On the Mechanisms of Collaborative Learning in VAE Recommenders
Authors: Long Tung Vuong
Julien Monteil
Hien Dang
Volodymyr Vaskovych
Trung Le
Vu Nguyen
Venue: ICLR 2026 Poster (2026)
Keywords: VAE-based collaborative filtering
Primary area: probabilistic methods (Bayesian methods, variational inference, sampling, UQ, etc.)

Abstract: Variational Autoencoders (VAEs) are a powerful alternative to matrix factorization for recommendation. A common technique in VAE-based collaborative filtering (CF) consists in applying binary input masking to user interaction vectors, which improves performance but remains underexplored theoretically. In this work, we analyze how collaboration arises in VAE-based CF and show it is governed by \emph{latent proximity}: we derive a latent sharing radius that informs when an SGD update on one user strictly reduces the loss on another user, with influence decaying as the latent Wasserstein distance increases. We further study the induced geometry: with clean inputs, VAE‑based CF primarily exploits \emph{local} collaboration between input‑similar users and under‑utilizes \emph{global} collaboration between far‑but‑related users. We compare two mechanisms that encourage \emph{global} mixing and characterize their trade‑offs: \ding{172} $\beta$‑KL regularization directly tightens the information bottleneck, promoting posterior overlap but risking representational collapse if too large; \ding{173} input masking induces stochastic \emph{geometric} contractions and expansions, which can bring distant users onto the same latent neighborhood but also introduce neighborhood drift.
To preserve user identity while enabling global consistency, we propose an anchor regularizer that aligns user posteriors with item embeddings, stabilizing users under masking and facilitating signal sharing across related items. Our analyses are validated on the Netflix, MovieLens-20M, and Million Song datasets. We also successfully deployed our proposed algorithm on an Amazon streaming platform following a successful online experiment.

Published as a conference paper at ICLR 2026
ON THE MECHANISMS OF COLLABORATIVE LEARNING IN VAE RECOMMENDERS
Tung-Long Vuong
Julien Monteil
Hien Dang
Amazon
Amazon
University of Texas at Austin hiendang@utexas. edu
Longvt@aamaoo..com
jul @ma z.on
Volodymyr Vaskovych Amazon vaskovyce amazon. com
Trung le
Vu Nguyen
Monash University
Amazon
trungimemonash.c com
vutngneamazon. com
ABSTRACT
Variational Autoencoders (VAEs) are powerful alternative to matrix factorization for recommendation, A common technique in VAE-based collaborative filtering (CF) consists in applying binary input masking to user interaction vectors, which improves performance but remains undercxplored theoretically. In this work, we analyze how collaboration arises in VAE-based CF and show it is governed by latent proximity: we derive a latent sharing radius that informs when an SGD update on one user strictly reduces the loss another user, with influence decaying as the latent Wasserstein distance increases. We further study the induced geometry: with clean inputs, VAE-based CF primarily exploits local collaboration between input-similar users and under-utilizes global collaboration between far- fur-but-related users. We compare two mechanisms that encourage global mixing and characterize their trade-offs: ① 8-KL. regularization directly tightens the information bottleneck, promoting posterior overlap but risking representational collapse if too large; input masking induces stochastic geometric contractions and expansions, which can bring distant users onto the same latent neighborhood but also introduce neighborhood drift. To preserve user identity while enabling global consistency, we propose an anchor regularizer that aligns user posteriors with item embeddings, stabilizing users under masking and facilitating signal sharing across related items. Our analyses are validated on the Netflix, MovieLLns--0MM, and Million Song datasets. We also successfully deployed our proposed algorithm on an Amazon streaming platform following successful online experiment.
INTRODUCTION
Recommender systems are essential for delivering personalized user experiences. Having benefited from three decades of research (Resnick et al.) 1994). Collaborative filtering (CF) remains an essential approach in today's 's recommender systems (Zhu et al.) 2025). CF predictive process consists in predicting user preferences by identifying and leveraging similarity patterns between users and items (Su & Khoshgoftaar 2009) Ricci al. 2010), which naturally aligns with the framework of latent variable models (LVMs) (Bishop & Nasrabadi 2006). where latent representations are used to capture the shared structure of user-item interactions. Due their simplicity and effectiveness, LVMs have historically played a central role in CF research. However, these models are inherently linear, which limits their capacity model the complex and non-linear nature of real-worke user behavior (Paterek) 2007|Mnil & Salakhutdinov, 2007). To overcome these limitations, researchers have increasingly explored the integration of neural networks (NNs) into CF frameworks, enabling more expressive modeling and yielding notable improvements in recommendation accuracy (He et al. 2017 Wu et al.)
2016 Liang et al. 2018 Truong et al. 2021 Li et al. (021). A particularly successful line of work VAE-based collaborative filtering (Liang et al. (018), which extends the variational autoencoder (VAE) framework (Kingma Welling 22033] Rezende et al. 2014) to collaborative filtering tasks.
Unlike traditional latent factor models (Hu al. 2008 Paterek 2007 Mnih & Salakhutdinov

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2007), which require learning separate latent vector for each user, VAE-based models offer a user- independent parameterization, where the number of trainable parameters remains fixed regardless of the number of users Lobel et al. (2019), leading to remarkable scalability. Additionally, empirically.
VAE-based CF models consistently outperform many existing L.M-based alternatives (Liang et al.
2018
Kim & Suh| 2019; Walker al. [202 Ma et al.
2019 Guo al.. [022] Wang al. 2023 2024 Husain & Monteil 2024 Li et al. 2021; Tran & Lauw 2025).
2022
Guo et al.
A key driver of the strong performance of VAE-based CF the use of binary mask that corrupts the user interaction vector, producing a partial history from which the model is trained to reconstruct the full interaction vector (Liang et al.] 2018). This masking strategy has been shown to significantly enhance recommendation accuracy (see Section 4.2 and Figure 2 comparing settings with and without masking). Although input noise has become standard component VAE-based CF models due to its empirical effectiveness, its underlying mechanisms and potential side effects remain largely unexplored. Existing works treat masking as a simple anfformancc-enhaaeeii thoroughly examining how it influences the learning process or affects the latent representations, Our work aims to fill this gap with a comprehensive study the effect of input noise in VAE-based CF. The contributions of this paper are summarized as follows:
heuristic, without
We conduct an in in-depth analysis of the collaboration mechanism in VAE-based collaborative filtering models and reveal that 1 collaboration in VAB-CF is fundamentally governed by latent proximity; @ VAE-CF with clean inputs primarily leverages local collaboration and fails to utilize global collaborative signals when input distances are large; @ Both 3-KL regularization and input masking can encourage global collaborative signals, but they operate through distinct mechanisms with different trade-offs i.e., B-KI. regularization promotes posterior mixing by directly constraining the information bottleneck, but suffers the risk of representational collapse when applied too aggressively while Input masking achieves mixing through geometric and stochastic means such that it can bring distant users into the same latent neighborhood, and latent space expansions can introduce neighborhood drift effects.
Guided by our theoretical analysis, we propose a regularization scheme that addresses the issues induced by input masking, mitigating the loss of local collaboration while preserving its benefits for global alignment. Specifically, we model items as learnable anchors in latent space, and during training, the masked encoder outputs are pulled toward the user's s anchor centroid. This acts as training-only auxiliary condition that helps stabilize user representations under input corruption without tightening the information bottleneck, promoting consistent, semantically grounded latent proximity. To our knowledge, ours is the first work to systematically analyze the collaboration mechanisms in VAE-based CF, showing that both 3 KL regularization and input masking can promote global collaboration. In contrast prior works that focus addressing the problems of 3-KL regularization (ref. Appendix fooo a detailed discussion). we address the issues induced by input masking.
Our experimental results demonstrate the strong benefits of the proposed PIA approach compared vanilla VAB-CF on benchmark datasets and especially the success the A/B testing at Amazon streaming platform. We conducted ablation studies across user groups segmented by interaction count validate the effectiveness of global collaborative signals. Additionally, we provide visualizations of the learned latent space that support our theoretical analysis.
2 COLLABORATION MECHANISM IN VAE-BASED CF
Notations. We index users by u E 21. U} and items by i E (1,2..... where U, are the number of users and items, respectively. X E (0, Uxl represents the user-item interaction matrix (e.g., click, watch, check-in, etc.) and x, (the u-th row of X) whereby X = implies that user u has interacted with item and X indicates otherwise. Note that x,, = 0 does not necessarily mean user u dislikes item i; the item may never be shown to the user. For simplicity, we use x to denote a general user interaction vector and retain x,, when specifically referring user Additionally, vectors with the E norm || || (Hamming) and between latent distributions with the 1- W-sssersttiin distance Wi (..).. We refer to the Appendix Table A for the notation summary.
Xx2... Xa/] is an T-dimensional binary vector
measure distances between input
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2.1 VAE- -ASED COLLABORATIVE FILTERING
Given a user's interaction history x XX X2, ,,, E {0. the goal is to predict the full
interaction behavior of this user with all remaining items. To simulate this process during training and to avoid overfitting to non-informative patterns (Steck, 2020). dropout-style random masking is commonly used in VAE-based CF (Wu et al. 2016 Liang et al. 2018 Lobel al. 2019 Shenbin et al., 2020; Vančura & Kordik 2021) ) as a form of stochastic imput corruption. Concretely, we introduce random binary mask b E {0, 1} is with the entry as un-masked, and O as masked. Thus, X₁2 = x ② b is the user's partial interaction history, the goal is to recover the full x given X
Training Objective. The parameters d, of the VAE-based collaborative filtering model are learnt by minimizing the negative 3-regularized Evidence Lower Bound (ELBO):
( 0, Ø) (x) log ( z)] + 3 KL(90 xx) ((
(1)
with standard reparameterizztioon
~ pr-Benouull(p)' X = x b. (H, )²) go (X,), c~N(O, = μ co
(2)
where p is the hyperparameter of a Bernoulli distribution, 4s is o-parameterized neural network, which outputs the mean μ and variance o² of the Gaussian distribution.
2.2 COLLABORATIVE LEARNING VIA VAE-CF
Before presenting our theoretical analysis, we briefly recall the goal of collaborative filtering (CF): to predict a user's preferences from other users' interaction patterns, without relying on user/item side information. Figure highlights two common forms of cross-user information in CF.
l
4
45
4,
L
X1
X2
(1) Neighborhood transfer. Users and X₃ are close in the input space (e.g., under {1), so each serves as a natural reference for the other: similar interaction histories should lead to similar predictions.
Valid Recommmeddation
(2) bar-aue-eel transfer. Users can be far in é, yet still mean- ingfully related through shared positives. Let Sx, {i: X = denote the set of positive items for user u. Sx2 C Sx, then
Figure 1: Local and global col- laborative signal example.
X1 is more active user with similar interests and can inform recommendations for x2 (c.g., items i i2, iz E Sx, \(Sx)). even though 1 and X2 need not be close in L,. We refer to this burlaae--el influence Global collaborative signal.
To formalize these notions, for > we define the input-space neighborhood of user u as
Ns(u)= = {u: ||x. x,|1i < }).
and the (nonzero) overlap indicator as
ov(X,, X.) = -ss. |20}'
Definition 2.1 (Local collaborative signal). The prediction for user depends on other users within the neighborhood N₂ (w).
Definition 2.2 (Global collaborative signal). A model exhibits global collaborative signal at scale 5 if there exist users u and v such that || strictly influence each other.
xx x,ll1 > 5 and ov (x,, x,) = 1, and their predictions
Cross-user influence via gradient transfer. In VAE-CF, cross-user information is exchanged primarily during training because the same parameters are updated using many different users. We therefore operationalize "influence" as training- time transfer: user v influences user u if an SGD step computed from v decreases u's expected loss to first order. The following theorem formalizes this notion and shows that such transfer is governed by proximity of the users' posteriors in latent space.
Theorem 2.3 (Latent-W; W1 sharing radius). Assume decoder gradient is Lipschitz in z such that for any given (- x.). uniformly in x and Vz', ||Volo(x, z) V (x, z')ll Lo Iz z'|l. Let
(n = [.( xx), qu go(. xx), (0): B.g. (lo(xx, (0) ooL.
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Define the content-mismatch term
(u, Egg [Volo z) Volo (x z)]
Dup Loz Wi (9us gu) + Ar(u,))
For one SGD step on user v, 0+ = -0-19- (0), the first-order change satisfies
L,(0t) (0) S -n (0)ll (19 - Da,v) + O(1²)).
Consequently, the step strictly decreases Lu first order whenever Du,v < (19,(0) i.e.
[1]9((0]1| Au,
Wilgus (o) Fsharo U;
Loz
Proof. See Appendix E.1
Result-1 (Collaboration is governed by latent proximity). Theorem 2.3 characterizes when an SGD step on user v is beneficial for user The key quantity is the transfer penalty Du, Le= W1 W1(qu: qu) + (u, v). which has two components: (i) latent mismatch term Wi qo) measuring how close the users' posteriors are in latent space, and (ii) content mismatch term (,, v) capturing how different the decoder gradients are even when evaluated at the same latent code. To first order, step decreases Ly whenever Da,v < I (0)ll- Therefore, gradient sharing effectively restricted to a latent neighborhood around u, and the strength collaboration decays users become latently farther apart.
Consequently, Theorem 2.3 reduces the distinction between local and global collaborative signals (Definitions 2.1 2.2) to geometric question: which user pairs become latently close enough to fall within the sharing radius. Local signals correspond to input-close pairs that remain latently close, whereas global signals require certain input-distant but overlap-related pairs to be mapped close in latent space. In the next section, we examine how the geometry of the input space (including masking) shapes the geometry of the latent space in VAE-based collaborative filtering.
2.3 IMPACT OF THE GROMETRY OF THE INPUT AND LATENT SPACES
We summarize the key theoretical results and present the discussion subsequently.
Lemma 2.4. Assume the encoder is Lipschit,, i.e., (xq) (oa(xx)-99(x4 S. Lo xx Xx VX., {0, 1 then Wi(gol= xu), xx)) I La ||x, xulli, VXa, X. E 13,
Theorem 2.5. Assume px(x x) regular exponential family with sufficient statistics T(x), natural parameter TTZz), and log-partition A. Let qu = 4o(-1 xx) and go = 4o(: Xx), and define Then the B-regularized pairwise objective satisfies
alz) qu(2)+
(2)
min n(-)
Σ Eyg log log 2)] +
Σ sE(uv)
Klga(z xi) x)))
(3)
iEfu,e)
C+ / (lu(z) (z(z)) A A x;: aZ)) da + 8
Σ
KI(Go(Z [()o((\x))lpp(z))
iE(u.))
where C is constant, A is the convex conjugate of A, and for [0,
A A Xvi = A-(T(xx))) (1 -1- A(T(x)))()))) - A*(T((xu) + +1- ( 2 0,
with equality if T(x.) = T(xx).
Additionally, assume the prior p satisfies the Bobkov- Gabkooo-Gttte//lllgggnnndd Ti (C) inequality (Babkov & Götze 1999) with a constant > 0 (e.g., Normal prior of(
W Wilg q.) s (V2CKL(qulP)) V2C
(4)
Proof. See Appendix E.2
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Result-2 (Clean inputs favor local over global collaboration).
Local neighborhoods are preserved. Lemma2.44impiie that & -near users induce nearby posteriors under WI (up to the encoder Lipschitz constant), so input-space locality naturally maps to latent- space locality, preserving local collaboration.
Reconstruction discourages overlap for mismatched users. Theorem 2.5 shows that when T(x.) o Txx.), overlapping posteriors incur a strictly positive "compromise gap" ['gu + qo) A dz in Eq. 3 This pushes the model separate qu and yo, making it difficult for input-distant, content- mismatched users to become latent-close, discouraging global collaboration.
3-KL encourages posterior overlap. Increasing 3 reduces the optimal KL terms, tightening the upper bound of Wi( 2o): thereby increasing latent overlap i.e., potentially bringing input-distant users closer in latent space and enabling global collaboration. However, overly strong KI. pressure risks posterior collapse and weakens recommendation quality; in practice / is typically kept small in canking-fcuuser CF.
Putting these pieces together, with clean (unmasked) inputs and moderate B, similar users remain latent-close while content-mist mismaachee users are pushed apart. yielding a clustered latent geometry that mirror input similarity (Setting-L, Figure 2). By Theorem 2.3] SGD updates are therefore shared predominantly within these latent neighborhoods (i.e., across pairs with Wi (Qu. qu) < Tshare (u, v; 0)). In other words, under clean inputs, VAE-CF primarily exploits local collaborative signals and suppresses global influence from input-distant users.
Theorem 2.6. Let Xu; Xy E 10 be binary inputs. Let bx,, bx. Bprn(p)' be independent masks and set x", = Xx @ bx.. and x,, = Xx O bx.- Denote the number of non-overlapped items X, X and the number of overlapped items s (xx, For any 8 >> 0, define
Ts = 61 and Ug = [0]. Then:
Contraction. Pr[lIx', -X,
6]
mmin(h.2s) (b) pd)p(111111 n-h (p² +1 p))) =
Expansion. Pr|lIx x,111
5) Ei=us (2p(1 p)) (1- (1-2p( 2p(1 p)) s-k
Proof. See Appendix
Result-3 (Masking induces stochastic neighborhood mixing). Theorem 2.6 quantifies how ran- dom masking can stochastically contract or expand the f distance between two users' interaction vectors. Under 3emma[2.4) contractions propagate to latent space; when the realized distance falls within the sharing radius (Theorem 2.3), an SGD step benefits u, even if the original (unmasked) pair was far apart. This creates intermittent long-range sharing events that inject global collaborative signal. Conversely, expansions can push genuine neighbors outside the sharing radius, increasing gradient variance and weakening local transfer. The net effect is global mixing through occasional contractions at the cost of neighborhood drift from expansions (Setting-2, Figure 2).
2.4 BEYOND LATENT GEOMETRY: 3-KL vs. MASKING
The previous section showed that collaboration is governed by latent proximity via the sharing radius (Theorem 2.3). Geometrically, both strengthening the KL penalty and introducing masking reduce latent distances and can enable global collaboration. We now turn these geometric insights into actionable guidance by linking latent distances to the KL terms optimized in the ELBO.
Recall the VAE-CF setting in Eq 1 & 2 with masked inputs X x 2 b, where ba Bern(p)) i.i.d. across items and p=1 recovers the clean-input setting.
For any users u, and masks b,, b. Theorem 2.5 (transportation inequality) yields
Wi(go(- x2 xbb,,, ( xb))) s / /2C x. xx.,b.)) (I)) + / 22 x, xb,,),,) llp).
(5)
Averaging uniformly over user pairs (u, v) and independently sampled masks b b, and using Jensen's 's incquality (concavity of the square root) gives
Ba W Wi Xx xx, bw), go(. x xb.)) S 2/2C / Ex, KI(go(: x xx (6)
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Define the aggregated (masked) posterior 9n (Z) Ex,s Ex X x and the encoder mutual information 190 (Xx; Z) Ex.b KL 9s ( (Z xxx b) 9b (2). standard identity then gives
|
b KL x (xxbb
1g (Xni 2) + KL(g. (2) p(Z))
Combining 6 and 7 any mechanism that lowers Las (Xn; 2) and/or (L lpp) shrinks expected pairwise latent distances, increasing the probability that user pairs fall within the sharing radius (Theorem 2.3 This leads to two directions for encouraging global collaboration:
8-KL (objective-level). Increasing 33 in the training objective (Eq. D strengthens the KL penalty, and by the decomposition in Eq. (7) this effectively penalizes the sum 4 (Xn; 2) + (L. lip). At convergence this typically drives both terms down, which in turn induces a near-uniform contraction of inter-user latent distances and shrinks the right-hand side of Eq. (6). The trade-off is that overly large /9 weakens the reconstruction signal and risks posterior collapse, degrading user semantics. A common solution to alleviate collapse is to use a more expressive prior (often multi-modal, e.g., mixtures, VampPrior, or flow-based priors). However, an expressive prior also weakens the global pairwise contraction effect compared to a simple prior such the standard normal prior. Specifically, with Gaussian prior, the KL term pulls all user posteriors toward a common zero-centered basin, so user pairs have higher chance of becoming latently close, strengthening sharing at fixed B. In contrast, expressive priors can satisfy the KL by distributing users across different modes rather than contracting them to single center, making collaboration locally dependent mode assignment.
Input masking (data-level). Smaller values of (Eq. 2 increase the masking strength, reducing the information available in X₁. By the data-processing inequality, this tends to decrease Tap (Xx: Z) and often also the aggregate mismatch (L( (p). tightening the bound in Eq. 6 However, masking affects the geometry of the latent space in a more stochastic manner than the uniform contraction produced by increasing B. Random masks cause sample-dependent contractions and expansions across batches: sometimes two users who are far apart in input space become close latent space, promoting desirable long-range sharing, while in other cases genuinely similar users may be pushed apart, weakening local reliability. For an individual user, each new mask realization slightly shifts the latent posterior, the user's nearest-neighbor set fluctuates from batch to batch. Over training, these shifts accumulate, producing what we refer to as neighborhood drift: the local structure of the user's neighborhood wanders, and the gradients shared among nearby users become noisy and inconsistent.
3 PROPOSED METHOD: PERSONALIZED ITEM ALIGNMENT (PIA)
Prior work has primarily pursued the objective-level pathway (adjusting or redesigning p(z); see Section B) while largely treating input masking as a benign training trick. In this section, we explore an alternative direction for improving VAE-CF: addressing the downside of masking by stabilizing the stochastic geometry it induces, so that beneficial long-range sharing occurs more consistently and with reduced drift. We introduce a training-one
regularizer that pushes the masked posterior (z | Xa.) toward user-specific target constructed from the user's positive items. This stabilizes masking-indee induced geometry without changing test-time inference, ensuring that different masked views of the same user map to consistent latent region while bringing users with overlapping items closer in a semantically grounded way. We define the overall objective as:
CPIA-VAE(x; 0,
EsD [VAE 0, d; xn)] + Aa LEd (x,, kD).
(8)
where E (e, E Ji=1 are learnable item anchors in latent space (same dimension as z), and AA > is small. In particular, let Sx = {ē: = 1} be the positives for user we have:
Rdy
1
LA 6,
E Ex-gg (x) x. e.
S
We use uppercase letters for random variables e.g., X and hold lowercase for their realizations x.

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Proposition 3.1. Assume the encoder posterior is Siagonal-Gaussee qo(z
| xh)
M((((x)), diag(o o (xx))) Let the item centroid be ex [S Dies, e, then
( X5 & B)
(x)) ex
(xpx))
+ consi(x, E);
(10)
aliggn maran üron controid
variance shrinkoge
where (x(xx)) diag(o) (xx)) and const E)
Eiesy |1 |1x
15
Proof. See Appendix E.4
Proposition 3.1 indicates that PIA ① centers masked latents near the user's item barycenter 0x and @ modestly reduces posterior spread. Two users u, u with similar positive-item sets have close centroids, so their masked posteriors become latently close more frequently, increasing the chance they fall within the sharing radius and benefit from each other's 's updates.
Proposition 3.2. Fix x and its neighhorkood in which the ELBO objective LvvE(x; 0 6; Xn), defined in Eq. ( written as a function of the encoder mean (x,),,, admits a quadratic approximation with Hessian H = mI and |||||
[| I L. Adding dA ( - -xxl2 to this objective yields an effective Hessian Hafs = H + I. Let fx (xx) be the unregularized minimizer over masks and p ()(A)(x))) (xx) the minimizer with alignment. Then with
(ZTZAR) we obtain the following inequalities
VarI[u(A)(xA) = 7² Varr[u (0) (xN)]
Eb (1 - -xx113] S +EE
(0) (x)) exl1
Proof. See Appendix
E.5
Proposition 3.2 indicates that adding the PIA term makes the masked encoder locally better condi- tioned and pulls its mean pa (x)) toward a per-user item centroid. Quantitatively, it shrinks O the variance of Us (xx) across different masks and @ the average drift of (x((x)) from the centroid by multiplicative factor T E (0, 1). Hence, masked views of the same user are more alike and less noisy, so the neighborhoods we train on are closer to the neighborhoods we infer on at test time.
In summary, PIA stabilizes the geometric pathway: aligning 4s (z x₂) to a fixed per-user Cx reduces masked-vs-clean drift and gradient variance; expansions are less likely to eject genuine neighbors from the sharing radius; @ promotes meaningful globul mixing: shared items pull users toward nearby centroids, creating consistent, semantically grounded latent proximity instead of relying purely on stochastic contractions ((Setting-3, 3, Figure 2): 3 introduces no test-time burden: E and the regularizer are estimated during training-only; inference the standard q x).
Remark: geometric view of collaborative filtering. The anchors e, form a semantic map where co-liked items organize into neighborhoods, and ex lies within the convex hull of the user's liked items. This implies:
Users with large/diverse interaction histories. When [Sx] is large and diverse, ēx may be less peaked; PIA then primarily improves stability rather than enforcing a specific prototype. Crucially, users who share more items (or items from the same neighborhoods) have closer centroids, making their representations neighbors and strengthening collaborative signal via the sharing radius (Theorem 2.3). For multi-modal users, the barycenter lies between item neighborhoods, keeping them close to multiple communities; shared (or nearby) items still pull such users into overlapping regions, allowing global signals to flow from both sides. In effect, PIA brings similar users closer without collapsing diverse preferences into a single artificial mode.
Cold-start users. Warm users sculpt the semantic map: items they co-like are pulled into coherent neighborhoods. Cold users, even with few interactions, are placed into this already-organized map by aligning toward their clicked items' anchors. Each positive item is a landmark surrounded by warm users who also liked it (and related items). Aligning cold users toward these landmarks means that even a single shared item can snap them into warm clusters. Moreover, because items sharing users are pulled closer under PIA, interacting with a similar item also places cold users in the right neighborhood. In click space, such users appear far from any warm user; in latent space, or two well-places items act as shortcuts to dense communities, enabling global collaborative signals to propagate to cold users.
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4 EXPERIMENTS
We validate our analysis using three real-world recommendation datasets: MoviieLens-20M, Netflix, and Million Song Dataset and the A/B testing on an Amazon streaming platform. Specifically:
First, we assess benefits of the proposed personalized item alignment approach compared to vanilla VAE-based CF (Multi-VAE (Liang et al. 2018) on these benchmark datasets.
Second, we provide visualizations of the learned latent space under three conditions: VAE without masking. VAE with masking, and VAE with PIA, support our theoretical analysis.
Finally, we conducted ablation studies across user groups segmented by interaction count to validate the effectiveness of global collaborative signals.
4.1 EFFECTIVENESS OF PERSONALIZED ITEM ALIGNMENT
Public dataset. Table presents the performance of our framework, which adds personalized item alignment to Multi VAE, and Vec (Shenbin et al. 2020) on the MoVieLens-20M, Netflix and Million Song datasets respectively. We follow the preprocessing procedure from (Liang et al.) 2018). The detailed data preprocessing steps and train/ mainn/vlliatioontestt split methodology are presented in Section C.I Our code for reproducibility is publicly available at httts::/ com/ amazon- wttpo-sccennccePPe
Table 1:
Our method (with PIA) achieves the best performance for MovieLens and Netflix Prize datasets while having the 3rd rank for Million Song. The best results are highlighted in bold.
MovieLens-20M
Neuflix Prize
Million Song
Model
Recall @20
Recall
NDCG
Recall
Recall
NDCG
Recall @00
Recall
NDCG 100
@50
100
@0
@0
@ 100
@50
Matrix factorization Linear regression
Popularity
0.162
0.235
0.191
0.116
0.175
0.159
0.043
0.068
0.058
EASE
0,391
0,521
0.420
0.362
0.445
0.393
0,333
0.428
0,389
MF
0.367
0.498
0.399
0.335
0.422
0.369
0.258
0.353
0.314
WMF
0,362
0.495
0.389
0.321
0.402
0.349
0,211
0.312
0.257
GRALS
0.376
0.505
0,401
0.335
0.416
0.365
0,201
0.275
0.245
PLRec
0.394
0.527
0.426
0.357
0.441
0.390
0.286
0.383
0.344
WARP
0.310
0.448
0.348
0.273
0.360
0.312
0.162
0.253
0.210
LambdaNet
0.395
0.534
0.427
0.352
0.441
0.386
0.259
0.355
0.308
Nonlinear autoencoders: ML. for encoder
CDAE RaCT
0,391
0.523
0.418
0.343
0.428
0.376
0.188
0.283
0.237
0.403
0.543
0,434
0.357
0.450
0.392
0.268
0.364
0.319
Multi VAE
0.395
0,537
0.426
0.351
0.444
0.386
0.266
0.364
0.316
Multi Aiti-VAE++ + PIA
0.408
0,546
0.437
0.360
0.448
0,392
0.275
0.372
0.326
Uplift (%)
3.29
1.68
2.58
2.56
0.90
1.55
3,38
2.20
3.16
Nonlinear autoencoders: densely connected layers for encoder
RecVAE RecVAE PIA
0.414
0.553
0.442
0.361
0.452
0.394
0.276
0.374
0.326
0.417
0.556
0.446
0.365
0.454
0.396
0.278
0.376
0.329
Uplift (%)
0.72
0.54
0.90
1.01
0.44
0.51
0.72
0.54
0.92
The results demonstrate that PIA consistently improves the performance over the base VAE recom- menders, in terms of nDCG and Recall. It also exhibits competitive performance across the three datasets considered, with RecVAE+PI being the top performing approach on MovieLens-200 and Netflix datasets, and the 3rd performing approach on Million Song dataset.
A/B testing on an Amazon streaming platform. On the basis of offline results, we run one week of A/B testing in September 2025 for the Multi- + PIA algorithm on one streaming platform of Amazon. The approach was implemented as offline system, with weekly training considering a 3-month window for collecting streaming behavior, and daily inference for active customers. The personalized scores computed daily include about 25 millions of users and 4000 movies. The performance of our system was evaluated on 2 movie cards present on the Homepage and on the Movie page. 50% of the customers were exposed to the algorithm (treatment group) for the duration
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of the experiment, while the rest was exposed the baseline algorithm (control group). As shown in Table 2 our approach outperformed the control group significantly, with improved performance on the card click rate by 117% 267% (per daily view) and 123% 283% (per daily user view). For statistical validation, we report the p-value which evaluates the mean difference between control and treatment groups, well the Bayesian probability that the mean difference is positive, considering a Normal-Normal conjugate historic prior which allows for closed form solutions to the posterior distribution. For click rate metrics we observed p-value 0.000 and (prob 0) 1.000; and for playtime, we observed p-value 0.000 and (prob > 0) 0.997. Since its launch, we have observed the performance of the ML system to be remarkably stable in playtime and click rate metrics.
4.2 LATENT SPACE VISUALIZATION
We present t-SNE visualizations (Maaten & Hinton 2008) of the latent spaces learned under three settings: @ clean input, @ input masking, and @ input masking with personalized item alignment, to examine the correspondence between the geometry of the input space and the latent space.
Setting-1: Clean input
Setting-2: Input masking
Setting-3:
Input masking
Personalized item alignment
Latent geometry:
Latent geometry:
Latent geometry:
Well-structured
Stochastic Global mixing
Semantically global mixing
Local collaboration
Local- collbbotllabo
Local collaberation
colbae--ol
Global collaboration
Global collaboration
nDCG@110: 0.409
nDCG@100: 0.426
nDCG@] (0: 0.437
Figure 2: t-SNE visualization of the latent representations for three user groups differentiated by the number of interactions from ML-20M dataset. Purple, Teal, and Orange denote users with 5, 50, and 350 interactions, respectively, correspond to different VAE model configurations. We select group of users with 5, 50, and 350 interactions as they are clearly separated (i.c., L!) on the input space.
Setup: We focus user cohorts with 50, and 350 interactions clearly contrast local versus global collaboration. Note that standard set-based distances (Hamming) inflate cross-cor cross-cohort dissimilarity: even two 5-interaction when the 50-interaction user subsumes the 5-interaction user's items; the same pattern holds for the 50-350 cohorts.
with disjoint histories are closer each other than any 5-50 pair, even
Setting-1:
As illustrated in Figure 2 when masking is disabled and interaction counts differ substan- tially, the learned representations are cleanly segregated by cohort. This indicates that the model in this setting primarily leverages local collaboration and has limited ability to capture global collabora- tive signals. Moreover, the latent geometry mis-aligns with the global structure of the input space: the 350-interaction cluster lies closer to the 5-interaction cluster than to the 50-interaction cluster which contrary to the expected ordering, where distance(350, 50) < distance(350, 5).
Setting-2: the representations from different cohorts become stochastically entangled, which encour- ages global sharing. However, within-cohort structure more diffuse, weakening local collaboration. Despite this trade-off, Setting-2 substantially outperforms Setting-1 (nDCG@ @ =00= 0.426 vs. 0.409), demonstrating the benefit encouraging global collaboration.
Setting-3 augments masking with PIA, which ① helps the VAE remain discriminative under input corruption, yielding a more structured latent space and @ promotes globally consistent user repre- sentations. The resulting latent manifold is both well organized and globally aligned, exhibiting smooth transitions from the 5-, to 50-, to 350- interaction cohorts. This balance local and global collaboration yields the best performance (nDCG@ 100 0.437).

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4.3
PERFORMANCE OF USER GROUPS WITH DIFFERENT NUMBER OF INTERACTIONS
Table 2: Offline and online results on an Amazon streaming Table Results across user groups for
platform.
MovieLens20M.
Medel
Recall
nDCG
Group
Model
Recall
nDCG
@:20
@550
10100
850
1100
Ofline
Multi-VAE VAE VAEii-VAE+PLA
0.592
0,288
0,386
MulniVAFF VAE
0.461
0.625
0.317
0.609
0,302
0,405
[5-10]
Muln-VAB- PIA
0.473
0.629
0.323
Uplint
2.87
4,88
5.13
Uplift
Mult-VAE
0:421
0.595
0.429
Model
Playtime (sec)
per user
Click Rate per
Click Rute (%) per user
111-50]
Mulni VAE PIA
Uplift (%)
0.424
0.598
0.434
Home Card
MAE
0.313
0.478
0.497
Contral Group Multi- VAE+PIA
27.7
4.4
5.3
[51-100]
Multi-ABB Uplätt (%)
Online
74.6
9.5
12.0
0.26
0.09
0.85
Uplitt (%)
169
117
123
Mulni VAR
0.418
0.386
0.474
Movie Card
[100+]
Mult-VAE
Uplift (%)
4.09
0.72
2,57
Control Group
16.8
3.4
4,2
Multi. VAE+PIA
102.6
12.5
16.2
Uplift
283
Our proposed framework provides both a well-structured latent space and the capacity to capture global collaborative signals. As a result, we expect it to benefit users across groups, including cold- start, neutral, and start users. In particular, cold-start performance Xu et al. [Moteel al. (2024); Liang et al.) (2025) is of particular importance in industry settings. To assess this, we partition the test-set users based on their number of interactions and evaluate the performance of our method within each group.
As shown in T3 our framework improves performance for all user groups. Notably, the cold-start group (within to 10 interactions) and the warm-start group (more than 100 interactions) benefit the most. This can be attributed to the inherent challenges each group faces: cold-start users have limited historical data, making recommendation difficult, while warm-start users, often found in the long tail of the user distribution, typically lack sufficient collaborative overlap. Our framework addresses both issues by enhancing access to global collahorative signals.
CONCLUSION
In this work, we analyzed how collaboration emerges in VAE WAE-CF and showed that it is fundamentally governed by latent proximity: SGD updates are shared within a data-dependent sharing radius, clean inputs bias the model toward local collaboration, and global signals can be induced by either the 3-KL/prror pathway (near-uniform contraction of latent distances, with collapse risk if over-used) or by input masking (stochastic neighborhood mixing with potential drift). Guided by these insights, we introduced Personalized Item Alignment (PIA), training-only regularizer that attaches learnable item anchors and softly pulls masked encodings toward each user's anchor centroid. PIA preserves instance information, stabilizes the geometry under masking, and promotes semantically grounded global mixing without adding test-time overhead. Empirically, PIA improves over vanilla VAE-CC on standard benchmarks and in an A/B test on a large-scale streaming platform, with ablations across user-activity strata and latent-space visualizations corroborating the theory.
Limitations. The benefits of capturing global collaborative signals still depend heavily on how well the input masking is designed (most current research relies on Bernoulli masking). If the masking is too noisy, even with alignment mechanisms, the model may struggle learn meaningful representations. Therefore, a promising direction for future research is to explore more effective masking strategies that better support global collaboration.
ACKNOWLEDGMENTS
We would like to thank Vy Vo for the valuable discussions during the preparation of this paper.
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THE USE OF LARGE LANGUAGE MODELS
We used large language model (ChatGPT) to help with editing this paper. It was only used for simple tasks such fixing typos, rephrasing sentences for clarity, and improving word choice. All ideas, experiments, and analyses were done by the authors, and the use of LLMs does not affect the reproducibility of our work.
We also used ChatGPT to assist with proof verification and theorem refinement. Our workflow involved providing initial drafts to ChatGPT, which would then suggest improvements to the mathe- matical presentation and formatting. We subsequently edited and refined these suggestions.
APPENDIX
This supplementary material provides summary of common notations, detailed experimental settings, and proofs for the theoretical results stated in the main paper. It is organized as follows:
We summarize common notation in Scction
We present the Related Work Section B
Detailed experimental settings and implementation details described in Section C
The pseudo-code of the algorithm is provided in Section C.2
Additional experiments on parameter sensitivity analysis are presented in Section
We present all proofs relevant to the theory developed in our paper in Section B
A NOTATION SUMMARY
Table 4: Table of Notations
Symbol
Description
Users and Items Input Data
U,T
Number of users and number of items I-dimensional binary vector (the u-th row of X); X implies that user has positive interaction with item Xai indicates otherwise
Xu (x11, Xu2,..., x,I]
E (0,1)/
binary mask, i.e., b~ Bern(p)
X4 xxb b
user's partial interaction history set of positive items from user x
Sx = (Vi SI: x; = 1}
VAE Models
6,0 0
VAE encoder Po and decoder parameters d6 Φ- d-parameterized and f-parameterized neural networks Latent space of the VAE, e.g., (μ, σ²) (xx), (0,, I), z learnable item embedding latent space (same dimension Z) and E {e, R N=
As Pe
6a
e; Rdd
Theoretical Constants and Bounds
Na(u) {v: ||x, X 1l S }
input-space neighborhood
Ln norm (sum of absolute values)
W((.)
1 Wasserstein distance
B RELATED WORKS
Motivated by our theoretical analysis, both (-weighted KL regularization and input masking can promote global collaboration, albeit with different trade-offs. Prior work has largely focused on
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controlling the KL term, primarily along two lines: (i) scheduling the / factor in the regularizer and (ii) adopting more flexible priors.
8-scheduling. Liang al. (Liang et al. 2018) introduce 8-scaling factor modulate the strength of the regularization [L(galz) x) p ( while Long et al. (Long et al. 2019) propose gradually increasing this weight over training to mitigate posterior collapse.
Flexible priors and architectures. Several works replace the standard normal prior with richer alternatives to better match the data. Examples include VampPrior and its hierarchical variants (e.g.. HVamp) (Tomczak Welling, 2018 Kim & Suh 2019), as well as implicit or learned priors (Walker al. 2022p. RecVAE (Shenbin al. 2020) combines redesigned encoder-decoder, composite prior, input-dependent (x) rescaling, alternating training, and a non-denoising decoder. Other lines incorporate user-dependent priors (Karamanolakis et al. 2018) or impose an arbitrary target prior via
adversarial training (Zhang et al.) 2018).
To our knowledge, ours is the first work to systematically analyze the collaboration mechanisms in VAE-base -AE-b CF, showing that both 8-weighted KL regularization and input masking can promote global collaboration. In contrast to prior works, guided by our theoretical analysis, we propose regularization scheme that addresses the issues induced by input masking, mitigating the loss of local collaboration while preserving its benefits for global alignment.
C EXPERIMENTAL SETTINGS
C.I DATASET
We validate our analysis using three real-world recommendation datasets: ens Netflix and Million Song (MSD) where each record consists of user-item pair along with rating that the user has given to the item. We follow the preprocessing procedure from MultVAE (Liang et al.) and Netflix, we retain users who have rated at least five movies and treat ratings of four higher as positive interactions. For MSD, we keep only users with at least 20 songs in their listening history and songs that have been listened to by at least 200 users.
2018). For MovieLens-222
Table Dataset statistics.
ML-20M
Netflix
MSD
of users
136,677
463,435
571,355
# of items
20.108
17,769
41,140
of interactions
10.0M
56.9M
33.6M
% of interactions
0.36%
0.69%
0.14%
of held-out users
10,000
40,000
50,000
The user data is split into training, validation, and test sets as presented in Table For every user in the training set, we utilize all interaction history, whereas for users in the validation or test set, fraction of the history (80%) is used to predict the remaining interaction.
C.2 IMPLEMENTATION DETAILS
Hyperparameters. We use batch size of 500 and train the model 200 epochs using the Adam optimizer with learning rate of x 10-3 across all experiments. The specific hyperparameters AA p. and Ascate are selected based on validation performance. An ablation study on the sensitivity of p. Asaale and AA with respect model performance is provided in Section D.I
Algorithm. The model trained by optimizing the objective defined in Eq. 8 However, for the hyperparameter λx, which controls the strength of the personalized item alignment regularization,
http://m11lonoonsottaett
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instead of consider it fixed nyper-parameter. gradually increase its value during training Specifically, we use the validation set to monitor whether the latent space is getting trapped in a local optimum ie., when the validation performance does not improve after consecutive epochs. If such a case is detected, we increase A by scaling factor Asale: as detailed in Algorithm |
Algorithm 1 Personalized Item Alignment VAE
1: Initialize:
Models: encoder qe, decoder pe and item-embeddings E.
Hyper-parameters: Ås Ascale and p. Variables: best.val. wal.hh == O, best ndcg :=
2: for epoch in n.epochs do
3: // 'Training
4: for iter in iterations do
5: Sample mini-batch x
6: z ~ (p(- x) // using reparametrization trick
7: Update q and E based on CPIA-VAE(x;0, 0) in Equation (8)
8:
end for
9:
//Validation
Compute nDCG@K on validation set: apochhndyy
11:
if epoch > best_val val_nddg
ndeg then cest_val := epoch_ndcg
12:
13:
best.val.epoch epoch end if
14:
15:
// Increase Aa if training is stuck in local optimum, i.e., when the validation performance does not improve after consecutive epochs. <, epoch + p then
if best_
17:
AA = Ascale x AA
end if
19:
end for
Return: the optimal encoder 9s and decoder po best val epoch.
C.3 BASELINES
We have selected following models as baselines:
Matrix factorization (MF); consider MF trained with ALS with uniform weights (Hu ct al. 2208)), which is a simple and computationally efficient baseline, and also weighted matrix factorization (wMF) (Hu et al. 2008);
Regularization based item-item interactions; here selected GRALS (Rao al. 2015 that employs graph regularization;
Linear models; we have chosen full-rank models EASE Steck (0019) and low-rank model PLRec (Sedhain et al., 2016);
Nonlinear autoencoders; here we consider the shallow autoencoder CDAE (Wu et al. 2016).
variational autoencoder MultVAE (Liang al. 2018), and its successors: RaCT (Lobel
et al. 2019) and Rec VAF (Shenbin et al. 2020
D ADDITIONAL EXPERIMENTS
D.I PARAMETER SENSITIVITY ANALYSIS A P AND ASCALE
Note that the hyperparameter ÅA was introduced in our main objective, where it controls the strength of the personalized item alignment regularization. In contrast, p and Ascale are two hyperparameters introduced in our algorithm to dynamically adjust AA during training. Specifically, we use p and Aucale to gradually increase the value of Xx We monitor the performance on the validation set to determine whether the latent space becomes trapped in local optimum i.e., when the performance
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does not improve after epochs. If such situation is detected, increase A by multiplying it with the scaling factor Ascale-
In this section, analyze the sensitivity of AA P. and Ascale with respect model performance. We fix the value AΛ = {2, 4, 8 and vary the values of p and Awale. Note that p is used to detect local optima by checking whether the validation performance fails to improve for p consecutive epochs. We evaluate p in the range from to 15. The hyperparameter Awale controls the rate at which X increases. Since large scaling factor may destabilize training, test Ascale values in the range from 1.0 to 3.0. 1.0 mean there will no scaling.
Validation NDCG@100
Test NDCG@100
A-
2-437
0.438
0.433
2.499
0.439
2-
0.432
0,433
2-434
0.424
0.434
0.443
0.18
0.433
0.437
0.43
0:437
0.440
0.400
3:441
0.440
0.432
0.435
0:436
0.436
0.435
-2.456
0.435
9.477
0.400
3,400
0:436
C-44
0.44
3.477
0.440
2.410
0,13
R-
0.432
2.456
0.632
-0
1.0
2.0
2.5
3.0
1.4
1.5
2.0
2.5
3.0
A_scale
A,scll
Figure Parameter sensitivity analysis on P and Ascale of PIA-VAR on MovieLens-20NG 20M. Fix AA 2.0 different values of E 5, 10, 15} and Ascale E {1.0, 2,,
Validation NDCG@100
Test NDCG@100
2.437
0.42)
2.400
0.432
D.434
0
0.434
C-49
0.43
0.488
g
0444
0.33
2.437
0.43
0.441
2.441
0.641
0.432
0.434
2:466
0.436
0.435
C-48
0.435
0.435
2445
0.440
0.431
2.4.9
0.415
-0433
0.222
0.455
2:454
0.414
0.4.1
0433
1.0
2.0
2.5
5.8
2.0
30
scale
Scale
Figure Parameter sensitivity analysis on P and Ascale of PIA-VVE on MovieL.nns222 Fix A different values of {3, 5, 7, 10, 15} and Ascate {1.0, 1.5, 2, 0, 3.0}
Figures 3 and 5 show the performance measured by nDCG@ 100 on the Movielens--00M dataset. It can be observed that the validation nDCG@ 100 remains relatively stable across XA values, for Ascale values in the range 1.5 to 2.3 and for p values in the range 5 to 10. Based on this analysis, we set p and Ascale for all experimental settings.
Analysis on AA To futher analyze the sensitivity of As, we fix the values of p 5 and Ascale (based on previous analyses) and vary the value of AA-
As described in the experimental setup, the hyperparameter Xa is selected using nDCG@ 100 on the validation set as the evaluation metric across all experiments. Figure presents the validation nDCG@ @ 100 for different values of Aa, along with the corresponding test nDCG@ @ 100. Recall and Recall @ 50 on MovieLens 20M. It can be seen that the validation and test performances are aligned, and the results also indicate that PIA-VAE is generally robust variations when X^ 0.
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Validation NDCG@100
Test NDCG@100
4-
2.488
0:423
0.423
CA10
2
0.424
5444
0.44
-.439
0.33
9.48
0.440
0.441
3.400
0.411
0.434
0.435
6:435
0.437
0.436
0.456
0.435
0.437
2430
0.440
0,640
2.440
0.443
0.414
0.435
24456
0.486
0.435
CA44
043
2.0
A,scale
A,scale
Figure 5: Parameter sensitivity analysis on P and Ascale of PIA-VAE on MovieLens-20MM Fix A = 8.0 different values of p {3,5,7, 5, 10, 15) and Ascale {1.0, 1.5, 2, 0, 2.5, 3.0)
0.56
0.52
0.50
Metric Score
NDDGGg100
Test Recaligg20 Recaligno
0.44
0.42
Paignmert
Figure 6: Performances MovieL.ens-20M dataset with different Aa
D.2 COMPUTATIONAL INFRASTRUCTURE AND RUNNING TIME
Infrastructure All experiments, including approach and the baseline models, were conducted on an ml. g5. 2x1 arge AWS EC2 instance equipped with an NVIDIA A10G GPU.
Table 6: Average training time per epoch (in seconds).
VAE
VAE Alignment
MovieLens-20M
8.207
9.516 (15.95%)
Netflix
29.
25.722 (15.90%)
Running Time Table reports the average training time per epoch (in seconds) for the base VAE model and our proposed PIA- VAE. The addition of the alignment component in PIA- VAE results in training overhead of approximately 15.9% compared the base VAE.
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E THEORETICAL DEVELOPMENT
In this Section, we present all proofs relevant to theory developed in our paper.
E.1 PROOF OF THEORRM
Theorem E.1 (Latent-Vi 11 Sharing Radius), Assume decoder gradient is Lipschitz in such that for any given z ~ qo(: Xu), uniformly in x and for all z' V (x, z) (xla(xx & Lez I|z - z']l Let
(0) (1xw)) (fo 2)],
gu( = VoLu(O),
and define the content-mismatch term
(u v) (ootlte) VVoo z) (x. 2)]||
For one SGD step user with step size 1j > O. setting 0+ = 0 - 179x(0), we have:
fu ( S -n Ilu (0) (0) Too Wi(go(. xx); 90(- xx)) + Au(u, +0
In particular, the step user strictly decreases Lu to first order whenever
Wa(gol: xx), 2o(. xx)) < Tshare (u, 0; == [19n(0)] - A.(
Loz
Proof. For shorthand, write qu gol: x.) and qu = gol. xx).
first-order Taylor expansion gives
Lu ng+) (i) n7 (9.(()).0(()) O(1²2)
(11)
Then, we decompose the inner product:
(Bur Bo) = -19111 (gus Ir -ga) S -199u11 1 + 119ull 11g. l-
Next, we bound
llg.
9ull
= Egg. Vole(xx, 2) - Eng Volo(Xu 2)
<
E Volo(xa: 2) - Volo 2)
+ Eg. Volo 2) - Eg Volo (x z
(1,(u,0)
Leu Wi(gu:w.)
For the last inequality, let (z) == Volo(x,, 2). By assumption decoder gradient Lipschitz, a is -ii-schsc in z; for any coupling a of (yus 4o).
/ (v((2) w²22)) dr 2 < Loz ||2 2'11 dx S Loz Wi(qu, go).
Bg. [bb] - Egg. [+]]] =
Combining the bounds and substituting into Eq. condition follows by inspecting the coefficient of
[II] yields the stated result, and the strict-decrease
E.2 PROOF OF THEOREM 2.5
Before proving the theorem, we recall some inequalities:
The Kantorovich-Rubinsteen dual form (Santambrogio 2015):
/ f d(j - v).
(i, = sup &-X (1
(12)
The Donsker- Varadhan variational formula (Donsker & Varadhan, 1975): for any measurable g with { ed dp oc.
/ g log / e dp.
KL(vIlp) 2
(13)
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The
Ti (C) inequality (Bobkov & Götze 1999) is known to be equivalent to the following sub-Gaussian moment generating function (mgf) bound for Lipschitz functions: p satisfies the Ti (C) inequality with constant C' 0, then for every 1-Lipschitz, f and every À E R,
C22
log exp(X(f Epf)) dp - 2
(14)
Lemma E.2. Assume the encoder is Lipiipschitz i.e., 190 (xx) (x(x))) || S Lollx, xx II for all Xus X, E 10 then Wi(gs(: xx), gs( |x,) S Lo ||x, Xulli for all Xus Xv E {0,
Proof. First, since go (z(x)) = (Hp(()))), (iag df
the Wasserstein-2 distance
(2((a(z)xi) 4o (x)xx)) has the following closed form:
(2(g0(2) x.), ( x,))² = (1 - (x+(x))11 +x - ax(xx)1?
(15)
[x)(x)
which, combined with the definition Qo(x))
[x( yields
(x.) (x,))1 = W2( (2) (olxx)) (x)))
(16)
Since Qs is L La-Liphchitz continuous, we have (x,) - Qo(x,)l S Tallxx xx and
W2(qo(z| xw). (z x.)) S Lø||x -xull-
(17)
Since W1 < W2, we have W1 (z x.). g0(z x.)) & L - -xvll-
Theorem E.3. Assume po(x z) is a regular exponential family with sufficient statistics T(x), 90(2/x;1
natural parameter 17(z) and log partition A. Let a(z) 20(x (4 {ęi + 92 > 0}. Then
2
2
min n(-)
E ( xx)) log |z)] + >
KL(gall x1) xi)
(18)
= =C+ f (go(z) x1) + 40(z x2)) A (x x2; dz + 8
KL xx)) llp()))
1=1
where A is the convex conjugate of A, C' is independent of (n-), and Ax-(x1, = a (x((())) + +1-1)) AT(T(x)) - - (*(x((x) + (1-x)T(xx)) 20 20, with equality iff either (- x1), ( x²) almost everywhere T(x:) T(x2).
Additionally, assume the prior satisfies the Boblon-Grötte/Tllagran (C) inequality (Bobkov & Göize 1999) with constant C (e.g., Normal prior (0,,
Wi(gs(z) x1), (z xz)) s 22CKI(g x1) [[)) + 2C (z xx) p(z))) (19)
Proof of Eq. 18). We write the conditional likelihood in its exponential-family form
px z) = h(x) exp (T)(x), - A(n(z))),
so that
log (x: iz) = A(n(z)) - (T(x;), m(2)) log (x;).
Let qı(z) = (z x;). 1,2, and define
(z(z)
Q(2) Q(z) > 0,
Q(z) = (z) (z))
a(z)
arbitrary in [0 1]. Q(z) 0,
and the a-mixture of sufficient statistics
(z(z) == (1-)
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(Any choice of on {Q = 0} is immaterial since all integrands below multiplied by Q.)
Summing the two reconstruction terms and using f q: = 1,
log (x 12) = (E (i(z)) A(n(z)) dz - / (T(x))q1(2) + ((xx)(((22)))) n(2)) Σ
Bg.
log h(x;)
1=1
Q(z)) (A(n(z)) (Ta(z). dz
log h(x,).
Recall the convex conjugate A and Fenchel- Young inequality (Fenchel 1949 Rockafellar 1970)
A (²()) = sup (v. n) - A(n)) A(n) (y. n) 2 (y),
with equality when y E aA()): in the regular (Legendre) case (Rockafellar 1970.. A is essentially smooth and strictly convex, so y VA(r) is the unique equality condition and A is strictly convex on its (convex) effective domain.
Because the integrand is separable in z and Q(z) 2 minimizing the integral over all measurable n(-) reduces to pointwise minimization:
min / @(()) -(a n())
(T)()).((z))) da / Q(z) min (A()) - (Ta(z), dz
/ (Tx(()) dz.
Hence
2 [2)] - f Q(z)) (((z) dz Σ log h(x;).
min x(-)
By
log
(20)
(When (z) lies the interior of dom(A"), the minimizer is (z) = VA (z)): equivalently, AA()"(z)) (z).) Add and subtract the quantity
2 / [(z)) ((T) + +11- dz Σ AT((xx)) / (((z)) dz,
and collect the terms independent of v7-)) into the constant
2
C:=
Σ
log)(x))) + AT(T(x))).
i=1
Using Eq. (00,, we obtain
lx; 2)] CC (ate + (1- (1= - -ATTa(
min 0(-)
Eg
dz
=C+ / (10))4((1)x221(1)) dz,
(21)
where
Ax.(X))x2:0) = a AT(((x)) + - a1 (T((x)) (*((((x) + - ())x)
By convexity of A", A (x,, X2: 2 for all a E [0, 1] (Jensen gap). In the regular (Legendre) case, A is strictly convex its effective domain, A (x1, X2; ai) = 0 iff either
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T(x;) (xx2), in which case the three arguments of A coincide, or
a E [0,1),ic i.e. ((2)a(z)( - a(z)) = 0 for Q-a.e. z. Equivalently, the posteriors have disjoint supports w.r.t. the measure Q(z) dz (on each point with Q > 0 exactly one of q1. 92 is zero).
(If A' were affine on the segment [T(x)); [x2)]] equality could also occur with 0 < a 1, but strict convexity rules this out unless T(x)) = T.x
Finally, the regularizer 3 - (T (z x:) || p())) does not depend on n7.), hence it carries through unchanged. Combining with Eq. (2l) yields Eq. (18).
Proof of Eq. 19. By the triangle inequality for W1,
Wilgo(: x1), go(- x2)) z Wilgs(: x1).P) + Wilgol- x2).
(22)
Thus it suffices to show that for any probability v with (L(vllp) co,
(i(pp)) & /2CKL(v/lp).
(23)
Fix a I-Lipschitz f and O. Apply Eq. 13 with g = A(s- - EEp)) to obtain
KL(w|lp) 2 A (s Epf) du log ʃ Texp(A(s - iE,()) dp.
Using the mgf bound Eq. [4 gives
/ f [ddv dd(--p) p) s ā KL(WlDD) + CA
2
Optimizing the right-hand side over À > 0 yields the minimizer x = /2KL(vlP)/C, and the minimum value
CA*
(L(Ullp)
(2CKL(U)p).
X
Therefore, for every 1-Lipschitz f.
J fdlv S (2CKL(v|p).
Taking the supremum over all 1-Lipschitz, f and invoking Eq. gives exactly Eq. 23
Applying Eq. 23 to gp(-) x1) and to 2-(-) X2) and combining with the triangle inequality
in Eq. yields Eq.
E.3 PROOF OF THEOREM 2.6
Theorem E.4 (Masked input: contraction and expansion). Let X1 (0, 10, be binary inputs. Let bxj- Dxg ~ Bern(p)) be independent masks and set x = x1 bx and X² = X2 O bx. Write h = |X] X2111 and (2) (so h is the number of disagreeing coordinates and s the count of shared 's). For any 6 > 0, define Ta = [8] - and Us = 15). Let = ||x x/ 1111 Then:
Contraction.
min min(h, (h)Ta)
Pr|D' < <6) 2 (0² + (1- p)
Σ
(n)
h
0 -p)
(24)
Expansion.
88)
Pr[D'20 2 N
Σ
(2p(1
- p))* 2p(1 - --)
(25)
k
k=Us
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Proof. Partition coordinates into
H = [j: æ1j + x2i),
[
S : æ1 æ2j = 13, |S|
For j E H, exactly one (æ1) 22j) equals 1, After masking, the post-mask difference at equals 1 iff the unique is kept, with probability Hence
:: Σ jEH
(post-maak difference at j 1 Binomial(h, p)-
For E S, both entries are 1. The post-mask difference equals |bı, b2yl. which is 1 iff the masks disagree; this happens with probability Pr(bij + b22) = p(1 p) + (1 - p)p = 2p(1 - p). Thus
Z ==
bbj
b2rl Binomial(s, 2p(1 - p)))
JES
Independence of masks across coordinates implies Y + Z. and the masked distance decomposes as
D' = ||x x2ll1
Y+ +
Contraction. Because D' is integer-valued. D' 8 is equivalent to D' S Tg. Consider the event = n < Ts}. On we have D' = Y + < Tg. hence
Pr[D' < 6) 2 Pr(E] = Pr[Z = 0) Pr(Y - Ts) by independence of Y and Z. Now Pr[Z 0] (Pr(bı, b2j)) (p2 (1 p) and
(h,T) h1
Pr[Y S Ta)
p p)
k
Multiplying the two factors yields Eq. (24
Expansion.
Using D' = Y + Z with Y Z and Us = [ō],
Pr[D's 2 8 = Pr + 2 2 Us} = Σ
Pr = m] Pr|Z 2 Ug - m
m=0
h Σ
h
pm 11 1-))h-
Σ
p)) (20(1
2p(1 p))
m
max (Us mm
Finally, since D' =Y + Z,
Pr[D's 2 8) Pr[Z 2 Us}
Σ
(0)
83
(20(1 (20(1- (2){ ~p))*(1 (1-2(11 -p))
k
k=U*
which gives Eq. (25 This completes the proof.
E.4 PROOF OF PROPOSITION
Proposition E.5. Assume the encoder posterior is Gaassaian gz(z
xx.)
N(Hx(x)), diag(o? (xx))) Let the item centroid be ex S Σies, e, then
CA(Xh, E)
||
ex
1|
(x(xn)
+ const(x, E).
(26)
align mean item centroid
variance shrinkaage
where Ex(xx) diag(o? (xx)) and const(x, E)
15x Eies, -
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Proof. Write (z(z|x))) (((ss()))) Es (xx)) with [x(x)) diag(o (xx)). have:
E E|llz e:l12 (x(s)) eill2 tr Eio
Averaging over E Sx yields
Lx, x; [Sx iE
Σ
(x)))(x) - oz 2 Ex()))
Given the item centroid be Cx [8x1
1 Dies, C₁ then, we obtain
Σ
((xs) -eill² [1 ex
Σ
1l::l2
||ex
S
S
iE8x
Combining the last two displays gives
LA (Xh,, x; x; E) = (x()))) - ex112 tr Ex(x)) +
Σ
le,1 - 11xx
S8
coust E)
which is exactly Eq. 26
E.5 PROOF OF PROPOSITION 3.2
Proposition E.6. Fix x and its neighborhood in which the ELBO objective LvvE(x; 0 6; xx), defined in Eq. ( written function of the encoder mean p.g RR., admits quadratic approximation with mask-indeeendee curvature
H Z mI, |1 ST (0<mSL<
Adding A (xll ex112 to this objective yields an effective Hessian Heff = H + 2A Let μ (xx)) be the unregularized minimizer over masks and (( (xx) the minimizer with alignment. Then with T = (1.t we obtain the following inequalities
Varb (xx))
111 5 72 Varb [u (0) (xn)]ll2
(27)
tr Varb ( (xx)
I 72 tr Varb 1 (0) (xxx)x
(28)
Ep || (x) Ex11
I T Eb || (xx) - cx112
(29)
Moreover, if Var |1 [ commutes with H (e.g., they are simultaneously diagonalizable). then the Löwner-order contraction
Varb (xn)) I 7² Varb [ee (0) (xx))
holds.
Proof. Fix and mask b, and let (H) denote the (unregularized) mask-conditioned denoising objective as function of the encoder mean E Rdd (all other quantities x, the masked input X decoder parameters, are held fixed).
Choose a reference point jú in a neighborhood where Fb admits quadratic approximation with mask-independent curvature matrix H, and assume
z mI,
|1 T.
0 m < I I< <00 00.
Equivalently, we approximate the Hessian uniformly across masks by 22Fb(1) H.
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Quadratic surrogate.
Define the quadratic model of Fb around ji by
Jb(u) Pb( VFb(A) (u (1) + (u [1) 11 (u po).
(30)
Let
gb
(p))
ab:= jr H gb.
Completing the square yields an equivalent form
Jb cb + 2 (u ab) H (μ ab),
(31)
where the (mask-dependent) constant
cb (p)()) 1 786
H gb
is independent of μ.. In particular, the unique minimizer Jb is ab:
arg min (b) = ab.
Fb is exactly quadratic with curvature H this neighborhood, then (xx)) = ab; otherwise, ab is the minimizer of the local quadratic approximation lbb.
Adding the alignment penalty Aallę ēx1ă gives the first-order condition
(I + μ = H ab + 2A
Define
L
: (H + +2 H, =: L + 2AA
E (0,1).
Then the aligned minimizer is the affine shrinkage of ab toward ēx:
μ (A) ab + (I- -MM cx
(32)
Spectral bounds on M. Diagonalize H QAQT with A diag m d L. Then
A
M Q diag
QT.
A + 2AA
Let a; == A/(Aa + 22A) E 1). It follows that
Amax (H)
0 M I
| max
S 7,
|| = |M < <t²
(33)
Amaxx (H) + 2AA
and, eigenwise, of < Ozg hence
2
M TI.
(34)
Variance contraction (operator norm).
Since ēx is mask-independent, Eq.
32 gives
Vars = M Var, [ab] M.
(35)
Taking spectral norms and using submultiplicatiiity.
Var (A)11 I [|M]3 Varblau]l2 s 72 3 Varb/abll2
which is Eq. 27 upon noting Vara(as) = (arl(u(0)).
Variance contraction (trace). From Eq. (35).
tr Varb (A) tr( (Varb M²) I ||M Vars(an) S 72 tr Vars[ab),
where the inequality uses M < ||M 1 and the fact that for A, 2 tr(AA) & BB]2 tr(A).
This yields Eq. (88)
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Löwner-order contraction under commutation (Higham & Lin 2013). If Varb |ab commutes with H, then it commutes with M. In the common eigenbasis, write Var [ap] = Q diag (v,) Q with 0j 0. Then
M Varb lap] M = Q diag(aft)) Q 3 Q (liag(?2u)) = -² Varb(ab).
proving the Löwner-order bound.
Mean-drift contraction.
From Eq. 32
1 (A) 8x = M(ab - -xx,,
hence
(()) exl12 (ab ex) TAA 2 ex)
I (ab 6x) (T)) ex)
(by Eq. 34
= r ab - 0x 12.
Taking EE, gives
Eb (bll (A) Ex112]
S r Eb 1 (0) cx
which is Eq. 29
26


Reviews:
[{"review_id": "LgHUM4DiV4", "reviewer": "Reviewer_4p7K", "summary": "This paper provides a theoretical and empirical analysis of collaboration mechanisms in VAE-based collaborative filtering. The authors establish that collaboration is governed by latent proximity, formalizing this concept through a derived latent sharing radius. This radius specifies the condition under which an SGD update for one user will also reduce the loss for another user, with the influence decaying as the Wasserstein distance between their latent distributions increases. The work further contrasts two pathways for enabling global collaboration: KL regularization, which acts on the objective to promote posterior overlap at the risk of representational collapse, and input masking, which operates on the data to stochastically alter input geometries, enabling global mixing but potentially introducing neighborhood drift. Guided by this analysis, the authors propose Personalized Item Alignment (PIA), a training-time regularizer that stabilizes the latent geometry under input masking by aligning a user's masked posterior toward a centroid defined by learnable item embeddings. This method aims to facilitate global collaboration in a semantically grounded way without incurring inference-time costs. Empirical validation on public benchmarks shows consistent improvements, and the method demonstrated significant metric lifts in a large-scale A/B test on an Amazon streaming platform. This paper is distinguished by its exemplary clarity in exposition, seamlessly integrating sophisticated theoretical derivations with practical algorithmic design and empirical validation.", "questions": "see Weaknesses", "limitations": "", "rating": 8, "confidence": 3, "soundness": 4, "presentation": 4, "contribution": 3, "strengths": "Novel Theoretical Framework: It establishes a rigorous, interpretable theory of collaboration in VAE-CF based on a latent sharing radius, providing a geometric condition for update transfer between users.\n\nElegant Algorithmic Design: The proposed PIA method is a direct, low-overhead application of this theory, using learnable item anchors and a training-only regularizer without inference costs.\n\nExtensive Empirical Support: The methodology is validated through consistent improvements on public benchmarks, detailed ablations, and supporting latent-space visualizations.\n\nDemonstrated Practical Impact: Significant performance gains reported from a large-scale A/B test on a production platform underscore its real-world applicability.\n\nExemplary Exposition: The paper is exceptionally clear, seamlessly bridging complex theory, proofs, and experimental result", "weaknesses": "A/B test reporting is incomplete. The online results are compelling but the paper omits key statistical details (sample sizes, confidence intervals or p-values) required to assess robustness and practical significance.\n\nLimited sensitivity analysis for hyperparameters. The geometric effects central to the paper depend on PIA hyperparameters. A more systematic ablation or robustness sweep would increase confidence that the method is stable across realistic settings.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "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": "YCOMfiwll2", "reviewer": "Reviewer_PHGG", "summary": "This paper investigates how (local/global) collaboration emerges in VAE-CF and shows it is governed by latent proximity. They compare the mechanisms and trade-offs of β-regularization and input masking. To address the latent drift, they propose PIA, a training-only regularizer that pulls each user’s masked posterior toward the centroid of their interacted item anchors. The analysis shows that PIA aligns user posteriors with their semantic item centroids, reduces variance, and stabilizes the encoder by improving local conditioning and mitigating mask-induced drift.", "questions": "1. I have a question regarding the definition and effect of the item centroid $\\bar e_x$ in PIA.\nAs I understand it, the posteriors $q_{\\phi}( z |x_h^{(1)}), q_{\\phi} (z|x_h^{(2)}), \\dots$ from multiple masked views are softly aligned toward the same semantic centroid $\\bar e_x$, making the user representation consistent across different masks. \nHowever, for users who have interacted with a very large and diverse set of items, the centroid $\\bar e _x = \\frac{1}{|S_x|} \\sum_{ i \\in S_x} e_i$ could become an almost uniform average over many anchors and lose semantic specificity. In such cases, does PIA still provide meaningful alignment?\n\n2. For large-scale item sets (e.g., millions of items), how does the additional anchor parameterization affect memory and training efficiency?\n\n3. I would be interested to hear the authors’ perspective on whether using a weighted (e.g. (reflecting interaction frequency) centroid could improve alignment.", "limitations": "", "rating": 8, "confidence": 2, "soundness": 3, "presentation": 3, "contribution": 3, "strengths": "1. Engaging and well-structured paper.\n\n2. Provides clear theoretical insight into how (local/global) collaboration in VAE–CF emerges.\n\n3. Proposes a noble regularizer (PIA) that stabilizes masking-induced noise through semantic alignment. \n\n4. Offers rigorous analysis showing that PIA reduces latent variance and improves encoder conditioning.\n\nThe paper is theoretically solid, and the large-scale experiments convincingly support its claims.", "weaknesses": "I did not find any major flaws in the theoretical analysis or experimental results. The paper appears technically sound and well-executed overall. I have only a few minor questions.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "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": "vLagx2jdW1", "reviewer": "Reviewer_2RrV", "summary": "The authors theoretically analyze the VAE-based collaborative filtering. Specifically, the authors claim that VAE-based CFs are governed by the latent proximity. Both the Local collaboration and global collaboration mechanism has been studied. The authors introduce the concept of a sharing radius via latent Wasserstein distance and compare the distinct operational mechanisms of β-KL regularization versus input masking. Building on this analysis, they propose Personalized Item Alignment (PIA) to mitigate the adverse effects of masking. PIA has four main advantages, which are preserving instance information, stabilizing the geometric pathway, promoting meaningful global mixing, and requiring no test-time burden. Performance improvements are reported on three benchmark datasets and an Amazon A/B test.", "questions": "- PIA targets the *average* of the item anchors that a user likes. However, when a user has diverse interests (e.g., 50% action movies, 50% romance movies), the *midpoint* between these two preferences may represent a meaningless (non-existent) preference. Isn't there a risk that this 'average' centroid distorts the representation of users with multi-modal interests?\n- How does the each component: item alignment, variance shrinkage, and λ_A scheduling, contribute towards claimed improvements? \n- Table 3 shows a 2.72% recall improvement for the [5-10] interaction group, but is this really due to global collaborative signals? By definition, cold-start users have small S_x, which means the item centroid ē_x has low reliability—how does PIA help in this case?", "limitations": "", "rating": 4, "confidence": 4, "soundness": 2, "presentation": 2, "contribution": 1, "strengths": "- The approach is well-motivated theoretically. \n- The claims have been supported through proofs which is provided in Appendix. \n- A/B testing has been conducted on industry-level datasets with real users.", "weaknesses": "- The paper lacks readability. Some of the terms are quite new, and hasn’t been defined well in the manuscript. For instance, local collaboration/ global collaboration are not well established terms in VAE-CF literature. Yet the authors claim that this is the first work to systematically analyze the collaboration mechanisms. \n- The statement on the base model is somewhat misleading. In line 105-106, the authors claim that the random binary mask is used across the VAE-based CF with citations. However, none of these works uses random masking. \n- The literature review is missing many representative VAE-based models. The baseline models are also missing models with strong performances. \n- PIA only exhibits modest improvements even on the conventional VAE CF models. These early models can be improved with less efforts compared to recent models. Is PIA applicable to recent VAE-based models?   \n- Computational complexity hasn't been discussed. No ablation study has been performed.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "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": "ECY4NHCSRk", "reviewer": "Reviewer_Mp4J", "summary": "In this paper, the authors theoretically analyzed two existing mechanisms, $\\beta$-KL regularization and input masking, on their effect of trade-off between local and global collaboration. To address shortcomings of these methods, the authors proposed Personalized Item Alignment (PIA), which stabilized the latent geometry without the risks of over regularization. The authors presented offline and online experiments and visualizations to validate the effectiveness of PIA.", "questions": "The effect of PIA seems to vary significantly with the encoder model, as provided in the offline results. Can the authors provide more results and discussion?", "limitations": "", "rating": 2, "confidence": 3, "soundness": 2, "presentation": 2, "contribution": 3, "strengths": "This paper provides a deep theoretical dive into how collaboration occurs in VAE-CF models. The derivation of latent sharing radius (Theorem 2.3) presents a formal mechanism to understand the interplay between users when updated. The analysis of the trade-offs achieved by $\\beta$-KL regularization and input masking is insightful for practitioners to understand and optimize these methods.\nThe proposed Personalized Item Alignment (PIA) is clean and intuitive. By introducing item anchors in latent space, PIA makes use of the semantics of user-item interaction records and mitigate the drawbacks of existing methods.", "weaknesses": "The experiment results are not very persuasive. The public datasets are relatively out-of-date so less convincing. The online results, though significant in uplift, draw comparison to a weak statistical baseline, which barely supports the validation.\nIntroducing learnable item anchors increases the number of parameters of the model. This is probably a huge gap as the size of item corpus is often quite large in realworld recommender systems. In this case, the experiments would be unfair.\nThe idea of introducing item anchor seems closely related to VQ-VAE, which is not cited nor discussed in this paper.\nThe provided visualization demonstrates the ability of PIA to yield more structured latent space under input corruption. However, there is no evidence showing the drift introduced by PIA encourages global collaboration between \"far but related\" users, which is the motivation of the idea.\nI believe the readibility of the paper would be improved with more visualization and case studies.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "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:

Decision: Accept (Poster)