Original: Recommender Transformers with Behavior Pathways
Revised: Recommender Transformers with Behavior Pathways

Original: Anonymous Author(s)
Revised: Anonymous Author(s)

Original: AfﬁliationAddress email
Revised: AffiliationAddress email

Original: Abstract
Revised: Abstract

Original: Sequential recommendation requires the recommender to capture the evolvingbehavior characteristics from logged user behavior data for accurate recommendations.
Revised: Sequential recommendation requires the recommender to capture the evolvingbehavior characteristics from logged user behavior data for accurate recommendations.

Original: However, user behavior sequences are viewed as a script with multipleongoing threads intertwined.
Revised: However, user behavior sequences are viewed as a script with multipleongoing threads intertwined.

Original: We ﬁnd that only a small set of pivotal behaviors canbe evolved into the user’s future action.
Revised: We find that only a small set of pivotal behaviors canbe evolved into the user’s future action.

Original: As a result, the future behavior of the useris hard to predict.
Revised: As a result, the future behavior of the useris hard to predict.

Original: We conclude this characteristic for sequential behaviors of eachuser as the Behavior Pathway .
Revised: We conclude this characteristic for sequential behaviors of eachuser as the Behavior Pathway .

Original: Different users have their unique behavior pathways.
Revised: Different users have their unique behavior pathways.

Original: Among existing sequential models, transformers have shown great capacity incapturing global-dependent characteristics.
Revised: Among existing sequential models, transformers have shown great capacity incapturing global-dependent characteristics.

Original: However, these models mainly providea dense distribution over all previous behaviors using the self-attention mechanism,making the ﬁnal predictions overwhelmed by the trivial behaviors not adjusted toeach user.
Revised: However, these models mainly providea dense distribution over all previous behaviors using the self-attention mechanism,making the final predictions overwhelmed by the trivial behaviors not adjusted toeach user.

Original: In this paper, we build the Recommender Transformer (RETR) with anovel Pathway Attention mechanism.
Revised: In this paper, we build the Recommender Transformer (RETR) with anovel Pathway Attention mechanism.

Original: RETR can dynamically plan the behaviorpathway speciﬁed for each user, and sparingly activate the network through thisbehavior pathway to effectively capture evolving patterns useful for recommendation.
Revised: RETR can dynamically plan the behaviorpathway specified for each user, and sparingly activate the network through thisbehavior pathway to effectively capture evolving patterns useful for recommendation.

Original: The key design is a learned binary route to prevent the behavior pathway frombeing overwhelmed by trivial behaviors.
Revised: The key design is a learned binary route to prevent the behavior pathway frombeing overwhelmed by trivial behaviors.

Original: We empirically verify the effectiveness of
Revised: We empirically verify the effectiveness of

Original: RETR on seven real-world datasets and RETR yields state-of-the-art performance.
Revised: RETR on seven real-world datasets and RETR yields state-of-the-art performance.

Original:  Introduction
Revised:  Introduction

Original: Recommender systems [14, 21, 39] have been widely adopted in real-world industrial applicationssuch as E-commerce and social media.
Revised: Recommender systems [16, 24, 42] have been widely adopted in real-world industrial applicationssuch as E-commerce and social media.

Original: Beneﬁting from the increase in computing power and modelcapacity, some recent efforts formulate recommendation as a time-series forecasting problem, knownas sequential recommendation [16, 28, 6].
Revised: Benefiting from the increase in computing power and modelcapacity, some recent efforts formulate recommendation as a time-series forecasting problem, knownas sequential recommendation [18, 31, 6].

Original: The core idea of this ﬁeld is to infer upcoming actionsbased on user’s historical behaviors, which are reorganized as time-ordered sequences.
Revised: The core idea of this field is to infer upcoming actionsbased on user’s historical behaviors, which are reorganized as time-ordered sequences.

Original: This intuitivemodeling of recommendation is proved time-sensitive and context-aware to make precise predictions.
Revised: This intuitivemodeling of recommendation is proved time-sensitive and context-aware to make precise predictions.

Original: Recent advanced sequential recommendation models, such as SASRec [16], Bert4Rec [28] and
Revised: Recent advanced sequential recommendation models, such as SASRec [18], Bert4Rec [31] and

Original: SMRec [6] have achieved signiﬁcant improvements.
Revised: SMRec [6] have achieved significant improvements.

Original: Transformers enable these models to recognizeglobal-range sequential patterns, and to model how future behaviors are anchored in historical ones.
Revised: Transformers enable these models to recognizeglobal-range sequential patterns and to model how future behaviors are anchored in historical ones.

Original: The self-attention mechanism does make it possible to explore all previous behaviors of each user,with the whole neural network activated.
Revised: The self-attention mechanism does make it possible to explore all previous behaviors of each user,with the whole neural network activated.

Original: However, misuse of user information, regardless of whetherthey are informative or not, ﬂoods models with trivial ones, makes models dense and inefﬁcient, andresults in key behaviors losing voice.
Revised: However, misuse of user information, regardless of whether they are informative or not, floods models with trivial ones, makes models dense and inefficient, and results in key behaviors losing voice.

Original: And this clearly contradicts with the way our brain works.
Revised: And this clearly contradicts with the way our brain works.

Original: The human being has many different parts of the brain specialized for various tasks, yet the brain onlycalls upon the relevant pieces for a given situation [37].
Revised: The human being has many different parts of the brain specialized for various tasks, yet the brain only calls upon the relevant pieces for a given situation [40].

Original: To some extent, user behavior sequences canbe viewed as a script with multiple ongoing threads intertwined.
Revised: To some extent, user behavior sequences can be viewed as a script with multiple ongoing threads intertwined.

Original: And only key clues suggest what willhappen next.
Revised: And only key clues suggest what will happen next.

Original: In sequential recommendation, we ﬁnd that only a small part of pivotal behaviors canbe evolved into the use’s future action.
Revised: In sequential recommendation, we find that only a small part of pivotal behaviors can be evolved into the user’s future action.

Original: And we conclude this characteristics of sequential behaviorsas the Behavior Pathway.
Revised: And we conclude this characteristics of sequential behaviors the Behavior Pathway

Original: [Figure]
Revised: [Figure]

Original: Different users have their unique behavior pathways and they can be grouped into three categories:
Revised: Different users have their unique behavior pathways and they can be grouped into three categories:

Original: • Correlated Behavior Pathway : A user’s behavior pathway is closely associated withbehaviors at a certain period.
Revised: • Correlated Behavior Pathway : A user’s behavior pathway is closely associated withbehaviors at a certain period.

Original: As shown in the second line of Figure 1, the mouse is clickedmany times recently, leading to the ﬁnal decision to buy a mouse.
Revised: As shown in the first line of Figure 1, the mouse is clickedmany times recently, leading to the final decision to buy a mouse.

Original: • Casual Behavior Pathway : A user’s behavior pathway is interested in a speciﬁc item atcasual times.
Revised: • Casual Behavior Pathway : A user’s behavior pathway is interested in a specific item atcasual times.

Original: As shown in the ﬁrst line of Figure 1, the backpack is randomly clicked
Revised: As shown in the second line of Figure 1, the backpack is randomly clicked

Original: sequentially.
Revised: sequentially.

Original: • Drifted Behavior Pathway : A user’s behavior pathway in a particular brand might drift
Revised: • Drifted Behavior Pathway : A user’s behavior pathway in a particular brand might drift

Original: over time.
Revised: over time.

Original: As shown in the third line of Figure 1, the user was initially interested in akeyboard, but suddenly became interested in buying a phone at last.
Revised: As shown in the third line of Figure 1, the user was initially interested in a keyboard, but suddenly became interested in buying a phone at last.

Original: It’s challenging to capture these aspects dynamically for each user to make precise recommendations.
Revised: It’s challenging to capture these aspects dynamically for each user to make precise recommendations.

Original: Motivated by the Pathways [8], a new way of thinking about AI, which builds a single model that issparsely activated for all tasks with small pathways through the network called into action as needed,we propose a novel Recommender Transformer (RETR) with a Pathway Attention mechanism.
Revised: Motivated by the Pathways [8], a new way of thinking about AI, which builds a single model that issparsely activated for all tasks with small pathways through the network called into action as needed,we propose a novel Recommender Transformer (RETR) with a Pathway Attention mechanism.

Original: RETRdynamically explores behavior pathways for different users and then captures evolving patternsthrough these pathways effectively.
Revised: RETRdynamically explores behavior pathways for different users and then captures evolving patternsthrough these pathways effectively.

Original: To be speciﬁc, the user-dependent pathway attention, whichincorporates a pathway router, determines whether or not a behavior token will be maintained in thebehavior pathway.
Revised: To be specific, the user-dependent pathway attention, whichincorporates a pathway router, determines whether or not a behavior token will be maintained in thebehavior pathway.

Original: Technically, the pathway router generates a customized binary route for each tokenbased on their information redundancy.
Revised: Technically, the pathway router generates a customized binary route for each tokenbased on their information redundancy.

Original: Recommender Transformers are stacked, and successivepathway routers constitute a hierarchical evolution pathway of user behaviors.
Revised: Recommender Transformers are stacked, and successivepathway routers constitute a hierarchical evolution pathway of user behaviors.

Original: To enable the pathwayrouter modules to be end-to-end optimized, we adopt the Gumbel-Softmax [15] sampling strategy toovercome the non-differentiable problem of sampling from a Bernoulli distribution.
Revised: To enable the pathwayrouter modules to be end-to-end optimized, we adopt the Gumbel-Softmax [17] sampling strategy toovercome the non-differentiable problem of sampling from a Bernoulli distribution.

Original: To effectively capture the evolving patterns via the behavior pathway, our pathway attention mechanism makes our RETR mainly attend to the obtained pathway.
Revised: To effectively capture the evolving patterns via the behavior pathway, our pathway attention mechanism makes our RETR mainly attend to the obtained pathway.

Original: We force the model to focus on themost informative behaviors by using the query routed through the behavior pathway.
Revised: We force the model to focus on themost informative behaviors by using the query routed through the behavior pathway.

Original: We cut off theinteraction from the off-pathway behaviors of the query.
Revised: We cut off theinteraction from the off-pathway behaviors of the query.

Original: Compared with using all previous behaviors,our pathway attention mechanism is obviously more effective and can avoid the most informativetokens being overwhelmed by trivial behaviors.
Revised: Compared with using all previous behaviors,our pathway attention mechanism is obviously more effective and can avoid the most informativetokens being overwhelmed by trivial behaviors.

Original: To validate the effectiveness of our approach, weconduct experiments on seven real-world competitive datasets for sequential recommendations and
Revised: To validate the effectiveness of our approach, weconduct experiments on seven real-world competitive datasets for sequential recommendations and

Original: RETR achieves state-of-the-art performance.
Revised: RETR achieves state-of-the-art performance.

Original: Our main contributions can be summarized as follows:
Revised: Our main contributions can be summarized as follows:

Original: • Our work is the ﬁrst to propose the concept of behavior pathway for sequential recommendation.
Revised: • Our work is the first to propose the concept of behavior pathway for sequential recommendation.

Original: We ﬁnd the key to the recommender is to dynamically capture the behavior pathwayfor each user.•
Revised: We find the key to the recommender is to dynamically capture the behavior pathwayfor each user.•

Original: We propose the novel recommender transformer (RETR) with a novel pathway attentionmechanism, which can generate the behavior pathway hierarchically and capture the evolvingpatterns dynamically through the pathway.•
Revised: We propose the novel recommender transformer (RETR) with a novel pathway attentionmechanism, which can generate the behavior pathway hierarchically and capture the evolvingpatterns dynamically through the pathway.•

Original: We validate the effectiveness of RETR on seven real-world datasets of different scales acrossdifferent scenarios for sequential recommendations and achieve state-of-the-art performance.  
Revised: We validate the effectiveness of RETR on seven real-world datasets of different scales acrossdifferent scenarios for sequential recommendations and achieve state-of-the-art performance.  Related Work

Original: Traditional recommendation approaches.
Revised: Traditional recommendation approaches.

Original: Capturing evolving behavior characteristics is crucialfor many online applications, such as advertising, social media and E-commerce, and it is the keychallenge for sequential recommendation [1, 16, 7, 36, 9, 24, 5, 41, 20].
Revised: Capturing evolving behavior characteristics is crucialfor many online applications, such as advertising, social media and E-commerce, and it is the keychallenge for sequential recommendation [1, 18, 7, 39, 11, 26, 5, 45, 23].

Original: Traditional recommendationapproach, such as the collaborative ﬁltering (CF) [13] based on matrix approximation [18, 19], alwaysassumes that the user’s behavior is static.
Revised: Traditional recommendationapproach, such as the collaborative filtering (CF) [15] based on matrix approximation [20, 21], alwaysassumes that the user’s behavior is static.

Original: However, in practice, user behaviors often change over timedue to various reasons, making the CF deteriorate in a real-world application.
Revised: However, in practice, user behaviors often change over timedue to various reasons, making the CF deteriorate in a real-world application.

Original: Sequential recommendation approaches.
Revised: Sequential recommendation approaches.

Original: To overcome this challenge, some methods, such as
Revised: To overcome this challenge, some methods, such as

Original: FPMC [12] and HRM [30], use Markov chains to capture sequential patterns by learning userspeciﬁc transition matrices.
Revised: FPMC [14] and HRM [34], use Markov chains to capture sequential patterns by learning userspecific transition matrices.

Original: Higher-order Markov Chains assume the next action is related to severalprevious actions.
Revised: Higher-order Markov Chains assume the next action is related to severalprevious actions.

Original: Beneﬁt from this strong inductive bias, MC-based methods [12, 11] show superiorperformance in capturing short-term patterns.
Revised: Benefit from this strong inductive bias, MC-based methods [14, 13] show superiorperformance in capturing short-term patterns.

Original: At the same time, there is a potential state spaceexplosion problem when these approaches are faced with different possible sequences [31].
Revised: At the same time, there is a potential state spaceexplosion problem when these approaches are faced with different possible sequences [35].

Original: In recentyears, many works have been using the deep neural network for sequential recommendation.
Revised: In recentyears, many works have been using the deep neural network for sequential recommendation.

Original: Forexample, the GRURec [14] and the RepeatNet [25] adopt the recurrent network to capture dynamicpatterns from the user behaviors dependent on sequence positions.
Revised: The GRU4Rec [16] and the RepeatNet [27] adopt the recurrent network to capture dynamic patterns fromthe user behaviors dependent on sequence positions.

Original: The RNN-based models achievecompetitive performance in capturing short-term behavior patterns but cannot capture long-termbehavior patterns effectively.
Revised: The RNN-based models achieve competitiveperformance in capturing short-term behavior patterns but cannot capture long-term behavior patternseffectively.

Original: The CNN-based model, such as Caser [29], applies convolutionaloperations to extract transitions while tending to overlook the intrinsic relationship across userbehaviors.
Revised: The CNN-based model, such as Caser [33], applies convolutional operations to extracttransitions while tending to overlook the intrinsic relationship across user behaviors.

Original: The GNN-based methods, such as SRGNN [33] and GCSAN [34], model behaviorsequences as graph-structured data and incorporate an attention mechanism for a session-basedrecommendation.
Revised: The GNNbased methods, such as SRGNN [37], GCSAN [38], Jodie [22] and TGN [28] model behaviorsequences as graph-structured data and incorporate an attention mechanism for a session-basedrecommendation.

Original: In addition, DIN [40] uses the gate mechanism to weight different user behaviors.
Revised: In addition, DIN [43] uses the gate mechanism to weight different user behaviors.

Original: However, concatenating all behaviors makes these models overlook the sequential characteristics.
Revised: However, concatenating all behaviors makes these models overlook the sequential characteristics.

Original: Transformer-based models for Sequential Recommendation.
Revised: Attention-based models for Sequential Recommendation.

Original: The transformer-based models havethe strong capacity to capture behavior patterns via the attention mechanism, achieving state-of-theart performance while involving many parameters.
Revised: The attention-based models like SINE[32] have the strong capacity to capture behavior patterns via the attention mechanism, achievingstate-of-the-art performance while involving many parameters.

Original:  SASRec [16], BertRec [28] and SSE-PT [32]introduce the transformer architecture into sequential recommendation, which might lead to theover-parameterized architecture of Transformer-based methods.
Revised: Especially, SASRec [18], BertRec[31], S3-Rec [44], TGSRec [10], LightSANs [9] and SSE-PT [36] introduce the transformer architecture into sequential recommendation, which might lead to the over-parameterized architectureof Transformer-based methods.

Original: These models capture the evolvingpatterns by the self-attention mechanism, interacting with all previous behaviors.
Revised: These models capture the evolving patterns by the self-attentionmechanism, interacting with all previous behaviors.

Original: However, denseinteractions will make the model not adapt to different users and overwhelm behavior pathways.
Revised: However, dense interactions will make themodel not adapt to different users and overwhelm behavior pathways.

Original: Totackle this challenge, our paper builds the Recommender Transformer (RETR) with a new Pathway Attention mechanism that is dynamically activated for the behavior pathway of all users.
Revised: To tackle this challenge, ourpaper builds the Recommender Transformer (RETR) with a new Pathway Attention mechanism thatis dynamically activated for the behavior pathway of all users.

Original: Distinctfrom the previous routing architecture like Switch Transformer [10] using the MoE [27] structure fornatural language tasks, our RETR is designed explicitly for sequential recommendation.
Revised: Distinct from the previous routingarchitecture like Switch Transformer [12] using the MoE [30] structure for natural language tasks, our RETR is designed explicitly for sequential recommendation.

Original: Our RETRuses the pathway router to adaptively route the sequential behavior of each user rather than routingthe experts of feed-forward networks in switch transformer.
Revised: Our RETR uses the pathway router toadaptively route the sequential behavior of each user rather than routing the experts of feed-forwardnetworks in switch transformer.

Original:  Method
Revised:  Method

Original: Suppose that we have a set of users and items, denoted by U and I respectively.
Revised: Suppose that we have a set of users and items, denoted by U and I respectively.

Original: In the task ofsequential recommendation, chronologically-ordered behaviors of a user u ∈ U could be representedby a user-interacted item sequence: { i 1 , · · · , i n } .
Revised: In the task ofsequential recommendation, chronologically-ordered behaviors of a user u ∈ U could be representedby a user-interacted item sequence: { i 1 , · · · , i n } .

Original: Formally, given a user u with her or his behavior 116 sequence { i 1 , · · · , i n } , the goal of sequential recommendation is to predict the next item the user u 117 would interact with at the ( n + 1) -th step, denoted as p ( i n + | i 1: n ) .
Revised: Formally, given a user u with her or his behavior 117 sequence { i 1 , · · · , i n } , the goal of sequential recommendation is to predict the next item the user u 118 would interact with at the ( n + 1) -th step, denoted as p ( i n + | i 1: n ) .

Original: As aforementioned, we highlight the key to sequential recommendation as the exploration of usertailored behavior pathways, through which evolving characteristics could be learned.
Revised: As aforementioned, we highlight the key to sequential recommendation as the exploration of usertailored behavior pathways, through which evolving characteristics could be learned.

Original: Motivated bythis, we propose a novel Recommender Transformer (RETR) with a new Pathway Attention , the coresubassembly of which is a pathway router.
Revised: Motivated bythis, we propose a novel Recommender Transformer (RETR) with a new Pathway Attention , the coresubassembly of which is a pathway router.

Original: Besides the modiﬁcation of architecture, we additionallyintroduce a hierarchical update strategy for the behavior pathway in the feed-forward procedure.
Revised: Besides the modification of architecture, we additionallyintroduce a hierarchical update strategy for the behavior pathway in the feed-forward procedure.

Original: 3.1 RecommenderTransformer
Revised: 3.1 Recommender

Original: Considering the limitation of Transformers [4] for sequential recommendation, we renovate the vanillaarchitecture to the Recommender Transformer (Figure 2) with a Pathway Attention mechanism.
Revised: Considering the limitation of Transformers [4] for sequential recommendation, we renovate the vanilla architecture to the Recommender Transformer (Figure 2) with a Pathway Attention mechanism.

Original: FFN
Revised: FFN

Original: LN
Revised: LN

Original: PathwayAttention ⇥
Revised: PathwayAttention ⇥

Original: LN ⇥ L ⇥
Revised: LN ⇥ L ⇥

Original: Embedding
Revised: Embedding

Original: Gumbel-Softmax l from u l,k todecidewhatblockstoselectorskipinthetask T k .
Revised: Gumbel-Softmax l from u l,k todecidewhatblockstoselectorskipinthetask T k .

Original: Speciﬁcally,withthe helpoftheselect-or-skipdecisions,weformanovelandnon-trivialnetworkarchitectureforMTLparameter-sharing,andshareknowledgeatdifferentlevelsacrossalltasksinaﬂexibleandefﬁcient way.
Revised: Speciﬁcally,withthe helpoftheselect-or-skipdecisions,weformanovelandnon-trivialnetworkarchitectureforMTLparameter-sharing,andshareknowledgeatdifferentlevelsacrossalltasksinaﬂexibleandefﬁcient way.

Original: Attesttime,whenanovelinputispresentedtothemulti-tasknetwork,theoptimalpolicyisfollowed,selectivelychoosingwhatblockstocomputeforeachtask.
Revised: Attesttime,whenanovelinputispresentedtothemulti-tasknetwork,theoptimalpolicyisfollowed,selectivelychoosingwhatblockstocomputeforeachtask.

Original: Ourproposedapproachnotonly encouragespositivesharingamongtasksviasharedblocksbutalsominimizesnegativeinterferencebyusingtask-speciﬁcblockswhennecessary.
Revised: Ourproposedapproachnotonly encouragespositivesharingamongtasksviasharedblocksbutalsominimizesnegativeinterferencebyusingtask-speciﬁcblockswhennecessary.

Original: LearningaTask-SpeciﬁcPolicy.
Revised: LearningaTask-SpeciﬁcPolicy.

Original: In AdaShare , welearntheselect-or-skippolicy U andnetwork weights W jointlythroughstandardback-propagationfromourdesignedlossfunctions.
Revised: In AdaShare , welearntheselect-or-skippolicy U andnetwork weights W jointlythroughstandardback-propagationfromourdesignedlossfunctions.

Original: However, eachselect-or-skippolicy u l,k isdiscreteandnon-differentiableandthismakesdirectoptimization difﬁcult.
Revised: However, eachselect-or-skippolicy u l,k isdiscreteandnon-differentiableandthismakesdirectoptimization difﬁcult.

Original: Therefore,weadoptGumbel-SoftmaxSampling[25]toresolvethisnon-differentiability andenabledirectoptimizationofthediscretepolicy u l,k usingback-propagation.
Revised: Therefore,weadoptGumbel-SoftmaxSampling[25]toresolvethisnon-differentiability andenabledirectoptimizationofthediscretepolicy u l,k usingback-propagation.

Original: Gumbel-SoftmaxSampling.
Revised: Gumbel-SoftmaxSampling.

Original: TheGumbel-Softmaxtrick[25,36]isasimpleandeffectivewayto substitutestheoriginalnon-differentiablesamplefromadiscretedistributionwithadifferentiable samplefromacorrespondingGumbel-Softmaxdistribution.
Revised: TheGumbel-Softmaxtrick[25,36]isasimpleandeffectivewayto substitutestheoriginalnon-differentiablesamplefromadiscretedistributionwithadifferentiable samplefromacorrespondingGumbel-Softmaxdistribution.

Original: Welet ⇡ l,k =
Revised: Welet ⇡ l,k =

Original: [1  ↵ l,k ,↵ l,k ] be the distributionvectorofthebinaryrandomvariable u l,k thatwewanttooptimize,wherethelogit ↵ l,k representstheprobabilitythatthe l -thblockisselectedtoexecuteinthetask T k .
Revised: [1  ↵ l,k ,↵ l,k ] be the distributionvectorofthebinaryrandomvariable u l,k thatwewanttooptimize,wherethelogit ↵ l,k representstheprobabilitythatthe l -thblockisselectedtoexecuteinthetask T k .

Original: InGumbel-SoftmaxSampling,insteadofdirectlysamplingaselect-or-skipdecision u l,k forthe l -th blockinthetask
Revised: InGumbel-SoftmaxSampling,insteadofdirectlysamplingaselect-or-skipdecision u l,k forthe l -th blockinthetask

Original: T k fromitsdistribution ⇡ l,k ,wegenerateitas, u l,k =argmax
Revised: T k fromitsdistribution ⇡ l,k ,wegenerateitas, u l,k =argmax

Original: j 2{ 0 , 1 }  log ⇡ l,k ( j )+ G l,k ( j )  , (1) where G l,k =  log(  log U l,k )
Revised: j 2{ 0 , 1 }  log ⇡ l,k ( j )+ G l,k ( j )  , (1) where G l,k =  log(  log U l,k )

Original: isastandardGumbeldistributionwith U l,k sampledfromauniform .d.
Revised: isastandardGumbeldistributionwith U l,k sampledfromauniform i.i.d.

Original: distributionUnif (0 , 1) .
Revised: distributionUnif (0 , 1) .

Original: Toremovethenon-differentiableargmaxoperationinEq.1,theGumbel Softmaxtrickrelaxesone-hot ( u l,k ) 2 { 0 , 1 } 2 (theone-hotencodingof u l,k )to v l,k 2 R 2 (thesoft select-or-skipdecisionforthe l -thblockin T k )withthereparameterizationtrick[25]: v l,k ( j )= exp  (log ⇡ l,k ( j )+ G l,k ( j )) /
Revised: Toremovethenon-differentiableargmaxoperationinEq.1,theGumbel Softmaxtrickrelaxesone-hot ( u l,k ) 2 { 0 , 1 } 2 (theone-hotencodingof u l,k )to v l,k 2 R 2 (thesoft select-or-skipdecisionforthe l -thblockin T k )withthereparameterizationtrick[25]: v l,k ( j ) [Equation]

Original: ⌧ 
Revised: [Equation] [Equation] [Equation]

Original: P i 2{ 0 , 1 } exp  (log ⇡ l,k
Revised: [Equation]

Original: ( i )+ G l,k ( i)) /
Revised: [Equation]  P i

Original: ⌧  , (2)
Revised: [Equation]

Original: Gumbel-Softmax encouragespositivesharingamongtasksviasharedblocksbutalsominimizesnegativeinterferencebyusingtask , eachselect or-skippolicy u l,k difﬁcult l k -Softmaxtrick j log
Revised: [Equation]

Original: ( j )
Revised: ( i )

Original: G
Revised: [Equation]

Original: ( j ) (1) where G l
Revised: ( i )) /

Original: = log
Revised: [Equation]

Original: ,k : v l,k ( j )= exp  (log ⇡ l,k (
Revised:  , (2)

Original: [Figure]
Revised: [Figure]

Revised: skippolicydecisionsampledfromthelearnedtask encouragespositivesharingamongtasksviasharedblocksbutalsominimizesnegativeinterferencebyusingtask weights

Original: As is with becomes to manually ﬁnd such a U to get to
Revised: However, eachselect-or-skippolicy u l,k isdiscreteandnon-differentiableandthismakesdirectoptimization difﬁcult ,weadoptGumbel-SoftmaxSampling -differentiability andenabledirectoptimizationofthediscretepolicy u l,k -propagation.

Revised: -SoftmaxSampling

Revised: -Softmaxtrick substitutestheoriginalnon where j )+ G l,k ( j )) /⌧

Revised: P i 2{ 0 , 1 } exp  (log ⇡ l,k

Revised: ( i )+ G l,k ( i )) /

Revised: ⌧  , ( encouragespositivesharingamongtasksviasharedblocksbutalsominimizesnegativeinterferencebyusingtask

Original: T k .
Revised: T k .

Original: InGumbel-SoftmaxSampling,insteadofdirectlysamplingaselect-or-skipdecision u l,k forthe l -th blockinthetask
Revised: InGumbel-SoftmaxSampling,insteadofdirectlysamplingaselect-or-skipdecision u l,k forthe l -th blockinthetask

Original: T k fromitsdistribution ⇡ l,k ,wegenerateitas, u l,k =argmax
Revised: T k fromitsdistribution ⇡ l,k ,wegenerateitas, u l,k =argmax

Original: j 2{ 0 , 1 }  log ⇡ l,k ( j )+ G l,k ( j )  , (1) where G l,k =  log(  log U l,k )
Revised: j 2{ 0 , 1 }  log ⇡ l,k ( j )+ G l,k ( j )  , (1) where G l,k =  log(  log U l,k )

Original: isastandardGumbeldistributionwith U l,k sampledfromauniform i.i.d.
Revised: isastandardGumbeldistributionwith U l,k sampledfromauniform i.i.d.

Original: distributionUnif (0 , 1) .
Revised: distributionUnif (0 , 1) .

Original: Toremovethenon-differentiableargmaxoperationinEq.1,theGumbel Softmaxtrickrelaxesone-hot ( u l,k ) 2 { 0 , 1 } 2 (theone-hotencodingof u l,k )to v l,k 2 R 2 (thesoft select-or-skipdecisionforthe l -thblockin T k )withthereparameterizationtrick[25]: vl,k ( j )= exp  (log ⇡ l,k ( j )+ G l,k ( j )) /
Revised: Toremovethenon-differentiableargmaxoperationinEq.1,theGumbel Softmaxtrickrelaxesone-hot ( u l,k ) 2 { 0 , 1 } 2 (theone-hotencodingof u l,k )to v l,k 2 R 2 (thesoft select-or-skipdecisionforthe l -thblockin T k )withthereparameterizationtrick[25]: v

Original: ⌧  P i 2{ 0 , 1 } exp  (log ⇡ l,k
Revised: [Figure]

Original: ( i )+ G l,k ( i )) / ⌧  , (2)
Revised: [Figure] )intraining.

Original: Gumbel-Softmax

Original: Bestviewedincolor.
Revised: Bestviewedincolor.

Original: onlyonetaskforpredictingtheoutput.
Revised: onlyonetaskforpredictingtheoutput.

Original: Inthisway,theselect or-skippolicyofallblocksandtasks ( U = { u l,k } l  L,k  K )determinestheadaptivefeaturesharingmechanismoverthegiventaskset T .
Revised: Inthisway,theselect-or-skippolicyofallblocksandtasks ( U = { u l,k } l  L,k  K )determinestheadaptivefeaturesharingmechanismoverthegiventaskset T .

Original: As the number of potential conﬁgurations for U is 2 L ⇥ K which grows exponentially with the number of blocks and tasks, it becomes intractable to manually ﬁnd such a U to get the optimal featuresharingpatterninmulti-tasklearning.
Revised: As the number of potential conﬁgurations for U is 2 L ⇥ K which grows exponentially with the number of blocks and tasks, it becomes intractable to manually ﬁnd such a U to get the optimal featuresharingpatterninmulti-tasklearning.

Original: Insteadofhandcraftingthispolicy,weadoptGumbelSoftmax
Revised: Insteadofhandcraftingthispolicy,weadoptGumbelSoftmax

Original: Sampling [25] to optimize U jointly with the network parameters W through standard back-propagation.
Revised: Sampling [25] to optimize U jointly with the network parameters W through standard back-propagation.

Original: Moreover,weintroducetwopolicyregularizationstoachieveeffectiveknowledge sharinginacompactmulti-tasknetwork,aswellasacurriculumlearningstrategytostabilizetheoptimizationintheearlystages.
Revised: Moreover,weintroducetwopolicyregularizationstoachieveeffectiveknowledge sharinginacompactmulti-tasknetwork,aswellasacurriculumlearningstrategytostabilizetheoptimizationintheearlystages.

Original: Afterthetrainingﬁnishes,wesamplethebinarydecision u l,k for eachblock l from u l,k todecidewhatblockstoselectorskipinthetask T k .
Revised: Afterthetrainingﬁnishes,wesamplethebinarydecision u l,k for eachblock l from u l,k todecidewhatblockstoselectorskipinthetask T k .

Original: Speciﬁcally,withthe helpoftheselect-or-skipdecisions,weformanovelandnon-trivialnetworkarchitectureforMTLparameter-sharing,andshareknowledgeatdifferentlevelsacrossalltasksinaﬂexibleandefﬁcient way.
Revised: Speciﬁcally,withthe helpoftheselect-or-skipdecisions,weformanovelandnon-trivialnetworkarchitectureforMTLparameter-sharing,andshareknowledgeatdifferentlevelsacrossalltasksinaﬂexibleandefﬁcient way.

Original: Attesttime,whenanovelinputispresentedtothemulti-tasknetwork,theoptimalpolicyisfollowed,selectivelychoosingwhatblockstocomputeforeachtask.
Revised: Attesttime,whenanovelinputispresentedtothemulti-tasknetwork,theoptimalpolicyisfollowed,selectivelychoosingwhatblockstocomputeforeachtask.

Original: Ourproposedapproachnotonly encouragespositivesharingamongtasksviasharedblocksbutalsominimizesnegativeinterferencebyusingtask-speciﬁcblockswhennecessary.
Revised: Ourproposedapproachnotonly encouragespositivesharingamongtasksviasharedblocksbutalsominimizesnegativeinterferencebyusingtask-speciﬁcblockswhennecessary.

Original: LearningaTask-SpeciﬁcPolicy.
Revised: LearningaTask-SpeciﬁcPolicy.

Original: In AdaShare , welearntheselect
Revised: In AdaShare , welearntheselect

Original: ( j ) ( j ) [25]: v l,k ( j )= exp  (log ⇡ l,k ( j )+ G l,k ( j )) /
Revised: [25]: v l,k ( j )= exp  (log ⇡ l,k ( j )+ G l,k ( j )) /

Original: ⌧ 
Revised: ⌧

Original: P i 2{ 0 , 1 } exp  (log ⇡ l,k
Revised: P i 2{ 0 , 1 } exp  (log ⇡ l,k

Original: ( i )+ G l,k ( i )) /
Revised: ( i )+ G l,k ( i )) /

Original: ⌧  , (2)
Revised: ⌧  , (2)

Original: Gumbel-Softmaxis
Revised: Gumbel-Softmax

Original: L K grows exponentiallywith and , it becomes intractable to manually ﬁnd such a U to get the optimal
Revised: K grows exponentially it becomes intractable to manually ﬁnd such a U to get the optimal

Original: Softmax Sampling [25] to optimize U jointly network parameters W  back  wherethelogit ↵ l,k representstheprobabilitythatthe l -thblockisselectedtoexecuteinthetask T k .
Revised: Softmax Sampling [25] to optimize U jointly with parameters W standard back [Table] [Table] wherethelogit ↵ l,k representstheprobabilitythatthe l -thblockisselectedtoexecuteinthetask T k .

Original: InGumbel-SoftmaxSampling,insteadofdirectlysamplingaselect-or-skipdecision u l,k forthe l -th blockinthetask
Revised: InGumbel-SoftmaxSampling,insteadofdirectlysamplingaselect-or-skipdecision u l,k forthe l -th blockinthetask

Original: T k fromitsdistribution ⇡ l,k ,wegenerateitas, u l,k =argmax
Revised: T k fromitsdistribution ⇡ l,k ,wegenerateitas, u l,k =argmax

Original: j 2{ 0 , 1 }  log ⇡ l,k ( j )+ G l,k [Equation] )  , (1) where G l,k =  log(  log U l,k ) isastandardGumbeldistributionwith U l,k sampledfromauniform i.i.d.
Revised: j 2{ 0 , 1 }  log ⇡ l,k ( j )+ G l,k ( j )  , (1) where G l,k =  log(  log U l,k ) isastandardGumbeldistributionwith U l,k sampledfromauniform i.i.d.

Original: distributionUnif (0 , 1) .
Revised: distributionUnif (0 , 1) .

Original: Toremovethenon-differentiableargmaxoperationinEq.1,theGumbel Softmaxtrickrelaxesone-hot ( u l,k ) 2 { 0 , 1 } 2 (theone-hotencodingof u l,k )to v l,k 2 R 2 (thesoft select-or-skipdecisionforthe l -thblockin T k )withthereparameterizationtrick[25]:
Revised: Toremovethenon-differentiableargmaxoperationinEq.1,theGumbel Softmaxtrickrelaxesone-hot ( u l,k ) 2 { 0 , 1 } 2 (theone-hotencodingof u l,k )to v l,k 2 R 2 (thesoft select-or-skipdecisionforthe l -thblockin T k )withthereparameterizationtrick[25]:

Original: [Equation]
Revised: [Equation]

Original: [Figure]
Revised: [Figure]

Original: )intraining. onlyonetaskforpredictingtheoutput.
Revised: [Table]

Original: Inthisway,theselect-or-skippolicyofallblocksandtasks ( U = { u l,k } l  L,k K )determinestheadaptivefeaturesharingmechanismoverthegiventaskset T .
Revised: l, [Table] [Table] L,k 

Original: As the number of potential conﬁgurations for U is 2 L ⇥ K which grows exponentially with the number of blocks and tasks, it becomes intractable to manually ﬁnd such a U to get the optimal featuresharingpatterninmulti-tasklearning.
Revised: [Table] [Table]

Original: Insteadofhandcraftingthispolicy,weadoptGumbelSoftmax
Revised: As [Table]

Original: Sampling [25] to optimize U jointly with the network parameters W through standard back-propagation.
Revised: [Table]

Original: Moreover,weintroducetwopolicyregularizationstoachieveeffectiveknowledge sharinginacompactmulti-tasknetwork,aswellasacurriculumlearningstrategytostabilizetheoptimizationintheearlystages.
Revised: ,weintroducetwopolicyregularizationstoachieveeffectiveknowledge sharinginacompactmulti [Table] [Table] optimizationintheearlystages.

Revised: [Table]

Original: Afterthetrainingﬁnishes,wesamplethebinarydecision u l,k for eachblock l from u l,k todecidewhatblockstoselectorskipinthetask T k .
Revised: [Table] [Table] eachblock l from [Table]

Revised: [Table]

Revised: todecidewhatblockstoselectorskipinthetask

Revised: [Table]

Revised: [Table]

Revised: [Table]

Revised: helpoftheselect

Revised: [Table]

Revised: or

Revised: [Table]

Revised: ,weformanovelandnon

Original: Speciﬁcally,withthe helpoftheselect-or-skipdecisions,weformanovelandnon-trivialnetworkarchitectureforMTLparameter-sharing,andshareknowledgeatdifferentlevelsacrossalltasksinaﬂexibleandefﬁcient way.
Revised: [Table] trivialnetworkarchitectureforMTLparameter [Table] ,andshareknowledgeatdifferentlevelsacrossalltasksinaﬂexibleandefﬁcient way.

Original: Attesttime,whenanovelinputispresentedtothemulti-tasknetwork,theoptimalpolicyisfollowed,selectivelychoosingwhatblockstocomputeforeachtask.
Revised: Attesttime,whenanovelinputispresentedtothemulti [Table] [Table] followed,selectivelychoosingwhatblockstocomputeforeachtask.

Original: Ourproposedapproachnotonly encouragespositivesharingamongtasksviasharedblocksbutalsominimizesnegativeinterferencebyusingtask-speciﬁcblockswhennecessary.
Revised: Ourproposedapproachnotonly encouragespositivesharingamongtasksviasharedblocksbutalsominimizesnegativeinterferencebyusingtask-speciﬁcblockswhennecessary.

Original: LearningaTask-SpeciﬁcPolicy.
Revised: SpeciﬁcPolicy

Original: AdaShare , 
Revised: AdaShare , or

Original: -or skippolicy U weights W propagationfromourdesignedlossfunctions. However, eachselect or-skippolicy u l,k
Revised: U or l differentiableandthismakesdirectoptimization u log

Original: -differentiableandthismakesdirectoptimization difﬁcult. -SoftmaxSampling[25]toresolvethisnon-differentiability andenabledirectoptimizationofthediscretepolicy u l,k -propagation. blockinthetask
Revised: ( j )

Original: T k ⇡ l,k ,wegenerateitas, u l,k =argmax j 2{ 0 , 1 }  log ⇡ l,k ( j ) + G l,k ( j )  , (1) where G l,k =  log(  log U l,k ) isastandardGumbeldistributionwith U l,k sampledfromauniform i.i.d. distributionUnif (0 , 1) .
Revised: G theone v

Original: Toremovethenon-differentiableargmaxoperationinEq.1,theGumbel Softmaxtrickrelaxesone-hot ( u l,k ) 2 { 0 , 1 } 2 (theone-hotencodingof u l,k )to v l,k 2 R 2 (thesoft select-or-skipdecisionforthe l -thblockin T k )withthereparameterizationtrick[25]: v l,k ( j )= exp  (log ⇡ l,k ( j )+ G l,k ( j )) /
Revised: ,k 2 R 2 (thesoft select-or-skipdecisionforthe l -thblockin T k )withthereparameterizationtrick[25]: v l,k ( j )= exp  (log ⇡ l,k ( j )+ G l,k ( j )) /

Original: ⌧ 
Revised: ⌧

Original: P i 2{ 0 , 1 } exp  (log ⇡ l,k
Revised: P i 2{ 0 , 1 } exp  (log ⇡ l,k

Original: ( i )+ G l,k ( i )) /
Revised: ( i )+ G l,k ( i )) /

Original: ⌧  , (2)
Revised: ⌧  , (2)

Original: [Figure]
Revised: [Figure]

Original: (logits).
Revised: (logits).

Original: These select-or-skip vectors deﬁne which blocks should be executed in different tasks.
Revised: These select-or-skip vectors deﬁne which blocks should be executed in different tasks.

Original: A block is said to be shared across two tasks if it is being used by both of them or task-speciﬁc if it is being used by only one task for predicting the output.
Revised: A block is said to be shared across two tasks if it is being used by both of them or task-speciﬁc if it is being used by only one task for predicting the output.

Original: During training, both policy logits and network parameters are jointly learned using standard back-propagation through Gumbel-Softmax Sampling.
Revised: During training, both policy logits and network parameters are jointly learned using standard back-propagation through Gumbel-Softmax Sampling.

Original: We use task-speciﬁc losses and policy regularizations (to encourage sparsity and sharing) in training.
Revised: We use task-speciﬁc losses and policy regularizations (to encourage sparsity and sharing) in training.

Original: Best viewed in color.
Revised: Best viewed in color.

Original: only one task for predicting the output.
Revised: only one task for predicting the output.

Original: In this way, the select-or-skip policy of all blocks and tasks ( U = { u l,k } l  L,k  K ) determines the adaptive feature sharing mechanism over the given task set T .
Revised: In this way, the select-or-skip policy of all blocks and tasks ( U = { u l,k } l  L,k  K ) determines the adaptive feature sharing mechanism over the given task set T .

Original: As the number of potential conﬁgurations for U is 2 L ⇥ K which grows exponentially with the number of blocks and tasks, it becomes intractable to manually ﬁnd such a U to get the optimal feature sharing pattern in multi-task learning.
Revised: As the number of potential conﬁgurations for U is 2 L ⇥ K which grows exponentially with the number of blocks and tasks, it becomes intractable to manually ﬁnd such a U to get the optimal feature sharing pattern in multi-task learning.

Original: Instead of handcrafting this policy, we adopt GumbelSoftmax Sampling [25] to optimize U jointly with the network parameters W through standard back-propagation.
Revised: Instead of handcrafting this policy, we adopt GumbelSoftmax Sampling [25] to optimize U jointly with the network parameters W through standard back-propagation.

Original: Moreover, we introduce two policy regularizations to achieve effective knowledge sharing in a compact multi-task network, as well as a curriculum learning strategy to stabilize the optimization in the early stages.
Revised: Moreover, we introduce two policy regularizations to achieve effective knowledge sharing in a compact multi-task network, as well as a curriculum learning strategy to stabilize the optimization in the early stages.

Original: After the training ﬁnishes, we sample the binary decision u l,k for each block l from u l,k to decide what blocks to select or skip in the task T k .
Revised: After the training ﬁnishes, we sample the binary decision u l,k for each block l from u l,k to decide what blocks to select or skip in the task T k .

Original: Speciﬁcally, with the help of the select-or-skip decisions, we form a novel and non-trivial network architecture for MTL parameter-sharing, and share knowledge at different levels across all tasks in a ﬂexible and efﬁcient way.
Revised: Speciﬁcally, with the help of the select-or-skip decisions, we form a novel and non-trivial network architecture for MTL parameter-sharing, and share knowledge at different levels across all tasks in a ﬂexible and efﬁcient way.

Original: At test time, when a novel input is presented to the multi-task network, the optimal policy is followed, selectively choosing what blocks to compute for each task.
Revised: At test time, when a novel input is presented to the multi-task network, the optimal policy is followed, selectively choosing what blocks to compute for each task.

Original: Our proposed approach not only encourages positive sharing among tasks via shared blocks but also minimizes negative interference by using task-speciﬁc blocks when necessary.
Revised: Our proposed approach not only encourages positive sharing among tasks via shared blocks but also minimizes negative interference by using task-speciﬁc blocks when necessary.

Original: Learning a Task-Speciﬁc Policy.
Revised: Learning a Task-Speciﬁc Policy.

Original: In AdaShare , we learn the select-or-skip policy U and network weights W jointly through standard back-propagation from our designed loss functions.
Revised: In AdaShare , we learn the select-or-skip policy U and network weights W jointly through standard back-propagation from our designed loss functions.

Original: However, each select-or-skip policy u l,k is discrete and non-differentiable and this makes direct optimization difﬁcult.
Revised: However, each select-or-skip policy u l,k is discrete and non-differentiable and this makes direct optimization difﬁcult.

Original: Therefore, we adopt Gumbel-Softmax Sampling [25] to resolve this non-differentiability and enable direct optimization of the discrete policy u l,k using back-propagation.
Revised: Therefore, we adopt Gumbel-Softmax Sampling [25] to resolve this non-differentiability and enable direct optimization of the discrete policy u l,k using back-propagation.

Original: Gumbel-Softmax Sampling.
Revised: Gumbel-Softmax Sampling.

Original: The Gumbel-Softmax trick [25, 36] is a simple and effective way to substitutes the original non-differentiable sample from a discrete distribution with a differentiable sample from a corresponding Gumbel-Softmax distribution.
Revised: The Gumbel-Softmax trick [25, 36] is a simple and effective way to substitutes the original non-differentiable sample from a discrete distribution with a differentiable sample from a corresponding Gumbel-Softmax distribution.

Original: We let ⇡ l,k =
Revised: We let ⇡ l,k =

Original: [1  ↵ l,k , ↵ l,k ] be the distribution vector of the binary random variable u l,k that we want to optimize, where the logit ↵ l,k represents the probability that the l -th block is selected to execute in the task T k .
Revised: [1  ↵ l,k , ↵ l,k ] be the distribution vector of the binary random variable u l,k that we want to optimize, where the logit ↵ l,k represents the probability that the l -th block is selected to execute in the task T k .

Original: In Gumbel-Softmax Sampling, instead of directly sampling a select-or-skip decision u l,k for the l -th block in the task T k from its distribution ⇡ l,k , we generate it as, u l,k = arg max j 2{ 0 , 1 }  log ⇡ l,k ( j ) + G l,k ( j )  , (1) where G l,k =  log(  log U l,k ) is a standard Gumbel distribution with U l,k sampled from a uniform i.i.d.
Revised: In Gumbel-Softmax Sampling, instead of directly sampling a select-or-skip decision u l,k for the l -th block in the task T k from its distribution ⇡ l,k , we generate it as, u l,k = arg max j 2{ 0 , 1 }  log ⇡ l,k ( j ) + G l,k ( j )  , (1) where G l,k =  log(  log U l,k ) is a standard Gumbel distribution with U l,k sampled from a uniform i.i.d.

Original: distribution Unif (0 , 1) .
Revised: distribution Unif (0 , 1) .

Original: To remove the non-differentiable argmax operation in Eq. 1, the Gumbel Softmax trick relaxes one-hot ( u l,k ) 2 { 0 , 1 } 2 (the one-hot encoding of u l,k ) to v l,k 2 R 2 (the soft select-or-skip decision for the l -th block in T k ) with the reparameterization trick [25]: v l,k ( j ) =
Revised: To remove the non-differentiable argmax operation in Eq. 1, the Gumbel Softmax trick relaxes one-hot ( u l,k ) 2 { 0 , 1 } 2 (the one-hot encoding of u l,k ) to v l,k 2 R 2 (the soft select-or-skip decision for the l -th block in T k ) with the reparameterization trick [25]: v l,k ( j ) =

Original: exp  (log ⇡ l,k ( j ) + G l,k ( j )) /
Revised: exp  (log ⇡ l,k ( j ) + G l,k ( j )) /

Original: ⌧  P i 2{ 0 , 1 } exp  (log ⇡ l,k
Revised: ⌧  P i 2{ 0 , 1 } exp  (log ⇡ l,k

Original: ( i ) + G l,k ( i )) /
Revised: ( i ) + G l,k ( i )) /

Original: ⌧  , (2)
Revised: ⌧  , (2)

Original: [Figure]
Revised: [Figure]

Original: Model inputs.
Revised: Model inputs.

Original: To obtain the model inputs, we follow the sliding window practice and transform theuser’s behavior sequence into a ﬁxed-length- N sequence s =
Revised: To obtain the model inputs, we follow the sliding window practice and transform theuser’s behavior sequence into a fixed-length-

Original:  ( s 1 , s 2 , . .
Revised: N sequence s = ( s 1 , s 2 , . .

Original: , s N ) .
Revised: , s N ) .

Original: Then we producean item embedding matrix E I ∈ R |I|× d , where d is the embedding dimensionality.
Revised: Then we producean item embedding matrix E I ∈ R |I|× d , where d is the embedding dimensionality.

Original: We perform 129 a look-up operation from
Revised: We perform 130 a look-up operation from

Original: E I to retrieve the input embedding matrix E s ∈ R N × d for sequence s .
Revised: E I to retrieve the input embedding matrix E s ∈ R N × d for sequence s .

Original: Besides, we also add a learnable position embedding
Revised: Besides, we also add a learnable position embedding

Original: P s ∈ R N × d for sequence s .
Revised: P s ∈ R N × d for sequence s .

Original: Finally, we cangenerate the input embedding of each behavior sequence s as X s =
Revised: Finally, we cangenerate the input embedding of each behavior sequence s as X s =

Original: E s + P s ∈ R N × d .
Revised: E s + P s ∈ R N × d .

Original: Overall architecture.
Revised: Overall architecture.

Original: Recommender Transformer is characterized by stacking the Pathway Attentionblocks and feed-forward layers alternately, containing L blocks.
Revised: Recommender Transformer is characterized by stacking the Pathway Attentionblocks and feed-forward layers alternately, containing L blocks.

Original: This stacking structure is conduciveto learning behavior representations hierarchically.
Revised: This stacking structure is conduciveto learning behavior representations hierarchically.

Original: The overall equations of block l are formalized as:
Revised: The overall equations of block l are formalized as:

Original: [Equation]
Revised: [Equation]

Original: where Z l ∈ R N × d , l ∈ { 1 , · · · , L } denotes the output of the l -th block.
Revised: where Z l ∈ R N × d , l ∈ { 1 , · · · , L } denotes the output of the l -th block.

Original: The initial input Z 0 = X s ∈
Revised: The initial input Z 0 = X s ∈

Original: R N × d represents the raw behavior embedding.
Revised: R N × d represents the raw behavior embedding.

Original: R l − 1 is the previous route from the block l − 1 andwe initialize all elements in the route R 0 to 1.
Revised: R l − 1 is the previous route from the block l − 1 andwe initialize all elements in the route R 0 to 1.

Original: Path-MSA( · ) is to conduct the pathway attention.
Revised: Path-MSA( · ) is to conduct the pathway attention.

Original: LN( · )is to conduct layer normalization [3] and FFN represents the point-wise feed-forward network [4].
Revised: LN( · )is to conduct layer normalization [3] and FFN represents the point-wise feed-forward network [4].

Original: 3.1.1 Pathway Attention
Revised: 3.1.1 Pathway Attention

Original: Note that the single-branch self-attention mechanism [4] in vanilla transformer cannot model thebehavior pathway dynamically, resulting in key behaviors being overwhelmed by these non-pivotalones.
Revised: Note that the single-branch self-attention mechanism [4] in vanilla transformer cannot model thebehavior pathway dynamically, resulting in key behaviors being overwhelmed by these non-pivotalones.

Original: To solve this problem, we propose the Pathway Attention mechanism, as shown in Figure 2,which can dynamically attend to the behavior pathway of pivotal behavior tokens.
Revised: To solve this problem, we propose the Pathway Attention mechanism, as shown in Figure 2,which can dynamically attend to the behavior pathway of pivotal behavior tokens.

Original: Pathway router.
Revised: Pathway router.

Original: The pathway attention employs a sequence-adaptive pathway router to custom-tailorbehavior pathway routes for users.
Revised: The pathway attention employs a sequence-adaptive pathway router to custom-tailorbehavior pathway routes for users.

Original: The router generates a binary route R l ∈ { 0 , 1 } N to determinewhether a behavior token would be part of the behavior pathway or not.
Revised: The router generates a binary route R l ∈ { 0 , 1 } N to determinewhether a behavior token would be part of the behavior pathway or not.

Original: Each router takes thepre-order route R l − 1 and user behavior tokens
Revised: Each router takes thepre-order route R l − 1 and user behavior tokens

Original: Z l − 1 ∈ R N × d of the block l − 1 as its inputs.
Revised: Z l − 1 ∈ R N × d of the block l − 1 as its inputs.

Original: Allelements in the route are initialized by 1 and are updated progressively in training.
Revised: Allelements in the route are initialized by 1 and are updated progressively in training.

Original: Foremost, to suppress the potential disturbance to the model caused by the local drifted interest(Figure 1), it is crucial to incorporate the global information in the route generation.
Revised: Foremost, to suppress the potential disturbance to the model caused by the local drifted interest(Figure 1), it is crucial to incorporate the global information in the route generation.

Original: We applythe average pooling to all the preserved behavior tokens routed by R l − 1 , and produce the globalsequential representation via a multilayer perceptrons (MLP) module.
Revised: We applythe average pooling to all the preserved behavior tokens routed by R l − 1 , and produce the globalsequential representation via a multilayer perceptrons (MLP) module.

Original: Then, we combine this globalrepresentation with the inputs and employ a residual connection to maintain the original inputinformation.
Revised: Then, we combine this globalrepresentation with the inputs and employ a residual connection to maintain the original inputinformation.

Original: Finally, we feed them to another MLP layer to predict the probabilities of keeping or dropping the behavior tokens.
Revised: Finally, we feed them to another MLP layer to predict the probabilities of keeping or dropping the behavior tokens.

Original: The above procedure can be formulated as follows:
Revised: The above procedure can be formulated as follows:

Original: [Equation]
Revised: [Equation]

Original: where (cid:12) is the Hadamard product.
Revised: where ⊙ is the Hadamard product.

Original: For t ∈ { 1 , 2 , · · · , N } , we let π t =
Revised: For t ∈ { 1 , 2 , · · · , N } , we let π t =

Original: [1 − α t , α t ] , where the logit 158 α t denotes the probability that the t -th behavior token is kept for the behavior pathway.
Revised: [1 − α t , α t ] , where the logit 159 α t denotes the probability that the t -th behavior token is kept for the behavior pathway.

Original: Gumbel-Softmax sampling from π for router.
Revised: Gumbel-Softmax sampling from π for router.

Original: Our goal is to generate the binary route from 160 π .
Revised: Our goal is to generate the binary route from 161 π .

Original: However, sampling from π directly is non-differentiable, and it will impede the gradient-basedtraining.
Revised: However, sampling from π directly is non-differentiable, and it will impede the gradient-basedtraining.

Original: Thus, we apply the Gumbel-Softmax [15] technique to such sample.
Revised: Thus, we apply the Gumbel-Softmax [17] technique to such sample.

Original: Gumbel-Softmax isan effective way to approximate the original non-differentiable sample from a discrete distributionwith a differentiable sample from a Gumbel-Softmax distribution.
Revised: Gumbel-Softmax isan effective way to approximate the original non-differentiable sample from a discrete distributionwith a differentiable sample from a Gumbel-Softmax distribution.

Original: Instead of directly sampling akeep-or-drop decision (cid:98) R lt for the t -th behavior token from the distribution π t , we generate it as:
Revised: Instead of directly sampling akeep-or-drop decision (cid:98) R lt for the t -th behavior token from the distribution π t , we generate it as:

Original: [Equation]
Revised: [Equation]

Original: where G t = − log( − log U t ) is a standard Gumbel distribution, and U t is sampled i.i.d.
Revised: where G t = − log( − log U t ) is a standard Gumbel distribution, and U t is sampled i.i.d.

Original: from auniform distribution Uniform (0 , 1) .
Revised: from auniform distribution Uniform (0 , 1) .

Original: To remove the non-differentiable argmax operation in Eq 3, the
Revised: To remove the non-differentiable argmax operation in Eq 3, the

Original: Gumbel-Softmax uses the reparameterization trick [15] as a differentiable approximation to relaxone-hot (cid:98) R lt ∈ { 0 , 1 } to v t ∈ R 2 :
Revised: Gumbel-Softmax uses the reparameterization trick [17] as a differentiable approximation to relaxone-hot (cid:98) R lt ∈ { 0 , 1 } to v t ∈ R 2 :

Original: [Equation]
Revised: [Equation]

Original: where τ is the temperature parameter of the Softmax, which is commonly set to 1 in deep networks.
Revised: where τ is the temperature parameter of the Softmax, which is commonly set to 1 in deep networks.

Original: Hierarchical update strategy for router.
Revised: Hierarchical update strategy for router.

Original: The preliminary route (cid:98) R l , sampled from π , is not a ﬁnaldecision.
Revised: The preliminary route (cid:98) R l , sampled from π , is not a finaldecision.

Original: In our design, once a token fails to be routed in a certain block, it would permanently losethe privilege to be part of the behavior pathway in the following feed-forward procedure, constitutinga hierarchical pathway router strategy.
Revised: In our design, once a token fails to be routed in a certain block, it would permanently losethe privilege to be part of the behavior pathway in the following feed-forward procedure, constitutinga hierarchical pathway router strategy.

Original: Thus ﬁnally we formulate the route R l as the Hadamardproduct of (cid:98) R l and the pre-order route R l − 1 in the block l − 1 :[Equation]
Revised: Thus finally we formulate the route R l as the Hadamardproduct of (cid:98) R l and the pre-order route R l − 1 in the block l − 1 :

Original: [Equation]
Revised: [Equation]

Original: Multi-head pathway attention.
Revised: Multi-head pathway attention.

Original: The standard self-attention mechanism retrieves sequential characteristics exploiting all behavior tokens, making the behavior pathway overwhelmed by the trivialbehaviors.
Revised: The standard self-attention mechanism retrieves sequentialcharacteristics exploiting all behavior tokens, making the behavior pathway overwhelmed by thetrivial behaviors.

Original: In the new pathway attention, the pathway router would be ﬁrstly applied to the inputbehavior tokens to route information.
Revised: In the new pathway attention, the pathway router would be firstly applied to the inputbehavior tokens to route information.

Original: The pathway router would not pare down the number of tokens,but only the interactions between the off-pathway and on-pathway tokens, as these off-pathwaytokens may also convey contextual information.
Revised: The pathway router would not pare down the number of tokens,but only the interactions between the off-pathway and on-pathway tokens, as these off-pathwaytokens may also convey contextual information.

Original: Speciﬁcally, for the query, key, and value in the pathway attention: the query is routed by the pathwayrouter, to prevent the pathway from being overwhelmed and to force the pathway attention to attendto the behavior pathway; the key and value are the original input behavior tokens, to ensure that thecontextual information from off-pathway behavior tokens can be captured as well:[Equation]
Revised: Specifically, for the query, key, and value in the pathway attention: the query is routed by the pathwayrouter, to prevent the pathway from being overwhelmed and to force the pathway attention to attendto the behavior pathway; the key and value are the original input behavior tokens, to ensure that thecontextual information from off-pathway behavior tokens can be captured as well:

Original: [Equation]
Revised: [Equation]

Original: where m ∈ { 1 , 2 , · · · , h } is the index of head in the multi-head self-attention; W l Q m , W l K m , W l V m ∈
Revised: where m ∈ { 1 , 2 , · · · , h } is the index of head in the multi-head self-attention; W l Q m , W l K m , W l V m ∈

Original: R d × d/h are transformation matrices learned from data.
Revised: R d × d/h are transformation matrices learned from data.

Original: Finally, the outputs (cid:8) (cid:98) Z lm ∈ R N × d/h (cid:9) 1 ≤ m ≤ hof multiple heads are concatenated into (cid:98) Z l ∈ R N × d .
Revised: Finally, the outputs (cid:8) (cid:98) Z lm ∈ R N × d/h (cid:9) 1 ≤ m ≤ hof multiple heads are concatenated into (cid:98) Z l ∈ R N × d .

Original: We use (cid:98) Z l , R l = Path-MSA ( Z l − 1 , R l − 1 ) tosummarize the above pathway attention.
Revised: We use (cid:98) Z l , R l = Path-MSA ( Z l − 1 , R l − 1 ) tosummarize the above pathway attention.

Original: Its output is further transformed by Eq.
Revised: Its output is further transformed by Eq.

Original: (1) to form the ﬁnaloutput of the l -th block Z l ∈ R N × d .
Revised: (1) to form the finaloutput of the l -th block Z l ∈ R N × d .

Original: Causality.
Revised: Causality.

Original: In the prediction of the ( t + 1 )-th behavior, only the ﬁrst t observable behaviors shouldbe taken into account.
Revised: In the prediction of the ( t + 1 )-th behavior, only the first t observable behaviors shouldbe taken into account.

Original: To avoid a future information leak and ensure causality, a look-ahead mask isemployed and all links between Q j and K i ( j > i ) are removed.
Revised: To avoid a future information leak and ensure causality, a look-ahead mask isemployed and all links between Q j and K i ( j > i ) are removed.

Original: 3.2 Prediction Layer and Training Objective
Revised: 3.2 Prediction Layer and Training Objective

Original: Prediction layer.
Revised: Prediction layer.

Original: In the ﬁnal layer of our RETR, we calculate the user’s preference score for theitem k in the step ( t + 1 ) in the context of user behavior history as p ( i t +1 =
Revised: In the final layer of our RETR, we calculate the user’s preference score for theitem k in the step ( t + 1 ) in the context of user behavior history as p ( i t +1 =

Original: k
Revised: k

Original: | i 1: t ) =
Revised: | i 1: t ) =

Original: e k · Z Lt ,where e k is the representation of item k from item embedding matrix E I , and Z Lt is the output of the 197 L -th RETR blocks at step t ( L is the number of RETR blocks).
Revised: e k · Z Lt ,where e k is the representation of item k from item embedding matrix E I , and Z Lt is the output of the 198 L -th RETR blocks at step t ( L is the number of RETR blocks).

Original: Training objective.
Revised: Training objective.

Original: We adopt the pairwise ranking loss to optimize the model parameters as:
Revised: We adopt the pairwise ranking loss to optimize the model parameters as:

Original: [Equation]
Revised: [Equation]

Original: where we pair each ground-truth item i t +1 with a randomly sampled negative item i − t +1 .
Revised: where we pair each ground-truth item i t +1 with a randomly sampled negative item i − t +1 .

Original: In eachepoch, we randomly generate one negative item for each time step in each sequence.
Revised: In eachepoch, we randomly generate one negative item for each time step in each sequence.

Original: This pairwiseranking loss is widely adopted in previous literature of sequential recommendation [16, 41].
Revised: This pairwiseranking loss is widely adopted in previous literature of sequential recommendation [18, 45].

Original:  Experiments
Revised:  Experiments

Original: We extensively evaluate the proposed Recommender Transformer on seven real-world benchmarks.
Revised: We extensively evaluate the proposed Recommender Transformer on seven real-world benchmarks.

Original: [Table]
Revised: [Table]

Original: Datasets.
Revised: Datasets.

Original: Here are descriptions ofthe seven datasets: (1) Beauty, Sports,and Toys : these three datasets are threesubcategories obtained from Amazon review [22] datasets.
Revised: Here are descriptions of the sevendatasets: (1) Netflix : Netflix dataset is a largescale movie rating dataset released by Netflix.(2) MSD : The Million Song Dataset (MSD) isa large-scale, metadata-rich and open-sourcedataset on Kaggle. (3) Taobao : Taobao dataset[32] contains user behaviors in Taobao’s recommender system.

Revised: In experiments, we only use theclick behaviors.

Original: (2) Yelp [2]: Yelp isa dataset for business recommendation.
Revised: (4) Yelp [2]: Yelp is a datasetfor business recommendation.

Original: We only use the transaction records after January 1st, 2019.
Revised: We only use thetransaction records after January 1st, 2019.

Original: (3) Tmall : Tmallcontains users’ shopping logs on Tmallonline shopping platform, which is fromthe IJCAI-15 competition.
Revised: Tmall : Tmall contains users’ shopping logs on Tmall online shopping platform, which is from the IJCAI-15 competition.

Original: (4) Steam[16]: Steam dataset is collected from alarge online video game distribution platform.
Revised: (6) Steam [18]: Steamdataset is collected from a large online video game distribution platform.

Original: This dataset includes 2,567,538 users, 15,474 gamesand 7,793,069 English reviews from October 2010 to January 2018.
Revised: This dataset includes2,567,538 users, 15,474 games and 7,793,069 English reviews from October 2010 to January 2018.(7)

Original: (5) MovieLens : this is a widelyused benchmark dataset for evaluating collaborative ﬁltering algorithms.
Revised: MovieLens : this is a widely used benchmark dataset for evaluating collaborative filtering algorithms.

Original: The version we use is MovieLens-1M, which includes 1 million user ratings.
Revised: The version we use is MovieLens-1M, which includes 1 million user ratings.

Revised: The statistics ofthe seven datasets are summarized in Table 1.

Revised: All datasets are widely used in the recommendationtask.

Revised: It is notable that Netflix, MSD, Taobao and Steam are large-scale recommendation datasets.

Original: We group the interaction records by users or sessions for all datasets and sort them by the timestampsin ascending order.
Revised: We group the interaction records by users or sessions for all datasets and sort them by the timestampsin ascending order.

Original: We follow the operation in SASRec [16] and split the historical sequence for eachuser into three parts: (1) the most recent behavior for testing, (2) the second most recent behavior forvalidation, and (3) all remaining behaviors for training.
Revised: We follow the operation in SASRec [18] and split the historical sequence for eachuser into three parts: (1) the most recent behavior for testing, (2) the second most recent behavior forvalidation, and (3) all remaining behaviors for training.

Original: During testing, the input sequences containtraining behaviors and validation behaviors.
Revised: During testing, the input sequences containtraining behaviors and validation behaviors.

Original: We ﬁlter less popular items and inactive users with fewerthan ﬁve interaction records.
Revised: We filter less popular items and inactive users with fewerthan five interaction records.

Original: The statistics of the above seven datasets are summarized in Table 1.

Original: Beauty, Sports, Toys and Yelp have fewer average actions per user and item.

Original: MovieLens, Tmall and

Original: Steam have more actions per item.

Original: Evaluation metrics.
Revised: Evaluation metrics.

Original: Following the previous literature [38, 41, 16], we apply top-k Hit Ratio(HR@k),
Revised: Following the previous literature [41, 45, 18], we apply top-k Hit Ratio(HR@k),

Original: top-k Normalized Discounted Cumulative Gain (NDCG@k) and Mean Reciprocal Rank(MRR) for evaluation.
Revised: top-k Normalized Discounted Cumulative Gain (NDCG@k) and Mean Reciprocal Rank(MRR) for evaluation.

Original: We report HR@10, NDCG@10 and MRR of the results.
Revised: We report HR@10, NDCG@10 and MRR of the results.

Original: Besides, followingthe standard strategy in SASRec [16], we pair the ground-truth item with 100 randomly samplednegative items that the user has not interacted with.
Revised: Besides, followingthe standard strategy in SASRec [18], we pair the ground-truth item with 100 randomly samplednegative items that the user has not interacted with.

Original: All metrics are calculated according to theranking of the items and we report the average score.
Revised: All metrics are calculated according to theranking of the items and we report the average score.

Original: Baseline methods.
Revised: Baseline methods.

Original: We compare our approach with seven baseline methods. The PopRec is a simplebaseline that ranks items according to their popularity.
Revised: We compare our RETR with GRU4Rec [16], a simple baseline that applies

Original: Besides, we select four latest state of-the-arttransformer-based models: SASRec [16], BertRec [28], SASRec+ [35] and SMRec [6].
Revised: GRU to model item sequences, and state-of-the-art sequential recommendation models: SASRec[18], BertRec [31], SMRec [6].

Original: We noticethat SASRec [16] applies the transformer [4] into the sequential recommendation task; BertRec [28]introduces a Cloze objective loss for sequential recommendation; SASRec+ [35] improves SASRecwith time embedding, which is inspired by the positional embedding in transformer; SMRec [6]adopts SASRec as the backbone, and it is associated with a novel self-modulating attention.
Revised: S3-Rec [44], SINE [32], TGSRec [10] and LightSANs [9].

Original: These recent transformer-based methods have achieved state-of-the-art performance in many benchmarks.
Revised: Thesemethods adopt the attention mechanism to make precise recommendations.

Original: Besides transformer-based methods, we also adopt an RNN-based model GRURec [14] and a CNNbased model Caser [29] as baseline models.
Revised: Besides, we also compareour RETR with state-of-the-art graph-based sequential recommendation methods: Jodie [22] and TGN [28].

Original: The GRURec [14] applies GRU to model item sequencesand the Caser [29] applies convolution operations for sequential recommendation.

Original: All baselinemethods are conﬁgured using default parameters of the original paper or optimal parameters whichcan produce the best results in a grid search.
Revised: All baseline methods are configured using default parameters of the original paper oroptimal parameters which can produce their best results through a grid search.

Original: Implementation details.
Revised: Implementation details.

Original: Our model is supervised by the pairwise rank loss in Equ 7, using the
Revised: Our model is supervised by the pairwise rank loss in Equ 7, using the

Original: ADAM [17] optimizer with an initial learning rate of 0.001.
Revised: ADAM [19] optimizer with an initial learning rate of 0.001.

Original: Batch size is set to 512.
Revised: Batch size is set to 512.

Original: The maximumnumber of training epochs for all methods is set to 200.
Revised: The maximumnumber of training epochs for all methods is set to 200.

Original: All hyperparameters are tuned on thevalidation set.
Revised: All hyperparameters are tuned on thevalidation set.

Original: The training process is early stopped within 10 epochs.
Revised: The training process is early stopped within 10 epochs.

Original: Our RETR has L = 2 layers,and each layer has h = 4 heads  and d is set to be 256.
Revised: Our RETR has L = 2 layers,and each layer has h = 4 heads (the ablation study of multi-head attention can be found in theappendix A) and d is set to be 256.

Original: The maximum sequence length N is set to200 for MovieLens-1m and 100 for the other six datasets.
Revised: The maximum sequence length N is set to 200 for MovieLens-1mand 100 for the other six datasets.

Original: All experiments are repeated three times,implemented in PyTorch [23], and conducted on a single NVIDIA 3090 GPU.[Table] [Table] [Table]
Revised: All experiments are repeated three times, implemented in PyTorch[25], and conducted on a single NVIDIA 3090 GPU.

Original: [Table]

Original: [Table]

Original: [Table]

Original: [Table]

Original: [Table]

Original: [Table]

Original: [Table]

Original: [Table]

Original: [Table]

Original: [Table]

Original: [Table]

Original: [Table]

Original: [Table]

Original: MRR 0.

Original: [Table]

Original: [Table]

Original: [Table]

Original: Tmall

Original: [Table]

Original: [Table]

Original: [Table]

Original: [Table]
Revised: [Table]

Original: MRR

Original: [Table]

Original: [Table]

Original: Steam

Original: [Table]

Original: [Table]

Original: [Table]

Original: [Table]

Original: [Table]

Original: [Table]

Original: [Table]

Original: [Table]

Original: MRR

Original: [Table]

Original: [Table]

Original: [Table]

Original: [Table]

Original: [Table]

Original: [Table]

Original: [Table]

Original: 4.1 Main Results
Revised: 4.1 Main Results

Original: The results of different methods on seven datasets are shown in Table 2.
Revised: The results of different methods on seven datasets are shown in Table 2.

Original: First, the non-sequentialrecommendation method PopRec performs worse than sequential recommendation methods, indicating that capturing the sequential pattern is essential for sequential recommendation.

Original: Next, we caneasily ﬁnd that transformer-based models, SASRec [16], BertRec [28], SASRec+ [35], and SMRec[6], achieve better performance than RNN-based model GRURec [14] and CNN-based model Caser[29] on most datasets.
Revised: We can easily find thatattention-based models, SASRec [18], BertRec [31], SMRec [6], S3-Rec [44], SINE [32], TGSRec[10] and LightSANs [9], achieve better performance than RNN-based model GRU4Rec [16] on mostdatasets.

Original: It indicates that the transformer has a better capacity to capture sequentialcharacteristics. The transformer-based models use the attention mechanism to capture the interactioninformation between all previous user behaviors, indicating that the attention mechanism is crucialfor sequential recommendation.
Revised: It indicates that the attention mechanism is crucial for sequential recommendation, makingthe model have a better capacity to capture sequential characteristics. These models can capture theinteraction information between all previous user behaviors via the attention mechanism.

Revised: Besides,the graph-based models like Jodie [22] and TGN [28] also achieve competitive performance.

Original: Our RETR can achieve state-of-the-art performance by a large margin on most datasets compared withall baseline models.
Revised: Besides,our RETR can achieve state-of-the-art performance by a large margin on most datasets comparedwith all baseline models.

Original: Speciﬁcally, our RETR achieves competitive performance on the Beauty, Sports, Toys, and Yelp.
Revised: Results on Yelp, MovieLens1M and Tmall. Specifically, our RETR achieves competitive performance on the Yelp and Tmall.

Original: These datasets are sparse, containing less action information.
Revised: These datasets are sparse, containing less action information.

Original: Thus they have lots ofnoisy logged information.
Revised: Thusthey have lots of noisy logged information.

Original: By effectively capturing the behavior pathway, our RETR is not affected bythis trivial behavior information and captures the most informative behavior representation to achieve better performance.
Revised: By effectively capturing the behavior pathway, our RETR is not affected by this trivial behavior information and captures the most informative behaviorrepresentation to achieve better performance.

Original: Besides, our RETR can also achieve better performance on the Tmall, Steam,and MovieLens, which contain a large number of actions.

Original: Note that under the Tmall benchmark, 
Revised: Note that under the Tmall benchmark, RETR gains 7%

Original: RETR gains 7% HR@10, 12% NDCG@10 and 14% MRR against the strongest baseline SMRec[6].
Revised: HR@10, 12% NDCG@10 and 14% MRR against the strongest baseline SMRec [6].

Original: Under the Steam benchmark, our RETR also yields state-of-the-art performance, achieving 6%
Revised: Besides, forthe MoveLens1M, our RETR also achieves the best performance among all competing baselines.

Original: MRR gains compared with the SASRec.
Revised: Results on large-scale datasets.

Original: For the MoveLens benchmarks, our RETR also achieves thebest performance among all competing baselines.
Revised: Our RETR can consistently achieve state-of-the-art results onlarge-scale datasets (Netflix, MSD, Taobao, and Steam).

Original: These results strongly indicate that our RETR isconsistently effective on both sparse and dense datasets. Unlike these transformer-based baselines, our RETR adopts a pathway router to detect the mostinformative behavior tokens dynamically. These informative behavior tokens are denoted as thebehavior pathway.
Revised: These datasets are challenging and difficultto capture pivotal behavior pathway useful for precise recommendation from the rich but noisy user’sbehaviors. Especially for the Taobao dataset, our RETR gains relative improvements of 12% HR@10,37% NDCG@10 and 20% MRR against the strongest baseline SINE [32].

Original: Our RETR uses the behavior pathway and discards the less informative behaviortokens from the query.
Revised: It provides evidence thatour RETR can achieve competitive performance in both small- and large-scale datasets.

Original: The substantial performance gains of our RETR indicate that focusing moreon the behavior pathway enables RETR to capture sequential characteristics more efﬁciently andeffectively than the vanilla self-attention mechanism, which considers all previous user behaviors.
Revised: The substantial performance gains of our RETR indicate that focusing more on the behavior pathwayenables RETR to capture sequential characteristics more efficiently and effectively than the vanillaself-attention mechanism, which considers all previous user behaviors

Original: 4.2 Ablation Study
Revised: 4.2 Ablation Study

Original: Effectiveness of each model component.
Revised: Effectiveness of each model component.

Original: In the left column of Table 3, we analyze the efﬁcacyof each component in RETR on the Beauty dataset and have the following observations.
Revised: In the left column of Table 3, we analyze the efficacyof each component in RETR on the Yelp dataset and have the following observations.

Original: First, weremove the pathway router module and randomly choose whether it can be maintained or droppedfor each input behavior token.
Revised: First, weremove the pathway router module and randomly choose whether it can be maintained or droppedfor each input behavior token.

Original: Removing the pathway router decreases the prediction performance alot (MRR: 0 . 3067{+
+} → 0 . 2703 ), showing the necessity of learning behavior pathway effectively basedon a data-dependent module.
Revised: Removing the pathway router decreases the prediction performance alot (MRR: 0 . {+
+} → 0 . 3887 ), showing the necessity of learning behavior pathway effectively basedon a data-dependent module.

Original: Second, discarding the hierarchical update strategy for the behaviorpathway also decreases the prediction performance, suggesting that this strategy is crucial for RETRto get a more accurate behavior pathway.
Revised: Second, discarding the hierarchical update strategy for the behaviorpathway also decreases the prediction performance, suggesting that this strategy is crucial for RETRto get a more accurate behavior pathway.

Original: Notably, SASRec is the particular case of removing thepathway router, making routing decision 1 for all behaviors.

Original: Our RETR signiﬁcantly outperformsthe SASRec, indicating that capturing the behavior pathway effectively interacts with all previousbehaviors.

Original: Number of blocks.
Revised: Number of blocks.

Original: In the right column of Table 3, we adjust the number of blocks for RETR on
Revised: In the right column of Table 3, we adjust the number of blocks for RETR on

Original: Beauty.
Revised: Yelp.

Original: We ﬁnd that the performance ﬁrst increases rapidly with the growth of the block number andachieves the best performance at N = 2 .
Revised: We find that the performance first increases rapidly with the growth of the block number andachieves the best performance at L = 2 .

Original: We perform a similar grid search on other datasets.
Revised: We perform a similar grid search on other datasets.

Original: [Table]
Revised: [Table]

Revised: [Table]

Original: [Table]
Revised: [Table]

Original: Effectiveness of temperature.
Revised: Effectiveness of temperature.

Original: In the left column of Table 4, we analyze the efﬁcacy of differenttemperatures for Gumbel-Softmax sampling in RETR on the Yelp dataset.
Revised: In the left column of Table 4, we analyze the efficacy of differenttemperatures for Gumbel-Softmax sampling in RETR on the Yelp dataset.

Original: We observe that the performance ﬁrst increases rapidly with the growth of the temperature and achieves the best performancewhen τ = 0 . 8 , while the performance degenerates a lot when τ > 1 .
Revised: We observe that the performance first increases rapidly with the growth of the temperature and achieves the best performancewhen τ = 0 . 8 , while the performance degenerates a lot when τ > 1 .

Original: The temperature τ softensthe softmax with τ > 1 .
Revised: The temperature τ softensthe softmax with τ > 1 .

Original: However, when τ → ∞ , the Gumbel-Softmax distribution p τ ( y t ) → 0 .
Revised: However, when τ → ∞ , the Gumbel-Softmax distribution p τ ( y t ) → 0 .

Original: 5becomes more smooth, leading to the maximum uncertainty.
Revised: 5becomes more smooth, leading to the maximum uncertainty.

Original: To make the sampling results moreconvincing, we apply the temperature calibration τ < 1 during training to avoid overconﬁdentpredictions.
Revised: To make the sampling results moreconvincing, we apply the temperature calibration τ < 1 during training to avoid overconfidentpredictions.

Original: These results show that Gumble-Softmax sampling with lower temperature ( τ < 1 )avoids overconﬁdent predictions, leading to better performance.
Revised: These results show that Gumble-Softmax sampling with lower temperature ( τ < 1 )avoids overconfident predictions, leading to better performance.

Original: Evaluation on efﬁciency.
Revised: Evaluation on efficiency.

Original: The efﬁciency is compared between SASRec, SASRec+ and SMRec onthe Yelp dataset.
Revised: The efficiency is compared between SASRec [18], SINE [32] and SMRec[6] on the Yelp dataset.

Original: The computation cost is measured with gigabit ﬂoating-point operations (GFLOPs)on the self-attention module with position encoding.
Revised: The computation cost is measured with gigabit floating-point operations(GFLOPs) on the self-attention module with position encoding.

Original: Meanwhile, the model scale measured withparameters is also presented.
Revised: Meanwhile, the model scale measuredwith parameters is also presented.

Original: As shown in Table 4, our RETR has almost the same number ofparameters or GFLOPs, compared with SASRec, indicating that our pathway router is a light-weightmodule.
Revised: As shown in Table 4, our RETR has almost the same number ofparameters or GFLOPs, compared with SASRec, indicating that our pathway router is a light-weightmodule.

Original: Our pathway attention does not bring more costs.
Revised: Our pathway attention does not bring more costs.

Original: It’s worth noticing that the parameterscales and GLOPs of other competing transformers (apart from SASRec) are larger than RETR, butour RETR achieves higher performance.
Revised: It’s worth noticing that the parameterscales and GLOPs of other competing transformers (apart from SASRec) are larger than RETR, butour RETR achieves higher performance.

Original: This result shows that our RETR is more efﬁcient andeffective than other competing transformer-based models.
Revised: This result shows that our RETR is more efficient andeffective than other competing attention-based models.

Original: 4.3 Visualization
Revised: 4.3 Case study

Original: Setups.
Revised: Setups.

Original: We also provide qualitative visualizations for our RETR,SASRec [16] and SMRec [6].
Revised: We also provide qualitative visualizations for our RETR, and SASRec [18].

Original: Technically, we use the GradCAM [26] to generate behavior heat maps of the output of the last layerin each model.
Revised: Technically, weuse the GradCAM [29] to generate behavior heatmaps of the output of the last layer in each model.

Original: A random user’s historical behaviors in the Steam dataset are given in sequentialorder (row-wise). The last item is an RPG game The Dwarves in the test set.
Revised: Three random examples of users’ historical behaviors in the Steam dataset are shown in sequentialorder through subplots (a)–(c) in Figure 3.

Original: We provide attentionheatmaps on the last ten positions at the last ten time steps in Figure 3.
Revised: We provide attention heatmaps of each example at the last ten time steps.

Original: As shown in Figure 3, twomain behavior pathway characteristics exist in this sequence: (1) Casual Behavior Pathway: RPGgames are randomly clicked by the user, while the user has a continuing interest in RPGs.
Revised: We can observe three main behavior pathway characteristics corresponding to threebehavior sequences respectively: (a) Casual behavior pathway: RPG games are randomly clicked bythe user, while the user has a continuing interest in RPGs.

Original: (2) Drifted Behavior Pathway: The user has recently been interested in adventure games but chooses the RPGat last.We hope that a sequential recommendation model can ﬁgure out the exact behavior pathway.
Revised: (b) Correlated behavior pathway: Theuser has recently been interested in indie games. (c) Drifted behavior pathway: The user has recentlybeen interested in simulation games but chooses an indie game at last.

Original: Visualzation results.
Revised: Visualization results.

Original: As shown in Figure 3, we can ﬁnd that the baseline method can not mitigatethe drifted behavior pathway and capture the casual pathway adaptively. It seems that these modelscan be misled by the recent Correlated Behavior Pathway .
Revised: We elaborate the three representative categories of behavior pathway inrecommender systems with model-learned attention heatmaps. (1) Casual behavior pathway:

Original: In the third row of Figure 3, the SASRecfocuses more on the recent adventure games and overlooks the user’s casual interest in RPGs, whichindicates the SASRec is easy to be overwhelmed by the drifted behavior pathway.
Revised: Asshown in Figure 3(a), the RGB game is randomly clicked at casual times. Our RETR can captureall the RPG casual behavior pathways, while the SASRec focuses on the incorrect recent adventuregames. The SASRec cannot capture the early clicked RPG game.

Original: The SASReccannot effectively mitigate the drifted behavior pathway and capture the casual behavior pathway.
Revised: This phenomenon proves thatour RETR can deal with the casual behavior pathway effectively. (2) Correlated behavior pathway:

Original: For SMRec, even though it adopts a time weight mechanism.
Revised: For the correlated behavior pathway, we also provide an example which is shown in Figure 3(b).

Original: However, only using the time weightmechanism can not help it capture the practical behavior pathway. 
Revised: The indie game is clicked many times recently, leading to the final decision to an indie game. Our RETR can effectively capture the correlated behavior pathway. However, the SASRec provides higherattention scores on the recent RPG games.

Original: On the contrary,as shown in thesecond row of Figure 3, our RETR can capture the casual behavior pathway precisely withhigherscores, and avoid being misled by the drifted behavior pathway.
Revised: On the contrary, our RETR pays no attention to thesewrong results, showing that it has a greater ability to cope with the correlated behavior pathway.(3) Drifted behavior pathway: As shown in Fig 3(c).

Revised: The user was initially interested in the indiegame, but suddenly became interested in simulation games recently and chose an indie game at last.

Revised: Our RETR captures the drifted behavior pathway for the indie game and has not concentrated onthe old drifted pathway – simulation games, while the SASRec is affected by the trivial behaviorsof simulation games.

Original: This visualization results stronglyshow that our RETR can capture the behavior pathway dynamically for each user.
Revised: These visualization results strongly show that our RETR can capture variousbehavior pathways dynamically for each user.

Original: [Figure]
Revised: [Figure]

Original: order to improve the performance of Semantic Segmentation.
Revised: order to improve the performance of Semantic Segmentation.

Original: In contrast, our approach is still able to improve the segmentation performance instead of suffering from the negative interference by the other two tasks.
Revised: In contrast, our approach is still able to improve the segmentation performance instead of suffering from the negative interference by the other two tasks.

Original: The same reduction in negative transfer is also observed in Surface Normal Prediction in Tiny-Taskonomy 5-Task Learning.
Revised: The same reduction in negative transfer is also observed in Surface Normal Prediction in Tiny-Taskonomy 5-Task Learning.

Original: However, our proposed approach AdaShare still performs the best using less than 1/5 parameters of most of the baselines (Table 4).
Revised: However, our proposed approach AdaShare still performs the best using less than 1/5 parameters of most of the baselines (Table 4)

Original: Moreover, our proposed AdaShare also achieves better overall performance across the same taskon different domains.
Revised: Moreover, our proposed AdaShare also achieves better overall performance across the same task

Original: For image classiﬁcation on DomainNet [42], AdaShare improves average accuracy over Multi-Task baseline on 6 different visual domains by 4.6% (62.2% vs. 57.6%), with the maximum 16% improvement in quickdraw domain.

Original: For text classiﬁcation task, AdaShare outperforms the Multi-Task baseline by 7.2% (76.1% vs. 68.9%) in average over 10 different NLP datasets [8] and maximally improves 27.8% in sogou_news dataset.

Original: Similar tasks are more correlated, such as real is closer to painting than quickdraw .

Original: Policy Visualization and Task Correlation.
Revised: Policy Visualization and Task Correlation.

Original: In Figure3: (a), we visualize our learned policy distributions (via logits) and the feature sharing policy in Tiny-Taskonomy 5-Task Learning (more visual- izations are included in supplementary material).
Revised: In Figure we visualize our learned policy distributions (via logits) and the feature sharing policy in Tiny-Taskonomy 5-Task Learning (more visual- izations are included in supplementary material).

Original: We also adopt the cosine similarity between task-speciﬁc policy logits as an effective representation of task correlations (Figure 3: (b), Figure 4).
Revised: We also adopt the cosine similarity between task-speciﬁc policy logits as an effective representation of task correlations (Figure 3: (b), Figure 4).

Original: We havethe following keyobservations.
Revised: We have key

Original: (a) Theexecution probability of eachblock for taskk shows that not all blocks contribute to the task equally and it allows AdaShare to mediate among tasks and decide task-speciﬁc blocks adaptive to the given task set.
Revised: The of each for task shows that not all blocks contribute to the task equally and it allows AdaShare to mediate among tasks and decide task-speciﬁc blocks adaptive to the given task set.

Original: (b) Our learned policy prefers to have more blocks shared only among a sub-group of tasks in ResNet’s conv3 _
Revised: (b) Our learned policy prefers to have more blocks shared only among a sub-group of tasks in ResNet’s conv3 _

Original: x layers, where middle/high-level features, which are more task speciﬁc, are starting to get captured.
Revised: x layers, where middle/high-level features, which are more task speciﬁc, are starting to get captured.

Original: By having blocks shared by a sub-group of tasks, AdaShare encourages the positive transfer and relieves the effect of negative transfer, resulting in better overall performance.
Revised: By having blocks shared by a sub-group of tasks, AdaShare encourages the positive transfer and relieves the effect of negative transfer, resulting in better overall performance.

Original: (c) We clearly observe that Surface Normal Prediction and Depth Prediction, two different 3D tasks, are more correlated, and that Keypoint prediction and Edge detection, two different 2D tasks are more correlated (see Figure 3: (b)).
Revised: (c) We clearly observe that Surface Normal Prediction and Depth Prediction, two different 3D tasks, are more correlated, and that Keypoint prediction and Edge detection, two different 2D tasks are more correlated (see Figure 3: (b)).

Original: Similarly, Figure 4 shows that the domain real is closer to painting than quickdraw in DomainNet.
Revised: Similarly, Figure 4 shows that the domain real is closer to painting than quickdraw in DomainNet.

Original: Both results follow the intuition that similar tasks should have similar execution distribution to share knowledge.
Revised: Both results follow the intuition that similar tasks should have similar execution distribution to share knowledge.

Original: Note that the cosine similarity purely measures the correlation between the normalized execution probabilities of different tasks, which is not inﬂuenced by the different optimization uncertainty of different tasks.
Revised: Note that the cosine similarity purely measures the correlation between the normalized execution probabilities of different tasks, which is not inﬂuenced by the different optimization uncertainty of different tasks.

Original: Computation Cost (FLOPs).
Revised: Computation Cost (FLOPs).

Original: AdaShare requires much less computation (FLOPs) as compared to existing MTL methods.
Revised: AdaShare requires much less computation (FLOPs) as compared to existing MTL methods.

Original: E.g., in Cityscapes 2-task, Cross-stitch/Sluice, NDDR, MTAN, DEN, and AdaShare use 37.06G, 38.32G, 44.31G, 39.18G and 33.35G FLOPs and in NYU v2 3-task, they use 55.59G, 57.21G, 58.43G, 57.71G and 50.13G FLOPs, respectively.
Revised: E.g., in Cityscapes 2-task, Cross-stitch/Sluice, NDDR, MTAN, DEN, and AdaShare use 37.06G, 38.32G, 44.31G, 39.18G and 33.35G FLOPs and in NYU v2 3-task, they use 55.59G, 57.21G, 58.43G, 57.71G and 50.13G FLOPs, respectively.

Original: Overall, AdaShare offers on average about 7.67%-18.71% computational savings compared to state-of-the-art methods over all the tasks while achieving better recognition accuracy with about 50%-80% less parameters.
Revised: Overall, AdaShare offers on average about 7.67%-18.71% computational savings compared to state-of-the-art methods over all the tasks while achieving better recognition accuracy with about 50%-80% less parameters.

Original: [Figure]
Revised: [Figure]

Original: GroundTruth

Original:  Conclusion
Revised:  Conclusion

Revised: [Figure]

Original: A sequential recommender is designed to make accurate recommendations based on users’ historicalbehaviors.
Revised: A sequential recommender is designed to make accurate recommendations based on users’ historicalbehaviors.

Original: The sequential recommendation system has beneﬁted many practical applications suchas online advertising and social media.
Revised: The sequential recommendation system has benefited many practical applications such asonline advertising.

Original: However, the users’ behaviors are dynamic and come in acontinually evolving manner due to various reasons.
Revised: However, the users’ behaviors are dynamic and come in a continually evolvingmanner.

Revised: A user’s current decision may only call upon the interest from the certain relevant behaviorsof the past.

Original: We conclude these sequential characteristicsas the behavior pathway.
Revised: We conclude these sequential characteristics as the behavior pathway.

Original: Previous models cannot capture the behavior pathway dynamically.
Revised: Previous modelscannot capture the behavior pathway dynamically.

Original: Wepropose the Recommender Transformer (RETR) with a novel pathway attention mechanism totackle these challenges.
Revised: We propose the Recommender Transformer(RETR) with a novel pathway attention mechanism to tackle these challenges.

Original: The pathway attention develops a pathway router to dynamically get thebehavior pathway for each user andcapture the evolving patterns.
Revised: The pathway attentiondevelops a pathway router to dynamically get the behavior pathway for each user and the patterns

Original: Our RETR achieves state-of-the-artperformance on seven real-world datasetsfor sequential recommendation.
Revised: RETR achieves -art performance -world datasets sequential recommendation visualization also that our RETR can dynamically capture the behavior pathway for each user.

Original: Checklist
Revised: Checklist

Original: For all authors...
Revised: For all authors...

Original: (a) Do the main claims made in the abstract and introduction accurately reﬂect the paper’s contributions and scope?
Revised: (a) Do the main claims made in the abstract and introduction accurately reflect the paper’s contribu- tions and scope?

Original: [Yes]
Revised: [Yes]

Original: (b) Did you describe the limitations of your work?
Revised: (b) Did you describe the limitations of your work?

Original: [Yes] Broader impact in the supplemental
Revised: [Yes] Broader impact in the supplemental

Original: material
Revised: material

Original: (c) Did you discuss any potential negative societal impacts of your work?
Revised: (c) Did you discuss any potential negative societal impacts of your work?

Original: [Yes] Broader impact in
Revised: [Yes] Broader impact in

Original: the supplemental material
Revised: the supplemental material

Original: (d) Have you read the ethics review guidelines and ensured that your paper conforms to them?
Revised: (d) Have you read the ethics review guidelines and ensured that your paper conforms to them?

Original: [Yes]
Revised: [Yes]

Original: If you are including theoretical results...
Revised: If you are including theoretical results...

Original: (a) Did you state the full set of assumptions of all theoretical results?
Revised: (a) Did you state the full set of assumptions of all theoretical results?

Original: [N/A]
Revised: [N/A]

Original: (b) Did you include complete proofs of all theoretical results?
Revised: (b) Did you include complete proofs of all theoretical results?

Original: [N/A]
Revised: [N/A]

Original: If you ran experiments...
Revised: If you ran experiments...

Original: (a) Did you include the code, data, and instructions needed to reproduce the main experimental
Revised: (a) Did you include the code, data, and instructions needed to reproduce the main experimental

Original: results (either in the supplemental material or as a URL)?
Revised: results (either in the supplemental material or as a URL)?

Original: [No] The code and the data are
Revised: [No] The code and the data are

Original: proprietary.
Revised: proprietary.

Original: (b) Did you specify all the training details (e
Revised: (b) Did you specify all the training details (e

Original: g., data splits, hyperparameters, how they were chosen)?
Revised: g., data splits, hyperparameters, how they were chosen)?

Original: [Yes] Section 4 in the main text.
Revised: [Yes] Section 4 in the main text.

Original: (c) Did you report error bars (e.g., with respect to the random seed after running experiments
Revised: (c) Did you report error bars (e g., with respect to the random seed after running experiments

Original: multiple times)?
Revised: multiple times)?

Original: [Yes] Section 4 in the main text.
Revised: [Yes] Section 4 in the main text.

Original: (d) Did you include the total amount of compute and the type of resources used (e g., type of GPUs,[Table]
Revised: (d) Did you include the total amount of compute and the type of resources used (e.g., type of GPUs,

Original: internal cluster, or cloud provider)?
Revised: internal cluster, or cloud provider)?

Original: [Yes] Section 4 in the main text.
Revised: [Yes] Section 4 in the main text.

Original: If you are using existing assets (e
Revised: If you are using existing assets (e.g.,

Original: g., code, data, models) or curating/releasing new assets...
Revised: a

Original: (a) Ifyour work uses existing assets, did you cite thecreators?
Revised: If uses existing assets, did you cite the

Original: [Yes] Section 4 in themain text.
Revised: [Yes] Section 4 in the text.

Original: (b) Did you mention the license of the assets?
Revised: (b Did you mention the license of the assets?

Original: [N/A]
Revised: [N/A

Revised: c

Original: (c) Did you include any newassets either inthe supplemental materialor as a URL?
Revised: any new either in supplemental material URL?

Original: [No]
Revised: No

Original: (d) Did you discuss whether and how consent was obtained from people whose data you’re us- [Table] ing/curating? [Yes] Section 4 in the main text.
Revised: d

Original: (e) Did you discuss whether the data you are using/curating contains personally identiﬁable
Revised: (e) Did you discuss whether the data you are using/curating contains personally identifiable

Original: informa-
Revised: informa-

Revised: [Table]

Original: tion or offensive content?
Revised: tion or offensive content?

Original: [Yes] Broader impact in the supplemental material. 
Revised: [Yes] Broader impact in the supplemental material. [Table]

Original: If you used crowdsourcing or conducted research with human subjects...
Revised: If you used crowdsourcing or conducted research with human subjects...

Original:  (a) Did you include the full text of instructions given to participants and screenshots, if applicable? 
Revised: [Table] (a) Did you include the full text of instructions given to participants and screenshots, if applicable? [Table]

Original: [N/A]
Revised: [N/A]

Original:  (b) Did you describe any potential participant risks, with links to Institutional Review Board (IRB) 
Revised: [Table] (b) Did you describe any potential participant risks, with links to Institutional Review Board (IRB) [Table]

Original: approvals, if applicable?
Revised: approvals, if applicable?

Original: [N/A]
Revised: [N/A]

Revised: [Table]

Original: (c) Did you include the estimated hourly wage paid to participants and the total amount spent on
Revised: (c) Did you include the estimated hourly wage paid to participants and the total amount spent on

Revised: [Table]

Original: participant compensation?
Revised: participant compensation?

Original: [N/A]
Revised: [N/A]

Revised: [Table]