a randomized sequence of episodes with different agent partners and kitchen layouts. After every two episodes, participants reported the direction and strength of their preference between their last two partners. "
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+        "type": "text",
+        "text": "5.1 Evaluation method: collaborative evaluation with human participants ",
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+        "type": "text",
+        "text": "To test how effectively FCP’s performance generalizes to human partners, we recruited participants from Prolific $\\mathbb { 1 1 8 } , \\lvert 5 5 \\rvert$ for an online collaboration study $N = 1 1 4$ ; $3 7 . 7 \\%$ female, $5 9 . 6 \\%$ male, $1 . 8 \\%$ nonbinary; median age between 25–34 years). We used a within-participant design for the study: each participant played with a full cohort of agents (i.e. generated through every training method). This design allowed us to evaluate both objective performance as well as subjective preferences. ",
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+        "type": "text",
+        "text": "Participants first read game instructions and played a short tutorial episode guiding them through the dish preparation sequence (see Appendix $\\dot { \\mathrm { \\bf D } } . 1 . 1$ for instruction text and study screenshots). Participants then played 20 episodes with a randomized sequence of agent partners and kitchen layouts. Episodes lasted $T = 3 0 0$ steps (1 minute) each. After every two episodes, participants reported their preference over the agent partners from those episodes on a five-point Likert-type scale. After playing all 20 episodes, participants completed a debrief questionnaire collecting standard demographic information and open-ended feedback on the study. Our statistical analysis below primarily relies upon the repeated-measures analysis of variance (ANOVA) method. See Appendix D for additional details of our study design and analysis, including independent ethical review. ",
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+        "type": "text",
+        "text": "5.2 Results ",
+        "text_level": 1,
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+        "type": "text",
+        "text": "Finding 1: FCP coordinates best with humans, achieving the highest score across maps To begin, we compare the objective team performance supported by our FCP and baseline agents. The strong FCP performance observed in agent-agent play generalizes to human-agent collaboration: ",
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+        "type": "text",
+        "text": "the FCP-human teams significantly outperform all other agent-human teams, achieving the highest average scores across maps, every $p < 0 . 0 0 1$ (Figure $\\mathrm { 7 a ) }$ , while performing as well as or better than the other teams on each individual map (see Appendix $\\mathbf { D } . 3 )$ . Echoing the results from our agent-agent ablation experiments (Table $\\perp )$ , the inclusion of past checkpoints in training proves critical to FCP’s strong performance, $p < 0 . 0 { \\overline { { 0 1 } } }$ (Figure $\\textcircled { 7 6 }$ . Similar to Carroll et al. $[ \\left[ 1 2 \\right] ]$ , we find that BCP outscores SP when collaborating with human players, $p < 0 . 0 0 1$ . ",
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+        "type": "text",
+        "text": "Finding 2: Participants prefer FCP over all baselines ",
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+        "type": "text",
+        "text": "FCP’s strong collaborative performance carries over to our participants’ subjective partner preferences. Participants expressed a significant preference for FCP partners over all other agents, including BCP, with every $p < 0 . 0 5$ (Figure $\\dot { \\bigtriangledown } \\dot { \\mathbf { c } } { \\big \\rVert }$ . Notably, while human-BCP and human-PP teams did not significantly differ in their completed deliveries, participants reported significantly preferring BCP over PP, $p = 0 . 0 0 3$ , highlighting the informativeness of our subjective analysis. ",
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+        "image_caption": [
+            "Figure 7: Human-agent collaborative evaluation: Evaluation and preference metrics from humanagent play in episodes of length $T = 3 0 0$ . Error bars represents $9 5 \\%$ confidence intervals, calculated over episodes. Plots aggregate data across kitchen layouts; results calculated by individual layout can be found in Appendix D.3. "
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+        "type": "text",
+        "text": "5.3 Exploratory behavioral analysis ",
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+        "type": "text",
+        "text": "To better understand how the human-agent scores and preferences may have arisen, here we analyze the resulting action trajectories of each human and agent player in our experiment. ",
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+        "img_path": "images/65959c0ab23a18c0f8de72bc451d199e7d9d9cc2698e7ca2ac4f320e26dac829.jpg",
+        "image_caption": [],
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+        "type": "text",
+        "text": "Figure 8: Behavioral analysis: (a) FCP is able to move most frequently $3 5 \\%$ of the time), corresponding to the best movement coordination with human partners. (b) FCP exhibits the most equal preferences over cooking pots (0.11 difference), aligning with human preferences. Values are calculated as the absolute difference in preferences between the two pots; 1 indicates that the player only uses one of the two available pots, while 0 indicates that the player uses both pots equally. ",
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+    {
+        "type": "text",
+        "text": "Finding 1: FCP exhibits the best movement coordination with humans ",
+        "text_level": 1,
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+        "type": "text",
+        "text": "First, we investigate how much each player moves in an episode (Figure $\\textcircled { 8 \\mathrm { a } }$ , where moving in a higher fraction of timesteps may suggest fewer collisions and thus better coordination with a partner. Notably, we observe two results: (1) humans rarely move, a behavior which is out-of-distribution for typical training methods (e.g. SP, PP) but is seen in the training distribution for BCP and FCP. ",
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+    {
+        "type": "text",
+        "text": "(2) FCP moves the most on all layouts other than Forced, suggesting it is better at coordinating its movement strategy with its partner. This result was also reported by human participants, for example: “I noticed that some of my partners seemed to know they needed to move around me, while others seemed to get ‘stuck’ until I moved out of their way” (see Appendix D for more examples). ",
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+    {
+        "type": "text",
+        "text": "Finding 2: FCP’s preferences over cooking pots aligns best with that of humans ",
+        "text_level": 1,
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+    {
+        "type": "text",
+        "text": "Next, we investigate whether there was a preference for a specific cooking pot in the layouts which included two cooking pots (Figure $\\textcircled { 8 6 }$ . To do this, we calculate the difference in the number of times each pot was used by each player, where a high value indicates a strong preference for one pot and a low value indicates more equal preference for the two pots. ",
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+    {
+        "type": "text",
+        "text": "As can be seen in the FCP column, our agent typically has the most aligned preferences with that of humans (0.11 for FCP to 0.14 for humans). Behaviorally speaking, this means that our agent prefers one cooking pot over the other $5 5 . 5 \\%$ of the time (i.e. a 0.11 point difference). In contrast, all other agents have a strong preference for a single pot. This is a non-adaptive strategy which generalizes poorly to typical human behavior of using both pots, leading to worse performance. ",
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+    {
+        "type": "text",
+        "text": "6 Discussion ",
+        "text_level": 1,
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+        "type": "text",
+        "text": "Summary In this work, we investigated the challenging problem of zero-shot collaboration with humans without using human data in the training pipeline. To accomplish this, we introduced Fictitious Co-Play (FCP) – a surprisingly simple yet effective method based on creating a diverse set of training partners. We found that FCP agents scored significantly higher than all baselines when partnered with both novel agent and human partners. Furthermore, through a rigorous human-agent experimental design, we also found that humans reported a strong subjective preference to partnering with FCP agents over all baselines. ",
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+    {
+        "type": "text",
+        "text": "Limitations and future work Our method currently relies on the manual process of initially training and selecting a diverse set of partners. This is not only time consuming, but also prone to researcher biases that may negatively influence the behavior of the created agents. Additionally, while we found FCP with a partner population size of $N = 3 2$ sufficient here, for more complex games, FCP may require an unrealistically large partner population size to represent sufficiently diverse strategies. To address these concerns, methods for automatically generating partner diversity for common-payoff games may be important. Possibilities include adaptive population matchmaking as been used in competitive zero-sum games $\\mathbb { \\lVert 6 9 \\rVert }$ , as well as auxiliary objectives that explicitly encourage behavioral diversity [19, 45, 46]. ",
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+    {
+        "type": "text",
+        "text": "Our method requires a known and fixed reward function. We also focus on one domain in order to compare with prior work which has argued that human-in-the-loop training is necessary. Consequently, the resulting agents are only designed to adaptively collaborate on a single task, and not to infer human preferences in general $\\textcircled { 1 1 } \\textcircled { 3 3 } \\textcircled { 5 9 }$ . Moreover, if a task’s reward function is poorly aligned with how humans approach the task, our method may well produce subpar partners, as would any method without access to human data. Thus, additional domains and tasks should be studied to better understand how our method generalizes. Targeted experiments to test specific forms of generalization may be especially helpful in this regard $\\overline { { [ 3 8 ] } }$ , as could approaches that procedurally generate environment layouts requiring diverse solutions $\\pmb { \\mathbb { Z } } 2 \\mathbf { l }$ ",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "Finally, it may be possible to produce even stronger agent assistants by combining the strengths of FCP (i.e. diversity) and BCP (i.e. human-like play). Indeed, Knott et al. $\\textcircled { \\lvert 3 8 \\rvert }$ recently demonstrated that modifying BCP to train with multiple BC partners produces more robust collaboration with held-out agents, a finding that would be interesting to test with human partners. ",
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+    {
+        "type": "text",
+        "text": "Societal impact A challenge for this line of work is ensuring agent behavior is aligned with human values (i.e. the AI value alignment problem [23, 59]). Our method has no guarantees that the resulting policy aligns with the preferences, intentions, or welfare of its potential partners. It likewise does not exclude the possibility that the target being optimized for is harmful (e.g. if the agent’s partner expresses preferences or intentions to harm others). This could therefore produce negative societal effects either if training leads to poor alignment or if agents are optimized for harmful metrics. ",
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+    {
+        "type": "text",
+        "text": "One potential strategy for mitigating these risks is the use of human preference data [15]. Such data could be used to fine-tune and filter trained agents before deployment, encouraging better alignment with human values. A key question in this line of research is how human preference data should be aggregated—or selected, in the case of expert preferences—when our aim is to create socially aligned agents (i.e. agents that are sufficiently aligned for everyone). Relatedly, targeted research on human beliefs and perceptions of AI $\\lVert \\overline { { 4 8 } } \\rVert$ , and how they steer human-agent interaction, would help inform agent design for positive societal impact. For instance, developers could incorporate specific priors into agents to reinforce tendencies for fair outcomes $\\pm \\mathbb { Z } 0 . \\pm \\mathbb { B } 2 \\mathbb { I }$ . ",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "",
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+    {
+        "type": "text",
+        "text": "Conclusion We proposed a method which is both effective at collaborating with humans and simple to implement. We also presented a rigorous and general methodology for evaluating with humans and eliciting their preferences. Together, these establish a strong foundation for future research on the important challenge of human-agent collaboration for benefiting society. ",
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+    {
+        "type": "text",
+        "text": "Acknowledgements ",
+        "text_level": 1,
+        "bbox": [
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+        ],
+        "page_idx": 9
+    },
+    {
+        "type": "text",
+        "text": "The authors would like to thank Mary Cassin for creating the game sprite art; Rohin Shah, Thore Graepel, and Iason Gabriel for feedback on the draft; Lucy Campbell-Gillingham, Tina Zhu, and Saffron Huang for support in evaluating agents with humans; and Max Kleiman-Weiner, Natasha Jaques, Marc Lanctot, Mike Bowling, and Dan Roberts for useful discussions. ",
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+    {
+        "type": "text",
+        "text": "Funding disclosure ",
+        "text_level": 1,
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "This work was funded solely by DeepMind. The authors declare no competing interests. ",
+        "bbox": [
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+        ],
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+    },
+    {
+        "type": "text",
+        "text": "References ",
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+        "bbox": [
+            174,
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+        "type": "text",
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parse/train/ARFshOO1Iu/ARFshOO1Iu.md

@@ -0,0 +1,355 @@
+# ADAPTIVE SELF-TRAINING FOR NEURAL SEQUENCE LABELING WITH FEW LABELS
+
+Anonymous authors Paper under double-blind review
+
+# ABSTRACT
+
+Neural sequence labeling is an important technique employed for many Natural Language Processing (NLP) tasks, such as Named Entity Recognition (NER), slot tagging for dialog systems and semantic parsing. Large-scale pre-trained language models obtain very good performance on these tasks when fine-tuned on large amounts of task-specific labeled data. However, such large-scale labeled datasets are difficult to obtain for several tasks and domains due to the high cost of human annotation as well as privacy and data access constraints for sensitive user applications. This is exacerbated for sequence labeling tasks requiring such annotations at token-level. In this work, we develop techniques to address the label scarcity challenge for neural sequence labeling models. Specifically, we develop self-training and meta-learning techniques for training neural sequence taggers with few labels. While self-training serves as an effective mechanism to learn from large amounts of unlabeled data – meta-learning helps in adaptive sample re-weighting to mitigate error propagation from noisy pseudo-labels. Extensive experiments on six benchmark datasets including two for massive multilingual NER and four slot tagging datasets for task-oriented dialog systems demonstrate the effectiveness of our method. With only 10 labeled examples for each class for each task, our method obtains $1 0 \%$ improvement over state-of-the-art systems demonstrating its effectiveness for the low-resource setting.
+
+# 1 INTRODUCTION
+
+Motivation. Deep neural networks typically require large amounts of training data to achieve stateof-the-art performance. Recent advances with pre-trained language models like BERT (Devlin et al., 2019), GPT-2 (Radford et al., 2019) and RoBERTa (Liu et al., 2019) have reduced this annotation bottleneck. In this paradigm, large neural network models are trained on massive amounts of unlabeled data in a self-supervised manner. However, the success of these large-scale models still relies on fine-tuning them on large amounts of labeled data for downstream tasks. For instance, our experiments show $\bar { 2 } 7 \%$ relative improvement on an average when fine-tuning BERT with the full training set (2.5K-705K labels) vs. fine-tuning with only 10 labels per class. This poses several challenges for many real-world tasks. Not only is acquiring large amounts of labeled data for every task expensive and time consuming, but also not feasible in many cases due to data access and privacy constraints. This issue is exacerbated for sequence labeling tasks that require annotations at token- and slot-level as opposed to instance-level classification tasks. For example, an NER task can have slots like B-PER, I-PER, O-PER marking the beginning, intermediate and out-of-span markers for person names, and similar slots for the names of location and organization. Similarly, language understanding models for dialog systems rely on effective identification of what the user intends to do (intents) and the corresponding values as arguments (slots) for use by downstream applications. Therefore, fully supervised neural sequence taggers are expensive to train for such tasks, given the requirement of thousands of annotations for hundreds of slots for the many different intents.
+
+Semi-supervised learning (SSL) (Chapelle et al., 2010) is one of the promising paradigms to address labeled data scarcity by making effective use of large amounts of unlabeled data in addition to task-specific labeled data. Self-training (ST, (III, 1965)) as one of the earliest SSL approaches has recently shown state-of-the-art performance for tasks like image classification (Li et al., 2019; Xie et al., 2020) performing at par with supervised systems while using very few training labels. In contrast to such instance-level classification tasks, sequence labeling tasks have dependencies between the slots demanding different design choices for slot-level loss optimization for the limited labeled data setting. For instance, prior work (Ruder & Plank, 2018) using classic self-training techniques for sequence labeling did not find much success in the low-data regime with $1 0 \%$ labeled data for the target domain. Although there has been some success with careful task-specific data selection (Petrov & McDonald, 2012) and more recently for distant supervision (Liang et al., 2020) using external resources like knowledge bases (e.g., Wikipedia). In contrast to these prior work, we develop techniques for self-training with limited labels and without any task-specific assumption or external knowledge.
+
+![](images/4716dc9424f650ad710d7db8d4aff2f8dd06b88c864da63dd6e410117264cc70.jpg)  
+Figure 1: MetaST framework.
+
+For self-training, a base model (teacher) is trained on some amount of labeled data and used to pseudo-annotate (task-specific) unlabeled data. The original labeled data is augmented with the pseudo-labeled data and used to train a student model. The student-teacher training is repeated until convergence. Traditionally in self-training frameworks, the teacher model pseudo-annotates unlabeled data without any sample selection. This may result in gradual drifts from self-training on noisy pseudo-labeled instances (Zhang et al., 2017). In order to deal with noisy labels and training set biases, Ren et al. (2018) propose a meta-learning technique to automatically re-weight noisy samples by their loss changes on a held-out clean labeled validation set. We adopt a similar principle in our work and leverage meta-learning to re-weight noisy pseudo-labeled examples from the teacher. While prior techniques for learning to re-weight examples have been developed for instance-level classification tasks, we extend them to operate at token-level for discrete sequence labeling tasks. To this end, we address some key challenges on how to construct an informative held-out validation set for token-level re-weighting. Prior works (Ren et al., 2018; Shu et al., 2019) for instance classification construct this validation set by random sampling. However, sequence labeling tasks involve many slots (e.g. WikiAnn has 123 slots over 41 languages) with variable difficulty and distribution in the data. In case of random sampling, the model oversamples from the most populous category and slots. This is particularly detrimental for low-resource languages in the multilingual setting. To this end, we develop an adaptive mechanism to create the validation set on the fly considering the diversity and uncertainty of the model for different slot types. Furthermore, we leverage this validation set for token-level loss estimation and re-weighting pseudo-labeled sequences from the teacher in the meta-learning setup. While prior works (Li et al., 2019; Sun et al., 2019; Bansal et al., 2020) on meta-learning for image and text classification leverage multi-task learning to improve a target classification task based on several similar tasks, in this work we focus on a single sequence labeling task – making our setup more challenging altogether.
+
+Our task and framework overview. We focus on sequence labeling tasks with only a few annotated samples (e.g., $K = \{ 5 , 1 0 , 2 0 , 1 0 0 \} )$ per slot type for training and large amounts of task-specific unlabeled data. Figure 1 shows an overview of our framework with the following components: (i) Self-training: Our self-training framework leverages a pre-trained language model as a teacher and co-trains a student model with iterative knowledge exchange (ii) Adaptive labeled data acquisition for validation: Our few-shot learning setup assumes a small number of labeled training samples per slot type. The labeled data from multiple slot types are not equally informative for the student model to learn from. While prior works in meta-learning randomly sample some labeled examples for held-out validation set, we develop an adaptive mechanism to create this set on the fly. To this end, we leverage loss decay as a proxy for model uncertainty to select informative labeled samples for the student model to learn from in conjunction with the re-weighting mechanism in the next step. (iii) Meta-learning for sample re-weighting: Since pseudo-labeled samples from the teacher can be noisy, we employ meta-learning to re-weight them to improve the student model performance on the held-out validation set obtained from the previous step. In contrast to prior work (Ren et al., 2018)
+
+on sample re-weighting operating at instance-level, we incorporate the re-weighting mechanism at token-level for sequence labeling tasks. Here the token-level weights are determined by the student model loss on the above validation set. Finally, we learn all of the above steps jointly with end-toend learning in the self-training framework. We refer to our adaptive self-training framework with meta-learning based sample re-weighting mechanism as MetaST.
+
+We perform extensive experiments on six benchmark datasets for several tasks including multilingual Named Entity Recognition and slot tagging for user utterances from task-oriented dialog systems to demonstrate the generalizability of our approach across diverse tasks and languages. We adopt BERT and multilingual BERT as encoder and show that its performance can be significantly improved by nearly $1 0 \%$ for low-resource settings with few training labels (e.g., 10 labeled examples per slot type) and large amounts of unlabeled data. In summary, our work makes the following contributions. (i) Develops a self-training framework for neural sequence tagging with few labeled training examples. (ii) Leverages an acquisition strategy to adaptively select a validation set from the labeled set for meta-learning of the student model. (iii) Develops a meta-learning framework for re-weighting pseudo-labeled samples at token-level to reduce drifts from noisy teacher predictions. (iv) Integrates the aforementioned components into an end-to-end learning framework and demonstrates its effectiveness for neural sequence labeling across six benchmark datasets with multiple slots, shots, domains and languages.
+
+# 2 BACKGROUND
+
+Sequence labeling and slot tagging. This is the task identifying the entity span of several slot types (e.g., names of person, organization, location, date, etc.) in a text sequence. Formally, given a sentence with $N$ tokens $\mathbf { \bar { \cal X } } ~ = ~ \{ x _ { 1 } , . . . , x _ { N } \}$ , an entity or slot value is a span of tokens $s = [ x _ { i } , . . . , x _ { j } ] ( 0 \leq i \leq j \leq N )$ associated with a type. This task assumes a pre-defined tagging policy like BIO (Tjong et al., 1999), where B marks the beginning of the slot, I marks an intermediate token in the span, and $\bigcirc$ marks out-of-span tokens. These span markers are used to extract multi-token values for each of the slot types with phrase-level evaluation for the performance.
+
+Self-training. Consider $f ( \cdot ; \theta _ { t e a } )$ and $f ( \cdot ; \theta _ { s t u } )$ to denote the teacher and student models respectively in the self-training framework. The role of the teacher model (e.g., a pre-trained language model) is to assign pseudo-labels to unlabeled data that is used to train a student model. The teacher and student model can exchange knowledge and the training schedules are repeated till convergence. The success of self-training with deep neural networks in recent works (He et al., 2019; Xie et al., 2020) has been attributed to a number of factors including stochastic regularization with dropouts and data regularization with unlabeled data. Formally, given $m$ -th unlabeled sentence with $N$ tokens $X _ { m } ^ { u } \doteq \{ x _ { 1 , m } ^ { u } , . . . , x _ { N , m } ^ { u } \}$ and $C$ pre-defined labels, consider the pseudo-labels $\hat { Y } _ { m } ^ { ( t ) } = [ \hat { y } _ { m , 1 } ^ { ( t ) } , . . . , \hat { y } _ { m , N } ^ { ( t ) } ]$ generated by the teacher model at the $t$ -th iteration where,
+
+$$
+\hat { y } _ { m , n } ^ { ( t ) } = \underset { c \in C } { \arg \operatorname* { m a x } } f _ { n , c } ( x _ { m , n } ^ { u } ; \theta _ { t e a } ^ { ( t ) } ) .
+$$
+
+The pseudo-labeled data set, denoted as $( X ^ { u } , \hat { Y } ^ { ( t ) } ) = \{ ( X _ { m } ^ { u } , \hat { Y } _ { m } ^ { ( t ) } ) \} _ { m } ^ { M }$ , is used to train the student model and learn its parameters as:
+
+$$
+\hat { \theta } _ { s t u } ^ { ( t ) } = \underset { \theta } { \arg \operatorname* { m i n } } \frac { 1 } { M } \sum _ { m = 1 } ^ { M } l ( \hat { Y } _ { m } ^ { ( t ) } , f ( X _ { m } ^ { u } ; \theta _ { s t u } ^ { ( t - 1 ) } ) ) ,
+$$
+
+where $l ( \cdot , \cdot )$ can be modeled as the cross-entropy loss.
+
+# 3 ADAPTIVE SELF TRAINING
+
+Given a pre-trained language model (e.g., BERT (Devlin et al., 2019)) as the teacher, we first finetune it on the small labeled data to make it aware of the underlying task. The fine-tuned teacher model is now used to pseudo-label the large unlabeled data. We consider the student model as another instantiation of the pre-trained language model that is trained over the pseudo-labeled data. However, our few-shot setting with limited labeled data results in a noisy teacher. A naive transfer of teacher knowledge to the student results in the propagation of noisy labels limiting the performance of the student model. To address this challenge, we develop an adaptive self-training framework to re-weight pseudo-labeled predictions from the teacher with a meta-learning objective that optimizes the token-level loss from the student model on a held-out labeled validation set. This held-out set is adaptively constructed via labeled data acquisition which selects labeled samples with high uncertainty for efficient data exploration.
+
+# 3.1 ADAPTIVE LABELED DATA ACQUISITION
+
+In standard meta-learning setup for instance-level classification tasks, the held-out validation set is usually constructed via random sampling (Ren et al., 2018; Shu et al., 2019). Sequence labeling tasks involve many slot types with variable difficulty and distribution in the data. For instance, NER tasks over WikiAnn operate over 123 slot types from 41 languages with additional complexity from variable model performance across different languages. A random sampling leads to oversampling instances with the most populous categories and slot types in the data. Therefore, we propose a novel labeled data acquisition strategy to construct the validation set for effective data exploration. We demonstrate its benefit over classic meta-learning approaches from prior works in experiments.
+
+In general, data acquisition strategies for prior works in meta-learning and active learning broadly leverage random sampling (Ren et al., 2018; Shu et al., 2019), easy (Kumar et al., 2010) and hard example mining (Shrivastava et al., 2016) or uncertainty-based methods (Chang et al., 2017a). These strategies have been compared in prior works (Chang et al., 2017a; Gal et al., 2017) that show uncertainty-based methods to have better generalizability across diverse settings. There are several approaches to uncertainty estimation including error decay (Konyushkova et al., 2017; Chang et al., 2020), Monte Carlo dropouts (Gal et al., 2017) and predictive variance (Chang et al., 2017a). We follow a similar principle of error decay to find samples that the model is uncertain about and can correspondingly benefit from knowing their labels (similar to active learning settings). To this end, we leverage stochastic loss decay from the model as a proxy for the model uncertainty to generate validation set on the fly. This is used for estimating token-level weights and re-weighting pseudo labeled data in Section 3.2.
+
+Consider the loss of the student model with parameters $\theta _ { s t u } ^ { ( t ) }$ on the labeled data $( X _ { m } ^ { l } , Y _ { m } )$ in the $t$ -th iteration as $l ( Y _ { m } , f ( X _ { m } ^ { l } ; \theta _ { s t u } ^ { ( t ) } ) )$ . To measure the loss decay value at any iteration, we use the difference between the current and previous loss values. Considering these values may fluctuate across iterations, we adopt the moving average of the loss values for $( X _ { m } ^ { l } , Y _ { m } )$ in the latest $R$ iterations as a baseline $l _ { b } ^ { m }$ for loss decay estimation. Baseline measure $l _ { b } ^ { m }$ is calculated as follows:
+
+$$
+l _ { b } ^ { m } = \frac { 1 } { R } \sum _ { r = 1 } ^ { R } l ( Y _ { m } , f ( X _ { m } ^ { l } ; \theta _ { s t u } ^ { ( t - r ) } ) ) .
+$$
+
+Since the loss decay values are estimated on the fly, we want to balance exploration and exploitation. To this end, we add a smoothness factor $\delta$ to prevent the low loss decay samples (i.e. samples with low uncertainty) from never being selected again. Considering all of the above factors, we obtain the sampling weight of labeled data $( X _ { m } ^ { l } , Y _ { m } ^ { l } )$ as follows:
+
+$$
+W _ { m } \propto \mathrm { m a x } ( l _ { b } ^ { m } - l ( Y _ { m } , f ( X _ { m } ^ { l } ; \theta _ { s t u } ^ { ( t ) } ) ) , 0 ) + \delta .
+$$
+
+The smoothness factor $\delta$ needs to be adaptive since the training loss is dynamic. Therefore, We adopt the maximum of the loss decay value as the smoothness factor $\delta$ to encourage exploration.
+
+The aforementioned acquisition function is re-estimated after a fixed number of steps to adapt to model changes. With labeled data acquisition, we rely on informative uncertain samples to improve learning efficiency. The sampled mini-batches of labeled data $\{ B _ { s } ^ { l } \}$ are used as a validation set for the student model in the next step for re-weighting pseudo-labeled data from the teacher model. We demonstrate its impact via ablation study in experiments. Note that the labeled data is only used to compute the acquisition function and not used for explicit training of the student model in this step.
+
+# 3.2 RE-WEIGHTING PSEUDO-LABELED DATA
+
+To mitigate error propagation from noisy pseudo-labeled sequences from the teacher, we leverage meta-learning to adaptively re-weight them based on the student model loss on the held-out validation set obtained via labeled data acquisition from the previous section. In contrast to prior work focusing on instance-level tasks like image classification – sequence labeling operates on discrete text sequences as input and assigns labels to each token in the sequence. Since teacher predictions vary for different slot labels and types, we adapt the meta-learning framework to re-weight samples at a token-level resolution.
+
+Token Re-weighting. Consider the pseudo-labels $\{ \hat { Y } _ { m } ^ { ( t ) } = [ \hat { y } _ { m , 1 } ^ { ( t ) } , . . . , \hat { y } _ { m , N } ^ { ( t ) } ] \} _ { m = 1 } ^ { M }$ from the teacher in the $t$ -th iteration with $m$ and $n$ indexing the instance and a token in the instance, respectively. In classic self-training, we update the student parameters leveraging pseudo-labels as follows:
+
+$$
+\hat { \theta } _ { s t u } ^ { ( t ) } = \hat { \theta } _ { s t u } ^ { ( t - 1 ) } - \alpha \nabla \big ( \frac { 1 } { M } \sum _ { m = 1 } ^ { M } l ( \hat { Y } _ { m } ^ { ( t ) } , f ( X _ { m } ^ { u } ; \theta _ { s t u } ^ { ( t - 1 ) } ) ) \big ) .
+$$
+
+Now, to downplay noisy token-level labels, we leverage meta-learning to re-weight the pseudolabeled data. To this end, we follow a similar analysis from (Koh & Liang, 2017) and (Ren et al., 2018) to perturb the weight for each token in the mini-batch by $\epsilon$ . Weight perturbation is used to discover data points that are most important to improve the model performance on a held-out validation set (Koh & Liang, 2017) where the sample importance is given by the magnitude of the the negative gradients. We extend prior techniques to obtain token-level perturbations as:
+
+$$
+\hat { \theta } _ { s t u } ^ { ( t ) } ( \epsilon ) = \hat { \theta } _ { s t u } ^ { ( t - 1 ) } - \alpha \nabla \big ( \frac { 1 } { M } \frac { 1 } { N } \sum _ { m = 1 } ^ { M } \sum _ { n = 1 } ^ { N } [ \epsilon _ { m , n } \cdot l ( \hat { y } _ { m , n } ^ { ( t ) } , f ( x _ { m , n } ^ { u } ; \hat { \theta } _ { s t u } ^ { ( t - 1 ) } ) ) ] \big ) .
+$$
+
+The token weights are obtained by minimizing the student model loss on the held-out validation set. Here, we employ the labeled data acquisition strategy from Eq. 4 to sample informative mini-batches of labeled data ${ \dot { B } } _ { s } ^ { l }$ locally at step $t$ . To obtain a cheap estimate of the meta-weight at step $t$ , we take a single gradient descent step for the sampled labeled mini-batch $B _ { s } ^ { l }$ :
+
+$$
+u _ { m , n , s } = - \frac { \partial } { \partial \epsilon _ { m , n , s } } \big ( \frac { 1 } { | \mathcal { B } _ { s } ^ { l } | } \frac { 1 } { N } \sum _ { m = 1 } ^ { | \mathcal { B } _ { s } ^ { l } | } \sum _ { n = 1 } ^ { N } [ l ( y _ { m , n } , f ( x _ { m , n } ^ { l } ; \hat { \theta } _ { s t u } ^ { ( t ) } ( \epsilon ) ) ] \big ) | _ { \epsilon _ { m , n , s } = 0 }
+$$
+
+We set the token weights to be proportional to the negative gradients to reflect the importance of pseudo-labeled tokens in the sequence. Since sequence labeling tasks have dependencies between the slot types and tokens, it is difficult to obtain a good estimation of the weights based on a single mini-batch of examples. Therefore, we sample $S$ mini-batches of labeled data $\{ B _ { 1 } ^ { l } , . . . , B _ { S } ^ { l } \}$ with the adaptive acquisition strategy and calculate the mean of the gradients to obtain a robust gradient estimate. Note that $S$ is a constant number that is the same for each token and the proportional sign in Eq. 8. Since a negative weight indicates a pseudo-label of poor quality that would potentially degrade the model performance, we set such weights to 0 to filter them out. The impact of $S$ is investigated in the experiments (refer to Appendix A.1). The overall meta-weight of pseudo-labeled token $\left( x _ { m , n } ^ { u } , \hat { y } _ { m , n } \right)$ is obtained as:
+
+$$
+w _ { m , n } \propto \mathrm { m a x } ( \sum _ { s = 1 } ^ { S } u _ { m , n , s } , 0 )
+$$
+
+To further ensure the stability of the loss function in each mini-batch, we normalise the weight $w _ { m , n }$ . Finally, we update the student model parameters while accounting for token-level re-weighting as:
+
+$$
+\hat { \theta } _ { s t u } ^ { ( t ) } = \hat { \theta } _ { s t u } ^ { ( t - 1 ) } - \alpha \nabla \big ( \frac { 1 } { M } \frac { 1 } { N } \sum _ { m = 1 } ^ { M } \sum _ { n = 1 } ^ { N } [ w _ { m , n } \cdot l ( \hat { y } _ { m , n } ^ { ( t ) } , f ( x _ { m , n } ^ { u } ; \hat { \theta } _ { s t u } ^ { ( t - 1 ) } ) ) ] \big ) .
+$$
+
+We demonstrate the impact of our re-weighting mechanism with an ablation study in experiments.
+
+# 3.3 TEACHER MODEL ITERATIVE UPDATES
+
+At the end of every self-training iteration, we assign the student model as a new teacher model (i.e., $\theta _ { t e a } = \theta _ { s t u } ^ { ( T ) } )$ . Since the student model uses the labeled data only as a held-out validation setl for meta-learning, we further utilize the labeled data
+
+$f ( \cdot , \theta _ { t e a } ^ { ( t ) } )$ with standard supervised loss minimization. We explore the effectiveness of this step with an ablation study in experiments. The overall training procedure is summarized in Algorithm 1.
+
+# Algorithm 1: MetaST Algorithm.
+
+<table><tr><td></td><td></td><td>Input:Labeled sequences (Xl,Y); Unlabeled sequences (X&quot;);Pre-trained BERT model with randomly initialized token classification layer f(;((O)); Batches S; Number of self-training iterations T.</td></tr><tr><td>Initialize teacher model 0tea =0(0) while not converged do</td><td></td><td></td></tr><tr><td></td><td>Fine-tune teacher model on small labeled data (Xl, Y);</td><td></td></tr><tr><td>Initialize the student model θ(0)</td><td>=0(0);</td><td></td></tr><tr><td></td><td>Generate hard pseudo-labels Y(t）for unlabeled samples Xu with model f(·,0tea);</td><td></td></tr><tr><td>fort←1toTdo</td><td></td><td></td></tr><tr><td></td><td>Compute labeled data acquisition function according to Eq. 4;</td><td></td></tr><tr><td>function;</td><td></td><td>Sample S mini-batches of labeled examples {Bl,.,B&#x27;s} from (Xl,Y）based on labeled data acquisition</td></tr><tr><td></td><td>Randomly sample abatch of pseudo-labeled examples B from(Xu,Y(t));</td><td></td></tr><tr><td></td><td></td><td></td></tr><tr><td></td><td>Compute token-level weights in B based on the loss on {Bl,..,B&#x27;s} according to Eq.8;</td><td></td></tr><tr><td></td><td></td><td></td></tr><tr><td>end</td><td></td><td>stu</td></tr><tr><td></td><td></td><td></td></tr><tr><td>Update the teacher:θtea</td><td></td><td></td></tr><tr><td>end</td><td></td><td></td></tr><tr><td></td><td></td><td></td></tr><tr><td></td><td></td><td></td></tr><tr><td></td><td></td><td></td></tr><tr><td></td><td></td><td></td></tr><tr><td></td><td></td><td></td></tr><tr><td></td><td></td><td></td></tr><tr><td></td><td></td><td></td></tr><tr><td></td><td></td><td></td></tr><tr><td></td><td></td><td></td></tr><tr><td></td><td></td><td></td></tr><tr><td></td><td></td><td></td></tr><tr><td></td><td></td><td></td></tr><tr><td></td><td></td><td></td></tr><tr><td></td><td></td><td></td></tr><tr><td></td><td></td><td></td></tr><tr><td></td><td></td><td></td></tr><tr><td></td><td></td><td></td></tr><tr><td></td><td></td><td></td></tr><tr><td></td><td></td><td></td></tr><tr><td></td><td></td><td></td></tr><tr><td></td><td></td><td></td></tr><tr><td></td><td></td><td></td></tr><tr><td></td><td></td><td></td></tr><tr><td></td><td></td><td></td></tr><tr><td></td><td></td><td></td></tr><tr><td></td><td></td><td></td></tr><tr><td></td><td></td><td></td></tr><tr><td></td><td></td><td></td></tr><tr><td></td><td></td><td></td></tr><tr><td></td><td></td><td></td></tr><tr><td></td><td></td><td></td></tr><tr><td></td><td></td><td></td></tr><tr><td></td><td></td><td></td></tr></table>
+
+# 4 EXPERIMENTS
+
+Encoder. Pre-trained language models like BERT (Devlin et al., 2019), GPT-2 (Radford et al., 2019) and RoBERTa (Liu et al., 2019) have shown state-of-the-art performance for various natural language processing tasks. In this work we adopt one of them as a base encoder by initializing the teacher with pre-trained BERT-base model and a randomly initialized token classification layer.
+
+Datasets. We perform large-scale experiments with six different datasets including user utterances for task-oriented dialog systems and multilingual Named Entity Recognition tasks as summarized in Table 1. (a) Email. This consists of natural language user utterances for email-oriented user actions like sending, receiving or searching emails with attributes like date, time, topics, people, etc. (b) SNIPS is a public benchmark
+
+<table><tr><td>Dataset</td><td># Slots</td><td>#Train</td><td>#Test</td><td>#Lang</td></tr><tr><td>Email</td><td>20</td><td>2.5K</td><td>1k</td><td>EN</td></tr><tr><td>SNIPS</td><td>39</td><td>13K</td><td>0.7K</td><td>EN</td></tr><tr><td>MIT Movie</td><td>12</td><td>8.8K</td><td>2.4K</td><td>EN</td></tr><tr><td>MIT Restaurant</td><td>8</td><td>6.9K</td><td>1.5K</td><td>EN</td></tr><tr><td>Wikiann (EN)</td><td>3</td><td>20K</td><td>10K</td><td>EN</td></tr><tr><td>CoNLL03 (EN)</td><td>4</td><td>15K</td><td>3.6K</td><td>EN</td></tr><tr><td>CoNLL03</td><td>16</td><td>38K</td><td>15K</td><td>4</td></tr><tr><td>Wikiann</td><td>123</td><td>705K</td><td>329K</td><td>41</td></tr></table>
+
+Table 1: Dataset summary.
+
+dataset (Coucke et al., 2018) of user queries from multiple domains including music, media, and weather. (c) MIT Movie and Restaurant corpus (Liu et al., 2013) consist of similar user utterances for movie and restaurant domains. (d) CoNLL03 (Sang & Meulder, 2003) and Wikiann (Pan et al., 2017) are public benchmark datasets for multilingual Named Entity Recognition. CoNLL03 is a collection of news wire articles from the Reuters Corpus from 4 languages with manual annotations, whereas Wikiann comprises of extractions from Wikipedia articles from 41 languages with automatic annotation leveraging meta-data for different entity types like ORG, PER, LOC etc. For every dataset, we sample $K \in \{ 5 , 1 0 , 2 0 , 1 0 0 \}$ labeled sequences for each slot type from the Train data, and add the remaining to the unlabeled set while ignoring their labels – following standard setups for semi-supervised learning. We repeatedly sample $K$ labeled instances three times for multiple runs to report average performance with standard deviation across the runs.
+
+Baselines. The first baseline we consider is the fully supervised BERT model trained on all available training data which provides the ceiling performance for every task. Each of the other models are trained on $K$ training labels per slot type. We adopt several state-of-the-art semi-supervised methods as baselines: (1) CVT (Clark et al., 2018) is a semi-supervised sequence labeling method based on cross-view training; (2) SeqVAT (Chen et al., 2020) incorporates adversarial training with conditional random field layer for semi-supervised sequence labeling; (3) Mean Teacher (MT) (Tarvainen & Valpola, 2017) averages model weights to obtain an aggregated teacher; (4) VAT (Miyato et al., 2018) adopts virtual adversarial training to make the model robust to noise; (5) classic ST (III, 1965) is simple self-training method with hard pseudo-labels; (6) BOND (Liang et al., 2020) is the most recent work on self-training for sequence labeling with confidence-based sample selection and forms a strong baseline for our work. We implement our framework in Pytorch and use Tesla V100 gpus for experiments. Hyper-parameter configurations with model settings presented in Appendix.
+
+Neural sequence labeling performance with few training labels. Table 2 shows the performance comparison among different models with $\mathrm { K } { = } 1 0$ labeled examples per slot type. The fully supervised BERT trained on thousands of labeled examples provides the ceiling performance for the few-shot setting. We observe our method MetaST to significantly outperform all methods across all datasets including the models that also use the same BERT encoder as ours like MT, VAT, Classic ST and BOND with corresponding average performance improvements as $1 4 . 2 2 \%$ , $1 4 . 9 0 \%$ , $8 . 4 6 \%$ and $8 . 8 2 \%$ . Non BERT models like CVT and ${ \tt S e q V A T }$ are consistently worse than other baselines.
+
+<table><tr><td>Method</td><td>SNIPS</td><td>Email</td><td>Movie</td><td>Restaurant</td><td>CoNLL03 (EN)</td><td>Wikiann (EN)</td></tr><tr><td># Slots</td><td>39</td><td>20</td><td>12</td><td>8</td><td>4</td><td>3</td></tr><tr><td colspan="7">Full-supervision</td></tr><tr><td>BERT</td><td>95.80</td><td>94.44</td><td>87.87</td><td>78.95</td><td>92.40</td><td>84.04</td></tr><tr><td>Few-shot supervision (10 labels per slot)</td><td></td><td></td><td>69.50</td><td>54.06</td><td>71.15</td><td>45.61</td></tr><tr><td colspan="7">BERT 79.01 87.85</td></tr><tr><td>Few-shot supervision (10 labels per slot) + unlabeled data</td><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>CVT</td><td>78.23</td><td>78.24</td><td>62.73</td><td>42.57</td><td>54.31</td><td>27.89</td></tr><tr><td>SeqVAT</td><td>78.67</td><td>72.65</td><td>67.10</td><td>51.55</td><td>67.21</td><td>35.16</td></tr><tr><td>MT</td><td>79.48</td><td>89.53</td><td>67.62</td><td>51.75</td><td>68.67</td><td>41.43</td></tr><tr><td>VAT</td><td>79.08</td><td>89.71</td><td>70.17</td><td>53.34</td><td>65.03</td><td>38.81</td></tr><tr><td>Classic ST</td><td>83.26</td><td>90.70</td><td>71.88</td><td>56.80</td><td>70.99</td><td>46.15</td></tr><tr><td>BOND</td><td>83.54</td><td>89.75</td><td>70.91</td><td>55.78</td><td>69.56</td><td>48.73</td></tr><tr><td rowspan="2">MetaST</td><td>88.23</td><td>92.18</td><td>77.67</td><td>63.83</td><td>76.65</td><td></td></tr><tr><td>(0.04;↑12%)</td><td>(0.47;↑4.93%)</td><td>(0.10;↑11.76%)</td><td>(1.62;↑18.07%)</td><td>(0.73;17.73%)</td><td>56.61 (0.4;↑24.12%)</td></tr></table>
+
+Table 2: F1 score comparison of models for sequence labeling on different datasets. All models (except CVT and ${ \tt S e q V A T } ,$ use the same BERT encoder. F1 score of our model for each task is followed by standard deviation and percentage improvement (↑) over BERT with few-shot supervision.
+
+We also observe variable performance of the models across different tasks. Specifically, the performance gap between the best few-shot model and the fully supervised model varies significantly. MetaST achieves close performance to the fully-supervised model in some datasets (e.g. SNIPS and Email) but has bigger room for improvement in others (e.g. CoNLL03 (EN) and Wikiann (EN)). This can be attributed to the following factors. (i) Labeled training examples and slots. The total number of labeled training instances for our K-shot setting is given by $K \times \# S l o t s$ . Therefore, for tasks with higher number of slots and consequently more training labels, most of the models perform better including MetaST. Task-oriented dialog systems with more slots and inherent dependency between the slot types benefit more than NER tasks. (ii) Task difficulty: User utterances from task-oriented dialog systems for some of the domains like weather, music and emails contain predictive query patterns and limited diversity. In contrast, Named Entity Recognition datasets are comparatively diverse and require more training labels to generalize well. Similar observations are also depicted in Table 3 for multilingual NER tasks with more slots and consequently more training labels from multiple languages as well as richer interactions across the slots from different languages.
+
+<table><tr><td>Dataset</td><td>#Lang</td><td>#Slots</td><td>Full Sup.</td><td>Few-shot Sup.</td><td colspan="5">Few-shot supervision + unlabeled data</td></tr><tr><td></td><td></td><td></td><td>BERT</td><td>BERT</td><td>MT</td><td>VAT</td><td>Classic ST</td><td>BOND</td><td>MetaST</td></tr><tr><td>CoNLL03</td><td>4</td><td>16</td><td>87.67</td><td>70.77</td><td>68.34</td><td>67.63</td><td>72.69</td><td>72.79</td><td>76.41 (0.47) (↑ 7.97%)</td></tr><tr><td>Wikiann</td><td>41</td><td>123</td><td>87.17</td><td>79.67</td><td>80.23</td><td>78.82</td><td>80.24</td><td>79.57</td><td>81.61 (0.14) (↑ 2.42%)</td></tr></table>
+
+Table 3: F1 score comparison of models for sequence labeling on multilingual datasets using the same BERT-Multilingual-Base encoder. F1 score of MetaST for each task is followed by standard deviation in parentheses and percentage improvement (↑) over BERT with few-shot supervision.
+
+Controlling for the total amount of labeled data. In order to control for the variable amount of training labels across different datasets, we perform another experiment where we vary the number of labels for different slot types while keeping the total number of labeled instances for each dataset similar (ca. 200). Results are shown in Table 4. To better illustrate the effect of the number of training labels, we choose tasks with lower performance in Table 2 for this experiment. Comparing the results in Tables 2 and 4, we observe the performance of MetaST to improve with more training labels for all the tasks .
+
+Effect of varying the number of labels $K$ per slot. Table 5 shows the improvement in the performance of MetaST when increasing the number of labels for each slot type in the SNIPS dataset.
+
+Table 4: F1 scores of different models with 200 labeled samples for each task. The percentage improvement $( \uparrow )$ is over the BERT model with few-shot supervision.   
+
+<table><tr><td>Dataset</td><td>BERT (Full Supervision)</td><td>BERT (Few-shot Supervision)</td><td>MetaST（%Improvement）</td></tr><tr><td>MIT Movie</td><td>87.87</td><td>75.81</td><td>80.33 (↑5.96%)</td></tr><tr><td>MIT Restaurant</td><td>78.95</td><td>60.12</td><td>67.86 (↑12.87%)</td></tr><tr><td>CoNLL03 (EN)</td><td>92.40</td><td>77.48</td><td>81.61 (↑ 5.33%)</td></tr><tr><td>Wikiann (EN)</td><td>84.04</td><td>62.04</td><td>71.27 (个14.88%)</td></tr><tr><td>Average</td><td>85.82</td><td>68.86</td><td>75.27 (↑ 9.31%)</td></tr></table>
+
+Similar trends can be found on other datasets (results in Appendix). As we increase the amount of labeled training instances, the performance of BERT also improves, and correspondingly the margin between MetaST and these baselines decreases although MetaST still improves over all of them. In the self-training framework, given the ceiling performance for every task and the improved performance of the teacher with more training labels, there is less room for (relative) improvement of the student over the teacher model. Consider SNIPS for example. Our model obtains $12 \%$ and $2 \%$ improvement over the few-shot BERT model for the 10-shot and 100-shot setting with F1-scores as $8 8 . 2 2 \%$ and $9 5 . 3 9 \%$ , respectively. The ceiling performance for this task is $9 5 . 8 \%$ on training BERT on the entire dataset with 13K labeled examples. This demonstrates that MetaST is most impactful for low-resource settings with few training labels for a given task.
+
+<table><tr><td>#Slots</td><td>Few-shot Supervision</td><td colspan="7">Few-shot supervision + unlabeled data</td></tr><tr><td></td><td>BERT</td><td>CVT</td><td>SeqVAT</td><td>MT</td><td>VAT</td><td>Classic ST</td><td>BOND</td><td>MetaST(%Improvement)</td></tr><tr><td>5</td><td>70.63</td><td>69.82</td><td>69.34</td><td>70.85</td><td>71.34</td><td>72.59</td><td>72.85</td><td>81.56 (↑15%)</td></tr><tr><td>10</td><td>79.01</td><td>78.23</td><td>78.67</td><td>79.48</td><td>79.08</td><td>83.26</td><td>83.54</td><td>88.22 (↑12%)</td></tr><tr><td>20</td><td>86.81</td><td>88.04</td><td>85.05</td><td>87.31</td><td>88.19</td><td>88.32</td><td>88.93</td><td>91.99 (↑6%)</td></tr><tr><td>100</td><td>93.90</td><td>94.61</td><td>91.46</td><td>94.26</td><td>94.53</td><td>93.92</td><td>94.22</td><td>95.39 (12%)</td></tr></table>
+
+Table 5: Variation in model performance on varying $K$ labels / slot on SNIPS dataset with 39 slots. The percentage improvement $( \uparrow )$ is relative to the BERT model with few-shot supervision.
+
+Ablation analysis. Table 6 demonstrates the impact of different MetaST components with ablation analysis. We observe that soft pseudo-labels hurt the model performance compared to hard pseudolabels, as also shown in recent work (Kumar et al., 2020). Such a performance drop may be attributed to soft labels being less informative compared to sharpened ones. Removing the iterative teacher fine-tuning step (Section 3.1) also hurts the overall performance.
+
+Table 6: Ablation analysis of our framework MetaST with 10 labeled examples per slot on SNIPS and CoNLL03 (EN).   
+
+<table><tr><td rowspan="2">Method</td><td colspan="2">Datasets</td></tr><tr><td>SNIPS</td><td>CoNLL03</td></tr><tr><td>BERT w/ Continued Pre-training +</td><td></td><td></td></tr><tr><td>Few-shot Supervision</td><td>83.96</td><td>69.84</td></tr><tr><td>Classic ST</td><td>83.26</td><td>70.99</td></tr><tr><td>Classic ST w/ Soft Pseudo-Labels</td><td>81.17</td><td>71.87</td></tr><tr><td>MetaST(ours) w/Hard Pseudo-Labels</td><td>88.23</td><td>76.65</td></tr><tr><td>MetaST w/ Soft Pseudo-Labels</td><td>86.16</td><td>75.84</td></tr><tr><td>MetaST w/o Iterative Teacher Fine-tune</td><td>85.64</td><td>72.74</td></tr><tr><td>MetaST w/o Labeled Data Acq.</td><td>86.63</td><td>75.02</td></tr><tr><td>Pseudo-labeled Data Re-weighting</td><td></td><td></td></tr><tr><td>MetaST w/o Re-weighting</td><td>85.48</td><td>73.02</td></tr><tr><td>MetaST (Easy)</td><td>85.56</td><td>74.53</td></tr><tr><td>MetaST (Difficult)</td><td>86.34</td><td>68.06</td></tr></table>
+
+![](images/6e003691b635563a0994ab8d5c2a1f4aff6b7c20f56ba95beaa0a166af22b000.jpg)  
+Figure 2: Visualization of MetaST reweighting on CoNLL03 (EN).
+
+Continued pre-training v.s. self-training. To contrast continued pre-training with self-training, we further pre-train BERT on in-domain unlabeled data and then fine-tune it with few labeled examples denoted as “BERT (Continued Pre-training $^ +$ Few-shot Supervision)”. The pre-training step improves the BERT performance over the baseline on SNIPS but degrades the performance on CoNLL03. This indicates that continued pre-training can improve the performance of few-shot supervised BERT on specialized tasks (e.g., SNIPS) with different data distribution than the original pre-training data (e.g., Wikipedia), but may not help for general domain ones like CoNLL03 with overlapping data from Wikipedia. In contrast to the above baseline, MetaST brings significant improvements on both datasets. This demonstrates the generality and flexibility of self-training over pre-training as also observed in contemporary work (Zoph et al., 2020) on image classification.
+
+Adaptive labeled data acquisition. We perform an ablation study by removing adaptive labeled data acquisition from MetaST (denoted as “MetaST w/o Labeled Data Acq.”). Removing this component leads to around $2 \%$ performance drop on an average demonstrating the impact of labeled data acquisition. Moreover, the performance drop on SNIPS (39 slots) is larger than that on CoNLL03 (4 slots). This demonstrates that adaptive acquisition is more helpful for tasks with more slot types – where diversity and data distribution necessitate a better exploration strategy in contrast to random sampling employed in prior meta-learning works.
+
+Re-weighting strategies. To explore the role of token-level re-weighting for pseudo-labeled sequences (discussed in Section 3.2), we replace our meta-learning component with different sample selection strategies based on the model confidence for different tokens. One sampling strategy chooses samples uniformly without any re-weighting (referred to as “MetaST w/o Re-weighting”). The sampling strategy with weights proportional to the model confidence favors easy samples (referred to as “MetaST-Easy”), whereas the converse favors difficult ones (referred to as “MetaSTDifficult”).We observe the meta-learning based re-weighting strategy to perform the best. Interestingly, MetaST-Easy outperforms MetaST-Difficult significantly on CoNLL03 (EN) but achieves slightly lower performance on SNIPS. This demonstrates that difficult samples are more helpful when the quality of pseudo-labeled data is relatively high. On the converse, the sample selection strategy focusing on difficult samples introduces noisy examples with lower pseudo-label quality. Therefore, sampling strategies may need to vary for different datasets, thereby, demonstrating the necessity of adaptive data re-weighting as in our framework MetaST. Moreover, MetaST significantly outperforms classic self-training strategies with hard and soft pseudo-labels demonstrating the effectiveness of our design.
+
+Analysis of pseudo-labeled data re-weighting. To visually explore the adaptive re-weighting mechanism, we illustrate token-level re-weighting of MetaST on CoNLL03 (EN) dataset with ${ \mathrm { K } } { = } 1 0$ shot at step 100 in Fig. 2. We include the re-weighting visualisation on SNIPS in Appendix A.1. We observe that the selection mechanism filters out most of the noisy pseudo-labels (colored in blue) even those with high teacher confidence as shown in Fig. 2.
+
+# 5 RELATED WORK
+
+Semi-supervised learning has been widely used for consistency training (Bachman et al., 2014; Rasmus et al., 2015; Laine & Aila, 2017; Tarvainen & Valpola, 2017; Miyato et al., 2018), latent variable models (Kingma et al., 2014) for sentence compression (Miao & Blunsom, 2016) and code generation (Yin et al., 2018). More recently, methods like UDA (Xie et al., 2019) leverage consistency training for few-shot learning of instance-classification tasks leveraging auxiliary resources like paraphrasing and back-translation (BT) (Sennrich et al., 2016).
+
+Sample selection. Curriculum learning (Bengio et al., 2009) techniques are based on the idea of learning easier aspects of the task first followed by the more complex ones. Prior work leveraging self-paced learning (Kumar et al., 2010) and more recently self-paced co-training (Ma et al., 2017) leverage teacher confidence to select easy samples during training. Sample selection for image classification tasks have been explored in recent works with meta-learning (Ren et al., 2018; Li et al., 2019) and active learning (Panagiota Mastoropoulou, 2019; Chang et al., 2017b). However, all of these techniques rely on only the model outputs applied to instance-level classification tasks.
+
+Semi-supervised sequence labeling. Miller et al. (2004); Peters et al. (2017) leverage large amounts of unlabeled data to improve token representation for sequence labeling tasks. Another line of research introduces latent variable modeling (Chen et al., 2019; Zhou & Neubig, 2017) to learn interpretable and structured latent representations. Recently, adversarial training based model SeqVAT (Chen et al., 2020) and cross-view training method CVT (Clark et al., 2018) have shown promising results for sequence labeling tasks.
+
+# 6 CONCLUSIONS
+
+In this work, we develop an adaptive self-training framework MetaST that leverages self-training and meta-learning for few-shot training of neural sequence taggers. We address the issue of error propagation from noisy pseudo-labels from the teacher in the self-training framework by adaptive sample selection and re-weighting with meta-learning. Extensive experiments on six benchmark datasets and different tasks including multilingual NER and slot tagging for task-oriented dialog systems demonstrate the effectiveness of the proposed method particularly for low-resource settings.
+
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+
+# A APPENDIX
+
+# A.1 EXPLORATIONS ON UNLABELED DATA AND MINI-BATCH S
+
+Variation in model performance with unlabeled data. Table 12 shows the improvement in model performance as we inject more unlabeled data with diminishing returns after a certain point.
+
+Variation in model performance with mini-batch S. We set the value of $S$ in Eq. 8 to $\{ 1 , 3 , 5 \}$ respectively to explore its impact on the re-weighting mechanism. From Figure 3 we observe that the model is not super sensitive to hyper-parameter $S$ but can achieve a better estimate of the weights of the pseudo-labeled data with increasing mini-batch values.
+
+Table 7: Varying proportion of unlabeled data for MetaST with 10 labels per slot.   
+
+<table><tr><td rowspan="2">Ratio of Unlabeled Data</td><td colspan="2">Datasets</td></tr><tr><td>SNIPS</td><td>CoNLL03</td></tr><tr><td>5%</td><td>84.47</td><td>72.92</td></tr><tr><td>25%</td><td>87.10</td><td>76.46</td></tr><tr><td>75%</td><td>87.50</td><td>76.56</td></tr></table>
+
+![](images/4acf5be292e2775588f2a99e982a0a9dfdc3fa3dd074d857771804a5f6d9f1ce.jpg)  
+Figure 3: Varying $S$ mini-batch labeled data for re-weighting.
+
+# A.2 ANALYSIS OF RE-WEIGHTING ON SNIPS AND CONLL03
+
+Analysis of pseudo-labeled data re-weighting. To visually explore the adaptive re-weighting mechanism, we illustrate token re-weighting of MetaST on CoNLL03 and SNIPS datasets with ${ \mathrm { K } } { = } 1 0$ shot at step 100 in Fig. 4. Besides the observation in the experimental section, we observe that many difficult and correct pseudo-labeled samples (low teacher confidence) are selected according to Fig. 4a.
+
+![](images/a1ce0ac42b92d98b8512da697f6121d4c41ab38cbc3fd9329203574c7580c82c.jpg)  
+Figure 4: Visualization of MetaST re-weighting examples on SNIPS and CoNLL03 (EN).
+
+# A.3 K-SHOTS
+
+Effect of varying the number of few-shots K. We show the performance changes with respect to varying number of few-shots K $\{ 5 , 1 0 , 2 0 , 1 0 0 \}$ on Wikiann (en), MIT movie, MIT Restaurant, CoNLL2003 (En), Multilingual CoNLL and Multilingual Wikiann in Table 9-13. Since the number of labeled examples for some slots in Email dataset is around 10, we only show 5 and 10 shots for Email dataset in Table 8.
+
+Table 8: Email Dataset.   
+
+<table><tr><td rowspan="2">Method</td><td colspan="2">Shots</td></tr><tr><td>5</td><td>10</td></tr><tr><td colspan="3">Full-supervision</td></tr><tr><td>BERT</td><td></td><td>0.9444</td></tr><tr><td colspan="3">Few-shot Supervision</td></tr><tr><td>BERT</td><td>0.8211</td><td>0.8785</td></tr><tr><td colspan="3">Few-shot Supervision + unlabeled data</td></tr><tr><td>CVT</td><td>67.44</td><td>78.24</td></tr><tr><td>SeqVAT</td><td>64.67</td><td>72.65</td></tr><tr><td>Mean Teacher</td><td>84.10</td><td>89.53</td></tr><tr><td>VAT</td><td>83.24</td><td>89.71</td></tr><tr><td>Classic ST</td><td>86.88</td><td>90.70</td></tr><tr><td>BOND</td><td>84.92</td><td>89.75</td></tr><tr><td>MetaST</td><td>89.21</td><td>92.18</td></tr></table>
+
+Table 9: Wikiann (En) Dataset.   
+
+<table><tr><td rowspan="2">Method</td><td colspan="4">Shots (3 Slot Types)</td></tr><tr><td>5</td><td>10</td><td>20</td><td>100</td></tr><tr><td colspan="5">Full-supervision</td></tr><tr><td>BERT</td><td colspan="3">84.04</td><td></td></tr><tr><td colspan="5">Few-shot Supervision</td></tr><tr><td>BERT</td><td>37.01</td><td>45.61</td><td>54.53</td><td>67.87</td></tr><tr><td colspan="5">Few-shot Supervision +unlabeled data</td></tr><tr><td>CVT</td><td>16.05</td><td>27.89</td><td>46.42</td><td>66.36</td></tr><tr><td>SeqVAT</td><td>21.11</td><td>35.16</td><td>42.26</td><td>62.37</td></tr><tr><td>Mean Teacher</td><td>30.92</td><td>41.43</td><td>50.61</td><td>67.16</td></tr><tr><td>VAT</td><td>24.72</td><td>38.81</td><td>50.15</td><td>66.31</td></tr><tr><td>Classic ST</td><td>32.72</td><td>46.15</td><td>54.41</td><td>68.64</td></tr><tr><td>BOND</td><td>34.22</td><td>48.73</td><td>52.45</td><td>68.89</td></tr><tr><td>MetaST</td><td>55.04</td><td>56.61</td><td>60.38</td><td>73.20</td></tr></table>
+
+Figure 5: MIT Movie Dataset.   
+
+<table><tr><td rowspan="2">Method</td><td colspan="4">Shots (12 Slot Types)</td></tr><tr><td>5</td><td>10</td><td>20</td><td>100</td></tr><tr><td>Full-supervision</td><td colspan="4">87.87</td></tr><tr><td>BERT</td><td colspan="4"></td></tr><tr><td>Few-shot Supervision</td><td></td><td></td><td></td><td></td></tr><tr><td>BERT</td><td>62.80</td><td>69.50</td><td>75.81</td><td>82.49</td></tr><tr><td colspan="5">Few-shot Supervision +unlabeled data</td></tr><tr><td>CVT</td><td>57.48</td><td>62.73</td><td>70.20</td><td>81.82</td></tr><tr><td>SeqVAT</td><td>60.94</td><td>67.10</td><td>74.15</td><td>82.73</td></tr><tr><td>Mean Teacher</td><td>58.92</td><td>67.62</td><td>75.24</td><td>82.20</td></tr><tr><td>VAT</td><td>60.75</td><td>70.17</td><td>75.41</td><td>82.39</td></tr><tr><td>Classic ST</td><td>63.39</td><td>71.88</td><td>76.58</td><td>83.06</td></tr><tr><td>BOND</td><td>62.50</td><td>70.91</td><td>75.52</td><td>82.65</td></tr><tr><td>MetaST</td><td>72.57</td><td>77.67</td><td>80.33</td><td>84.35</td></tr></table>
+
+Table 10: MIT Restaurant Dataset.   
+
+<table><tr><td rowspan="2">Method</td><td colspan="4">Shots (8 Slot Types)</td></tr><tr><td>5</td><td>10</td><td>20</td><td>100</td></tr><tr><td colspan="5">Full-supervision</td></tr><tr><td>BERT</td><td colspan="4">78.95</td></tr><tr><td colspan="5">Few-shot Supervision</td></tr><tr><td>BERT</td><td>41.39</td><td>54.06</td><td>60.12</td><td>72.24</td></tr><tr><td colspan="5">Few-shot Supervision +unlabeled data</td></tr><tr><td>CVT</td><td>33.74</td><td>42.57</td><td>51.33</td><td>70.84</td></tr><tr><td>SeqVAT</td><td>41.94</td><td>51.55</td><td>56.15</td><td>71.39</td></tr><tr><td>Mean Teacher</td><td>40.37</td><td>51.75</td><td>57.34</td><td>72.40</td></tr><tr><td>VAT</td><td>41.29</td><td>53.34</td><td>59.68</td><td>72.65</td></tr><tr><td>Classic ST</td><td>44.35</td><td>56.80</td><td>60.28</td><td>73.13</td></tr><tr><td>BOND</td><td>43.01</td><td>55.78</td><td>59.96</td><td>73.60</td></tr><tr><td>MetaST</td><td>53.02</td><td>63.83</td><td>67.86</td><td>75.25</td></tr></table>
+
+Table 11: CoNLL2003 (EN)   
+
+<table><tr><td rowspan="2">Method</td><td colspan="4">Shots (4 Slot Types)</td></tr><tr><td>5</td><td>10</td><td>20</td><td>100</td></tr><tr><td>Full-supervision</td><td colspan="4">92.40</td></tr><tr><td>BERT</td><td colspan="4"></td></tr><tr><td>Few-shot Supervision</td><td></td><td></td><td></td><td></td></tr><tr><td>BERT</td><td>63.87</td><td>71.15</td><td>73.57</td><td>84.36</td></tr><tr><td colspan="5">Few-shot Supervision +unlabeled data</td></tr><tr><td>CVT</td><td>51.15</td><td>54.31</td><td>66.11</td><td>81.99</td></tr><tr><td>SeqVAT</td><td>58.02</td><td>67.21</td><td>74.15</td><td>82.20</td></tr><tr><td>Mean Teacher</td><td>59.04</td><td>68.67</td><td>72.62</td><td>84.17</td></tr><tr><td>VAT</td><td>57.03</td><td>65.03</td><td>72.69</td><td>84.43</td></tr><tr><td>Classic ST</td><td>64.04</td><td>70.99</td><td>74.65</td><td>84.93</td></tr><tr><td>BOND</td><td>62.52</td><td>69.56</td><td>74.19</td><td>83.87</td></tr><tr><td>MetaST</td><td>71.49</td><td>76.65</td><td>78.54</td><td>85.77</td></tr></table>
+
+Table 12: Multilingual CoNLL03.   
+
+<table><tr><td rowspan="2">Method</td><td colspan="4">Shots (4 Slot Types)</td></tr><tr><td>5</td><td>10</td><td>20</td><td>100</td></tr><tr><td colspan="5">Full-supervision</td></tr><tr><td>BERT</td><td colspan="3"></td><td></td></tr><tr><td colspan="5">Few-shot Supervision</td></tr><tr><td>BERT</td><td>64.80</td><td>70.77</td><td>73.89</td><td>80.61</td></tr><tr><td colspan="5">Few-shot Supervision +unlabeled data</td></tr><tr><td>Mean Teacher</td><td>64.55</td><td>68.34</td><td>73.87</td><td>79.21</td></tr><tr><td>VAT</td><td>64.97</td><td>67.63</td><td>74.26</td><td>80.70</td></tr><tr><td>Classic ST</td><td>67.95</td><td>72.69</td><td>73.79</td><td>81.82</td></tr><tr><td>BOND</td><td>69.42</td><td>72.79</td><td>76.02</td><td>80.62</td></tr><tr><td>MetaST</td><td>73.34</td><td>76.65</td><td>77.01</td><td>82.11</td></tr></table>
+
+Table 13: Multilingual Wikiann   
+
+<table><tr><td rowspan="2">Method</td><td colspan="4">Shots (3 Slot Types X 41 languages)</td></tr><tr><td>5</td><td>10</td><td>20</td><td>100</td></tr><tr><td colspan="5">Full-supervision</td></tr><tr><td>BERT</td><td colspan="3"></td></tr><tr><td>Few-shot Supervision</td><td></td><td></td><td>82.33</td><td>85.70</td></tr><tr><td>BERT</td><td>77.68</td><td>79.67</td><td></td><td></td></tr><tr><td colspan="5">Few-shot Supervision +unlabeled data</td></tr><tr><td>Mean Teacher</td><td>77.09</td><td>80.23</td><td>82.19</td><td>85.34</td></tr><tr><td>VAT</td><td>74.71</td><td>78.82</td><td>82.60</td><td>85.82</td></tr><tr><td>Classic ST</td><td>76.73</td><td>80.24</td><td>82.39</td><td>86.08</td></tr><tr><td>BOND</td><td>78.81</td><td>79.57</td><td>82.19</td><td>86.14</td></tr><tr><td>MetaST</td><td>79.10</td><td>81.61</td><td>83.14</td><td>85.57</td></tr></table>
+
+# A.4 IMPLEMENTATIONS AND HYPER-PARAMETER
+
+We do not perform any hyper-parameter tuning for different datasets. The batch size and maximum sequence length varies due to data characteristics and are as shown in Tbale 14. The hyperparameters are as shown in Table 14.
+
+Also, we retain parameters from original BERT implementation from https://github.com/ huggingface/transformers.
+
+We implement SeqVAT based on https://github.com/jiesutd/NCRFpp and implement CVT following https://github.com/tensorflow/models/tree/master/ research/cvt_text.
+
+Table 14: Batch size, sequence length and BERT encoder choices across datasets   
+
+<table><tr><td>Dataset</td><td>Sequence Length</td><td></td><td>Batch SizeLabeled data sample size B|</td><td>Unlabeled Batch Size</td><td>BERT Encoder</td></tr><tr><td>SNIPS</td><td>64</td><td>16</td><td>32</td><td>32</td><td>BERT-base-uncased</td></tr><tr><td>Email</td><td>64</td><td>16</td><td>32</td><td>32</td><td>BERT-base-cased</td></tr><tr><td>Movie</td><td>64</td><td>16</td><td>32</td><td>32</td><td>BERT-base-uncased</td></tr><tr><td>Restaurant</td><td>64</td><td>16</td><td>16</td><td>32</td><td>BERT-base-uncased</td></tr><tr><td>CoNLL03 (EN)</td><td>128</td><td>16</td><td>8</td><td>32</td><td>BERT-base-cased</td></tr><tr><td>Wikiann (EN)</td><td>128</td><td>16</td><td>8</td><td>32</td><td>BERT-base-cased</td></tr><tr><td>CoNLLO3 (multilingual)</td><td>128</td><td>16</td><td>32</td><td>32</td><td>BERT-multilingual-base-cased</td></tr><tr><td>Wikiann (multilingaul)</td><td>128</td><td>16</td><td>32</td><td>32</td><td>BERT-multilingual-base-cased</td></tr></table>
+
+Table 15: Hyper-parameters.   
+
+<table><tr><td>BERT attention dropout BERT hidden dropout Latest Iteration R in labeled data acquisition BERT output hidden size h</td><td>0.3 0.3 5 768</td></tr><tr><td>Steps for fine-tuning teacher model on labeled data</td><td>2000</td></tr><tr><td>Steps T for self-training model on unlabeled data</td><td>3000</td></tr><tr><td>Mini-batch S Re-initialize Student</td><td>5</td></tr><tr><td>Pseudo-label Type</td><td>Y Hard</td></tr><tr><td>Warmup steps</td><td>20</td></tr><tr><td>learning rate α</td><td>5e-5</td></tr><tr><td>Weight_decay</td><td>5e-6</td></tr></table>

parse/train/B1l8BtlCb/B1l8BtlCb.md

@@ -0,0 +1,318 @@
+# NON-AUTOREGRESSIVE NEURAL MACHINE TRANSLATION
+
+Jiatao $\mathbf { G u } ^ { \dagger }$ ∗, James Bradbury‡, Caiming Xiong‡, Victor O.K. Li†& Richard Socher‡
+
+‡Salesforce Research   
+{james.bradbury,cxiong,rsocher}@salesforce.com   
+†The University of Hong Kong   
+{jiataogu, vli}@eee.hku.hk
+
+# ABSTRACT
+
+Existing approaches to neural machine translation condition each output word on previously generated outputs. We introduce a model that avoids this autoregressive property and produces its outputs in parallel, allowing an order of magnitude lower latency during inference. Through knowledge distillation, the use of input token fertilities as a latent variable, and policy gradient fine-tuning, we achieve this at a cost of as little as 2.0 BLEU points relative to the autoregressive Transformer network used as a teacher. We demonstrate substantial cumulative improvements associated with each of the three aspects of our training strategy, and validate our approach on IWSLT 2016 English–German and two WMT language pairs. By sampling fertilities in parallel at inference time, our non-autoregressive model achieves near-state-of-the-art performance of 29.8 BLEU on WMT 2016 English– Romanian.
+
+# 1 INTRODUCTION
+
+Neural network based models outperform traditional statistical models for machine translation (MT) (Bahdanau et al., 2015; Luong et al., 2015). However, state-of-the-art neural models are much slower than statistical MT approaches at inference time (Wu et al., 2016). Both model families use autoregressive decoders that operate one step at a time: they generate each token conditioned on the sequence of tokens previously generated. This process is not parallelizable, and, in the case of neural MT models, it is particularly slow because a computationally intensive neural network is used to generate each token.
+
+While several recently proposed models avoid recurrence at train time by leveraging convolutions (Kalchbrenner et al., 2016; Gehring et al., 2017; Kaiser et al., 2017) or self-attention (Vaswani et al., 2017) as more-parallelizable alternatives to recurrent neural networks (RNNs), use of autoregressive decoding makes it impossible to take full advantage of parallelism during inference.
+
+We introduce a non-autoregressive translation model based on the Transformer network (Vaswani et al., 2017). We modify the encoder of the original Transformer network by adding a module that predicts fertilities, sequences of numbers that form an important component of many traditional machine translation models (Brown et al., 1993). These fertilities are supervised during training and provide the decoder at inference time with a globally consistent plan on which to condition its simultaneously computed outputs.
+
+# 2 BACKGROUND
+
+# 2.1 AUTOREGRESSIVE NEURAL MACHINE TRANSLATION
+
+Given a source sentence $X = \{ x _ { 1 } , . . . , x _ { T ^ { \prime } } \}$ , a neural machine translation model factors the distribution over possible output sentences $Y = \{ y _ { 1 } , . . . , y _ { T } \}$ into a chain of conditional probabilities with a
+
+left-to-right causal structure:
+
+$$
+p _ { \mathcal { A } \mathcal { R } } ( \boldsymbol { Y } | \boldsymbol { X } ; \theta ) = \prod _ { t = 1 } ^ { T + 1 } p ( y _ { t } | y _ { 0 : t - 1 } , x _ { 1 : T ^ { \prime } } ; \theta ) ,
+$$
+
+where the special tokens $y _ { 0 }$ (e.g. $\left. \mathrm { b o s } \right.$ ) and $y _ { T + 1 }$ (e.g. $\langle \cos \rangle$ ) are used to represent the beginning and end of all target sentences. These conditional probabilities are parameterized using a neural network. Typically, an encoder-decoder architecture (Sutskever et al., 2014) with a unidirectional RNN-based decoder is used to capture the causal structure of the output distribution.
+
+Maximum Likelihood training Choosing to factorize the machine translation output distribution autoregressively enables straightforward maximum likelihood training with a cross-entropy loss applied at each decoding step:
+
+$$
+\mathcal { L } _ { \mathrm { M L } } = \log p _ { \mathcal { A R } } ( Y | X ; \theta ) = \sum _ { t = 1 } ^ { T + 1 } \log p ( y _ { t } | y _ { 0 : t - 1 } , x _ { 1 : T ^ { \prime } } ; \theta ) .
+$$
+
+This loss provides direct supervision for each conditional probability prediction.
+
+Autoregressive NMT without RNNs Since the entire target translation is known at training time, the calculation of later conditional probabilities (and their corresponding losses) does not depend on the output words chosen during earlier decoding steps. Even though decoding must remain entirely sequential during inference, models can take advantage of this parallelism during training. One such approach replaces recurrent layers in the decoder with masked convolution layers (Kalchbrenner et al., 2016; Gehring et al., 2017) that provide the causal structure required by the autoregressive factorization.
+
+A recently introduced option which reduces sequential computation still further is to construct the decoder layers out of self-attention computations that have been causally masked in an analogous way. The state-of-the-art Transformer network takes this approach, which allows information to flow in the decoder across arbitrarily long distances in a constant number of operations, asymptotically fewer than required by convolutional architectures (Vaswani et al., 2017).
+
+# 2.2 NON-AUTOREGRESSIVE DECODING
+
+Pros and cons of autoregressive decoding The autoregressive factorization used by conventional NMT models has several benefits. It corresponds to the word-by-word nature of human language production and effectively captures the distribution of real translations. Autoregressive models achieve state-of-the-art performance on large-scale corpora and are easy to train, while beam search provides an effective local search method for finding approximately-optimal output translations.
+
+But there are also drawbacks. As the individual steps of the decoder must be run sequentially rather than in parallel, autoregressive decoding prevents architectures like the Transformer from fully realizing their train-time performance advantage during inference. Meanwhile, beam search suffers from diminishing returns with respect to beam size (Koehn & Knowles, 2017) and exhibits limited search parallelism because it introduces computational dependence between beams.
+
+Towards non-autoregressive decoding A na¨ıve solution is to remove the autoregressive connection directly from an existing encoder-decoder model. Assuming that the target sequence length $T$ can be modeled with a separate conditional distribution $p _ { L }$ , this becomes
+
+![](images/fb73e32da81d3465f857ae37043ab008349971a74c732394fc409a62ee78d60d.jpg)  
+Figure 1: Translating “A B C” to $^ { 6 6 } \mathrm { X }$ Y” using autoregressive and non-autoregressive neural MT architectures. The latter generates all output tokens in parallel.
+
+$$
+p _ { \mathcal N A } ( Y | X ; \theta ) = p _ { L } ( T | x _ { 1 : T ^ { \prime } } ; \theta ) \cdot \prod _ { t = 1 } ^ { T } p ( y _ { t } | x _ { 1 : T ^ { \prime } } ; \theta ) .
+$$
+
+This model still has an explicit likelihood function, and it can still be trained using independent cross-entropy losses on each output distribution. Now, however, these distributions can be computed in parallel at inference time.
+
+![](images/899dc15129b43e72de49a617f813130a25104e3d34171cb067e8d5c905671e3e.jpg)  
+Figure 2: The architecture of the NAT, where the black solid arrows represent differentiable connections and the purple dashed arrows are non-differentiable operations. Each sublayer inside the encoder and decoder stacks also includes layer normalization and a residual connection.
+
+# 2.3 THE MULTIMODALITY PROBLEM
+
+However, this na¨ıve approach does not yield good results, because such a model exhibits complete conditional independence. Each token’s distribution $p ( y _ { t } )$ depends only on the source sentence $X$ . This makes it a poor approximation to the true target distribution, which exhibits strong correlation across time. Intuitively, such a decoder is akin to a panel of human translators each asked to provide a single word of a translation independently of the words their colleagues choose.
+
+In particular, consider an English source sentence like “Thank you.” This can be accurately translated into German as any one of “Danke.”, “Danke schon.”, or “Vielen Dank.”, all of which may ¨ occur in a given training corpus. This target distribution cannot be represented as a product of independent probability distributions for each of the first, second, and third words, because a conditionally independent distribution cannot allow “Danke schon.” and “Vielen Dank.” without also ¨ licensing “Danke Dank.” and “Vielen schon.”¨
+
+The conditional independence assumption prevents a model from properly capturing the highly multimodal distribution of target translations. We call this the “multimodality problem” and introduce both a modified model and new training techniques to tackle this issue.
+
+# 3 THE NON-AUTOREGRESSIVE TRANSFORMER (NAT)
+
+We introduce a novel NMT model—the Non-Autoregressive Transformer (NAT)—that can produce an entire output translation in parallel. As shown in Fig. 2, the model is composed of the following four modules: an encoder stack, a decoder stack, a newly added fertility predictor (details in 3.3), and a translation predictor for token decoding.
+
+# 3.1 ENCODER STACK
+
+Similar to the autoregressive Transformer, both the encoder and decoder stacks are composed entirely of feed-forward networks (MLPs) and multi-head attention modules. Since no RNNs are used, there is no inherent requirement for sequential execution, making non-autoregressive decoding possible. For our proposed NAT, the encoder stays unchanged from the original Transformer network.
+
+# 3.2 DECODER STACK
+
+In order to translate non-autoregressively and parallelize the decoding process, we modify the decoder stack as follows.
+
+Decoder Inputs Before decoding starts, the NAT needs to know how long the target sentence will be in order to generate all words in parallel. More crucially, we cannot use time-shifted target outputs (during training) or previously predicted outputs (during inference) as the inputs to the first decoder layer. Omitting inputs to the first decoder layer entirely, or using only positional embeddings, resulted in very poor performance. Instead, we initialize the decoding process using copied source inputs from the encoder side. As the source and target sentences are often of different lengths, we propose two methods:
+
+• Copy source inputs uniformly: Each decoder input $t$ is a copy of the Round $( T ^ { \prime } t / T )$ -th encoder input. This is equivalent to “scanning” source inputs from left to right with a constant “speed,” and results in a decoding process that is deterministic given a (predicted) target length. • Copy source inputs using fertilities: A more powerful way, depicted in Fig. 2 and discussed in more detail below, is to copy each encoder input as a decoder input zero or more times, with the number of times each input is copied referred to as that input word’s “fertility.” In this case the source inputs are scanned from left to right at a “speed” that varies inversely with the fertility of each input; the decoding process is now conditioned on the sequence of fertilities, while the resulting output length is determined by the sum of all fertility values.
+
+Non-causal self-attention Without the constraint of an autoregressive factorization of the output distribution, we no longer need to prevent earlier decoding steps from accessing information from later steps. Thus we can avoid the causal mask used in the self-attention module of the conventional Transformer’s decoder. Instead, we mask out each query position only from attending to itself, which we found to improve decoder performance relative to unmasked self-attention.
+
+Positional attention We also include an additional positional attention module in each decoder layer, which is a multi-head attention module with the same general attention mechanism used in other parts of the Transformer network, i.e.
+
+$$
+{ \mathrm { A t t e n t i o n } } ( Q , K , V ) = { \mathrm { s o f t m a x } } \left( { \frac { Q K ^ { T } } { \sqrt { d _ { \mathrm { m o d e l } } } } } \right) \cdot V ,
+$$
+
+where $d _ { \mathrm { m o d e l } }$ is the model hidden size, but with the positional encoding1 as both query and key and the decoder states as the value. This incorporates positional information directly into the attention process and provides a stronger positional signal than the embedding layer alone. We also hypothesize that this additional information improves the decoder’s ability to perform local reordering.
+
+# 3.3 MODELING FERTILITY TO TACKLE THE MULTIMODALITY PROBLEM
+
+The multimodality problem can be attacked by introducing a latent variable $z$ to directly model the nondeterminism in the translation process: we first sample $z$ from a prior distribution and then condition on $z$ to non-autoregressively generate a translation.
+
+One way to interpret this latent variable is as a sentence-level “plan” akin to those discussed in the language production literature (Martin et al., 2010). There are several desirable properties for this latent variable:
+
+• It should be simple to infer a value for the latent variable given a particular input-output pair, as this is needed to train the model end-to-end. • Adding $z$ to the conditioning context should account as much as possible for the correlations across time between different outputs, so that the remaining marginal probabilities at each output location are as close as possible to satisfying conditional independence. • It should not account for the variation in output translations so directly that $p ( y | x , z )$ becomes trivial to learn, since that is the function our decoder neural network will approximate.
+
+The factorization by length introduced in Eq. 3 provides a very weak example of a latent variable model, satisfying the first and third property but not the first. We propose the use of fertilities instead. These are integers for each word in the source sentence that correspond to the number of words in the target sentence that can be aligned to that source word using a hard alignment algorithm like IBM Model 2 (Brown et al., 1993).
+
+One of the most important properties of the proposed NAT is that it naturally introduces an informative latent variable when we choose to copy the encoder inputs based on predicted fertilities. More precisely, given a source sentence $X$ , the conditional probability of a target translation $Y$ is:
+
+$$
+p _ { \mathcal N \mathcal M } ( Y | X ; \theta ) = \sum _ { f _ { 1 } , . . . , f _ { T ^ { \prime } } \in \mathcal F } \left( \prod _ { t ^ { \prime } = 1 } ^ { T ^ { \prime } } p _ { F } ( f _ { t ^ { \prime } } | x _ { 1 : T ^ { \prime } } ; \theta ) \cdot \prod _ { t = 1 } ^ { T } p ( y _ { t } | x _ { 1 } \{ f _ { 1 } \} , . . , x _ { T ^ { \prime } } \{ f _ { T ^ { \prime } } \} ; \theta ) \right)
+$$
+
+where value $\begin{array} { r } { \mathcal { F } = \{ f _ { 1 } , . . . , f _ { T ^ { \prime } } | \sum _ { t ^ { \prime } = 1 } ^ { T ^ { \prime } } f _ { t ^ { \prime } } = T , f _ { t ^ { \prime } } \in \mathbb { Z } ^ { * } \} } \end{array}$ is thand of all fertility sequdenotes the token ces—onerepeated ertilitytimes. $Y$ $x \{ f \}$ $x$ $f$
+
+Fertility prediction As shown in Fig. 2, we model the fertility $p _ { F } \big ( f _ { t ^ { \prime } } | x _ { 1 : T ^ { \prime } } \big )$ at each position independently using a one-layer neural network with a softmax classifier $L = 5 0$ in our experiments) on top of the output of the last encoder layer. This models the way that fertility values are a property of each input word but depend on information and context from the entire sentence.
+
+Benefits of fertility Fertilities possess all three of the properties listed earlier as desired of a latent variable for non-autoregressive machine translation:
+
+• An external aligner provides a simple and fast approximate inference model that effectively reduces the unsupervised training problem to two supervised ones.   
+• Using fertilities as a latent variable makes significant progress towards solving the multimodality problem by providing a natural factorization of the output space. Given a source sentence, restricting the output distribution to those target sentences consistent with a particular fertility sequence dramatically reduces the mode space. Furthermore, the global choice of mode is factored into a set of local mode choices: namely, how to translate each input word. These local mode choices can be effectively supervised because the fertilities provide a fixed “scaffold.”   
+Including both fertilities and reordering in the latent variable would provide complete alignment statistics. This would make the decoding function trivially easy to approximate given the latent variable and force all of the modeling complexity into the encoder. Using fertilities alone allows the decoder to take some of this burden off of the encoder.
+
+Our use of fertilities as a latent variable also means that there is no need to have a separate means of explicitly modeling the length of the translation, which is simply the sum of fertilities. And fertilities provide a powerful way to condition the decoding process, allowing the model to generate diverse translations by sampling over the fertility space.
+
+# 3.4 TRANSLATION PREDICTOR AND THE DECODING PROCESS
+
+At inference time, the model can identify the translation with the highest conditional probability (see Eq. 5) by marginalizing over all possible latent fertility sequences. Given a fertility sequence, however, identifying the optimal translation only requires independently maximizing the local probability for each output position. We define $Y \overset { \cdot } { = } G ( x _ { 1 : T ^ { \prime } } , f _ { 1 : T ^ { \prime } } ; \theta )$ to represent the optimal translation given a source sentence and a sequence of fertility values.
+
+But searching and marginalizing over the whole fertility space is still intractable. We propose three heuristic decoding algorithms to reduce the search space of the NAT model:
+
+Argmax decoding Since the fertility sequence is also modeled with a conditionally independent factorization, we can simply estimate the best translation by choosing the highest-probability fertility for each input word:
+
+$$
+\hat { Y } _ { \mathrm { a r g m a x } } = G ( x _ { 1 : T ^ { \prime } } , \hat { f } _ { 1 : T ^ { \prime } } ; \theta ) , \mathrm { w h e r e \ } \hat { f } _ { t ^ { \prime } } = \underset { f } { \operatorname { a r g m a x } } p _ { F } ( f _ { t ^ { \prime } } | x _ { 1 : T ^ { \prime } } ; \theta )
+$$
+
+Average decoding We can also estimate each fertility as the expectation of its corresponding softmax distribution:
+
+$$
+\hat { Y } _ { \mathrm { a v e r a g e } } = G ( x _ { 1 : T ^ { \prime } } , \hat { f } _ { 1 : T ^ { \prime } } ; \theta ) , \mathrm { w h e r e } \hat { f } _ { t ^ { \prime } } = \mathrm { R o u n d } \left( \sum _ { f _ { t ^ { \prime } } = 1 } ^ { L } p _ { F } \big ( f _ { t ^ { \prime } } | x _ { 1 : T ^ { \prime } } ; \theta \big ) f _ { t ^ { \prime } } \right)
+$$
+
+Noisy parallel decoding (NPD) A more accurate approximation of the true optimum of the target distribution, inspired by Cho (2016), is to draw samples from the fertility space and compute the best translation for each fertility sequence. We can then use the autoregressive teacher to identify the best overall translation:
+
+$$
+\hat { Y } _ { \mathrm { N P D } } = G ( x _ { 1 : T ^ { \prime } } , \underset { f _ { t ^ { \prime } } \sim p _ { F } } { \mathrm { a r g m a x } } p _ { \mathcal { A R } } ( G ( x _ { 1 : T ^ { \prime } } , f _ { 1 : T ^ { \prime } } ; \theta ) | X ; \theta ) ; \theta )
+$$
+
+Note that, when using an autoregressive model as a scoring function for a set of decoded translations, it can run as fast as it does at train time because it can be provided with all decoder inputs in parallel.
+
+NPD is a stochastic search method, and it also increases the computational resources required linearly by the sample size. However, because all the search samples can be computed and scored entirely independently, the process only doubles the latency compared to computing a single translation if sufficient parallelism is available.
+
+# 4 TRAINING
+
+The proposed NAT contains a discrete sequential latent variable $f _ { 1 : T ^ { \prime } }$ , whose conditional posterior distribution $p ( f _ { 1 : T ^ { \prime } } | x _ { 1 : T ^ { \prime } } , y _ { 1 : T } ; \theta )$ we can approximate using a proposal distribution $q ( f _ { 1 : T ^ { \prime } } | x _ { 1 : T ^ { \prime } } , y _ { 1 : T } )$ . This provides a variational bound for the overall maximum likelihood loss:
+
+$$
+\begin{array} { r l } & { \mathcal { L } _ { \mathrm { M L } } = \log p _ { \mathcal { N A } } ( Y | X ; \theta ) = \log \displaystyle \sum _ { f _ { 1 : T ^ { \prime } } \in \mathcal { F } } p _ { F } ( f _ { 1 : T ^ { \prime } } | x _ { 1 : T ^ { \prime } } ; \theta ) \cdot p ( y _ { 1 : T } | x _ { 1 : T ^ { \prime } } , f _ { 1 : T ^ { \prime } } ; \theta ) } \\ & { \geq \displaystyle \sum _ { f _ { 1 : T ^ { \prime } \sim \mathcal { I } } } \left( \underbrace { T } _ { \mathrm { t - 1 } } \log p ( y _ { t } | x _ { 1 } \{ f _ { 1 } \} , . . . , x _ { T ^ { \prime } } \{ f _ { T ^ { \prime } } \} ; \theta ) \right)} _ { \mathrm { T r a n s l a t i o n ~ L o s s } } + \underbrace { \sum _ { t ^ { \prime } = 1 } ^ { T ^ { \prime } } \log p _ { F } ( f _ { t ^ { \prime } } | x _ { 1 : T ^ { \prime } } ; \theta ) } _ { \mathrm { F e r t i l i t y ~ L o s s } }  + \mathcal { H } ( q )  \end{array}
+$$
+
+We choose a proposal distribution $q$ defined by a separate, fixed fertility model. Possible options include the output of an external aligner, which produces a deterministic sequence of integer fertilities for each (source, target) pair in a training corpus, or fertilities computed from the attention weights used in our fixed autoregressive teacher model. This simplifies the inference process considerably, as the expectation over $q$ is deterministic.
+
+The resulting loss function, consisting of the two bracketed terms in Eq. 9, allows us to train the entire model in a supervised fashion, using the inferred fertilities to simultaneously train the translation model $p$ and supervise the fertility neural network model $p _ { F }$ .
+
+# 4.1 SEQUENCE-LEVEL KNOWLEDGE DISTILLATION
+
+While the latent fertility model substantially improves the ability of the non-autoregressive output distribution to approximate the multimodal target distribution, it does not completely solve the problem of nondeterminism in the training data. In many cases, there are multiple correct translations consistent with a single sequence of fertilities—for instance, both “Danke schon.” and “Vielen ¨ dank.” are consistent with the English input “Thank you.” and the fertility sequence [2, 0, 1], because “you” is not directly translated in either German sentence.
+
+Thus we additionally apply sequence-level knowledge distillation (Kim & Rush, 2016) to construct a new corpus by training an autoregressive machine translation model, known as the teacher, on an existing training corpus, then using that model’s greedy outputs as the targets for training the nonautoregressive student. The resulting targets are less noisy and more deterministic, as the trained model will consistently translate a sentence like “Thank you.” into the same German translation every time; on the other hand, they are also lower in quality than the original dataset.
+
+# 4.2 FINE-TUNING
+
+Our supervised fertility model enables a decomposition of the overall maximum likelihood loss into translation and fertility terms, but it has some drawbacks compared to variational training. In particular, it heavily relies on the deterministic, approximate inference model provided by the external alignment system, while it would be desirable to train the entire model, including the fertility predictor, end to end.
+
+Thus we propose a fine-tuning step after training the NAT to convergence. We introduce an additional loss term consisting of the reverse K-L divergence with the teacher output distribution, a form of word-level knowledge distillation:
+
+$$
+\mathcal { L } _ { \mathrm { R K L } } \left( f _ { 1 : T ^ { \prime } } ; \theta \right) = \sum _ { t = 1 } ^ { T } \sum _ { y _ { t } } \left[ \log p _ { \mathcal { A R } } \left( y _ { t } | \hat { y } _ { 1 : t - 1 } , x _ { 1 : T ^ { \prime } } \right) \cdot p _ { \mathcal { N A } } \left( y _ { t } | x _ { 1 : T ^ { \prime } } , f _ { 1 : T ^ { \prime } } ; \theta \right) \right] ,
+$$
+
+where $\hat { y } _ { 1 : T } = G ( x _ { 1 : T ^ { \prime } } , f _ { 1 : T ^ { \prime } } ; \theta )$ . Such a loss is more favorable towards highly peaked student output distributions than a standard cross-entropy error would be.
+
+Then we train the whole model jointly with a weighted sum of the original distillation loss and two such terms, one an expectation over the predicted fertility distribution, normalized with a baseline, and the other based on the external fertility inference model:
+
+$$
+\mathcal { L } _ { \mathrm { F T } } = \lambda \left( \underbrace { \mathbb { E } } _ { \int _ { \mathrm { I : T : } } r \sim p _ { F } } \left( \mathcal { L } _ { \mathrm { R K L } } \left( f _ { 1 : T ^ { \prime } } \right) - \mathcal { L } _ { \mathrm { R K L } } \left( \bar { f } _ { 1 : T ^ { \prime } } \right) \right) + \underbrace { \mathbb { E } } _ { f _ { 1 : T ^ { \prime } \sim q } } \left( \mathcal { L } _ { \mathrm { R K L } } \left( f _ { 1 : T ^ { \prime } } \right) \right)  _ { \mathcal { L } _ { \mathrm { R P } } } \right) + ( 1 - \lambda ) \mathcal { L } _ { \mathrm { K D } } ,
+$$
+
+where ${ \bar { f } } _ { 1 : T ^ { \prime } }$ is the average fertility computed by Eq. 7. The gradient with respect to the nondifferentiable ${ \mathcal { L } } _ { \mathrm { R L } }$ term can be estimated with REINFORCE (Williams, 1992), while the $\mathcal { L } _ { \mathrm { B P } }$ term can be trained using ordinary backpropagation.
+
+# 5 EXPERIMENTS
+
+# 5.1 EXPERIMENTAL SETTINGS
+
+Dataset We evaluate the proposed NAT on three widely used public machine translation corpora: IWSLT16 En–De2, WMT14 En–De,3 and WMT16 En–Ro4. We use IWSLT—which is smaller than the other two datasets—as the development dataset for ablation experiments, and additionally train and test our primary models on both directions of both WMT datasets. All the data are tokenized and segmented into subword symbols using byte-pair encoding (BPE) (Sennrich et al., 2015) to restrict the size of the vocabulary. For both WMT datasets, we use shared BPE vocabulary and additionally share encoder and decoder word embeddings; for IWSLT, we use separate English and German vocabulary and embeddings.
+
+Teacher Sequence-level knowledge distillation is applied to alleviate multimodality in the training dataset, using autoregressive models as the teachers. The same teacher model used for distillation is also used as a scoring function for fine-tuning and noisy parallel decoding.
+
+To enable a fair comparison, and benefit from its high translation quality, we implemented the autoregressive teachers using the state-of-the-art Transformer architecture. In addition, we use the same sizes and hyperparameters for each student and its respective teacher, with the exception of the newly added positional self-attention and fertility prediction modules.
+
+<table><tr><td rowspan="2">Models</td><td colspan="2">WMT14</td><td colspan="2">WMT16</td><td colspan="2">IWSLT16</td><td></td></tr><tr><td>En→De</td><td>De→En</td><td>En→Ro</td><td>Ro→En</td><td>En→De</td><td>Latency / Speedup</td><td></td></tr><tr><td>NAT</td><td>17.35</td><td>20.62</td><td>26.22</td><td>27.83</td><td>25.20</td><td>39 ms</td><td>15.6×</td></tr><tr><td>NAT (+FT)</td><td>17.69</td><td>21.47</td><td>27.29</td><td>29.06</td><td>26.52</td><td>39 ms</td><td>15.6×</td></tr><tr><td>NAT (+FT + NPD s = 10)</td><td>18.66</td><td>22.41</td><td>29.02</td><td>30.76</td><td>27.44</td><td>79 ms</td><td>7.68×</td></tr><tr><td>NAT (+FT + NPD s = 100)</td><td>19.17</td><td>23.20</td><td>29.79</td><td>31.44</td><td>28.16</td><td>257 ms</td><td>2.36×</td></tr><tr><td>Autoregressive (b = 1)</td><td>22.71</td><td>26.39</td><td>31.35</td><td>31.03</td><td>28.89</td><td>408 ms</td><td>1.49×</td></tr><tr><td>Autoregressive (b = 4)</td><td>23.45</td><td>27.02</td><td>31.91</td><td>31.76</td><td>29.70</td><td>607ms</td><td>1.00×</td></tr></table>
+
+Table 1: BLEU scores on official test sets (newstest2014 for WMT En-De and newstest2016 for WMT En-Ro) or the development set for IWSLT. NAT models without NPD use argmax decoding. Latency is computed as the time to decode a single sentence without minibatching, averaged over the whole test set; decoding is implemented in PyTorch on a single NVIDIA Tesla P100.
+
+Preparation for knowledge distillation We first train all teacher models using maximum likelihood, then freeze their parameters. To avoid the redundancy of running fixed teacher models repeatedly on the same data, we decode the entire training set once using each teacher to create a new training dataset for its respective student.
+
+Encoder initialization We find it helpful to initialize the weights in the NAT student’s encoder with the encoder weights from its teacher, as the autoregressive and non-autoregressive models share the same encoder input and architecture.
+
+Fertility supervision during training As described above, we supervise the fertility predictions at train time by using a fixed aligner as a fertility inference function. We use the fast align5 implementation of IBM Model 2 for this purpose, with default parameters (Dyer et al., 2013).
+
+![](images/ff2cfd4d2f25ef6e98d968d65066c8e02ea0f947a91d09952aa8c8ffbab3302a.jpg)  
+Figure 3: BLEU scores on IWSLT development set as a function of sample size for noisy parallel decoding. NPD matches the performance of the other two decoding strategies after two samples, and exceeds the performance of the autoregressive teacher with around 1000.
+
+Hyperparameters For experiments on WMT datasets, we use the hyperparameter settings of the base Transformer model described in Vaswani et al. (2017), though without label smoothing. As IWSLT is a smaller corpus, and to reduce training time, we use a set of smaller hyperparameters $( d _ { \mathrm { m o d e l } } = 2 8 7 , d _ { \mathrm { h i d d e n } } = 5 0 7 , n _ { \mathrm { l a y e r } } = 5 , n _ { \mathrm { h e a d } } = \mathrm { \Omega } ^ { \ast }$ , and $t _ { \mathrm { w a r m u p } } = 7 4 6 )$ for all experiments on that dataset. For fine-tuning we use $\lambda = 0 . 2 5$ .
+
+Evaluation metrics We evaluate using tokenized and cased BLEU scores (Papineni et al., 2002).
+
+Implementation We have open-sourced our PyTorch implementation of the $\mathrm { N A T ^ { 6 } }$ .
+
+# 5.2 RESULTS
+
+Across the three datasets we used, the NAT performs between 2-5 BLEU points worse than its autoregressive teacher, with part or all of this gap addressed by the use of noisy parallel decoding. In the case of WMT16 English–Romanian, NPD improves the performance of our non-autoregressive model to within 0.2 BLEU points of the previous overall state of the art (Gehring et al., 2017).
+
+Comparing latencies on the development model shows a speedup of more than a factor of 10 over greedy autoregressive decoding, or a factor of 15 over beam search. Latencies for decoding with NPD, regardless of sample size, could be reduced to about $8 0 \mathrm { m s }$ by parallelizing across multiple GPUs because each sample can be generated, then scored, independently from the others.
+
+# 5.3 ABLATION STUDY
+
+We also conduct an extensive ablation study with the proposed NAT on the IWSLT dataset. First, we note that the model fails to train when provided with only positional embeddings as input to the decoder. Second, we see that training on the distillation corpus rather than the ground truth provides a fairly consistent improvement of around 5 BLEU points. Third, switching from uniform copying of source inputs to fertility-based copying improves performance by four BLEU points when using ground-truth training or two when using distillation.
+
+<table><tr><td>Distillation b=1 b=4</td><td>Decoder Inputs +uniform</td><td>+fertility</td><td>+PosAtt</td><td>Fine-tuning +LKD +LBP</td><td>BLEU +CRL</td><td>BLEU (T)</td></tr><tr><td></td><td></td><td></td><td></td><td></td><td>~2</td><td></td></tr><tr><td></td><td>√</td><td></td><td></td><td></td><td>16.51</td><td></td></tr><tr><td></td><td></td><td></td><td>√</td><td></td><td>18.87</td><td></td></tr><tr><td>√</td><td>√</td><td></td><td>√</td><td></td><td>20.72</td><td></td></tr><tr><td></td><td>√</td><td></td><td>√</td><td></td><td>21.12</td><td></td></tr><tr><td>&lt;</td><td></td><td></td><td>√</td><td></td><td>24.02</td><td>43.91</td></tr><tr><td></td><td></td><td></td><td>√</td><td></td><td>25.20</td><td>45.41</td></tr><tr><td></td><td>√</td><td></td><td></td><td>√</td><td>22.44 厂</td><td></td></tr><tr><td>兴 √</td><td></td><td>√</td><td></td><td></td><td>×</td><td>×</td></tr><tr><td></td><td></td><td>√</td><td></td><td>√</td><td>×</td><td>×</td></tr><tr><td>√</td><td></td><td>√</td><td>√</td><td>√</td><td>25.76</td><td>46.11</td></tr><tr><td>√</td><td></td><td>√</td><td>√</td><td>√</td><td>26.52</td><td>47.38</td></tr></table>
+
+Table 2: Ablation performance on the IWSLT development set. BLEU (T) refers to the BLEU score on a version of the development set that has been translated by the teacher model. An $\times$ indicates that fine-tuning caused that model to get worse. When uniform copying is used as the decoder inputs, the ground-truth target lengths are provided. All models use argmax decoding.
+
+Fine-tuning does not converge with reinforcement learning alone, or with the $\mathcal { L } _ { \mathrm { B P } }$ term alone, but use of all three fine-tuning terms together leads to an improvement of around 1.5 BLEU points. Training the student model from a distillation corpus produced using beam search is similar to training from the greedily-distilled corpus.
+
+Figure 4: Two examples comparing translations produced by an autoregressive (AR) and nonautoregressive Transformer as well as the result of noisy parallel decoding with sample size 100. Repeated words are highlighted in gray.   
+
+<table><tr><td>Source:</td><td>politicians try to pick wordsand use words to shape realityand control reality,butin fact,reality changes words</td></tr><tr><td></td><td>far more than words can ever change reality.</td></tr><tr><td rowspan="3">Target: AR:</td><td>Politiker versuchen Worte zu benutzen,um die Realitat zu formen und die Realitat zu kontrolieren,aber</td></tr><tr><td>tatsächlich verandert die Realitat Worte viel mehr,als Worte die Realitat jemals verändern konnten.</td></tr><tr><td>Politikerversuchen Worter zu wahlen und Worter zur Realitat zu gestalten und Realitätzu steuern,aber in</td></tr><tr><td rowspan="2">NAT:</td><td>Wirklichkeit verändert sich die Realitat viel mehrals Worte,die die Realität verändern konnen.</td></tr><tr><td>Politikerversuchen,Worter wahlen und zu verwenden,um Realitatzu formen und Realitatzu formen,aber</td></tr><tr><td rowspan="2">NAT+NPD:</td><td>tatsächlich ändert Realitat Realitat viel mehrals Wortedie Realität Realitat verändern.</td></tr><tr><td>Politikerversuchen,Worter wahlenund zu verwenden,um Realitat Realitat formenund die Realitatzu formen， aber tatsächlich ändert die Realität Worte viel mehrals Worte jemals die Realität verändern konnen.</td></tr><tr><td>Source:</td><td>Isee wheelchairs bought and sold like used cars.</td></tr><tr><td>Target:</td><td>ich erlebe,dass Rollstuhle gekauft und verkauft werden wie Gebrauchtwagen</td></tr><tr><td>AR: NAT:</td><td>ich sehe Rollstuhlen,die wie Autos verkauft und verkauft werden.</td></tr><tr><td>NAT+NPD:</td><td>ich sehe,dass Stuhle Stuhle und verkauftwie Autos verkauft.</td></tr><tr><td></td><td>ich sehe Rollühle kauften und verkaufte wie Autos.</td></tr></table>
+
+We include two examples of translations from the IWSLT development set in Fig. 4. Instances of repeated words or phrases, highlighted in gray, are most prevalent in the non-autoregressive output for the relatively complex first example sentence. Two pairs of repeated words in the first example, as
+
+se lucreaza la soluti de genul acesta .
+
+se la solutii de genul acesta .   
+se lucreaza la solutii de acesta .   
+se lucreaza solutii de genul acesta .   
+se se lucreaza la solutii de acesta .   
+se lucreaza lucreaza la solutii de acesta .   
+se se lucreaza lucreaza la solutii de acesta .   
+se se lucreaza lucreaza la solutii de de acesta .   
+se se lucreaza lucreaza la solutii de genul acesta . solutions on this kind are done.   
+work done on solutions like this .   
+solutions on this kind is done .   
+work is done on solutions like this .   
+work is done on solutions like this .   
+work is being done on solutions like this .   
+work is being done on solutions such as this.   
+work is being done on solutions such this kind .
+
+Figure 5: A Romanian–English example translated with noisy parallel decoding. At left are eight sampled fertility sequences from the encoder, represented with their corresponding decoder input sequences. Each of these values for the latent variable leads to a different possible output translation, shown at right. The autoregressive Transformer then picks the best translation, shown in red, a process which is much faster than directly using it to generate output.
+
+well as a pair in the second, are not present in the versions with noisy parallel decoding, suggesting that NPD scoring using the teacher model can filter out such mistakes. The translations produced by the NAT with NPD, while of a similar quality to those produced by the autoregressive model, are also noticeably more literal.
+
+We also show an example of the noisy parallel decoding process in Fig. 5, demonstrating the diversity of translations that can be found by sampling from the fertility space.
+
+# 6 CONCLUSION
+
+We introduce a latent variable model for non-autoregressive machine translation that enables a decoder based on Vaswani et al. (2017) to take full advantage of its exceptional degree of internal parallelism even at inference time. As a result, we measure translation latencies of one-tenth that of an equal-sized autoregressive model, while maintaining competitive BLEU scores.
+
+# REFERENCES
+
+Dzmitry Bahdanau, Kyunghyun Cho, and Yoshua Bengio. Neural machine translation by jointly learning to align and translate. In ICLR, 2015.
+
+Peter Brown, Vincent della Pietra, Stephen della Pietra, and Robert Mercer. The mathematics of statistical machine translation: Parameter estimation. Computational Linguistics, 19(2):263–311, 1993.
+
+Kyunghyun Cho. Noisy parallel approximate decoding for conditional recurrent language model. arXiv preprint arXiv:1605.03835, 2016.
+
+Chris Dyer, Victor Chahuneau, and Noah Smith. A simple, fast, and effective reparameterization of IBM Model 2. In NAACL, 2013.
+
+Jonas Gehring, Michael Auli, David Grangier, Denis Yarats, and Yann Dauphin. Convolutional sequence to sequence learning. arXiv preprint arXiv:1705.03122, 2017.
+
+Łukasz Kaiser, Aidan Gomez, and Franc¸ois Chollet. Depthwise separable convolutions for neural machine translation. arXiv preprint arXiv:1706.03059, 2017.
+
+Nal Kalchbrenner, Lasse Espeholt, Karen Simonyan, Aaron van den Oord, Alex Graves, and Koray Kavukc¸uoglu. Neural machine translation in linear time. ˇ arXiv preprint arXiv:1610.10099, 2016.
+
+Yoon Kim and Alexander Rush. Sequence-level knowledge distillation. In EMNLP, 2016.
+
+Philipp Koehn and Rebecca Knowles. Six challenges for neural machine translation. arXiv preprint arXiv:1706.03872, 2017.
+
+Minh-Thang Luong, Hieu Pham, and Christopher D Manning. Effective approaches to attentionbased neural machine translation. In EMNLP, 2015.
+
+Randi Martin, Jason Crowther, Meredith Knight, Franklin Tamborello, and Chin-Lung Yang. Planning in sentence production: Evidence for the phrase as a default planning scope. Cognition, 116 (2):177–192, 2010.
+
+Kishore Papineni, Salim Roukos, Todd Ward, and Wei-Jing Zhu. BLEU: A method for automatic evaluation of machine translation. In ACL, pp. 311–318, 2002.
+
+Rico Sennrich, Barry Haddow, and Alexandra Birch. Neural machine translation of rare words with subword units. arXiv preprint arXiv:1508.07909, 2015.
+
+Ilya Sutskever, Oriol Vinyals, and Quoc L ˆ e. Sequence to sequence learning with neural networks. ˆ In NIPS, 2014.
+
+Ashish Vaswani, Noam Shazeer, Niki Parmar, Jakob Uszkoreit, Llion Jones, Aidan Gomez, Łukasz Kaiser, and Illia Polosukhin. Attention is all you need. arXiv preprint arXiv:1706.03762, 2017.
+
+Ronald Williams. Simple statistical gradient-following algorithms for connectionist reinforcement learning. Machine Learning, 8(3-4):229–256, 1992.
+
+Y. Wu, M. Schuster, Z. Chen, Q. V. Le, M. Norouzi, W. Macherey, M. Krikun, Y. Cao, Q. Gao, K. Macherey, J. Klingner, A. Shah, M. Johnson, X. Liu, Ł. Kaiser, S. Gouws, Y. Kato, T. Kudo, H. Kazawa, K. Stevens, G. Kurian, N. Patil, W. Wang, C. Young, J. Smith, J. Riesa, A. Rudnick, O. Vinyals, G. Corrado, M. Hughes, and J. Dean. Google’s neural machine translation system: Bridging the gap between human and machine translation. arXiv preprint arXiv:1609.08144, 2016.
+
+![](images/8397d58044f6d9c8a19dcbb03ac376664021ffaa63d7eac01c5e0d5c288a1df7.jpg)  
+Figure 6: The schematic structure of training and inference for the NAT. The “distilled data” contains target sentences decoded by the autoregressive model and ground-truth source sentences.
+
+![](images/65e35fd7ac2e233ef8cdae03751ebce2756e57bc1378b23f1a59c83c62823be8.jpg)  
+Figure 7: The translation latency, computed as the time to decode a single sentence without minibatching, for each sentence in the IWSLT development set as a function of its length. The autoregressive model has latency linear in the decoding length, while the latency of the NAT is nearly constant for typical lengths, even with NPD with sample size 10. When using NPD with sample size 100, the level of parallelism is enough to more than saturate the GPU, leading again to linear latencies.
+
+![](images/19326d4ac73a662073b026f5ada8aa0be903a2801d0ffdb32756ff0c9f97cdcc.jpg)  
+Figure 8: Learning curves for training and fine-tuning of the NAT on IWSLT. BLEU scores are on the development set.

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+        "type": "text",
+        "text": "NON-AUTOREGRESSIVE NEURAL MACHINE TRANSLATION ",
+        "text_level": 1,
+        "bbox": [
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+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "Jiatao $\\mathbf { G u } ^ { \\dagger }$ ∗, James Bradbury‡, Caiming Xiong‡, Victor O.K. Li†& Richard Socher‡ ",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "‡Salesforce Research   \n{james.bradbury,cxiong,rsocher}@salesforce.com   \n†The University of Hong Kong   \n{jiataogu, vli}@eee.hku.hk ",
+        "bbox": [
+            184,
+            186,
+            633,
+            242
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "ABSTRACT ",
+        "text_level": 1,
+        "bbox": [
+            454,
+            279,
+            544,
+            294
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "Existing approaches to neural machine translation condition each output word on previously generated outputs. We introduce a model that avoids this autoregressive property and produces its outputs in parallel, allowing an order of magnitude lower latency during inference. Through knowledge distillation, the use of input token fertilities as a latent variable, and policy gradient fine-tuning, we achieve this at a cost of as little as 2.0 BLEU points relative to the autoregressive Transformer network used as a teacher. We demonstrate substantial cumulative improvements associated with each of the three aspects of our training strategy, and validate our approach on IWSLT 2016 English–German and two WMT language pairs. By sampling fertilities in parallel at inference time, our non-autoregressive model achieves near-state-of-the-art performance of 29.8 BLEU on WMT 2016 English– Romanian. ",
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+    {
+        "type": "text",
+        "text": "1 INTRODUCTION ",
+        "text_level": 1,
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+            336,
+            522
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "Neural network based models outperform traditional statistical models for machine translation (MT) (Bahdanau et al., 2015; Luong et al., 2015). However, state-of-the-art neural models are much slower than statistical MT approaches at inference time (Wu et al., 2016). Both model families use autoregressive decoders that operate one step at a time: they generate each token conditioned on the sequence of tokens previously generated. This process is not parallelizable, and, in the case of neural MT models, it is particularly slow because a computationally intensive neural network is used to generate each token. ",
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+    {
+        "type": "text",
+        "text": "While several recently proposed models avoid recurrence at train time by leveraging convolutions (Kalchbrenner et al., 2016; Gehring et al., 2017; Kaiser et al., 2017) or self-attention (Vaswani et al., 2017) as more-parallelizable alternatives to recurrent neural networks (RNNs), use of autoregressive decoding makes it impossible to take full advantage of parallelism during inference. ",
+        "bbox": [
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+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "We introduce a non-autoregressive translation model based on the Transformer network (Vaswani et al., 2017). We modify the encoder of the original Transformer network by adding a module that predicts fertilities, sequences of numbers that form an important component of many traditional machine translation models (Brown et al., 1993). These fertilities are supervised during training and provide the decoder at inference time with a globally consistent plan on which to condition its simultaneously computed outputs. ",
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+        "type": "text",
+        "text": "2 BACKGROUND ",
+        "text_level": 1,
+        "bbox": [
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+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "2.1 AUTOREGRESSIVE NEURAL MACHINE TRANSLATION ",
+        "text_level": 1,
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "Given a source sentence $X = \\{ x _ { 1 } , . . . , x _ { T ^ { \\prime } } \\}$ , a neural machine translation model factors the distribution over possible output sentences $Y = \\{ y _ { 1 } , . . . , y _ { T } \\}$ into a chain of conditional probabilities with a ",
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+    {
+        "type": "text",
+        "text": "left-to-right causal structure: ",
+        "bbox": [
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+    {
+        "type": "equation",
+        "img_path": "images/633a748a4002cb496ac4d94d9bde49381f4173fa71b235023f3e7a76c5656215.jpg",
+        "text": "$$\np _ { \\mathcal { A } \\mathcal { R } } ( \\boldsymbol { Y } | \\boldsymbol { X } ; \\theta ) = \\prod _ { t = 1 } ^ { T + 1 } p ( y _ { t } | y _ { 0 : t - 1 } , x _ { 1 : T ^ { \\prime } } ; \\theta ) ,\n$$",
+        "text_format": "latex",
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+        "type": "text",
+        "text": "where the special tokens $y _ { 0 }$ (e.g. $\\left. \\mathrm { b o s } \\right.$ ) and $y _ { T + 1 }$ (e.g. $\\langle \\cos \\rangle$ ) are used to represent the beginning and end of all target sentences. These conditional probabilities are parameterized using a neural network. Typically, an encoder-decoder architecture (Sutskever et al., 2014) with a unidirectional RNN-based decoder is used to capture the causal structure of the output distribution. ",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "Maximum Likelihood training Choosing to factorize the machine translation output distribution autoregressively enables straightforward maximum likelihood training with a cross-entropy loss applied at each decoding step: ",
+        "bbox": [
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+        "text": "$$\n\\mathcal { L } _ { \\mathrm { M L } } = \\log p _ { \\mathcal { A R } } ( Y | X ; \\theta ) = \\sum _ { t = 1 } ^ { T + 1 } \\log p ( y _ { t } | y _ { 0 : t - 1 } , x _ { 1 : T ^ { \\prime } } ; \\theta ) .\n$$",
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+        "type": "text",
+        "text": "This loss provides direct supervision for each conditional probability prediction. ",
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+    },
+    {
+        "type": "text",
+        "text": "Autoregressive NMT without RNNs Since the entire target translation is known at training time, the calculation of later conditional probabilities (and their corresponding losses) does not depend on the output words chosen during earlier decoding steps. Even though decoding must remain entirely sequential during inference, models can take advantage of this parallelism during training. One such approach replaces recurrent layers in the decoder with masked convolution layers (Kalchbrenner et al., 2016; Gehring et al., 2017) that provide the causal structure required by the autoregressive factorization. ",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "A recently introduced option which reduces sequential computation still further is to construct the decoder layers out of self-attention computations that have been causally masked in an analogous way. The state-of-the-art Transformer network takes this approach, which allows information to flow in the decoder across arbitrarily long distances in a constant number of operations, asymptotically fewer than required by convolutional architectures (Vaswani et al., 2017). ",
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+    {
+        "type": "text",
+        "text": "2.2 NON-AUTOREGRESSIVE DECODING ",
+        "text_level": 1,
+        "bbox": [
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+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "Pros and cons of autoregressive decoding The autoregressive factorization used by conventional NMT models has several benefits. It corresponds to the word-by-word nature of human language production and effectively captures the distribution of real translations. Autoregressive models achieve state-of-the-art performance on large-scale corpora and are easy to train, while beam search provides an effective local search method for finding approximately-optimal output translations. ",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "But there are also drawbacks. As the individual steps of the decoder must be run sequentially rather than in parallel, autoregressive decoding prevents architectures like the Transformer from fully realizing their train-time performance advantage during inference. Meanwhile, beam search suffers from diminishing returns with respect to beam size (Koehn & Knowles, 2017) and exhibits limited search parallelism because it introduces computational dependence between beams. ",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "Towards non-autoregressive decoding A na¨ıve solution is to remove the autoregressive connection directly from an existing encoder-decoder model. Assuming that the target sequence length $T$ can be modeled with a separate conditional distribution $p _ { L }$ , this becomes ",
+        "bbox": [
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+    {
+        "type": "image",
+        "img_path": "images/fb73e32da81d3465f857ae37043ab008349971a74c732394fc409a62ee78d60d.jpg",
+        "image_caption": [
+            "Figure 1: Translating “A B C” to $^ { 6 6 } \\mathrm { X }$ Y” using autoregressive and non-autoregressive neural MT architectures. The latter generates all output tokens in parallel. "
+        ],
+        "image_footnote": [],
+        "bbox": [
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+        "page_idx": 1
+    },
+    {
+        "type": "equation",
+        "img_path": "images/d97e3003546373ed25378b0bc946fe1615293facf85f3967deae841210d37fb1.jpg",
+        "text": "$$\np _ { \\mathcal N A } ( Y | X ; \\theta ) = p _ { L } ( T | x _ { 1 : T ^ { \\prime } } ; \\theta ) \\cdot \\prod _ { t = 1 } ^ { T } p ( y _ { t } | x _ { 1 : T ^ { \\prime } } ; \\theta ) .\n$$",
+        "text_format": "latex",
+        "bbox": [
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+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "This model still has an explicit likelihood function, and it can still be trained using independent cross-entropy losses on each output distribution. Now, however, these distributions can be computed in parallel at inference time. ",
+        "bbox": [
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+        "page_idx": 1
+    },
+    {
+        "type": "image",
+        "img_path": "images/899dc15129b43e72de49a617f813130a25104e3d34171cb067e8d5c905671e3e.jpg",
+        "image_caption": [
+            "Figure 2: The architecture of the NAT, where the black solid arrows represent differentiable connections and the purple dashed arrows are non-differentiable operations. Each sublayer inside the encoder and decoder stacks also includes layer normalization and a residual connection. "
+        ],
+        "image_footnote": [],
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "2.3 THE MULTIMODALITY PROBLEM ",
+        "text_level": 1,
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "However, this na¨ıve approach does not yield good results, because such a model exhibits complete conditional independence. Each token’s distribution $p ( y _ { t } )$ depends only on the source sentence $X$ . This makes it a poor approximation to the true target distribution, which exhibits strong correlation across time. Intuitively, such a decoder is akin to a panel of human translators each asked to provide a single word of a translation independently of the words their colleagues choose. ",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "In particular, consider an English source sentence like “Thank you.” This can be accurately translated into German as any one of “Danke.”, “Danke schon.”, or “Vielen Dank.”, all of which may ¨ occur in a given training corpus. This target distribution cannot be represented as a product of independent probability distributions for each of the first, second, and third words, because a conditionally independent distribution cannot allow “Danke schon.” and “Vielen Dank.” without also ¨ licensing “Danke Dank.” and “Vielen schon.”¨ ",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "The conditional independence assumption prevents a model from properly capturing the highly multimodal distribution of target translations. We call this the “multimodality problem” and introduce both a modified model and new training techniques to tackle this issue. ",
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+    {
+        "type": "text",
+        "text": "3 THE NON-AUTOREGRESSIVE TRANSFORMER (NAT) ",
+        "text_level": 1,
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+    {
+        "type": "text",
+        "text": "We introduce a novel NMT model—the Non-Autoregressive Transformer (NAT)—that can produce an entire output translation in parallel. As shown in Fig. 2, the model is composed of the following four modules: an encoder stack, a decoder stack, a newly added fertility predictor (details in 3.3), and a translation predictor for token decoding. ",
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+    {
+        "type": "text",
+        "text": "3.1 ENCODER STACK ",
+        "text_level": 1,
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "Similar to the autoregressive Transformer, both the encoder and decoder stacks are composed entirely of feed-forward networks (MLPs) and multi-head attention modules. Since no RNNs are used, there is no inherent requirement for sequential execution, making non-autoregressive decoding possible. For our proposed NAT, the encoder stays unchanged from the original Transformer network. ",
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+    {
+        "type": "text",
+        "text": "3.2 DECODER STACK ",
+        "text_level": 1,
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "In order to translate non-autoregressively and parallelize the decoding process, we modify the decoder stack as follows. ",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "Decoder Inputs Before decoding starts, the NAT needs to know how long the target sentence will be in order to generate all words in parallel. More crucially, we cannot use time-shifted target outputs (during training) or previously predicted outputs (during inference) as the inputs to the first decoder layer. Omitting inputs to the first decoder layer entirely, or using only positional embeddings, resulted in very poor performance. Instead, we initialize the decoding process using copied source inputs from the encoder side. As the source and target sentences are often of different lengths, we propose two methods: ",
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "• Copy source inputs uniformly: Each decoder input $t$ is a copy of the Round $( T ^ { \\prime } t / T )$ -th encoder input. This is equivalent to “scanning” source inputs from left to right with a constant “speed,” and results in a decoding process that is deterministic given a (predicted) target length. • Copy source inputs using fertilities: A more powerful way, depicted in Fig. 2 and discussed in more detail below, is to copy each encoder input as a decoder input zero or more times, with the number of times each input is copied referred to as that input word’s “fertility.” In this case the source inputs are scanned from left to right at a “speed” that varies inversely with the fertility of each input; the decoding process is now conditioned on the sequence of fertilities, while the resulting output length is determined by the sum of all fertility values. ",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "Non-causal self-attention Without the constraint of an autoregressive factorization of the output distribution, we no longer need to prevent earlier decoding steps from accessing information from later steps. Thus we can avoid the causal mask used in the self-attention module of the conventional Transformer’s decoder. Instead, we mask out each query position only from attending to itself, which we found to improve decoder performance relative to unmasked self-attention. ",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "Positional attention We also include an additional positional attention module in each decoder layer, which is a multi-head attention module with the same general attention mechanism used in other parts of the Transformer network, i.e. ",
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "equation",
+        "img_path": "images/7591f42425b5f5d9a239ca6fc7711621177920ae7db10daccd0a298639ff6dee.jpg",
+        "text": "$$\n{ \\mathrm { A t t e n t i o n } } ( Q , K , V ) = { \\mathrm { s o f t m a x } } \\left( { \\frac { Q K ^ { T } } { \\sqrt { d _ { \\mathrm { m o d e l } } } } } \\right) \\cdot V ,\n$$",
+        "text_format": "latex",
+        "bbox": [
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "where $d _ { \\mathrm { m o d e l } }$ is the model hidden size, but with the positional encoding1 as both query and key and the decoder states as the value. This incorporates positional information directly into the attention process and provides a stronger positional signal than the embedding layer alone. We also hypothesize that this additional information improves the decoder’s ability to perform local reordering. ",
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "3.3 MODELING FERTILITY TO TACKLE THE MULTIMODALITY PROBLEM ",
+        "text_level": 1,
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "The multimodality problem can be attacked by introducing a latent variable $z$ to directly model the nondeterminism in the translation process: we first sample $z$ from a prior distribution and then condition on $z$ to non-autoregressively generate a translation. ",
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "One way to interpret this latent variable is as a sentence-level “plan” akin to those discussed in the language production literature (Martin et al., 2010). There are several desirable properties for this latent variable: ",
+        "bbox": [
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+        "page_idx": 3
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+    {
+        "type": "text",
+        "text": "• It should be simple to infer a value for the latent variable given a particular input-output pair, as this is needed to train the model end-to-end. • Adding $z$ to the conditioning context should account as much as possible for the correlations across time between different outputs, so that the remaining marginal probabilities at each output location are as close as possible to satisfying conditional independence. • It should not account for the variation in output translations so directly that $p ( y | x , z )$ becomes trivial to learn, since that is the function our decoder neural network will approximate. ",
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "The factorization by length introduced in Eq. 3 provides a very weak example of a latent variable model, satisfying the first and third property but not the first. We propose the use of fertilities instead. These are integers for each word in the source sentence that correspond to the number of words in the target sentence that can be aligned to that source word using a hard alignment algorithm like IBM Model 2 (Brown et al., 1993). ",
+        "bbox": [
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+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "One of the most important properties of the proposed NAT is that it naturally introduces an informative latent variable when we choose to copy the encoder inputs based on predicted fertilities. More precisely, given a source sentence $X$ , the conditional probability of a target translation $Y$ is: ",
+        "bbox": [
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+        "page_idx": 4
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+    {
+        "type": "equation",
+        "img_path": "images/addbc095e30bd0f2ec3e327b7ac2d196aff125984ec04b5d2c19836176794d07.jpg",
+        "text": "$$\np _ { \\mathcal N \\mathcal M } ( Y | X ; \\theta ) = \\sum _ { f _ { 1 } , . . . , f _ { T ^ { \\prime } } \\in \\mathcal F } \\left( \\prod _ { t ^ { \\prime } = 1 } ^ { T ^ { \\prime } } p _ { F } ( f _ { t ^ { \\prime } } | x _ { 1 : T ^ { \\prime } } ; \\theta ) \\cdot \\prod _ { t = 1 } ^ { T } p ( y _ { t } | x _ { 1 } \\{ f _ { 1 } \\} , . . , x _ { T ^ { \\prime } } \\{ f _ { T ^ { \\prime } } \\} ; \\theta ) \\right)\n$$",
+        "text_format": "latex",
+        "bbox": [
+            199,
+            229,
+            777,
+            280
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "where value $\\begin{array} { r } { \\mathcal { F } = \\{ f _ { 1 } , . . . , f _ { T ^ { \\prime } } | \\sum _ { t ^ { \\prime } = 1 } ^ { T ^ { \\prime } } f _ { t ^ { \\prime } } = T , f _ { t ^ { \\prime } } \\in \\mathbb { Z } ^ { * } \\} } \\end{array}$ is thand of all fertility sequdenotes the token ces—onerepeated ertilitytimes. $Y$ $x \\{ f \\}$ $x$ $f$ ",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "Fertility prediction As shown in Fig. 2, we model the fertility $p _ { F } \\big ( f _ { t ^ { \\prime } } | x _ { 1 : T ^ { \\prime } } \\big )$ at each position independently using a one-layer neural network with a softmax classifier $L = 5 0$ in our experiments) on top of the output of the last encoder layer. This models the way that fertility values are a property of each input word but depend on information and context from the entire sentence. ",
+        "bbox": [
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+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "Benefits of fertility Fertilities possess all three of the properties listed earlier as desired of a latent variable for non-autoregressive machine translation: ",
+        "bbox": [
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+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "• An external aligner provides a simple and fast approximate inference model that effectively reduces the unsupervised training problem to two supervised ones.   \n• Using fertilities as a latent variable makes significant progress towards solving the multimodality problem by providing a natural factorization of the output space. Given a source sentence, restricting the output distribution to those target sentences consistent with a particular fertility sequence dramatically reduces the mode space. Furthermore, the global choice of mode is factored into a set of local mode choices: namely, how to translate each input word. These local mode choices can be effectively supervised because the fertilities provide a fixed “scaffold.”   \nIncluding both fertilities and reordering in the latent variable would provide complete alignment statistics. This would make the decoding function trivially easy to approximate given the latent variable and force all of the modeling complexity into the encoder. Using fertilities alone allows the decoder to take some of this burden off of the encoder. ",
+        "bbox": [
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+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "Our use of fertilities as a latent variable also means that there is no need to have a separate means of explicitly modeling the length of the translation, which is simply the sum of fertilities. And fertilities provide a powerful way to condition the decoding process, allowing the model to generate diverse translations by sampling over the fertility space. ",
+        "bbox": [
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+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "3.4 TRANSLATION PREDICTOR AND THE DECODING PROCESS ",
+        "text_level": 1,
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "At inference time, the model can identify the translation with the highest conditional probability (see Eq. 5) by marginalizing over all possible latent fertility sequences. Given a fertility sequence, however, identifying the optimal translation only requires independently maximizing the local probability for each output position. We define $Y \\overset { \\cdot } { = } G ( x _ { 1 : T ^ { \\prime } } , f _ { 1 : T ^ { \\prime } } ; \\theta )$ to represent the optimal translation given a source sentence and a sequence of fertility values. ",
+        "bbox": [
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+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "But searching and marginalizing over the whole fertility space is still intractable. We propose three heuristic decoding algorithms to reduce the search space of the NAT model: ",
+        "bbox": [
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+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "Argmax decoding Since the fertility sequence is also modeled with a conditionally independent factorization, we can simply estimate the best translation by choosing the highest-probability fertility for each input word: ",
+        "bbox": [
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+        "page_idx": 4
+    },
+    {
+        "type": "equation",
+        "img_path": "images/c87b82f443ad023fe764cc137a25c0b5f30813f1855f5398ec17018f945487d0.jpg",
+        "text": "$$\n\\hat { Y } _ { \\mathrm { a r g m a x } } = G ( x _ { 1 : T ^ { \\prime } } , \\hat { f } _ { 1 : T ^ { \\prime } } ; \\theta ) , \\mathrm { w h e r e \\ } \\hat { f } _ { t ^ { \\prime } } = \\underset { f } { \\operatorname { a r g m a x } } p _ { F } ( f _ { t ^ { \\prime } } | x _ { 1 : T ^ { \\prime } } ; \\theta )\n$$",
+        "text_format": "latex",
+        "bbox": [
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+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "Average decoding We can also estimate each fertility as the expectation of its corresponding softmax distribution: ",
+        "bbox": [
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+        "page_idx": 5
+    },
+    {
+        "type": "equation",
+        "img_path": "images/cddc8316aa514a2040ceed5ae75c4f96052fd7ea9df38f637de3023bdc4c2c2c.jpg",
+        "text": "$$\n\\hat { Y } _ { \\mathrm { a v e r a g e } } = G ( x _ { 1 : T ^ { \\prime } } , \\hat { f } _ { 1 : T ^ { \\prime } } ; \\theta ) , \\mathrm { w h e r e } \\hat { f } _ { t ^ { \\prime } } = \\mathrm { R o u n d } \\left( \\sum _ { f _ { t ^ { \\prime } } = 1 } ^ { L } p _ { F } \\big ( f _ { t ^ { \\prime } } | x _ { 1 : T ^ { \\prime } } ; \\theta \\big ) f _ { t ^ { \\prime } } \\right)\n$$",
+        "text_format": "latex",
+        "bbox": [
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "Noisy parallel decoding (NPD) A more accurate approximation of the true optimum of the target distribution, inspired by Cho (2016), is to draw samples from the fertility space and compute the best translation for each fertility sequence. We can then use the autoregressive teacher to identify the best overall translation: ",
+        "bbox": [
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+        "page_idx": 5
+    },
+    {
+        "type": "equation",
+        "img_path": "images/ddb83a2f54effd61e8585241161c5ecfe255d9b7958c6a9e1d1be0a28272f922.jpg",
+        "text": "$$\n\\hat { Y } _ { \\mathrm { N P D } } = G ( x _ { 1 : T ^ { \\prime } } , \\underset { f _ { t ^ { \\prime } } \\sim p _ { F } } { \\mathrm { a r g m a x } } p _ { \\mathcal { A R } } ( G ( x _ { 1 : T ^ { \\prime } } , f _ { 1 : T ^ { \\prime } } ; \\theta ) | X ; \\theta ) ; \\theta )\n$$",
+        "text_format": "latex",
+        "bbox": [
+            303,
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "Note that, when using an autoregressive model as a scoring function for a set of decoded translations, it can run as fast as it does at train time because it can be provided with all decoder inputs in parallel. ",
+        "bbox": [
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+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "NPD is a stochastic search method, and it also increases the computational resources required linearly by the sample size. However, because all the search samples can be computed and scored entirely independently, the process only doubles the latency compared to computing a single translation if sufficient parallelism is available. ",
+        "bbox": [
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+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "4 TRAINING ",
+        "text_level": 1,
+        "bbox": [
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+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "The proposed NAT contains a discrete sequential latent variable $f _ { 1 : T ^ { \\prime } }$ , whose conditional posterior distribution $p ( f _ { 1 : T ^ { \\prime } } | x _ { 1 : T ^ { \\prime } } , y _ { 1 : T } ; \\theta )$ we can approximate using a proposal distribution $q ( f _ { 1 : T ^ { \\prime } } | x _ { 1 : T ^ { \\prime } } , y _ { 1 : T } )$ . This provides a variational bound for the overall maximum likelihood loss: ",
+        "bbox": [
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+        "page_idx": 5
+    },
+    {
+        "type": "equation",
+        "img_path": "images/98d5a44ed0ad3d2976698667125e9e76d3327aac64ae197046cd812c046fa407.jpg",
+        "text": "$$\n\\begin{array} { r l } & { \\mathcal { L } _ { \\mathrm { M L } } = \\log p _ { \\mathcal { N A } } ( Y | X ; \\theta ) = \\log \\displaystyle \\sum _ { f _ { 1 : T ^ { \\prime } } \\in \\mathcal { F } } p _ { F } ( f _ { 1 : T ^ { \\prime } } | x _ { 1 : T ^ { \\prime } } ; \\theta ) \\cdot p ( y _ { 1 : T } | x _ { 1 : T ^ { \\prime } } , f _ { 1 : T ^ { \\prime } } ; \\theta ) } \\\\ & { \\geq \\displaystyle \\sum _ { f _ { 1 : T ^ { \\prime } \\sim \\mathcal { I } } } \\left( \\underbrace { T } _ { \\mathrm { t - 1 } } \\log p ( y _ { t } | x _ { 1 } \\{ f _ { 1 } \\} , . . . , x _ { T ^ { \\prime } } \\{ f _ { T ^ { \\prime } } \\} ; \\theta ) \\right)} _ { \\mathrm { T r a n s l a t i o n ~ L o s s } } + \\underbrace { \\sum _ { t ^ { \\prime } = 1 } ^ { T ^ { \\prime } } \\log p _ { F } ( f _ { t ^ { \\prime } } | x _ { 1 : T ^ { \\prime } } ; \\theta ) } _ { \\mathrm { F e r t i l i t y ~ L o s s } }  + \\mathcal { H } ( q )  \\end{array}\n$$",
+        "text_format": "latex",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "We choose a proposal distribution $q$ defined by a separate, fixed fertility model. Possible options include the output of an external aligner, which produces a deterministic sequence of integer fertilities for each (source, target) pair in a training corpus, or fertilities computed from the attention weights used in our fixed autoregressive teacher model. This simplifies the inference process considerably, as the expectation over $q$ is deterministic. ",
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+    },
+    {
+        "type": "text",
+        "text": "The resulting loss function, consisting of the two bracketed terms in Eq. 9, allows us to train the entire model in a supervised fashion, using the inferred fertilities to simultaneously train the translation model $p$ and supervise the fertility neural network model $p _ { F }$ . ",
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+    },
+    {
+        "type": "text",
+        "text": "4.1 SEQUENCE-LEVEL KNOWLEDGE DISTILLATION ",
+        "text_level": 1,
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "While the latent fertility model substantially improves the ability of the non-autoregressive output distribution to approximate the multimodal target distribution, it does not completely solve the problem of nondeterminism in the training data. In many cases, there are multiple correct translations consistent with a single sequence of fertilities—for instance, both “Danke schon.” and “Vielen ¨ dank.” are consistent with the English input “Thank you.” and the fertility sequence [2, 0, 1], because “you” is not directly translated in either German sentence. ",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "Thus we additionally apply sequence-level knowledge distillation (Kim & Rush, 2016) to construct a new corpus by training an autoregressive machine translation model, known as the teacher, on an existing training corpus, then using that model’s greedy outputs as the targets for training the nonautoregressive student. The resulting targets are less noisy and more deterministic, as the trained model will consistently translate a sentence like “Thank you.” into the same German translation every time; on the other hand, they are also lower in quality than the original dataset. ",
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+    {
+        "type": "text",
+        "text": "",
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+    },
+    {
+        "type": "text",
+        "text": "4.2 FINE-TUNING ",
+        "text_level": 1,
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "Our supervised fertility model enables a decomposition of the overall maximum likelihood loss into translation and fertility terms, but it has some drawbacks compared to variational training. In particular, it heavily relies on the deterministic, approximate inference model provided by the external alignment system, while it would be desirable to train the entire model, including the fertility predictor, end to end. ",
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+    {
+        "type": "text",
+        "text": "Thus we propose a fine-tuning step after training the NAT to convergence. We introduce an additional loss term consisting of the reverse K-L divergence with the teacher output distribution, a form of word-level knowledge distillation: ",
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+        "page_idx": 6
+    },
+    {
+        "type": "equation",
+        "img_path": "images/e65993392162bd75d4d5f03dbe09c11504275ad6f8a4d1ecdf2eaf6fe3d240bf.jpg",
+        "text": "$$\n\\mathcal { L } _ { \\mathrm { R K L } } \\left( f _ { 1 : T ^ { \\prime } } ; \\theta \\right) = \\sum _ { t = 1 } ^ { T } \\sum _ { y _ { t } } \\left[ \\log p _ { \\mathcal { A R } } \\left( y _ { t } | \\hat { y } _ { 1 : t - 1 } , x _ { 1 : T ^ { \\prime } } \\right) \\cdot p _ { \\mathcal { N A } } \\left( y _ { t } | x _ { 1 : T ^ { \\prime } } , f _ { 1 : T ^ { \\prime } } ; \\theta \\right) \\right] ,\n$$",
+        "text_format": "latex",
+        "bbox": [
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "where $\\hat { y } _ { 1 : T } = G ( x _ { 1 : T ^ { \\prime } } , f _ { 1 : T ^ { \\prime } } ; \\theta )$ . Such a loss is more favorable towards highly peaked student output distributions than a standard cross-entropy error would be. ",
+        "bbox": [
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+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "Then we train the whole model jointly with a weighted sum of the original distillation loss and two such terms, one an expectation over the predicted fertility distribution, normalized with a baseline, and the other based on the external fertility inference model: ",
+        "bbox": [
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+        "page_idx": 6
+    },
+    {
+        "type": "equation",
+        "img_path": "images/57b8b0401c44a9da9dffb4a771b588d3f01db84a0e94c59950fcea341c8459e4.jpg",
+        "text": "$$\n\\mathcal { L } _ { \\mathrm { F T } } = \\lambda \\left( \\underbrace { \\mathbb { E } } _ { \\int _ { \\mathrm { I : T : } } r \\sim p _ { F } } \\left( \\mathcal { L } _ { \\mathrm { R K L } } \\left( f _ { 1 : T ^ { \\prime } } \\right) - \\mathcal { L } _ { \\mathrm { R K L } } \\left( \\bar { f } _ { 1 : T ^ { \\prime } } \\right) \\right) + \\underbrace { \\mathbb { E } } _ { f _ { 1 : T ^ { \\prime } \\sim q } } \\left( \\mathcal { L } _ { \\mathrm { R K L } } \\left( f _ { 1 : T ^ { \\prime } } \\right) \\right)  _ { \\mathcal { L } _ { \\mathrm { R P } } } \\right) + ( 1 - \\lambda ) \\mathcal { L } _ { \\mathrm { K D } } ,\n$$",
+        "text_format": "latex",
+        "bbox": [
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "where ${ \\bar { f } } _ { 1 : T ^ { \\prime } }$ is the average fertility computed by Eq. 7. The gradient with respect to the nondifferentiable ${ \\mathcal { L } } _ { \\mathrm { R L } }$ term can be estimated with REINFORCE (Williams, 1992), while the $\\mathcal { L } _ { \\mathrm { B P } }$ term can be trained using ordinary backpropagation. ",
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+    },
+    {
+        "type": "text",
+        "text": "5 EXPERIMENTS ",
+        "text_level": 1,
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+    },
+    {
+        "type": "text",
+        "text": "5.1 EXPERIMENTAL SETTINGS ",
+        "text_level": 1,
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "Dataset We evaluate the proposed NAT on three widely used public machine translation corpora: IWSLT16 En–De2, WMT14 En–De,3 and WMT16 En–Ro4. We use IWSLT—which is smaller than the other two datasets—as the development dataset for ablation experiments, and additionally train and test our primary models on both directions of both WMT datasets. All the data are tokenized and segmented into subword symbols using byte-pair encoding (BPE) (Sennrich et al., 2015) to restrict the size of the vocabulary. For both WMT datasets, we use shared BPE vocabulary and additionally share encoder and decoder word embeddings; for IWSLT, we use separate English and German vocabulary and embeddings. ",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "Teacher Sequence-level knowledge distillation is applied to alleviate multimodality in the training dataset, using autoregressive models as the teachers. The same teacher model used for distillation is also used as a scoring function for fine-tuning and noisy parallel decoding. ",
+        "bbox": [
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "To enable a fair comparison, and benefit from its high translation quality, we implemented the autoregressive teachers using the state-of-the-art Transformer architecture. In addition, we use the same sizes and hyperparameters for each student and its respective teacher, with the exception of the newly added positional self-attention and fertility prediction modules. ",
+        "bbox": [
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+        "page_idx": 6
+    },
+    {
+        "type": "table",
+        "img_path": "images/b27d229f92b1dc501a1101859c66ddaef0b786b8513588c7b5b795ee0a526bb9.jpg",
+        "table_caption": [],
+        "table_footnote": [],
+        "table_body": "<table><tr><td rowspan=\"2\">Models</td><td colspan=\"2\">WMT14</td><td colspan=\"2\">WMT16</td><td colspan=\"2\">IWSLT16</td><td></td></tr><tr><td>En→De</td><td>De→En</td><td>En→Ro</td><td>Ro→En</td><td>En→De</td><td>Latency / Speedup</td><td></td></tr><tr><td>NAT</td><td>17.35</td><td>20.62</td><td>26.22</td><td>27.83</td><td>25.20</td><td>39 ms</td><td>15.6×</td></tr><tr><td>NAT (+FT)</td><td>17.69</td><td>21.47</td><td>27.29</td><td>29.06</td><td>26.52</td><td>39 ms</td><td>15.6×</td></tr><tr><td>NAT (+FT + NPD s = 10)</td><td>18.66</td><td>22.41</td><td>29.02</td><td>30.76</td><td>27.44</td><td>79 ms</td><td>7.68×</td></tr><tr><td>NAT (+FT + NPD s = 100)</td><td>19.17</td><td>23.20</td><td>29.79</td><td>31.44</td><td>28.16</td><td>257 ms</td><td>2.36×</td></tr><tr><td>Autoregressive (b = 1)</td><td>22.71</td><td>26.39</td><td>31.35</td><td>31.03</td><td>28.89</td><td>408 ms</td><td>1.49×</td></tr><tr><td>Autoregressive (b = 4)</td><td>23.45</td><td>27.02</td><td>31.91</td><td>31.76</td><td>29.70</td><td>607ms</td><td>1.00×</td></tr></table>",
+        "bbox": [
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+            101,
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+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "Table 1: BLEU scores on official test sets (newstest2014 for WMT En-De and newstest2016 for WMT En-Ro) or the development set for IWSLT. NAT models without NPD use argmax decoding. Latency is computed as the time to decode a single sentence without minibatching, averaged over the whole test set; decoding is implemented in PyTorch on a single NVIDIA Tesla P100. ",
+        "bbox": [
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+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "Preparation for knowledge distillation We first train all teacher models using maximum likelihood, then freeze their parameters. To avoid the redundancy of running fixed teacher models repeatedly on the same data, we decode the entire training set once using each teacher to create a new training dataset for its respective student. ",
+        "bbox": [
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+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "Encoder initialization We find it helpful to initialize the weights in the NAT student’s encoder with the encoder weights from its teacher, as the autoregressive and non-autoregressive models share the same encoder input and architecture. ",
+        "bbox": [
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+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "Fertility supervision during training As described above, we supervise the fertility predictions at train time by using a fixed aligner as a fertility inference function. We use the fast align5 implementation of IBM Model 2 for this purpose, with default parameters (Dyer et al., 2013). ",
+        "bbox": [
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+        "page_idx": 7
+    },
+    {
+        "type": "image",
+        "img_path": "images/ff2cfd4d2f25ef6e98d968d65066c8e02ea0f947a91d09952aa8c8ffbab3302a.jpg",
+        "image_caption": [
+            "Figure 3: BLEU scores on IWSLT development set as a function of sample size for noisy parallel decoding. NPD matches the performance of the other two decoding strategies after two samples, and exceeds the performance of the autoregressive teacher with around 1000. "
+        ],
+        "image_footnote": [],
+        "bbox": [
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+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "Hyperparameters For experiments on WMT datasets, we use the hyperparameter settings of the base Transformer model described in Vaswani et al. (2017), though without label smoothing. As IWSLT is a smaller corpus, and to reduce training time, we use a set of smaller hyperparameters $( d _ { \\mathrm { m o d e l } } = 2 8 7 , d _ { \\mathrm { h i d d e n } } = 5 0 7 , n _ { \\mathrm { l a y e r } } = 5 , n _ { \\mathrm { h e a d } } = \\mathrm { \\Omega } ^ { \\ast }$ , and $t _ { \\mathrm { w a r m u p } } = 7 4 6 )$ for all experiments on that dataset. For fine-tuning we use $\\lambda = 0 . 2 5$ . ",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "Evaluation metrics We evaluate using tokenized and cased BLEU scores (Papineni et al., 2002). ",
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+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "Implementation We have open-sourced our PyTorch implementation of the $\\mathrm { N A T ^ { 6 } }$ . ",
+        "bbox": [
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+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "5.2 RESULTS ",
+        "text_level": 1,
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "Across the three datasets we used, the NAT performs between 2-5 BLEU points worse than its autoregressive teacher, with part or all of this gap addressed by the use of noisy parallel decoding. In the case of WMT16 English–Romanian, NPD improves the performance of our non-autoregressive model to within 0.2 BLEU points of the previous overall state of the art (Gehring et al., 2017). ",
+        "bbox": [
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+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "Comparing latencies on the development model shows a speedup of more than a factor of 10 over greedy autoregressive decoding, or a factor of 15 over beam search. Latencies for decoding with NPD, regardless of sample size, could be reduced to about $8 0 \\mathrm { m s }$ by parallelizing across multiple GPUs because each sample can be generated, then scored, independently from the others. ",
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+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "5.3 ABLATION STUDY ",
+        "text_level": 1,
+        "bbox": [
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+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "We also conduct an extensive ablation study with the proposed NAT on the IWSLT dataset. First, we note that the model fails to train when provided with only positional embeddings as input to the decoder. Second, we see that training on the distillation corpus rather than the ground truth provides a fairly consistent improvement of around 5 BLEU points. Third, switching from uniform copying of source inputs to fertility-based copying improves performance by four BLEU points when using ground-truth training or two when using distillation. ",
+        "bbox": [
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+        "page_idx": 8
+    },
+    {
+        "type": "table",
+        "img_path": "images/e54d8b7021cfac76f841f708bf7c607fe1294c5aa3739137af72c28cad0aff7f.jpg",
+        "table_caption": [],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>Distillation b=1 b=4</td><td>Decoder Inputs +uniform</td><td>+fertility</td><td>+PosAtt</td><td>Fine-tuning +LKD +LBP</td><td>BLEU +CRL</td><td>BLEU (T)</td></tr><tr><td></td><td></td><td></td><td></td><td></td><td>~2</td><td></td></tr><tr><td></td><td>√</td><td></td><td></td><td></td><td>16.51</td><td></td></tr><tr><td></td><td></td><td></td><td>√</td><td></td><td>18.87</td><td></td></tr><tr><td>√</td><td>√</td><td></td><td>√</td><td></td><td>20.72</td><td></td></tr><tr><td></td><td>√</td><td></td><td>√</td><td></td><td>21.12</td><td></td></tr><tr><td>&lt;</td><td></td><td></td><td>√</td><td></td><td>24.02</td><td>43.91</td></tr><tr><td></td><td></td><td></td><td>√</td><td></td><td>25.20</td><td>45.41</td></tr><tr><td></td><td>√</td><td></td><td></td><td>√</td><td>22.44 厂</td><td></td></tr><tr><td>兴 √</td><td></td><td>√</td><td></td><td></td><td>×</td><td>×</td></tr><tr><td></td><td></td><td>√</td><td></td><td>√</td><td>×</td><td>×</td></tr><tr><td>√</td><td></td><td>√</td><td>√</td><td>√</td><td>25.76</td><td>46.11</td></tr><tr><td>√</td><td></td><td>√</td><td>√</td><td>√</td><td>26.52</td><td>47.38</td></tr></table>",
+        "bbox": [
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+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "Table 2: Ablation performance on the IWSLT development set. BLEU (T) refers to the BLEU score on a version of the development set that has been translated by the teacher model. An $\\times$ indicates that fine-tuning caused that model to get worse. When uniform copying is used as the decoder inputs, the ground-truth target lengths are provided. All models use argmax decoding. ",
+        "bbox": [
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+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "Fine-tuning does not converge with reinforcement learning alone, or with the $\\mathcal { L } _ { \\mathrm { B P } }$ term alone, but use of all three fine-tuning terms together leads to an improvement of around 1.5 BLEU points. Training the student model from a distillation corpus produced using beam search is similar to training from the greedily-distilled corpus. ",
+        "bbox": [
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+        "page_idx": 8
+    },
+    {
+        "type": "table",
+        "img_path": "images/f8421f544ec54c247fda2ccf5acde08a1d896cc7e4be518f611e266b0beaaf82.jpg",
+        "table_caption": [
+            "Figure 4: Two examples comparing translations produced by an autoregressive (AR) and nonautoregressive Transformer as well as the result of noisy parallel decoding with sample size 100. Repeated words are highlighted in gray. "
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>Source:</td><td>politicians try to pick wordsand use words to shape realityand control reality,butin fact,reality changes words</td></tr><tr><td></td><td>far more than words can ever change reality.</td></tr><tr><td rowspan=\"3\">Target: AR:</td><td>Politiker versuchen Worte zu benutzen,um die Realitat zu formen und die Realitat zu kontrolieren,aber</td></tr><tr><td>tatsächlich verandert die Realitat Worte viel mehr,als Worte die Realitat jemals verändern konnten.</td></tr><tr><td>Politikerversuchen Worter zu wahlen und Worter zur Realitat zu gestalten und Realitätzu steuern,aber in</td></tr><tr><td rowspan=\"2\">NAT:</td><td>Wirklichkeit verändert sich die Realitat viel mehrals Worte,die die Realität verändern konnen.</td></tr><tr><td>Politikerversuchen,Worter wahlen und zu verwenden,um Realitatzu formen und Realitatzu formen,aber</td></tr><tr><td rowspan=\"2\">NAT+NPD:</td><td>tatsächlich ändert Realitat Realitat viel mehrals Wortedie Realität Realitat verändern.</td></tr><tr><td>Politikerversuchen,Worter wahlenund zu verwenden,um Realitat Realitat formenund die Realitatzu formen， aber tatsächlich ändert die Realität Worte viel mehrals Worte jemals die Realität verändern konnen.</td></tr><tr><td>Source:</td><td>Isee wheelchairs bought and sold like used cars.</td></tr><tr><td>Target:</td><td>ich erlebe,dass Rollstuhle gekauft und verkauft werden wie Gebrauchtwagen</td></tr><tr><td>AR: NAT:</td><td>ich sehe Rollstuhlen,die wie Autos verkauft und verkauft werden.</td></tr><tr><td>NAT+NPD:</td><td>ich sehe,dass Stuhle Stuhle und verkauftwie Autos verkauft.</td></tr><tr><td></td><td>ich sehe Rollühle kauften und verkaufte wie Autos.</td></tr></table>",
+        "bbox": [
+            184,
+            597,
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+            801
+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "We include two examples of translations from the IWSLT development set in Fig. 4. Instances of repeated words or phrases, highlighted in gray, are most prevalent in the non-autoregressive output for the relatively complex first example sentence. Two pairs of repeated words in the first example, as ",
+        "bbox": [
+            176,
+            882,
+            825,
+            924
+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "se lucreaza la soluti de genul acesta . ",
+        "bbox": [
+            210,
+            107,
+            428,
+            119
+        ],
+        "page_idx": 9
+    },
+    {
+        "type": "text",
+        "text": "se la solutii de genul acesta .   \nse lucreaza la solutii de acesta .   \nse lucreaza solutii de genul acesta .   \nse se lucreaza la solutii de acesta .   \nse lucreaza lucreaza la solutii de acesta .   \nse se lucreaza lucreaza la solutii de acesta .   \nse se lucreaza lucreaza la solutii de de acesta .   \nse se lucreaza lucreaza la solutii de genul acesta . solutions on this kind are done.   \nwork done on solutions like this .   \nsolutions on this kind is done .   \nwork is done on solutions like this .   \nwork is done on solutions like this .   \nwork is being done on solutions like this .   \nwork is being done on solutions such as this.   \nwork is being done on solutions such this kind . ",
+        "bbox": [
+            207,
+            132,
+            493,
+            255
+        ],
+        "page_idx": 9
+    },
+    {
+        "type": "text",
+        "text": "",
+        "bbox": [
+            521,
+            132,
+            790,
+            256
+        ],
+        "page_idx": 9
+    },
+    {
+        "type": "text",
+        "text": "Figure 5: A Romanian–English example translated with noisy parallel decoding. At left are eight sampled fertility sequences from the encoder, represented with their corresponding decoder input sequences. Each of these values for the latent variable leads to a different possible output translation, shown at right. The autoregressive Transformer then picks the best translation, shown in red, a process which is much faster than directly using it to generate output. ",
+        "bbox": [
+            173,
+            276,
+            826,
+            345
+        ],
+        "page_idx": 9
+    },
+    {
+        "type": "text",
+        "text": "well as a pair in the second, are not present in the versions with noisy parallel decoding, suggesting that NPD scoring using the teacher model can filter out such mistakes. The translations produced by the NAT with NPD, while of a similar quality to those produced by the autoregressive model, are also noticeably more literal. ",
+        "bbox": [
+            174,
+            372,
+            825,
+            428
+        ],
+        "page_idx": 9
+    },
+    {
+        "type": "text",
+        "text": "We also show an example of the noisy parallel decoding process in Fig. 5, demonstrating the diversity of translations that can be found by sampling from the fertility space. ",
+        "bbox": [
+            174,
+            435,
+            823,
+            463
+        ],
+        "page_idx": 9
+    },
+    {
+        "type": "text",
+        "text": "6 CONCLUSION ",
+        "text_level": 1,
+        "bbox": [
+            176,
+            484,
+            318,
+            501
+        ],
+        "page_idx": 9
+    },
+    {
+        "type": "text",
+        "text": "We introduce a latent variable model for non-autoregressive machine translation that enables a decoder based on Vaswani et al. (2017) to take full advantage of its exceptional degree of internal parallelism even at inference time. As a result, we measure translation latencies of one-tenth that of an equal-sized autoregressive model, while maintaining competitive BLEU scores. ",
+        "bbox": [
+            174,
+            517,
+            825,
+            573
+        ],
+        "page_idx": 9
+    },
+    {
+        "type": "text",
+        "text": "REFERENCES ",
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+        "text": "Ashish Vaswani, Noam Shazeer, Niki Parmar, Jakob Uszkoreit, Llion Jones, Aidan Gomez, Łukasz Kaiser, and Illia Polosukhin. Attention is all you need. arXiv preprint arXiv:1706.03762, 2017. ",
+        "bbox": [
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+        "text": "Ronald Williams. Simple statistical gradient-following algorithms for connectionist reinforcement learning. Machine Learning, 8(3-4):229–256, 1992. ",
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+        "page_idx": 10
+    },
+    {
+        "type": "text",
+        "text": "Y. Wu, M. Schuster, Z. Chen, Q. V. Le, M. Norouzi, W. Macherey, M. Krikun, Y. Cao, Q. Gao, K. Macherey, J. Klingner, A. Shah, M. Johnson, X. Liu, Ł. Kaiser, S. Gouws, Y. Kato, T. Kudo, H. Kazawa, K. Stevens, G. Kurian, N. Patil, W. Wang, C. Young, J. Smith, J. Riesa, A. Rudnick, O. Vinyals, G. Corrado, M. Hughes, and J. Dean. Google’s neural machine translation system: Bridging the gap between human and machine translation. arXiv preprint arXiv:1609.08144, 2016. ",
+        "bbox": [
+            176,
+            419,
+            826,
+            502
+        ],
+        "page_idx": 10
+    },
+    {
+        "type": "image",
+        "img_path": "images/8397d58044f6d9c8a19dcbb03ac376664021ffaa63d7eac01c5e0d5c288a1df7.jpg",
+        "image_caption": [
+            "Figure 6: The schematic structure of training and inference for the NAT. The “distilled data” contains target sentences decoded by the autoregressive model and ground-truth source sentences. "
+        ],
+        "image_footnote": [],
+        "bbox": [
+            179,
+            135,
+            815,
+            446
+        ],
+        "page_idx": 11
+    },
+    {
+        "type": "image",
+        "img_path": "images/65e35fd7ac2e233ef8cdae03751ebce2756e57bc1378b23f1a59c83c62823be8.jpg",
+        "image_caption": [
+            "Figure 7: The translation latency, computed as the time to decode a single sentence without minibatching, for each sentence in the IWSLT development set as a function of its length. The autoregressive model has latency linear in the decoding length, while the latency of the NAT is nearly constant for typical lengths, even with NPD with sample size 10. When using NPD with sample size 100, the level of parallelism is enough to more than saturate the GPU, leading again to linear latencies. "
+        ],
+        "image_footnote": [],
+        "bbox": [
+            230,
+            541,
+            733,
+            790
+        ],
+        "page_idx": 11
+    },
+    {
+        "type": "image",
+        "img_path": "images/19326d4ac73a662073b026f5ada8aa0be903a2801d0ffdb32756ff0c9f97cdcc.jpg",
+        "image_caption": [
+            "Figure 8: Learning curves for training and fine-tuning of the NAT on IWSLT. BLEU scores are on the development set. "
+        ],
+        "image_footnote": [],
+        "bbox": [
+            246,
+            381,
+            720,
+            627
+        ],
+        "page_idx": 12
+    }
+]

parse/train/BkxfshNYwB/BkxfshNYwB.md

@@ -0,0 +1,333 @@
+# MINCUT POOLING IN GRAPH NEURAL NETWORKS
+
+Anonymous authors Paper under double-blind review
+
+# ABSTRACT
+
+The advance of node pooling operations in Graph Neural Networks (GNNs) has lagged behind the feverish design of new message-passing techniques, and pooling remains an important and challenging endeavor for the design of deep architectures. In this paper, we propose a pooling operation for GNNs that leverages a differentiable unsupervised loss based on the minCUT optimization objective. For each node, our method learns a soft cluster assignment vector that depends on the node features, the target inference task (e.g., a graph classification loss), and, thanks to the minCUT objective, also on the connectivity structure of the graph. Graph pooling is obtained by applying the matrix of assignment vectors to the adjacency matrix and the node features. The proposed method can also be used as a stand-alone module to cluster vertexes in annotated graphs and solve unsupervised problems. We validate the effectiveness of the proposed pooling method on downstream tasks, including supervised graph classification and a set of unsupervised tasks, which reveal the limitations of existing GNN pooling approaches.
+
+# 1 INTRODUCTION
+
+A fundamental component in deep convolutional neural networks is the pooling operation, which replaces the output of convolutions with local summaries of nearby points and is usually implemented by maximum or average operations (Lee et al., 2016). State-of-the-art architectures alternate convolutions, which extrapolate local patterns irrespective of the specific location on the input signal, and pooling, which lets the ensuing convolutions capture aggregated patterns. Pooling allows to learn abstract representations in deeper layers of the network by discarding information that is superfluous for the task, and keeps model complexity under control by limiting the growth of intermediate features.
+
+Graph Neural Networks (GNNs) extend the convolution operation from regular domains, such as images or time series, to data with arbitrary topologies and unordered structures described by graphs (Battaglia et al., 2018). The development of pooling strategies for GNNs, however, has lagged behind the design of newer and more effective message-passing (MP) operations (Gilmer et al., 2017), such as graph convolutions, mainly due to the difficulty of defining an aggregated version of the original graph that supports the pooled signal.
+
+A na¨ıve pooling strategy in GNNs is to average all nodes features (Li et al., 2016), but it has limited flexibility since it does not extract local summaries of the graph structure, and no further MP operations can be applied afterwards. An alternative approach consists in pre-computing coarsened versions of the original graph and then fit the data to these deterministic structures (Bruna et al., 2013). While this aggregation accounts for the connectivity of the graph, it ignores task-specific objectives as well as the node features.
+
+In this paper, we propose a differentiable pooling operation implemented as a neural network layer, which can be seamlessly combined with other MP layers (see Fig. 1). The parameters in the pooling layer are learned by combining the task-specific loss with an unsupervised regularization term, which optimizes a continuous relaxation of the normalized minCUT objective. The minCUT identifies dense graph components, where the nodes features become locally homogeneous after the message-passing. By gradually aggregating these components, the GNN learns to distil global properties from the graph. The proposed minCUT pooling operator (minCUTpool) yields partitions that 1) cluster together nodes which have similar features and are strongly connected on the graph, and 2) take into account the objective of the downstream task.
+
+![](images/2f1bdb5271287007bfb404fabc54a4bd48a828a415e925e71e65dd38e08b6950.jpg)  
+Figure 1: A deep GNN architecture where message-passing is followed by minCUT pooling.
+
+# 2 BACKGROUND
+
+# 2.1 MINCUT AND SPECTRAL CLUSTERING
+
+Given a graph $G = \{ \nu , \mathcal { E } \}$ , $| \nu | = N$ , and the associated adjacency matrix $\mathbf { A } \in \mathbb { R } ^ { N \times N }$ , the $K$ -way normalized minCUT (simply referred to as minCUT) aims at partitioning $\nu$ in $K$ disjoint subsets by removing the minimum volume of edges. The problem is equivalent to maximizing
+
+$$
+\frac { 1 } { K } \sum _ { k = 1 } ^ { K } \frac { \operatorname* { l i n k s } ( \mathcal { V } _ { k } ) } { \deg \mathrm { r e e } ( \mathcal { V } _ { k } ) } = \frac { 1 } { K } \sum _ { k = 1 } ^ { K } \frac { \sum _ { i , j \in \mathcal { V } _ { k } } \mathcal { E } _ { i , j } } { \sum _ { i \in \mathcal { V } _ { k } , j \in \mathcal { V } \backslash \mathcal { V } _ { k } } \mathcal { E } _ { i , j } } ,
+$$
+
+where the numerator counts the edge volume within each cluster, and the denominator counts the edges between the nodes in a cluster and the rest of the graph (Shi & Malik, 2000). Let $\mathbf { C } \in \mathbb { R } ^ { N \times K }$ be a cluster assignment matrix, so that $\mathbf { C } _ { i , j } = 1$ if node $i$ belongs to cluster $j$ , and 0 otherwise. The minCUT problem can be expressed as
+
+$$
+\mathrm { m a x i m i z e } \frac { 1 } { K } \sum _ { k = 1 } ^ { K } \frac { { \bf C } _ { k } ^ { T } { \bf A } { \bf C } _ { k } } { { \bf C } _ { k } ^ { T } { \bf D } { \bf C } _ { k } } , \mathrm { s . t . } { \bf C } \in \{ 0 , 1 \} ^ { N \times K } , { \bf C } { \bf 1 } _ { K } = { \bf 1 } _ { N } ,
+$$
+
+where $\mathbf { D } = \mathrm { d i a g } ( \mathbf { A } \mathbf { 1 } _ { N } )$ is the degree matrix (Dhillon et al., 2004). Since problem (2) is NP-hard, it is usually recast in a relaxed formulation that can be solved in polynomial time and guarantees a near-optimal solution (Yu & Shi, 2003):
+
+$$
+\arg \operatorname* { m a x } _ { \mathbf { Q } \in \mathbb { R } ^ { N \times K } } \frac { 1 } { K } \sum _ { k = 1 } ^ { K } \mathbf { Q } _ { k } ^ { T } \mathbf { A } \mathbf { Q } _ { k } , \quad \mathrm { s . t . } \mathbf { Q } = \mathbf { C } ( \mathbf { C } ^ { T } \mathbf { D } \mathbf { C } ) ^ { - \frac { 1 } { 2 } } , \ \mathbf { Q } ^ { T } \mathbf { Q } = \mathbf { I } _ { K } .
+$$
+
+While the optimization problem (3) is still non-convex, there exists an optimal solution $\mathbf { Q } ^ { * } = \mathbf { U } _ { K } \mathbf { O }$ , where ${ \bf U } _ { K } \dot { } \in \mathbb { R } ^ { N \times K }$ contains the eigenvectors of A corresponding to the $K$ largest eigenvalues, and $\mathbf { O } \in \mathbb { R } ^ { K \times K }$ is an orthogonal transformation (Ikebe et al., 1987).
+
+Since the elements of $\mathbf { Q } ^ { * }$ are real values rather than binary cluster indicators, the spectral clustering (SC) approach can be used to find discrete cluster assignments. In SC, the rows of $\mathbf { Q } ^ { * }$ are treated as node representations embedded in the eigenspace of the Laplacian, and are clustered together with standard algorithms such as $k$ -means (Von Luxburg, 2007). One of the main limitations of SC lies in the computation of the spectrum of A, which has a memory complexity of $\mathcal { O } ( N ^ { 2 } )$ and a computational complexity of $\mathcal { O } ( \bar { N } ^ { 3 } )$ . This prevents its applicability to large datasets.
+
+To deal with such scalability issues, the constrained optimization in (3) can be solved by gradient descent algorithms that refine the solution by iterating operations whose individual complexity is $\mathcal { O } ( N ^ { 2 } )$ , or even $\mathcal { O } ( N )$ (Han & Filippone, 2017). Those algorithms search the solution on the manifold induced by the orthogonality constraint on the columns of $\mathbf { Q }$ , by performing gradient updates along the geodesics (Wen & Yin, 2013; Collins et al., 2014). Alternative approaches rely on the QR factorization to constrain the space of feasible solutions (Damle et al., 2016), and alleviate the cost $\mathcal { O } ( N ^ { 3 } )$ of the factorization by ensuring that orthogonality holds only on one minibatch at a time (Shaham et al., 2018).
+
+Other works based on neural networks include an autoencoder trained to map the $i$ th row of the Laplacian to the ith components of the first $K$ eigenvectors, to avoid the spectral decomposition (Tian et al., 2014). Yi et al. (2017) use a soft orthogonality constraint to learn spectral embeddings as a volumetric reparametrization of a precomputed Laplacian eigenbase. Shaham et al. (2018); Kampffmeyer et al. (2019) propose differentiable loss functions to partition generic data and process out-of-sample data at inference time. Nazi et al. (2019) generate balanced node partitions with a GNN, but adopt an optimization that does not encourage cluster assignments to be orthogonal.
+
+# 2.2 GRAPH NEURAL NETWORKS
+
+Many approaches have been proposed to process graphs with neural networks, including recurrent architectures (Scarselli et al., 2009; Li et al., 2016) or convolutional operations inspired by filters used in graph signal processing (Defferrard et al., 2016; Bianchi et al., 2019). Since our focus is on graph pooling, we base our GNN implementation on a simple MP operation, which combines the features of each node with its 1st-order neighbors. To account for the initial node features, it is possible to introduce self-loops by adding a (scaled) identity matrix to the diagonal of A (Kipf & Welling, 2017). Since our pooling will modify the structure of the adjacency matrix, we prefer a MP implementation that leaves the original A unaltered and accounts for the initial node features by means of skip connections.
+
+Let $\tilde { \mathbf { A } } = \mathbf { D } ^ { - \frac { 1 } { 2 } } \mathbf { A } \mathbf { D } ^ { - \frac { 1 } { 2 } } \in \mathbb { R } ^ { N \times N }$ be the symmetrically normalized adjacency matrix and $\mathbf { X } \in \mathbb { R } ^ { N \times F }$ the matrix containing the node features. The output of the MP layer is
+
+$$
+\mathbf { X } ^ { ( t + 1 ) } = M P ( \mathbf { X } ^ { ( t ) } , \tilde { \mathbf { A } } ) = \operatorname { R e L U } ( \tilde { \mathbf { A } } \mathbf { X } ^ { ( t ) } \mathbf { W } _ { m } + \mathbf { X } ^ { ( t ) } \mathbf { W } _ { s } ) ,
+$$
+
+where $\boldsymbol { \Theta } _ { M P } = \{ \mathbf { W } _ { m } , \mathbf { W } _ { s } \}$ are the trainable weights relative to the mixing and skip component of the layer, respectively.
+
+# 3 PROPOSED METHOD
+
+The minCUT pooling strategy computes a cluster assignment matrix $\mathbf { S } \in \mathbb { R } ^ { N \times K }$ by means of a multi-layer perceptron, which maps each node feature $\mathbf { x } _ { i }$ into the ith row of S:
+
+$$
+\begin{array} { r } { \mathbf { S } = s o f t m a x ( \mathbf { R e L U } ( \mathbf { X } \mathbf { W } _ { 1 } ) \mathbf { W } _ { 2 } ) , } \end{array}
+$$
+
+where $\boldsymbol { \Theta } _ { P o o l } = \{ \mathbf { W } _ { 1 } \in \mathbb { R } ^ { F \times H } , \mathbf { W } _ { 2 } \in \mathbb { R } ^ { H \times K } \}$ are trainable parameters. The softmax function guarantees that $s _ { i , j } \in [ 0 , 1 ]$ and enforces the constraints $\mathbf { S 1 } _ { K } = \mathbf { 1 } _ { N }$ inherited from the optimization problem in (2). The parameters $\Theta _ { M P }$ and $\Theta _ { P o o l }$ are jointly optimized by minimizing the usual task-specific loss, as well as an unsupervised loss $\mathcal { L } _ { u }$ , which is composed of two terms
+
+$$
+\mathcal { L } _ { u } = \mathcal { L } _ { c } + \mathcal { L } _ { o } = \underbrace { - \frac { T r ( \mathbf { S } ^ { T } \tilde { \mathbf { A } } \mathbf { S } ) } { T r ( \mathbf { S } ^ { T } \tilde { \mathbf { D } } \mathbf { S } ) } } _ { \mathcal { L } _ { c } } + \underbrace { \left\| \frac { \mathbf { S } ^ { T } \mathbf { S } } { \| \mathbf { S } ^ { T } \mathbf { S } \| _ { F } } - \frac { \mathbf { I } _ { K } } { \sqrt { K } } \right\| _ { F } } _ { \mathcal { L } _ { o } } ,
+$$
+
+where $\| \cdot \| _ { F }$ indicates the Frobenius norm.
+
+The cut loss term, $\mathcal { L } _ { c }$ , evaluates the minCUT given by the cluster assignment S, and is bounded by $- 1 \leq \mathcal { L } _ { c } \leq 0$ . Minimizing $\mathcal { L } _ { c }$ encourages strongly connected nodes to be clustered together, since the inner product $\left. \mathbf { s } _ { i } , \mathbf { s } _ { j } \right.$ increases when $\tilde { a } _ { i , j }$ is large. $\mathcal { L } _ { c }$ has a single maximum, reached when the numerator $\begin{array} { r } { T r ( \mathbf { S } ^ { T } \tilde { \mathbf { A } } \mathbf { S } ) = \frac { 1 } { K } \sum _ { k = 1 } ^ { K } \mathbf { S } _ { k } ^ { T } \tilde { \mathbf { A } } \mathbf { S } _ { k } = 0 } \end{array}$ . This occurs if, for each pair of connected nodes (i.e., $\tilde { a } _ { i , j } > 0 \rangle$ ), the cluster assignments are orthogonal (i.e., $\langle \mathbf { s } _ { i } , \mathbf { s } _ { j } \rangle = 0 ,$ ). $\mathcal { L } _ { c }$ reaches its minimum, $- 1$ , when $T r ( \mathbf { S } ^ { T } \tilde { \mathbf { A } } \mathbf { S } ) = T r ( \mathbf { S } ^ { T } \tilde { \mathbf { D } } \mathbf { S } )$ . This occurs when in a graph with $K$ disconnected components the cluster assignments are equal for all the nodes in the same component and orthogonal to the cluster assignments of nodes in different components. However, $\mathcal { L } _ { c }$ is a non-convex function and its minimization can lead to local minima or degenerate solutions. For example, given a connected graph, a trivial optimal solution is the one that assigns all nodes to the same cluster. As a consequence of the continuous relaxation, another degenerate minimum occurs when the cluster assignments are all uniform, that is, all nodes are equally assigned to all clusters. This problem is exacerbated by prior message-passing operations, which make the node features more uniform.
+
+The orthogonality loss term, $\mathcal { L } _ { o }$ , penalizes the degenerate minima of $\mathcal { L } _ { c }$ by encouraging the cluster assignments to be orthogonal and the clusters to be of similar size. Since the two matrices in $\mathcal { L } _ { o }$ have unitary norm it is easy to see that $0 \leq \mathcal { L } _ { o } \leq 2$ . Therefore, $\mathcal { L } _ { o }$ does not dominate over $\mathcal { L } _ { c }$ and the two terms can be safely summed directly (see Fig. 4 for an example). ${ \mathbf { I } } _ { K }$ can be interpreted as a (rescaled) clustering matrix $\mathbf { I } _ { K } = \hat { \mathbf { S } } ^ { T } \hat { \mathbf { S } }$ , where $\hat { \bf S }$ assigns exactly $N / K$ points to each cluster. The value of the Frobenius norm between clustering matrices is not dominated by the performance on the largest clusters (Law et al., 2017) and, thus, can be used to optimize intra-cluster variance.
+
+Contrarily to SC methods that search for feasible solutions only within the space of orthogonal matrices, $\mathcal { L } _ { o }$ only introduces a soft constraint that could be violated during the learning procedure. Since $\mathcal { L } _ { c }$ is non-convex, the violation compromises the theoretical guarantee of convergence to the optimum of (3). However, we note that:
+
+1. the cluster assignments S are well initialized: after the MP operation, the features of the connected vertices become similar and, since the MLP is a smooth function (Nelles, 2013), it yields similar cluster assignments for those vertices;   
+2. in the GNN architecture, the minCUT objective is a regularization term and, therefore, a solution which is sub-optimal for (3) could instead be adequate for the specific objective of the downstream task;   
+3. optimizing the task-specific loss helps the GNN to avoid the degenerate minima of $\mathcal { L } _ { c }$ .
+
+# 3.1 COARSENING
+
+The coarsened version of the adjacency matrix and the graph signal are computed as
+
+$$
+{ \bf A } ^ { p o o l } = { \bf S } ^ { T } { \tilde { \bf A } } { \bf S } ; ~ { \bf X } ^ { p o o l } = { \bf S } ^ { T } { \bf X } ,
+$$
+
+where the entry xpooi,j in $\mathbf { X } ^ { p o o l } ~ \in ~ \mathbb { R } ^ { K \times F }$ is the weighted average value of feature $j$ among the elements in cluster $i$ . $\mathbf { A } ^ { p o o l } ~ \in ~ \mathbb { R } ^ { K \times K }$ is a symmetric matrix, whose entries $a _ { i , i } ^ { p o o l }$ are the total number of edges between the nodes in the cluster i, while apooi,j is the number of edges between cluster $i$ and $j$ . Since $\mathbf { A } ^ { p o o l }$ corresponds to the numerator of $\mathcal { L } _ { c }$ in (7), the trace maximization yields clusters with many internal connections and weakly connected to each other. Hence, $\mathbf { A } ^ { p o o l }$ will be a diagonal-dominant matrix, which describes a graph with self-loops much stronger than any other connection. Because self-loops hamper the propagation across adjacent nodes in the MP operations following the pooling layer, we compute the new adjacency matrix $\tilde { \mathbf { A } } ^ { p o o l }$ by zeroing the diagonal and by applying the degree normalization
+
+$$
+\hat { \bf A } = { \bf A } ^ { p o o l } - { \bf I } _ { K } d i a g ( { \bf A } ^ { p o o l } ) ; \quad \tilde { \bf A } ^ { p o o l } = \hat { \bf D } ^ { - \frac { 1 } { 2 } } \hat { \bf A } \hat { \bf D } ^ { - \frac { 1 } { 2 } } .
+$$
+
+where $d i a g ( \cdot )$ returns the matrix diagonal.
+
+# 3.2 DISCUSSION AND RELATIONSHIP WITH SPECTRAL CLUSTERING
+
+The proposed method is straightforward to implement: the cluster assignments, the loss, graph coarsening, and feature pooling are all computed with standard linear algebra operations.
+
+There are several differences between minCUTpool and classic SC methods. SC partitions the graph based on the Laplacian, but does not account for the node features. Instead, the cluster assignments $\mathbf { s } _ { i }$ found by minCUTpool depend on $\mathbf { x } _ { i }$ , which works well if connected nodes have similar features. This is a reasonable assumption in GNNs since, even in disassortative graphs (i.e., networks where dissimilar nodes are likely to be connected (Newman, 2003)), the features tend to become similar due to the MP operations.
+
+Another difference is that SC handles a single graph and is not conceived for tasks with multiple graphs to be partitioned independently. Instead, thanks to the independence of the model parameters from the number of nodes $N$ and from the graph spectrum, minCUTpool can generalize to outof-sample data. This feature is fundamental in problems such as graph classification, where each sample is a graph with a different structure, and allows to train the model on small graphs and process larger ones at inference time. Finally, minCUTpool directly uses the soft cluster assignments rather than performing $k$ -means afterwards.
+
+# 4 RELATED WORK ON POOLING IN GNNS
+
+Trainable pooling methods. Similarly to our method, these approaches learn how to generate coarsened version of the graph through differentiable functions, which take as input the nodes features $\mathbf { X }$ and are parametrized by weights optimized on the task at hand.
+
+Diffpool (Ying et al., 2018) is a pooling module that includes two parallel MP layers: one to compute the new node features $\mathbf { X } ^ { ( t + 1 ) }$ and another to generate the cluster assignments S. Diffpool implements an unsupervised loss that consists of two terms. First, the link prediction term $\| \mathbf { A } - \mathbf { S } \mathbf { \dot { S } } ^ { T } \| _ { F }$ minimizes the Frobenius norm of the difference between the adjacency and the Gram matrix of the cluster assignments, encouraging nearby nodes to be clustered together. The second term $\begin{array} { r } { \frac { 1 } { N } \sum _ { i = 1 } ^ { N } H ( \mathbf { S } _ { i } ) } \end{array}$ minimizes the entropy of the cluster assignments to make them alike to one-hot vectors. Like minCUTpool, Diffpool clusters the vertices of annotated graphs, but yields completely different partitions, since it computes differently the clustering assignments, the coarsened adjacency matrix and, most importantly, the unsupervised loss. In Diffpool, such a loss shows pathological behaviors that are discussed later in the experiments.
+
+The approach dubbed Top- $K$ pooling (Hongyang Gao, 2019; Lee et al., 2019), learns a projection vector that is applied to each node feature to obtain a score. The nodes with the $K$ highest scores are retained, the others are dropped. Since the top- $K$ selection is not differentiable, the scores are also used as a gate/attention for the node features, letting the projection vector to be trained with backpropagation. Top- $K$ is memory efficient as it avoids generating cluster assignments. To prevent A from becoming disconnected after nodes removal, Top- $K$ drops the rows and the columns from ${ \bf A } ^ { 2 }$ and uses it as the new adjacency matrix. However, computing ${ \bf A } ^ { 2 }$ costs $\mathcal { O } ( N ^ { 2 } )$ and it is inefficient to implement with sparse operations.
+
+Topological pooling methods. These methods pre-compute a pyramid of coarsened graphs, only taking into account the topology (A), but not the node features $\mathbf { \Pi } ( \mathbf { X } )$ . During training, the node features are pooled with standard procedures and are fit into these deterministic graph structures. These methods are less flexible, but provide a stronger bias that can prevent degenerate solutions (e.g., coarsened graphs collapsing in a single node).
+
+The approach proposed by Bruna et al. (2013), which has been adopted also in other GNN architectures (Defferrard et al., 2016; Fey et al., 2018), exploits GRACLUS (Dhillon et al., 2004), a hierarchical algorithm based on SC. At each pooling level $l$ , GRACLUS indetifies the pairs of maximally similar nodes $i _ { l }$ and $j _ { l }$ to be clustered together into a new vertex $k _ { ( l + 1 ) }$ . At inference phase, max-pooling is used to determine which node in the pair is kept. Fake vertices are added so that the number of nodes can be halved each time, but this injects noisy information in the graph.
+
+Node decimation is a method originally proposed in graph signal processing literature (Shuman et al., 2016), which as been adapted also for GNNs (Simonovsky & Komodakis, 2017). The nodes are partitioned in two sets, according to the signs of the Laplacian eigenvector associated to the largest eigenvalue. One of the two sets is dropped, reducing the number of nodes each time approximately by half. Kron reduction is used to compute a pyramid of coarsened Laplacians from the remaining nodes.
+
+A procedure proposed in Gama et al. (2018) diffuses a signal from designated nodes on the graph and stores the observed sequence of diffused components. The resulting stream of information is interpreted as a time signal, where standard CNN pooling is applied. We also mention a pooling operation for coarsening binary unweighted graphs by aggregating maximal cliques (Luzhnica et al., 2019). Nodes assigned to the same clique are summarized by max or average pooling and become a new node in the coarsened graph.
+
+# 5 EXPERIMENTS
+
+We consider both supervised and unsupervised tasks, and compare minCUTpool with other GNN pooling strategies. The Appendix provides further details on the experiments and a schematic depiction of the architectures used in each task. In addition, the Appendix reports two additional experiments: i) graph reconstruction by means of an Auto Encoder with bottleneck, implemented with pooling and un-pooling layers, ii) an architecture with pooling for graph regression.
+
+# 5.1 CLUSTERING THE GRAPH NODES
+
+To study the effectiveness of the proposed loss, we perform different node clustering tasks with a simple GNN composed of a single MP layer followed by a pooling layer. The GNN is trained by minimizing $\mathcal { L } _ { u }$ only, so that its effect is evaluated without the “interference” of a supervised loss.
+
+Clustering on synthetic networks We consider two simple graphs: the first is a network with 6 communities and the second is a regular grid. The adjacency matrix A is binary and the features X are the 2-D node coordinates. Fig. 2 depicts the node partitions generated by SC (a, d), Diffpool (b, e), and minCUTpool (c, f). Cluster indexes for Diffpool and minCUTpool are obtained by taking the argmax of S row-wise. Compared to SC, Diffpool and minCUTpool leverage the information contained in X. minCUTpool generates very accurate and balanced partitions, demonstrating that the cluster assignment matrix S is well formed. On the other hand, Diffpool assigns some nodes to the wrong community in the first example, and produces an imbalanced partition of the grid.
+
+![](images/f54a1747a2f3fb20dd6df85e294051b41f7c8f617ba05ec5ba321652a3688701.jpg)  
+Figure 2: Node clustering on a community network $K { = } 6 )$ and on a grid graph $( K { = } 5 )$
+
+Image segmentation Given an image, we build a Region Adjacency Graph (Tremeau & Colan- ´ toni, 2000) using as nodes the regions generated by an oversegmentation procedure (Felzenszwalb & Huttenlocher, 2004). The SC technique used in this example is the recursive normalized cut (Shi & Malik, 2000), which recursively clusters the nodes until convergence. For Diffpool and minCUTpool, we include node features consisting of the average and total color in each oversegmented region. We set the number of desired clusters to $K = 4$ . The results in Fig. 3 show that minCUTpool yields a more precise segmentation. On the other hand, SC and Diffpool aggregate wrong regions and, in addition, SC finds too many segments.
+
+Clustering on citation networks We cluster the nodes of three popular citation networks: Cora, Citeseer, and Pubmed. The nodes are documents represented by sparse bag-of-words feature vectors stored in $\mathbf { X }$ and the binary undirected edges in $\mathbf { A }$ indicate citation links between documents. Each node $i$ is labeled with the document class $y _ { i }$ . Once the training is over, to test the quality of the partitions generated by each method we check the agreement between the cluster assignments and the true class labels. Tab. 1 reports the Completeness Score $\begin{array} { r } { \mathrm { C S } ( \tilde { \bf y } , { \bf y } ) = 1 - \frac { H ( \tilde { \bf y } | { \bf y } ) } { H ( \tilde { \bf y } ) } } \end{array}$ and Normalized Mutual Information $\begin{array} { r } { \mathbf { N M I } ( \tilde { \mathbf { y } } , \mathbf { y } ) = \frac { H ( \tilde { \mathbf { y } } ) - H ( \tilde { \mathbf { y } } | \mathbf { y } ) } { \sqrt { H ( \tilde { \mathbf { y } } ) - H ( \mathbf { y } ) } } } \end{array}$ where $H ( \cdot )$ is the entropy.
+
+The GNN architecture configured with minCUTpool achieves a higher NMI score than SC, which does not account for the node features $\mathbf { X }$ when generating the partitions. Our pooling operation outperforms also Diffpool, since the minimization of the unsupervised loss in Diffpool yields degenerate solutions. The pathological behavior is shown in Fig. 4, which depicts the evolution of the NMI scores as the unsupervised losses in Diffpool and minCUTpool are minimized in training.
+
+![](images/81a3f7ffc1776e74fbc56b414ab1c318578c5dc39e05ac6ea084422888017b44.jpg)  
+Figure 3: Image segmentation by clustering the nodes of the Region Adjacency Graph.
+
+![](images/4067d319802597da0f8a99d17f9a05ae75ef1d9974bd1b46567b315150d067c6.jpg)  
+Figure 4: Unsupervised losses and NMI of Diffpool and minCUTpool on Cora.
+
+Table 1: NMI and CS obtained by clustering the nodes on citation networks over 10 different runs. The number of clusters $K$ is equal to the number of node classes.   
+
+<table><tr><td>Dataset</td><td>K</td><td colspan="2">Spectral clustering</td><td colspan="2">Diffpool</td><td colspan="2">minCUTpool</td></tr><tr><td></td><td></td><td>NMI</td><td>cs</td><td>NMI</td><td>CS</td><td>NMI</td><td>CS</td></tr><tr><td>Cora</td><td>7</td><td>0.025 ± 0.014</td><td>0.126 ± 0.042</td><td>0.315 ± 0.005</td><td>0.309 ±0.005</td><td>0.404 ± 0.018</td><td>0.392 ± 0.018</td></tr><tr><td>Citeseer</td><td>6</td><td>0.014 ± 0.003</td><td>0.033 ±0.000</td><td>0.139 ± 0.016</td><td>0.153 ± 0.020</td><td>0.287 ±0.047</td><td>0.283 ± 0.046</td></tr><tr><td>Pubmed</td><td>3</td><td>0.182 ± 0.000</td><td>0.261 ± 0.000</td><td>0.079 ±0.001</td><td>0.085 ±0.001</td><td>0.200 ± 0.020</td><td>0.197 ± 0.019</td></tr></table>
+
+# 5.2 SUPERVISED GRAPH CLASSIFICATION
+
+In this task, the $i$ -th datum is a graph with $N _ { i }$ nodes represented by a pair $\{ \mathbf { A } _ { i } , \mathbf { X } _ { i } \}$ and must be associated to the correct label $\mathbf { y } _ { i }$ . We test the models on different graph classification datasets. For featureless graphs, we used the node degree information and the clustering coefficient as surrogate node features. We evaluate model performance with a 10-fold train/test split, using $1 0 \%$ of the training set in each fold as validation for early stopping. We adopt a fixed network architecture, MP(32)-poolMP(32)-pool-MP(32)-GlobalAvgPool-softmax, where MP is the message-passing operation in (4)
+
+with 32 hidden units. The pooling module is implemented either by Graclus, Decimation pooling, Top- $K$ , SAGPool (Lee et al., 2019), Diffpool, or the proposed minCUTpool. Each pooling method is configured to drop half of the nodes in a graph $K = N / 2$ in Top- $K$ , Diffpool, and minCUTpool). As baselines, we consider the popular Weisfeiler-Lehman (WL) graph kernel (Shervashidze et al., 2011), a network with only MP layers (Flat), and a fully connected network (Dense).
+
+Table 2: Graph classification accuracy. Significantly better results $( p < 0 . 0 5 )$ are in bold.   
+
+<table><tr><td>Dataset</td><td>WL</td><td>Dense</td><td>Flat</td><td>Graclus</td><td>Decim.</td><td>Diffpool</td><td>Top-K</td><td>SAGpool</td><td>minCUT</td></tr><tr><td>Bench-easy</td><td>92.6</td><td>29.3±0.3</td><td>98.5±0.3</td><td>97.5±0.5</td><td>97.9±0.5</td><td>98.6±0.4</td><td>82.4±8.9</td><td>84.2±2.3</td><td>99.0±0.0</td></tr><tr><td>Bench-hard</td><td>60.0</td><td>29.4±0.3</td><td>67.6±2.8</td><td>69.0±1.5</td><td>72.6±0.9</td><td>69.9±1.9</td><td>42.7±15.2</td><td>37.7±14.5</td><td>73.8±1.9</td></tr><tr><td>Mutagenicity</td><td>81.7±1.1</td><td>68.4±0.3</td><td>78.0±1.3</td><td>74.4±1.8</td><td>77.8±2.3</td><td>77.6±2.7</td><td>71.9±3.7</td><td>72.4±2.4</td><td>79.9±2.1</td></tr><tr><td>Proteins</td><td>71.2±2.6</td><td>68.7±3.3</td><td>72.6±4.8</td><td>68.6±4.6</td><td>73.3±3.7</td><td>72.7±3.8</td><td>69.6±3.5</td><td>70.5±2.6</td><td>76.5±2.6</td></tr><tr><td>DD</td><td>78.6±2.7</td><td>70.6±5.2</td><td>76.8±1.5</td><td>70.5±4.8</td><td>72.0±3.1</td><td>79.3±2.4</td><td>69.4±7.8</td><td>71.5±4.5</td><td>80.8±2.3</td></tr><tr><td>COLLAB</td><td>74.8±1.3</td><td>79.3±1.6</td><td>82.1±1.8</td><td>77.1±2.1</td><td>79.1±1.5</td><td>81.8±1.4</td><td>79.3±1.8</td><td>79.2±2.0</td><td>83.4±1.7</td></tr><tr><td>Reddit-Binary</td><td>68.2±1.7</td><td>48.5±2.6</td><td>80.3±2.6</td><td>79.2±0.4</td><td>84.3±2.4</td><td>86.8±2.1</td><td>74.7±4.5</td><td>73.9±5.1</td><td>91.4±1.5</td></tr></table>
+
+Tab. 2 reports the classification results, highlighting those that are significantly better ( $\dot { p }$ -value $< ~ 0 . 0 5$ w.r.t. the method with the highest mean accuracy). The comparison with Flat helps to understand if a pooling operation is useful or not. The results of Dense, instead, help to quantify how much additional information is brought by the graph structure, with respect to the node features alone. It can be seen that minCUTpool obtains always equal or better results with respect to every other GNN architecture. On the other hand, some pooling procedures do not always improve the performance compared to the Flat baseline, making them not advisable to use in some cases. The WL kernel generally performs worse than the GNNs, except for the Mutagenicity dataset. This is probably because Mutagenicity has smaller graphs than the other datasets, and the adopted GNN architecture is overparametrized for this task. Interestingly, in some dataset such as Proteins and COLLAB it is possible to obtain fairly good classification accuracy with the Dense architecture, meaning that the graph structure only adds limited information.
+
+![](images/e375310d148f5976514d2295a7d3c8830c48da3e0966c6040f4a07d9c8821927.jpg)  
+Figure 5: Average duration of one epoch using the same GNN with different pooling operations. Times were computed with an Nvidia GeForce GTX 1050, on the DD dataset with batch size of 1.
+
+Fig. 5 reports a comparison of the execution time per training epoch for each pooling algorithm. Graclus and Decimation are understandably the fastest methods, since the coarsened graphs are precomputed. Among the differentiable pooling methods, minCUTpool is faster than Diffpool, which uses a slower MP layer rather than a MLP to compute cluster assignments, and than Top- $K$ , which computes the square of A at every forward pass.
+
+# 6 CONCLUSIONS
+
+We proposed a pooling layer for GNNs that coarsens a graph by taking into account both the the connectivity structure and the node features. The layer optimizes a regularization term based on the minCUT objective, which is minimized in conjunction with the task-specific loss to produce node partitions that are optimal for the task at hand.
+
+We tested the effectiveness of our pooling strategy on unsupervised node clustering tasks, by optimizing only the unsupervised clustering loss, as well as supervised graph classification tasks on several popular benchmark datasets. Results show that minCUTpool performs significantly better than existing pooling strategies for GNNs.
+
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+David I Shuman, Mohammad Javad Faraji, and Pierre Vandergheynst. A multiscale pyramid transform for graph signals. IEEE Transactions on Signal Processing, 64(8):2119–2134, 2016.
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+Martin Simonovsky and Nikos Komodakis. Dynamic edgeconditioned filters in convolutional neural networks on graphs. In Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, 2017.
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+
+Yu and Shi. Multiclass spectral clustering. In Proceedings Ninth IEEE International Conference on Computer Vision, pp. 313–319 vol.1, Oct 2003.
+
+# APPENDIX
+
+A ADDITIONAL EXPERIMENTS
+
+# A.1 GNN AUTOENCODER
+
+To compare the amount of information retained by the pooling layers in the coarsened graphs, we train an autoencoder (AE) to reconstruct a input graph signal $\mathbf { X }$ from its pooled version. The AE architecture is MP(32)-MP(32)-pool-unpool-MP(32)-MP(32)-MP, and is trained by minimizing the mean squared error between the original and the reconstructed graph signal, $\lVert \bf { X } - \bf { X } ^ { \mathrm { { r e c } } } \rVert ^ { 2 }$ . All the pooling operations are configured to retain $2 5 \%$ of the original nodes.
+
+In Diffpool and minCUTpool, the unpool step is simply implemented by transposing the original pooling operations
+
+$$
+{ \bf X } ^ { \mathrm { r e c } } = { \bf S } { \bf X } ^ { \mathrm { p o o l } } ; ~ { \bf A } ^ { \mathrm { r e c } } = { \bf S } { \bf A } ^ { \mathrm { p o o l } } { \bf S } ^ { T } .
+$$
+
+Top- $K$ does not generate a cluster assignment matrix, but returns a binary mask $\mathbf { m } = \{ 0 , 1 \} ^ { N }$ that indicates the nodes to drop (0) or to retain (1). Therefore, an upsamplig matrix $\mathbf { U }$ is built by dropping the columns of the identity matrix ${ \mathbf { I } } _ { N }$ that correspond to a 0 in $\mathbf { m }$ , $\bar { \mathbf { U } } = [ \mathbf { I } _ { N } ] _ { : , \mathbf { m } = = 1 }$ . The unpooling operation is performed by replacing S with $\mathbf { U }$ in (9), and the resulting upscaled graph is a version of the original graph with zeroes in correspondence of the dropped nodes.
+
+![](images/441bd5ff28bf0dbad772497856fe6d0256f85ad6ae1cfa337d7be79956b30a09.jpg)  
+Figure 6: AE reconstruction of a ring graph
+
+![](images/4b22636cf4edd79e814a6d27c3e71aeabc0f8293196e377e997385878fcd0602.jpg)  
+Figure 7: AE reconstruction of a grid graph
+
+Fig. 6 and 7 report the original graph signal $\mathbf { X }$ (the node features are the 2-D coordinates of the nodes) and the reconstruction $\mathbf { X } ^ { \mathrm { r e c } }$ obtained by using the different pooling methods, for a ring graph and a regular grid graph. The reconstruction produced by Diffpool is worse for the ring graph, but is almost perfect for the grid graph, while minCUTpool yields good results in both cases. On the other hand, Top- $K$ clearly fails in generating a coarsened representation that maintains enough information from the original graph.
+
+This experiment highlights a major issue in Top- $K$ pooling, which retains the nodes associated to the highest $K$ values of a score vector s, computed by projecting the node features onto a trainable vector p: $\mathbf { s } = \mathbf { X } \mathbf { p } $ . Nodes that are connected on the graph usually share similar features, and their similarity further increases after the MP operations, which combine the features of neighboring nodes. Retaining the nodes associated to the top $K$ scores in s corresponds to keeping those nodes that are alike and highly connected, as it can be seen in Fig. 6-7. Therefore, Top- $K$ discards entire portions of the graphs, which might contain important information. This explains why Top- $K$ fails to recover the original graph signal when used as bottleneck for the AE, and yields the worse performance among all GNN methods in the graph classification task.
+
+# A.2 GRAPH REGRESSION OF MOLECULAR PROPERTIES ON QM9
+
+The QM9 chemical database is a collection of ${ \approx } 1 3 5 \mathrm { k }$ small organic molecules, associated to continuous labels describing several geometric, energetic, electronic, and thermodynamic properties1. Each molecule in the dataset is represented as a graph $\{ \mathbf { A } _ { i } , \mathbf { X } _ { i } \}$ , where atoms are associated to nodes, and edges represent chemical bonds. The atomic number of each atom (one-hot encoded; C, N, F, O) is taken as node feature and the type of bond (one-hot encoded; single, double, triple, aromatic) can be used as edge attribute. In this experiment, we ignore the edge attributes in order to use all pooling algorithms without modifications.
+
+The purpose of this experiment is to compare the trainable pooling methods also on a graph regression task, but it must be intended as a proof of concept. In fact, the graphs in this dataset are extremely small (the average number of nodes is 8) and, therefore, a pooling operation is arguably not necessary. We consider a GNN with architecture MP(32)-pool-MP(32)-GlobalAvgPool-Dense, where pool is implemented by Top- $K$ , Diffpool, or minCUTpool. The network is trained to predict a given chemical property from the input molecular graphs. Performance is evaluated with a 10-fold cross-validation, using $1 \dot { 0 } \%$ of the training set for validation in each split. The GNNs are trained for 50 epochs, using Adam with learning rate 5e-4, batch size 32, and ReLU activations. We use the mean squared error (MSE) as supervised loss.
+
+The MSE obtained on the prediction of each property for different pooling methods is reported in Tab. 3. As expected, the flat baseline with no pooling operation (MP(32)-MP(32)-GlobalAvgPoolDense) yields a lower error in most cases. Contrarily to the graph classification and the AE task, Top- $K$ achieves better results than Diffpool in average. Once again, minCUTpool significantly outperforms the other methods on each regression task and, in one case, also the flat baseline.
+
+<table><tr><td>Property</td><td>Top-K</td><td>Diffpool</td><td>minCUTpool</td><td>Flat baseline</td></tr><tr><td>mu</td><td>0.600±0.085</td><td>0.651±0.026</td><td>0.538±0.012</td><td>0.559±0.007</td></tr><tr><td>alpha</td><td>0.197±0.087</td><td>0.114±0.001</td><td>0.078±0.007</td><td>0.065±0.006</td></tr><tr><td>homo</td><td>0.698±0.102</td><td>0.712±0.015</td><td>0.526±0.021</td><td>0.435±0.013</td></tr><tr><td>lumo</td><td>0.601±0.050</td><td>0.646±0.013</td><td>0.540±0.005</td><td>0.515±0.007</td></tr><tr><td>gap</td><td>0.630±0.044</td><td>0.698±0.004</td><td>0.584±0.007</td><td>0.552±0.008</td></tr><tr><td>r2</td><td>0.452±0.087</td><td>0.440±0.024</td><td>0.261±0.006</td><td>0.204±0.006</td></tr><tr><td>zpve</td><td>0.402±0.032</td><td>0.410±0.004</td><td>0.328±0.005</td><td>0.284±0.005</td></tr><tr><td>uO_atom</td><td>0.308±0.055</td><td>0.245±0.006</td><td>0.193±0.002</td><td>0.163±0.001</td></tr><tr><td>cv</td><td>0.291±0.118</td><td>0.337±0.018</td><td>0.148±0.004</td><td>0.127±0.002</td></tr></table>
+
+Table 3: MSE on the graph regression task. The best results with a statistical significance of $p < 0 . 0 5$ are highlighted: the best overall are in bold, the best among pooling methods are underlined.
+
+# B EXPERIMENTAL DETAILS
+
+For the WL kernel, we used the implementation provided in the GraKeL library2. The pooling strategy based on Graclus, is taken from the ChebyNets repository3.
+
+# B.1 CLUSTERING ON CITATION NETWORKS
+
+Diffpool and minCUTpool are configured with 16 hidden neurons with linear activations in the MLP and MP layer, respectively used to compute the cluster assignment matrix S. The MP layer used to compute the propagated node features $\mathbf { X } ^ { ( 1 ) }$ uses an ELU activation in both architectures. The learning rate for Adam is 5e-4, and the models are trained for 10000 iterations. The details of the citation networks dataset are reported in Tab. 4.
+
+Table 4: Details of the citation networks datasets   
+
+<table><tr><td>Dataset</td><td>Nodes</td><td>Edges</td><td>Node features</td><td>Node classes</td></tr><tr><td>Cora</td><td>2708</td><td>5429</td><td>1433</td><td>7</td></tr><tr><td>Citeseer</td><td>3327</td><td>9228</td><td>3703</td><td>6</td></tr><tr><td>Pubmed</td><td>19717</td><td>88651</td><td>500</td><td>3</td></tr></table>
+
+# B.2 GRAPH CLASSIFICATION
+
+We train the GNN architectures with Adam, an $\mathrm { L } _ { 2 }$ penalty loss with weight 1e-4, and 16 hidden units $( H )$ both in the MLP of minCUTpool and in the internal MP of Diffpool. Mutagenicity, Proteins, DD, COLLAB, and Reddit- ${ \it 2 k }$ are datasets representing real-world graphs and are taken from the repository of benchmark datasets for graph kernels4. Bench-easy and Bench-hard5 are datasets where the node features $\mathbf { X }$ and the adjacency matrix A are completely uninformative if considered alone. Hence, algorithms that account only for the node features or the graph structure will fail to classify the graphs. Since Bench-easy and Bench-hard come with a train/validation/test split, the 10-fold split is not necessary to evaluate the performance. The statistics of all the datasets are reported in Tab. 5.
+
+Table 5: Summary of statistics of the graph classification datasets   
+
+<table><tr><td>Dataset</td><td>samples</td><td>classes</td><td>avg. nodes</td><td>avg. edges</td><td>node attr.</td><td>node labels</td></tr><tr><td>Bench-easy</td><td>1800</td><td>3</td><td>147.82</td><td>922.66</td><td></td><td>yes</td></tr><tr><td>Bench-hard</td><td>1800</td><td>3</td><td>148.32</td><td>572.32</td><td></td><td>yes</td></tr><tr><td>Mutagenicity</td><td>4337</td><td>2</td><td>30.32</td><td>30.77</td><td></td><td>yes</td></tr><tr><td>Proteins</td><td>1113</td><td>2</td><td>39.06</td><td>72.82</td><td>1</td><td>no</td></tr><tr><td>DD</td><td>1178</td><td>2</td><td>284.32</td><td>715.66</td><td>1</td><td>yes</td></tr><tr><td>COLLAB</td><td>5000</td><td>3</td><td>74.49</td><td>2457.78</td><td></td><td>no</td></tr><tr><td>Reddit-2K</td><td>2000</td><td>2</td><td>429.63</td><td>497.75</td><td>1</td><td>no</td></tr></table>
+
+# C ARCHITECTURES SCHEMATA
+
+Fig. 8 reports the schematic representation of the minCUTpool layer; Fig. 9 the GNN architecture used in the clustering and segmentation tasks; Fig. 10 the GNN architecture used in the graph classification task; Fig. 12 the GNN architecture used in the graph regression task; Fig. 11 the graph autoencoder used in the graph signal reconstruction task.
+
+![](images/d9ade9085ab54361a1aa6626d8499f13441a1f331f8a266df6a2b0894a69a6db.jpg)  
+Figure 8: Schema of the minCUTpool layer.
+
+![](images/d710cb546df4f56d39a534e37d809d53060d1d9bc2b6ee1c45fe2367b58e3ef9.jpg)  
+Figure 9: Architecture for clustering/segmentation.
+
+![](images/da255a17d1270f108c2393a35c6f5725d6c431af5f91c472b5369ec2db9913d6.jpg)  
+Figure 10: Architecture for graph classification.
+
+![](images/969e11240083f473509da7280d39c4b88009ae72ad1c88f632f5a4207bc0742d.jpg)  
+Figure 11: Architecture for the autoencoder.
+
+![](images/031a97e555c2460b138d4ed99d26909b098af1b3775c29da264c3560104df77d.jpg)  
+Figure 12: Architecture for graph regression.

parse/train/BkxfshNYwB/BkxfshNYwB_content_list.json

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+[
+    {
+        "type": "text",
+        "text": "MINCUT POOLING IN GRAPH NEURAL NETWORKS ",
+        "text_level": 1,
+        "bbox": [
+            176,
+            98,
+            782,
+            121
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "Anonymous authors Paper under double-blind review ",
+        "bbox": [
+            183,
+            145,
+            398,
+            172
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "ABSTRACT ",
+        "text_level": 1,
+        "bbox": [
+            454,
+            210,
+            544,
+            226
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "The advance of node pooling operations in Graph Neural Networks (GNNs) has lagged behind the feverish design of new message-passing techniques, and pooling remains an important and challenging endeavor for the design of deep architectures. In this paper, we propose a pooling operation for GNNs that leverages a differentiable unsupervised loss based on the minCUT optimization objective. For each node, our method learns a soft cluster assignment vector that depends on the node features, the target inference task (e.g., a graph classification loss), and, thanks to the minCUT objective, also on the connectivity structure of the graph. Graph pooling is obtained by applying the matrix of assignment vectors to the adjacency matrix and the node features. The proposed method can also be used as a stand-alone module to cluster vertexes in annotated graphs and solve unsupervised problems. We validate the effectiveness of the proposed pooling method on downstream tasks, including supervised graph classification and a set of unsupervised tasks, which reveal the limitations of existing GNN pooling approaches. ",
+        "bbox": [
+            233,
+            242,
+            764,
+            436
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "1 INTRODUCTION ",
+        "text_level": 1,
+        "bbox": [
+            176,
+            467,
+            334,
+            482
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "A fundamental component in deep convolutional neural networks is the pooling operation, which replaces the output of convolutions with local summaries of nearby points and is usually implemented by maximum or average operations (Lee et al., 2016). State-of-the-art architectures alternate convolutions, which extrapolate local patterns irrespective of the specific location on the input signal, and pooling, which lets the ensuing convolutions capture aggregated patterns. Pooling allows to learn abstract representations in deeper layers of the network by discarding information that is superfluous for the task, and keeps model complexity under control by limiting the growth of intermediate features. ",
+        "bbox": [
+            174,
+            498,
+            825,
+            609
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "Graph Neural Networks (GNNs) extend the convolution operation from regular domains, such as images or time series, to data with arbitrary topologies and unordered structures described by graphs (Battaglia et al., 2018). The development of pooling strategies for GNNs, however, has lagged behind the design of newer and more effective message-passing (MP) operations (Gilmer et al., 2017), such as graph convolutions, mainly due to the difficulty of defining an aggregated version of the original graph that supports the pooled signal. ",
+        "bbox": [
+            174,
+            617,
+            825,
+            702
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "A na¨ıve pooling strategy in GNNs is to average all nodes features (Li et al., 2016), but it has limited flexibility since it does not extract local summaries of the graph structure, and no further MP operations can be applied afterwards. An alternative approach consists in pre-computing coarsened versions of the original graph and then fit the data to these deterministic structures (Bruna et al., 2013). While this aggregation accounts for the connectivity of the graph, it ignores task-specific objectives as well as the node features. ",
+        "bbox": [
+            174,
+            708,
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+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "In this paper, we propose a differentiable pooling operation implemented as a neural network layer, which can be seamlessly combined with other MP layers (see Fig. 1). The parameters in the pooling layer are learned by combining the task-specific loss with an unsupervised regularization term, which optimizes a continuous relaxation of the normalized minCUT objective. The minCUT identifies dense graph components, where the nodes features become locally homogeneous after the message-passing. By gradually aggregating these components, the GNN learns to distil global properties from the graph. The proposed minCUT pooling operator (minCUTpool) yields partitions that 1) cluster together nodes which have similar features and are strongly connected on the graph, and 2) take into account the objective of the downstream task. ",
+        "bbox": [
+            174,
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+        "page_idx": 0
+    },
+    {
+        "type": "image",
+        "img_path": "images/2f1bdb5271287007bfb404fabc54a4bd48a828a415e925e71e65dd38e08b6950.jpg",
+        "image_caption": [
+            "Figure 1: A deep GNN architecture where message-passing is followed by minCUT pooling. "
+        ],
+        "image_footnote": [],
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "2 BACKGROUND ",
+        "text_level": 1,
+        "bbox": [
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+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "2.1 MINCUT AND SPECTRAL CLUSTERING ",
+        "text_level": 1,
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "Given a graph $G = \\{ \\nu , \\mathcal { E } \\}$ , $| \\nu | = N$ , and the associated adjacency matrix $\\mathbf { A } \\in \\mathbb { R } ^ { N \\times N }$ , the $K$ -way normalized minCUT (simply referred to as minCUT) aims at partitioning $\\nu$ in $K$ disjoint subsets by removing the minimum volume of edges. The problem is equivalent to maximizing ",
+        "bbox": [
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+    },
+    {
+        "type": "equation",
+        "img_path": "images/bed538315cdc4b11b03e72a1f8508838e1bc29db0005bb3d50c0b887200c4dfa.jpg",
+        "text": "$$\n\\frac { 1 } { K } \\sum _ { k = 1 } ^ { K } \\frac { \\operatorname* { l i n k s } ( \\mathcal { V } _ { k } ) } { \\deg \\mathrm { r e e } ( \\mathcal { V } _ { k } ) } = \\frac { 1 } { K } \\sum _ { k = 1 } ^ { K } \\frac { \\sum _ { i , j \\in \\mathcal { V } _ { k } } \\mathcal { E } _ { i , j } } { \\sum _ { i \\in \\mathcal { V } _ { k } , j \\in \\mathcal { V } \\backslash \\mathcal { V } _ { k } } \\mathcal { E } _ { i , j } } ,\n$$",
+        "text_format": "latex",
+        "bbox": [
+            333,
+            411,
+            665,
+            455
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+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "where the numerator counts the edge volume within each cluster, and the denominator counts the edges between the nodes in a cluster and the rest of the graph (Shi & Malik, 2000). Let $\\mathbf { C } \\in \\mathbb { R } ^ { N \\times K }$ be a cluster assignment matrix, so that $\\mathbf { C } _ { i , j } = 1$ if node $i$ belongs to cluster $j$ , and 0 otherwise. The minCUT problem can be expressed as ",
+        "bbox": [
+            174,
+            460,
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+        "page_idx": 1
+    },
+    {
+        "type": "equation",
+        "img_path": "images/1bc8a238d93fae41b9a6b3f91c0e932f6d25110d313c304a11065a033efcef83.jpg",
+        "text": "$$\n\\mathrm { m a x i m i z e } \\frac { 1 } { K } \\sum _ { k = 1 } ^ { K } \\frac { { \\bf C } _ { k } ^ { T } { \\bf A } { \\bf C } _ { k } } { { \\bf C } _ { k } ^ { T } { \\bf D } { \\bf C } _ { k } } , \\mathrm { s . t . } { \\bf C } \\in \\{ 0 , 1 \\} ^ { N \\times K } , { \\bf C } { \\bf 1 } _ { K } = { \\bf 1 } _ { N } ,\n$$",
+        "text_format": "latex",
+        "bbox": [
+            274,
+            523,
+            722,
+            568
+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "where $\\mathbf { D } = \\mathrm { d i a g } ( \\mathbf { A } \\mathbf { 1 } _ { N } )$ is the degree matrix (Dhillon et al., 2004). Since problem (2) is NP-hard, it is usually recast in a relaxed formulation that can be solved in polynomial time and guarantees a near-optimal solution (Yu & Shi, 2003): ",
+        "bbox": [
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+        "page_idx": 1
+    },
+    {
+        "type": "equation",
+        "img_path": "images/8b4a96c5fa8a262b25a42766484b99a8cfede951176181e475f73ecda54a5854.jpg",
+        "text": "$$\n\\arg \\operatorname* { m a x } _ { \\mathbf { Q } \\in \\mathbb { R } ^ { N \\times K } } \\frac { 1 } { K } \\sum _ { k = 1 } ^ { K } \\mathbf { Q } _ { k } ^ { T } \\mathbf { A } \\mathbf { Q } _ { k } , \\quad \\mathrm { s . t . } \\mathbf { Q } = \\mathbf { C } ( \\mathbf { C } ^ { T } \\mathbf { D } \\mathbf { C } ) ^ { - \\frac { 1 } { 2 } } , \\ \\mathbf { Q } ^ { T } \\mathbf { Q } = \\mathbf { I } _ { K } .\n$$",
+        "text_format": "latex",
+        "bbox": [
+            269,
+            623,
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+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "While the optimization problem (3) is still non-convex, there exists an optimal solution $\\mathbf { Q } ^ { * } = \\mathbf { U } _ { K } \\mathbf { O }$ , where ${ \\bf U } _ { K } \\dot { } \\in \\mathbb { R } ^ { N \\times K }$ contains the eigenvectors of A corresponding to the $K$ largest eigenvalues, and $\\mathbf { O } \\in \\mathbb { R } ^ { K \\times K }$ is an orthogonal transformation (Ikebe et al., 1987). ",
+        "bbox": [
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+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "Since the elements of $\\mathbf { Q } ^ { * }$ are real values rather than binary cluster indicators, the spectral clustering (SC) approach can be used to find discrete cluster assignments. In SC, the rows of $\\mathbf { Q } ^ { * }$ are treated as node representations embedded in the eigenspace of the Laplacian, and are clustered together with standard algorithms such as $k$ -means (Von Luxburg, 2007). One of the main limitations of SC lies in the computation of the spectrum of A, which has a memory complexity of $\\mathcal { O } ( N ^ { 2 } )$ and a computational complexity of $\\mathcal { O } ( \\bar { N } ^ { 3 } )$ . This prevents its applicability to large datasets. ",
+        "bbox": [
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+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "To deal with such scalability issues, the constrained optimization in (3) can be solved by gradient descent algorithms that refine the solution by iterating operations whose individual complexity is $\\mathcal { O } ( N ^ { 2 } )$ , or even $\\mathcal { O } ( N )$ (Han & Filippone, 2017). Those algorithms search the solution on the manifold induced by the orthogonality constraint on the columns of $\\mathbf { Q }$ , by performing gradient updates along the geodesics (Wen & Yin, 2013; Collins et al., 2014). Alternative approaches rely on the QR factorization to constrain the space of feasible solutions (Damle et al., 2016), and alleviate the cost $\\mathcal { O } ( N ^ { 3 } )$ of the factorization by ensuring that orthogonality holds only on one minibatch at a time (Shaham et al., 2018). ",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "Other works based on neural networks include an autoencoder trained to map the $i$ th row of the Laplacian to the ith components of the first $K$ eigenvectors, to avoid the spectral decomposition (Tian et al., 2014). Yi et al. (2017) use a soft orthogonality constraint to learn spectral embeddings as a volumetric reparametrization of a precomputed Laplacian eigenbase. Shaham et al. (2018); Kampffmeyer et al. (2019) propose differentiable loss functions to partition generic data and process out-of-sample data at inference time. Nazi et al. (2019) generate balanced node partitions with a GNN, but adopt an optimization that does not encourage cluster assignments to be orthogonal. ",
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "2.2 GRAPH NEURAL NETWORKS ",
+        "text_level": 1,
+        "bbox": [
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+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "Many approaches have been proposed to process graphs with neural networks, including recurrent architectures (Scarselli et al., 2009; Li et al., 2016) or convolutional operations inspired by filters used in graph signal processing (Defferrard et al., 2016; Bianchi et al., 2019). Since our focus is on graph pooling, we base our GNN implementation on a simple MP operation, which combines the features of each node with its 1st-order neighbors. To account for the initial node features, it is possible to introduce self-loops by adding a (scaled) identity matrix to the diagonal of A (Kipf & Welling, 2017). Since our pooling will modify the structure of the adjacency matrix, we prefer a MP implementation that leaves the original A unaltered and accounts for the initial node features by means of skip connections. ",
+        "bbox": [
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+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "Let $\\tilde { \\mathbf { A } } = \\mathbf { D } ^ { - \\frac { 1 } { 2 } } \\mathbf { A } \\mathbf { D } ^ { - \\frac { 1 } { 2 } } \\in \\mathbb { R } ^ { N \\times N }$ be the symmetrically normalized adjacency matrix and $\\mathbf { X } \\in \\mathbb { R } ^ { N \\times F }$ the matrix containing the node features. The output of the MP layer is ",
+        "bbox": [
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+            378,
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+        "page_idx": 2
+    },
+    {
+        "type": "equation",
+        "img_path": "images/34c777764a42e47800439e8acb679c0fc313d00d93b57909084dfaca360baee8.jpg",
+        "text": "$$\n\\mathbf { X } ^ { ( t + 1 ) } = M P ( \\mathbf { X } ^ { ( t ) } , \\tilde { \\mathbf { A } } ) = \\operatorname { R e L U } ( \\tilde { \\mathbf { A } } \\mathbf { X } ^ { ( t ) } \\mathbf { W } _ { m } + \\mathbf { X } ^ { ( t ) } \\mathbf { W } _ { s } ) ,\n$$",
+        "text_format": "latex",
+        "bbox": [
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+            416,
+            696,
+            436
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "where $\\boldsymbol { \\Theta } _ { M P } = \\{ \\mathbf { W } _ { m } , \\mathbf { W } _ { s } \\}$ are the trainable weights relative to the mixing and skip component of the layer, respectively. ",
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "3 PROPOSED METHOD ",
+        "text_level": 1,
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "The minCUT pooling strategy computes a cluster assignment matrix $\\mathbf { S } \\in \\mathbb { R } ^ { N \\times K }$ by means of a multi-layer perceptron, which maps each node feature $\\mathbf { x } _ { i }$ into the ith row of S: ",
+        "bbox": [
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+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "equation",
+        "img_path": "images/eb9b8566cc8d18dce23ac90d2d6d28532fcd23484c72c59fadfa52de34d9d2e9.jpg",
+        "text": "$$\n\\begin{array} { r } { \\mathbf { S } = s o f t m a x ( \\mathbf { R e L U } ( \\mathbf { X } \\mathbf { W } _ { 1 } ) \\mathbf { W } _ { 2 } ) , } \\end{array}\n$$",
+        "text_format": "latex",
+        "bbox": [
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+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "where $\\boldsymbol { \\Theta } _ { P o o l } = \\{ \\mathbf { W } _ { 1 } \\in \\mathbb { R } ^ { F \\times H } , \\mathbf { W } _ { 2 } \\in \\mathbb { R } ^ { H \\times K } \\}$ are trainable parameters. The softmax function guarantees that $s _ { i , j } \\in [ 0 , 1 ]$ and enforces the constraints $\\mathbf { S 1 } _ { K } = \\mathbf { 1 } _ { N }$ inherited from the optimization problem in (2). The parameters $\\Theta _ { M P }$ and $\\Theta _ { P o o l }$ are jointly optimized by minimizing the usual task-specific loss, as well as an unsupervised loss $\\mathcal { L } _ { u }$ , which is composed of two terms ",
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "equation",
+        "img_path": "images/093c5d20482e4733720500e265f3b4b47793157e111ce4ec091ed8c0b6c46652.jpg",
+        "text": "$$\n\\mathcal { L } _ { u } = \\mathcal { L } _ { c } + \\mathcal { L } _ { o } = \\underbrace { - \\frac { T r ( \\mathbf { S } ^ { T } \\tilde { \\mathbf { A } } \\mathbf { S } ) } { T r ( \\mathbf { S } ^ { T } \\tilde { \\mathbf { D } } \\mathbf { S } ) } } _ { \\mathcal { L } _ { c } } + \\underbrace { \\left\\| \\frac { \\mathbf { S } ^ { T } \\mathbf { S } } { \\| \\mathbf { S } ^ { T } \\mathbf { S } \\| _ { F } } - \\frac { \\mathbf { I } _ { K } } { \\sqrt { K } } \\right\\| _ { F } } _ { \\mathcal { L } _ { o } } ,\n$$",
+        "text_format": "latex",
+        "bbox": [
+            305,
+            651,
+            689,
+            708
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "where $\\| \\cdot \\| _ { F }$ indicates the Frobenius norm. ",
+        "bbox": [
+            174,
+            715,
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+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "The cut loss term, $\\mathcal { L } _ { c }$ , evaluates the minCUT given by the cluster assignment S, and is bounded by $- 1 \\leq \\mathcal { L } _ { c } \\leq 0$ . Minimizing $\\mathcal { L } _ { c }$ encourages strongly connected nodes to be clustered together, since the inner product $\\left. \\mathbf { s } _ { i } , \\mathbf { s } _ { j } \\right.$ increases when $\\tilde { a } _ { i , j }$ is large. $\\mathcal { L } _ { c }$ has a single maximum, reached when the numerator $\\begin{array} { r } { T r ( \\mathbf { S } ^ { T } \\tilde { \\mathbf { A } } \\mathbf { S } ) = \\frac { 1 } { K } \\sum _ { k = 1 } ^ { K } \\mathbf { S } _ { k } ^ { T } \\tilde { \\mathbf { A } } \\mathbf { S } _ { k } = 0 } \\end{array}$ . This occurs if, for each pair of connected nodes (i.e., $\\tilde { a } _ { i , j } > 0 \\rangle$ ), the cluster assignments are orthogonal (i.e., $\\langle \\mathbf { s } _ { i } , \\mathbf { s } _ { j } \\rangle = 0 ,$ ). $\\mathcal { L } _ { c }$ reaches its minimum, $- 1$ , when $T r ( \\mathbf { S } ^ { T } \\tilde { \\mathbf { A } } \\mathbf { S } ) = T r ( \\mathbf { S } ^ { T } \\tilde { \\mathbf { D } } \\mathbf { S } )$ . This occurs when in a graph with $K$ disconnected components the cluster assignments are equal for all the nodes in the same component and orthogonal to the cluster assignments of nodes in different components. However, $\\mathcal { L } _ { c }$ is a non-convex function and its minimization can lead to local minima or degenerate solutions. For example, given a connected graph, a trivial optimal solution is the one that assigns all nodes to the same cluster. As a consequence of the continuous relaxation, another degenerate minimum occurs when the cluster assignments are all uniform, that is, all nodes are equally assigned to all clusters. This problem is exacerbated by prior message-passing operations, which make the node features more uniform. ",
+        "bbox": [
+            173,
+            736,
+            825,
+            924
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "The orthogonality loss term, $\\mathcal { L } _ { o }$ , penalizes the degenerate minima of $\\mathcal { L } _ { c }$ by encouraging the cluster assignments to be orthogonal and the clusters to be of similar size. Since the two matrices in $\\mathcal { L } _ { o }$ have unitary norm it is easy to see that $0 \\leq \\mathcal { L } _ { o } \\leq 2$ . Therefore, $\\mathcal { L } _ { o }$ does not dominate over $\\mathcal { L } _ { c }$ and the two terms can be safely summed directly (see Fig. 4 for an example). ${ \\mathbf { I } } _ { K }$ can be interpreted as a (rescaled) clustering matrix $\\mathbf { I } _ { K } = \\hat { \\mathbf { S } } ^ { T } \\hat { \\mathbf { S } }$ , where $\\hat { \\bf S }$ assigns exactly $N / K$ points to each cluster. The value of the Frobenius norm between clustering matrices is not dominated by the performance on the largest clusters (Law et al., 2017) and, thus, can be used to optimize intra-cluster variance. ",
+        "bbox": [
+            173,
+            103,
+            825,
+            204
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "Contrarily to SC methods that search for feasible solutions only within the space of orthogonal matrices, $\\mathcal { L } _ { o }$ only introduces a soft constraint that could be violated during the learning procedure. Since $\\mathcal { L } _ { c }$ is non-convex, the violation compromises the theoretical guarantee of convergence to the optimum of (3). However, we note that: ",
+        "bbox": [
+            176,
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "1. the cluster assignments S are well initialized: after the MP operation, the features of the connected vertices become similar and, since the MLP is a smooth function (Nelles, 2013), it yields similar cluster assignments for those vertices;   \n2. in the GNN architecture, the minCUT objective is a regularization term and, therefore, a solution which is sub-optimal for (3) could instead be adequate for the specific objective of the downstream task;   \n3. optimizing the task-specific loss helps the GNN to avoid the degenerate minima of $\\mathcal { L } _ { c }$ . ",
+        "bbox": [
+            210,
+            276,
+            825,
+            386
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "3.1 COARSENING ",
+        "text_level": 1,
+        "bbox": [
+            174,
+            401,
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+            416
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "The coarsened version of the adjacency matrix and the graph signal are computed as ",
+        "bbox": [
+            174,
+            426,
+            725,
+            443
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "equation",
+        "img_path": "images/c14e7c61c40a2f766857a297640952b7ad643866d8ac0d1f6858958d0c1eb67a.jpg",
+        "text": "$$\n{ \\bf A } ^ { p o o l } = { \\bf S } ^ { T } { \\tilde { \\bf A } } { \\bf S } ; ~ { \\bf X } ^ { p o o l } = { \\bf S } ^ { T } { \\bf X } ,\n$$",
+        "text_format": "latex",
+        "bbox": [
+            382,
+            446,
+            612,
+            465
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "where the entry xpooi,j in $\\mathbf { X } ^ { p o o l } ~ \\in ~ \\mathbb { R } ^ { K \\times F }$ is the weighted average value of feature $j$ among the elements in cluster $i$ . $\\mathbf { A } ^ { p o o l } ~ \\in ~ \\mathbb { R } ^ { K \\times K }$ is a symmetric matrix, whose entries $a _ { i , i } ^ { p o o l }$ are the total number of edges between the nodes in the cluster i, while apooi,j is the number of edges between cluster $i$ and $j$ . Since $\\mathbf { A } ^ { p o o l }$ corresponds to the numerator of $\\mathcal { L } _ { c }$ in (7), the trace maximization yields clusters with many internal connections and weakly connected to each other. Hence, $\\mathbf { A } ^ { p o o l }$ will be a diagonal-dominant matrix, which describes a graph with self-loops much stronger than any other connection. Because self-loops hamper the propagation across adjacent nodes in the MP operations following the pooling layer, we compute the new adjacency matrix $\\tilde { \\mathbf { A } } ^ { p o o l }$ by zeroing the diagonal and by applying the degree normalization ",
+        "bbox": [
+            173,
+            470,
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "equation",
+        "img_path": "images/cdc85379486e51b65f69e07f035aec1a89b20127fdc77e297c858fa7fe2513dd.jpg",
+        "text": "$$\n\\hat { \\bf A } = { \\bf A } ^ { p o o l } - { \\bf I } _ { K } d i a g ( { \\bf A } ^ { p o o l } ) ; \\quad \\tilde { \\bf A } ^ { p o o l } = \\hat { \\bf D } ^ { - \\frac { 1 } { 2 } } \\hat { \\bf A } \\hat { \\bf D } ^ { - \\frac { 1 } { 2 } } .\n$$",
+        "text_format": "latex",
+        "bbox": [
+            312,
+            617,
+            684,
+            638
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "where $d i a g ( \\cdot )$ returns the matrix diagonal. ",
+        "bbox": [
+            176,
+            643,
+            452,
+            659
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "3.2 DISCUSSION AND RELATIONSHIP WITH SPECTRAL CLUSTERING ",
+        "text_level": 1,
+        "bbox": [
+            176,
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+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "The proposed method is straightforward to implement: the cluster assignments, the loss, graph coarsening, and feature pooling are all computed with standard linear algebra operations. ",
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "There are several differences between minCUTpool and classic SC methods. SC partitions the graph based on the Laplacian, but does not account for the node features. Instead, the cluster assignments $\\mathbf { s } _ { i }$ found by minCUTpool depend on $\\mathbf { x } _ { i }$ , which works well if connected nodes have similar features. This is a reasonable assumption in GNNs since, even in disassortative graphs (i.e., networks where dissimilar nodes are likely to be connected (Newman, 2003)), the features tend to become similar due to the MP operations. ",
+        "bbox": [
+            174,
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "Another difference is that SC handles a single graph and is not conceived for tasks with multiple graphs to be partitioned independently. Instead, thanks to the independence of the model parameters from the number of nodes $N$ and from the graph spectrum, minCUTpool can generalize to outof-sample data. This feature is fundamental in problems such as graph classification, where each sample is a graph with a different structure, and allows to train the model on small graphs and process larger ones at inference time. Finally, minCUTpool directly uses the soft cluster assignments rather than performing $k$ -means afterwards. ",
+        "bbox": [
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "4 RELATED WORK ON POOLING IN GNNS ",
+        "text_level": 1,
+        "bbox": [
+            174,
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "Trainable pooling methods. Similarly to our method, these approaches learn how to generate coarsened version of the graph through differentiable functions, which take as input the nodes features $\\mathbf { X }$ and are parametrized by weights optimized on the task at hand. ",
+        "bbox": [
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "Diffpool (Ying et al., 2018) is a pooling module that includes two parallel MP layers: one to compute the new node features $\\mathbf { X } ^ { ( t + 1 ) }$ and another to generate the cluster assignments S. Diffpool implements an unsupervised loss that consists of two terms. First, the link prediction term $\\| \\mathbf { A } - \\mathbf { S } \\mathbf { \\dot { S } } ^ { T } \\| _ { F }$ minimizes the Frobenius norm of the difference between the adjacency and the Gram matrix of the cluster assignments, encouraging nearby nodes to be clustered together. The second term $\\begin{array} { r } { \\frac { 1 } { N } \\sum _ { i = 1 } ^ { N } H ( \\mathbf { S } _ { i } ) } \\end{array}$ minimizes the entropy of the cluster assignments to make them alike to one-hot vectors. Like minCUTpool, Diffpool clusters the vertices of annotated graphs, but yields completely different partitions, since it computes differently the clustering assignments, the coarsened adjacency matrix and, most importantly, the unsupervised loss. In Diffpool, such a loss shows pathological behaviors that are discussed later in the experiments. ",
+        "bbox": [
+            174,
+            183,
+            825,
+            325
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "The approach dubbed Top- $K$ pooling (Hongyang Gao, 2019; Lee et al., 2019), learns a projection vector that is applied to each node feature to obtain a score. The nodes with the $K$ highest scores are retained, the others are dropped. Since the top- $K$ selection is not differentiable, the scores are also used as a gate/attention for the node features, letting the projection vector to be trained with backpropagation. Top- $K$ is memory efficient as it avoids generating cluster assignments. To prevent A from becoming disconnected after nodes removal, Top- $K$ drops the rows and the columns from ${ \\bf A } ^ { 2 }$ and uses it as the new adjacency matrix. However, computing ${ \\bf A } ^ { 2 }$ costs $\\mathcal { O } ( N ^ { 2 } )$ and it is inefficient to implement with sparse operations. ",
+        "bbox": [
+            174,
+            332,
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "Topological pooling methods. These methods pre-compute a pyramid of coarsened graphs, only taking into account the topology (A), but not the node features $\\mathbf { \\Pi } ( \\mathbf { X } )$ . During training, the node features are pooled with standard procedures and are fit into these deterministic graph structures. These methods are less flexible, but provide a stronger bias that can prevent degenerate solutions (e.g., coarsened graphs collapsing in a single node). ",
+        "bbox": [
+            174,
+            460,
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "The approach proposed by Bruna et al. (2013), which has been adopted also in other GNN architectures (Defferrard et al., 2016; Fey et al., 2018), exploits GRACLUS (Dhillon et al., 2004), a hierarchical algorithm based on SC. At each pooling level $l$ , GRACLUS indetifies the pairs of maximally similar nodes $i _ { l }$ and $j _ { l }$ to be clustered together into a new vertex $k _ { ( l + 1 ) }$ . At inference phase, max-pooling is used to determine which node in the pair is kept. Fake vertices are added so that the number of nodes can be halved each time, but this injects noisy information in the graph. ",
+        "bbox": [
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "Node decimation is a method originally proposed in graph signal processing literature (Shuman et al., 2016), which as been adapted also for GNNs (Simonovsky & Komodakis, 2017). The nodes are partitioned in two sets, according to the signs of the Laplacian eigenvector associated to the largest eigenvalue. One of the two sets is dropped, reducing the number of nodes each time approximately by half. Kron reduction is used to compute a pyramid of coarsened Laplacians from the remaining nodes. ",
+        "bbox": [
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "A procedure proposed in Gama et al. (2018) diffuses a signal from designated nodes on the graph and stores the observed sequence of diffused components. The resulting stream of information is interpreted as a time signal, where standard CNN pooling is applied. We also mention a pooling operation for coarsening binary unweighted graphs by aggregating maximal cliques (Luzhnica et al., 2019). Nodes assigned to the same clique are summarized by max or average pooling and become a new node in the coarsened graph. ",
+        "bbox": [
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+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "5 EXPERIMENTS ",
+        "text_level": 1,
+        "bbox": [
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+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "We consider both supervised and unsupervised tasks, and compare minCUTpool with other GNN pooling strategies. The Appendix provides further details on the experiments and a schematic depiction of the architectures used in each task. In addition, the Appendix reports two additional experiments: i) graph reconstruction by means of an Auto Encoder with bottleneck, implemented with pooling and un-pooling layers, ii) an architecture with pooling for graph regression. ",
+        "bbox": [
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+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "5.1 CLUSTERING THE GRAPH NODES ",
+        "text_level": 1,
+        "bbox": [
+            176,
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "To study the effectiveness of the proposed loss, we perform different node clustering tasks with a simple GNN composed of a single MP layer followed by a pooling layer. The GNN is trained by minimizing $\\mathcal { L } _ { u }$ only, so that its effect is evaluated without the “interference” of a supervised loss. ",
+        "bbox": [
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+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "Clustering on synthetic networks We consider two simple graphs: the first is a network with 6 communities and the second is a regular grid. The adjacency matrix A is binary and the features X are the 2-D node coordinates. Fig. 2 depicts the node partitions generated by SC (a, d), Diffpool (b, e), and minCUTpool (c, f). Cluster indexes for Diffpool and minCUTpool are obtained by taking the argmax of S row-wise. Compared to SC, Diffpool and minCUTpool leverage the information contained in X. minCUTpool generates very accurate and balanced partitions, demonstrating that the cluster assignment matrix S is well formed. On the other hand, Diffpool assigns some nodes to the wrong community in the first example, and produces an imbalanced partition of the grid. ",
+        "bbox": [
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+        "page_idx": 5
+    },
+    {
+        "type": "image",
+        "img_path": "images/f54a1747a2f3fb20dd6df85e294051b41f7c8f617ba05ec5ba321652a3688701.jpg",
+        "image_caption": [
+            "Figure 2: Node clustering on a community network $K { = } 6 )$ and on a grid graph $( K { = } 5 )$ "
+        ],
+        "image_footnote": [],
+        "bbox": [
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "Image segmentation Given an image, we build a Region Adjacency Graph (Tremeau & Colan- ´ toni, 2000) using as nodes the regions generated by an oversegmentation procedure (Felzenszwalb & Huttenlocher, 2004). The SC technique used in this example is the recursive normalized cut (Shi & Malik, 2000), which recursively clusters the nodes until convergence. For Diffpool and minCUTpool, we include node features consisting of the average and total color in each oversegmented region. We set the number of desired clusters to $K = 4$ . The results in Fig. 3 show that minCUTpool yields a more precise segmentation. On the other hand, SC and Diffpool aggregate wrong regions and, in addition, SC finds too many segments. ",
+        "bbox": [
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+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "Clustering on citation networks We cluster the nodes of three popular citation networks: Cora, Citeseer, and Pubmed. The nodes are documents represented by sparse bag-of-words feature vectors stored in $\\mathbf { X }$ and the binary undirected edges in $\\mathbf { A }$ indicate citation links between documents. Each node $i$ is labeled with the document class $y _ { i }$ . Once the training is over, to test the quality of the partitions generated by each method we check the agreement between the cluster assignments and the true class labels. Tab. 1 reports the Completeness Score $\\begin{array} { r } { \\mathrm { C S } ( \\tilde { \\bf y } , { \\bf y } ) = 1 - \\frac { H ( \\tilde { \\bf y } | { \\bf y } ) } { H ( \\tilde { \\bf y } ) } } \\end{array}$ and Normalized Mutual Information $\\begin{array} { r } { \\mathbf { N M I } ( \\tilde { \\mathbf { y } } , \\mathbf { y } ) = \\frac { H ( \\tilde { \\mathbf { y } } ) - H ( \\tilde { \\mathbf { y } } | \\mathbf { y } ) } { \\sqrt { H ( \\tilde { \\mathbf { y } } ) - H ( \\mathbf { y } ) } } } \\end{array}$ where $H ( \\cdot )$ is the entropy. ",
+        "bbox": [
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+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "The GNN architecture configured with minCUTpool achieves a higher NMI score than SC, which does not account for the node features $\\mathbf { X }$ when generating the partitions. Our pooling operation outperforms also Diffpool, since the minimization of the unsupervised loss in Diffpool yields degenerate solutions. The pathological behavior is shown in Fig. 4, which depicts the evolution of the NMI scores as the unsupervised losses in Diffpool and minCUTpool are minimized in training. ",
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+        "img_path": "images/81a3f7ffc1776e74fbc56b414ab1c318578c5dc39e05ac6ea084422888017b44.jpg",
+        "image_caption": [
+            "Figure 3: Image segmentation by clustering the nodes of the Region Adjacency Graph. "
+        ],
+        "image_footnote": [],
+        "bbox": [
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+        "img_path": "images/4067d319802597da0f8a99d17f9a05ae75ef1d9974bd1b46567b315150d067c6.jpg",
+        "image_caption": [
+            "Figure 4: Unsupervised losses and NMI of Diffpool and minCUTpool on Cora. "
+        ],
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+    {
+        "type": "table",
+        "img_path": "images/4158255af3330a03321c8d25f82fd169f90fca4a4f87f98e57d954019d96471f.jpg",
+        "table_caption": [
+            "Table 1: NMI and CS obtained by clustering the nodes on citation networks over 10 different runs. The number of clusters $K$ is equal to the number of node classes. "
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>Dataset</td><td>K</td><td colspan=\"2\">Spectral clustering</td><td colspan=\"2\">Diffpool</td><td colspan=\"2\">minCUTpool</td></tr><tr><td></td><td></td><td>NMI</td><td>cs</td><td>NMI</td><td>CS</td><td>NMI</td><td>CS</td></tr><tr><td>Cora</td><td>7</td><td>0.025 ± 0.014</td><td>0.126 ± 0.042</td><td>0.315 ± 0.005</td><td>0.309 ±0.005</td><td>0.404 ± 0.018</td><td>0.392 ± 0.018</td></tr><tr><td>Citeseer</td><td>6</td><td>0.014 ± 0.003</td><td>0.033 ±0.000</td><td>0.139 ± 0.016</td><td>0.153 ± 0.020</td><td>0.287 ±0.047</td><td>0.283 ± 0.046</td></tr><tr><td>Pubmed</td><td>3</td><td>0.182 ± 0.000</td><td>0.261 ± 0.000</td><td>0.079 ±0.001</td><td>0.085 ±0.001</td><td>0.200 ± 0.020</td><td>0.197 ± 0.019</td></tr></table>",
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+    },
+    {
+        "type": "text",
+        "text": "5.2 SUPERVISED GRAPH CLASSIFICATION ",
+        "text_level": 1,
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "In this task, the $i$ -th datum is a graph with $N _ { i }$ nodes represented by a pair $\\{ \\mathbf { A } _ { i } , \\mathbf { X } _ { i } \\}$ and must be associated to the correct label $\\mathbf { y } _ { i }$ . We test the models on different graph classification datasets. For featureless graphs, we used the node degree information and the clustering coefficient as surrogate node features. We evaluate model performance with a 10-fold train/test split, using $1 0 \\%$ of the training set in each fold as validation for early stopping. We adopt a fixed network architecture, MP(32)-poolMP(32)-pool-MP(32)-GlobalAvgPool-softmax, where MP is the message-passing operation in (4) ",
+        "bbox": [
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+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "with 32 hidden units. The pooling module is implemented either by Graclus, Decimation pooling, Top- $K$ , SAGPool (Lee et al., 2019), Diffpool, or the proposed minCUTpool. Each pooling method is configured to drop half of the nodes in a graph $K = N / 2$ in Top- $K$ , Diffpool, and minCUTpool). As baselines, we consider the popular Weisfeiler-Lehman (WL) graph kernel (Shervashidze et al., 2011), a network with only MP layers (Flat), and a fully connected network (Dense). ",
+        "bbox": [
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+    },
+    {
+        "type": "table",
+        "img_path": "images/f42ea0a0a3ed9e12ba04e59f7afa9d42c08e5d9a16acdb713d983a07264519c7.jpg",
+        "table_caption": [
+            "Table 2: Graph classification accuracy. Significantly better results $( p < 0 . 0 5 )$ are in bold. "
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>Dataset</td><td>WL</td><td>Dense</td><td>Flat</td><td>Graclus</td><td>Decim.</td><td>Diffpool</td><td>Top-K</td><td>SAGpool</td><td>minCUT</td></tr><tr><td>Bench-easy</td><td>92.6</td><td>29.3±0.3</td><td>98.5±0.3</td><td>97.5±0.5</td><td>97.9±0.5</td><td>98.6±0.4</td><td>82.4±8.9</td><td>84.2±2.3</td><td>99.0±0.0</td></tr><tr><td>Bench-hard</td><td>60.0</td><td>29.4±0.3</td><td>67.6±2.8</td><td>69.0±1.5</td><td>72.6±0.9</td><td>69.9±1.9</td><td>42.7±15.2</td><td>37.7±14.5</td><td>73.8±1.9</td></tr><tr><td>Mutagenicity</td><td>81.7±1.1</td><td>68.4±0.3</td><td>78.0±1.3</td><td>74.4±1.8</td><td>77.8±2.3</td><td>77.6±2.7</td><td>71.9±3.7</td><td>72.4±2.4</td><td>79.9±2.1</td></tr><tr><td>Proteins</td><td>71.2±2.6</td><td>68.7±3.3</td><td>72.6±4.8</td><td>68.6±4.6</td><td>73.3±3.7</td><td>72.7±3.8</td><td>69.6±3.5</td><td>70.5±2.6</td><td>76.5±2.6</td></tr><tr><td>DD</td><td>78.6±2.7</td><td>70.6±5.2</td><td>76.8±1.5</td><td>70.5±4.8</td><td>72.0±3.1</td><td>79.3±2.4</td><td>69.4±7.8</td><td>71.5±4.5</td><td>80.8±2.3</td></tr><tr><td>COLLAB</td><td>74.8±1.3</td><td>79.3±1.6</td><td>82.1±1.8</td><td>77.1±2.1</td><td>79.1±1.5</td><td>81.8±1.4</td><td>79.3±1.8</td><td>79.2±2.0</td><td>83.4±1.7</td></tr><tr><td>Reddit-Binary</td><td>68.2±1.7</td><td>48.5±2.6</td><td>80.3±2.6</td><td>79.2±0.4</td><td>84.3±2.4</td><td>86.8±2.1</td><td>74.7±4.5</td><td>73.9±5.1</td><td>91.4±1.5</td></tr></table>",
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+    },
+    {
+        "type": "text",
+        "text": "Tab. 2 reports the classification results, highlighting those that are significantly better ( $\\dot { p }$ -value $< ~ 0 . 0 5$ w.r.t. the method with the highest mean accuracy). The comparison with Flat helps to understand if a pooling operation is useful or not. The results of Dense, instead, help to quantify how much additional information is brought by the graph structure, with respect to the node features alone. It can be seen that minCUTpool obtains always equal or better results with respect to every other GNN architecture. On the other hand, some pooling procedures do not always improve the performance compared to the Flat baseline, making them not advisable to use in some cases. The WL kernel generally performs worse than the GNNs, except for the Mutagenicity dataset. This is probably because Mutagenicity has smaller graphs than the other datasets, and the adopted GNN architecture is overparametrized for this task. Interestingly, in some dataset such as Proteins and COLLAB it is possible to obtain fairly good classification accuracy with the Dense architecture, meaning that the graph structure only adds limited information. ",
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+    },
+    {
+        "type": "image",
+        "img_path": "images/e375310d148f5976514d2295a7d3c8830c48da3e0966c6040f4a07d9c8821927.jpg",
+        "image_caption": [
+            "Figure 5: Average duration of one epoch using the same GNN with different pooling operations. Times were computed with an Nvidia GeForce GTX 1050, on the DD dataset with batch size of 1. "
+        ],
+        "image_footnote": [],
+        "bbox": [
+            178,
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+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "Fig. 5 reports a comparison of the execution time per training epoch for each pooling algorithm. Graclus and Decimation are understandably the fastest methods, since the coarsened graphs are precomputed. Among the differentiable pooling methods, minCUTpool is faster than Diffpool, which uses a slower MP layer rather than a MLP to compute cluster assignments, and than Top- $K$ , which computes the square of A at every forward pass. ",
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+    {
+        "type": "text",
+        "text": "6 CONCLUSIONS ",
+        "text_level": 1,
+        "bbox": [
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+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "We proposed a pooling layer for GNNs that coarsens a graph by taking into account both the the connectivity structure and the node features. The layer optimizes a regularization term based on the minCUT objective, which is minimized in conjunction with the task-specific loss to produce node partitions that are optimal for the task at hand. ",
+        "bbox": [
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+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "We tested the effectiveness of our pooling strategy on unsupervised node clustering tasks, by optimizing only the unsupervised clustering loss, as well as supervised graph classification tasks on several popular benchmark datasets. Results show that minCUTpool performs significantly better than existing pooling strategies for GNNs. ",
+        "bbox": [
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+    {
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+        "text": "Li Yi, Hao Su, Xingwen Guo, and Leonidas J Guibas. Syncspeccnn: Synchronized spectral cnn for 3d shape segmentation. In Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, pp. 2282–2290, 2017. ",
+        "bbox": [
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+        ],
+        "page_idx": 9
+    },
+    {
+        "type": "text",
+        "text": "Zhitao Ying, Jiaxuan You, Christopher Morris, Xiang Ren, Will Hamilton, and Jure Leskovec. Hierarchical graph representation learning with differentiable pooling. In Advances in Neural Information Processing Systems, pp. 4800–4810, 2018. ",
+        "bbox": [
+            173,
+            837,
+            823,
+            881
+        ],
+        "page_idx": 9
+    },
+    {
+        "type": "text",
+        "text": "Yu and Shi. Multiclass spectral clustering. In Proceedings Ninth IEEE International Conference on Computer Vision, pp. 313–319 vol.1, Oct 2003. ",
+        "bbox": [
+            174,
+            888,
+            823,
+            917
+        ],
+        "page_idx": 9
+    },
+    {
+        "type": "text",
+        "text": "APPENDIX ",
+        "text_level": 1,
+        "bbox": [
+            176,
+            102,
+            263,
+            118
+        ],
+        "page_idx": 10
+    },
+    {
+        "type": "text",
+        "text": "A ADDITIONAL EXPERIMENTS ",
+        "bbox": [
+            178,
+            137,
+            442,
+            154
+        ],
+        "page_idx": 10
+    },
+    {
+        "type": "text",
+        "text": "A.1 GNN AUTOENCODER ",
+        "text_level": 1,
+        "bbox": [
+            176,
+            169,
+            367,
+            184
+        ],
+        "page_idx": 10
+    },
+    {
+        "type": "text",
+        "text": "To compare the amount of information retained by the pooling layers in the coarsened graphs, we train an autoencoder (AE) to reconstruct a input graph signal $\\mathbf { X }$ from its pooled version. The AE architecture is MP(32)-MP(32)-pool-unpool-MP(32)-MP(32)-MP, and is trained by minimizing the mean squared error between the original and the reconstructed graph signal, $\\lVert \\bf { X } - \\bf { X } ^ { \\mathrm { { r e c } } } \\rVert ^ { 2 }$ . All the pooling operations are configured to retain $2 5 \\%$ of the original nodes. ",
+        "bbox": [
+            174,
+            195,
+            825,
+            267
+        ],
+        "page_idx": 10
+    },
+    {
+        "type": "text",
+        "text": "In Diffpool and minCUTpool, the unpool step is simply implemented by transposing the original pooling operations ",
+        "bbox": [
+            173,
+            272,
+            823,
+            301
+        ],
+        "page_idx": 10
+    },
+    {
+        "type": "equation",
+        "img_path": "images/8bbce8dd36526a6342dc4574ef8b5dab6566229c68e0a0326d22de1f3f93de0b.jpg",
+        "text": "$$\n{ \\bf X } ^ { \\mathrm { r e c } } = { \\bf S } { \\bf X } ^ { \\mathrm { p o o l } } ; ~ { \\bf A } ^ { \\mathrm { r e c } } = { \\bf S } { \\bf A } ^ { \\mathrm { p o o l } } { \\bf S } ^ { T } .\n$$",
+        "text_format": "latex",
+        "bbox": [
+            379,
+            301,
+            619,
+            319
+        ],
+        "page_idx": 10
+    },
+    {
+        "type": "text",
+        "text": "Top- $K$ does not generate a cluster assignment matrix, but returns a binary mask $\\mathbf { m } = \\{ 0 , 1 \\} ^ { N }$ that indicates the nodes to drop (0) or to retain (1). Therefore, an upsamplig matrix $\\mathbf { U }$ is built by dropping the columns of the identity matrix ${ \\mathbf { I } } _ { N }$ that correspond to a 0 in $\\mathbf { m }$ , $\\bar { \\mathbf { U } } = [ \\mathbf { I } _ { N } ] _ { : , \\mathbf { m } = = 1 }$ . The unpooling operation is performed by replacing S with $\\mathbf { U }$ in (9), and the resulting upscaled graph is a version of the original graph with zeroes in correspondence of the dropped nodes. ",
+        "bbox": [
+            174,
+            333,
+            825,
+            404
+        ],
+        "page_idx": 10
+    },
+    {
+        "type": "image",
+        "img_path": "images/441bd5ff28bf0dbad772497856fe6d0256f85ad6ae1cfa337d7be79956b30a09.jpg",
+        "image_caption": [
+            "Figure 6: AE reconstruction of a ring graph "
+        ],
+        "image_footnote": [],
+        "bbox": [
+            200,
+            425,
+            795,
+            555
+        ],
+        "page_idx": 10
+    },
+    {
+        "type": "image",
+        "img_path": "images/4b22636cf4edd79e814a6d27c3e71aeabc0f8293196e377e997385878fcd0602.jpg",
+        "image_caption": [
+            "Figure 7: AE reconstruction of a grid graph "
+        ],
+        "image_footnote": [],
+        "bbox": [
+            202,
+            614,
+            795,
+            744
+        ],
+        "page_idx": 10
+    },
+    {
+        "type": "text",
+        "text": "Fig. 6 and 7 report the original graph signal $\\mathbf { X }$ (the node features are the 2-D coordinates of the nodes) and the reconstruction $\\mathbf { X } ^ { \\mathrm { r e c } }$ obtained by using the different pooling methods, for a ring graph and a regular grid graph. The reconstruction produced by Diffpool is worse for the ring graph, but is almost perfect for the grid graph, while minCUTpool yields good results in both cases. On the other hand, Top- $K$ clearly fails in generating a coarsened representation that maintains enough information from the original graph. ",
+        "bbox": [
+            173,
+            790,
+            825,
+            875
+        ],
+        "page_idx": 10
+    },
+    {
+        "type": "text",
+        "text": "This experiment highlights a major issue in Top- $K$ pooling, which retains the nodes associated to the highest $K$ values of a score vector s, computed by projecting the node features onto a trainable vector p: $\\mathbf { s } = \\mathbf { X } \\mathbf { p } $ . Nodes that are connected on the graph usually share similar features, and their similarity further increases after the MP operations, which combine the features of neighboring nodes. Retaining the nodes associated to the top $K$ scores in s corresponds to keeping those nodes that are alike and highly connected, as it can be seen in Fig. 6-7. Therefore, Top- $K$ discards entire portions of the graphs, which might contain important information. This explains why Top- $K$ fails to recover the original graph signal when used as bottleneck for the AE, and yields the worse performance among all GNN methods in the graph classification task. ",
+        "bbox": [
+            176,
+            881,
+            825,
+            924
+        ],
+        "page_idx": 10
+    },
+    {
+        "type": "text",
+        "text": "",
+        "bbox": [
+            174,
+            103,
+            825,
+            188
+        ],
+        "page_idx": 11
+    },
+    {
+        "type": "text",
+        "text": "A.2 GRAPH REGRESSION OF MOLECULAR PROPERTIES ON QM9",
+        "text_level": 1,
+        "bbox": [
+            176,
+            212,
+            629,
+            226
+        ],
+        "page_idx": 11
+    },
+    {
+        "type": "text",
+        "text": "The QM9 chemical database is a collection of ${ \\approx } 1 3 5 \\mathrm { k }$ small organic molecules, associated to continuous labels describing several geometric, energetic, electronic, and thermodynamic properties1. Each molecule in the dataset is represented as a graph $\\{ \\mathbf { A } _ { i } , \\mathbf { X } _ { i } \\}$ , where atoms are associated to nodes, and edges represent chemical bonds. The atomic number of each atom (one-hot encoded; C, N, F, O) is taken as node feature and the type of bond (one-hot encoded; single, double, triple, aromatic) can be used as edge attribute. In this experiment, we ignore the edge attributes in order to use all pooling algorithms without modifications. ",
+        "bbox": [
+            174,
+            239,
+            825,
+            337
+        ],
+        "page_idx": 11
+    },
+    {
+        "type": "text",
+        "text": "The purpose of this experiment is to compare the trainable pooling methods also on a graph regression task, but it must be intended as a proof of concept. In fact, the graphs in this dataset are extremely small (the average number of nodes is 8) and, therefore, a pooling operation is arguably not necessary. We consider a GNN with architecture MP(32)-pool-MP(32)-GlobalAvgPool-Dense, where pool is implemented by Top- $K$ , Diffpool, or minCUTpool. The network is trained to predict a given chemical property from the input molecular graphs. Performance is evaluated with a 10-fold cross-validation, using $1 \\dot { 0 } \\%$ of the training set for validation in each split. The GNNs are trained for 50 epochs, using Adam with learning rate 5e-4, batch size 32, and ReLU activations. We use the mean squared error (MSE) as supervised loss. ",
+        "bbox": [
+            173,
+            344,
+            825,
+            469
+        ],
+        "page_idx": 11
+    },
+    {
+        "type": "text",
+        "text": "The MSE obtained on the prediction of each property for different pooling methods is reported in Tab. 3. As expected, the flat baseline with no pooling operation (MP(32)-MP(32)-GlobalAvgPoolDense) yields a lower error in most cases. Contrarily to the graph classification and the AE task, Top- $K$ achieves better results than Diffpool in average. Once again, minCUTpool significantly outperforms the other methods on each regression task and, in one case, also the flat baseline. ",
+        "bbox": [
+            174,
+            477,
+            823,
+            546
+        ],
+        "page_idx": 11
+    },
+    {
+        "type": "table",
+        "img_path": "images/abf2e28f0c4594a1f795c78d14e892f9e76511066dff22a973092bd24eabf709.jpg",
+        "table_caption": [],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>Property</td><td>Top-K</td><td>Diffpool</td><td>minCUTpool</td><td>Flat baseline</td></tr><tr><td>mu</td><td>0.600±0.085</td><td>0.651±0.026</td><td>0.538±0.012</td><td>0.559±0.007</td></tr><tr><td>alpha</td><td>0.197±0.087</td><td>0.114±0.001</td><td>0.078±0.007</td><td>0.065±0.006</td></tr><tr><td>homo</td><td>0.698±0.102</td><td>0.712±0.015</td><td>0.526±0.021</td><td>0.435±0.013</td></tr><tr><td>lumo</td><td>0.601±0.050</td><td>0.646±0.013</td><td>0.540±0.005</td><td>0.515±0.007</td></tr><tr><td>gap</td><td>0.630±0.044</td><td>0.698±0.004</td><td>0.584±0.007</td><td>0.552±0.008</td></tr><tr><td>r2</td><td>0.452±0.087</td><td>0.440±0.024</td><td>0.261±0.006</td><td>0.204±0.006</td></tr><tr><td>zpve</td><td>0.402±0.032</td><td>0.410±0.004</td><td>0.328±0.005</td><td>0.284±0.005</td></tr><tr><td>uO_atom</td><td>0.308±0.055</td><td>0.245±0.006</td><td>0.193±0.002</td><td>0.163±0.001</td></tr><tr><td>cv</td><td>0.291±0.118</td><td>0.337±0.018</td><td>0.148±0.004</td><td>0.127±0.002</td></tr></table>",
+        "bbox": [
+            259,
+            568,
+            736,
+            712
+        ],
+        "page_idx": 11
+    },
+    {
+        "type": "text",
+        "text": "Table 3: MSE on the graph regression task. The best results with a statistical significance of $p < 0 . 0 5$ are highlighted: the best overall are in bold, the best among pooling methods are underlined. ",
+        "bbox": [
+            169,
+            726,
+            825,
+            755
+        ],
+        "page_idx": 11
+    },
+    {
+        "type": "text",
+        "text": "B EXPERIMENTAL DETAILS ",
+        "text_level": 1,
+        "bbox": [
+            176,
+            796,
+            416,
+            811
+        ],
+        "page_idx": 11
+    },
+    {
+        "type": "text",
+        "text": "For the WL kernel, we used the implementation provided in the GraKeL library2. The pooling strategy based on Graclus, is taken from the ChebyNets repository3. ",
+        "bbox": [
+            171,
+            830,
+            823,
+            859
+        ],
+        "page_idx": 11
+    },
+    {
+        "type": "text",
+        "text": "B.1 CLUSTERING ON CITATION NETWORKS ",
+        "text_level": 1,
+        "bbox": [
+            176,
+            103,
+            485,
+            118
+        ],
+        "page_idx": 12
+    },
+    {
+        "type": "text",
+        "text": "Diffpool and minCUTpool are configured with 16 hidden neurons with linear activations in the MLP and MP layer, respectively used to compute the cluster assignment matrix S. The MP layer used to compute the propagated node features $\\mathbf { X } ^ { ( 1 ) }$ uses an ELU activation in both architectures. The learning rate for Adam is 5e-4, and the models are trained for 10000 iterations. The details of the citation networks dataset are reported in Tab. 4. ",
+        "bbox": [
+            174,
+            128,
+            825,
+            200
+        ],
+        "page_idx": 12
+    },
+    {
+        "type": "table",
+        "img_path": "images/83643cb5b85febe056dfd089e5192e8b209287c5ac7b40081e179d6e516f65fb.jpg",
+        "table_caption": [
+            "Table 4: Details of the citation networks datasets "
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>Dataset</td><td>Nodes</td><td>Edges</td><td>Node features</td><td>Node classes</td></tr><tr><td>Cora</td><td>2708</td><td>5429</td><td>1433</td><td>7</td></tr><tr><td>Citeseer</td><td>3327</td><td>9228</td><td>3703</td><td>6</td></tr><tr><td>Pubmed</td><td>19717</td><td>88651</td><td>500</td><td>3</td></tr></table>",
+        "bbox": [
+            312,
+            239,
+            684,
+            308
+        ],
+        "page_idx": 12
+    },
+    {
+        "type": "text",
+        "text": "B.2 GRAPH CLASSIFICATION ",
+        "text_level": 1,
+        "bbox": [
+            174,
+            334,
+            387,
+            349
+        ],
+        "page_idx": 12
+    },
+    {
+        "type": "text",
+        "text": "We train the GNN architectures with Adam, an $\\mathrm { L } _ { 2 }$ penalty loss with weight 1e-4, and 16 hidden units $( H )$ both in the MLP of minCUTpool and in the internal MP of Diffpool. Mutagenicity, Proteins, DD, COLLAB, and Reddit- ${ \\it 2 k }$ are datasets representing real-world graphs and are taken from the repository of benchmark datasets for graph kernels4. Bench-easy and Bench-hard5 are datasets where the node features $\\mathbf { X }$ and the adjacency matrix A are completely uninformative if considered alone. Hence, algorithms that account only for the node features or the graph structure will fail to classify the graphs. Since Bench-easy and Bench-hard come with a train/validation/test split, the 10-fold split is not necessary to evaluate the performance. The statistics of all the datasets are reported in Tab. 5. ",
+        "bbox": [
+            173,
+            359,
+            826,
+            486
+        ],
+        "page_idx": 12
+    },
+    {
+        "type": "table",
+        "img_path": "images/8139375cff6db7f44f94bbb4867d33a66608ffa28a0ec65a6dcfdb33bd0f0efa.jpg",
+        "table_caption": [
+            "Table 5: Summary of statistics of the graph classification datasets "
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>Dataset</td><td>samples</td><td>classes</td><td>avg. nodes</td><td>avg. edges</td><td>node attr.</td><td>node labels</td></tr><tr><td>Bench-easy</td><td>1800</td><td>3</td><td>147.82</td><td>922.66</td><td></td><td>yes</td></tr><tr><td>Bench-hard</td><td>1800</td><td>3</td><td>148.32</td><td>572.32</td><td></td><td>yes</td></tr><tr><td>Mutagenicity</td><td>4337</td><td>2</td><td>30.32</td><td>30.77</td><td></td><td>yes</td></tr><tr><td>Proteins</td><td>1113</td><td>2</td><td>39.06</td><td>72.82</td><td>1</td><td>no</td></tr><tr><td>DD</td><td>1178</td><td>2</td><td>284.32</td><td>715.66</td><td>1</td><td>yes</td></tr><tr><td>COLLAB</td><td>5000</td><td>3</td><td>74.49</td><td>2457.78</td><td></td><td>no</td></tr><tr><td>Reddit-2K</td><td>2000</td><td>2</td><td>429.63</td><td>497.75</td><td>1</td><td>no</td></tr></table>",
+        "bbox": [
+            225,
+            527,
+            772,
+            645
+        ],
+        "page_idx": 12
+    },
+    {
+        "type": "text",
+        "text": "C ARCHITECTURES SCHEMATA ",
+        "text_level": 1,
+        "bbox": [
+            176,
+            676,
+            446,
+            693
+        ],
+        "page_idx": 12
+    },
+    {
+        "type": "text",
+        "text": "Fig. 8 reports the schematic representation of the minCUTpool layer; Fig. 9 the GNN architecture used in the clustering and segmentation tasks; Fig. 10 the GNN architecture used in the graph classification task; Fig. 12 the GNN architecture used in the graph regression task; Fig. 11 the graph autoencoder used in the graph signal reconstruction task. ",
+        "bbox": [
+            173,
+            707,
+            825,
+            763
+        ],
+        "page_idx": 12
+    },
+    {
+        "type": "image",
+        "img_path": "images/d9ade9085ab54361a1aa6626d8499f13441a1f331f8a266df6a2b0894a69a6db.jpg",
+        "image_caption": [
+            "Figure 8: Schema of the minCUTpool layer. "
+        ],
+        "image_footnote": [],
+        "bbox": [
+            299,
+            103,
+            699,
+            236
+        ],
+        "page_idx": 13
+    },
+    {
+        "type": "image",
+        "img_path": "images/d710cb546df4f56d39a534e37d809d53060d1d9bc2b6ee1c45fe2367b58e3ef9.jpg",
+        "image_caption": [
+            "Figure 9: Architecture for clustering/segmentation. "
+        ],
+        "image_footnote": [],
+        "bbox": [
+            400,
+            304,
+            591,
+            361
+        ],
+        "page_idx": 13
+    },
+    {
+        "type": "image",
+        "img_path": "images/da255a17d1270f108c2393a35c6f5725d6c431af5f91c472b5369ec2db9913d6.jpg",
+        "image_caption": [
+            "Figure 10: Architecture for graph classification. "
+        ],
+        "image_footnote": [],
+        "bbox": [
+            230,
+            426,
+            766,
+            482
+        ],
+        "page_idx": 13
+    },
+    {
+        "type": "image",
+        "img_path": "images/969e11240083f473509da7280d39c4b88009ae72ad1c88f632f5a4207bc0742d.jpg",
+        "image_caption": [
+            "Figure 11: Architecture for the autoencoder. "
+        ],
+        "image_footnote": [],
+        "bbox": [
+            222,
+            541,
+            774,
+            599
+        ],
+        "page_idx": 13
+    },
+    {
+        "type": "image",
+        "img_path": "images/031a97e555c2460b138d4ed99d26909b098af1b3775c29da264c3560104df77d.jpg",
+        "image_caption": [
+            "Figure 12: Architecture for graph regression. "
+        ],
+        "image_footnote": [],
+        "bbox": [
+            294,
+            659,
+            700,
+            715
+        ],
+        "page_idx": 13
+    }
+]

parse/train/Byf5-30qFX/Byf5-30qFX.md

@@ -0,0 +1,271 @@
+# DHER: HINDSIGHT EXPERIENCE REPLAY FOR DYNAMIC GOALS
+
+Meng Fang∗, Cheng Zhou, Bei Shi, Boqing Gong, Jia Xu, Tong Zhang Tencent AI Lab
+
+# ABSTRACT
+
+Dealing with sparse rewards is one of the most important challenges in reinforcement learning (RL), especially when a goal is dynamic (e.g., to grasp a moving object). Hindsight experience replay (HER) has been shown an effective solution to handling sparse rewards with fixed goals. However, it does not account for dynamic goals in its vanilla form and, as a result, even degrades the performance of existing off-policy RL algorithms when the goal is changing over time.
+
+In this paper, we present Dynamic Hindsight Experience Replay (DHER), a novel approach for tasks with dynamic goals in the presence of sparse rewards. DHER automatically assembles successful experiences from two relevant failures and can be used to enhance an arbitrary off-policy RL algorithm when the tasks’ goals are dynamic. We evaluate DHER on tasks of robotic manipulation and moving object tracking, and transfer the polices from simulation to physical robots. Extensive comparison and ablation studies demonstrate the superiority of our approach, showing that DHER is a crucial ingredient to enable RL to solve tasks with dynamic goals in manipulation and grid world domains.
+
+# 1 INTRODUCTION
+
+Deep reinforcement learning has been shown an effective framework for solving a rich repertoire of complex control problems. In simulated domains, agents have been trained to perform a diverse array of challenging tasks (Mnih et al., 2015; Lillicrap et al., 2015; Duan et al., 2016). In order to train such agents, it is often the case that one has to design a reward function that not only reflects the task at hand but also is carefully shaped $\mathrm { N g }$ et al., 1999) to guide the policy optimization. Unfortunately, many of the capabilities demonstrated by reward engineering are often limited to specific tasks. Moreover, it requires both RL expertise and domain-specific knowledge to reshape the reward functions. For situations where we do not know what admissible behavior may look like, for example, using LEGO bricks to build a desired architecture, it is difficult to apply reward engineering. Therefore, it is essential to develop algorithms which can learn from unshaped and usually sparse reward signals.
+
+Learning with sparse rewards is challenging, especially when a goal is dynamic. Dynamic goals are common in games and planning problems, often addressed using reward shaping or search (Kaelbling, 1993; Mnih et al., 2015; Di Rocco et al., 2013). However, the difficulty posed by a sparse reward is exacerbated by the complicated environment dynamics in robotics (Andrychowicz et al., 2017). For instance, system dynamics around contacts are difficult to model and induce sensitivity in the system to small errors. Many robotic tasks also need executing multiple steps successfully over a long horizon, involve enormous search space, and require generalization to varying task instances. Policy gradient methods are breakthroughs in the challenging environments, such as PPO (Heess et al., 2017; Schulman et al., 2017), ACER (Wang et al., 2016), TRPO (Schulman et al., 2015) and so on. They are used in environments, where an agent tries to reach a target, learns to walk, runs, and so on. Recently, sampling-efficient learning is introduced and demonstrates a significant increase in performance for off-policy actor-critic DQN (Mnih et al., 2015) and DDPG (Lillicrap et al., 2015) algorithms. Hindsight experience replay (HER) is very effective for improving the performance of off-policy RL algorithms in solving goal-based tasks with sparse rewards (Andrychowicz et al., 2017). Similar to UVFA (Schaul et al., 2015a), it takes a goal state as part of input. However, it assumes the goal is fixed. As a result, this assumption actually impedes the learning of RL agents in the environments of moving goals.
+
+![](images/a34ff9c3bf9148b8d43e21b58e1ea68fe1bcb07b8ac12d22cc17bf9a91fd4060.jpg)  
+Figure 1: The framework of DHER. DHER is a kind of experience replay method. It searches relevant failed experiences and then assembles them into successful experiences.
+
+In this paper, we address this challenge with a new method, Dynamic Hindsight Experience Replay (DHER), for accomplishing tasks with moving goals. We follow the multi-goal setting in UVFA (Schaul et al., 2015a) and HER (Andrychowicz et al., 2017). It assumes that the goal being pursued does not influence the environment dynamics. We also need to have the knowledge of goal similarity. For example, in manipulation or grid world domains, we can use Euclidean distance between positions to measure the goal similarity. HER turns a failed episode to a success by composing a new task whose goal is achieved by that episode. Our idea allows an agent to learn from the failure one step further than HER: the agent not only sets a new goal but also hallucinates how to reach the original goal from the new one. Take playing frisbee for instance. When an agent jumps to catch the frisbee and yet misses it, the agent receives no positive feedback under the sparse reward setting. Using HER, the agent could set the end of its episode as the new goal — position of the frisbee; with DHER, however, the agent finds a trajectory from its past experiences as the imagined path of the frisbee, and thereby extrapolates towards the original goal.
+
+In particular, we do the following for DHER. To finish the tasks with dynamic goals needs to explore experience and understand multiple goals. DHER uses replay buffers to allow the agent to learn from a couple of failures by assembling new ‘experience’ from different episodes. The proposed method retrieves memories to find the connection between the experience of different episodes. It largely improves the sample efficiency in dynamic goal task settings. More importantly, this strategy makes it possible to learn in the setting that both sparse rewards and dynamic goals exist.
+
+We evaluate our method along with the state-of-the-art baselines on new environments and manipulation tasks, which have sparse rewards and dynamic goals. Our results demonstrate that DHER is clearly better than others for these tasks. We also transfer policies trained in our simulation based on DHER to a physical robot and show that DHER can be applied to solving real-world robotics problems.
+
+We summarize our main contributions as follows: (1) We demonstrate that, both in simulation and real worlds, DHER succeeds in continuous control with a moving target. To our knowledge, this is the first empirical result on manipulation tasks that demonstrates model-free learning methods can tackle tasks of this complexity. (2) We show that with assembling new experience from two failures, the sample complexity can be reduced dramatically. We attribute this to global knowledge learning in a set of failed experience which breaks the constraint of local one-episode experience towards more robust strategies. (3) We design and implement a set of new environments and continuous tasks with dynamic goals, which would be of interest to researchers at the intersection of robotics and reinforcement learning.1
+
+# 2 RELATED WORK
+
+Recent works in deep RL have shown impressive results in different domains, such as games (Bellemare et al., 2013; Silver et al., 2016), simulated control tasks (Brockman et al., 2016) and so on. There have been several proposed RL methods for playing Atari games, including DQN (Mnih et al., 2015), UVFA (Schaul et al., 2015b) and so on. UVFA trains a single neural network approximating multiple value functions for state and goal. For the continuous control, DDPG (Lillicrap et al., 2015) is a popular actor-critic algorithm that has shown impressive results in continuous control tasks. Dynamic goals appear in games and planning, often addressed by rewards shaping or search (Kaelbling, 1993; Mnih et al., 2015; Di Rocco et al., 2013). When the rewards are sparse, there is few work studying the dynamic goals to the best of our knowledge.
+
+Curriculum learning is also used for reinforcement learning scenarios. The idea is that solving easier problems first has advantages to learn more complex goals later and thus that learning can be optimized by presenting the problems in an optimal order, a curriculum (Bengio et al., 2009). Narvekar et al. (2017) and Florensa et al. (2018) proposed methods to automatically produce subtasks or subgoals for a given target. Narvekar et al. (2017) produce subtasks according to predefined tasks of a given domain problem. Florensa et al. (2018) use a Generative Adversarial Network (GAN) to produce goals with different difficulties. Different from these methods, our approach produces a series of goals for an episode from failed experience.
+
+Experience replay is an important technique and introduced to break temporal correlations by mixing more and less recent experience for updating policies (Lin, 1992). It was demonstrated for its efficiency in DQN (Mnih et al., 2015). Prioritized experience replay improves the speed of training by considering prioritizing transitions in the replay buffer (Schaul et al., 2015b). HER considers modifying experience in the replay buffer for continuous control (Andrychowicz et al., 2017). By contrary, our approach assembles successful experience from two failures. Comparing with these methods, which do not consider dynamic goals, our approach uses a series of goals to assemble successful experience. As a result, our method is able to accomplish the tasks with sparse rewards and dynamic goals.
+
+# 3 METHODOLOGY
+
+We first review how HER works (Andrychowicz et al., 2017), followed by details of the proposed DHER for dealing with dynamic goals.
+
+HER is a simple and effective method of manipulating the replay buffer used in off-policy RL algorithms that allows it to learn policies more efficiently from sparse rewards. It assumes the goal being pursued does not influence the environment dynamics. After experiencing an episode $\bar { \{ } s _ { 0 } , s _ { 1 } , \dotsb , s _ { T } \}$ , every transition $s _ { t } \to s _ { t + 1 }$ along with the goal for this episode is usually stored in the replay buffer. Some of the saved episodes fail to reach the goal, providing no positive feedback to the agent. However, with HER, the failed experience is modified and also stored in the replay buffer in the following manner. The idea is to replace the original goal with a state visited by the failed episode. As the reward function remains unchanged, this change of goals hints the agent how to achieve the new goal in the environment. HER assumes that the mechanism of reaching the new goal helps the agent learn for the original goal.
+
+# 3.1 DYNAMIC GOALS
+
+Dynamic goals are not static and change at every timestep. We follow the multi-goal setting of Andrychowicz et al. (2017). The goals are part of the environment and do not influence the environment dynamics. We also assume that a dynamic goal $g _ { t } \in \mathcal G$ moves by following some law $g _ { t } = g ( t ; \gamma )$ , where $\gamma$ parameterizes the law (e.g., acceleration in Newton’s law of motion), and yet its underlying moving law is unknown to the agent.
+
+Moreover, we need to have some basic knowledge of goals, i.e., the measure of goal similarity on $\mathcal { G }$ . We assume that $g _ { t } \in \mathcal G$ corresponds to some predicate $f _ { g _ { t } } : S  \{ 0 , 1 \}$ and that the agent’s goal is to achieve any state $s$ that satisfies $f _ { g _ { t } } ( s ) = 1$ . We use $S = \mathcal { G }$ and define $f _ { g _ { t } } ( s ) : = [ s = g _ { t } ]$ , which can be considered as a measure of goal similarity between $g _ { t }$ and $s$ . The goals can also specify only some properties of the state. Take manipulation tasks for instance: $\mathcal { G } = \mathbb { R } ^ { 3 }$ corresponds to the 3D
+
+# Algorithm 1 Dynamic Hindsight Experience Replay with Experience Assembling
+
+Require: an off-policy RL algorithm A, replay buffer $R$ , a reward function $r$
+
+1: Initialize A and replay buffer $R$   
+2: for episode $\mathbf { \Omega } = 1 , 2 , \cdots , M$ do   
+3: Sample an initial goal $g _ { 0 }$ and an initial state $s _ { 0 }$   
+4: for $t = 0 , \cdots , T - 1$ do   
+5: Sample an action $a _ { t }$ using the behavioral policy from A:   
+6: $a _ { t }  \pi ( s _ { t } | g _ { t } )$   
+7: Execute the action $a _ { t }$ and observe a new state $s _ { t + 1 }$ and a new goal $g _ { t + 1 }$   
+8: end for   
+9: for $t = 0 , \cdots , T - 1$ do   
+10: $r _ { t } : = r ( s _ { t } , a _ { t } , g _ { t + 1 } )$   
+11: Store the transitions $\left( s _ { t } | g _ { t } , a _ { t } , r _ { t } , s _ { t + 1 } | g _ { t + 1 } \right)$ in $R$ (Standard experience replay)   
+12: end for   
+13: Collect failed episodes to $\mathcal { E }$   
+14: 15: for S $E _ { i } \in \mathcal { E }$ donother $E _ { j } ( i \neq j ) \in \mathcal { E }$ where $g _ { i , p } ^ { a c } = g _ { j , q } ^ { d e }$   
+16: if $E _ { j } \neq \boldsymbol { \mathcal { O } }$ then   
+17: Clone a goal trajectory $\{ g _ { 0 } ^ { \prime } , \cdot \cdot \cdot , g _ { m } ^ { \prime } \} _ { m = \operatorname* { m i n } \{ p , q \} }$ in which $g _ { t } ^ { \prime } = g _ { j , q - m + t } ^ { d e }$ from $E _ { j }$   
+18: for $t = \{ 0 , \cdots , m - 1 \}$ do   
+19: $r _ { t } ^ { \prime } : = r ( s _ { i , p - m + t } , a _ { i , p - m + t } , g _ { t + 1 } ^ { \prime } )$   
+20: Store the transition $\left( s _ { i , p - m + t } | g _ { t } ^ { \prime } , a _ { i , p - m + t } , r _ { t } ^ { \prime } , s _ { i , p - m + t + 1 } | g _ { t + 1 } ^ { \prime } \right) \mathrm { i n } R \left( \mathrm { D H E R } \right)$   
+21: end for   
+22: end if   
+23: end for   
+24: for $t = 1 , \cdots , N$ do   
+25: Sample a minibatch $B$ from the replay buffer $R$   
+26: Optimize A using the minibatch $B$   
+27: end for   
+28: end for
+
+positions of an object $s ^ { \mathrm { o b j } }$ about which the observation could include additional properties of the object. For a more concrete example, consider pushing a block towards a moving target position. The success of a task is defined as $f \big ( s _ { t } , g _ { t } \big ) = \mathbf { 1 } _ { \mathrm { c o n d i t i o n } } \big ( \| s _ { t } ^ { \mathrm { o b j } } - g _ { t } \| \leq \epsilon \big )$ , where $s _ { t } ^ { \mathrm { o b j } }$ is the position of the object in the state $s _ { t }$ and $\epsilon$ denotes a tolerance by the environment. $\mathbf { 1 } _ { \mathrm { c o n d i t i o n } }$ is an indicator function. The agent aims to achieve any state $s _ { t }$ that satisfies $f ( s _ { t } , g _ { t } ) = 1$ . It receives a sparse reward $r _ { t } : = r ( \tilde { s } _ { t } , a _ { t } , g _ { t + 1 } ) = - \mathbf { 1 } _ { \mathrm { c o n d i t i o n } } ( f ( s _ { t + 1 } , g _ { t + 1 } ) \neq 1 )$ upon making an action $a _ { t }$ .
+
+It is worth discussing the main difference between the implications of the dynamic goals and the static ones. Expressing a static goal in the following way, $g _ { t } ^ { \mathrm { s t a t i c } } = g ^ { \mathrm { s t a t i c } } , \forall t$ , highlights the key challenge of dealing with the dynamic goal. Namely, the agent has no access to the underlying law of the dynamic goal in our setting, whereas the law of being static is known to the agent in Andrychowicz et al. (2017). In other words, the agent has no clue at all how to construct a new dynamic goal that is admissible by the environment.
+
+# 3.2 DYNAMIC HINDSIGHT EXPERIENCE REPLAY
+
+At the first glance, we shall compose a new dynamic goal $g ^ { \mathrm { d y n a m i c } } = \{ s _ { t _ { 0 } } ^ { \mathrm { o b j } } , s _ { t _ { 1 } } ^ { \mathrm { o b j } } , \cdot \cdot \cdot , s _ { t _ { T ^ { \prime } } } ^ { \mathrm { o b j } } \}$ from a in order to apply HER (Andrychowicz et al., 2017) to our problem setting. However, per the discussion above, this new dynamic goal $g ^ { \mathrm { d y n a m i c } }$ may be inadmissible by the environment, leading to no positive feedback to the agent at all.
+
+We tackle the challenge by drawing the following two observations. One is that many episodes fail in the replay buffer, implying that the agent can actually build a new goal upon more than one episodes. The other is that the more failed experience the agent has, the more possible for the agent to use the connection between achieved goals in an episode and desired goals in some other episode. Take the example of a moving object that the agent must reach, desired goals are the positions of the moving object and achieved goals are the positions of a gripper (controlled by the agent). There may exist some positions that both the object and the gripper have ever reached respectively.
+
+![](images/685259757917f2907f387b49a9224aabd57ab150ad7074e7a37b24515868d9cf.jpg)  
+Figure 2: The proposed tasks with dynamic goals (red objects). Arrow indicates the movement of a goal. The first row indicates initial states. The second row indicates final states.
+
+After experiencing some episode $s _ { 0 } , s _ { 1 } , \cdots , s _ { T }$ , we store in the replay buffer every transition $s _ { t } \ \to \ s _ { t + 1 }$ for this episode, defined as $\left( { { s _ { t } } , { a _ { t } } , { r _ { t } } , { s _ { t + 1 } } } \right)$ , where $s _ { t }$ indicates a state $s _ { t }$ at timestep $t$ , and $a _ { t }$ indicates an action and $r _ { t }$ indicates a reward. Thus before $t$ , there are a series of records $\left\{ \left( s _ { 0 } , a _ { 0 } , r _ { 0 } , s _ { 1 } \right) \cdot \cdot \cdot , \left( s _ { t } , a _ { t } , r _ { t } , s _ { t + 1 } \right) \right\}$ . A state consists of three parts: observation $o _ { t }$ , desired goal $g _ { t } ^ { d e }$ and achieved goal $g _ { t } ^ { a c }$ , define as $\dot { s } _ { t } = \langle o _ { t } , g _ { t } ^ { a c } , g _ { t } ^ { d e } \rangle$ , where normally $g _ { t } ^ { d e } = g _ { t }$ and $g _ { t } ^ { a c }$ indicates goals that the agent has achieved.
+
+We reuse the failed experience from the replay buffer with inverse simulation to create successful rewards for the agent, as shown in Algorithm 1 (lines 13-23). Our inverse simulation contains two main steps: First, given a failed episode, for its achieved goal trajectory, we try to find a desired goal trajectory from other episodes that could match it (line 15). Second, we assemble a new episode by matching the achieved goal trajectory of the given episode to the desired goal trajectory of the founded one (lines 17-21). Let $g _ { i , q } ^ { a c }$ indicate the achieved goal of the agent at timestep $q$ in episodxperience $i$ $g _ { j , p } ^ { d e }$ te the desired goal at timestep , we search and draw two faile $p$ in episoepisodes $j$ . Gand n of failed), where $\{ E _ { 0 } , E _ { 1 } , \stackrel { \cdot } { E } _ { 2 } , \cdot \cdot \cdot \}$ $E _ { i }$ $E _ { j }$ $( i \neq j )$ $\exists i , j , p , q ,$ s.t. $g _ { i , p } ^ { a c } = g _ { j , q } ^ { d e }$ . If we find two such failed episodes, we combine the two experience by replacing the desired goals in $E _ { i }$ by $\{ g _ { j , t } ^ { d e } \}$ , where $j$ indicates $E _ { j }$ and $t \leq \operatorname* { m i n } \{ p , q \}$ . Based on this, we end up assembling a new experience $E _ { i } ^ { \prime }$ based on $E _ { i }$ with a new “imagined” goal trajectory $\{ g _ { j , 0 } ^ { d e } , \cdot \cdot \cdot , g _ { j , t } ^ { d e } \}$ where $t \leq \operatorname* { m i n } \{ p , q \}$ .
+
+More details of the complete $\mathrm { R L + D H E R }$ method are shown in Algorithm 1. Unlike HER, our DHER needs to search all failed experiences to compose a “imagined” goal trajectory. Hence, the efficiency of searching the memory is important. In our implementation, we use two hash tables to store the trajectories of achieved goals and desired goals, respectively.
+
+# 4 EXPERIMENT
+
+We run extensive experiments to examine the proposed DHER for moving goals and compare it with some competing baselines. We first introduce the environments and tasks that we want to address, followed by the experimental results. Demo videos from our experiments are available at https://sites.google.com/view/dher.
+
+![](images/868b5ca50a241e6883855868e5cdc6d4e2e4a7d4f491d103d018de67c19012a7.jpg)  
+Figure 3: Results on different environments.
+
+# 4.1 ENVIRONMENTS
+
+Whereas grasping moving targets are fairly common in robotic applications, there are rarely existing environments featuring dynamic goals. We modify the robotic manipulation environments created by OpenAI (Brockman et al., 2016) for our experiments. As shown in Figure 2, we assign certain rules to the goals so that they accordingly move in the environments while an agent is required to control the robotic arm’s grippers to reach the goal that moves along a straight line (Dy-Reaching), to reach the goal that moves in a circle (Dy-Circling), or to push a block to the goal that moves along a straight line (Dy-Pushing). In addition, we also develop a new GREEDY SNAKE environment (DySnake), in which the goal moves from one discrete cell to another. The greedy snake aims to reach the goal (and eat it). No matter what actions are taken by the agent, the underlying rule of changing the goals’ positions remain the same. We assume that the law of the goal’s motion is unknown to the agent. More details of the tasks are described in the appendix.
+
+For the first three tasks, we follow the basic settings of OpenAI robotics environments (Brockman et al., 2016). States are read from the MuJoCo physics engine. An observation consists of relative positions of the object and the target (grippers are blocked) Goals are positions in the 3D world coordinate system with a fixed tolerance (we use $\epsilon = 0 . 0 1$ for the tolerance). Note the goals are able to move in our tasks. The velocity we use is $v = 0 . 0 1 1$ . 1 epoch indicates 100 episodes. The start positions of the goals are randomly chosen. Rewards are binary and sparse: $r ( s _ { t } , a _ { t } , g _ { t } ) =$ $- \mathbf { 1 } _ { \mathrm { c o n d i t i o n } } \big ( | s _ { t + 1 } ^ { \mathrm { o b j } } - g _ { t + 1 } | \geq \epsilon \big )$ where $s _ { t + 1 }$ and $g _ { t + 1 }$ are respectively the state and dynamic goal after the execution of the action $a _ { t }$ in the state $s _ { t }$ . Two positions are overlapped if they are close within the tolerance $\epsilon$ . We use 3-dimensional actions, in which three dimensions correspond to the desired relative gripper position at the next timestep.
+
+For the last task, it is very similar to the standard snake game. There is a 2D plane grid whose size is $3 0 \times 4 0$ . A snake and a goal (food) both move in this grid. We use a $1 \times 1$ square as the body of the snake and do not allow the snake to grow any longer as it moves. The states of the system are represented by using the positions of the snake and food. Goals are the positions of the food. The snake has to move itself such that it resides in the same cell as the food at a certain timestep. The velocity of the goal is set to $( 0 , 1 )$ . The start positions of the goal are set randomly in different episodes of the game, so are the start positions of the snake. Rewards are binary and sparse: $r \big ( s _ { t } , \bar { a } _ { t } , g _ { t + 1 } \big ) = - \bar { \mathbf { 1 } } _ { \mathrm { c o n d i t i o n } } \big ( \big | s _ { t + 1 } ^ { \mathrm { s n a k e } } - g _ { t + 1 } \big | \bar { \neq } 0 \big )$ where $s _ { t + 1 }$ and $g _ { t + 1 }$ are the environment’s state and goal after the agent executes action $a _ { t }$ in the state $s _ { t }$ . Observations are represented by the positions of the snake and food. We also add to the state the distance between the snake and food. Actions allowed in the game are the following: move up, move down, move left, and move right, for one cell per timestep.
+
+# 4.2 BASELINES
+
+For the first three tasks which call for continuous control, we consider two competing baselines:2 • DDPG, which is a model-free RL algorithm for continuous control (Lillicrap et al., 2015). It learns a deterministic policy by using a stochastic counterpart to explore in the training.
+
+![](images/732a387a80c212738b2fb410b777a5c71d62a4dacb48b29dd438871f23abaf26.jpg)  
+Figure 4: Low velocity: 0.001.
+
+![](images/f8c0fd7014d07719a2c477eef04492742d4a9d1ff91065b3d850a3053e6e0ee6.jpg)  
+Figure 5: High velocity: 0.016.
+
+• $\mathrm { D D P G } + \mathrm { H E R }$ , which improves the replay buffer of DDPG by the hindsight experience replay (Andrychowicz et al., 2017).   
+DDPG (dense), which employs the negative distance $( - d )$ as dense rewards.   
+DDPG (dense-2), which employs the negative distance $( - d )$ as dense rewards if $d \geq \epsilon$ . However, if $d < \epsilon$ (i.e., success) it uses $( - d + 1 . 0 )$ as rewards. 1.0 is a bonus.
+
+For the last task of discrete control, we use the following baselines in the experiments: DQN (Mnih et al., 2015) and $\mathrm { D Q N + H E R }$ , which uses HER to enhance the replay in DQN.
+
+• DQN, which is a powerful model-free RL algorithm for discrete action spaces (Mnih et al., 2015).   
+• $\mathrm { D Q N + H E R }$ , which uses HER to enhance the replay in DQN.   
+• DQN (dense), which uses the negative distance $( - d )$ as dense rewards.   
+• DQN (dense-2), which uses the negative distance $( - d )$ as dense rewards. However, if $d = 0 . 0$ (i.e., success) it uses $( - d + 1 . 0 )$ as rewards instead. 1.0 is a bonus.
+
+# 4.3 COMPARISON RESULTS ON THE ROBOTIC ENVIRONMENTS
+
+For the continuous control, we present three sets of comparison results in Figure 3 for the first three tasks, respectively. Consistently, the results show our DHER algorithm outperforms the others. The two baselines are not able to catch up even after we train them for thousands of iterations. Vanilla DDPG is slightly better than the version with HER. HER does not benefit DDPG in these tasks because the goals in HER are fixed, fundamentally misleading the agent in the attempt of solving the tasks with dynamic goals. The results of DDPG (dense) and DDPG (dense-2) suggest that even the dense rewards do not work well as they are agnostic to the task of interest. A good reward shaping may give rise to better performance by carefully tuning it for the task of dynamic goals.
+
+Comparing Figure 3a and Figure 3b with Figure 3c, we find that DHER learns faster in Dy-Reaching and Dy-Circling than Dy-Pushing probably because Dy-Reaching and Dy-Circling are easier tasks than Dy-Pushing. In Dy-Pushing, all the algorithms take a fairly big amount of time to explore without receiving any positive feedback. However, the more failed experiences the agent encounters, the better change our algorithm is able to identify relevant episodes from them for assembling useful dynamic goals. As a result, DHER is able to pick up the momentum and learns faster and better than the baselines after a certain point. In Figure 3a, the performance decreases a little. The reason may be that as successful experience increases, some assembled experience is inconsistent with these successful experience.
+
+# 4.3.1 COMPARISON USING DIFFERENT VELOCITIES OF GOALS
+
+To show the performance of our method on more complex tasks with different velocities, we study different methods in Dy-Reaching environment as shown in Figures 4 and 5 with the same physical properties as the previous experiments. Overall the results show our method is much better than DDPG and HER. As a reminder, the threshold for calculating rewards we used is 0.01. In Figure 4, the task becomes an easier task because of the slower velocity. It shows that our method quickly achieves to a good result around 5 epoch. Comparing with Figure 3a, it shows that the performance with $v = 0 . 0 0 1$ is better than the performance with $v = 0 . 0 1 1$ and get $1 5 \%$ improvements. However, it also shows the performance with $v = 0 . 0 1 6$ is worse than the performance with $v = 0 . 0 1 1$ . Both DDPG and $\mathrm { \Delta D D P G + H E R }$ failed when $v = 0 . 0 1 6$ and their performance is 0. This performance is consistent because the task becomes more difficult when the velocity increases.
+
+![](images/14dd0b3e1878d3f49fb1b7d44ca84006cca0ac15133dc036aef116910149f401.jpg)  
+Figure 6: Snake with dynamic goals.
+
+![](images/97b49eb4c50a91b591b5c09b7c8417f90a64b3336f8b06a8631418b78f185b01.jpg)  
+Figure 7: Special: $\mathrm { H E R + }$ knows how goals move.
+
+# 4.4 COMPARISON ON THE DYNAMIC SNAKE ENVIRONMENT
+
+In the Dy-Snake environment, which is a discrete control environment, we present the results of the chasing food task in Figure 6. The results show that the proposed algorithm works best. DQN is better than HER. HER fails for this task. That HER fails for this task shows just using achieved goals is not enough for the tasks with dynamic goals and can lead wrong direction. The results also show that around 800 episodes, the performance of DQN and DHER is close and DHER is slightly better than DQN. This is because the chasing food task is a simple task. The action space is very small and just 4 types of actions. After enough exploration, DQN also has competitive performance. However, at the beginning, DHER quickly achieves very good performance. It shows that assembling experience from two failures improves the performance very efficiently in this task. DQN (dense) and DQN (dense-2) help learn the policy at the early stage. However, in the long run, it does not lead to any particular benefits.
+
+# 4.5 SIM TO REAL ADAPTATION
+
+We used policies for Dy-Circling task and a new Pouring task trained in our simulator 3 to deploy them on a physical robot. As shown in Figure 8, the policies were trained by using DHER and adapted to the real robot without any finetuning. However, the policy requires accurate localizations of the gripper and the goal. For Dy-Circling task, the robot’s gripper was blocked. There were a toy turntable, whose speed is unknown, and a blue block on the turntable. We set the position 1cm above the block as the target position. The position of the block was predicted based on traditional contour shape analysis using camera images. For Pouring task, the robot gripped a can. A man held a cup and moved it. The cup was set as the target and with a green marker. We used the marker to estimate its position.
+
+Our policies were transferred successfully for both tasks. With the accurate positions, we have $100 \%$ success rate for 5 trials. It was observed that the robot had learned to not only follow the current target but also step forward to the future target position. Demo videos about the experiments are available at https://sites.google.com/view/dher.
+
+![](images/ff03243dba37e8e374b610dab429ef50349cfd9bf2cd37e4c19e2d40e16ac98c.jpg)  
+Figure 8: Adapting the policies trained based on DHER from our simulation to a real robotic arm.
+
+4.6 SPECIAL CASE: HOW ABOUT IF HER KNOWS THE LAW OF THE MOTION OF A GOAL
+
+We use Dy-Snake to demonstrate the experimental results for a special case that the law of the motion of the target (food) is known to agents. Because the motion of the food is very simple and controllable in Dy-Snake environment. We develop a direct extension of HER, called $\mathrm { H E R + }$ , that modifies desired goals at every timestep based on the law of the motion of the food to create successful experience. More details of $\mathrm { H E R + }$ are described in the appendix.
+
+We show the results in Figure 7. DHER and $\mathrm { H E R + }$ are both better than DQN at the beginning. DHER is slightly better than $\mathrm { H E R + }$ , which shows the efficiency of DHER is comparable in this simple task.
+
+# 5 CONCLUSION
+
+We introduced a novel technique that assembles successful experience from a couple of failures. With this technique, our proposed algorithm called DHER ( Dynamic Hindsight Experience Replay) is able to address the tasks with sparse rewards and dynamic goals. Our technique can be combined with an arbitrary off-policy RL algorithm and we experimentally demonstrated that with DQN and DDPG. As far as we know, it is the first time that an agent is allowed to learn from assembled experience from two failures.
+
+# ACKNOWLEDGMENTS
+
+We would like to thank Weitao Xi, Tianzhou Wang, Tingguang Li for performing some additional transfer experiments. We would also like to thank Han Liu and the whole RL team for fruitful discussions as well as the anonymous reviewers for their comments.
+
+# REFERENCES
+
+Marcin Andrychowicz, Filip Wolski, Alex Ray, Jonas Schneider, Rachel Fong, Peter Welinder, Bob McGrew, Josh Tobin, OpenAI. Pieter Abbeel, and Wojciech Zaremba. Hindsight experience replay. In Advances in Neural Information Processing Systems, pp. 5048–5058, 2017.   
+Marc G. Bellemare, Yavar Naddaf, Joel Veness, and Michael Bowling. The arcade learning environment: An evaluation platform for general agents. Journal of Artificial Intelligence Research, 47:253–279, 2013. ISSN 1076-9757.   
+Yoshua Bengio, Jrme Louradour, Ronan Collobert, and Jason Weston. Curriculum learning. In Proceedings of the 26th International Conference on Machine Learning, pp. 41–48. ACM, 2009.   
+Greg Brockman, Vicki Cheung, Ludwig Pettersson, Jonas Schneider, John Schulman, Jie Tang, and Wojciech Zaremba. Openai gym, 2016.   
+Maurizio Di Rocco, Federico Pecora, Prasanna Kumar Sivakumar, and Alessandro Saffiotti. Configuration planning with multiple dynamic goals. In AAAI Spring Symposium: Designing Intelligent Robots, 2013.   
+Yan Duan, Xi Chen, Rein Houthooft, John Schulman, and Pieter Abbeel. Benchmarking deep reinforcement learning for continuous control. In Proceedings of the 33rd International Conference on Machine Learning, pp. 1329–1338, 2016.
+
+Carlos Florensa, David Held, Xinyang Geng, and Pieter Abbeel. Automatic goal generation for reinforcement learning agents. In Proceedings of the 35th International Conference on Machine Learning, volume 80, pp. 1515–1528, 2018.
+
+Nicolas Heess, Dhruva TB, Srinivasan Sriram, Jay Lemmon, Josh Merel, Greg Wayne, Yuval Tassa, Tom Erez, Ziyu Wang, S. M. Ali Eslami, Martin A. Riedmiller, and David Silver. Emergence of locomotion behaviours in rich environments. CoRR, abs/1707.02286, 2017.
+
+Leslie Pack Kaelbling. Learning to achieve goals. In Proceedings of the 13th International Joint Conference on Artificial Intelligence, pp. 1094–1099. Citeseer, 1993.
+
+Timothy P. Lillicrap, Jonathan J. Hunt, Alexander Pritzel, Nicolas Heess, Tom Erez, Yuval Tassa, David Silver, and Daan Wierstra. Continuous control with deep reinforcement learning. arXiv preprint arXiv:1509.02971, 2015.
+
+Long-Ji Lin. Self-improving reactive agents based on reinforcement learning, planning and teaching. Machine Learning, 8(3-4):293–321, 1992.
+
+Volodymyr Mnih, Koray Kavukcuoglu, David Silver, Andrei A. Rusu, Joel Veness, Marc G. Bellemare, Alex Graves, Martin Riedmiller, Andreas K. Fidjeland, Georg Ostrovski, Stig Petersen, Charles Beattie, Amir Sadik, Ioannis Antonoglou, Helen King, Dharshan Kumaran, Daan Wierstra, Shane Legg, and Demis Hassabis. Human-level control through deep reinforcement learning. Nature, 518:529, 2015.
+
+Sanmit Narvekar, Jivko Sinapov, and Peter Stone. Autonomous task sequencing for customized curriculum design in reinforcement learning. In Proceedings of the 27th International Joint Conference on Artificial Intelligence, volume 147, pp. 149, 2017.
+
+Andrew Y. Ng, Daishi Harada, and Stuart Russell. Policy invariance under reward transformations: Theory and application to reward shaping. In Proceedings of the 16th International Conference on Machine Learning, volume 99, pp. 278–287, 1999.
+
+Tom Schaul, Daniel Horgan, Karol Gregor, and David Silver. Universal value function approximators. In Proceedings of the 32nd International Conference on Machine Learning, pp. 1312–1320, 2015a.
+
+Tom Schaul, John Quan, Ioannis Antonoglou, and David Silver. Prioritized experience replay. arXiv preprint arXiv:1511.05952, 2015b.
+
+John Schulman, Sergey Levine, Philipp Moritz, Michael I. Jordan, and Pieter Abbeel. Trust region policy optimization. CoRR, abs/1502.05477, 2015.
+
+John Schulman, Filip Wolski, Prafulla Dhariwal, Alec Radford, and Oleg Klimov. Proximal policy optimization algorithms. CoRR, abs/1707.06347, 2017.
+
+David Silver, Aja Huang, Chris J Maddison, Arthur Guez, Laurent Sifre, George Van Den Driessche, Julian Schrittwieser, Ioannis Antonoglou, Veda Panneershelvam, Marc Lanctot, et al. Mastering the game of go with deep neural networks and tree search. Nature, 529(7587):484, 2016.
+
+Emanuel Todorov, Tom Erez, and Yuval Tassa. Mujoco: A physics engine for model-based control. In 2012 IEEE/RSJ International Conference on Intelligent Robots and Systems, pp. 5026–5033. IEEE, 2012.
+
+Ziyu Wang, Victor Bapst, Nicolas Heess, Volodymyr Mnih, Remi Munos, Koray Kavukcuoglu, and ´ Nando de Freitas. Sample efficient actor-critic with experience replay. CoRR, abs/1611.01224, 2016.
+
+# APPENDIX
+
+# TASKS WITH DYNAMIC GOALS
+
+We have created four tasks as described below and illustrated by Figure 2. The first three tasks are based on the robotic environments. The last is based on the GREEDY SNAKE environment.
+
+• Dy-Reaching: The task is to control the robotic arm so that its gripper can reach the target position. The target position moves from one point to another along a straight line with a constant velocity.   
+• Dy-Circling: The task is to control the robotic arm so that its gripper can reach the target position. The target position moves along a circle with a constant velocity. Dy-Pushing: in this task, a box is placed on a table in front of the robotic arm. The robot is required to move the box to the target location on the table. The target location moves from one position to another with a fixed velocity. Note that the robot’s grippers are locked to prevent it from grasping. The learned behavior is actually a mixture of pushing and rolling.   
+Dy-Snake: in this task, a snake and food are placed on a rectangle map and the task is to control the snake to eat the food. The food is moving from one position to another position with a fixed velocity.
+
+# HARDWARE
+
+We use the Universal Robots UR10 with a gripper. We use a RealSense Camera SR300 to track the position of objects. The gripper is blocked. We use a marker on the gripper for camera calibration. During adapting the robot, for the position of the target, we use the camera to estimate it.
+
+# SIMULATION
+
+We simulate the physical system using the MuJoCo physics engine (Todorov et al., 2012) and also use MuJoCo to render the images. In our tasks, we use positions provided by MuJoCo for training policies in the simulation.
+
+In Figure 9, we demonstrate our simulation and the physics environment.
+
+![](images/0ab0a04331e1ed7ee05503beb83d72a71ddd08962ea6776f4dbc386edf14fc2c.jpg)  
+Figure 9: Our simulation and the physics environment.
+
+A SPECIAL AND SIMPLER CASE - HER+
+
+The paper considers a general situation that the law of the motion of goals is invisible to an agent. However, we relax this assumption and assume that in some situations the law of the motion of goals is easy to obtain, i.e., the parameters of $g ( t ; \gamma )$ are known. For example, it is able to calculate the velocity of an object by observing the trajectories of the object.
+
+In this situation, we do not need to search failed experience. With the knowledge of the velocity of an object, it is straightforward that we can calculate any trajectory of desired goals. Thus for every failed experience, at any time step $t$ , based on the achieved goal $g _ { t } ^ { a c }$ , we calculate new desired goals $g _ { t } ^ { d e } = g ( { \dot { t } } )$ corresponding to the achieved goals in order to construct successful experience.
+
+The details of $\mathrm { H E R + }$ are described in Algorithm 2. $\mathrm { H E R + }$ can be seen as a direct extension of HER. HER and $\mathrm { H E R + }$ can modify any failed experience to successful experience because they both assume the law of the motion of goals is known.
+
+# Algorithm 2 Hindsight Experience Replay Plus
+
+Require: an off-policy RL algorithm A, replay buffer $R$ , a reward function $r$   
+1: Initialize A and replay buffer $R$   
+2: for episode $\mathbf { \Omega } = 1 , 2 , \cdots , M$ do   
+3: Sample an initial goal $g _ { 0 }$ and an initial state $s _ { 0 }$   
+4: for $t = 0 , \cdots , T - 1$ do   
+5: Sample an action $a _ { t }$ using the behavioral policy from A:   
+6: $a _ { t } \doteq \pi ( s _ { t } | g _ { t } )$   
+7: Execute the action $a _ { t }$ and observe a new state $s _ { t + 1 }$ and a new goal $g _ { t + 1 }$   
+8: end for   
+9: for $t = 0 , \cdots , T - 1$ do   
+10: $r _ { t } : = r ( s _ { t } , a _ { t } , g _ { t + 1 } )$   
+11: Store the transitions $\left( s _ { t } | g _ { t } , a _ { t } , r _ { t } , s _ { t + 1 } | g _ { t + 1 } \right)$ in $R$ (Standard experience replay)   
+12: Sample a set of the achieved goals of $E _ { i }$ as additional goals for reply $G ^ { \prime }$   
+13: for $\bar { g _ { p } ^ { \prime } } \in G ^ { \prime }$ do   
+14: Calculate a goal trajectory $\{ g _ { 0 } ^ { \prime } , \cdots , g _ { p } ^ { \prime } \}$ where $g _ { t } ^ { \prime } = g ( t ; \gamma )$ $\mathrm { ( H E R + ) }$   
+15: for $t = \{ 0 , \cdots , p - 1 \}$ do   
+16: $r _ { t } ^ { \prime } : = r ( s _ { i , t } , a _ { i , t } , g _ { t + 1 } ^ { \prime } )$   
+17: Store the transition $\left( s _ { i , t } | g _ { t } ^ { \prime } , a _ { i , t } , r _ { t } ^ { \prime } , s _ { i , t + 1 } | g _ { t + 1 } ^ { \prime } \right) \mathrm { i n } R$   
+18: end for   
+19: end for   
+20: end for   
+21: end for

parse/train/Byf5-30qFX/Byf5-30qFX_content_list.json

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+    {
+        "type": "text",
+        "text": "DHER: HINDSIGHT EXPERIENCE REPLAY FOR DYNAMIC GOALS ",
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+    {
+        "type": "text",
+        "text": "Meng Fang∗, Cheng Zhou, Bei Shi, Boqing Gong, Jia Xu, Tong Zhang Tencent AI Lab ",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "ABSTRACT ",
+        "text_level": 1,
+        "bbox": [
+            454,
+            234,
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+            251
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "Dealing with sparse rewards is one of the most important challenges in reinforcement learning (RL), especially when a goal is dynamic (e.g., to grasp a moving object). Hindsight experience replay (HER) has been shown an effective solution to handling sparse rewards with fixed goals. However, it does not account for dynamic goals in its vanilla form and, as a result, even degrades the performance of existing off-policy RL algorithms when the goal is changing over time. ",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "In this paper, we present Dynamic Hindsight Experience Replay (DHER), a novel approach for tasks with dynamic goals in the presence of sparse rewards. DHER automatically assembles successful experiences from two relevant failures and can be used to enhance an arbitrary off-policy RL algorithm when the tasks’ goals are dynamic. We evaluate DHER on tasks of robotic manipulation and moving object tracking, and transfer the polices from simulation to physical robots. Extensive comparison and ablation studies demonstrate the superiority of our approach, showing that DHER is a crucial ingredient to enable RL to solve tasks with dynamic goals in manipulation and grid world domains. ",
+        "bbox": [
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+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "1 INTRODUCTION ",
+        "text_level": 1,
+        "bbox": [
+            176,
+            502,
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+            518
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "Deep reinforcement learning has been shown an effective framework for solving a rich repertoire of complex control problems. In simulated domains, agents have been trained to perform a diverse array of challenging tasks (Mnih et al., 2015; Lillicrap et al., 2015; Duan et al., 2016). In order to train such agents, it is often the case that one has to design a reward function that not only reflects the task at hand but also is carefully shaped $\\mathrm { N g }$ et al., 1999) to guide the policy optimization. Unfortunately, many of the capabilities demonstrated by reward engineering are often limited to specific tasks. Moreover, it requires both RL expertise and domain-specific knowledge to reshape the reward functions. For situations where we do not know what admissible behavior may look like, for example, using LEGO bricks to build a desired architecture, it is difficult to apply reward engineering. Therefore, it is essential to develop algorithms which can learn from unshaped and usually sparse reward signals. ",
+        "bbox": [
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+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "Learning with sparse rewards is challenging, especially when a goal is dynamic. Dynamic goals are common in games and planning problems, often addressed using reward shaping or search (Kaelbling, 1993; Mnih et al., 2015; Di Rocco et al., 2013). However, the difficulty posed by a sparse reward is exacerbated by the complicated environment dynamics in robotics (Andrychowicz et al., 2017). For instance, system dynamics around contacts are difficult to model and induce sensitivity in the system to small errors. Many robotic tasks also need executing multiple steps successfully over a long horizon, involve enormous search space, and require generalization to varying task instances. Policy gradient methods are breakthroughs in the challenging environments, such as PPO (Heess et al., 2017; Schulman et al., 2017), ACER (Wang et al., 2016), TRPO (Schulman et al., 2015) and so on. They are used in environments, where an agent tries to reach a target, learns to walk, runs, and so on. Recently, sampling-efficient learning is introduced and demonstrates a significant increase in performance for off-policy actor-critic DQN (Mnih et al., 2015) and DDPG (Lillicrap et al., 2015) algorithms. Hindsight experience replay (HER) is very effective for improving the performance of off-policy RL algorithms in solving goal-based tasks with sparse rewards (Andrychowicz et al., 2017). Similar to UVFA (Schaul et al., 2015a), it takes a goal state as part of input. However, it assumes the goal is fixed. As a result, this assumption actually impedes the learning of RL agents in the environments of moving goals. ",
+        "bbox": [
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+    {
+        "type": "image",
+        "img_path": "images/a34ff9c3bf9148b8d43e21b58e1ea68fe1bcb07b8ac12d22cc17bf9a91fd4060.jpg",
+        "image_caption": [
+            "Figure 1: The framework of DHER. DHER is a kind of experience replay method. It searches relevant failed experiences and then assembles them into successful experiences. "
+        ],
+        "image_footnote": [],
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "In this paper, we address this challenge with a new method, Dynamic Hindsight Experience Replay (DHER), for accomplishing tasks with moving goals. We follow the multi-goal setting in UVFA (Schaul et al., 2015a) and HER (Andrychowicz et al., 2017). It assumes that the goal being pursued does not influence the environment dynamics. We also need to have the knowledge of goal similarity. For example, in manipulation or grid world domains, we can use Euclidean distance between positions to measure the goal similarity. HER turns a failed episode to a success by composing a new task whose goal is achieved by that episode. Our idea allows an agent to learn from the failure one step further than HER: the agent not only sets a new goal but also hallucinates how to reach the original goal from the new one. Take playing frisbee for instance. When an agent jumps to catch the frisbee and yet misses it, the agent receives no positive feedback under the sparse reward setting. Using HER, the agent could set the end of its episode as the new goal — position of the frisbee; with DHER, however, the agent finds a trajectory from its past experiences as the imagined path of the frisbee, and thereby extrapolates towards the original goal. ",
+        "bbox": [
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+            382,
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+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "In particular, we do the following for DHER. To finish the tasks with dynamic goals needs to explore experience and understand multiple goals. DHER uses replay buffers to allow the agent to learn from a couple of failures by assembling new ‘experience’ from different episodes. The proposed method retrieves memories to find the connection between the experience of different episodes. It largely improves the sample efficiency in dynamic goal task settings. More importantly, this strategy makes it possible to learn in the setting that both sparse rewards and dynamic goals exist. ",
+        "bbox": [
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+            570,
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+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "We evaluate our method along with the state-of-the-art baselines on new environments and manipulation tasks, which have sparse rewards and dynamic goals. Our results demonstrate that DHER is clearly better than others for these tasks. We also transfer policies trained in our simulation based on DHER to a physical robot and show that DHER can be applied to solving real-world robotics problems. ",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "We summarize our main contributions as follows: (1) We demonstrate that, both in simulation and real worlds, DHER succeeds in continuous control with a moving target. To our knowledge, this is the first empirical result on manipulation tasks that demonstrates model-free learning methods can tackle tasks of this complexity. (2) We show that with assembling new experience from two failures, the sample complexity can be reduced dramatically. We attribute this to global knowledge learning in a set of failed experience which breaks the constraint of local one-episode experience towards more robust strategies. (3) We design and implement a set of new environments and continuous tasks with dynamic goals, which would be of interest to researchers at the intersection of robotics and reinforcement learning.1 ",
+        "bbox": [
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+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "2 RELATED WORK ",
+        "text_level": 1,
+        "bbox": [
+            176,
+            102,
+            339,
+            117
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "Recent works in deep RL have shown impressive results in different domains, such as games (Bellemare et al., 2013; Silver et al., 2016), simulated control tasks (Brockman et al., 2016) and so on. There have been several proposed RL methods for playing Atari games, including DQN (Mnih et al., 2015), UVFA (Schaul et al., 2015b) and so on. UVFA trains a single neural network approximating multiple value functions for state and goal. For the continuous control, DDPG (Lillicrap et al., 2015) is a popular actor-critic algorithm that has shown impressive results in continuous control tasks. Dynamic goals appear in games and planning, often addressed by rewards shaping or search (Kaelbling, 1993; Mnih et al., 2015; Di Rocco et al., 2013). When the rewards are sparse, there is few work studying the dynamic goals to the best of our knowledge. ",
+        "bbox": [
+            174,
+            132,
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+            258
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "Curriculum learning is also used for reinforcement learning scenarios. The idea is that solving easier problems first has advantages to learn more complex goals later and thus that learning can be optimized by presenting the problems in an optimal order, a curriculum (Bengio et al., 2009). Narvekar et al. (2017) and Florensa et al. (2018) proposed methods to automatically produce subtasks or subgoals for a given target. Narvekar et al. (2017) produce subtasks according to predefined tasks of a given domain problem. Florensa et al. (2018) use a Generative Adversarial Network (GAN) to produce goals with different difficulties. Different from these methods, our approach produces a series of goals for an episode from failed experience. ",
+        "bbox": [
+            174,
+            265,
+            825,
+            377
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "Experience replay is an important technique and introduced to break temporal correlations by mixing more and less recent experience for updating policies (Lin, 1992). It was demonstrated for its efficiency in DQN (Mnih et al., 2015). Prioritized experience replay improves the speed of training by considering prioritizing transitions in the replay buffer (Schaul et al., 2015b). HER considers modifying experience in the replay buffer for continuous control (Andrychowicz et al., 2017). By contrary, our approach assembles successful experience from two failures. Comparing with these methods, which do not consider dynamic goals, our approach uses a series of goals to assemble successful experience. As a result, our method is able to accomplish the tasks with sparse rewards and dynamic goals. ",
+        "bbox": [
+            174,
+            383,
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+            508
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "3 METHODOLOGY ",
+        "text_level": 1,
+        "bbox": [
+            176,
+            529,
+            341,
+            545
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "We first review how HER works (Andrychowicz et al., 2017), followed by details of the proposed DHER for dealing with dynamic goals. ",
+        "bbox": [
+            176,
+            559,
+            823,
+            588
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "HER is a simple and effective method of manipulating the replay buffer used in off-policy RL algorithms that allows it to learn policies more efficiently from sparse rewards. It assumes the goal being pursued does not influence the environment dynamics. After experiencing an episode $\\bar { \\{ } s _ { 0 } , s _ { 1 } , \\dotsb , s _ { T } \\}$ , every transition $s _ { t } \\to s _ { t + 1 }$ along with the goal for this episode is usually stored in the replay buffer. Some of the saved episodes fail to reach the goal, providing no positive feedback to the agent. However, with HER, the failed experience is modified and also stored in the replay buffer in the following manner. The idea is to replace the original goal with a state visited by the failed episode. As the reward function remains unchanged, this change of goals hints the agent how to achieve the new goal in the environment. HER assumes that the mechanism of reaching the new goal helps the agent learn for the original goal. ",
+        "bbox": [
+            174,
+            594,
+            825,
+            734
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "3.1 DYNAMIC GOALS",
+        "text_level": 1,
+        "bbox": [
+            176,
+            751,
+            338,
+            765
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "Dynamic goals are not static and change at every timestep. We follow the multi-goal setting of Andrychowicz et al. (2017). The goals are part of the environment and do not influence the environment dynamics. We also assume that a dynamic goal $g _ { t } \\in \\mathcal G$ moves by following some law $g _ { t } = g ( t ; \\gamma )$ , where $\\gamma$ parameterizes the law (e.g., acceleration in Newton’s law of motion), and yet its underlying moving law is unknown to the agent. ",
+        "bbox": [
+            174,
+            776,
+            825,
+            847
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "Moreover, we need to have some basic knowledge of goals, i.e., the measure of goal similarity on $\\mathcal { G }$ . We assume that $g _ { t } \\in \\mathcal G$ corresponds to some predicate $f _ { g _ { t } } : S  \\{ 0 , 1 \\}$ and that the agent’s goal is to achieve any state $s$ that satisfies $f _ { g _ { t } } ( s ) = 1$ . We use $S = \\mathcal { G }$ and define $f _ { g _ { t } } ( s ) : = [ s = g _ { t } ]$ , which can be considered as a measure of goal similarity between $g _ { t }$ and $s$ . The goals can also specify only some properties of the state. Take manipulation tasks for instance: $\\mathcal { G } = \\mathbb { R } ^ { 3 }$ corresponds to the 3D ",
+        "bbox": [
+            174,
+            854,
+            823,
+            924
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "Algorithm 1 Dynamic Hindsight Experience Replay with Experience Assembling ",
+        "text_level": 1,
+        "bbox": [
+            173,
+            102,
+            717,
+            118
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "Require: an off-policy RL algorithm A, replay buffer $R$ , a reward function $r$ ",
+        "bbox": [
+            176,
+            123,
+            679,
+            137
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "1: Initialize A and replay buffer $R$   \n2: for episode $\\mathbf { \\Omega } = 1 , 2 , \\cdots , M$ do   \n3: Sample an initial goal $g _ { 0 }$ and an initial state $s _ { 0 }$   \n4: for $t = 0 , \\cdots , T - 1$ do   \n5: Sample an action $a _ { t }$ using the behavioral policy from A:   \n6: $a _ { t }  \\pi ( s _ { t } | g _ { t } )$   \n7: Execute the action $a _ { t }$ and observe a new state $s _ { t + 1 }$ and a new goal $g _ { t + 1 }$   \n8: end for   \n9: for $t = 0 , \\cdots , T - 1$ do   \n10: $r _ { t } : = r ( s _ { t } , a _ { t } , g _ { t + 1 } )$   \n11: Store the transitions $\\left( s _ { t } | g _ { t } , a _ { t } , r _ { t } , s _ { t + 1 } | g _ { t + 1 } \\right)$ in $R$ (Standard experience replay)   \n12: end for   \n13: Collect failed episodes to $\\mathcal { E }$   \n14: 15: for S $E _ { i } \\in \\mathcal { E }$ donother $E _ { j } ( i \\neq j ) \\in \\mathcal { E }$ where $g _ { i , p } ^ { a c } = g _ { j , q } ^ { d e }$   \n16: if $E _ { j } \\neq \\boldsymbol { \\mathcal { O } }$ then   \n17: Clone a goal trajectory $\\{ g _ { 0 } ^ { \\prime } , \\cdot \\cdot \\cdot , g _ { m } ^ { \\prime } \\} _ { m = \\operatorname* { m i n } \\{ p , q \\} }$ in which $g _ { t } ^ { \\prime } = g _ { j , q - m + t } ^ { d e }$ from $E _ { j }$   \n18: for $t = \\{ 0 , \\cdots , m - 1 \\}$ do   \n19: $r _ { t } ^ { \\prime } : = r ( s _ { i , p - m + t } , a _ { i , p - m + t } , g _ { t + 1 } ^ { \\prime } )$   \n20: Store the transition $\\left( s _ { i , p - m + t } | g _ { t } ^ { \\prime } , a _ { i , p - m + t } , r _ { t } ^ { \\prime } , s _ { i , p - m + t + 1 } | g _ { t + 1 } ^ { \\prime } \\right) \\mathrm { i n } R \\left( \\mathrm { D H E R } \\right)$   \n21: end for   \n22: end if   \n23: end for   \n24: for $t = 1 , \\cdots , N$ do   \n25: Sample a minibatch $B$ from the replay buffer $R$   \n26: Optimize A using the minibatch $B$   \n27: end for   \n28: end for ",
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+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "positions of an object $s ^ { \\mathrm { o b j } }$ about which the observation could include additional properties of the object. For a more concrete example, consider pushing a block towards a moving target position. The success of a task is defined as $f \\big ( s _ { t } , g _ { t } \\big ) = \\mathbf { 1 } _ { \\mathrm { c o n d i t i o n } } \\big ( \\| s _ { t } ^ { \\mathrm { o b j } } - g _ { t } \\| \\leq \\epsilon \\big )$ , where $s _ { t } ^ { \\mathrm { o b j } }$ is the position of the object in the state $s _ { t }$ and $\\epsilon$ denotes a tolerance by the environment. $\\mathbf { 1 } _ { \\mathrm { c o n d i t i o n } }$ is an indicator function. The agent aims to achieve any state $s _ { t }$ that satisfies $f ( s _ { t } , g _ { t } ) = 1$ . It receives a sparse reward $r _ { t } : = r ( \\tilde { s } _ { t } , a _ { t } , g _ { t + 1 } ) = - \\mathbf { 1 } _ { \\mathrm { c o n d i t i o n } } ( f ( s _ { t + 1 } , g _ { t + 1 } ) \\neq 1 )$ upon making an action $a _ { t }$ . ",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "It is worth discussing the main difference between the implications of the dynamic goals and the static ones. Expressing a static goal in the following way, $g _ { t } ^ { \\mathrm { s t a t i c } } = g ^ { \\mathrm { s t a t i c } } , \\forall t$ , highlights the key challenge of dealing with the dynamic goal. Namely, the agent has no access to the underlying law of the dynamic goal in our setting, whereas the law of being static is known to the agent in Andrychowicz et al. (2017). In other words, the agent has no clue at all how to construct a new dynamic goal that is admissible by the environment. ",
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+    {
+        "type": "text",
+        "text": "3.2 DYNAMIC HINDSIGHT EXPERIENCE REPLAY",
+        "text_level": 1,
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "At the first glance, we shall compose a new dynamic goal $g ^ { \\mathrm { d y n a m i c } } = \\{ s _ { t _ { 0 } } ^ { \\mathrm { o b j } } , s _ { t _ { 1 } } ^ { \\mathrm { o b j } } , \\cdot \\cdot \\cdot , s _ { t _ { T ^ { \\prime } } } ^ { \\mathrm { o b j } } \\}$ from a in order to apply HER (Andrychowicz et al., 2017) to our problem setting. However, per the discussion above, this new dynamic goal $g ^ { \\mathrm { d y n a m i c } }$ may be inadmissible by the environment, leading to no positive feedback to the agent at all. ",
+        "bbox": [
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+        "page_idx": 3
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+    {
+        "type": "text",
+        "text": "We tackle the challenge by drawing the following two observations. One is that many episodes fail in the replay buffer, implying that the agent can actually build a new goal upon more than one episodes. The other is that the more failed experience the agent has, the more possible for the agent to use the connection between achieved goals in an episode and desired goals in some other episode. Take the example of a moving object that the agent must reach, desired goals are the positions of the moving object and achieved goals are the positions of a gripper (controlled by the agent). There may exist some positions that both the object and the gripper have ever reached respectively. ",
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+    {
+        "type": "image",
+        "img_path": "images/685259757917f2907f387b49a9224aabd57ab150ad7074e7a37b24515868d9cf.jpg",
+        "image_caption": [
+            "Figure 2: The proposed tasks with dynamic goals (red objects). Arrow indicates the movement of a goal. The first row indicates initial states. The second row indicates final states. "
+        ],
+        "image_footnote": [],
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "After experiencing some episode $s _ { 0 } , s _ { 1 } , \\cdots , s _ { T }$ , we store in the replay buffer every transition $s _ { t } \\ \\to \\ s _ { t + 1 }$ for this episode, defined as $\\left( { { s _ { t } } , { a _ { t } } , { r _ { t } } , { s _ { t + 1 } } } \\right)$ , where $s _ { t }$ indicates a state $s _ { t }$ at timestep $t$ , and $a _ { t }$ indicates an action and $r _ { t }$ indicates a reward. Thus before $t$ , there are a series of records $\\left\\{ \\left( s _ { 0 } , a _ { 0 } , r _ { 0 } , s _ { 1 } \\right) \\cdot \\cdot \\cdot , \\left( s _ { t } , a _ { t } , r _ { t } , s _ { t + 1 } \\right) \\right\\}$ . A state consists of three parts: observation $o _ { t }$ , desired goal $g _ { t } ^ { d e }$ and achieved goal $g _ { t } ^ { a c }$ , define as $\\dot { s } _ { t } = \\langle o _ { t } , g _ { t } ^ { a c } , g _ { t } ^ { d e } \\rangle$ , where normally $g _ { t } ^ { d e } = g _ { t }$ and $g _ { t } ^ { a c }$ indicates goals that the agent has achieved. ",
+        "bbox": [
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+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "We reuse the failed experience from the replay buffer with inverse simulation to create successful rewards for the agent, as shown in Algorithm 1 (lines 13-23). Our inverse simulation contains two main steps: First, given a failed episode, for its achieved goal trajectory, we try to find a desired goal trajectory from other episodes that could match it (line 15). Second, we assemble a new episode by matching the achieved goal trajectory of the given episode to the desired goal trajectory of the founded one (lines 17-21). Let $g _ { i , q } ^ { a c }$ indicate the achieved goal of the agent at timestep $q$ in episodxperience $i$ $g _ { j , p } ^ { d e }$ te the desired goal at timestep , we search and draw two faile $p$ in episoepisodes $j$ . Gand n of failed), where $\\{ E _ { 0 } , E _ { 1 } , \\stackrel { \\cdot } { E } _ { 2 } , \\cdot \\cdot \\cdot \\}$ $E _ { i }$ $E _ { j }$ $( i \\neq j )$ $\\exists i , j , p , q ,$ s.t. $g _ { i , p } ^ { a c } = g _ { j , q } ^ { d e }$ . If we find two such failed episodes, we combine the two experience by replacing the desired goals in $E _ { i }$ by $\\{ g _ { j , t } ^ { d e } \\}$ , where $j$ indicates $E _ { j }$ and $t \\leq \\operatorname* { m i n } \\{ p , q \\}$ . Based on this, we end up assembling a new experience $E _ { i } ^ { \\prime }$ based on $E _ { i }$ with a new “imagined” goal trajectory $\\{ g _ { j , 0 } ^ { d e } , \\cdot \\cdot \\cdot , g _ { j , t } ^ { d e } \\}$ where $t \\leq \\operatorname* { m i n } \\{ p , q \\}$ . ",
+        "bbox": [
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+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "More details of the complete $\\mathrm { R L + D H E R }$ method are shown in Algorithm 1. Unlike HER, our DHER needs to search all failed experiences to compose a “imagined” goal trajectory. Hence, the efficiency of searching the memory is important. In our implementation, we use two hash tables to store the trajectories of achieved goals and desired goals, respectively. ",
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+    {
+        "type": "text",
+        "text": "4 EXPERIMENT ",
+        "text_level": 1,
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+        "text": "We run extensive experiments to examine the proposed DHER for moving goals and compare it with some competing baselines. We first introduce the environments and tasks that we want to address, followed by the experimental results. Demo videos from our experiments are available at https://sites.google.com/view/dher. ",
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+        "img_path": "images/868b5ca50a241e6883855868e5cdc6d4e2e4a7d4f491d103d018de67c19012a7.jpg",
+        "image_caption": [
+            "Figure 3: Results on different environments. "
+        ],
+        "image_footnote": [],
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "4.1 ENVIRONMENTS ",
+        "text_level": 1,
+        "bbox": [
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+        "type": "text",
+        "text": "Whereas grasping moving targets are fairly common in robotic applications, there are rarely existing environments featuring dynamic goals. We modify the robotic manipulation environments created by OpenAI (Brockman et al., 2016) for our experiments. As shown in Figure 2, we assign certain rules to the goals so that they accordingly move in the environments while an agent is required to control the robotic arm’s grippers to reach the goal that moves along a straight line (Dy-Reaching), to reach the goal that moves in a circle (Dy-Circling), or to push a block to the goal that moves along a straight line (Dy-Pushing). In addition, we also develop a new GREEDY SNAKE environment (DySnake), in which the goal moves from one discrete cell to another. The greedy snake aims to reach the goal (and eat it). No matter what actions are taken by the agent, the underlying rule of changing the goals’ positions remain the same. We assume that the law of the goal’s motion is unknown to the agent. More details of the tasks are described in the appendix. ",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "For the first three tasks, we follow the basic settings of OpenAI robotics environments (Brockman et al., 2016). States are read from the MuJoCo physics engine. An observation consists of relative positions of the object and the target (grippers are blocked) Goals are positions in the 3D world coordinate system with a fixed tolerance (we use $\\epsilon = 0 . 0 1$ for the tolerance). Note the goals are able to move in our tasks. The velocity we use is $v = 0 . 0 1 1$ . 1 epoch indicates 100 episodes. The start positions of the goals are randomly chosen. Rewards are binary and sparse: $r ( s _ { t } , a _ { t } , g _ { t } ) =$ $- \\mathbf { 1 } _ { \\mathrm { c o n d i t i o n } } \\big ( | s _ { t + 1 } ^ { \\mathrm { o b j } } - g _ { t + 1 } | \\geq \\epsilon \\big )$ where $s _ { t + 1 }$ and $g _ { t + 1 }$ are respectively the state and dynamic goal after the execution of the action $a _ { t }$ in the state $s _ { t }$ . Two positions are overlapped if they are close within the tolerance $\\epsilon$ . We use 3-dimensional actions, in which three dimensions correspond to the desired relative gripper position at the next timestep. ",
+        "bbox": [
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+        "type": "text",
+        "text": "For the last task, it is very similar to the standard snake game. There is a 2D plane grid whose size is $3 0 \\times 4 0$ . A snake and a goal (food) both move in this grid. We use a $1 \\times 1$ square as the body of the snake and do not allow the snake to grow any longer as it moves. The states of the system are represented by using the positions of the snake and food. Goals are the positions of the food. The snake has to move itself such that it resides in the same cell as the food at a certain timestep. The velocity of the goal is set to $( 0 , 1 )$ . The start positions of the goal are set randomly in different episodes of the game, so are the start positions of the snake. Rewards are binary and sparse: $r \\big ( s _ { t } , \\bar { a } _ { t } , g _ { t + 1 } \\big ) = - \\bar { \\mathbf { 1 } } _ { \\mathrm { c o n d i t i o n } } \\big ( \\big | s _ { t + 1 } ^ { \\mathrm { s n a k e } } - g _ { t + 1 } \\big | \\bar { \\neq } 0 \\big )$ where $s _ { t + 1 }$ and $g _ { t + 1 }$ are the environment’s state and goal after the agent executes action $a _ { t }$ in the state $s _ { t }$ . Observations are represented by the positions of the snake and food. We also add to the state the distance between the snake and food. Actions allowed in the game are the following: move up, move down, move left, and move right, for one cell per timestep. ",
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+    {
+        "type": "text",
+        "text": "4.2 BASELINES",
+        "text_level": 1,
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+        "type": "text",
+        "text": "For the first three tasks which call for continuous control, we consider two competing baselines:2 • DDPG, which is a model-free RL algorithm for continuous control (Lillicrap et al., 2015). It learns a deterministic policy by using a stochastic counterpart to explore in the training. ",
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+    {
+        "type": "image",
+        "img_path": "images/732a387a80c212738b2fb410b777a5c71d62a4dacb48b29dd438871f23abaf26.jpg",
+        "image_caption": [
+            "Figure 4: Low velocity: 0.001. "
+        ],
+        "image_footnote": [],
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+    {
+        "type": "image",
+        "img_path": "images/f8c0fd7014d07719a2c477eef04492742d4a9d1ff91065b3d850a3053e6e0ee6.jpg",
+        "image_caption": [
+            "Figure 5: High velocity: 0.016. "
+        ],
+        "image_footnote": [],
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+        "text": "",
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+    {
+        "type": "text",
+        "text": "• $\\mathrm { D D P G } + \\mathrm { H E R }$ , which improves the replay buffer of DDPG by the hindsight experience replay (Andrychowicz et al., 2017).   \nDDPG (dense), which employs the negative distance $( - d )$ as dense rewards.   \nDDPG (dense-2), which employs the negative distance $( - d )$ as dense rewards if $d \\geq \\epsilon$ . However, if $d < \\epsilon$ (i.e., success) it uses $( - d + 1 . 0 )$ as rewards. 1.0 is a bonus. ",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "For the last task of discrete control, we use the following baselines in the experiments: DQN (Mnih et al., 2015) and $\\mathrm { D Q N + H E R }$ , which uses HER to enhance the replay in DQN. ",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "• DQN, which is a powerful model-free RL algorithm for discrete action spaces (Mnih et al., 2015).   \n• $\\mathrm { D Q N + H E R }$ , which uses HER to enhance the replay in DQN.   \n• DQN (dense), which uses the negative distance $( - d )$ as dense rewards.   \n• DQN (dense-2), which uses the negative distance $( - d )$ as dense rewards. However, if $d = 0 . 0$ (i.e., success) it uses $( - d + 1 . 0 )$ as rewards instead. 1.0 is a bonus. ",
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+        "page_idx": 6
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+    {
+        "type": "text",
+        "text": "4.3 COMPARISON RESULTS ON THE ROBOTIC ENVIRONMENTS ",
+        "text_level": 1,
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "For the continuous control, we present three sets of comparison results in Figure 3 for the first three tasks, respectively. Consistently, the results show our DHER algorithm outperforms the others. The two baselines are not able to catch up even after we train them for thousands of iterations. Vanilla DDPG is slightly better than the version with HER. HER does not benefit DDPG in these tasks because the goals in HER are fixed, fundamentally misleading the agent in the attempt of solving the tasks with dynamic goals. The results of DDPG (dense) and DDPG (dense-2) suggest that even the dense rewards do not work well as they are agnostic to the task of interest. A good reward shaping may give rise to better performance by carefully tuning it for the task of dynamic goals. ",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "Comparing Figure 3a and Figure 3b with Figure 3c, we find that DHER learns faster in Dy-Reaching and Dy-Circling than Dy-Pushing probably because Dy-Reaching and Dy-Circling are easier tasks than Dy-Pushing. In Dy-Pushing, all the algorithms take a fairly big amount of time to explore without receiving any positive feedback. However, the more failed experiences the agent encounters, the better change our algorithm is able to identify relevant episodes from them for assembling useful dynamic goals. As a result, DHER is able to pick up the momentum and learns faster and better than the baselines after a certain point. In Figure 3a, the performance decreases a little. The reason may be that as successful experience increases, some assembled experience is inconsistent with these successful experience. ",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "4.3.1 COMPARISON USING DIFFERENT VELOCITIES OF GOALS",
+        "text_level": 1,
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "To show the performance of our method on more complex tasks with different velocities, we study different methods in Dy-Reaching environment as shown in Figures 4 and 5 with the same physical properties as the previous experiments. Overall the results show our method is much better than DDPG and HER. As a reminder, the threshold for calculating rewards we used is 0.01. In Figure 4, the task becomes an easier task because of the slower velocity. It shows that our method quickly achieves to a good result around 5 epoch. Comparing with Figure 3a, it shows that the performance with $v = 0 . 0 0 1$ is better than the performance with $v = 0 . 0 1 1$ and get $1 5 \\%$ improvements. However, it also shows the performance with $v = 0 . 0 1 6$ is worse than the performance with $v = 0 . 0 1 1$ . Both DDPG and $\\mathrm { \\Delta D D P G + H E R }$ failed when $v = 0 . 0 1 6$ and their performance is 0. This performance is consistent because the task becomes more difficult when the velocity increases. ",
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+    {
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+        "img_path": "images/14dd0b3e1878d3f49fb1b7d44ca84006cca0ac15133dc036aef116910149f401.jpg",
+        "image_caption": [
+            "Figure 6: Snake with dynamic goals. "
+        ],
+        "image_footnote": [],
+        "bbox": [
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+    },
+    {
+        "type": "image",
+        "img_path": "images/97b49eb4c50a91b591b5c09b7c8417f90a64b3336f8b06a8631418b78f185b01.jpg",
+        "image_caption": [
+            "Figure 7: Special: $\\mathrm { H E R + }$ knows how goals move. "
+        ],
+        "image_footnote": [],
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+        "text": "",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "4.4 COMPARISON ON THE DYNAMIC SNAKE ENVIRONMENT ",
+        "text_level": 1,
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "In the Dy-Snake environment, which is a discrete control environment, we present the results of the chasing food task in Figure 6. The results show that the proposed algorithm works best. DQN is better than HER. HER fails for this task. That HER fails for this task shows just using achieved goals is not enough for the tasks with dynamic goals and can lead wrong direction. The results also show that around 800 episodes, the performance of DQN and DHER is close and DHER is slightly better than DQN. This is because the chasing food task is a simple task. The action space is very small and just 4 types of actions. After enough exploration, DQN also has competitive performance. However, at the beginning, DHER quickly achieves very good performance. It shows that assembling experience from two failures improves the performance very efficiently in this task. DQN (dense) and DQN (dense-2) help learn the policy at the early stage. However, in the long run, it does not lead to any particular benefits. ",
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+    {
+        "type": "text",
+        "text": "4.5 SIM TO REAL ADAPTATION ",
+        "text_level": 1,
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+    {
+        "type": "text",
+        "text": "We used policies for Dy-Circling task and a new Pouring task trained in our simulator 3 to deploy them on a physical robot. As shown in Figure 8, the policies were trained by using DHER and adapted to the real robot without any finetuning. However, the policy requires accurate localizations of the gripper and the goal. For Dy-Circling task, the robot’s gripper was blocked. There were a toy turntable, whose speed is unknown, and a blue block on the turntable. We set the position 1cm above the block as the target position. The position of the block was predicted based on traditional contour shape analysis using camera images. For Pouring task, the robot gripped a can. A man held a cup and moved it. The cup was set as the target and with a green marker. We used the marker to estimate its position. ",
+        "bbox": [
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+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "Our policies were transferred successfully for both tasks. With the accurate positions, we have $100 \\%$ success rate for 5 trials. It was observed that the robot had learned to not only follow the current target but also step forward to the future target position. Demo videos about the experiments are available at https://sites.google.com/view/dher. ",
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+        "page_idx": 7
+    },
+    {
+        "type": "image",
+        "img_path": "images/ff03243dba37e8e374b610dab429ef50349cfd9bf2cd37e4c19e2d40e16ac98c.jpg",
+        "image_caption": [
+            "Figure 8: Adapting the policies trained based on DHER from our simulation to a real robotic arm. "
+        ],
+        "image_footnote": [],
+        "bbox": [
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+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "4.6 SPECIAL CASE: HOW ABOUT IF HER KNOWS THE LAW OF THE MOTION OF A GOAL",
+        "bbox": [
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+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "We use Dy-Snake to demonstrate the experimental results for a special case that the law of the motion of the target (food) is known to agents. Because the motion of the food is very simple and controllable in Dy-Snake environment. We develop a direct extension of HER, called $\\mathrm { H E R + }$ , that modifies desired goals at every timestep based on the law of the motion of the food to create successful experience. More details of $\\mathrm { H E R + }$ are described in the appendix. ",
+        "bbox": [
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+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "We show the results in Figure 7. DHER and $\\mathrm { H E R + }$ are both better than DQN at the beginning. DHER is slightly better than $\\mathrm { H E R + }$ , which shows the efficiency of DHER is comparable in this simple task. ",
+        "bbox": [
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+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "5 CONCLUSION ",
+        "text_level": 1,
+        "bbox": [
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+            401,
+            318,
+            417
+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "We introduced a novel technique that assembles successful experience from a couple of failures. With this technique, our proposed algorithm called DHER ( Dynamic Hindsight Experience Replay) is able to address the tasks with sparse rewards and dynamic goals. Our technique can be combined with an arbitrary off-policy RL algorithm and we experimentally demonstrated that with DQN and DDPG. As far as we know, it is the first time that an agent is allowed to learn from assembled experience from two failures. ",
+        "bbox": [
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+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "ACKNOWLEDGMENTS ",
+        "text_level": 1,
+        "bbox": [
+            176,
+            537,
+            356,
+            553
+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "We would like to thank Weitao Xi, Tianzhou Wang, Tingguang Li for performing some additional transfer experiments. We would also like to thank Han Liu and the whole RL team for fruitful discussions as well as the anonymous reviewers for their comments. ",
+        "bbox": [
+            174,
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+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "REFERENCES ",
+        "text_level": 1,
+        "bbox": [
+            176,
+            631,
+            285,
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+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "Marcin Andrychowicz, Filip Wolski, Alex Ray, Jonas Schneider, Rachel Fong, Peter Welinder, Bob McGrew, Josh Tobin, OpenAI. Pieter Abbeel, and Wojciech Zaremba. Hindsight experience replay. In Advances in Neural Information Processing Systems, pp. 5048–5058, 2017.   \nMarc G. Bellemare, Yavar Naddaf, Joel Veness, and Michael Bowling. The arcade learning environment: An evaluation platform for general agents. Journal of Artificial Intelligence Research, 47:253–279, 2013. ISSN 1076-9757.   \nYoshua Bengio, Jrme Louradour, Ronan Collobert, and Jason Weston. Curriculum learning. In Proceedings of the 26th International Conference on Machine Learning, pp. 41–48. ACM, 2009.   \nGreg Brockman, Vicki Cheung, Ludwig Pettersson, Jonas Schneider, John Schulman, Jie Tang, and Wojciech Zaremba. Openai gym, 2016.   \nMaurizio Di Rocco, Federico Pecora, Prasanna Kumar Sivakumar, and Alessandro Saffiotti. Configuration planning with multiple dynamic goals. In AAAI Spring Symposium: Designing Intelligent Robots, 2013.   \nYan Duan, Xi Chen, Rein Houthooft, John Schulman, and Pieter Abbeel. Benchmarking deep reinforcement learning for continuous control. In Proceedings of the 33rd International Conference on Machine Learning, pp. 1329–1338, 2016. ",
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+        "text": "Tom Schaul, John Quan, Ioannis Antonoglou, and David Silver. Prioritized experience replay. arXiv preprint arXiv:1511.05952, 2015b. ",
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+        "type": "text",
+        "text": "David Silver, Aja Huang, Chris J Maddison, Arthur Guez, Laurent Sifre, George Van Den Driessche, Julian Schrittwieser, Ioannis Antonoglou, Veda Panneershelvam, Marc Lanctot, et al. Mastering the game of go with deep neural networks and tree search. Nature, 529(7587):484, 2016. ",
+        "bbox": [
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+        "page_idx": 9
+    },
+    {
+        "type": "text",
+        "text": "Emanuel Todorov, Tom Erez, and Yuval Tassa. Mujoco: A physics engine for model-based control. In 2012 IEEE/RSJ International Conference on Intelligent Robots and Systems, pp. 5026–5033. IEEE, 2012. ",
+        "bbox": [
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+        ],
+        "page_idx": 9
+    },
+    {
+        "type": "text",
+        "text": "Ziyu Wang, Victor Bapst, Nicolas Heess, Volodymyr Mnih, Remi Munos, Koray Kavukcuoglu, and ´ Nando de Freitas. Sample efficient actor-critic with experience replay. CoRR, abs/1611.01224, 2016. ",
+        "bbox": [
+            174,
+            784,
+            825,
+            827
+        ],
+        "page_idx": 9
+    },
+    {
+        "type": "text",
+        "text": "APPENDIX ",
+        "text_level": 1,
+        "bbox": [
+            176,
+            103,
+            263,
+            117
+        ],
+        "page_idx": 10
+    },
+    {
+        "type": "text",
+        "text": "TASKS WITH DYNAMIC GOALS ",
+        "text_level": 1,
+        "bbox": [
+            176,
+            135,
+            385,
+            148
+        ],
+        "page_idx": 10
+    },
+    {
+        "type": "text",
+        "text": "We have created four tasks as described below and illustrated by Figure 2. The first three tasks are based on the robotic environments. The last is based on the GREEDY SNAKE environment. ",
+        "bbox": [
+            173,
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+        ],
+        "page_idx": 10
+    },
+    {
+        "type": "text",
+        "text": "• Dy-Reaching: The task is to control the robotic arm so that its gripper can reach the target position. The target position moves from one point to another along a straight line with a constant velocity.   \n• Dy-Circling: The task is to control the robotic arm so that its gripper can reach the target position. The target position moves along a circle with a constant velocity. Dy-Pushing: in this task, a box is placed on a table in front of the robotic arm. The robot is required to move the box to the target location on the table. The target location moves from one position to another with a fixed velocity. Note that the robot’s grippers are locked to prevent it from grasping. The learned behavior is actually a mixture of pushing and rolling.   \nDy-Snake: in this task, a snake and food are placed on a rectangle map and the task is to control the snake to eat the food. The food is moving from one position to another position with a fixed velocity. ",
+        "bbox": [
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+        "page_idx": 10
+    },
+    {
+        "type": "text",
+        "text": "HARDWARE ",
+        "text_level": 1,
+        "bbox": [
+            174,
+            407,
+            258,
+            421
+        ],
+        "page_idx": 10
+    },
+    {
+        "type": "text",
+        "text": "We use the Universal Robots UR10 with a gripper. We use a RealSense Camera SR300 to track the position of objects. The gripper is blocked. We use a marker on the gripper for camera calibration. During adapting the robot, for the position of the target, we use the camera to estimate it. ",
+        "bbox": [
+            176,
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+        ],
+        "page_idx": 10
+    },
+    {
+        "type": "text",
+        "text": "SIMULATION ",
+        "text_level": 1,
+        "bbox": [
+            176,
+            496,
+            264,
+            508
+        ],
+        "page_idx": 10
+    },
+    {
+        "type": "text",
+        "text": "We simulate the physical system using the MuJoCo physics engine (Todorov et al., 2012) and also use MuJoCo to render the images. In our tasks, we use positions provided by MuJoCo for training policies in the simulation. ",
+        "bbox": [
+            176,
+            522,
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+        ],
+        "page_idx": 10
+    },
+    {
+        "type": "text",
+        "text": "In Figure 9, we demonstrate our simulation and the physics environment. ",
+        "bbox": [
+            173,
+            570,
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+            585
+        ],
+        "page_idx": 10
+    },
+    {
+        "type": "image",
+        "img_path": "images/0ab0a04331e1ed7ee05503beb83d72a71ddd08962ea6776f4dbc386edf14fc2c.jpg",
+        "image_caption": [
+            "Figure 9: Our simulation and the physics environment. "
+        ],
+        "image_footnote": [],
+        "bbox": [
+            215,
+            604,
+            782,
+            800
+        ],
+        "page_idx": 10
+    },
+    {
+        "type": "text",
+        "text": "A SPECIAL AND SIMPLER CASE - HER+",
+        "bbox": [
+            176,
+            868,
+            455,
+            882
+        ],
+        "page_idx": 10
+    },
+    {
+        "type": "text",
+        "text": "The paper considers a general situation that the law of the motion of goals is invisible to an agent. However, we relax this assumption and assume that in some situations the law of the motion of goals is easy to obtain, i.e., the parameters of $g ( t ; \\gamma )$ are known. For example, it is able to calculate the velocity of an object by observing the trajectories of the object. ",
+        "bbox": [
+            173,
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+        ],
+        "page_idx": 10
+    },
+    {
+        "type": "text",
+        "text": "",
+        "bbox": [
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+        ],
+        "page_idx": 11
+    },
+    {
+        "type": "text",
+        "text": "In this situation, we do not need to search failed experience. With the knowledge of the velocity of an object, it is straightforward that we can calculate any trajectory of desired goals. Thus for every failed experience, at any time step $t$ , based on the achieved goal $g _ { t } ^ { a c }$ , we calculate new desired goals $g _ { t } ^ { d e } = g ( { \\dot { t } } )$ corresponding to the achieved goals in order to construct successful experience. ",
+        "bbox": [
+            174,
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+        ],
+        "page_idx": 11
+    },
+    {
+        "type": "text",
+        "text": "The details of $\\mathrm { H E R + }$ are described in Algorithm 2. $\\mathrm { H E R + }$ can be seen as a direct extension of HER. HER and $\\mathrm { H E R + }$ can modify any failed experience to successful experience because they both assume the law of the motion of goals is known. ",
+        "bbox": [
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+            202,
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+        ],
+        "page_idx": 11
+    },
+    {
+        "type": "text",
+        "text": "Algorithm 2 Hindsight Experience Replay Plus ",
+        "text_level": 1,
+        "bbox": [
+            176,
+            260,
+            490,
+            275
+        ],
+        "page_idx": 11
+    },
+    {
+        "type": "text",
+        "text": "Require: an off-policy RL algorithm A, replay buffer $R$ , a reward function $r$   \n1: Initialize A and replay buffer $R$   \n2: for episode $\\mathbf { \\Omega } = 1 , 2 , \\cdots , M$ do   \n3: Sample an initial goal $g _ { 0 }$ and an initial state $s _ { 0 }$   \n4: for $t = 0 , \\cdots , T - 1$ do   \n5: Sample an action $a _ { t }$ using the behavioral policy from A:   \n6: $a _ { t } \\doteq \\pi ( s _ { t } | g _ { t } )$   \n7: Execute the action $a _ { t }$ and observe a new state $s _ { t + 1 }$ and a new goal $g _ { t + 1 }$   \n8: end for   \n9: for $t = 0 , \\cdots , T - 1$ do   \n10: $r _ { t } : = r ( s _ { t } , a _ { t } , g _ { t + 1 } )$   \n11: Store the transitions $\\left( s _ { t } | g _ { t } , a _ { t } , r _ { t } , s _ { t + 1 } | g _ { t + 1 } \\right)$ in $R$ (Standard experience replay)   \n12: Sample a set of the achieved goals of $E _ { i }$ as additional goals for reply $G ^ { \\prime }$   \n13: for $\\bar { g _ { p } ^ { \\prime } } \\in G ^ { \\prime }$ do   \n14: Calculate a goal trajectory $\\{ g _ { 0 } ^ { \\prime } , \\cdots , g _ { p } ^ { \\prime } \\}$ where $g _ { t } ^ { \\prime } = g ( t ; \\gamma )$ $\\mathrm { ( H E R + ) }$   \n15: for $t = \\{ 0 , \\cdots , p - 1 \\}$ do   \n16: $r _ { t } ^ { \\prime } : = r ( s _ { i , t } , a _ { i , t } , g _ { t + 1 } ^ { \\prime } )$   \n17: Store the transition $\\left( s _ { i , t } | g _ { t } ^ { \\prime } , a _ { i , t } , r _ { t } ^ { \\prime } , s _ { i , t + 1 } | g _ { t + 1 } ^ { \\prime } \\right) \\mathrm { i n } R$   \n18: end for   \n19: end for   \n20: end for   \n21: end for ",
+        "bbox": [
+            176,
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+            589
+        ],
+        "page_idx": 11
+    }
+]

parse/train/HygrdpVKvr/HygrdpVKvr_content_list.json

@@ -0,0 +1,1647 @@
+[
+    {
+        "type": "text",
+        "text": "NAS EVALUATION IS FRUSTRATINGLY HARD ",
+        "text_level": 1,
+        "bbox": [
+            174,
+            101,
+            705,
+            121
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "Antoine Yang∗ Ecole Polytechnique ´ † France ",
+        "bbox": [
+            184,
+            145,
+            325,
+            188
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "Pedro M Esperanc¸a Huawei Noah’s Ark Lab London, UK ",
+        "bbox": [
+            382,
+            145,
+            545,
+            186
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "Fabio Maria Carlucci Huawei Noah’s Ark Lab London, UK ",
+        "bbox": [
+            606,
+            145,
+            769,
+            186
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "ABSTRACT ",
+        "text_level": 1,
+        "bbox": [
+            454,
+            226,
+            544,
+            241
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "Neural Architecture Search (NAS) is an exciting new field which promises to be as much as a game-changer as Convolutional Neural Networks were in 2012. Despite many great works leading to substantial improvements on a variety of tasks, comparison between different methods is still very much an open issue. While most algorithms are tested on the same datasets, there is no shared experimental protocol followed by all. As such, and due to the under-use of ablation studies, there is a lack of clarity regarding why certain methods are more effective than others. Our first contribution is a benchmark of 8 NAS methods on 5 datasets. To overcome the hurdle of comparing methods with different search spaces, we propose using a method’s relative improvement over the randomly sampled average architecture, which effectively removes advantages arising from expertly engineered search spaces or training protocols. Surprisingly, we find that many NAS techniques struggle to significantly beat the average architecture baseline. We perform further experiments with the commonly used DARTS search space in order to understand the contribution of each component in the NAS pipeline. These experiments highlight that: (i) the use of tricks in the evaluation protocol has a predominant impact on the reported performance of architectures; (ii) the cell-based search space has a very narrow accuracy range, such that the seed has a considerable impact on architecture rankings; (iii) the hand-designed macrostructure (cells) is more important than the searched micro-structure (operations); and (iv) the depth-gap is a real phenomenon, evidenced by the change in rankings between 8 and 20 cell architectures. To conclude, we suggest best practices, that we hope will prove useful for the community and help mitigate current NAS pitfalls, e.g. difficulties in reproducibility and comparison of search methods. The code used is available at https://github.com/antoyang/NAS-Benchmark. ",
+        "bbox": [
+            232,
+            256,
+            764,
+            603
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "1 INTRODUCTION ",
+        "text_level": 1,
+        "bbox": [
+            176,
+            628,
+            336,
+            643
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "As the deep learning revolution helped us move away from hand crafted features (Krizhevsky et al., 2012) and reach new heights (He et al., 2016; Szegedy et al., 2017), so does Neural Architecture Search (NAS) hold the promise of freeing us from hand-crafted architectures, which requires tedious and expensive tuning for each new task or dataset. Identifying the optimal architecture is indeed a key pillar of any Automated Machine Learning (AutoML) pipeline. Research in the last two years has proceeded at a rapid pace and many search strategies have been proposed, from Reinforcement Learning (Zoph & Le, 2017; Pham et al., 2018), to Evolutionary Algorithms (Real et al., 2017), to Gradient-based methods (Liu et al., 2019; Liang et al., 2019). Still, it remains unclear which approach and search algorithm is preferable. Typically, methods have been evaluated on accuracy alone, even though accuracy is influenced by many other factors besides the search algorithm. Comparison between published search algorithms for NAS is therefore either very difficult (complex training protocols with no code available) or simply impossible (different search spaces), as previously pointed out (Li & Talwalkar, 2019; Sciuto et al., 2019; Lindauer & Hutter, 2019). ",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "NAS methods have been typically decomposed into three components (Elsken et al., 2019; Li & Talwalkar, 2019): search space, search strategy and model evaluation strategy. This division is important to keep in mind, as an improvement in any of these elements will lead to a better final performance. But is a method with a more (manually) tuned search space a better AutoML algorithm? If the key idea behind NAS is to find the optimal architecture, without human intervention, why are we devoting so much energy to infuse expert knowledge into the pipeline? Furthermore, the lack of ablation studies in most works makes it harder to pinpoint which components are instrumental to the final performance, which can easily lead to Hypothesizing After the Results are Known (HARKing; Gencoglu et al., 2019). ",
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+        "type": "text",
+        "text": "",
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+        "type": "text",
+        "text": "Paradoxically, the huge effort invested in finding better search spaces and training protocols, has led to a situation in which any randomly sampled architecture performs almost as well as those obtained by the search strategies. Our findings suggest that most of the gains in accuracy in recent contributions to NAS have come from manual improvements in the training protocol, not in the search algorithms. ",
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+    {
+        "type": "text",
+        "text": "As a step towards understanding which methods are more effective, we have collected code for 8 reasonably fast (search time of less than 4 days) NAS algorithms, and benchmarked them on 5 well known CV datasets. Using a simple metric—the relative improvement over the average architecture of the search space—we find that most NAS methods perform very similarly and rarely substantially above this baseline. The methods used are DARTS, StacNAS, PDARTS, MANAS, CNAS, NSGANET, ENAS and NAO. The datasets used are CIFAR10, CIFAR100, SPORT8, MIT67 and FLOWERS102. ",
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+        "type": "text",
+        "text": "Through a number of additional experiments on the widely used DARTS search space (Liu et al., 2019), we will show that: (a) how you train your model has a much bigger impact than the actual architecture chosen; (b) different architectures from the same search space perform very similarly, so much so that (c) hyperparameters, like the number of cells, or the seed itself have a very significant effect on the ranking; and (d) the specific operations themselves have less impact on the final accuracy than the hand-designed macro-structure of the network. Notably, we find that the $2 0 0 +$ architectures sampled from this search space (available from the link in the abstract) are all within a range of one percentage point (top-1 accuracy) after a standard full training on CIFAR10. Finally, we include some observations on how to foster reproducibility and a discussion on how to potentially avoid some of the encountered pitfalls. ",
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+    {
+        "type": "text",
+        "text": "2 RELATED WORK ",
+        "text_level": 1,
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+        "type": "text",
+        "text": "As mentioned, NAS methods have the potential to truly revolutionize the field, but to do so it is crucial that future research avoids common mistakes. Some of these concerns have been recently raised by the community. ",
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+        "type": "text",
+        "text": "For example, Li & Talwalkar (2019) highlight that most NAS methods a) fail to compare against an adequate baseline, such as a properly implemented random search strategy, b) are overly complex, with no ablation to properly assign credit to the important components, and c) fail to provide all details needed for successfully reproducing their results. In our paper we go one step further and argue that the relative improvement over the average (randomly sampled) architecture is an useful tool to quantify the effectiveness of a proposed solution and compare it with competing methods. To partly answer their second point, and understand how much the final accuracy depends on the specific architecture, we implement an in-depth study of the widely employed DARTS (Liu et al., 2019) search space and perform an ablation on the commonly used training techniques (e.g. Cutout, DropPath, AutoAugment). ",
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+        "type": "text",
+        "text": "In addition, Sciuto et al. (2019) also took the important step of systematically using fair baselines, and suggest random search with early stopping, averaged over multiple seeds, as an extremely competitive baseline. They find that the search spaces of three methods investigated (DARTS, ENAS, NAO) have been expertly engineered to the extent that any randomly selected architecture performs very well. In contrast, we show that even random sampling (without search) provides an incredibly competitive baseline. Our relative improvement metric allows us to isolate the contribution of the search strategy from the effects of the search space and training pipeline. Thus, we further confirm the authors’ claim, showing that indeed the average architecture performs extremely well and that how you train a model has more impact than any specific architecture. ",
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+    {
+        "type": "text",
+        "text": "3 NAS BENCHMARK ",
+        "text_level": 1,
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+    {
+        "type": "text",
+        "text": "In this section we present a systematic evaluation of 8 methods on 5 datasets using a strategy that is designed to reveal the quality of each method’s search strategy, removing the effect of the manuallyengineered training protocol and search space. The goal is to find general trends and highlight common features rather than just pin-pointing the most accurate algorithm. ",
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+    {
+        "type": "text",
+        "text": "Understanding why methods are effective is not an easy task: most introduce variations to previous search spaces, search strategies, and training protocols—with ablations disentangling the contribution of each component often incomplete or missing. In other words, how can we be sure that a new state-of-the-art method is not so simply due to a better engineered search space or training protocol? To address this issue we compare a set of 8 methods with randomly sampled architectures from their respective search spaces, and trained with the same protocol as the searched architectures. ",
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+        "type": "text",
+        "text": "The ultimate goal behind NAS should be to return the optimal model for any dataset given, at least within the limits of a certain task, and we feel that the current practices of searching almost exclusively on CIFAR10 go against this principle. Indeed, to avoid the very concrete risk of overfitting to this set of data, NAS methods should be tested on a variety of tasks. For this reason we run experiments on 5 different datasets. ",
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+    {
+        "type": "text",
+        "text": "3.1 METHODOLOGY ",
+        "text_level": 1,
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+    {
+        "type": "text",
+        "text": "Criteria for dataset selection. We selected datasets to cover a variety of subtasks within image classification. In addition to the standard CIFAR10 we select CIFAR100 for a more challenging object classification problem (Krizhevsky, 2009); SPORT8 for action classification (Li & Fei-Fei, 2007); MIT67 for scene classification (Quattoni & Torralba, 2009); and FLOWERS102 for finegrained object classification (Nilsback & Zisserman, 2008). More details are given in the Appendix. ",
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+    {
+        "type": "text",
+        "text": "Criteria for method selection. We selected methods which (a) have open-source code, or provided it upon request, and (b) have a reasonable running time, specifically a search time under 4 GPU-days on CIFAR10. The selected methods are: DARTS (Liu et al., 2019), StacNAS (Li et al., 2019), PDARTS (Xin Chen, 2019), MANAS (Carlucci et al., 2019), CNAS (Weng et al., 2019), NSGANET (Lu et al., 2018), ENAS (Pham et al., 2018), and NAO (Luo et al., 2018). With the exception of NAO and NSGANET, all methods are DARTS variants and use weight sharing. ",
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+    {
+        "type": "text",
+        "text": "Evaluation protocol. NAS algorithms usually consist of two phases: (i) search, producing the best architecture according to the search algorithm used; (ii) augmentation, consisting in training from scratch the best model found in the search phase. We evaluate methods as follows: 1. Sample 8 architectures from the search space, uniformly at random, and use the method’s code to augment these architectures (same augment seed for all); 2. Use the method’s code to search for 8 architectures and augment them (different search seed, same augment seed); 3. Report mean and standard deviation of the top-1 test accuracy, obtained at the end of the augmentation, for both the randomly sampled and the searched architectures; ",
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+    {
+        "type": "text",
+        "text": "Since both learned and randomly sampled architectures share the same search space and training protocol, calculating a relative improvement over this random baseline as $R I = 1 0 0 \\times ( A c c _ { m } -$ $A c c _ { r } ) / A c c _ { r }$ can offer insights into the quality of the search strategy alone. $A c c _ { m }$ and $A c c _ { r }$ represent the top-1 accuracy of the search method and random sampling strategies, respectively. A good, general-purpose NAS method is expected to yield $R I > 0$ consistently over different searches and across different subtasks. We emphasize that the comparison is not against random search, but rather against random sampling, i.e., the average architecture of the search space. For example, in the DARTS search space, for each edge in the graph that defines a cell we select one out of eight possible operations (e.g. pooling or convolutions) with uniform probability $1 / 8$ . ",
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+    {
+        "type": "text",
+        "text": "Hyperparameters are optimized on CIFAR10, according to the values reported by the corresponding authors. Since most methods do not include their optimization as part of the search routine, we assumed them to be robust and generalizable to other tasks. As such, aside from scaling down the architecture depending on dataset size, experiments on other datasets use the same hyperparameters. Other training details and references are given in the Appendix. ",
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+    {
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+        "img_path": "images/edf5f8a33f5bb147c60a4fc8d6e36c6306bb7276930131c944ec9914b79e4870.jpg",
+        "image_caption": [
+            "Figure 1: Comparison of search methods and random sampling from their respective search spaces. Methods lying in the diagonal perform the same as the average architecture, while methods above the diagonal outperform it. See also Table 1. "
+        ],
+        "image_footnote": [],
+        "bbox": [
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+    {
+        "type": "image",
+        "img_path": "images/3203460b279ee612939f03c89b01e0c7ce0f8773d113c8c7e58f41bc3d8a1d1d.jpg",
+        "image_caption": [
+            "Figure 2: Performance and computational cost of the search phase on CIFAR10. "
+        ],
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+    {
+        "type": "table",
+        "img_path": "images/c01388e0b766ac927995cde360d93dfc9a5de1b355216979bcf6a2dd53aecde9.jpg",
+        "table_caption": [
+            "Table 1: Relative improvement metric, $\\begin{array} { r l } { R I } & { { } = } \\end{array}$ $1 0 0 \\times ( A c c _ { m } - A c c _ { r } ) / A c c _ { r }$ (in $\\%$ ), where $A c c _ { m }$ and $A c c _ { r }$ are the accuracies of the search method and random sampling baseline, respectively. "
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td></td><td>C10</td><td>C100</td><td>S8</td><td>M67</td><td>F102</td></tr><tr><td>DARTS</td><td>0.32</td><td>0.23</td><td>-0.13</td><td>0.10</td><td>0.25</td></tr><tr><td>PDARTS</td><td>0.52</td><td>1.20</td><td>0.51</td><td>1.19</td><td>0.20</td></tr><tr><td>NSGANET</td><td>-0.48</td><td>1.37</td><td>0.43</td><td>2.00</td><td>1.47</td></tr><tr><td>ENAS</td><td>0.01</td><td>-3.44</td><td>0.67</td><td>0.13</td><td>0.47</td></tr><tr><td>CNAS</td><td>0.74</td><td>-0.89</td><td>-1.06</td><td>-0.66</td><td>-2.48</td></tr><tr><td>MANAS</td><td>0.18</td><td>-0.20</td><td>0.33</td><td>1.48</td><td>0.70</td></tr><tr><td>StacNAS NAO</td><td>0.43 0.44</td><td>2.87 -0.01</td><td>0.38 -2.05</td><td>0.05 -1.53</td><td>-0.16 -0.13</td></tr></table>",
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+    {
+        "type": "text",
+        "text": "3.2 RESULTS ",
+        "text_level": 1,
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "Figure 1 shows the evaluation results on the 5 datasets, from which we draw two main conclusions. First, the improvements over random sampling tend to be small. In some cases the average performance of a method is even below the average randomly sampled architecture, which suggests that the search methods are not converging to desirable architectures. Second, the small range of accuracies obtained hints at narrow search spaces, where even the worst architectures perform reasonably well. See Section 5 for more experiments corroborating this conclusion. ",
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+    {
+        "type": "text",
+        "text": "We observe also that, on CIFAR10, the top half of best-performing methods (PDARTS, MANAS, DARTS, StacNAS) all perform similarly and positively in relation to their respective search spaces, but more variance is seen on the other datasets. This could be explained by the fact that most methods’ hyperparameters have been optimized on CIFAR10 and might not generalize as well on different datasets. As a matter of fact, we found that all NAS methods neglect to report the time needed to optimize hyperparameters. In addition, Table 1 shows the relative improvement metric $R I$ (see intro to Section 3) for each method and dataset. ",
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+        "type": "text",
+        "text": "",
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+    {
+        "type": "text",
+        "text": "The computational cost of searching for architectures is a limiting factor in their applicability and, therefore, an important variable in the evaluation of NAS algorithms. Figure 2 shows the performance as well and the computational cost of the search phase on CIFAR10. ",
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+    {
+        "type": "text",
+        "text": "4 COMPARISON OF TRAINING PROTOCOLS ",
+        "text_level": 1,
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+    {
+        "type": "text",
+        "text": "In this section we attempt to shed some light on the surprising results of the previous section. We noticed that there was a much larger differences between the random baselines of different methods than the actual increase in performance of each approach. We hypothesized that how a network is trained (the training protocol) has a larger impact on the final accuracy than which architecture is trained, for each search space. To test this, we performed sensitivity analysis using the most common performanceboosting training protocols. ",
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+    {
+        "type": "text",
+        "text": "4.1 METHODOLOGY ",
+        "text_level": 1,
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+    {
+        "type": "text",
+        "text": "We decided to evaluate architectures from the commonly used DARTS search space (Liu et al., 2019) on the CIFAR10 dataset. We use the following process: 1) sample 8 random architectures, 2) train them with different training protocols (details below) and 3) report mean, standard deviation and maximum of the top-1 test accuracy at the end of the training process. ",
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+    {
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+        "img_path": "images/caa55a31af78adab243a490ab57323412ef1ea1347232a5cd9f8350973a2321e.jpg",
+        "image_caption": [
+            "Figure 3: Comparison of different augmentation protocols for the DARTS search space on CIFAR10. Same colored dots represent minimum and maximum accuracies in the 8 runs. "
+        ],
+        "image_footnote": [],
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+        "type": "text",
+        "text": "Training protocols. The simplest training protocol, which we will call Base is similar to the one used in DARTS, but with all tricks disabled: the model is simply trained for 600 epochs. On the other extreme, our full protocol uses several tricks which have been used in recent works (Xie et al., 2019b; Nayman et al., 2019): Auxiliary Towers (A), DropPath (D; Larsson & Shakhnarovich, 2017), Cutout (C; DeVries & Taylor, 2017), AutoAugment (AA; Cubuk et al., 2018), extended training for 1500 epochs (1500E), and increased number of channels (50C). In between these two extremes, by selectively enabling and disabling each component, we evaluated a further 8 intermediate training protocols. When active, DropPath probability is 0.2, cutout length is 16, auxiliary tower weight is 0.4, and AutoAugment combined with Cutout are used after standard data pre-processing techniques previously described, as in Popien (2019). ",
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+    {
+        "type": "text",
+        "text": "4.2 RESULTS ",
+        "text_level": 1,
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+    {
+        "type": "text",
+        "text": "As shown in Figure 3, a large difference of over 3 percentage points (p.p.) exists between the simplest and the most advanced training protocols. Indeed, this is much higher than any improvement over random sampling observed in the previous section: for example, on CIFAR10, the best improvement observed was 0.69 p.p. In other words, the training protocol is often far more important than the architecture used. Note that the best accuracy of the 8 random architectures training with the best protocol is $9 8 . 1 5 \\%$ , which is only 0.25 p.p. below state-of-the-art (Nayman et al., 2019). ",
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+    {
+        "type": "text",
+        "text": "To summarize, it seems that most recent state-of-the-art results, though impressive, cannot always be attributed to superior search strategies. Rather, they are often the result of expert knowledge applied to the evaluation protocol. In Figure 10 (Appendix A.3.1) we show similar results when training a ResNet-50 (He et al., 2016) with the same protocols. ",
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+        "img_path": "images/f9ef12213677fc9a4669a42a87f74fd716606dd30dbac4f7517b2b24659054a0.jpg",
+        "image_caption": [
+            "Figure 4: Training curves for the 214 randomly sampled architectures. Inset plot shows the histogram of accuracies at different epochs. "
+        ],
+        "image_footnote": [],
+        "bbox": [
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+    {
+        "type": "image",
+        "img_path": "images/3ab1d0af1522db09538fa5918d8022741f2b541c8dfb7d338233ba12f9eb1f4f.jpg",
+        "image_caption": [
+            "Figure 5: Correlation between accuracies at different epochs and final accuracy, using raw and smoothed accuracies over a window $w$ . "
+        ],
+        "image_footnote": [],
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+    {
+        "type": "text",
+        "text": "5 STUDY OF DARTS’ SEARCH SPACE ",
+        "text_level": 1,
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+    {
+        "type": "text",
+        "text": "5.1 DISTRIBUTION OF THE RANDOM SAMPLING WITHIN DARTS SEARCH SPACE ",
+        "text_level": 1,
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+    {
+        "type": "text",
+        "text": "To better understand the results from the previous section, we sampled a considerable number of architectures (214) from the most commonly used search space (Liu et al., 2019) and fully trained them with the matching training protocol (Cutout+DropPath+Auxiliary Towers). This allows us to get a sense of how much variance exists between the different models (training statistics are made available at the link in the abstract). ",
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+    {
+        "type": "text",
+        "text": "As we can observe from Figure 4, architectures sampled from this search space all perform similarly, with a mean of $9 7 . 0 3 \\pm 0 . 2 3$ . The worst architecture we found had an accuracy of 96.18, while the best achieved 97.56. ",
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+    {
+        "type": "text",
+        "text": "To put this into perspective, many methods using the same training protocol, fall within (or very close to) the standard deviation of the average architecture. Furthermore, as we can observe in Figure 7, the number of cells (a human-picked hyperparameter) has a much larger impact on the final accuracy. ",
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+    {
+        "type": "text",
+        "text": "In Figure 5 we used the training statistics of the 214 models to plot the correlation between test accuracies at different epochs: it grows slowly in an almost linear fashion. We note that using the moving average of the accuracies yields a stronger correlation, which could be useful for methods using early stopping. ",
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+    {
+        "type": "text",
+        "text": "5.2 OPERATIONS",
+        "text_level": 1,
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+    {
+        "type": "text",
+        "text": "To test whether the results from the previous section were due to the choice of available operations, we developed an intentionally sub-optimal search space containing 4 plain convolutions $( 1 \\times 1 , 3 \\times 3$ , $7 \\times 7 .$ , $1 1 \\times 1 1$ ), 2 max pooling operators $( 3 \\times 3 , 5 \\times 5 )$ plus the none and skip connect operations. This proposed search space is clearly more parameter inefficient compared to the commonly used DARTS one (which uses both dilated and separable ones), and we expect it to perform worse. ",
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+    {
+        "type": "text",
+        "text": "We sampled 56 architectures from this new search space and trained them with the DARTS training protocol (Cutout $^ +$ DropPath $^ +$ Auxiliary Towers), for fair comparison with the results from the previous section. Figure 6 shows the resulting histogram, together with the one obtained from the classical DARTS space of operations. The two distributions are only shifted by 0.18 accuracy points. Given the minor difference in performance, the specific operations are not a key ingredient in the success of this search space. Very likely, it’s the well engineered cell structure that allows the model to perform as well as it does. ",
+        "bbox": [
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+    {
+        "type": "image",
+        "img_path": "images/5e91248ab0a2f0aabd9ab36f7d3f7c4ee456017c62591d2c5a5bc19fc63e0e6f.jpg",
+        "image_caption": [
+            "Figure 6: Histograms of the final accuracies (600 epochs) for architectures sampled from the DARTS search space (214 models) and our modified version (56 models). "
+        ],
+        "image_footnote": [],
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+        "image_caption": [
+            "Figure 7: Performance of 16 randomly sampled architectures with different numbers of cells. Error bars represent standard deviation. "
+        ],
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+        "image_caption": [
+            "Figure 8: Changes in the ranking of different architectures when trained with two different seeds (A and B). "
+        ],
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+    {
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+        "img_path": "images/5f3c33ff2e3ac55ede03bb632eba1c2d1e204c46b832377bf24ea864a9fd54c4.jpg",
+        "image_caption": [
+            "Figure 9: Changes in the ranking of different architectures when trained with different numbers of cells (same seed). "
+        ],
+        "image_footnote": [],
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "5.3 DOES CHANGING SEED AND NUMBER OF CELLS AFFECT RANKING? ",
+        "text_level": 1,
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "A necessary practice for many weight-sharing methods (Liu et al., 2019; Pham et al., 2018) is to restart the training from scratch after the search phase, with a different number of cells. Recent works have warned that this procedure might negatively affect ranking; similarly, the role of the seed has been previously recognized as as a fundamental element in reproducibility (Li & Talwalkar, 2019; Sciuto et al., 2019). ",
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+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "To test the impact of seed, we randomly sampled 32 architectures and trained them with two different seeds (Figure 8). Ranking is heavily influenced, as the Kendall tau correlation between the two sets of training is 0.48. On average, the test accuracy changes by $0 . 1 3 \\% \\pm 0 . 0 8$ (max change is $0 . 3 9 \\%$ , which is substantial considering the small gap between random architectures and NAS methods. ",
+        "bbox": [
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+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "To test the depth-gap we trained another 32 with different number of cells (Figure 9). The correlation between the two different depths is not very strong as measured by Kendall Tau (0.54), with architectures shifting up and down the rankings by up to 18 positions (out of 32). Methods employing weight sharing (WS) would see an even more pronounced effect as the architectures normally chosen at 8 cells would have been training sub-optimally due to the WS itself (Sciuto et al., 2019). ",
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+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "These findings point towards two issues. The first is that since the seed has such a large effect on ranking, it stands to reason that the final accuracy reported should be averaged over multiple seeds. The second is that, if the lottery ticket hypothesis holds—so that specific sub-networks are better mainly due to their lucky initialization; Frankle & Carbin., 2018—together with our findings, this could be an additional reason why methods searching on a different number of cells than the final model, struggle to significantly improve on the average randomly sampled architecture. ",
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+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "6 DISCUSSION AND BEST PRACTICES ",
+        "text_level": 1,
+        "bbox": [
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+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "In this section we offer some suggestions on how to mitigate the issues in NAS research. ",
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+    {
+        "type": "text",
+        "text": "Augmention tricks: while achieving higher accuracies is clearly a desirable goal, we have shown in section 4, that using well engineered training protocols can hide the contribution of the search algorithm. We therefore suggest that both results, with and without training tricks, should be reported. An example of best practice is found in Hundt et al. (2019). ",
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+    {
+        "type": "text",
+        "text": "Search Space: it is difficult to evaluate the effectiveness of any given proposed method without a measure of how good randomly sampled architectures are. This is not the same thing as performing a random search which is a search strategy in itself; random sampling is simply used to establish how good the average model is. A simple approach to measure the variability of any new given search space could be to randomly sample $k$ architectures and report mean and standard deviation. We hope that future works will attempt to develop more expressive search spaces, capable of producing both good and bad network designs. Restricted search spaces, while guaranteeing good performance and quick results, will inevitably be constrained by the bounds of expert knowledge (local optima) and will be incapable of reaching more truly innovative solutions (closer to the global optima). As our findings in section 5.2 suggest, the overall wiring (the macro-structure) is an extremely influential component in the final performance. As such, future research could investigate the optimal wiring at a global level: an interesting work in this direction is Xie et al. (2019a). ",
+        "bbox": [
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+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "Multiple datasets: as the true goal of AutoML is to minimize the need for human experts, focusing the research efforts on a single dataset will inevitably lead to algorithmic overfitting and/or methods heavily dependent on hyperparameter tuning. The best solution for this is likely to test NAS algorithms on a battery of datasets, with different characteristics: image sizes, number of samples, class granularity and learning task. ",
+        "bbox": [
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+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "Investigating hidden components: as our experiments in Sections 4 and 5.2 show, the DARTS search space is not only effective due to specific operations that are being chosen, but in greater part due to the overall macro-structure and the training protocol used. We suggest that proper ablation studies can lead to better understanding of the contributions of each element of the pipeline. ",
+        "bbox": [
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+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "The importance of reproducibility: reproducibility is of extreme relevance in all sciences. To this end, it is very important that authors release not only their best found architecture but also the corresponding seed (if they did not average over multiple ones), as well as the code and the detailed training protocol (including hyperparameters). To this end, NAS-Bench-101 (Ying et al., 2019), a dataset mapping architectures to their accuracy, can be extremely useful, as it allows the quality of search strategies to be assessed in isolation from other NAS components (e.g. search space, training protocol) in a quick and reproducible fashion. The code for this paper is open-source (link in the abstract). We also open-source the 270 trained architectures used in Section 5. ",
+        "bbox": [
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+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "Hyperparameter tuning cost: tuning hyperparameters in NAS is an extremely costly component. Therefore, we argue that either (i) hyperparameters are general enough so that they do not require tuning for further tasks, or (2) the cost is included in the search budget. ",
+        "bbox": [
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+        "page_idx": 7
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+    {
+        "type": "text",
+        "text": "7 CONCLUSIONS ",
+        "text_level": 1,
+        "bbox": [
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+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "AutoML, and NAS in particular, have the potential to truly democratize the use of machine learning for all, and could bring forth very notable improvements on a variety of tasks. To truly step forward, a principled approach, with a focus on fairness and reproducibility is needed. ",
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+        "page_idx": 7
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+    {
+        "type": "text",
+        "text": "In this paper we have shown that, for many NAS methods, the search space has been engineered such that all architectures perform similarly well and that their relative ranking can easily shift. We have furthermore showed that the training protocol itself has a higher impact on the final accuracy than the actual network. Finally, we have provided some suggestions on how to make future research more robust to these issues. ",
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+    {
+        "type": "text",
+        "text": "We hope that our findings will help the community focus their efforts towards a more general approach to automated neural architecture design. Only then can we expect to learn from NASgenerated architectures as opposed to the current paradigm where search spaces are heavily influenced by our current (human) expert knowledge. ",
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+    {
+        "type": "text",
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+        "bbox": [
+            176,
+            837,
+            823,
+            880
+        ],
+        "page_idx": 9
+    },
+    {
+        "type": "text",
+        "text": "Barret Zoph and Quoc Le. Neural architecture search with reinforcement learning. In International Conference on Learning Representations (ICLR), 2017. ",
+        "bbox": [
+            174,
+            888,
+            823,
+            917
+        ],
+        "page_idx": 9
+    },
+    {
+        "type": "table",
+        "img_path": "images/320203340cda9ff05fec56f6573c4eaf1ef276b1e36acceee02cf27a14c0f25e.jpg",
+        "table_caption": [
+            "Table 2: Hyperparameters for different NAS methods. “S” denotes search stage and “A” denotes augmentation stage. For learning rates, $a \\downarrow b$ means cosine annealing from $a$ to $b$ . "
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td rowspan=\"2\"></td><td colspan=\"5\">Method</td></tr><tr><td>DARTS</td><td>StacNAS</td><td>PDARTS</td><td>MANAS</td><td>CNAS</td></tr><tr><td>batch size S</td><td>64</td><td>64</td><td>96</td><td>64</td><td>64</td></tr><tr><td>batch size A</td><td>96</td><td>96</td><td>128</td><td>128</td><td>64</td></tr><tr><td>init channels S</td><td>16</td><td>16</td><td>16</td><td>16</td><td>16</td></tr><tr><td>init channels A</td><td>36</td><td>36</td><td>36</td><td>36</td><td>36</td></tr><tr><td>epochs S</td><td>50</td><td>100+100</td><td>25+25+25</td><td>50</td><td>60</td></tr><tr><td>epochs A</td><td>600</td><td>600</td><td>600</td><td>600</td><td>200</td></tr><tr><td>optimizer S/A</td><td>SGD</td><td>SGD</td><td>SGD</td><td>SGD</td><td>Adam</td></tr><tr><td>learning rates S</td><td>.025↓.001</td><td>.025↓.001</td><td>.025↓.0</td><td>.025↓.001</td><td>.025-.003</td></tr><tr><td>learning rates A</td><td>.025↓.0</td><td>.025↓.0</td><td>.025↓.0</td><td>.025←.0</td><td>.025-.001</td></tr><tr><td>weight decay S/A</td><td>3 ×10-4</td><td>3×10-4</td><td>3×10-4</td><td>3×10-4</td><td>3×10-4</td></tr><tr><td>optimizer arch</td><td>Adam</td><td>Adam</td><td>Adam</td><td></td><td>Adam</td></tr><tr><td>learning rates arch</td><td>3×10-4</td><td>3×10-4</td><td>6×10-4</td><td></td><td>3×10-4</td></tr><tr><td>weight decay arch</td><td>10-3</td><td>10-3</td><td>10-3</td><td></td><td>10-3</td></tr><tr><td>nb cells S CIFAR</td><td>8</td><td>14/20</td><td>5/11/17</td><td>8</td><td>6</td></tr><tr><td>nb cells A CIFAR</td><td>20</td><td>20</td><td>20</td><td>20</td><td>20</td></tr><tr><td>nb cells S other datasets</td><td>8</td><td>8/8</td><td>8/8/8</td><td>8</td><td>6</td></tr><tr><td>nb cellsA other datasets</td><td>8</td><td>8</td><td>8</td><td>8</td><td>8</td></tr><tr><td>nb intermediate nodes</td><td>4</td><td>4</td><td>4</td><td>4</td><td>6</td></tr></table>",
+        "bbox": [
+            176,
+            145,
+            820,
+            428
+        ],
+        "page_idx": 10
+    },
+    {
+        "type": "text",
+        "text": "A APPENDIX ",
+        "text_level": 1,
+        "bbox": [
+            174,
+            460,
+            299,
+            476
+        ],
+        "page_idx": 10
+    },
+    {
+        "type": "text",
+        "text": "This section details the datasets and the hyperparameters used for each method on each dataset. Search spaces were naturally left unchanged. Hyperparameters were chosen as close as possible to the original paper and occasionally updated to more recent implementations. The network size was tuned similarly for all methods for SPORT8, MIT67 and FLOWERS102. All experiments were run on NVIDIA Tesla V100 GPUs. ",
+        "bbox": [
+            174,
+            493,
+            825,
+            563
+        ],
+        "page_idx": 10
+    },
+    {
+        "type": "text",
+        "text": "A.1 METHODS AND HYPERPARAMETERS ",
+        "text_level": 1,
+        "bbox": [
+            176,
+            582,
+            467,
+            595
+        ],
+        "page_idx": 10
+    },
+    {
+        "type": "text",
+        "text": "During search, models are trained/validated on the training/validation subsets, respectively During the final evaluation, the model is trained on the training $^ +$ validation subsets and tested on the test subset. ",
+        "bbox": [
+            174,
+            608,
+            825,
+            650
+        ],
+        "page_idx": 10
+    },
+    {
+        "type": "text",
+        "text": "Common hyperparameters. All 8 methods share a common number of hyperparameters precised here. When SGD optimizer is used, momentum is .9 while when Adam is used, momentum is $\\beta = ( 0 . 5 , 0 . 9 9 9 )$ . Gradient clipping is set at 5. ",
+        "bbox": [
+            174,
+            657,
+            825,
+            700
+        ],
+        "page_idx": 10
+    },
+    {
+        "type": "text",
+        "text": "DARTS, StacNAS, PDARTS, MANAS, CNAS common hyperparameters. These methods are inspired by DARTS code-wise and consequently share a common number of hyperparameters, which we precise in table 1. ",
+        "bbox": [
+            174,
+            707,
+            825,
+            748
+        ],
+        "page_idx": 10
+    },
+    {
+        "type": "text",
+        "text": "DARTS. We used the following repository : https://github.com/khanrc/pt.darts. It notably updates the official implementation to a pytorch version posterior to 0.4. Additional enhancements include cutout of size 16 (DeVries & Taylor, 2017), path dropout of probability 0.2 (Larsson & Shakhnarovich, 2017), and auxiliary tower with weight 0.4. ",
+        "bbox": [
+            174,
+            756,
+            825,
+            811
+        ],
+        "page_idx": 10
+    },
+    {
+        "type": "text",
+        "text": "StacNAS. We used an unofficial implementation provided by the authors. The search process consists of 2 stages, of which the details are given in table 1. Additional enhancements are the same as DARTS. ",
+        "bbox": [
+            174,
+            819,
+            825,
+            861
+        ],
+        "page_idx": 10
+    },
+    {
+        "type": "text",
+        "text": "PDARTS. We used the official implementation $:$ https://github.com/chenxin061/pdarts. The search process consists of 3 stages, of which general details are given in table 1. At stage 1, 2 and 3 respectively, the number of operations decreases from 8 to 5 to 3, and the dropout probability on skip-connect increases from 0.0 to 0.4 to 0.7 for CIFAR10, SPORT8, MIT67 and FLOWERS102 (0.1 to 0.2 to 0.3 for CIFAR100). Discovered cells are restricted to keep at most 2 skip-connect operations. Additional enhancements include cutout of size 16 (DeVries & Taylor, 2017), DropPath of probability 0.3 (Larsson & Shakhnarovich, 2017) and auxiliary tower with weight 0.4. ",
+        "bbox": [
+            174,
+            867,
+            823,
+            922
+        ],
+        "page_idx": 10
+    },
+    {
+        "type": "text",
+        "text": "",
+        "bbox": [
+            173,
+            103,
+            823,
+            146
+        ],
+        "page_idx": 11
+    },
+    {
+        "type": "text",
+        "text": "MANAS. We used an unofficial implementation provided by the authors. The reward baseline is 5, gamma is 0.1 (0.07 for SPORT8, 0.05 for FLOWERS102, 0.01 for MIT67) and the Boltzmann temperature decays from 1000 to 200 (300 to 100 for SPORT8, 5000 to 2000 for MIT67). Additional enhancements are the same as DARTS. ",
+        "bbox": [
+            174,
+            152,
+            823,
+            208
+        ],
+        "page_idx": 11
+    },
+    {
+        "type": "text",
+        "text": "CNAS. We used the official implementation : https://github.com/tianbaochou/CNAS. Label Smoothing is used with epsilon 0.1. Other additional enhancements include cutout of size 16 (DeVries & Taylor, 2017), DropPath of probability 0.25 (Larsson & Shakhnarovich, 2017). ",
+        "bbox": [
+            174,
+            215,
+            821,
+            257
+        ],
+        "page_idx": 11
+    },
+    {
+        "type": "text",
+        "text": "NSGANET. We used the official implementation: https://github.com/ianwhale/nsga-net. The search is done in the micro search space (with 2 cells to search, 9 operations in the search space, 5 blocks in each cell) on 8 layers networks. The population size is 40, the number of generations is 30 and the number of offsprings created by generation is 20. Networks are trained for 20 epochs, with batch size 128, and the initial number of channels is 16. For architecture evaluation, the network is composed of 20 cells for CIFAR10 and CIFAR100, and 8 cells for SPORT8, MIT67 and FLOWERS102. The final selected models are trained for 600 epochs with batch size 96 and the initial number of channels 34. Momentum SGD is used with initial learning rate $\\eta _ { w } = 0 . 0 2 5$ (annealed down to zero following a cosine schedule), and weight decay $3 \\times 1 0 ^ { - \\hat { 4 } }$ . The filter increment is set to 4, and squeeze and excitation is used. Additional enhancements include cutout of size 16 (DeVries & Taylor, 2017), DropPath of probability 0.2 (Larsson & Shakhnarovich, 2017) and auxiliary tower with weight 0.4. ",
+        "bbox": [
+            173,
+            263,
+            825,
+            417
+        ],
+        "page_idx": 11
+    },
+    {
+        "type": "text",
+        "text": "NAO. We used the official Pytorch implementation: https://github.com/renqianluo/NAO pytorch. The LSTM model used to encode architecture has a token embedding size of 48 and a hidden state size of 96. The LSTM model used to decode architecture has a hidden state size of 96. The encoder and decoder are trained using Adam for 1000 epochs with a learning rate of 0.001. The trade-off parameters is $\\lambda = 0 . 9$ . The step size to perform continuous optimization is $\\eta = 1 0$ . The number of nodes is fixed to 5, normal cell is stacked 3 (2 for SPORT8, MIT67 and FLOWERS102) times to form the CNN architecture, which corresponds to a 11 (8 for SPORT8, MIT67 and FLOWERS102) cells network and the initial number of channels is 20. Networks are trained for 100 epochs with batch size 64 for training, and validated for 20 epochs with batch size 500. For architecture evaluation, the final CNN architecture is a 20 cells network (8 cells network). This network is trained for 600 epochs with batch size 128 for the training set (96 for both for SPORT8, MIT67 and FLOWERS102), 500 for the validation set (128 for both for SPORT8, MIT67 and FLOWERS102) and the initial number of channels is 36. Momentum SGD is used with initial learning rate $\\eta _ { w } = 0 . 0 2 5$ (annealed down to zero following a cosine schedule) and weight decay $3 \\times 1 0 ^ { - \\overline { { 4 } } }$ . Additional enhancements include cutout of size 16 (DeVries & Taylor, 2017), DropPath of probability 0.2 (Larsson & Shakhnarovich, 2017), dropout of probability 0.4 (Srivastava et al., 2014), and auxiliary tower with weight 0.4. ",
+        "bbox": [
+            173,
+            424,
+            825,
+            660
+        ],
+        "page_idx": 11
+    },
+    {
+        "type": "text",
+        "text": "ENAS. We used the official tensorflow implementation for experiments on CIFAR10 and CIFAR100: https://github.com/melodyguan/enas Experiments on SPORT8, MIT67 and FLOWERS102 are done using a more recent version in Pytorch for the search : https://github.com/MengTianjian/enas-pytorch. Because only the search process is implemented there, the evaluation code used is the same as DARTS. During the search, networks are composed of 8 cells. The shared parameters $w$ are trained with Nesterov momentum (Nesterov, 1983), weight decay $1 0 ^ { - 4 }$ , gradient clipping 5, batch size 160, 20 output filters, and a cosine learning rate schedule with $l _ { m } a x = 0 . 0 5$ , $l _ { m } i n = 0 . 0 0 1$ , $T _ { 0 } = 1 0$ , $T _ { m } u l = 2$ (Loshchilov & Hutter, 2017). Each architecture search is run for 150 epochs. $w$ are initialized with He initialization (He & Sun, 2015). The policy parameters $\\theta$ are initialized uniformly in [-0.1, 0.1], and trained with Adam at a learning rate of 0.00035. A tanh constant of 1.10 and a temperature of 2.5 is applied to the controllers logits, and the controller entropy is added to the reward with weight 0.1. For the evaluation, the architecture searched is extended to 17 cells (8 for SPORT8, MIT67 and FLOWERS102), trained for 630 epochs, with batch size 144, and a cosine learning rate schedule with $l _ { \\mathrm { m a x } } = 0 . 0 5$ , $l _ { \\mathrm { m i n } } = 0 . 0 0 1$ , $T _ { 0 } = 1 0$ , $T _ { \\mathrm { m u l } } = 2$ . ",
+        "bbox": [
+            173,
+            667,
+            825,
+            876
+        ],
+        "page_idx": 11
+    },
+    {
+        "type": "text",
+        "text": "A.2 DATASETS ",
+        "text_level": 1,
+        "bbox": [
+            176,
+            103,
+            290,
+            117
+        ],
+        "page_idx": 12
+    },
+    {
+        "type": "text",
+        "text": "We present here the datasets used and how they are pre-processed. ",
+        "bbox": [
+            174,
+            130,
+            609,
+            143
+        ],
+        "page_idx": 12
+    },
+    {
+        "type": "text",
+        "text": "CIFAR10. The CIFAR10 dataset (Krizhevsky, 2009) is a dataset of 10 classes and consists of 50, 000 training images and 10, 000 test images of size $3 2 \\times 3 2$ . ",
+        "bbox": [
+            174,
+            150,
+            823,
+            179
+        ],
+        "page_idx": 12
+    },
+    {
+        "type": "text",
+        "text": "CIFAR100. The CIFAR100 dataset (Krizhevsky, 2009) is a dataset of 100 classes and consists of 50, 000 training images and 10, 000 test images of size $3 2 \\times 3 2$ . ",
+        "bbox": [
+            174,
+            185,
+            821,
+            214
+        ],
+        "page_idx": 12
+    },
+    {
+        "type": "text",
+        "text": "Each of these datasets is split into a training, validation and testing subsets of size 25, 000, 25, 000 and 10, 000 respectively. For both these datasets, we use standard data pre-processing and augmentation techniques, i.e. subtracting the channel mean and dividing by the channel standard deviation; centrally padding the training images to $4 0 \\times 4 0$ and randomly cropping them back to $3 2 \\times 3 2$ ; and randomly clipping them horizontally. ",
+        "bbox": [
+            174,
+            220,
+            825,
+            291
+        ],
+        "page_idx": 12
+    },
+    {
+        "type": "text",
+        "text": "SPORT8. This is an action recognition dataset containing 8 sport event categories and a total of 1579 images (Li & Fei-Fei, 2007). The tiny size of this dataset stresses the generalization capabilities of any NAS method applied to it. ",
+        "bbox": [
+            174,
+            297,
+            825,
+            340
+        ],
+        "page_idx": 12
+    },
+    {
+        "type": "text",
+        "text": "MIT67. This is a dataset of 67 classes representing different indoor scenes and consists of 15, 620 images of different sizes (Quattoni & Torralba, 2009). ",
+        "bbox": [
+            176,
+            347,
+            823,
+            376
+        ],
+        "page_idx": 12
+    },
+    {
+        "type": "text",
+        "text": "FLOWERS102. This is a dataset of 102 classes representing different species of flowers and consists of 8, 189 images of different sizes (Nilsback & Zisserman, 2008). ",
+        "bbox": [
+            176,
+            382,
+            820,
+            411
+        ],
+        "page_idx": 12
+    },
+    {
+        "type": "text",
+        "text": "Each of these datasets is split into a training, validation and testing subsets with proportions $4 0 / 4 0 / 2 0 \\ ( \\% )$ . For each one, we use use standard data pre-processing and augmentation techniques, i.e. subtracting the channel mean and dividing the channel standard deviation, cropping the training images to random size and aspect ratio, resizing them to $2 2 4 \\times 2 2 4$ , and randomly changing their brightness, contrast, and saturation, while resizing test images to $2 5 6 \\times 2 5 6$ and cropping them at the center. ",
+        "bbox": [
+            173,
+            417,
+            825,
+            501
+        ],
+        "page_idx": 12
+    },
+    {
+        "type": "text",
+        "text": "A.3 ADDITIONAL RESULTS ",
+        "text_level": 1,
+        "bbox": [
+            176,
+            518,
+            374,
+            532
+        ],
+        "page_idx": 12
+    },
+    {
+        "type": "image",
+        "img_path": "images/ce230d7557a836be95b1c534a22b98a18804cb6ce095b27f9043206e3ab14ff8.jpg",
+        "image_caption": [
+            "A.3.1 DIFFERENT TRAINING PROTOCOLS FOR RESNET-50 ",
+            "Figure 10: Extension of Figure 3, including results obtained by training a ResNet-50 on CIFAR10. Bars with darker shade are for ResNet-50 and bars with lighter shade are for DARTS (same as Figure 3). Result are for 8 runs of each training protocol. For ResNet-50, the auxiliary tower was added after layer 2. As DropPath (Larsson & Shakhnarovich, 2017) would not have been straightforward to apply, we instead implemented Stocastic Depth (Huang et al., 2016), to a similar effect. "
+        ],
+        "image_footnote": [],
+        "bbox": [
+            269,
+            573,
+            723,
+            712
+        ],
+        "page_idx": 12
+    }
+]

parse/train/QmxFsofRvW9/QmxFsofRvW9.md

@@ -0,0 +1,287 @@
+# Unsupervised Speech Recognition
+
+Alexei Baevski4 Wei-Ning Hsu4 Alexis Conneau∗ Michael Auli4
+
+4 Facebook AI  Google AI
+
+# Abstract
+
+Despite rapid progress in the recent past, current speech recognition systems still require labeled training data which limits this technology to a small fraction of the languages spoken around the globe. This paper describes wav2vec-U, short for wav2vec Unsupervised, a method to train speech recognition models without any labeled data. We leverage self-supervised speech representations to segment unlabeled audio and learn a mapping from these representations to phonemes via adversarial training. The right representations are key to the success of our method. Compared to the best previous unsupervised work, wav2vec-U reduces the phone error rate on the TIMIT benchmark from 26.1 to 11.3. On the larger English Librispeech benchmark, wav2vec-U achieves a word error rate of 5.9 on test-other, rivaling some of the best published systems trained on 960 hours of labeled data from only two years ago. We also experiment on nine other languages, including low-resource languages such as Kyrgyz, Swahili and Tatar. The code is available at https://github.com/pytorch/fairseq/tree/ master/examples/wav2vec/unsupervised
+
+# 1 Introduction
+
+Speech recognition performance on the much studied English Librispeech benchmark [Panayotov et al., 2015] has seen rapid improvement over the last few years due to advances in model architectures [Dong et al., 2018, Synnaeve et al., 2020, Gulati et al., 2020], semi-supervised learning [Xu et al., 2020b, Park et al., 2020] and self-supervised learning [van den Oord et al., 2018, Chung and Glass, 2018, Chung et al., 2019b, Baevski et al., 2020c]. However, all of these techniques require transcribed speech data which is not available for the vast majority of the nearly 7,000 languages of the world [Lewis et al., 2016]. As a result, speech recognition technology is only available for about 125 different languages [Google, 2021]. On the other hand, humans learn a lot about speech simply by listening to others around them and without explicit supervision [Werker and Tees, 1984, Hirsh-Pasek et al., 1987, Polka and Werker, 1994, Jusczyk et al., 1999, Johnson and Jusczyk, 2001].
+
+Unsupervised learning has been very successful in machine translation resulting in systems that obtain remarkable accuracy given no labeled training data at all [Conneau et al., 2018, Lample et al., 2018, Artetxe et al., 2018]. Inspired by this, there has been some work on unsupervised speech recognition based on learning to align unlabeled text and audio [Yeh et al., 2019] or adversarial learning [Liu et al., 2018, Chen et al., 2019]. These approaches showed promising initial results but their error rates are still high, with evaluation being limited to the small-scale and clean TIMIT benchmark.
+
+In this work, we introduce a framework for unsupervised learning of speech recognition models. Wav2vec-U, or wav2vec Unsupervised, leverages self-supervised representations from wav2vec 2.0 [Baevski et al., 2020c] to embed the speech audio and to segment the audio into units with a simple $\mathrm { k }$ -means clustering method (see Figure 1 for an illustration of our approach). We find that the quality of the audio representations is key to the success of unsupervised speech recognition. Similar to Liu et al. [2018] and Chen et al. [2019], we learn a mapping between segments and phonemes using adversarial training but different to their work, we also enable the algorithm to label segments as silences. We also introduce an unsupervised cross-validation metric to enable model development without labeled development data. Our unsupervised speech recognition model, the generator, is very lightweight: it consists of a single temporal convolution comprising only about 90k parameters to which we input frozen wav2vec 2.0 representations.
+
+![](images/0b5b4f3465570676296b5d72eebf6d66830b97659f2ec44658268dac36522d53.jpg)  
+Figure 1: Illustration of wav2vec Unsupervised: we learn self-supervised representations with wav2vec 2.0 on unlabeled speech audio (Step 1), identify clusters in the representations with $\mathbf { k }$ -means (Step 2) to segment the audio (Step 3). Next, we build segment representations by mean pooling the wav2vec 2.0 representations, performing PCA and a second mean pooling step between adjacent segments (Step 4). This is input to the generator which outputs a phoneme sequence (Step 5) fed to the discriminator, similar to phonemized unlabeled text (Step 6), for adversarial training (Step 7).
+
+Experimental results demonstrate the viability of the framework for a variety of settings and languages. wav2vec-U improves the phone error rate (PER) on the small-scale TIMIT benchmark from 26.1 to 11.3 compared to the next best known unsupervised approach. To get a better sense of the performance compared to the best supervised methods, we measure performance on the larger Librispeech benchmark where our method achieves word error rate (WER) 5.9 on test-other. We also evaluate on six other European languages of the multilingual Librispeech benchmark [Pratap et al., 2020] and on three non-European low-resource languages.
+
+# 2 Speech and Text Representations
+
+Next, we describe how we build suitable speech and text representations for unsupervised learning.   
+Good representations are essential to learning a mapping from speech to text without supervision.
+
+# 2.1 Self-supervised Learning of Speech Audio Representations
+
+In the first step, we learn representations of the speech audio signal using self-supervised learning. There has been a lot of recent work in this direction which has shown strong performance in extremely low-labeled data setups across a range of languages [Conneau et al., 2020] and tasks [Fan et al., 2021, Pepino et al., 2021, Wang et al., 2021].
+
+Wav2vec 2.0 consists of a convolutional feature encoder $f : \mathcal X \mapsto \mathcal Z$ that maps a raw audio sequence $X$ to latent speech representations $z _ { 1 } , \dots , z _ { T }$ , which a Transformer $g : { \mathcal { Z } } \mapsto { \mathcal { C } }$ then turns into context representations $c _ { 1 } , \ldots , c _ { T }$ [Baevski et al., 2020b,a]. Each $z _ { t }$ represents about $2 5 \mathrm { m s }$ of audio strided by $2 0 \mathrm { m s }$ and the Transformer architecture follows BERT [Vaswani et al., 2017, Devlin et al., 2019]. During training, latent representations are discretized to $q _ { 1 } , \ldots , q _ { T }$ with a quantization module ${ \mathcal { Z } } \mapsto { \mathcal { Q } }$ to represent the targets in the objective. Quantization uses a Gumbel softmax to choose entries from two codebooks [Jegou et al., 2011, Jang et al., 2016, Baevski et al., 2020b].
+
+In our experiments, we use the publicly available English model pre-trained on $5 3 \mathrm { k }$ hours of LibriLight [Kahn et al., 2020b] as well as XLSR-53 which was pre-trained on nearly 60k hours of speech audio in 53 languages [Conneau et al., 2020].
+
+# 2.2 Pre-processing and Embedding the Audio Data
+
+Removing Silences. Most datasets we use for our experiments have audio data with silences. However, these parts of the audio do not correspond to any transcription and we therefore remove silences as much as possible. We apply rVAD, an unsupervised voice activity detection (VAD) model which determines the segments in the audio data corresponding to silences, and we remove these sections [Tan et al., 2020]. We ablate this choice in Appendix C.
+
+Speech Audio Representations. After silence removal, we embed the unlabeled speech audio with wav2vec 2.0 to obtain speech representations. Specifically, we use the representations of the context Transformer network $c _ { 1 } , \ldots , c _ { T }$ $( \ S 2 . 1 )$ . The context network contains 24 Transformer blocks and we denote the output of block $l$ at time-step $t$ as $c _ { t } ^ { l }$ . Our goal is to learn a model which can map from audio representations $c _ { t } ^ { l }$ to phonemes using no supervision. However, the representations of the uppermost block of wav2vec 2.0 may not be well suited for this task. These features are trained to directly predict masked latent representations spanning $2 5 \mathrm { m s }$ of speech audio which is much shorter than the typical duration of a phoneme.
+
+To get a better sense of this, we train supervised phoneme recognizers with a CTC loss [Graves et al., 2006] on top of the frozen representations of each of the 24 blocks of the English wav2vec 2.0 LARGE model pre-trained on Libri-Light. We then evaluate phone error rate (PER) with respect to the phonemized transcriptions of Librispeech dev-other. The classifier takes as input $c _ { t } ^ { l }$ and contains a single softmax-normalized linear layer mapping to the phoneme inventory. Figure 2 shows that most of the first ten blocks as well as the final blocks provide very poor performance, while blocks 15-19 provide error rates below $9 \%$ PER. Block 15 achieves the best error rate of $7 . 5 \%$ PER. A similar insight has been used in the concurrent work of Hsu et al. [2021b]. Appendix A shows that this choice generalizes to other languages. For brevity we drop the superscript $l$ and refer to block 15 representations simply as $c _ { 1 } , \ldots , c _ { T }$ .
+
+![](images/4893afedc781e5fe6ccd0b0db23368e07e04f56d069fce1ae7128f54dac18113.jpg)  
+Figure 2: Supervised phoneme recognition using representations from different wav2vec 2.0 blocks on dev-other of English Librispeech. Low and high blocks do not provide good features, while as blocks 14-19 do. Block 15 performs best.
+
+# 2.3 Segmenting the Audio Signal
+
+Once the speech signal is embedded, we identify segments corresponding to meaningful units that can be mapped to phonemes. Segmentation has been shown to be crucial in prior work [Chung et al., 2018] since the right boundaries in the input representations make it more aligned to phonetic sequences. There has been a lot of prior work in unsupervised speech segmentation [Kamper et al., 2017a,b, Rasanen et al., 2015, Kreuk et al., 2020] but here we simply use a method based on clustering the wav2vec 2.0 speech representations $c _ { 1 } , \ldots , c _ { T }$ . In a first step, we collect all the speech representations for the unlabeled speech data and perform k-means clustering to identify $K = 1 2 8$ clusters. We use the FAISS library to do fast clustering on GPUs [Johnson et al., 2019]. Next, each $c _ { t }$ is labeled with the corresponding cluster ID $i _ { t } \in \{ 1 , \ldots , K \}$ and we introduce speech segment boundaries whenever the cluster ID changes.
+
+Once the speech audio representations are segmented, we compute a 512-dimensional PCA over all speech representations output by wav2vec 2.0 for the training set. Next, we mean-pool the PCA representations for a particular segment to obtain an average representation of the segment. The PCA retains only the most important features and we found this to be effective. Segment boundaries are noisy due to the lack of supervision and we therefore found it useful to also mean-pool pairs of adjacent segment representations to increase robustness. This results in sequences of speech segment representation $S = s _ { 1 } , \ldots , s _ { T } , S \sim { \mathcal { S } }$ for a given utterance. Appendix B shows an illustration of the segmentation strategy on an actual example as well as a quantitative evaluation of the strategy compared to human segmented data.
+
+# 2.4 Pre-processing the Text Data
+
+Similar to how we segment the unlabeled speech audio data into suitable units for unsupervised learning, we do the same for the unlabeled text data. We apply two pre-processing steps to the text data: phonemization and silence token insertion.
+
+Phonemes characterize the different sounds which distinguish words from each other, e.g., for the word cat there are three phonemes corresponding to the three distinct sounds in the pronunciation of the word: /K/, /AE/, $/ \mathrm { T } / .$ . We phonemize the text data because we found it easier to learn a mapping between speech audio and the different sounds of a word rather than between audio and words or letters. Phonemization converts a sequence of words $Y$ into a sequence of phonemes $P = [ p _ { 1 } , \cdots , p _ { M } ]$ , where $p _ { m } \in O$ and $O$ is the phoneme inventory. We use off-the-shelf tools for this step which we detail in Appendix $\ S \operatorname { E } . 2$ .
+
+The unlabeled speech audio data is pre-processed by applying unsupervised silence removal. However, this process is not always accurate and many silences in the speech audio remain. To deal with this, we enable the unsupervised model to label some segments with a phonemic silence token (SIL; $\ S \ 3 . 1 \AA .$ ). However, the phonemized unlabeled text data does not contain any silence tokens and this may pose difficulties for adversarial learning $( \ S 3 )$ . We remedy this by inserting silence markers at the beginning and end of the phonemized unlabeled text data; we also randomly insert SIL between words, or groups of phonemes corresponding to words at a rate of $2 5 \%$ . Appendix C evaluates these choices.
+
+# 3 Unsupervised Learning
+
+We use adversarial training to train an unsupervised speech recognition model using the representations of the unlabeled speech audio data and the unlabeled phonemized text data [Liu et al., 2018, Chen et al., 2019]. In the following, we detail the model architecture, the training objective as well as the unsupervised cross-validation metric we developed.
+
+# 3.1 Model Architecture
+
+Generative adversarial networks (GAN; Goodfellow et al. 2014) train a generator network $\mathcal { G }$ and a discriminator/critic network $\mathcal { C }$ where the generator produces samples which are then judged by the discriminator. The discriminator is trained to classify whether samples are from the generator or from the real data distribution. The objective of the generator is to produce samples that are indistinguishable by the discriminator.
+
+Concretely, $\mathcal { G }$ takes as input a sequence of $T$ segment representations $S = [ s _ { 1 } , \dotsc , s _ { T } ]$ (§ 2.3) which are then mapped to a sequence of $M$ phonemes $\mathcal { G } ( S ) \bar { = } [ p _ { 1 } , \dotsc , p _ { M } ]$ . The generator predicts a distribution over the phoneme set $O$ for each segment and outputs the phoneme with the highest probability. If the argmax prediction of consecutive segments result in the same phoneme, then we sample one of these segments, therefore $M \leq T$ .
+
+The phoneme set $O$ includes a silence label SIL to enable labeling silences in the speech audio as such. Without a silence label, we noticed that the model was repurposing a particular phoneme to label silences which resulted in much lower performance since it interfered with subsequent language model (LM) decoding. In the backward pass, we back-propagate through segments sampled at the generator output. We do not modify the segment representations $S$ during unsupervised training. The generator is parameterized as a single layer convolutional neural network (CNN).
+
+The discriminator takes as input either a sequence $P ^ { r } \sim \mathcal { P } ^ { r }$ of one-hot vectors denoting phonemized text from the real data distribution ${ \mathcal { P } } ^ { r }$ or a sequence of output distributions from the generator $\mathcal { G } ( S )$ . Each input vector has $| O |$ dimensions to represent the distribution over phonemes for each segment. The discriminator is also a CNN which outputs a probability indicating how likely the sample is to be from the data distribution.
+
+# 3.2 Objective
+
+In our setup we use the original GAN objective with a gradient penalty [Goodfellow et al., 2014, Arjovsky et al., 2017], a segment smoothness penalty and a phoneme diversity penalty:
+
+$$
+\operatorname* { m i n } _ { \mathcal { G } } \operatorname* { m a x } _ { \mathcal { C } } \quad \mathbb { E } _ { \mathcal { P } ^ { r } \sim \mathcal { P } ^ { r } } \left[ \log \mathcal { C } ( \boldsymbol { P } ^ { r } ) \right] - \underset { S \sim \mathcal { S } } { \mathbb { E } } \left[ \log \left( 1 - \mathcal { C } ( \mathcal { G } ( S ) ) \right) \right] - \lambda \mathcal { L } _ { g p } + \gamma \mathcal { L } _ { s p } + \eta \mathcal { L } _ { p d }
+$$
+
+where $P ^ { r } \sim \mathcal { P } ^ { r }$ is phonemized unlabeled text, $\mathcal { G } ( S )$ is the transcription output by the generator of input segment representations $S$ for some unlabeled speech audio. The first term trains the discriminator to assign high probability to real transcriptions, the second term encourages the discriminator to assign low probability to generator outputs, $\mathcal { L } _ { g p }$ is a gradient penalty, $\mathcal { L } _ { s p }$ is a smoothness penalty and $\mathcal { L } _ { p d }$ is a phoneme diversity loss which we detail next. During training we alternate updates for the discriminator and the generator. We also alternate batches of predicted transcriptions from the generator and phonemized unlabeled text.
+
+Gradient penalty. To stabilize training, we penalize the gradient norm of the discriminator with respect to the input [Gulrajani et al., 2017]. The penalty is computed for random samples $\tilde { P } \sim \tilde { \mathcal { P } }$ which are a linear combination of the activations of pairs of real and fake samples.2
+
+$$
+\mathcal { L } _ { g p } = \underset { \tilde { P } \sim \tilde { \mathcal { P } } } { \mathbb { E } } \left[ \left( \| \nabla \mathcal { C } ( \tilde { P } ) \| - 1 \right) ^ { 2 } \right]
+$$
+
+Segment smoothness penalty. The $\mathbf { k }$ -means segmentation of the speech audio is more granular than a typical phonemized transcription and neighboring representations are highly correlated. We therefore found it useful to add a penalty which encourages the generator to produce similar outputs for adjacent segments where $p _ { t } \in \mathbb { R } ^ { | O | }$ :
+
+$$
+\mathcal { L } _ { s p } = \sum _ { ( p _ { t } , p _ { t + 1 } ) \in \mathcal { G } ( S ) } \| p _ { t } - p _ { t + 1 } \| ^ { 2 }
+$$
+
+Phoneme diversity loss. We also found it helpful to penalize low usage of the phoneme vocabulary by the generator on the batch level. In particular, we maximize the entropy of the averaged softmax distribution $H _ { \mathcal { G } } ( \mathcal { G } ( S ) )$ of the generator over the phoneme vocabulary across a batch $B$ of utterances:
+
+$$
+\mathcal { L } _ { p d } = \frac { 1 } { | B | } \sum _ { S \in B } - H _ { \mathcal { G } } ( \mathcal { G } ( S ) )
+$$
+
+# 3.3 Unsupervised Cross-Validation Metric
+
+Our goal is to build speech recognition models without any supervision. To this end, we developed a cross-validation metric which does not require labeled data. We use the metric for early stopping, selecting a random seed, and hyper-parameter selection $( \lambda , \gamma , \eta )$ .
+
+We consider two quantities in our metric: LM negative log-likelihood (NLL) and vocabulary usage. LM-NLL serves as an indicator of fluency for a given transcription and it is measured with a language model $p _ { L M }$ trained on phonemized text data $( \ S ~ 2 . 4 )$ . Vocabulary usage is the proportion of the phoneme vocabulary being output by the model via Viterbi decoding. Measuring vocabulary usage identifies degenerate models which output fluent but trivial transcriptions.
+
+We deaudio rbias criptions for a given generator configuration . LM-NLL is measured in the standard way o $\mathcal { G }$ and unlabeled speechr the phonemized tran$\{ X _ { j } \} _ { j = 1 } ^ { N _ { s } }$ $\mathbf { \bar { \mathcal { P } } } = \{ P _ { j } \} _ { j = 1 } ^ { N _ { s } }$ scriptions: $\begin{array} { r } { N L L _ { L M } ( \mathcal { P } ) = \frac { 1 } { N _ { s } } \sum _ { j = 1 } ^ { N _ { s } } N L L _ { L M } ( P _ { j } ) } \end{array}$ where $\begin{array} { r } { N L L _ { L M } ( P ) = - \frac { 1 } { M } \sum _ { t = 1 } ^ { M } \log p _ { L M } ( p _ { t } ) } \end{array}$ using $p _ { L M } ( p _ { t } )$ as shorthand for $p _ { L M } ( p _ { t } | p _ { t - 1 } , . . . , p _ { 1 } )$ .3 On the other hand, we use $U ( { \mathcal { P } } ) =$ $\begin{array} { r } { \frac { 1 } { | O | } \bar { \sum _ { o \in O } } [ o \in \mathcal { P } ] \in [ 0 , 1 ] } \end{array}$ to denote the vocabulary usage of $\mathcal { P }$ .
+
+In a first step, we generate phoneme transcriptions for different training checkpoints or hyperparameter settings and denote the transcriptions of the configuration with the lowest vocabulary-usage adjusted NLL as $\begin{array} { r } { \hat { \mathcal { P } } = \arg \operatorname* { m i n } _ { \mathcal { P } } N L L _ { L M } ( \mathcal { P } ) - \log U ( \mathcal { P } ) } \end{array}$ .4 Next, we discard model configurations which do not satisfy the following using $\hat { \mathcal { P } }$ as the anchor:
+
+$$
+N L L _ { L M } ( \mathcal { P } ) < N L L _ { L M } ( \hat { \mathcal { P } } ) + \log \left( \frac { U ( \mathcal { P } ) } { U ( \hat { \mathcal { P } } ) } \right) + \log 1 . 2
+$$
+
+The second term on the right hand side introduces a margin over the NLL of the anchor transcription $N L L _ { L M } ( \hat { \mathcal { P } } )$ based on the vocabulary usage of $\mathcal { P }$ and $\hat { \mathcal { P } }$ : If $U ( \hat { \mathcal { P } } )$ is much lower compared to $U ( \mathcal { P } )$ , then we allow model configurations which produce transcriptions with higher NLL compared to $\hat { \mathcal { P } }$ . However, if $U ( \hat { \mathcal { P } } )$ is a lot higher than $U ( \mathcal { P } )$ , then the model configuration will not satisfy the constraint. The $\log 1 . 2$ factor serves as another margin allowing checkpoints with slightly worse vocabulary-usage adjusted NLL to be included.
+
+In a final step, we take into account the length of the transcriptions: out of the configurations ${ \mathcal { P } } ^ { \prime }$ which satisfy the above constraint, we select the one which has the highest sum of log probability without normalizing the length:
+
+$$
+\mathcal { P } ^ { * } = \arg \operatorname* { m a x } _ { \mathcal { P } ^ { \prime } } \sum _ { j = 1 } ^ { N _ { s } } \sum _ { t = 1 } ^ { M } \log p _ { L M } ( p _ { t } ^ { j } ) , M = | P ^ { j } | , P ^ { j } = [ p _ { 1 } ^ { j } , \dots , p _ { M } ^ { j } ]
+$$
+
+This selects model configurations which produce phoneme sequences that score high under the language model but are not too long. Appendix D compares accuracy when developing with this metric compared to a labeled development set.
+
+# 4 Results
+
+# 4.1 Comparison to Supervised Speech Recognition on Librispeech
+
+We first test our approach on Librispeech to get a sense of how unsupervised speech recognition compares to the best supervised systems trained on a large amount of labeled data. Librispeech is a standard benchmark in the speech recognition community which provides about 960 hours of transcribed read audiobooks. We use the language modeling data of Librispeech as unlabeled text data for unsupervised training. In Appendix G we show that far less unlabeled text and speech audio are sufficient to reach a similar level of performance. We experiment with the frozen representations of a wav2vec 2.0 LARGE model trained on the $5 3 . 2 \mathrm { k }$ hours of Libri-Light (LL-60k) which we denote as wav2vec-U LARGE. We also consider self-training over three iterations by first training an HMM on the labels generated by the GANm then fine-tuning the original wav2vec 2.0 model on the labels of the HMM for Librispeech followed by then fine-tuning on Libri-Light; Appendix F investigates alternatives.
+
+wav2vec-U LARGE with self-training (wav2vec- $\mathbf { \partial } . \mathbf { U } + \mathbf { S } \mathbf { T } ,$ ) and a Transformer language model achieves WER 5.9 on test-other, the noisy test set. This shows that unsupervised speech recognition can perform remarkably well compared to the best supervised systems of the recent past on this much studied benchmark. Also, self-training is effective even when the teacher model is unsupervised as per the improvement over GAN training (wav2vec-U). Interestingly, self-training on just Librispeech, or 960 hours of unlabeled speech audio, achieves already very good performance of WER 6.4 on dev-other compared to self-training on all of Libri-Light (53.2k hours) which compares at 6.0 WER. We note that the number of parameters trained during adversarial training is very small: the generator contains only about 90k parameters for a single temporal convolution mapping to the phoneme set from frozen wav2vec 2.0 representations.
+
+Table 1: WER on Librispeech dev/test sets when using 960 hours of unlabeled audio from Librispeech (LS-960) or $5 3 . 2 \mathrm { k }$ hours from Libri-Light (LL-60k) using representations from wav2vec 2.0 LARGE. Librispeech provides clean dev/test sets which are less challenging than the other sets. We report results for GAN training only (wav2vec-U) and with subsequent self-training (wav2vec- $\mathbf { \partial } . \mathbf { U } + \mathbf { S } \mathbf { T } ,$ .   
+
+<table><tr><td rowspan="2">Model</td><td rowspan="2">Unlabeled data</td><td rowspan="2">LM</td><td colspan="2">dev</td><td colspan="2">test</td></tr><tr><td>clean</td><td>other</td><td>clean</td><td>other</td></tr><tr><td>960h - Supervised learning</td><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>DeepSpeech 2 [Amodei et al.,2016]</td><td></td><td>5-gram</td><td></td><td></td><td>5.33</td><td>13.25</td></tr><tr><td>Fully Conv [Zeghidour et al., 2018]</td><td></td><td>ConvLM</td><td>3.08</td><td>9.94</td><td>3.26</td><td>10.47</td></tr><tr><td>TDNN+Kaldi [Xu et al., 2018]</td><td></td><td>4-gram</td><td>2.71</td><td>7.37</td><td>3.12</td><td>7.63</td></tr><tr><td>SpecAugment [Park et al., 2019]</td><td></td><td>RNN</td><td>1</td><td>-</td><td>2.5</td><td>5.8</td></tr><tr><td>ContextNet [Han et al.,2020]</td><td></td><td>LSTM</td><td>1.9</td><td>3.9</td><td>1.9</td><td>4.1</td></tr><tr><td>Conformer [Gulati et al.,2020]</td><td></td><td>LSTM</td><td>2.1</td><td>4.3</td><td>1.9</td><td>3.9</td></tr><tr><td>960h - Self and semi-supervised learning</td><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>Transf.+ PL [Synnaeve et al.,2020]</td><td>LL-60k</td><td>CLM+Transf.</td><td>2.00</td><td>3.65</td><td>2.09</td><td>4.11</td></tr><tr><td>IPL [Xu et al., 2020b]</td><td>LL-60k</td><td>4-gram+Transf.</td><td>1.85</td><td>3.26</td><td>2.10</td><td>4.01</td></tr><tr><td>NST [Park et al., 2020]</td><td>LL-60k</td><td>LSTM</td><td>1.6</td><td>3.4</td><td>1.7</td><td>3.4</td></tr><tr><td>wav2vec 2.0 [Baevski et al.,2020c]</td><td>LL-60k</td><td>Transf.</td><td>1.6</td><td>3.0</td><td>1.8</td><td>3.3</td></tr><tr><td>wav2vec 2.0 + NST [Zhang et al.,2020b]</td><td>LL-60k</td><td>LSTM</td><td>1.3</td><td>2.6</td><td>1.4</td><td>2.6</td></tr><tr><td>Unsupervised learning</td><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>wav2vec-ULARGE</td><td>LL-60k</td><td>4-gram</td><td>13.3</td><td>15.1</td><td>13.8</td><td>18.0</td></tr><tr><td>wav2vec-ULARGE+ ST</td><td>LL-60k</td><td>4-gram</td><td>3.4</td><td>6.0</td><td>3.8</td><td>6.5</td></tr><tr><td></td><td>LL-60k</td><td>Transf.</td><td>3.2</td><td>5.5</td><td>3.4</td><td>5.9</td></tr></table>
+
+# 4.2 Comparison to Prior Unsupervised Work
+
+Prior work on unsupervised speech recognition focused on the TIMIT benchmark. In order to perform a direct comparison to these approaches, we report results on this benchmark as well. We consider two setups to compare to previous work: in the matched setting, the unlabeled text data is simply the transcriptions of the unlabeled audio data but unpaired. In the unmatched setup, the unlabeled text data does not contain the transcriptions for the audio data which is a more realistic setting.
+
+We measure performance on the standard Kaldi dev and test sets (core-dev/core-test) as well as a slightly larger version of the test set (all-test) to be able to compare to Liu et al. [2018] and Chen et al. [2019]. Further details of the two setups can be found in Appendix $\ S \operatorname { E } . 1$ . We report performance for wav2vec-U with a 4-gram language model trained on the language modeling data of TIMIT and we also consider self-training (wav2vec- $\mathbf { \partial } . \mathbf { U } + \mathbf { S } \mathbf { T }$ ).
+
+Table 2 shows that wav2vec-U outperforms prior unsupervised work in both the matched and unmatched settings, reducing PER on all-test in the matched setup by $57 \%$ relative compared to Chen et al. [2019]. Our method has lower performance than the best supervised methods but it performs still very well at PER 12 on core-test in the matched setup compared to PER 8.3 for the state of the art [Baevski et al., 2020c].
+
+# 4.3 Performance on non-English languages
+
+To get a sense of how well the method works on non-English data, we experiment on six languages of the multilingual Librispeech corpus (MLS; Pratap et al. 2020). As baseline we consider the supervised systems of Pratap et al. [2020] trained on between $2 \mathrm { k }$ and 161 hours of labeled data, depending on the language. For adversarial learning we use 100 hours of unlabeled audio data from MLS for every language as well as the MLS language modeling data. As input to wav2vec-U we use the representations from XLSR-53 [Conneau et al., 2020], a wav2vec 2.0 model pre-trained on 53 languages. Table 3 shows that wav2vec-U generalizes across a range of languages. Performance is lower than supervised systems but it shows the viability for other languages.
+
+Next, we turn to three low-resource languages, Swahili, Kyrgyz, and Tatar. Swahili is an African language, Kyrgyz and Tatar are Turkic languages with only about $4 . 3 \mathrm { m }$ and $5 . 2 \mathrm { m }$ speakers, respectively.5 We use between 1.8 hours (Kyrgyz) and 9.2 hours of unlabeled audio (Swahili), see Appendix $\ S \operatorname { E } . 1$ .
+
+Table 2: TIMIT Phoneme Error Rate (PER) in comparison to previous work for the matched and unmatched training data setups (Appendix $\ S \operatorname { E . 1 }$ ). PER is measured on the Kaldi dev and test sets (core-dev/core-test) as well as a slightly larger version of the test set (all-test) as used by some of the prior work. $( ^ { * } )$ indicates experiments that do not use the standard split excluding SA utterances.   
+
+<table><tr><td>Model</td><td>LM</td><td>core-dev</td><td>core-test</td><td>all-test</td></tr><tr><td colspan="5">Supervised learning</td></tr><tr><td>LiGRU [Ravanelli et al., 2018]</td><td></td><td></td><td>14.9</td><td></td></tr><tr><td>LiGRU [Ravanelli et al., 2019]</td><td></td><td></td><td>14.2</td><td></td></tr><tr><td colspan="5">Self and semi-supervised learning</td></tr><tr><td>vq-wav2vec [Baevski et al.,2020b]</td><td></td><td>9.6</td><td>11.6</td><td></td></tr><tr><td>wav2vec 2.0 [Baevski et al.,2020c]</td><td></td><td>7.4</td><td>8.3</td><td></td></tr><tr><td colspan="5">Unsupervised learning - matched setup</td></tr><tr><td>EODM[Yeh et al.,2019]</td><td>5-gram</td><td></td><td>36.5</td><td>=</td></tr><tr><td>GAN*[Chen et al., 2019]</td><td>9-gram</td><td></td><td>=</td><td>48.6</td></tr><tr><td>GAN + HMM* [Chen et al.,2019]</td><td>9-gram</td><td>■</td><td>-</td><td>26.1</td></tr><tr><td>wav2vec-U</td><td>4-gram</td><td>17.0</td><td>17.8</td><td>16.6</td></tr><tr><td>wav2vec-U + ST</td><td>4-gram</td><td>11.3</td><td>12.0</td><td>11.3</td></tr><tr><td colspan="5">Unsupervised learning - unmatched setup</td></tr><tr><td>EODM[Yeh et al., 2019]</td><td>5-gram</td><td></td><td>41.6</td><td>■</td></tr><tr><td>GAN* [Chen et al.,2019]</td><td>9-gram</td><td></td><td>=</td><td>50.0</td></tr><tr><td>GAN + HMM* [Chen et al., 2019]</td><td>9-gram</td><td>=</td><td>-</td><td>33.1</td></tr><tr><td>wav2vec-U*</td><td>4-gram</td><td>21.3</td><td>22.3</td><td>24.4</td></tr><tr><td>wav2vec-U + ST*</td><td>4-gram</td><td>13.8</td><td>15.0</td><td>18.6</td></tr></table>
+
+Table 3: WER on the Multilingual Librispeech (MLS) dataset using representations from the wav2vec 2.0 XLSR-53 model. We consider German (de), Dutch (nl), French (fr), Spanish (es), Italian (it), Portuguese (pt).   
+
+<table><tr><td>Model</td><td>Labeled data used</td><td>LM</td><td>de</td><td>nl</td><td>fr</td><td>es</td><td>it</td><td>pt</td><td>Avg</td></tr><tr><td>Labeled training hours (full)</td><td></td><td></td><td>2k</td><td>1.6k</td><td>1.1k</td><td>918</td><td>247</td><td>161</td><td></td></tr><tr><td>Supervised learning</td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>Pratap et al. [2020]</td><td>full</td><td> 5-gram</td><td>6.49</td><td>12.02</td><td>5.58</td><td>6.07</td><td>10.54</td><td>19.49</td><td>10.0</td></tr><tr><td>Unsupervised learning</td><td>0h</td><td></td><td></td><td></td><td></td><td>33.3</td><td></td><td></td><td></td></tr><tr><td>wav2vec-U</td><td></td><td> 4-gram</td><td>32.5</td><td>40.2</td><td>39.8</td><td></td><td>58.1</td><td>59.8</td><td>43.9</td></tr><tr><td>wav2vec-U + ST</td><td>0h</td><td>4-gram</td><td>11.8</td><td>21.4</td><td>14.7</td><td>11.3</td><td>26.3</td><td>26.3</td><td>18.6</td></tr></table>
+
+To compare to prior work, we measure WER for Swahili and PER for Kyrgyz and Tatar. For Tatar and Kyrgyz we opted to use a reduced self-training regime for faster experimental turn-around where we only perform HMM self-training and we expect better performance with the full self-training setup (Appendix F). Table 4 and Table 5 show that wav2vec-U achieves good performance on these low-resource languages compared to previous work that utilized labeled data. We note that for Tatar and Kyrgyz we use a much smaller amount of speech audio than prior work: compared to XLSR-53 we use $1 . 8 \mathrm { h }$ unlabeled data vs 17h of labeled data for Kyrgyz and 4.6h vs. 17h for Tatar.
+
+# 5 Related Work
+
+This paper builds on a large body of prior work which includes semi-supervised speech recognition such as self-training [Kahn et al., 2020a, Xu et al., 2020b, Park et al., 2020]. Some of the earliest work in self-supervised learning of speech representations was was done by van den Oord et al. [2018] for phoneme recognition which was simplified in Schneider et al. [2019] who applied it to full speech recognition. Other work includes language model-style pre-training [Chung et al., 2019a] and learning fixed size representations of audio segments [Chung and Glass, 2018]. There is also work on quantization of the continuous speech data [Baevski et al., 2020b,a, Liu et al., 2019, van Niekerk et al., 2020, Baevski et al., 2020c, Hsu et al., 2021b] and on robustness to domain shift [Hsu et al., 2021a], multilingual pre-training [Kawakami et al., 2020, Conneau et al., 2020] as well as combining speech and vision [Harwath et al., 2020].
+
+Table 4: PER for low-resource languages, Tatar (tt) and Kyrgyz (ky).   
+
+<table><tr><td>Model</td><td>tt</td><td>ky</td></tr><tr><td colspan="3">Supervised learning</td></tr><tr><td>Fer et al. [2017]</td><td>42.5</td><td>38.7</td></tr><tr><td>m-CPC [Riviere et al., 2020]</td><td>42.0</td><td>41.2</td></tr><tr><td>XLSR-53 [Conneau et al.,2020]</td><td>5.1</td><td>6.1</td></tr><tr><td colspan="3">Unsupervised learning</td></tr><tr><td>wav2vec-U</td><td>25.7</td><td>24.1</td></tr><tr><td>wav2vec-U + HMM</td><td>13.7</td><td>14.9</td></tr></table>
+
+Table 5: WER for Swahili from the ALFFA corpus. We compare to the supervised baseline of the ALFFA project.   
+
+<table><tr><td>Model</td><td>sw</td></tr><tr><td>Supervised learning</td><td></td></tr><tr><td>Besacier et al. [2015]</td><td>27.36</td></tr><tr><td>Unsupervised learning</td><td></td></tr><tr><td>wav2vec-U</td><td>52.6</td></tr><tr><td>wav2vec-U + ST</td><td>32.2</td></tr></table>
+
+Learning to map speech to phonemes without supervision using adversarial learning has been explored by Liu et al. [2018] who learn a mapping matrix between segment identifiers and phonemes. However, their work still relied on data segmented into phonemes by human annotators. This has been later extended to use an automatic segmentation [Chen et al., 2019] which is iteratively refined with HMMs. However, cross validation is still performed using labeled data (personal communication with authors). We also explored HMMs to refine segmentation boundaries (Table A2) but did not find it as effective as self-training. Our work is in part inspired by aligning word embedding spaces of different languages [Mikolov et al., 2013, Artetxe et al., 2017, Conneau et al., 2018] and full unsupervised machine translation [Lample et al., 2018, Artetxe et al., 2018, Conneau and Lample, 2019].
+
+# 6 Conclusion and Future Work
+
+wav2vec-U is a framework which enables building speech recognition models without labeled data. It embeds and segments the speech audio with self-supervised representations from wav2vec 2.0, learns a mapping to phonemes with adversarial learning, and cross-validates hyper-parameter choices as well as early stopping with an unsupervised metric. Experiments on the standard Librispeech benchmark show performance close to the state of the art models from only a few years ago, even though these models relied on nearly 1,000 hours of labeled data.
+
+Compared to the previous best unsupervised speech recognition approach, wav2vec-U reduces TIMIT phone error rate from 26.1 to 11.3. We also demonstrate the viability of our approach on several languages other than English, some of which are low-resource. The ability to build speech recognition models solely from unlabeled speech audio and unlabeled text drastically lowers the effort to build speech technology for many more languages of the world.
+
+Our approach requires phonemization of the text for the language of interest. Moreover, phonemizers are not available for all languages and this presents a bottleneck. To address this, future work may develop phonemizers for more languages, explore phonemization approaches that generalize across languages, or unsupervised training with graphemic text units such as letters.
+
+We explored a simple segmentation technique based on self-supervised representations, however, there is a large body of research on segmentation and some of these techniques may lead to improvements over our simple approach [Varadarajan et al., 2008, Zhang and Glass, 2009, Gish et al., 2009, Lee and Glass, 2012, Lee et al., 2015, Ondel et al., 2016, Kamper et al., 2017a,b, Kreuk et al., 2020]. Also, wav2vec 2.0 learns representations for fixed size units with a fixed stride, however, phonemic units are of variable size. Another direction is to learn variable sized representations during pre-training.
+
+# Acknowledgments and Disclosure of Funding
+
+We thank Zhouhan Lin for helping with initial explorations in this project, Tatiana Likhomanenko for helpful discussions about self-training, Da-Rong Liu for sharing details to reproduce the setup of Chen et al. [2019], Marc’Aurelio Ranzato for general helpful discussions, and Ruth Kipng’eno, Ruth Ndila Ndeto as well as Mark Mutitu for error analysis of our Swahili model.
+
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parse/train/QmxFsofRvW9/QmxFsofRvW9_content_list.json

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+    {
+        "type": "text",
+        "text": "Unsupervised Speech Recognition ",
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+        "text": "Alexei Baevski4 Wei-Ning Hsu4 Alexis Conneau\u0003∗ Michael Auli4 ",
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+    {
+        "type": "text",
+        "text": "4 Facebook AI \u0003 Google AI ",
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+    {
+        "type": "text",
+        "text": "Abstract ",
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+        "text": "Despite rapid progress in the recent past, current speech recognition systems still require labeled training data which limits this technology to a small fraction of the languages spoken around the globe. This paper describes wav2vec-U, short for wav2vec Unsupervised, a method to train speech recognition models without any labeled data. We leverage self-supervised speech representations to segment unlabeled audio and learn a mapping from these representations to phonemes via adversarial training. The right representations are key to the success of our method. Compared to the best previous unsupervised work, wav2vec-U reduces the phone error rate on the TIMIT benchmark from 26.1 to 11.3. On the larger English Librispeech benchmark, wav2vec-U achieves a word error rate of 5.9 on test-other, rivaling some of the best published systems trained on 960 hours of labeled data from only two years ago. We also experiment on nine other languages, including low-resource languages such as Kyrgyz, Swahili and Tatar. The code is available at https://github.com/pytorch/fairseq/tree/ master/examples/wav2vec/unsupervised ",
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+    {
+        "type": "text",
+        "text": "1 Introduction ",
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+        "text": "Speech recognition performance on the much studied English Librispeech benchmark [Panayotov et al., 2015] has seen rapid improvement over the last few years due to advances in model architectures [Dong et al., 2018, Synnaeve et al., 2020, Gulati et al., 2020], semi-supervised learning [Xu et al., 2020b, Park et al., 2020] and self-supervised learning [van den Oord et al., 2018, Chung and Glass, 2018, Chung et al., 2019b, Baevski et al., 2020c]. However, all of these techniques require transcribed speech data which is not available for the vast majority of the nearly 7,000 languages of the world [Lewis et al., 2016]. As a result, speech recognition technology is only available for about 125 different languages [Google, 2021]. On the other hand, humans learn a lot about speech simply by listening to others around them and without explicit supervision [Werker and Tees, 1984, Hirsh-Pasek et al., 1987, Polka and Werker, 1994, Jusczyk et al., 1999, Johnson and Jusczyk, 2001]. ",
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+        "text": "Unsupervised learning has been very successful in machine translation resulting in systems that obtain remarkable accuracy given no labeled training data at all [Conneau et al., 2018, Lample et al., 2018, Artetxe et al., 2018]. Inspired by this, there has been some work on unsupervised speech recognition based on learning to align unlabeled text and audio [Yeh et al., 2019] or adversarial learning [Liu et al., 2018, Chen et al., 2019]. These approaches showed promising initial results but their error rates are still high, with evaluation being limited to the small-scale and clean TIMIT benchmark. ",
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+        "text": "In this work, we introduce a framework for unsupervised learning of speech recognition models. Wav2vec-U, or wav2vec Unsupervised, leverages self-supervised representations from wav2vec 2.0 [Baevski et al., 2020c] to embed the speech audio and to segment the audio into units with a simple $\\mathrm { k }$ -means clustering method (see Figure 1 for an illustration of our approach). We find that the quality of the audio representations is key to the success of unsupervised speech recognition. Similar to Liu et al. [2018] and Chen et al. [2019], we learn a mapping between segments and phonemes using adversarial training but different to their work, we also enable the algorithm to label segments as silences. We also introduce an unsupervised cross-validation metric to enable model development without labeled development data. Our unsupervised speech recognition model, the generator, is very lightweight: it consists of a single temporal convolution comprising only about 90k parameters to which we input frozen wav2vec 2.0 representations. ",
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+        "img_path": "images/0b5b4f3465570676296b5d72eebf6d66830b97659f2ec44658268dac36522d53.jpg",
+        "image_caption": [
+            "Figure 1: Illustration of wav2vec Unsupervised: we learn self-supervised representations with wav2vec 2.0 on unlabeled speech audio (Step 1), identify clusters in the representations with $\\mathbf { k }$ -means (Step 2) to segment the audio (Step 3). Next, we build segment representations by mean pooling the wav2vec 2.0 representations, performing PCA and a second mean pooling step between adjacent segments (Step 4). This is input to the generator which outputs a phoneme sequence (Step 5) fed to the discriminator, similar to phonemized unlabeled text (Step 6), for adversarial training (Step 7). "
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+        "text": "Experimental results demonstrate the viability of the framework for a variety of settings and languages. wav2vec-U improves the phone error rate (PER) on the small-scale TIMIT benchmark from 26.1 to 11.3 compared to the next best known unsupervised approach. To get a better sense of the performance compared to the best supervised methods, we measure performance on the larger Librispeech benchmark where our method achieves word error rate (WER) 5.9 on test-other. We also evaluate on six other European languages of the multilingual Librispeech benchmark [Pratap et al., 2020] and on three non-European low-resource languages. ",
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+        "text": "2 Speech and Text Representations ",
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+        "text": "Next, we describe how we build suitable speech and text representations for unsupervised learning.   \nGood representations are essential to learning a mapping from speech to text without supervision. ",
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+        "text": "2.1 Self-supervised Learning of Speech Audio Representations ",
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+        "text": "In the first step, we learn representations of the speech audio signal using self-supervised learning. There has been a lot of recent work in this direction which has shown strong performance in extremely low-labeled data setups across a range of languages [Conneau et al., 2020] and tasks [Fan et al., 2021, Pepino et al., 2021, Wang et al., 2021]. ",
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+        "text": "Wav2vec 2.0 consists of a convolutional feature encoder $f : \\mathcal X \\mapsto \\mathcal Z$ that maps a raw audio sequence $X$ to latent speech representations $z _ { 1 } , \\dots , z _ { T }$ , which a Transformer $g : { \\mathcal { Z } } \\mapsto { \\mathcal { C } }$ then turns into context representations $c _ { 1 } , \\ldots , c _ { T }$ [Baevski et al., 2020b,a]. Each $z _ { t }$ represents about $2 5 \\mathrm { m s }$ of audio strided by $2 0 \\mathrm { m s }$ and the Transformer architecture follows BERT [Vaswani et al., 2017, Devlin et al., 2019]. During training, latent representations are discretized to $q _ { 1 } , \\ldots , q _ { T }$ with a quantization module ${ \\mathcal { Z } } \\mapsto { \\mathcal { Q } }$ to represent the targets in the objective. Quantization uses a Gumbel softmax to choose entries from two codebooks [Jegou et al., 2011, Jang et al., 2016, Baevski et al., 2020b]. ",
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+        "text": "In our experiments, we use the publicly available English model pre-trained on $5 3 \\mathrm { k }$ hours of LibriLight [Kahn et al., 2020b] as well as XLSR-53 which was pre-trained on nearly 60k hours of speech audio in 53 languages [Conneau et al., 2020]. ",
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+        "type": "text",
+        "text": "2.2 Pre-processing and Embedding the Audio Data ",
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+        "type": "text",
+        "text": "Removing Silences. Most datasets we use for our experiments have audio data with silences. However, these parts of the audio do not correspond to any transcription and we therefore remove silences as much as possible. We apply rVAD, an unsupervised voice activity detection (VAD) model which determines the segments in the audio data corresponding to silences, and we remove these sections [Tan et al., 2020]. We ablate this choice in Appendix C. ",
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+        "type": "text",
+        "text": "Speech Audio Representations. After silence removal, we embed the unlabeled speech audio with wav2vec 2.0 to obtain speech representations. Specifically, we use the representations of the context Transformer network $c _ { 1 } , \\ldots , c _ { T }$ $( \\ S 2 . 1 )$ . The context network contains 24 Transformer blocks and we denote the output of block $l$ at time-step $t$ as $c _ { t } ^ { l }$ . Our goal is to learn a model which can map from audio representations $c _ { t } ^ { l }$ to phonemes using no supervision. However, the representations of the uppermost block of wav2vec 2.0 may not be well suited for this task. These features are trained to directly predict masked latent representations spanning $2 5 \\mathrm { m s }$ of speech audio which is much shorter than the typical duration of a phoneme. ",
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+    {
+        "type": "text",
+        "text": "To get a better sense of this, we train supervised phoneme recognizers with a CTC loss [Graves et al., 2006] on top of the frozen representations of each of the 24 blocks of the English wav2vec 2.0 LARGE model pre-trained on Libri-Light. We then evaluate phone error rate (PER) with respect to the phonemized transcriptions of Librispeech dev-other. The classifier takes as input $c _ { t } ^ { l }$ and contains a single softmax-normalized linear layer mapping to the phoneme inventory. Figure 2 shows that most of the first ten blocks as well as the final blocks provide very poor performance, while blocks 15-19 provide error rates below $9 \\%$ PER. Block 15 achieves the best error rate of $7 . 5 \\%$ PER. A similar insight has been used in the concurrent work of Hsu et al. [2021b]. Appendix A shows that this choice generalizes to other languages. For brevity we drop the superscript $l$ and refer to block 15 representations simply as $c _ { 1 } , \\ldots , c _ { T }$ . ",
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+        "image_caption": [
+            "Figure 2: Supervised phoneme recognition using representations from different wav2vec 2.0 blocks on dev-other of English Librispeech. Low and high blocks do not provide good features, while as blocks 14-19 do. Block 15 performs best. "
+        ],
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+        "text": "2.3 Segmenting the Audio Signal ",
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+        "type": "text",
+        "text": "Once the speech signal is embedded, we identify segments corresponding to meaningful units that can be mapped to phonemes. Segmentation has been shown to be crucial in prior work [Chung et al., 2018] since the right boundaries in the input representations make it more aligned to phonetic sequences. There has been a lot of prior work in unsupervised speech segmentation [Kamper et al., 2017a,b, Rasanen et al., 2015, Kreuk et al., 2020] but here we simply use a method based on clustering the wav2vec 2.0 speech representations $c _ { 1 } , \\ldots , c _ { T }$ . In a first step, we collect all the speech representations for the unlabeled speech data and perform k-means clustering to identify $K = 1 2 8$ clusters. We use the FAISS library to do fast clustering on GPUs [Johnson et al., 2019]. Next, each $c _ { t }$ is labeled with the corresponding cluster ID $i _ { t } \\in \\{ 1 , \\ldots , K \\}$ and we introduce speech segment boundaries whenever the cluster ID changes. ",
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+        "type": "text",
+        "text": "Once the speech audio representations are segmented, we compute a 512-dimensional PCA over all speech representations output by wav2vec 2.0 for the training set. Next, we mean-pool the PCA representations for a particular segment to obtain an average representation of the segment. The PCA retains only the most important features and we found this to be effective. Segment boundaries are noisy due to the lack of supervision and we therefore found it useful to also mean-pool pairs of adjacent segment representations to increase robustness. This results in sequences of speech segment representation $S = s _ { 1 } , \\ldots , s _ { T } , S \\sim { \\mathcal { S } }$ for a given utterance. Appendix B shows an illustration of the segmentation strategy on an actual example as well as a quantitative evaluation of the strategy compared to human segmented data. ",
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+        "text": "2.4 Pre-processing the Text Data ",
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+        "type": "text",
+        "text": "Similar to how we segment the unlabeled speech audio data into suitable units for unsupervised learning, we do the same for the unlabeled text data. We apply two pre-processing steps to the text data: phonemization and silence token insertion. ",
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+        "text": "Phonemes characterize the different sounds which distinguish words from each other, e.g., for the word cat there are three phonemes corresponding to the three distinct sounds in the pronunciation of the word: /K/, /AE/, $/ \\mathrm { T } / .$ . We phonemize the text data because we found it easier to learn a mapping between speech audio and the different sounds of a word rather than between audio and words or letters. Phonemization converts a sequence of words $Y$ into a sequence of phonemes $P = [ p _ { 1 } , \\cdots , p _ { M } ]$ , where $p _ { m } \\in O$ and $O$ is the phoneme inventory. We use off-the-shelf tools for this step which we detail in Appendix $\\ S \\operatorname { E } . 2$ . ",
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+        "type": "text",
+        "text": "The unlabeled speech audio data is pre-processed by applying unsupervised silence removal. However, this process is not always accurate and many silences in the speech audio remain. To deal with this, we enable the unsupervised model to label some segments with a phonemic silence token (SIL; $\\ S \\ 3 . 1 \\AA .$ ). However, the phonemized unlabeled text data does not contain any silence tokens and this may pose difficulties for adversarial learning $( \\ S 3 )$ . We remedy this by inserting silence markers at the beginning and end of the phonemized unlabeled text data; we also randomly insert SIL between words, or groups of phonemes corresponding to words at a rate of $2 5 \\%$ . Appendix C evaluates these choices. ",
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+        "text": "3 Unsupervised Learning ",
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+        "text": "We use adversarial training to train an unsupervised speech recognition model using the representations of the unlabeled speech audio data and the unlabeled phonemized text data [Liu et al., 2018, Chen et al., 2019]. In the following, we detail the model architecture, the training objective as well as the unsupervised cross-validation metric we developed. ",
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+        "text": "3.1 Model Architecture ",
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+        "text": "Generative adversarial networks (GAN; Goodfellow et al. 2014) train a generator network $\\mathcal { G }$ and a discriminator/critic network $\\mathcal { C }$ where the generator produces samples which are then judged by the discriminator. The discriminator is trained to classify whether samples are from the generator or from the real data distribution. The objective of the generator is to produce samples that are indistinguishable by the discriminator. ",
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+        "text": "Concretely, $\\mathcal { G }$ takes as input a sequence of $T$ segment representations $S = [ s _ { 1 } , \\dotsc , s _ { T } ]$ (§ 2.3) which are then mapped to a sequence of $M$ phonemes $\\mathcal { G } ( S ) \\bar { = } [ p _ { 1 } , \\dotsc , p _ { M } ]$ . The generator predicts a distribution over the phoneme set $O$ for each segment and outputs the phoneme with the highest probability. If the argmax prediction of consecutive segments result in the same phoneme, then we sample one of these segments, therefore $M \\leq T$ . ",
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+        "type": "text",
+        "text": "The phoneme set $O$ includes a silence label SIL to enable labeling silences in the speech audio as such. Without a silence label, we noticed that the model was repurposing a particular phoneme to label silences which resulted in much lower performance since it interfered with subsequent language model (LM) decoding. In the backward pass, we back-propagate through segments sampled at the generator output. We do not modify the segment representations $S$ during unsupervised training. The generator is parameterized as a single layer convolutional neural network (CNN). ",
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+        "type": "text",
+        "text": "The discriminator takes as input either a sequence $P ^ { r } \\sim \\mathcal { P } ^ { r }$ of one-hot vectors denoting phonemized text from the real data distribution ${ \\mathcal { P } } ^ { r }$ or a sequence of output distributions from the generator $\\mathcal { G } ( S )$ . Each input vector has $| O |$ dimensions to represent the distribution over phonemes for each segment. The discriminator is also a CNN which outputs a probability indicating how likely the sample is to be from the data distribution. ",
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+        "text": "3.2 Objective ",
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+        "type": "text",
+        "text": "In our setup we use the original GAN objective with a gradient penalty [Goodfellow et al., 2014, Arjovsky et al., 2017], a segment smoothness penalty and a phoneme diversity penalty: ",
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+    {
+        "type": "equation",
+        "img_path": "images/a15593f8fdca0cdc2e5a2bf415cdd52fd286427c617f23aeff5dbf4f23d44a11.jpg",
+        "text": "$$\n\\operatorname* { m i n } _ { \\mathcal { G } } \\operatorname* { m a x } _ { \\mathcal { C } } \\quad \\mathbb { E } _ { \\mathcal { P } ^ { r } \\sim \\mathcal { P } ^ { r } } \\left[ \\log \\mathcal { C } ( \\boldsymbol { P } ^ { r } ) \\right] - \\underset { S \\sim \\mathcal { S } } { \\mathbb { E } } \\left[ \\log \\left( 1 - \\mathcal { C } ( \\mathcal { G } ( S ) ) \\right) \\right] - \\lambda \\mathcal { L } _ { g p } + \\gamma \\mathcal { L } _ { s p } + \\eta \\mathcal { L } _ { p d }\n$$",
+        "text_format": "latex",
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+    {
+        "type": "text",
+        "text": "where $P ^ { r } \\sim \\mathcal { P } ^ { r }$ is phonemized unlabeled text, $\\mathcal { G } ( S )$ is the transcription output by the generator of input segment representations $S$ for some unlabeled speech audio. The first term trains the discriminator to assign high probability to real transcriptions, the second term encourages the discriminator to assign low probability to generator outputs, $\\mathcal { L } _ { g p }$ is a gradient penalty, $\\mathcal { L } _ { s p }$ is a smoothness penalty and $\\mathcal { L } _ { p d }$ is a phoneme diversity loss which we detail next. During training we alternate updates for the discriminator and the generator. We also alternate batches of predicted transcriptions from the generator and phonemized unlabeled text. ",
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+        "text": "Gradient penalty. To stabilize training, we penalize the gradient norm of the discriminator with respect to the input [Gulrajani et al., 2017]. The penalty is computed for random samples $\\tilde { P } \\sim \\tilde { \\mathcal { P } }$ which are a linear combination of the activations of pairs of real and fake samples.2 ",
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+    {
+        "type": "equation",
+        "img_path": "images/0a8f6af23cdb1998f6ef4e92c36819c82eb870dd5b721a5d19fc4f0384f93881.jpg",
+        "text": "$$\n\\mathcal { L } _ { g p } = \\underset { \\tilde { P } \\sim \\tilde { \\mathcal { P } } } { \\mathbb { E } } \\left[ \\left( \\| \\nabla \\mathcal { C } ( \\tilde { P } ) \\| - 1 \\right) ^ { 2 } \\right]\n$$",
+        "text_format": "latex",
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+        "type": "text",
+        "text": "Segment smoothness penalty. The $\\mathbf { k }$ -means segmentation of the speech audio is more granular than a typical phonemized transcription and neighboring representations are highly correlated. We therefore found it useful to add a penalty which encourages the generator to produce similar outputs for adjacent segments where $p _ { t } \\in \\mathbb { R } ^ { | O | }$ : ",
+        "bbox": [
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+    {
+        "type": "equation",
+        "img_path": "images/dc18aa35eab1ad24f09a6f15551a94289a62fd2eada4a74b608bff6bec0d7c91.jpg",
+        "text": "$$\n\\mathcal { L } _ { s p } = \\sum _ { ( p _ { t } , p _ { t + 1 } ) \\in \\mathcal { G } ( S ) } \\| p _ { t } - p _ { t + 1 } \\| ^ { 2 }\n$$",
+        "text_format": "latex",
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+        "type": "text",
+        "text": "Phoneme diversity loss. We also found it helpful to penalize low usage of the phoneme vocabulary by the generator on the batch level. In particular, we maximize the entropy of the averaged softmax distribution $H _ { \\mathcal { G } } ( \\mathcal { G } ( S ) )$ of the generator over the phoneme vocabulary across a batch $B$ of utterances: ",
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+        "type": "equation",
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+        "text": "$$\n\\mathcal { L } _ { p d } = \\frac { 1 } { | B | } \\sum _ { S \\in B } - H _ { \\mathcal { G } } ( \\mathcal { G } ( S ) )\n$$",
+        "text_format": "latex",
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+        "type": "text",
+        "text": "3.3 Unsupervised Cross-Validation Metric ",
+        "text_level": 1,
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+        "type": "text",
+        "text": "Our goal is to build speech recognition models without any supervision. To this end, we developed a cross-validation metric which does not require labeled data. We use the metric for early stopping, selecting a random seed, and hyper-parameter selection $( \\lambda , \\gamma , \\eta )$ . ",
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+        "text": "We consider two quantities in our metric: LM negative log-likelihood (NLL) and vocabulary usage. LM-NLL serves as an indicator of fluency for a given transcription and it is measured with a language model $p _ { L M }$ trained on phonemized text data $( \\ S ~ 2 . 4 )$ . Vocabulary usage is the proportion of the phoneme vocabulary being output by the model via Viterbi decoding. Measuring vocabulary usage identifies degenerate models which output fluent but trivial transcriptions. ",
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+    {
+        "type": "text",
+        "text": "We deaudio rbias criptions for a given generator configuration . LM-NLL is measured in the standard way o $\\mathcal { G }$ and unlabeled speechr the phonemized tran$\\{ X _ { j } \\} _ { j = 1 } ^ { N _ { s } }$ $\\mathbf { \\bar { \\mathcal { P } } } = \\{ P _ { j } \\} _ { j = 1 } ^ { N _ { s } }$ scriptions: $\\begin{array} { r } { N L L _ { L M } ( \\mathcal { P } ) = \\frac { 1 } { N _ { s } } \\sum _ { j = 1 } ^ { N _ { s } } N L L _ { L M } ( P _ { j } ) } \\end{array}$ where $\\begin{array} { r } { N L L _ { L M } ( P ) = - \\frac { 1 } { M } \\sum _ { t = 1 } ^ { M } \\log p _ { L M } ( p _ { t } ) } \\end{array}$ using $p _ { L M } ( p _ { t } )$ as shorthand for $p _ { L M } ( p _ { t } | p _ { t - 1 } , . . . , p _ { 1 } )$ .3 On the other hand, we use $U ( { \\mathcal { P } } ) =$ $\\begin{array} { r } { \\frac { 1 } { | O | } \\bar { \\sum _ { o \\in O } } [ o \\in \\mathcal { P } ] \\in [ 0 , 1 ] } \\end{array}$ to denote the vocabulary usage of $\\mathcal { P }$ . ",
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+        "type": "text",
+        "text": "",
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+    {
+        "type": "text",
+        "text": "In a first step, we generate phoneme transcriptions for different training checkpoints or hyperparameter settings and denote the transcriptions of the configuration with the lowest vocabulary-usage adjusted NLL as $\\begin{array} { r } { \\hat { \\mathcal { P } } = \\arg \\operatorname* { m i n } _ { \\mathcal { P } } N L L _ { L M } ( \\mathcal { P } ) - \\log U ( \\mathcal { P } ) } \\end{array}$ .4 Next, we discard model configurations which do not satisfy the following using $\\hat { \\mathcal { P } }$ as the anchor: ",
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+    {
+        "type": "equation",
+        "img_path": "images/b07976d07eb1264788bb86ec8c503a84fc3c183351681c48efba85a9d06b98dd.jpg",
+        "text": "$$\nN L L _ { L M } ( \\mathcal { P } ) < N L L _ { L M } ( \\hat { \\mathcal { P } } ) + \\log \\left( \\frac { U ( \\mathcal { P } ) } { U ( \\hat { \\mathcal { P } } ) } \\right) + \\log 1 . 2\n$$",
+        "text_format": "latex",
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+    {
+        "type": "text",
+        "text": "The second term on the right hand side introduces a margin over the NLL of the anchor transcription $N L L _ { L M } ( \\hat { \\mathcal { P } } )$ based on the vocabulary usage of $\\mathcal { P }$ and $\\hat { \\mathcal { P } }$ : If $U ( \\hat { \\mathcal { P } } )$ is much lower compared to $U ( \\mathcal { P } )$ , then we allow model configurations which produce transcriptions with higher NLL compared to $\\hat { \\mathcal { P } }$ . However, if $U ( \\hat { \\mathcal { P } } )$ is a lot higher than $U ( \\mathcal { P } )$ , then the model configuration will not satisfy the constraint. The $\\log 1 . 2$ factor serves as another margin allowing checkpoints with slightly worse vocabulary-usage adjusted NLL to be included. ",
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+        "type": "text",
+        "text": "In a final step, we take into account the length of the transcriptions: out of the configurations ${ \\mathcal { P } } ^ { \\prime }$ which satisfy the above constraint, we select the one which has the highest sum of log probability without normalizing the length: ",
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+    {
+        "type": "equation",
+        "img_path": "images/2930d2c4de9bfc9242467fc6ca39076d0e51025e6eb1f2125a1e21c64638989c.jpg",
+        "text": "$$\n\\mathcal { P } ^ { * } = \\arg \\operatorname* { m a x } _ { \\mathcal { P } ^ { \\prime } } \\sum _ { j = 1 } ^ { N _ { s } } \\sum _ { t = 1 } ^ { M } \\log p _ { L M } ( p _ { t } ^ { j } ) , M = | P ^ { j } | , P ^ { j } = [ p _ { 1 } ^ { j } , \\dots , p _ { M } ^ { j } ]\n$$",
+        "text_format": "latex",
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+    {
+        "type": "text",
+        "text": "This selects model configurations which produce phoneme sequences that score high under the language model but are not too long. Appendix D compares accuracy when developing with this metric compared to a labeled development set. ",
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+    {
+        "type": "text",
+        "text": "4 Results ",
+        "text_level": 1,
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+    },
+    {
+        "type": "text",
+        "text": "4.1 Comparison to Supervised Speech Recognition on Librispeech ",
+        "text_level": 1,
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+    {
+        "type": "text",
+        "text": "We first test our approach on Librispeech to get a sense of how unsupervised speech recognition compares to the best supervised systems trained on a large amount of labeled data. Librispeech is a standard benchmark in the speech recognition community which provides about 960 hours of transcribed read audiobooks. We use the language modeling data of Librispeech as unlabeled text data for unsupervised training. In Appendix G we show that far less unlabeled text and speech audio are sufficient to reach a similar level of performance. We experiment with the frozen representations of a wav2vec 2.0 LARGE model trained on the $5 3 . 2 \\mathrm { k }$ hours of Libri-Light (LL-60k) which we denote as wav2vec-U LARGE. We also consider self-training over three iterations by first training an HMM on the labels generated by the GANm then fine-tuning the original wav2vec 2.0 model on the labels of the HMM for Librispeech followed by then fine-tuning on Libri-Light; Appendix F investigates alternatives. ",
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+    },
+    {
+        "type": "text",
+        "text": "wav2vec-U LARGE with self-training (wav2vec- $\\mathbf { \\partial } . \\mathbf { U } + \\mathbf { S } \\mathbf { T } ,$ ) and a Transformer language model achieves WER 5.9 on test-other, the noisy test set. This shows that unsupervised speech recognition can perform remarkably well compared to the best supervised systems of the recent past on this much studied benchmark. Also, self-training is effective even when the teacher model is unsupervised as per the improvement over GAN training (wav2vec-U). Interestingly, self-training on just Librispeech, or 960 hours of unlabeled speech audio, achieves already very good performance of WER 6.4 on dev-other compared to self-training on all of Libri-Light (53.2k hours) which compares at 6.0 WER. We note that the number of parameters trained during adversarial training is very small: the generator contains only about 90k parameters for a single temporal convolution mapping to the phoneme set from frozen wav2vec 2.0 representations. ",
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+    },
+    {
+        "type": "table",
+        "img_path": "images/7d5f6a9816458b5d9d90dd620c97a44d70ecc200d9e2e077d3e3e3e887499080.jpg",
+        "table_caption": [
+            "Table 1: WER on Librispeech dev/test sets when using 960 hours of unlabeled audio from Librispeech (LS-960) or $5 3 . 2 \\mathrm { k }$ hours from Libri-Light (LL-60k) using representations from wav2vec 2.0 LARGE. Librispeech provides clean dev/test sets which are less challenging than the other sets. We report results for GAN training only (wav2vec-U) and with subsequent self-training (wav2vec- $\\mathbf { \\partial } . \\mathbf { U } + \\mathbf { S } \\mathbf { T } ,$ . "
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td rowspan=\"2\">Model</td><td rowspan=\"2\">Unlabeled data</td><td rowspan=\"2\">LM</td><td colspan=\"2\">dev</td><td colspan=\"2\">test</td></tr><tr><td>clean</td><td>other</td><td>clean</td><td>other</td></tr><tr><td>960h - Supervised learning</td><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>DeepSpeech 2 [Amodei et al.,2016]</td><td></td><td>5-gram</td><td></td><td></td><td>5.33</td><td>13.25</td></tr><tr><td>Fully Conv [Zeghidour et al., 2018]</td><td></td><td>ConvLM</td><td>3.08</td><td>9.94</td><td>3.26</td><td>10.47</td></tr><tr><td>TDNN+Kaldi [Xu et al., 2018]</td><td></td><td>4-gram</td><td>2.71</td><td>7.37</td><td>3.12</td><td>7.63</td></tr><tr><td>SpecAugment [Park et al., 2019]</td><td></td><td>RNN</td><td>1</td><td>-</td><td>2.5</td><td>5.8</td></tr><tr><td>ContextNet [Han et al.,2020]</td><td></td><td>LSTM</td><td>1.9</td><td>3.9</td><td>1.9</td><td>4.1</td></tr><tr><td>Conformer [Gulati et al.,2020]</td><td></td><td>LSTM</td><td>2.1</td><td>4.3</td><td>1.9</td><td>3.9</td></tr><tr><td>960h - Self and semi-supervised learning</td><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>Transf.+ PL [Synnaeve et al.,2020]</td><td>LL-60k</td><td>CLM+Transf.</td><td>2.00</td><td>3.65</td><td>2.09</td><td>4.11</td></tr><tr><td>IPL [Xu et al., 2020b]</td><td>LL-60k</td><td>4-gram+Transf.</td><td>1.85</td><td>3.26</td><td>2.10</td><td>4.01</td></tr><tr><td>NST [Park et al., 2020]</td><td>LL-60k</td><td>LSTM</td><td>1.6</td><td>3.4</td><td>1.7</td><td>3.4</td></tr><tr><td>wav2vec 2.0 [Baevski et al.,2020c]</td><td>LL-60k</td><td>Transf.</td><td>1.6</td><td>3.0</td><td>1.8</td><td>3.3</td></tr><tr><td>wav2vec 2.0 + NST [Zhang et al.,2020b]</td><td>LL-60k</td><td>LSTM</td><td>1.3</td><td>2.6</td><td>1.4</td><td>2.6</td></tr><tr><td>Unsupervised learning</td><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>wav2vec-ULARGE</td><td>LL-60k</td><td>4-gram</td><td>13.3</td><td>15.1</td><td>13.8</td><td>18.0</td></tr><tr><td>wav2vec-ULARGE+ ST</td><td>LL-60k</td><td>4-gram</td><td>3.4</td><td>6.0</td><td>3.8</td><td>6.5</td></tr><tr><td></td><td>LL-60k</td><td>Transf.</td><td>3.2</td><td>5.5</td><td>3.4</td><td>5.9</td></tr></table>",
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+    },
+    {
+        "type": "text",
+        "text": "4.2 Comparison to Prior Unsupervised Work ",
+        "text_level": 1,
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+    {
+        "type": "text",
+        "text": "Prior work on unsupervised speech recognition focused on the TIMIT benchmark. In order to perform a direct comparison to these approaches, we report results on this benchmark as well. We consider two setups to compare to previous work: in the matched setting, the unlabeled text data is simply the transcriptions of the unlabeled audio data but unpaired. In the unmatched setup, the unlabeled text data does not contain the transcriptions for the audio data which is a more realistic setting. ",
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+    {
+        "type": "text",
+        "text": "We measure performance on the standard Kaldi dev and test sets (core-dev/core-test) as well as a slightly larger version of the test set (all-test) to be able to compare to Liu et al. [2018] and Chen et al. [2019]. Further details of the two setups can be found in Appendix $\\ S \\operatorname { E } . 1$ . We report performance for wav2vec-U with a 4-gram language model trained on the language modeling data of TIMIT and we also consider self-training (wav2vec- $\\mathbf { \\partial } . \\mathbf { U } + \\mathbf { S } \\mathbf { T }$ ). ",
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+    {
+        "type": "text",
+        "text": "Table 2 shows that wav2vec-U outperforms prior unsupervised work in both the matched and unmatched settings, reducing PER on all-test in the matched setup by $57 \\%$ relative compared to Chen et al. [2019]. Our method has lower performance than the best supervised methods but it performs still very well at PER 12 on core-test in the matched setup compared to PER 8.3 for the state of the art [Baevski et al., 2020c]. ",
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+    {
+        "type": "text",
+        "text": "4.3 Performance on non-English languages ",
+        "text_level": 1,
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "To get a sense of how well the method works on non-English data, we experiment on six languages of the multilingual Librispeech corpus (MLS; Pratap et al. 2020). As baseline we consider the supervised systems of Pratap et al. [2020] trained on between $2 \\mathrm { k }$ and 161 hours of labeled data, depending on the language. For adversarial learning we use 100 hours of unlabeled audio data from MLS for every language as well as the MLS language modeling data. As input to wav2vec-U we use the representations from XLSR-53 [Conneau et al., 2020], a wav2vec 2.0 model pre-trained on 53 languages. Table 3 shows that wav2vec-U generalizes across a range of languages. Performance is lower than supervised systems but it shows the viability for other languages. ",
+        "bbox": [
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+        "page_idx": 6
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+    {
+        "type": "text",
+        "text": "Next, we turn to three low-resource languages, Swahili, Kyrgyz, and Tatar. Swahili is an African language, Kyrgyz and Tatar are Turkic languages with only about $4 . 3 \\mathrm { m }$ and $5 . 2 \\mathrm { m }$ speakers, respectively.5 We use between 1.8 hours (Kyrgyz) and 9.2 hours of unlabeled audio (Swahili), see Appendix $\\ S \\operatorname { E } . 1$ . ",
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+    },
+    {
+        "type": "table",
+        "img_path": "images/77fd4860fa4ec19b6701be89b6868bc4fe53c80cb80e10678edaf6050869d0ac.jpg",
+        "table_caption": [
+            "Table 2: TIMIT Phoneme Error Rate (PER) in comparison to previous work for the matched and unmatched training data setups (Appendix $\\ S \\operatorname { E . 1 }$ ). PER is measured on the Kaldi dev and test sets (core-dev/core-test) as well as a slightly larger version of the test set (all-test) as used by some of the prior work. $( ^ { * } )$ indicates experiments that do not use the standard split excluding SA utterances. "
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>Model</td><td>LM</td><td>core-dev</td><td>core-test</td><td>all-test</td></tr><tr><td colspan=\"5\">Supervised learning</td></tr><tr><td>LiGRU [Ravanelli et al., 2018]</td><td></td><td></td><td>14.9</td><td></td></tr><tr><td>LiGRU [Ravanelli et al., 2019]</td><td></td><td></td><td>14.2</td><td></td></tr><tr><td colspan=\"5\">Self and semi-supervised learning</td></tr><tr><td>vq-wav2vec [Baevski et al.,2020b]</td><td></td><td>9.6</td><td>11.6</td><td></td></tr><tr><td>wav2vec 2.0 [Baevski et al.,2020c]</td><td></td><td>7.4</td><td>8.3</td><td></td></tr><tr><td colspan=\"5\">Unsupervised learning - matched setup</td></tr><tr><td>EODM[Yeh et al.,2019]</td><td>5-gram</td><td></td><td>36.5</td><td>=</td></tr><tr><td>GAN*[Chen et al., 2019]</td><td>9-gram</td><td></td><td>=</td><td>48.6</td></tr><tr><td>GAN + HMM* [Chen et al.,2019]</td><td>9-gram</td><td>■</td><td>-</td><td>26.1</td></tr><tr><td>wav2vec-U</td><td>4-gram</td><td>17.0</td><td>17.8</td><td>16.6</td></tr><tr><td>wav2vec-U + ST</td><td>4-gram</td><td>11.3</td><td>12.0</td><td>11.3</td></tr><tr><td colspan=\"5\">Unsupervised learning - unmatched setup</td></tr><tr><td>EODM[Yeh et al., 2019]</td><td>5-gram</td><td></td><td>41.6</td><td>■</td></tr><tr><td>GAN* [Chen et al.,2019]</td><td>9-gram</td><td></td><td>=</td><td>50.0</td></tr><tr><td>GAN + HMM* [Chen et al., 2019]</td><td>9-gram</td><td>=</td><td>-</td><td>33.1</td></tr><tr><td>wav2vec-U*</td><td>4-gram</td><td>21.3</td><td>22.3</td><td>24.4</td></tr><tr><td>wav2vec-U + ST*</td><td>4-gram</td><td>13.8</td><td>15.0</td><td>18.6</td></tr></table>",
+        "bbox": [
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+        "page_idx": 7
+    },
+    {
+        "type": "table",
+        "img_path": "images/b406f6c833d0575a5f43e3163dc4e9bbbbefc546de30a4f3e6945916da6d56ac.jpg",
+        "table_caption": [
+            "Table 3: WER on the Multilingual Librispeech (MLS) dataset using representations from the wav2vec 2.0 XLSR-53 model. We consider German (de), Dutch (nl), French (fr), Spanish (es), Italian (it), Portuguese (pt). "
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>Model</td><td>Labeled data used</td><td>LM</td><td>de</td><td>nl</td><td>fr</td><td>es</td><td>it</td><td>pt</td><td>Avg</td></tr><tr><td>Labeled training hours (full)</td><td></td><td></td><td>2k</td><td>1.6k</td><td>1.1k</td><td>918</td><td>247</td><td>161</td><td></td></tr><tr><td>Supervised learning</td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>Pratap et al. [2020]</td><td>full</td><td> 5-gram</td><td>6.49</td><td>12.02</td><td>5.58</td><td>6.07</td><td>10.54</td><td>19.49</td><td>10.0</td></tr><tr><td>Unsupervised learning</td><td>0h</td><td></td><td></td><td></td><td></td><td>33.3</td><td></td><td></td><td></td></tr><tr><td>wav2vec-U</td><td></td><td> 4-gram</td><td>32.5</td><td>40.2</td><td>39.8</td><td></td><td>58.1</td><td>59.8</td><td>43.9</td></tr><tr><td>wav2vec-U + ST</td><td>0h</td><td>4-gram</td><td>11.8</td><td>21.4</td><td>14.7</td><td>11.3</td><td>26.3</td><td>26.3</td><td>18.6</td></tr></table>",
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+    },
+    {
+        "type": "text",
+        "text": "To compare to prior work, we measure WER for Swahili and PER for Kyrgyz and Tatar. For Tatar and Kyrgyz we opted to use a reduced self-training regime for faster experimental turn-around where we only perform HMM self-training and we expect better performance with the full self-training setup (Appendix F). Table 4 and Table 5 show that wav2vec-U achieves good performance on these low-resource languages compared to previous work that utilized labeled data. We note that for Tatar and Kyrgyz we use a much smaller amount of speech audio than prior work: compared to XLSR-53 we use $1 . 8 \\mathrm { h }$ unlabeled data vs 17h of labeled data for Kyrgyz and 4.6h vs. 17h for Tatar. ",
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+    },
+    {
+        "type": "text",
+        "text": "5 Related Work ",
+        "text_level": 1,
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "This paper builds on a large body of prior work which includes semi-supervised speech recognition such as self-training [Kahn et al., 2020a, Xu et al., 2020b, Park et al., 2020]. Some of the earliest work in self-supervised learning of speech representations was was done by van den Oord et al. [2018] for phoneme recognition which was simplified in Schneider et al. [2019] who applied it to full speech recognition. Other work includes language model-style pre-training [Chung et al., 2019a] and learning fixed size representations of audio segments [Chung and Glass, 2018]. There is also work on quantization of the continuous speech data [Baevski et al., 2020b,a, Liu et al., 2019, van Niekerk et al., 2020, Baevski et al., 2020c, Hsu et al., 2021b] and on robustness to domain shift [Hsu et al., 2021a], multilingual pre-training [Kawakami et al., 2020, Conneau et al., 2020] as well as combining speech and vision [Harwath et al., 2020]. ",
+        "bbox": [
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+    },
+    {
+        "type": "table",
+        "img_path": "images/2681bd270ee947c4735ec6105ffa578b603c0a8f14a89fb155bf16d2679be651.jpg",
+        "table_caption": [
+            "Table 4: PER for low-resource languages, Tatar (tt) and Kyrgyz (ky). "
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>Model</td><td>tt</td><td>ky</td></tr><tr><td colspan=\"3\">Supervised learning</td></tr><tr><td>Fer et al. [2017]</td><td>42.5</td><td>38.7</td></tr><tr><td>m-CPC [Riviere et al., 2020]</td><td>42.0</td><td>41.2</td></tr><tr><td>XLSR-53 [Conneau et al.,2020]</td><td>5.1</td><td>6.1</td></tr><tr><td colspan=\"3\">Unsupervised learning</td></tr><tr><td>wav2vec-U</td><td>25.7</td><td>24.1</td></tr><tr><td>wav2vec-U + HMM</td><td>13.7</td><td>14.9</td></tr></table>",
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+        "img_path": "images/75c82e8aef7073d98bca3ee508ceb7960d3a4e7ae6963489d1130fb03b1695b7.jpg",
+        "table_caption": [
+            "Table 5: WER for Swahili from the ALFFA corpus. We compare to the supervised baseline of the ALFFA project. "
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>Model</td><td>sw</td></tr><tr><td>Supervised learning</td><td></td></tr><tr><td>Besacier et al. [2015]</td><td>27.36</td></tr><tr><td>Unsupervised learning</td><td></td></tr><tr><td>wav2vec-U</td><td>52.6</td></tr><tr><td>wav2vec-U + ST</td><td>32.2</td></tr></table>",
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+    {
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+    {
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+        "text": "Learning to map speech to phonemes without supervision using adversarial learning has been explored by Liu et al. [2018] who learn a mapping matrix between segment identifiers and phonemes. However, their work still relied on data segmented into phonemes by human annotators. This has been later extended to use an automatic segmentation [Chen et al., 2019] which is iteratively refined with HMMs. However, cross validation is still performed using labeled data (personal communication with authors). We also explored HMMs to refine segmentation boundaries (Table A2) but did not find it as effective as self-training. Our work is in part inspired by aligning word embedding spaces of different languages [Mikolov et al., 2013, Artetxe et al., 2017, Conneau et al., 2018] and full unsupervised machine translation [Lample et al., 2018, Artetxe et al., 2018, Conneau and Lample, 2019]. ",
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+    {
+        "type": "text",
+        "text": "6 Conclusion and Future Work ",
+        "text_level": 1,
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+    {
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+        "text": "wav2vec-U is a framework which enables building speech recognition models without labeled data. It embeds and segments the speech audio with self-supervised representations from wav2vec 2.0, learns a mapping to phonemes with adversarial learning, and cross-validates hyper-parameter choices as well as early stopping with an unsupervised metric. Experiments on the standard Librispeech benchmark show performance close to the state of the art models from only a few years ago, even though these models relied on nearly 1,000 hours of labeled data. ",
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+    {
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+        "text": "Compared to the previous best unsupervised speech recognition approach, wav2vec-U reduces TIMIT phone error rate from 26.1 to 11.3. We also demonstrate the viability of our approach on several languages other than English, some of which are low-resource. The ability to build speech recognition models solely from unlabeled speech audio and unlabeled text drastically lowers the effort to build speech technology for many more languages of the world. ",
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+    {
+        "type": "text",
+        "text": "Our approach requires phonemization of the text for the language of interest. Moreover, phonemizers are not available for all languages and this presents a bottleneck. To address this, future work may develop phonemizers for more languages, explore phonemization approaches that generalize across languages, or unsupervised training with graphemic text units such as letters. ",
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+    {
+        "type": "text",
+        "text": "We explored a simple segmentation technique based on self-supervised representations, however, there is a large body of research on segmentation and some of these techniques may lead to improvements over our simple approach [Varadarajan et al., 2008, Zhang and Glass, 2009, Gish et al., 2009, Lee and Glass, 2012, Lee et al., 2015, Ondel et al., 2016, Kamper et al., 2017a,b, Kreuk et al., 2020]. Also, wav2vec 2.0 learns representations for fixed size units with a fixed stride, however, phonemic units are of variable size. Another direction is to learn variable sized representations during pre-training. ",
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+    {
+        "type": "text",
+        "text": "Acknowledgments and Disclosure of Funding ",
+        "text_level": 1,
+        "bbox": [
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+        "page_idx": 9
+    },
+    {
+        "type": "text",
+        "text": "We thank Zhouhan Lin for helping with initial explorations in this project, Tatiana Likhomanenko for helpful discussions about self-training, Da-Rong Liu for sharing details to reproduce the setup of Chen et al. [2019], Marc’Aurelio Ranzato for general helpful discussions, and Ruth Kipng’eno, Ruth Ndila Ndeto as well as Mark Mutitu for error analysis of our Swahili model. ",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "References ",
+        "text_level": 1,
+        "bbox": [
+            174,
+            195,
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+            212
+        ],
+        "page_idx": 9
+    },
+    {
+        "type": "text",
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parse/train/SySaJ0xCZ/SySaJ0xCZ.md

@@ -0,0 +1,259 @@
+# SIMPLE AND EFFICIENT ARCHITECTURE SEARCH FOR CONVOLUTIONAL NEURAL NETWORKS
+
+Anonymous authors Paper under double-blind review
+
+# ABSTRACT
+
+Neural networks have recently had a lot of success for many tasks. However, neural network architectures that perform well are still typically designed manually by experts in a cumbersome trial-and-error process. We propose a new method to automatically search for well-performing CNN architectures based on a simple hill climbing procedure whose operators apply network morphisms, followed by short optimization runs by cosine annealing. Surprisingly, this simple method yields competitive results, despite only requiring resources in the same order of magnitude as training a single network. E.g., on CIFAR-10, our method designs and trains networks with an error rate below $6 \%$ in only 12 hours on a single GPU; training for one day reduces this error further, to almost $5 \%$ .
+
+# 1 INTRODUCTION
+
+Neural networks have rapidly gained popularity over the last few years due to their success in a variety of tasks, such as image recognition (Krizhevsky et al., 2012), speech recognition (Hinton et al., 2012) and machine translation (Bahdanau et al., 2015). In most cases, these neural networks are still designed by hand, which is an exhausting, time-consuming process. Additionally, the vast amount of possible configurations requires expert knowledge to restrict the search. Therefore, a natural goal is to design optimization algorithms that automate this neural architecture search.
+
+However, most classic optimization algorithms do not apply to this problem, since the architecture search space is discrete (e.g., number of layers, layer types) and conditional (e.g., the number of parameters defining a layer depends on the layer type). Thus, methods that rely on, e.g., differentiability or independent parameters are not applicable. This led to a growing interest in using evolutionary algorithms (Real et al., 2017; Suganuma et al., 2017) and reinforcement learning (Baker et al., 2016; Cai et al., 2017; Zoph & Le, 2017) for automatically designing CNN architectures. Unfortunately, most proposed methods are either very costly (requiring hundreds or thousands of GPU days) or yield non-competitive performance.
+
+In this work, we aim to dramatically reduce these computational costs while still achieving competitive performance. Specifically, our contributions are as follows:
+
+• We propose a baseline method that randomly constructs networks and trains them with SGDR (Loshchilov & Hutter, 2017). We demonstrate that this simple baseline achieves $6 \% - 7 \%$ test error on CIFAR-10, which already rivals several existing methods for neural archictecture search. Due to its simplicity, we hope that this baseline provides a valuable starting point for the development of more sophisticated methods in the future.   
+• We formalize and extend the work on network morphisms (Chen et al., 2015; Wei et al., 2016; Cai et al., 2017) in order to provide popular network building blocks, such as skip connections and batch normalization.   
+• We propose Neural Architecture Search by Hillclimbing (NASH), a simple iterative approach that, at each step, applies a set of alternative network morphisms to the current network, trains the resulting child networks with short optimization runs of cosine annealing (Loshchilov & Hutter, 2017), and moves to the most promising child network. NASH finds and trains competitive architectures at a computational cost of the same order of magnitude as training a single network; e.g., on CIFAR-10, NASH finds and trains CNNs with an error rate below $6 \%$ in roughly 12 hours on
+
+a single GPU. After one day the error is reduced to almost $5 \%$ . Models from different stages of our algorithm can be combined to achieve an error of $4 . 7 \%$ within two days on a single GPU. On CIFAR-100, we achieve an error below $24 \%$ in one day and get close to $20 \%$ after two days.
+
+• Our method is easy to use and easy to extend, so it hopefully can serve as a basis for future work.
+
+We first discuss related work in Section 2. Then, we formalize the concept of network morphisms in Section 3 and propose our architecture search methods based on them in Section 4. We evaluate our methods in Section 5 and conclude in Section 6.
+
+# 2 RELATED WORK
+
+Hyperparameter optimization. Neural networks are known to be quite sensitive to the setting of various hyperparameters, such as learning rates and regularization constants. There exists a long line of research on automated methods for setting these hyperparameters, including, e.g., random search (Bergstra & Bengio, 2012), Bayesian optimization (Bergstra et al., 2011; Snoek et al., 2012), bandit-based approaches (Li et al., 2016a), and evolutionary strategies (Loshchilov & Hutter, 2016).
+
+Automated architecture search. In recent years, the research focus has shifted from optimizing hyperparameters to optimizing architectures. While architectural choices can be treated as categorical hyperparameters and be optimized with standard hyperparameter optimization methods (Bergstra et al., 2011; Mendoza et al., 2016), the current focus is on the development of special techniques for architectural optimization. One very popular approach is to train a reinforcement learning agent with the objective of designing well-performing convolutional neural networks (Baker et al., 2016; Zoph & Le, 2017; Cai et al., 2017). Baker et al. (2016) train an RL agent to sequentially choose the type of layers (convolution, pooling, fully connected) and their parameters. Zoph & Le (2017) use a recurrent neural network controller to sequentially generate a string representing the network architecture. Both approaches train their generated networks from scratch and evaluate their performance on a validation set, which represents a very costly step. In a follow-up work (Zoph et al., 2017), the RL agent learned to build cells, which are then used as building blocks for a neural network with a fixed global structure. Unfortunately, training an RL agent with the objective of designing architecture is extremely expensive: both Baker et al. (2016) and Zoph & Le (2017) required over 10.000 fully trained networks, requiring hundreds to thousands of GPU days. To overcome this drawback, Cai et al. (2017) proposed to apply the concept of network transformations/morphisms within RL. As in our (independent, parallel) work, the basic idea is to use the these transformation to generate new pre-trained architectures to avoid the large cost of training all networks from scratch. Compared to this work, our approach is much simpler and 15 times faster while obtaining better performance.
+
+Real et al. (2017) and Suganuma et al. (2017) utilized evolutionary algorithms to iteratively generate powerful networks from a small network. Operations like inserting a layer, modifying the parameters of a layer or adding skip connections serve as ”mutations” in their framework of evolution. Whereas Real et al. (2017) also used enormous computational resources (250 GPUs, 10 days), Suganuma et al. (2017) were restricted to relatively small networks due to handling a population of networks. In contrast to the previous methods where network capacity increases over time, Saxena & Verbeek (2016) start with training a large network (a ”convolution neural fabric”) and prune this in the end. Very recently, Brock et al. (2017) used hypernetworks (Ha et al., 2017) to generate the weights for a randomly sampled network architecture with the goal of eliminating the costly process of training a vast amount of networks.
+
+Network morphism/ transformation. Network transformations were (to our knowledge) first introduced by Chen et al. (2015) in the context of transfer learning. The authors described a function preserving operation to make a network deeper (dubbed ”Net2Deeper”) or wider (”Net2Wider”) with the goal of speeding up training and exploring network architectures. Wei et al. (2016) proposed additional operations, e.g., for handling non-idempotent activation functions or altering the kernel size and introduced the term network morphism. As mentioned above, Cai et al. (2017) used network morphisms for architecture search, though they just employ the Net2Deeper and Net2Wider operators from Chen et al. (2015) as well as altering the kernel size, i.e., they limit their search space to simple architectures without, e.g., skip connections.
+
+# 3 NETWORK MORPHISM
+
+Let $\mathcal { N } ( \mathcal { X } )$ denote a set of neural networks defined on $\mathcal { X } \subset \mathbb { R } ^ { n }$ . A network morphism is a mapping $M : \dot { \mathcal { N } } ( \dot { \mathcal { X } } ) \times \mathbb { R } ^ { k }  \mathcal { N } ( \underline { { \mathcal { X } } } ) \times \mathbb { R } ^ { j }$ from a neural network $f ^ { w } \in \mathcal { N } ( \mathcal { X } )$ with parameters $w \in \mathbb { R } ^ { k }$ to another neural network $g ^ { \tilde { w } } \in \mathcal { N } ( \mathcal { X } )$ with parameters $\tilde { w } \in \mathbb { R } ^ { j }$ so that
+
+$$
+f ^ { w } ( x ) = g ^ { \tilde { w } } ( x ) \mathrm { f o r e v e r y } x \in \mathcal { X } .
+$$
+
+In the following we give a few examples of network morphisms and how standard operations for building neural networks (e.g., adding a convolutional layer) can be expressed as a network morphism. For this, let $f _ { i } ^ { w _ { i } } ( x )$ be some part of a NN $f ^ { w } ( x )$ , e.g., a layer or a subnetwork.
+
+Network morphism Type I. We replace $f _ { i } ^ { w _ { i } }$ by
+
+$$
+\tilde { f } _ { i } ^ { \tilde { w } _ { i } } ( x ) = A f _ { i } ^ { w _ { i } } ( x ) + b ,
+$$
+
+with $\tilde { w } _ { i } = ( w _ { i } , A , b ) ^ { 1 }$ . Equation (1) obviously holds for $A = \mathbf { 1 } , b = \mathbf { 0 }$ . This morphism can be used to add a fully-connected or convolutional layer, as these layers are simply linear mappings. Chen et al. (2015) dubbed this morphism ”Net2DeeperNet”. Alternatively to the above replacement, one could also choose
+
+$$
+\tilde { f } _ { i } ^ { \tilde { w } _ { i } } ( x ) = C ( A f _ { i } ^ { w _ { i } } ( x ) + b ) + d ,
+$$
+
+with $\tilde { w } _ { i } = ( w _ { i } , C , d )$ . $A , b$ are fixed, non-learnable. In this case network morphism Equation (1) holds if $C = A ^ { - 1 } , d = - C b$ . A Batch Normalization layer (or other normalization layers) can be written in the above form: $A , b$ represent the batch statistics and $C , d$ the learnable scaling and shifting.
+
+Network morphism Type II. Assume $f _ { i } ^ { w _ { i } }$ has the form $f _ { i } ^ { w _ { i } } ( x ) = A h ^ { w _ { h } } ( x ) + b$ for an arbitrary function $h$ . We replace $f _ { i } ^ { w _ { i } }$ , $w _ { i } = ( w _ { h } , \dot { A } , b )$ , by
+
+$$
+\tilde { f } _ { i } ^ { \tilde { w } _ { i } } ( x ) = \left( A \quad \tilde { A } \right) \binom { h ^ { w _ { h } } ( x ) } { \tilde { h } ^ { w _ { h } } ( x ) } + b
+$$
+
+with an arbitrary function $\tilde { h } ^ { w _ { \tilde { h } } } ( x )$ . The new parameters are $\tilde { w } _ { i } = ( w _ { i } , w _ { \tilde { h } } , \tilde { A } )$ . Again, Equation (1) can trivially be satisfied by setting $\tilde { A } = 0$ . We think of two modifications of a NN which can be expressed by this morphism. Firstly, a layer can be widened (i.e., increasing the number of units in a fully connected layer or the number of channels in a CNN - the Net2WiderNet transformation from Chen et al. (2015)). Think of $h ( x )$ as the layer to be widened. For example, we can then set $\tilde { h } = h$ to simply double the width. Secondly, skip-connections by concatenation as used by Huang et al. (2016) can be formulated as a network morphism. If $h ( x )$ itself is a sequence of layers, $h ( x ) = h _ { n } ( x ) \circ \cdots \circ h _ { 0 } ( x )$ , then one could choose $\tilde { h } ( x ) = x$ to realize a skip from $h _ { 0 }$ to the layer subsequent to $h _ { n }$ .
+
+Network morphism Type III. By definition, every idempotent function $f _ { i } ^ { w _ { i } }$ can simply be replaced by
+
+$$
+f _ { i } ^ { ( w _ { i } , \tilde { w } _ { i } ) } = f _ { i } ^ { \tilde { w } _ { i } } \circ f _ { i } ^ { w _ { i } }
+$$
+
+with the initialization $\tilde { w } _ { i } = w _ { i }$ . This trivially also holds for idempotent function without weights, e.g., Relu.
+
+Network morphism Type IV. Every layer $f _ { i } ^ { w _ { i } }$ is replaceable by
+
+$$
+\tilde { f } _ { i } ^ { \tilde { w } _ { i } } ( x ) = \lambda f _ { i } ^ { w _ { i } } ( x ) + ( 1 - \lambda ) h ^ { w _ { h } } ( x ) , \quad \tilde { w } _ { i } = ( w _ { i } , \lambda , w _ { h } )
+$$
+
+with an arbitrary function $h$ and Equation (1) holds if $\lambda$ is initialized as 1. This morphism can be used to incorporate any function, especially any non-linearities. For example, Wei et al. (2016) use a special case of this operator to deal with non-linear, non-idempotent activation functions. Another example wou(2016) to sim insertioing: If $f _ { i } ^ { w _ { i } }$ f an additiv itself is a s p connection,nce of layers, $f _ { i } ^ { w _ { i } } = f _ { i _ { n } } ^ { w _ { i _ { n } } } \circ \cdot \cdot \cdot \circ f _ { i _ { 0 } } ^ { w _ { i _ { 0 } } }$ He et al., then one $h ( x ) = x$ to realize a skip from $f _ { i _ { 0 } } ^ { w _ { i _ { 0 } } }$ to the layer subsequent to $f _ { i _ { n } } ^ { w _ { i _ { n } } }$
+
+Note that every combinations of the network morphisms again yields a morphism. So one could for example insert a block ”Conv-BatchNorm-Relu” subsequent to a Relu layer by using equations (2), (3) and (5).
+
+![](images/f8ca3cbd2a4cdfcdcf35ac65c139d715df875d1be2779a18db0872654bca035b.jpg)  
+Figure 1: Visualization of our method. Based on the current best model, new models are generated and trained afterwards. The best model is than updated.
+
+# 4 ARCHITECTURE SEARCH BY NETWORK MORPHISMS
+
+Our proposed algorithm is a simple hill climbing strategy (Russell & Norvig, 2009). We start with a small, (possibly) pretrained network. Then, we apply network morphisms to this initial network to generate larger ones that may perform better when trained further. These new “child” networks can be seen as neighbors of the initial “parent” network in the space of network architectures. Due to the network morphism Equation (1), the child networks start at the same performance as their parent. In essence, network morphisms can thus be seen as a way to initialize child networks to perform well, avoiding the expensive step of training them from scratch and thereby reducing the cost of their evaluation. The various child networks can then be trained further for a brief period of time to exploit the additional capacity obtained by the network morphism, and the search can move on to the best resulting child network. This constitutes one step of our proposed algorithm, which we dub Neural Architecture Search by Hill-climbing (NASH). NASH can execute this step several times until performance on a validation set saturates; we note that this greedy process may in principle get stuck in a poorly-performing region, from which it can never escape, but we did not find evidence for this in our experiments.
+
+Figure 1 visualizes one step of the NASH approach, and Algorithm 1 provides full details for the algorithm. In our implementation, the function $A p p l y N e t M o r p h ( m o d e l , n )$ (line 15) applies $n$ network morphisms, each of them sampled uniformly at random from the following three:
+
+• Make the network deeper, i.e., add a ”Conv-BatchNorm-Relu” block as described at the end of Section 3. The position where to add the block, as well as the kernel size $( \in \{ 3 , 5 \} )$ , are uniformly sampled. The number of channels is chosen to be equal to he number of channels of the closest preceding convolution.   
+• Make the network wider, i.e., increase the number of channels by using the network morphism type II. The conv layer to be widened, as well as the widening factor $( \in \{ 2 , 4 \} )$ are sampled uniformly at random.   
+• Add a skip connection from layer i to layer j (either by concatenation or addition – uniformly sampled) by using network morphism type II or IV, respectively. Layers i and j are also sampled uniformly.
+
+Note that the current best model is also considered as a child, i.e. our algorithm is not forced to select a new model but can rather also keep the old one if no other one improves upon it.
+
+# Algorithm 1 Network architecture search by hill climbing
+
+$1 \backslash \mathrm { ~ f u n c t i o n ~ N A S H } ( m o d e l _ { 0 } , n _ { s t e p s } , n _ { n e i g h } , n _ { N M } , e p o c h _ { n e i g h } , e p o c h _ { f i n a l } , \lambda _ { e n d } , \lambda _ { s t a r t } )$   
+2:   
+3: # $m o d e l _ { 0 }$ , model to start with, $n _ { s t e p s } \triangleq$ number of hill climbining steps   
+4: # $n _ { n e i g h } \triangleq$ number of neighbours, $n _ { N M } \triangleq$ number of net. morph. applied   
+5: # $e p o c h _ { n e i g h } \triangleq$ number of epochs for training every neighbour   
+6: # $e p o c h _ { f i n a l } \triangleq$ number of epochs for final training   
+7: # initial LR $\lambda _ { s t a r t }$ is annealed to $\lambda _ { e n d }$ during SGDR training   
+8:   
+9: $m o d e l _ { b e s t }  m o d e l _ { 0 }$   
+10: # start hill climbing   
+11: for $i \gets 1 , \dots , n _ { s t e p s } \ { \bf d }$ o   
+12: #get $n _ { n e i g h }$ neighbors of $m o d e l _ { 0 }$ by applying $n _ { N M }$ network morphisms to $m o d e l _ { b e s t }$   
+13: for $j \gets 1 , \dots , n _ { n e i g h } - 1$ do   
+14: $m o d e l _ { j } \gets A p p l y N e t M o r p h s ( m o d e l _ { b e s t } , n _ { N M } )$   
+15: # train for a few epochs on training set with SGDR   
+16: $m o d e l _ { j } \gets \mathrm { S G D R t r a i n } ( m o d e l _ { j } , e \bar { p } o c h _ { n e i g h } , \lambda _ { s t a r t } , \lambda _ { e n d } )$   
+17: end for   
+18: # in fact, last neighbor is always just the current best   
+19: $m o d e l _ { n _ { n e i g h } } \gets \mathrm { S G D R t r a i n } ( m o d e l _ { b e s t } , e p o c h _ { n e i g h } , \lambda _ { s t a r t } , \lambda _ { e n d } )$   
+20: # get best model on validation set   
+21: $\underbrace { \Bre { \_ } { a } } { m o d } e l _ { b e s t }  \underbrace { a r g m a x } _ { j = 1 , \dots , n _ { n e i g h } } \{ p e r f o r m a n c e _ { v a l i } ( m o d e l _ { j } ) \}$   
+22: end for   
+23: # train the final model on training and validation set   
+24: $m o d e l _ { b e s t } \gets \mathrm { S G D R t r a i n } ( m o d e \bar { l } _ { b e s t } , e p o c h _ { f i n a l } , \lambda _ { s t a r t } , \lambda _ { e n d } )$   
+25: return modelbest   
+26: end function
+
+It is important for our method that child networks only need to be trained for a few epochs2 (line 17). Hence, an optimization algorithm with good anytime performance is required. Therefore, we chose the cosine annealing strategy from Loshchilov & Hutter (2017), whereas the learning rate is implicitly restarted: the training in line 17 always starts with a learning rate $\lambda _ { s t a r t }$ which is annealed to $\lambda _ { e n d }$ after epochneigh epochs. We use the same learning rate scheduler in the final training (aside from a different number of epochs).
+
+While we presented our method as a simple hill-climbing method, we note that it can also be interpreted as a very simple evolutionary algorithm with a population size of $n _ { n e i g h }$ , no cross-over, network morphisms as mutations, and a selection mechanism that only considers the best-performing population member as the parent for the next generation. This interpretation also suggests several promising possibilities for extending our simple method.
+
+# 5 EXPERIMENTS
+
+We evaluate our method on CIFAR-10 and CIFAR-100. First, we investigate whether our considerations from the previous chapter coincide with empirical results. We also check if the interplay of modifying and training networks harms their eventual performance. Finally, we compare our proposed method with other automated architecture algorithms as well as hand crafted architectures.
+
+We use the same standard data augmentation scheme for both CIFAR datasets used by Loshchilov & Hutter (2017) in all of the following experiments. The training set (50.000 samples) is split up in training (40.000) and validation (10.000) set for the purpose of architecture search. Eventually the performance is evaluated on the test set. All experiments where run on Nvidia Titan X (Maxwell)
+
+GPUs, with code implemented in Keras (Chollet et al., 2015) with a TensorFlow (Abadi et al., 2015) backend.
+
+# 5.1 EXPERIMENTS ON CIFAR-10
+
+# 5.1.1 BASELINES
+
+Before comparing our method to others, we run some baseline experiments to see whether our considerations from the previous chapter coincide with empirical data.
+
+Random model selection. First, we investigate if the simple hill climbing strategy is able to distinguish between models with high and low performance. For this, we set $n _ { n e i g h } = 1$ , i.e., there is no model selction - we simply construct random networks and train them. We then run experiments with $n _ { n e i g h } = 8$ and compare both results. All other parameters are the same in this experiment, namely $n _ { s t e p s } = 5 , n _ { N M } = 5 , e p o c h _ { n e i g h } = 1 7 , e p o c h _ { f i n a l } = 1 0 0$ . We choose $\lambda _ { s t a r t } = 0 . 0 5$ , $\lambda _ { e n d } = 0 . { \overset { \cdot } { 0 } }$ as done in Loshchilov & Hutter (2017). model0 was a simple conv net: Conv-MaxPool-Conv-MaxPool-Conv-FC-Softmax3, which is pretrained for 20 epochs, achieving $\approx 7 5 \%$ validation accuracy (up to $9 1 \%$ when trained till convergence), see Figure 5 in the appendix. If our algorithm is able to identify better networks, one would expect to get better results with the setting $n _ { n e i g h } = 8$ .
+
+Retraining from scratch. In the this experiment we investigate whether the ”weight inheritance” due to the network morphisms used in our algorithm harms the final performance of the final model. This weight inheritance can be seen as a strong prior on the weights and one could suspect that the new, larger model may not be able to overcome a possibly poor prior. Additionally we were interested in measuring the overhead of the architecture search process, so we compared the times for generating and training a model with the time needed when training the final model from scratch. The retraining from scratch is done for the same number of epochs as the total number of epochs spent to train the model returned by our algorithm4 .
+
+No SGDR. We now turn off the cosine annealing with restarts (SGDR) during the hill climbing stage, i.e., the training in line 17 of Algorithm 1 is done with a constant learning rate. We tried $\lambda \in \{ 0 . 0 1 , 0 . 0 2 5 , 0 . 0 5 \}$ , 10 runs each and averaged the results. Note that we still use the cosine decay for the final training.
+
+No network morphism. Lastly, we turn off the network morphism constraint for initializing the neighbor networks. In detail, we proceeded as Real et al. (2017): All weights from layer where now changes occur are inherited, whereas the weights of new/modified layers are initialized by random.
+
+The results for these experiments are summarized in Table 1 . The hill climbing strategy is actually able to identify better performing models. (first and second line: $5 . 7 \%$ vs. $6 . 5 \%$ ). Notice how hill climbing prefers larger models (5.7 million parameters on average vs. 4.4 million). Performance slightly decreases when the models are retrained from scratch (line 3). This experiments indicates that our algorithm does not harm the final performance of a model. Regarding the runtime, the overhead for first having to search for the architecture is roughly a factor 3. We think this is a big advantage of our method and shows that architecture search can be done in the same order of magnitude as training a single model. In line 4 we can see that SGDR plays an important role. The resulting models chosen by our algorithm when training is done with a constant learning rate perform similarly to the models without any model selection strategy $( 6 . 4 \%$ and $6 . 5 \%$ , respectively), which indicates that the performance after a few epochs on the validation set when trained without SGDR correlates less with the final performance on the test set as it is the case for training with SGDR. Indeed, we computed the Pearson correlation coefficient and obtained $R ^ { 2 } = 0 . 6 4$ for training with SGDR and and $\mathrm { \bar { \it R } ^ { 2 } = 0 . 3 6 }$ for training with a constant learning rate. See appendix A. Also, with the constant learning rate, the few epochs spent are not sufficient to improve the performance of the model. Figure 2 shows the progress while running our algorithm with and without SGDR, averaged over all runs. When turning off the network morphism constraint, performance also decreases.
+
+![](images/5bffa50e24c866e7a85ea7102470da8aa121189925b47b5e0807ef32b1fb1234.jpg)  
+Figure 2: The best model found by Algorithm 1 tracked over time (in terms of hill climbing iterations). With (red) and without (blue) using SGDR for the training within the hill climbing (line 17). Final training (line 24) is not plotted. Dashed line denotes mean, shaded area $\pm 2 \sigma$ intervalls.
+
+Table 1: Baseline experiments. Runtime, # params, and error rates are averaged over 10 runs (for $n _ { n e i g h } = 8 $ ) and 30 runs $( n _ { n e i g h } = 1 )$ ) runs, respectively. $n _ { s t e p s } = 5$ in all experiments.   
+
+<table><tr><td>algorithm setting</td><td>runtime (hrs)</td><td># params (mil.)</td><td>error ± std.( %)</td></tr><tr><td>nneigh =8</td><td>12.8</td><td>5.7</td><td>5.7 ± 0.35</td></tr><tr><td>Random networks (nneigh = 1)</td><td>4.5</td><td>4.4</td><td>6.5 ± 0.76</td></tr><tr><td>models from line 1 retrained from scratch</td><td>5.3</td><td>5.7</td><td>6.1 ± 0.92</td></tr><tr><td>nneigh = 8, no SGDR</td><td>10.6</td><td>5.8</td><td>6.4±0.70</td></tr><tr><td>nneigh = 8, no net. morph.</td><td>6.6</td><td>2.9</td><td>6.1 ±0.30</td></tr></table>
+
+Interestingly the number of parameters heavily decreases. This indicates that our algorithm prefers models without new parameters.
+
+# 5.1.2 COMPARISON TO HAND CRAFTED AND OTHER AUTOMATICALLY GENERATED ARCHITECTURES
+
+We now compare our algorithm against the popular wide residual networks (Zagoruyko & Komodakis, 2016), the state of the art model from Gastaldi (2017) as well as other automated architecture search methods. Beside our results for $n _ { s t e p s } = 5$ from the previous section, we also tried $n _ { s t e p s } = 8$ to generate larger models.
+
+For further improving the results, we take snapshots of the best models from every iteration while running our algorithm following the idea of Huang et al. (2017) when using SGDR (Loshchilov & Hutter, 2017) for training. However different from Huang et al. (2017), we do not immediately get fully trained models for free, as our snapshots are not yet trained on the validation set but rather only on the training set. Hence we spent some additional resources and train the snapshots on both sets. Afterwards the ensemble model is build by combining the snapshot models with uniform weights. Lastly, we also build an ensemble from the models returned by our algorithm across all runs. Results are listed in Table 2.
+
+The proposed method is able to generate competitive network architectures in only 12 hours. By spending another 12 hours, it outperforms most automated architecture search methods although all of them require (partially far) more time and GPUs. We do not reach the performance of the two handcrafted architectures as well as the ones found by Zoph & Le (2017) and Brock et al. (2017). However note that Zoph & Le (2017) spent by far more resources than we did.
+
+Unsurprisingly, the ensemble models perform better. It is a simple and cheap way to improve results which everyone can consider when the number of parameters is not relevant.
+
+Table 2: Results for CIFAR-10. For our methods the stated resources, # parameters and errors are averaged over all runs. ”Resources spent” denotes training costs in case of the handcrafted models.   
+
+<table><tr><td>model</td><td>resources spent</td><td># params (mil.)</td><td>error(%)</td></tr><tr><td></td><td></td><td></td><td></td></tr><tr><td>Shake-Shake (Gastaldi,2017)</td><td>4 GPU days,2 GPUs</td><td>26</td><td>2.9</td></tr><tr><td>WRN 28-10 (Loshchilov &amp; Hutter,2017)</td><td>1 GPU day</td><td>36.5</td><td>3.86</td></tr><tr><td>Baker et al. (2016)</td><td>80-100 GPU days</td><td>11</td><td>6.9</td></tr><tr><td>Cai et al. (2017)</td><td>15 GPU days</td><td>19.7</td><td>5.7</td></tr><tr><td>Zoph &amp; Le (2017)</td><td>16.000-24.000 GPU days</td><td>37.5</td><td>3.65</td></tr><tr><td>Real et al. (2017)</td><td>2500 GPU days</td><td>5.4</td><td>5.4</td></tr><tr><td>Saxena &amp; Verbeek (2016)</td><td>？</td><td>21</td><td>7.4</td></tr><tr><td>Brock et al. (2017)</td><td>3 GPU days</td><td>16.0</td><td>4.0</td></tr><tr><td>Ours (random networks,nsteps = 5, nneigh =1)</td><td>0.2 GPU days</td><td>4.4</td><td>6.5</td></tr><tr><td>Ours (nsteps = 5,nneigh =8,10 runs)</td><td>0.5 GPU days</td><td>5.7</td><td>5.7</td></tr><tr><td>Ours (nsteps = 8,nneigh = 8,4 runs)</td><td>1 GPU day</td><td>19.7</td><td>5.2</td></tr><tr><td>Ours (snapshot ensemble,4 runs)</td><td>2 GPU days</td><td>57.8</td><td>4.7</td></tr><tr><td>Ours (ensemble across runs)</td><td>4 GPU days</td><td>88</td><td>4.4</td></tr></table>
+
+Table 3: Results for CIFAR-100. For our methods the stated resources, # parameters and errors are averaged over all runs. ”Resources spent” denotes training costs in case of the handcrafted models.   
+
+<table><tr><td>model</td><td>resources spent</td><td># params (mil.)</td><td>error(%)</td></tr><tr><td></td><td></td><td></td><td>15.9</td></tr><tr><td>Shake-Shake (Gastaldi, 2017) WRN 28-10 (Loshchilov &amp; Hutter,2017)</td><td>14 GPU days</td><td>34.4</td><td></td></tr><tr><td></td><td>1 GPU day</td><td>36.5</td><td>19.6</td></tr><tr><td>Real et al. (2017)</td><td>250 GPUs</td><td>40.4</td><td>23.7</td></tr><tr><td>Brock et al. (2017)</td><td>3 GPU days</td><td>16.0</td><td>20.6</td></tr><tr><td>Ours (nsteps = 8,nneigh = 8,5 runs)</td><td>1 GPU day</td><td>22.3</td><td>23.4</td></tr><tr><td>Ours (snapshot ensemble,5 runs)</td><td>2 GPU days</td><td>73.3</td><td>20.9</td></tr><tr><td>Ours (ensemble across runs)</td><td>5 GPU days</td><td>111.5</td><td>19.6</td></tr></table>
+
+# 5.2 EXPERIMENTS ON CIFAR-100
+
+We repeat the previous experiment on CIFAR-100; hyperparameters were not changed. The results are listed in Table 3. Unfortunately most automated architecture methods did not consider CIFAR100. Our method is on a par with Real et al. (2017) after one day with a single GPU. The snapshot ensemble performs similar to Brock et al. (2017) and an ensemble model build from the 5 runs can compete with the hand crafted WRN 28-10. The performance of the Shake-Shake network (Gastaldi, 2017) is again not reached.
+
+# 6 CONCLUSION
+
+We proposed NASH, a simple and fast method for automated architecture search based on a hill climbing strategy, network morphisms, and training via SGDR. Experiments on CIFAR-10 and CIFAR-100 showed that our method yields competitive results while requiring considerably less computational resources than most alternative approaches. Our algorithm is easily extendable, e.g., by other network morphisms, evolutionary approaches for generating new models, other methods for cheap performance evaluation (such as, e.g., learning curve prediction (Klein et al., 2017) or hypernetworks (Ha et al., 2017; Brock et al., 2017)), or better resource handling strategies (such as Hyperband (Li et al., 2016b)). In this sense, we hope that our approach can serve as a basis for the development of more sophisticated methods that yield further improvements of performance.
+
+# REFERENCES
+
+Mart´ın Abadi, Ashish Agarwal, Paul Barham, Eugene Brevdo, Zhifeng Chen, Craig Citro, Greg S. Corrado, Andy Davis, Jeffrey Dean, Matthieu Devin, Sanjay Ghemawat, Ian Goodfellow, Andrew Harp, Geoffrey Irving, Michael Isard, Yangqing Jia, Rafal Jozefowicz, Lukasz Kaiser, Manjunath Kudlur, Josh Levenberg, Dan Mane, Rajat Monga, Sherry Moore, Derek Murray, Chris Olah, ´ Mike Schuster, Jonathon Shlens, Benoit Steiner, Ilya Sutskever, Kunal Talwar, Paul Tucker, Vincent Vanhoucke, Vijay Vasudevan, Fernanda Viegas, Oriol Vinyals, Pete Warden, Martin Watten- ´ berg, Martin Wicke, Yuan Yu, and Xiaoqiang Zheng. TensorFlow: Large-scale machine learning on heterogeneous systems, 2015. URL https://www.tensorflow.org/. Software available from tensorflow.org.
+
+Dzmitry Bahdanau, Kyunghyun Cho, and Yoshua Bengio. Neural machine translation by jointly learning to align and translate. ICLR, 2015.
+
+Bowen Baker, Otkrist Gupta, Nikhil Naik, and Ramesh Raskar. Designing neural network architectures using reinforcement learning. ICLR 2017, 2016.
+
+J. Bergstra and Y. Bengio. Random search for hyper-parameter optimization. 13(1):281–305, 2012.
+
+J. Bergstra, R. Bardenet, Y. Bengio, and B. Kegl. Algorithms for hyper-parameter optimization. In ´ NIPS, 2011.
+
+Andrew Brock, Theodore Lim, James M. Ritchie, and Nick Weston. SMASH: one-shot model architecture search through hypernetworks. arXiv preprint, 2017.
+
+Han Cai, Tianyao Chen, Weinan Zhang, Yong Yu, and Jun Wang. Reinforcement learning for architecture search by network transformation. 2017.
+
+Tianqi Chen, Ian J. Goodfellow, and Jonathon Shlens. Net2net: Accelerating learning via knowledge transfer. arXiv preprint, 2015.
+
+Franc¸ois Chollet et al. Keras. https://github.com/fchollet/keras, 2015.
+
+Xavier Gastaldi. Shake-shake regularization. ICLR 2017 Workshop, 2017.
+
+David Ha, Andrew M. Dai, and Quoc V. Le. Hypernetworks. ICLR, 2017.
+
+Kaiming He, Xiangyu Zhang, Shaoqing Ren, and Jian Sun. Deep residual learning for image recognition. CVPR, 2016.
+
+Geoffrey Hinton, Li Deng, Dong Yu, George Dahl, Abdel rahman Mohamed, Navdeep Jaitly, Andrew Senior, Vincent Vanhoucke, Patrick Nguyen, Tara Sainath, and Brian Kingsbury. Deep neural networks for acoustic modeling in speech recognition. IEEE Signal Processing Magazine, 2012.
+
+Gao Huang, Zhuang Liu, and Kilian Q. Weinberger. Densely connected convolutional networks. 2016.
+
+Gao Huang, Yixuan Li, Geoff Pleiss, Zhuang Liu, John E. Hopcroft, and Kilian Q. Weinberger. Snapshot ensembles: Train 1, get M for free. ICLR 2017, 2017.
+
+A. Klein, S. Falkner, J. T. Springenberg, and F. Hutter. Learning curve prediction with Bayesian neural networks. In International Conference on Learning Representations (ICLR) 2017 Conference Track, April 2017.
+
+Alex Krizhevsky, Ilya Sutskever, and Geoffrey E Hinton. Imagenet classification with deep convolutional neural networks. In F. Pereira, C. J. C. Burges, L. Bottou, and K. Q. Weinberger (eds.), Advances in Neural Information Processing Systems 25, pp. 1097–1105. Curran Associates, Inc., 2012.
+
+L. Li, K. G. Jamieson, G. DeSalvo, A. Rostamizadeh, and A. Talwalkar. Efficient hyperparameter optimization and infinitely many armed bandits. CoRR, abs/1603.06560, 2016a.
+
+Lisha Li, Kevin G. Jamieson, Giulia DeSalvo, Afshin Rostamizadeh, and Ameet Talwalkar. Efficient hyperparameter optimization and infinitely many armed bandits. arXiv preprint, 2016b.   
+I. Loshchilov and F. Hutter. CMA-ES for hyperparameter optimization of deep neural networks. CoRR, abs/1604.07269, 2016.   
+I. Loshchilov and F. Hutter. Sgdr: Stochastic gradient descent with warm restarts. In International Conference on Learning Representations (ICLR) 2017 Conference Track, April 2017.   
+H. Mendoza, A. Klein, M. Feurer, T. Springenberg, and F. Hutter. Towards automatically-tuned neural networks. In AutoML, 2016.   
+Esteban Real, Sherry Moore, Andrew Selle, Saurabh Saxena, Yutaka Leon Suematsu, Quoc V. Le, and Alex Kurakin. Large-scale evolution of image classifiers. arXiv preprint, 2017.   
+Stuart Russell and Peter Norvig. Artificial Intelligence: A Modern Approach (3rd Edition). Pearson, 3 edition, December 2009. ISBN 0136042597.   
+Shreyas Saxena and Jakob Verbeek. Convolutional neural fabrics. arXiv preprint, 2016.   
+J. Snoek, H. Larochelle, and R.P. Adams. Practical Bayesian optimization of machine learning algorithms. In NIPS, 2012.   
+Masanori Suganuma, Shinichi Shirakawa, and Tomoharu Nagao. A genetic programming approach to designing convolutional neural network architectures. arXiv preprint, 2017.   
+Tao Wei, Changhu Wang, Yong Rui, and Chang Wen Chen. Network morphism. arXiv preprint, 2016.   
+Sergey Zagoruyko and Nikos Komodakis. Wide residual networks. arXiv preprint, 2016.   
+Barret Zoph and Quoc V. Le. Neural architecture search with reinforcement learning. 2017.   
+Barret Zoph, Vijay Vasudevan, Jonathon Shlens, and Quoc V. Le. Learning transferable architectures for scalable image recognition. 2017.
+
+![](images/2edbb1405729ce5dc046dc80f49bd9380081ebed874aa93e2d296d2395a7ddf0.jpg)  
+Figure 3: Initial network for our algorithm.
+
+![](images/213925428f8eea0c7c284680e760c96a1baa86df2685b0480330288a33417347.jpg)  
+Figure 4: Initial network for our algorithm.
+
+![](images/926480ca8e0fe0b1fac91e9b0c6c21dd16e70a4e522edfe39777971a2e331b4d.jpg)  
+Figure 5: Initial network for our algorithm.
+
+![](images/091ad5bd88208c13ba32695bfc45a25363ea4c4e47109a8acba5e63354b8c3d1.jpg)  
+Figure 6: Network generated by our algorithm with $n _ { s t e p s } = 5$ .
+
+![](images/e810d4abf64e5a83ec8d5f1149515b76d979a3c8fc66b0153106f09e2b3c3c2d.jpg)  
+Figure 7: Network generated by our algorithm with $n _ { s t e p s } = 8$ .

parse/train/SySaJ0xCZ/SySaJ0xCZ_content_list.json

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+    {
+        "type": "text",
+        "text": "SIMPLE AND EFFICIENT ARCHITECTURE SEARCH FOR CONVOLUTIONAL NEURAL NETWORKS ",
+        "text_level": 1,
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "Anonymous authors Paper under double-blind review ",
+        "bbox": [
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+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "ABSTRACT ",
+        "text_level": 1,
+        "bbox": [
+            454,
+            234,
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+            251
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "Neural networks have recently had a lot of success for many tasks. However, neural network architectures that perform well are still typically designed manually by experts in a cumbersome trial-and-error process. We propose a new method to automatically search for well-performing CNN architectures based on a simple hill climbing procedure whose operators apply network morphisms, followed by short optimization runs by cosine annealing. Surprisingly, this simple method yields competitive results, despite only requiring resources in the same order of magnitude as training a single network. E.g., on CIFAR-10, our method designs and trains networks with an error rate below $6 \\%$ in only 12 hours on a single GPU; training for one day reduces this error further, to almost $5 \\%$ . ",
+        "bbox": [
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+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "1 INTRODUCTION ",
+        "text_level": 1,
+        "bbox": [
+            176,
+            435,
+            336,
+            450
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "Neural networks have rapidly gained popularity over the last few years due to their success in a variety of tasks, such as image recognition (Krizhevsky et al., 2012), speech recognition (Hinton et al., 2012) and machine translation (Bahdanau et al., 2015). In most cases, these neural networks are still designed by hand, which is an exhausting, time-consuming process. Additionally, the vast amount of possible configurations requires expert knowledge to restrict the search. Therefore, a natural goal is to design optimization algorithms that automate this neural architecture search. ",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "However, most classic optimization algorithms do not apply to this problem, since the architecture search space is discrete (e.g., number of layers, layer types) and conditional (e.g., the number of parameters defining a layer depends on the layer type). Thus, methods that rely on, e.g., differentiability or independent parameters are not applicable. This led to a growing interest in using evolutionary algorithms (Real et al., 2017; Suganuma et al., 2017) and reinforcement learning (Baker et al., 2016; Cai et al., 2017; Zoph & Le, 2017) for automatically designing CNN architectures. Unfortunately, most proposed methods are either very costly (requiring hundreds or thousands of GPU days) or yield non-competitive performance. ",
+        "bbox": [
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+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "In this work, we aim to dramatically reduce these computational costs while still achieving competitive performance. Specifically, our contributions are as follows: ",
+        "bbox": [
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+        "page_idx": 0
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+    {
+        "type": "text",
+        "text": "• We propose a baseline method that randomly constructs networks and trains them with SGDR (Loshchilov & Hutter, 2017). We demonstrate that this simple baseline achieves $6 \\% - 7 \\%$ test error on CIFAR-10, which already rivals several existing methods for neural archictecture search. Due to its simplicity, we hope that this baseline provides a valuable starting point for the development of more sophisticated methods in the future.   \n• We formalize and extend the work on network morphisms (Chen et al., 2015; Wei et al., 2016; Cai et al., 2017) in order to provide popular network building blocks, such as skip connections and batch normalization.   \n• We propose Neural Architecture Search by Hillclimbing (NASH), a simple iterative approach that, at each step, applies a set of alternative network morphisms to the current network, trains the resulting child networks with short optimization runs of cosine annealing (Loshchilov & Hutter, 2017), and moves to the most promising child network. NASH finds and trains competitive architectures at a computational cost of the same order of magnitude as training a single network; e.g., on CIFAR-10, NASH finds and trains CNNs with an error rate below $6 \\%$ in roughly 12 hours on ",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "a single GPU. After one day the error is reduced to almost $5 \\%$ . Models from different stages of our algorithm can be combined to achieve an error of $4 . 7 \\%$ within two days on a single GPU. On CIFAR-100, we achieve an error below $24 \\%$ in one day and get close to $20 \\%$ after two days. ",
+        "bbox": [
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+        "page_idx": 1
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+    {
+        "type": "text",
+        "text": "• Our method is easy to use and easy to extend, so it hopefully can serve as a basis for future work. ",
+        "bbox": [
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+        "page_idx": 1
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+    {
+        "type": "text",
+        "text": "We first discuss related work in Section 2. Then, we formalize the concept of network morphisms in Section 3 and propose our architecture search methods based on them in Section 4. We evaluate our methods in Section 5 and conclude in Section 6. ",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "2 RELATED WORK ",
+        "text_level": 1,
+        "bbox": [
+            176,
+            267,
+            341,
+            282
+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "Hyperparameter optimization. Neural networks are known to be quite sensitive to the setting of various hyperparameters, such as learning rates and regularization constants. There exists a long line of research on automated methods for setting these hyperparameters, including, e.g., random search (Bergstra & Bengio, 2012), Bayesian optimization (Bergstra et al., 2011; Snoek et al., 2012), bandit-based approaches (Li et al., 2016a), and evolutionary strategies (Loshchilov & Hutter, 2016). ",
+        "bbox": [
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+        "page_idx": 1
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+    {
+        "type": "text",
+        "text": "Automated architecture search. In recent years, the research focus has shifted from optimizing hyperparameters to optimizing architectures. While architectural choices can be treated as categorical hyperparameters and be optimized with standard hyperparameter optimization methods (Bergstra et al., 2011; Mendoza et al., 2016), the current focus is on the development of special techniques for architectural optimization. One very popular approach is to train a reinforcement learning agent with the objective of designing well-performing convolutional neural networks (Baker et al., 2016; Zoph & Le, 2017; Cai et al., 2017). Baker et al. (2016) train an RL agent to sequentially choose the type of layers (convolution, pooling, fully connected) and their parameters. Zoph & Le (2017) use a recurrent neural network controller to sequentially generate a string representing the network architecture. Both approaches train their generated networks from scratch and evaluate their performance on a validation set, which represents a very costly step. In a follow-up work (Zoph et al., 2017), the RL agent learned to build cells, which are then used as building blocks for a neural network with a fixed global structure. Unfortunately, training an RL agent with the objective of designing architecture is extremely expensive: both Baker et al. (2016) and Zoph & Le (2017) required over 10.000 fully trained networks, requiring hundreds to thousands of GPU days. To overcome this drawback, Cai et al. (2017) proposed to apply the concept of network transformations/morphisms within RL. As in our (independent, parallel) work, the basic idea is to use the these transformation to generate new pre-trained architectures to avoid the large cost of training all networks from scratch. Compared to this work, our approach is much simpler and 15 times faster while obtaining better performance. ",
+        "bbox": [
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+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "Real et al. (2017) and Suganuma et al. (2017) utilized evolutionary algorithms to iteratively generate powerful networks from a small network. Operations like inserting a layer, modifying the parameters of a layer or adding skip connections serve as ”mutations” in their framework of evolution. Whereas Real et al. (2017) also used enormous computational resources (250 GPUs, 10 days), Suganuma et al. (2017) were restricted to relatively small networks due to handling a population of networks. In contrast to the previous methods where network capacity increases over time, Saxena & Verbeek (2016) start with training a large network (a ”convolution neural fabric”) and prune this in the end. Very recently, Brock et al. (2017) used hypernetworks (Ha et al., 2017) to generate the weights for a randomly sampled network architecture with the goal of eliminating the costly process of training a vast amount of networks. ",
+        "bbox": [
+            174,
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+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "Network morphism/ transformation. Network transformations were (to our knowledge) first introduced by Chen et al. (2015) in the context of transfer learning. The authors described a function preserving operation to make a network deeper (dubbed ”Net2Deeper”) or wider (”Net2Wider”) with the goal of speeding up training and exploring network architectures. Wei et al. (2016) proposed additional operations, e.g., for handling non-idempotent activation functions or altering the kernel size and introduced the term network morphism. As mentioned above, Cai et al. (2017) used network morphisms for architecture search, though they just employ the Net2Deeper and Net2Wider operators from Chen et al. (2015) as well as altering the kernel size, i.e., they limit their search space to simple architectures without, e.g., skip connections. ",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "3 NETWORK MORPHISM ",
+        "text_level": 1,
+        "bbox": [
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+        "page_idx": 2
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+    {
+        "type": "text",
+        "text": "Let $\\mathcal { N } ( \\mathcal { X } )$ denote a set of neural networks defined on $\\mathcal { X } \\subset \\mathbb { R } ^ { n }$ . A network morphism is a mapping $M : \\dot { \\mathcal { N } } ( \\dot { \\mathcal { X } } ) \\times \\mathbb { R } ^ { k }  \\mathcal { N } ( \\underline { { \\mathcal { X } } } ) \\times \\mathbb { R } ^ { j }$ from a neural network $f ^ { w } \\in \\mathcal { N } ( \\mathcal { X } )$ with parameters $w \\in \\mathbb { R } ^ { k }$ to another neural network $g ^ { \\tilde { w } } \\in \\mathcal { N } ( \\mathcal { X } )$ with parameters $\\tilde { w } \\in \\mathbb { R } ^ { j }$ so that ",
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "equation",
+        "img_path": "images/01da69f32520eccbef16ce0ecf9fbbcf2637c41fb3974f8b8230761a9c0e4b45.jpg",
+        "text": "$$\nf ^ { w } ( x ) = g ^ { \\tilde { w } } ( x ) \\mathrm { f o r e v e r y } x \\in \\mathcal { X } .\n$$",
+        "text_format": "latex",
+        "bbox": [
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+        "page_idx": 2
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+    {
+        "type": "text",
+        "text": "In the following we give a few examples of network morphisms and how standard operations for building neural networks (e.g., adding a convolutional layer) can be expressed as a network morphism. For this, let $f _ { i } ^ { w _ { i } } ( x )$ be some part of a NN $f ^ { w } ( x )$ , e.g., a layer or a subnetwork. ",
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "Network morphism Type I. We replace $f _ { i } ^ { w _ { i } }$ by ",
+        "bbox": [
+            174,
+            253,
+            491,
+            268
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "equation",
+        "img_path": "images/739fb4573c092613f8d0559923d6bb3981e5fbbefbec26a727c76f98d046b2eb.jpg",
+        "text": "$$\n\\tilde { f } _ { i } ^ { \\tilde { w } _ { i } } ( x ) = A f _ { i } ^ { w _ { i } } ( x ) + b ,\n$$",
+        "text_format": "latex",
+        "bbox": [
+            416,
+            271,
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+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "with $\\tilde { w } _ { i } = ( w _ { i } , A , b ) ^ { 1 }$ . Equation (1) obviously holds for $A = \\mathbf { 1 } , b = \\mathbf { 0 }$ . This morphism can be used to add a fully-connected or convolutional layer, as these layers are simply linear mappings. Chen et al. (2015) dubbed this morphism ”Net2DeeperNet”. Alternatively to the above replacement, one could also choose ",
+        "bbox": [
+            173,
+            292,
+            825,
+            347
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "equation",
+        "img_path": "images/7999d9061602778300a91a1b4c09054ac86a6cafaa7aa40fb422aa6a160d5ca7.jpg",
+        "text": "$$\n\\tilde { f } _ { i } ^ { \\tilde { w } _ { i } } ( x ) = C ( A f _ { i } ^ { w _ { i } } ( x ) + b ) + d ,\n$$",
+        "text_format": "latex",
+        "bbox": [
+            390,
+            345,
+            606,
+            366
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "with $\\tilde { w } _ { i } = ( w _ { i } , C , d )$ . $A , b$ are fixed, non-learnable. In this case network morphism Equation (1) holds if $C = A ^ { - 1 } , d = - C b$ . A Batch Normalization layer (or other normalization layers) can be written in the above form: $A , b$ represent the batch statistics and $C , d$ the learnable scaling and shifting. ",
+        "bbox": [
+            173,
+            372,
+            825,
+            429
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "Network morphism Type II. Assume $f _ { i } ^ { w _ { i } }$ has the form $f _ { i } ^ { w _ { i } } ( x ) = A h ^ { w _ { h } } ( x ) + b$ for an arbitrary function $h$ . We replace $f _ { i } ^ { w _ { i } }$ , $w _ { i } = ( w _ { h } , \\dot { A } , b )$ , by ",
+        "bbox": [
+            173,
+            434,
+            820,
+            464
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "equation",
+        "img_path": "images/f4578e30ebce96eb214241b79c83d5935f0306cd6cc67ef9b418c714979d56e3.jpg",
+        "text": "$$\n\\tilde { f } _ { i } ^ { \\tilde { w } _ { i } } ( x ) = \\left( A \\quad \\tilde { A } \\right) \\binom { h ^ { w _ { h } } ( x ) } { \\tilde { h } ^ { w _ { h } } ( x ) } + b\n$$",
+        "text_format": "latex",
+        "bbox": [
+            382,
+            465,
+            616,
+            501
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "with an arbitrary function $\\tilde { h } ^ { w _ { \\tilde { h } } } ( x )$ . The new parameters are $\\tilde { w } _ { i } = ( w _ { i } , w _ { \\tilde { h } } , \\tilde { A } )$ . Again, Equation (1) can trivially be satisfied by setting $\\tilde { A } = 0$ . We think of two modifications of a NN which can be expressed by this morphism. Firstly, a layer can be widened (i.e., increasing the number of units in a fully connected layer or the number of channels in a CNN - the Net2WiderNet transformation from Chen et al. (2015)). Think of $h ( x )$ as the layer to be widened. For example, we can then set $\\tilde { h } = h$ to simply double the width. Secondly, skip-connections by concatenation as used by Huang et al. (2016) can be formulated as a network morphism. If $h ( x )$ itself is a sequence of layers, $h ( x ) = h _ { n } ( x ) \\circ \\cdots \\circ h _ { 0 } ( x )$ , then one could choose $\\tilde { h } ( x ) = x$ to realize a skip from $h _ { 0 }$ to the layer subsequent to $h _ { n }$ . ",
+        "bbox": [
+            173,
+            503,
+            825,
+            638
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "Network morphism Type III. By definition, every idempotent function $f _ { i } ^ { w _ { i } }$ can simply be replaced by ",
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+    {
+        "type": "equation",
+        "img_path": "images/eacf17365fe1bb32a28659b1c5a881dee0fdc9ac4b0b594b9ccefe3e1423f078.jpg",
+        "text": "$$\nf _ { i } ^ { ( w _ { i } , \\tilde { w } _ { i } ) } = f _ { i } ^ { \\tilde { w } _ { i } } \\circ f _ { i } ^ { w _ { i } }\n$$",
+        "text_format": "latex",
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+        "page_idx": 2
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+    {
+        "type": "text",
+        "text": "with the initialization $\\tilde { w } _ { i } = w _ { i }$ . This trivially also holds for idempotent function without weights, e.g., Relu. ",
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+        "type": "text",
+        "text": "Network morphism Type IV. Every layer $f _ { i } ^ { w _ { i } }$ is replaceable by ",
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+    {
+        "type": "equation",
+        "img_path": "images/fd47040a01a63f7e977805f8e17a1b0019034a8e830d36d15a69e1bb6c4d3d41.jpg",
+        "text": "$$\n\\tilde { f } _ { i } ^ { \\tilde { w } _ { i } } ( x ) = \\lambda f _ { i } ^ { w _ { i } } ( x ) + ( 1 - \\lambda ) h ^ { w _ { h } } ( x ) , \\quad \\tilde { w } _ { i } = ( w _ { i } , \\lambda , w _ { h } )\n$$",
+        "text_format": "latex",
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+    {
+        "type": "text",
+        "text": "with an arbitrary function $h$ and Equation (1) holds if $\\lambda$ is initialized as 1. This morphism can be used to incorporate any function, especially any non-linearities. For example, Wei et al. (2016) use a special case of this operator to deal with non-linear, non-idempotent activation functions. Another example wou(2016) to sim insertioing: If $f _ { i } ^ { w _ { i } }$ f an additiv itself is a s p connection,nce of layers, $f _ { i } ^ { w _ { i } } = f _ { i _ { n } } ^ { w _ { i _ { n } } } \\circ \\cdot \\cdot \\cdot \\circ f _ { i _ { 0 } } ^ { w _ { i _ { 0 } } }$ He et al., then one $h ( x ) = x$ to realize a skip from $f _ { i _ { 0 } } ^ { w _ { i _ { 0 } } }$ to the layer subsequent to $f _ { i _ { n } } ^ { w _ { i _ { n } } }$ ",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "Note that every combinations of the network morphisms again yields a morphism. So one could for example insert a block ”Conv-BatchNorm-Relu” subsequent to a Relu layer by using equations (2), (3) and (5). ",
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+        "img_path": "images/f8ca3cbd2a4cdfcdcf35ac65c139d715df875d1be2779a18db0872654bca035b.jpg",
+        "image_caption": [
+            "Figure 1: Visualization of our method. Based on the current best model, new models are generated and trained afterwards. The best model is than updated. "
+        ],
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+    {
+        "type": "text",
+        "text": "4 ARCHITECTURE SEARCH BY NETWORK MORPHISMS ",
+        "text_level": 1,
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+        "type": "text",
+        "text": "Our proposed algorithm is a simple hill climbing strategy (Russell & Norvig, 2009). We start with a small, (possibly) pretrained network. Then, we apply network morphisms to this initial network to generate larger ones that may perform better when trained further. These new “child” networks can be seen as neighbors of the initial “parent” network in the space of network architectures. Due to the network morphism Equation (1), the child networks start at the same performance as their parent. In essence, network morphisms can thus be seen as a way to initialize child networks to perform well, avoiding the expensive step of training them from scratch and thereby reducing the cost of their evaluation. The various child networks can then be trained further for a brief period of time to exploit the additional capacity obtained by the network morphism, and the search can move on to the best resulting child network. This constitutes one step of our proposed algorithm, which we dub Neural Architecture Search by Hill-climbing (NASH). NASH can execute this step several times until performance on a validation set saturates; we note that this greedy process may in principle get stuck in a poorly-performing region, from which it can never escape, but we did not find evidence for this in our experiments. ",
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+        "text": "Figure 1 visualizes one step of the NASH approach, and Algorithm 1 provides full details for the algorithm. In our implementation, the function $A p p l y N e t M o r p h ( m o d e l , n )$ (line 15) applies $n$ network morphisms, each of them sampled uniformly at random from the following three: ",
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+        "type": "text",
+        "text": "• Make the network deeper, i.e., add a ”Conv-BatchNorm-Relu” block as described at the end of Section 3. The position where to add the block, as well as the kernel size $( \\in \\{ 3 , 5 \\} )$ , are uniformly sampled. The number of channels is chosen to be equal to he number of channels of the closest preceding convolution.   \n• Make the network wider, i.e., increase the number of channels by using the network morphism type II. The conv layer to be widened, as well as the widening factor $( \\in \\{ 2 , 4 \\} )$ are sampled uniformly at random.   \n• Add a skip connection from layer i to layer j (either by concatenation or addition – uniformly sampled) by using network morphism type II or IV, respectively. Layers i and j are also sampled uniformly. ",
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+    {
+        "type": "text",
+        "text": "Note that the current best model is also considered as a child, i.e. our algorithm is not forced to select a new model but can rather also keep the old one if no other one improves upon it. ",
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+    {
+        "type": "text",
+        "text": "Algorithm 1 Network architecture search by hill climbing ",
+        "text_level": 1,
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+    {
+        "type": "text",
+        "text": "$1 \\backslash \\mathrm { ~ f u n c t i o n ~ N A S H } ( m o d e l _ { 0 } , n _ { s t e p s } , n _ { n e i g h } , n _ { N M } , e p o c h _ { n e i g h } , e p o c h _ { f i n a l } , \\lambda _ { e n d } , \\lambda _ { s t a r t } )$   \n2:   \n3: # $m o d e l _ { 0 }$ , model to start with, $n _ { s t e p s } \\triangleq$ number of hill climbining steps   \n4: # $n _ { n e i g h } \\triangleq$ number of neighbours, $n _ { N M } \\triangleq$ number of net. morph. applied   \n5: # $e p o c h _ { n e i g h } \\triangleq$ number of epochs for training every neighbour   \n6: # $e p o c h _ { f i n a l } \\triangleq$ number of epochs for final training   \n7: # initial LR $\\lambda _ { s t a r t }$ is annealed to $\\lambda _ { e n d }$ during SGDR training   \n8:   \n9: $m o d e l _ { b e s t }  m o d e l _ { 0 }$   \n10: # start hill climbing   \n11: for $i \\gets 1 , \\dots , n _ { s t e p s } \\ { \\bf d }$ o   \n12: #get $n _ { n e i g h }$ neighbors of $m o d e l _ { 0 }$ by applying $n _ { N M }$ network morphisms to $m o d e l _ { b e s t }$   \n13: for $j \\gets 1 , \\dots , n _ { n e i g h } - 1$ do   \n14: $m o d e l _ { j } \\gets A p p l y N e t M o r p h s ( m o d e l _ { b e s t } , n _ { N M } )$   \n15: # train for a few epochs on training set with SGDR   \n16: $m o d e l _ { j } \\gets \\mathrm { S G D R t r a i n } ( m o d e l _ { j } , e \\bar { p } o c h _ { n e i g h } , \\lambda _ { s t a r t } , \\lambda _ { e n d } )$   \n17: end for   \n18: # in fact, last neighbor is always just the current best   \n19: $m o d e l _ { n _ { n e i g h } } \\gets \\mathrm { S G D R t r a i n } ( m o d e l _ { b e s t } , e p o c h _ { n e i g h } , \\lambda _ { s t a r t } , \\lambda _ { e n d } )$   \n20: # get best model on validation set   \n21: $\\underbrace { \\Bre { \\_ } { a } } { m o d } e l _ { b e s t }  \\underbrace { a r g m a x } _ { j = 1 , \\dots , n _ { n e i g h } } \\{ p e r f o r m a n c e _ { v a l i } ( m o d e l _ { j } ) \\}$   \n22: end for   \n23: # train the final model on training and validation set   \n24: $m o d e l _ { b e s t } \\gets \\mathrm { S G D R t r a i n } ( m o d e \\bar { l } _ { b e s t } , e p o c h _ { f i n a l } , \\lambda _ { s t a r t } , \\lambda _ { e n d } )$   \n25: return modelbest   \n26: end function ",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "It is important for our method that child networks only need to be trained for a few epochs2 (line 17). Hence, an optimization algorithm with good anytime performance is required. Therefore, we chose the cosine annealing strategy from Loshchilov & Hutter (2017), whereas the learning rate is implicitly restarted: the training in line 17 always starts with a learning rate $\\lambda _ { s t a r t }$ which is annealed to $\\lambda _ { e n d }$ after epochneigh epochs. We use the same learning rate scheduler in the final training (aside from a different number of epochs). ",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "While we presented our method as a simple hill-climbing method, we note that it can also be interpreted as a very simple evolutionary algorithm with a population size of $n _ { n e i g h }$ , no cross-over, network morphisms as mutations, and a selection mechanism that only considers the best-performing population member as the parent for the next generation. This interpretation also suggests several promising possibilities for extending our simple method. ",
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+    {
+        "type": "text",
+        "text": "5 EXPERIMENTS ",
+        "text_level": 1,
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+    {
+        "type": "text",
+        "text": "We evaluate our method on CIFAR-10 and CIFAR-100. First, we investigate whether our considerations from the previous chapter coincide with empirical results. We also check if the interplay of modifying and training networks harms their eventual performance. Finally, we compare our proposed method with other automated architecture algorithms as well as hand crafted architectures. ",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "We use the same standard data augmentation scheme for both CIFAR datasets used by Loshchilov & Hutter (2017) in all of the following experiments. The training set (50.000 samples) is split up in training (40.000) and validation (10.000) set for the purpose of architecture search. Eventually the performance is evaluated on the test set. All experiments where run on Nvidia Titan X (Maxwell) ",
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+    {
+        "type": "text",
+        "text": "GPUs, with code implemented in Keras (Chollet et al., 2015) with a TensorFlow (Abadi et al., 2015) backend. ",
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+    {
+        "type": "text",
+        "text": "5.1 EXPERIMENTS ON CIFAR-10 ",
+        "text_level": 1,
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+    {
+        "type": "text",
+        "text": "5.1.1 BASELINES",
+        "text_level": 1,
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "Before comparing our method to others, we run some baseline experiments to see whether our considerations from the previous chapter coincide with empirical data. ",
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+    {
+        "type": "text",
+        "text": "Random model selection. First, we investigate if the simple hill climbing strategy is able to distinguish between models with high and low performance. For this, we set $n _ { n e i g h } = 1$ , i.e., there is no model selction - we simply construct random networks and train them. We then run experiments with $n _ { n e i g h } = 8$ and compare both results. All other parameters are the same in this experiment, namely $n _ { s t e p s } = 5 , n _ { N M } = 5 , e p o c h _ { n e i g h } = 1 7 , e p o c h _ { f i n a l } = 1 0 0$ . We choose $\\lambda _ { s t a r t } = 0 . 0 5$ , $\\lambda _ { e n d } = 0 . { \\overset { \\cdot } { 0 } }$ as done in Loshchilov & Hutter (2017). model0 was a simple conv net: Conv-MaxPool-Conv-MaxPool-Conv-FC-Softmax3, which is pretrained for 20 epochs, achieving $\\approx 7 5 \\%$ validation accuracy (up to $9 1 \\%$ when trained till convergence), see Figure 5 in the appendix. If our algorithm is able to identify better networks, one would expect to get better results with the setting $n _ { n e i g h } = 8$ . ",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "Retraining from scratch. In the this experiment we investigate whether the ”weight inheritance” due to the network morphisms used in our algorithm harms the final performance of the final model. This weight inheritance can be seen as a strong prior on the weights and one could suspect that the new, larger model may not be able to overcome a possibly poor prior. Additionally we were interested in measuring the overhead of the architecture search process, so we compared the times for generating and training a model with the time needed when training the final model from scratch. The retraining from scratch is done for the same number of epochs as the total number of epochs spent to train the model returned by our algorithm4 . ",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "No SGDR. We now turn off the cosine annealing with restarts (SGDR) during the hill climbing stage, i.e., the training in line 17 of Algorithm 1 is done with a constant learning rate. We tried $\\lambda \\in \\{ 0 . 0 1 , 0 . 0 2 5 , 0 . 0 5 \\}$ , 10 runs each and averaged the results. Note that we still use the cosine decay for the final training. ",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "No network morphism. Lastly, we turn off the network morphism constraint for initializing the neighbor networks. In detail, we proceeded as Real et al. (2017): All weights from layer where now changes occur are inherited, whereas the weights of new/modified layers are initialized by random. ",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "The results for these experiments are summarized in Table 1 . The hill climbing strategy is actually able to identify better performing models. (first and second line: $5 . 7 \\%$ vs. $6 . 5 \\%$ ). Notice how hill climbing prefers larger models (5.7 million parameters on average vs. 4.4 million). Performance slightly decreases when the models are retrained from scratch (line 3). This experiments indicates that our algorithm does not harm the final performance of a model. Regarding the runtime, the overhead for first having to search for the architecture is roughly a factor 3. We think this is a big advantage of our method and shows that architecture search can be done in the same order of magnitude as training a single model. In line 4 we can see that SGDR plays an important role. The resulting models chosen by our algorithm when training is done with a constant learning rate perform similarly to the models without any model selection strategy $( 6 . 4 \\%$ and $6 . 5 \\%$ , respectively), which indicates that the performance after a few epochs on the validation set when trained without SGDR correlates less with the final performance on the test set as it is the case for training with SGDR. Indeed, we computed the Pearson correlation coefficient and obtained $R ^ { 2 } = 0 . 6 4$ for training with SGDR and and $\\mathrm { \\bar { \\it R } ^ { 2 } = 0 . 3 6 }$ for training with a constant learning rate. See appendix A. Also, with the constant learning rate, the few epochs spent are not sufficient to improve the performance of the model. Figure 2 shows the progress while running our algorithm with and without SGDR, averaged over all runs. When turning off the network morphism constraint, performance also decreases. ",
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+    {
+        "type": "image",
+        "img_path": "images/5bffa50e24c866e7a85ea7102470da8aa121189925b47b5e0807ef32b1fb1234.jpg",
+        "image_caption": [
+            "Figure 2: The best model found by Algorithm 1 tracked over time (in terms of hill climbing iterations). With (red) and without (blue) using SGDR for the training within the hill climbing (line 17). Final training (line 24) is not plotted. Dashed line denotes mean, shaded area $\\pm 2 \\sigma$ intervalls. "
+        ],
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+        "bbox": [
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+    {
+        "type": "table",
+        "img_path": "images/399c4ad8f3e36610cb71bf824ac3a3e315a7c2b733f1dcf09b58c5f4d7dfd8a5.jpg",
+        "table_caption": [
+            "Table 1: Baseline experiments. Runtime, # params, and error rates are averaged over 10 runs (for $n _ { n e i g h } = 8 $ ) and 30 runs $( n _ { n e i g h } = 1 )$ ) runs, respectively. $n _ { s t e p s } = 5$ in all experiments. "
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>algorithm setting</td><td>runtime (hrs)</td><td># params (mil.)</td><td>error ± std.( %)</td></tr><tr><td>nneigh =8</td><td>12.8</td><td>5.7</td><td>5.7 ± 0.35</td></tr><tr><td>Random networks (nneigh = 1)</td><td>4.5</td><td>4.4</td><td>6.5 ± 0.76</td></tr><tr><td>models from line 1 retrained from scratch</td><td>5.3</td><td>5.7</td><td>6.1 ± 0.92</td></tr><tr><td>nneigh = 8, no SGDR</td><td>10.6</td><td>5.8</td><td>6.4±0.70</td></tr><tr><td>nneigh = 8, no net. morph.</td><td>6.6</td><td>2.9</td><td>6.1 ±0.30</td></tr></table>",
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+    {
+        "type": "text",
+        "text": "Interestingly the number of parameters heavily decreases. This indicates that our algorithm prefers models without new parameters. ",
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+    {
+        "type": "text",
+        "text": "5.1.2 COMPARISON TO HAND CRAFTED AND OTHER AUTOMATICALLY GENERATED ARCHITECTURES ",
+        "text_level": 1,
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+    {
+        "type": "text",
+        "text": "We now compare our algorithm against the popular wide residual networks (Zagoruyko & Komodakis, 2016), the state of the art model from Gastaldi (2017) as well as other automated architecture search methods. Beside our results for $n _ { s t e p s } = 5$ from the previous section, we also tried $n _ { s t e p s } = 8$ to generate larger models. ",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "For further improving the results, we take snapshots of the best models from every iteration while running our algorithm following the idea of Huang et al. (2017) when using SGDR (Loshchilov & Hutter, 2017) for training. However different from Huang et al. (2017), we do not immediately get fully trained models for free, as our snapshots are not yet trained on the validation set but rather only on the training set. Hence we spent some additional resources and train the snapshots on both sets. Afterwards the ensemble model is build by combining the snapshot models with uniform weights. Lastly, we also build an ensemble from the models returned by our algorithm across all runs. Results are listed in Table 2. ",
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+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "The proposed method is able to generate competitive network architectures in only 12 hours. By spending another 12 hours, it outperforms most automated architecture search methods although all of them require (partially far) more time and GPUs. We do not reach the performance of the two handcrafted architectures as well as the ones found by Zoph & Le (2017) and Brock et al. (2017). However note that Zoph & Le (2017) spent by far more resources than we did. ",
+        "bbox": [
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+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "Unsurprisingly, the ensemble models perform better. It is a simple and cheap way to improve results which everyone can consider when the number of parameters is not relevant. ",
+        "bbox": [
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+        "page_idx": 6
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+    {
+        "type": "table",
+        "img_path": "images/40ffbbc485084b4e3fbd3f84be67a619447ee95d3fffcf9f34d4d00c8ce93c36.jpg",
+        "table_caption": [
+            "Table 2: Results for CIFAR-10. For our methods the stated resources, # parameters and errors are averaged over all runs. ”Resources spent” denotes training costs in case of the handcrafted models. "
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>model</td><td>resources spent</td><td># params (mil.)</td><td>error(%)</td></tr><tr><td></td><td></td><td></td><td></td></tr><tr><td>Shake-Shake (Gastaldi,2017)</td><td>4 GPU days,2 GPUs</td><td>26</td><td>2.9</td></tr><tr><td>WRN 28-10 (Loshchilov &amp; Hutter,2017)</td><td>1 GPU day</td><td>36.5</td><td>3.86</td></tr><tr><td>Baker et al. (2016)</td><td>80-100 GPU days</td><td>11</td><td>6.9</td></tr><tr><td>Cai et al. (2017)</td><td>15 GPU days</td><td>19.7</td><td>5.7</td></tr><tr><td>Zoph &amp; Le (2017)</td><td>16.000-24.000 GPU days</td><td>37.5</td><td>3.65</td></tr><tr><td>Real et al. (2017)</td><td>2500 GPU days</td><td>5.4</td><td>5.4</td></tr><tr><td>Saxena &amp; Verbeek (2016)</td><td>？</td><td>21</td><td>7.4</td></tr><tr><td>Brock et al. (2017)</td><td>3 GPU days</td><td>16.0</td><td>4.0</td></tr><tr><td>Ours (random networks,nsteps = 5, nneigh =1)</td><td>0.2 GPU days</td><td>4.4</td><td>6.5</td></tr><tr><td>Ours (nsteps = 5,nneigh =8,10 runs)</td><td>0.5 GPU days</td><td>5.7</td><td>5.7</td></tr><tr><td>Ours (nsteps = 8,nneigh = 8,4 runs)</td><td>1 GPU day</td><td>19.7</td><td>5.2</td></tr><tr><td>Ours (snapshot ensemble,4 runs)</td><td>2 GPU days</td><td>57.8</td><td>4.7</td></tr><tr><td>Ours (ensemble across runs)</td><td>4 GPU days</td><td>88</td><td>4.4</td></tr></table>",
+        "bbox": [
+            173,
+            155,
+            825,
+            343
+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "table",
+        "img_path": "images/4a47d8eceb003bb23f38bfb4ad16df746a77c1f78312b59d11e2951c2db318cd.jpg",
+        "table_caption": [
+            "Table 3: Results for CIFAR-100. For our methods the stated resources, # parameters and errors are averaged over all runs. ”Resources spent” denotes training costs in case of the handcrafted models. "
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>model</td><td>resources spent</td><td># params (mil.)</td><td>error(%)</td></tr><tr><td></td><td></td><td></td><td>15.9</td></tr><tr><td>Shake-Shake (Gastaldi, 2017) WRN 28-10 (Loshchilov &amp; Hutter,2017)</td><td>14 GPU days</td><td>34.4</td><td></td></tr><tr><td></td><td>1 GPU day</td><td>36.5</td><td>19.6</td></tr><tr><td>Real et al. (2017)</td><td>250 GPUs</td><td>40.4</td><td>23.7</td></tr><tr><td>Brock et al. (2017)</td><td>3 GPU days</td><td>16.0</td><td>20.6</td></tr><tr><td>Ours (nsteps = 8,nneigh = 8,5 runs)</td><td>1 GPU day</td><td>22.3</td><td>23.4</td></tr><tr><td>Ours (snapshot ensemble,5 runs)</td><td>2 GPU days</td><td>73.3</td><td>20.9</td></tr><tr><td>Ours (ensemble across runs)</td><td>5 GPU days</td><td>111.5</td><td>19.6</td></tr></table>",
+        "bbox": [
+            179,
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+            536
+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "5.2 EXPERIMENTS ON CIFAR-100 ",
+        "text_level": 1,
+        "bbox": [
+            176,
+            566,
+            428,
+            582
+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "We repeat the previous experiment on CIFAR-100; hyperparameters were not changed. The results are listed in Table 3. Unfortunately most automated architecture methods did not consider CIFAR100. Our method is on a par with Real et al. (2017) after one day with a single GPU. The snapshot ensemble performs similar to Brock et al. (2017) and an ensemble model build from the 5 runs can compete with the hand crafted WRN 28-10. The performance of the Shake-Shake network (Gastaldi, 2017) is again not reached. ",
+        "bbox": [
+            173,
+            593,
+            825,
+            676
+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "6 CONCLUSION ",
+        "text_level": 1,
+        "bbox": [
+            176,
+            696,
+            318,
+            713
+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "We proposed NASH, a simple and fast method for automated architecture search based on a hill climbing strategy, network morphisms, and training via SGDR. Experiments on CIFAR-10 and CIFAR-100 showed that our method yields competitive results while requiring considerably less computational resources than most alternative approaches. Our algorithm is easily extendable, e.g., by other network morphisms, evolutionary approaches for generating new models, other methods for cheap performance evaluation (such as, e.g., learning curve prediction (Klein et al., 2017) or hypernetworks (Ha et al., 2017; Brock et al., 2017)), or better resource handling strategies (such as Hyperband (Li et al., 2016b)). In this sense, we hope that our approach can serve as a basis for the development of more sophisticated methods that yield further improvements of performance. ",
+        "bbox": [
+            173,
+            728,
+            825,
+            854
+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
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+        "page_idx": 9
+    },
+    {
+        "type": "image",
+        "img_path": "images/2edbb1405729ce5dc046dc80f49bd9380081ebed874aa93e2d296d2395a7ddf0.jpg",
+        "image_caption": [
+            "Figure 3: Initial network for our algorithm. "
+        ],
+        "image_footnote": [],
+        "bbox": [
+            191,
+            155,
+            761,
+            391
+        ],
+        "page_idx": 10
+    },
+    {
+        "type": "image",
+        "img_path": "images/213925428f8eea0c7c284680e760c96a1baa86df2685b0480330288a33417347.jpg",
+        "image_caption": [
+            "Figure 4: Initial network for our algorithm. "
+        ],
+        "image_footnote": [],
+        "bbox": [
+            197,
+            469,
+            761,
+            707
+        ],
+        "page_idx": 10
+    },
+    {
+        "type": "image",
+        "img_path": "images/926480ca8e0fe0b1fac91e9b0c6c21dd16e70a4e522edfe39777971a2e331b4d.jpg",
+        "image_caption": [
+            "Figure 5: Initial network for our algorithm. "
+        ],
+        "image_footnote": [],
+        "bbox": [
+            410,
+            169,
+            581,
+            825
+        ],
+        "page_idx": 11
+    },
+    {
+        "type": "image",
+        "img_path": "images/091ad5bd88208c13ba32695bfc45a25363ea4c4e47109a8acba5e63354b8c3d1.jpg",
+        "image_caption": [
+            "Figure 6: Network generated by our algorithm with $n _ { s t e p s } = 5$ . "
+        ],
+        "image_footnote": [],
+        "bbox": [
+            406,
+            116,
+            586,
+            867
+        ],
+        "page_idx": 12
+    },
+    {
+        "type": "image",
+        "img_path": "images/e810d4abf64e5a83ec8d5f1149515b76d979a3c8fc66b0153106f09e2b3c3c2d.jpg",
+        "image_caption": [
+            "Figure 7: Network generated by our algorithm with $n _ { s t e p s } = 8$ . "
+        ],
+        "image_footnote": [],
+        "bbox": [
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+        "page_idx": 13
+    }
+]

parse/train/rkgZaT4tDr/rkgZaT4tDr.md

@@ -0,0 +1,257 @@
+# PARAMETERIZED ACTION REINFORCEMENT LEARNING FOR INVERTED INDEX MATCH PLAN GENERATION
+
+Anonymous authors Paper under double-blind review
+
+# ABSTRACT
+
+Match plan generation in the inverted index at Microsoft Bing is used to be based on hand-crafted rules. We formulate the generation process as a Parameterized Action MDP with sharing parameters and purpose a reinforcement learning algorithm on such formulation. We combine deterministic policy learning on discrete and continuous action spaces and several recent advances in deep reinforcement learning. For exploring in the parameterized action space, the agent outputs softmax values for discrete actions and applies Parameter Space Noise on policy network to unify the exploration direction in both spaces. We apply prioritized recurrent replay on match plan sequences and pad short match plans. We also use invertible value function rescaling and $n$ -step return to stabilize the training. The agent is evaluated on our environment and some benchmarks. It outperforms the well-designed production match plan and beats the baselines on the benchmarks.
+
+# 1 INTRODUCTION
+
+Using machine learning to optimize and accelerate software and hardware systems is an emerging field in the past few years (Mirhoseini et al. (2017); Rosset et al. (2018)). The process of decisionmaking in those systems is usually hand-crafted by human engineers, which is less explored to be automatically done by learning algorithms. A promising direction is to formulate such sequential decision-making problems as Reinforcement Learning (RL) problems, such as search plan generation problem in inverted indexes (Rosset et al. (2018)).
+
+The inverted index is a specialized data structure that is commonly used in search engines, including Microsoft $\mathrm { B i n g ^ { 1 } }$ . An inverted index provides an inverted mapping from term to documents. Each term has a posting list which contains all the (document, location) pairs that the term appears. By combining the posting lists of the terms in a user query, the initial document candidates are generated (Witten et al. (1999); Zobel & Moffat (2006)).
+
+In Bing, documents are scanned with specified match plans, either predefined or generated in realtime. A match plan has a sequence of rewrites (match rules, e.g., it treats the query as a phrase which should appear in the document exactly as it is), where each rewrite can be controlled by several quotas (stopping criteria). There are several types of rewrites, and all these types share the same continuous quotas. A pair of a rewrite type and the quotas forms a single action which determines if a document will be a ranking candidate.
+
+We formulate the generation problem as a RL problem. The state consists of system runtime signals and semantic embeddings of queries. The action space is called parameterized or discretecontinuous hybrid, where an action has a discrete action and continuous action-parameters. The reward is weighted by result quality and query latency. It is similar to Parameterized Action RL (Masson et al. (2016)) (PARL), while our setting requires all actions to share same parameters.
+
+Previously, the match plans are predefined manually for each query. It hardly utilizes the rich information in the state to dynamically adjust the rewrites and quotas for specific query online. Rosset et al. (2018) tries to automatically generate match plans using tabular Q-learning with discretized state space and predefined action-parameters. They learn the generation policy for a specific query class each time and solve it only in discretized spaces with tabular methods. We extend the generation process to the general case, such that the match plans are fully parameterized and learned from scratch without any predefined knowledge (e.g., limited match rules).
+
+![](images/7459112fc13a2ca51b6133f349d4373e932db4f4ab389ec3ae4eb649b28ac3c6.jpg)  
+Figure 1: Match plan example: for the query “Reinforcement Learning”, the search engine firstly gets a document posting list for each term from the inverted index, and then scans the document candidates following a serial of rewrites (match rules) according to the match plan.
+
+In this paper, we purpose a parameterized action RL algorithm that learns to act on parameterized action space environments, such as the match plan generation process. We introduce normalized softmax values of discrete actions to form a categorical distributions to enable gradients backpropagation. We also combine several recent advances in RL to accelerate and stabilize the training. We investigate parameter space noise (Plappert et al. (2017)) on parameters of the policy for unifying directions in exploring the structured action space. We explore recurrent deterministic policies (Heess et al. (2015)) with prioritized replay buffer (Schaul et al. (2015)) on sequence, due to the inherent nature of partial observability and sparse feedback in our setting. We also use $n$ -step return and invertible value function rescaling (Kapturowski et al. (2018)) for further stability.
+
+We present an agent to integrate these techniques and evaluate on offline training on a query dataset collected from Bing search. When training on the dataset with uniformly sampling, the agent outperforms the currently deployed production match plan, which is generated based on well-designed hand-crafted rules. We study the performance of training on the dataset or only with several selected complicated queries individually, as well as ablation studies for the various components. We test on a few existing PARL benchmarks, where our agent beats our baseline methods and performs the state-of-the-art results.
+
+# 2 BACKGROUND
+
+# 2.1 REINFORCEMENT LEARNING
+
+We address the problem using reinforcement learning (RL) framework with a parameterized action space. An agent interacts with an environment to maximize the accumulated reward with discount factor $\gamma \in \ [ 0 , 1 )$ . We model the environment with a discrete-time Partially Observable Markov Decision Process (POMDP). A POMDP is given by a tuple $( S , \mathcal { A } , T , R , \Omega , \dot { \mathcal { O } } )$ , and the underlying Markov Decision Process (MDP) is defined by $( S , { \mathcal { A } } , T , R )$ , where $s$ is the state space, $\mathcal { A }$ the parameterized action space, $T$ the transition function $\mathcal { T } : \mathcal { S } \times \mathcal { S } \times \mathcal { A }  \mathbb { R } _ { + }$ , and $R : S \times \mathcal { A }  \mathbb { R }$ is the reward function. The set of observations is given by $\Omega$ and the the observation function mapping underlying states to probability distributions over observations is given by $\mathcal { O }$ .
+
+Specifically, the environment in the match plan generation has a parameterized action space. In Masson et al. (2016); Bester et al. (2019), such formulation in fully observable settings is referred as Parameterized Action MDP (PAMDP), where the action space is denoted as
+
+$$
+\mathcal { A } = \bigcup _ { k \in \mathcal { A } _ { d } } \left\{ ( k , x _ { k } ) | x _ { k } \in \mathcal { X } _ { k } \right\} ,
+$$
+
+where each discrete action $a \in \mathcal { A } _ { d } = [ K ]$ has a corresponding continuous action-parameter space $\mathcal { X } _ { a }$ . However, our setting requires a slightly different formulation:
+
+$$
+\mathcal { A } = \{ ( k , x ) | k \in \mathcal { A } _ { d } , x \in \mathcal { X } \} = \mathcal { A } _ { d } \times \mathcal { X } ,
+$$
+
+where the discrete action space (rewrite) $\mathbf { \mathcal { A } } _ { d }$ share the action-parameter space $\mathcal { X }$ . Such formulation results in a disentangled action space between discrete and continuous actions which a class of parameterized action (P-DQN (Xiong et al. (2018)) and MP-DQN (Bester et al. (2019))) may not be trivially applicable to. Considering the notational simplicity in partially observable environment (POMDP), we do not explicitly denote it when there is no ambiguity in action settings.
+
+# 2.2 FORMULATION OF MATCH PLAN GENERATION
+
+In Rosset et al. (2018), the action-parameters are predefined for the match plan generation, where the action space is then a set of discrete rewrites (actions). We fully parameterize a match plan to allow the agent to generate any valid plans.
+
+State. At each time step, the agent receives a state with two parts. First part has selected run-time system signals from the inverted index system. Since the query is uniformly sampled in different episode, we include some statistical features and semantic embeddings of queries to allow the agent to identify different queries and then generate corresponding match plans. Such statistical features are used in the current production system, such as the length of a query. All signals and embeddings are normalized to a reasonable range around $[ - 1 , 1 ]$ based on empirical estimations.
+
+Action. The agent selects a parameterized action $a _ { t }$ including a rewrite id and its allocated quotas at each step. There are 29 types of rewrites in $\mathbf { \mathcal { A } } _ { d }$ and also a 5-dimensional quota parameter space $\mathcal { X }$ for each rewrite in int64 type. However, the range of each quota is empirically set to valid values and then normalized to $[ - 1 , 1 ]$ . All outputted quotas are effective for the current step.
+
+There is also a special action to note: stop (by agent). Normally, the environment will return a terminal signal, but it happens in extreme cases, such as low system resources. To allow a better balance of latency and performance, we allow the agent to choose stop or not as another type of discrete action, which is the same level as other 29 rewrites.
+
+Reward. We use two criterions in the design: latency and performance. For latency consideration, we use a signal Seek Count that is constant for a same query in different runs with same match plan, instead of executed time. We weight the Ranking Scores of top five returned documents as an indicator of performance with weights [0.4, 0.2, 0.2, 0.1, 0.1]. When there are less than five documents returned, the scores of missing documents are treated as a minimum possible ranking score. The final scalar reward is weighted by these two objectives to balance them. We do not use the division in Rosset et al. (2018), since the loss surfaces may become more non-convex for optimizing.
+
+We also have punishments (negative rewards) for some special cases. One is to assign a punishment when the agent selects to illegally stop at the first step or some unsupported rewrites (for some special queries). However, unsupported rewrites do not necessarily cause a terminal state, since the production system has same hand-crafted match plans for a class of queries, in which the unsupported rewrites are simply omitted.
+
+# 3 METHOD
+
+For generating match plans, we introduce a method that works on the aforementioned formulation with slightly different parameterized action space than standard PAMDPs in the literature. We start from the intuition with deterministic policy learning (Silver et al. (2014)) and how it relates to parameterized actions. PAMDP often refers to the formulation that each individual discrete action $k \in \mathcal { A } _ { d } = [ K ]$ has a corresponding continuous action-parameter space. Thus, there are $K$ continuous action-parameter spaces corresponding to $K$ discrete action (Xiong et al. (2018)). In our shared-parameter PAMDP, the Bellman equation incorporated both discrete action $k$ and continuous action-parameters $x$ is given by:
+
+$$
+\begin{array} { r } { Q \left( s , k , x \right) = \underset { r , s ^ { \prime } } { \mathbb { E } } \left[ r + \gamma \underset { k ^ { \prime } } { \operatorname* { m a x } } \ \underset { x ^ { \prime } \in \mathcal { X } } { \operatorname* { s u p } } Q \left( s ^ { \prime } , k ^ { \prime } , x ^ { \prime } \right) \vert s , k , x \right] . } \end{array}
+$$
+
+P-DQN (Xiong et al. (2018)) tackles PAMDP by incorporating multiple action-parameter policies $x _ { k } ( s ; \theta _ { x } ) : { \cal { S } }  { \mathcal { X } } _ { k }$ for each action $k$ and update them with $\begin{array} { r } { \operatorname* { m a x } _ { k ^ { \prime } } \operatorname* { s u p } _ { x _ { k ^ { \prime } } \in \mathcal { X } _ { k ^ { \prime } } } Q \left( s ^ { \prime } , k ^ { \prime } , x _ { k ^ { \prime } } \right) } \end{array}$ simultaneously. However, since all parameters $x$ are shared for actions $k$ in our case, we do not require multiple policies. The policy loss in P-DQN (Xiong et al. (2018)) given by
+
+$$
+L _ { x } \left( \theta _ { x } \right) = \underset { s \sim D } { \mathbb { E } } \left[ - \sum _ { k = 1 } ^ { K } Q \left( s , k , x _ { k } \left( s ; \theta _ { x } \right) ; \theta _ { Q } \right) \right]
+$$
+
+![](images/908f0f5be906ce40a46112737a183c610852cc851433f4f94d61674bb007f08e.jpg)  
+Figure 2: The diagram of the process.
+
+naturally degenerates to a single policy in next case, where the gradient $\nabla L _ { x } \left( \theta _ { x } \right)$ exactly is the deterministic policy gradient (DPG, Silver et al. (2014)). MP-DQN (Bester et al. (2019)) states a problem regarding to the erroneous gradients of Q-network $\nabla L _ { Q }$ in P-DQN caused by multiple action-parameter policies backpropagating gradients at the same time. However, it does not exist in such single network situation. This is a desired architecture since separating multiple actionparameter policies loses the knowledge that they share same potential meanings.
+
+Following this intuition, we directly parameterize the policy with two heads $\mu : \mathcal { S } \to \mathbb { R } ^ { K } \times \mathcal { X }$ with $\theta _ { \mu }$ $\mathrm { ~ ` ~ } _ { \mu } \mathrm { ~ a s : ~ } k _ { t } ^ { s o f t } , x _ { t } = a _ { t } ^ { s o f t } = \mu ( s _ { t } ; \theta _ { \mu } )$ , where $k _ { t } ^ { s o f t }$ and $a _ { t } ^ { s o f t }$ refers to action-parameters or actions with softmax values. One head outputs the sof tmax values for all discrete actions. For another head, it outputs normalized action-parameter values with hyperbolic tangent $( t a n h )$ activation after the continuous head. The environment will denormalize it to a valid range. This corresponds to the Squashing Gradients method for bounded-continuous action spaces in Hausknecht & Stone (2015).
+
+Exploration with Parameter Space Noise and action sampling. In DQN (Mnih et al. (2015)), the behavioral policy is given by $\epsilon$ -greedy strategy for exploration purpose, where an agent randomly selects a discrete action with probability $\epsilon < 1$ . In DDPG (Lillicrap et al. (2015)), although the policy learned is deterministic, to explore the action space, the behavioral policy needs to be different because of the off-policy nature. It uses action space noise such as uncorrelated Gaussian noise or correlated Ornstein-Uhlenbeck process (Lillicrap et al. (2015)).
+
+Directly combining such two exploration strategies is straightforward. However, it may induce a problem that the exploration in two action spaces $\mathcal { A } = \mathcal { A } _ { d } \times \mathcal { X }$ in different paces. For example, the match plan may need another rewrite with larger quotas in a step. However, if the exploration strategy is to use $\epsilon$ -greedy for a rewrite $k$ and Gaussian noise for its quotas $x$ , the agent may require more samples to discover the potential rewards (positive documents). We instead use parameter space noise (Plappert et al. (2017)) on parameterized action space to tackle such issue.
+
+We denote the discrete and continuous action heads as $( \pi _ { k } ^ { s o f t } ( s ) , \pi _ { x } ( s ) ) = \mu ( s ; \theta _ { \mu } ) .$ . To compute the distance $d ( \pi , \widetilde { \pi } ) = D _ { \mathrm { K L } } ( \pi \| \widetilde { \pi } )$ of non-perturbed and perturbed policies $\mu ( s ; \theta _ { \mu } ) , \widetilde { \mu } ( s ; \theta _ { \mu } )$ , we e e euse weighted sum of the distance of discrete and continuous actions. For the continuous actions $\widetilde { \pi } _ { x } ( s )$ , the distance is given by $\mathbb { E } _ { s } \left[ \left( \pi _ { x } ( s ) _ { i } - \widetilde { \pi } _ { x } ( s ) _ { i } \right) ^ { 2 } \right]$ to estimate KL-divergence empirically. For e ethe discrete actions, we use outputted softmax probabilities to compute The state and action pairs are sampled from a replay memory. The varianc $D _ { \mathrm { K L } } ( \pi _ { k } ^ { s o f t } ( s ) \Vert \widetilde { \pi } _ { k } ^ { s o f t } ( s ) )$ $\sigma$ after a policy update based on the distance and threhold $\delta$ (Plappert et al. (2017)). The policy and target networks with layer normalization (Ba et al. (2016)) are perturbed per episode.
+
+Prioritized replay and recurrent policies. We use recurrent architecture to obtain the underlying system state of the POMDP for both value and policy networks (Heess et al. (2015)). To avoid recurrent state staleness (Kapturowski et al. (2018)), we store and replay a sequence of $( s , k ^ { s o f t } , x , r )$ with softmax values into a replay memory. Since a match plan is usually short, we set a maximum length and pad shorter episodes with zero or randomly sampled states and actions.
+
+The sampling from a replay memory can be prioritized with a probability $p _ { i }$ proportional to TDerrors (Schaul et al. (2015)) to increase the sample efficiency in such structured action space. To prioritize the transitions with well-matched documents, we slightly modify the sampling strategy. With a half probability, the agent uses regular prioritization, otherwise partitions the memory to multiple bins and retrieve a transition (sequence) with max reward from each bin. Our strategy provides a more efficient and balanced exploration strategy of the evaluation.
+
+Policy update. In the update, we use clipped double $Q$ -learning and delayed policy update (Fujimoto et al. (2018)) to stabilizing the training. After the agent samples a batch of (sequences), it perturbs the target policy network and computes the perturbed actions for target policy smoothing. The parameter space noise variance $\sigma$ is then updated with the sampled states and actions.
+
+The policy is still deterministic since it is learned in off-policy and only the exploration involves stochasticity. The update is given by deterministic policy gradients theorem (Silver et al. (2014)):
+
+$$
+\nabla L _ { \mu } \left( \theta _ { \mu } \right) = \nabla _ { s \sim D } \left[ Q \left( s , \mu ( s ; \theta _ { \mu } ) ; \theta _ { Q } \right) \right] = \nabla \frac { 1 } { \left| D \right| } \sum _ { s \in D } Q \left( s , k ^ { s o f t } , x ; \theta _ { Q } \right) ,
+$$
+
+where $D$ is a replay memory. We found this policy architecture is similar to PA-DDPG (Hausknecht $\&$ Stone (2015)), while it does not including sof tmax activation for discrete actions and other advanced techniques. We also build upon other useful techniques such as invertible value function rescaling $h ( x ) = \mathrm { { s i g n } } ( x ) ( \sqrt { | x | } + 1 - 1 ) + \epsilon x$ (Kapturowski et al. (2018)):
+
+$$
+y = h \left( \sum _ { k = 0 } ^ { n - 1 } r _ { t + k } \gamma ^ { k } + \gamma ^ { n } h ^ { - 1 } \left( Q \left( s _ { t + n } , a ^ { \ast } ; \theta _ { Q } ^ { - } \right) \right) \right) ,
+$$
+
+where $a ^ { * } = ( \operatorname* { m a x } k _ { t } ^ { s o f t } , x _ { t } ) = ( k _ { t } , x _ { t } )$ is the greedy action, $y$ the target for updating Q-network, and $\theta _ { Q } ^ { - }$ denotes the target Q-network. The policy network outputs differentiable softmax values and is updated by the gradients backpropagated from the Q-network:
+
+$$
+\nabla L _ { Q } \left( \theta _ { Q } \right) = \nabla \mathbb { E } \left[ \frac { 1 } { 2 } \left( y - Q \left( s , k ^ { s o f t } , x ; \theta _ { Q } \right) \right) ^ { 2 } \right] ,
+$$
+
+where the expectation is took over samples from a memory.
+
+The pseudocode for the algorithm with more details can be found in the Appendix.
+
+# 4 EXPERIMENTS
+
+In this section, we apply the purposed agent on the inverted index match plan generation problem. We create a dataset which contains a set of queries and corresponding query embeddings. We perform various ablation study on how each component interacts and the benefits of them. We also test on other Paramterized Action RL benchmarking baselines.
+
+# 4.1 EXPERIMENT SETTINGS
+
+For match plan generation, we experiment on a dataset that has about 100,000 queries sampled from Bing search log. In the current production system, each query is classified to a predefined query classes online based on a set of rules which are related to statistical features of the query. Each query class has some hand-crafted rules which outputs a match plan for the classified query. We use each query’s production match plan as baseline. The match plan for each query is generated by the hand-crafted rules and does not change over each running. We only skip a few special queries that do not have embeddings or need additional operations beyond match plans.
+
+The generated match plan is evaluated by the delta values of both Ranking Score and Seek Count and overall reward. We provide learning curves of delta values of evaluation rewards. Note that the reward are not symmetrical around 0, since the ranking scores has a minimum value and is sparse since a few queries are hard to find good documents and will be assigned a very low score. It may significantly pull down the average rewards shown in the curves, thus we present histograms for fair comparison. For the benchmarks, we report the results on evaluation reward curves during tuning.
+
+# .2 MATCH PLAN GENERATION PERFORMANCE EVALUATION
+
+We first visualize the query embeddings in Figure 3 using UMAP (McInnes et al. (2018)) to demonstrate our learned models. We evaluate 6,000 queries and draw the colormap based on the difference between evaluation reward and production baseline reward. Although most queries perform similar to the well-designed production rules, there are some clusters of queries and some patterns exist. We notice that there is a main cluster at the center (about $( - 7 , - 1 ) )$ ) that gathers most queries on which our agent does not perform well. That cluster contains some random inputs from the users, which may have some typos. For the queries that the agent outperforms the baseline, we find they are quite scattered. We guess the reason is that the baseline with hand-crafted rules do not consider the embeddings, thus it is less affected by embeddings. This may suggest us to look for more informative embeddings of queries to better distinguish some clustered queries.
+
+![](images/1b912e4438fe0c4576fc52e07dd81917a7cf3148fcc9fac32a9a96a543cd4db8.jpg)  
+Figure 3: Visualization of query embeddings.
+
+![](images/5ea9b9c596510988cdcbdc7742ad1ba606263fb7aae0db82cd463ab8f11bfb27.jpg)  
+Figure 4: Different techniques.
+
+![](images/6f60df92f6ce68b3bc8a05d04a9fa957d6cb5bab0fe7d16ef5692b5aaa72f95a.jpg)  
+Figure 5: Delta Reward Distribution in Evaluation Phrase.
+
+In the plots shown in Figure 6, we visualize the distribution of delta rewards, ranking scores and seek count values comparing to the well-designed production rules. For most of the queries the agent learns promising match plan without any prior knowledge just based on the reward signals. There are also some hard queries to find a pattern that have poor reward (about $- 1 0 0 )$ and usually lies in the main cluster and around a few more small clusters. Other than some meaningless queries around the center, they also include some non-English queries, such as French and Chinese, which are possibly clustered around their centroid and are challenging to learn the policy for all of them.
+
+Reward design. We consider different weights to trade-off between the query latency from the input and the quality of the returned documents. The quality is evaluated by Ranking Scores of top five documents. We found that it is sparse since the good documents are hard to match. When we weight more on ranking score, the agent tends to stop the search early.
+
+We also investigate a few punishments and try to use less of them to avoid manual design. We found the agent learns some common patterns guided by the reward and punishments. It tries to avoid ”stop” at the first step because we set a huge punishment on such invalid stop. This punishment is necessary since it prevents the agent stops at first step for better value than trying more steps but get no documents matched. In other words, the agent is encouraged to explore different rewrites instead of using empty match plans. Without such punishment, the performance significantly drops since it is hard to explore good documents at first. We also punish the agent to avoid unsupported rewrites, since the production system uses designed rules for each class of the queries and simply omits a rewrite without any useful feedback. We test punishing repeated rewrites, however, it helps seek count (more efficient) but may harm ranking scores.
+
+Table 1: Improved Scores of Different Noise Compared to RNN Gaussian Noise. Ranking Score and Seek Count are scaled to match Overall $=$ RankingScore−SeekCount for easy comparison.   
+
+<table><tr><td></td><td>Overall</td><td>Ranking Score (Quality)</td><td>Seek Count (Efficiency)</td></tr><tr><td>OU Noise</td><td>+1.00</td><td>+1.20</td><td>-0.20</td></tr><tr><td>Param Noise</td><td>+1.69</td><td>+0.82</td><td>-0.87</td></tr></table>
+
+Table 2: Improved Scores of Different Model Compared to MLP   
+
+<table><tr><td></td><td>Overall</td><td>Ranking Score (Quality)</td><td>Seek Count (Efficiency)</td></tr><tr><td>MLP+Prioritized</td><td>+14.54</td><td>+8.56</td><td>-5.98</td></tr><tr><td>RNN+Prioritized</td><td>+32.63</td><td>+14.44</td><td>-18.19</td></tr><tr><td>RNN + Prioritized Sample</td><td>+32.67</td><td>+15.29</td><td>-17.38</td></tr></table>
+
+# 4.3 ABLATION STUDY
+
+We compare different exploration noise, including action space noise and parameter space noise. For the action space noise, the noise on discrete and continuous actions are applied separately. We test Gaussian and OrnsteinUhlenbeck noise on continuous actions, while the discrete actions only use $\epsilon$ -greedy. To keep the comparison fair, we also test $\epsilon$ -greedy strategy on continuous actions by uniformly sampling a point with probability $\epsilon$ . The parameter noise is directly applied on policy network $\widetilde \mu ( s ; \theta _ { \mu } )$ . We found the parameter space noise performs more stable than all types of action espace noise. The uniform sampling on both discrete and continous action with $\epsilon$ -greedy failed for sometimes, thus we did not include it in comparison. We give the relative improvement in Table 1 compared to RNN with Gaussian Noise. The results show that parameter space noise has best performance overall.
+
+The results in Figure 6(a) and Table 2 show that RNN got significantly better performance than MLP with or without parameterization on our environment. It indicates that the environment is highly non-Markov. We guess one obvious possibility is that the system signals of the state space cannot include all the information, while recurrent networks try to extract latent state from the history. Note that each episode will sample one query, thus the query embedding is constant for all steps in one episode. Another possible reason is that some rewrites may not be supported by special queries or have too small change for the state signals.
+
+We compare different parameterization methods on recurrent networks. The results are shown in Figure 4(b) and Table 2. We empirically found that our modified strategy using reward bin is more stable from the beginning. It is possible that the agent repeatedly replays not only good experience on matching documents, but also learns to avoid punishment we set, as we expect. In general prioritized replay, the sampling probability is just based on TD-error and may be biased to worse samples since value function may not update towards possible results.
+
+# 4.4 BENCHMARKING GAMES
+
+We experiment on Platform-v0 and Goal-v0 from Bester et al. (2019). Note that, in all these games, each discrete action has a separate continuous action-parameter space. Our algorithm is designed for shared action-parameters and does not utilize such prior, thus we do not compare with P-DQN-style algorithms. We apply n-step return since the episode in these games is much longer. We assume the environment is fully observable and do not use recurrent networks in comparison.
+
+Hyperparameters. We examine the games with different combinations of hyperparameters, since they are easy to parallize on each training nodes without the need to connect to an production environment emulator. With NNI, the learning rates for value and policy network are set to log-uniform in $[ 3 \times 1 0 ^ { - 4 } , 3 \times 1 0 ^ { - 3 } ]$ and $[ 1 \times 1 0 ^ { - 4 } , 1 \times \mathsf { \bar { 1 } 0 ^ { - 3 } } ]$ . The $\alpha$ in parameterized replay is set to log-uniform in [0.2, 1.0]. The action noise threshold $\delta$ in parameter space noise is set to log-uniform between [0.05, 0.8]. Tn soft parameter update, the $\tau$ is set to log-uniform in $[ 1 \times 1 0 ^ { - 3 } , 1 \times 1 0 ^ { - 2 } ]$ .
+
+In Platform-v0 and Goal-v0, we found the agent is not very sensitive to the range we set, such as $\alpha , \delta$ and $\tau$ . The $\delta$ values of top $20 \%$ trials vary between [0.05, 0.3], while $\alpha$ and $\tau$ values are evenly scattered in the defined range. In these settings, usually the agent prefers slightly larger value learning rate than policy learning rate.
+
+<table><tr><td>Average Eval Return</td><td>Our</td><td>PA-DDPG</td></tr><tr><td>Platform-v0</td><td>0.9573</td><td>0.3113</td></tr><tr><td>Goal-v0</td><td>34.20</td><td>-6.208</td></tr></table>
+
+Table 3: Average evaluation results (the average of all training rewards and final evaluation reward) on benchmarks Platform-v0 and Goal-v0 with PA-DDPG (Hausknecht & Stone (2015)), MP-DQN (Bester et al. (2019)) and P-DQN (Xiong et al. (2018)). We use reported number from the papers, while last two methods report another metric on Goal-v0.
+
+# 5 RELATED WORK
+
+While the aforementioned algorithms and techniques work on discrete or continuous action spaces, it is not trivial to apply them on parameterized action space, since such discrete-continuous hybrid action space is hard to parameterized by a single distribution. A related series of work is to combine DDPG and DQN to optimize Q-value function on parameter actions. There are two classes of methods that belong to them: PA-DDPG (Hausknecht & Stone (2015)) based on DDPG and PDQN (Xiong et al. (2018)) based on DQN. They are Q-Learning-based methods which select the best action by maximizing the Q-value function on discrete action space or learning a deterministic policy outputting best continuous action. However, they use different strategies to combine discrete and continuous actions. Bester et al. (2019) (MP-DQN) extends P-DQN to tackle the problem that Q-value is a function of the joint action-parameter vector $Q ( s ^ { \prime } , k ^ { \prime } , { \bf x } ^ { \tilde { Q } } ( s ^ { \prime } ) )$ in normal PAMDP, which may results in fault gradients. However, such problem does not exist in our slightly modified setting, since the action-parameter space $\mathcal { X }$ in the match plan generation is inherently defined to be shared for each $k \in \mathcal { A } _ { d }$ . Masson et al. (2016) purposes a method to iteratively optimizing discrete and continuous actions by alternating between them. Another perspective (Klimek et al. (2017); Wei et al. (2018); Fu et al. (2019)) for a parameterized action space is to regard it as a twohierarchy action space, where an agent selects discrete action first and continuous parameter later. However, we do not consider this direction in current scheme because we share the same parameters for all discrete action in not very large scale. Therefore, the hierarchical methods may not bring a significant performance gain.
+
+# 6 DISCUSSIONS
+
+In this paper, we present a parameterized action RL match plan generation method which extends the plan generation to the general case without any predefined knowledge. Key to address the problem are normalized softmax values of discrete actions to enable gradients backpropagation, parameter space noise on parameters of the policy for unifying the exploration direction in both discrete and continuous spaces, and recurrent deterministic policies with prioritized replay buffer to accelerate and stabilize the training. Our algorithm can be applied to not only the match plan generation environment, but also other similar parameteried action environments. The experiment results demonstrate our method outperforms the well-designed hand-crafted rules in Bing and serveral baseline results in some existing PARL benchmarks. In this paper, we mainly discuss about offline training procedure. In the future, we plan to apply learned policy to the production environment.
+
+# REFERENCES
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+
+# A APPENDIX
+
+# A.1 PSEUDOCODE
+
+Algorithm pseudocode for the algorithm is provided in Algorithm 1 which includes all aforementioned details.
+
+# Algorithm 1
+
+<table><tr><td>Input: Empty replay buffer D, init parameter noise std δparam, action noise threshold δ Initialize policy parameters 0,value parameters Φ ←0Q for each episode do Perturb policy parameters θ ← θ +(O,Oparam) and target policy parameters θtarget Observe state St, output a disturbed action embedding A =p(st；0） Compute executing action at by taking max over k</td></tr><tr><td>Execute parameterized action at in the environment server Observe next state St+1,reward rt, done signal dt denoting if St+1 is terminal t,rt, St+1,dt) to the buffer D If St+1 is terminal, reset to an initial state so for each update if update-condition do</td></tr><tr><td>Sample a minibatch from prioritized replay buffer D with specific priorities Compute and transform target actions with disturbed target policy network</td></tr><tr><td>Update parameter noise std Oparam using empirical distance d(μ, μ)</td></tr><tr><td>Compute targets for TD-error with min Q-value in the twin Q-networks Update Q-network parameters using gradient descent</td></tr><tr><td>if policy update frequency then</td></tr><tr><td>Update policy network parameters θ with Update target parameters with polyak averaging end if</td></tr></table>
+
+# A.2 FURTHER EXPERIMENTAL DETAILS
+
+Hyperparameter search. We use Microsoft $\mathrm { N N I } ^ { 2 }$ and OpenPAI3 to search hyperparameters. The final metric to report to NNI is set to the sum of average training reward and final evaluation reward (repeated 1,000 times) final_metric $=$ (avg_reward+eval_reward)/2. The intermediate metric is set to evaluation reward per 1,000 episodes. We also use the early stop assessor. Each GPU server node connects to a production environment emulator with ethernet.
+
+Model architecture. Both policy and value networks use two fully connected layers with 512 hidden units and a LSTM layer (Hochreiter & Schmidhuber (1997)). Each layer also uses a layer normalization (LayerNorm, Ba et al. (2016)) as suggested by Plappert et al. (2017) in consideration of stability for noise applied on parameters, and follows a ReLU activation. Both output heads of the policy network has a hidden layer with sof tmax or tanh activations.
+
+# A.3 FURTHER ENVIRONMENTAL DETAILS
+
+Accumulated values. Note that, for accumulated values in received states, rewards and outputted action-parameters, we use the difference (delta values) from the last step. For states and rewards, it is $s _ { t } = s _ { t } ^ { \prime } - s _ { t - 1 }$ , $r _ { t } = r _ { t } ^ { \prime } - r _ { t - 1 }$ , where where $s ^ { \prime }$ and $r ^ { \prime }$ denote raw state and reward. For actions, the agent outputs raw action-parameter output $a ^ { \prime }$ , and the emulator converts it to accumulated value $a _ { t } = a _ { t } ^ { \prime } + a _ { t - 1 }$ .
+
+![](images/6d04d136c67be4f2400a72fd7e2f02c247f2d8e0e0954f2f1782df4d09b152ff.jpg)  
+Figure 6: Best evaluation learning curves on both environments during tuning. The agent achieves maximum possible reward on both environments (50 and 1).
+
+Inverted index in Bing. In the inverted index system in Bing, there are two key steps: (i) the system rewrites the query to enlarge candidate set with specified match plan (or search plan), (ii) it returns candidates with top ranking scores. We just refer to the math plan part regarding to generation, but not user-input content. In the match plan generation, the goal is to generate the optimal search plan (policy) for each query.
+
+Closed-loop and open-loop control. The production match plan is generated online in open-loop (feedforward) without taking runtime system signals into consideration for the latency and implementation consideration. However, RL is closed-loop which takes feedback from system signals to make decisions. This may increase the online overhead, but it can be tackled by converting the reflective policy to a shooting-style action sequence by predicting with learned transition dynamics. In the implementation, the environment emulator receives an action sequence $a _ { 0 } , . . . , a _ { t }$ and return $s _ { t + 1 }$ to simulate the open-loop style.
+
+# A.4 MORE TRAINING FOR BENCHMARKS
+
+We provide the best evaluation learning curves on both environments during tuning.

parse/train/rkgZaT4tDr/rkgZaT4tDr_content_list.json

@@ -0,0 +1,1397 @@
+[
+    {
+        "type": "text",
+        "text": "PARAMETERIZED ACTION REINFORCEMENT LEARNING FOR INVERTED INDEX MATCH PLAN GENERATION ",
+        "text_level": 1,
+        "bbox": [
+            176,
+            98,
+            821,
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+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "Anonymous authors Paper under double-blind review ",
+        "bbox": [
+            183,
+            171,
+            398,
+            198
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "ABSTRACT ",
+        "text_level": 1,
+        "bbox": [
+            454,
+            234,
+            544,
+            251
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "Match plan generation in the inverted index at Microsoft Bing is used to be based on hand-crafted rules. We formulate the generation process as a Parameterized Action MDP with sharing parameters and purpose a reinforcement learning algorithm on such formulation. We combine deterministic policy learning on discrete and continuous action spaces and several recent advances in deep reinforcement learning. For exploring in the parameterized action space, the agent outputs softmax values for discrete actions and applies Parameter Space Noise on policy network to unify the exploration direction in both spaces. We apply prioritized recurrent replay on match plan sequences and pad short match plans. We also use invertible value function rescaling and $n$ -step return to stabilize the training. The agent is evaluated on our environment and some benchmarks. It outperforms the well-designed production match plan and beats the baselines on the benchmarks. ",
+        "bbox": [
+            233,
+            267,
+            764,
+            434
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "1 INTRODUCTION ",
+        "text_level": 1,
+        "bbox": [
+            176,
+            462,
+            334,
+            478
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "Using machine learning to optimize and accelerate software and hardware systems is an emerging field in the past few years (Mirhoseini et al. (2017); Rosset et al. (2018)). The process of decisionmaking in those systems is usually hand-crafted by human engineers, which is less explored to be automatically done by learning algorithms. A promising direction is to formulate such sequential decision-making problems as Reinforcement Learning (RL) problems, such as search plan generation problem in inverted indexes (Rosset et al. (2018)). ",
+        "bbox": [
+            174,
+            494,
+            825,
+            577
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "The inverted index is a specialized data structure that is commonly used in search engines, including Microsoft $\\mathrm { B i n g ^ { 1 } }$ . An inverted index provides an inverted mapping from term to documents. Each term has a posting list which contains all the (document, location) pairs that the term appears. By combining the posting lists of the terms in a user query, the initial document candidates are generated (Witten et al. (1999); Zobel & Moffat (2006)). ",
+        "bbox": [
+            174,
+            584,
+            823,
+            654
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "In Bing, documents are scanned with specified match plans, either predefined or generated in realtime. A match plan has a sequence of rewrites (match rules, e.g., it treats the query as a phrase which should appear in the document exactly as it is), where each rewrite can be controlled by several quotas (stopping criteria). There are several types of rewrites, and all these types share the same continuous quotas. A pair of a rewrite type and the quotas forms a single action which determines if a document will be a ranking candidate. ",
+        "bbox": [
+            174,
+            661,
+            823,
+            744
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "We formulate the generation problem as a RL problem. The state consists of system runtime signals and semantic embeddings of queries. The action space is called parameterized or discretecontinuous hybrid, where an action has a discrete action and continuous action-parameters. The reward is weighted by result quality and query latency. It is similar to Parameterized Action RL (Masson et al. (2016)) (PARL), while our setting requires all actions to share same parameters. ",
+        "bbox": [
+            174,
+            752,
+            823,
+            821
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "Previously, the match plans are predefined manually for each query. It hardly utilizes the rich information in the state to dynamically adjust the rewrites and quotas for specific query online. Rosset et al. (2018) tries to automatically generate match plans using tabular Q-learning with discretized state space and predefined action-parameters. They learn the generation policy for a specific query class each time and solve it only in discretized spaces with tabular methods. We extend the generation process to the general case, such that the match plans are fully parameterized and learned from scratch without any predefined knowledge (e.g., limited match rules). ",
+        "bbox": [
+            174,
+            828,
+            823,
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+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "image",
+        "img_path": "images/7459112fc13a2ca51b6133f349d4373e932db4f4ab389ec3ae4eb649b28ac3c6.jpg",
+        "image_caption": [
+            "Figure 1: Match plan example: for the query “Reinforcement Learning”, the search engine firstly gets a document posting list for each term from the inverted index, and then scans the document candidates following a serial of rewrites (match rules) according to the match plan. "
+        ],
+        "image_footnote": [],
+        "bbox": [
+            310,
+            108,
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+            184
+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "",
+        "bbox": [
+            171,
+            263,
+            821,
+            292
+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "In this paper, we purpose a parameterized action RL algorithm that learns to act on parameterized action space environments, such as the match plan generation process. We introduce normalized softmax values of discrete actions to form a categorical distributions to enable gradients backpropagation. We also combine several recent advances in RL to accelerate and stabilize the training. We investigate parameter space noise (Plappert et al. (2017)) on parameters of the policy for unifying directions in exploring the structured action space. We explore recurrent deterministic policies (Heess et al. (2015)) with prioritized replay buffer (Schaul et al. (2015)) on sequence, due to the inherent nature of partial observability and sparse feedback in our setting. We also use $n$ -step return and invertible value function rescaling (Kapturowski et al. (2018)) for further stability. ",
+        "bbox": [
+            173,
+            299,
+            825,
+            425
+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "We present an agent to integrate these techniques and evaluate on offline training on a query dataset collected from Bing search. When training on the dataset with uniformly sampling, the agent outperforms the currently deployed production match plan, which is generated based on well-designed hand-crafted rules. We study the performance of training on the dataset or only with several selected complicated queries individually, as well as ablation studies for the various components. We test on a few existing PARL benchmarks, where our agent beats our baseline methods and performs the state-of-the-art results. ",
+        "bbox": [
+            173,
+            431,
+            825,
+            529
+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "2 BACKGROUND ",
+        "text_level": 1,
+        "bbox": [
+            176,
+            547,
+            326,
+            565
+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "2.1 REINFORCEMENT LEARNING ",
+        "text_level": 1,
+        "bbox": [
+            176,
+            579,
+            415,
+            594
+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "We address the problem using reinforcement learning (RL) framework with a parameterized action space. An agent interacts with an environment to maximize the accumulated reward with discount factor $\\gamma \\in \\ [ 0 , 1 )$ . We model the environment with a discrete-time Partially Observable Markov Decision Process (POMDP). A POMDP is given by a tuple $( S , \\mathcal { A } , T , R , \\Omega , \\dot { \\mathcal { O } } )$ , and the underlying Markov Decision Process (MDP) is defined by $( S , { \\mathcal { A } } , T , R )$ , where $s$ is the state space, $\\mathcal { A }$ the parameterized action space, $T$ the transition function $\\mathcal { T } : \\mathcal { S } \\times \\mathcal { S } \\times \\mathcal { A }  \\mathbb { R } _ { + }$ , and $R : S \\times \\mathcal { A }  \\mathbb { R }$ is the reward function. The set of observations is given by $\\Omega$ and the the observation function mapping underlying states to probability distributions over observations is given by $\\mathcal { O }$ . ",
+        "bbox": [
+            173,
+            604,
+            825,
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+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "Specifically, the environment in the match plan generation has a parameterized action space. In Masson et al. (2016); Bester et al. (2019), such formulation in fully observable settings is referred as Parameterized Action MDP (PAMDP), where the action space is denoted as ",
+        "bbox": [
+            174,
+            723,
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+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "equation",
+        "img_path": "images/76ea0d7a9eb735ac9b64468a264943b9eec3b340c391396f2eb432de507a6511.jpg",
+        "text": "$$\n\\mathcal { A } = \\bigcup _ { k \\in \\mathcal { A } _ { d } } \\left\\{ ( k , x _ { k } ) | x _ { k } \\in \\mathcal { X } _ { k } \\right\\} ,\n$$",
+        "text_format": "latex",
+        "bbox": [
+            395,
+            768,
+            599,
+            803
+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "where each discrete action $a \\in \\mathcal { A } _ { d } = [ K ]$ has a corresponding continuous action-parameter space $\\mathcal { X } _ { a }$ . However, our setting requires a slightly different formulation: ",
+        "bbox": [
+            173,
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+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "equation",
+        "img_path": "images/243001bdfb8447abcdd89869de2d2453c03e6261b0ef47f965d0d6494f259a02.jpg",
+        "text": "$$\n\\mathcal { A } = \\{ ( k , x ) | k \\in \\mathcal { A } _ { d } , x \\in \\mathcal { X } \\} = \\mathcal { A } _ { d } \\times \\mathcal { X } ,\n$$",
+        "text_format": "latex",
+        "bbox": [
+            359,
+            835,
+            635,
+            852
+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "where the discrete action space (rewrite) $\\mathbf { \\mathcal { A } } _ { d }$ share the action-parameter space $\\mathcal { X }$ . Such formulation results in a disentangled action space between discrete and continuous actions which a class of parameterized action (P-DQN (Xiong et al. (2018)) and MP-DQN (Bester et al. (2019))) may not be trivially applicable to. Considering the notational simplicity in partially observable environment (POMDP), we do not explicitly denote it when there is no ambiguity in action settings. ",
+        "bbox": [
+            174,
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+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "2.2 FORMULATION OF MATCH PLAN GENERATION ",
+        "text_level": 1,
+        "bbox": [
+            173,
+            103,
+            539,
+            118
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "In Rosset et al. (2018), the action-parameters are predefined for the match plan generation, where the action space is then a set of discrete rewrites (actions). We fully parameterize a match plan to allow the agent to generate any valid plans. ",
+        "bbox": [
+            176,
+            128,
+            823,
+            171
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "State. At each time step, the agent receives a state with two parts. First part has selected run-time system signals from the inverted index system. Since the query is uniformly sampled in different episode, we include some statistical features and semantic embeddings of queries to allow the agent to identify different queries and then generate corresponding match plans. Such statistical features are used in the current production system, such as the length of a query. All signals and embeddings are normalized to a reasonable range around $[ - 1 , 1 ]$ based on empirical estimations. ",
+        "bbox": [
+            173,
+            188,
+            825,
+            271
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "Action. The agent selects a parameterized action $a _ { t }$ including a rewrite id and its allocated quotas at each step. There are 29 types of rewrites in $\\mathbf { \\mathcal { A } } _ { d }$ and also a 5-dimensional quota parameter space $\\mathcal { X }$ for each rewrite in int64 type. However, the range of each quota is empirically set to valid values and then normalized to $[ - 1 , 1 ]$ . All outputted quotas are effective for the current step. ",
+        "bbox": [
+            174,
+            286,
+            825,
+            343
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "There is also a special action to note: stop (by agent). Normally, the environment will return a terminal signal, but it happens in extreme cases, such as low system resources. To allow a better balance of latency and performance, we allow the agent to choose stop or not as another type of discrete action, which is the same level as other 29 rewrites. ",
+        "bbox": [
+            174,
+            349,
+            825,
+            405
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "Reward. We use two criterions in the design: latency and performance. For latency consideration, we use a signal Seek Count that is constant for a same query in different runs with same match plan, instead of executed time. We weight the Ranking Scores of top five returned documents as an indicator of performance with weights [0.4, 0.2, 0.2, 0.1, 0.1]. When there are less than five documents returned, the scores of missing documents are treated as a minimum possible ranking score. The final scalar reward is weighted by these two objectives to balance them. We do not use the division in Rosset et al. (2018), since the loss surfaces may become more non-convex for optimizing. ",
+        "bbox": [
+            174,
+            420,
+            825,
+            518
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "We also have punishments (negative rewards) for some special cases. One is to assign a punishment when the agent selects to illegally stop at the first step or some unsupported rewrites (for some special queries). However, unsupported rewrites do not necessarily cause a terminal state, since the production system has same hand-crafted match plans for a class of queries, in which the unsupported rewrites are simply omitted. ",
+        "bbox": [
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+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "3 METHOD ",
+        "text_level": 1,
+        "bbox": [
+            174,
+            614,
+            282,
+            631
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "For generating match plans, we introduce a method that works on the aforementioned formulation with slightly different parameterized action space than standard PAMDPs in the literature. We start from the intuition with deterministic policy learning (Silver et al. (2014)) and how it relates to parameterized actions. PAMDP often refers to the formulation that each individual discrete action $k \\in \\mathcal { A } _ { d } = [ K ]$ has a corresponding continuous action-parameter space. Thus, there are $K$ continuous action-parameter spaces corresponding to $K$ discrete action (Xiong et al. (2018)). In our shared-parameter PAMDP, the Bellman equation incorporated both discrete action $k$ and continuous action-parameters $x$ is given by: ",
+        "bbox": [
+            173,
+            646,
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+            758
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "equation",
+        "img_path": "images/4baf652d557a9988b78e9d6b9f883817be7d2229b913710040c6d0deac8aada0.jpg",
+        "text": "$$\n\\begin{array} { r } { Q \\left( s , k , x \\right) = \\underset { r , s ^ { \\prime } } { \\mathbb { E } } \\left[ r + \\gamma \\underset { k ^ { \\prime } } { \\operatorname* { m a x } } \\ \\underset { x ^ { \\prime } \\in \\mathcal { X } } { \\operatorname* { s u p } } Q \\left( s ^ { \\prime } , k ^ { \\prime } , x ^ { \\prime } \\right) \\vert s , k , x \\right] . } \\end{array}\n$$",
+        "text_format": "latex",
+        "bbox": [
+            308,
+            775,
+            687,
+            810
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "P-DQN (Xiong et al. (2018)) tackles PAMDP by incorporating multiple action-parameter policies $x _ { k } ( s ; \\theta _ { x } ) : { \\cal { S } }  { \\mathcal { X } } _ { k }$ for each action $k$ and update them with $\\begin{array} { r } { \\operatorname* { m a x } _ { k ^ { \\prime } } \\operatorname* { s u p } _ { x _ { k ^ { \\prime } } \\in \\mathcal { X } _ { k ^ { \\prime } } } Q \\left( s ^ { \\prime } , k ^ { \\prime } , x _ { k ^ { \\prime } } \\right) } \\end{array}$ simultaneously. However, since all parameters $x$ are shared for actions $k$ in our case, we do not require multiple policies. The policy loss in P-DQN (Xiong et al. (2018)) given by ",
+        "bbox": [
+            173,
+            819,
+            825,
+            878
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "equation",
+        "img_path": "images/38a0ce4a63eabe51e761e09dd8728767079ede8cf87f9111a5e7ab29f0c3a281.jpg",
+        "text": "$$\nL _ { x } \\left( \\theta _ { x } \\right) = \\underset { s \\sim D } { \\mathbb { E } } \\left[ - \\sum _ { k = 1 } ^ { K } Q \\left( s , k , x _ { k } \\left( s ; \\theta _ { x } \\right) ; \\theta _ { Q } \\right) \\right]\n$$",
+        "text_format": "latex",
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "image",
+        "img_path": "images/908f0f5be906ce40a46112737a183c610852cc851433f4f94d61674bb007f08e.jpg",
+        "image_caption": [
+            "Figure 2: The diagram of the process. "
+        ],
+        "image_footnote": [],
+        "bbox": [
+            284,
+            98,
+            704,
+            164
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "naturally degenerates to a single policy in next case, where the gradient $\\nabla L _ { x } \\left( \\theta _ { x } \\right)$ exactly is the deterministic policy gradient (DPG, Silver et al. (2014)). MP-DQN (Bester et al. (2019)) states a problem regarding to the erroneous gradients of Q-network $\\nabla L _ { Q }$ in P-DQN caused by multiple action-parameter policies backpropagating gradients at the same time. However, it does not exist in such single network situation. This is a desired architecture since separating multiple actionparameter policies loses the knowledge that they share same potential meanings. ",
+        "bbox": [
+            174,
+            228,
+            825,
+            313
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "Following this intuition, we directly parameterize the policy with two heads $\\mu : \\mathcal { S } \\to \\mathbb { R } ^ { K } \\times \\mathcal { X }$ with $\\theta _ { \\mu }$ $\\mathrm { ~ ` ~ } _ { \\mu } \\mathrm { ~ a s : ~ } k _ { t } ^ { s o f t } , x _ { t } = a _ { t } ^ { s o f t } = \\mu ( s _ { t } ; \\theta _ { \\mu } )$ , where $k _ { t } ^ { s o f t }$ and $a _ { t } ^ { s o f t }$ refers to action-parameters or actions with softmax values. One head outputs the sof tmax values for all discrete actions. For another head, it outputs normalized action-parameter values with hyperbolic tangent $( t a n h )$ activation after the continuous head. The environment will denormalize it to a valid range. This corresponds to the Squashing Gradients method for bounded-continuous action spaces in Hausknecht & Stone (2015). ",
+        "bbox": [
+            173,
+            319,
+            825,
+            405
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "Exploration with Parameter Space Noise and action sampling. In DQN (Mnih et al. (2015)), the behavioral policy is given by $\\epsilon$ -greedy strategy for exploration purpose, where an agent randomly selects a discrete action with probability $\\epsilon < 1$ . In DDPG (Lillicrap et al. (2015)), although the policy learned is deterministic, to explore the action space, the behavioral policy needs to be different because of the off-policy nature. It uses action space noise such as uncorrelated Gaussian noise or correlated Ornstein-Uhlenbeck process (Lillicrap et al. (2015)). ",
+        "bbox": [
+            173,
+            430,
+            825,
+            515
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "Directly combining such two exploration strategies is straightforward. However, it may induce a problem that the exploration in two action spaces $\\mathcal { A } = \\mathcal { A } _ { d } \\times \\mathcal { X }$ in different paces. For example, the match plan may need another rewrite with larger quotas in a step. However, if the exploration strategy is to use $\\epsilon$ -greedy for a rewrite $k$ and Gaussian noise for its quotas $x$ , the agent may require more samples to discover the potential rewards (positive documents). We instead use parameter space noise (Plappert et al. (2017)) on parameterized action space to tackle such issue. ",
+        "bbox": [
+            173,
+            521,
+            825,
+            604
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "We denote the discrete and continuous action heads as $( \\pi _ { k } ^ { s o f t } ( s ) , \\pi _ { x } ( s ) ) = \\mu ( s ; \\theta _ { \\mu } ) .$ . To compute the distance $d ( \\pi , \\widetilde { \\pi } ) = D _ { \\mathrm { K L } } ( \\pi \\| \\widetilde { \\pi } )$ of non-perturbed and perturbed policies $\\mu ( s ; \\theta _ { \\mu } ) , \\widetilde { \\mu } ( s ; \\theta _ { \\mu } )$ , we e e euse weighted sum of the distance of discrete and continuous actions. For the continuous actions $\\widetilde { \\pi } _ { x } ( s )$ , the distance is given by $\\mathbb { E } _ { s } \\left[ \\left( \\pi _ { x } ( s ) _ { i } - \\widetilde { \\pi } _ { x } ( s ) _ { i } \\right) ^ { 2 } \\right]$ to estimate KL-divergence empirically. For e ethe discrete actions, we use outputted softmax probabilities to compute The state and action pairs are sampled from a replay memory. The varianc $D _ { \\mathrm { K L } } ( \\pi _ { k } ^ { s o f t } ( s ) \\Vert \\widetilde { \\pi } _ { k } ^ { s o f t } ( s ) )$ $\\sigma$ after a policy update based on the distance and threhold $\\delta$ (Plappert et al. (2017)). The policy and target networks with layer normalization (Ba et al. (2016)) are perturbed per episode. ",
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+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "Prioritized replay and recurrent policies. We use recurrent architecture to obtain the underlying system state of the POMDP for both value and policy networks (Heess et al. (2015)). To avoid recurrent state staleness (Kapturowski et al. (2018)), we store and replay a sequence of $( s , k ^ { s o f t } , x , r )$ with softmax values into a replay memory. Since a match plan is usually short, we set a maximum length and pad shorter episodes with zero or randomly sampled states and actions. ",
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+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "The sampling from a replay memory can be prioritized with a probability $p _ { i }$ proportional to TDerrors (Schaul et al. (2015)) to increase the sample efficiency in such structured action space. To prioritize the transitions with well-matched documents, we slightly modify the sampling strategy. With a half probability, the agent uses regular prioritization, otherwise partitions the memory to multiple bins and retrieve a transition (sequence) with max reward from each bin. Our strategy provides a more efficient and balanced exploration strategy of the evaluation. ",
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "Policy update. In the update, we use clipped double $Q$ -learning and delayed policy update (Fujimoto et al. (2018)) to stabilizing the training. After the agent samples a batch of (sequences), it perturbs the target policy network and computes the perturbed actions for target policy smoothing. The parameter space noise variance $\\sigma$ is then updated with the sampled states and actions. ",
+        "bbox": [
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+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "The policy is still deterministic since it is learned in off-policy and only the exploration involves stochasticity. The update is given by deterministic policy gradients theorem (Silver et al. (2014)): ",
+        "bbox": [
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+        "page_idx": 4
+    },
+    {
+        "type": "equation",
+        "img_path": "images/3562b5ab1968d6fce4dd58258e2c12c671f3fadb5d89d26146c9a6856a9e24a7.jpg",
+        "text": "$$\n\\nabla L _ { \\mu } \\left( \\theta _ { \\mu } \\right) = \\nabla _ { s \\sim D } \\left[ Q \\left( s , \\mu ( s ; \\theta _ { \\mu } ) ; \\theta _ { Q } \\right) \\right] = \\nabla \\frac { 1 } { \\left| D \\right| } \\sum _ { s \\in D } Q \\left( s , k ^ { s o f t } , x ; \\theta _ { Q } \\right) ,\n$$",
+        "text_format": "latex",
+        "bbox": [
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "where $D$ is a replay memory. We found this policy architecture is similar to PA-DDPG (Hausknecht $\\&$ Stone (2015)), while it does not including sof tmax activation for discrete actions and other advanced techniques. We also build upon other useful techniques such as invertible value function rescaling $h ( x ) = \\mathrm { { s i g n } } ( x ) ( \\sqrt { | x | } + 1 - 1 ) + \\epsilon x$ (Kapturowski et al. (2018)): ",
+        "bbox": [
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+        "page_idx": 4
+    },
+    {
+        "type": "equation",
+        "img_path": "images/fce58c5a07a0c3febf35ee414e9539f1e4ea20fd2393bb65923f45a0fdcb7751.jpg",
+        "text": "$$\ny = h \\left( \\sum _ { k = 0 } ^ { n - 1 } r _ { t + k } \\gamma ^ { k } + \\gamma ^ { n } h ^ { - 1 } \\left( Q \\left( s _ { t + n } , a ^ { \\ast } ; \\theta _ { Q } ^ { - } \\right) \\right) \\right) ,\n$$",
+        "text_format": "latex",
+        "bbox": [
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "where $a ^ { * } = ( \\operatorname* { m a x } k _ { t } ^ { s o f t } , x _ { t } ) = ( k _ { t } , x _ { t } )$ is the greedy action, $y$ the target for updating Q-network, and $\\theta _ { Q } ^ { - }$ denotes the target Q-network. The policy network outputs differentiable softmax values and is updated by the gradients backpropagated from the Q-network: ",
+        "bbox": [
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+        "page_idx": 4
+    },
+    {
+        "type": "equation",
+        "img_path": "images/d951c0efa2af92e644a3128d1ed4e8b66e025fb64e2e4c6797ccd5e0e6c726fd.jpg",
+        "text": "$$\n\\nabla L _ { Q } \\left( \\theta _ { Q } \\right) = \\nabla \\mathbb { E } \\left[ \\frac { 1 } { 2 } \\left( y - Q \\left( s , k ^ { s o f t } , x ; \\theta _ { Q } \\right) \\right) ^ { 2 } \\right] ,\n$$",
+        "text_format": "latex",
+        "bbox": [
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "where the expectation is took over samples from a memory. ",
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "The pseudocode for the algorithm with more details can be found in the Appendix. ",
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+    },
+    {
+        "type": "text",
+        "text": "4 EXPERIMENTS ",
+        "text_level": 1,
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "In this section, we apply the purposed agent on the inverted index match plan generation problem. We create a dataset which contains a set of queries and corresponding query embeddings. We perform various ablation study on how each component interacts and the benefits of them. We also test on other Paramterized Action RL benchmarking baselines. ",
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+    },
+    {
+        "type": "text",
+        "text": "4.1 EXPERIMENT SETTINGS ",
+        "text_level": 1,
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "For match plan generation, we experiment on a dataset that has about 100,000 queries sampled from Bing search log. In the current production system, each query is classified to a predefined query classes online based on a set of rules which are related to statistical features of the query. Each query class has some hand-crafted rules which outputs a match plan for the classified query. We use each query’s production match plan as baseline. The match plan for each query is generated by the hand-crafted rules and does not change over each running. We only skip a few special queries that do not have embeddings or need additional operations beyond match plans. ",
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+    },
+    {
+        "type": "text",
+        "text": "The generated match plan is evaluated by the delta values of both Ranking Score and Seek Count and overall reward. We provide learning curves of delta values of evaluation rewards. Note that the reward are not symmetrical around 0, since the ranking scores has a minimum value and is sparse since a few queries are hard to find good documents and will be assigned a very low score. It may significantly pull down the average rewards shown in the curves, thus we present histograms for fair comparison. For the benchmarks, we report the results on evaluation reward curves during tuning. ",
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+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": ".2 MATCH PLAN GENERATION PERFORMANCE EVALUATION ",
+        "text_level": 1,
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "We first visualize the query embeddings in Figure 3 using UMAP (McInnes et al. (2018)) to demonstrate our learned models. We evaluate 6,000 queries and draw the colormap based on the difference between evaluation reward and production baseline reward. Although most queries perform similar to the well-designed production rules, there are some clusters of queries and some patterns exist. We notice that there is a main cluster at the center (about $( - 7 , - 1 ) )$ ) that gathers most queries on which our agent does not perform well. That cluster contains some random inputs from the users, which may have some typos. For the queries that the agent outperforms the baseline, we find they are quite scattered. We guess the reason is that the baseline with hand-crafted rules do not consider the embeddings, thus it is less affected by embeddings. This may suggest us to look for more informative embeddings of queries to better distinguish some clustered queries. ",
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+        "page_idx": 4
+    },
+    {
+        "type": "image",
+        "img_path": "images/1b912e4438fe0c4576fc52e07dd81917a7cf3148fcc9fac32a9a96a543cd4db8.jpg",
+        "image_caption": [
+            "Figure 3: Visualization of query embeddings. "
+        ],
+        "image_footnote": [],
+        "bbox": [
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "image",
+        "img_path": "images/5ea9b9c596510988cdcbdc7742ad1ba606263fb7aae0db82cd463ab8f11bfb27.jpg",
+        "image_caption": [
+            "Figure 4: Different techniques. "
+        ],
+        "image_footnote": [],
+        "bbox": [
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+        "page_idx": 5
+    },
+    {
+        "type": "image",
+        "img_path": "images/6f60df92f6ce68b3bc8a05d04a9fa957d6cb5bab0fe7d16ef5692b5aaa72f95a.jpg",
+        "image_caption": [
+            "Figure 5: Delta Reward Distribution in Evaluation Phrase. "
+        ],
+        "image_footnote": [],
+        "bbox": [
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+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "In the plots shown in Figure 6, we visualize the distribution of delta rewards, ranking scores and seek count values comparing to the well-designed production rules. For most of the queries the agent learns promising match plan without any prior knowledge just based on the reward signals. There are also some hard queries to find a pattern that have poor reward (about $- 1 0 0 )$ and usually lies in the main cluster and around a few more small clusters. Other than some meaningless queries around the center, they also include some non-English queries, such as French and Chinese, which are possibly clustered around their centroid and are challenging to learn the policy for all of them. ",
+        "bbox": [
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+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "Reward design. We consider different weights to trade-off between the query latency from the input and the quality of the returned documents. The quality is evaluated by Ranking Scores of top five documents. We found that it is sparse since the good documents are hard to match. When we weight more on ranking score, the agent tends to stop the search early. ",
+        "bbox": [
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "We also investigate a few punishments and try to use less of them to avoid manual design. We found the agent learns some common patterns guided by the reward and punishments. It tries to avoid ”stop” at the first step because we set a huge punishment on such invalid stop. This punishment is necessary since it prevents the agent stops at first step for better value than trying more steps but get no documents matched. In other words, the agent is encouraged to explore different rewrites instead of using empty match plans. Without such punishment, the performance significantly drops since it is hard to explore good documents at first. We also punish the agent to avoid unsupported rewrites, since the production system uses designed rules for each class of the queries and simply omits a rewrite without any useful feedback. We test punishing repeated rewrites, however, it helps seek count (more efficient) but may harm ranking scores. ",
+        "bbox": [
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+        "page_idx": 5
+    },
+    {
+        "type": "table",
+        "img_path": "images/e3a1464f0b6cd2d71b46e2251154e906a70ddf2e498fb4263bde557589df6bb7.jpg",
+        "table_caption": [
+            "Table 1: Improved Scores of Different Noise Compared to RNN Gaussian Noise. Ranking Score and Seek Count are scaled to match Overall $=$ RankingScore−SeekCount for easy comparison. "
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td></td><td>Overall</td><td>Ranking Score (Quality)</td><td>Seek Count (Efficiency)</td></tr><tr><td>OU Noise</td><td>+1.00</td><td>+1.20</td><td>-0.20</td></tr><tr><td>Param Noise</td><td>+1.69</td><td>+0.82</td><td>-0.87</td></tr></table>",
+        "bbox": [
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "table",
+        "img_path": "images/7320f38c5eca22be88d47fec5b5f6b8be13097a72a46698ca9f2671a3e8e7c6c.jpg",
+        "table_caption": [
+            "Table 2: Improved Scores of Different Model Compared to MLP "
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td></td><td>Overall</td><td>Ranking Score (Quality)</td><td>Seek Count (Efficiency)</td></tr><tr><td>MLP+Prioritized</td><td>+14.54</td><td>+8.56</td><td>-5.98</td></tr><tr><td>RNN+Prioritized</td><td>+32.63</td><td>+14.44</td><td>-18.19</td></tr><tr><td>RNN + Prioritized Sample</td><td>+32.67</td><td>+15.29</td><td>-17.38</td></tr></table>",
+        "bbox": [
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+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "",
+        "bbox": [
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+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "4.3 ABLATION STUDY ",
+        "text_level": 1,
+        "bbox": [
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "We compare different exploration noise, including action space noise and parameter space noise. For the action space noise, the noise on discrete and continuous actions are applied separately. We test Gaussian and OrnsteinUhlenbeck noise on continuous actions, while the discrete actions only use $\\epsilon$ -greedy. To keep the comparison fair, we also test $\\epsilon$ -greedy strategy on continuous actions by uniformly sampling a point with probability $\\epsilon$ . The parameter noise is directly applied on policy network $\\widetilde \\mu ( s ; \\theta _ { \\mu } )$ . We found the parameter space noise performs more stable than all types of action espace noise. The uniform sampling on both discrete and continous action with $\\epsilon$ -greedy failed for sometimes, thus we did not include it in comparison. We give the relative improvement in Table 1 compared to RNN with Gaussian Noise. The results show that parameter space noise has best performance overall. ",
+        "bbox": [
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+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "The results in Figure 6(a) and Table 2 show that RNN got significantly better performance than MLP with or without parameterization on our environment. It indicates that the environment is highly non-Markov. We guess one obvious possibility is that the system signals of the state space cannot include all the information, while recurrent networks try to extract latent state from the history. Note that each episode will sample one query, thus the query embedding is constant for all steps in one episode. Another possible reason is that some rewrites may not be supported by special queries or have too small change for the state signals. ",
+        "bbox": [
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+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "We compare different parameterization methods on recurrent networks. The results are shown in Figure 4(b) and Table 2. We empirically found that our modified strategy using reward bin is more stable from the beginning. It is possible that the agent repeatedly replays not only good experience on matching documents, but also learns to avoid punishment we set, as we expect. In general prioritized replay, the sampling probability is just based on TD-error and may be biased to worse samples since value function may not update towards possible results. ",
+        "bbox": [
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+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "4.4 BENCHMARKING GAMES ",
+        "text_level": 1,
+        "bbox": [
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "We experiment on Platform-v0 and Goal-v0 from Bester et al. (2019). Note that, in all these games, each discrete action has a separate continuous action-parameter space. Our algorithm is designed for shared action-parameters and does not utilize such prior, thus we do not compare with P-DQN-style algorithms. We apply n-step return since the episode in these games is much longer. We assume the environment is fully observable and do not use recurrent networks in comparison. ",
+        "bbox": [
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+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "Hyperparameters. We examine the games with different combinations of hyperparameters, since they are easy to parallize on each training nodes without the need to connect to an production environment emulator. With NNI, the learning rates for value and policy network are set to log-uniform in $[ 3 \\times 1 0 ^ { - 4 } , 3 \\times 1 0 ^ { - 3 } ]$ and $[ 1 \\times 1 0 ^ { - 4 } , 1 \\times \\mathsf { \\bar { 1 } 0 ^ { - 3 } } ]$ . The $\\alpha$ in parameterized replay is set to log-uniform in [0.2, 1.0]. The action noise threshold $\\delta$ in parameter space noise is set to log-uniform between [0.05, 0.8]. Tn soft parameter update, the $\\tau$ is set to log-uniform in $[ 1 \\times 1 0 ^ { - 3 } , 1 \\times 1 0 ^ { - 2 } ]$ . ",
+        "bbox": [
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+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "In Platform-v0 and Goal-v0, we found the agent is not very sensitive to the range we set, such as $\\alpha , \\delta$ and $\\tau$ . The $\\delta$ values of top $20 \\%$ trials vary between [0.05, 0.3], while $\\alpha$ and $\\tau$ values are evenly scattered in the defined range. In these settings, usually the agent prefers slightly larger value learning rate than policy learning rate. ",
+        "bbox": [
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+        "page_idx": 7
+    },
+    {
+        "type": "table",
+        "img_path": "images/43fb6a7fec969297f5ab873d3137dea0d0470694b6859f537189d55399ea27e8.jpg",
+        "table_caption": [],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>Average Eval Return</td><td>Our</td><td>PA-DDPG</td></tr><tr><td>Platform-v0</td><td>0.9573</td><td>0.3113</td></tr><tr><td>Goal-v0</td><td>34.20</td><td>-6.208</td></tr></table>",
+        "bbox": [
+            346,
+            266,
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+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "Table 3: Average evaluation results (the average of all training rewards and final evaluation reward) on benchmarks Platform-v0 and Goal-v0 with PA-DDPG (Hausknecht & Stone (2015)), MP-DQN (Bester et al. (2019)) and P-DQN (Xiong et al. (2018)). We use reported number from the papers, while last two methods report another metric on Goal-v0. ",
+        "bbox": [
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+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "5 RELATED WORK ",
+        "text_level": 1,
+        "bbox": [
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+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "While the aforementioned algorithms and techniques work on discrete or continuous action spaces, it is not trivial to apply them on parameterized action space, since such discrete-continuous hybrid action space is hard to parameterized by a single distribution. A related series of work is to combine DDPG and DQN to optimize Q-value function on parameter actions. There are two classes of methods that belong to them: PA-DDPG (Hausknecht & Stone (2015)) based on DDPG and PDQN (Xiong et al. (2018)) based on DQN. They are Q-Learning-based methods which select the best action by maximizing the Q-value function on discrete action space or learning a deterministic policy outputting best continuous action. However, they use different strategies to combine discrete and continuous actions. Bester et al. (2019) (MP-DQN) extends P-DQN to tackle the problem that Q-value is a function of the joint action-parameter vector $Q ( s ^ { \\prime } , k ^ { \\prime } , { \\bf x } ^ { \\tilde { Q } } ( s ^ { \\prime } ) )$ in normal PAMDP, which may results in fault gradients. However, such problem does not exist in our slightly modified setting, since the action-parameter space $\\mathcal { X }$ in the match plan generation is inherently defined to be shared for each $k \\in \\mathcal { A } _ { d }$ . Masson et al. (2016) purposes a method to iteratively optimizing discrete and continuous actions by alternating between them. Another perspective (Klimek et al. (2017); Wei et al. (2018); Fu et al. (2019)) for a parameterized action space is to regard it as a twohierarchy action space, where an agent selects discrete action first and continuous parameter later. However, we do not consider this direction in current scheme because we share the same parameters for all discrete action in not very large scale. Therefore, the hierarchical methods may not bring a significant performance gain. ",
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+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "6 DISCUSSIONS ",
+        "text_level": 1,
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "In this paper, we present a parameterized action RL match plan generation method which extends the plan generation to the general case without any predefined knowledge. Key to address the problem are normalized softmax values of discrete actions to enable gradients backpropagation, parameter space noise on parameters of the policy for unifying the exploration direction in both discrete and continuous spaces, and recurrent deterministic policies with prioritized replay buffer to accelerate and stabilize the training. Our algorithm can be applied to not only the match plan generation environment, but also other similar parameteried action environments. The experiment results demonstrate our method outperforms the well-designed hand-crafted rules in Bing and serveral baseline results in some existing PARL benchmarks. In this paper, we mainly discuss about offline training procedure. In the future, we plan to apply learned policy to the production environment. ",
+        "bbox": [
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+        "page_idx": 7
+    },
+    {
+        "type": "text",
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+    {
+        "type": "text",
+        "text": "A APPENDIX ",
+        "text_level": 1,
+        "bbox": [
+            176,
+            102,
+            299,
+            117
+        ],
+        "page_idx": 10
+    },
+    {
+        "type": "text",
+        "text": "A.1 PSEUDOCODE ",
+        "text_level": 1,
+        "bbox": [
+            176,
+            133,
+            315,
+            148
+        ],
+        "page_idx": 10
+    },
+    {
+        "type": "text",
+        "text": "Algorithm pseudocode for the algorithm is provided in Algorithm 1 which includes all aforementioned details. ",
+        "bbox": [
+            176,
+            161,
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+        ],
+        "page_idx": 10
+    },
+    {
+        "type": "text",
+        "text": "Algorithm 1 ",
+        "text_level": 1,
+        "bbox": [
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+            259,
+            218
+        ],
+        "page_idx": 10
+    },
+    {
+        "type": "table",
+        "img_path": "images/6805768dc1374f48ea940804c4f043f9541f672a807ee8463e41885f8a35b386.jpg",
+        "table_caption": [],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>Input: Empty replay buffer D, init parameter noise std δparam, action noise threshold δ Initialize policy parameters 0,value parameters Φ ←0Q for each episode do Perturb policy parameters θ ← θ +(O,Oparam) and target policy parameters θtarget Observe state St, output a disturbed action embedding A =p(st；0） Compute executing action at by taking max over k</td></tr><tr><td>Execute parameterized action at in the environment server Observe next state St+1,reward rt, done signal dt denoting if St+1 is terminal t,rt, St+1,dt) to the buffer D If St+1 is terminal, reset to an initial state so for each update if update-condition do</td></tr><tr><td>Sample a minibatch from prioritized replay buffer D with specific priorities Compute and transform target actions with disturbed target policy network</td></tr><tr><td>Update parameter noise std Oparam using empirical distance d(μ, μ)</td></tr><tr><td>Compute targets for TD-error with min Q-value in the twin Q-networks Update Q-network parameters using gradient descent</td></tr><tr><td>if policy update frequency then</td></tr><tr><td>Update policy network parameters θ with Update target parameters with polyak averaging end if</td></tr></table>",
+        "bbox": [
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+        ],
+        "page_idx": 10
+    },
+    {
+        "type": "text",
+        "text": "A.2 FURTHER EXPERIMENTAL DETAILS ",
+        "text_level": 1,
+        "bbox": [
+            176,
+            583,
+            464,
+            598
+        ],
+        "page_idx": 10
+    },
+    {
+        "type": "text",
+        "text": "Hyperparameter search. We use Microsoft $\\mathrm { N N I } ^ { 2 }$ and OpenPAI3 to search hyperparameters. The final metric to report to NNI is set to the sum of average training reward and final evaluation reward (repeated 1,000 times) final_metric $=$ (avg_reward+eval_reward)/2. The intermediate metric is set to evaluation reward per 1,000 episodes. We also use the early stop assessor. Each GPU server node connects to a production environment emulator with ethernet. ",
+        "bbox": [
+            173,
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+        ],
+        "page_idx": 10
+    },
+    {
+        "type": "text",
+        "text": "Model architecture. Both policy and value networks use two fully connected layers with 512 hidden units and a LSTM layer (Hochreiter & Schmidhuber (1997)). Each layer also uses a layer normalization (LayerNorm, Ba et al. (2016)) as suggested by Plappert et al. (2017) in consideration of stability for noise applied on parameters, and follows a ReLU activation. Both output heads of the policy network has a hidden layer with sof tmax or tanh activations. ",
+        "bbox": [
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+        ],
+        "page_idx": 10
+    },
+    {
+        "type": "text",
+        "text": "A.3 FURTHER ENVIRONMENTAL DETAILS ",
+        "text_level": 1,
+        "bbox": [
+            176,
+            785,
+            477,
+            800
+        ],
+        "page_idx": 10
+    },
+    {
+        "type": "text",
+        "text": "Accumulated values. Note that, for accumulated values in received states, rewards and outputted action-parameters, we use the difference (delta values) from the last step. For states and rewards, it is $s _ { t } = s _ { t } ^ { \\prime } - s _ { t - 1 }$ , $r _ { t } = r _ { t } ^ { \\prime } - r _ { t - 1 }$ , where where $s ^ { \\prime }$ and $r ^ { \\prime }$ denote raw state and reward. For actions, the agent outputs raw action-parameter output $a ^ { \\prime }$ , and the emulator converts it to accumulated value $a _ { t } = a _ { t } ^ { \\prime } + a _ { t - 1 }$ . ",
+        "bbox": [
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+        ],
+        "page_idx": 10
+    },
+    {
+        "type": "image",
+        "img_path": "images/6d04d136c67be4f2400a72fd7e2f02c247f2d8e0e0954f2f1782df4d09b152ff.jpg",
+        "image_caption": [
+            "Figure 6: Best evaluation learning curves on both environments during tuning. The agent achieves maximum possible reward on both environments (50 and 1). "
+        ],
+        "image_footnote": [],
+        "bbox": [
+            218,
+            106,
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+            297
+        ],
+        "page_idx": 11
+    },
+    {
+        "type": "text",
+        "text": "Inverted index in Bing. In the inverted index system in Bing, there are two key steps: (i) the system rewrites the query to enlarge candidate set with specified match plan (or search plan), (ii) it returns candidates with top ranking scores. We just refer to the math plan part regarding to generation, but not user-input content. In the match plan generation, the goal is to generate the optimal search plan (policy) for each query. ",
+        "bbox": [
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+        ],
+        "page_idx": 11
+    },
+    {
+        "type": "text",
+        "text": "Closed-loop and open-loop control. The production match plan is generated online in open-loop (feedforward) without taking runtime system signals into consideration for the latency and implementation consideration. However, RL is closed-loop which takes feedback from system signals to make decisions. This may increase the online overhead, but it can be tackled by converting the reflective policy to a shooting-style action sequence by predicting with learned transition dynamics. In the implementation, the environment emulator receives an action sequence $a _ { 0 } , . . . , a _ { t }$ and return $s _ { t + 1 }$ to simulate the open-loop style. ",
+        "bbox": [
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+        ],
+        "page_idx": 11
+    },
+    {
+        "type": "text",
+        "text": "A.4 MORE TRAINING FOR BENCHMARKS ",
+        "text_level": 1,
+        "bbox": [
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+        ],
+        "page_idx": 11
+    },
+    {
+        "type": "text",
+        "text": "We provide the best evaluation learning curves on both environments during tuning. ",
+        "bbox": [
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+        "page_idx": 11
+    }
+]