Evidential Stochastic Differential Equations for Time-Aware Sequential Recommendation
Authors: Krishna Prasad Neupane
Ervine Zheng
Qi Yu
Venue: NeurIPS 2024 poster (2024)
Keywords: Sequential recommendation
time-evolving behavior
Primary area: machine_learning_for_other_sciences_and_fields
TL;DR: We formulate a novel Evidential Neural Stochastic Differential Equation (E-NSDE) to seamlessly integrate NSDE and evidential learning for effective time-aware sequential recommendations.

Abstract: Sequential recommender systems are designed to capture users' evolving interests over time. Existing methods typically assume a uniform time interval among consecutive user interactions and may not capture users' continuously evolving behavior in the short and long term. In reality, the actual time intervals of user interactions vary dramatically. Consequently, as the time interval between interactions increases, so does the uncertainty in user behavior. Intuitively, it is beneficial to establish a correlation between the interaction time interval and the model uncertainty to provide effective recommendations. To this end, we formulate a novel Evidential Neural Stochastic Differential Equation (*E-NSDE*) to seamlessly integrate NSDE and evidential learning for effective time-aware sequential recommendations. The NSDE enables the model to learn users' fine-grained time-evolving behavior by capturing continuous user representation while evidential learning quantifies both aleatoric and epistemic uncertainties considering interaction time interval to provide model confidence during prediction. Furthermore, we derive a mathematical relationship between the interaction time interval and model uncertainty to guide the learning process. Experiments on real-world data demonstrate the effectiveness of the proposed method compared to the SOTA methods.

Evidential Stochastic Differential Equations for Time-Aware Sequential Recommendation
Krishna Prasad Neupane, Ervine Zheng, Qi Yu"
Rochester Institute of Technology mx25733, gttp:s/....y/ri..eeeee
mx27333,,,
Abstract
Sequential recommender systems are designed capture users' evolving interests over time. Existing methods typically assume uniform time interval among consecutive user interactions and may not capture users' continuously evolving behavior in the short and long term. In reality, the actual time intervals of user inter- actions vary dramatically. Consequently, as time interval between interactions increases, does the uncertainty in user behavior. Intuitively, it is beneficial tablish a correlation between the interaction time interval and the model uncertainty provide effective recommendations. To this end, formulate novel Evidential Neural Stochastic Differential Equation (E-NSDE) to seamlessly integrate NSDE and evidential learning for effective time-aware sequential recommendations. The NSDE enables the model to learn users' fine-grained time-evolving behavior by capturing continuous user representation while evidential learning quantifies both aleatoric and epistemic uncertainties considering interaction time interval to pro- vide model confidence during prediction. Furthermore, we derive mathematical relationship between the interaction time interval and model uncertainty to guide the learning process. Experiments on real-world data demonstrate the effectiveness of the proposed method compared to the SOTA methods.
Introduction
Recommender systems have been used in various domains, such e-commerce, entertainment, education, health care, social media, and many more 32
In these domains, users' interests and behaviors dynamically evolve over time. Therefore, capturing users' evolving behavior plays an essential role in effective recommendations. Various sequential recommendation models B8 40 4 have been proposed accordingly. They mainly leverage the user's historical sequential interactions and aim to predict the next item that a user likes to interact with. These methods usually assume uniform time interval of user interactions. However, in reality, the actual time interval between two consecutive interactions may vary dramatically, and a large time interval may be accompanied by a change users' preferences.
B5
The unrealistic assumption of uniform inter- action interval could significantly impact the model's capability to capture users' continu- ously evolving behavior and subsequently hurt the recommendation performance. Table pro- vides an illustrative example of the issues as outlined above. In this example, we follow the standard sequential recommendation similar to [9 35 by predicting the next item considering
Table 1: Impact of interaction interval
Ranking J
Interaction Interval (Seconds)
BERT4Rec
E-NSDE
6
623,591
24
116 + 117
62
6
150 + 151
896,291
56
"Coresponding author
38th Conference on Neural Information Processing Systems (NcurIPS 2024).

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Table 2: Epistemic uncertainty and recommended movie genres for random user considering
sequential interaction intervals
Model
Interval (Seconds)
Epistemic uncertainty
Ground-truth genre
Recommended genre
44
N/A
'Comedyy' 'Romance")
['Comedy', 'Dramaa)
GRU-ODE
623,591
62
N/A
N/A
l'Action' 'Adventure', 'Thriller'
I'Drama', 'Romance", "War)
l'Action'. 'Romunce', "Drama'l
["Comedy" . 'Romance"
896,291
N/A
['Homor', "Thrillrr)
['Drama', 'Romance")
44
0.4016
l'Comedyy', y 'Romance"]
I'Comedy', 'Romance', "Thriller")
E-NSDE
623.591
0.6725
I'Drmma' 'Romance', 'War1 ['Action', 'Adventure', , "Thriller')
I'Drama', 'Horror'. 'Fci_FF'
0.4463
['Action' "Mystery"l
896,291
0.7104
['Horror, "Thriller)
[Thrilllr 'Crime" 'Adventure']
other 100 negative items from the item pool. We select a random user from the Movielens- dataset and provide recommended ranking results together with the interaction time intervals in the sequence. The recommendation performance for a sequential model BERT4Rec [35] deteriorates significantly when the gap between the consecutive interactions becomes large. For example, when the next interaction occurs soon after the first one, BERT4Rec usually ranks the ground-truth item in a top- 10 list. However, for much larger interval, the ground-truth item drops out of the top-20 or even the top-50 recommendation list.
Neural Ordinary Differential Equations (NODE) have been recently introduced that map the existing discrete neural networks to a continuous model (
36 [6]. which can naturally capture users' continuously evolving preferences. However, one key limitation of these NODE models is the lack of uncertainty quantification capability, which is essential to understand user behavior when recommending the next item, especially when learning from extremely sparse user interactions given a large item space. Intuitively, the uncertainty of user behavior should increase along with the length of the interval since the last active interaction. For example, if the user has no activity for long time, the user's prior interest tends to decrease. As a result, we become more uncertain about the user's s preference. At the same time, a high uncertainty also presents a unique opportunity effectively explore the item space by providing diverse recommendation list to the users so that they may be attracted to a new category of items to keep them in the system.
Uncertainty can serve as a useful guidance to the recommender system to adapt to users' changing preferences and explore new items effectively. Table 2 further highlights the limitation of an existing ODE-based sequential recommendation method GRU-ODE [16). where recommended genres come from frequently watched 'Drama' and 'Romance' movies in the past. This issue becomes even worse when the interaction gap becomes large (i.e., the fourth row of the GRU-ODE model), and the recommended genres significantly deviate from the ground truth. The recommendation list again concentrates on the same 'Drama' and 'Romance' genres, which are misaligned with the user's s long-term interests. It is evident that conducting a more effective exploration is crucial to uncover the long-term and varied interests of users, aiming to optimize potential future benefits.
To address this critical gap as outlined Table 3: Comparison of related recommendation models above, we propose uncertainty augmented Neural Stochastic Differential Equations (NSDE) and integrate it into a novel se- quential recommendation model. NSDE is a variant of NODE that adds Brownian motion terms incorporate stochasticity via a diffusion function. NSDE has been successfully applied in other fields, such as computer vision (20 41) It provides an effective means to capture users' continuously changing behavior, and also model the noise via stochasticity in user and item representations. However, recommender systems involve uncertainty from multiple sources: uncer- tainty caused by evolving user preferences and uncertainty arising from user-item interactions. While the standard NSDE can naturally capture the former, it is not designed to cover the latter. To this end, we further incorporate evidential deep learning (EDL) [3 to gather evidence from user-item interactions and systematically capture uncertainty from multiple sources. Table 3 summarizes the key differences between the proposed model and existing relevant models.
Key functions
Sequential
NODE
NSDE
E-NSDE
Varied interval
x
/
Uncertainty preference
Uncertainty interaction
The proposed E-NSDE seamlessly integrates an NSDE module and an EDL module, where the former is responsible for learning user and item representations over time and the latter utilizes these rich representations to identify important and diverse items that the model needs to learn to capture users' actual behavior with the help of uncertainty-awarr exploration. Table shows that E-NSDE places a pronounced emphasis a wider array of genres, and substantial portion of these manage
2

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to capture sustained interest over the long term. In each sequence, E-NSDE attempts to provide diverse genres as shown in the first row ('Thriller') and second row ('Sci of the E-NSDE result. When there is a long time interval, the model can leverage this opportunity guided by its predicted epistemic uncertainty and recommend novel genre ("Crime") to explore the diverse items that can help to capture the user's long-term interest. The ability to quantify time-aware uncertainty also allows E-NSDE to outperform SOTA sequential recommendation models as shown in Table [
As key innovation, we connect NSDE-based user-item representation learning with EDL using a monotonic network to provide an evidence- evidence-guided recommendation to capture sensitive rating prediction augmented with uncertainty estimation. Intuitively, the model's uncertainty of a user's s interest should increase with respect the time interval since the last observed user-item interaction. To model üime-sensitive uncertainty, we integrate EDL using an uncertaint--awai regression model to infer evidential distributions that allow us to quantify both aleatoric and epistemic uncertainties. Similarly, the monotonic network captures the underlying constraint of monotonicity between the time interval and the predicted uncertainty: a longer time interval leads to a higher uncertainty. With accurately estimated uncertainty, the proposed framework effectively explores user preference from large item space. The main contribution of this paper fourfold:
a novel recommendation model that integrates neural stochastic differential equations with eviden- tial learning for time-aware uncertainty quantification for effective sequential recommendations, leveraging interaction and time-guided evidential uncertainty to maximize information gain through exploration of large item pool,
a monotonic network to ensure positive correlation between interaction gap and uncertainty, an end-to-end integrated training process with seamless integration of NSDE and EDL modules.
To assess the feasibility of our method in comparison with existing state-of-the-art methods, we perform wide range of experiments on publicly available real-world datasets. We also conduct ablation and case studies to analyze the effectiveness and interpretability of our method.
2 Related Work
In this section, we provide existing works most relevant to our proposed approach. Some additional related works are discussed in the Appendix.
Sequential recommendation models. Sequential models utilize users' historical interactions to capture users' preferences over time. Tang al. utilized a CNN architecture capture union level and point level contributions (37. Kang et al. leveraged transformer- user representation to better capture their interest [19]. Sun et al. utilized a bidirectional encoder for sequential recommendation [35 Similarly, Zhou et al. 4 have leveraged auxiliary self-supervised objectives to learn correlation among attributes, items, sub-sequences, and sequences by utilizing mutual information maximization. Recently, contrastive learning has been used in sequential recommendation 440 43 to learn high- quality user representation leveraging different forms of data augmentation strategies. Recently, SAR 3 has leveraged an actor-critic network, where the action is generated as adaptive sequence length better represent the user's sequential pattern. Similarly, ResAct [42 utilizes residual actor- network to reconstruct policy that is close but better than online policy more efficiently in sequential recommendation. However, most existing sequential models are inadequate to capture long-term users' preferences, which is a critical gap that the proposed work aims to address.
NODE based recommender systems. Neural ODE solvers have recently been introduced into recommender systems [9] [36. For example, the learnable time ODE-based collaborative filtering [ redesigns linear graph convolution networks on top of the NODE that learns the optimal ar- chitecture and smooth ODE solutions for effective collaborative filtering. Similarly, (36) utilizes meta-learning enhanced neural ODE for citywide next POI Recommendation. It models city-invariant and city isteiiieee information separately to achieve accurate citywide next POI recommendation. As discussed earlier, standard NODE models do not explicitly capture uncertainty, which is critical for recommendation model to explore a large item space to capture user's long-term preference.
3 Preliminaries
Problem formulation. The input to recommendation model include user set (U) and item set
(T), respectively. We represent a user as u, U and item as i, E time L. In a sequential recommendation setting, users' interactions are organized in the chronological order and we use
3

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(io, f1, fi.... " to represent interaction sequences for user at time t. We perform recommenda- tion and uncertainty quantification for each user using function:
fe(u, it) ((,,,))) (x). ((u,, (()).
where (( is the recommendation score for item assigned by user u, V(ar,te) and (( are the
model evidence, and B((u,5)) is total uncertainty arising from the user-item interaction at time
Evidential learning. Evidential learning an evidence acquisition process where every training sample adds support to learn higher order evidential distribution [33 M Given that the target Y/.
drawn i..d. from a Gaussian distribution with unknown mean and variance (ju, o²) the model evidence can be introduced by further placing prior distribution prior on the unknown mean and the Inverse- Inverse-Gammn Germme prior on the unknown variance, the posterior of (j,, ad) is the Normal-Invers, Inverse-Gamma (NIG) distribution. The Gaussian and the Inverse-Gane Gamma priors are chosen to ensure conjugacy:
(μ, o²). Placing Gaussian
p(yn 02) NN, )²), p(u17, o p(u17,02v-1) N(T, p(a² a B) Inv-Gamma(a, 3)
where Inv-Gamma(z/a, 3) Maa (4) exp(- with r(-) being a gamma function; (7, a. 3) are parameters of the corresponding prior distributions. The posterior of (μ, o²) follows a Normal Sverse-Gaami (NIG):
8r
p(u, m) = 3a
exp { 23 + (()-1)² v²²
{
I(a)22T0²
20
Given a NIG posterior, one can derive the mean (E(p)), aleatoric (EEoo)) and epistemic (Varfu)) uncertainty as:
Elu] 7, Elo²) B Varlu] v(ax -1 1)
B
(1)
Neural ordinary differential equations (NODE). Ordinary Differential Equations (ODEs) are used to model continuous-tine hidden dynamics in neural networks (7) that can be defined as:
dh, (he, ()dl, ho E Rd
where f()) is a neural network with parameter vb and ho an initial value. Leveraging Eq (2 and
integrating these dynamics forward, one can compute h(ts+1) from h(t;) by solving the following Riemann integral problem:
h(t++1)= h((s) +
((h(t))t;))dd
Neural stochastic differential equations (NSDE). We could view Stochastic Differential Equations (SDE) as an ODE with infinitesimal noise added throughout time:
dh, = f (he, t)dt + 9u (h+, t)dB,
where f() and g() are drift and diffusion functions respectively. B, is a Brownian motion. Similar to NODE, we are also able to compute the forward dynamics of NSDE i.c. h(T) from initial value h(oo) integrating Eq 4 as:
k(T) h((t)) + S' ((b(1) + '' g(h(t),
(5)
4 Time-Aware Sequential Recommendations
Overview. We propose a novel time-aware sequential recommendation model as shown in Figure [] The model leverages 1) NSDE to capture continuous time-evolving user dynamics and 2) an eviden- tial module to capture uncertainty in user-item interactions and also to provide uncertainty-awee exploration that takes into consideration the interaction interval. The NSDE module takes the initial representations of users and items as inputs, and uses the interaction time gap to generate refined user and item representations. Subsequently, these improved user and item representations are fed into the EDL module. The rating network then generates a rating score, while the monotonic network produces evidential parameters that incorporate the interaction time gap, establishing direct link to the model's 's predicted uncertainty. Our approach adheres to the conventional sequential training strategy and incorporates supervised signals derived from evidential learning. We delve into detailed discussions in the subsequent sections.

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User Embrddiin
User NSDE
module
Rating network
futtUit
Final user representation
Predicted matnn
wgRR)
Diffusion
NSDE diachantic process
Monatonically incressing
NSDE stochastic
Dritt serm Raltt
AIX
spistemic uncertainty
Final Item representation
Monotonically decreasing
(100)
Biffusion QUUSUU1
Monotomic network
Mitl
Bam Embedding
Item NSDE
Time intervtl
Figure I:
Overview of E-NSDE framework, which includes user and item NSDE modules to generate the final user and item representation and EDL module to provide an uncertainty-aware prediction.
4.1 NSDE Based User and Item Representations
The NSDE includes two key components: drift and diffusion functions. The drift component captures the system's evolving nature, and the diffusion component captures its stochasticity. The proposed NSDE for recommender system advances contemporary sequential models from the following aspects: 1) existing methods require partitioning the time into uniform intervals to support model training and inference, while NSDE removes this requirement, providing additional flexibility; 2) the existing methods largely negate stochasticity in the system, but the NSDE incorporates into the form of inherent noise. The above issues suggest better fit of the NSDE into sequential recommendation and essentially support generating richer user and item representations. This because SDE can capture users' continuously evolving preferences sequential and deterministic ODE methods cannot. The fine- grained user representation (based on NSDE formulation) can be written following (5)
time, while previous discrete
u uTT) u(to) + [.' f(u(t), ti dt
[" g(u(t),
(6)
where u(fo) is the user's initial representation which aggregates of initially interacted items: u(to)= = agg(()..iz) and 7' is the final time.
In the setting of recommender systems, the drift component naturally encodes the evolution of the user's ' preference, while the diffusion component captures inherent noise that occurs when the user interacts with the environment. In particular, we leverage the diffusion function with Brownian motion to capture the user's inherent noise over each interaction. This term crucial in SDE to capture stochasticity in the system. By capturing stochasticity, we incorporate the impact of noisy user-item interactions. As it includes the Brownian motion for stochasticity, we relate this in recommender systems incorporate noise considering the time interval of interaction. We first provide the standard definition and properties of the Brownian motion and then present its applicability in the recommendation setting.
Definition (Standard Brownian Motion), A standard Brownian motion B, is stochastic process that satisfies the following properties: a) B, B, is normally distributed with zero mean and (t -)) variance: NO t for all 2 0: b) For every pair of disjoint time intervals [t1, t2] and (t, 14), with L < 12 < la S 14, the increments B -B,, and Br Brg are independent random variables.
Theorem 1. For user representation defined by the Brownian motion in Eq. 6 with two adjacent timestamps of interaction denoted as la and Lı, larger interaction time interval (12 - (1) guarantees higher uncertainty of user representation.
Given Theorem the final term in Eq. (6) captures the user's time deviation and its impact in increasing large variance or noise in the system. Further, the first term captures the user's initial representation with some interactions, and the second drift component provides the user's evolving
5

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interest. Considering all of these three components, the SDE solver captures the user's richer representation over time. Similarly, NSDE- based item representation processes can be formulated as:
((T) i(to) ['' t(i(t),t; '." g(i(t),t:))dl
where, i(4)) represents item's s initial representation
4.2 Evidential Module
We leverage an evidential learning technique to provide an uncertainty-aware model prediction for effective recommendations, The evidential module consists of two key networks: Rating Network and Monotonic Network.
Rating Network. The rating network utilizes the fine- fine-grained user and item in representations from the NSDE and predicts the score (()...)) of the corresponding user item interactions. We adopt an evidential loss as the marginal likelihood while computing the predicted loss. This includes the negative log-likelihood (CNLL [fe]) to maximize the marginal likelihood and an evidential regularizer (C*1 (C"()e)) to impose a high penalty the predicted error with low uncertainty (i.e., high confidence). first formulate the negative log-likelihodd, given by
(8) where, m(ue (e) (Turrde)) (() (fua)d)): ((,,, model parameters time and ((r(a1)))) mm,, +))== (t(T(au (urk):: Plasss (1+ (w.,.)) is student t-distribution ac- quired after placing NIG evidential prior on Gaussian likelihood function. We formalize our own evidence regularizer, which considers epistemic uncertainty to penalize confidently predicted errors. We multiply the predicted error with the inverse epistemic uncertainty that scales up the error, which encourages high inverse epistemic uncertainty when the predicted evidence is high (and vice-versa). Conversely, it will be less penalized if the prediction is close to the target score:
[f it) = (oooo(p((((uaa)) (aneeeaa))mm/n/aa [m(u,, it)
((eevi))
[f in] (1((a (- ((us,te) ((
(9)
B(ur.se)
The regularized EDL loss for each sequential update is: CEDL(UE, in) = C.V. [fe + (fo 4t)
(10)
where À is regularization coefficient.
Monotonic Network. We adopt the concept of monotonic network 34 in the context of building the relationship between the interaction time gap and model uncertainty. Intuitively, the monotonic network is designed in such way that the increase in input, i.e., time interval (At), increases the output, i.e., the variance of the predicted rating. The variance or epistemic uncertainty is computed as given by Eq (T). For this, the nominator term, i.e., total uncertainty B(o..).) should need to be increased with the increase in At, and the denominator terms, i.c., pscudo-observation d/ and should need to decreased with the increase in At. We theoretically show this intuition in the following theoretical section and show mathematical relation. We maintain this by performing exponential transformation of the network weights as: & = exp (Qinit), where Pinst is the network's initial weight. To ensure f to monotonically increase, we assign all positive weights to the network layers. Similarly, to ensure v and a to monotonically decrease, we assign negative weights to the last layer and positive weights to other layers of the network. We update the network utilizing the total loss similar to the rating network.
Lemma (Monotonic increase total uncertainty B). Let the total uncertainty of user-item interac- tion B(ue.ke) be the output of the evidential monotonic network with weights & exp (denit). Given time interval At, the outpul of the network is guaranteed to monotonicully increase.
Lemma 2 (Monotonic decrease of pseudo-observations and v). Let At the increased time interval AI, weights Wr. of the last layer be negative, and weights Wo....I-11 for other layers be positive, the output i.e., pseudo-observalinn di)p and M(oee))) of the evidential monotonic network decreases monotonically.

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Theorem 2. (Increased time interval Êt results in increased in epistemic uncertainty Var(p)). Given the monotonic network formulated by Lemmas [ad X an increase of the input time interval (At) of the evidential monotonic network guarantees an increase of the oulpul epistemic uncertainty Varli [u]
Proof. The epistemic uncertainty equation from Eq T
P((na)))
U Mane,e)
Variu]]
M((ueSe) (((
Given the increase ((m from Lemma I and decrease in (((a)))) and P(u,.i.) from Lemma the nominator of the epistemic uncertainty increases, and the denominator decreases. This proves that the increase in the time interval (At) increases the epistemic uncertainty var[u] of the evidential monotonic network. We enforce the constraints on (8(ua.i)) ((ur,)s)) ((u..))) with a soflplus activation and adding (((eee)) since (M),)))) > 1).
Interpreting hyper-parameters. Besides serving as the parameters of the evidential prior distri- butions, the hyper-parameters (V(a,.)); d.),, (()...)) offer very intuitive meanings. First, both M(a).s)) and (e are essentially the "pseudo' prior observations, and their posterior can be treated as the evidence to support prediction. In the context of the recommendation, their relation with time interval is inverse, because the large time gap causes decrease in the number of pseudo items, as mentioned in Lemma 2 Second, the ((,,,..) hyperparameter combines total uncertainty from pseudo samples and observed data. Lemma shows that increase in time interval will result in increase in the uncertainty (due to a smaller number of pseudo and interacted items to the user), and therefore, the model will be less confident in providing accurate prediction.
Weighted Bayesian personalized ranking (WBPR) loss. To leverage the effective exploration for the long-term, we formulate weighted BPR loss which is computed from non-interacted (i.e., negative) items, Jt E N₁ that are similar to the user's 's future interacted items. We first select similar negative items from the user non-interacted item pool and then leverage cosine similarity with future positive item embeddings. Further, the model provides uncertainty-awan predicted rating score for those negative items leveraging both rating and monotonic network output as:
(i) = (w..d)) + 1j
(11)
where jt represents non-interacted items time and r7 scalar to control the influence of epistemic uncertainty. We then compute weight coefficients based on uncertainty-awee aware predicted scores with cosine similarity S Sim(.) as:
max [Sim ( (f_emb, b j_emb) ], ((w..d)) > T
((
min [Sim (f _e__mb, i_emb) ]. otherwise
where f_emb,j_ent are future and negative item embedding, respectively. We then formulate weighted BPR loss utilizing a negative likelihoooo function as:
LWAPR (ut, it)
Σ
In
(12)
(M
where (().))) = ((a..))) - ((unde)) (.) is the sigmoid.
Remark. The intuition behind this weighted BPR formulation is learn effective exploration by providing higher weight to the non- on-inrtrected items which are quite similar to user future positive items that model can learn quickly a diverse range of evolving behavior to benefit the future.
The overall loss of the end-to-end model training obtained by combining the EDL and WBPR loss:
L(u,, it) LEDL (u,, 4,)
[LurR (uz, ie)
(13)
where ( represents the balancing factor between EDL and WBPR loss. Training and inference details are provided in Appendix D Experiments
Experimental setup. Our experiment setting of sequential recommendation is based on next-item recommendation tasks, which was used in [35]. We first split users by 70% into train and 30% in
7

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Table 4: Recommendation performance comparison
Categacy
Model
MovieLene 100K
Moriclens-MM
Nettix
Amnzon Book
PG5
aDCGG5
PG5
nDCG@5
P05
mDCG@5
P85
nDCGB5
Dynomic MF
Vime
CKF
0.3916=0.017
0,5620+0001
0.392=00016
0:991:00066
0:3508-00.01
0.5552=0.015
0,3600
0,875-+0.066
+0.077
0-251-0011
0.2086-0:04
0.360 +0014
0.8923+00066
0.31%6-0003
0.3214-00055
Graph
LightiiN
NCCF
0.005500.044
0.389-00014
0.5702+00013
0.562200022
03906-00066
04228=0017
0.5587 -0.01
0.3632-0.015
0.87400015
0,3617+0.033
0:316700017
0.124-00016
0.554400012
0.5678+00013
0.382200003
CASPR
0-4036 +0.02
0.56620001
0-021-0014
0:3626-00.055
0 0,966 +0.013
0:3199-0022
0.922240012
0.344-00013
SASRRc
04105=00013
0,5740
+0.011
04112:0015
0.5208+0.017
0.376++0.012
0:3257-0014
0.8812+00014
0.345-00122
BERTSRax
04149:00014
0.5081+0.001
04163=00012
0.5754 =0.013
0
0.325-00013
0.3846-0..013
0.365-00113
Sequeutal
0:4125 20012
0.9755100014
0413620013
0,5715
20.014
0,5786100006
0.3244-0.133
0.5725
0:3550-0011
Cl ASikee
04210:0:016
0:5021100077
04205:00013
0,5781 20.015
0.8114 10006
03318-0012
0.88
5:051
SAR
0.5741+0012
04225-0014
0.3247-0.014
0
0.124-00133
0.865+00122
03350-0014
ResAct
04466:00004
0,5948+0.012
04286-0014
0.881400.01
0 0.367200012
0.150000:11
0 0.8884000013
0.3472-0013
ODE
GRU ODE
LTTOCF
0.2262-0.013
04398:00014
0.3902
0.3785500:0:5
10.017
0414120001
04275500013
0.392250.012
0,3673 20,044
0.808100012
0,394220003
03313300013
0.347__00015
0.300010.111
0.384110.014
0.346220112
0.345500011
Proposed
E-NSDE
0.711
0,4122:0.013
04511-0011
0.3962:0.016
0,414
0.367-00015
0,0111200014
03321
test. For each user, we leverage the fixed sequence length and hold out the next item of the behavior sequence the target item. We follow the standard strategy in [35] for easy and fair evaluation. We leverage the actual time of interactions (in UNIX timestamp) to provide user preference evolution.
Datasets and baselines. We conduct extensive experiments on four real-world datasets that contain explicit ratings: Movielens- 100K, Movielens-IMM /M, Netflix, and Amazon Book.
Movielens-1009 2. This dataset contains 100,000 explicit ratings on a scale of (1-5) from 943 users on 1,682 movies. Each user least rated 20 movies from September 19, 1997 through April
22, 1998.
Movielens- 1M This dataset includes IM explicit feedback (i.e. ratings) made by 6,040 anony- mous users on 3,900 distinct movies from 04/2000 to 02/2003.
Netflix 4 This dataset has around 100 million interactions, 480,000 users, and nearly 18,000 movies rated between 1998 to 2005. We pre-processed the dataset and selected 6,042 users with user-item interactions from 01/2002 to 12/2005.
Amazon Book (39: This data set contains 2,984, 108 ratings applied to 91,599 books by 52,643
users with at least ten interactions in each user sequence
For comparisons, we include a comprehensive list of SOTA baselines from diverse groups, including Dynamic models: timeSVD++ [22] and CKF 14); Sequential models: CASER (37), SASRec [9),
BERT4Rec [35, S Re-RRe 45). (5)
CL4SRee 44). SAR [3]. and ResAct 42 Graph-based models:
3GCF and LightGCN [8]; ODE-based models: LT-OCF
(9) and GRU-ODE [6].
Evaluation metrics. To evaluate the proposed and baseline recommendation models, we follow the
sequential recommendation setup similar (35 We consider one ground truth item in each sequential recommendation. We use two standard metrics to measure the recommendation performance.
Precision @N (P@N) N): It is the fraction of the top-N items recommended in each sequence to the user. We reported the average overall sequence precision value as the final precision. Further, due to only one ground truth in the target, the P@N N is equivalent to Recall @ N.
nDCG@N: Normalized Discounted Cumulative Gain (nDCG) measures ranking quality, consid- ering the relevant items within the top-N of the ranking list in each recommendation.
For more details about datasets, and implementation please refer the Appendix.
Recommendation performance comparison. Table summariizs the recommendation perfor- mance from all models for four real-wor world datasets. The proposed model benefits from both the SDE module, which continuously captures user evolving preferences, and the evidential module, which estimates prediction confidence, and thus achieves better results in all four datasets. The dynamic models achieve less ideal performance due to their focus on discrete-term user interest and inability to provide continuous user preference. Graph-based methods take advantage of recently interacted items and have shown better performance than traditional dynamic methods. However, they may not be good enough to capture user sequential interest, Further, sequential methods benefit from sequential learning and have promising results. However, they do not consider the time component in the recommendation and are less effective than the proposed method. ODE-based methods have
8

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04:
CRU-EE
3RU
BEN Ahee
CRU -EC
0.50
154 oPfec
M5.
0.5
0.45
0.40
0.40
0.40
0.35
18
25
25 30
10
26
25
40
05
18
15
26
25
35
46
45
15
28
25 36
40
45
tpoch
1poch
1pach
1poch
Cc-Cc Limmsc
GAU-GIE
0.40
0.45
GMnGEN
GRI
03
0.5
--- CC
G OTE
0.5
DE citer
0.4
0.35-
2
03:
Coech
4poch
1posh
Figure 2: P@5 and nDCG@5 Performance: MovieLens-10015 MovieLens-IMM IM, Netflix, and Amazon from top down.
Table 5: (a) Diverse recommendations by E-NSDE; (b) Ablation of key components
Model
Important Movies (Genre)
Future Movie's Genre
Performance
NSDE
RDL
WBPR
Dead Man Walking ('Drama')
'Thriller'
P@5
nDCG@5
GRU-ODE
Richard III (" ('Drama))
"Drama'
Mad Love 'Romancee)
"Mystery'
x
x
0.4065
0.3677
x
0.4523
0.3962
GoldenEye ("Thriller')
"Crime"
0,4120
0.3715
E-NSDE
Taxi Driver ('Drama')
'Sci_i' Fi"
Twelve Monkeys ( ("Sci_i))
0.4711
0,4112
(a)
(b)
shown clear advantage due to their focus on capturing users' continuous behavior over time, but they cannot estimate model confidence predictions and hence have lower performance value than the proposed method. We provided a detailed plot of precision and nDCG @5 in Figure eggureeconiidriiig test users each training epoch. Further, we report the precision and NDCG @ 10 and @ 20 as the increased top-N metric (i.e., N 10, 20) for several baselines in the appendix. The results show the proposed model is consistently outperforming other baselines.
Uncertainty vs. Interaction gap We further investigate the impact of the user-item interaction gap and the corre- sponding uncertainty in providing important and diverse items. Table 5 (a) shows the proposed E-NSDE model
Total uncertainty
0.8
0.6
provides diverse (i.e., 'Thriller' and 'S'i_Fi') movies for the larger interaction time gap At = 896, 291 seconds
0.4
Average User Single User
that help to capture the future interest of the user. On the other hand, the existing GRU-ODE model recommends only popular genres like 'Drama' and fails explore others adequately. We further provided the simulation results of 5 users considering increasing time intervals: (10?, 103,, 10t, 105. 106, 10²) in seconds with random item interactions on those timestamps and the corresponding predicted uncertainty in Figure The total uncertainty 3 monotonically increases with the time intervals which shows that E-NSDE effectively captures user's uncertainty coming from longer interaction gaps.
0.2
1e2
1e3 led 1e5 1e6 1e7
Time interval(in seconds)
Figure 3: , vs. At
Effectiveness of exploration. ration, we measure the diversity of the recommended items. We consider three commonly used diversity measures: Gini index (G), Coverage (C',, and Novelty (N):
To demonstrate the effectiveness of the uncertainty-basee explo-
Gini index can be calculated by leveraging the different genres categories for each recommended D c=1 P(c) where C' is the number of categories and P(c),c [1, C*] is the probability for each category.
top K items in a sequence: G
Coverage represents the number of categories that are included the recommendation list. For the recommended top K items, we compute item coverage as: C' C==3 # categories /total categories. Novelty defined by the ratio of recommended items from new categories not interacted by the user. It is computed as N # new categories KK.

---

Table Gini index, coverage, and novelty comparisons
Models
Gini
Coverage
Novelty
Moviel Len- IM
Netfix
MovieL.ens-IM
Netfix
Moviel IM
Netfix
BHRT4Rec GRU-ODE
0.6845
0.6926
0.4103
0.3718
0.1434
0.1752
0.6632
0.6784
0.4142
0.3812
0.1482
0.1866
E-NSDE
0.7413
0.7811
0.4416
0,4026
0.2402
0.2236
0.50
0.45
0.45
0.45
2.55
0.35
0.33
0:30
0.30
3.25
0.25
0.02
0.0001
0.25
Emoedeing
C
(a) Embedding size
(b) Uncertainty-aware rating
(c) WBPR loss
Figure Average nDCG@5 plot for different embedding sizes, and balancing factors
Table T shows that E-NSDE recommends more diverse items based on all three evaluation metrics as compared with the two competitive baselines thanks to its uncertainty- -uiiddd exploration strategy.
Table 7: Average P@5 and nDCG @5 for E-NSDE with different regularizer values
Regularizer
MovieLens 1M
Netflix
(A)
P@5
nDCG@5
P@5
nDCG@5
0
0.4236
0.3786
0.4022
0.3574
0.0001
0.4412
0.3914
0.4134
0.3615
0.001
0.4551
0.3982
0.4194
0.3637
0.01
0.4518
0.3942
0.4096
0,3605
0.1
0.4224
0.3756
0.4064
0.3586
1
0.4116
0.3711
0.3923
0,3502
Ablation study. We conduct an ablation study and details are summarized below:
Impact key components. We evaluate the impact of each key component in the proposed E-NSDE. Table55 (b) shows each component contributes to improved recommendation performance.
Evidential regularization parameter. One of the key hyperparameters of the E-NSDE model is the regularizer constant (X) for the evidential learning. We cross-validated this parameter with empirical results of the model for the different values in two datasets as shown in Table 7 From
the table, our model achieves the best performance in both datasets with A = 0.001.
Embedding dimension. We generate user and item embeddings using the embedding network.
We perform grid search for the embedding dimension (d) of the user and item representation in E-NSDE model as shown in Figure From the plot, it shows that E-NSDE has the best performance with d = 64.
Balancing factors. We leverage grid search on uncertainty-aware ranking factor y,, and WBPR loss balancing factor Ç on three datasets shown in Figure 4b and Figure respectively. The figure shows a clear advantage with 7 = 0.01, which indicates that the uncertainty-aware exploration component takes effective role in providing the best performance for our proposed E-NSED model. Similarly, for Ç balancing factor integrated overall loss has the best performance when equal to 0.001.
6 Conclusion
We propose a novel evidential stochastic differential equations (E-NSDE) model for the time- sequential recommendations. E-NSDE seamlessly integrates an NSDE module and an EDL module to capture users' continuously evolving behavior and model predictive uncertainty at the same time. Our proposed model effectively leverages the interaction time gap and provides uncertainty-awee recommendations with diverse items to the user. Further, we theoretically derive mathematical relationships between the interaction time gap and model uncertainty enhance the learning process, as demonstrated in extensive experiments multiple real-world datascts.
10

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Acknowledgments
This research was supported in part by an NSF IIS award IIS-18144 181450. The views and conclusions contained in this paper are those of the authors and should not be interpreted representing any funding agency. We would like to thank the anonymous reviewers for their constructive comments.
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Appendix
Organization of Appendix In this Appendix, we first summarize all notations used in our paper. Next we provide additional related work. Further, we provide the theoretical proof for Theorem 1, Lemma I, and Lemma 2. Followed by that, we provide algorithms for the training and inference pro- cess. Further, we provide additional results for the extra baselines in terms of precision, NDCG@ 10 and NDCG@ 20. Finally, we provide a broader impact, limitation, future work, link to the source code, and checklist.
A Summary of Notations
We summarize the major notations used throughout the paper in Table g
Table 8: Summary of Notations
Notation
Description
U. I
user set and item set
Ms. fe
user and item continuous representations time f total model uncertainty for user u item at time item 8 at time predlccte score for user on item i at time
model evidence for for user
M(ueds)
Uncertainty -awar predicted raling and ground truth for user a item al time
Predicted rating score difference between ground truth item and nogative item ý for user u at time r Overall model parameters i.e. @=(t) on, 6, di
R. w. 8, Ø At
SDE drift, SDE diffusion, rating, and monotonic networks parameters
interaction time gap between two consecutive items
Weight coefficients for negative item j based on uneertainty- Threshold for uncertainty- aware predicted rating score
predicted scores
T
No
Negative items at time t Epistemic uncertainty for user a and item v interaction al time I
S
Balancing coellicient for EDL regularizer, uncertainty rating, and WBPR loss respectively
B Additional Related Work
In this section, we discuss some commonly used reoemmendation models to complement the related works covered in the main paper.
Static and dynamic recommendation models. Matrix Factorization (MF) leverages user and item latent factors to infer user preferences 23
MF further extended with Bayesian Personalized Ranking (BPR) [30] and Factorization Machine (FM) [29] Recently, deep learning-
21
based recommender systems [5] have achieved impressive performance. DeepFM [15] integrates traditional FM and deep learning to learn low- and high-order feature interactions. Both wide and deep networks are jointly trained in [ for better memorization and generalization. The dynamic model shifts latent user preference over time to incorporate temporal information. TimeSVD++ [22 considers time-specific factors, which uses additive bias to model user and item-related temporal changes. Gaussian state-space models introduce time-evolving factors with a one-way Kalman filter [4]. To process implicit data, Sahoo et al. extended the hidden Markov model (31), and Charlin et al. 66] further augmented it with the Poisson emission. Nevertheless, these models grasp the evolving preferences of users, yet they exhibit limited foresight into future interactions, leading to poor recommendations performance.
Graph-based recommendation models. Another popular line of recommendation systems is graph-bases models. A graph captures high-order user-item interactions through an iterative process to provide effective recommendations [77. Users and items are represented as a bipartite graph in 5 and links are predicted to provide recommendations. Similarly, a graph- framework called Neural Graph Collaborative Filtering (NGCF) (39 explicitly encodes the collaborative signal in the form of high-order connectivities in a user-item bipartite graph via embedding propagation. However, these methods are unable to capture long-term user preferences or deal with cold-start problems.
14

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C Proof of Theoretical Results
In this section, we provide proofs of the theoretical results in the main paper.
C.1 Proof of Theorem
show that the increase in interaction time gap (t2 (1) increases the chance that the user may deviate from the current interest. It turns out that the last term of Eq (6) has larger variance, ie., there is higher deviation in the user interest, if there is longer time gap in the interaction. Suppose la > 12, then we have
Proof. Given Definition
=E [[, olu(t),
27 )
[ g(u(t), t:w)
Var
o(u(t),:W)dBB
=E
E
((u(t),;;))
t(u(t),t;w)?dd 2 g(u(t), (tt
(14)
Var
glu(t),;:)ddB
where we applicd the Ito Isometry in the second step. This result indicates that there is longer interaction gap t1, then the state is more uncertain.
C.2 Proof of Lemma
Given the user final representation ut, item final representation é, and interaction time gap At. The monotonic network produces ((me)))) as:
((w.)))) = (W) concat(ue, 4, At)
Ut
-[T
W.T
WAi]
it
Hence
03 8(A = WAr 2 O.
C.3 Proof of Lemma 2
Given the same setup as Lemma the monotonic network outputs (u,,)))) and V(uu,))) We first consider (.).
og..g.o........................ oo h2 g h hil[concattuu, i,, At)), (( = [h, o
where (x) is the transformation induced by the ith affine layer, h,(2) Wix + bi, o is the composition of functions, and is an increasing activation function.
According to the backpropagation, have
io (m).)))
WT
W
WT W
WI WT o (hL-)1)) o (hL-2)) .... o g' (hz)) o g'(h1)
T
W W W
where @ is element-wise product of two matrices with the same size. The matrix
is just WT..
where we rewrite WT the same blocks as that in Lemma Therefore.
da(a).5))
2)] ... @ of (he) o @ gh(hi) 0(At) WT. W [W3 [... [W [WZ @ of (hL-1)) @ g (h)
Since the entries W,, WT-1 are negative, and g (h1), o (hr,-) are all positive. Therefore, if entries in Wy are all negative, we have aacur < 0. J(A
dv Similarly, we can show that ((Ae) ELU(.) to satisfy this condition.
< 0. We leverage the monotonic non-lineat activation function i.e.
15

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Table Higher Order top-N metric comparisons with several baselines
Models
MovieLens-IN IM
Amazon Book
P@
P@
N@
N@20
P@
P@20
N@ 10
N@:21 20
BERT4Rec 35
0.7258
0.8370
0.5131
0.5545
0.6583
0.7671
0.4833
0.5014
ResAct 42
0.7443
0.8572
0.5276
0.5697
0.6759
0.7863
0.4976
0.5160
GRU-ODEL6
0.7392
0.85156
0.5226
0,5645
0.6732
0.7830
0.4911
0,5095
DiffuRec 26
0.7478
0.8616
0.5336
0.5759
0.6805
0.7868
0.4994
0.5179
TiSASRec 24
0.7401
0.8532
0.5297
0.5717
0.6813
0.7889
0.4951
0,5135
STOSA 12
0.7484
0.8622
0,5310
0,5733
0.6788
0.7902
0.5025
0.5210
DuoRec 28
0.7489
0,8659
0.5259
0.5682
0.6831
0.7945
0.5001
0.5186
GDERee 27
0.7503
0.8649
0.5324
0.5750
0.6808
0.7928
0.5077
0.5264
E-NSDE
0.7745
0.8926
0.5467
0.5907
0.7021
0.8175
0.5198
0.5390
D Training and Inference Processes
The training procedure involves the end-to-end parameter updates associated with the NSDE module and evidential module. Both modules utilize the overall loss mentioned in Eq (3), which includes supervised signal from evidential loss and ranking loss from WBPR loss. The rating network (0) and monotonic network (Φ) are updated with the Adam optimizer, and the SDE module with model parameters (1,, w) is updated with SDE adjoint method (25). Algorithm shows the training process that learns the model parameters. During inference, we consider test users (i.e. distinct users from the training set) and perform standard sequential recommendations respecting the time interval of interactions.
Algorithm E-NSDE Training
Require: Hyperparameters: X, S, V, Initialize both NSDE and EDL modules:O- = (vb, w0,,w,0 0,
while not converge do Sample train user Tú from user pool U for all u To do
Compute user and item final representations using Eg (6) and Eq 7 respectively from SDE module.
Compute interaction time gap At with target item Compute EDL loss for each sequence using Eq (10) Compute weighted BPR loss for each sequence using Eq 12
Perform end-to-end update using overall loss Eq (13
end for end while
E Additional Experimental Results
Higher order top-N results. We report the results using top-N metric with larger N value (i.e., 10 and @20) Table g 95.75% sparsity and Amazon Book with 99.98% sparsity. In both datasets, proposal models outperform other baselines in those metrics and show consistent performance over metrics.
We reported those results on two sparse datasets: Movielens- 1M with
Additional datasets. We conduct experiments on two additional datasets from the book and music domains to cover a broader range. The Book-Crossing dataset a collection book ratings, including both explicit ratings (1-10 stars) and implicit ratings (interaction) [46]. The Yahoo! Music dataset is a collection user ratings for songs, albums, artists, and genres, with fine-resolution timestamps for ratings [10]. The proposed E-NSDE consistently outperforms the competitive baselines.
16

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Table 10: Recommendation Performance on More Datasets
BookCrossing
Yahoo Music
Model
P@5
nDCG@5
P@5
nDCG @5
BERT4Rec
0.4811
0.4585
0.5269
0.4773
GRU-ODE
0.4965
0.4662
0.5316
0.4825
E-NSDE 0.5217
0.4834
0.5621
0.5145
F Broader Societal Impact, Limitation, and Future Work
This paper presents novel stochastic neural ODE and evidential learning- based recommendation model to capture users' continuously evolving behavior. This work aims understand the user's dynamic interest considering an actual time interval of user interaction with the system. This is very useful in many time-series user interaction fields like e-commerce, social media, health care, and gaming sectors.
As potential limitation of this work, if user-item interactions have uniform time intervals like in click-through, then the impact of time-aware interval is less effective in capturing uncertainty.
Future work could be applying the E-NSDE method to other areas of recommender systems, such as healtheare, where patient behaviors evolve over time, and capturing their real-time behavior is crucial to handling their problem. Similarly, understanding behavior in the gaming sector is also a potential area to explore in the future.
G Source Code
For the source code, please click this link: httpps///tthhhb.mm//zztttiigaaaa
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NeurIPS Paper Checklist
1. Claims
Question: Do the main claims made in the abstract and introduction accurately reflect the paper's contributions and scope?
Answer: [Yes]
Justification: Introduction section includes contribution and scope of the work.
2. Limitations
Question: Does the paper discuss the limitations of the work performed by the authors?
Answer: [Yes]
Justification: Please refer Appendix Forr limitation of our work.
3. Theory Assumptions and Proofs
Question: For each theoretical result, does the paper provide the full set of assumptions and a complete (and correct) proof?
Answer: [Yes]
Justification: We provide assumptions and complete proof of lemmas and theorems in Appendix.
4. Experimental Result Reproducibility
Question: Does the paper fully disclose all the information needed to reproduce the main ex- perimental results of the paper to the extent that it affects the main claims and/or conclusions of the paper (regardless of whether the code and data are provided or not)?
Answer: [Yes]
Justification: We fully disclose the dataset, and experiment settings in Appendix.
5. Open access to data and code
Question: Does the paper provide open access to the data and code, with sufficient instruc- tions faithfully reproduce the main experimental results, described in supplemental material?
Answer: [Yes]
Justification: We provide data open access with in the anonymous source code link in Appendix.
6. Experimental Setting/Details
Question: Does the paper specify all the training and test details (e.g., data splits, hyper- parameters, how they were chosen, type of optimizer, etc.) necessary to understand the results?
Answer: [Yes]
Justification: We provide all details of experiment settings in Appendix.
7. Experiment Statistical Significance
Question: Does the paper report error bars suitably and correctly defined or other appropriate information about the statistical significance of the experiments?
Answer: [Yes]
Justification: We provide statistical testing results in main table.
8. Experiments Compute Resources
Question: For each experiment, does the paper provide sufficient information on the com- puter resources (type of compute workers, memory, time of execution) needed to reproduce the experiments?
Answer: [Yes]
Justification: We provide the computing details in the Appendix.
9. Code Of Ethics
18

---

Question: Does the research conducted in the paper conform, in every respect, with the NeurIPS Code of Ethics httpp//www...aa......./oo//////a
Answer: [Yes]
Justification: We confirm that we follow the NeurlPS Code of Ethics.
10. Broader Impacts
Question: Does the paper discuss both potential positive societal impacts and negative societal impacts of the work performed?
Answer: [Yes]
Justification:
We mention broader societal impacts in Appendix.
11. Safeguards
Does the paper describe safeguards that have been put in place for responsible release of data or models that have high risk for misuse (e.g., pretrained language models, image generators, or scraped datasets)?
Question:
Answer: [NA]
Justification: We exclusively utilize public data and release models to promote research in recommender systems.
Licenses for existing assets
Question: Are the creators or original owners of assets (e.g., code, data, models), used in the paper, properly credited and are the license and terms of use explicitly mentioned and properly respected?
Answer: [Yes]
Justification: We acknowledge the contributions of open-source baselines and public datasets by citing them as references.
13. New Assets
Question: Are assets introduced in the paper well documented and is the documentation provided alongside the assets?
Answer: [Yes]
Justification: We provide ccode asset via an anonymized URL in Appendix G 14. Crowdsourcing and Research with Human Subjects
Question: For crowdsourcing experiments and research with human subjects, does the paper include the full text of instructions given to participants and screenshots, if applicable, as well as details about compensation (if any)?
Answer: [NA]
Justification: We haven't used human-subjeet subject based crowd sourcing dataset to our experi- ment.
15. Institutional Review Board (IRB) Approvals or Equivalent for Research with Human Subjects
Question: Does the paper describe potential risks incurred by study participants, whether such risks were disclosed to the subjects, and whether Institutional Review Board (IRB) approvals (or equivalent approval/review based the requirements of your country or institution) were obtained?
Answer: [NA]
Justification: We haven't done any human subjects experiment in our work.
19


Reviews:
[{"review_id": "pfsAPsNBnD", "reviewer": "Reviewer_p7WH", "summary": "This work investigates sequential recommendation, and proposes a new method that utilizes stochastic differential equations (SDEs) to model dynamic time intervals and estimate uncertainty.\n\nOverall, this study addresses an engaging problem and provides a novel and reasonable solution. Extensive experiments have been conducted. Consequently, I lean towards accept.", "questions": "Please refer to weaknesses.", "limitations": "No concern.", "rating": 7, "confidence": 2, "soundness": 3, "presentation": 3, "contribution": 3, "strengths": "1.\tThis work studies on an interesting and important problem --- how to capture dynamic time interval as well as estimate model uncertainty. \n\n2.\tThe paper is well-written, with clear motivations.\n\n3.\tThe application of stochastic differential equations to model sequential recommendation is both novel and reasonable.\n\n4.\tExtensive experiments are conducted to validate the effectiveness of the proposal.", "weaknesses": "1.\tIt would be advantageous to include diffusion model-based sequential recommendation baselines for comparison in the experiments, such as [a1][a2], especially since SDEs have been utilized in these methods as well.\n\n2.\tThe work reports performance metrics only for P@5 and NDCG@5. It would be better to include the results with different @N, particularly @20, which is commonly adopted by recent work.\n\n3.\tA discussion on the limitations and future directions of the research in Section 6 would be beneficial.\n\n4.\tThere are some typos. For example, in the eq.(13), ‘BPR’->’WBPR’; In the line 316, removing ‘vs’. \n\n\n5.\tSome important relate work is omitted:\n[a1] TOIS’23: Diffurec: A diffusion model for sequential recommendation\n[a2] NIPS’23: Generate what you prefer: Reshaping sequential recommendation via guided diffusion", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "**Q1:  Diffusion model-based sequential recommendation baselines for comparison.**\n\nThanks for suggesting those important related works. We will cite them and add a discussion in the revised paper. More specifically, DiffuRec [a1]  models item representations as distributions by corrupting the target item embedding into a Gaussian distribution through adding noise and reversing the Gaussian noise into the target item representation based on historical interactions. DreamRec [a2] formulates sequential recommendation as a learning-to-generate task. It uses a guided diffusion model with a transformer encoder to generate the distribution of representations from historical items and adds noise to items to explore the item space distribution.\nIn summary, the two papers leverage explicit augmentation of noises to representations, which are technically different from the proposed method.\n\nAs suggested by the reviewer, we have conducted experiments to compare with the diffusion model-based sequential recommendation, i.e., DiffuRec and the results are presented in the Table in the general response to all reviewers. Since DiffuRec represents compact item representation with construction and injection of uncertainty, it does not properly address continuous time-evolving aspects of user interest and hence has lower performance than the proposed E-NSDE model. Limited by time, we will include a comparison with DreamRec [a2] in the revised paper. \n\n**Q2:  Better to include the results with different @N, particularly @20**\n\nThanks for the suggestion. We have conducted additional experiments and reported the top @N =10 and 20 results in the Table of the general response to all reviewers. \n\n**Q3:  Limitations and future directions of the research**\n\nThanks for the suggestion. We have included a discussion of limitations and future work in Appendix G.", "claims_and_evidence": "", "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": "", "extra_scores": {}}, {"review_id": "WvU3cSljIx", "reviewer": "Reviewer_LeEA", "summary": "The paper revolves around enhancing sequential recommendation systems by incorporating time-awareness through the utilization of Evidential Neural Stochastic Differential Equations (E-NSDE). Traditional recommendation systems often overlook the temporal dynamics of user interactions, leading to suboptimal recommendations. The authors aim to bridge this gap by developing a novel framework that captures the evolving behavior of users over time intervals, thereby improving the accuracy and reliability of recommendations.\nIt acknowledges the limitations of existing methods in effectively modeling temporal dynamics and uncertainty in user behavior. By integrating NSDE and evidential learning, the authors build upon the foundations laid by previous works on stochastic differential equations and recommendation systems. This integration allows for a more robust modeling of user preferences and interactions over time, setting the stage for more accurate predictions.", "questions": "1.\tCould the authors provide a detailed explanation of how NSDE and evidential learning are integrated within the E-NSDE framework?\n\n2.\tCan the authors elaborate on the characteristics of the real-world datasets used in their experiments? How diverse are these datasets, and do they encompass a broad spectrum of recommendation scenarios to validate the generalizability of the E-NSDE framework?\n\n3.\tAre there specific techniques or methodologies incorporated to enhance the transparency and explainability of the recommendation process?\n\n4.\tIn the context of large-scale recommendation systems, how does the E-NSDE framework address challenges related to scalability and computational efficiency? Have any experiments been conducted to evaluate the framework's scalability as dataset sizes or user interactions increase?", "limitations": "The authors have adequately addressed the limitations and identified no potential negative societal impacts of their work.", "rating": 5, "confidence": 4, "soundness": 3, "presentation": 4, "contribution": 3, "strengths": "1.\tThe E-NSDE framework dynamically models user behaviors over time, effectively addressing a crucial gap in traditional recommendation systems that often overlook temporal dynamics.\n2.\tBy incorporating NSDEs to capture the continuous-time dynamics of user interactions, along with evidential learning to assess recommendation uncertainty, this dual approach ensures that the recommendations are not only time-sensitive but also carry a higher degree of confidence.\n3.\tThe integration of NSDE and evidential learning into a unified framework facilitates comprehensive modeling of both the evolution of user preferences and the inherent uncertainty in predicting user behavior.", "weaknesses": "1.\tWhen user-item interactions have uniform time intervals, such as in click-through scenarios, the model's time-aware approach may be less effective in capturing uncertainty.\n2.\tThe paper acknowledges the interpretability of the E-NSDE framework but falls short in providing detailed explanations of the decision-making process and incorporating feature importance analysis, which would significantly enhance transparency and build user trust.\n3.\tThe discussion regarding the generalizability of the E-NSDE framework across various domains and datasets is inadequate. Providing more detailed insights into the model's performance in diverse settings would clarify its robustness and broader applicability.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "**Q1: When user-item interactions have uniform time intervals, such as in click-through scenarios, the model's time-aware approach may be less effective in capturing uncertainty.**\n\nWe agree with the reviewer that when interaction intervals are uniform, the time-aware uncertainty component is less effective. We have pointed out this as we discuss the limitation of our approach in Appendix G. Meanwhile,  we would like to clarify that the proposed model's performance will not degrade when interaction intervals are uniform when compared to existing state-of-the-art models.\n\n**Q2: The paper acknowledges the interpretability of the E-NSDE framework but falls short in providing detailed explanations of the decision-making process and incorporating feature importance analysis, which would significantly enhance transparency and build user trust.**\n\nThank you for the suggestion; it would indeed be valuable to examine details at the feature level. However, we would like to emphasize that our approach aims to improve interpretability at the module level using epistemic uncertainty. In particular, our epistemic uncertainty indicates the model's confidence in recommending the next item, which increases the transparency of the recommendation process and can help build user trust. \n\n**Q3: Providing more detailed insights into the model's performance in diverse settings would clarify its robustness and broader applicability.**\n\nThank you for the great suggestion! The datasets used in our experiments indeed cover very diverse settings. First, the datasets possess different levels of sparsity that varies from 95\\% to over 99.9\\%: Movielens-1M with a sparsity of 95.75\\%, Netflix with a sparsity of 98.82\\%, and Amazon Books with a sparsity of 99.98\\%. The level of sparsity is usually tied to the difficulty of the dataset when making recommendations. Meanwhile, different datasets also encode diverse interaction behaviors from users. For example, the interaction patterns vary significantly based on the timing of interactions. In the Movielens-1M dataset, most interactions occur within seconds, minutes, and days. For Netflix, interactions predominantly happen with day-long gaps. However, in the Amazon Books dataset, user interactions span months or even years. We selected these datasets to particularly demonstrate the proposed model's effectiveness across different interaction time intervals. Our model exhibits robust performance across all these datasets, providing evidence of its broad applicability in any time-aware user-interaction settings.\n\n\n**Q4:Detailed explanation of how NSDE and evidential learning are integrated within the E-NSDE framework**\n\nOur NSDE module generates richer user and item representations by explicitly considering their interaction time. Those representations are fed to the EDL module to capture interaction uncertainty and generate predicted scores, as shown in Figure 1 of the main paper. We further leverage a monotonic network in building the relationship between the interaction time gap and model uncertainty. The monotonic network ensures the increase of the uncertainty (i.e., variance) of the predicted rating along with the increase of time interval ($\\Delta t$). This novel integration leads to an end-to-end E-NSDE framework that provides an effective time-aware sequential recommendation model.\n\n**Q5: Elaborate on the characteristics of the real-world datasets used in their experiments? How diverse are these datasets, and do they encompass a broad spectrum of recommendation scenarios to validate the generalizability of the E-NSDE framework?**\n\nPlease refer to the answer to Q3.\n\n**Q6: Are there specific techniques or methodologies incorporated to enhance the transparency and explainability of the recommendation process?**\n\nA key component to enhance transparency and explainability of the recommendation process is the evidential learning module, which allows us to perform fine-grained uncertainty decomposition. As a result, the decomposed epistemic uncertainty indicates the model's confidence in recommending the next item, which increases the transparency of the recommendation process and can help to build user trust. \n\n\n**Q7: In the context of large-scale recommendation systems, how does the E-NSDE framework address challenges related to scalability and computational efficiency? Have any experiments been conducted to evaluate the framework's scalability as dataset sizes or user interactions increase?**\n\nWe would like to clarify that our training setup leverages incremental time computation for the stochastic differential equation, progressing from the previous time step $t-1$ to the current step $t$ rather than starting from the beginning ($t_0$). This approach, which uses the previous step's computation for the next step, enhances both the forward and backward passes of the NSDE module. Consequently, this improves the model's scalability, as demonstrated by its applicability to datasets ranging from smaller ones(e.g., Movielens) to larger ones (e.g., Netflix and Amazon). For more details on the training setup, please refer to the experimental setting section in the main paper.", "claims_and_evidence": "", "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": "", "extra_scores": {}}, {"review_id": "bu2yFzmc1i", "reviewer": "Reviewer_V8wq", "summary": "This paper investigates the modeling of interaction time intervals in sequential recommendation. Considering both time interval and model uncertainty, this paper formulates E-NSDE to integrate NSDE and evidential learning to model effective time-aware sequential recommendation.  Experimental results on four real-world datasets prove the effectiveness of proposed method.", "questions": "1. Please refer to weakness 1, and give more clarification on Table 2.\n\n2. Please explain the relationship between this work and [1],[2],[3]. The baselines lack the time-interval awarded by the sequential model and diversity model.\n\n3. Pleas refer to weakness3, more n in top-n results should be given.\n\n\n\n[1]Time interval aware self-attention for sequential recommendation,WSDM20\n\n[2]Learning Graph ODE for Continuous-Time Sequential Recommendation,TKDE\n\n[3]Temporal Conformity-aware Hawkes Graph Network for Recommendations,Webconf 24", "limitations": "Yes", "rating": 4, "confidence": 3, "soundness": 2, "presentation": 3, "contribution": 2, "strengths": "1. The problem is interesting. The time interval between interactions is really an important factor in the sequential recommendation. Meanwhile, time-aware uncertainty guides the recommendation to adapt to users' changing preferences.\n\n2. Combining two existing techniques is well-motivated. Overall, both user NSDE and item NSDE are introduced here to encode the evaluation of the preference and inherent noise. The evidential module then provides uncertainty-aware rating prediction. All the stack techniques are combined reasonably.\n\n3. Experiments are conducted to verify the effectiveness. And the results are statically reliable.", "weaknesses": "1. The motivation in the introduction is unclear. As the authors argue, GRU-ODE recommends genres that come from past behaviors, while NSDE recommends genres which have potential future benefits in Table 2. It is not sure if some genres recommended by NSDE are in accordance with long-term interests. For example, Sci_Fi, Mystery, and Crime in Table 2. My concern is whether motivation is not the real need of the user.\n\n2.  As to method, in Figure 1, users also have evolved into representation. It is clear that the user interfaces with items in an evolving manner. But not so clear that the users also evolved into different user.\n\n3. The experiments in Table 4 report the P@5, nDCG@5. However, in the movielens datasets, 1m and 100k are used, so more top-n results should be given to verify the effectiveness. In line 316, \"Uncertainty vs. Interaction gap vs.\" may be a typo.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "**Q1: The motivation in the introduction is unclear. As the authors argue, GRU-ODE recommends genres that come from past behaviors, while NSDE recommends genres which have potential future benefits in Table 2. It is not sure if some genres recommended by NSDE are in accordance with long-term interests. For example, Sci\\_Fi, Mystery, and Crime in Table 2. My concern is whether motivation is not the real need of the user.**\n\nThank you for the comment. We would like to clarify that we included motivating examples (in Table 2 of the main paper) to demonstrate the need for an effective means of exploration, which is essential and critical to uncover the user's long-term interests. Especially, if a user is inactive for a longer period, maintaining their engagement in the system requires more aggressive exploration, as indicated by the larger time-interval gap in Table 2. While there is no total guarantee that every explored item will be successful, our epistemic uncertainty-guided exploration (see Eq. 11) allows the model to recommend items that are largely unknown to the users (due to the second term) while potentially interesting to them (due to the first term). Both our quantitative (shown in Table 4) and qualitative results (shown in Table 5a) clearly demonstrate the effectiveness of our approach. \n\n\n**Q2: As to method, in Figure 1, users also have evolved into representation. It is clear that the user interfaces with items in an evolving manner. But not so clear that the users also evolved into different user.**\n\nWe would like to clarify that our NSDE module consists of two key components: diffusion and drift. The diffusion component captures the user's extrinsic behavior, while the drift component captures the user's intrinsic behavior. This module is responsible for modeling the user's evolving interests over time. Additionally, as the reviewer pointed out, the user-item interface also evolves over time, and the uncertainty of these interactions is captured through the evidential module.\n\n**Q3: More top-n results**\n\nThanks for the suggestion. We have reported additional higher-order top-N (@10 and @20) results in the table presented in the general response to all reviewers.\n\n\n**Q4: Please explain the relationship between this work and [1],[2],[3]. The baselines lack the time-interval awarded by the sequential model and diversity model.**\n\nThanks for pointing out those papers.\n\nFor prior efforts on time interval-aware recommendations, [1] introduces a self-attention mechanism that considers both the absolute positions of items and the time intervals between them in interaction history, in order to allow the system to be aware of the influence of different time intervals on predicting the next item. However, the architecture leverages the black-box embedding and attention mechanisms for time intervals. In comparison, the proposed approach introduces differential equations and monotonic networks to explicitly encourage the system to generate higher uncertainty to longer time intervals.\n\n[2] is published in July 2024, and therefore, it is impossible for us to be aware of it during submission. [2] introduces a Graph Ordinary Differential Equation model to capture continuous-time dynamics in sequential recommendation systems. The key differences between [2] and the proposed method are: 1) Ordinary differential equations are deterministic, while our approach leverages stochastic differential equations, which involve a noisy process to model how the uncertainty of users' and items' representation evolves over time.\n2) The proposed approach explicitly encourages the system to assign higher uncertainty to longer time intervals.\n\n[3] introduces Hawkes processes to model the intensity of user interactions and leverages graph neural networks to learn from the complex user-item interactions. Hawkes process is a point process to model the occurrence of sequential events with irregular inter-arrival time. Unlike the proposed method, it does not explicitly model the uncertainty or enforce higher uncertainty to longer time intervals.\n\nWe will incorporate them into the related work section of the revised paper. Further, we have provided results for TiSASRec ([1] Time interval aware self-attention for sequential recommendation, WSDM20) and compared with the proposed method in the table of the general response, which shows the proposed approach achieves a better recommendation performance.", "claims_and_evidence": "", "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": "", "extra_scores": {}}, {"review_id": "gMjNa9ZRqV", "reviewer": "Reviewer_zE4M", "summary": "The authors note that existing methods assume a uniform time interval among user behaviors. This paper posits that the time intervals in sequential recommendation increase the uncertainty of users' behavior. Therefore, it proposes NSDE to learn users’ fine-grained time-evolving behavior, while evidential learning quantifies both aleatoric and epistemic uncertainties. The authors believe that this is something other sequential learning methods have not considered.", "questions": "1.Why do the authors believe that sequential recommendation methods typically use uniform time intervals and overlook changes in user interests? Many earlier works have addressed this issue, such as \"Uniform Sequence Better: Time Interval Aware Data Augmentation for Sequential Recommendation\".\n2.See weeknesses", "limitations": "N/A", "rating": 4, "confidence": 4, "soundness": 2, "presentation": 3, "contribution": 2, "strengths": "1. The paper starts from the uncertainty of time intervals to capture the evolution and uncertainty of user behavior, which is a valuable insight. However, this perspective lacks innovation, as \"Sequential recommendation via stochastic self-attention\" (2022) also approaches the problem from the same insight.\n2. The straightforward derivation of the relationship between increasing time intervals and uncertainty to guide learning demonstrates a degree of innovation and robustness in modeling.", "weaknesses": "1.\tThere are formatting issues in lines 99-105. The abbreviation for Normalized Discounted Cumulative Gain is generally NDCG.The combination of metrics chosen in the paper is uncommon and lacks persuasiveness. According to line 294, the metrics are derived from Bert4Rec. However, Bert4Rec's metrics are Hit Ratio (HR), Normalized Discounted Cumulative Gain (NDCG), and Mean Reciprocal Rank (MRR). \n\n2.The selected baselines could include more recent state-of-the-art models, such as STOSA, DuoRec, CoSeRec, GDERec,TiCoSeRec and GCG-ODE. The baselines particularly lack ODE-related sequential recommendation models. Among the two ODE-related models, LT-OCF is not specifically designed to address sequential recommendation.\n\n3.The increase in time intervals may lead to changes in user interests. Addressing this issue within NODE-based recommender systems, the paper proposes corresponding solutions and offers a relatively novel perspective.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "**Q1: The abbreviation for Normalized Discounted Cumulative Gain is generally NDCG.The combination of metrics chosen in the paper is uncommon and lacks persuasiveness. According to line 294, the metrics are derived from Bert4Rec. However, Bert4Rec's metrics are Hit Ratio (HR), Normalized Discounted Cumulative Gain (NDCG), and Mean Reciprocal Rank (MRR).**\n\nThanks for the suggestion to clarify the metrics. We follow a similar setup in Bert4Rec as a next-item prediction. However, we selected three popular metrics (i.e., Precision, Recall, and NDCG) that are widely used in evaluating recommendation models. Here, Precision is equivalent to Hit Ratio (HR), and due to next-item prediction, it is also equivalent to Recall. Further, NDCG is a metric that considers position by assigning greater weights to higher positions. We will clarify these in the revised paper. \n\n**Q2: The selected baselines could include more recent state-of-the-art models, such as STOSA, DuoRec, CoSeRec, GDERec, TiCoSeRec and GCG-ODE. The baselines particularly lack ODE-related sequential recommendation models. Among the two ODE-related models, LT-OCF is not specifically designed to address sequential recommendation.**\n\nThanks for pointing out recent baselines. Limited by time, we have provided results for three of the additional baselines, including STOSA, DuoRec, and GDERec, and compared them with our approach (please refer to the table presented in the overall rebuttal to all reviewers). The results clearly show that the proposed E-NSDE model outperforms these baselines by effectively leveraging the interaction time gap in novel ways to offer uncertainty-aware recommendations with diverse items that better align with the user interest. We will provide a more complete comparison in the revised paper. \n\n**Q3: Why do the authors believe that sequential recommendation methods typically use uniform time intervals and overlook changes in user interests? Many earlier works have addressed this issue, such as \"Uniform Sequence Better: Time Interval Aware Data Augmentation for Sequential Recommendation\".**\n\nThank you for the comment. In the paper suggested by the reviewer, the authors propose to address the issue of varying time intervals for sequential recommendations. Instead of leveraging the varied intervals, it argues that sequences with uniformly distributed time intervals are more beneficial for performance improvement and introduces new approaches to transform non-uniform sequences into uniform ones. While there may also be other works that consider time intervals in user interactions, none of these works address the increasing uncertainty arising from the extended interaction intervals. We believe our paper is the first work that establishes a correlation between the interaction time interval and the model uncertainty, and leverages this important connection to improve recommendations through time-aware uncertainty guided exploration.", "claims_and_evidence": "", "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": "", "extra_scores": {}}]

Author rebuttal:
We thank all the reviewers for their constructive comments and suggestions. Here, we provide results for several suggested baselines and top-$N$ metrics with a higher $N$ value as requested by the reviewers:

| **Datasets** | **Metric**   | **Bert4Rec** | **ResAct** |**GRU-ODE** |**DiffuRec** |**TiSASRec** |**STOSA** |**DuoRec** |**GDERec** |**E-NSDE** |
|--|--|--|--|--|--|--|--|--|--|--|
| *MovieLens-1M*     | P@5   |  0.4163   | 0.4286   | 0.4275 |  0.4212 |   0.4253 | 0.4314 | 0.4337    | 0.4301   | **0.4551** | 
|    | P@10   | 0.7258    | 0.7443   |  0.7392|  0.7478 |0.7401    |0.7484 | 0.7489    |  0.7503  | **0.7745**| 
|   | P@20  | 0.8370    | 0.8572   | 0.8515 | 0.8616  | 0.8532|  0.8622   |0.8659    |0.8649 |**0.8926**| 
|    | NDCG@5   | 0.3754     |   0.3814  | 0.3792 |  0.3795 |0.3829    |0.3801 |   0.3852  |  0.3805  | **0.3982**| 
|     | NDCG@10   | 0.5131    |  0.5276  |0.5226  |  0.5336  |0.5297    | 0.5310|   0.5259  |  0.5324  | **0.5467**| 
|    | NDCG@20   |0.5545    | 0.5697  | 0.5645 | 0.5759    | 0.5717   | 0.5733|   0.5682  |  0.5750  | **0.5907**| 
| *Amazon Book*      | P@5  |  0.3846    |0.3884    | 0.3856| 0.3870    | 0.3940 |0.3899 |   0.3902 |  0.3935  |**0.4021** |
|     | P@10  | 0.6583    |   0.6759 | 0.6732 |   0.6805  |  0.6813  | 0.6788|    0.6831 |    0.6808 |**0.7021** |
|       | P@20  | 0.7671    | 0.7863   | 0.7830  |   0.7868 | 0.7889| 0.7902    | 0.7945   |0.7928 |**0.8175** |
|      | NDCG@5  |  0.3463   | 0.3472| 0.3455 | 0.3415  | 0.3521  |0.3538|  0.3504  | 0.3563   | **0.3621**|
|      | NDCG@10  |  0.4833   | 0.4976   | 0.4911 |    0.4994    |0.4951 |   0.5025  |    0.5001| 0.5077| **0.5198**|
|      | NDCG@20  | 0.5014    | 0.5160   |0.5095  |   0.5179  | 0.5135   | 0.5210| 0.5186    |  0.5264  |**0.5390** |

Meta-review: Very slightly on the positive side according to review scores, though arguably mostly saved by one reviewer. Reviewers find the problem interesting, straightforward, and reasonably convincing in terms of experiments. Reviewers complain about interpretability issues, lack of metrics (and other experimental details), and some problems with the motivation.

All of the reviews (including the most positive one) aren't particularly detailed, so it's hard to be confident of the recommendation. Not that that's the authors' fault.
Decision: Accept (poster)