Personalized Negative Reservoir for Incremental Learning in Recommender Systems
Authors: Antonios Valkanas
Yuening Wang
Yingxue Zhang
Mark Coates
Venue: Accepted by TMLR ()

Abstract: Recommender systems have become an integral part of online platforms. Every day the volume of training data is expanding and the number of user interactions is constantly increasing. The exploration of larger and more expressive models has become a necessary pursuit to improve user experience. However, this progression carries with it an increased computational burden. In commercial settings, once a recommendation system model has been trained and deployed it typically needs to be updated frequently as new client data arrive. Cumulatively, the mounting volume of data is guaranteed to eventually make full batch retraining of the model from scratch computationally infeasible. Naively fine-tuning solely on the new data runs into the well-documented problem of catastrophic forgetting. Despite the fact that negative sampling is a crucial part of training with implicit feedback, no specialized technique exists that is tailored to the incremental learning framework. In this work, we propose a personalized negative reservoir strategy, which is used to obtain negative samples for the standard triplet loss of graph-based recommendation systems. Our technique balances alleviation of forgetting with plasticity by encouraging the model to remember stable user preferences and selectively forget when user interests change. We derive the mathematical formulation of a negative sampler to populate and update the reservoir. We integrate our design in three SOTA and commonly used incremental recommendation models. We show that these concrete realizations of our negative reservoir framework achieve state-of-the-art results for standard benchmarks using multiple top-k evaluation metrics.

Published in Transactions on Machine Learning Research (02/2025)
Personalized Negative Reservoir for Incremental Learning in Recommender Systems
Antonios Valkanas
antonios. antonios. www..aaaaaaaaammiiiiimllmlaolmm.
McGill University, Mila, ILLS
Yuening Wang
Buening.wanngghhuuurre
Huawei Noah's Ark Lab
Yingxue Zhang
Shmopmee.zhnn@@haues..com
Huowei Noah's Ark
Mark Coates
mark. markscoates@mmogill.c
McGill University, Mila, ILLS
Reviewed on OpenReview: https: // openreview. net/ forum? id- jrUUks5sKk
Abstract
Recommender systems have become integral part of online platforms. Every day the volume of training data is expanding and the number of user interactions is constantly in- crcasing. The exploration of larger and more expressive models has become a necossary pursuit to improve user experience. However, this progression carries with it an increased computational burden. In commercial settings, once a recommendation system model has been trained and deployed typically needs be updated frequently as new client data arrive. Cumulatively, the mounting volume of data is guaranteed to eventually make full batch retraining of the model from scratch computationally infeasible. Naively fine-tuning solely on the new data runs into the well-documented problem of catastrophic forgetting. Despite the fact that negative sampling is a crucial part of training with implicit feedback, no specialized technique exists that is tailored to the incremental learning framework. In this work, we propose a personalized negative reservoir strategy. which is used to obtain negative samples for the standard triplet loss graph-based recommendation systems. Our technique balances alleviation of forgetting with plasticity by encouraging the model to re- member stable user preferences and selectively forget when interests change. We derive the mathematical formulation of negative sampler to populate and update the reservoir. We integrale our design in three SOTA and commonly used incremental recommendation models. We show that these concrete realizations of our negative reservoir framework achieve statc-of-the-art results for standard benchmarks using multiple top-k evaluation metrics.
1 Introduction
Recommender systems have become crucial part of online services. Delivering highly relevant item ommendations not only enhances experience but also bolsters the revenue of service providers. The advent of deep learning-based recommender systems has significantly elevated the quality of user and item representations (Covington et al. 2016 Guo el. al. 2017 Cheng et al. 2016 He et al. 2023). To more accurately represent user behavior, there has been a substantial expansion in the volume of training data, accumulated from the long user-item interaction history (He et al. 2023 Xu al.] 2020). Thus, the ex- ploration of larger and more expressive models has become vital research direction. For example, Graph Neural Network (GNN) based recommendation methods can achieve compelling performance on recommen-

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dation tasks because of their ability to model the rich relational information of the data through the message
passing paradigm (van den Berg et. al. 2018 Wang et al. 2019b 2021a Sun et al. 2019).
However, this evolution brings with it a potential increase in computational burden. An industrial-scale recommendation serving model, once integrated into an online system, usually requires regular updates to accommodate the arrival of recent. client. data. The constant arrival of new data inevitably leads to a point where full-batch retraining of the model from scratch becomes infeasible. One straightforward way to tackle this computational challenge is to train the backbone model in an incremental fashion, updating it only when new data block arrives, instead of full batch retraining with older data. In industrial-Ievel rocommender systems, the new data block can arrive in daily, hourly or even in shorter interval (Xu) et al. 2020; Wang et al., 2021b), depending on the application. Unfortunately, naively fine-tuning the model with new data leads to the well-known issue of "catastrophic forgetting" (Kirkpatrick et al.) 2017). í.e., the model discards information from earlier data blocks and overfits to the newly acquired data. There are two mainstream methods to alleviate the catastrophic forgetting problem: (i) experience (rescrvoir) knowledge distillation (Castro et al. 2018 Kirkpatrick et al. 2017 Xu et al. 2020 Wang et al. 2021b 2023). Reservoir replay methods retrain on some previously observed user interactions from past data blocks while jointly training with the new data. Regularization techniques are typically formulated as knowledge distillation problem where the model trained on the old data takes the role of the "teacher" model and the model fine-tuned on the new data is regarded as the "student" model. A knowledge distillation loss is applied to preserve the information from the teacher to the student model through model weight (Castro et al. 2018 Kirkpatrick et al. 2017). structural (Xu et al. 2020), contrastive distillation (Wang et al. 2021b).
replay (Prabhu et. al. 2020 Ahrabian et al. 2021]: 1; and (ii) regularization-
We note there is one important aspect of the incremental learning framework for graph based recommender systems that has received very little attention. Negative sampling plays critical role in recommendation system training. This is because when training with implicit feedback we do not have access to explicit user dislikes so we need a mechanism to select low-user interest items for training. Sampling negative items is necessary as training on all possible positive and negative item pairs would be too costly. A good negative sampler can lead to increased convergence speed. This is key in live deployment settings where there is limited amount of time to train before new batch of data is generated. The most common strategy for negative sampling involves uniform sampling (Rendle et al., 2009). While subsequent works improve upon the negative sampler for the static setting, there are no works dedicated to addressing negative sampling in incremental learning. We identify two unique challenges for designing a good negative sampler for an incremental lcarning framework. First, the negative reservoir must be personalized for cach user and it should model a user's interests or preference shift across time blocks. This can provide a significant distribution bias in the negative sampling process. This relates to a classic tradc-off in continual learning, namely achieving a correct balance between retaining knowledge learned from prior training (stability), and being flexible enough to adapt to new patterns (plasticity) in a delta-regime (Oreshkin et al. 2024) that combines the two. Second, the ranking (prediction) produced by the model from the previous time block should be exploited as a bascline for informative negative samples in the new block. We note that the focus of our work is on accounting for user interest shifts rather addressing the problem from a traditional continual learning perspective that focuses on preventing catastrophic forgetting (Wang et al.) 2023). The reason for this is that, as we show in the experiments and case study, existing incremental learning techniques are too focused on slability and neglect model plasticily.
Considering the abovenmentioned challenges, we design the first negative reservoir strategy tailored for the incremental learning framework. This negative rescrvoir contains the most effective negative samples in cach incremental training block based on the user change of interest. Methodologically this translates into two hypotheses concerning the properties of a good sampling distribution for negative items. Firstly, the negative sampler should respond to user changes of interest and sample more items from item categories that the user is losing interest in over time and secondly the sampler should prefer items that are ranked highly (hard negatives) to induce larger gradients and learn faster. Our negative reservoir design is compatible with any incremental learning framework that employs negative sampling, which includes the standard incremental learning frameworks for recommender systems. In our experiments, we integrate our negative reservoir design into three recent incremental learning frameworks. Our designed negative reservoir achieves state-
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of-the-art performance when incorporated in three standard incremental learning frameworks, improving GraphSATL. (Xu et al. 2020), SGCT (Wang et al. 2021b), and LWC-KD (Wang et al. 2021bp by an average of 11.2%, 8.3% and 6.4%, respectively, across six large-scale recommender system datasets. Our main contributions can be summarized as:
This is the first work to propose negative reservoir design tailored for incremental learning in graph- based recommender systems. The approach, for which we provide principled mathematical derivation in Section 5_1 is compatible with existing learning frameworks that involve triplet loss.
We demonstrate the effectiveness of our personalized negative reservoir via thorough comparison six diverse datasets. We strongly and consistently improve upon recent SOTA incremental learning techniques (Sections 6.3 These results are not achievable with other negative samplers (Section 6.4)
We propose a personalized negative reservoir based on the user-specific preference change. All prior works assume static user interests when selecting negative items. In Section 666 demonstrate that for users with high interest shift model can quickly adapt and clearly improves recommendations.
2 Related Work
2.1
Incremental Learning for Recommendation Systems
Incremental Icarning is a training strategy that allows models to update continually as new data arrive. However, naively fine-tuning the model with new data leads to "catastrophic lorgetting" (Kirkpatrick el al. 2017 Shmelkov al., 2017 Castro al. 2018), i.e., the model overfits to the newly acquired data and loses the ability to generalize well on data from previous blocks. There are two main research branches that aim to alleviate the catastrophic forgetting issue. The first direction is called reservoir replay experience replay. Well known works such as iCarl (Rebuffi et al. 2017) and GDumb (Prabhu et al. 2020 construct a reservoir from the old data and replay the reservoir while training with the new data. The reservoir is usually constructed via direct optimization or heuristics. In the next paragraph we discuss methods related to incremental learning for graph- based recommendation systems. We note that there is extensive literature outside this area, for example online learning for CTR prediction (Aharon et al. 2017) and general online or incremental learning (Valkanas et al. 2024 Waxman & Djuric 2024) that we do not cover because it is beyond the scope of this work.
A recent incremental framework for graph-based recommender systems extended the core idea of the GDumb heuristic and proposed a reservoir sampler based on node degrees (Ahrabian et al. 2021). Another line of research focuses on regularization-bassl knowledge distillation (KD). The model trained using old data blocks serves as the teacher model, and the model that fine-tuned using the new data is the student. A KD loss (Hinton et al.) 2015) is applied to preserve certain propertics that were learned from the historical data. In GraphSAIL (Xu et al., 2020), each node's local and global structure in the user-item bipartite graph is preserved. By contrast, in SGCT and LWC-KD (Wang et al. 2021b), layer-wise contrastive distillation loss is applied to enable intermediate layer embeddings and structure-aware knowledge to be transferred between the teacher model and the student model. However, one important aspect of the incremental learning framework that has received very little attention is how to properly design a negative sample reservoir. This is a key omission considering the important role of negative sampling in recommendation. In this paper, we shed some light on how to design a negative reservoir tailored to the special characteristics of incremental learning in recommender systems.
2.2 Negative Sampling in Recommendation Systems
Since the number of non-observed interactions in recommendation datasct is vast (often in the billions Ying et al. 2018a) sampling a small number of negative items is necessary for efficient learning. Random negalive sampling is the default sampling strategy in Bayesian Personalized Ranking (BPR) (Rendle et al. 2009 Some more recent attempts aim to design better hcuristic negative sampling stratogy to obtain more effective negative samples from non-interacting items (Rendle & Freudenthaler 2014
et al., 2018 Zhao et. al. 2015 Ying et. al. 2018a). In general, the intuition is that presenting "harder" negative
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samples during training should encourage the model to learn better item and user representations. Some heuristics select negative samples based on the popularity of the item (Rendle & Freudenthaler 2014) or the node degree "Caselles-Dupré et al. 2018). Some strive to identify hard negative samples by rejection (Zhao ct al. 2015), or via personalized PageRank (Ying et al., 2018a). Other works focus on a more sophisticated model- based negalive sampler. For example, DNS (Zhang et al. 2013) chooses negative samples from the
top ranking list produced by the current prediction model. IRGAN (Wang et al., 2017) uses a minimax game realized by generative adversarial network framework to produce negative sample candidates. (Yu et al.] (002)) address the issue of class imbalance of negatives in static recommendation setting. While not strictly proposed for recommendation systems, Yao et al.] (2022) and Chen et al. (2023) propose negative samplers for knowledge graphs that aim to sample "hard" negatives while minimizing the chance of sampling false negatives, i.e,, unobserved true positives. Although these negative sampling strategies yield improvement when applied naively to incremental recommendation, they do not take the time-evolving interests of users into account and as such leave substantial room for improvement in this specific sctting. Additionally, the GAN techniques often rely on reinforcement learning for the optimization. In industrial setlings, the instability of GAN optimization is highly undesirable.
3 Problem Statement
In this section, provide clear definition of the incremental learning setting and our problem statement. Consider bipartite graph G: = (e, Eg) with a node set Vi = Ue Uz, that consists of two types: user nodes Uz and item nodes I, A set of edges & interconnects elements of Ur and I; thus each edge of G. encodes one user-item interaction. As is done frequently, in a recommendation setting, we only have access to implicit feedback data. Concretely, this means that for each user u we have access to the set of itemn that a user interacts with It {i : (u, i) E 8} but no explicit set of user dislikes I, We consider learning in discrete intervals, and use the integer I to index the 1-th interval. This corresponds to continuous time interval [tAT, (t + 1)AT). When refer to the interactions at time t, indicated as E(,,+1), all interactions in the interval [tAT, (t + 1))T). The graph and its component nodes and edges are indexed by integer time t as they evolve over time in a discrete fashion. The graph update rule is:
thus mean
(1) where E,, represent the cumulative user-item interactions up to and including time tAT and Mcc.+11) Te, ((.2+1) represent the user-item interactions accrued during the time interval [LAT, (1+1)AT)) Note that in our setting we do not construct a graph using the old set of edges &; we merely have the ob- served edges from the current time block and all the user and item nodes from previous and current time blocks. For the rest of this analysis, the user-item interactions in the interval (0. are called "base block data" and interactions belonging to subsequent time intervals {(t, + (t, (t "incremental block data". The goal resembles a standard recommendation task; given G. = (44, Ie, E(-), we are expected to provide a matrix R|4|x|Iz ranking all items in order of relevance to each user. The main difference with respect to standard static rocommendation task is that, due to the temporal nature of the incremental learning, our training set includes data up to block tr but we aim to predict item ranking for time ITTAT. To measure the quality of recommended items we employ the standard evaluation metries for the "topk" " recommendation task, Recall@K, Precision@K, MAP@K, NDCG@K (definitions in Appendix A).
g = (u UU Ie U ((stt))
1, (f+1, 2]. .)..... } are referred to
We note the difference between our setting and the distinct problem of sequential learning. Incremental learning aims to ameliorate the computational bottleneck for training, which usually limits the training instances to the most recent time block. To better inherit knowledge from the past data and the previously trained model, a specially designed knowledge distillation experience (reservoir) replay is usually applied. In contrast, the sequential recommendation problem focuses on designing time-sensitive encoders (Hidasi & Karatzoglou 2018 Kang & McAAley 2018 Fan et al.) 2021) (c.g., memory units, attention mechanisms) to betler capture users' short and long-term preferences. Thus, incremental learning is a training strategy, whereas sequential learning focuses on specific model design for sequential data. Indeed, incremental learning training stratogics can be applicd to different types of backbone models that may be sequential or not. Our negative reservoir tracks shifts in user interest over time; however, we do not apply this approach to new users, there is historical interaction data available to observe such shifts. We consider the cold-start
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problem to be distinct from setting. We note that, since our framework assumes small and frequent updates for each data block, the proportion of new users and items within each incremental training block is generally small. The cold-start user and item representations are learned via the standard GNN backbone and improving performance for them is beyond our scope.
4 Preliminaries
In this section, we provide the relevant background for our methodology. We succinetly review how modern recommender system is trained using triplet loss and how knowledge distillation is applied in the incremental learning sctting to alloviate forgetting. This section also serves to introduce notation.
4.1 Graph Based Recommendation Systems
Consider a standard static recommendation task given bipartite graph 9 representing interactions ween users and items. The typical model uses message passing framework implemented as graph neural network (GNN) where initial user and item features or learnable embeddings e2 and e are passed through a K K-layer GNN, The messages across layers for user node u can be recursively defined as:
ag (k) AGGREGATE ((h :u (WE)))))),
(2)
h (k) COMBINE( (h(*-1), aa, (1)).
(3)
Here, ay (R) summarizes the information coming from node v's neighborhood (denoted by M())). The following step, COMBINE, combines this neighborhood representation with the previous node representation h. (k-1) At the input layer of the GNN, the initial user node embedding is fed directly to the network, i.c., h Cu. Ttem nodes go through identical aggregation and combination steps with h = = GNN we obtaín node representations emb, = h and emb; = h for the user and item nodes respectively. The exact choice of the sampling method for the aggregation function and the choice of pooling for the combination operation vary by architecture. To produce an estimate of the relevance of item i to user we typically consider the dot product of the user and item embeddings fus emb, emb;
e;. At the final layer of the
4.2 Knowledge Distillation for Incremental Learning
Knowledge Distillation (KD) was originally designed to facilitate transferring the performance of a complex "teacher" model to simpler "student" model (Hinton et al. 2015). In the setting of incremental learning for recommendation, the teacher model is the model trained on old data and the student model is trained on the most recent incremental block. The overall loss that we minimize takes the form:
LBASE LTRIPLET + ARD
(4)
where LTRIPLET is standard triplet loss for recommendation such the BPR loss (Redlee et al. 2009
(defined in the Appendix B] of the student model on the incremental data batch and LKD represents the realization of the KD loss of teacher and student models, Mr and Ms. The constant AKD is the KD weight hyperparameter. Depending on the specific incremental learning technique, LKD can take a different form and more components may be added to the overall loss function (Xu et al. 2020 Wang et al. For concrete examples of realizations of KD losses in our setting see the Appendix
2020 2021b)
5 Proposed Method: GraphSANE
In this section we describe our proposed approach, the Graph Structure Aware NEgative (Graph-SANE) Reservoir for incremental learning of graph recommender systems. Our technique works by estimating the user interest shift with respoct to item clusters between time blocks. It then uses the estimated user change of preferences bias a negative sampler to provide high quality negative samples for the triplet loss. The following subsections describe how construct, update and sample from our proposed personalized negative
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reservoir, and how the item clusters are obtained. We also present overall training objective, which is end-to-end trainable. We note that our framework can be used by any graph neural network backbone that uses triplet loss and is compatible with existing incremental learning approaches.
On a high level, our method consists of three components. First, we introduce the negative reservoir in Section 5.1 where we define loss term CSANE- We detail how to update the contents of this reservoir for each user in Section 5.2 The user interest shift is computed based on clustering the items the user interacts with. One such end-to-end trainable clustering technique (with loss component LKI.) from the literature is reviewed in Section 5.3 Fimally, Section 5.4 where the incremental learning negative reservoir loss LSANE and differentiable clustering loss LKL is combined with the base model loss LBASE to produce the overall objective that is optimized via backpropagation.
5.1 Derivation
To optimize the model parameters O, triplet loss approaches randomly sample small number of items with which user has observed interactions: IT Itt where Itt I represents the complementary set of IT. Thus, I, is randomly selected set of items that user u does not interact with (Rendle et al. 2009). Existing approaches sample each negative item once per user. However, in general, repeating some highly informative negatives multiple times (or weighting them more) can increase the speed of convergence. Furthermore, in the context of incremental learning the user interest shift can be used to drive a higher number of negatives from item categories that the user is losing interest The likelihood of positive item being ranked above negative item j for user is:
p Q) abbui Duy)-
Our proposed method proposes sampling negative items with replacement. Concretely, the proposed function SANFOPT with respect which we optimize may consider multiple copies Nu., of negative example j for user u. This leads Nuj 2 independent observations, each obeying the likelihood from equation
SANEoPT == Inp(O (>w) x In (p(> (p)>>x)))p(O))
In
II
(Bus - Bus) No.s p(0)
Nuj In - Duy) - xe|l0112
(6)
(
where p(O) is an isotropic normal distribution. In practice minimize the negative of equation using backpropagation: LSANE -SANEOPT. Our loss is now defined. In the next section we demonstrate a concrete procedure to obtain
Nu.,z))
5.2 Negative Reservoir for Incremental Learning
Notation and Setup: At time L, using backbone recommendation model's user and item embeddings emb,, and emb; we can obtain the estimated ranking of items for user u by considering P.. = emb, emb; for all i e Z. Ordering the items by the scores Jui ranks items for user (this yields row u of matrix R from the problem statement).
Determining user interest shift: We propose tracking user interests by measuring the number of inter- actions of each user with item categories every time step. For example, in the toy example depicted in that there are K 3 item categorics. By counting the proportion of items that each user interacts with (in Fig. (b)) we obtain histograms of user-item calegory interactions H RK These histograms are then normalized and projected to the simplex Ax-1 (in Fig. [ (c)). By tracking the trajec- tory of each on the simplex can surmise the user's interest shift: shift (u, t 1,t) H... I where denotes the L1 norm. Note that our mothod is robust to the case where item categorics are not given. this case we cluster the items and interpret the item clusters as induced pseudo-categories
Fig.
H.,. H...-

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(4)
100%
Hyds
Hads
30
79%
50%
15
25%4
Monday
Tuesday
Wednesday
Thursday
Friday
0
Tuesday
Wednesday' Car Parts
Thursday
Friday
Car Parts
Coffee
Pets
Coffee
(d)
Negative
Negative Reservoir Q
Reservoir Q
Parts
B
Pets
Madd
Coffee
Pets
Coffee
Tuesday to Wednesday
Wednesday to Thursday
Wednesday
Thursday
Figure 1: Toy example with daily model updates and 3 item categories: pets, car parts and coffee itemss The figure shows user's interactions with these categorics over a week. (a) Cumulative user interest over time: A larger fraction of user u's interactions comes from pet items at the start of the week, but his interests change over time and he interacts with more part items by the end of the week. (b) The change of preference is reflected on the daily histograms of user-itemm-categryy interactions H (c) The histograms
normalized H.,t and projected on the simplex Åg. There we see the interest shift on the simplex representing the user's interest shift from 2, (Tuesdayy
3, (Wednesday) and on the right the user's interest shift from 3, (Wednesday) to 4, (Thursday). We that the user exhibits large change in interests the second simplex (moves far away from current neighborhood in simplex denoted by red dashed circle). (d) We propose to sample more negatives from pet category when fine tuning the model on Thursday to allow the model to quickly adjust to new user interests (in the figure the right bucket has many more pet items).
Level Dirichlet Hyperparameter User item clster interaction histograms: High interest shift at cluster (red) large
Negative items: Consider the top ranked Q negative items for user (by sorting row of R) at time t. This is the set of size Q that contains the items that the model ranks the highest for user u, but which the user does not inter- act with. For the top Q negative items per user we note the item category (or item cluster membership if categories are not available in the data) of each item. We denote K as the number of item aategories/clusters top negative item interactions per item category for each user Cu,t = (Cu,t,1y.... (............kk) Cu..K),, such that E Ca,ti = Q. For exai- ple, in Fig. (d), this vector would contain the counts nega- tive pet, car and coffee items associated with a particular user at specific time step. We interpret the observed top negative user cetoory interactions Cu,t N (c..t, Cu.t,K) k) Q samples of multinomial distribution with unknown pa- rameters o,, E TBK = (f..t.,...,, .,.,,K). where luttk repre- sents the probability of sampling a negative item from category for user u at time 1.
H
H.
Key Multinomial Parameter
This yields count of
Goel: Infer this parameter, that drives negative ttem samping eq, (9)
pl
Level 3: Dirichiet Observations
Observed multinomial realizetion high rank negative items por cluster
fultu (.)) Gesp mel
Figure 2: The hierarchical model in equa- tion 7 & From time loses interest the i-th category, this in- creases OG, Thus 0, has high prior value sample negatives with higher probabil- ity from that item category in equation [I]
to t, a user
Our hypothesis: A good sampling distribution for negatives should prioritize sampling negative interactions that simulta- neously: (i) correspond to item categories for which the

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exhibits reduced interest at the present time when compared to his/her historical preferences; and (ii) are ranked highly (hard negatives)
We model the prior distribution of Ou. as a Dirichlet Ou.e ~ Dir(a Our frame- work obtains posterior distribution over ou, by fusing information from our prior model with the observed distribution of negative items across categories. The parameters of the prior Cu, are derived from the his- togram of user ttem-category interaction counts Hy, and Ha,-- Hu,: E NK is histogram that summarizes the number of items that user interacted with from each of the K categories, i.c., H.,, [k] denotes that at time t user interacted with items from category k. Recall that Q is the mumber of negative items in each user's negative rescrvoir. We then define the following hicrarchical model (shown in Fig. 2
Hierarchical Model:
LEVEL 1: au,t = XQ softmax (-1
H H...
H HH,,-1l 1).
Hu,t-1
(7)
where |. denotes the L1 norm and Qu, E EK Our choice for prior in equation reflects the fact that 0, then user is interacting with fewer items belonging to category k, and hence may be losing interest in the item category with index k, want to sample more negative items from it. Conversoly, if the difference is positive, this indicates an increase in user interest in items from the category k so the softmax function will decrease the probability of sampling a negative item from this category. The next levels are a Multinomial- Diriiiomall--iicchee conjugate pair:
if Hu.t Ha...
H...l H &
T(aa,1.))
K II @0aak-1
LEVEL 2:
p(Ou..)= Dir((a.,)) I(a ... I(au,s
a,tk
k=1
K
LEVEL 3: Su.t Ou,t)
N
II
@0ati u,ti
(8)
[ Cu.ee
T(-) is the Gamma function, Σ, Ou,e. 1, an,t.0 is a positive valued hyperparameter. The posterior p(O..t Cu, an,)) is:
Ex= Ohuniis Cugi is the i-th element of Cu, and X E IR.,
I(ao)
K II
N!
p(O,, Cu,e, au,1) x p(0,,,) (u,t) I(a1)...
goz-1
II 0
Dir(a + Ca.t)
I G!
k=1
Ha,t
H Hu,t-1
= -Dir XQsoftmax
+ Cu.e
(9)
Ha.e
Hu,t-1
We can then estimate a.t as the mcan of the posterior:
XQsoftmax
Hu.td Hundd
Ha.t-
Hu.t-id
+ Ca.ti
Ôu,,. = Elou. Ca.t.i)
(10)
Σ; AQsoftmax
H.ddd Ha.dd
H..1-. 14
+ Ca,ti
H4. 1.
Sampler for Reservoir: Denote iu,,c as the C-th entry of i.., (C (1...., K} is the item category that belongs to). To sample negalive items from the reservoir, we define the sampler for negalive item n, Z:
p(ny j.....)= (i)e
(11)
Σ, Iie (1) (1)
where and (i) is an indicator function that is one when item belongs to the set Q top negative items for user u time and g(i) function that returns the category index of item index Connecting this the derivation in Section 5.1, vector .N..,...,,N..pp. from equation 0 is a draw from the multinomial with parameters defined in equation 11
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5.3 Clustering
Recall that we often do not have pre-specified categories item altributes that clearly identify suitable item categories. We overcome this problem by defining item pseudo-categories based on item clusters. The deep structural clustering method we use is adapted from two recont works by Bo et al. (Bo et al. 2020) and Wang et al. [Wang et al. 2019a). We note that the clustering algorithm we utilize is not a research contribution but simply an adopted method. We select this method because the clusters are learned using both node attributes and the graph adjacency, in an end-to-end trainable fashion.
For item i, use the kernel of the Student's t-distribution embedding at time f, h,, and the k-th cluster centroid μ
similarity measure between the item
(1 1I /1) =
d (1 + || 2 11/11) 4
(12)
where K is the total number of item clusters and represents the degrees of freedom of the distribution. We consider o to be the probability of assigning item i to cluster k. Then, Q . -g.kl is a discrete probability mass function that summarizes the probability of item i belonging to cach cluster at time t. The assignment of all items can be described by Q' = [d] An issue is that Q' can sometimes provide diffuse cluster assignments (close to uniform). This is why [Bo et al. (2020) obtain confident cluster assignments, i.e., more mass concentration to a single cluster per item through a transformation:
(d/,)) Ei L.
PL. Σn (0% )2/ / th
(13)
Then P' consists of the elements of Q' after being transformed by square and normalization operation. By minimizing the Kullback Leibler (KL) divergence encourage more concentrated assignment to clusters.
LKL. = (P' Q1 = -- log
(14)
m
In practice we first initialize μ1, M.. uk via K-means and then optimize equation 14 in subsequent training iterations so that the centroids are updated via back-propagation based on the gradients of LKL. We then model the probability of item i belonging to cluster using pl. by applying a softmax function with temperature E R4:
exp(p(,))/7
c/ = Σe exp(pp 3/T
(15)
5.4 Overall Framework
In this section, we present the overall objective function, and provide an algorithm that summarizes our proposed incremental training framework. We emphasize that our proposed framework facilitates end-to- end training with any GNN backbone and any incremental learning framework. This includes both knowledge distillation and reservoir replay techniques.
While training using hard negative items can help improve gradient magnitudes and speed up convergence, it can cause instability (Ying al.] 20188)). To address this use two sources of negative samples: (i) hard negatives from our proposed reservoir; and (ii) negatives selected randomly according to a uniform distribution. By including randomly selected negatives, we introduce diversity as well as improving stability by modcrating the effects of large gradients obtained from hard negatives during the initial epochs YYngg et al. 201 The proposed objective is:
LIOAAL =
LBASE
+
LSANE + Neg. Reservoir
B LKL
(16)
CTRIPLET: LND
Cluster
Here LBASE consists of the base incremental learning model loss components, i.e., the knowledge distillation loss LKD and triplet loss LTRILETT such as BPR loss, of the randomly sampled negatives. LSANE is
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LWCKD- LWCKD-SANE" SANE SGCT-SANE
WARP
0.0850
PinSage
LWCKD
0.0825
PNS
GSAIL- GSAIL-SANE' SANE
R
0.0800
NS Cache
SGCT
0.0775
DeMix
Inv. Degree
0.0750
ESNS
LSPs
0.0725
GSAIL
0.0700
Uniform
0.0675
Fine Tune
5 Rank
10
425
450
475
500
525 550 575
Time (s)
Figure 3: Left: Boxplot of ranks of the algorithms across the 6 datasets. The medians and means of the ranks are shown by the vertical lines and the black triangles respectively; whiskers extend to the minimum and maximum ranks. Stars **" represent methods that integrate our proposed negative reservoir. We abbreviate GraphSail "GSAIL" Right: Comparison of recall performance and training time required per incremental block for various negative samplers of Yelp discussed in Table 3 Our method (SANE) outperforms with time complexity in line with the basclines. Note that full batch retraining takes more than hour.
proposed loss from the hard negative reservoir, and LKL is the KI. loss component for the clustering. Note that both CBASE and CSANE are triplet loss based so they operate on the same scale. However, we require weighing the clustering loss term with hyperparameter 3 balance the contributions of the loss components. completely different scale proprely tuning /3 is necessary to prevent clustering from being ignored during the optimization dompletely dominating the objective. K for hyperparameter luning details. The training process with our method is detailed in
That is because the clustering loss operates
See Appendix
Algorithm 2
6
Experiments
This section empirically evaluates the proposed method GraphSANE. Our discussion is centered the following rescarch questions (RQ). Experiment code and method implementation are available onling
RQ1 How does our method compare to standard SOTA incremental learning methods?
RQ2 our sampler better than generic negative samplers in the incremental learning setting?
RQ3 How does the time complexity of our sampler compare other samplers? Is our approach scalable?
RQ4 Where the performance gains coming from? For which users do improve recommendation?
6.1 Datasets
We empirically evaluate our proposed method on six rainstream recommender system datasets: Gowalla, Yelp, Taobao-14, Taobao-15, Netflix and 10V. These datasets vary significantly in the total mum- ber of interactions, sparsity, average item and user node degrees, well as the time span they cover. Detailed dataset statistics are provided in Appendix C Tab. 4 In this work adopt the data pre-processing ap- proach from the literature. Our data setup is identical to the basclines GraphSAII, (Xu et al. 2020), Inverse Degree (Ahrabian et al. 2021). SGCT and LWC-KD (Wang et al.) 2021a). To simulate an incremental learning setting, the datasets are separated to 60% base blocks and four incremental blocks each with 10% of the remaining data in chronological order. For additional information on how the blocks are constructed see Appendix Fig. depicts the data split per block. For the metrics, we record the performance for each incremental block and report the average.
Link code repository: http:///hhhuu.cccc/am/maaaaaaaaa
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Table 1: Comparison (R) of baselines and recent knowledge distillation algorithms with our SANE
reservoir. Our method indicated by a star (*). Best performers are in bold. Blue cell colors indicate stat.
significant improvement of particular method when our reservoir is introduced (p- 0.05 on Wilcoxon test).
Gowalla-20
Taobao2014
Taobao2015
Yelp
Netflix
MovieLensI0M
Average
Average
Average
Average
Average
Average
Methods
A%
A%
A%
4%
A%
4%
Rec@20
Rec@20
Rec@20
Rec@20
Rec@20
Rec@20
Fine Tune
0.1705
0.0
0.0153
0.0
0.0950
0.0
0.0661
0.0
0.1036
0.0
0.0918
0.0
LSP 8
0.1783
4.6
0.0152
-0.7
0.0968
1.9
0.0676
2.3
0.1128
8.7
0.0925
0.8
Uniform
0.1728
1.3
0.0157
2.6
0.0982
3.4
0.0654
-1.1
0.0957
-7.6
0.0885
-3.6
Inv degree
0.1738
1.9
0.0175
14.6
0.0989
4.2
0.0677
2.4
0.0957
-7.6
0.0915
-0.3
GraphSATL
0.1849
8.4
0.0155
1.3
0.0963
1.4
0.0639
-3.3
0.1051
1.4
0.0890
-3.1
GraphSATT-SANE
0.1925
12.9
0.0171
11.8
0.1107
16.5
0.0857
29.7
0.1088
4.8
0.0921
0.3
SGCT
0.1870
9.7
0.0160
1.7
0.0999
5.2
0.0668
1.06
0.1135
9.6
0.0919
0.1
SGCT-SANE*
0.1897
11.3
0.0178
16.3
0.1128
18.7
0.0862
30.4
0.1155
11.5
0.0946
3.1
LWC-KD
0.1977
15.9
0.0176
15.3
0. 0.10
8.4
0.0679
2.7
0.1142
10.2
0.0928
1.1
LWC-KD-SANE"
0.1881
10.3
0.0188
22.9
0.1114
17.2
0.0898
35.9
0.1182
14.1
0.0964
5.0
6.2 Baselines
Our base model recommendation system is MGCCF Sun et al. 2019). a commonly used architecture in the incremental recommendation setting (Xu et al. 2020 Wang et al.) 2021b) that is specifically designed to handle bipartite graphs. All the incremental learning algorithms are built on top of this backbone model. In our first set of experiments summarized in Table (even finer-grained results per incremental block are available in Appendix Table [2], we evaluate our model in comparison to multiple baselines, including the current SOTA graph incremental learning approaches. Fine Tune: Fine-tune naively trains new incremental data of each time block to update the model that was trained using the previous time block's 's data. Tt is prone to "catastrophic forgetting". LSP 8 (Yang et al. 2020): T.PP is a know snowledge distillation technique tailored to Graph Convolution Network (GCN) models. Uniform: This method randomly samples and replays a subset of old data along with the incremental data to alleviate forgelting. Inv degree (Ahrabian et al. 2021): Inv _ewgreeeeee_ee is a state-of-art art reservoir replay method. The reservoir is constructed from historical user-item interactions. The inclusion probability of an interaction is proportional to the inverse degree of the user. SOTA Graph Rec. Sys. Incremental Learning methods: GraphSail (Xu et al. 2020), SGCT (Wang et al. (021b) and LWC-KD (Wang et al. 2021b) are state-of- of-the-rrtttttt knowledge distillation techniques. We integrate our design into these models and compare.
In the second set of experiments, we investigate whether the proposed SANE reservoir design is effective compared to alternatives. We investigate how several prominent existing negative sampling strategies perform in incremental learning. The experiment demonstrates that the specialized sampler we propose is better than existing generic negative samplers. The methods we compare to are WARP (Weston et al.] 2010 PNS (Rendle & Freudenthaler 2014). PinSage (sampler) (Ying et al. 2018a), NS Cache (Zhang et. al.
2019 ESNS (Yao et al.) 2022], DeMix (Chen et al. 2023). For more information on the selected negative
samplers see Appendix D
Hyperparameters and Reproducibilitty We make our experimental code available. We use GNN layers in the MGCCF model with an embodding dimension of 128 and update the reservoir every two epochs. For full set of hyperparameters please consult Appendix H A detailed description on how to deploy the model and tune the hyperparameters in practical settings is in Appendix K
6.3 Comparison to SOTA Incremental Learning (RQ1)
Our first set of experiments compares our method to the standard incremental learning baselines on six main- stream datasets. We use the exact same base MGCCF (Sun et al. 2019) backbone model instance trained on the base block for all incremental learning methods. We integrate our negative reservoir design SANE in three SOTA and commonly used incremental recommendation models, including GraphSAIL (Xu et al. 2020). SGCT Wang et al. 2021b), and LWC-KD (Wang et al. 2021b). The experiment convincingly demonstrates the value of considering a negative reservoir in conjunction with standard incremental learning approaches.
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We show in Table I that method strongly outperforms for almost all datasets, achieving top performance in all but the smallest dataset (Gowalla-20). This is not unexpected since the smallest. dataset, Gowalla, has only ~5000 items. With an average user degree of ~50, and assumiin we select 10 negative samples per observed interaction for the optimiza- tion, even randomly sampling the nega- lives without replacement yields a neg- ative sample size that is approximate 10/5000 10% of the total item population per epoch. Training for 10-20 epochs virtually guaranlees that the pool of all potential negatives is exhausted, thus reducing the effectiveness of any non-trivial negative sampler relative to brute force sam- pling of all the negatives. On moderate and large datasets our method is the top performer by convincing margin, often offering more than 10% compared to the top-performing baselines that do not use our nega- tive reservoir. Overall, our designed negative reservoir can boost the average performance of three SOTA incremental learning frameworks, GraphSAIL, SGCT, and LWC-KD by 11.2%, 8.3% and 6.4%, respectively, across six datasets. Furthermore, as summarized in Fig. 3 LWC-KD-SANE is top-performing method overall.
Table 2: Average ranks of models for key metrics across Gowalla, Yelp, Taobao14, Taobao15. Lower rank is better (4). Bold indi- cates improvement over base model.
Recall8220 Rank (L)
NDCG&20 Rank (L)
Precision::20 Rank (4)
MAP@20
Rank (4)
GraphSail
6.00
4.75
5.00
5.00
GraphSall+SANe
3.00
3.75
3.25
3.50
SCCT
4.75
4.75
4.50
4.50
SCGT+SANE
2.25
2.75
3.25
2.00
LWOKD
3,25
3.25
3.75
3.25
LWCKD4SANE
1.50
2.00
1.50
2.50
Precision, MAP, NDCG In the previous subsection and Table T we only presented Re- call@20 metrics. Here, we present a summary of the results of the same experimental setup as in Ta-
More Metrics:
Table 3: Comparison of mainstream negative samplers with our proposed reservoir in terms Recall@20. Inc 1, 2, columns indicate performance for each incremental data block. Last col- umn compares average performance across blocks. Our proposed method the average recall. Blue color cells indicate statistically significant improvement.
ble and Fig. 3 but also include results for Precision@k, mean av- erage precision (MAP@k) and nor- malized discounted cumulative gain (NDCG@k). We show results that depict the overall rank of the meth- ods, averaged across the datasets experiments
Dataset
Methods
Inc
Inc 2
Inc
Avg.
SGCT+ Warpl
0.0740
0.0656
0.0608
O. 0.06688
SGCT+ PinSage)
0.0794
0.0663
0.0651
0.0703
SGCT+ PNS)
0.0933
0.0798
0.0748
0.0827
Yelp
SGCT+ NS Cache]
0.0794
0.0681
0.0670
0.0715
SGCT+ DeMix)
0.0783
0.0740
0.0694
0.0739
for k 20. We for k E (0,10, 15, and obtained very similar results to Table 2 in all cases. Our results span 5 datasets, distinct & values for differ- ent metrics and pairwise compari- son of incremental models (using our reservoir versus not using it).
SGCT+ ESNS
0.0786
0.0754
0.0690
0.0743
SGCTT+ SANE (ours)
0.0966
0.0877
0.0744
0.0862
SGCT+ Warpl
0.0240
0.0092
0.0148
0.0160
SGCT+ PinSage
0.0241
0.0099
0.0151
0.0164
SGCT+ PNS)
0.0220
0.0114
0.0113
0.0149
Taobao14
SGCT+ NS Cache]
0.0237
0.0124
0.0121
0.0165
SGCT+ DeMix
0.0196
0.0097
0.0T13
0.0135
SGCT+ ESNS
0.0218
0.0113
0.0128
0.0153
S SANE (ours)
0.0224
0.0136
0.0173
0.0178
This yields 6 x 4 x = 288 distinct comparisons. Our method improves upon the baseline in
226/288 (78.5%) of the cases, and the improvement is larger than 5% in 193/288 (67.0%) of the cases. We note that the majority of the cases where our model does not improve upon the base model is Gowalla-20, which as explained earlier is a pathological case. If we exclude Gowalla-20, our model improves the base models 933 of the time.
6.4 Comparison to Generic Neg. Samplers (RQ2)
Our second experiment focuses on evaluating the proposed negative sampler for the reservoir. The goal of this experiment to demonstrate the effectiveness of our negative sampler in the context of incremental learning. For the baselines, we replace LSANE with standard triplet loss, i.c., BPR, and draw the negatives according to the baseline negative sampler algorithms. We select one incremental learning framework, SGCT, replicate
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the same incremental learning setup for Yelp and Taobao2014 and vary the choice of negative samplers. As shown in Table B our method offers a consistent improvement. We conjecture that the performance gain arises because our sampler is the only one that is designed explicitly for the incremental setting, rather than being designed for a static setting and then adapted (this is investigated in the case study in a subsequent section). We compare the performance and the time to train one incremental block of Yelp for different samplers in Fig. 3 Our approach takes approximately the same amount of time as PNS, NS Caching, DeMix and ESNS and 20% more time than vanilla WARP.
6.5 Time Complexity Efficient Scaling (RQ3)
For training complexity the main cost comes from ranking the items. Our approach exploits the fact that in real world setting recommender systems that are trained incrementally start with a rank the items from the previous data block. We only need to rank the items 2-3 times as the number of training epochs until model convergence is usually very low (between 5-15) for all of our datasets, even though they vary in size dramatically. Therefore, the computational cost of ranking the itemss handful of times is not unreasonable. Inference time is not affected by our algorithm BPR (Redlle et al. 2009) and WARP (Zhao et al. 2015) select negatives at random so they are the most efficient. The PinSage sampler (Ying et al. 2018b) requires running a personalized PageRank algorithm to rank the items. In settings where the incremental block data do not. radically change the graph topology, the PageRank iterations converge quickly the previous block's PageRank vector is used to initializo the iterative PageRank algorithm. Score and rank based models require computing dot products between user and item embeddings, which costs ((Z) These are typically the most expensive models, but they often provide "hard" negatives that can significantly improve training convergence. Such methods include our method as well as (Zhang el al. 2019 Rendle & Freudenthaler 2014 Zhang et al. 2013). In general, ranking all the items incurs a computational cost of [[
we do not cluster or sample negatives during evaluation.
We note that we only rank the top [Q] items, which reduces the complexity to Z[) on average when using QuickSelect (Hoare 1961
6.6 Case Study: GraphSANE Improves Recommendation for Dynamic Users (RQ4)
We conduct a case study Taobao14 the users with high interest shift to in- vestigate their negative items drawn from the various samplers. Since our approach aims to model user interest shift, we ex-
0.013
Pct. postives in negative samples
0012
0.011
Recal 620
pect our model to (i) draw more negatives from old positive items, thus validating our hypothesis that explicitly targeting user loss of interest in items for negalive
0.010
0.000
0.008
samples is sensible; and (ii) outperform in the recall metric, since our algorithm focuses on this subset of users. As we can see in Fig. 4 our algorithm increases the proportion of negative samples from old positives by sevenfold and offers clear improvement of about 20% in Recall@20 This compares to an improvement of 15% for the remaining 85% of users with lower interest shift. Note that this shows that our approach is particularly effective for high shift users relative to the general population. This further val- idates our hypothesis about the effectiveness of tracking user interest shift when drawing negative samples. Details for the case study are available in Appendix
0.007
0.005
Ware
NS Caching
PanSage
SANE
Worp
PNS
Caching
PinSage
SANE
Figure Case Study: Among the 15% of users with the highest interest shift on Taobao14 we observe that Graph-SANE increases the amount of old positives sampled as current negatives by 7 times. Our sampler strongly improves Recall@20.
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7 Conclusion
This work proposes a novel incremental learning technique for recommendation systems to sample the neg- atives in the triplet loss. The method is not applicable to the case where users or items are not represented by their identity, but rather only by their features (i.e. no user item nodes at all). Our approach is easy to implement on top any graph-based recommendation system backbone such as PinSage Ying et all 2018a), MGCCF (Sun al., 2019), or LightGCN (He al. (020a), and can be easily combined with base incremental learning methods. When used in conjunction with standard knowledge distillation approaches, our method demonstrates very strong improvement over the current state-of-the-art models.
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Rex Ying, Ruining He, Kaifeng Chen, Pong Eksombatchai, William I. Hamilton, and Jure Leskovec. Graph convolutional neural networks for web-scale rocommender systems. In Proc. Int. Conf. Knowledge Discov- ery & Dala Mining (KDD), pp. 974 974-983, London, UK, Aug. 2018a.
Rex Ying, Jiaxuan You, Christopher Morris, Xiang Ren, William L. Hamilton, and Jure Leskovec. Hierar- chical graph representation learning with differentiable pooling. In Proc. Adv. Neural Inf. Process. Syst. (NeurIPS). pp. 1805-4815, Montréal, Canada, Dec. 2018b.
Lu Yu, Shichao Pei, Feng Zhu, Longlei Li, Jun Zhou, Chuxu Zhang, and Xiangliang Zhang. A biased sampling method for imbalanced personalized ranking. In Proc. ACM Int. Conf. Info. Knowledge Management (CIKM), pp. 2393 2402, Oct. 2022.
Weinan Zhang, Tianqi Chen, Jun Wang, and Yong Yu. Optimizing top-n collaborative filtering via dynamic negative item sampling. In Proc. Int. Conf. Research and Development in Info. Retrieval (SIGIR), pp. 785-788, Dublin, Treland, Jul. 2013.
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Yongqi Zhang, Quamming Yao, Yingxia Shao, and Lei Chen. Nscaching: simple and efficient negative sampling for knowledge graph embedding. In Proc. IEEE Iul. Conf. Dala Engineering (ICDE), pp. 614- 625, Macao, China, Apr. 2019.
Tong Zhao, Julian McAuley, and Trwin King. Improving latent factor models via personalized feature projection for one class recommendation. In Proc. ACM Int. Conf. Info. & Knowledge Monagement (CIKM), pp. 821 830, Melbourne, Australia, Oct. 2015.
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Personalized Negative Reservoir for Incremental Learning in Recommender Systems Supplementary material
Table of Contents
Metrics
19
A.1 Normalized Discounted Cumulative Gain (NDCG)
19
A.2 Mean Average Precision (MAP)
19
13 Standard Losses
20
B.1 Bayesian Pairwise (BPR) Loss
20
B.2 Knowledge Distillation (KD) Loss for Incremental Learning in Recommendation
20
Dataset Statistics
D Negative Sampler Baseline Details
E Algorithms
22
Case Study Details
22
G Loss Ablation Study & Sensitivity Analysis
23
G.1 Ablation study
23
Clustering Algorithm Sensitivity
23
H Hyperparameter Settings
25
Experimental Results per Incremental Training Block
26
Dataset Preprocessing Data Block Deñnition
27
K Practical Recommendation for Model Deployment
28
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A Metrics
In this section, we provide a review of some standard metrics for recommendation system evaluation that we use in our experiments. Recommendation systems return ranked list. of relevant items for each We typically care about the top K itemss returned by the model. There are number of different methods that evaluate the quality of the predicted list of items versus the ground truth.
Some simple methods include evaluating standard classification metries such as the precision and recall. There are also some other information retrieval specific metrics that we use: the Normalized Discounted Cumulative Gain and the Mean Average Precision. This section reviews these two metrics.
A.1 Normalized Discounted Cumulative Gain (NDCG)
To define NDCG we first define its components. The cumulative gain (CG) can be defined as the number of items that a user interacts with that were among the top K predicted by the model:
CGOK = Σ 1ikeI+1 (k)
Σ GR.
(17)
A disadvantage of this metric is that it assigns the same weight to all correct predictions. Predicting 2 items correctly among the top yields the same CG irrespective of the relative rank of these two items. In general we would especially like the top recommended items to be positive.
To address this we introduce discount function that weights the cumulative gain from correctly identified item by its relative ranking. For example, choosing the logarithm function:
K
I I (k) 1og,(1 (1 + k)
K
GR
DCG@K = Σ
(18)
loga (1 + k)
Finally, to make the DCG score easily comparable across choices of K may normalize to produce the Normalized DCG (NDCG) by the highest value DCG could attain to produce values in the range [0, 1]:
Jizz- (N) NDCG@K = 2k=1 loRg(1+R)
GL k= long [1+)
(19)
Ek logu
k=1 (1+kk)
We may then report the average NDCG for all users.
A.2 Mean Average Precision (MAP)
Precision at K, denoted as Prec(K) or prec@k, is the fraction of relevant items in the top K items ranked by the model. Similarly to CG from the previous section, a disadvantage of this metric is that it assigns the same weight to all correct predictions. In practice it is more important to identify relevant items at the top of the model's ranking. To address this Average Precision (AP) for user u is used:
APOK(u)
nezzh (k) Prec(k))
(20)
where [ is the number of relevant items for u. To aggregate this metric may average over the entire user set U:
MAP@K
Σ AP@K(u).
(21)
U
WEW
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B Standard Losses
B.1 Bayesian Pairwise (BPR) Loss
Reintroducing the notation from the main text, recall that for each user we have access to the set of items that user interacts with It = {i: (u, E E} but no explicit set of user dislikes In To optimize the model parameters θ the Bayesian Pairwise (BPR) loss randomly samples a small number of items with which user u has no observed interactions (Rendle et al., 2009p. During training, the overall objective takes the form:
CBPR
Σ
lIno Duy) )o||o1?
(22)
(U.
where a(r) is the standard sigmoid function, and λy is a regularization parameter. The BPR objective is differentiable, so the model parameters are trainable via standard backpropagation.
Our main contribution, discussed in the methodology section, is novel approach for selecting In that is specifically designed for incremental learning setting. We also propose a modified triplet loss.
B.2 Knowledge Distillation (KD) Loss for Incremental Learning in Recommendation
In this section we provide some examples concrete realizations of standard KD) techniques in the context of incremental learning for recommendation systems.
GCNs utilize neural networks to aggregate local information, enabling nodes to benefit from rich contextual
data within their neighborhoods and learn generalized representations. Preserving this local neighborhood representation is essential in incrementally trained graph-based recomnender systems. To accomplish this, Xu et al. (2020) propose distilling the dot product between the central node embedding and its neighborhood representation. Practically, this can be achieved by applying a KD objective on the dot product between the embedding from time t-1 of user u, denoted embb-1, and the average embedding of the items in its neighborhood c'1 u.A--1 and the dot product of emb,, with et w, A similar procedure is carried out for item reprosentations and the average embedding of their neighborhoods. Concretely this objective takes the form:
2
fLOCAL
1
emii-
d-1 uNV
emb co.Ns
+
emb
1-1 iN--1
emb? ctNt
(23)
U
I
WEW
KEI
where CLA M
Σ PENT
emb' and C. W
Σ W'NN
embt,
Wang al. (2021b) propose contrastive distillation objective. The positive pairs and negative pairs are constructed from the user-item bipartite graph in order to capture the important structural information. The distillation objective is:
exp (hi,0 11/00//1 /T7
Laget = CkD +
log
(24)
U
W
1EAT-1 (w) EiEDy (w) exp hhip h//l//))
wEll
where h is the embedding for node u at time t, MM7 (u) is the neighborhood set of user node u from the user-item interaction graph at time t-1, which provides the positive samples, and D
(u) is the collection (union) of positive and negatives samples of the user u generated from the user-item bipartite graph from time / --1 1. - is a temperature that adjusts the concentration level.
There are other KD losses such as global structure distillation, which maintains each node's global positional information the user-item graph (Xu et al. 2020), and personalized distillation objectives tailored each individual user (Wang al. 2023
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C Dataset Statistics
We evaluate our proposed method empirically on six mainstream recommender system datasets: Gowalla, Yelp, Taobao-14, Taobao-15, Netflix and MovieLens These datasets vary siguificantly in the total num- ber of interactions, sparsity, average item and user node degrees as well as the time span they cover. Detailed dataset statistics are provided in Appendix Table To simulate an incremental learning setting, each dataset is separated into base block, containing 60% of the data, followed by four incremental blocks each with 10% of the remaining data, with partitioning applied in chronological order.
Table Statistics of the six datasets used the experiments.
Gowalla
Yelp
Taobao2014
Taobao2015
Netflix
MovieLens10M
Num. edges
281412
942395
749438
1332602
12402763
10000054
Num. users
5992
40863
8844
92605
63691
71567
Avg. user degrees
46.96
23.06
84.74
14.39
194.73
143.11 11
Num. items
5639
25338
39103
9842
10271
10681
Avg. item degrees
49.90
37.19
19.17
135.40
1207.56
936.59
Avg. % new users
2.67
3.94
1.67
2.67
4.36
4.87
Avg. % new items
0.67
1.72
2.60
0.22
0.72
7.12
Time span (months)
19
6
5
6
168
D Negative Sampler Baseline Details
In the second set of experiments, we investigate if our user interest shift aware negative reservoir design tailored specifically for incremental learning is effective compared to alternative designs. We investigate how several prominent existing negative sampling strategies perform in incremental learning, The experiment demonstrraes that the specialized sampler propose is better than existing generic negalive samplers. The methods we compare to are:
1. WARP Weston al. 2010): This method randomly samples negatives from the pool of unobserved interactions.
Popularity-based Negative Sampling (PNS) (Rendle & Freudenthaler 2014): This method
ranks the top negatives and samples them with a fixed parametric distribution, e.g., a geometric.
3. PinSage Sampler (Ying et al. 2018a]): This negative sampler ranks items based on personalized PageRank and then samples high rank negatives. Note, this is not to be confused with the overall PinSage GNN recommender system backbone we merely use the negative sampler.
4. Negative Sample Caching (NS Cache) (Zhang et al. 2019 This is knowledge graph negative sampler which we adapt to our setting. It samples negative items and compares them to cache content. The negative samples randomly replace cachod entrics proportionally to their likelihood following an importance sampling approach. This algorithm has fewer parameters than GAN-based negative samplers, such as KGAN (Cai & Wang. 2018) and IGAN (Wang et al. 2018 Besides, it fully trainable using back-propagation and has equal or better performance than GAN methods.
5. Entity Similarity-Based Negative Sampling (ESNS) Yao et al. 2022) is knowledge graph method that we adapt to our setting. improves negative sampling by considering the semantic similarity between entities and using a shift-based logistic loss function, resulting in higher-quality negative samples and better performance compared existing methods in link prediction tasks.
6. DeMix (Chen et al.) 2023) is also adapted from the knowledge graph literature. DeMix works by not only proposing highly scored negative samples but also implements a strategy to alleviate accidental sampling false negative (but unobserved) interactions.
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E
Algorithms
This section summarizes our algorithm and provides a pseudo-code implementation of the updates of the Additionally, we also show how the reservoir is used
reservoir at each incremental training block in Alg. 1 during training to sample negatives in Alg.
Algorithm Updating the Graph-SANE Reservoir
Require: R, E [Q
P top neg. items per user histogram of user-item category interactions at times 1, f item to category one-hot map at time > stores probability of sampling neg. item for user u
Require: H,, H E N
Require: C, E g|
M. E | f-1 0
2: for u 0; S [M];
do
3:
for i= 0; <
1 do
0u, E R update sampling params from eq. equation 10
5: C' <- arg max :
b get category i belongs to b from eq. equation 11
M, p(n; ilé E C, 0,,,,)
7: end for
end for
Algorithm 2 Incremental Training with Graph-SANE Reservoir
Require: o
D params of model from block t 1 refresh rate of reservoir, max epochs
Require: f, max epochs
Require: R, E [
SANE reservoir mum. random negatives, reservoir samples
Require: N2
ITER <-
2: repeat
3:
if N ITER mod f == 0 then
4:
Update item cluster memberships using eq. equation Update R2 using Algorithm I
5:
end if
Draw batch of incremental data B S {(u,i) {1)1
Draw Nj random negatives Iı Sample N₂ reservoir negatives It Compute loss components from eq. equation 16
10:
11:
Update parameters
12:
N _ITER + N ITER
13:
until convergence
F
Case Study Details
To conduct this case study we chose a clustering algorithm that differs from the one used in our method. This is done to provide an alternative estimate of high shift users that is not part of our model. Note that the user shift indicator, í.c. the technique to identify high interest shift users, we use follows the process introduced by Wang el al. (Wang et al. 2023). For completeness we explicitly list. the steps taken by Wang al. /Wang al. )
1. Apply K-means on item embeddings time block obtained from the SGCT model to identify K clusters.
2. Obtain jt E R by counting number of items from each calegory a user interacts with for all
3. Normalize je to calculate I = - Evex T'
4. Obtain interest shift indicator: ISS. * EK
ii I 12-1112.
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5.
We define users with top 15% interest shift indicator the high shift user set.
6. Calculate average recall for the high shift users using all the different negative samplers on top of SGCT.
G Loss Ablation Study & Sensitivity Analysis
G.1 Ablation study
In this section we conduct a loss ablation study on our proposed objective, as well as sensitivity studies on key components of our method: the choice of specific clustering algorithm, the number of clusters of our clustering algorithm
well the size of our proposed negative reservoir. The dataset choice for the ablation and sensitivity experiments can be explained by the fact that Netflix, which is our biggest dataset, is prohibitively big to run many experiments on as it takes over 2 days per experiment Taobao14 14 as they have the most representative number of user and items compared to the average dataset (they are neither the biggest nor the smallest).
opt for Yelp and
Table 5: Loss components ablation Taobao14 and Yelp for SGCT-SANE (Recall@20). We check the impact of removing cach loss term from our overall proposed optimization objective. As we can see, removing any of our proposed components impacts performance and/or end-to-end trainability.
Method
LBPR
LKD
LSANE
LRL
End-to-Fam Trainable
Taobao14
Yelp
Fine Tune
X
X
X
Yes
0.0153
0.0661
SGCT
/
X
X
Yes
0.0160
0.0668
SGCT-hard-cluster
V
X
No
0.0178
0.0845
SGCT-SANE (ours)
V
Yes
0.0178
0.0857
Table 6: Loss components ablation on Taobao14 and Yelp for LWCKD-SANE (Recall@20). As we can see, removing any of our proposed components impacts performance and/or end-to-end trainability.
Method
CAPR
LKD
LSANE
L
And-to-End Trainable
Taobao14
Yelp
Fine Tune
X
Yes
0.0153
0.0661
LWCKD
/
X
X
Yes
0.0176
0.0679
WWCCK--hardcllssfe
V
X
No
0.0185
0.0857
IWCKD-SANE (ours)
V
V
Yes
0.0188
0.0898
Our loss ablation study validates each term in the proposed loss. Concretely, we check the impact of removing each loss term from our overall proposed optimization objective. As can in Tables 5 and 6 removing any of our proposed components impacts performance and/or end-to-end trainability.
G.2 Clustering Algorithm Sensitivity
In this sensitivity study check if ad-hoc training scheme where we cluster the items using K-means between epochs can produce similar results to our approach, which uses an end-to-end structural based clustering method (Bo et al. 2020). In Table observe that our method performs within 1-3% with either clustering algorithm, thus validating the low sensitivity towards clustering algorithm selection. We obtain similar results when we vary the dataset choice and the number of clusters. The attributed clustering algorithm maintains end-to-end trainability so it converges faster than K-mcans.
In the second sensitivity study, shown in Table g conduct an analysis the number of clusters used in our method. As we can see, once the number of clusters reaches sufficient number (~ 10), the performance remains stable.
Thirdly, in Table 10 we conduct a sensitivity analysis on the size of the user negal ive reservoir |Q]- As we can see, the method is not sensitive to the size of the reservoir. This implies that introducing even a few hard nogatives the incremental training can be sufficient improve performance.
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Table 7: Sensitivity to clustering algorithm choice in Yelp. Results demonstrate low sensitivity to specific algorithm choice.
Methods
Inc. 1
Inc. 2
Inc.3
Avg.
SraE (K- (K-means)
0.0877
0.0871
0.0791
0.0846
GraphSAIL+SANE (end-to-end ours)
0.0939
0.0842
0.0791
0.0857
SGCT+SANE (K-means)
0.0946
0.0858
0.0732
0.0845
SGCT+SANE, (end-to-end ours)
0.0966
0.0877
0.0744
0.0857
LWC-KD+SANE (K-means)
0.0931
0.0853
0.0787
0.0857
LWC-KD++SANE (end-to-end ours)
0.0924
0.0855
0.0798
0.0859
Table 8: Sensitivity to clustering algo. choice in Taobao14. Results demonstrate low sensitivity to specific
algorithm choice.
Methods
Inc.
Inc.
Inc.3
Avg.
GraphSAITL+SANE (K-means)
0.0222
0.0139
0.0165
0.0175
GraphSAIIL+SANE (end-to-end)
0.0231
0.0131
0.0150
0.0171
SGCT+SANE (K-means)
0.0228
0.0154
0.0153
0.0178
SGCT+SANE (end-to-end)
0.0224
0.0136
0.0173
0.0178
LWC-KD+SANE (K-mcans)
0.0228
0.0174
0.0154
0.0185
LWC-KD+SANE (end-Lo-end)
0.0222
0.0188
0.0156
0.0188
Table 9: Sensitivity analysis for the cluster number K. We present Recall@20 results the Gowalla and Taobao2015 datasets for SGCT-SANE and LWC-KD-SANE. Results demonstrate low sensitivity to number of clusters.
Distillation Stralegies
Dataset
K
Inc
Ine 2
Inc 3
Avg. Recall@20
0.0240
0.0133
0.0127
0.0167
10
0.0224
0.0136
0.0173
0.0178
SGCT-SANE
15
0.0237
0.0143
0.0143
0.0174
20
0.0237
0.0154
0.0165
0.0185
25
0.0234
0.0156
0.0166
0.0185
Taobao14 14
0.0265
0.0121
0.0150
0.0179
10
0.0222
0.0188
0.0155
0.0188
LWC-KD-SANE
15
0.0251
0.0138
0.0161
0.0183
20
0.0247
0.0128
0.0145
0.0173
25
0.0247
0.0141
0.0162
0.0183
Table 10: Sensitivity analysis the size of the user negative reservoir Q We present Recall@20 results
on the Gowalla and Taobao2015 datasets for SGCT-SANE and AWC-KD-SANC Results demonstrate low sensitivity to negative reservoir size.
Distillation Strategies
Dataset
Q
Inc 1
Inc 2
Inc 3
Avg. Recall@20
50
0.0237
0.0156
0.0160
0.0184
SGCT-SANE
100
0.0224
0.0136
0.0173
0.0178
300
0.0254
0.0140
0.0160
0.0185
Taobao14
0.0238
0.0140
0.0162
0.0180
IWC-KD-SANE
100
0.0222
0.0188
0.0155
0.0188
300
0.0246
0.0133
0.0180
0.0186
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H Hyperparameter Settings
Our method is implemented in TensorFlow. The backbone graph neural network is the MGCCF (Sun et al. 2019 trained using the hyperparameters shown in Table [1 Incremental learning methods are not used during the base block training so the loss during the base block is only LBPR, i.e, (no LKD; LSANE, LKI. components).
Table 11: Hyperparameters of our model on all benchmarks.
Hyperparameter
Value
Min Epochs Base Block
10
Min Epochs Incremental
3
Max Epochs Base Block
N/A
Max Epochs Incremental
15
Early Stopping Patience
2
Batch size
64
Optimizer
Adam
Cache Update Frequency f
2 epochs
Cache Size per user [Ω]
100
Learning rate (max)
5e-4
Dropout.
0.2
Losses
KD, BPR, SANE, KL
GNN Num Layers (L)
2
Num Clusters (K)
10
Embedding dimensionality
128
Augmentations
NONE
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Experimental Results per Incremental Training Block
In this section we provide a more detailed version of the results from Tab. with breakdown of the performance for each incremental block.
Table 12:
Comparison (R)) of baselines and 3 recent knowledge distillation algorithms with our SANE reservoir, our methods are accompanied by star (+). Best performers are in bold, second best are underlined. Blue cell colors indicate improvement of a particular method when our reservoir is introduced.
Yelp
Netflix
Model
Inc
Inc 2
Inc 3
Average
A%
Inc
Inc 2
Inc 3
Average
%%
Fine Tune
0.0705
0.0638
0.0640
0.0661
0.0
0,1092
0.1041
0.0977
0.1036
0.0
LSP
0.0722
0.0661
0.0644
0.0676
2.3
0.1173
0.1136
1076
0.1128
8.7
U Uniform
0.0718
0.0635
0.0610
0.0654
-1.1
0,1018
0.1055
0.0800
0.0957
-7.6
Inv degree
0.0727
0.0699
0.0605
0.0677
2.4
0,1000
0.1050
0.0820
0.0957
-7.6
GraphSATI
0.0674
0.0617
0.0625
0.0639
-3.3
0.1163
0.1023
0.0968
0.1051
1.4
GraphSAIL-SANT
0.0939
0.0842
0.0791
0.0857
29.7
0,1153
0.1091
0.01014
0.1086
4.8
SGCT
0.0740
0.0656
0.0608
0.0668
1.06
0.1166
0.1161
0.1077
0.1135
9.6
SGCT-SANE*
0.0966
0.0877
0.0744
0.0862
30.4
0.1182
0.1164
0.1120
0.1155
11.5
LWC-KD
0.0739
0.0661
0.0637
0.0679
2.7
0.1185
0.1170
0.1071
0.1142
10.2
LWC-KD-SANE*
0.0970
0.0891
0.0834
0.0898
35.9
0.1192
0.1196
0.1157
0,1182
14.1
Taobao14
Taobao15
Model
Inc
Tne 2
Inc
Average
A%
Tnc
Inc 2
Inc 3
Average
A%
Fine Tune
0.0208
0.0112
0.0138
0.0153
0.0
0.0933
0.0952
0.0965
0.0950
0.0
LSP
0.0213
0.0106
0.0138
0.0152
-0.7
0.0993
0.0952
0.0957
0.0968
1.9
Uniform
0.0195
0.0127
0.0148
0.0157
2.6
0.0988
0.0954
O. 1004
0.0982
3.4
Inv degree
0.0228
0.0140
0.0159
0.0175
14.6
0.0991
0.0977
O. 0.1000
0.0989
4.2
GraphSAIL
0.0222
0.0105
0.0139
0.0155
1.31
0.0959
0.0959
0.0972
0.0963
GraphSAII-SANE
0.0231
0.0131
0.0150
0.0171
11.8
0.1114
0.1087
0.1121
0.1107
16.5
SGCT
0.0240
0.0092
0.0148
0.0160
1.74
0,1030
0.0983
0.0984
0.0999
5.2
SGCT-SANE*
0.0224
0.0136
0.0173
0.0178
16.3
0.1117
0.1129
0.1138
0.1128
18.7
LWC-KD
0.0254
0.0119
0.0156
0.0176
15.3
0,1039
0.1022
0.1029
0,1030
8.4
LWC-KD-SANE*
0.0222
0,0188
0.0155
0.0188
22.9
0,1106
0.1108
0.1128
0.1114
17.2
Gowalla-20
MovieLens 10M
Model
Inc
Inc 2
Inc
Average
A%
Inc
2
Inc 3
Average
A%
Fine Tune
0.1412
0.1637
0.2065
0.1705
0.0
0.0923
0.0904
0.0957
0.0918
0.0
LSP S
0.1512
0.1741
0.2097
0.1783
4.57
0.0912
0.0923
0.0941
0.0925
0.76
Uniforma
0.1480
0.1653
0.2051
0.1728
1.34
0.0874
0.0879
0.0902
0.0885
-3.59
Inv dogree
0.1483
0.1680
0.2001
0.1738
1.93
0.0906
0.0911
O. 0.0928
0.0915
-0.32
GraphSAlL
0.1529
0.1823
0.2195
0.1849
8.44
0.0867
0.0887
0.0917
0.0890
-3.05
GraphSAIT.SSANS
0.1646
0.1907
0.2221
0.1925
12.9
0.0887
0.0915
0.0961
0.0921
0.33
SGCT
0.1588
0.1815
0.2207
0.1870
9.68
0.0894
0.0902
0.0960
0.0919
0.11
SGCT-SANE*
0.1611
0.1843
0.2237
0.1897
11.3
0.0927
0.0932
0.0980
0.0946
3.05
LWC-KD
0.1639
0.1921
0.2368
0.1977
15.9
0.0902
0.0910
0.0973
0.0928
1.09
LWC-KD-SANE
0.1698
0.1835
0.2173
0.1881
10.3
0.0928
0.0953
0.1012
0.0964
5.01
26

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Published in Transactions on Machine Learning Research (02/2025)
J Dataset Preprocessing Data Block Definition
For all data sets we follow the setup from literature (Xu et al. 2020 Ahrabian et al. 2021 We divide the data in chronological order into a base block and incremental blocks. The base block contains 60% of the data. The remaining 40% of the data is evenly separated into four incremental blocks. Note that during training the blocks can be further subdivided to allow for a validation set. In our setting for each block we reserve 5% of the data as a validation dataset following from the baselines (Xu et al.) 2020 Ahrabian al.,
2021 Note that this does not induce data leakage all splits in chronological order. For visualization Fig.
50%
10%
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10%
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Base Model
Train
Test
Transfer Knowledge
T=1
Model 1
Train
Test
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Figure 5: Data is separated to base block with 60% of the data and 4 incremental blocks, cach with 10% of the remaining data.
27

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a practice adopted form the Published in Transactions on Machine Learning Research (02/2025)
K Practical Recommendation for Model Deployment
Tuning the framework hyperparameters can be achieved in similar fashion to the setup in Fig. 5 Here, we again split the data into temporally sorted blocks. The base block contains 60% of the data. The remaining 40% the data evenly separated into four incremental blocks. During training, when block is used as the training set, the first half of block t + used as the validation set and the second half used as the testing set (Figure 0 Note this setup prevents data Ieakage the test data are all from interactions that occur after the validation set. For example, if a block contains 10 days worth of data, the validation dataset would contain days 1-5 and the test set days 6-10.
50%
5%
5%
10%
10%
10%
10%
Train
Val
Test
B1
B2
B3
B4
Base Model
Train
Val
Test
Transfe: Knowledge
T-1
Model 1
Train
Transfer Knowledge
T=2
Model 2
Figure 6: Incremental learning hyperparameter tuning setup. Note this setup prevents data leakage as the test data are all from interactions that occur after the validation data. For example, if block contains a 10 days worth of data, the validation dataset would contain days 1-5 and the test set days 6-10.
To deploy GraphSANE on top of an existing recommendation system, we recommend the following steps:
Accumulate data equal to 10 times the incremental block size. For example, if the model is expected to be updated daily we recommend accumulating 10 days worth of data for hyperparameter tuning.
2. Split the data chronologically in blocks as shown in Fig. G The reason that we put validation sets in the data immediately following the block is the we wish to create back-testing style setup where the hyperpameters are tuned based on the typical distribution shift between the train and test steps. Note that since the blocks are chronologically ordered this does not leak any interaction from the test set the validation set. This placement of the validation literature (Xu al. 2020: Ahrabian et al. 2021).
3. Train a base GNN model on the base block data. Note that any base backbone recommendation system model, such as MGCCF (Sun et al.) 2019 or LightGCN (He et al., 2020b) has its own hyperparameters which can be tuned on the validation portion of the base block. These base GNN architectures have their own hyperparameters that are not related our incremental learning framework we omit further discussion on how to tune the base models and focus how to shift hyperparameterss related to our method.
Tune parameter by checking the training loss the first incremental block. It suffices select B values such that at the start of training the KI. loss component of the loss is in the same scale
28

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Published in Transactions on Machine Learning Research (02/2025)
the triplet loss component. Note that the source code provide tracks these components this process is easy to perform.
For the number of clusters K and the size of the reservoir [Q] we recommend running a grid search, Note that since these two hyperparameters the sensitivity tests experiments, the parameter luming process could be further oplimized using Bayesian optimization hyperparameter tuning tools such as Optuna
may search over the values used in in Tables and 10 Note even though run grid search in our
/https://optuma.org
29


Reviews:
[{"review_id": "B8udCE4L1R", "reviewer": "Reviewer_2utX", "summary": "", "questions": "", "limitations": "", "rating": null, "confidence": null, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "# Strengths\n- Solves an extremely important problem of adapting to the changing marketplace of users and items quickly and efficiently. In many practical applications, the latency between events happening, and a model trained on those events being deployed and used has a tremendous effect on the performance in practice.\n- Shows significantly positive results on some recsys datasets.\n- The method does not degrade the inference time in any way, which is extremely important in practical recommender systems. The cost of recommendation in many cases makes the difference between a useful and a useless method.\n\nBeyond the strengths, it appears the paper needs some over-haul before it's ready for publication. See weaknesses and requested changes. \n\n# Weaknesses\nThe weaknesses are divided into weaknesses concerning the scientific contribution and content, and weaknesses concerning the structure.\n\n## Contribution weaknesses\n1. One important paradigm of incremental learning is the paradigm of online learning - training on each example only once. It should be explained why this method is not applicable for the discussed setup of the model, or be added as a baseline.\n2. The method appears to be non-extensible to the case when users or items are *not* represented by their identity, but rather only by their features (i.e. no user / item nodes at all). This needs to be explicitly written in the conclusion section, since many recsys where there isn’t a huge amount of training data and sparsity is abundant (such as ads, for example), work this way. \n3. A well-known benchmark family for RecSys are the movie lens datasets. They appear to be missing.\n4. A simple online-learning baseline without triplet loss is missing. It's another common method of adapting to the changing trends. See [1] for example. (i.e. binary labels, positive and negative, where the negatives are randomly sampled).\n5. Lacks a link to the code (anonymized with some service, such as https://anonymous.4open.science service)\n\n## Structural weaknesses\n1. The paper appears to lack crispness and polish. It's not clear where the boundary between the core contribution and the 'peripheral' things goes, and it needs to be deduced as we read. For example:\n  1.1 The paper does not explain from the very beginning, the abstract and the intro, that the main focus is GNNs for rankings. Many recommenders are not of this structure, i.e. Factorization-Machine based ad recommenders.\n  1.2 In Section 5.3, it is not clear from the text weather the T distribution as the cluster assignment probability is the authors’ contribution, or the review of previous works cited at the beginning of the section. The same for the clustering method, and the square+normalization operation.\n2. Section 5.2 - if the item categories are not given, how do you update the assignment of item to categories in the incremental learning setting? Based on which embeddings? How does it work if the embeddings constantly change? What about new items from the current batch for which we don't have reasonable embeddings yet? Or is the negative reservior only from the previous batches? A lot of missing details here. The code, again, would help, even if these details are not in the paper.\n3. In Section 5.3 -  what does “ To obtain confident cluster assignments” mean? “Confident” in what sense?\n4. The content 5.4 should probably appear before the components of the framework are described. A top-down approach is typically more readable than a bottom-up approach. Moreover, why is $beta_1 = 1$ a reasonable choice?\n5.  Section 5.1 is hard to follow, and there’s no intuition on *why* we should consider several independent observations of the same negative item. The hypothesis on page 7 should come earlier, to make the paper more readable.\n6. It's not clear in the experiment section how the measurements are conducted (per-block? Only last block? Something else? How the blocks are aggregated?), and how the data-sets are divided into blocks.\n\n\n[1]: Aharon, M., Kagian, A., & Somekh, O. (2017, April). Adaptive online hyper-parameters tuning for ad event-prediction models. In Proceedings of the 26th International Conference on World Wide Web Companion (pp. 672-679).", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "No", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "paper_topic_and_main_contributions": "", "excitement": null, "reproducibility": null, "ethical_concerns": "", "main_review": "", "summary_of_the_paper": "", "summary_of_the_review": "", "strength_and_weaknesses": "", "limitations_and_societal_impact": "", "review_text": "", "summary_of_contributions": "The paper proposes a framework for continually learning a GNN recommendation model to quickly adapt to the changing sets of users, items, and trends in their affinity. This is an important and fundamental problem in many recommendation systems, ranging from ads, to news and video recommendation. The framework includes a non-uniform reservoir sampling technique, where the sampling distribution is based on clusters of items, either statically determined by a taxonomy, or dynamically learned by clustering.", "claims_and_evidence_yn": "No", "claims_explanation": "", "audience_yn": "Yes", "audience_explanation": "", "requested_changes": "1. Please move the hypothesis from page 7 to section 5.1 to to emphasize that this is a hypothesis, and not something that we know to be true\n2. Separate the core contribution from the 'peripherals' more clearly. For example, the 'framework' in section 5.4 may be with or without clustering, since the taxonomy of items may be given.\n3. Explain from the very beginning that the paper is about GNN recommenders with user/item identity.\n4. Clarify, as explained in the weaknesses, what exactly is the contribution of this paper, and what is adoption of ideas from other papers. The distinction needs to be more clear (i.e. the T distribution).\n5. Clarify how the experiments were conducted, and how the measurements were made. Otherwise, it's hard to judge the evidence provided.\n6. Anonymizer and add a link to the code.", "broader_impact_concerns": "I do not see broader impact concerns.", "additional_comments": "", "extra_scores": {}, "extra_text": {}}, {"review_id": "XYbFpfs0fC", "reviewer": "Reviewer_r8Jp", "summary": "", "questions": "", "limitations": "", "rating": null, "confidence": null, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "S1: mitigates the issue of catastrophic forgetting: The proposed approach effectively addresses the problem of catastrophic forgetting in incremental learning by maintaining a personalized negative reservoir that balances stability and plasticity. This ensures the system retains past knowledge while adapting to new user interaction data.\n\nS2: can be integrated with SOTA graph NN algorithms\n\nS3: strong performance across different datasets: empirical results demonstrate significant improvements in metrics like Recall@20 and NDCG on five diverse datasets, showing the method enhances the performance of SOTA algorithms in many different scenarios.\n\nS4: very interesting ablation studies: The paper includes thorough ablation studies that validate the importance of key components, such as the negative reservoir and clustering mechanisms.\n\n---\n---\n\nW1: Increased complexity: the proposed approach increases the complexity, both computational and conceptual. It increases the computational complexity because it requires a set of additional steps, such as tracking user interest shifts, maintaining and updating a negative reservoir, and clustering items dynamically over time. These steps increase the overall complexity of training and may require additional computational resources, which may be problematic for large-scale systems with millions of users and items. \n\nW2: no investigation of cold-start scenarios: The paper does not explicitly address how the approach handles cold-start users (new users with little interaction history) or cold-start items (new items with few interactions). Since incremental learning often struggles with cold-start issues, the lack of a dedicated strategy in this method could limit its applicability in such scenarios. It would be nice if the paper explored such scenarios.\n\nW3: Presence of many hyperparameters: The approach introduces several hyperparameters, such as reservoir size and loss weights, which require careful tuning.", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "Yes", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "paper_topic_and_main_contributions": "", "excitement": null, "reproducibility": null, "ethical_concerns": "", "main_review": "", "summary_of_the_paper": "", "summary_of_the_review": "", "strength_and_weaknesses": "", "limitations_and_societal_impact": "", "review_text": "", "summary_of_contributions": "The paper, titled Personalized Negative Reservoir for Incremental Learning in Recommender Systems, proposes a novel strategy to address the challenge of maintaining efficient and accurate recommendation systems as user interactions evolve over time. The proposed framework can be intergrated with existing graph-based recommendation systems and incremental learning models and it is used to improve performance of state-of-the-art Graph Incremental Learning methods (GraphSAIL, SGCT, and LWC-KD) across five datasets.", "claims_and_evidence_yn": "Yes", "claims_explanation": "", "audience_yn": "Yes", "audience_explanation": "", "requested_changes": "- Address Cold-Start Scenarios:\n\nYou could try to incorporate strategies to handle cold-start users and items, such as leveraging content-based features or meta-learning techniques. You could include experiments to evaluate the method’s performance in cold-start scenarios.\n\n- Improve Clustering Mechanisms\n\nYou could try to improve the clustering process by e.g. integrating multi-modal features (e.g., textual or visual data) or adaptive clustering techniques to ensure high-quality item categorization.\n\n- Provide Practical Guidelines\n\nPlease include practical recommendations for deploying the method, such as resource requirements and tips for hyperparameter tuning. This is fundamental for such a complicated method. Also, if possible, explore automated tuning strategies like Bayesian optimization to reduce the complexity of selecting the many hyperparameters of the proposed approach.\n\n- Expand Dataset Diversity\n\nIf possible, test the method on additional datasets. Useful scenarios may be the datasets with extreme sparsity, dense interactions, or highly dynamic user-item relationships. This can further validate the generalizability of the proposed approach", "broader_impact_concerns": "No issues.", "additional_comments": "", "extra_scores": {}, "extra_text": {}}, {"review_id": "6HM6Qrhtw4", "reviewer": "Reviewer_UQg6", "summary": "", "questions": "", "limitations": "", "rating": null, "confidence": null, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "**Strengths**:\n\n1. The paper addresses the important but underexplored issue of negative sampling in incremental learning, which is crucial for the performance of recommender systems.\n\n2. The proposed method shows significant improvements across multiple metrics (e.g., Recall@20), especially when combined with SOTA models.\n\n3. The personalized negative reservoir strategy effectively handles user interest shifts, making it highly valuable for practical recommender system applications.\n\n**Weaknesses**:\n\n1. The benchmark used in this paper does not clearly specify how the test set is defined, which is important for interpreting the assumptions in Section 5.2 and understanding the reasons for performance improvements. My understanding is that the incremental split dataset is sorted by time, and after each incremental block is learned, all the remaining data including the most recent training data should be used as the test set.\n\n2. SANE improves plasticity in incremental learning by considering user interest shifts, but a thorough incremental learning framework also needs to consider stability, as catastrophic forgetting has a detrimental impact on system performance. I suggest further explaining how the proposed method contributes to system stability.\n\n3. The generalizability of calculating interest shifts based solely on user interactions from the previous time block is questionable. While this approach is reasonable in scenarios with rapid user interest changes, it may not be applicable to all incremental cases. It is recommended to add an ablation study by replacing $\\mathbf{H}_{u,t-1}$ in Eq.7 with prefix sum or sliding average and to provide related discussions to support the stability and generalizability of the SANE system.\n\n4. The paper lacks the comparison with the Oracle method Joint Training in the incremental learning. Further, if user interest shifts are rapid and significant, would learning only on the incremental blocks achieve good results? I suggest adding a relevant comparison.\n\n5. The choice of baseline negative sampling methods could be more comprehensive. It is recommended to refer to the latest survey[1] and add a comparison with *at least one* recent negative sampling technique, such as ESNS[2] or DeMix[3], to strengthen the evaluation.\n\n**Minor Question**\n\n* In Section 6.3, the statement \"Furthermore, as summarized in Fig.3, LWC-KD-SANE is the top-performing method overall\" seems inconsistent with the average rank shown in Fig.3, where SGCT-SANE appears to perform better.\n\n**Reference**:\n\n[1] Madushanka, T., & Ichise, R. (2024). Negative Sampling in Knowledge Graph Representation Learning: A Review. ArXiv, abs/2402.19195.\n\n[2] Yao, N., Liu, Q., Li, X., Yang, Y., & Bai, Q. (2022). Entity Similarity-Based Negative Sampling for Knowledge Graph Embedding. Pacific Rim International Conference on Artificial Intelligence.\n\n[3] Chen, X., Zhang, W., Yao, Z., Chen, M., & Tang, S. (2023). Negative Sampling with Adaptive Denoising Mixup for Knowledge Graph Embedding. International Workshop on the Semantic Web.", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "Yes", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "paper_topic_and_main_contributions": "", "excitement": null, "reproducibility": null, "ethical_concerns": "", "main_review": "", "summary_of_the_paper": "", "summary_of_the_review": "", "strength_and_weaknesses": "", "limitations_and_societal_impact": "", "review_text": "", "summary_of_contributions": "This paper proposes a personalized negative reservoir strategy for incremental learning in recommender systems, addressing the issue of catastrophic forgetting while adapting to changes in user preferences. The authors introduce a novel negative sampling strategy tailored for incremental learning, validated through integration with three state-of-the-art (SOTA) models. The key contributions include a mathematical derivation of a personalized negative reservoir, integration with incremental recommendation frameworks, and experimental results verified on five large-scale datasets.", "claims_and_evidence_yn": "Yes", "claims_explanation": "", "audience_yn": "Yes", "audience_explanation": "", "requested_changes": "1. Provide detailed information on how the test set is determined in the incremental learning setup of recommender system datasets.\n\n2. Further discuss how the proposed negative reservoir strategy enhances the stability of the incremental learning system, helping to address the issue of catastrophic forgetting.\n\n3. Replace $\\mathbf{H}_{u,t-1}$ in Eq.7 with prefix sum or sliding average to perform an ablation study.\n\n4. Include the Joint Training method.\n\n5. Include a baseline that learns only on incremental blocks.\n\n6. Add a comparison with *at least one* recent negative sampling methods.", "broader_impact_concerns": "No concerns in this regard.", "additional_comments": "", "extra_scores": {}, "extra_text": {}}]

Author rebuttal:

Meta-review: After the discussion, the reviewers were unanimous that this paper should be accepted. Your responses and updated manuscript answered all of the reviewers' questions and comments. 

As you had promised in your response to reviewer UQg6, please add a discussion "indicating that the focus of our work is on accounting for user interest shifts rather addressing the problem from a traditional continual learning perspective that focuses on preventing catastrophic forgetting in the final version of the manuscript." That's the only requested revision. 

Congratulations!
Decision: Accept (poster)