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+# A Hierarchical Reinforcement Learning Based Optimization Framework for Large-scale Dynamic Pickup and Delivery Problems
+
+Yi $\mathbf { M } \mathbf { a } ^ { 1 }$ ∗, Xiaotian Hao1∗, Jianye $\mathbf { H } \mathbf { a } \mathbf { o } ^ { 1 2 }$ †, Jiawen $\mathbf { L } \mathbf { u } ^ { 2 }$ , Xing Liu2, Xialiang $\mathbf { T o n g } ^ { 2 }$ , Mingxuan Yuan2, Zhigang $\mathbf { L i } ^ { 1 }$ , Jie $\mathbf { T a n g } ^ { 3 }$ , Zhaopeng Meng1 1College of Intelligence and Computing, Tianjin University {mayi,xiaotianhao, jianye.hao, scs_lzg, mengzp} $@$ tju.edu.cn 2Noah’s Ark Lab, Huawei, {jiawen.lu, tongxialiang, Yuan.Mingxuan} $@$ huawei.com 3Tsinghua University, jietang $@$ tsinghua.edu.cn
+
+# Abstract
+
+The Dynamic Pickup and Delivery Problem (DPDP) is an essential problem in the logistics domain, which is NP-hard. The objective is to dynamically schedule vehicles among multiple sites to serve the online generated orders such that the overall transportation cost could be minimized. The critical challenge of DPDP is the orders are not known a priori, i.e., the orders are dynamically generated in real-time. To address this problem, existing methods partition the overall DPDP into fixed-size sub-problems by caching online generated orders and solve each sub-problem, or on this basis to utilize the predicted future orders to optimize each sub-problem further. However, the solution quality and efficiency of these methods are unsatisfactory, especially when the problem scale is very large. In this paper, we propose a novel hierarchical optimization framework to better solve large-scale DPDPs. Specifically, we design an upper-level agent to dynamically partition the DPDP into a series of sub-problems with different scales to optimize vehicles routes towards globally better solutions. Besides, a lower-level agent is designed to efficiently solve each sub-problem by incorporating the strengths of classical operational research-based methods with reinforcement learning-based policies. To verify the effectiveness of the proposed framework, real historical data is collected from the order dispatching system of Huawei Supply Chain Business Unit and used to build a functional simulator. Extensive offline simulation and online testing conducted on the industrial order dispatching system justify the superior performance of our framework over existing baselines.
+
+# 1 Introduction
+
+The Dynamic Pickup and Delivery Problem (DPDP) constitutes an important family of routing problems, which generally contains three key elements: orders, goods and vehicles as shown in Figure 1. Orders are generated in real-time. Different orders contain different types and quantities of goods. A number of vehicles are scheduled to serve the orders by transporting the desired goods from different origins to different destinations. The objective of DPDP is to dynamically assign each order to the most appropriate vehicle so that the overall transportation cost (e.g., overall distances) could be minimized. DPDPs are widespread in order dispatching systems of the supply chain, express mail delivery services and elsewhere.
+
+DPDP is a complex variant of the Travelling Salesman Problem (TSP) and Vehicle Routing Problem (VRP), which are both NP-Hard combinatorial optimization problems [25]. The main difficulty of DPDP comes from the dynamically generated orders in real-time, thus the order dispatching decisions cannot be made beforehand in an offline style. Besides, compared with TSP and VRP, there exist various additional complex constraints in DPDP such as pickup and delivery constraint, Last-In-First-Out (LIFO) constraint, time window constraint, split demand constraint, etc.
+
+Traditional methods for DPDP. Existing solutions for DPDP fall into two categories. The first category maintains a fixed buffer to cache the most recent generated orders and periodically dispatches all cached orders in a delayed mode. By this way, the overall dynamic problem is partitioned into a series of static sub-problems with subsets of known orders, i.e., static Pickup and Delivery Problems (PDPs). Then, operational research-based (OR) methods [22, 20], heuristic and
+
+![](images/cffab4ad3c0adfcdecee9a0e263d0743d9661055b3ec7556369c0d85dc0c97b8.jpg)  
+Figure 1: Demonstration of DPDP
+
+meta-heuristic methods [7, 16, 25, 4, 5, 3, 11, 26, 23, 9] are designed to solve each sub-problem. However, myopically optimizing each static sub-problem cannot guarantee the overall dynamic problem could be optimized from a long-term perspective since the split sub-problems are not independent of each other. The main reasons are previous orders assignment results will influence (1) the number of remaining orders to be dispatched, (2) the vehicle’s remaining capacity and (3) the relative positions to the following orders. To acquire better solutions, the second category methods [24, 8, 12] try to predict the distribution of future orders and take the predicted orders into consideration when computing the solution for each sub-problem. However, predicting future orders is not realistic due to the high uncertainty in the real world. Inaccurate predictions will mislead the order dispatcher and route planner, and result in poor solution quality.
+
+Learning-based methods for VRP. Additionally, a common flaw of traditional OR and metaheuristic methods is that they are computationally expensive and normally unable to obtain a desired solution within the allowable time. Besides, the design of them heavily relies on complex domain knowledge. To improve the solution computing efficiency and ease the difficulty of the algorithm design, recently, several learning-based methods are proposed [27, 1, 18, 6, 13]. These methods have demonstrated that the solution computing efficiency can be significantly improved by leveraging the generalization ability of the trained models. Besides, they could obtain solutions with competitive qualities compared with the state-of-the-art traditional methods. Although these methods mainly focus on TSPs or VRPs, of which all orders’ information is known in advance and much fewer constraints are considered comparing with DPDP, learning-based methods have shown great potential to help solve large-scale DPDPs and reach superior performance.
+
+In this paper, we propose a novel hierarchical reinforcement learning (RL) based optimization framework to solve the real-world large-scale DPDPs. Considering that order dispatching has a longterm impact on the overall optimization objective, the upper-level RL agent dynamically determines whether to wait longer at each moment for caching more future orders. In this way, the orders can be more flexibly assigned to vehicles (since each vehicle will have more candidate orders to choose) and the routes of vehicles could be optimized towards globally better solutions. The lower-level RL agent is responsible for assigning the cached orders to the most appropriate vehicles by sequentially manipulating heuristic operators to improve the solution quality iteratively. To verify the effectiveness of the framework, we collected real historical data from the order dispatching system of Huawei Supply Chain and built a simulator to simulate the order dispatching and vehicle transportation process. Further, we deployed our method on the company’s Supply Chain Business Unit. Extensive offline simulation and online testing showed the superior performance of our algorithm.
+
+Our main contributions are as follows:
+
+• We are the first to propose a practical hierarchical RL framework to efficiently and farsightedly compute superior solutions for the real-world large-scale DPDPs with complex constraints.   
+• We design a simulator using real industrial data to be the experimental benchmark to verify the proposed method, which is available here for interested researchers.   
+• We show that our approach considerably improves the optimization objectives compared with existing algorithms both in the offline evaluation and online testing. The ablation study indicates our approach can obtain high-quality solutions with fast running speed and has strong generalization ability.
+
+# 2 Problem Formulation
+
+We now give the formulation of DPDP in our logistics scenario. For the orders dynamically generated in real-time at different nodes (i.e., factories and warehouses) within a day, vehicles should be scheduled to transport the goods from pickup nodes to delivery nodes to fulfil the orders with minimal transportation cost. In our case, the objective is to minimize $K$ vehicles average travelling distances $D ( K )$ of the entire DPDP:
+
+$$
+\operatorname* { m i n } D ( K )
+$$
+
+while meeting several constraints: Pickup and Delivery Constraint, Capacity Constraint, LIFO Constraint, Time Window Constraint, etc. Detailed constraints are shown in Appendix A.
+
+In practice, however, some orders are destined to violate time window constraints2. Thus, we add it to the objective function as an associated penalty to convert the hard time window constraint to a soft one. The penalty function is defined as the overtime beyond the specified completion time of each order. The optimization objective is then reformulated as minimizing the weighted sum 3 of average vehicles travelling distances (kilometers) $D ( K )$ and total overtime (seconds) $O T$ of all orders $C$ :
+
+$$
+\operatorname* { m i n } D ( K ) + \lambda * O T ( C )
+$$
+
+Apart from the various complex constraints mentioned above, the additional difficulties of this problem mainly come from two aspects:
+
+(1) The problem scale is very large. In practical logistic scenarios of the company, millions of products and intermediate materials are manufactured every day. As these products and materials might be used in the subsequent phases (e.g., assembling or selling), they have to be scheduled and transported between hundreds of factories and warehouses by dozens of vehicles within stringent timeline constraints, which constitutes a very large-scale and complex DPDP.   
+(2) Besides, as the orders are generated online in real-time, the schedule planning cannot be made aforehand in an offline style. From the oracle’s point of view, i.e., when all orders of a day are known in advance, the uncertainty is eliminated and this DPDP can be formulated as a complex Mixed Integer Programming (MIP) Problem, of which the optimal solution could be obtained utilizing exact algorithms (e.g., cutting plane algorithms, branch-and-bound algorithms or modern solvers such as Gurobi[20]) [22]. However, in reality, it’s impossible to know all the orders in advance, thus these approaches are not applicable.
+
+To eliminate the uncertainties brought by the unknown orders, a practical way is to utilize a buffer to cache the most recent generated orders and periodically dispatches all cached orders in a little delayed mode. With the known orders in the cache, the static PDP can be formulated as an MIP as shown in Appendix A. We could resort to modern solvers to solve this MIP. However, even for the static PDP with very few orders, it still costs several hours to compute a feasible solution, which is beyond the acceptable limits (details are shown in Table 2 and 3). Besides, even if we could obtain the optimal solution for each fixed split static PDP, we still cannot guarantee the global DPDP can be optimized as these static sub-problems are not independent of each other.
+
+# 3 Method
+
+# 3.1 Overall Framework
+
+![](images/a63fc2ac3eace80d601a066183cb4bf3c1da3b9a4dbf769b433fc8344b19c7a8.jpg)  
+Figure 2: Hierarchical Optimization Framework
+
+In this paper, considering the challenges mentioned above, we propose a novel hierarchical reinforcement learning based optimization framework, which contains two levels of agents. As shown in Figure 2, we maintain a buffer to cache the newly generated orders and periodically dispatch all cached orders at once. But instead of dispatching the cached orders of fixed numbers or predicting future orders, we design an upper-level agent to dynamically determine whether to wait longer for caching more future orders at each moment. Though waiting longer will postpone the dispatching and transportation of the earlier cached orders, additional future orders can be taken into account for the vehicle-order matching. In this way, each vehicle will have more candidate orders to choose, thus the overall travelling distances will be more potentially to be optimized for shorter4. This process could be regarded as sacrificing a little time in exchange for a precise estimation of future orders. However, waiting for too long will also increase the risk of overtime of the earlier cached orders. Thus, whether to wait longer to cache more orders at each moment will have a long-term impact on the overall dispatching results, and can be naturally modeled as a sequential decision-making problem. We model this procedure as a Markov Decision Process (MDP). Depending on whether to wait longer at each moment, the overall DPDP can be dynamically partitioned into a series of static sub-problems, each of which includes different numbers of orders. As shown in Figure 2, the generated orders are accumulated in the buffer until the upper-level agent decides to stop caching at time $t _ { i + k }$ . Then, the agent releases the cached orders to the lower-level agent and clears the buffer.
+
+Given the released orders (which form a static sub-problem, i.e., a PDP), the lower-level agent is appointed to assign the orders to the most appropriate vehicles and arrange the transportation route of each vehicle, such that the transportation cost of these orders could be minimized. First, a set of basic operators are maintained, whose roles are converting one feasible solution to another. For instance, given an initial solution’s route $\{ \mathrm { A } \mathrm { - } \mathrm { > B } \mathrm { - } \mathrm { > C } \}$ with three nodes A, B and C, a typical operator is swapping two nodes[13], e.g., swapping A and B. After applying this operator, $\{ \mathrm { A } \mathrm { - } \mathrm { > B } \mathrm { - } \mathrm { > C } \}$ is converted to $\{ { \bf B } { \bf - } { \bf > } { \bf A } { \bf - } { \bf > } { \bf C } \}$ . If the travelling cost of $\{ { \bf B } { \cdot } { > } { \bf A } { \cdot } { > } { \bf C } \}$ is less than $\{ \mathrm { A } \mathrm { - } \mathrm { > B } \mathrm { - } \mathrm { > C } \}$ , the initial solution is improved. On this basis, we design the lower-level agent similar to the traditional metaheuristic algorithms which sequentially manipulates these operators to improve the solution of each PDP. The difference is that we model the process of sequentially manipulating these operators as an MDP and incorporate RL methods to optimize the policy instead of manually designing complex rules. Finally, the best found solution is adopted by the order dispatching system to assign the orders to the vehicles and arrange their transportation routes. In the following two subsections, we will go into more details of the designed two agents.
+
+# 3.2 Upper-level Agent
+
+# 3.2.1 Workflow
+
+The workflow of the upper-level agent is described in Figure 2. We partition a day into $T = 1 4 4$ fixed time intervals, and the time span of each interval is ten minutes. Each time interval starts at time $t _ { i - 1 }$ and ends at time $t _ { i }$ , $i \leq T$ is a positive integer. We name $t _ { 1 } , . . . , t _ { i } , . . . , t _ { T }$ as decision points. At each decision point $t _ { i }$ , the upper-level agent decides whether to release the accumulated orders to the lower-level agent according to their overtime risk. Taking Figure 2 as an example, at decision point $t _ { i - 1 }$ , the buffer already cached some orders $O _ { i - 1 }$ . At $t _ { i - 1 }$ , the upper-level agent makes a decision and determines to wait longer and not to release $O _ { i - 1 }$ to the lower-level agent. Thus $O _ { i - 1 }$ are still maintained in the buffer. Thereafter, at all decision points before $t _ { i + k }$ , the upper-level agent makes the same decisions as at $t _ { i - 1 }$ , i.e., ’not release’. Therefore, new generated orders $\langle \bar { O _ { i } } , . . . , O _ { i + k } \rangle$ between $t _ { i - 1 }$ and $t _ { i + K }$ are all appended to the buffer as well. At $t _ { i + k }$ , the upper-level agent makes a change and determines to release all accumulated orders $\langle O _ { i - 1 } , O _ { i } , . . . , O _ { i + k } \rangle$ to the lower-level agent. At this time, all accumulated orders together with the remaining orders $O _ { \mathrm { r e m a i n } }$ (assigned to the vehicles before $t _ { i - 1 }$ but the goods of the orders are still not loaded onto the vehicles even at $t _ { i + k }$ ) will be released by the upper-level agent. In this way, we get a static sub-problem constituting of orders $\langle O _ { i - 1 } , O _ { i } , . . . , O _ { i + k } , O _ { \mathrm { r e m a i n } } \rangle$ for the lower-level agent. By analogy, the overall DPDP can be divided into a series of static PDPs with different scales. We model the procedure of whether to wait longer at each decision moment as an MDP described in the following subsection.
+
+# 3.2.2 Markov Decision Process (MDP)
+
+State: The state includes the number of orders accumulated in the buffer, the number of available vehicles, the amount of time left before exceeding the time limit of each order, etc. All these features are normalized and concatenated together. Detailed descriptions are postponed to the Appendix F due to the space limitation.
+
+Action: The action is a binary variable indicates whether to release orders to the lower-level agent.
+
+Reward: Our ultimate goal is to minimize the optimization objective for the entire dynamic problem. Therefore, we first get the the overtime of the orders completed and the corresponding vehicle travelling distances between two consecutive decision moments $t _ { i - 1 }$ and $t _ { i }$ as shown in Figure 2, i.e., avg_distance $+ \lambda *$ overtime. Then we set the immediate reward of action executed at $t _ { i - 1 }$ as $- ( \mathrm { a v g \_ d i s t a n c e } + \lambda *$ overtime). By this rule, the sum of the immediate rewards forms the negative value of the total objective for the entire dynamic problem. With this reward, the overall objective for the entire dynamic problem could be optimized. In other words, we encourage the upper-level agent to optimize the overall dynamic problem from a long-term perspective when making decisions.
+
+# 3.2.3 Agent Model
+
+For the upper-level agent, we use Deep Q Network (DQN) [17]. We parameterize a value function $Q \left( s , a ; \phi _ { l } \right)$ using the deep neural network of MLPs in which $\phi _ { l }$ are the parameters of the Q-network at updating iteration $l$ . When reaching decision point $t _ { i }$ , we obtain the state $s _ { t _ { i } }$ , action $\boldsymbol { a } _ { t _ { i } }$ , and reward $r _ { t _ { i } }$ according to Section 3.2.2 for the current static problem and save them to the replay buffer. When reaching decision point $t _ { i + 1 }$ , we obtain the state $s _ { t _ { i + 1 } }$ , which is the next state of the previous static sub-problem and we get a new transition $e _ { t _ { i } } = ( s _ { t _ { i } } , a _ { t _ { i } } , r _ { t _ { i } } , s _ { t _ { i + 1 } } )$ . We store the transitions into buffer $D = \{ e _ { t _ { 1 } } , \ldots , e _ { t _ { i } } , \ldots \}$ during the running of simulator. During the training, we apply Q-learning updates on uniformly sampled transitions $( s , a , r , s ^ { \prime } ) \sim U ( D )$ from the replay buffer. The model updates at iteration $l$ uses the following Temporal Difference (TD) loss function:
+
+$$
+L _ { i } \left( \phi _ { l } \right) = \mathbb { E } _ { ( s , a , r , s ^ { \prime } ) \sim U ( D ) } \left[ \left( r + \gamma \operatorname* { m a x } _ { a ^ { \prime } } Q \left( s ^ { \prime } , a ^ { \prime } ; \phi _ { l } ^ { - } \right) - Q \left( s , a ; \phi _ { l } \right) \right) ^ { 2 } \right]
+$$
+
+where $\gamma$ is the discount factor, $\phi _ { l }$ are the parameters of the Q-network at iteration $l$ and ${ \phi } _ { l } ^ { - }$ are the parameters of the target network at iteration $\it l$ .
+
+![](images/505766d775cc3d9cb4f45b38bdff6c77c1c8f417fd7954bc4287b3a99b8c0f78.jpg)  
+Figure 3: Workflow of Lower-level Agent
+
+# 3.3 Lower-level Agent
+
+# 3.3.1 Workflow
+
+The workflow of the lower-level agent is described in Figure 3. We first generate a feasible initial solution of the static sub-problem using greedy algorithm (described in Section 4.2). Given the initial solution, the lower-level agent iteratively improves the solution by manipulating different operators according to solution states as mentioned in Section 3.1 (we call this step Improvement [6, 13]). When the improved solution reaches a local optimum (i.e., the solution could not be improved further for a series of steps), we will partially or entirely re-assigning the orders using the greedy algorithm (we call this step Reconstruction). The improvement of the next iteration will start from the reconstructed solution. Note that the lower-level agent only selects improvement operators as reconstruction operator has a long-lasting effect on solutions compared with improvement operators and we found mixing up them will lead to instability during the training. The process of improvement and reconstruction alternates until reaching the maximum number of steps or the maximum allowable running time. The best generated solution during the improvements and reconstructions will be adopted to dispatch orders to vehicles. Note that the final accepted solution is ensured to be at least as good as the initial solution. Overall, by transferring the knowledge learned from previously solved PDPs to the new ones, the agent could efficiently and monotonically improve the solution quality. The MDP definition of the operators-manipulating procedure is described in the following subsection.
+
+# 3.3.2 Markov Decision Process (MDP)
+
+State: The state of the current solution consists of the states of all nodes, i.e., $s = \{ s _ { 1 } , s _ { 2 } , . . . , s _ { | V | } \}$ where $s _ { v }$ is the state of node $v$ . Each $s _ { v }$ includes the position information, order information, vehicle information and objective-related information. Details can be found in Appendix F.
+
+Action: The action set consists of 4 carefully designed operators, i.e., inner-exchange, inner-relocate, inter-exchange and inter-relocate. We provide a proof in Appendix G that any feasible solution (including the optimal one) could be obtained by iteratively applying these 4 operators from any given initial solution. Details are described in Appendix G.
+
+Reward: We find that the total objective can be easily reduced by a large margin during the first few improvement steps of an initial solution or reconstructed solution in the experiments (See Figure 4). If we assign the actions at these improvement steps a large reward, it’s not fair for the actions in the subsequent steps. This is because the actions in the subsequent steps also play important roles in improving solutions in the complex solution space. Therefore, the overall objective $\mathrm { O B J } _ { b }$ of the sub-problem after the first iteration (e.g., Iteration 1 in Figure 3) is used as the baseline following [13]. For each subsequent iteration $i$ , we first get the optimized objective after the iteration as $\mathrm { O B J } _ { i }$ and then assign $( | \mathbf { O B } \mathbf { J } _ { b } - \mathbf { O B J } _ { i } | ) / n _ { i }$ to all $n _ { i }$ actions executed in iteration $i$ as reward.
+
+# 3.3.3 Agent Policy Network
+
+The policy network of the lower-level agent inputs the state of the current solution and outputs action probabilities of length $| A |$ where $A$ is the set of operators. In our case, a critical challenge of designing the policy network is the number of orders and the number of available vehicles are different for each static sub-problem. As the quantity of the combination of orders and vehicles are extremely huge, we cannot train a separate model for every combination of different numbers of orders and vehicles. Thus, the desired model should be able to transfer the knowledge learned from the previously solved problems and generalize to new problems of any scale without fine-tuning. Besides, the routes of a solution naturally form a certain topological graph structure as shown in Figure 3. Therefore, in this paper, we incorporate GIN (Graph Isomorphism Network)[30], a powerful Graph Neural Network (GNN), to be the basis of the policy network of the lower-level agent. We use the REINFORCE algorithm [28] to train the policy network. Details of the policy network are shown in Appendix H.
+
+# 4 Offline Evaluation
+
+# 4.1 Experiments Settings
+
+We start with designing a simulator to shed light on the contributions of the proposed framework under more controlled settings. Details of the simulator can be found in Appendix C. To comprehensively verify the effectiveness of our approach on problems of different scales, we use four types of datasets of different sizes, i.e., 15 orders with 5 vehicles, 50 orders with 5 vehicles, 300 orders with 20 vehicles, 1000 orders with 50 vehicles (matching the practical problem of thousand scales). Note that the orders/vehicles ratios are set according to realistic business settings. Each type of datasets contains 10 datasets, including 7 training sets and 3 test sets according to the ratio of 7:3 (e.g., 300-1, 300-2 and 300-3 are test sets with 300 orders). The vehicles have the same load capacity. Details of the datasets are described in Appendix D. According to the realistic business settings, the time span between two consecutive decision points is set to 10 minutes in the simulator.
+
+The comparisons of different methods proceed as follows. For our approach, we first train a shared model on each type of training datasets and then evaluate the model on the test datasets of the same size. At each decision point, the upper-level agent decides whether to release orders to the lower-level agent. The lower-level agent is executed for no more than 10 minutes after receiving orders from the upper-level agent. Both agents are trained simultaneously. This training process is relatively stable due to the following reasons. The iterative solution optimization process (starts from an initial greedy solution) of our lower-level agent can ensure the obtained solutions have relatively high quality even at the initial training stages. In other words, the solutions given by the lower-level agent are relatively stable. Therefore, the unstable issue of co-training both levels of policies in our case is negligible, and thus both levels can be trained simultaneously. For baselines showed in Section 4.2, we also run them for up to 10 minutes at each decision point. We run the simulator until all the orders of the dataset are dispatched and completed to ensure fair comparisons. All the results in the experiments are obtained by running each algorithm ten times to get the mean and variance value of the optimization objective.
+
+# 4.2 Baselines
+
+To help readers better understand the baselines, we name them in the format of ’upper-level method $^ +$ lower-level method’ except for the Optimal baseline. ’10min-Interval’ means the dynamic problem is partitioned into static sub-problems with a fixed interval of ten minutes. ’1order-Interval’ means the dynamic problem is partitioned into static sub-problems consists of a single order.
+
+10min-Interval $^ +$ Greedy: Greedy [15] is the most widely-used method in industry, which is also the online deployed baseline method. The solution routes are expanded by greedily inserting new pickup and delivery nodes until all the orders are inserted.
+
+10min-Interval $^ +$ ALNS: ALNS [29] is one of the most representative meta-heuristic local search frameworks for solving DPDP that uses a series of operators to improve the solution. In each iteration, an operator is selected to destroy the current solution, and an operator is selected to repair the solution.
+
+1order-Interval $^ +$ E2ERL: According to [14], we use a DQN model to assign vehicles to each generated order and insert each order into the vehicle’s order queue using the Greedy algorithm. It’s an E2ERL (end-to-end RL) algorithm.
+
+10min-Interval $^ +$ ST-DDGN: ST-DDGN [12] is the state-of-the-art method that predicts future orders of DPDP. Then both the predicted orders and real generated orders are considered when solving each sub-problem using E2ERL.
+
+Optimal: We convert DPDPs to static PDPs as we can obtain all the orders’ information beforehand in offline style. Then we use Gurobi to solve the corresponding MIP model to get the optimal solution. As Gurobi can only solve small-scale PDPs within acceptable time due to the NP-hard property, we only compare with the optimal solution on problems of 15 and 50 orders in Section 4.4.1.
+
+# 4.3 Main Results
+
+Here we show part of the experimental results in Table 1. The complete results are shown in Table 6 of Appendix I. The objective improvement measurement is the improvement percentage of each algorithm compared with the Greedy algorithm. Our approach consistently outperforms all baselines
+
+Table 1: Main results of different methods on test datasets   
+
+<table><tr><td>Dataset</td><td>Algorithm</td><td>Overtime</td><td>Avg_Dis</td><td>Objective</td><td>Obj Impro</td></tr><tr><td rowspan="5">50-1</td><td>10min-Interval + Greedy</td><td>0</td><td>109.30</td><td>109.30</td><td>0.00%</td></tr><tr><td>lorder-Interval +E2ERL</td><td>0</td><td>96.56</td><td>96.56</td><td>11.66%</td></tr><tr><td>10min-Interval + ALNS</td><td>0</td><td>107.95</td><td>107.95</td><td>1.24%</td></tr><tr><td>10min-Interval + ST-DDGN</td><td>0</td><td>108.95</td><td>108.95</td><td>0.32%</td></tr><tr><td>Our (Upper-level RL + Lower-level RL)</td><td>0</td><td>93.70</td><td>93.70</td><td>14.27%</td></tr><tr><td rowspan="5">300-1</td><td>10min-Interval+Greedy</td><td>0</td><td>147.78</td><td>147.78</td><td>0.00%</td></tr><tr><td>lorder-Interval + E2ERL</td><td>0</td><td>158.39</td><td>158.39</td><td>-7.18%</td></tr><tr><td>10min-Interval + ALNS</td><td>0</td><td>137.31</td><td>137.31</td><td>7.08%</td></tr><tr><td>10min-Interval + ST-DDGN</td><td>0</td><td>131.99</td><td>131.99</td><td>10.68%</td></tr><tr><td>Our (Upper-level RL + Lower-level RL)</td><td>0</td><td>122.42</td><td>122.42</td><td>17.16%</td></tr><tr><td rowspan="5">1000-1</td><td>10min-Interval+Greedy</td><td>0</td><td>183.04</td><td>183.04</td><td>0.00%</td></tr><tr><td>lorder-Interval + E2ERL</td><td>0</td><td>180.36</td><td>180.36</td><td>1.46%</td></tr><tr><td>10min-Interval + ALNS</td><td>0</td><td>174.68</td><td>174.68</td><td>4.57%</td></tr><tr><td>10min-Interval + ST-DDGN</td><td>0</td><td>171.09</td><td>171.09</td><td>6.53%</td></tr><tr><td>Our(Upper-level RL +Lower-level RL)</td><td>0</td><td>159.18</td><td>159.18</td><td>13.04%</td></tr></table>
+
+on all datasets (lower total objective is better). On some datasets, the baselines have overtime results due to their lack of long-term planning and exhaustively optimization of each static problem from a myopic perspective. As a result, dispatching of some orders is delayed for too long, and finally, overtime is inevitable in any case. In contrast to this, our upper-level RL partitions the dynamic problem into sub-problems considering the balance between the orders overtime (seconds) risk and optimization of vehicle travelling distances (kilometers), and our lower-level RL is responsible for the optimization of each static sub-problem. The cooperation of the two agents enables our method to find solutions with less overtime and vehicle travelling distances on the overall dynamic problem from a long-term perspective. The comparison of the learning curves of all learning-based methods on 50-1 are shown in Figure 11 in Appendix I.
+
+# 4.4 Ablation Studies
+
+# 4.4.1 How far is our lower-level agent from the optimal one on static PDP?
+
+We convert the DPDP to a single static PDP as described in Section 4.2. As the orders should be assigned to vehicles all at once, there is no need to use an upper-level agent. Similarly, without the prediction of future orders, ST-DDGN is essentially the same as E2ERL. Therefore we only use the lower-level agent and E2ERL in the static PDP. Each algorithm is run without time or step limitation to discover its full potential. As shown in Table 2 and 3, the difference of the total objective of our method with the optimal solution is much smaller than the baselines (as all the overtime is 0, the column is omitted from the two Tables). The time consumption is much shorter than ALNS and Gurobi. It is because our method can exert the generalization ability to quickly improve the initial solution by using the most appropriate operators based on the experiences obtained from training, without the need of manually designing complicated search as in ALNS and Gurobi. Note that the time consumption of Gurobi on problems of 50 orders is represented using hyphen symbol ’-’, which means we can’t get results even after 100 hours due to the various complex constraints as described in Appendix A. Comparing with baselines, our method is the most qualified to meet the online deployment requirements that the algorithm should obtain high-quality solutions with fast speed.
+
+Table 2: Results on static 15-1, 15-2, 15-3   
+
+<table><tr><td>Algorithm</td><td>Avg_Dis</td><td>Objective</td><td>Obj Impro</td><td>Time</td></tr><tr><td>Greedy</td><td>53.85</td><td>53.85</td><td>0.00%</td><td>0.38s</td></tr><tr><td>E2ERL</td><td>51.70</td><td>51.70</td><td>3.99%</td><td>0.58s</td></tr><tr><td>ALNS</td><td>51.58</td><td>51.58</td><td>4.22%</td><td>405s</td></tr><tr><td>Our</td><td>45.72</td><td>45.72</td><td>15.10%</td><td>68.21s</td></tr><tr><td>(Lower-level RL) Optimal</td><td>44.35</td><td>44.35</td><td>17.64%</td><td>141360s</td></tr><tr><td>Greedy</td><td>69.61</td><td>69.61</td><td>0.00%</td><td>0.40s</td></tr><tr><td>E2ERL</td><td>68.00</td><td>68.00</td><td>2.31%</td><td>0.79s</td></tr><tr><td>ALNS</td><td>62.62</td><td>62.62</td><td>10.04%</td><td>606s</td></tr><tr><td>Our</td><td>62.32</td><td>62.32</td><td>10.47%</td><td>27.96s</td></tr><tr><td>(Lower-level RL) Optimal</td><td>57.48</td><td>57.48</td><td>17.43%</td><td>193680s</td></tr><tr><td>Greedy</td><td>78.73</td><td>78.73</td><td>0.00%</td><td>0.34s</td></tr><tr><td>E2ERL</td><td>59.02</td><td>59.02</td><td>25.03%</td><td>0.83s</td></tr><tr><td>ALNS</td><td>52.21</td><td>52.21</td><td>33.68%</td><td>920s</td></tr><tr><td>Our</td><td>50.95</td><td>50.95</td><td>35.29%</td><td>71.98s</td></tr><tr><td>(Lower-level RL) Optimal</td><td>50.75</td><td>50.75</td><td>35.54%</td><td>28651s</td></tr></table>
+
+Table 3: Results on static 50-1, 50-2, 50-3   
+
+<table><tr><td>Algorithm</td><td>Avg_Dis</td><td>Objective</td><td>Obj Impro</td><td>Time</td></tr><tr><td>Greedy</td><td>98.68</td><td>98.68</td><td>0.00%</td><td>66.73s</td></tr><tr><td>E2ERL</td><td>94.94</td><td>94.94</td><td>3.79%</td><td>52.64s</td></tr><tr><td>ALNS</td><td>96.98</td><td>96.98</td><td>1.72%</td><td>10728.34s</td></tr><tr><td>Our (Lower-level RL)</td><td>82.43</td><td>82.43</td><td>16.47%</td><td>1459.23s</td></tr><tr><td>Optimal</td><td>-</td><td>-</td><td>-</td><td>-</td></tr><tr><td>Greedy</td><td>80.67</td><td>80.67</td><td>0.00%</td><td>22.27s</td></tr><tr><td>E2ERL</td><td>76.04</td><td>76.04</td><td>5.74%</td><td>16.66s</td></tr><tr><td>ALNS</td><td>65.31</td><td>65.31</td><td>19.04%</td><td>6012.56s</td></tr><tr><td>Our (Lower-level RL)</td><td>58.42</td><td>58.42</td><td>27.58%</td><td>1152.64s</td></tr><tr><td>Optimal</td><td>=</td><td>=</td><td>=</td><td>=</td></tr><tr><td>Greedy</td><td>83.34</td><td>83.34</td><td>0.00%</td><td>44.31s</td></tr><tr><td>E2ERL</td><td>80.92</td><td>80.92</td><td>2.90%</td><td>20.34s</td></tr><tr><td>ALNS</td><td>80.51</td><td>80.51</td><td>3.40%</td><td>4140.15s</td></tr><tr><td>Our (Lower-level RL)</td><td>72.66</td><td>72.66</td><td>12.81%</td><td>1998.09s</td></tr><tr><td>Optimal</td><td>-</td><td>-</td><td>-</td><td>-</td></tr></table>
+
+# 4.4.2 Does lower-level agent learn how to select operators?
+
+To verify that our lower-level agent learns to choose the most suitable operators at different states, we compare the results of different operator selection methods on both static problems and dynamic problems. We first compare the total objective during the solution improvement process on the static problems using the lower-level agent with the method that randomly selects operators. As the improvement-reconstruct iteration process designed in Section 3.3 ensures the quality of the solution can be monotonically improved, selecting operators randomly is also a powerful baseline that can achieve satisfactory performance for the static PDP.
+
+Therefore, for the static problem, we mainly focus on whether the lower-level agent can improve the solving speed. As we can see in Figure 4, at the same step, choosing operators using lower-level RL can reach a better objective than randomly choosing operators, which indicates our lower-level method learned to accelerate the searching for better solutions. Since the static sub-problems of a dynamic problem are not independent of each other, the small gap between the above
+
+![](images/bd810fb7e2b2140648402ff44b3c03029bbb2ec9151bf3b8de37d65eaf513284.jpg)  
+Figure 4: Comparison of different selection methods of operators on static problems
+
+two methods in a static sub-problem will continue to enlarge in the subsequent sub-problems, resulting in a very large result gap on the entire dynamic problem. We compare the total objectives of the entire dynamic problems in Table 4. To ensure fairness, we control the upper-level methods to be ’10min-Interval’ and use the lower-level agent and random selection as lower-level methods, respectively. As we can see in Table 4, using the lower-level agent can help find better solutions on the entire dynamic problems.
+
+# 4.4.3 Does the upper-level agent learn to partition DPDP from a long-term perspective?
+
+To verify that our upper-level agent learns to partition the dynamic problem into static subproblems from a long-term perspective, we compare the results of differ
+
+Table 4: Effectiveness of lower-level agent and upper-level agent   
+
+<table><tr><td>Dataset</td><td>Method</td><td>Overtime</td><td>Avg_Dis</td><td>Objective</td><td>ObjImpro</td></tr><tr><td rowspan="3">300-1</td><td>10min-Interval+Random Search</td><td>0</td><td>139.16 ± 8.59</td><td>139.16</td><td>0.00%</td></tr><tr><td>10min-Interval + Lower-level RL</td><td>0</td><td>126.95 ± 4.80</td><td>126.95</td><td>8.77%</td></tr><tr><td>Our(Upper-level RL +Lower-level RL)</td><td>0</td><td>122.42 ± 4.02</td><td>122.42</td><td>12.03%</td></tr><tr><td rowspan="3">300-2</td><td>10min-Interval+RandomSearch</td><td>0</td><td>166.31 ± 10.20</td><td>166.31</td><td>0.00%</td></tr><tr><td>10min-Interval + Lower-level RL</td><td>0</td><td>154.39 ± 8.13</td><td>154.39</td><td>7.17%</td></tr><tr><td>Our (Upper-level RL + Lower-level RL)</td><td>0</td><td>142.33 ± 7.47</td><td>142.33</td><td>14.42%</td></tr><tr><td rowspan="3">300-3</td><td>10min-Interval+RandomSearch</td><td>0</td><td>168.69±7.70</td><td>168.69</td><td>0.00%</td></tr><tr><td>10min-Interval + Lower-level RL</td><td>0</td><td>156.64 ± 7.50</td><td>156.64</td><td>7.14%</td></tr><tr><td>Our(Upper-level RL +Lower-level RL)</td><td>0</td><td>146.88 ±13.91</td><td>146.88</td><td>12.93%</td></tr></table>
+
+ent static sub-problems partitioning methods. We compare our upper-level agent with the $\mathrm { \Omega } ^ { , } 1 0 \mathrm { m i n } .$ Interval’ method. As we can see in Table 4, using an upper-level agent to partition the dynamic problem reaches the best objective. The results illustrate that our upper-level agent can partition the problem from a long-term perspective to balance the orders overtime risk and optimization of vehicle travelling distances.
+
+# 4.4.4 Can our method generalized to larger-scale problems?
+
+To verify our method’s generalization ability, we evaluate the models trained using datasets of 300 orders / 20 vehicles on larger-scale datasets, i.e., 1000 orders / 50 vehicles. As shown in Table 5, the model trained on datasets of 300 orders achieves similar performance with the one trained on datasets of 1000 orders.
+
+Table 5: Generalization verification   
+
+<table><tr><td>Dataset</td><td>Model</td><td>Overtime</td><td>Avg_Dis</td><td>Objective</td></tr><tr><td rowspan="2">1000-1</td><td>Trained on 1000</td><td>0</td><td>159.18 ± 4.10</td><td>159.18</td></tr><tr><td>Trained on 300</td><td>0</td><td>170.78 ± 10.27</td><td>170.78</td></tr><tr><td rowspan="2">1000-2</td><td>Trained on 1000</td><td>0</td><td>196.66± 9.52</td><td>196.66</td></tr><tr><td>Trained on 300</td><td>0</td><td>209.48±8.68</td><td>209.48</td></tr><tr><td rowspan="2">1000-3</td><td>Trained on 1000</td><td>0</td><td>176.39 ± 7.61</td><td>176.39</td></tr><tr><td>Trained on 300</td><td>0</td><td>182.83 ± 5.64</td><td>182.83</td></tr></table>
+
+Note that the model trained on datasets of 300 orders also outperforms the baselines in Table 1. It verifies that our method can be generalized to new problems of different scales without fine-tuning after well trained on existing problems.
+
+# 5 Online Testing
+
+We deployed our method on the order dispatching system in Huawei supply chain. In the online experiments, we compare our method with the previously online deployed greedy algorithm (10min-Interval $^ +$ Greedy). For a fair comparison, we control the vehicles and the nodes (factories and warehouses) involved in the online testing to be the same. Normally, a standard A/B testing is required to be performed on homogeneous experimental groups using different methods
+
+![](images/03c50a505ccc16ad888407a2571a88d5e637c0de5e647de57cf281efeb8016a4.jpg)  
+Figure 5: Online Results
+
+at the same time dimension. Then experimental data of each group are collected and evaluated to choose the best method. However, in our situation, it’s unrealistic to split each order into two sub-orders to ensure the experimental groups are homogeneous. Besides, a large number of offline experiments have demonstrated that our method is significantly better than the greedy algorithm. Even in the worst case when there is no improvement in each sub-problem, our method is still the same with Greedy. Thus, we directly replaced the greedy algorithm for online deployment. Figure 5 summarises the results from Nov 2020 to Apr 2021. The points of Nov and Dec 2020 shown in Figure 5 are generated by greedy algorithm and our method is deployed from Jan to Apr 2021. As we can see, our method can reduce the average orders’ overtime and vehicles’ travelling distances compared with the greedy baseline. Even with more orders, our method can still reach a better optimization objective. Note that in the actual business scenario, orders generated in each day follow a similar distribution with a small variance. These results indicate that our method could achieve a better performance in the realistic deployment environment with varied data distributions.
+
+# 6 Conclusions
+
+In this paper, we propose a novel hierarchical reinforcement learning based optimization framework to solve the large-scale DPDP in the real world. The upper-level agent is equipped with the far-sight ability whose target is to optimize the long-term cumulative objective. The lower-level agent exerts the generalization ability of GNN to quickly improve the solution quality by transferring the knowledge (policy) learned from training. The cooperation of the upper-level and lower-level agents enables our method to find globally better solutions. Extensive offline simulation on the simulator built on real historical data and online testing verify that our method can obtain higher-quality solutions with faster running speed.
+
+The core idea of our learning-based framework are beneficial to a number of similar problems in the supply chain community that have time-evolving components (e.g., orders/customers/tasks), such as dynamic routing problems, dynamic flow shop scheduling, dynamic job shop scheduling, dynamic bin packing and so on. As orders/customers/tasks of all these dynamic problems are online generated that are not known a priori, the orders/customers/tasks should first be cached and then be dispatched. In this way, these problems can be modeled as hierarchical optimization problems like DPDP that the upper-level problem is ”how to cache orders/customers/tasks” and the lower-level problem is ”how to dispatch cached orders/customers/tasks”. We will verify our proposed framework in these fields in the future work.
+
+# Acknowledgments and Disclosure of Funding
+
+The work is supported by the National Natural Science Foundation of China (Grant Nos: U1836214) and the New Generation of Artificial Intelligence Science and Technology Major Project of Tianjin under grant: 19ZXZNGX00010.
+
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+        "text": "A Hierarchical Reinforcement Learning Based Optimization Framework for Large-scale Dynamic Pickup and Delivery Problems ",
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+        "text": "Yi $\\mathbf { M } \\mathbf { a } ^ { 1 }$ ∗, Xiaotian Hao1∗, Jianye $\\mathbf { H } \\mathbf { a } \\mathbf { o } ^ { 1 2 }$ †, Jiawen $\\mathbf { L } \\mathbf { u } ^ { 2 }$ , Xing Liu2, Xialiang $\\mathbf { T o n g } ^ { 2 }$ , Mingxuan Yuan2, Zhigang $\\mathbf { L i } ^ { 1 }$ , Jie $\\mathbf { T a n g } ^ { 3 }$ , Zhaopeng Meng1 1College of Intelligence and Computing, Tianjin University {mayi,xiaotianhao, jianye.hao, scs_lzg, mengzp} $@$ tju.edu.cn 2Noah’s Ark Lab, Huawei, {jiawen.lu, tongxialiang, Yuan.Mingxuan} $@$ huawei.com 3Tsinghua University, jietang $@$ tsinghua.edu.cn ",
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+        "text": "The Dynamic Pickup and Delivery Problem (DPDP) is an essential problem in the logistics domain, which is NP-hard. The objective is to dynamically schedule vehicles among multiple sites to serve the online generated orders such that the overall transportation cost could be minimized. The critical challenge of DPDP is the orders are not known a priori, i.e., the orders are dynamically generated in real-time. To address this problem, existing methods partition the overall DPDP into fixed-size sub-problems by caching online generated orders and solve each sub-problem, or on this basis to utilize the predicted future orders to optimize each sub-problem further. However, the solution quality and efficiency of these methods are unsatisfactory, especially when the problem scale is very large. In this paper, we propose a novel hierarchical optimization framework to better solve large-scale DPDPs. Specifically, we design an upper-level agent to dynamically partition the DPDP into a series of sub-problems with different scales to optimize vehicles routes towards globally better solutions. Besides, a lower-level agent is designed to efficiently solve each sub-problem by incorporating the strengths of classical operational research-based methods with reinforcement learning-based policies. To verify the effectiveness of the proposed framework, real historical data is collected from the order dispatching system of Huawei Supply Chain Business Unit and used to build a functional simulator. Extensive offline simulation and online testing conducted on the industrial order dispatching system justify the superior performance of our framework over existing baselines. ",
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+    {
+        "type": "text",
+        "text": "1 Introduction ",
+        "text_level": 1,
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+        "text": "The Dynamic Pickup and Delivery Problem (DPDP) constitutes an important family of routing problems, which generally contains three key elements: orders, goods and vehicles as shown in Figure 1. Orders are generated in real-time. Different orders contain different types and quantities of goods. A number of vehicles are scheduled to serve the orders by transporting the desired goods from different origins to different destinations. The objective of DPDP is to dynamically assign each order to the most appropriate vehicle so that the overall transportation cost (e.g., overall distances) could be minimized. DPDPs are widespread in order dispatching systems of the supply chain, express mail delivery services and elsewhere. ",
+        "bbox": [
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+        "type": "text",
+        "text": "DPDP is a complex variant of the Travelling Salesman Problem (TSP) and Vehicle Routing Problem (VRP), which are both NP-Hard combinatorial optimization problems [25]. The main difficulty of DPDP comes from the dynamically generated orders in real-time, thus the order dispatching decisions cannot be made beforehand in an offline style. Besides, compared with TSP and VRP, there exist various additional complex constraints in DPDP such as pickup and delivery constraint, Last-In-First-Out (LIFO) constraint, time window constraint, split demand constraint, etc. ",
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+        "text": "Traditional methods for DPDP. Existing solutions for DPDP fall into two categories. The first category maintains a fixed buffer to cache the most recent generated orders and periodically dispatches all cached orders in a delayed mode. By this way, the overall dynamic problem is partitioned into a series of static sub-problems with subsets of known orders, i.e., static Pickup and Delivery Problems (PDPs). Then, operational research-based (OR) methods [22, 20], heuristic and ",
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+        "image_caption": [
+            "Figure 1: Demonstration of DPDP "
+        ],
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+    },
+    {
+        "type": "text",
+        "text": "meta-heuristic methods [7, 16, 25, 4, 5, 3, 11, 26, 23, 9] are designed to solve each sub-problem. However, myopically optimizing each static sub-problem cannot guarantee the overall dynamic problem could be optimized from a long-term perspective since the split sub-problems are not independent of each other. The main reasons are previous orders assignment results will influence (1) the number of remaining orders to be dispatched, (2) the vehicle’s remaining capacity and (3) the relative positions to the following orders. To acquire better solutions, the second category methods [24, 8, 12] try to predict the distribution of future orders and take the predicted orders into consideration when computing the solution for each sub-problem. However, predicting future orders is not realistic due to the high uncertainty in the real world. Inaccurate predictions will mislead the order dispatcher and route planner, and result in poor solution quality. ",
+        "bbox": [
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+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "Learning-based methods for VRP. Additionally, a common flaw of traditional OR and metaheuristic methods is that they are computationally expensive and normally unable to obtain a desired solution within the allowable time. Besides, the design of them heavily relies on complex domain knowledge. To improve the solution computing efficiency and ease the difficulty of the algorithm design, recently, several learning-based methods are proposed [27, 1, 18, 6, 13]. These methods have demonstrated that the solution computing efficiency can be significantly improved by leveraging the generalization ability of the trained models. Besides, they could obtain solutions with competitive qualities compared with the state-of-the-art traditional methods. Although these methods mainly focus on TSPs or VRPs, of which all orders’ information is known in advance and much fewer constraints are considered comparing with DPDP, learning-based methods have shown great potential to help solve large-scale DPDPs and reach superior performance. ",
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+    {
+        "type": "text",
+        "text": "In this paper, we propose a novel hierarchical reinforcement learning (RL) based optimization framework to solve the real-world large-scale DPDPs. Considering that order dispatching has a longterm impact on the overall optimization objective, the upper-level RL agent dynamically determines whether to wait longer at each moment for caching more future orders. In this way, the orders can be more flexibly assigned to vehicles (since each vehicle will have more candidate orders to choose) and the routes of vehicles could be optimized towards globally better solutions. The lower-level RL agent is responsible for assigning the cached orders to the most appropriate vehicles by sequentially manipulating heuristic operators to improve the solution quality iteratively. To verify the effectiveness of the framework, we collected real historical data from the order dispatching system of Huawei Supply Chain and built a simulator to simulate the order dispatching and vehicle transportation process. Further, we deployed our method on the company’s Supply Chain Business Unit. Extensive offline simulation and online testing showed the superior performance of our algorithm. ",
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+    {
+        "type": "text",
+        "text": "Our main contributions are as follows: ",
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+        "text": "• We are the first to propose a practical hierarchical RL framework to efficiently and farsightedly compute superior solutions for the real-world large-scale DPDPs with complex constraints.   \n• We design a simulator using real industrial data to be the experimental benchmark to verify the proposed method, which is available here for interested researchers.   \n• We show that our approach considerably improves the optimization objectives compared with existing algorithms both in the offline evaluation and online testing. The ablation study indicates our approach can obtain high-quality solutions with fast running speed and has strong generalization ability. ",
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+    {
+        "type": "text",
+        "text": "2 Problem Formulation ",
+        "text_level": 1,
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+        "type": "text",
+        "text": "We now give the formulation of DPDP in our logistics scenario. For the orders dynamically generated in real-time at different nodes (i.e., factories and warehouses) within a day, vehicles should be scheduled to transport the goods from pickup nodes to delivery nodes to fulfil the orders with minimal transportation cost. In our case, the objective is to minimize $K$ vehicles average travelling distances $D ( K )$ of the entire DPDP: ",
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+    {
+        "type": "equation",
+        "img_path": "images/fbb1306a5d2c874e3898029fb02a44400a1b445c5eeb155f51902b6f4023aa7b.jpg",
+        "text": "$$\n\\operatorname* { m i n } D ( K )\n$$",
+        "text_format": "latex",
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+    {
+        "type": "text",
+        "text": "while meeting several constraints: Pickup and Delivery Constraint, Capacity Constraint, LIFO Constraint, Time Window Constraint, etc. Detailed constraints are shown in Appendix A. ",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "In practice, however, some orders are destined to violate time window constraints2. Thus, we add it to the objective function as an associated penalty to convert the hard time window constraint to a soft one. The penalty function is defined as the overtime beyond the specified completion time of each order. The optimization objective is then reformulated as minimizing the weighted sum 3 of average vehicles travelling distances (kilometers) $D ( K )$ and total overtime (seconds) $O T$ of all orders $C$ : ",
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+    {
+        "type": "equation",
+        "img_path": "images/b56976e96f1c129f139647dee4da696cef5bbfcc1f71184966c068988b7e8bba.jpg",
+        "text": "$$\n\\operatorname* { m i n } D ( K ) + \\lambda * O T ( C )\n$$",
+        "text_format": "latex",
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+    {
+        "type": "text",
+        "text": "Apart from the various complex constraints mentioned above, the additional difficulties of this problem mainly come from two aspects: ",
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+        "type": "text",
+        "text": "(1) The problem scale is very large. In practical logistic scenarios of the company, millions of products and intermediate materials are manufactured every day. As these products and materials might be used in the subsequent phases (e.g., assembling or selling), they have to be scheduled and transported between hundreds of factories and warehouses by dozens of vehicles within stringent timeline constraints, which constitutes a very large-scale and complex DPDP.   \n(2) Besides, as the orders are generated online in real-time, the schedule planning cannot be made aforehand in an offline style. From the oracle’s point of view, i.e., when all orders of a day are known in advance, the uncertainty is eliminated and this DPDP can be formulated as a complex Mixed Integer Programming (MIP) Problem, of which the optimal solution could be obtained utilizing exact algorithms (e.g., cutting plane algorithms, branch-and-bound algorithms or modern solvers such as Gurobi[20]) [22]. However, in reality, it’s impossible to know all the orders in advance, thus these approaches are not applicable. ",
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+        "page_idx": 2
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+    {
+        "type": "text",
+        "text": "To eliminate the uncertainties brought by the unknown orders, a practical way is to utilize a buffer to cache the most recent generated orders and periodically dispatches all cached orders in a little delayed mode. With the known orders in the cache, the static PDP can be formulated as an MIP as shown in Appendix A. We could resort to modern solvers to solve this MIP. However, even for the static PDP with very few orders, it still costs several hours to compute a feasible solution, which is beyond the acceptable limits (details are shown in Table 2 and 3). Besides, even if we could obtain the optimal solution for each fixed split static PDP, we still cannot guarantee the global DPDP can be optimized as these static sub-problems are not independent of each other. ",
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+    {
+        "type": "text",
+        "text": "3 Method ",
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+    {
+        "type": "text",
+        "text": "3.1 Overall Framework ",
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+    },
+    {
+        "type": "image",
+        "img_path": "images/a63fc2ac3eace80d601a066183cb4bf3c1da3b9a4dbf769b433fc8344b19c7a8.jpg",
+        "image_caption": [
+            "Figure 2: Hierarchical Optimization Framework "
+        ],
+        "image_footnote": [],
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "In this paper, considering the challenges mentioned above, we propose a novel hierarchical reinforcement learning based optimization framework, which contains two levels of agents. As shown in Figure 2, we maintain a buffer to cache the newly generated orders and periodically dispatch all cached orders at once. But instead of dispatching the cached orders of fixed numbers or predicting future orders, we design an upper-level agent to dynamically determine whether to wait longer for caching more future orders at each moment. Though waiting longer will postpone the dispatching and transportation of the earlier cached orders, additional future orders can be taken into account for the vehicle-order matching. In this way, each vehicle will have more candidate orders to choose, thus the overall travelling distances will be more potentially to be optimized for shorter4. This process could be regarded as sacrificing a little time in exchange for a precise estimation of future orders. However, waiting for too long will also increase the risk of overtime of the earlier cached orders. Thus, whether to wait longer to cache more orders at each moment will have a long-term impact on the overall dispatching results, and can be naturally modeled as a sequential decision-making problem. We model this procedure as a Markov Decision Process (MDP). Depending on whether to wait longer at each moment, the overall DPDP can be dynamically partitioned into a series of static sub-problems, each of which includes different numbers of orders. As shown in Figure 2, the generated orders are accumulated in the buffer until the upper-level agent decides to stop caching at time $t _ { i + k }$ . Then, the agent releases the cached orders to the lower-level agent and clears the buffer. ",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "Given the released orders (which form a static sub-problem, i.e., a PDP), the lower-level agent is appointed to assign the orders to the most appropriate vehicles and arrange the transportation route of each vehicle, such that the transportation cost of these orders could be minimized. First, a set of basic operators are maintained, whose roles are converting one feasible solution to another. For instance, given an initial solution’s route $\\{ \\mathrm { A } \\mathrm { - } \\mathrm { > B } \\mathrm { - } \\mathrm { > C } \\}$ with three nodes A, B and C, a typical operator is swapping two nodes[13], e.g., swapping A and B. After applying this operator, $\\{ \\mathrm { A } \\mathrm { - } \\mathrm { > B } \\mathrm { - } \\mathrm { > C } \\}$ is converted to $\\{ { \\bf B } { \\bf - } { \\bf > } { \\bf A } { \\bf - } { \\bf > } { \\bf C } \\}$ . If the travelling cost of $\\{ { \\bf B } { \\cdot } { > } { \\bf A } { \\cdot } { > } { \\bf C } \\}$ is less than $\\{ \\mathrm { A } \\mathrm { - } \\mathrm { > B } \\mathrm { - } \\mathrm { > C } \\}$ , the initial solution is improved. On this basis, we design the lower-level agent similar to the traditional metaheuristic algorithms which sequentially manipulates these operators to improve the solution of each PDP. The difference is that we model the process of sequentially manipulating these operators as an MDP and incorporate RL methods to optimize the policy instead of manually designing complex rules. Finally, the best found solution is adopted by the order dispatching system to assign the orders to the vehicles and arrange their transportation routes. In the following two subsections, we will go into more details of the designed two agents. ",
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+    {
+        "type": "text",
+        "text": "3.2 Upper-level Agent ",
+        "text_level": 1,
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+    {
+        "type": "text",
+        "text": "3.2.1 Workflow ",
+        "text_level": 1,
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+    {
+        "type": "text",
+        "text": "The workflow of the upper-level agent is described in Figure 2. We partition a day into $T = 1 4 4$ fixed time intervals, and the time span of each interval is ten minutes. Each time interval starts at time $t _ { i - 1 }$ and ends at time $t _ { i }$ , $i \\leq T$ is a positive integer. We name $t _ { 1 } , . . . , t _ { i } , . . . , t _ { T }$ as decision points. At each decision point $t _ { i }$ , the upper-level agent decides whether to release the accumulated orders to the lower-level agent according to their overtime risk. Taking Figure 2 as an example, at decision point $t _ { i - 1 }$ , the buffer already cached some orders $O _ { i - 1 }$ . At $t _ { i - 1 }$ , the upper-level agent makes a decision and determines to wait longer and not to release $O _ { i - 1 }$ to the lower-level agent. Thus $O _ { i - 1 }$ are still maintained in the buffer. Thereafter, at all decision points before $t _ { i + k }$ , the upper-level agent makes the same decisions as at $t _ { i - 1 }$ , i.e., ’not release’. Therefore, new generated orders $\\langle \\bar { O _ { i } } , . . . , O _ { i + k } \\rangle$ between $t _ { i - 1 }$ and $t _ { i + K }$ are all appended to the buffer as well. At $t _ { i + k }$ , the upper-level agent makes a change and determines to release all accumulated orders $\\langle O _ { i - 1 } , O _ { i } , . . . , O _ { i + k } \\rangle$ to the lower-level agent. At this time, all accumulated orders together with the remaining orders $O _ { \\mathrm { r e m a i n } }$ (assigned to the vehicles before $t _ { i - 1 }$ but the goods of the orders are still not loaded onto the vehicles even at $t _ { i + k }$ ) will be released by the upper-level agent. In this way, we get a static sub-problem constituting of orders $\\langle O _ { i - 1 } , O _ { i } , . . . , O _ { i + k } , O _ { \\mathrm { r e m a i n } } \\rangle$ for the lower-level agent. By analogy, the overall DPDP can be divided into a series of static PDPs with different scales. We model the procedure of whether to wait longer at each decision moment as an MDP described in the following subsection. ",
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+    {
+        "type": "text",
+        "text": "3.2.2 Markov Decision Process (MDP) ",
+        "text_level": 1,
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+        "type": "text",
+        "text": "State: The state includes the number of orders accumulated in the buffer, the number of available vehicles, the amount of time left before exceeding the time limit of each order, etc. All these features are normalized and concatenated together. Detailed descriptions are postponed to the Appendix F due to the space limitation. ",
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+    {
+        "type": "text",
+        "text": "Action: The action is a binary variable indicates whether to release orders to the lower-level agent. ",
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+        "type": "text",
+        "text": "Reward: Our ultimate goal is to minimize the optimization objective for the entire dynamic problem. Therefore, we first get the the overtime of the orders completed and the corresponding vehicle travelling distances between two consecutive decision moments $t _ { i - 1 }$ and $t _ { i }$ as shown in Figure 2, i.e., avg_distance $+ \\lambda *$ overtime. Then we set the immediate reward of action executed at $t _ { i - 1 }$ as $- ( \\mathrm { a v g \\_ d i s t a n c e } + \\lambda *$ overtime). By this rule, the sum of the immediate rewards forms the negative value of the total objective for the entire dynamic problem. With this reward, the overall objective for the entire dynamic problem could be optimized. In other words, we encourage the upper-level agent to optimize the overall dynamic problem from a long-term perspective when making decisions. ",
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+        "type": "text",
+        "text": "3.2.3 Agent Model ",
+        "text_level": 1,
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+        "type": "text",
+        "text": "For the upper-level agent, we use Deep Q Network (DQN) [17]. We parameterize a value function $Q \\left( s , a ; \\phi _ { l } \\right)$ using the deep neural network of MLPs in which $\\phi _ { l }$ are the parameters of the Q-network at updating iteration $l$ . When reaching decision point $t _ { i }$ , we obtain the state $s _ { t _ { i } }$ , action $\\boldsymbol { a } _ { t _ { i } }$ , and reward $r _ { t _ { i } }$ according to Section 3.2.2 for the current static problem and save them to the replay buffer. When reaching decision point $t _ { i + 1 }$ , we obtain the state $s _ { t _ { i + 1 } }$ , which is the next state of the previous static sub-problem and we get a new transition $e _ { t _ { i } } = ( s _ { t _ { i } } , a _ { t _ { i } } , r _ { t _ { i } } , s _ { t _ { i + 1 } } )$ . We store the transitions into buffer $D = \\{ e _ { t _ { 1 } } , \\ldots , e _ { t _ { i } } , \\ldots \\}$ during the running of simulator. During the training, we apply Q-learning updates on uniformly sampled transitions $( s , a , r , s ^ { \\prime } ) \\sim U ( D )$ from the replay buffer. The model updates at iteration $l$ uses the following Temporal Difference (TD) loss function: ",
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+        "type": "equation",
+        "img_path": "images/b0e8b8af5ae5c96e7a7b4efcb758d48aef40fd75c24324f5ea6cd281e3125faa.jpg",
+        "text": "$$\nL _ { i } \\left( \\phi _ { l } \\right) = \\mathbb { E } _ { ( s , a , r , s ^ { \\prime } ) \\sim U ( D ) } \\left[ \\left( r + \\gamma \\operatorname* { m a x } _ { a ^ { \\prime } } Q \\left( s ^ { \\prime } , a ^ { \\prime } ; \\phi _ { l } ^ { - } \\right) - Q \\left( s , a ; \\phi _ { l } \\right) \\right) ^ { 2 } \\right]\n$$",
+        "text_format": "latex",
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+    {
+        "type": "text",
+        "text": "where $\\gamma$ is the discount factor, $\\phi _ { l }$ are the parameters of the Q-network at iteration $l$ and ${ \\phi } _ { l } ^ { - }$ are the parameters of the target network at iteration $\\it l$ . ",
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+    {
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+        "image_caption": [
+            "Figure 3: Workflow of Lower-level Agent "
+        ],
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+    {
+        "type": "text",
+        "text": "3.3 Lower-level Agent ",
+        "text_level": 1,
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+    {
+        "type": "text",
+        "text": "3.3.1 Workflow ",
+        "text_level": 1,
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+    {
+        "type": "text",
+        "text": "The workflow of the lower-level agent is described in Figure 3. We first generate a feasible initial solution of the static sub-problem using greedy algorithm (described in Section 4.2). Given the initial solution, the lower-level agent iteratively improves the solution by manipulating different operators according to solution states as mentioned in Section 3.1 (we call this step Improvement [6, 13]). When the improved solution reaches a local optimum (i.e., the solution could not be improved further for a series of steps), we will partially or entirely re-assigning the orders using the greedy algorithm (we call this step Reconstruction). The improvement of the next iteration will start from the reconstructed solution. Note that the lower-level agent only selects improvement operators as reconstruction operator has a long-lasting effect on solutions compared with improvement operators and we found mixing up them will lead to instability during the training. The process of improvement and reconstruction alternates until reaching the maximum number of steps or the maximum allowable running time. The best generated solution during the improvements and reconstructions will be adopted to dispatch orders to vehicles. Note that the final accepted solution is ensured to be at least as good as the initial solution. Overall, by transferring the knowledge learned from previously solved PDPs to the new ones, the agent could efficiently and monotonically improve the solution quality. The MDP definition of the operators-manipulating procedure is described in the following subsection. ",
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+    {
+        "type": "text",
+        "text": "3.3.2 Markov Decision Process (MDP) ",
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+        "type": "text",
+        "text": "State: The state of the current solution consists of the states of all nodes, i.e., $s = \\{ s _ { 1 } , s _ { 2 } , . . . , s _ { | V | } \\}$ where $s _ { v }$ is the state of node $v$ . Each $s _ { v }$ includes the position information, order information, vehicle information and objective-related information. Details can be found in Appendix F. ",
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+    {
+        "type": "text",
+        "text": "Action: The action set consists of 4 carefully designed operators, i.e., inner-exchange, inner-relocate, inter-exchange and inter-relocate. We provide a proof in Appendix G that any feasible solution (including the optimal one) could be obtained by iteratively applying these 4 operators from any given initial solution. Details are described in Appendix G. ",
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+    {
+        "type": "text",
+        "text": "Reward: We find that the total objective can be easily reduced by a large margin during the first few improvement steps of an initial solution or reconstructed solution in the experiments (See Figure 4). If we assign the actions at these improvement steps a large reward, it’s not fair for the actions in the subsequent steps. This is because the actions in the subsequent steps also play important roles in improving solutions in the complex solution space. Therefore, the overall objective $\\mathrm { O B J } _ { b }$ of the sub-problem after the first iteration (e.g., Iteration 1 in Figure 3) is used as the baseline following [13]. For each subsequent iteration $i$ , we first get the optimized objective after the iteration as $\\mathrm { O B J } _ { i }$ and then assign $( | \\mathbf { O B } \\mathbf { J } _ { b } - \\mathbf { O B J } _ { i } | ) / n _ { i }$ to all $n _ { i }$ actions executed in iteration $i$ as reward. ",
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+    {
+        "type": "text",
+        "text": "3.3.3 Agent Policy Network ",
+        "text_level": 1,
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+        "type": "text",
+        "text": "The policy network of the lower-level agent inputs the state of the current solution and outputs action probabilities of length $| A |$ where $A$ is the set of operators. In our case, a critical challenge of designing the policy network is the number of orders and the number of available vehicles are different for each static sub-problem. As the quantity of the combination of orders and vehicles are extremely huge, we cannot train a separate model for every combination of different numbers of orders and vehicles. Thus, the desired model should be able to transfer the knowledge learned from the previously solved problems and generalize to new problems of any scale without fine-tuning. Besides, the routes of a solution naturally form a certain topological graph structure as shown in Figure 3. Therefore, in this paper, we incorporate GIN (Graph Isomorphism Network)[30], a powerful Graph Neural Network (GNN), to be the basis of the policy network of the lower-level agent. We use the REINFORCE algorithm [28] to train the policy network. Details of the policy network are shown in Appendix H. ",
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+        "type": "text",
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "4 Offline Evaluation ",
+        "text_level": 1,
+        "bbox": [
+            176,
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "4.1 Experiments Settings ",
+        "text_level": 1,
+        "bbox": [
+            176,
+            209,
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "We start with designing a simulator to shed light on the contributions of the proposed framework under more controlled settings. Details of the simulator can be found in Appendix C. To comprehensively verify the effectiveness of our approach on problems of different scales, we use four types of datasets of different sizes, i.e., 15 orders with 5 vehicles, 50 orders with 5 vehicles, 300 orders with 20 vehicles, 1000 orders with 50 vehicles (matching the practical problem of thousand scales). Note that the orders/vehicles ratios are set according to realistic business settings. Each type of datasets contains 10 datasets, including 7 training sets and 3 test sets according to the ratio of 7:3 (e.g., 300-1, 300-2 and 300-3 are test sets with 300 orders). The vehicles have the same load capacity. Details of the datasets are described in Appendix D. According to the realistic business settings, the time span between two consecutive decision points is set to 10 minutes in the simulator. ",
+        "bbox": [
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "The comparisons of different methods proceed as follows. For our approach, we first train a shared model on each type of training datasets and then evaluate the model on the test datasets of the same size. At each decision point, the upper-level agent decides whether to release orders to the lower-level agent. The lower-level agent is executed for no more than 10 minutes after receiving orders from the upper-level agent. Both agents are trained simultaneously. This training process is relatively stable due to the following reasons. The iterative solution optimization process (starts from an initial greedy solution) of our lower-level agent can ensure the obtained solutions have relatively high quality even at the initial training stages. In other words, the solutions given by the lower-level agent are relatively stable. Therefore, the unstable issue of co-training both levels of policies in our case is negligible, and thus both levels can be trained simultaneously. For baselines showed in Section 4.2, we also run them for up to 10 minutes at each decision point. We run the simulator until all the orders of the dataset are dispatched and completed to ensure fair comparisons. All the results in the experiments are obtained by running each algorithm ten times to get the mean and variance value of the optimization objective. ",
+        "bbox": [
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+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "4.2 Baselines ",
+        "text_level": 1,
+        "bbox": [
+            174,
+            575,
+            276,
+            589
+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "To help readers better understand the baselines, we name them in the format of ’upper-level method $^ +$ lower-level method’ except for the Optimal baseline. ’10min-Interval’ means the dynamic problem is partitioned into static sub-problems with a fixed interval of ten minutes. ’1order-Interval’ means the dynamic problem is partitioned into static sub-problems consists of a single order. ",
+        "bbox": [
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "10min-Interval $^ +$ Greedy: Greedy [15] is the most widely-used method in industry, which is also the online deployed baseline method. The solution routes are expanded by greedily inserting new pickup and delivery nodes until all the orders are inserted. ",
+        "bbox": [
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+            662,
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+            704
+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "10min-Interval $^ +$ ALNS: ALNS [29] is one of the most representative meta-heuristic local search frameworks for solving DPDP that uses a series of operators to improve the solution. In each iteration, an operator is selected to destroy the current solution, and an operator is selected to repair the solution. ",
+        "bbox": [
+            174,
+            710,
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "1order-Interval $^ +$ E2ERL: According to [14], we use a DQN model to assign vehicles to each generated order and insert each order into the vehicle’s order queue using the Greedy algorithm. It’s an E2ERL (end-to-end RL) algorithm. ",
+        "bbox": [
+            174,
+            758,
+            825,
+            801
+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "10min-Interval $^ +$ ST-DDGN: ST-DDGN [12] is the state-of-the-art method that predicts future orders of DPDP. Then both the predicted orders and real generated orders are considered when solving each sub-problem using E2ERL. ",
+        "bbox": [
+            174,
+            806,
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "Optimal: We convert DPDPs to static PDPs as we can obtain all the orders’ information beforehand in offline style. Then we use Gurobi to solve the corresponding MIP model to get the optimal solution. As Gurobi can only solve small-scale PDPs within acceptable time due to the NP-hard property, we only compare with the optimal solution on problems of 15 and 50 orders in Section 4.4.1. ",
+        "bbox": [
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "4.3 Main Results ",
+        "text_level": 1,
+        "bbox": [
+            174,
+            92,
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+            106
+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "Here we show part of the experimental results in Table 1. The complete results are shown in Table 6 of Appendix I. The objective improvement measurement is the improvement percentage of each algorithm compared with the Greedy algorithm. Our approach consistently outperforms all baselines ",
+        "bbox": [
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+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "table",
+        "img_path": "images/a6e5a7e490192470b1dc6f14adedb3484e3d2145722ab798d031bf71ef690dbd.jpg",
+        "table_caption": [
+            "Table 1: Main results of different methods on test datasets "
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>Dataset</td><td>Algorithm</td><td>Overtime</td><td>Avg_Dis</td><td>Objective</td><td>Obj Impro</td></tr><tr><td rowspan=\"5\">50-1</td><td>10min-Interval + Greedy</td><td>0</td><td>109.30</td><td>109.30</td><td>0.00%</td></tr><tr><td>lorder-Interval +E2ERL</td><td>0</td><td>96.56</td><td>96.56</td><td>11.66%</td></tr><tr><td>10min-Interval + ALNS</td><td>0</td><td>107.95</td><td>107.95</td><td>1.24%</td></tr><tr><td>10min-Interval + ST-DDGN</td><td>0</td><td>108.95</td><td>108.95</td><td>0.32%</td></tr><tr><td>Our (Upper-level RL + Lower-level RL)</td><td>0</td><td>93.70</td><td>93.70</td><td>14.27%</td></tr><tr><td rowspan=\"5\">300-1</td><td>10min-Interval+Greedy</td><td>0</td><td>147.78</td><td>147.78</td><td>0.00%</td></tr><tr><td>lorder-Interval + E2ERL</td><td>0</td><td>158.39</td><td>158.39</td><td>-7.18%</td></tr><tr><td>10min-Interval + ALNS</td><td>0</td><td>137.31</td><td>137.31</td><td>7.08%</td></tr><tr><td>10min-Interval + ST-DDGN</td><td>0</td><td>131.99</td><td>131.99</td><td>10.68%</td></tr><tr><td>Our (Upper-level RL + Lower-level RL)</td><td>0</td><td>122.42</td><td>122.42</td><td>17.16%</td></tr><tr><td rowspan=\"5\">1000-1</td><td>10min-Interval+Greedy</td><td>0</td><td>183.04</td><td>183.04</td><td>0.00%</td></tr><tr><td>lorder-Interval + E2ERL</td><td>0</td><td>180.36</td><td>180.36</td><td>1.46%</td></tr><tr><td>10min-Interval + ALNS</td><td>0</td><td>174.68</td><td>174.68</td><td>4.57%</td></tr><tr><td>10min-Interval + ST-DDGN</td><td>0</td><td>171.09</td><td>171.09</td><td>6.53%</td></tr><tr><td>Our(Upper-level RL +Lower-level RL)</td><td>0</td><td>159.18</td><td>159.18</td><td>13.04%</td></tr></table>",
+        "bbox": [
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+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "on all datasets (lower total objective is better). On some datasets, the baselines have overtime results due to their lack of long-term planning and exhaustively optimization of each static problem from a myopic perspective. As a result, dispatching of some orders is delayed for too long, and finally, overtime is inevitable in any case. In contrast to this, our upper-level RL partitions the dynamic problem into sub-problems considering the balance between the orders overtime (seconds) risk and optimization of vehicle travelling distances (kilometers), and our lower-level RL is responsible for the optimization of each static sub-problem. The cooperation of the two agents enables our method to find solutions with less overtime and vehicle travelling distances on the overall dynamic problem from a long-term perspective. The comparison of the learning curves of all learning-based methods on 50-1 are shown in Figure 11 in Appendix I. ",
+        "bbox": [
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+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "4.4 Ablation Studies ",
+        "text_level": 1,
+        "bbox": [
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+            455,
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+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "4.4.1 How far is our lower-level agent from the optimal one on static PDP? ",
+        "text_level": 1,
+        "bbox": [
+            176,
+            482,
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+            497
+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "We convert the DPDP to a single static PDP as described in Section 4.2. As the orders should be assigned to vehicles all at once, there is no need to use an upper-level agent. Similarly, without the prediction of future orders, ST-DDGN is essentially the same as E2ERL. Therefore we only use the lower-level agent and E2ERL in the static PDP. Each algorithm is run without time or step limitation to discover its full potential. As shown in Table 2 and 3, the difference of the total objective of our method with the optimal solution is much smaller than the baselines (as all the overtime is 0, the column is omitted from the two Tables). The time consumption is much shorter than ALNS and Gurobi. It is because our method can exert the generalization ability to quickly improve the initial solution by using the most appropriate operators based on the experiences obtained from training, without the need of manually designing complicated search as in ALNS and Gurobi. Note that the time consumption of Gurobi on problems of 50 orders is represented using hyphen symbol ’-’, which means we can’t get results even after 100 hours due to the various complex constraints as described in Appendix A. Comparing with baselines, our method is the most qualified to meet the online deployment requirements that the algorithm should obtain high-quality solutions with fast speed. ",
+        "bbox": [
+            173,
+            507,
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+            700
+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "table",
+        "img_path": "images/410429e88fb44a084612f20c0a962b435d1f34920667aa33b61c66fe5e5ad191.jpg",
+        "table_caption": [
+            "Table 2: Results on static 15-1, 15-2, 15-3 "
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>Algorithm</td><td>Avg_Dis</td><td>Objective</td><td>Obj Impro</td><td>Time</td></tr><tr><td>Greedy</td><td>53.85</td><td>53.85</td><td>0.00%</td><td>0.38s</td></tr><tr><td>E2ERL</td><td>51.70</td><td>51.70</td><td>3.99%</td><td>0.58s</td></tr><tr><td>ALNS</td><td>51.58</td><td>51.58</td><td>4.22%</td><td>405s</td></tr><tr><td>Our</td><td>45.72</td><td>45.72</td><td>15.10%</td><td>68.21s</td></tr><tr><td>(Lower-level RL) Optimal</td><td>44.35</td><td>44.35</td><td>17.64%</td><td>141360s</td></tr><tr><td>Greedy</td><td>69.61</td><td>69.61</td><td>0.00%</td><td>0.40s</td></tr><tr><td>E2ERL</td><td>68.00</td><td>68.00</td><td>2.31%</td><td>0.79s</td></tr><tr><td>ALNS</td><td>62.62</td><td>62.62</td><td>10.04%</td><td>606s</td></tr><tr><td>Our</td><td>62.32</td><td>62.32</td><td>10.47%</td><td>27.96s</td></tr><tr><td>(Lower-level RL) Optimal</td><td>57.48</td><td>57.48</td><td>17.43%</td><td>193680s</td></tr><tr><td>Greedy</td><td>78.73</td><td>78.73</td><td>0.00%</td><td>0.34s</td></tr><tr><td>E2ERL</td><td>59.02</td><td>59.02</td><td>25.03%</td><td>0.83s</td></tr><tr><td>ALNS</td><td>52.21</td><td>52.21</td><td>33.68%</td><td>920s</td></tr><tr><td>Our</td><td>50.95</td><td>50.95</td><td>35.29%</td><td>71.98s</td></tr><tr><td>(Lower-level RL) Optimal</td><td>50.75</td><td>50.75</td><td>35.54%</td><td>28651s</td></tr></table>",
+        "bbox": [
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+            729,
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+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "table",
+        "img_path": "images/93c1a41a9be6fffb2ac4d30f75f040f569e2a3686e588663e0926b1bc6d794ff.jpg",
+        "table_caption": [
+            "Table 3: Results on static 50-1, 50-2, 50-3 "
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>Algorithm</td><td>Avg_Dis</td><td>Objective</td><td>Obj Impro</td><td>Time</td></tr><tr><td>Greedy</td><td>98.68</td><td>98.68</td><td>0.00%</td><td>66.73s</td></tr><tr><td>E2ERL</td><td>94.94</td><td>94.94</td><td>3.79%</td><td>52.64s</td></tr><tr><td>ALNS</td><td>96.98</td><td>96.98</td><td>1.72%</td><td>10728.34s</td></tr><tr><td>Our (Lower-level RL)</td><td>82.43</td><td>82.43</td><td>16.47%</td><td>1459.23s</td></tr><tr><td>Optimal</td><td>-</td><td>-</td><td>-</td><td>-</td></tr><tr><td>Greedy</td><td>80.67</td><td>80.67</td><td>0.00%</td><td>22.27s</td></tr><tr><td>E2ERL</td><td>76.04</td><td>76.04</td><td>5.74%</td><td>16.66s</td></tr><tr><td>ALNS</td><td>65.31</td><td>65.31</td><td>19.04%</td><td>6012.56s</td></tr><tr><td>Our (Lower-level RL)</td><td>58.42</td><td>58.42</td><td>27.58%</td><td>1152.64s</td></tr><tr><td>Optimal</td><td>=</td><td>=</td><td>=</td><td>=</td></tr><tr><td>Greedy</td><td>83.34</td><td>83.34</td><td>0.00%</td><td>44.31s</td></tr><tr><td>E2ERL</td><td>80.92</td><td>80.92</td><td>2.90%</td><td>20.34s</td></tr><tr><td>ALNS</td><td>80.51</td><td>80.51</td><td>3.40%</td><td>4140.15s</td></tr><tr><td>Our (Lower-level RL)</td><td>72.66</td><td>72.66</td><td>12.81%</td><td>1998.09s</td></tr><tr><td>Optimal</td><td>-</td><td>-</td><td>-</td><td>-</td></tr></table>",
+        "bbox": [
+            493,
+            729,
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+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "4.4.2 Does lower-level agent learn how to select operators? ",
+        "text_level": 1,
+        "bbox": [
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+            92,
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+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "To verify that our lower-level agent learns to choose the most suitable operators at different states, we compare the results of different operator selection methods on both static problems and dynamic problems. We first compare the total objective during the solution improvement process on the static problems using the lower-level agent with the method that randomly selects operators. As the improvement-reconstruct iteration process designed in Section 3.3 ensures the quality of the solution can be monotonically improved, selecting operators randomly is also a powerful baseline that can achieve satisfactory performance for the static PDP. ",
+        "bbox": [
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+            114,
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+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "Therefore, for the static problem, we mainly focus on whether the lower-level agent can improve the solving speed. As we can see in Figure 4, at the same step, choosing operators using lower-level RL can reach a better objective than randomly choosing operators, which indicates our lower-level method learned to accelerate the searching for better solutions. Since the static sub-problems of a dynamic problem are not independent of each other, the small gap between the above ",
+        "bbox": [
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+            213,
+            408,
+            404
+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "image",
+        "img_path": "images/bd810fb7e2b2140648402ff44b3c03029bbb2ec9151bf3b8de37d65eaf513284.jpg",
+        "image_caption": [
+            "Figure 4: Comparison of different selection methods of operators on static problems "
+        ],
+        "image_footnote": [],
+        "bbox": [
+            426,
+            234,
+            816,
+            348
+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "two methods in a static sub-problem will continue to enlarge in the subsequent sub-problems, resulting in a very large result gap on the entire dynamic problem. We compare the total objectives of the entire dynamic problems in Table 4. To ensure fairness, we control the upper-level methods to be ’10min-Interval’ and use the lower-level agent and random selection as lower-level methods, respectively. As we can see in Table 4, using the lower-level agent can help find better solutions on the entire dynamic problems. ",
+        "bbox": [
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+            405,
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+            488
+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "4.4.3 Does the upper-level agent learn to partition DPDP from a long-term perspective? ",
+        "text_level": 1,
+        "bbox": [
+            173,
+            502,
+            792,
+            518
+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "To verify that our upper-level agent learns to partition the dynamic problem into static subproblems from a long-term perspective, we compare the results of differ",
+        "bbox": [
+            174,
+            526,
+            299,
+            650
+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "table",
+        "img_path": "images/9453374922488b327a5fc2f47b189d248010047d77e4eb62a45c386536e9eae1.jpg",
+        "table_caption": [
+            "Table 4: Effectiveness of lower-level agent and upper-level agent "
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>Dataset</td><td>Method</td><td>Overtime</td><td>Avg_Dis</td><td>Objective</td><td>ObjImpro</td></tr><tr><td rowspan=\"3\">300-1</td><td>10min-Interval+Random Search</td><td>0</td><td>139.16 ± 8.59</td><td>139.16</td><td>0.00%</td></tr><tr><td>10min-Interval + Lower-level RL</td><td>0</td><td>126.95 ± 4.80</td><td>126.95</td><td>8.77%</td></tr><tr><td>Our(Upper-level RL +Lower-level RL)</td><td>0</td><td>122.42 ± 4.02</td><td>122.42</td><td>12.03%</td></tr><tr><td rowspan=\"3\">300-2</td><td>10min-Interval+RandomSearch</td><td>0</td><td>166.31 ± 10.20</td><td>166.31</td><td>0.00%</td></tr><tr><td>10min-Interval + Lower-level RL</td><td>0</td><td>154.39 ± 8.13</td><td>154.39</td><td>7.17%</td></tr><tr><td>Our (Upper-level RL + Lower-level RL)</td><td>0</td><td>142.33 ± 7.47</td><td>142.33</td><td>14.42%</td></tr><tr><td rowspan=\"3\">300-3</td><td>10min-Interval+RandomSearch</td><td>0</td><td>168.69±7.70</td><td>168.69</td><td>0.00%</td></tr><tr><td>10min-Interval + Lower-level RL</td><td>0</td><td>156.64 ± 7.50</td><td>156.64</td><td>7.14%</td></tr><tr><td>Our(Upper-level RL +Lower-level RL)</td><td>0</td><td>146.88 ±13.91</td><td>146.88</td><td>12.93%</td></tr></table>",
+        "bbox": [
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+            547,
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+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "ent static sub-problems partitioning methods. We compare our upper-level agent with the $\\mathrm { \\Omega } ^ { , } 1 0 \\mathrm { m i n } .$ Interval’ method. As we can see in Table 4, using an upper-level agent to partition the dynamic problem reaches the best objective. The results illustrate that our upper-level agent can partition the problem from a long-term perspective to balance the orders overtime risk and optimization of vehicle travelling distances. ",
+        "bbox": [
+            173,
+            651,
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+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "4.4.4 Can our method generalized to larger-scale problems? ",
+        "text_level": 1,
+        "bbox": [
+            173,
+            736,
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+            750
+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "To verify our method’s generalization ability, we evaluate the models trained using datasets of 300 orders / 20 vehicles on larger-scale datasets, i.e., 1000 orders / 50 vehicles. As shown in Table 5, the model trained on datasets of 300 orders achieves similar performance with the one trained on datasets of 1000 orders. ",
+        "bbox": [
+            174,
+            760,
+            437,
+            869
+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "table",
+        "img_path": "images/9878aaa0f8430644e217ecb135677ba679d7c97de63230885577a67d2fb4d4f0.jpg",
+        "table_caption": [
+            "Table 5: Generalization verification "
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>Dataset</td><td>Model</td><td>Overtime</td><td>Avg_Dis</td><td>Objective</td></tr><tr><td rowspan=\"2\">1000-1</td><td>Trained on 1000</td><td>0</td><td>159.18 ± 4.10</td><td>159.18</td></tr><tr><td>Trained on 300</td><td>0</td><td>170.78 ± 10.27</td><td>170.78</td></tr><tr><td rowspan=\"2\">1000-2</td><td>Trained on 1000</td><td>0</td><td>196.66± 9.52</td><td>196.66</td></tr><tr><td>Trained on 300</td><td>0</td><td>209.48±8.68</td><td>209.48</td></tr><tr><td rowspan=\"2\">1000-3</td><td>Trained on 1000</td><td>0</td><td>176.39 ± 7.61</td><td>176.39</td></tr><tr><td>Trained on 300</td><td>0</td><td>182.83 ± 5.64</td><td>182.83</td></tr></table>",
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+        "page_idx": 8
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+    {
+        "type": "text",
+        "text": "Note that the model trained on datasets of 300 orders also outperforms the baselines in Table 1. It verifies that our method can be generalized to new problems of different scales without fine-tuning after well trained on existing problems. ",
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+    {
+        "type": "text",
+        "text": "5 Online Testing ",
+        "text_level": 1,
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+        "page_idx": 9
+    },
+    {
+        "type": "text",
+        "text": "We deployed our method on the order dispatching system in Huawei supply chain. In the online experiments, we compare our method with the previously online deployed greedy algorithm (10min-Interval $^ +$ Greedy). For a fair comparison, we control the vehicles and the nodes (factories and warehouses) involved in the online testing to be the same. Normally, a standard A/B testing is required to be performed on homogeneous experimental groups using different methods ",
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+    {
+        "type": "image",
+        "img_path": "images/03c50a505ccc16ad888407a2571a88d5e637c0de5e647de57cf281efeb8016a4.jpg",
+        "image_caption": [
+            "Figure 5: Online Results "
+        ],
+        "image_footnote": [],
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+    },
+    {
+        "type": "text",
+        "text": "at the same time dimension. Then experimental data of each group are collected and evaluated to choose the best method. However, in our situation, it’s unrealistic to split each order into two sub-orders to ensure the experimental groups are homogeneous. Besides, a large number of offline experiments have demonstrated that our method is significantly better than the greedy algorithm. Even in the worst case when there is no improvement in each sub-problem, our method is still the same with Greedy. Thus, we directly replaced the greedy algorithm for online deployment. Figure 5 summarises the results from Nov 2020 to Apr 2021. The points of Nov and Dec 2020 shown in Figure 5 are generated by greedy algorithm and our method is deployed from Jan to Apr 2021. As we can see, our method can reduce the average orders’ overtime and vehicles’ travelling distances compared with the greedy baseline. Even with more orders, our method can still reach a better optimization objective. Note that in the actual business scenario, orders generated in each day follow a similar distribution with a small variance. These results indicate that our method could achieve a better performance in the realistic deployment environment with varied data distributions. ",
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+    {
+        "type": "text",
+        "text": "6 Conclusions ",
+        "text_level": 1,
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+    },
+    {
+        "type": "text",
+        "text": "In this paper, we propose a novel hierarchical reinforcement learning based optimization framework to solve the large-scale DPDP in the real world. The upper-level agent is equipped with the far-sight ability whose target is to optimize the long-term cumulative objective. The lower-level agent exerts the generalization ability of GNN to quickly improve the solution quality by transferring the knowledge (policy) learned from training. The cooperation of the upper-level and lower-level agents enables our method to find globally better solutions. Extensive offline simulation on the simulator built on real historical data and online testing verify that our method can obtain higher-quality solutions with faster running speed. ",
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+    {
+        "type": "text",
+        "text": "The core idea of our learning-based framework are beneficial to a number of similar problems in the supply chain community that have time-evolving components (e.g., orders/customers/tasks), such as dynamic routing problems, dynamic flow shop scheduling, dynamic job shop scheduling, dynamic bin packing and so on. As orders/customers/tasks of all these dynamic problems are online generated that are not known a priori, the orders/customers/tasks should first be cached and then be dispatched. In this way, these problems can be modeled as hierarchical optimization problems like DPDP that the upper-level problem is ”how to cache orders/customers/tasks” and the lower-level problem is ”how to dispatch cached orders/customers/tasks”. We will verify our proposed framework in these fields in the future work. ",
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+    {
+        "type": "text",
+        "text": "Acknowledgments and Disclosure of Funding ",
+        "text_level": 1,
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+    {
+        "type": "text",
+        "text": "The work is supported by the National Natural Science Foundation of China (Grant Nos: U1836214) and the New Generation of Artificial Intelligence Science and Technology Major Project of Tianjin under grant: 19ZXZNGX00010. ",
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+        "text": "References   \n[1] Irwan Bello, Hieu Pham, Quoc V Le, Mohammad Norouzi, and Samy Bengio. Neural combinatorial optimization with reinforcement learning. arXiv preprint arXiv:1611.09940, 2016.   \n[2] Enrique Benavent, Mercedes Landete, Enrique Mota, and Gregorio Tirado. The multiple vehicle pickup and delivery problem with lifo constraints. European Journal of Operational Research, 243(3):752–762, 2015.   \n[3] Gerardo Berbeglia, Jean-François Cordeau, and Gilbert Laporte. Dynamic pickup and delivery problems. European journal of operational research, 202(1):8–15, 2010.   \n[4] Francesco Carrabs, Jean-François Cordeau, and Gilbert Laporte. Variable neighborhood search for the pickup and delivery traveling salesman problem with lifo loading. INFORMS Journal on Computing, 19 (4):618–632, 2007.   \n[5] Brenda Cheang, Xiang Gao, Andrew Lim, Hu Qin, and Wenbin Zhu. Multiple pickup and delivery traveling salesman problem with last-in-first-out loading and distance constraints. European journal of operational research, 223(1):60–75, 2012.   \n[6] Xinyun Chen and Yuandong Tian. Learning to perform local rewriting for combinatorial optimization. In Hanna M. Wallach, Hugo Larochelle, Alina Beygelzimer, Florence d’Alché-Buc, Emily B. Fox, and Roman Garnett, editors, Advances in Neural Information Processing Systems 32: Annual Conference on Neural Information Processing Systems 2019, NeurIPS 2019, December 8-14, 2019, Vancouver, BC, Canada, pages 6278–6289, 2019. URL https://proceedings.neurips.cc/paper/2019/hash/ 131f383b434fdf48079bff1e44e2d9a5-Abstract.html.   \n[7] Michel Gendreau, Francois Guertin, Jean-Yves Potvin, and René Séguin. Neighborhood search heuristics for a dynamic vehicle dispatching problem with pick-ups and deliveries. Transportation Research Part C: Emerging Technologies, 14(3):157–174, 2006.   \n[8] Gianpaolo Ghiani, Emanuele Manni, Antonella Quaranta, and Chefi Triki. Anticipatory algorithms for same-day courier dispatching. Transportation Research Part E: Logistics and Transportation Review, 45 (1):96–106, 2009.   \n[9] Péter Györgyi and Tamás Kis. A probabilistic approach to pickup and delivery problems with time window uncertainty. European Journal of Operational Research, 274(3):909–923, 2019.   \n[10] Matheus Nohra Haddad, Rafael Martinelli, Thibaut Vidal, Simone Martins, Luiz Satoru Ochi, Marcone Jamilson Freitas Souza, and Richard Hartl. Large neighborhood-based metaheuristic and branch-and-price for the pickup and delivery problem with split loads. European Journal of Operational Research, 270(3): 1014–1027, 2018.   \n[11] Farzaneh Karami, Wim Vancroonenburg, and Greet Vanden Berghe. A periodic optimization approach to dynamic pickup and delivery problems with time windows. Journal of Scheduling, 23(6):711–731, 2020.   \n[12] Xijun Li, Weilin Luo, Mingxuan Yuan, Jun Wang, Jiawen Lu, Jie Wang, Jinhu Lv, and Jia Zeng. Learning to optimize industry-scale dynamic pickup and delivery problems. 37th IEEE International Conference on Data Engineering, 2021.   \n[13] Hao Lu, Xingwen Zhang, and Shuang Yang. A learning-based iterative method for solving vehicle routing problems. In 8th International Conference on Learning Representations, ICLR 2020, Addis Ababa, Ethiopia, April 26-30, 2020. OpenReview.net, 2020. URL https://openreview.net/forum?id=BJe1334YDH.   \n[14] Hongzi Mao, Malte Schwarzkopf, Shaileshh Bojja Venkatakrishnan, Zili Meng, and Mohammad Alizadeh. Learning scheduling algorithms for data processing clusters. In Proceedings of the ACM Special Interest Group on Data Communication, pages 270–288. 2019.   \n[15] Snežana Mitrovic-Mini ´ c and Gilbert Laporte. Waiting strategies for the dynamic pickup and delivery ´ problem with time windows. Transportation Research Part B: Methodological, 38(7):635–655, 2004.   \n[16] Snezana Mitrovic-Minic, Ramesh Krishnamurti, Gilbert Laporte, et al. Double-horizon based heuristics for the dynamic pickup and delivery problem with time windows. Transportation Research Part B: Methodological, 38(8):669–685, 2004.   \n[17] Volodymyr Mnih, Koray Kavukcuoglu, David Silver, Andrei A Rusu, Joel Veness, Marc G Bellemare, Alex Graves, Martin Riedmiller, Andreas K Fidjeland, Georg Ostrovski, et al. Human-level control through deep reinforcement learning. nature, 518(7540):529–533, 2015. ",
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+    {
+        "type": "text",
+        "text": "FLOWTRON: AN AUTOREGRESSIVE FLOW-BASED GENERATIVE NETWORK FOR TEXT-TO-SPEECH SYNTHESIS ",
+        "text_level": 1,
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+        "type": "text",
+        "text": "Rafael Valle, Kevin J. Shih, Ryan Prenger & Bryan Catanzaro   \nNVIDIA   \nrafaelvalle@nvidia.com ",
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+        "type": "text",
+        "text": "ABSTRACT ",
+        "text_level": 1,
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+    },
+    {
+        "type": "text",
+        "text": "In this paper we propose Flowtron: an autoregressive flow-based generative network for text-to-speech synthesis with style transfer and speech variation. Flowtron borrows insights from Autoregressive Flows and revamps Tacotron 2 in order to provide high-quality and expressive mel-spectrogram synthesis. Flowtron is optimized by maximizing the likelihood of the training data, which makes training simple and stable. Flowtron learns an invertible mapping of data to a latent space that can be used to modulate many aspects of speech synthesis (timbre, expressivity, accent). Our mean opinion scores (MOS) show that Flowtron matches state-ofthe-art TTS models in terms of speech quality. We provide results on speech variation, interpolation over time between samples and style transfer between seen and unseen speakers. Code and pre-trained models are publicly available at https://github.com/NVIDIA/flowtron. ",
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+    {
+        "type": "text",
+        "text": "1 INTRODUCTION ",
+        "text_level": 1,
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+        "type": "text",
+        "text": "Current speech synthesis methods do not give the user enough control over how speech actually sounds. Automatically converting text to audio that successfully communicates the text was achieved a long time ago (Umeda et al., 1968; Badham et al., 1983). However, communicating only the text information leaves out the acoustic properties of the voice that convey much of the meaning and human expressiveness. In spite of this, the typical speech synthesis problem is formulated as a text to speech (TTS) problem in which the user inputs only text since the 1960s. This work proposes a normalizing flow model (Kingma & Dhariwal, 2018; Huang et al., 2018) that learns an unsupervised mapping from non-textual information to manipulable latent Gaussian distributions. ",
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+        "text": "Taming the non-textual information in speech is difficult because the non-textual is unlabeled. A voice actor may speak the same text with different emphasis or emotion based on context, but it is unclear how to label a particular reading. Without labels for the non-textual information, recent approaches (Shen et al., 2017; Arik et al., 2017a;b; Ping et al., 2017) have formulated speech synthesis as a TTS problem wherein the non-textual information is implicitly learned. Despite their success in recreating non-textual information in the training set, the user has limited insight and control over it. ",
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+        "type": "text",
+        "text": "It is possible to formulate an unsupervised learning problem in such a way that the user can exploit the unlabeled characteristics of a data set. One way is to formulate the problem such that the data is assumed to have a representation in some latent space, and have the model learn that representation. This latent space can then be investigated and manipulated to give the user more control over the generative model’s output. Such approaches have been popular in image generation, allowing users to interpolate smoothly between images and to identify portions of the latent space that correlate with various features (Radford et al., 2015; Kingma & Dhariwal, 2018; Izmailov et al., 2019). ",
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+        "text": "Recent deep learning approaches to expressive speech synthesis have combined text and learned latent embeddings for non-textual information (Wang et al., 2018; Skerry-Ryan et al., 2018; Hsu et al., 2018; Habib et al., 2019; Sun et al., 2020). These approaches impose an undesirable paradox: they require making assumptions before hand about the dimensionality of the embeddings when the correct dimensionality can only be determined after the model is trained. Even then, these embeddings are not guaranteed to contain all the non-textual information it takes to reconstruct speech, often ",
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+        "type": "text",
+        "text": "(a) Time-averaged $_ { z }$ -values from multiple samples from 3 speakers with different timbres. $^ +$ is the centroid computed over samples from the same speaker. ",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "(b) Time-averaged $_ { z }$ -values from multiple samples from 123 LibriTTS speakers. Each color represents a speaker. $^ +$ is Male (lower $F _ { 0 }$ , third quadrant). is Female (higher $F _ { 0 }$ , first quadrant). ",
+        "bbox": [
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+        "text": "Figure 1: T-SNE plot showing Flowtron partitioning the $_ z$ -space according to acoustic characteristics. ",
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+    {
+        "type": "text",
+        "text": "resulting in models with dummy or uninterpretable latent dimensions and not enough capacity, as the appendices in Wang et al. (2018); Skerry-Ryan et al. (2018); Hsu et al. (2018) confirm. ",
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+        "type": "text",
+        "text": "Furthermore, most models are not able to manipulate speech characteristics over time due to fixedlength embeddings. Their assumption is that variable-length embeddings are not robust to text and speaker perturbations (Skerry-Ryan et al., 2018), which we show not to be the case. Finally, although VAEs and GANs (Sun et al., 2020; Habib et al., 2019; Hsu et al., 2018; Binkowski et al., 2019; ´ Akuzawa et al., 2018) provide a latent embedding that can be manipulated, they may be difficult to train, are limited to approximate latent variable prediction, and rely on an implicit generative model or ELBO estimate to perform MLE in the latent space (Kingma & Dhariwal, 2018; Lucic et al., 2018; Kingma et al., 2016). ",
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+    {
+        "type": "text",
+        "text": "In this paper we propose Flowtron: an autoregressive flow-based generative network for melspectrogram synthesis with style transfer over time and speech variation. Flowtron learns an invertible function that maps a distribution over mel-spectrograms to a latent $_ z$ -space parameterized by a spherical Gaussian. Figure 1 shows that acoustic characteristics like timbre and $F _ { 0 }$ correlate with portions of the $_ z$ -space of Flowtron models trained without speaker embeddings. ",
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+        "type": "text",
+        "text": "With our formalization, we can generate samples containing specific speech characteristics manifested in mel-space by finding and sampling the corresponding region in $_ z$ -space (Gambardella et al., 2019). Our formulation also allows us to impose a structure to the $_ z$ -space and to parametrize it with a Gaussian mixture, similar to Hsu et al. (2018). In our simplest setup, we generate samples with a zero mean spherical Gaussian prior and control the amount of variation by adjusting its variance. ",
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+        "text": "Compared to VAEs and GANs and their disadvantages enumerated in Kingma & Dhariwal (2018), manipulating a latent prior in Flowtron comes at no cost in speech quality nor optimization challenges. Flowtron is able to generalize and produce sharp mel-spectrograms, even at high $\\sigma ^ { 2 }$ values, by simply maximizing the likelihood of the data while not requiring any additional Prenet or Postnet layer (Wang et al., 2017), nor compound loss functions required by most SOTA models (Shen et al., 2017; Ping et al., 2017; Skerry-Ryan et al., 2018; Wang et al., 2018; Binkowski et al., 2019). ´ ",
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+        "type": "text",
+        "text": "In summary, Flowtron is optimized by maximizing the exact likelihood of the training data, which makes training simple and stable. Using normalizing flows, it learns an invertible mapping from data to latent space that can be manipulated to modulate many aspects of speech synthesis. Concurrent with this work are Glow-TTS (Kim et al., 2020) and Flow-TTS (Miao et al., 2020), both of which incorporate normalizing flows into the TTS task. Our work differs from these two in that Flowtron is an autoregressive architecture where we explore the use of flow to modulate speech and style variation. In contrast, Glow-TTS and Flow-TTS are parallel architectures that focus on inference speed. Our mean opinion scores (MOS) show that Flowtron matches SOTA TTS models in terms of speech quality. Further, we provide results on speech variation, interpolation between samples and interpolation between styles over time, and style transfer between seen and unseen speakers with equal or different sentences. We hope this work, the first to show evidence that normalizing flows can be used for expressive text-to-speech synthesis and style transfer, will further stimulate developments in normalizing flows. ",
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+        "type": "text",
+        "text": "2 FLOWTRON ",
+        "text_level": 1,
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+        "text": "Flowtron is an autoregressive flow that generates a sequence of mel-spectrogram frames. A normalizing flow generates samples by first sampling a latent variable from a known distribution $p ( z )$ , and applying a series of invertible transformations to produce a sample from the target distribution $p ( { \\pmb x } )$ . These invertible transformations $f$ are known as steps of flow: ",
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+        "type": "equation",
+        "img_path": "images/bce7fd2e095f9f60885bbc94f18a3627704417c762e441e07a4a9bdea500a29a.jpg",
+        "text": "$$\n\\pmb { x } = \\pmb { f } _ { 1 } \\circ \\pmb { f } _ { 2 } \\circ . . . \\pmb { f } _ { k } ( z )\n$$",
+        "text_format": "latex",
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+    {
+        "type": "text",
+        "text": "Because each transformation is invertible, we can directly evaluate the exact log-likelihood of the target distribution $p ( { \\pmb x } )$ using the change of variables: ",
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+    {
+        "type": "equation",
+        "img_path": "images/d14b588d480f4157aa78b744b410bce81a8aa766a42e149540deb4d4c9953e57.jpg",
+        "text": "$$\n\\begin{array} { l } { \\log p _ { \\theta } ( \\pmb { x } ) = \\log p _ { \\theta } ( z ) + \\displaystyle \\sum _ { i = 1 } ^ { k } \\log \\vert \\operatorname* { d e t } ( \\pmb { J } ( \\pmb { f } _ { i } ^ { - 1 } ( \\pmb { x } ) ) ) \\vert } \\\\ { z = \\pmb { f } _ { k } ^ { - 1 } \\circ \\pmb { f } _ { k - 1 } ^ { - 1 } \\circ . . . \\pmb { f } _ { 1 } ^ { - 1 } ( \\pmb { x } ) } \\end{array}\n$$",
+        "text_format": "latex",
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+    {
+        "type": "text",
+        "text": "Where $\\textbf {  { J } }$ is the Jacobian of the inverse transform $f _ { i } ^ { - 1 } ( { \\pmb x } )$ . By cleverly choosing the latent distribution $p ( z )$ and the invertible transformations, the exact log-likelihood becomes simple and tractable. ",
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+    {
+        "type": "text",
+        "text": "2.1 LATENT DISTRIBUTIONS ",
+        "text_level": 1,
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+        "type": "text",
+        "text": "We consider two simple distributions for the latent distribution $_ z$ : a zero-mean spherical Gaussian and a mixture of spherical Gaussians with fixed or learnable parameters. ",
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+    {
+        "type": "equation",
+        "img_path": "images/00bf64d9ae66304b7a9361df0f33d02fcf971960cbc84d548832fef138204b14.jpg",
+        "text": "$$\nz \\sim \\mathcal { N } ( z ; 0 , I ) \\quad \\mathrm { o r } \\quad z \\sim \\sum _ { k } \\hat { \\phi } _ { k } \\mathcal { N } ( z ; \\hat { \\mu } _ { k } , \\hat { \\Sigma } _ { k } )\n$$",
+        "text_format": "latex",
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+    {
+        "type": "text",
+        "text": "The zero-mean spherical Gaussian has a simple log-likelihood. The mixture of the spherical Gaussians, has inherent clusters that might result in interesting aspects of the audio information. ",
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+        "type": "text",
+        "text": "2.2 INVERTIBLE TRANSFORMATIONS ",
+        "text_level": 1,
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+        "type": "text",
+        "text": "Normalizing flows are typically constructed using coupling layers (Dinh et al., 2014; 2016; Kingma & Dhariwal, 2018). In our case, we use an autoregressive affine coupling layer (Dinh et al., 2016). The latent variable $_ z$ has the same number of dimensions and frames as the resulting mel-spectrogram sample. The previous frames $z _ { 1 : t - 1 }$ produce scale and bias terms, $\\mathbf { } _ { s _ { t } }$ and $\\mathbf { } _ { b _ { t } }$ respectively, that affine-transform the succeeding time step ${ \\boldsymbol { z } } _ { t }$ : ",
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+    {
+        "type": "equation",
+        "img_path": "images/ea1735f175b2137a148a3626abac1fe1572348dac1e78f521cf5366136fe0121.jpg",
+        "text": "$$\n\\begin{array} { c } { { ( \\log s _ { t } , b _ { t } ) = N N ( z _ { 1 : t - 1 } , t e x t , s p e a k e r ) } } \\\\ { { f ( z _ { t } ) = ( z _ { t } - b _ { t } ) \\div s _ { t } } } \\\\ { { f ^ { - 1 } ( z _ { t } ) = s _ { t } \\odot z _ { t } + b _ { t } } } \\end{array}\n$$",
+        "text_format": "latex",
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+    {
+        "type": "text",
+        "text": "Here, $N N ( )$ can be any autoregressive causal transformation (Shumway & Stoffer, 2017). The affine coupling layer is a reversible transformation, even though $N N ( )$ itself need not be invertible. We use a 0-vector for obtaining the scaling and bias terms what will affine transform $z _ { 1 }$ . This 0-vector constant also guarantees that the first $_ z$ is always known. ",
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+        "page_idx": 2
+    },
+    {
+        "type": "image",
+        "img_path": "images/a0d01da5631791f09e9056942672608e597522f1883e26e701c1ed9de4deae52.jpg",
+        "image_caption": [
+            "Figure 2: Mapping data $\\mathbf { \\rho } ( \\mathbf { x } )$ to the latent dimension ${ \\bf \\Pi } ( { \\bf z } )$ for K steps of flow. The right side shows a unrolled view of the $N N ( )$ architecture. Text and speaker embeddings are channel-wise concatenated to produce context matrix $c$ . At every time step $t$ , a recurrent attention mechanism computes a weighting distribution over the context matrix $c$ to produce a weighted-sum reduction over $c$ , which is then passed through an LSTM-Conv decoder architecture to generate affine parameters for transforming $x _ { t + 1 } \\to x _ { t + 1 } ^ { \\prime }$ . As predicted parameters are always for the next time step, the first iteration is conditioned on a pre-defined 0-vector. "
+        ],
+        "image_footnote": [],
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "With an affine coupling layer, only the $\\mathbf { \\delta } _ { s _ { t } }$ term changes the volume of the mapping and adds a change of variables term to the loss. This term also penalizes the model for non-invertible affine mappings. ",
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+    {
+        "type": "equation",
+        "img_path": "images/920afdfc5b16d7a6544216cdbcfd8c60379014edcaa64c38c2eca61a2a803374.jpg",
+        "text": "$$\n\\log | \\operatorname* { d e t } ( J ( f _ { c o u p l i n g } ^ { - 1 } ( \\pmb { x } ) ) ) | = \\log | s |\n$$",
+        "text_format": "latex",
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+    {
+        "type": "text",
+        "text": "To evaluate the likelihood, we take the mel-spectrograms and pass them through the inverse steps of flow conditioned on the text and optional speaker ids, adding the corresponding $\\log | s |$ penalties, and evaluate the result based on the Gaussian likelihoods. ",
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+    {
+        "type": "text",
+        "text": "With this setup, it is also possible to reverse the ordering of the mel-spectrogram frames in time without loss of generality. We reverse the order of frames on even steps of flow, defining a step of flow as a full pass over the input sequence. This allows the model to learn dependencies both forward and backwards in time while remaining causal and invertible. ",
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+    {
+        "type": "text",
+        "text": "2.3 MODEL ARCHITECTURE ",
+        "text_level": 1,
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "Our text encoder modifies the text encoder in Tacotron 2 by replacing batch-norm with instance-norm. Our decoder and $N N$ architecture, depicted in Figure 2, removes the Prenet and Postnet layers from Tacotron previously thought to be essential (Shen et al., 2017). Please compare Figure 2 describing our architecture and Figure 8 in A.4.4 describing Tacotron’s architecture. We also provide model summary views in A.6 ",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "We use the content-based tanh attention described in Vinyals et al. (2015), which can be easily modified to become also location sensitive. We use the Mel Encoder described in Hsu et al. (2018) to predict the parameters of the Gaussian Mixture. Following (Valle et al., 2019b), we use speakerembeddings channel-wise concatenated with the encoder outputs at every token. We use a single shared embedding for models not conditioned on speaker id. ",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "The step of flow closest to the latent variable $_ { z }$ has a gating mechanism that prunes extra frames from the $_ z$ -values provided to the model during inference. The length of $_ z$ -values remains fixed on the next steps of flow. ",
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+    {
+        "type": "text",
+        "text": "2.4 INFERENCE ",
+        "text_level": 1,
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "Inference, given a trained model, is simply a matter of sampling $_ z$ values from a spherical Gaussian, or Gaussian Mixture, and running them through the network in the forward direction $f$ , e.g. Eq. 1. The parameters of the Gaussian mixture are either fixed or predicted by Flowtron. Training was conducted with $\\sigma ^ { 2 } = 1$ , but we explore the effects of different values for $\\sigma ^ { \\bar { 2 } }$ in section 3.3. In general, we found that sampling $_ z$ from a Gaussian with lower standard deviation than used during training resulted in better sounding mel-spectrograms, as similarly concluded in Kingma & Dhariwal (2018) and (Parmar et al., 2018). Our inference results use $\\sigma ^ { \\mathrm { 2 } } = 0 . 5$ while sampling the prior and the posterior variance while sampling the posterior. ",
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+    {
+        "type": "text",
+        "text": "2.5 POSTERIOR INFERENCE ",
+        "text_level": 1,
+        "bbox": [
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+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "Figure 1 shows that several speech characteristics present in mel-spectrograms are clustered into regions of the $_ z$ -space. Knowing this, we can treat the latent distribution as a prior $q ( z ) = \\mathcal { N } ( 0 , I )$ and obtain a posterior over the latent space of the flow model $q ( z | \\zeta _ { 1 : m } )$ conditioned on the evidence $\\zeta _ { 1 : m }$ , which are $m$ data observations $\\mathbf { \\Delta } _ { \\mathbf { \\mathcal { X } } _ { i } }$ mapped to the latent space using $\\zeta _ { i } = f ^ { - 1 } ( { \\pmb x } _ { i } )$ . We can use a Gaussian likelihood function with covariance matrix $\\Sigma$ to compute the posterior above analytically, $q ( z | \\boldsymbol { \\zeta } _ { 1 : m } ) = \\mathcal { N } ( \\mu _ { p } , \\boldsymbol { \\Sigma } _ { p } )$ . Following the approach in Gambardella et al. (2019), defining $\\bar { \\zeta }$ as the mean of $\\zeta _ { i }$ and using $\\lambda$ as a hyperparameter, we define the parameters of the posterior below. Please see A.2, Algorithm 1 and Gambardella et al. (2019) for implementation details and a full derivation. ",
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+        "page_idx": 4
+    },
+    {
+        "type": "equation",
+        "img_path": "images/d9f54447ea9be14a88028cfcfd0b0c16ca546e7c3cbce839d9aa383b06dc26de.jpg",
+        "text": "$$\n\\pmb { \\mu } _ { p } = \\frac { \\frac { m } { \\lambda } \\bar { \\zeta } } { \\frac { m } { \\lambda } + 1 } \\quad \\pmb { \\Sigma } _ { p } = \\frac { 1 } { \\frac { m } { \\lambda } + 1 } \\pmb { I }\n$$",
+        "text_format": "latex",
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+    {
+        "type": "text",
+        "text": "3 EXPERIMENTS ",
+        "text_level": 1,
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+    {
+        "type": "text",
+        "text": "This section describes our training setup and provides quantitative and qualitative results. Our quantitative results show that Flowtron has mean opinion scores that are comparable to the state of the art. Our qualitative results demonstrate many features that are either impossible or inefficient to achieve using Tacotron, Tacotron 2 GST and Tacotron GM-VAE. These features include variation control in speech, interpolation between samples, and style transfer over time. ",
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+    {
+        "type": "text",
+        "text": "We decode all mel-spectrograms into waveforms with a WaveGlow (Prenger et al., 2019) model available on github (Valle et al., 2019a). This suggests that WaveGlow can be used as an universal decoder. In addition to our illustrated and quantitative results, we ask that the readers listen to Flowtron samples in our supplementary materials corresponding to our qualitative experiments. ",
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+    {
+        "type": "text",
+        "text": "3.1 TRAINING SETUP ",
+        "text_level": 1,
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+    {
+        "type": "text",
+        "text": "We train Flowtron, Tacotron 2 and Tacotron 2 GST models using a dataset (LSH) that combines the LJSpeech dataset (Ito et al., 2017) with two proprietary single speaker datasets with 20 and 10 hours each (Sally and Helen). We also train a Flowtron model on the train-clean-100 subset of LibriTTS (Zen et al., 2019) with 123 speakers and 25 minutes on average per speaker. Speakers with less than 5 minutes of data and files that are larger than 10 seconds are filtered out. For each dataset, we use at least 180 samples for the validation set, and the remainder for the training set. ",
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+    {
+        "type": "text",
+        "text": "The models are trained on uniformly sampled normalized text and ARPAbet encodings obtained from the CMU Pronouncing Dictionary (Weide, 1998). We do not perform any data augmentation. We adapt public Tacotron 2 and Tacotron 2 GST repos to include speaker embeddings as described in Section 2. We use the same mel-spectrogram representation used in WaveGlow (Prenger et al., 2019). We train Flowtron with a pre-trained text encoder, progressively adding steps of flow once the last step of flow has learned to attend to text. Flowtron models used in our experiments have 2 steps of flow. We forward readers to A.3 and A.4 for details on our training setup and ablation studies. ",
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+    {
+        "type": "text",
+        "text": "3.2 MEAN OPINION SCORE (MOS) COMPARISON ",
+        "text_level": 1,
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+    {
+        "type": "text",
+        "text": "We use the LJS voice as a reference and compare MOS between real samples, samples from Flowtron with 2 steps of flow, and samples from Tacotron 2. Following guidelines in (Prenger et al., 2019), we crowd-sourced MOS tests on Amazon Mechanical Turk using 30 volume normalized utterances disjoint from the training set for evaluation, and randomly chose the utterances for each subject. The scores provided in (Prenger et al., 2019) are used for real samples. ",
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+    {
+        "type": "text",
+        "text": "The mean opinion scores are shown in Table 1 with $9 5 \\%$ confidence intervals computed over approximately 250 scores per source. The results roughly match our subjective qualitative assessment. The larger advantage of Flowtron is in the control over the amount of speech variation and the manipulation of the latent space. ",
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+    {
+        "type": "table",
+        "img_path": "images/b678e53a40114694eafea8eb842877b0e74bf89c25747a97d752a8948fcf2033.jpg",
+        "table_caption": [
+            "Table 1: Mean Opinion Scores "
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td> Source</td><td>Flows</td><td>MOS</td></tr><tr><td>Real</td><td>1</td><td>4.27 ± 0.13</td></tr><tr><td>Flowtron</td><td>2</td><td>3.66 ± 0.16</td></tr><tr><td>Tacotron 2</td><td>1</td><td>3.52 ± 0.17</td></tr></table>",
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+    {
+        "type": "text",
+        "text": "3.3 SAMPLING THE PRIOR ",
+        "text_level": 1,
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+        "page_idx": 5
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+    {
+        "type": "text",
+        "text": "The simplest approach to generating samples with Flowtron is to sample from a prior distribution $z \\sim \\mathcal { N } ( 0 , \\sigma ^ { 2 } )$ and adjust $\\sigma ^ { 2 }$ to control the amount of variation. Whereas $\\sigma ^ { 2 } = { \\overset { \\cdot } { 0 } }$ completely removes variation and produces outputs based on the model bias, increasing $\\sigma ^ { 2 }$ will increase the amount of variation in speech. ",
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+    {
+        "type": "text",
+        "text": "3.3.1 SPEECH VARIATION ",
+        "text_level": 1,
+        "bbox": [
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+        "page_idx": 5
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+    {
+        "type": "text",
+        "text": "We illustrate the relationship between $\\sigma ^ { 2 }$ and control over variability by synthesizing Flowtron samples with $\\sigma ^ { 2 } \\in \\{ 0 . 0 , 0 . 5 , 1 . 0 \\}$ . All samples are generated conditioned on the speaker Sally and the text “How much variation is there?\". Despite the variability added by increasing $\\sigma ^ { 2 }$ , all Flowtron-synthesized samples produce high quality speech. ",
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+    {
+        "type": "text",
+        "text": "Figure 3 shows that contrary to commonly held wisdom (Shen et al., 2017; Arik et al., 2017a;b; Ping et al., 2017; Skerry-Ryan et al., 2018; Wang et al., 2018; Binkowski et al., 2019), Flowtron generates ´ sharp harmonics and well resolved formants without a compound loss nor Prenet or Postnet layers. ",
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+        "page_idx": 5
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+    {
+        "type": "image",
+        "img_path": "images/e7c8b410365c954bd6e9c021768b7bcaf98aa8346bf4d800c4fd74a32b969a41.jpg",
+        "image_caption": [
+            "Figure 3: Flowtron Mel-spectrograms illustrate increasing variability by using different $\\sigma ^ { 2 }$ and that Flowtron is able to produce sharp harmonics with high $\\sigma ^ { \\tilde { 2 } }$ and without Prenet or Postnet layers. "
+        ],
+        "image_footnote": [],
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+    {
+        "type": "text",
+        "text": "Now we show that adjusting $\\sigma ^ { 2 }$ is a simple and valuable approach that provides more variation and control thereof than Tacotron, without sacrificing speech quality and despite of having a similar but simpler architecture. For this, we synthesize 10 samples with Tacotron 2 using different values for the Prenet dropout probability $p \\in \\{ 0 . 4 5 , 0 . 5 , 0 . 5 5 \\}$ , scaling outputs accordingly. Samples computed on values of $p \\in [ 0 . 3 , 0 . 8 ]$ are not included because they sound unintelligible. ",
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+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "Figure 4 provides plots of $F _ { 0 }$ contours extracted with the YIN algorithm (De Cheveigné & Kawahara, 2002), with minimum $F _ { 0 }$ , maximum $F _ { 0 }$ , and harmonicity threshold equal to $8 0 \\mathrm { H z }$ , $4 0 0 \\mathrm { H z }$ and 0.3 respectively. Our results are similar to the previous sample duration analysis. As expected, $\\sigma ^ { 2 } = 0$ provides no variation in $F _ { 0 }$ contour1, while increasing $\\sigma ^ { \\bar { 2 } }$ will increase variation in $F _ { 0 }$ contours. ",
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+    {
+        "type": "text",
+        "text": "Our results in Figure 4 also show that Flowtron samples are considerably less monotonous than the samples produced with Tacotron 2 at no cost and with a similar but simpler architecture. Whereas increasing $\\sigma ^ { 2 }$ considerably increases variation in $F _ { 0 }$ , modifying $p$ barely produces any variation. This is valuable because expressive speech is associated with non-monotonic $F _ { 0 }$ contours. In A.1 we show similar results with respect to sentence duration. ",
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+    },
+    {
+        "type": "text",
+        "text": "3.3.2 INTERPOLATION BETWEEN SAMPLES ",
+        "text_level": 1,
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "With Flowtron, we can perform interpolation in $_ { z }$ -space to achieve interpolation in mel-spectrogram space. This experiment evaluates Flowtron models with and without speaker embeddings. For the experiment with speaker embeddings, we choose the speaker Sally and the phrase $^ { 6 6 } I t$ is well known that deep generative models have a rich latent space.\". We generate mel-spectrograms by sampling $z \\sim \\mathcal { N } ( 0 , 0 . 8 )$ twice and interpolating between them over 100 timesteps. For the experiment without speaker embeddings we interpolate between Sally and Helen using the phrase “We are testing this model.\". ",
+        "bbox": [
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+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "First, we perform inference by sampling $z \\sim \\mathcal { N } ( 0 , 0 . 5 )$ until we find $_ z$ values, $_ { z _ { h } }$ and $z _ { s }$ , that produce mel-spectrograms with Helen’s and Sally’s voice respectively. We then generate samples by performing inference while linearly interpolating between $z _ { h }$ and $z _ { s }$ . Our same speaker interpolation samples show that Flowtron is able to interpolate between multiple samples while producing correct alignment maps. Our different speaker interpolation samples show that Flowtron is able to gradually and smoothly morph one voice into another. ",
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+        "page_idx": 5
+    },
+    {
+        "type": "image",
+        "img_path": "images/f30f9cb2befac46a0eb35ffb6087c92348c0aedb6f0ca808d2b43b9d9b9d1998.jpg",
+        "image_caption": [
+            "Figure 4: $F _ { 0 }$ contours obtained from samples generated by Flowtron and Tacotron 2 with different values for $\\sigma ^ { 2 }$ and $p$ . Flowtron provides more variability and expressivity than Tacotron 2. "
+        ],
+        "image_footnote": [],
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+        "type": "text",
+        "text": "",
+        "bbox": [
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+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "3.4 SAMPLING THE POSTERIOR (STYLE TRANSFER) ",
+        "text_level": 1,
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "We generate samples with Flowtron by sampling a posterior distribution conditioned on the evidence containing speech characteristics of interest, as described in 2.5 and Gambardella et al. (2019). Tacotron 2 GST Wang et al. (2018) has an equivalent posterior sampling approach. During inference, the model is conditioned on a weighted sum of global style tokens (posterior) queried through an embedding of existing audio samples (evidence). We evaluate Tacotron 2 GST using a single sample to query a style token, or multiple samples to compute an average style token. For complete results, please refer to audio samples in the supplemental material corresponding to the following sections. ",
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+    },
+    {
+        "type": "text",
+        "text": "3.4.1 SEEN SPEAKER",
+        "text_level": 1,
+        "bbox": [
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+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "In this section we run two style transfer experiments: the first one (Expressive) uses samples with high variance in pitch, which we use as a proxy for comparing expressivity in speech; the second (High Pitch), uses samples with high average pitch. In these experiments, we provide comparisons between Pitch Mean and Pitch Standard Deviation from the Reference samples providing the style, a Flowtron Baseline and after style transfer using Flowtron Posterior and Tacotron 2 GST. ",
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+    },
+    {
+        "type": "text",
+        "text": "Our experiments show that by sampling from the posterior or interpolating between the posterior and the Gaussian prior over time, Flowtron makes a monotonic speaker gradually sound more expressive. Architectures similar to Tacotron 2 GST with fixed-latent embeddings are not able to perform gradual changes in style over time. Table 2 provides pitch summary statistics computed over 5 phrases and 10 takes each and shows that Flowtron is overall closer to the reference providing the style than Tacotron 2 GST. Our supplemental materials also show that Tacotron 2 GST sentences are repetitive and contain vocal-fry like distortions. ",
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+    },
+    {
+        "type": "table",
+        "img_path": "images/78cb70863916da84a2512860053e3537d678234725071d3f79d80b3259c9a31f.jpg",
+        "table_caption": [],
+        "table_footnote": [],
+        "table_body": "<table><tr><td colspan=\"2\"></td><td colspan=\"2\">Pitch Mean</td><td colspan=\"3\">Pitch Standard Deviation</td></tr><tr><td>Model</td><td>Style Expressive</td><td>High Pitch</td><td>Surprised</td><td>Expressive</td><td>High Pitch</td><td>Surprised</td></tr><tr><td>Reference</td><td>53.6</td><td>55.2</td><td>58.2</td><td>4.5</td><td>2.3</td><td>1.0</td></tr><tr><td>FTA Posterior</td><td>53.4</td><td>53.3</td><td>55.5</td><td>2.5</td><td>2.3</td><td>3.0</td></tr><tr><td>FTA Baseline</td><td>53.1</td><td>52.6</td><td>52.8</td><td>2.2</td><td>1.9</td><td>1.9</td></tr><tr><td>Tacotron 2 GST</td><td>51.7</td><td>53.6</td><td>51.6</td><td>2.0</td><td>2.4</td><td>1.7</td></tr></table>",
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+    },
+    {
+        "type": "text",
+        "text": "Table 2: Values closer to the Reference are better. Comparison between pitch (MIDI number) summary statistics from Reference providing the style, Flowtron with standard Gaussian prior (FTA Baseline) and samples after style transfer with Flowtron (FTA Posterior) and Tacotron 2 GST. Our results show that FTA Posterior is overall more effective than Tacotron 2 GST in emulating the Reference by better matching its pitch summary statistics. ",
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+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "3.4.2 SEEN SPEAKER WITH UNSEEN STYLE",
+        "text_level": 1,
+        "bbox": [
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+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "We compare samples generated with Flowtron and Tacotron 2 GST to evaluate their ability to emulate a speaking style unseen during training of a speaker seen during training. While Sally’s data used during training consists of news article readings, the evaluation samples contain Sally’s interpretation of the somber and vampiresque novel, Born of Darkness (BOD). ",
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+    },
+    {
+        "type": "text",
+        "text": "Our samples show that while Tacotron 2 GST fails to emulate the somber timbre in Born of Darkness, Flowtron succeeds in transferring not only the somber timbre, but also the low $F _ { 0 }$ and the long pauses associated with the narrative style. ",
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+    },
+    {
+        "type": "text",
+        "text": "3.4.3 UNSEEN SPEAKER",
+        "text_level": 1,
+        "bbox": [
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+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "In this experiment we compare Flowtron and Tacotron 2 GST samples to evaluate their ability to emulate the speaking style of a speaker not seen during training. The styles comes from speaker ID 24 and her “surprised\" samples in RAVDESS (Livingstone & Russo, 2018), a dataset with emotion labels. Table 2 shows that while the samples generated with Tacotron 2 GST are not able to emulate the high-pitched style from RAVDESS, Flowtron is able to make Sally sound high-pitched as in the “surprised\" style. ",
+        "bbox": [
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+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "3.5 INTERPOLATION BETWEEN STYLES (PRIOR AND POSTERIOR) ",
+        "text_level": 1,
+        "bbox": [
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+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "In this experiment we illustrate how to control the speaking style at inference time by adjusting the parameter $\\lambda$ in Equation 9 to interpolate between a baseline style (prior) and a target style (posterior). We use a model trained on LibriTTS and use a single sample from Sally’s (unseen speaker) Born of Darkness dataset as evidence providing the target style. We synthesize posterior samples generated with Flowtron with $\\lambda \\in \\{ 0 . 1 , \\bar { 0 } . 6 6 6 , \\bar { 1 . 0 } , 2 . 0 \\}$ . Figure 5 reflects the interpolation in style as interpolation in spectral profiles. Our supplemental materials aurally reflect a similar interpolation in other non-textual characteristics. ",
+        "bbox": [
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+        "page_idx": 7
+    },
+    {
+        "type": "image",
+        "img_path": "images/3aff932d2f12339fcd2f2fce3f3076915313ae7641a2cba1b3937ff1976cb0df.jpg",
+        "image_caption": [
+            "Figure 5: Spectral profiles from the target style, from the Flowtron baseline generated using the prior, and from Flowtron samples generated using the posterior with different values for $\\lambda$ . These images show that by decreasing the value of $\\lambda$ we gradually move the spectral profile from the baseline style (prior) to the target style (posterior). "
+        ],
+        "image_footnote": [],
+        "bbox": [
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+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "3.6 SAMPLING THE GAUSSIAN MIXTURE ",
+        "text_level": 1,
+        "bbox": [
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+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "In this last section we provide samples from Flowtron Gaussian Mixture (GM) and visualizations. We replicate the experiments in Tacotron GM-VAE (Hsu et al., 2018) to visualize how speakers are assigned to mixture components and provide samples in which we modulate speech characteristics by translating one of the dimensions of an individual mixture component. ",
+        "bbox": [
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+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "For these experiments, Flowtron GM-LibriTTS is trained on LibriTTS without speaker embeddings and a Gaussian mixture with 8 component with predicted mean, covariance and component assignment probabilities; Flowtron GM-LSH is trained on LSH with speaker embeddings and a Gaussian Mixture with 8 components, fixed mean and covariances and predicted component assignment probabilities. ",
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+    {
+        "type": "text",
+        "text": "",
+        "bbox": [
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+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "3.6.1 VISUALIZING ASSIGNMENTS ",
+        "text_level": 1,
+        "bbox": [
+            176,
+            147,
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+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "We evaluate model interpretability on a subset of LibriTTS with 123 speakers and 1410 utterances, 180 of which come from the validation set. Following Hsu et al. (2018), each utterance is assigned to the component with the highest posterior probability a $\\cdot \\mathrm { g } \\operatorname* { m a x } _ { k } p ( \\hat { \\phi } _ { k } \\mid \\mathbf { x } )$ . We obtain posterior probabilities per utterance by using the Mel Encoder described in Section 2.3 and averaging the predicted component assignment probabilities over time. Figure 6 suggests that information in each component of Flowtron GM-LibriTTS is gender dependent. ",
+        "bbox": [
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+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "e quant al. (201 the association between gender and mixture components with the The assignment consistency with respect to gender is defined as $\\begin{array} { r } { \\frac { 1 } { M } \\sum _ { i = 1 } ^ { N } \\sum _ { j = 1 } ^ { N _ { i } } \\mathbb { 1 } y _ { i j } = } \\end{array}$ $\\hat { y } _ { i }$ $M$ is the component assignment of utterance $j$ from speaker $i$ , and ugge $\\hat { y } _ { i }$ is the mode of ng that the co $\\{ y _ { i j } \\} _ { j = 1 } ^ { N _ { i } }$ . The assignment consistency in Flowtron GM-LibriTTS is  group utterances by speaker and group speakers by gend $8 2 . 4 \\%$ provide visualizations in Figure 6. ",
+        "bbox": [
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+        "page_idx": 8
+    },
+    {
+        "type": "image",
+        "img_path": "images/e736b3bc02eb0a38f6cdff0b56f42799339468a72f5b49b7e13d7cb79dfaa76d.jpg",
+        "image_caption": [
+            "Figure 6: Component assignments suggest that information in each component is gender dependent. "
+        ],
+        "image_footnote": [],
+        "bbox": [
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+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "3.6.2 TRANSLATING DIMENSIONS ",
+        "text_level": 1,
+        "bbox": [
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+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "We use the model Flowtron GM-LSH and focus on translating one of the dimensions of a single mixture component by adding an offset. The samples in our supplementary material show that we are able to modulate specific speech characteristics like pitch and word duration. Although the samples generated by translating one the dimensions associated with pitch height have different pitch contours, they have the same duration. Similarly, our samples show that translating the dimension associated with length of the first word does not modulate the pitch of the first word. We provide visualizations in Figure 9 in A.5. ",
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+    },
+    {
+        "type": "text",
+        "text": "4 CONCLUSION ",
+        "text_level": 1,
+        "bbox": [
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+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "We propose a new text to mel-spectrogram synthesis model based on autoregressive flows that is optimized by maximizing the likelihood and allows for speech variation and style transfer. Our results show that samples generated with Flowtron achieve mean opinion scores similar to SOTA TTS models. We demonstrate that our model learns a latent space that stores non-textual information, supervised using only MLE. Flowtron is able to produce high quality speech with high variability by adjusting $\\sigma ^ { 2 }$ . ",
+        "bbox": [
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+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "Our results show that the latent space over non-textual features that can be investigated and manipulated to give the user more control over the generative model’s output. We provide many examples that showcase this, including transferring the style from speakers seen and unseen during training to another speaker using sentences with similar or different text, and making a monotonic speaker sound more expressive. For future work, we are interested in using normalizing flows for few-shot speech synthesis, speech compression and in semi-supervised settings to exploit datasets with limited labels. ",
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+    {
+        "type": "text",
+        "text": "REFERENCES ",
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+        "text": "Heiga Zen, Viet Dang, Rob Clark, Yu Zhang, Ron J Weiss, Ye Jia, Zhifeng Chen, and Yonghui Wu. Libritts: A corpus derived from librispeech for text-to-speech. arXiv preprint arXiv:1904.02882, 2019. ",
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+    {
+        "type": "text",
+        "text": "A APPENDIX ",
+        "text_level": 1,
+        "bbox": [
+            176,
+            102,
+            297,
+            117
+        ],
+        "page_idx": 11
+    },
+    {
+        "type": "text",
+        "text": "A.1 SPEECH VARIATION ",
+        "text_level": 1,
+        "bbox": [
+            176,
+            142,
+            356,
+            157
+        ],
+        "page_idx": 11
+    },
+    {
+        "type": "text",
+        "text": "Figure 7 provides plots from sample durations in seconds. Our results show that larger values of $\\sigma ^ { 2 }$ produces samples with more variation in duration, whereas $\\sigma ^ { 2 } = 0$ is fully deterministic. These results demonstrate that our latent space is able to model duration, which is a critical non-textual component to expressiveness in speech. ",
+        "bbox": [
+            173,
+            175,
+            826,
+            231
+        ],
+        "page_idx": 11
+    },
+    {
+        "type": "image",
+        "img_path": "images/a1d117d71899bdbad6fd981f8c746b3fe210e9afcef209fbdbb739e32933e0c9.jpg",
+        "image_caption": [
+            "Figure 7: Sample duration given $\\sigma ^ { 2 }$ and $p$ show that Flowtron provides more variation in sample duration than Tacotron. "
+        ],
+        "image_footnote": [],
+        "bbox": [
+            370,
+            261,
+            627,
+            366
+        ],
+        "page_idx": 11
+    },
+    {
+        "type": "text",
+        "text": "A.2 POSTERIOR INFERENCE ",
+        "text_level": 1,
+        "bbox": [
+            176,
+            464,
+            383,
+            478
+        ],
+        "page_idx": 11
+    },
+    {
+        "type": "text",
+        "text": "We generate posterior samples with Flowtron by sampling a posterior distribution conditioned on evidence containing speech characteristics of interest, as described in (Gambardella et al., 2019). We collect the evidence by performing a forward pass with Flowtron using with a speaker embedding, $( s \\sim \\mathcal { N } ( 0 , I ) )$ , the observed mel-spectrogram, and the text from a set of samples with the speech characteristics of interest. We use a specific speaker embedding when we want to factor out information about a specific speaker from $\\zeta$ . ",
+        "bbox": [
+            174,
+            496,
+            826,
+            580
+        ],
+        "page_idx": 11
+    },
+    {
+        "type": "text",
+        "text": "Next, we compute $\\bar { \\zeta }$ by averaging $\\zeta _ { i , k }$ over batch $( i )$ or over batch and time $( i , k )$ and use Equation 9 to compute the parameters of the posterior. When averaging over batch, we repeat the $\\mathbf { Z }$ -values over the time dimension until they reach the desired length. We find in our experiments that averaging over batch is more efficient for transfering the style than averaging over batch and time. In all experiments, we select the best performing samples given $\\lambda$ values between $m * 0 . 1$ and $m * 4$ , where $m$ is the number of samples in the evidence. While small $\\lambda$ values move the mean of the posterior closer to the evidence and decreases its variance, large $\\lambda$ values move the mean of the posterior closer to the prior and increase the variance. ",
+        "bbox": [
+            174,
+            585,
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+        ],
+        "page_idx": 11
+    },
+    {
+        "type": "text",
+        "text": "Once the parameters of the posterior distribution are computed, we can sample the posterior distribution and perform inference with the desired text and speaker. Algorithm 1 provides a description of posterior inference with Flowtron. ",
+        "bbox": [
+            176,
+            705,
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+        ],
+        "page_idx": 11
+    },
+    {
+        "type": "text",
+        "text": "A.3 TRAINING DETAILS ",
+        "text_level": 1,
+        "bbox": [
+            176,
+            780,
+            354,
+            794
+        ],
+        "page_idx": 11
+    },
+    {
+        "type": "text",
+        "text": "We use the ADAM (Kingma & Ba, 2014) optimizer with default parameters, 1e-4 learning rate and1e-6 weight decay for Flowtron and 1e-3 learning rate and 1e-5 weight decay for the other models,following Wang et al. (2017). We anneal the learning rate once the generalization error starts toplateau and stop training once the the generalization error stops significantly decreasing or startsincreasing. Flowtron models with 2 steps of flow were trained on the LSH dataset for approximately1000 epochs, then fine-tuned on LibriTTS for 500 epochs. Tacotron 2 and Tacotron 2 GST are trained for approximately 500 epochs. Each model is trained on a single NVIDIA DGX-1 with 8 GPUs. ",
+        "bbox": [
+            174,
+            811,
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+        ],
+        "page_idx": 11
+    },
+    {
+        "type": "text",
+        "text": "Algorithm 1: Flowtron Posterior inference ",
+        "bbox": [
+            176,
+            107,
+            457,
+            122
+        ],
+        "page_idx": 12
+    },
+    {
+        "type": "text",
+        "text": "Input : Trained Flowtron model $f$ , evidence audio samples ${ \\boldsymbol { \\mathbf { \\mathit { x } } } } _ { 1 : m }$ Output : Posterior sample ",
+        "bbox": [
+            173,
+            126,
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+        ],
+        "page_idx": 12
+    },
+    {
+        "type": "text",
+        "text": "1 For each $m e l _ { i , k } , t e x t _ { i }$ , speakeri ∈ x1:m ",
+        "bbox": [
+            165,
+            154,
+            442,
+            166
+        ],
+        "page_idx": 12
+    },
+    {
+        "type": "text",
+        "text": "2 if average over batch then ",
+        "bbox": [
+            161,
+            196,
+            351,
+            210
+        ],
+        "page_idx": 12
+    },
+    {
+        "type": "text",
+        "text": "3 repeat each $\\zeta _ { k }$ over the time dimension until target length is achieve   \n4 $\\bar { \\zeta _ { k } } \\gets \\mathrm { C o m p u }$ te $\\zeta _ { i , k }$ average over batch $k$   \n5 else   \n6 ¯ζ ← Compute $\\zeta _ { i , k }$ average over batch and time $k$   \n7 end   \n8 $\\mu _ { p }$ , $\\Sigma _ { p } $ Compute posterior parameters using Equation 9   \n9 Initialize $\\boldsymbol { Z } _ { p } \\sim \\mathcal { N } ( \\pmb { \\mu } _ { p } , \\pmb { \\Sigma } _ { p } )$   \n10 Sample $z _ { p }$ from $Z _ { p }$   \n11 Perform inference with Flowtron using $z _ { p }$ , text and speaker ",
+        "bbox": [
+            158,
+            210,
+            642,
+            345
+        ],
+        "page_idx": 12
+    },
+    {
+        "type": "text",
+        "text": "A.4 ABLATION STUDIES ",
+        "text_level": 1,
+        "bbox": [
+            176,
+            378,
+            356,
+            392
+        ],
+        "page_idx": 12
+    },
+    {
+        "type": "text",
+        "text": "A.4.1 COMPOSING FLOWS",
+        "text_level": 1,
+        "bbox": [
+            176,
+            404,
+            370,
+            417
+        ],
+        "page_idx": 12
+    },
+    {
+        "type": "text",
+        "text": "We evaluated Flowtron models with 2, 3 and 6 steps of flow and found that more steps of flow have better likelihood but no significant qualitative improvement, while increasing inference time significantly. Hence, we chose to report results on Flowtron models with 2 steps of flow. ",
+        "bbox": [
+            174,
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+            470
+        ],
+        "page_idx": 12
+    },
+    {
+        "type": "text",
+        "text": "A.4.2 BIDIRECTIONAL PROCESSING",
+        "text_level": 1,
+        "bbox": [
+            176,
+            486,
+            436,
+            501
+        ],
+        "page_idx": 12
+    },
+    {
+        "type": "text",
+        "text": "We compared the bidirectional (reversing the ordering of the mel-spectrogram frames in time on even numbered steps of flows) and unidirectional processing and found that bidirectional processing provides better likelihood and audio quality. Hence, we use bidirectional processing in all our Flowtron models. ",
+        "bbox": [
+            174,
+            510,
+            825,
+            565
+        ],
+        "page_idx": 12
+    },
+    {
+        "type": "text",
+        "text": "A.4.3 ADDITIVE VS AFFINE TRANSFORMATIONS ",
+        "text_level": 1,
+        "bbox": [
+            174,
+            582,
+            524,
+            595
+        ],
+        "page_idx": 12
+    },
+    {
+        "type": "text",
+        "text": "The Tacotron 2 baseline without the postnet layer can be interpreted as additive single step autoregressive normalizing flow (ASSANF). By comparing Flowtron with Tacotron 2, we’re comparing with a model that is better than an (ASSANF), as Tacotron 2 sans Postnet does not have sharp harmonics. Hence, we prefer affine over additive transformations. ",
+        "bbox": [
+            174,
+            606,
+            826,
+            661
+        ],
+        "page_idx": 12
+    },
+    {
+        "type": "text",
+        "text": "A.4.4 COMPARISON WITH TACOTRON 2 ",
+        "text_level": 1,
+        "bbox": [
+            176,
+            676,
+            460,
+            690
+        ],
+        "page_idx": 12
+    },
+    {
+        "type": "text",
+        "text": "The Tacotron 2 baseline without the postnet layer can be interpreted as additive single step autoregressive normalizing flow (ASSANF). By comparing Flowtron with Tacotron 2, we’re comparing with a model that is better than an (ASSANF), as Tacotron 2 sans Postnet does not have sharp harmonics. Hence, we prefer affine over additive transformations. ",
+        "bbox": [
+            174,
+            700,
+            826,
+            757
+        ],
+        "page_idx": 12
+    },
+    {
+        "type": "image",
+        "img_path": "images/cefdc8f2171b60bd2119214eca1bde41063f24f86b63edf5cfab97efff387eb2.jpg",
+        "image_caption": [
+            "Figure 8: Visualization of the decoder in Tacotron 2 during training. Unlike Flowtron, Tacotron 2 requires Prenet and Postnet layers to learn attention and produce sharp harmonics. "
+        ],
+        "image_footnote": [],
+        "bbox": [
+            173,
+            98,
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+            303
+        ],
+        "page_idx": 13
+    },
+    {
+        "type": "image",
+        "img_path": "images/62ef8251c7a9a869a84ca1e2925c939f73e3784e68dce95f76c876c37514717f.jpg",
+        "image_caption": [
+            "Figure 9: (a) shows that by translating one of the dimensions of $_ z$ we are able to alter the pitch contour of the sentence while keeping the length fixed. (b) shows that by translation one of the dimensions of $_ z$ we are able to alter the length of the sentence while keeping a similar pitch contour. "
+        ],
+        "image_footnote": [],
+        "bbox": [
+            179,
+            547,
+            826,
+            815
+        ],
+        "page_idx": 13
+    },
+    {
+        "type": "text",
+        "text": "A.6 FLOWTRON AND TACOTRON SUMMARY VIEW ",
+        "text_level": 1,
+        "bbox": [
+            178,
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+        ],
+        "page_idx": 14
+    },
+    {
+        "type": "text",
+        "text": "Flowtron( (speaker_embedding): Embedding(3, 128) (embedding): Embedding(185, 512) (flows): ModuleList( (0): AR_Step( (conv): Conv1d(1024, 160, kernel_size $=$ (1,), stride $=$ (1,)) (lstm): LSTM(1664, 1024, num_layers $^ { = 2 }$ ) (attention_lstm): LSTM(80, 1024) (attention_layer): Attention( (softmax): Softmax(dim $^ { = 2 }$ ) (query): LinearNorm( (linear_layer): Linear(in_features=1024, out_features $= 6 4 0$ , bias=False) ) (key): LinearNorm( (linear_layer): Linear(in_features $= 6 4 0$ , out_feature $_ { 3 } = 6 4 0$ , bias $\\mathbf { \\tau } = \\dot { }$ False) ) (value): LinearNorm( (linear_layer): Linear(in_features $= 6 4 0$ , out_feature $\\mathord { : } = 6 4 0$ , bias=False) ) (v): LinearNorm( (linear_layer): Linear(in_features $= 6 4 0$ , out_features $: = 1$ , bias=False) ) ) (dense_layer): DenseLayer( (layers): ModuleList( (0): LinearNorm( (linear_layer): Linear(in_features=1024, out_features=1024, bias=True) ) (1): LinearNorm( (linear_layer): Linear(in_feature $\\mathord { \\mathrm { 3 } } = 1 0 2 4$ , out_features $_ { \\mathrm { : = 1 0 2 4 } }$ , bias $= \"$ True) ) ",
+        "bbox": [
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+        "page_idx": 14
+    },
+    {
+        "type": "text",
+        "text": "(1): AR_Back_Step( (ar_step): AR_Step( (conv): Conv1d(1024, 160, kernel_size $=$ (1,), stride $=$ (1,)) (lstm): LSTM(1664, 1024, num_layers $^ { = 2 }$ ) (attention_lstm): LSTM(80, 1024) (attention_layer): Attention( (softmax): Softmax(dim $^ { = 2 }$ ) (query): LinearNorm( (linear_layer): Linear(in_feature $\\mathord { \\mathrm { 3 } } = 1 0 2 4$ , out_feature $\\mathtt { s } = 6 4 0$ , bias $=$ False) ) (key): LinearNorm( (linear_layer): Linear(in_feature $\\mathord { : } = 6 4 0$ , out_features $= 6 4 0$ , bias ${ } = \\mathbb { E }$ alse) (value): LinearNorm( (linear_layer): Linear(in_features $_ { : = 6 4 0 }$ , out_features $= 6 4 0$ , bias=False) ) (v): LinearNorm( (linear_layer): Linear(in_features $_ { : = 6 4 0 }$ , out_features $^ { = 1 }$ , bias $=$ False) ) ) (dense_layer): DenseLayer( (layers): ModuleList( (0): LinearNorm( (linear_layer): Linear(in_features $\\mathbf { \\Psi } = \\mathbf { \\dot { \\Psi } }$ 1024, out_features $\\mathbf { \\Psi } = \\mathbf { \\dot { \\Psi } }$ 1024, bias ${ } , = { }$ True) ) (1): LinearNorm( (linear_layer): Linear(in_features $= 1$ 1024, out_features $=$ 1024, bias $=$ True) ) (gate_layer): LinearNorm( (linear_layer): Linear(in_features $^ { = 1 }$ 664, out_features $^ { = 1 }$ , bias $= \"$ True) )   \n)   \n(encoder): Encoder( (convolutions): ModuleList( (0): Sequential( (0): ConvNorm( (conv): Conv1d(512, 512, kernel_size $=$ (5,), stride $=$ (1,), padding=(2,)) ) (1): InstanceNorm1d(512, eps=1e-05, momentum=0.1, affine $=$ True, track_running_ ) ",
+        "bbox": [
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+        ],
+        "page_idx": 14
+    },
+    {
+        "type": "text",
+        "text": "(1): Sequential( (0): ConvNorm( (conv): Conv1d(512, 512, kernel_size $=$ (5,), stride $=$ (1,), padding=(2,)) ) (1): InstanceNorm1d(512, ep $\\mathrm { 3 } { = } 1 \\mathrm { e } { - } 0 5$ , momentum $\\ i { = } 0 \\cdot 1$ , affine $= ^ { \\prime }$ True, track_running_stats=False) ) (2): Sequential( (0): ConvNorm( (conv): Conv1d(512, 512, kernel_size $=$ (5,), stride $=$ (1,), padding=(2,)) ) (1): InstanceNorm1d(512, eps $=$ 1e-05, momentum $\\ i { = } 0 \\cdot 1$ , affine $=$ True, track_running_stats=False) ) ) (lstm): LSTM(512, 256, batch_first $= \"$ True, bidirectional $=$ True) ) ) ",
+        "bbox": [
+            171,
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+        ],
+        "page_idx": 15
+    },
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parse/train/SkgHtkrYPH/SkgHtkrYPH.md

@@ -0,0 +1,261 @@
+# FAST SPARSE CONVNETS
+
+Anonymous authors Paper under double-blind review
+
+# ABSTRACT
+
+Historically, the pursuit of efficient inference has been one of the driving forces behind the research into new deep learning architectures and building blocks. Some of the recent examples include: the squeeze-and-excitation module of (Hu et al., 2018), depthwise separable convolutions in Xception (Chollet, 2017), and the inverted bottleneck in MobileNet v2 (Sandler et al., 2018). Notably, in all of these cases, the resulting building blocks enabled not only higher efficiency, but also higher accuracy, and found wide adoption in the field. In this work, we further expand the arsenal of efficient building blocks for neural network architectures; but instead of combining standard primitives (such as convolution), we advocate for the replacement of these dense primitives with their sparse counterparts. While the idea of using sparsity to decrease the parameter count is not new (Mozer & Smolensky, 1989), the conventional wisdom is that this reduction in theoretical FLOPs does not translate into real-world efficiency gains. We aim to correct this misconception by introducing a family of efficient sparse kernels for several hardware platforms, which we plan to open-source for the benefit of the community. Equipped with our efficient implementation of sparse primitives, we show that sparse versions of MobileNet v1 and MobileNet v2 architectures substantially outperform strong dense baselines on the efficiency-accuracy curve. On Snapdragon 835 our sparse networks outperform their dense equivalents by $1 . 1 - 2 . 2 \times$ – equivalent to approximately one entire generation of improvement. We hope that our findings will facilitate wider adoption of sparsity as a tool for creating efficient and accurate deep learning architectures.
+
+# 1 INTRODUCTION
+
+Convolutional neural networks (CNNs) have proven to be excellent at solving a diverse range of tasks (Bhandare et al., 2016). Standard network architectures are used in classification, segmentation, object detection and generation tasks (Pan et al., 2019; Long et al., 2015; Zhao et al., 2019). Given their wide utility, there has been significant effort to design efficient architectures that are capable of being run on mobile and other low power devices while still achieving high classification accuracy on benchmarks such as ImageNet (Russakovsky et al., 2015). For example, MobileNets (Howard et al., 2017; Sandler et al., 2018) employ the depthwise separable convolutions introduced in (Sifre & Mallat, 2014) to significantly reduce resource requirements over previous architectures. Inference time and computational complexity in these architectures are dominated by the $1 \times 1$ convolutions, which directly map to matrix-matrix multiplications.
+
+Weight sparsity is generally known to lead (Cheng et al., 2017) to theoretically smaller and more computationally efficient (in terms of number of floating-point operations) models, but it is often disregarded as a practical means of accelerating models because of the misconception that sparse operations cannot be fast enough to achieve actual speedups during inference. In this work we introduce fast kernels for Sparse Matrix-Dense Matrix Multiplication (SpMM) specifically targeted at the accceleration of sparse neural networks. The main distinction of our $\mathbf { S p M M }$ kernel from prior art (Nagasaka et al., 2018; Yang et al., 2018) is that we focus on a different point in the design space. While prior work focused on extremely sparse problems (typically ${ > } 9 9 \%$ , found in scientific and graph problems), we target the sparsity range of $\bar { 7 } 0 { - } 9 5 \%$ , more common when inducing weight sparsity in neural networks. As a result our kernels outperform both the Intel MKL (Intel, 2009) and the TACO compiler (Kjolstad et al., 2017).
+
+Using these kernels, we demonstrate the effectiveness of weight sparsity across three generations of MobileNet (Howard et al., 2017; Sandler et al., 2018; Tan et al., 2018; Tan & Le, 2019) architectures.
+
+![](images/768643c4b40a648f50103e2de8234d672275a600f8aa66150d8daaf370fb367d.jpg)  
+Figure 1: MobileNet v1 and v2 and EfficientNet models. Sparse models: blue, dense models: red. Sparse models include the cost of storing the location of non-zeros for sparse tensors as a bitmask converted back into parameter count. That is every 32 values in the bitmask contributes one “parameter”.
+
+Sparsity leads to an approximately one generation improvement in each architecture, with a sparse EfficientNet significantly more efficient than all previous models. These models represent a new generation of efficient CNNs, which reduces inference times by $1 . 1 - 2 . 2 \times$ , parameter counts by over $2 \times$ and number of floating-point operations (FLOPs) by up to $3 \times$ relative to the previous generations.
+
+# 2 RELATED WORK
+
+Improvements in convolutional network architectures (Krizhevsky et al., 2012; Simonyan & Zisserman, 2015; He et al., 2016; Huang et al., 2017), as measured by increased classification accuracy on benchmark tasks such as ImageNet (Russakovsky et al., 2015), have generally been concomitant with increases in model parameter counts, FLOPs and memory requirements. Recently this evolution has led to networks found through neural architecture search (Zoph et al., 2017; Real et al., 2019) which can achieve over $82 \%$ top-1 accuracy, but require nearly 25 GFLOPs for one inference.
+
+Given these prohibitive inference costs, there have been many lines of work attempting to improve CNN efficiency, which is often defined as one of three metrics:
+
+1. Inference speedup on real hardware   
+2. Theoretical speedup through FLOPs reduction   
+3. Model size reduction
+
+These axes are neither parallel nor orthogonal. The effect of (3) and (2) on (1) in particular can be quite complicated and highly varied depending on the hardware in question.
+
+The MobileNet family of architectures (Howard et al., 2017; Sandler et al., 2018) has focused on improving efficiency by taking advantage of the depthwise separable convolutions introduced in (Sifre & Mallat, 2014), which can be thought of as a hand-crafted sparsification of full convolutions with a predefined sparse topology, and which are responsible for the parameter efficiency of these architectures. MobileNet v1 (MBv1) used layers of $1 \times 1$ convolutions followed by depthwise convolutions. MobileNet v2 (MBv2) introduced the inverted residual block which consists of a $1 \times 1$ convolution expanding the channel count, a depthwise convolution on the expanded channel count, and then a $1 \times 1$ convolution reducing the parameter count. Across MobileNet architectures, the depthwise convolutions account for only a small fraction of the total FLOPs, parameters, and inference time of these models. In MBv1, they account for less than $2 \%$ of the total FLOPs and in MBv2 less than $3 \%$ .
+
+A different line of work attempted to make more efficient CNNs by directly pruning the weights of full convolutional filters accompanied by the necessary inference kernels (Park et al., 2016; Liu et al., 2015). Park et al. (2016) was not able to accelerate $1 \times 1$ convolutions, Liu et al. (2015) did not attempt it. The latter also required generating a new set of kernels for each instance of a model, which is often impractical for deployment. Due to the difficultly of accelerating sparse computation, channel pruning approaches have been preferred (Gordon et al., 2018; Dai et al., 2018; Luo et al., 2017; Louizos et al., 2018; Theis et al., 2018; He et al., 2018). These approaches prune away entire filters leaving the final model dense, and function more as an architecture search over channel counts.
+
+![](images/1de64d6d12d49e76835e08cf1c6c167b10b266c2dbaa3a3429f353302587b36a.jpg)  
+Figure 2: Sparse 1x1 Convolution as SpMM. Left: Unstructured sparsity (or block size 1). Right: Output channel block size of 4
+
+Full Neural Architecture Search has also been applied directly to architectures resembling MBv2 resulting in MobileNet v3 (Tan et al., 2018), FBNet (Wu et al., 2019), and EfficientNet (Tan & Le, 2019).
+
+Alternatively, factorizations of the $1 \times 1$ convolutions have been considered in ShuffleNet (Zhang et al., 2017) and Learnable Butterfly Factorizations (Dao et al., 2019). ShuffleNet factorizes the weight matrix into a product of a permutation matrix and block diagonal matrix. Butterfly Factorizations factorize the weight matrix into a sequence of permutation matrices and weight matrices with special structure that can represent many common $\bar { O } ( N l o g N )$ transforms such as Fast Fourier Transforms.
+
+Work in Text-to-Speech (TTS) (Kalchbrenner et al., 2018) demonstrated that increasing sparsity and concomitant increase in state size in RNN models lead to increased model quality for a given non-zero parameter count. They additionally demonstrated fast block-sparse matrix-vector (SpMV) multiplication routines necessary for RNN inference.
+
+# 3 METHODS
+
+To understand how to design the most efficient convolutional models, we investigate both how to construct and train sparse MBv1, MBv2 and EfficientNet models and also the performance of our SpMM kernels.
+
+# 3.1 SPARSIFYING NETWORKS
+
+We train on the ImageNet (Russakovsky et al., 2015) dataset with standard augmentation and report top-1 accuracies on the provided 50k example validation set. To make the networks sparse we use the gradual magnitude pruning technique of (Zhu & Gupta, 2018).
+
+We do not prune the first dense convolution at the beginning of all three networks. Its overall contribution to the parameter count, FLOP count, and runtime is small and does not warrant introducing a new sparse operator. Instead, we implement a dense convolutional kernel which takes as input the image in the standard HWC layout and outputs the CHW layout consumed by the sparse operators in the rest of the network. In HWC layout, the values for different channels corresponding to one spatial location are adjacent in memory. In CHW layout, the values of all the spatial locations for one channel are adjacent in memory.
+
+We also do not prune the squeeze-excitation (Hu et al., 2018) blocks in EfficientNet as they contribute ${ < } 1 \%$ of the total FLOPs to the dense model. The last fully-connected layer in all models also contributes insignificantly $( < 1 \% )$ to the total FLOP count, but does contribute a significant fraction $( 2 0 - 5 0 \% )$ of total parameters, especially after the rest of the model is pruned. As we are concerned with maximizing top-1 accuracy for a given runtime, we do not prune the final layer in MobileNet v1 and v2 as doing so leads to a small decrease in top-1 accuracy. Standard EfficientNets do not scale the number of filters in the last convolution by the width of the model, however we find that when introducing sparsity it is beneficial to do this; in all sparse EfficientNet models we double the units from 1280 to 2560. We also find that it is possible to make the fully-connected layer sparse without loss of accuracy in EfficientNet, so we do so.
+
+![](images/da03981655f6665941f3caadd1aaf775acf28a3e2ac9da30bac322f9e308566f.jpg)  
+Figure 3: Visualization of the memory reads and writes of our algorithm. In step 1, we load 8 spatial locations simultaneously for each of the non-zero weights in the first row of the weight matrix. We multiply each scalar weight by its corresponding row, accumulate the results, and in the end write them out. Step 2 performs the same calculation for the next output channel. After steps 1 and 2, all values for these spatial locations are in the cache, so future loads in steps 3 and 4 will be fast, despite being random access.
+
+# 3.2 KERNEL IMPLEMENTATION
+
+A diagram of the $1 \times 1$ convolution as a SpMM is seen in figure 2. Our scheme requires activation tensors be stored in CHW format, in contrast to dense mobile inference libraries (Jacob, 2017; Dukhan et al., 2019; Jacob, 2019) which favor HWC.
+
+There are two key insights enabling the high performance of our kernels:
+
+1. While the weight matrix is sparse, the activation matrix is dense. This means that we can perform vector loads from the activation matrix and process multiple spatial locations simultaneously. 2. By processing the matrix in the right order we can keep values that will be randomly accessed in the L1 cache, from which random access is fast and constant time.
+
+Figure 3 shows the memory read and write patterns of a few steps of the kernel. The figure shows 8 elements being processed together but other values are possible and we also implement 4 and 16. The outer loop is over columns and the inner loop is over rows; this allows each strip of 4, 8 or 16 spatial locations in the activations to remain in the L1 cache until it is no longer needed. In figure 3 steps 1 and 2 prime the cache, while subsequent steps 3 and 4 load all right hand side values from the L1 cache.
+
+In addition to the vectorization in the $H W$ dimension, taking advantage of small amounts of structure in the weight matrix can offer significant performance boosts by increasing data reuse after values are loaded into registers. Constraining the sparsity pattern so that multiple output or input channels all share the same zero/non-zero pattern creates ‘blocks’ in the weight matrix (see figure 3 right). Blocks in the output channel dimension allow for more data reuse than blocks in the input channel dimension. Experiments (see figure 6) show that either choice has the same effect on accuracy, so we implement output channel blocking with sizes of 2 and 4. Our nomenclature for kernels is to give their spatial vectorization width followed by the output channel block size $- 1 6 \times 2$ means 16 pixels and 2 output channels are processed in the inner loop.
+
+We implement the ARM kernels in C with NEON intrinsics unlike current production libraries (Jacob, 2017; Dukhan et al., 2019; Jacob, 2019) which rely on expert-optimized assembly. As reference, the code for the $4 \times 1$ inner loop is available in appendix A.
+
+# 3.3 LIBRARY
+
+We provide a library that can run sparse models trained with the model pruning library in TensorFlow (Abadi et al., 2015). This includes conversion from a dense representation to a Block Compressed Sparse Row (BCSR)-like representation suitable for inference. In addition to the high performance $1 \times 1$ convolutions, we also provide all supporting CHW kernels – depthwise convolutions, global average pooling and a $3 \times 3$ stride-2 dense convolution – necessary for running all three generations of models. While we provide high performance versions of these kernels, we do not detail them here. They are included in end-to-end measurements.
+
+![](images/2c914fc93fcd7c7874de5f6a5570203dedee21ec0aaac10f59265e4c7d76da34.jpg)  
+Figure 4: FLOPs with increasing layer depth. All measurements taken on a Snapdragon (SD) 835.
+
+# 4 RESULTS
+
+In the main text we mainly include results for MBv1 and MBv2 due to space limitations. EfficientNets generally follow the same trends as MBv2 models, plots for EfficientNet can be found in appendix C.
+
+First we reveal performance results for our SpMM kernels, then we show how the networks respond to sparsity and then finally we combine this information to find the models with the lowest inference time.
+
+# 4.1 ARM KERNEL PERFORMANCE
+
+We use Ruy (Jacob, 2019), the current TensorFlow Lite ARM64 backend written largely in handcoded assembly, as the dense baseline. For a sparse baseline we use the kernel generated by the TACO compiler (Kjolstad et al., 2017). We present results by plotting the FLOPs achieved at each layer in the model, with increasing depth to the right in figure 4. For MBv1 we use a width multiplier of 1.4 and $90 \%$ sparse and for MBV2 we use a width multiplier of 1.4 and $80 \%$ sparse as these configurations approximately match the top-1 accuracy of the width 1 dense models. The kernel variants that process 16 spatial locations at a time (e.g. $1 6 \times 1$ , etc.) are the highest performing and all reported numbers are from these kernel variants. TACO only supports unstructured sparsity and should be compared with the $\beth 6 \times \beth$ kernels.
+
+The raw performance of the sparse kernels falls in the range of $40 { - } 9 0 \%$ of the dense kernels. And as they must do much less work, when taking the sparsity of the layer into account, the effective FLOPs are in the $2 { - } 7 \times$ range. In MBv1 performance falls significantly in the last two layers of the model when the number of channels (1024) causes the size of one “strip” of spatial locations to exceed the size of the L1 cache. In MBv2 the sawtooth pattern is caused by the alternating expand and contract operations. The performance is higher for the expand kernels due to greater data reuse of each “strip” that is brought into the L1 cache.
+
+# 4.2 X86-64 KERNEL PERFORMANCE
+
+We implement an AVX-512 version of our scheme with intrinsics to compare with the Intel MKL (Intel, 2009) SpMM. Results are in figure 5. In the majority of layers our scheme outperforms the MKL. The geometric mean speedup over all layers is 1.20 in both MBv1 and MBv2.
+
+![](images/b6c45c9416d3f0ac6d6c761e8eb479eb446169d3b083c2f67404b9191619ddb8.jpg)  
+Figure 5: FLOPs with increasing layer depth. Measurements taken on an Intel Xeon W-2135.
+
+![](images/c98b84fb2984a8ce8f09802ba2592c14a82879a3f5637a60da4f466ea6dc9ee2.jpg)  
+Figure 6: Effect of block size on top-1 accuracy. It only matters how many elements are in a block, the configuration is unimportant.
+
+# 4.3 MODEL PERFORMANCE
+
+The hyper-parameters used to train MBv1 and MBv2 are listed in table 2, they were found with a grid search on dense models with a width multiplier of 1.0 to reproduce the original results, which used RMSProp, with SGD with momentum. The same hyper-parameters are used to train sparse models. This change allows us to match or exceed the reported accuracies with only $4 5 \mathrm { k }$ iterations of training.
+
+The hyper-parameters used to train EfficientNet are largely unmodified from their code release, with the exception of extending training from 350 to 550 epochs and increasing the learning rate decay exponent to .985 from .97 so that the learning rate decays more slowly. These changes do not improve the dense baseline.
+
+We induce sparsity in MBv1 and MBv2 by starting the sparsification process at iteration 7,000 and stopping at 28,000 with a pruning frequency of 2,000. For EfficientNet we start at iteration 23,000 and end at iteration 105,000, also with a pruning frequency of 2,000.
+
+We train on the ImageNet (Russakovsky et al., 2015) dataset with standard data augmentation. Top-1 accuracies are reported on the validation set with center single-crops.
+
+To understand the effect of block size, we plot in figure 6 accuracy against flops for different block sizes. In these plots, every sparse tensor in the network uses the same output channel block size. The tradeoff for block sparsity only appears to involve how many elements are in each block, and not their configuration. For example, in MBv1, the $1 \times 4$ , $4 \times 1$ and $2 \times 2$ curves all lie on top of one another. The loss in accuracy due to blocking seems to decrease slightly for larger width models.
+
+![](images/09c9cc79d70434e98c44f4a4bc5600c27a87cde93b25f6c6814dab0d90fef9d1.jpg)  
+Figure 7: Effect of sparsity on top-1 accuracy. The sparser a model is, the fewer flops it requires to achieve a given Top-1 accuracy.
+
+![](images/8c1dd0f325bbe87b6efc5642f1e222319a6579f93f9c9836e15fcf70671329d2.jpg)  
+Figure 8: The $\mathbf { X }$ -axis corresponds to turning that layer and all following layers to block size 4, the prior layers are unstructured. The y-axis is the efficiency of making this change over an unstructured model given as a ratio where the numerator is the speedup of changing the block(s) from unstructured to block size 4 and the denominator is the decrease in top-1 accuracy that occurs by making this change.
+
+To understand how the sparsity level affects the efficiency of the models, we train models at $70 \%$ , $80 \%$ and $90 \%$ unstructured sparsity which is constant throughout the model. The results are plotted in figure 7. MBv1 and MBv2 are more efficient the more sparse they become, confirming that the results of Kalchbrenner et al. (2018) hold not just for RNNs, but also for convolutional models as well.
+
+In figure 1 we plot Top-1 accuracy vs. FLOPs for all three generations of sparse and dense models. MobileNet v1 is $90 \%$ sparse, the other models are $80 \%$ sparse. A sparse MBv1 exceeds MBv2 in terms of FLOP and parameter efficiency; a sparse MBv2 matches EfficientNet in terms of FLOP and parameter efficiency; and a sparse EfficientNet exceeds all other models in both categories.
+
+# 4.4 MODEL DESIGN
+
+To design the models with the best top-1 accuracy vs. inference time frontiers we make the following assumptions to reduce the search space:
+
+1. We leave the models themselves unchanged.   
+2. We consider only block size 1 and block size 4 variants.   
+3. We induce the same level of sparsity in all $1 \times 1$ convolutions.
+
+Table 1: All input image sizes are $2 2 4 \mathbf { x } 2 2 4$ . Sparse MBv1 models are $90 \%$ sparse, Sparse MBv2 models are $80 \%$ sparse. In sparse MBv1 models, layer 12 uses a block size of 4. This is almost as efficient as the models in 4.4 and matches the top-1 scores of the dense models more closely. In sparse MBv2 width multiplier 2.0 model, layers 14-16 use block size of 4. In all other MBv2 models, layers 11-16 use a block size of 4.   
+
+<table><tr><td></td><td>Model</td><td>Width</td><td>Top-1</td><td>Mega-Params</td><td>Time (ms) SD835</td><td>Time (ms) SD670</td></tr><tr><td rowspan="2">MBv1</td><td>Dense</td><td>1.0</td><td>70.9</td><td>4.24</td><td>125</td><td>106</td></tr><tr><td>Sparse</td><td>1.4</td><td>72.0</td><td>2.31</td><td>63</td><td>63</td></tr><tr><td rowspan="2">MBv1</td><td>Dense</td><td>.75</td><td>68.4</td><td>2.59</td><td>73</td><td>64</td></tr><tr><td>Sparse</td><td>1.0</td><td>68.4</td><td>1.48</td><td>33</td><td>34</td></tr><tr><td rowspan="2">MBv1</td><td>Dense</td><td>.5</td><td>63.3</td><td>1.34</td><td>36</td><td>33</td></tr><tr><td>Sparse</td><td>.75</td><td>64.4</td><td>1.29</td><td>21</td><td>20</td></tr><tr><td rowspan="2">MBv2</td><td>Dense</td><td>1.4</td><td>75.0</td><td>6.06</td><td>150</td><td>129</td></tr><tr><td>Sparse</td><td>2.0</td><td>74.9</td><td>4.63</td><td>127</td><td>118</td></tr><tr><td rowspan="2">MBv2</td><td>Dense</td><td>1.0</td><td>71.8</td><td>3.47</td><td>83</td><td>74</td></tr><tr><td>Sparse</td><td>1.4</td><td>72.0</td><td>2.86</td><td>63</td><td>56</td></tr><tr><td rowspan="2">MBv2</td><td>Dense</td><td>.75</td><td>69.8</td><td>2.61</td><td>64</td><td>57</td></tr><tr><td>Sparse</td><td>1.0</td><td>68.6</td><td>1.85</td><td>35</td><td>33</td></tr><tr><td rowspan="2">MBv2</td><td>Dense</td><td>.5</td><td>65.4</td><td>2.61</td><td>33</td><td>30</td></tr><tr><td>Sparse</td><td>.75</td><td>65.2</td><td>1.65</td><td>29</td><td>25</td></tr></table>
+
+Then we do a search at width multiplier 1.4 over $N$ models when there are $N$ residual blocks in a model. An $\mathbf { X }$ -axis location of $n$ corresponds to a model in which the first $n$ residual blocks are unstructured and the last $N - n$ residual blocks have an output channel block size of 4. We train each model, note its top-1 accuracy and then measure its inference time. From this we can calculate the ratio of inference time reduction relative to a fully unstructured model and top-1 lost, which are plotted in figure 9. We choose the model with the highest ratio and train models at all widths with this choice. This amounts to making layers 6 and deeper block size 4 in MBv1 models and layers 11 and deeper block size 4 in MBv2.
+
+A full Neural Architecture Search (Zoph & Le, 2017; Liu et al., 2019) will likely lead to even more efficient models, but we leave this to future work.
+
+Table 1 contains the timings for running our sparse models on a single big core of two different processors, a Snapdragon 835 and a Snapdragon 670. We compare them with MBv1 and MBv2 models from their official repositories (Google, 2018a;b) run on the dense-inference TF Lite framework with the standard Ruy backend.
+
+# 5 CONCLUSION
+
+We demonstrate that for a constant computational budget, sparse convolutional networks are more accurate than dense ones; this corroborates the findings of Kalchbrenner et al. (2018), which demonstrated that for a set number of floating-point operations, sparse RNNs are more accurate than dense RNNs. We enable the use of weight sparsity to accelerate state-of-the-art convolutional networks by providing fast SpMM kernels along with all necessary supporting kernels for ARM processors. On Snapdragon 835 the sparse networks we present in this paper outperform their dense equivalents by $1 . 1 - 2 . 2 \times$ – equivalent to approximately one entire generation of improvement. By overturning the misconception that “sparsity is slow”, we hope to open new avenues of research that would previously not be considered.
+
+# A CODE LISTING
+
+We present the code for the $4 \times 1$ kernel here for reference. ARM intrinsics have been renamed for clarity and casts have been removed for brevity.
+
+size_t $\mathrm { ~ n ~ } = \mathrm { ~ H W ~ }$ ;   
+while $\mathrm { ~  ~ { ~ \langle ~ n ~ \rangle ~ } ~ } ! = \mathrm { ~  ~ { ~ 0 ~ } ~ }$ ) { // Loop over spatial positions float $\star$ w; // Weights, non-zeros are stored consecutively int32_t $\star$ widx_dmap; // Deltas between columns in bytes uint32_t $\star$ nnzmap; // Non-zeros per row size_t k $=$ OutputChannels; do { // Loop over output channels uint32_t nnz $=$ \*nnzmap++; // This next line loads the bias float32x4_t vacc $=$ load_1_f32_value_and_broadcast $( \mathbb { W } ^ { + + } )$ ; while (nnz-- ! $\ : \ 0$ ) { // Loop over non-zero input channels intptr_t diff $=$ \*dmap++; // get delta in bytes and advance float32x4_t vx $=$ load_4_f32_values(x); // Load activations x $+ =$ diff; // advance the activations for the next non-zero float32x4_t vw $=$ load_1_f32_value_and_broadcast $( \mathbb { w } + + )$ ; vacc $=$ multiply_add_4_f32(vacc, vx, vw); // vacc $\begin{array} { r l } { + = } & { { } \nabla \times } \end{array}$ \* vw } store_4_f32_values(y, vacc); y $+ =$ HW; // advance down the output strip } while $\mathrm { ~  ~ \omega ~ } : = \mathrm { ~  ~ 0 ~ }$ ); // Reset pointers for the next strip of spatial locations   
+y $- =$ OutputChannels $\star$ HW; y $+ = 4$ ; x $+ = 4$ ; $\mathrm { ~ n ~ \ -- = ~ 4 ~ }$ ;   
+}
+
+# B HYPER PARAMETERS
+
+Table 2: Hyper-parameters for MBv1 and MBv2 training. Learning rates are specified in a reduced space and then multiplied by a factor of 16 due to the batch size.   
+
+<table><tr><td></td><td>MBv1</td><td>MBv2</td></tr><tr><td>learning rate</td><td>.35 *16= 5.6</td><td>.24 *16= 3.84</td></tr><tr><td>momentum</td><td>0.9</td><td>0.92</td></tr><tr><td>12 coefficient</td><td>5e-5</td><td>4e-5</td></tr></table>
+
+# C EFFICIENTNET PLOTS
+
+Here we present the plots for EfficientNet corresponding to those in the main text for scaling with sparsity and block size. The same trend for block size is observed - the configuration of the blocks isn’t important, only the total size of the block. EfficientNet exhibits less improvement as sparsity increases.
+
+# REFERENCES
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+![](images/48393732b4c5652a71f98c4f9db45179e073f49780b9d2454071b950283dab9b.jpg)  
+Figure 9: (left) EfficientNet scaling with block size. (right) EfficientNet scaling with sparsity.
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+        "text": "FAST SPARSE CONVNETS ",
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+        "text": "Anonymous authors Paper under double-blind review ",
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+    {
+        "type": "text",
+        "text": "ABSTRACT ",
+        "text_level": 1,
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+        "page_idx": 0
+    },
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+        "type": "text",
+        "text": "Historically, the pursuit of efficient inference has been one of the driving forces behind the research into new deep learning architectures and building blocks. Some of the recent examples include: the squeeze-and-excitation module of (Hu et al., 2018), depthwise separable convolutions in Xception (Chollet, 2017), and the inverted bottleneck in MobileNet v2 (Sandler et al., 2018). Notably, in all of these cases, the resulting building blocks enabled not only higher efficiency, but also higher accuracy, and found wide adoption in the field. In this work, we further expand the arsenal of efficient building blocks for neural network architectures; but instead of combining standard primitives (such as convolution), we advocate for the replacement of these dense primitives with their sparse counterparts. While the idea of using sparsity to decrease the parameter count is not new (Mozer & Smolensky, 1989), the conventional wisdom is that this reduction in theoretical FLOPs does not translate into real-world efficiency gains. We aim to correct this misconception by introducing a family of efficient sparse kernels for several hardware platforms, which we plan to open-source for the benefit of the community. Equipped with our efficient implementation of sparse primitives, we show that sparse versions of MobileNet v1 and MobileNet v2 architectures substantially outperform strong dense baselines on the efficiency-accuracy curve. On Snapdragon 835 our sparse networks outperform their dense equivalents by $1 . 1 - 2 . 2 \\times$ – equivalent to approximately one entire generation of improvement. We hope that our findings will facilitate wider adoption of sparsity as a tool for creating efficient and accurate deep learning architectures. ",
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+        "text": "1 INTRODUCTION ",
+        "text_level": 1,
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+        "type": "text",
+        "text": "Convolutional neural networks (CNNs) have proven to be excellent at solving a diverse range of tasks (Bhandare et al., 2016). Standard network architectures are used in classification, segmentation, object detection and generation tasks (Pan et al., 2019; Long et al., 2015; Zhao et al., 2019). Given their wide utility, there has been significant effort to design efficient architectures that are capable of being run on mobile and other low power devices while still achieving high classification accuracy on benchmarks such as ImageNet (Russakovsky et al., 2015). For example, MobileNets (Howard et al., 2017; Sandler et al., 2018) employ the depthwise separable convolutions introduced in (Sifre & Mallat, 2014) to significantly reduce resource requirements over previous architectures. Inference time and computational complexity in these architectures are dominated by the $1 \\times 1$ convolutions, which directly map to matrix-matrix multiplications. ",
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+        "text": "Weight sparsity is generally known to lead (Cheng et al., 2017) to theoretically smaller and more computationally efficient (in terms of number of floating-point operations) models, but it is often disregarded as a practical means of accelerating models because of the misconception that sparse operations cannot be fast enough to achieve actual speedups during inference. In this work we introduce fast kernels for Sparse Matrix-Dense Matrix Multiplication (SpMM) specifically targeted at the accceleration of sparse neural networks. The main distinction of our $\\mathbf { S p M M }$ kernel from prior art (Nagasaka et al., 2018; Yang et al., 2018) is that we focus on a different point in the design space. While prior work focused on extremely sparse problems (typically ${ > } 9 9 \\%$ , found in scientific and graph problems), we target the sparsity range of $\\bar { 7 } 0 { - } 9 5 \\%$ , more common when inducing weight sparsity in neural networks. As a result our kernels outperform both the Intel MKL (Intel, 2009) and the TACO compiler (Kjolstad et al., 2017). ",
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+        "text": "Using these kernels, we demonstrate the effectiveness of weight sparsity across three generations of MobileNet (Howard et al., 2017; Sandler et al., 2018; Tan et al., 2018; Tan & Le, 2019) architectures. ",
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+            "Figure 1: MobileNet v1 and v2 and EfficientNet models. Sparse models: blue, dense models: red. Sparse models include the cost of storing the location of non-zeros for sparse tensors as a bitmask converted back into parameter count. That is every 32 values in the bitmask contributes one “parameter”. "
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+        "text": "Sparsity leads to an approximately one generation improvement in each architecture, with a sparse EfficientNet significantly more efficient than all previous models. These models represent a new generation of efficient CNNs, which reduces inference times by $1 . 1 - 2 . 2 \\times$ , parameter counts by over $2 \\times$ and number of floating-point operations (FLOPs) by up to $3 \\times$ relative to the previous generations. ",
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+        "text": "2 RELATED WORK ",
+        "text_level": 1,
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+        "text": "Improvements in convolutional network architectures (Krizhevsky et al., 2012; Simonyan & Zisserman, 2015; He et al., 2016; Huang et al., 2017), as measured by increased classification accuracy on benchmark tasks such as ImageNet (Russakovsky et al., 2015), have generally been concomitant with increases in model parameter counts, FLOPs and memory requirements. Recently this evolution has led to networks found through neural architecture search (Zoph et al., 2017; Real et al., 2019) which can achieve over $82 \\%$ top-1 accuracy, but require nearly 25 GFLOPs for one inference. ",
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+        "text": "Given these prohibitive inference costs, there have been many lines of work attempting to improve CNN efficiency, which is often defined as one of three metrics: ",
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+        "text": "1. Inference speedup on real hardware   \n2. Theoretical speedup through FLOPs reduction   \n3. Model size reduction ",
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+        "text": "These axes are neither parallel nor orthogonal. The effect of (3) and (2) on (1) in particular can be quite complicated and highly varied depending on the hardware in question. ",
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+        "text": "The MobileNet family of architectures (Howard et al., 2017; Sandler et al., 2018) has focused on improving efficiency by taking advantage of the depthwise separable convolutions introduced in (Sifre & Mallat, 2014), which can be thought of as a hand-crafted sparsification of full convolutions with a predefined sparse topology, and which are responsible for the parameter efficiency of these architectures. MobileNet v1 (MBv1) used layers of $1 \\times 1$ convolutions followed by depthwise convolutions. MobileNet v2 (MBv2) introduced the inverted residual block which consists of a $1 \\times 1$ convolution expanding the channel count, a depthwise convolution on the expanded channel count, and then a $1 \\times 1$ convolution reducing the parameter count. Across MobileNet architectures, the depthwise convolutions account for only a small fraction of the total FLOPs, parameters, and inference time of these models. In MBv1, they account for less than $2 \\%$ of the total FLOPs and in MBv2 less than $3 \\%$ . ",
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+        "type": "text",
+        "text": "A different line of work attempted to make more efficient CNNs by directly pruning the weights of full convolutional filters accompanied by the necessary inference kernels (Park et al., 2016; Liu et al., 2015). Park et al. (2016) was not able to accelerate $1 \\times 1$ convolutions, Liu et al. (2015) did not attempt it. The latter also required generating a new set of kernels for each instance of a model, which is often impractical for deployment. Due to the difficultly of accelerating sparse computation, channel pruning approaches have been preferred (Gordon et al., 2018; Dai et al., 2018; Luo et al., 2017; Louizos et al., 2018; Theis et al., 2018; He et al., 2018). These approaches prune away entire filters leaving the final model dense, and function more as an architecture search over channel counts. ",
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+        "image_caption": [
+            "Figure 2: Sparse 1x1 Convolution as SpMM. Left: Unstructured sparsity (or block size 1). Right: Output channel block size of 4 "
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+        "text": "Full Neural Architecture Search has also been applied directly to architectures resembling MBv2 resulting in MobileNet v3 (Tan et al., 2018), FBNet (Wu et al., 2019), and EfficientNet (Tan & Le, 2019). ",
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+        "text": "Alternatively, factorizations of the $1 \\times 1$ convolutions have been considered in ShuffleNet (Zhang et al., 2017) and Learnable Butterfly Factorizations (Dao et al., 2019). ShuffleNet factorizes the weight matrix into a product of a permutation matrix and block diagonal matrix. Butterfly Factorizations factorize the weight matrix into a sequence of permutation matrices and weight matrices with special structure that can represent many common $\\bar { O } ( N l o g N )$ transforms such as Fast Fourier Transforms. ",
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+    {
+        "type": "text",
+        "text": "Work in Text-to-Speech (TTS) (Kalchbrenner et al., 2018) demonstrated that increasing sparsity and concomitant increase in state size in RNN models lead to increased model quality for a given non-zero parameter count. They additionally demonstrated fast block-sparse matrix-vector (SpMV) multiplication routines necessary for RNN inference. ",
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+        "type": "text",
+        "text": "3 METHODS ",
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+        "type": "text",
+        "text": "To understand how to design the most efficient convolutional models, we investigate both how to construct and train sparse MBv1, MBv2 and EfficientNet models and also the performance of our SpMM kernels. ",
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+    {
+        "type": "text",
+        "text": "3.1 SPARSIFYING NETWORKS ",
+        "text_level": 1,
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+        "type": "text",
+        "text": "We train on the ImageNet (Russakovsky et al., 2015) dataset with standard augmentation and report top-1 accuracies on the provided 50k example validation set. To make the networks sparse we use the gradual magnitude pruning technique of (Zhu & Gupta, 2018). ",
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+        "type": "text",
+        "text": "We do not prune the first dense convolution at the beginning of all three networks. Its overall contribution to the parameter count, FLOP count, and runtime is small and does not warrant introducing a new sparse operator. Instead, we implement a dense convolutional kernel which takes as input the image in the standard HWC layout and outputs the CHW layout consumed by the sparse operators in the rest of the network. In HWC layout, the values for different channels corresponding to one spatial location are adjacent in memory. In CHW layout, the values of all the spatial locations for one channel are adjacent in memory. ",
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+        "type": "text",
+        "text": "We also do not prune the squeeze-excitation (Hu et al., 2018) blocks in EfficientNet as they contribute ${ < } 1 \\%$ of the total FLOPs to the dense model. The last fully-connected layer in all models also contributes insignificantly $( < 1 \\% )$ to the total FLOP count, but does contribute a significant fraction $( 2 0 - 5 0 \\% )$ of total parameters, especially after the rest of the model is pruned. As we are concerned with maximizing top-1 accuracy for a given runtime, we do not prune the final layer in MobileNet v1 and v2 as doing so leads to a small decrease in top-1 accuracy. Standard EfficientNets do not scale the number of filters in the last convolution by the width of the model, however we find that when introducing sparsity it is beneficial to do this; in all sparse EfficientNet models we double the units from 1280 to 2560. We also find that it is possible to make the fully-connected layer sparse without loss of accuracy in EfficientNet, so we do so. ",
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+        "img_path": "images/da03981655f6665941f3caadd1aaf775acf28a3e2ac9da30bac322f9e308566f.jpg",
+        "image_caption": [
+            "Figure 3: Visualization of the memory reads and writes of our algorithm. In step 1, we load 8 spatial locations simultaneously for each of the non-zero weights in the first row of the weight matrix. We multiply each scalar weight by its corresponding row, accumulate the results, and in the end write them out. Step 2 performs the same calculation for the next output channel. After steps 1 and 2, all values for these spatial locations are in the cache, so future loads in steps 3 and 4 will be fast, despite being random access. "
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+    {
+        "type": "text",
+        "text": "3.2 KERNEL IMPLEMENTATION ",
+        "text_level": 1,
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+    {
+        "type": "text",
+        "text": "A diagram of the $1 \\times 1$ convolution as a SpMM is seen in figure 2. Our scheme requires activation tensors be stored in CHW format, in contrast to dense mobile inference libraries (Jacob, 2017; Dukhan et al., 2019; Jacob, 2019) which favor HWC. ",
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+        "text": "There are two key insights enabling the high performance of our kernels: ",
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+    {
+        "type": "text",
+        "text": "1. While the weight matrix is sparse, the activation matrix is dense. This means that we can perform vector loads from the activation matrix and process multiple spatial locations simultaneously. 2. By processing the matrix in the right order we can keep values that will be randomly accessed in the L1 cache, from which random access is fast and constant time. ",
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+    {
+        "type": "text",
+        "text": "Figure 3 shows the memory read and write patterns of a few steps of the kernel. The figure shows 8 elements being processed together but other values are possible and we also implement 4 and 16. The outer loop is over columns and the inner loop is over rows; this allows each strip of 4, 8 or 16 spatial locations in the activations to remain in the L1 cache until it is no longer needed. In figure 3 steps 1 and 2 prime the cache, while subsequent steps 3 and 4 load all right hand side values from the L1 cache. ",
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+    {
+        "type": "text",
+        "text": "In addition to the vectorization in the $H W$ dimension, taking advantage of small amounts of structure in the weight matrix can offer significant performance boosts by increasing data reuse after values are loaded into registers. Constraining the sparsity pattern so that multiple output or input channels all share the same zero/non-zero pattern creates ‘blocks’ in the weight matrix (see figure 3 right). Blocks in the output channel dimension allow for more data reuse than blocks in the input channel dimension. Experiments (see figure 6) show that either choice has the same effect on accuracy, so we implement output channel blocking with sizes of 2 and 4. Our nomenclature for kernels is to give their spatial vectorization width followed by the output channel block size $- 1 6 \\times 2$ means 16 pixels and 2 output channels are processed in the inner loop. ",
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+    {
+        "type": "text",
+        "text": "We implement the ARM kernels in C with NEON intrinsics unlike current production libraries (Jacob, 2017; Dukhan et al., 2019; Jacob, 2019) which rely on expert-optimized assembly. As reference, the code for the $4 \\times 1$ inner loop is available in appendix A. ",
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+    {
+        "type": "text",
+        "text": "3.3 LIBRARY ",
+        "text_level": 1,
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "We provide a library that can run sparse models trained with the model pruning library in TensorFlow (Abadi et al., 2015). This includes conversion from a dense representation to a Block Compressed Sparse Row (BCSR)-like representation suitable for inference. In addition to the high performance $1 \\times 1$ convolutions, we also provide all supporting CHW kernels – depthwise convolutions, global average pooling and a $3 \\times 3$ stride-2 dense convolution – necessary for running all three generations of models. While we provide high performance versions of these kernels, we do not detail them here. They are included in end-to-end measurements. ",
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+        "img_path": "images/2c914fc93fcd7c7874de5f6a5570203dedee21ec0aaac10f59265e4c7d76da34.jpg",
+        "image_caption": [
+            "Figure 4: FLOPs with increasing layer depth. All measurements taken on a Snapdragon (SD) 835. "
+        ],
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+    {
+        "type": "text",
+        "text": "4 RESULTS ",
+        "text_level": 1,
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+        "type": "text",
+        "text": "In the main text we mainly include results for MBv1 and MBv2 due to space limitations. EfficientNets generally follow the same trends as MBv2 models, plots for EfficientNet can be found in appendix C. ",
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+        "type": "text",
+        "text": "First we reveal performance results for our SpMM kernels, then we show how the networks respond to sparsity and then finally we combine this information to find the models with the lowest inference time. ",
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+    {
+        "type": "text",
+        "text": "4.1 ARM KERNEL PERFORMANCE ",
+        "text_level": 1,
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+    {
+        "type": "text",
+        "text": "We use Ruy (Jacob, 2019), the current TensorFlow Lite ARM64 backend written largely in handcoded assembly, as the dense baseline. For a sparse baseline we use the kernel generated by the TACO compiler (Kjolstad et al., 2017). We present results by plotting the FLOPs achieved at each layer in the model, with increasing depth to the right in figure 4. For MBv1 we use a width multiplier of 1.4 and $90 \\%$ sparse and for MBV2 we use a width multiplier of 1.4 and $80 \\%$ sparse as these configurations approximately match the top-1 accuracy of the width 1 dense models. The kernel variants that process 16 spatial locations at a time (e.g. $1 6 \\times 1$ , etc.) are the highest performing and all reported numbers are from these kernel variants. TACO only supports unstructured sparsity and should be compared with the $\\beth 6 \\times \\beth$ kernels. ",
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+        "type": "text",
+        "text": "The raw performance of the sparse kernels falls in the range of $40 { - } 9 0 \\%$ of the dense kernels. And as they must do much less work, when taking the sparsity of the layer into account, the effective FLOPs are in the $2 { - } 7 \\times$ range. In MBv1 performance falls significantly in the last two layers of the model when the number of channels (1024) causes the size of one “strip” of spatial locations to exceed the size of the L1 cache. In MBv2 the sawtooth pattern is caused by the alternating expand and contract operations. The performance is higher for the expand kernels due to greater data reuse of each “strip” that is brought into the L1 cache. ",
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+    {
+        "type": "text",
+        "text": "4.2 X86-64 KERNEL PERFORMANCE ",
+        "text_level": 1,
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "We implement an AVX-512 version of our scheme with intrinsics to compare with the Intel MKL (Intel, 2009) SpMM. Results are in figure 5. In the majority of layers our scheme outperforms the MKL. The geometric mean speedup over all layers is 1.20 in both MBv1 and MBv2. ",
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+    {
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+        "img_path": "images/b6c45c9416d3f0ac6d6c761e8eb479eb446169d3b083c2f67404b9191619ddb8.jpg",
+        "image_caption": [
+            "Figure 5: FLOPs with increasing layer depth. Measurements taken on an Intel Xeon W-2135. "
+        ],
+        "image_footnote": [],
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+    {
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+        "img_path": "images/c98b84fb2984a8ce8f09802ba2592c14a82879a3f5637a60da4f466ea6dc9ee2.jpg",
+        "image_caption": [
+            "Figure 6: Effect of block size on top-1 accuracy. It only matters how many elements are in a block, the configuration is unimportant. "
+        ],
+        "image_footnote": [],
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+    {
+        "type": "text",
+        "text": "4.3 MODEL PERFORMANCE ",
+        "text_level": 1,
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "The hyper-parameters used to train MBv1 and MBv2 are listed in table 2, they were found with a grid search on dense models with a width multiplier of 1.0 to reproduce the original results, which used RMSProp, with SGD with momentum. The same hyper-parameters are used to train sparse models. This change allows us to match or exceed the reported accuracies with only $4 5 \\mathrm { k }$ iterations of training. ",
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+    {
+        "type": "text",
+        "text": "The hyper-parameters used to train EfficientNet are largely unmodified from their code release, with the exception of extending training from 350 to 550 epochs and increasing the learning rate decay exponent to .985 from .97 so that the learning rate decays more slowly. These changes do not improve the dense baseline. ",
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+    {
+        "type": "text",
+        "text": "We induce sparsity in MBv1 and MBv2 by starting the sparsification process at iteration 7,000 and stopping at 28,000 with a pruning frequency of 2,000. For EfficientNet we start at iteration 23,000 and end at iteration 105,000, also with a pruning frequency of 2,000. ",
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+    {
+        "type": "text",
+        "text": "We train on the ImageNet (Russakovsky et al., 2015) dataset with standard data augmentation. Top-1 accuracies are reported on the validation set with center single-crops. ",
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+    {
+        "type": "text",
+        "text": "To understand the effect of block size, we plot in figure 6 accuracy against flops for different block sizes. In these plots, every sparse tensor in the network uses the same output channel block size. The tradeoff for block sparsity only appears to involve how many elements are in each block, and not their configuration. For example, in MBv1, the $1 \\times 4$ , $4 \\times 1$ and $2 \\times 2$ curves all lie on top of one another. The loss in accuracy due to blocking seems to decrease slightly for larger width models. ",
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+        "image_caption": [
+            "Figure 7: Effect of sparsity on top-1 accuracy. The sparser a model is, the fewer flops it requires to achieve a given Top-1 accuracy. "
+        ],
+        "image_footnote": [],
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+    {
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+        "img_path": "images/8c1dd0f325bbe87b6efc5642f1e222319a6579f93f9c9836e15fcf70671329d2.jpg",
+        "image_caption": [
+            "Figure 8: The $\\mathbf { X }$ -axis corresponds to turning that layer and all following layers to block size 4, the prior layers are unstructured. The y-axis is the efficiency of making this change over an unstructured model given as a ratio where the numerator is the speedup of changing the block(s) from unstructured to block size 4 and the denominator is the decrease in top-1 accuracy that occurs by making this change. "
+        ],
+        "image_footnote": [],
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+        "page_idx": 6
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+    {
+        "type": "text",
+        "text": "To understand how the sparsity level affects the efficiency of the models, we train models at $70 \\%$ , $80 \\%$ and $90 \\%$ unstructured sparsity which is constant throughout the model. The results are plotted in figure 7. MBv1 and MBv2 are more efficient the more sparse they become, confirming that the results of Kalchbrenner et al. (2018) hold not just for RNNs, but also for convolutional models as well. ",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "In figure 1 we plot Top-1 accuracy vs. FLOPs for all three generations of sparse and dense models. MobileNet v1 is $90 \\%$ sparse, the other models are $80 \\%$ sparse. A sparse MBv1 exceeds MBv2 in terms of FLOP and parameter efficiency; a sparse MBv2 matches EfficientNet in terms of FLOP and parameter efficiency; and a sparse EfficientNet exceeds all other models in both categories. ",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "4.4 MODEL DESIGN ",
+        "text_level": 1,
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+    {
+        "type": "text",
+        "text": "To design the models with the best top-1 accuracy vs. inference time frontiers we make the following assumptions to reduce the search space: ",
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+    {
+        "type": "text",
+        "text": "1. We leave the models themselves unchanged.   \n2. We consider only block size 1 and block size 4 variants.   \n3. We induce the same level of sparsity in all $1 \\times 1$ convolutions. ",
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+    {
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+        "table_caption": [
+            "Table 1: All input image sizes are $2 2 4 \\mathbf { x } 2 2 4$ . Sparse MBv1 models are $90 \\%$ sparse, Sparse MBv2 models are $80 \\%$ sparse. In sparse MBv1 models, layer 12 uses a block size of 4. This is almost as efficient as the models in 4.4 and matches the top-1 scores of the dense models more closely. In sparse MBv2 width multiplier 2.0 model, layers 14-16 use block size of 4. In all other MBv2 models, layers 11-16 use a block size of 4. "
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td></td><td>Model</td><td>Width</td><td>Top-1</td><td>Mega-Params</td><td>Time (ms) SD835</td><td>Time (ms) SD670</td></tr><tr><td rowspan=\"2\">MBv1</td><td>Dense</td><td>1.0</td><td>70.9</td><td>4.24</td><td>125</td><td>106</td></tr><tr><td>Sparse</td><td>1.4</td><td>72.0</td><td>2.31</td><td>63</td><td>63</td></tr><tr><td rowspan=\"2\">MBv1</td><td>Dense</td><td>.75</td><td>68.4</td><td>2.59</td><td>73</td><td>64</td></tr><tr><td>Sparse</td><td>1.0</td><td>68.4</td><td>1.48</td><td>33</td><td>34</td></tr><tr><td rowspan=\"2\">MBv1</td><td>Dense</td><td>.5</td><td>63.3</td><td>1.34</td><td>36</td><td>33</td></tr><tr><td>Sparse</td><td>.75</td><td>64.4</td><td>1.29</td><td>21</td><td>20</td></tr><tr><td rowspan=\"2\">MBv2</td><td>Dense</td><td>1.4</td><td>75.0</td><td>6.06</td><td>150</td><td>129</td></tr><tr><td>Sparse</td><td>2.0</td><td>74.9</td><td>4.63</td><td>127</td><td>118</td></tr><tr><td rowspan=\"2\">MBv2</td><td>Dense</td><td>1.0</td><td>71.8</td><td>3.47</td><td>83</td><td>74</td></tr><tr><td>Sparse</td><td>1.4</td><td>72.0</td><td>2.86</td><td>63</td><td>56</td></tr><tr><td rowspan=\"2\">MBv2</td><td>Dense</td><td>.75</td><td>69.8</td><td>2.61</td><td>64</td><td>57</td></tr><tr><td>Sparse</td><td>1.0</td><td>68.6</td><td>1.85</td><td>35</td><td>33</td></tr><tr><td rowspan=\"2\">MBv2</td><td>Dense</td><td>.5</td><td>65.4</td><td>2.61</td><td>33</td><td>30</td></tr><tr><td>Sparse</td><td>.75</td><td>65.2</td><td>1.65</td><td>29</td><td>25</td></tr></table>",
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+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "Then we do a search at width multiplier 1.4 over $N$ models when there are $N$ residual blocks in a model. An $\\mathbf { X }$ -axis location of $n$ corresponds to a model in which the first $n$ residual blocks are unstructured and the last $N - n$ residual blocks have an output channel block size of 4. We train each model, note its top-1 accuracy and then measure its inference time. From this we can calculate the ratio of inference time reduction relative to a fully unstructured model and top-1 lost, which are plotted in figure 9. We choose the model with the highest ratio and train models at all widths with this choice. This amounts to making layers 6 and deeper block size 4 in MBv1 models and layers 11 and deeper block size 4 in MBv2. ",
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+    {
+        "type": "text",
+        "text": "A full Neural Architecture Search (Zoph & Le, 2017; Liu et al., 2019) will likely lead to even more efficient models, but we leave this to future work. ",
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+    },
+    {
+        "type": "text",
+        "text": "Table 1 contains the timings for running our sparse models on a single big core of two different processors, a Snapdragon 835 and a Snapdragon 670. We compare them with MBv1 and MBv2 models from their official repositories (Google, 2018a;b) run on the dense-inference TF Lite framework with the standard Ruy backend. ",
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+    },
+    {
+        "type": "text",
+        "text": "5 CONCLUSION ",
+        "text_level": 1,
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "We demonstrate that for a constant computational budget, sparse convolutional networks are more accurate than dense ones; this corroborates the findings of Kalchbrenner et al. (2018), which demonstrated that for a set number of floating-point operations, sparse RNNs are more accurate than dense RNNs. We enable the use of weight sparsity to accelerate state-of-the-art convolutional networks by providing fast SpMM kernels along with all necessary supporting kernels for ARM processors. On Snapdragon 835 the sparse networks we present in this paper outperform their dense equivalents by $1 . 1 - 2 . 2 \\times$ – equivalent to approximately one entire generation of improvement. By overturning the misconception that “sparsity is slow”, we hope to open new avenues of research that would previously not be considered. ",
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+    },
+    {
+        "type": "text",
+        "text": "A CODE LISTING ",
+        "text_level": 1,
+        "bbox": [
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+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "We present the code for the $4 \\times 1$ kernel here for reference. ARM intrinsics have been renamed for clarity and casts have been removed for brevity. ",
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+    },
+    {
+        "type": "text",
+        "text": "size_t $\\mathrm { ~ n ~ } = \\mathrm { ~ H W ~ }$ ;   \nwhile $\\mathrm { ~  ~ { ~ \\langle ~ n ~ \\rangle ~ } ~ } ! = \\mathrm { ~  ~ { ~ 0 ~ } ~ }$ ) { // Loop over spatial positions float $\\star$ w; // Weights, non-zeros are stored consecutively int32_t $\\star$ widx_dmap; // Deltas between columns in bytes uint32_t $\\star$ nnzmap; // Non-zeros per row size_t k $=$ OutputChannels; do { // Loop over output channels uint32_t nnz $=$ \\*nnzmap++; // This next line loads the bias float32x4_t vacc $=$ load_1_f32_value_and_broadcast $( \\mathbb { W } ^ { + + } )$ ; while (nnz-- ! $\\ : \\ 0$ ) { // Loop over non-zero input channels intptr_t diff $=$ \\*dmap++; // get delta in bytes and advance float32x4_t vx $=$ load_4_f32_values(x); // Load activations x $+ =$ diff; // advance the activations for the next non-zero float32x4_t vw $=$ load_1_f32_value_and_broadcast $( \\mathbb { w } + + )$ ; vacc $=$ multiply_add_4_f32(vacc, vx, vw); // vacc $\\begin{array} { r l } { + = } & { { } \\nabla \\times } \\end{array}$ \\* vw } store_4_f32_values(y, vacc); y $+ =$ HW; // advance down the output strip } while $\\mathrm { ~  ~ \\omega ~ } : = \\mathrm { ~  ~ 0 ~ }$ ); // Reset pointers for the next strip of spatial locations   \ny $- =$ OutputChannels $\\star$ HW; y $+ = 4$ ; x $+ = 4$ ; $\\mathrm { ~ n ~ \\ -- = ~ 4 ~ }$ ;   \n} ",
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+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "B HYPER PARAMETERS ",
+        "text_level": 1,
+        "bbox": [
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+    },
+    {
+        "type": "table",
+        "img_path": "images/f5173eb91312159b2a31c21ee4648447a413c5f8574dcf3f294a3e60966521de.jpg",
+        "table_caption": [
+            "Table 2: Hyper-parameters for MBv1 and MBv2 training. Learning rates are specified in a reduced space and then multiplied by a factor of 16 due to the batch size. "
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td></td><td>MBv1</td><td>MBv2</td></tr><tr><td>learning rate</td><td>.35 *16= 5.6</td><td>.24 *16= 3.84</td></tr><tr><td>momentum</td><td>0.9</td><td>0.92</td></tr><tr><td>12 coefficient</td><td>5e-5</td><td>4e-5</td></tr></table>",
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+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "C EFFICIENTNET PLOTS ",
+        "text_level": 1,
+        "bbox": [
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+            656,
+            392,
+            672
+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "Here we present the plots for EfficientNet corresponding to those in the main text for scaling with sparsity and block size. The same trend for block size is observed - the configuration of the blocks isn’t important, only the total size of the block. EfficientNet exhibits less improvement as sparsity increases. ",
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+    },
+    {
+        "type": "text",
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parse/train/SkxKPDv5xl/SkxKPDv5xl.md

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+# SAMPLERNN: AN UNCONDITIONAL END-TO-END NEURAL AUDIO GENERATION MODEL
+
+Soroush Mehri University of Montreal
+
+Kundan Kumar IIT Kanpur
+
+Ishaan Gulrajani University of Montreal
+
+Rithesh Kumar SSNCE
+
+Shubham Jain IIT Kanpur
+
+Jose Sotelo University of Montreal
+
+Aaron Courville University of Montreal CIFAR Fellow
+
+Yoshua Bengio University of Montreal CIFAR Senior Fellow
+
+# ABSTRACT
+
+In this paper we propose a novel model for unconditional audio generation based on generating one audio sample at a time. We show that our model, which profits from combining memory-less modules, namely autoregressive multilayer perceptrons, and stateful recurrent neural networks in a hierarchical structure is able to capture underlying sources of variations in the temporal sequences over very long time spans, on three datasets of different nature. Human evaluation on the generated samples indicate that our model is preferred over competing models. We also show how each component of the model contributes to the exhibited performance.
+
+# 1 INTRODUCTION
+
+Audio generation is a challenging task at the core of many problems of interest, such as text-tospeech synthesis, music synthesis and voice conversion. The particular difficulty of audio generation is that there is often a very large discrepancy between the dimensionality of the the raw audio signal and that of the effective semantic-level signal. Consider the task of speech synthesis, where we are typically interested in generating utterances corresponding to full sentences. Even at a relatively low sample rate of 16kHz, on average we will have 6,000 samples per word generated. 1
+
+Traditionally, the high-dimensionality of raw audio signal is dealt with by first compressing it into spectral or hand-engineered features and defining the generative model over these features. However, when the generated signal is eventually decompressed into audio waveforms, the sample quality is often degraded and requires extensive domain-expert corrective measures. This results in complicated signal processing pipelines that are to adapt to new tasks or domains. Here we propose a step in the direction of replacing these handcrafted systems.
+
+In this work, we investigate the use of recurrent neural networks (RNNs) to model the dependencies in audio data. We believe RNNs are well suited as they have been designed and are suited solutions for these tasks (see Graves (2013), Karpathy (2015), and Siegelmann (1999)). However, in practice it is a known problem of these models to not scale well at such a high temporal resolution as is found when generating acoustic signals one sample at a time, e.g., 16000 times per second. This is one of the reasons that Oord et al. (2016) profits from other neural modules such as one presented by Yu & Koltun (2015) to show extremely good performance.
+
+In this paper, an end-to-end unconditional audio synthesis model for raw waveforms is presented while keeping all the computations tractable.2 Since our model has different modules operating at different clock-rates (which is in contrast to WaveNet), we have the flexibility in allocating the amount of computational resources in modeling different levels of abstraction. In particular, we can potentially allocate very limited resource to the module responsible for sample level alignments operating at the clock-rate equivalent to sample-rate of the audio, while allocating more resources in modeling dependencies which vary very slowly in audio, for example identity of phoneme being spoken. This advantage makes our model arbitrarily flexible in handling sequential dependencies at multiple levels of abstraction.
+
+Hence, our contribution is threefold:
+
+1. We present a novel method that utilizes RNNs at different scales to model longer term dependencies in audio waveforms while training on short sequences which results in memory efficiency during training.   
+2. We extensively explore and compare variants of models achieving the above effect.   
+3. We study and empirically evaluate the impact of different components of our model on three audio datasets. Human evaluation also has been conducted to test these generative models.
+
+# 2 SAMPLERNN MODEL
+
+In this paper we propose SampleRNN (shown in Fig. 1), a density model for audio waveforms. SampleRNN models the probability of a sequence of waveform samples $X ~ = ~ \{ x _ { 1 } , x _ { 2 } , \ldots , x _ { T } \}$ (a random variable over input data sequences) as the product of the probabilities of each sample conditioned on all previous samples:
+
+$$
+p ( X ) = \prod _ { i = 0 } ^ { T - 1 } p ( x _ { i + 1 } \vert x _ { 1 } , \dotsc , x _ { i } )
+$$
+
+RNNs are commonly used to model sequential data which can be formulated as:
+
+$$
+\begin{array} { c } { h _ { t } = \mathcal { H } ( h _ { t - 1 } , x _ { i = t } ) } \\ { p ( x _ { i + 1 } | x _ { 1 } , \dots , x _ { i } ) = S o f t m a x ( M L P ( h _ { t } ) ) } \end{array}
+$$
+
+with $\mathcal { H }$ being one of the known memory cells, Gated Recurrent Units (GRUs) (Chung et al., 2014), Long Short Term Memory Units (LSTMs) (Hochreiter & Schmidhuber, 1997), or their deep variations (Section 3). However, raw audio signals are challenging to model because they contain structure at very different scales: correlations exist between neighboring samples as well as between ones thousands of samples apart.
+
+SampleRNN helps to address this challenge by using a hierarchy of modules, each operating at a different temporal resolution. The lowest module processes individual samples, and each higher module operates on an increasingly longer timescale and a lower temporal resolution. Each module conditions the module below it, with the lowest module outputting sample-level predictions. The entire hierarchy is trained jointly end-to-end by backpropagation.
+
+# 2.1 FRAME-LEVEL MODULES
+
+Rather than operating on individual samples, the higher-level modules in SampleRNN operate on non-overlapping frames of $F S ^ { ( k ) }$ (“Frame Size”) samples at the $k ^ { \mathrm { { t h } } }$ level up in the hierarchy at a time (frames denoted by $f ^ { ( k ) }$ ). Each frame-level module is a deep RNN which summarizes the history of its inputs into a conditioning vector for the next module downward.
+
+The variable number of frames we condition upon up to timestep $t - 1$ is expressed by a fixed length hidden state or memory $h _ { t } ^ { ( k ) }$ where $t$ is related to clock rate at that tier. The RNN makes a memory update at timestep $t$ as a function of the previous memory $h _ { t - 1 } ^ { ( k ) }$ and an input ${ i n p } _ { t } ^ { ( k ) }$ . This input for top tier $k = K$ is simply the input frame. For intermediate tiers $1 < k < K$ ) this input is a linear combination of conditioning vector from higher tier and current input frame. See Eqs. 4–5.
+
+Because different modules operate at different temporal resolutions, we need to upsample each vector $c$ at the output of a module into a series of $r ^ { ( k ) }$ vectors (where $r ^ { ( k ) }$ is the ratio between the temporal resolutions of the modules) before feeding it into the input of the next module downward (Eq. 6). We do this with a set of $r ^ { ( k ) }$ separate linear projections.
+
+![](images/e8280be33b3609b1d7afc26585a66c21aae4bf4ccb693864961aa5c90ebb6cc5.jpg)  
+Figure 1: Snapshot of the unrolled model at timestep $i$ with $K = 3$ tiers. As a simplification only one RNN and up-sampling ratio $r = 4$ is used for all tiers.
+
+Here we are formalizing the frame-level module in tier $k$ . Note that following equations are exclusive to tier $k$ and timestep $t$ for that specific tier. To increase the readability, unless necessary superscript $( k )$ is not shown for $\bar { t } , i n p ^ { ( k ) } , \bar { W } _ { x } ^ { ( k ) } , h ^ { ( k ) } , \mathcal { H } ^ { ( k ) } , W _ { j } ^ { ( k ) }$ , and $r ^ { ( k ) }$ .
+
+$$
+\begin{array} { c c } { i n p _ { t } = \left\{ \begin{array} { l l } { W _ { x } f _ { t } ^ { ( k ) } + c _ { t } ^ { ( k + 1 ) } ; } & { 1 < k < K } \\ { f _ { t } ^ { ( k = K ) } ; } & { k = K } \end{array} \right. } \\ { h _ { t } = \mathcal { H } ( h _ { t - 1 } , i n p _ { t } ) } \\ { c _ { ( t - 1 ) * r + j } ^ { ( k ) } = W _ { j } h _ { t } ; } & { 1 \leq j \leq r } \end{array}
+$$
+
+Our approach of upsampling with $r ^ { ( k ) }$ linear projections is exactly equivalent to upsampling by adding zeros and then applying a linear convolution. This is sometimes called “perforated” upsampling in the context of convolutional neural networks (CNNs). It was first demonstrated to work well in Dosovitskiy et al. (2016) and is a fairly common upsampling technique.
+
+# 2.2 SAMPLE-LEVEL MODULE
+
+The lowest module (tier $k = 1$ ; Eqs. 7–9) in the SampleRNN hierarchy outputs a distribution over a sample $x _ { i + 1 }$ , conditioned on the $F S ^ { ( 1 ) }$ preceding samples as well as a vector $c _ { i } ^ { ( k = 2 ) }$ from the next higher module which encodes information about the sequence prior to that frame. As $F S ^ { ( 1 ) }$ is usually a small value and correlations in nearby samples are easy to model by a simple memoryless module, we implement it with a multilayer perceptron (MLP) rather than RNN which slightly speeds up the training. Assuming $e _ { i }$ represents $x _ { i }$ after passing through embedding layer (section 2.2.1), conditional distribution in Eq. 1 can be achieved by following and for further clarity two consecutive sample-level frames are shown. In addition, $W _ { x }$ in Eq. 8 is simply used to linearly combine a frame and conditioning vector from above.
+
+$$
+\begin{array} { r } { f _ { i - 1 } ^ { ( 1 ) } = f l a t t e n ( \left[ e _ { i - F S ^ { ( 1 ) } } , \dots , e _ { i - 1 } \right] ) } \\ { f _ { i } ^ { ( 1 ) } = f l a t t e n ( \left[ e _ { i - F S ^ { ( 1 ) } + 1 } , \dots , e _ { i } \right] ) } \\ { i n p _ { i } ^ { ( 1 ) } = W _ { x } ^ { ( 1 ) } f _ { i } ^ { ( 1 ) } + c _ { i } ^ { ( 2 ) } \qquad } \\ { p ( x _ { i + 1 } | x _ { 1 } , \dots , x _ { i } ) = S o f t m a x ( M L P ( i n p _ { i } ^ { ( 1 ) } ) ) } \end{array}
+$$
+
+We use a Softmax because we found that better results were obtained by discretizing the audio signals (also see van den Oord et al. (2016)) and outputting a Multinoulli distribution rather than using a Gaussian or Gaussian mixture to represent the conditional density of the original real-valued signal. When processing an audio sequence, the MLP is convolved over the sequence, processing each window of $F S ^ { ( 1 ) }$ samples and predicting the next sample. At generation time, the MLP is run repeatedly to generate one sample at a time. Table 1 shows a considerable gap between the baseline model RNN and this model, suggesting that the proposed hierarchically structured architecture of SampleRNN makes a big difference.
+
+# 2.2.1 OUTPUT QUANTIZATION
+
+The sample-level module models its output as a $q$ -way discrete distribution over possible quantized values of $x _ { i }$ (that is, the output layer of the MLP is a $q$ -way Softmax).
+
+To demonstrate the importance of a discrete output distribution, we apply the same architecture on real-valued data by replacing the $q$ -way Softmax with a Gaussian Mixture Models (GMM) output distribution. Table 2 shows that our model outperforms an RNN baseline even when both models use real-valued outputs. However, samples from the real-valued model are almost indistinguishable from random noise.
+
+In this work we use linear quantization with $q = 2 5 6$ , corresponding to a per-sample bit depth of 8. Unintuitively, we realized that even linearly decreasing the bit depth (resolution of each audio sample) from 16 to 8 can ease the optimization procedure while generated samples still have reasonable quality and are artifact-free.
+
+In addition, early on we noticed that the model can achieve better performance and generation quality when we embed the quantized input values before passing them through the sample-level MLP (see Table 4). The embedding steps maps each of the $q$ discrete values to a real-valued vector embedding. However, real-valued raw samples are still used as input to the higher modules.
+
+# 2.2.2 CONDITIONALLY INDEPENDENT SAMPLE OUTPUTS
+
+To demonstrate the importance of a sample-level autoregressive module, we try replacing it with “Multi-Softmax” (see Table 4), where the prediction of each sample $x _ { i }$ depends only on the conditioning vector $c$ from Eq. 9. In this configuration, the model outputs an entire frame of $F S ^ { ( 1 ) }$ samples at a time, modeling all samples in a frame as conditionally independent of each other. We find that this Multi-Softmax model (which lacks a sample-level autoregressive module) scores significantly worse in terms of log-likelihood and fails to generate convincing samples. This suggests that modeling the joint distribution of the acoustic samples inside each frame is very important in order to obtain good acoustic generation. We found this to be true even when the frame size is reduced, with best results always with a frame size of 1, i.e., generating only one acoustic sample at a time.
+
+# 2.3 TRUNCATED BPTT
+
+Training recurrent neural networks on long sequences can be very computationally expensive. Oord et al. (2016) avoid this problem by using a stack of dilated convolutions instead of any recurrent connections. However, when they can be trained efficiently, recurrent networks have been shown to be very powerful and expressive sequence models. We enable efficient training of our recurrent model using truncated backpropagation through time, splitting each sequence into short subsequences and propagating gradients only to the beginning of each subsequence. We experiment with different subsequence lengths and demonstrate that we are able to train our networks, which model very long-term dependencies, despite backpropagating through relatively short subsequences.
+
+Table 3 shows that by increasing the subsequence length, performance substantially increases alongside with train-time memory usage and convergence time. Yet it is noteworthy that our best models have been trained on subsequences of length 512, which corresponds to 32 milliseconds, a small fraction of the length of a single a phoneme of human speech while generated samples exhibit longer word-like structures.
+
+Despite the aforementioned fact, this generative model can mimic the existing long-term structure of the data which results in more natural and coherent samples that is preferred by human listeners. (More on this in Sections 3.2–3.3.) This is due to the fast updates from TBPTT and specialized frame-level modules (Section 2.1) with top tiers designed to model a lower resolution of signal while leaving the process of filling the details to lower tiers.
+
+# 3 EXPERIMENTS AND RESULTS
+
+In this section we are introducing three datasets which have been chosen to evaluate the proposed architecture for modeling raw acoustic sequences. The description of each dataset and their preprocessing is as follows:
+
+Blizzard which is a dataset presented by Prahallad et al. (2013) for speech synthesis task, contains 315 hours of a single female voice actor in English; however, for our experiments we are using only 20.5 hours. The training/validation/test split is $8 6 \% - 7 \% - 7 \%$ .
+
+Onomatopoeia3, a relatively small dataset with 6,738 sequences adding up to 3.5 hours, is human vocal sounds like grunting, screaming, panting, heavy breathing, and coughing. Diversity of sound type and the fact that these sounds were recorded from 51 actors and many categories makes it a challenging task. To add to that, this data is extremely unbalanced. The training/validation/test split is $9 2 \% - 4 \% - 4 \%$ .
+
+Music dataset is the collection of all 32 Beethoven’s piano sonatas publicly available on https://archive.org/ amounting to 10 hours of non-vocal audio. The training/validation/test split is $8 8 \% - 6 \% - 6 \%$ .
+
+See Fig. 2 for a visual demonstration of examples from datasets and generated samples. For all the datasets we are using a $1 6 ~ \mathrm { k H z }$ sample rate and 16 bit depth. For the Blizzard and Music datasets, preprocessing simply amounts to chunking the long audio files into 8 seconds long sequences on which we will perform truncated backpropagation through time. Each sequence in the Onomatopoeia dataset is few seconds long, ranging from 1 to 11 seconds. To train the models on this dataset, zero-padding has been applied to make all the sequences in a mini-batch have the same length and corresponding cost values (for the predictions over the added 0s) would be ignored when computing the gradients.
+
+We particularly explored two gated variants of RNNs—GRUs and LSTMs. For the case of LSTMs, the forget gate bias is initialized with a large positive value of 3, as recommended by Zaremba (2015) and Gers (2001), which has been shown to be beneficial for learning long-term dependencies.
+
+As for models that take real-valued input, e.g. the RNN-GMM and SampleRNN-GMM (with 4 components), normalization is applied per audio sample with the global mean and standard deviation obtained from the train split. For most of our experiments where the model demands discrete input, binning was applied per audio sample.
+
+All the models have been trained with teacher forcing and stochastic gradient decent (mini-batch size 128) to minimize the Negative Log-Likelihood (NLL) in bits per dimension (per audio sample). Gradients were hard-clipped to remain in [-1, 1] range. Update rules from the Adam optimizer (Kingma & Ba, 2014) $\beta _ { 1 } = 0 . 9$ , $\beta _ { 2 } ~ = ~ 0 . 9 9 9$ , and $\epsilon = 1 e { - 8 } )$ with an initial learning rate of 0.001 was used to adjust the parameters. For training each model, random search over hyper-parameter values (Bergstra & Bengio, 2012) was conducted. The initial RNN state of all the RNN-based models was always learnable. Weight Normalization (Salimans & Kingma, 2016) has been used for all the linear layers in the model (except for the embedding layer) to accelerate the training procedure. Size of the embedding layer was 256 and initialized by standard normal distribution. Orthogonal weight matrices used for hidden-to-hidden connections and other weight matrices initialized similar to He et al. (2015). In final model, we found GRU to work best (slightly better than LSTM). 1024 was the the number of hidden units for all GRUs (1 layer per tier for 3-tier and 3 layer for 2-tier model) and MLPs (3 fully connected layers with ReLU activation with output dimension being 1024 for first two layers and 256 for the final layer before softmax). Also $F \bar { S } ^ { ( 1 ) } = F S ^ { ( 2 ) } = 2$ and $F S ^ { ( 3 ) } = 8 $ were found to result in lowest NLL.
+
+# 3.1 WAVENET RE-IMPLEMENTATION
+
+We implemented the WaveNet architecture as described in Oord et al. (2016). Ideally, we would have liked to replicate their model exactly but owing to missing details of architecture and hyperparameters, as well as limited compute power at our disposal, we made our own design choices so that the model would fit on a single GPU while having a receptive field of around 250 milliseconds, while having a reasonable number of updates per unit time. Although our model is very similar to WaveNet, the design choices, e.g. number of convolution filters in each dilated convolution layer, length of target sequence to train on simultaneously (one can train with a single target with all samples in the receptive field as input or with target sequence length of size T with input of size receptive field $+ \mathrm { ~ T ~ } - 1$ ), batch-size, etc. might make our implementation different from what the authors have done in the original WaveNet model. Hence, we note here that although we did our best at exactly reproducing their results, there would very likely be different choice of hyper-parameters between our implementation and the one of the authors.
+
+![](images/095574c20ff2a204bedf1e789a109edb8ab60a841da04859134aaf954e818b5e.jpg)  
+Figure 2: Examples from the datasets compared to samples from our models. In the first 3 rows, 2 seconds of audio are shown. In the bottom 3 rows, 100 milliseconds of audio are shown. Rows 1 and 4 are ground truth from which one can see how the datasets look different and have complex structure in low resolution which the frame-level component of the SampleRNN is designed to capture. Samples also to some extent mimic the same global structure. At the same time, zoomed-in samples of our model shows that it can perfectly resemble the high resolution structure present in the data as well.
+
+Table 1: Test NLL in bits for three presented datasets.   
+
+<table><tr><td>Model</td><td>Blizzard</td><td>Onomatopoeia</td><td>Music</td></tr><tr><td>RNN (Eq.2)</td><td>1.434</td><td>2.034</td><td>1.410</td></tr><tr><td>WaveNet (re-impl.)</td><td>1.480</td><td>2.285</td><td>1.464</td></tr><tr><td>SampleRNN (2-tier)</td><td>1.392</td><td>2.026</td><td>1.076</td></tr><tr><td>SampleRNN (3-tier)</td><td>1.387</td><td>1.990</td><td>1.159</td></tr></table>
+
+Table 2: Average NLL on Blizzard test set for real-valued models.   
+
+<table><tr><td>Model</td><td>Average Test NLL</td></tr><tr><td>RNN-GMM</td><td>-2.415</td></tr><tr><td>SampleRNN-GMM (2-tier)</td><td>-2.782</td></tr></table>
+
+Table 3: Effect of subsequence length on NLL (bits per audio sample) computed on the Blizzard validation set.   
+
+<table><tr><td>Subsequence Length</td><td>32</td><td>64</td><td>128</td><td>256</td><td>512</td></tr><tr><td>NLL Validation</td><td>1.575</td><td>1.468</td><td>1.412</td><td>1.391</td><td>1.364</td></tr></table>
+
+Table 4: Test (validation) set NLL (bits per audio sample) for Blizzard. Variants of SampleRNN are provided to compare the contribution of each component in performance.   
+
+<table><tr><td>Model</td><td>NLL Test (Validation)</td></tr><tr><td>SampleRNN (2-tier)</td><td>1.392 (1.369)</td></tr><tr><td>Without Embedding</td><td>1.566 (1.539)</td></tr><tr><td>Multi-Softmax</td><td>1.685 (1.656)</td></tr></table>
+
+For our WaveNet implementation, we have used 4 dilated convolution blocks each having 10 dilated convolution layers with dilation 1, 2, 4, 8 up to 512. Hence, our network has a receptive field of 4092 acoustic samples i.e. the parameters of multinomial distribution of sample at time step t, $p ( x _ { i } ) = f _ { \boldsymbol { \theta } } ( x _ { i - 1 } , \bar { x _ { i - 2 } } , \dots x _ { i - 4 0 9 2 } )$ where $\theta$ is model parameters. We train on target sequence length of 1600 and use batch size of 8. Each dilated convolution filter has size 2 and the number of output channels is 64 for each dilated convolutional layer (128 filters in total due to gated nonlinearity). We trained this model using Adam optimizer with a fixed global learning rate of 0.001 for Blizzard dataset and 0.0001 for Onomatopoeia and Music datasets. We trained these models for about one week on a GeForce GTX TITAN X. We dropped the learning rate in the Blizzard experiment to 0.0001 after around 3 days of training.
+
+# 3.2 HUMAN EVALUATION
+
+Apart from reporting NLL, we conducted AB preference tests for random samples from four models trained on the Blizzard dataset. For unconditional generation of speech which at best sounds like mumbling, this type of test is the one which is more suited. Competing models were the RNN, SampleRNN (2-tier), SampleRNN (3-tier), and our implementation of WaveNet. The rest of the models were excluded as the quality of samples were definitely lower and also to keep the number of pair comparison tests manageable. We will release the samples that have been used in this test too.
+
+All the samples were set to have the same volume. Every user is then shown a set of twenty pairs of samples with one random pair at a time. Each pair had samples from two different models. The human evaluator is asked to listen to the samples and had the option of choosing between the two model or choosing not to prefer any of them. Hence, we have a quantification of preference between every pair of models. We used the online tool made publicly available by Jillings et al. (2015).
+
+Results in Fig. 3 clearly points out that SampleRNN (3-tier) is a winner by a huge margin in terms of preference by human raters, then SampleRNN (2-tier) and afterward two other models, which matches with the performance comparison in Table 1.
+
+The same evaluation was conducted for Music dataset except for an additional filtering process of samples. Specific to only this dataset, we observed that a batch of generated samples from competing models (this time restricted to RNN, SampleRNN (2-tier), and SampleRNN (3-tier)) were either music-like or random noise. For all these models we only considered random samples that were not random noise. Fig. 4 is dedicated to result of human evaluation on Music dataset.
+
+![](images/2d96293eb1cfa3e42560f06229017eae1d46d950502c02d79fe8cdd1fbcdb740.jpg)  
+Figure 3: Pairwise comparison of 4 best models based on the votes from listeners conducted on samples generated from models trained on Blizzard dataset.
+
+![](images/3f4065b402e4c76a71a4ce716fe699ae6b8f5f5dd56e968b020de62c176579b7.jpg)  
+Figure 4: Pairwise comparison of 3 best models based on the votes from listeners conducted on samples generated from models trained on Music dataset.
+
+# 3.3 QUANTIFYING INFORMATION RETENTION
+
+For the last experiment we are interested in measuring the memory span of the model. We trained our model, SampleRNN (3-tier), with best hyper-parameters on a dataset of 2 speakers reading audio books, one male and one female, respectively, with mean fundamental frequency of 125.3 and $2 0 1 . 8 \mathrm { H z }$ . Each speaker has roughly 10 hours of audio in the dataset that has been preprocessed similar to Blizzard. We observed that it learned to stay consistent generating samples from the same speaker without having any knowledge about the speaker ID or any other conditioning information. This effect is more apparent here in comparison to the unbalanced Onomatopoeia that sometimes mixes two different categories of sounds.
+
+Another experiment was conducted to test the effect of memory and study the effective memory horizon. We inject 1 second of silence in the middle of sampling procedure in order to see if it will remember to generate from the same speaker or not. Initially when sampling we let the model generate 2 seconds of audio as it normally do. From 2 to 3 seconds instead of feeding back the generated sample at that timestep a silent token (zero amplitude) would be fed. From 3 to 5 seconds again we sample normally; feeding back the generated token.
+
+We did classification based on mean fundamental frequency of speakers for the first and last 2 seconds. In $83 \%$ of samples SampleRNN generated from the same person in two separate segments.
+
+This is in contrast to a model with fixed past window like WaveNet where injecting 16000 silent tokens (3.3 times the receptive field size) is equivalent to generating from scratch which has $50 \%$ chance (assuming each 2-second segment is coherent and not a mixed sound of two speakers).
+
+# 4 RELATED WORK
+
+Our work is related to earlier work on auto-regressive multi-layer neural networks, starting with Bengio & Bengio (1999), then NADE (Larochelle & Murray, 2011) and more recently PixelRNN (van den Oord et al., 2016). Similar to how they tractably model joint distribution over units of the data (e.g. words in sentences, pixels in images, etc.) through an auto-regressive decomposition, we transform the joint distribution of acoustic samples using Eq. 1.
+
+The idea of having part of the model running at different clock rates is related to multi-scale RNNs (Schmidhuber, 1992; El Hihi & Bengio, 1995; Koutnik et al., 2014; Sordoni et al., 2015; Serban et al., 2016).
+
+Chung et al. (2015) also attempt to model raw audio waveforms which is in contrast to traditional approaches which use spectral features as in Tokuda et al. (2013), Bertrand et al. (2008), and Lee et al. (2009).
+
+Our work is closely related to WaveNet (Oord et al., 2016), which is why we have made the above comparisons, and makes it interesting to compare the effect of adding higher-level RNN stages working at a low resolution. Similar to this work, our models generate one acoustic sample at a time conditioned on all previously generated samples. We also share the preprocessing step of quantizing the acoustics into bins. Unlike this model, we have different modules in our models running at different clock-rates. In contrast to WaveNets, we mitigate the problem of long-term dependency with hierarchical structure and using stateful RNNs, i.e. we will always propagate hidden states to the next training sequence although the gradient of the loss will not take into account the samples in previous training sequence.
+
+# 5 DISCUSSION AND CONCLUSION
+
+We propose a novel model that can address unconditional audio generation in the raw acoustic domain, which typically has been done until recently with hand-crafted features. We are able to show that a hierarchy of time scales and frequent updates will help to overcome the problem of modeling extremely high-resolution temporal data. That allows us, for this particular application, to learn the data manifold directly from audio samples. We show that this model can generalize well and generate samples on three datasets that are different in nature. We also show that the samples generated by this model are preferred by human raters.
+
+Success in this application, with a general-purpose solution as proposed here, opens up room for more improvement when specific domain knowledge is applied. This method, however, proposed with audio generation application in mind, can easily be adapted to other tasks that require learning the representation of sequential data with high temporal resolution and long-range complex structure.
+
+# ACKNOWLEDGMENTS
+
+The authors would like to thank Joao Felipe Santos and Kyle Kastner for insightful comments and ˜ discussion. We would like to thank the Theano Development Team $\left( 2 0 1 6 \right) ^ { 4 }$ and MILA staff. We acknowledge the support of the following agencies for research funding and computing support: NSERC, Calcul Quebec, Compute Canada, the Canada Research Chairs and CIFAR. Jose Sotelo ´ also thanks the Consejo Nacional de Ciencia y Tecnolog´ıa (CONACyT) as well as the Secretar´ıa de Educacion P ´ ublica (SEP) for their support. This work was a collaboration with Ubisoft. ´
+
+# REFERENCES
+
+Yoshua Bengio and Samy Bengio. Modeling high-dimensional discrete data with multi-layer neural networks. In NIPS, volume 99, pp. 400–406, 1999.
+
+James Bergstra and Yoshua Bengio. Random search for hyper-parameter optimization. Journal of Machine Learning Research, 13(Feb):281–305, 2012.
+
+Alexander Bertrand, Kris Demuynck, Veronique Stouten, et al. Unsupervised learning of auditory filter banks using non-negative matrix factorisation. In 2008 IEEE International Conference on Acoustics, Speech and Signal Processing, pp. 4713–4716. IEEE, 2008.
+
+Junyoung Chung, Caglar Gulcehre, KyungHyun Cho, and Yoshua Bengio. Empirical evaluation of gated recurrent neural networks on sequence modeling. arXiv preprint arXiv:1412.3555, 2014.
+
+Junyoung Chung, Kyle Kastner, Laurent Dinh, Kratarth Goel, Aaron C Courville, and Yoshua Bengio. A recurrent latent variable model for sequential data. In Advances in neural information processing systems, pp. 2980–2988, 2015.
+
+Alexey Dosovitskiy, Jost Springenberg, Maxim Tatarchenko, and Thomas Brox. Learning to generate chairs, tables and cars with convolutional networks. 2016.
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+Salah El Hihi and Yoshua Bengio. Hierarchical recurrent neural networks for long-term dependencies. In NIPS, volume 400, pp. 409. Citeseer, 1995.
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+Felix Gers. Long short-term memory in recurrent neural networks. PhD thesis, Universitat Han- ¨ nover, 2001.
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+Alex Graves. Generating sequences with recurrent neural networks. arXiv preprint arXiv:1308.0850, 2013.
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+Kaiming He, Xiangyu Zhang, Shaoqing Ren, and Jian Sun. Delving deep into rectifiers: Surpassing human-level performance on imagenet classification. In Proceedings of the IEEE International Conference on Computer Vision, pp. 1026–1034, 2015.
+
+Sepp Hochreiter and Jurgen Schmidhuber. Long short-term memory. ¨ Neural computation, 9(8): 1735–1780, 1997.
+
+Nicholas Jillings, David Moffat, Brecht De Man, and Joshua D. Reiss. Web Audio Evaluation Tool: A browser-based listening test environment. In 12th Sound and Music Computing Conference, July 2015.
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+Andrej Karpathy. The unreasonable effectiveness of recurrent neural networks. Andrej Karpathy blog, 2015.
+
+Diederik Kingma and Jimmy Ba. Adam: A method for stochastic optimization. arXiv preprint arXiv:1412.6980, 2014.
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+Jan Koutnik, Klaus Greff, Faustino Gomez, and Juergen Schmidhuber. A clockwork rnn. arXiv preprint arXiv:1402.3511, 2014.
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+Hugo Larochelle and Iain Murray. The neural autoregressive distribution estimator. In AISTATS, volume 1, pp. 2, 2011.
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+Honglak Lee, Peter Pham, Yan Largman, and Andrew Y Ng. Unsupervised feature learning for audio classification using convolutional deep belief networks. In Advances in neural information processing systems, pp. 1096–1104, 2009.
+
+Aaron van den Oord, Sander Dieleman, Heiga Zen, Karen Simonyan, Oriol Vinyals, Alex Graves, Nal Kalchbrenner, Andrew Senior, and Koray Kavukcuoglu. Wavenet: A generative model for raw audio. arXiv preprint arXiv:1609.03499, 2016.
+
+Kishore Prahallad, Anandaswarup Vadapalli, Naresh Elluru, G Mantena, B Pulugundla, P Bhaskararao, HA Murthy, S King, V Karaiskos, and AW Black. The blizzard challenge 2013– indian language task. In Blizzard Challenge Workshop 2013, 2013.
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+Tim Salimans and Diederik P Kingma. Weight normalization: A simple reparameterization to accelerate training of deep neural networks. arXiv preprint arXiv:1602.07868, 2016.
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+Jurgen Schmidhuber. Learning complex, extended sequences using the principle of history com-¨ pression. Neural Computation, 4(2):234–242, 1992.
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+Iulian V Serban, Alessandro Sordoni, Yoshua Bengio, Aaron Courville, and Joelle Pineau. Building end-to-end dialogue systems using generative hierarchical neural network models. In Proceedings of the 30th AAAI Conference on Artificial Intelligence (AAAI-16), 2016.
+
+Hava T Siegelmann. Computation beyond the turing limit. In Neural Networks and Analog Computation, pp. 153–164. Springer, 1999.
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+Alessandro Sordoni, Yoshua Bengio, Hossein Vahabi, Christina Lioma, Jakob Grue Simonsen, and Jian-Yun Nie. A hierarchical recurrent encoder-decoder for generative context-aware query suggestion. In Proceedings of the 24th ACM International on Conference on Information and Knowledge Management, pp. 553–562. ACM, 2015.
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+Theano Development Team. Theano: A Python framework for fast computation of mathematical expressions. arXiv e-prints, abs/1605.02688, May 2016. URL http://arxiv.org/abs/ 1605.02688.
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+Keiichi Tokuda, Yoshihiko Nankaku, Tomoki Toda, Heiga Zen, Junichi Yamagishi, and Keiichiro Oura. Speech synthesis based on hidden markov models. Proceedings of the IEEE, 101(5): 1234–1252, 2013.
+
+Aaron van den Oord, Nal Kalchbrenner, and Koray Kavukcuoglu. Pixel recurrent neural networks. arXiv preprint arXiv:1601.06759, 2016.
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+Fisher Yu and Vladlen Koltun. Multi-scale context aggregation by dilated convolutions. arXiv preprint arXiv:1511.07122, 2015.
+
+Wojciech Zaremba. An empirical exploration of recurrent network architectures. 2015.
+
+# APPENDIX A
+
+A MODEL VARIANT: SAMPLERNN-WAVENET HYBRID
+
+SampleRNN-WaveNet model has two modules operating at two different clock-rate. The slower clock-rate module (frame-level module) sees one frame (each of which has size $F S$ ) at a time while the faster clock-rate component(sample-level component) sees one acoustic sample at a time i.e. the ratio of clock-rates for these two modules would be the size of a single frame. Number of sequential steps for frame-level component would be $F S$ times lower. We repeat the output of each step of frame-level component $F S$ times so that number of time-steps for output of both the components match. The output of both these modules are concatenated for every time-step which is further operated by non-linearities for every time-step independently before generating the final output.
+
+In our experiments, we kept size of a single frame $( F S )$ to be 128. We tried two variants of this model: 1. fully convolutional WaveNet and 2. RNN-WaveNet. In fully convolutional WaveNet, both modules described above are implemented using dilated convolutions as described in original WaveNet model. In RNN-WaveNet, we use high capacity RNN in the frame-level module to model the dependency between frames. The sample-level WaveNet in RNN-WaveNet has receptive field of size 509 samples from the past.
+
+Although these models are designed with the intention of combining the two models to harness their best features, preliminary experiments show that this variant is not meeting our expectations at the moment which directs us to a possible future work.

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+        "text": "SAMPLERNN: AN UNCONDITIONAL END-TO-END NEURAL AUDIO GENERATION MODEL ",
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+    {
+        "type": "text",
+        "text": "Soroush Mehri University of Montreal ",
+        "bbox": [
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+            334,
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+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "Kundan Kumar IIT Kanpur ",
+        "bbox": [
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+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "Ishaan Gulrajani University of Montreal ",
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+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "Rithesh Kumar SSNCE ",
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+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "Shubham Jain IIT Kanpur ",
+        "bbox": [
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+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "Jose Sotelo University of Montreal ",
+        "bbox": [
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+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "Aaron Courville University of Montreal CIFAR Fellow ",
+        "bbox": [
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+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "Yoshua Bengio University of Montreal CIFAR Senior Fellow ",
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+    },
+    {
+        "type": "text",
+        "text": "ABSTRACT ",
+        "text_level": 1,
+        "bbox": [
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+        "type": "text",
+        "text": "In this paper we propose a novel model for unconditional audio generation based on generating one audio sample at a time. We show that our model, which profits from combining memory-less modules, namely autoregressive multilayer perceptrons, and stateful recurrent neural networks in a hierarchical structure is able to capture underlying sources of variations in the temporal sequences over very long time spans, on three datasets of different nature. Human evaluation on the generated samples indicate that our model is preferred over competing models. We also show how each component of the model contributes to the exhibited performance. ",
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+    {
+        "type": "text",
+        "text": "1 INTRODUCTION ",
+        "text_level": 1,
+        "bbox": [
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+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "Audio generation is a challenging task at the core of many problems of interest, such as text-tospeech synthesis, music synthesis and voice conversion. The particular difficulty of audio generation is that there is often a very large discrepancy between the dimensionality of the the raw audio signal and that of the effective semantic-level signal. Consider the task of speech synthesis, where we are typically interested in generating utterances corresponding to full sentences. Even at a relatively low sample rate of 16kHz, on average we will have 6,000 samples per word generated. 1 ",
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+    {
+        "type": "text",
+        "text": "Traditionally, the high-dimensionality of raw audio signal is dealt with by first compressing it into spectral or hand-engineered features and defining the generative model over these features. However, when the generated signal is eventually decompressed into audio waveforms, the sample quality is often degraded and requires extensive domain-expert corrective measures. This results in complicated signal processing pipelines that are to adapt to new tasks or domains. Here we propose a step in the direction of replacing these handcrafted systems. ",
+        "bbox": [
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+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "In this work, we investigate the use of recurrent neural networks (RNNs) to model the dependencies in audio data. We believe RNNs are well suited as they have been designed and are suited solutions for these tasks (see Graves (2013), Karpathy (2015), and Siegelmann (1999)). However, in practice it is a known problem of these models to not scale well at such a high temporal resolution as is found when generating acoustic signals one sample at a time, e.g., 16000 times per second. This is one of the reasons that Oord et al. (2016) profits from other neural modules such as one presented by Yu & Koltun (2015) to show extremely good performance. ",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "In this paper, an end-to-end unconditional audio synthesis model for raw waveforms is presented while keeping all the computations tractable.2 Since our model has different modules operating at different clock-rates (which is in contrast to WaveNet), we have the flexibility in allocating the amount of computational resources in modeling different levels of abstraction. In particular, we can potentially allocate very limited resource to the module responsible for sample level alignments operating at the clock-rate equivalent to sample-rate of the audio, while allocating more resources in modeling dependencies which vary very slowly in audio, for example identity of phoneme being spoken. This advantage makes our model arbitrarily flexible in handling sequential dependencies at multiple levels of abstraction. ",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "Hence, our contribution is threefold: ",
+        "bbox": [
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+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "1. We present a novel method that utilizes RNNs at different scales to model longer term dependencies in audio waveforms while training on short sequences which results in memory efficiency during training.   \n2. We extensively explore and compare variants of models achieving the above effect.   \n3. We study and empirically evaluate the impact of different components of our model on three audio datasets. Human evaluation also has been conducted to test these generative models. ",
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+    {
+        "type": "text",
+        "text": "2 SAMPLERNN MODEL ",
+        "text_level": 1,
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+    {
+        "type": "text",
+        "text": "In this paper we propose SampleRNN (shown in Fig. 1), a density model for audio waveforms. SampleRNN models the probability of a sequence of waveform samples $X ~ = ~ \\{ x _ { 1 } , x _ { 2 } , \\ldots , x _ { T } \\}$ (a random variable over input data sequences) as the product of the probabilities of each sample conditioned on all previous samples: ",
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+        "img_path": "images/722521ef84b3ac668f48f46d9fce61dd9a97268c5d94b6ebc1f33a3d63eca7e8.jpg",
+        "text": "$$\np ( X ) = \\prod _ { i = 0 } ^ { T - 1 } p ( x _ { i + 1 } \\vert x _ { 1 } , \\dotsc , x _ { i } )\n$$",
+        "text_format": "latex",
+        "bbox": [
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+        "type": "text",
+        "text": "RNNs are commonly used to model sequential data which can be formulated as: ",
+        "bbox": [
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+    {
+        "type": "equation",
+        "img_path": "images/ccabcbd280ece86d2af2a0bacac3ee9629eafdf953ffec46c1c144757955aa01.jpg",
+        "text": "$$\n\\begin{array} { c } { h _ { t } = \\mathcal { H } ( h _ { t - 1 } , x _ { i = t } ) } \\\\ { p ( x _ { i + 1 } | x _ { 1 } , \\dots , x _ { i } ) = S o f t m a x ( M L P ( h _ { t } ) ) } \\end{array}\n$$",
+        "text_format": "latex",
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+    {
+        "type": "text",
+        "text": "with $\\mathcal { H }$ being one of the known memory cells, Gated Recurrent Units (GRUs) (Chung et al., 2014), Long Short Term Memory Units (LSTMs) (Hochreiter & Schmidhuber, 1997), or their deep variations (Section 3). However, raw audio signals are challenging to model because they contain structure at very different scales: correlations exist between neighboring samples as well as between ones thousands of samples apart. ",
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+        "type": "text",
+        "text": "SampleRNN helps to address this challenge by using a hierarchy of modules, each operating at a different temporal resolution. The lowest module processes individual samples, and each higher module operates on an increasingly longer timescale and a lower temporal resolution. Each module conditions the module below it, with the lowest module outputting sample-level predictions. The entire hierarchy is trained jointly end-to-end by backpropagation. ",
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+        "type": "text",
+        "text": "2.1 FRAME-LEVEL MODULES ",
+        "text_level": 1,
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+    {
+        "type": "text",
+        "text": "Rather than operating on individual samples, the higher-level modules in SampleRNN operate on non-overlapping frames of $F S ^ { ( k ) }$ (“Frame Size”) samples at the $k ^ { \\mathrm { { t h } } }$ level up in the hierarchy at a time (frames denoted by $f ^ { ( k ) }$ ). Each frame-level module is a deep RNN which summarizes the history of its inputs into a conditioning vector for the next module downward. ",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "The variable number of frames we condition upon up to timestep $t - 1$ is expressed by a fixed length hidden state or memory $h _ { t } ^ { ( k ) }$ where $t$ is related to clock rate at that tier. The RNN makes a memory update at timestep $t$ as a function of the previous memory $h _ { t - 1 } ^ { ( k ) }$ and an input ${ i n p } _ { t } ^ { ( k ) }$ . This input for top tier $k = K$ is simply the input frame. For intermediate tiers $1 < k < K$ ) this input is a linear combination of conditioning vector from higher tier and current input frame. See Eqs. 4–5. ",
+        "bbox": [
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+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "Because different modules operate at different temporal resolutions, we need to upsample each vector $c$ at the output of a module into a series of $r ^ { ( k ) }$ vectors (where $r ^ { ( k ) }$ is the ratio between the temporal resolutions of the modules) before feeding it into the input of the next module downward (Eq. 6). We do this with a set of $r ^ { ( k ) }$ separate linear projections. ",
+        "bbox": [
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+        "page_idx": 1
+    },
+    {
+        "type": "image",
+        "img_path": "images/e8280be33b3609b1d7afc26585a66c21aae4bf4ccb693864961aa5c90ebb6cc5.jpg",
+        "image_caption": [
+            "Figure 1: Snapshot of the unrolled model at timestep $i$ with $K = 3$ tiers. As a simplification only one RNN and up-sampling ratio $r = 4$ is used for all tiers. "
+        ],
+        "image_footnote": [],
+        "bbox": [
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+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "Here we are formalizing the frame-level module in tier $k$ . Note that following equations are exclusive to tier $k$ and timestep $t$ for that specific tier. To increase the readability, unless necessary superscript $( k )$ is not shown for $\\bar { t } , i n p ^ { ( k ) } , \\bar { W } _ { x } ^ { ( k ) } , h ^ { ( k ) } , \\mathcal { H } ^ { ( k ) } , W _ { j } ^ { ( k ) }$ , and $r ^ { ( k ) }$ . ",
+        "bbox": [
+            174,
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+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "equation",
+        "img_path": "images/478faea9a499304d61608dd1cfa764565b8d50e3dcb308b7d97936bc648020aa.jpg",
+        "text": "$$\n\\begin{array} { c c } { i n p _ { t } = \\left\\{ \\begin{array} { l l } { W _ { x } f _ { t } ^ { ( k ) } + c _ { t } ^ { ( k + 1 ) } ; } & { 1 < k < K } \\\\ { f _ { t } ^ { ( k = K ) } ; } & { k = K } \\end{array} \\right. } \\\\ { h _ { t } = \\mathcal { H } ( h _ { t - 1 } , i n p _ { t } ) } \\\\ { c _ { ( t - 1 ) * r + j } ^ { ( k ) } = W _ { j } h _ { t } ; } & { 1 \\leq j \\leq r } \\end{array}\n$$",
+        "text_format": "latex",
+        "bbox": [
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+            436,
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+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "Our approach of upsampling with $r ^ { ( k ) }$ linear projections is exactly equivalent to upsampling by adding zeros and then applying a linear convolution. This is sometimes called “perforated” upsampling in the context of convolutional neural networks (CNNs). It was first demonstrated to work well in Dosovitskiy et al. (2016) and is a fairly common upsampling technique. ",
+        "bbox": [
+            174,
+            530,
+            825,
+            587
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "2.2 SAMPLE-LEVEL MODULE ",
+        "text_level": 1,
+        "bbox": [
+            174,
+            603,
+            392,
+            618
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "The lowest module (tier $k = 1$ ; Eqs. 7–9) in the SampleRNN hierarchy outputs a distribution over a sample $x _ { i + 1 }$ , conditioned on the $F S ^ { ( 1 ) }$ preceding samples as well as a vector $c _ { i } ^ { ( k = 2 ) }$ from the next higher module which encodes information about the sequence prior to that frame. As $F S ^ { ( 1 ) }$ is usually a small value and correlations in nearby samples are easy to model by a simple memoryless module, we implement it with a multilayer perceptron (MLP) rather than RNN which slightly speeds up the training. Assuming $e _ { i }$ represents $x _ { i }$ after passing through embedding layer (section 2.2.1), conditional distribution in Eq. 1 can be achieved by following and for further clarity two consecutive sample-level frames are shown. In addition, $W _ { x }$ in Eq. 8 is simply used to linearly combine a frame and conditioning vector from above. ",
+        "bbox": [
+            173,
+            628,
+            826,
+            760
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "equation",
+        "img_path": "images/d5acba725dee8e51e6eb7d827ecf3e77d9fbfd70d244b6cc0a4016eaafde8a27.jpg",
+        "text": "$$\n\\begin{array} { r } { f _ { i - 1 } ^ { ( 1 ) } = f l a t t e n ( \\left[ e _ { i - F S ^ { ( 1 ) } } , \\dots , e _ { i - 1 } \\right] ) } \\\\ { f _ { i } ^ { ( 1 ) } = f l a t t e n ( \\left[ e _ { i - F S ^ { ( 1 ) } + 1 } , \\dots , e _ { i } \\right] ) } \\\\ { i n p _ { i } ^ { ( 1 ) } = W _ { x } ^ { ( 1 ) } f _ { i } ^ { ( 1 ) } + c _ { i } ^ { ( 2 ) } \\qquad } \\\\ { p ( x _ { i + 1 } | x _ { 1 } , \\dots , x _ { i } ) = S o f t m a x ( M L P ( i n p _ { i } ^ { ( 1 ) } ) ) } \\end{array}\n$$",
+        "text_format": "latex",
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "We use a Softmax because we found that better results were obtained by discretizing the audio signals (also see van den Oord et al. (2016)) and outputting a Multinoulli distribution rather than using a Gaussian or Gaussian mixture to represent the conditional density of the original real-valued signal. When processing an audio sequence, the MLP is convolved over the sequence, processing each window of $F S ^ { ( 1 ) }$ samples and predicting the next sample. At generation time, the MLP is run repeatedly to generate one sample at a time. Table 1 shows a considerable gap between the baseline model RNN and this model, suggesting that the proposed hierarchically structured architecture of SampleRNN makes a big difference. ",
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+        "page_idx": 2
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+    {
+        "type": "text",
+        "text": "",
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "2.2.1 OUTPUT QUANTIZATION ",
+        "text_level": 1,
+        "bbox": [
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "The sample-level module models its output as a $q$ -way discrete distribution over possible quantized values of $x _ { i }$ (that is, the output layer of the MLP is a $q$ -way Softmax). ",
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "To demonstrate the importance of a discrete output distribution, we apply the same architecture on real-valued data by replacing the $q$ -way Softmax with a Gaussian Mixture Models (GMM) output distribution. Table 2 shows that our model outperforms an RNN baseline even when both models use real-valued outputs. However, samples from the real-valued model are almost indistinguishable from random noise. ",
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "In this work we use linear quantization with $q = 2 5 6$ , corresponding to a per-sample bit depth of 8. Unintuitively, we realized that even linearly decreasing the bit depth (resolution of each audio sample) from 16 to 8 can ease the optimization procedure while generated samples still have reasonable quality and are artifact-free. ",
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "In addition, early on we noticed that the model can achieve better performance and generation quality when we embed the quantized input values before passing them through the sample-level MLP (see Table 4). The embedding steps maps each of the $q$ discrete values to a real-valued vector embedding. However, real-valued raw samples are still used as input to the higher modules. ",
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "2.2.2 CONDITIONALLY INDEPENDENT SAMPLE OUTPUTS ",
+        "text_level": 1,
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "To demonstrate the importance of a sample-level autoregressive module, we try replacing it with “Multi-Softmax” (see Table 4), where the prediction of each sample $x _ { i }$ depends only on the conditioning vector $c$ from Eq. 9. In this configuration, the model outputs an entire frame of $F S ^ { ( 1 ) }$ samples at a time, modeling all samples in a frame as conditionally independent of each other. We find that this Multi-Softmax model (which lacks a sample-level autoregressive module) scores significantly worse in terms of log-likelihood and fails to generate convincing samples. This suggests that modeling the joint distribution of the acoustic samples inside each frame is very important in order to obtain good acoustic generation. We found this to be true even when the frame size is reduced, with best results always with a frame size of 1, i.e., generating only one acoustic sample at a time. ",
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+    {
+        "type": "text",
+        "text": "2.3 TRUNCATED BPTT ",
+        "text_level": 1,
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "Training recurrent neural networks on long sequences can be very computationally expensive. Oord et al. (2016) avoid this problem by using a stack of dilated convolutions instead of any recurrent connections. However, when they can be trained efficiently, recurrent networks have been shown to be very powerful and expressive sequence models. We enable efficient training of our recurrent model using truncated backpropagation through time, splitting each sequence into short subsequences and propagating gradients only to the beginning of each subsequence. We experiment with different subsequence lengths and demonstrate that we are able to train our networks, which model very long-term dependencies, despite backpropagating through relatively short subsequences. ",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "Table 3 shows that by increasing the subsequence length, performance substantially increases alongside with train-time memory usage and convergence time. Yet it is noteworthy that our best models have been trained on subsequences of length 512, which corresponds to 32 milliseconds, a small fraction of the length of a single a phoneme of human speech while generated samples exhibit longer word-like structures. ",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "Despite the aforementioned fact, this generative model can mimic the existing long-term structure of the data which results in more natural and coherent samples that is preferred by human listeners. (More on this in Sections 3.2–3.3.) This is due to the fast updates from TBPTT and specialized frame-level modules (Section 2.1) with top tiers designed to model a lower resolution of signal while leaving the process of filling the details to lower tiers. ",
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+    {
+        "type": "text",
+        "text": "3 EXPERIMENTS AND RESULTS ",
+        "text_level": 1,
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "In this section we are introducing three datasets which have been chosen to evaluate the proposed architecture for modeling raw acoustic sequences. The description of each dataset and their preprocessing is as follows: ",
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+    {
+        "type": "text",
+        "text": "Blizzard which is a dataset presented by Prahallad et al. (2013) for speech synthesis task, contains 315 hours of a single female voice actor in English; however, for our experiments we are using only 20.5 hours. The training/validation/test split is $8 6 \\% - 7 \\% - 7 \\%$ . ",
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+    },
+    {
+        "type": "text",
+        "text": "Onomatopoeia3, a relatively small dataset with 6,738 sequences adding up to 3.5 hours, is human vocal sounds like grunting, screaming, panting, heavy breathing, and coughing. Diversity of sound type and the fact that these sounds were recorded from 51 actors and many categories makes it a challenging task. To add to that, this data is extremely unbalanced. The training/validation/test split is $9 2 \\% - 4 \\% - 4 \\%$ . ",
+        "bbox": [
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+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "Music dataset is the collection of all 32 Beethoven’s piano sonatas publicly available on https://archive.org/ amounting to 10 hours of non-vocal audio. The training/validation/test split is $8 8 \\% - 6 \\% - 6 \\%$ . ",
+        "bbox": [
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+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "See Fig. 2 for a visual demonstration of examples from datasets and generated samples. For all the datasets we are using a $1 6 ~ \\mathrm { k H z }$ sample rate and 16 bit depth. For the Blizzard and Music datasets, preprocessing simply amounts to chunking the long audio files into 8 seconds long sequences on which we will perform truncated backpropagation through time. Each sequence in the Onomatopoeia dataset is few seconds long, ranging from 1 to 11 seconds. To train the models on this dataset, zero-padding has been applied to make all the sequences in a mini-batch have the same length and corresponding cost values (for the predictions over the added 0s) would be ignored when computing the gradients. ",
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+    {
+        "type": "text",
+        "text": "We particularly explored two gated variants of RNNs—GRUs and LSTMs. For the case of LSTMs, the forget gate bias is initialized with a large positive value of 3, as recommended by Zaremba (2015) and Gers (2001), which has been shown to be beneficial for learning long-term dependencies. ",
+        "bbox": [
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+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "As for models that take real-valued input, e.g. the RNN-GMM and SampleRNN-GMM (with 4 components), normalization is applied per audio sample with the global mean and standard deviation obtained from the train split. For most of our experiments where the model demands discrete input, binning was applied per audio sample. ",
+        "bbox": [
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+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "All the models have been trained with teacher forcing and stochastic gradient decent (mini-batch size 128) to minimize the Negative Log-Likelihood (NLL) in bits per dimension (per audio sample). Gradients were hard-clipped to remain in [-1, 1] range. Update rules from the Adam optimizer (Kingma & Ba, 2014) $\\beta _ { 1 } = 0 . 9$ , $\\beta _ { 2 } ~ = ~ 0 . 9 9 9$ , and $\\epsilon = 1 e { - 8 } )$ with an initial learning rate of 0.001 was used to adjust the parameters. For training each model, random search over hyper-parameter values (Bergstra & Bengio, 2012) was conducted. The initial RNN state of all the RNN-based models was always learnable. Weight Normalization (Salimans & Kingma, 2016) has been used for all the linear layers in the model (except for the embedding layer) to accelerate the training procedure. Size of the embedding layer was 256 and initialized by standard normal distribution. Orthogonal weight matrices used for hidden-to-hidden connections and other weight matrices initialized similar to He et al. (2015). In final model, we found GRU to work best (slightly better than LSTM). 1024 was the the number of hidden units for all GRUs (1 layer per tier for 3-tier and 3 layer for 2-tier model) and MLPs (3 fully connected layers with ReLU activation with output dimension being 1024 for first two layers and 256 for the final layer before softmax). Also $F \\bar { S } ^ { ( 1 ) } = F S ^ { ( 2 ) } = 2$ and $F S ^ { ( 3 ) } = 8 $ were found to result in lowest NLL. ",
+        "bbox": [
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+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "3.1 WAVENET RE-IMPLEMENTATION ",
+        "text_level": 1,
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "We implemented the WaveNet architecture as described in Oord et al. (2016). Ideally, we would have liked to replicate their model exactly but owing to missing details of architecture and hyperparameters, as well as limited compute power at our disposal, we made our own design choices so that the model would fit on a single GPU while having a receptive field of around 250 milliseconds, while having a reasonable number of updates per unit time. Although our model is very similar to WaveNet, the design choices, e.g. number of convolution filters in each dilated convolution layer, length of target sequence to train on simultaneously (one can train with a single target with all samples in the receptive field as input or with target sequence length of size T with input of size receptive field $+ \\mathrm { ~ T ~ } - 1$ ), batch-size, etc. might make our implementation different from what the authors have done in the original WaveNet model. Hence, we note here that although we did our best at exactly reproducing their results, there would very likely be different choice of hyper-parameters between our implementation and the one of the authors. ",
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+        "page_idx": 4
+    },
+    {
+        "type": "image",
+        "img_path": "images/095574c20ff2a204bedf1e789a109edb8ab60a841da04859134aaf954e818b5e.jpg",
+        "image_caption": [
+            "Figure 2: Examples from the datasets compared to samples from our models. In the first 3 rows, 2 seconds of audio are shown. In the bottom 3 rows, 100 milliseconds of audio are shown. Rows 1 and 4 are ground truth from which one can see how the datasets look different and have complex structure in low resolution which the frame-level component of the SampleRNN is designed to capture. Samples also to some extent mimic the same global structure. At the same time, zoomed-in samples of our model shows that it can perfectly resemble the high resolution structure present in the data as well. "
+        ],
+        "image_footnote": [],
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+    },
+    {
+        "type": "table",
+        "img_path": "images/c233dce22334f3eef34c534948c6a3214414b8b1030397610a781c439d9d6c59.jpg",
+        "table_caption": [
+            "Table 1: Test NLL in bits for three presented datasets. "
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>Model</td><td>Blizzard</td><td>Onomatopoeia</td><td>Music</td></tr><tr><td>RNN (Eq.2)</td><td>1.434</td><td>2.034</td><td>1.410</td></tr><tr><td>WaveNet (re-impl.)</td><td>1.480</td><td>2.285</td><td>1.464</td></tr><tr><td>SampleRNN (2-tier)</td><td>1.392</td><td>2.026</td><td>1.076</td></tr><tr><td>SampleRNN (3-tier)</td><td>1.387</td><td>1.990</td><td>1.159</td></tr></table>",
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+    },
+    {
+        "type": "table",
+        "img_path": "images/316cc8398763837a820468e8942732f67c7bfaa44413acd31e62637b4bc5124c.jpg",
+        "table_caption": [
+            "Table 2: Average NLL on Blizzard test set for real-valued models. "
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>Model</td><td>Average Test NLL</td></tr><tr><td>RNN-GMM</td><td>-2.415</td></tr><tr><td>SampleRNN-GMM (2-tier)</td><td>-2.782</td></tr></table>",
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+    },
+    {
+        "type": "table",
+        "img_path": "images/9a5606f1f8ce6d42bf0b929a9026ad7eafda452c27c5baae3a6d9c8f1b1db8ef.jpg",
+        "table_caption": [
+            "Table 3: Effect of subsequence length on NLL (bits per audio sample) computed on the Blizzard validation set. "
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>Subsequence Length</td><td>32</td><td>64</td><td>128</td><td>256</td><td>512</td></tr><tr><td>NLL Validation</td><td>1.575</td><td>1.468</td><td>1.412</td><td>1.391</td><td>1.364</td></tr></table>",
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+    },
+    {
+        "type": "table",
+        "img_path": "images/eeeb66b7772c54b66bef3e7e38e57499182b59d7daeb8a120439c4f2b9b8a668.jpg",
+        "table_caption": [
+            "Table 4: Test (validation) set NLL (bits per audio sample) for Blizzard. Variants of SampleRNN are provided to compare the contribution of each component in performance. "
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>Model</td><td>NLL Test (Validation)</td></tr><tr><td>SampleRNN (2-tier)</td><td>1.392 (1.369)</td></tr><tr><td>Without Embedding</td><td>1.566 (1.539)</td></tr><tr><td>Multi-Softmax</td><td>1.685 (1.656)</td></tr></table>",
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+    },
+    {
+        "type": "text",
+        "text": "",
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+    {
+        "type": "text",
+        "text": "For our WaveNet implementation, we have used 4 dilated convolution blocks each having 10 dilated convolution layers with dilation 1, 2, 4, 8 up to 512. Hence, our network has a receptive field of 4092 acoustic samples i.e. the parameters of multinomial distribution of sample at time step t, $p ( x _ { i } ) = f _ { \\boldsymbol { \\theta } } ( x _ { i - 1 } , \\bar { x _ { i - 2 } } , \\dots x _ { i - 4 0 9 2 } )$ where $\\theta$ is model parameters. We train on target sequence length of 1600 and use batch size of 8. Each dilated convolution filter has size 2 and the number of output channels is 64 for each dilated convolutional layer (128 filters in total due to gated nonlinearity). We trained this model using Adam optimizer with a fixed global learning rate of 0.001 for Blizzard dataset and 0.0001 for Onomatopoeia and Music datasets. We trained these models for about one week on a GeForce GTX TITAN X. We dropped the learning rate in the Blizzard experiment to 0.0001 after around 3 days of training. ",
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+    },
+    {
+        "type": "text",
+        "text": "3.2 HUMAN EVALUATION ",
+        "text_level": 1,
+        "bbox": [
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+        "page_idx": 6
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+    {
+        "type": "text",
+        "text": "Apart from reporting NLL, we conducted AB preference tests for random samples from four models trained on the Blizzard dataset. For unconditional generation of speech which at best sounds like mumbling, this type of test is the one which is more suited. Competing models were the RNN, SampleRNN (2-tier), SampleRNN (3-tier), and our implementation of WaveNet. The rest of the models were excluded as the quality of samples were definitely lower and also to keep the number of pair comparison tests manageable. We will release the samples that have been used in this test too. ",
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+    {
+        "type": "text",
+        "text": "All the samples were set to have the same volume. Every user is then shown a set of twenty pairs of samples with one random pair at a time. Each pair had samples from two different models. The human evaluator is asked to listen to the samples and had the option of choosing between the two model or choosing not to prefer any of them. Hence, we have a quantification of preference between every pair of models. We used the online tool made publicly available by Jillings et al. (2015). ",
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+    {
+        "type": "text",
+        "text": "Results in Fig. 3 clearly points out that SampleRNN (3-tier) is a winner by a huge margin in terms of preference by human raters, then SampleRNN (2-tier) and afterward two other models, which matches with the performance comparison in Table 1. ",
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+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "The same evaluation was conducted for Music dataset except for an additional filtering process of samples. Specific to only this dataset, we observed that a batch of generated samples from competing models (this time restricted to RNN, SampleRNN (2-tier), and SampleRNN (3-tier)) were either music-like or random noise. For all these models we only considered random samples that were not random noise. Fig. 4 is dedicated to result of human evaluation on Music dataset. ",
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+        "page_idx": 6
+    },
+    {
+        "type": "image",
+        "img_path": "images/2d96293eb1cfa3e42560f06229017eae1d46d950502c02d79fe8cdd1fbcdb740.jpg",
+        "image_caption": [
+            "Figure 3: Pairwise comparison of 4 best models based on the votes from listeners conducted on samples generated from models trained on Blizzard dataset. "
+        ],
+        "image_footnote": [],
+        "bbox": [
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+        "page_idx": 7
+    },
+    {
+        "type": "image",
+        "img_path": "images/3f4065b402e4c76a71a4ce716fe699ae6b8f5f5dd56e968b020de62c176579b7.jpg",
+        "image_caption": [
+            "Figure 4: Pairwise comparison of 3 best models based on the votes from listeners conducted on samples generated from models trained on Music dataset. "
+        ],
+        "image_footnote": [],
+        "bbox": [
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+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "3.3 QUANTIFYING INFORMATION RETENTION ",
+        "text_level": 1,
+        "bbox": [
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+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "For the last experiment we are interested in measuring the memory span of the model. We trained our model, SampleRNN (3-tier), with best hyper-parameters on a dataset of 2 speakers reading audio books, one male and one female, respectively, with mean fundamental frequency of 125.3 and $2 0 1 . 8 \\mathrm { H z }$ . Each speaker has roughly 10 hours of audio in the dataset that has been preprocessed similar to Blizzard. We observed that it learned to stay consistent generating samples from the same speaker without having any knowledge about the speaker ID or any other conditioning information. This effect is more apparent here in comparison to the unbalanced Onomatopoeia that sometimes mixes two different categories of sounds. ",
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+        "page_idx": 7
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+    {
+        "type": "text",
+        "text": "Another experiment was conducted to test the effect of memory and study the effective memory horizon. We inject 1 second of silence in the middle of sampling procedure in order to see if it will remember to generate from the same speaker or not. Initially when sampling we let the model generate 2 seconds of audio as it normally do. From 2 to 3 seconds instead of feeding back the generated sample at that timestep a silent token (zero amplitude) would be fed. From 3 to 5 seconds again we sample normally; feeding back the generated token. ",
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+    {
+        "type": "text",
+        "text": "We did classification based on mean fundamental frequency of speakers for the first and last 2 seconds. In $83 \\%$ of samples SampleRNN generated from the same person in two separate segments. ",
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+    {
+        "type": "text",
+        "text": "This is in contrast to a model with fixed past window like WaveNet where injecting 16000 silent tokens (3.3 times the receptive field size) is equivalent to generating from scratch which has $50 \\%$ chance (assuming each 2-second segment is coherent and not a mixed sound of two speakers). ",
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+            174,
+            103,
+            825,
+            146
+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "4 RELATED WORK ",
+        "text_level": 1,
+        "bbox": [
+            176,
+            174,
+            344,
+            190
+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "Our work is related to earlier work on auto-regressive multi-layer neural networks, starting with Bengio & Bengio (1999), then NADE (Larochelle & Murray, 2011) and more recently PixelRNN (van den Oord et al., 2016). Similar to how they tractably model joint distribution over units of the data (e.g. words in sentences, pixels in images, etc.) through an auto-regressive decomposition, we transform the joint distribution of acoustic samples using Eq. 1. ",
+        "bbox": [
+            174,
+            210,
+            823,
+            281
+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "The idea of having part of the model running at different clock rates is related to multi-scale RNNs (Schmidhuber, 1992; El Hihi & Bengio, 1995; Koutnik et al., 2014; Sordoni et al., 2015; Serban et al., 2016). ",
+        "bbox": [
+            176,
+            287,
+            825,
+            329
+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "Chung et al. (2015) also attempt to model raw audio waveforms which is in contrast to traditional approaches which use spectral features as in Tokuda et al. (2013), Bertrand et al. (2008), and Lee et al. (2009). ",
+        "bbox": [
+            176,
+            337,
+            825,
+            378
+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "Our work is closely related to WaveNet (Oord et al., 2016), which is why we have made the above comparisons, and makes it interesting to compare the effect of adding higher-level RNN stages working at a low resolution. Similar to this work, our models generate one acoustic sample at a time conditioned on all previously generated samples. We also share the preprocessing step of quantizing the acoustics into bins. Unlike this model, we have different modules in our models running at different clock-rates. In contrast to WaveNets, we mitigate the problem of long-term dependency with hierarchical structure and using stateful RNNs, i.e. we will always propagate hidden states to the next training sequence although the gradient of the loss will not take into account the samples in previous training sequence. ",
+        "bbox": [
+            174,
+            386,
+            825,
+            511
+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "5 DISCUSSION AND CONCLUSION ",
+        "text_level": 1,
+        "bbox": [
+            176,
+            540,
+            467,
+            555
+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "We propose a novel model that can address unconditional audio generation in the raw acoustic domain, which typically has been done until recently with hand-crafted features. We are able to show that a hierarchy of time scales and frequent updates will help to overcome the problem of modeling extremely high-resolution temporal data. That allows us, for this particular application, to learn the data manifold directly from audio samples. We show that this model can generalize well and generate samples on three datasets that are different in nature. We also show that the samples generated by this model are preferred by human raters. ",
+        "bbox": [
+            174,
+            575,
+            825,
+            672
+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "Success in this application, with a general-purpose solution as proposed here, opens up room for more improvement when specific domain knowledge is applied. This method, however, proposed with audio generation application in mind, can easily be adapted to other tasks that require learning the representation of sequential data with high temporal resolution and long-range complex structure. ",
+        "bbox": [
+            176,
+            680,
+            825,
+            750
+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "ACKNOWLEDGMENTS ",
+        "text_level": 1,
+        "bbox": [
+            176,
+            775,
+            326,
+            787
+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "The authors would like to thank Joao Felipe Santos and Kyle Kastner for insightful comments and ˜ discussion. We would like to thank the Theano Development Team $\\left( 2 0 1 6 \\right) ^ { 4 }$ and MILA staff. We acknowledge the support of the following agencies for research funding and computing support: NSERC, Calcul Quebec, Compute Canada, the Canada Research Chairs and CIFAR. Jose Sotelo ´ also thanks the Consejo Nacional de Ciencia y Tecnolog´ıa (CONACyT) as well as the Secretar´ıa de Educacion P ´ ublica (SEP) for their support. This work was a collaboration with Ubisoft. ´ ",
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+        "page_idx": 8
+    },
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+    {
+        "type": "text",
+        "text": "APPENDIX A ",
+        "text_level": 1,
+        "bbox": [
+            176,
+            554,
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+        ],
+        "page_idx": 10
+    },
+    {
+        "type": "text",
+        "text": "A MODEL VARIANT: SAMPLERNN-WAVENET HYBRID ",
+        "bbox": [
+            174,
+            584,
+            553,
+            599
+        ],
+        "page_idx": 10
+    },
+    {
+        "type": "text",
+        "text": "SampleRNN-WaveNet model has two modules operating at two different clock-rate. The slower clock-rate module (frame-level module) sees one frame (each of which has size $F S$ ) at a time while the faster clock-rate component(sample-level component) sees one acoustic sample at a time i.e. the ratio of clock-rates for these two modules would be the size of a single frame. Number of sequential steps for frame-level component would be $F S$ times lower. We repeat the output of each step of frame-level component $F S$ times so that number of time-steps for output of both the components match. The output of both these modules are concatenated for every time-step which is further operated by non-linearities for every time-step independently before generating the final output. ",
+        "bbox": [
+            174,
+            611,
+            825,
+            722
+        ],
+        "page_idx": 10
+    },
+    {
+        "type": "text",
+        "text": "In our experiments, we kept size of a single frame $( F S )$ to be 128. We tried two variants of this model: 1. fully convolutional WaveNet and 2. RNN-WaveNet. In fully convolutional WaveNet, both modules described above are implemented using dilated convolutions as described in original WaveNet model. In RNN-WaveNet, we use high capacity RNN in the frame-level module to model the dependency between frames. The sample-level WaveNet in RNN-WaveNet has receptive field of size 509 samples from the past. ",
+        "bbox": [
+            174,
+            728,
+            823,
+            813
+        ],
+        "page_idx": 10
+    },
+    {
+        "type": "text",
+        "text": "Although these models are designed with the intention of combining the two models to harness their best features, preliminary experiments show that this variant is not meeting our expectations at the moment which directs us to a possible future work. ",
+        "bbox": [
+            176,
+            820,
+            825,
+            862
+        ],
+        "page_idx": 10
+    }
+]

parse/train/UZgGf92u5N0/UZgGf92u5N0.md

@@ -0,0 +1,457 @@
+# On the Effects of Data Distortion on Model Analysis and Training
+
+Anonymous Author(s)   
+Affiliation   
+Address   
+email
+
+# Abstract
+
+1 Data modification can introduce artificial information. It is often assumed that   
+2 the resulting artefacts are detrimental to training, whilst being negligible when   
+3 analysing models. We investigate these assumptions and conclude that in some   
+4 cases they are unfounded and lead to incorrect results. Specifically, we show current   
+5 shape bias identification methods and occlusion robustness measures are biased   
+6 and propose a fairer alternative for the latter. Subsequently, through a series of   
+7 experiments we seek to correct and strengthen the community’s perception of how   
+8 distorting data affects learning. Based on our empirical results we argue that the   
+9 impact of the artefacts must be understood and exploited rather than eliminated.
+
+# 10 1 Motivation
+
+11 Modifying data has become commonplace both when training and analysing models, yet the wider   
+12 implications are often disregarded. We delve into some of the side-effects and point out that this   
+13 practice has resulted in the creation of biased model interpretation tools and poorly informed theories.   
+14 On the analysis side, we take as examples occlusion robustness and shape bias identification methods.   
+15 On the training side, we focus on some instances of Mixed Sample Data Augmentation (MSDA),   
+16 where two images are combined to obtain a new training sample. Visual examples of each can   
+17 be found in Figure 1. In this paper we study a number of assumptions that lie at the heart of the   
+18 aforementioned methods, which we briefly introduce below.   
+19 Shape-texture bias: Deep models are known to be sensitive to interventions that are imperceptible   
+20 to humans [35, 13], as well as to other forms of distribution shifts [1, 6, 8]. It has been argued that   
+21 this is intimately linked to networks tending to use texture rather than shape information [2, 11].   
+22 Recently, input distortions have become a popular way of assessing a model’s texture bias. To this end,   
+23 images are divided into a grid and the resulting patches are randomly shuffled such that information   
+24 is preserved locally, while the global shape is altered [32, 27, 25, 41]. It is implicitly assumed that   
+25 patch-shuffling does not introduce misleading shape or texture that could affect model evaluation.   
+26 Occlusion robustness: A widely adopted method for measuring occlusion robustness is through the   
+27 accuracy obtained after superimposing a rectangular patch on an image [5, 9, 39, 42, 20]. We refer   
+28 to this approach as CutOcclusion throughout the paper. Just as for shape bias, this method relies on   
+29 information introduced not to interfere with a model’s learnt representations such that a decrease in   
+30 performance can be directly attributed to lack of robustness.   
+31 Data augmentation studies: In statistical learning, training with augmented data is termed Vicinal   
+32 Risk Minimisation (VRM) [37, 4] and it is seen as injecting prior knowledge about the neighbourhood   
+33 of the data samples. The intuition behind augmentation caused researchers to interpret its effect   
+34 through the similarity between original and augmented data distributions. This perspective is often   
+35 challenged by methods which, despite generating samples that do not appear to fall under the   
+36 distribution of natural images, lead to strong learners. Gontijo-Lopes et al. [12] argue it is the   
+37 perceived distribution shift that needs to be minimised, while maximising the sample vicinity.   
+38 Formalising these concepts, they introduce augmentation “diversity” and “affinity”. Diversity is   
+39 defined as the training loss when learning with artificial samples, while affinity quantifies the   
+40 difference between the accuracy on original test data and augmented test data for a reference model.   
+41 The latter penalises augmentations that introduce artificial information to which the model is not   
+42 invariant, implicitly assuming that training with that information is detrimental to generalisation.   
+43 In summary, it is currently assumed that the artefacts introduced by changes in the data are negligible   
+44 when evaluating models, while those introduced when training are important and undesirable. Does   
+45 the artificial information added by analysis methods not have major side-effects or does it lead to   
+46 biased results? Conversely, are the artefacts important when training with modified data? Do they   
+47 cause models to learn better or worse representations?   
+48 We set out to answer these questions and find that when the secondary effects of data manipulation   
+49 are not accounted for, results can be misleading, especially in comparative studies. Subsequently, we   
+50 construct empirical counter-examples which disprove common beliefs in the literature and highlight   
+51 the importance of understanding the changes MSDAs introduce. Our contributions are:
+
+![](images/c60398d309119af7ef6dce4ba96a96def6d83386bbef24d7aa21c2ed9b677914.jpg)  
+Figure 1: Examples of image distortions. For test-time distortions (Occlusion and Shuffled grid) only Image 1 was used. For mixing augmentations, the first row was generated with a mixing factor of 0.2, while the second one with 0.5.
+
+• We show that increasingly popular model interpretation and analysis methods are biased, relying on unfounded assumptions (Section 2);   
+• For measuring occlusion robustness, we propose a fairer alternative (Section 3);   
+• We show that, in contrast to what is widely assumed, not preserving the data distribution can lead to learning better representations (Section 4).
+
+# 57 2 Are artefacts negligible when analysing classifiers?
+
+58 To verify whether distorting data at evaluation time could have side-effects previously not considered,   
+59 we look at the increase in misclassifications per category. That is, from the number of incorrect   
+60 predictions of a model evaluated on modified data, we subtract the incorrect predictions when testing   
+61 on original data. If there is a significant increase for a specific class, it indicates that the distortion   
+62 introduces features the model associates with that class. We refer to this phenomenon as “data   
+63 interference”. Considering only positive differences, we denote the increase in the percentage of   
+64 misclassifications for class $c$ of a given model $m$ by $i _ { c } ^ { m }$ . We define the Data Interference $D I$ index as
+
+$$
+D I = \frac { i _ { c _ { m a x } } } { \sum _ { c } i _ { c } } i _ { c _ { m a x } } ,
+$$
+
+65 where $c _ { m a x }$ is the class with highest mean increase across all runs. The $D I$ index measures the   
+66 percentage represented by the dominant class $c _ { m a x }$ weighted by its increase. A high index value   
+67 indicates a sharp increase for a particular class which is consistent across runs. We associate this with   
+68 an overlap between introduced artefacts and learnt representations. In Appendix B.1 we experiment   
+69 with an alternative index, where we weight by the highest increase of a model across the 5 runs, so as   
+70 to obtain a worst-case analysis. As expected, we observe a more accentuated bias in this case.   
+71 To obtain models with different behaviours in a controlled manner, we make use of data augmentation.   
+72 Since it is sufficient to identify some common cases in which models are disfavoured, we choose to   
+73 reduce our environmental impact by restricting the analysis to simple MSDAs that combine images   
+74 without incurring additional computation time or external models. As will be argued in Section 3, we   
+75 expect the unfairness to be present in most settings, thus the exact choice of augmentation is irrelevant.   
+76 We focus on two popular MSDAs, MixUp [40] and CutMix [39]. MixUp linearly interpolates between   
+77 two images to obtain a new training example, while CutMix masks out a rectangular region of an   
+78 image with the corresponding region of another image. Besides the aforementioned methods, we   
+79 also employ FMix due to its irregularly shaped masks sampled from Fourier space, which will play   
+80 an important role in our analysis. Note that although the masking methods sample the size of the   
+81 occluding patch from the same distribution, in CutMix part of the rectangle can be outside the image,   
+82 which leads to less occluded samples overall. We refer to models by the augmentations they were   
+83 trained with and use “basic” to label the models trained without MSDA.   
+84 Throughout the paper, we do 5 runs of each experiment with PreAct-ResNet18 [15] as the default   
+85 architecture. We include results for BagNet [2] and VGG [33] in the Appendices. The main data sets   
+86 we report results on are CIFAR-10/100 [21], Tiny ImageNet [34], FashionMNIST [38], ImageNet [29].   
+87 For ImageNet we use pretrained ResNet-101 models made publicly available by Harris et al. [14].   
+88 Note that the only experiments for which we are unable to run repeats are those on ImageNet, since   
+89 only one model per augmentation is provided. For full experimental details, see Appendix A. Total   
+90 emissions of training the models evaluated in this paper are estimated [22] to be $3 8 . 0 7 \mathrm { k g C O _ { 2 } e q }$ , to   
+91 which $1 3 . 1 1 \mathrm { k g C O _ { 2 } e q }$ more are added during the analysis. The hope is that our findings will lead to a   
+92 better understanding which in the long run would help reduce erroneous research directions without   
+93 needing to empirically disprove them, lessening the future carbon footprint of the community.
+
+Table 1: DI index $( \% )$ for PreAct-ResNet18 on grid-shuffled images for four different types of models. Results with the highest average are given in italic and the lowest in bold. Information introduced when shuffling tends to interfere less with the representations of FMix and CutMix models.   
+
+<table><tr><td></td><td>basic</td><td>MixUp</td><td>FMix</td><td>CutMix</td></tr><tr><td>CIFAR-10</td><td>2.90±1.10</td><td>2.54±1.29</td><td>0.60±0.26</td><td>0.33±0.17</td></tr><tr><td>CIFAR-100</td><td>1.05±0.59</td><td>0.93±0.44</td><td>0.23±0.29</td><td>0.11±0.10</td></tr><tr><td>FashionMNIST</td><td>1.12±0.63</td><td>2.73±1.64</td><td>1.12±0.61</td><td>0.70±0.22</td></tr><tr><td>Tiny ImageNet</td><td>2.58±4.73</td><td>0.54±0.27</td><td>0.38±0.12</td><td>0.14±0.12</td></tr><tr><td>ImageNet</td><td>0.82</td><td>1.49</td><td>0.58</td><td>1</td></tr></table>
+
+# 94 2.1 Shape bias
+
+95 For assessing shape bias through sample manipulation, the standard procedure is to choose between   
+96 dividing the image in 4, 16 or 64 patches to be shuffled. Since FashionMNIST images are smaller,   
+97 we choose a $2 \times 2$ grid, for CIFAR-10/100 and Tiny ImageNet $4 \times 4$ , while for ImageNet we use   
+98 an $8 \times 8$ grid. However, similar results are obtained for different grid sizes (Appendix B.2). The   
+99 large DI index in Table 1 indicates that either basic or MixUp models tend to associate the features   
+100 artificially introduced by patch-shuffling with a certain class. We take a closer look at the distribution   
+101 of misclassifications for CIFAR-10 and notice that the basic model tends to wrongly predict the class   
+102 “Truck” (Figure 2). This is not at all surprising, given that the strong horizontal and vertical edges are   
+103 highly indicative of this class. Similar observations can be made for other data sets (Appendix B.3).   
+104 Thus, we believe the grid-shuffling approach is causing models which are not invariant to strong   
+105 horizontal and vertical edges to appear to rely more heavily on shape information. A model not   
+106 affected by this transformation could be considered texture-biased if we accept the larger definition   
+107 of texture as local information. However, there is a question about the extent to which the reciprocal   
+108 is true; A model can be invariant to the aforementioned edges because it is indeed relying on texture   
+109 information or simply because it uses different shape-related features.   
+110 Is a model necessarily more affected by patch-shuffling if it has a higher shape bias? To answer   
+111 this question, we can use another method of determining shape and texture bias to find a counter  
+112 example. We analyse the ImageNet models on the Geirhos Style-Transfer (GST) [11] data set. GST   
+113 contains artificially generated images where the shape belongs to one class and the texture to another.   
+114 There are 16 coarse classes that encompass a number of ImageNet categories to which they are   
+115 mapped. The bias of the models is given by the accuracy obtained when the label is set to either the   
+116 shape or texture. Using this well-known method of identifying shape bias we want to find models   
+117 which have similar biases but different DI indices when patch-shuffling. This would indicate that   
+118 sensitivity to shuffling is not necessarily linked to increased shape bias.   
+119 The results in Table 2 show that the basic model does not have a higher shape bias than masking   
+120 methods although it has a significantly higher DI index, as we have seen in Table 1. We repeat the   
+121 same experiment on the Tiny ImageNet [34] data set. Geirhos et al. [11] use WordNet [26] to map the   
+122 1000 categories to the 16 classes of the GST data set. A number of ImageNet categories that belong   
+123 to the 16 higher-level classes of GST are missing. For this reason, a poorer overall performance is   
+124 expected and the results could differ slightly given a better fit between the sets. Nonetheless, we find   
+125 again no significant correlation between masking augmentation and texture bias. We also include in   
+126 Table B.2 the results for BagNet models, which have smaller receptive fields and so are forced to use   
+127 more local information. Even in this case, we find a high DI for the basic model and no difference   
+128 in texture bias compared to MSDA. Thus, a model which is more affected by patch-shuffling is not   
+129 necessary more shaped-bias. In other words, models can appear to have vastly different shape bias   
+130 when evaluated on randomly rearranged patches, albeit in reality their bias is similar. The inability of   
+131 this method to account for artefacts makes it unfair and unreliable.
+
+Table 2: Accuracy of augmentation-trained ImageNet and Tiny ImageNet models on the GST data set when the label is taken to be either the shape or texture. There is no clear correlation between masking methods and low texture bias.   
+
+<table><tr><td colspan="3">ImageNet</td><td colspan="2">Tiny ImageNet</td></tr><tr><td></td><td>Shape</td><td>Texture</td><td>Shape</td><td>Texture</td></tr><tr><td>basic</td><td>20.31</td><td>53.28</td><td>10.56±0.65</td><td>26.04±1.77</td></tr><tr><td>MixUp</td><td>24.14</td><td>60.31</td><td>12.02±0.33</td><td>27.77±1.56</td></tr><tr><td>FMix</td><td>21.25</td><td>53.43</td><td>10.40±0.39</td><td>19.90±2.12</td></tr><tr><td>CutMix</td><td>1</td><td>1</td><td>10.54±0.38</td><td>23.72±2.42</td></tr></table>
+
+![](images/90d416994389419c06e2ed3c99f10e5e22c66a3a72e7c7adbbcc7f6219c23af3.jpg)  
+Figure 2: Difference in incorrect predictions on CIFAR-10 for the basic model.
+
+# 2.2 Occlusion measurement
+
+133 We want to determine whether the same issue identified in the case of shape bias evaluation applies   
+134 to occlusion robustness measures. We focus on CutOcclusion, where a rectangular black patch is   
+135 superimposed on test images and the robustness is given by the resulting accuracy. We perform   
+136 the same experiment as before, where the $D I$ index is now measured when testing on rectangle  
+137 occluded images. There is no standardised distortion when measuring CutOcclusion, with the size   
+138 and positioning of the obstructing patch varying between studies. Most often in prior art a lack of   
+139 robustness is noted for large occluders [e.g. 5, 42]. For this reason, we sample the size of the patch   
+140 from a Beta(2,1) distribution, allowing the occluding patch to lie outside the image (as it is done for   
+141 augmenting with CutMix and CutOut [7]). This allows us to capture both the cases in which either   
+142 the centre or the border area is masked out but requires a non-uniform distribution to counter for the   
+143 patches existing outside the image. We also sample from a uniform distribution where the occluder is   
+144 restricted to be positioned within the image boundaries and obtain similar results (See Appendix C.1).   
+145 Table 3 shows that a significant gap in the DI index can be identified for each of the data sets. This   
+146 indicates that some models will again be disadvantaged. We additionally find that data interference is   
+147 present for different architectures, when overlapping patches from external images or using differently   
+148 shaped masks (Appendix B.4). Thus, the result of CutOcclusion and its variants is highly dependent   
+149 on the problem at hand. That is, whether the artefacts introduced by the artificial occlusion are   
+150 salient features of the model depends on what features are naturally distinctive for the model. Just as   
+151 for randomly shuffling tiles, by occluding images using a particularly shaped patch, one implicitly   
+152 measures a model’s affinity to certain features, albeit those features might be discriminative. This   
+153 deems such methods inappropriate for fairly assessing robustness and texture bias.   
+154 A related observation was made by Hooker et al. [17] who note the pitfalls of manipulating data to   
+155 determine feature importance. They point out that when simply superimposing uniform patches over   
+156 image features, it is difficult to asses how much of the reduction in accuracy is caused by the absence   
+157 of those features and how much is due to images becoming out of distribution. To address this, the   
+158 most important features identified by an estimator are masked out both on train and test data, closing   
+159 the gap between the two sets. Hooker et al. then train and evaluate models on the newly generated   
+160 images. Unlike for interpretability methods, the subject of occlusion robustness studies is the model   
+161 itself, which makes training with a modified version of the data an inviable option. In the following   
+162 section we explore ways of overcoming this bias when measuring occlusion robustness.
+
+Table 3: DI index $( \% )$ when occluding with black patches. The highest results are given in italic and the lowest in bold. For each data set, there exists a non-negligible gap in the DI index.   
+
+<table><tr><td></td><td>basic</td><td>MixUp</td><td>FMix</td><td>CutMix</td></tr><tr><td>CIFAR-10</td><td>5.48±1.31</td><td>0.75±0.55</td><td>0.87±0.92</td><td>2.87±3.04</td></tr><tr><td>CIFAR-100</td><td>3.25±1.31</td><td>0.80±0.46</td><td>1.28±2.48</td><td>1.36±0.63</td></tr><tr><td>FashionMNIST</td><td>0.44±0.34</td><td>2.59±1.05</td><td>0.92±1.79</td><td>0.97±1.82</td></tr><tr><td>Tiny</td><td>2.40±0.82</td><td>1.88±0.61</td><td>0.47±0.41</td><td>4.62±4.93</td></tr><tr><td>Imagenet</td><td>1.28</td><td>4.50</td><td>1.02</td><td></td></tr></table>
+
+# 163 3 What are fairer alternatives?
+
+164 We propose a simple, more carefully defined measure that aims to decouple the machine’s edge bias   
+165 from the occlusion robustness, which we refer to as “interplay occlusion” (iOcclusion). Interplay   
+166 occlusion reflects the change in the interplay between performance on seen and unseen data. Formally,
+
+$$
+i O c c l u s i o n _ { i } = \left| \frac { \mathcal { A } ( \mathcal { D } _ { t r a i n } ^ { i } ) - \mathcal { A } ( \mathcal { D } _ { t e s t } ^ { i } ) } { \mathcal { A } ( \mathcal { D } _ { t r a i n } ) - \mathcal { A } ( \mathcal { D } _ { t e s t } ) } \right| ,
+$$
+
+167 where $\mathcal A ( \mathcal D )$ denotes the accuracy on a given data set $\mathcal { D }$ , and $\mathcal { D } ^ { i }$ is the data set resulting from   
+168 removing $i \%$ pixels of each image. The intuition is that on train data robust models are less sensitive   
+169 to the artefacts of the occlusion policy for small levels of occlusion, resulting in a large difference in   
+170 accuracy from that on unseen data. The performance of both train and test gets close to random as   
+171 the percentage of occluded data approaches $90 \%$ and we expect the gap to fall off quicker for less   
+172 robust models. This change in interplay is taken with respect to the generalisation gap of the model,   
+173 such that the quality of the model fit in itself does not interfere with the robustness measure.   
+174 Although iOcclusion reduces data interference, other factors have to also be considered when choosing   
+175 a masking method for computing $\mathcal { D } ^ { i }$ , such as the number of contiguous components or the amount of   
+176 salient information masked out. In this paper we choose to generate masks using Grad-CAM [30],   
+177 such that the area with most salient $\mathrm { i } \%$ pixels is covered. It must be noted that this method implicitly   
+178 assumes there could be multiple occluders and has the downside of incurring a higher environmental   
+179 cost. For this, we also experiment with using rectangular or Fourier-sampled masks and conclude   
+180 that although random masking makes the process noisier, the exact choice of masking method is of   
+181 secondary importance as long as the occluder’s granularity is accounted for. Appendix C.4 provides   
+182 discussion and results on these alternative instances of iOcclusion, as well as differences in their   
+183 carbon footprint. For a fair comparison, throughout this section we do not allow the obstructing patch   
+184 when measuring CutOcclusion to lie outside the image such that the fraction removed is exact.   
+185 Assessing the correctness of such a measure is difficult in the absence of a baseline. For the remainder   
+186 of this section we will build varied experiments to attest the validity of our method. We focus on the   
+187 key results, but include additional ones and further experiments in Appendix C. Since occlusion in   
+188 real-life scenarios could be caused by non-uniformly coloured objects, an appropriate measure must   
+189 generalise across colour patterns. When computing iOcclusion and CutOcclusion, we superimpose   
+190 patches from images belonging to a different data set and compare the results to those obtained   
+191 when occluding with black patches only. For visual clarity, Figure 3 presents the results for the   
+192 least and most robust models (see Appendix C.2 for a full comparison). For iOcclusion, using   
+193 uniform occluders gives similar results to its non-uniform version, whereas the CutOcclusion measure   
+194 provides an inconsistent model evaluation.   
+195 As we have argued, in addition to not being sensitive to the colour pattern of the patch, a fair measure   
+196 must also be invariant to the shape of the patch. To empirically confirm iOcclusion reduces the   
+197 importance of edge information, we aim to obtain a model that is robust to occlusion, but at the same   
+198 time has a high DI index (it is sensitive to edge information). To this end, we create a variation of   
+199 FMix, Random Masks (RM), where at the beginning of the training process three masks are randomly   
+200 sampled from Fourier space. For each batch, one of the three is chosen uniformly at random. While   
+201 the RM models are not sensitive to black-patch occlusion, when masking with patterned patches they   
+202 have a higher DI index than FMix, as desired. Table 4 gives results for a fraction of 0.3 pixels covered   
+203 by a non-uniform occluder. Our measure reflects the robustness of training with RM, situating it close   
+204 to other masking methods. On the other hand, because CutOcclusion implicitly penalises models   
+205 with high DI index, according to this measure RM appears almost as sensitive to occlusion as MixUp.   
+206 Figure B.4 shows results for a wider range of fractions.   
+207 Another problem that occurs when purely looking at post-masking accuracy is weaker models would   
+208 erroneously appear less robust. We show this by reversing the problem: we evaluate the same model   
+209 on two different subsets of the CIFAR-100 data set: typical and tail images as categorised by Feldman   
+210 and Zhang [10]. They consider a train-test sample pair to belong to the tail of the data distribution if   
+211 the test sample is correctly classified when a model is trained with the train sample and incorrectly   
+212 without it. CutOcclusion would indicate that models are significantly more robust to occluding typical   
+213 examples. However, a closer analysis makes us doubt this conclusion. The raw accuracy on both   
+214 train and test data for tail examples is lower than for the typical ones. In fact, the performance when   
+215 occluding images decreases at the same rate for the two subsets. By way of definition, iOcclusion   
+216 allows a fair comparison of robustness regardless of the overall performance of a model (Figure 4).   
+217 As we evidenced through controlled experiments, there are many cases that CutOcclusion does not   
+218 properly address. From a model analysis perspective, correctly assessing the occlusion robustness   
+219 could lead to better understanding and development of models and training procedures. Equally   
+220 important, it has applicability for real-world deployments where no prior knowledge exists about the
+
+![](images/e551cc1ecfbeb68fefe5795596197f7407ea4247c54f483da25a921da06b6e03.jpg)  
+Figure 3: CutOcclusion (left) and iOcclusion (right) when occluding with black patches (uniform) and patches taken from other images (nonuniform). iOcclusion gives more consistent results.
+
+Table 4: DI index $( \% )$ and occlusion robustness for models trained on CIFAR-10 when obstructing $30 \%$ of the image pixels with non-uniform patches. When measuring the robustness with CutOcclusion, RM appears significantly less robust than CutMix due to its sensitivity to patching with rectangles, while iOcclusion highlights the robustness specific to training with FMix-like masks. Given in bold is the closest result to that of RM for each evaluation.   
+
+<table><tr><td></td><td>basic</td><td>MixUp</td><td>CutMix</td><td>FMix</td><td>RM</td></tr><tr><td>DI index</td><td>1.67±0.27</td><td>1.00±0.31</td><td>0.17±0.16</td><td>0.15±0.03</td><td>0.39±0.07</td></tr><tr><td>CutOcclusion</td><td>47.97±0.52</td><td>58.65±1.01</td><td>76.56±6.36</td><td>78.00±0.45</td><td>60.79±5.03</td></tr><tr><td>iOcclusion</td><td>0.21±0.10</td><td>0.57±0.18</td><td>1.09±0.17</td><td>1.46±0.07</td><td>1.20±0.23</td></tr></table>
+
+![](images/65a8e783befee46722765dbd36fdc4b45482b8cf690fcfb225f9686c5ea7be1c.jpg)  
+Figure 4: CutOcclusion (left) and iOcclusion (right) for the basic and FMix models on two subsets of the same data set: tail and typical. Evaluating the models with iOcclusion on the two types of samples leads to mostly overlapping robustness levels. That is, they do not differ outside the margin of error. On the contrary, CutOcclusion incorrectly finds the models to be less robust on tail data.
+
+Table 5: Augmentation comparison on CIFAR-10. We consider two variants when calculating diversity. One is computing the cross-entropy loss using the label of the majority class (Diversity), as for mixing in [19]. The alternative, MixDiversity, takes a linear combination of the two cross-entropy losses.   
+Table 6: DI index $( \% )$ measured for nonuniform occlusion when training without the class with highest increase in incorrect predictions. Again, a gap can be noted, supporting the idea that data interference is not specific to peculiar cases.   
+
+<table><tr><td></td><td>Affinity</td><td>Diversity</td><td>MixDiversity</td><td></td><td>CIFAR-10</td><td>CIFAR-100</td></tr><tr><td>MixUp</td><td>-12.58±0.14</td><td>0.41±0.01</td><td>0.84±0.00</td><td>MixUp</td><td>0.39±0.15</td><td>1.22±0.19</td></tr><tr><td>FMix</td><td>-25.55±0.26</td><td>0.34±0.01</td><td>0.65±0.00</td><td>FMix</td><td>0.08±0.06</td><td>0.50±0.21</td></tr></table>
+
+possible shapes of the obstructions. While this aspect of generality is the strength of our approach, it must be stressed that when there exists a limited set of known possible occluders, evaluating robustness specifically to them could be safer. Incorrectly assessing robustness can have severe effects especially when applied to autonomous vehicles or medical imaging. We do not propose a universal solution, but rather suggest an alternative to the biased approach for the common scenario in which the environment is not controlled and little is known about all the potential occluders. However, even in this case, our metric should be taken as a guide when analysing models. Although iOcclusion aims to address data interference, since a ground-truth does not exist, it cannot be guaranteed that this method provides fair results in the absolute.
+
+230 The strength of the bias will depend on the data in question and some applications will be more heavily   
+231 affected than others. We have seen that for natural images this bias does exist. To confirm that we have   
+232 not just identified isolated cases, we remove the class that has the highest increase in mispredictions   
+233 and retrain the models on the remaining classes. We find that the bias is again present (Table 6),   
+234 but with respect to another class. For example, in the case of CIFAR-10, after removing the “Truck”   
+235 class, models mispredict rectangle-occluded images as “Boat” (Appendix D). Thus, the edge artefacts   
+236 are very likely to interfere with learnt representations since they are such fundamental features. From   
+237 an evaluation perspective, as we have seen, this impacts assessment methods and must be accounted   
+238 for. From the training perspective, such a widespread data interference of masking distortions would   
+239 indicate a large perceptual shift in the data when performing MSDA. In the following section we   
+240 investigate the importance of the artefacts in this case and their implications.
+
+# 241 4 Is the magnitude of the distribution shift important?
+
+Traditionally it was believed that a good augmentation should have minimal distribution shift. Most recently, it has been argued that it is the degree of the perceived shift that determines augmentation quality [12]. We start with the perceptual gap of training with MSDA, as proposed in Gontijo-Lopes et al. [12]. Reiterating, this is given by the difference between the performance of the baseline model when presented with original test data and augmented test data and is termed “affinity”. Subsequently,
+
+247 we address the gap in the wider sense, as is often sought in prior art. We first argue that high affinity   
+248 and high diversity are not necessarily desirable. Indeed, on CIFAR-10, we find FMix, a better   
+249 performing augmentation, to have both lower affinity and lower diversity than MixUp (Table 5). For   
+250 diversity, we compute the cross-entropy loss where the label is taken to be that of the majority class.   
+251 Similar results are obtained with the MixUp loss, where a weighted average of the true labels is taken.   
+252 While intuitively for a high level of affinity, high diversity could correspond to better methods,   
+253 the converse does not hold. We argue this is because affinity is rather an analysis of the learnt   
+254 representations of the reference model and cannot give an insight into the quality of the augmentation   
+255 or its effect on learning. The limitations of affinity are intimately linked to those of CutOcclusion.   
+256 We have seen in Section 3 that the bias of the basic model is present not only when obstructing an   
+257 image with a uniform patch, but also when mask-mixing. As such, an augmentation will have a   
+258 lower affinity if it introduces artefacts that could otherwise lead to learning better representations   
+259 when used in the training process. We believe this issue extends to other approaches that aim to   
+260 motivate the success of MSDA through reduced distribution shift. Henceforth, we focus on bringing   
+261 further supporting evidence that the importance lies in the invariance introduced by the shift and its   
+262 interaction with the given problem rather than its magnitude.
+
+# 263 4.1 If it is not the magnitude that matters, is it the direction?
+
+264 We use empirical evidence to argue against previous assumptions behind the success of MSDA and   
+265 propose the study of introduced bias as a more informative research direction. Here we use the term   
+266 “bias” to refer to a drift in the learnt representations introduced by the change in the training procedure.   
+267 A fundamental difference to classical training is that in the case of augmentation the samples are no   
+268 longer independent. Mixed-sampling takes this even further. An immediate question is, does the   
+269 added correlation lead to more meaningful representations? It is claimed that the strength of MixUp   
+270 lies in causing the model to behave linearly between two images [40] or in pushing the examples   
+271 towards their mean [3]. Both of these claims rely on the combined images to be generated from the   
+272 same distribution. We want to verify to which extent this is necessary for a successful augmentation.
+
+It has been argued that label mixing has a negligible effect on the final model performance [19, 18, 14, 24]. We use the reformulated objective setting [18, 14], where targets are not mixed and the mixing coefficient is drawn from an imbalanced Beta distribution. This allows us to apply MSDA between data sets. Thus, for training a model on a data set, we use an additional one whose targets will be ignored. As an example, a model that is learning to predict CIFAR-10 images will be trained on a combination of CIFAR-10 and CIFAR-100 images, with the target of the former. This scenario breaks the added correlation between training examples. Note that when mixing between data sets we use the same procedure as when performing regular MSDA, without improving the process.
+
+281 Table 7 contains the results of this experiment, showing that an accuracy similar to or better than that   
+282 of regular MSDA can be obtained by performing inter-dataset MSDA.This invalidates the argument   
+283 that the power of MixUp resides in causing the model to act linearly between samples. Another   
+284 observation is that for FMix and MixUp, introducing elements from CIFAR-100 when training   
+285 models on the CIFAR-10 problem does not harm the learning process. The reciprocal, however, does   
+286 not hold. Hence, the “distribution shift” is more intimately linked to the problem at hand and aiming   
+287 to characterise an augmentation based on the distance from the original distribution is a limiting   
+288 approach, especially when the distance is measured as perceived by a reference model.   
+289 We believe an explanation is that the artefacts created when putting together images from CIFAR-10   
+290 with those of CIFAR-100 could introduce information that makes the separation of the 10 classes   
+291 easier. However, if the information happens to interfere with a feature that is important for separating   
+292 the CIFAR-100 categories, the performance could degrade on this data set. This singular experiment   
+293 is not sufficient to draw any general conclusions. However, it does show that shifting two distributions   
+294 by the same amount can have different effects on the model performance. Thus, the specifics of the   
+295 bias introduced could be more important than its magnitude. While some level of data similarity has   
+296 to be preserved when performing MSDA, it is far from being the objective of such data-distorting   
+297 approaches which, as we will argue further, should be rather seen as forms of regularisation.   
+298 We have seen that for all considered data sets, artefacts introduced by masking methods seem to   
+299 overlap with common features. This has led us to believe that MSDA training could help bypass   
+300 some of the simplicity bias. The simplicity bias refers to the tendency of deep models to find simple   
+301 representations and has been used to justify the success of deep models [28, 36]. Recent research   
+302 shows that this propensity causes models to ignore complex features that explain the data well in   
+303 favour of elementary features, even when they lead to worse performance [31, 16].
+
+Table 7: Accuracy on CIFAR-10 (left) and CIFAR-100 (right) upon mixing with samples from a different data set. The baseline is the accuracy when training with a single data set using the reformulated objective. In the interest of space, CIFAR-110 is used to refer to mixing with CIFAR100 when training on the CIFAR-10 problem and vice-versa.   
+
+<table><tr><td></td><td>MixUp</td><td>FMix</td><td>CutMix</td><td>MixUp</td><td>FMix</td><td>CutMix</td></tr><tr><td>baseline</td><td>94.18±0.34</td><td>94.36±0.28</td><td>94.67±0.20</td><td>74.68±0.37</td><td>75.75±0.31</td><td>74.19±0.50</td></tr><tr><td>CIFAR-110</td><td>94.70±0.27</td><td>94.80±0.32</td><td>94.66±0.12</td><td>72.36±1.04</td><td>74.80±0.55</td><td>74.47±0.39</td></tr><tr><td>Fashion</td><td>92.28±0.28</td><td>95.03±0.10</td><td>94.61±0.19</td><td>66.40±1.86</td><td>74.46±0.57</td><td>74.06±0.28</td></tr></table>
+
+Although it could seem natural that since MSDAs are not augmentations in the VRM sense, they will increase the complexity of the problem, we design an experiment to support this claim. Similarly to Shah et al. [31], we combine CIFAR-10 and MNIST [23] samples. Since they have the same number of classes, we can easily associate each class of one data set with a corresponding one from the other. Thus, we stack a padded image from the $k$ th class of MNIST on top of a sample from the kth class of CIFAR-10, such that a $3 \times 6 4 \times 3 2$ image is obtained. We then randomly combine the test images and separately compute the accuracy with respect to the targets of each data set.
+
+311 The predictions with respect to the CIFAR-10 labels are no better than random $( 1 0 . 0 4 _ { \pm 0 . 1 1 } )$ , while   
+312 the accuracy with respect to the MNIST images remains high $( 9 9 . 5 7 _ { \pm 0 . 7 2 } )$ . Thus, models trained   
+313 on this combination are mostly relying on MNIST images to make predictions. Similar behaviours   
+314 have previously been associated with simplicity bias. Subsequently, when training, we perform FMix   
+315 only on MNIST images and observe that this is enough to reverse the results. Evaluating against the   
+316 CIFAR-10 label gives an accuracy of $8 6 . 6 0 _ { \pm 0 . 3 4 }$ , while testing against the MNIST label only gives   
+317 $1 1 . 6 1 _ { \pm 0 . 3 0 }$ . We find that this also holds true for the other MSDAs. Thus, performing these distortions   
+318 on the simpler data set increases its complexity to the point where it surpasses that of CIFAR-10.   
+319 Previously, we presented evidence that masking MSDA does not necessarily promote learning neither   
+320 more shape nor texture information. In the light of this fact along with the results from this section,   
+321 we believe image distortions force the model to learn more complex both shape and texture-specific   
+322 features. Thus, in this paper we pointed out that the shift in learnt representations can lead to better   
+323 models and simply quantifying the distribution shift can be misleading. An open question remains:   
+324 How can we better capture the bias that is introduced and its quality? We believe understanding how   
+325 a relatively small change in the data distribution impacts learnt representations could lead the way to   
+326 characterising the relationship between data and model generalisation.
+
+# 327 5 Conclusions
+
+328 Distorting data is such a commonplace procedure, yet little effort has been devoted to investigating its   
+329 broader effects. This is particularly problematic when image modifications are applied in analyses. We   
+330 show a number of cases in which this leads to biased results. For occlusion robustness measurement,   
+331 we propose an alternative. The insights we gain from this endeavour point towards the study of data   
+332 characteristics as a cornerstone of our understanding and raise a number of questions about mixed   
+333 sample data augmentation, on which we subsequently focus. We note that they interfere with features   
+334 that are consistently found across a number of data sets and conclude that the methods commonly   
+335 used are forms of mixed sample regularisation rather than augmentation. A limitation of previous   
+336 studies that aim to explain their success is the focus on trying to argue similarity with original data,   
+337 rather than explaining the bias introduced by the distortion. Correctly interpreting it is important   
+338 not only for making the models trustable but also for injecting more informed prior knowledge in   
+339 future applications. Beyond their practical benefits, we believe MSDAs have the potential to help   
+340 characterise the interplay between data and learnt representations. Overall, the purpose of our paper   
+341 is to encourage better practice when dealing with all forms of data distortions.
+
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+
+# Checklist
+
+1. For all authors...
+
+(a) Do the main claims made in the abstract and introduction accurately reflect the paper’s contributions and scope? [Yes] (b) Did you describe the limitations of your work? [Yes] See lines 174–184, 221–229,   
+292–294. (c) Did you discuss any potential negative societal impacts of your work? [Yes] See lines   
+221–229 as well as 89–93 and Appendix C.4. (d) Have you read the ethics review guidelines and ensured that your paper conforms to them? [Yes]
+
+2. If you are including theoretical results...
+
+(a) Did you state the full set of assumptions of all theoretical results? [N/A] (b) Did you include complete proofs of all theoretical results? [N/A]
+
+3. If you ran experiments...
+
+(a) Did you include the code, data, and instructions needed to reproduce the main experimental results (either in the supplemental material or as a URL)? [Yes]   
+(b) Did you specify all the training details (e.g., data splits, hyperparameters, how they were chosen)? [Yes] See Appendix A.   
+(c) Did you report error bars (e.g., with respect to the random seed after running experiments multiple times)? [Yes] The only exception is when using publicly available models, as mentioned in Section 2.   
+(d) Did you include the total amount of compute and the type of resources used (e.g., type of GPUs, internal cluster, or cloud provider)? [Yes] See Appendix A.
+
+4. If you are using existing assets (e.g., code, data, models) or curating/releasing new assets...
+
+(a) If your work uses existing assets, did you cite the creators? [Yes] See lines 84–93 and Appendix A.   
+(b) Did you mention the license of the assets? [N/A]   
+(c) Did you include any new assets either in the supplemental material or as a URL? [N/A]   
+(d) Did you discuss whether and how consent was obtained from people whose data you’re using/curating? [N/A]   
+(e) Did you discuss whether the data you are using/curating contains personally identifiable information or offensive content? [N/A]
+
+5. If you used crowdsourcing or conducted research with human subjects...
+
+(a) Did you include the full text of instructions given to participants and screenshots, if applicable? [N/A]   
+(b) Did you describe any potential participant risks, with links to Institutional Review Board (IRB) approvals, if applicable? [N/A]   
+(c) Did you include the estimated hourly wage paid to participants and the total amount spent on participant compensation? [N/A]

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+        "text": "1 Data modification can introduce artificial information. It is often assumed that   \n2 the resulting artefacts are detrimental to training, whilst being negligible when   \n3 analysing models. We investigate these assumptions and conclude that in some   \n4 cases they are unfounded and lead to incorrect results. Specifically, we show current   \n5 shape bias identification methods and occlusion robustness measures are biased   \n6 and propose a fairer alternative for the latter. Subsequently, through a series of   \n7 experiments we seek to correct and strengthen the community’s perception of how   \n8 distorting data affects learning. Based on our empirical results we argue that the   \n9 impact of the artefacts must be understood and exploited rather than eliminated. ",
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+        "text": "10 1 Motivation ",
+        "text_level": 1,
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+        "text": "11 Modifying data has become commonplace both when training and analysing models, yet the wider   \n12 implications are often disregarded. We delve into some of the side-effects and point out that this   \n13 practice has resulted in the creation of biased model interpretation tools and poorly informed theories.   \n14 On the analysis side, we take as examples occlusion robustness and shape bias identification methods.   \n15 On the training side, we focus on some instances of Mixed Sample Data Augmentation (MSDA),   \n16 where two images are combined to obtain a new training sample. Visual examples of each can   \n17 be found in Figure 1. In this paper we study a number of assumptions that lie at the heart of the   \n18 aforementioned methods, which we briefly introduce below.   \n19 Shape-texture bias: Deep models are known to be sensitive to interventions that are imperceptible   \n20 to humans [35, 13], as well as to other forms of distribution shifts [1, 6, 8]. It has been argued that   \n21 this is intimately linked to networks tending to use texture rather than shape information [2, 11].   \n22 Recently, input distortions have become a popular way of assessing a model’s texture bias. To this end,   \n23 images are divided into a grid and the resulting patches are randomly shuffled such that information   \n24 is preserved locally, while the global shape is altered [32, 27, 25, 41]. It is implicitly assumed that   \n25 patch-shuffling does not introduce misleading shape or texture that could affect model evaluation.   \n26 Occlusion robustness: A widely adopted method for measuring occlusion robustness is through the   \n27 accuracy obtained after superimposing a rectangular patch on an image [5, 9, 39, 42, 20]. We refer   \n28 to this approach as CutOcclusion throughout the paper. Just as for shape bias, this method relies on   \n29 information introduced not to interfere with a model’s learnt representations such that a decrease in   \n30 performance can be directly attributed to lack of robustness.   \n31 Data augmentation studies: In statistical learning, training with augmented data is termed Vicinal   \n32 Risk Minimisation (VRM) [37, 4] and it is seen as injecting prior knowledge about the neighbourhood   \n33 of the data samples. The intuition behind augmentation caused researchers to interpret its effect   \n34 through the similarity between original and augmented data distributions. This perspective is often   \n35 challenged by methods which, despite generating samples that do not appear to fall under the   \n36 distribution of natural images, lead to strong learners. Gontijo-Lopes et al. [12] argue it is the   \n37 perceived distribution shift that needs to be minimised, while maximising the sample vicinity.   \n38 Formalising these concepts, they introduce augmentation “diversity” and “affinity”. Diversity is   \n39 defined as the training loss when learning with artificial samples, while affinity quantifies the   \n40 difference between the accuracy on original test data and augmented test data for a reference model.   \n41 The latter penalises augmentations that introduce artificial information to which the model is not   \n42 invariant, implicitly assuming that training with that information is detrimental to generalisation.   \n43 In summary, it is currently assumed that the artefacts introduced by changes in the data are negligible   \n44 when evaluating models, while those introduced when training are important and undesirable. Does   \n45 the artificial information added by analysis methods not have major side-effects or does it lead to   \n46 biased results? Conversely, are the artefacts important when training with modified data? Do they   \n47 cause models to learn better or worse representations?   \n48 We set out to answer these questions and find that when the secondary effects of data manipulation   \n49 are not accounted for, results can be misleading, especially in comparative studies. Subsequently, we   \n50 construct empirical counter-examples which disprove common beliefs in the literature and highlight   \n51 the importance of understanding the changes MSDAs introduce. Our contributions are: ",
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+            "Figure 1: Examples of image distortions. For test-time distortions (Occlusion and Shuffled grid) only Image 1 was used. For mixing augmentations, the first row was generated with a mixing factor of 0.2, while the second one with 0.5. "
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+        "text": "• We show that increasingly popular model interpretation and analysis methods are biased, relying on unfounded assumptions (Section 2);   \n• For measuring occlusion robustness, we propose a fairer alternative (Section 3);   \n• We show that, in contrast to what is widely assumed, not preserving the data distribution can lead to learning better representations (Section 4). ",
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+        "text": "58 To verify whether distorting data at evaluation time could have side-effects previously not considered,   \n59 we look at the increase in misclassifications per category. That is, from the number of incorrect   \n60 predictions of a model evaluated on modified data, we subtract the incorrect predictions when testing   \n61 on original data. If there is a significant increase for a specific class, it indicates that the distortion   \n62 introduces features the model associates with that class. We refer to this phenomenon as “data   \n63 interference”. Considering only positive differences, we denote the increase in the percentage of   \n64 misclassifications for class $c$ of a given model $m$ by $i _ { c } ^ { m }$ . We define the Data Interference $D I$ index as ",
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+        "text": "$$\nD I = \\frac { i _ { c _ { m a x } } } { \\sum _ { c } i _ { c } } i _ { c _ { m a x } } ,\n$$",
+        "text_format": "latex",
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+        "text": "65 where $c _ { m a x }$ is the class with highest mean increase across all runs. The $D I$ index measures the   \n66 percentage represented by the dominant class $c _ { m a x }$ weighted by its increase. A high index value   \n67 indicates a sharp increase for a particular class which is consistent across runs. We associate this with   \n68 an overlap between introduced artefacts and learnt representations. In Appendix B.1 we experiment   \n69 with an alternative index, where we weight by the highest increase of a model across the 5 runs, so as   \n70 to obtain a worst-case analysis. As expected, we observe a more accentuated bias in this case.   \n71 To obtain models with different behaviours in a controlled manner, we make use of data augmentation.   \n72 Since it is sufficient to identify some common cases in which models are disfavoured, we choose to   \n73 reduce our environmental impact by restricting the analysis to simple MSDAs that combine images   \n74 without incurring additional computation time or external models. As will be argued in Section 3, we   \n75 expect the unfairness to be present in most settings, thus the exact choice of augmentation is irrelevant.   \n76 We focus on two popular MSDAs, MixUp [40] and CutMix [39]. MixUp linearly interpolates between   \n77 two images to obtain a new training example, while CutMix masks out a rectangular region of an   \n78 image with the corresponding region of another image. Besides the aforementioned methods, we   \n79 also employ FMix due to its irregularly shaped masks sampled from Fourier space, which will play   \n80 an important role in our analysis. Note that although the masking methods sample the size of the   \n81 occluding patch from the same distribution, in CutMix part of the rectangle can be outside the image,   \n82 which leads to less occluded samples overall. We refer to models by the augmentations they were   \n83 trained with and use “basic” to label the models trained without MSDA.   \n84 Throughout the paper, we do 5 runs of each experiment with PreAct-ResNet18 [15] as the default   \n85 architecture. We include results for BagNet [2] and VGG [33] in the Appendices. The main data sets   \n86 we report results on are CIFAR-10/100 [21], Tiny ImageNet [34], FashionMNIST [38], ImageNet [29].   \n87 For ImageNet we use pretrained ResNet-101 models made publicly available by Harris et al. [14].   \n88 Note that the only experiments for which we are unable to run repeats are those on ImageNet, since   \n89 only one model per augmentation is provided. For full experimental details, see Appendix A. Total   \n90 emissions of training the models evaluated in this paper are estimated [22] to be $3 8 . 0 7 \\mathrm { k g C O _ { 2 } e q }$ , to   \n91 which $1 3 . 1 1 \\mathrm { k g C O _ { 2 } e q }$ more are added during the analysis. The hope is that our findings will lead to a   \n92 better understanding which in the long run would help reduce erroneous research directions without   \n93 needing to empirically disprove them, lessening the future carbon footprint of the community. ",
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+        "table_caption": [
+            "Table 1: DI index $( \\% )$ for PreAct-ResNet18 on grid-shuffled images for four different types of models. Results with the highest average are given in italic and the lowest in bold. Information introduced when shuffling tends to interfere less with the representations of FMix and CutMix models. "
+        ],
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+        "table_body": "<table><tr><td></td><td>basic</td><td>MixUp</td><td>FMix</td><td>CutMix</td></tr><tr><td>CIFAR-10</td><td>2.90±1.10</td><td>2.54±1.29</td><td>0.60±0.26</td><td>0.33±0.17</td></tr><tr><td>CIFAR-100</td><td>1.05±0.59</td><td>0.93±0.44</td><td>0.23±0.29</td><td>0.11±0.10</td></tr><tr><td>FashionMNIST</td><td>1.12±0.63</td><td>2.73±1.64</td><td>1.12±0.61</td><td>0.70±0.22</td></tr><tr><td>Tiny ImageNet</td><td>2.58±4.73</td><td>0.54±0.27</td><td>0.38±0.12</td><td>0.14±0.12</td></tr><tr><td>ImageNet</td><td>0.82</td><td>1.49</td><td>0.58</td><td>1</td></tr></table>",
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+        "type": "text",
+        "text": "94 2.1 Shape bias ",
+        "text_level": 1,
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+        "text": "95 For assessing shape bias through sample manipulation, the standard procedure is to choose between   \n96 dividing the image in 4, 16 or 64 patches to be shuffled. Since FashionMNIST images are smaller,   \n97 we choose a $2 \\times 2$ grid, for CIFAR-10/100 and Tiny ImageNet $4 \\times 4$ , while for ImageNet we use   \n98 an $8 \\times 8$ grid. However, similar results are obtained for different grid sizes (Appendix B.2). The   \n99 large DI index in Table 1 indicates that either basic or MixUp models tend to associate the features   \n100 artificially introduced by patch-shuffling with a certain class. We take a closer look at the distribution   \n101 of misclassifications for CIFAR-10 and notice that the basic model tends to wrongly predict the class   \n102 “Truck” (Figure 2). This is not at all surprising, given that the strong horizontal and vertical edges are   \n103 highly indicative of this class. Similar observations can be made for other data sets (Appendix B.3).   \n104 Thus, we believe the grid-shuffling approach is causing models which are not invariant to strong   \n105 horizontal and vertical edges to appear to rely more heavily on shape information. A model not   \n106 affected by this transformation could be considered texture-biased if we accept the larger definition   \n107 of texture as local information. However, there is a question about the extent to which the reciprocal   \n108 is true; A model can be invariant to the aforementioned edges because it is indeed relying on texture   \n109 information or simply because it uses different shape-related features.   \n110 Is a model necessarily more affected by patch-shuffling if it has a higher shape bias? To answer   \n111 this question, we can use another method of determining shape and texture bias to find a counter  \n112 example. We analyse the ImageNet models on the Geirhos Style-Transfer (GST) [11] data set. GST   \n113 contains artificially generated images where the shape belongs to one class and the texture to another.   \n114 There are 16 coarse classes that encompass a number of ImageNet categories to which they are   \n115 mapped. The bias of the models is given by the accuracy obtained when the label is set to either the   \n116 shape or texture. Using this well-known method of identifying shape bias we want to find models   \n117 which have similar biases but different DI indices when patch-shuffling. This would indicate that   \n118 sensitivity to shuffling is not necessarily linked to increased shape bias.   \n119 The results in Table 2 show that the basic model does not have a higher shape bias than masking   \n120 methods although it has a significantly higher DI index, as we have seen in Table 1. We repeat the   \n121 same experiment on the Tiny ImageNet [34] data set. Geirhos et al. [11] use WordNet [26] to map the   \n122 1000 categories to the 16 classes of the GST data set. A number of ImageNet categories that belong   \n123 to the 16 higher-level classes of GST are missing. For this reason, a poorer overall performance is   \n124 expected and the results could differ slightly given a better fit between the sets. Nonetheless, we find   \n125 again no significant correlation between masking augmentation and texture bias. We also include in   \n126 Table B.2 the results for BagNet models, which have smaller receptive fields and so are forced to use   \n127 more local information. Even in this case, we find a high DI for the basic model and no difference   \n128 in texture bias compared to MSDA. Thus, a model which is more affected by patch-shuffling is not   \n129 necessary more shaped-bias. In other words, models can appear to have vastly different shape bias   \n130 when evaluated on randomly rearranged patches, albeit in reality their bias is similar. The inability of   \n131 this method to account for artefacts makes it unfair and unreliable. ",
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+            "Table 2: Accuracy of augmentation-trained ImageNet and Tiny ImageNet models on the GST data set when the label is taken to be either the shape or texture. There is no clear correlation between masking methods and low texture bias. "
+        ],
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+        "table_body": "<table><tr><td colspan=\"3\">ImageNet</td><td colspan=\"2\">Tiny ImageNet</td></tr><tr><td></td><td>Shape</td><td>Texture</td><td>Shape</td><td>Texture</td></tr><tr><td>basic</td><td>20.31</td><td>53.28</td><td>10.56±0.65</td><td>26.04±1.77</td></tr><tr><td>MixUp</td><td>24.14</td><td>60.31</td><td>12.02±0.33</td><td>27.77±1.56</td></tr><tr><td>FMix</td><td>21.25</td><td>53.43</td><td>10.40±0.39</td><td>19.90±2.12</td></tr><tr><td>CutMix</td><td>1</td><td>1</td><td>10.54±0.38</td><td>23.72±2.42</td></tr></table>",
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+        "image_caption": [
+            "Figure 2: Difference in incorrect predictions on CIFAR-10 for the basic model. "
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+        "text": "2.2 Occlusion measurement ",
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+        "text": "133 We want to determine whether the same issue identified in the case of shape bias evaluation applies   \n134 to occlusion robustness measures. We focus on CutOcclusion, where a rectangular black patch is   \n135 superimposed on test images and the robustness is given by the resulting accuracy. We perform   \n136 the same experiment as before, where the $D I$ index is now measured when testing on rectangle  \n137 occluded images. There is no standardised distortion when measuring CutOcclusion, with the size   \n138 and positioning of the obstructing patch varying between studies. Most often in prior art a lack of   \n139 robustness is noted for large occluders [e.g. 5, 42]. For this reason, we sample the size of the patch   \n140 from a Beta(2,1) distribution, allowing the occluding patch to lie outside the image (as it is done for   \n141 augmenting with CutMix and CutOut [7]). This allows us to capture both the cases in which either   \n142 the centre or the border area is masked out but requires a non-uniform distribution to counter for the   \n143 patches existing outside the image. We also sample from a uniform distribution where the occluder is   \n144 restricted to be positioned within the image boundaries and obtain similar results (See Appendix C.1).   \n145 Table 3 shows that a significant gap in the DI index can be identified for each of the data sets. This   \n146 indicates that some models will again be disadvantaged. We additionally find that data interference is   \n147 present for different architectures, when overlapping patches from external images or using differently   \n148 shaped masks (Appendix B.4). Thus, the result of CutOcclusion and its variants is highly dependent   \n149 on the problem at hand. That is, whether the artefacts introduced by the artificial occlusion are   \n150 salient features of the model depends on what features are naturally distinctive for the model. Just as   \n151 for randomly shuffling tiles, by occluding images using a particularly shaped patch, one implicitly   \n152 measures a model’s affinity to certain features, albeit those features might be discriminative. This   \n153 deems such methods inappropriate for fairly assessing robustness and texture bias.   \n154 A related observation was made by Hooker et al. [17] who note the pitfalls of manipulating data to   \n155 determine feature importance. They point out that when simply superimposing uniform patches over   \n156 image features, it is difficult to asses how much of the reduction in accuracy is caused by the absence   \n157 of those features and how much is due to images becoming out of distribution. To address this, the   \n158 most important features identified by an estimator are masked out both on train and test data, closing   \n159 the gap between the two sets. Hooker et al. then train and evaluate models on the newly generated   \n160 images. Unlike for interpretability methods, the subject of occlusion robustness studies is the model   \n161 itself, which makes training with a modified version of the data an inviable option. In the following   \n162 section we explore ways of overcoming this bias when measuring occlusion robustness. ",
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+        "table_caption": [
+            "Table 3: DI index $( \\% )$ when occluding with black patches. The highest results are given in italic and the lowest in bold. For each data set, there exists a non-negligible gap in the DI index. "
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td></td><td>basic</td><td>MixUp</td><td>FMix</td><td>CutMix</td></tr><tr><td>CIFAR-10</td><td>5.48±1.31</td><td>0.75±0.55</td><td>0.87±0.92</td><td>2.87±3.04</td></tr><tr><td>CIFAR-100</td><td>3.25±1.31</td><td>0.80±0.46</td><td>1.28±2.48</td><td>1.36±0.63</td></tr><tr><td>FashionMNIST</td><td>0.44±0.34</td><td>2.59±1.05</td><td>0.92±1.79</td><td>0.97±1.82</td></tr><tr><td>Tiny</td><td>2.40±0.82</td><td>1.88±0.61</td><td>0.47±0.41</td><td>4.62±4.93</td></tr><tr><td>Imagenet</td><td>1.28</td><td>4.50</td><td>1.02</td><td></td></tr></table>",
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+        "type": "text",
+        "text": "163 3 What are fairer alternatives? ",
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+        "text": "164 We propose a simple, more carefully defined measure that aims to decouple the machine’s edge bias   \n165 from the occlusion robustness, which we refer to as “interplay occlusion” (iOcclusion). Interplay   \n166 occlusion reflects the change in the interplay between performance on seen and unseen data. Formally, ",
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+        "text": "$$\ni O c c l u s i o n _ { i } = \\left| \\frac { \\mathcal { A } ( \\mathcal { D } _ { t r a i n } ^ { i } ) - \\mathcal { A } ( \\mathcal { D } _ { t e s t } ^ { i } ) } { \\mathcal { A } ( \\mathcal { D } _ { t r a i n } ) - \\mathcal { A } ( \\mathcal { D } _ { t e s t } ) } \\right| ,\n$$",
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+        "text": "167 where $\\mathcal A ( \\mathcal D )$ denotes the accuracy on a given data set $\\mathcal { D }$ , and $\\mathcal { D } ^ { i }$ is the data set resulting from   \n168 removing $i \\%$ pixels of each image. The intuition is that on train data robust models are less sensitive   \n169 to the artefacts of the occlusion policy for small levels of occlusion, resulting in a large difference in   \n170 accuracy from that on unseen data. The performance of both train and test gets close to random as   \n171 the percentage of occluded data approaches $90 \\%$ and we expect the gap to fall off quicker for less   \n172 robust models. This change in interplay is taken with respect to the generalisation gap of the model,   \n173 such that the quality of the model fit in itself does not interfere with the robustness measure.   \n174 Although iOcclusion reduces data interference, other factors have to also be considered when choosing   \n175 a masking method for computing $\\mathcal { D } ^ { i }$ , such as the number of contiguous components or the amount of   \n176 salient information masked out. In this paper we choose to generate masks using Grad-CAM [30],   \n177 such that the area with most salient $\\mathrm { i } \\%$ pixels is covered. It must be noted that this method implicitly   \n178 assumes there could be multiple occluders and has the downside of incurring a higher environmental   \n179 cost. For this, we also experiment with using rectangular or Fourier-sampled masks and conclude   \n180 that although random masking makes the process noisier, the exact choice of masking method is of   \n181 secondary importance as long as the occluder’s granularity is accounted for. Appendix C.4 provides   \n182 discussion and results on these alternative instances of iOcclusion, as well as differences in their   \n183 carbon footprint. For a fair comparison, throughout this section we do not allow the obstructing patch   \n184 when measuring CutOcclusion to lie outside the image such that the fraction removed is exact.   \n185 Assessing the correctness of such a measure is difficult in the absence of a baseline. For the remainder   \n186 of this section we will build varied experiments to attest the validity of our method. We focus on the   \n187 key results, but include additional ones and further experiments in Appendix C. Since occlusion in   \n188 real-life scenarios could be caused by non-uniformly coloured objects, an appropriate measure must   \n189 generalise across colour patterns. When computing iOcclusion and CutOcclusion, we superimpose   \n190 patches from images belonging to a different data set and compare the results to those obtained   \n191 when occluding with black patches only. For visual clarity, Figure 3 presents the results for the   \n192 least and most robust models (see Appendix C.2 for a full comparison). For iOcclusion, using   \n193 uniform occluders gives similar results to its non-uniform version, whereas the CutOcclusion measure   \n194 provides an inconsistent model evaluation.   \n195 As we have argued, in addition to not being sensitive to the colour pattern of the patch, a fair measure   \n196 must also be invariant to the shape of the patch. To empirically confirm iOcclusion reduces the   \n197 importance of edge information, we aim to obtain a model that is robust to occlusion, but at the same   \n198 time has a high DI index (it is sensitive to edge information). To this end, we create a variation of   \n199 FMix, Random Masks (RM), where at the beginning of the training process three masks are randomly   \n200 sampled from Fourier space. For each batch, one of the three is chosen uniformly at random. While   \n201 the RM models are not sensitive to black-patch occlusion, when masking with patterned patches they   \n202 have a higher DI index than FMix, as desired. Table 4 gives results for a fraction of 0.3 pixels covered   \n203 by a non-uniform occluder. Our measure reflects the robustness of training with RM, situating it close   \n204 to other masking methods. On the other hand, because CutOcclusion implicitly penalises models   \n205 with high DI index, according to this measure RM appears almost as sensitive to occlusion as MixUp.   \n206 Figure B.4 shows results for a wider range of fractions.   \n207 Another problem that occurs when purely looking at post-masking accuracy is weaker models would   \n208 erroneously appear less robust. We show this by reversing the problem: we evaluate the same model   \n209 on two different subsets of the CIFAR-100 data set: typical and tail images as categorised by Feldman   \n210 and Zhang [10]. They consider a train-test sample pair to belong to the tail of the data distribution if   \n211 the test sample is correctly classified when a model is trained with the train sample and incorrectly   \n212 without it. CutOcclusion would indicate that models are significantly more robust to occluding typical   \n213 examples. However, a closer analysis makes us doubt this conclusion. The raw accuracy on both   \n214 train and test data for tail examples is lower than for the typical ones. In fact, the performance when   \n215 occluding images decreases at the same rate for the two subsets. By way of definition, iOcclusion   \n216 allows a fair comparison of robustness regardless of the overall performance of a model (Figure 4).   \n217 As we evidenced through controlled experiments, there are many cases that CutOcclusion does not   \n218 properly address. From a model analysis perspective, correctly assessing the occlusion robustness   \n219 could lead to better understanding and development of models and training procedures. Equally   \n220 important, it has applicability for real-world deployments where no prior knowledge exists about the ",
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+        "image_caption": [
+            "Figure 3: CutOcclusion (left) and iOcclusion (right) when occluding with black patches (uniform) and patches taken from other images (nonuniform). iOcclusion gives more consistent results. "
+        ],
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+        "table_caption": [
+            "Table 4: DI index $( \\% )$ and occlusion robustness for models trained on CIFAR-10 when obstructing $30 \\%$ of the image pixels with non-uniform patches. When measuring the robustness with CutOcclusion, RM appears significantly less robust than CutMix due to its sensitivity to patching with rectangles, while iOcclusion highlights the robustness specific to training with FMix-like masks. Given in bold is the closest result to that of RM for each evaluation. "
+        ],
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+        "table_body": "<table><tr><td></td><td>basic</td><td>MixUp</td><td>CutMix</td><td>FMix</td><td>RM</td></tr><tr><td>DI index</td><td>1.67±0.27</td><td>1.00±0.31</td><td>0.17±0.16</td><td>0.15±0.03</td><td>0.39±0.07</td></tr><tr><td>CutOcclusion</td><td>47.97±0.52</td><td>58.65±1.01</td><td>76.56±6.36</td><td>78.00±0.45</td><td>60.79±5.03</td></tr><tr><td>iOcclusion</td><td>0.21±0.10</td><td>0.57±0.18</td><td>1.09±0.17</td><td>1.46±0.07</td><td>1.20±0.23</td></tr></table>",
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+        "image_caption": [
+            "Figure 4: CutOcclusion (left) and iOcclusion (right) for the basic and FMix models on two subsets of the same data set: tail and typical. Evaluating the models with iOcclusion on the two types of samples leads to mostly overlapping robustness levels. That is, they do not differ outside the margin of error. On the contrary, CutOcclusion incorrectly finds the models to be less robust on tail data. "
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+        "table_caption": [
+            "Table 5: Augmentation comparison on CIFAR-10. We consider two variants when calculating diversity. One is computing the cross-entropy loss using the label of the majority class (Diversity), as for mixing in [19]. The alternative, MixDiversity, takes a linear combination of the two cross-entropy losses. ",
+            "Table 6: DI index $( \\% )$ measured for nonuniform occlusion when training without the class with highest increase in incorrect predictions. Again, a gap can be noted, supporting the idea that data interference is not specific to peculiar cases. "
+        ],
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+        "table_body": "<table><tr><td></td><td>Affinity</td><td>Diversity</td><td>MixDiversity</td><td></td><td>CIFAR-10</td><td>CIFAR-100</td></tr><tr><td>MixUp</td><td>-12.58±0.14</td><td>0.41±0.01</td><td>0.84±0.00</td><td>MixUp</td><td>0.39±0.15</td><td>1.22±0.19</td></tr><tr><td>FMix</td><td>-25.55±0.26</td><td>0.34±0.01</td><td>0.65±0.00</td><td>FMix</td><td>0.08±0.06</td><td>0.50±0.21</td></tr></table>",
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+        "text": "possible shapes of the obstructions. While this aspect of generality is the strength of our approach, it must be stressed that when there exists a limited set of known possible occluders, evaluating robustness specifically to them could be safer. Incorrectly assessing robustness can have severe effects especially when applied to autonomous vehicles or medical imaging. We do not propose a universal solution, but rather suggest an alternative to the biased approach for the common scenario in which the environment is not controlled and little is known about all the potential occluders. However, even in this case, our metric should be taken as a guide when analysing models. Although iOcclusion aims to address data interference, since a ground-truth does not exist, it cannot be guaranteed that this method provides fair results in the absolute. ",
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+        "text": "230 The strength of the bias will depend on the data in question and some applications will be more heavily   \n231 affected than others. We have seen that for natural images this bias does exist. To confirm that we have   \n232 not just identified isolated cases, we remove the class that has the highest increase in mispredictions   \n233 and retrain the models on the remaining classes. We find that the bias is again present (Table 6),   \n234 but with respect to another class. For example, in the case of CIFAR-10, after removing the “Truck”   \n235 class, models mispredict rectangle-occluded images as “Boat” (Appendix D). Thus, the edge artefacts   \n236 are very likely to interfere with learnt representations since they are such fundamental features. From   \n237 an evaluation perspective, as we have seen, this impacts assessment methods and must be accounted   \n238 for. From the training perspective, such a widespread data interference of masking distortions would   \n239 indicate a large perceptual shift in the data when performing MSDA. In the following section we   \n240 investigate the importance of the artefacts in this case and their implications. ",
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+        "type": "text",
+        "text": "241 4 Is the magnitude of the distribution shift important? ",
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+        "text": "Traditionally it was believed that a good augmentation should have minimal distribution shift. Most recently, it has been argued that it is the degree of the perceived shift that determines augmentation quality [12]. We start with the perceptual gap of training with MSDA, as proposed in Gontijo-Lopes et al. [12]. Reiterating, this is given by the difference between the performance of the baseline model when presented with original test data and augmented test data and is termed “affinity”. Subsequently, ",
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+        "text": "247 we address the gap in the wider sense, as is often sought in prior art. We first argue that high affinity   \n248 and high diversity are not necessarily desirable. Indeed, on CIFAR-10, we find FMix, a better   \n249 performing augmentation, to have both lower affinity and lower diversity than MixUp (Table 5). For   \n250 diversity, we compute the cross-entropy loss where the label is taken to be that of the majority class.   \n251 Similar results are obtained with the MixUp loss, where a weighted average of the true labels is taken.   \n252 While intuitively for a high level of affinity, high diversity could correspond to better methods,   \n253 the converse does not hold. We argue this is because affinity is rather an analysis of the learnt   \n254 representations of the reference model and cannot give an insight into the quality of the augmentation   \n255 or its effect on learning. The limitations of affinity are intimately linked to those of CutOcclusion.   \n256 We have seen in Section 3 that the bias of the basic model is present not only when obstructing an   \n257 image with a uniform patch, but also when mask-mixing. As such, an augmentation will have a   \n258 lower affinity if it introduces artefacts that could otherwise lead to learning better representations   \n259 when used in the training process. We believe this issue extends to other approaches that aim to   \n260 motivate the success of MSDA through reduced distribution shift. Henceforth, we focus on bringing   \n261 further supporting evidence that the importance lies in the invariance introduced by the shift and its   \n262 interaction with the given problem rather than its magnitude. ",
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+        "type": "text",
+        "text": "263 4.1 If it is not the magnitude that matters, is it the direction? ",
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+        "text": "264 We use empirical evidence to argue against previous assumptions behind the success of MSDA and   \n265 propose the study of introduced bias as a more informative research direction. Here we use the term   \n266 “bias” to refer to a drift in the learnt representations introduced by the change in the training procedure.   \n267 A fundamental difference to classical training is that in the case of augmentation the samples are no   \n268 longer independent. Mixed-sampling takes this even further. An immediate question is, does the   \n269 added correlation lead to more meaningful representations? It is claimed that the strength of MixUp   \n270 lies in causing the model to behave linearly between two images [40] or in pushing the examples   \n271 towards their mean [3]. Both of these claims rely on the combined images to be generated from the   \n272 same distribution. We want to verify to which extent this is necessary for a successful augmentation. ",
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+        "text": "It has been argued that label mixing has a negligible effect on the final model performance [19, 18, 14, 24]. We use the reformulated objective setting [18, 14], where targets are not mixed and the mixing coefficient is drawn from an imbalanced Beta distribution. This allows us to apply MSDA between data sets. Thus, for training a model on a data set, we use an additional one whose targets will be ignored. As an example, a model that is learning to predict CIFAR-10 images will be trained on a combination of CIFAR-10 and CIFAR-100 images, with the target of the former. This scenario breaks the added correlation between training examples. Note that when mixing between data sets we use the same procedure as when performing regular MSDA, without improving the process. ",
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+        "text": "281 Table 7 contains the results of this experiment, showing that an accuracy similar to or better than that   \n282 of regular MSDA can be obtained by performing inter-dataset MSDA.This invalidates the argument   \n283 that the power of MixUp resides in causing the model to act linearly between samples. Another   \n284 observation is that for FMix and MixUp, introducing elements from CIFAR-100 when training   \n285 models on the CIFAR-10 problem does not harm the learning process. The reciprocal, however, does   \n286 not hold. Hence, the “distribution shift” is more intimately linked to the problem at hand and aiming   \n287 to characterise an augmentation based on the distance from the original distribution is a limiting   \n288 approach, especially when the distance is measured as perceived by a reference model.   \n289 We believe an explanation is that the artefacts created when putting together images from CIFAR-10   \n290 with those of CIFAR-100 could introduce information that makes the separation of the 10 classes   \n291 easier. However, if the information happens to interfere with a feature that is important for separating   \n292 the CIFAR-100 categories, the performance could degrade on this data set. This singular experiment   \n293 is not sufficient to draw any general conclusions. However, it does show that shifting two distributions   \n294 by the same amount can have different effects on the model performance. Thus, the specifics of the   \n295 bias introduced could be more important than its magnitude. While some level of data similarity has   \n296 to be preserved when performing MSDA, it is far from being the objective of such data-distorting   \n297 approaches which, as we will argue further, should be rather seen as forms of regularisation.   \n298 We have seen that for all considered data sets, artefacts introduced by masking methods seem to   \n299 overlap with common features. This has led us to believe that MSDA training could help bypass   \n300 some of the simplicity bias. The simplicity bias refers to the tendency of deep models to find simple   \n301 representations and has been used to justify the success of deep models [28, 36]. Recent research   \n302 shows that this propensity causes models to ignore complex features that explain the data well in   \n303 favour of elementary features, even when they lead to worse performance [31, 16]. ",
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+            "Table 7: Accuracy on CIFAR-10 (left) and CIFAR-100 (right) upon mixing with samples from a different data set. The baseline is the accuracy when training with a single data set using the reformulated objective. In the interest of space, CIFAR-110 is used to refer to mixing with CIFAR100 when training on the CIFAR-10 problem and vice-versa. "
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+        "table_body": "<table><tr><td></td><td>MixUp</td><td>FMix</td><td>CutMix</td><td>MixUp</td><td>FMix</td><td>CutMix</td></tr><tr><td>baseline</td><td>94.18±0.34</td><td>94.36±0.28</td><td>94.67±0.20</td><td>74.68±0.37</td><td>75.75±0.31</td><td>74.19±0.50</td></tr><tr><td>CIFAR-110</td><td>94.70±0.27</td><td>94.80±0.32</td><td>94.66±0.12</td><td>72.36±1.04</td><td>74.80±0.55</td><td>74.47±0.39</td></tr><tr><td>Fashion</td><td>92.28±0.28</td><td>95.03±0.10</td><td>94.61±0.19</td><td>66.40±1.86</td><td>74.46±0.57</td><td>74.06±0.28</td></tr></table>",
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+        "text": "Although it could seem natural that since MSDAs are not augmentations in the VRM sense, they will increase the complexity of the problem, we design an experiment to support this claim. Similarly to Shah et al. [31], we combine CIFAR-10 and MNIST [23] samples. Since they have the same number of classes, we can easily associate each class of one data set with a corresponding one from the other. Thus, we stack a padded image from the $k$ th class of MNIST on top of a sample from the kth class of CIFAR-10, such that a $3 \\times 6 4 \\times 3 2$ image is obtained. We then randomly combine the test images and separately compute the accuracy with respect to the targets of each data set. ",
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+        "text": "311 The predictions with respect to the CIFAR-10 labels are no better than random $( 1 0 . 0 4 _ { \\pm 0 . 1 1 } )$ , while   \n312 the accuracy with respect to the MNIST images remains high $( 9 9 . 5 7 _ { \\pm 0 . 7 2 } )$ . Thus, models trained   \n313 on this combination are mostly relying on MNIST images to make predictions. Similar behaviours   \n314 have previously been associated with simplicity bias. Subsequently, when training, we perform FMix   \n315 only on MNIST images and observe that this is enough to reverse the results. Evaluating against the   \n316 CIFAR-10 label gives an accuracy of $8 6 . 6 0 _ { \\pm 0 . 3 4 }$ , while testing against the MNIST label only gives   \n317 $1 1 . 6 1 _ { \\pm 0 . 3 0 }$ . We find that this also holds true for the other MSDAs. Thus, performing these distortions   \n318 on the simpler data set increases its complexity to the point where it surpasses that of CIFAR-10.   \n319 Previously, we presented evidence that masking MSDA does not necessarily promote learning neither   \n320 more shape nor texture information. In the light of this fact along with the results from this section,   \n321 we believe image distortions force the model to learn more complex both shape and texture-specific   \n322 features. Thus, in this paper we pointed out that the shift in learnt representations can lead to better   \n323 models and simply quantifying the distribution shift can be misleading. An open question remains:   \n324 How can we better capture the bias that is introduced and its quality? We believe understanding how   \n325 a relatively small change in the data distribution impacts learnt representations could lead the way to   \n326 characterising the relationship between data and model generalisation. ",
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+        "type": "text",
+        "text": "327 5 Conclusions ",
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+        "text": "328 Distorting data is such a commonplace procedure, yet little effort has been devoted to investigating its   \n329 broader effects. This is particularly problematic when image modifications are applied in analyses. We   \n330 show a number of cases in which this leads to biased results. For occlusion robustness measurement,   \n331 we propose an alternative. The insights we gain from this endeavour point towards the study of data   \n332 characteristics as a cornerstone of our understanding and raise a number of questions about mixed   \n333 sample data augmentation, on which we subsequently focus. We note that they interfere with features   \n334 that are consistently found across a number of data sets and conclude that the methods commonly   \n335 used are forms of mixed sample regularisation rather than augmentation. A limitation of previous   \n336 studies that aim to explain their success is the focus on trying to argue similarity with original data,   \n337 rather than explaining the bias introduced by the distortion. Correctly interpreting it is important   \n338 not only for making the models trustable but also for injecting more informed prior knowledge in   \n339 future applications. Beyond their practical benefits, we believe MSDAs have the potential to help   \n340 characterise the interplay between data and learnt representations. Overall, the purpose of our paper   \n341 is to encourage better practice when dealing with all forms of data distortions. ",
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+        "text": "References   \n[1] Rocío Alaiz-Rodríguez and Nathalie Japkowicz. Assessing the impact of changing environments on classifier performance. In Conference of the Canadian Society for Computational Studies of Intelligence, pages 13–24. Springer, 2008.   \n[2] Wieland Brendel and Matthias Bethge. Approximating CNNs with bag-of-local-features models works surprisingly well on imagenet. In International Conference on Learning Representations, 2019. URL https://openreview.net/forum?id $\\equiv$ SkfMWhAqYQ.   \n[3] Luigi Carratino, Moustapha Cissé, Rodolphe Jenatton, and Jean-Philippe Vert. On mixup regularization. arXiv preprint arXiv:2006.06049, 2020.   \n[4] Olivier Chapelle, Jason Weston, Léon Bottou, and Vladimir Vapnik. Vicinal risk minimization. In Advances in neural information processing systems, pages 416–422, 2001.   \n[5] Sanghyuk Chun, Seong Joon Oh, Sangdoo Yun, Dongyoon Han, Junsuk Choe, and Youngjoon Yoo. 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Lin, editors, Advances in Neural Information Processing Systems, volume 33, pages 9573–9585. Curran Associates, Inc., 2020. URL https://proceedings.neurips. cc/paper/2020/file/6cfe0e6127fa25df2a0ef2ae1067d915-Paper.pdf.   \n431 [32] Baifeng Shi, Dinghuai Zhang, Qi Dai, Zhanxing Zhu, Yadong Mu, and Jingdong Wang. Informative dropout for robust representation learning: A shape-bias perspective. In International Conference on Machine Learning, pages 8828–8839. PMLR, 2020. [33] Karen Simonyan and Andrew Zisserman. Very deep convolutional networks for large-scale image recognition. In International Conference on Learning Representations, 2015.   \n[34] Stanford. Tiny imagenet visual recognition challenge, 2015. URL https://tiny-imagenet. herokuapp.com/.   \n[35] Christian Szegedy, Wojciech Zaremba, Ilya Sutskever, Joan Bruna, Dumitru Erhan, Ian Goodfellow, and Rob Fergus. Intriguing properties of neural networks. arXiv preprint arXiv:1312.6199, 2013.   \n[36] Guillermo Valle-Perez, Chico Q. Camargo, and Ard A. Louis. Deep learning generalizes because the parameter-function map is biased towards simple functions. In International Conference on Learning Representations, 2019. URL https://openreview.net/forum?id ${ } = { }$ rye4g3AqFm.   \n[37] Vladimir Vapnik. The nature of statistical learning theory. Springer science & business media, 1999.   \n[38] Han Xiao, Kashif Rasul, and Roland Vollgraf. Fashion-MNIST: a novel image dataset for benchmarking machine learning algorithms. arXiv preprint arXiv:1708.07747, 2017.   \n[39] Sangdoo Yun, Dongyoon Han, Seong Joon Oh, Sanghyuk Chun, Junsuk Choe, and Youngjoon Yoo. Cutmix: Regularization strategy to train strong classifiers with localizable features. In Proceedings of the IEEE International Conference on Computer Vision, pages 6023–6032, 2019.   \n[40] Hongyi Zhang, Moustapha Cisse, Yann N. Dauphin, and David Lopez-Paz. mixup: Beyond empirical risk minimization. In International Conference on Learning Representations, 2018. URL https://openreview.net/forum?id=r1Ddp1-Rb.   \n[41] Tianyuan Zhang and Zhanxing Zhu. Interpreting adversarially trained convolutional neural networks. In International Conference on Machine Learning, pages 7502–7511. PMLR, 2019.   \n[42] Zhun Zhong, Liang Zheng, Guoliang Kang, Shaozi Li, and Yi Yang. Random erasing data augmentation. In Proceedings of the AAAI Conference on Artificial Intelligence, number 34(07), pages 13001–13008, 2020. ",
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+        "text": "1. For all authors... ",
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+        "text": "(a) Do the main claims made in the abstract and introduction accurately reflect the paper’s contributions and scope? [Yes] (b) Did you describe the limitations of your work? [Yes] See lines 174–184, 221–229,   \n292–294. (c) Did you discuss any potential negative societal impacts of your work? [Yes] See lines   \n221–229 as well as 89–93 and Appendix C.4. (d) Have you read the ethics review guidelines and ensured that your paper conforms to them? [Yes] ",
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+        "text": "(a) Did you state the full set of assumptions of all theoretical results? [N/A] (b) Did you include complete proofs of all theoretical results? [N/A] ",
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