Path-Enhanced Contrastive Learning for Recommendation
Authors: Haoran Sun
Fei Xiong
Yuanzhe Hu
Liang Wang
Venue: NeurIPS 2025 spotlight ()
Keywords: graph mining
recommender systems
self-supervised learning
Contrastive Learning
Data Augmentation
Primary area: applications

Abstract: Collaborative filtering (CF) methods are now facing the challenge of data sparsity in recommender systems. In order to reduce the effect of data sparsity, researchers proposed contrastive learning methods to extract self-supervised signals from raw data. Contrastive learning methods address this problem by graph augmentation and maximizing the consistency of node representations between different augmented graphs. However, these methods tends to unintentionally distance the target node from its path nodes on the interaction path, thus limiting its effectiveness. In this regard, we propose a solution that uses paths as samples in the contrastive loss function. In order to obtain the path samples, we design a path sampling method. In addition to the contrast of the relationship between the target node and the nodes within the path (intra-path contrast), we also designed a method of contrasting the relationship between the paths (inter-path contrast) to better pull the target node and its path nodes closer to each other. We use Simplifying and Powering Graph Convolution Network (LightGCN) as the basis and combine with a new path-enhanced graph approach proposed for graph augmentation. It effectively improves the performance of recommendation models. Our proposed Path Enhanced Contrastive Loss (PECL) model replaces the common contrastive loss function with our novel loss function, showing significant performance improvement. Experiments on three real-world datasets demonstrate the effectiveness of our model.

Path-Enhanced Contrastive Learning for Recommendation
Haoran Sun
Fei Xiong
Beijing Jiaotong University haoran.. sun@bj tu. edu. en
Beijing Jiaotong University xi ongf@bjee tu. edu.
Yuanzhe Hut
Liang Wang
Institute of Software Chinese Academy of Sciences yuanzheliscas.dt ac.
Northwestern Polytechnical University 1iangvang01230gaaill com
Abstract
Collaborative filtering (CF) methods are now facing the challenge of data sparsity in recommender systems, In order to reduce the effect of data sparsity, researchers proposed contrastive learning methods extract supervised signals from raw data. Contrastive learning methods address this problem by graph augmentation and maximizing the consistency of node representations between different aug- mented graphs. However, these methods tends to unintentionally distance the target node from its path nodes on the interaction path, thus limiting its effectiveness. In this regard, we propose solution that uses paths as samples in the contrastive loss function. In order to obtain the path samples, we design a path sampling method. In addition to the contrast of the relationship between the target node and the nodes within the path (intra-path contrast), we also designed a method of contrasting the relationship between the paths Linter-path contrast) to better pull the target node and its path nodes closer to each other. We use Simplifying and Powering Graph Convolution Network (LightGCN) as the basis and combine with a new path-enhanced graph approach proposed for graph augmentation. It effectively improves the performance of recommendation models. Our proposed Path Enhanced Contrastive Loss (PECL) model replaces the common contrastive loss function with our novel loss function, showing significant performance im- provement. Experiments on three real-world datasets demonstrate the effectiveness of our model.
Introduction
In the era of information explosion, recommender systems play crucial role in identifying users' preferences and delivering personalized experiences effectively [18). Among the various techniques,
CF 21 has become cornerstone approach to generate recommendations utilizing implicit feedback such as clicks, purchases, and comments. The core idea of CF methods is that users with similar behaviors are likely share similar preferences. CF methods are broadly classified into memory- b5sed 4 120) and model-based approaches 17 TO 12). Recent research trends focus on model- based CF techniques due to their superior performance and scalability. However, methods are often challenged by the data sparsity problem. To address this, researchers proposed various models
to enhance the representations users and items by using additional information[10 25 13 27 [5)
For instance, models like SVD++ incorporate implicit feedback from user-item interactions to refine
"oorreponnding author
I 'These authors contributed equally to this research.
39th Conference on Neural Information Processing Systems (NcurIPS 2025).

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predictions 12], while LightGCN effectively captures higher-order collaborative signals to improve the embedding quality of users and items
Recently, contrastive learning has emerged as powerful paradigm in representation learning, achiev- ing remarkable success in various domains such computer vision 3 7 and natural language processing [6] [28 311. By leveraging self-supervised signals, contrastive learning can effectively extract meaningful features from large-scale unlabeled data, offering promising solution the prob- lem of data sparsity (2 233] Given its ability to provide additional supervisory signals, an increasing number of studies 14 26 331 have applied contrastive learning techniques to recommender systems, resulting in significant improvements in recommendation performance. The core concept behind contrastive learning creating additional supervised instances and applying a self-designed task to this augmented data, thereby tackling the challenge of data scarcity. Specifically, we randomly select node from the interaction graph to be the target node and paths extending from the target node as center paths. Data augmentation is achieved by perturbing the interaction graph. During training, the augmentation of the target node represented as its positive samples and other nodes as negative samples. However, disturbing interaction graph may generate irrelevant connections or discard critical training information, thereby weakening the reliability and overall performance of contrastive learning models. Moreover, treating other nodes negative nodes will unintentionally distance the target node from its node neighbors along the interaction path. However, these neighbors exert positive influence on the target node.
To overcome these challenges, we propose a path-enhanced contrastive learning method (PECL) that focuses on path-level representations, offering neighborhood-basee perspective for contrastive learning approaches. We first propose an intra-path contrastive learning strategy that effectively selects nodes for contrastive learning, so that the target node is pulled closer to the nodes along the interaction path. Nevertheless, the semantics of a single node can often be diverse or ambiguous, which motivates to further design an inter-path contrastive learning method. Since path consists of multiple sequentially connected nodes, naturally encodes contextual constraints and thus helps to mitigate noise. To enable inter-path contrast, we devise general path sampling strategy that selects representative paths extending from the target node as positive samples of the center path, thereby enabling the model to align semantically similar paths more effectively.
In summary, our main contributions are summarized as follows:
We propose an efficient path contrastive learning model that utilizes multiple positive path samples to guide the updating of the representation of the center path. The experiments show that multiple positive samples together influence the representation of the center path and enhance the recommendation performance of the model.
We design a path sampling method that can sample paths similar to the center path as positive samples. The positive samples provided allow model to perform inter-path contrastive learning, which in turn brings the target node closer to its collaborative nodes on other paths.
By utilizing three datasets derived from actual real-world situations, we conducted empirical research that revealed a distinct advantage of PECL compared state-of-the-art baseline models.
2 Related Work
Graph Neural Network Based Recommender Systems. Graph Neural Networks (GNNs) have emerged as a powerful tool for recommendation tasks, particularly because they can capture intricate relationships between users and items in graph-based setting. Traditional collaborative filtering (CF) models, such as matrix factorization, have been widely adopted in recommender systems. However, these models often struggle with data sparsity and fail to capture complex higher-order interactions between users and items. GNN-based models, such as NGCF (Neural Graph Col- laborative Filtering) (25), address these limitations by leveraging message-passe passing mechanisms to propagate information across the user-item graph. NGCF captures both direct and indirect collab- orative signals, making it particularly suitable for recommendation tasks in sparse data scenarios. Despite the improvements offered by NGCF, its heavy reliance on deep message-passiene paaagggg layers and non-linear activations leads to potential over-smoothing and overfitting, making the model in- efficient and computationally expensive. LightGCN addresses these issues by simplifying the

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architecture Sehioviture-removingg the non-linear activation functions and transformation parameters typically used in GNN models. This reduction in complexity not only improves computational efficiency but also enhances the model's ability to focus on essential collaborative signals. However, such aggregation- modeling paradigm does not explicitly account for the sequential or semantic continuity of nodes along interaction paths.
SuperSupe Learning Techniques in Recommender Systems. In recent years, Self- supervised learning has become an important technique in enhancing recommendation models, especially when dealing with sparse or noisy data. In contrastive self-supervised learning, the goal is to pull positive samples closer together while pushing negative samples further apart, thus improving the robustness of learned representations. SimGCI,33 proposes contrastive learning framework for graph-basel recommendation models, where the authors introduce augmented views of users and items enhance the model's is ability to distinguish between relevant and irrelevant interactions. By incorporating contrastive loss, SimGCL not only improves the robustness of the learned embeddings but also helps address the issue of negative sampling, which is often problematic in collaborative filtering- bitering-based systems. Furthermore, NCL(14] enhances this approach by clustering users and items into meaningful groups, allowing the model to leverage these clusters as positive samples. This clustering technique, combined with contrastive loss, significantly improves the quality of the learned representations, particularly in sparse scenarios. IHGCL leverages meta-paths in heterogeneous graphs to extract user intents and enhances recommendation via intent-intent and intent-interaction contrastive learning. However, existing work does not fully consider the relationships between target nodes and nodes the interaction path in recommendation scenario. In this paper, use contrastive learning to interpretively model these potential node relationships.
3
The PECL framework
In this section, we introduce the PECL framework. The PECL. framework is composed by four parts: graph collaborative filtration backbone LightGCN, path node-aware contrastive learning method, path sampling network and the path-aware contrastive learning method. The overall framework is shown in Fig 1
3.1 Graph Collaborative Filtering Backbone
In PECL, we use LightGCN as the backbone model. The LightGCN model focuses on effectively capturing high-order collaborative signals in user-item interaction graph by leveraging a simplified GCN structure. Given bipartite graph g EV.E), the node set V = 2/ U I includes both users and items, and the edge set & = [[u, Rui = 1} captures observed interactions that connects users and items. LightGCN updates node embeddings over i layers, where each layer aggregates information from increasingly distant neighbors. The embedding at the k-th layer, HK represents knowledge collected from k-hop neighbors. To counteract the over-smoothing commonly observed in deep GCNs, LightGCN constructs the final node representations by combining embeddings from all layers, including the input embeddings:
H H() + H() + (2 +
+ o (K)
on H +aIHH 0)) +az H
+ ak A K (()
A . AD
(2)
where A is the symmetrically normalized matrix and D is (M + [Z] x (14 + IZ) diagonal matrix. The 0-th layer embedding matrix ()) e [[((++/Z)) where E is the embedding size.
These final embeddings represented by h, and h;, respectively. The predicted interaction score between user u and item i is then computed using the inner product operation:
used to represent users and deess-speifiiallyy, user and item i are
fui haghT
(3)
The model is trained using ranking loss function, encouraging observed interactions (positive samples from R*) to have higher scores than unobserved ones (negative samples from R ), with a sigmoid function a (x) 1/(1 + e=>) used to map predictions probabilities:
LAPR
Σ
Σ
log(a - -fu))
wed
FR JER
3

---

Encode
Postive Noilss
Contrastive
Or
Negatbe Node
Cauta
Lintr
Negothan Paths
H
LightGCN
Car
U- Interaction Graph
Figure 1: Method framework.
3.2 Path Node Aware Contrastive Learning
Existing graph augmentation contrastive learning methods mainly augment graph collaborative filtering by utilizing similar structural neighbors 14 22]. These methods ignore the internal nodes of the interaction paths, however, in fact, the nodes inside the interaction paths also have influence on the target nodes. In order take full advantage of contrastive learning, we argue that when constructing the contrast loss of a target node, it is also important to consider the representatives of nodes inside its interaction path as positive samples. Computing nodes on paths may make computation too large, we use the random walk with restart for path sampling based on length classification proposed by Xiong et al. (30]
Pry
restart;
p
random selection of neighbors,
[Nnesghorll
where Nneighbor denotes the set of neighbors and the probability of the next move in a random walk is governed by two distinct scenarios. We obtain our set of center paths P. of the target node utilizing the above sampling approach. In order to find the positive nodes n of the target node w.we define positive node selection method:
V (n/a l P}|}
(6)

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where P denotes the path and a is a hyperparameter that determines the minimum number of positive nodes in sample paths. Then, other nodes are treated as negative samples. During the contrast loss construction process, specifically, we learn the embeddings of the target nodes themselves and the sampled intra-path nodes by contrast. Building on the principles InfoNCH([6]] we introduce an intra-path contrastive learning framework aimed at encouraging closer alignment between related representations by reducing their mutual divergence:
exp(h, /T)
Cintra
Σ Log
Σ
(xp(h(h)))))
BE
nEVT
where h denotes the embedding vector of the node and denotes the negative node.
3.3 Preparation for Path Aware Contrastive Learning
This section will introduce how find sample paths of the path-aware contrastive learning. Our ultimate target is to bring the target node on the center path closer to the nodes on the positive path through the path. Random walk sampling with the target node the starting point is an option. However, since we define our own way of obtaining the center path, the path obtained by random walk sampling is not guaranteed to have high similarity with our center path, since it only determine that it has the same starting point. The meta-path sampling approach is not available for the recommendation task we study because we only have a simple user-item binary graph. To our knowledge, few studies have performed contrastive learning between paths, while our study has center paths that we define, so we need a corresponding positive path sampling method which can ensure that the computation is not too large and the similarity is also good. Meanwhile, negative sampling is performed other paths.
To better capture the time dynamics and structural patterns in user-item interaction graphs, we propose two-stage path sampling method termed Target-guided Random Walk. This strategy integrates deterministic time traversal with stochastic exploration, enabling sampled paths to reflect both the structured information flow and the inherent uncertainty of user behavior.
Formally, each edge iu paths P. of the target node v, we define center path C' = (v1, (2,, .... Un), C' E Pu. constructed by following the time interaction sequence such that:
is associated with a timestamp t(u, T. For the set of center
t(v, U+41) S (11411 U(42), Vi= I..,...,
(8)
This path reflects a plausible trajectory of user or item interaction based on actual historical data.
We divide the sampling process into two stages to obtain path C's positive path set P
Stage 1 (Target-guided traversal): We deterministically follow one center path C' E Po from the start node e1 to the intermediate node vg, where / is hyperparameter controlling the number of steps before random walking. The partial path is denoted as:
p()) (V1, U2, u2, (1))
Stage (Conditional random walk): Starting from node ug, we conduct time-aware conditional random walk to generate the remaining nodes. At each step j. the next node 2/ 1 is sampled from the neighborhood N(²)) based on temporally-biasee transition probability TP(c)):
(P())) = Softmax,
D) w witch,.))
(10)
where (((r), = t(05, last captures the relative time gap, and wi('), v) denotes a tunable edge
weight that can incorporate interaction frequency node similarity. The second-stage path p(2) is defined as a sequence of nodes generated via time-aware random walk process:
p(2) = (v/441...., vk),, where V/411 ~ TP(())
for j = B..... nn
(11)
The final sampled path defined as:
P p()) p(2) (u,,..., Ug 2/
(12)
This hybrid sampling mechanism ensures that the sampled paths maintain time consistency with real- world interaction sequences while introducing stochasticity to enhance path diversity and coverage.
5

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3.4 Path Aware Contrastive Learning
The inter-path loss introduced this section leverages representative paths extending from the target node as positive counterparts of the center path, enabling the model to align semantically similar paths and mitigate the ambiguity of single-node semantics.
To perform inter-path contrastive learning, we need to encode the paths. Since we are sampling the paths based on time series, we consider incorporating time information in the encoding of the paths. We use Temporal Context Encoding to get the encoding of the timestamps We show specific coding methods in A.5 Since the timestamp the recommender system is an attribute of the user-item relationship, i.e., is a time code corresponding to each edge on the graph. So it is necessary to choose a suitable way to fuse node and edge information. In this paper, the Hermitian inner product is chosen the interaction between node embedding and time embedding. The rotation on the complex plane maintains the invariance of the relationship between the node embedding and that the distance between the two in the complex plane does not change
the time embedding, due to the rotation. Normalizing the time embedding and then doing the Hermitian inner product operation with the node embedding, i.e., rotating the node embedding by certain angle in the complex plane. For node embeddings and time embeddings, first treat the first half of the dimension of the embedding vector the real part reall erraa and the second half of the dimension as the imaginary part " emmo Perform the Hermitian inner product with the edges from the farthest node of the path towards the center node in the following order:
Wp Fo
w, ;-1 to @ egeal + wi-1 C ej img img
1 = - roal @ img
img
+ w, @ geal
(13)
w 10 real || 1
iigg
Wi = 2, + w/-11
hp
Wn
where @ denotes the elemental product of vectors, is the intermediate computation, denotes the order nodes on the path, E [o, T.). and I, is the path length.
Similar to Eq the contrast loss between paths is defined as follows:
Linter =- - Σ log Σ cxp(hc(hp)"/1)
(14)
Esep, L.ER (hs) /
WCV CEP
PEP:
3.5 Gradient Analysis and Comparative Study of Contrastive Losses
Contrastive learning enhances representation learning by encouraging proximity between positive samples and separation from negatives. In this section, provide detailed gradient derivation for the intra-path and inter-path contrastive losses and analyze their roles in optimization.
Gradient of Intra- Intra-path Contrastive Loss. the target node embedding, we differentiate the Eq[7]
For the gradient of the intra-pati loss with respect to
Linnra
exp(hohT, hn +
exp(hahh/ hg
Σ
(15)
Oh
Zintra
Zintra
nEVE
jev
where Zintra is the partition function given by:
Zintra Σ exp(h,h)77))
Σ exp(hinhTTT)
(16)
EEV
JEV
The gradient analysis reveals that the intra- parr--pathhaa loss encourages positive nodes closer to the target node while pushing negative nodes away. The strength of this attraction-eepulsion mechanism modulated by the temperature parameter

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Gradient of Inter-path Contrastive Loss. Recalling the inter-path loss from Eq 14 the gradient w.r.t. with respect the center path embedding hc:
we compute
iiner
exp(hchip/T) hp
exp(hohy//T) hJ
Σ
+
Σ
(17)
Ōhc
Zinter
Zimter
PEPO
JEP
where Zinter is the partition function defined as:
Zinter
Σ
exp(holip7)) + Σ
exp(hchl//
(18)
PEPÉ
JEP
The gradient analysis indicates that the inter-path loss minimizes the discrepancy between the center path and positive paths while distinguishing them from negative paths.
From the gradient perspective, the intra-path loss directly updates node embeddings through their pairwise similarities weighted by influence functions, resulting in localized embedding refinement. In contrast, the inter-path loss updates path-level representations that indirectly influence the node embeddings through path encoding networks, promoting global consistency across paths. Combining these two losses yiclds a complementary synergy: intra-path loss strengthens local neighborhood coherence within sampled paths, while inter-path loss encourages global structural alignment across diverse paths. This joint optimization facilitates learning robust and discriminative representations for recommendation tasks. We provide further analysis in A.6
3.6 Model Training
In this section, we will present the overall loss of the model. As with most contrastive learning methods, our model loss composed of the BPR loss for interactions between user items and the contrastive learning loss.
L = LBAr + X Linaa + X2 An
As 1
(19)
where [}, A2, Aal denotes the regularized penalty coefficient and @ corresponds to the parameters of the model. We give the values of lambda in A.7
4 Experimental Results
4.1 Experimental Settings
Our experiments utilize three publicty available, real-world zon zon-that offer rich information, including both user-item ratings and the corresponding timestamps of user interactions. Each dataset divided into training and test by randomly selecting 80% of the rating entries for training purposes, while the leftover 20% is reserved to evaluate the model's performance during testing. To assess the effectiveness of our recommendation approach, we rely on two widely adopted evaluation metrics: Recall @ K and NDCG@ K. In our experiment, K is set 10 and 20. To evaluate performance differences, we conduct a comparison between PECL and nine state-of-the-aan recommendation approaches: SimGCL (3) SGL[26),SCFF22 LightGCN
Ciao and Ama-
25 SelfCF 34), SEPT (2), GAIPSRec 30
[HGCL
4.2 Comparative Experiments
To validate the effectiveness and generalizability of the proposed PECL, we conducted compre- hensive performance comparison against several baseline models using three distinct datasets. We compute the average results 5 times for each dataset. The results of these experiments are presented in Table I and the key findings are summarized as follows: The experimental results demonstrate that PECL outperforms all baseline models in both Recall@1 K and NDCG@K K across the evaluated datasets. In particular, PECL achieves significant gains over best-performing baseline models in terms of NDCG@ 10 on the Ciao, with improvement rate of 4.52%. The improvement can be attributed to the following key factors: (1) PECL generates multiple complementary nodes and paths through its contrastive learning framework. These nodes and paths are not simply based on

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Datasets
Metrics
NGCF
SGL
LighTCCN
SEPT
SafCF
SanGEL
SCCF
GAIPSRec
IHGCL
PECL
NDCG@10
0.3279
0,3645
0.3542
0,3470
0.3629
0,3667
2DCG@20
0,3115
0.3981
0.3462
0.3475
0,3523
0.3274
0.3985
0,4006
0.4024
ML-IM
Recal
0.1275
0,1429
0,1440 S44T4
0.1357
0.1514
0,1542
0,1437
0.1582
0.1001
0.1676
2ecall@
0.2161
0,2510
0,2419
0.2218
0.2259
0,2373
0,2501
0.2514
0.2565
0.2605
NDCG
0.0298
0.0376
030354
0.0354
0.0371
0.0369
0.0297
0.0362
0.0364
0.0393
Ciao
2DCG@20
0.0353
0.0447
0.0435
0.0368
0.0451
0.0471
0,0360
0.0473
0.0450
0.0486
Recall 10
0.0338
0.0483
0.0420
0.0435
0.0439
0,0476
0.0424
0.0481
0,0476
0.03%
2ccall@20
0.0520
0.0713
0.0687
0.0678
0.0709
0.0721
0.0663
0.0728
0.0691
0.0745
NDCG$10
0.0785
0,1091
0.1016
0.1013
0.1054
0,1021
0.1086
0.1105
0.1132
0.1169
NDCG@20
0.0913
0.1256
0.1195
0.1243
0.1240
0.1354
Amazon
Recall 10
0,0813
0.1135
0. 1084
0.1044
0.1089
0,1145
0,10
0.1128
0.1193
0.1241
Recall@20
0.1257
0.1501
0.1528
0.1486
0.1548
0,1691
0.1494
0.1664
0.1764
0.1820
Table
1: NDCG and Recall of PECL and baseline models.
random augmentations, but on the rich paths formed through both direct interactions and higher-order connections within the user-item graph. This mechanism ensures that PECL can effectively learn diverse representations that better capture the complex relationships between users and items. (2) Unlike traditional recommendation models that focus solely on direct user-item interactions, PECL introduces novel contrastive learning strategy that incorporates path-based comparisons. By lever- aging multiple interaction paths between users and items, PECL ensures that richer and more diverse representations of user preferences are captured. This path-based contrast helps the model discern nuanced patterns in the data, allowing for more accurate recommendations. (3) The combination
of temporal information and collaborative filtering principles enables PECL to balance historical interaction patterns with the evolving preferences users, resulting in improved predictive accuracy and user satisfaction.
When analyzing the performance of all baseline models, it is clear that self eeff-superiieed learning (SSL)-enhanced methods consistently outperform traditional recommendation approaches. This trend especially noticeable in models such as SimGCL and SGL, which incorporate SSL techniques into the learning process. While these methods are useful, they fail to fully capture the complexity of user-item interactions and their higher-order relationships. On the other hand, PECL's path-based contrastive learning directly addresses this issue by comparing different paths within the user-item interaction graph. This allows PECL to learn richer and more meaningful representations.
4.3 Ablation Study
To verify the effectiveness of the core components in PECL,, we conducted ablation studies by designing the following model variants: PECL w/o Inter-Path Contrast(w/o inter): This variant removes the inter-path contrastive learning mechanism. PECL w/o Intra-Path Contrast(w/o intra): This version excludes the intra-path contrast mechanism. PECL w/o Path Sampling(w/o PS): In this variant, we replace our proposed path sampling method with a standard random walk sampling technique. PECL (Full): The complete model incorporating all three components, serving as the baseline for comparison. The performance of these variants is summarized Fig in terms of Recall @ 10, NDCG@ @ 10 on the ML-1M and Ciao.
When the inter-path contrast mechanism is removed, the model experiences substantial performance degradation, with decline of 27.4% in Recall @ 10 on ML-IM. This demonstrates that contrasting multiple paths effectively enhances the model's capability to capture diverse interaction patterns across different user-item paths, leading to more comprehensive and robust representations. The exclusion
344-
16
100E
3022
350
(a) ML- IM N 10
(b) ML- MM Recall @
(c) Ciao NDCG@ 10
(d) Ciao Recall 10
Figure 2: PECL and its variants.
8

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342
42M
347
534015
9201
0%6
(a) cx
(b) 9
(c) T
Figure 3: Effect of hyperparameters on ML-IM.
of intra-pate path contrast also results in noticeable performance drops, particularly in both metrics, where the model shows 7.3% reduction NDCG@ 10 and a 13.7% reduction on ML-IM. This indicates that contrasting within a single path helps the model refine its representations by reinforcing the consistency of the learned embeddings within each path, thus preventing noisy or trivial patterns from dominating. Replacing our path sampling method with random walk sampling (PECL w/o PS) leads declines both Recall and NDCG scores, with a 11.3% drop Recall 10 on ML-IM. This demonstrates that our proposed path sampling strategy is more effective in selecting informative and diverse paths that contribute to more discriminative and expressive user-item representations. PECL w/o PS's decline is least because it does not ablate any contrast loss. The full model (PECL) consistently outperforms all ablation variants, indicating that each proposed component contributes to the overall performance improvement. Notably, the inter-pate contrast mechanism exhibits the most significant impact, highlighting its crucial role in capturing diverse and informative paths.
4.4 Hyperparameter Analysis
To comprchensively evaluate the impact of hyperparameters on PECL performanc, we performed a series of controlled experiments by varying key hyperparameters. Specifically, we focus three crucial hyperparameters: a (Eq 6). B (Eq 9 and 7 (Eqs) 7 14 We conducted these experiments on the ML-IM with NDCG@ 10 and Recall @ 10. Experiments Ciao shown in [..555
We vary a in 21,2,3, 4] to assess how the number of positive nodes influences the model's ability to capture various interaction patterns. As depicted in Fig Fa] increasing the from 1 to 2 improves the performance, with an 4.4% gain in NDCG@ 10 on ML-IM. However, further increasing a to leads to performance decreases. When the value of alpha is too small, the model tends to capture too many positive nodes, leading to overfitting. Conversely, when alpha is too large, the model may fail to capture sufficient path nodes, resulting in potential information loss. Therefore, setting alpha to 2 can effectively balance the model's generalization ability and the capture of path nodes, thereby enhancing the overall performance.
We examine
21,2,3,4, 4, 5) to verify the effect of this parameter on our path sampling method. As shown in Fig 3b) increasing the number of positive nodes generally improves performance, with the optimal performance observed at = 4. further increase ,3 beyond leads to performance degradation. This is likely because excessive positive nodes introduce redundant, diluting the effectiveness of contrastive learning. is worth noting that the performance improvement when changing from odd to even is higher when alpha is less than 5. This is due to the fact that in the user-item bipartite graph, paths grow even lengths with the addition of nodes of the same type, which allows for the learning of more efficient path node information.
We vary 7 in f0.01, 0.03, 0.05, 0.07, 0.09) to investigate its effect on representation discrimination. As depicted in Fi the impact of T is evident in both metrics. When 7 is set to 0.05, the model achieves the highest performance, indicating that a moderate temperature provides balanced contrastive distribution. Setting too low results in overly sharp distributions, making it difficult for the model to differentiate similar paths. Conversely, a higher 7 produces excessively smooth distributions, weakening the contrastive effect.

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5 Conclusion
In this work, we proposed novel path-enhanced contrastive learning framework for recommenda- tion, which leverages the structural information embedded in multiple interaction paths to enhance representation learning. Unlike conventional contrastive learning methods that primarily focus on node-level or edge-level interactions, PECL explores both inter-path and intra-path relationships, effectively capturing richer contextual dependencies among users and items. Additionally, our tailored path sampling strategy mitigates the risk of redundant or noisy paths, enabling more informative contrastive learning signals. Extensive experiments conducted on three real world datasets, ML-1M, Ciao and Amazon, demonstrate the effectivvness of the proposed framework, highlighting the im- portance of path-level contrastive learning and the proposed path sampling strategy. In summary. this study underscores the potential of integrating path-level information into contrastive learning for recommendation tasks, offering promising direction for further exploration. Future work may extend this framework by incorporating adaptive path sampling techniques or integrating additional auxiliary information to further improve recommendation accuracy and robustness.
Acknowledgments
This work has been supported by the Fundamental Research Funds for the Central Universities under Grant 2024YIS203 and the National Natural Science Foundation of China under Grant 62472024.
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A Technical Appendices and Supplementary Material
A.1 Notation and Description
Symbol
Description
U
Set of users
I
Set of items
R
User-item interaction matrix
g
Bipartite graph representing interactions
V
Set of nodes (users and items)
Set of edges (interactions) Node embeddings at layer ls
H
A
Symmetrically normalized adjacency matrix
Pr
Restart probability in random walk
Nenighbor
Set of neighbors
T
Temperature parameter in contrastive loss Path set for node
Po
has hi
Embeddings of user and item i
LBPR BPR loss function
Liotra
Intra-path contrastive loss
Linter
Inter-path contrastive loss
Table 2: Symbols and descriptions used in the PECL model
A.2 Preliminary
CF is foundational technique in recommender systems, designed to identify and suggest items that users are likely to engage with, inferred from implicit feedback such as clicks, purchases, or other forms of interaction. Consider set of users U {u} and a set of items I {i}. The user-item interaction data is captured in binary matrix R E {0, 1) || where an entry R,, 1 indicates that user u has interacted with item i, and R.s 0 otherwise. Using this matrix R. recommendation models aim infer unobserved interactions and predict user preferences.
In recent approaches, GNNs have been leveraged enhance collaborative filtering by modeling the user-item interactions as bipartite graph 9 = (V. E), where the node set V = L/ U includes both users and items, and the edge set = [(u, i) Ru. = 1) captures observed interactions. GNN- based methods learn expressive user and item embeddings by recursively aggregating information from neighboring nodes in the graph. Typically, this process involves two major phases: infor- mation propagation to propagate neighborhood signals, and update operations to generate refined representations:
h AGGREGATEW!) (I E ee(w))) ha UPDATE (1 h ,..,..., .....n(h) (x)).
(20)
where (k) is the updated representation of node u at layer and (u) denotes the neighboring nodes of node
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A.3
Pesudo Code
Algorithm 1: PECL Framework Training Algorithm
Input: User-item interaction graph g = (L4 U., E) Embedding dimension E, number of LightGCN layers K Number of sampled paths per node 5, path length
Two-stage path sampling parameter 3
Number of positive/negative samples N,, Na.
Learning rate v). total training epochs T
Output: Learned embeddings H* for users and items
Initialize embeddings H for all nodes randomly;
2 Precompute normalized adjacency matrix A; for epoch to 7 do
// LightGCN Embedding Propagation ()) - initial embeddings;
for k to K do
(k) À ();;));
Compute final embeddings:
H'
Σ ag H
where Og are layer weights; // Path Node Aware Contrastive Learning foreach node v E U UI do
P, empty for s to S do
store sampled paths;
10
11
p Sample path of length L from node via random walk with restart (temporal constraints): Add p to Pe:
12
// Construct positive node set V
V ():
14
foreach path in P. do
15
For positive node in p. add u to Vi::
16
Sample N, negative nodes;
17
Compute intra-path contrastive loss Linta using Eq. ( on embeddings H' for node v,
V and negatives:
// Path Aware Contrastive Learning foreach node E 4ZZ do
18
19
Qo < empty set sampled paths; for 8 to S do
20
21
p f- Two-stage path sampling of length from node e: Deterministic walk 3 steps along center path
Conditional random walk for remaining L 3 steps;
Add p to Q.:
22
foreach p; in Q, do
23
Sample negative path pj;
24
Encode path into vector embeddings using temporal context encoding and Hermitian
inner product;
25
Compute inter-path contrastive loss Cinter on pairs;
// Update embeddings
Update O))) using gradients from Liata and Limter via optimizer with learning rate 77;
26
27
return H':
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A.4
Complexity Analysis
In this section, we analyze the computational complexity of the PECL framework, focusing on its main components: the LightGCN backbone, path node-aware contrastive learning, and the path-aware contrastive learning with path sampling.
A.4.1 Complexity of LightGCN Backbone
The LightGCN backbone operates on bipartite graph G (44 U.,E) with [4] users, []] items, and [E] edges representing observed interactions.
At each layer k of LightGCN, the embedding update is sparse matrix multiplication of the normalized adjacency matrix Å with the embedding matrix H(k-1), Since Á has 2| non-zero entries (due to the bipartite graph symmetry), the cost per layer is approximately:
O x E),
(21)
where is the embedding dimension.
For K layers, the total complexity for embedding propagation is:
O(K |8] E).
(22)
Finally, the weighted sum aggregation of embeddings from all layers has a cost of:
(((M4 + [Z] x K x E):
(23)
which is typically negligible compared the sparse matrix multiplications.
A.4.2 Complexity of Path Node Aware Contrastive Learning
The path node-aware contrastive learning module involves:
Random walk with restart path sampling: For each target node v. paths of length are sampled by random walks guided by temporal constraints. Assuming paths per node, the sampling complexity per node is roughly:
O x L).
(24)
Since the random walk step involves selecting neighbors, and the neighbor size is generally small compared to [ or [Z], this step is efficient.
Positive node selection and influence computation: For each node the positive node set VJ is constructed by checking path membership. This involves checking paths of length thus:
O(S x L).
(25)
Contrastive loss computation: The intra-path contrastive loss in Eq. involves computing dot products between the target node and positive nodes, and between the target node and all negative nodes. Let Np | be the number of positive nodes and N,, the number of negative samples per node. The cost per node is:
O(NN, + N.) x E).
(26)
Typically, Np and N,, are kept small by sampling maintain efficiency.
Overall, the complexity of this module
O(KI + IZ]) x (SxL+ + No) x E).
(27)
A.4.3 Complexity of Path Aware Contrastive Learning with Path Sampling The path-aware contrastive learning involves:
22

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Two-stage path sampling: 'The first stage deterministically traverses 3 nodes along the center path, costing:
(
(28)
The second stage performs conditional random walks of length L - 3, each step involving softmax over the neighbors. Assuming average degree d, the complexity per step is:
O(d),
(29)
thus for the random walk:
O[(L 3) d).
(30)
The total sampling complexity per path is:
O + (L B) d).
(31)
Path encoding and contrastive loss: Encoding path of length L. using temporal context encoding and Hermitian inner products involves:
OLL E))
(32)
operations per path.
The inter-path contrastive loss computes similarity between pairs of paths or between center path and positive paths. If M positive paths are sampled per center path, the cost per target path is:
O(M L E).
(33)
Considering all target nodes and their sampled paths, the total complexity is approximately:
0((14) + (Z) x (S x (3 + (L 3)d) + M x L x E)).
(34)
A.4.4 Summary
The overall computational complexity of PECL is dominated by the LightGCN embedding propa- gation and the path-aware contrastive learning components. Given typical sparse user-item graphs where [8] >> [4]| + [Z], and carefully controlled sampling parameters S, L,, 3, M, Np. and Nn, the model remains scalable and efficient for large-scale recommendation tasks.
A.5 Encoding of Timestamps
The time embedding is computed follows:
{{
timestamp 2k/d k%2 0
sin
[k]
10000
(35)
cos
timestamp
10000
2(k-1)/4 1)/d
11%2 + 0
where certain dimension of temporal embedding e, d denotes the dimension of temporal embedding, and timestamp denotes the timestamp. The model can learn certain temporal dependencies of information dissemination paths through the temporal context of t.
A.6 Comparison of the Two Loss Functions
Aspect
Intra-path Contrastive Loss
Inter-path Contrastive Loss
Granularity
Node-level
Path-level
Positives Definition
Nodes frequently appearing in paths
Paths with spatiotemporal consistency
Optimization
Pulls nodes closer within same path Lower (scales with node set)
Pulls similar paths together, separates others Higher (depends on path sampling)
Computational Cost
Expressiveness
Local semantic focus
Global structural discrimination
Table Comparison the Two Loss Functions
The gradient expressions of both losses show common structure: positive embeddings attract while negative embeddings repel. The interaction between these two contrastive losses provides
23

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multi-level optimization strategy: the intra antra-path loss fine-tunes local relations between nodes, while the inter-path loss preserves the global path consistency. The balance between these gradients is controlled by the temperature т, which affects the sharpness of the similarity distribution. Both intra-path and inter-path contrastive losses are designed to improve the quality of node representations by leveraging structural information in the user-item interaction graph, but they operate at different granularities:
Intra-Path Loss focuses on the local structure within a single path by contrasting the target node against nodes inside its sampled paths. It captures fine-grained relationships and encourages tight clustering of nodes that co-occur frequently within interaction paths. This helps the model learn nuanced user-item correlations informed by intermediate nodes the paths.
Inter-Path Loss, on the other hand, operates at the path level by contrasting entire paths against each other. This loss mitigates the randomness and potential noise introduced by path sampling by encouraging the model to pull positive paths closer and push apart negative or unrelated paths. It effectively smooths the representation space by aligning semantically or temporally related paths.
A.7 Gradient Normalization Strategy for Balancing Loss Terms
To ensure balanced optimization when combining the BPR loss with contrastive components, adopt a gradient normalization strategy to determine the weighting coefficients A1 and X2 in the total loss Eq 19 This strategy ensures that the gradients of all loss components have similar magnitudes during backpropagation, thereby avoiding dominance by any single term. The weighting coefficients computed as follows:
VoCBPR| 122
V l2
A1 V l
A2
(36)
Ve
Here, O denotes the full set of model parameters, and V Ve is the gradient of loss component L; with respect to @ Each gradient norm computed as:
ac 2
VoCill2
Σ PEB
(37)
Op
To reduce the variance caused by mini-batch noise, we optionally apply exponential moving average smoothing over multiple batches:
g = aa. 9; (1) + (1- a)- J. (t-1)
(38)
where a E [0.9, 0.99] is the decay rate, and 9," denotes the raw gradient norm at batch t.
This normalization-hant based tuning of X₁ and A2 leads to more stable convergence and improved model performance by balancing the optimization pressures from different loss components.
A.8
Experimental
A.8.1
Device
All experiments conducted are performed with Intel(R) Xeon(R) Bronze 3204 CPU @ 1.90GHz, Tesla A A100, and 256GB memory, running the Ubuntu 20.04.4 LTS operating system.
A.8.2 Datases
We present information on the three real-world datasets use in Tabl
24

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ML-1M
Ciao
Amazon
Number of users
6,040
101,998
6,170
Number of items
3,706
5,441
2,753
Number of ratings
1,000,209 95.53%
268,975
195,791
Sparssity
99.95%
98.85%
Table Features of the evaluation datasets
A.8.3 Baselines
SimGCL introduces contrastive learning into graph collaborative filtering by generating per- turbed graph views and maximizing agreement between them. It effectively enhances graph- based recommendation by mitigating oversmoothing issues.
SGL[26 employs contrastive learning to leverage both graph structure and node attributes, creating multiple views of the graph to learn robust user and item embeddings.
SCCF unifies contrastive learning and collaborative filtering by jointly optimizing self-supervised signals and recommendation loss, enhancing robustness and generalization.
Ligh simplifies traditional GCNs by removing unnecessary components such as feature transformation and nonlinear activation, focusing purely on message passing to improve recommen- dation performance.
NGCF (25) integrates user-item interaction data into graph neural networks, allowing for richer and deeper embeddings that capture higher-order connectivity patterns.
SelfCF 34] adopts self-supervised contrastive learning to generate self- augmented views for collabo- rative filtering, aiming to mitigate data sparsity and improve recommendation accuracy.
SEPT leverages contrastive learning to generate positive and negative samples for self-supervised learning, effectively improving collaborative filtering by aligning and contrasting multiple graph views.
GAIPSRec 30 introduces graph attention network that captures high-order neighbor information through a heterogeneous graph sampling and path aggregation mechanism. It leverages attention and gating integrate multi-hop dependencies and mitigate wer-smoothing.
IHGCL[[9) introduces an intent-guides heterogencous graph contrastive learning framework. It leverages meta-path based intent representations with dual contrastive learning and employs a bottle- necked autoencoder to reduce noise, improving recommendation accuracy.
A.8.4 Ablation Study
1. w/b P8
wild PS
0,2605
0.4024
wil intor
0.3645
0.3701
0.30
(a) ML-IM NDCG@20
(b) ML-IM Recall @
Figure 4: PECL and its variants on ML-1M.
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6.42
0.3488
0.09
0,0745
0088
weo Intr
0.73
0,72
0.0719
D.49
0.0463
0.071
0.0708
0.0451
0.070
0.0883
0.011
0.0427
0.088
0.007
D.42
0.099
0.00
(a) Ciao NDCG @0
(b) Ciao Recall @0
Figure PECL and its variants on Ciao.
We supplement the top-20 results from the ablation experimentssFigs 45 with experimental conclu- sions consistent with the main text section.
A.8.5 Hyperparameter Analysis
The experimental supplement for hyperparameters the Ciao dataset is showed in Figs. CM
5.42
REcog Rioa ME1
0.34-
0.0496 00005
0
1078
40 0.0099
0.0771
wh, 0473
N0000010
0.000
0.045
Roco
0.0049
0:80
0.0402
E002
0,0012
3.50
0.0004
0033
3.80
Figure 6: a on Ciao
Figure 7: on Ciao
5091
5017
Recalig
0.0063
0.00
0.0300
0.0382
0.2879
0054
Rocal 1210
3.04
0,0057
0.22
0050
6. 0.0499
0048
5023
0.0471
5022
Figure 8: Ciao
In Fig we can see that the performance growth when alpha changes from to 2 not very much. However, if we fix alpha to can eliminate the positive node sampling work (Eql)), which
26

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reduces certain computational complexity, and this problem can be analyzed specifically in specific scenario.
A.9
Ethic Impact Statements
Our paper uses real-world, publicly available datasets that do not raise ethical impact.
27


Reviews:
[{"review_id": "jRmsRcBIxh", "reviewer": "Reviewer_Gc9N", "summary": "This paper proposes a novel PECL framework for collaborative filtering recommendation. While previous contrastive learning methods focus primarily on node-level consistency using graph augmentation, this work innovatively integrates both intra-path and inter-path contrastive learning strategies to enhance the representation of users and items. Specifically, the authors design a time-aware path sampling strategy and path-level contrastive loss that bring semantically similar paths closer, thereby mitigating issues arising from graph perturbations in conventional methods. Experiments demonstrate PECL’s performance.", "questions": "Q1: Is there a risk of overfitting if sampled paths are highly similar?\n\nQ2:  While ML-1M and Ciao are popular benchmarks, have the authors considered testing PECL on larger-scale datasets (e.g., Amazon, Yelp)? \n\nQ3: Could the authors comment on whether longer or redundant paths may sometimes harm performance?", "limitations": "Yes", "rating": 5, "confidence": 4, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 3, "clarity": 4, "significance": 3, "originality": 4, "strengths_and_weaknesses": "Strengths:\n\nS1: The paper presents a technically sound and well-motivated framework. The derivation of contrastive loss functions, the path encoding design using Hermitian inner products, and the integration of time-aware sampling are all carefully described. Experimental results are thorough and convincing, with statistically significant improvements over recent baselines across multiple datasets.\n\nS2: The contribution is meaningful to the recommender system and self-supervised learning communities. By explicitly modeling both intra- and inter-path relations, the paper expands the scope of contrastive learning in recommendation beyond node-level augmentation. This can inspire further research in structured or temporal-aware contrastive objectives.\n\nS3: The idea of contrasting sampled paths instead of just nodes is a notable and original extension to existing self-supervised learning methods in recommendation. PECL introduces a new level of abstraction by leveraging paths as the unit of contrast, which is both novel and effective.\n\nWeaknesses:\n\nW1: There are occasional grammatical errors and formatting inconsistencies (e.g., duplicated phrases like “effectively extract meaningful features from large-scale unlabeled data effectively”), which can be polished in a revision.\n\nW2: The use of Hermitian inner product in complex space is technically novel, but readers may find it hard to interpret how it improves path representation in practice, especially without visualizations or ablations isolating this factor.\n\nW3: The current framework seems closely tied to bipartite user-item graphs; it is unclear how flexible the method is when applied to more complex graph structures, such as heterogeneous.", "was_revised": true, "final_justification": "The authores have addressed my concerns in the rebuttal. I keep my rating unchaged.", "rebuttal": "We thank reviewer for the constructive comments. We provide our feedbacks as follows.\n\nMain Comments:\n\nW1: Language and Formatting Issues.\nComment: “There are occasional grammatical errors and formatting inconsistencies (e.g., duplicated phrases like ‘effectively extract meaningful features from large-scale unlabeled data effectively’)...”\n\nResponse: We appreciate your attention to language quality. The current manuscript indeed contains occasional issues such as duplicated phrases and inconsistent spacing. We carefully revise the paper to remove duplicated expressions and polish the language throughout. For example, the sentence mentioned will be corrected to “effectively extract meaningful features from large-scale unlabeled data.”; “But this will unintentionally distance the target node from its node neighbors on the interaction path, which will affect the performance of the model.” will be corrected to “However, this will unintentionally increase the distance between the target node and its neighboring nodes along the interaction path, which may negatively affect the model's performance. ” \n\nW2: Interpretability of Hermitian Inner Product.\nComment: “The use of Hermitian inner product in complex space is technically novel, but readers may find it hard to interpret how it improves path representation in practice...”\n\nResponse: Thank you for raising this point. We acknowledge that the use of Hermitian inner product in complex vector space introduces conceptual and practical novelty that deserves more precise explanation.\nThe motivation stems from the need to jointly encode both structural and temporal signals in interaction paths. In recommender systems, especially with timestamped user-item graphs, edge time information encodes behavioral evolution. Traditional dot-product-based aggregation fails to capture how temporal order influences the strength or semantics of user-item interactions along a path.\nThe Hermitian inner product allows us to incorporate directional and temporal bias by rotating node embeddings in the complex plane based on normalized edge timestamps. Concretely:\nEach node embedding vector x is split into real and imaginary parts, corresponding to two orthogonal components of its latent representation.\nEach edge timestamp is encoded into a time embedding e using sinusoidal encoding (Eq. 36), then used to rotate the downstream node representation by a complex multiplication with the prior hidden state.\nThe Hermitian inner product accumulates these complex rotations recursively from the end of the path to the target node, modeling how historical interactions progressively influence the current preference.\nMathematically, this approach can be viewed as applying a temporal transformation kernel to the node sequence, where the influence of earlier nodes is modulated by the time-difference-aware rotation. Compared to dot product or attention-based pooling, the Hermitian operator has the following advantages:\nTime-aware modulation: The same node will have a different contribution depending on when it appeared along the path, allowing the model to distinguish, e.g., early behavior vs. recent behavior.\nCompositional semantics: By applying the rotation recursively, we effectively encode how multiple interactions jointly influence a node's representation over time.\nPhase-preserving aggregation: The Hermitian inner product preserves both magnitude (strength of similarity) and phase (relative position in time), giving richer representational capacity.\nWe conduct an ablation study isolating the impact of the Hermitian inner product (e.g., by replacing it with a standard dot product), to better demonstrate its effectiveness. In our experiments, replacing the Hermitian interaction with dot product results in consistent performance drops (e.g., −2.3% in NDCG@10 on ML-1M), validating that the complex-space formulation is not merely decorative but substantively beneficial.\n\nW3: Generalizability Beyond Bipartite Graphs.\nComment: “It is unclear how flexible the method is when applied to more complex graph structures, such as heterogeneous...”\n\nResponse: We appreciate the reviewer’s insightful comment. While our current experiments are conducted on bipartite user-item graphs, we would like to clarify that the proposed PECL framework is not inherently restricted to this structure. In fact, the underlying methodology—particularly the path sampling strategy and the intra-/inter-path contrastive learning mechanisms—is fully compatible with more general graph structures, including heterogeneous graphs.\nFor heterogeneous graphs, PECL can be extended by incorporating type-aware path sampling (e.g., using meta-paths or schema-guided traversal) and adjusting the contrastive objectives to respect node and edge semantics. The time-aware and structure-aware contrastive principles that PECL is built upon remain applicable in such settings.\nTherefore, we believe PECL offers a flexible and extensible framework that can serve as a foundation for future work in heterogeneous recommendation or general graph-based tasks. We will add a clarification of this point to the revised version.\n\nQ1: Is there a risk of overfitting if sampled paths are highly similar?\n\nThank you for raising this important concern. We agree that excessive similarity among sampled paths may lead to overfitting or reduced diversity in the learned representations. To mitigate this risk, our method incorporates several mechanisms:\nStochasticity in Sampling: Our two-stage path sampling strategy introduces controlled randomness in the second stage via time-aware conditional random walks. This encourages diversity among sampled paths even when they share the same target node.\nTemporal Constraints: By enforcing a time-aware constraint on the directionality of path traversal, we avoid repeatedly sampling structurally similar or redundant paths that differ only trivially in topology.\nHyperparameter Tuning: We have explicitly studied this issue in our hyperparameter analysis (Section 4.4, Figure 3). For instance, increasing the number of positive paths (via α and β) initially improves performance, but further increases lead to diminishing returns or slight drops—indicating the trade-off between informativeness and redundancy. We choose optimal values (e.g., α = 2, β = 4) to balance this effect.\n\nQ2: While ML-1M and Ciao are popular benchmarks, have the authors considered testing PECL on larger-scale datasets (e.g., Amazon, Yelp)?\n\nResponse: We appreciate the reviewer’s suggestion. In response, we have conducted additional experiments on a dataset Amazon, which is widely used in recommendation research and contains rich user-item interactions with timestamps. The experimental results are as follows:\n\nNGCF: Recall@10: 0.0813, Recall@20: 0.1257, NDCG@10: 0.0785, NDCG@20: 0.0913.\n\nSGL: Recall@10: 0.1135, Recall@20: 0.1501, NDCG@10: 0.1091, NDCG@20: 0.1256. \n\nLightGCN: Recall@10: 0.1084, Recall@20: 0.1528, NDCG@10: 0.1016, NDCG@20: 0.1183.\n\nSEPT: Recall@10: 0.1034, Recall@20: 0.1486, NDCG@10: 0.1013, NDCG@20: 0.1156.\n\nSelfCF: Recall@10: 0.1089, Recall@20: 0.1548, NDCG@10: 0.1054, NDCG@20: 0.1195.\n\nSimGCL: Recall@10: 0.1145, Recall@20: 0.1691, NDCG@10: 0.1013, NDCG@20: 0.1243.\n\nSCCF: Recall@10: 0.1029, Recall@20: 0.1494, NDCG@10: 0.1086, NDCG@20: 0.1208.\n\nPECL: Recall@10: 0.1231, Recall@20: 0.1808, NDCG@10: 0.1165, NDCG@20: 0.1343.\n\nQ3: Could the authors comment on whether longer or redundant paths may sometimes harm performance?\n\nResponse: We thank the reviewer for raising this insightful question. Indeed, excessively long or redundant paths can introduce noise, dilute useful signals, or increase representation overlap, potentially harming performance.\nTo address this, our framework incorporates explicit control mechanisms through hyperparameters such as α (positive node frequency threshold) and β (deterministic prefix length), which help regulate the number, length, and diversity of sampled paths.\nAs shown in Figure 3b, we empirically observe that increasing β (i.e., allowing longer deterministic prefix in sampled paths) improves performance up to a point (β = 4), after which further increases lead to performance degradation. This confirms that overly long or redundant paths can negatively affect contrastive learning."}, {"review_id": "OX1BMEbsvj", "reviewer": "Reviewer_Z83u", "summary": "This paper introduces PECL, a novel framework that enhances collaborative filtering by explicitly modeling contrastive signals between and within sampled interaction paths. Unlike prior methods that treat contrastive learning at the node or neighbor level, PECL constructs center paths and mines time-aligned positive paths to form more semantically coherent self-supervision signals. The intra-path loss encourages local consistency between a node and its path neighbors, while the inter-path loss aligns global structure across multiple paths. The authors also introduce a two-stage path sampling mechanism guided by temporal behavior. Experimental evaluations show that PECL consistently outperforms state-of-the-art methods, supported by extensive ablation and hyperparameter analysis.", "questions": "(1) Could the authors provide a rough estimate of training time or memory usage compared to LightGCN or SGL?\n\n(2) Would the model still perform well with a simpler temporal encoding scheme, such as scalar time embeddings?\n\n(3) Since PECL depends on pre-sampled and encoded paths, can the model be efficiently used in an online recommendation service?", "limitations": "yes.", "rating": 6, "confidence": 4, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 3, "clarity": 3, "significance": 3, "originality": 4, "strengths_and_weaknesses": "Strengths:\n\n(1) PECL is built on LightGCN and adopts a plug-in architecture, allowing its contrastive objectives to be easily integrated into other GNN-based recommenders, improving usability and adaptability in practice.\n\n(2) The model’s use of multi-hop paths enhances its ability to represent users and items in sparse environments, making it more robust to data imbalance and cold-start scenarios.\n\n(3) Experiments show consistent improvements over baselines, especially on ML-1M. Ablation studies validate the contributions of each component, reinforcing the method’s effectiveness.\n\n(4) The core ideas—path-based contrast and time-aware sampling—are generalizable, with potential use in temporal graphs, session data, and sequential modeling beyond recommendation.\n\nWeaknesses:\n\n(1) While the method is well-motivated, its reliance on multiple hyperparameters may limit applicability. The paper could benefit from providing practical guidelines or heuristics for tuning these values in new datasets.\n\n(2) The inter-path loss introduces some additional computational complexity. Discussion or benchmarking on runtime and memory usage would strengthen the claims of scalability.\n\n(3) The gains on the Ciao dataset, though consistent, are relatively modest. It would be helpful if the authors could comment on why the performance gap is narrower compared to ML-1M (e.g., sparsity).", "was_revised": true, "final_justification": "The rebuttal is clear and convincing, with helpful clarifications on hyperparameter tuning, computational efficiency, and temporal encoding scheme. The paper proposes a path-enhanced contrastive learning framework that leverages temporal interaction paths to improve recommendation performance through intra- and inter-path objectives. I am satisfied with the authors' responses and willing to raise my score.", "rebuttal": "We thank reviewer for the constructive comments. We provide our feedbacks as follows.\n\nMain Comments:\n\nW(1): While the method is well-motivated, its reliance on multiple hyperparameters may limit applicability. The paper could benefit from providing practical guidelines or heuristics for tuning these values in new datasets.\n\nResponse: We appreciate the reviewer’s thoughtful comment. It is true that our method involves several hyperparameters—particularly α (path node threshold), β (deterministic prefix length), and τ (temperature for contrastive loss)—which play important roles in balancing path informativeness and sampling diversity. To address this, we have conducted a thorough hyperparameter analysis in Section 4.4 and Appendix A.9.6, where we vary each parameter independently and report its effect on performance across different metrics and datasets. Based on these results, we summarize some practical guidelines for tuning: \n\nα (positive node threshold): Set to 2 by default. Lower values (e.g., 1) may overfit on noisy nodes; higher values (>3) risk discarding informative neighbors. A value of 2 works well across both dense (ML-1M) and sparse (Ciao) datasets. \n\nβ (path prefix length): We recommend setting β to be one less than the path length (e.g., β = 4 if L = 5) to ensure both time consistency and stochastic diversity. \n\nτ (temperature): A moderate value (e.g., 0.05) is generally effective; smaller τ leads to sharp, overconfident similarity distributions, while larger τ may weaken contrast signals. \nWe added a summary table of these heuristics in the revised Appendix A.9 for clarity.\n\nW(2): The inter-path loss introduces some additional computational complexity. Discussion or benchmarking on runtime and memory usage would strengthen the claims of scalability.\n\nResponse: We appreciate the reviewer’s suggestion. While it is true that the inter-path contrastive loss introduces additional computation (primarily due to path sampling and encoding), we have carefully designed PECL to remain scalable and efficient. In particular: Efficient Design: We use LightGCN as the backbone for its low computational overhead. The two-stage path sampling is designed to minimize redundancy while maintaining diversity. Path encoding uses a Hermitian inner product structure, which is lightweight and parallelizable. Theoretical Analysis: We provide a detailed computational complexity breakdown in Appendix A.5, showing that the overall complexity scales linearly with the number of nodes and sampled paths, and remains practical under reasonable sampling parameters (e.g., small path length L, limited positive paths per node).\n\nW(3): The gains on the Ciao dataset, though consistent, are relatively modest. It would be helpful if the authors could comment on why the performance gap is narrower compared to ML-1M (e.g., sparsity).\n\nResponse: We thank the reviewer for the thoughtful observation. Indeed, while PECL consistently outperforms all baselines on both datasets, the performance gains on Ciao are relatively smaller compared to those on ML-1M.\nWe believe this difference is primarily due to Ciao’s significantly higher sparsity. As reported in Appendix A.9.3 (Table 4), Ciao has a sparsity of 99.96%, compared to 95.53% for ML-1M. This extreme sparsity leads to:\nFewer meaningful paths available for contrastive learning;\nReduced overlap between users and items, limiting shared structure across paths;\nShorter and noisier paths, which dilute the effectiveness of intra- and inter-path contrast.\nDespite this, PECL still achieves the best performance among all baselines, demonstrating its robustness under severe data sparsity. Additionally, we find that the relative improvement on Ciao remains consistent across all metrics and variants, as shown in our ablation study (Fig. 2c, 2d), further validating the method’s effectiveness.\n\nQ(1): Could the authors provide a rough estimate of training time or memory usage compared to LightGCN or SGL?\n\nResponse: We thank the reviewer for this practical and important question.\nTo provide a rough comparison, we benchmarked PECL, LightGCN, and SGL on the ML-1M dataset using an NVIDIA A100 GPU with 40GB memory. All models were trained using the same batch size (2048) and embedding dimension (64).\n\nLightGCN-13 seconds/Epoch;\nSGL-20seconds/Epoch;\nPECL-25 seconds/Epoch.\n\nCompared to LightGCN, PECL introduces a 2x increase in training time per epoch, primarily due to contrastive losses and path sampling. Compared to SGL, the increase is modest (16%), while achieving stronger performance. The GPU memory usage remains comfortably under 5GB, making the method feasible on most modern hardware.\nWe will add this runtime and memory benchmarking table to the revised Appendix to support our scalability claims. Thank you for encouraging this addition.\n\nQ(2): Would the model still perform well with a simpler temporal encoding scheme, such as scalar time embeddings?\n\nResponse: We appreciate the reviewer’s insightful question. This is indeed an important consideration for improving efficiency and simplifying implementation in practical deployments.\nIn our current design, we adopt temporal context encoding combined with Hermitian inner product, which allows the model to capture directional and cyclic time dependencies along user-item interaction paths. This structure-aware time modeling helps improve temporal alignment across paths, especially for the inter-path contrastive objective.\nWe have conducted a preliminary ablation using scalar time embeddings (concatenated to node embeddings), and found that while performance drops slightly (around 1.8% on NDCG@10 on ML-1M), the model still outperforms most baselines. This suggests that our framework is robust to simpler temporal encodings.In future work, we plan to explore adaptive or learnable time embeddings that balance expressiveness and efficiency. We will also include this ablation in the final version for completeness.\n\nQ(3): Since PECL depends on pre-sampled and encoded paths, can the model be efficiently used in an online recommendation service?\n\nResponse: Thank you for this important question. We fully agree that inference efficiency is critical for online recommendation systems.\nWe would like to clarify that while PECL does rely on path sampling and encoding, these operations are performed only during training to optimize the representations via contrastive learning. During inference, the model does not require any path sampling or temporal encoding. Instead, it simply uses the final user and item embeddings, just as in standard collaborative filtering models.\nAs a result, PECL maintains the similar inference speed and memory footprint as LightGCN, making it fully compatible with real-time recommendation pipelines. We believe this separation of training-time complexity and inference-time simplicity is a key advantage of PECL."}, {"review_id": "LAVpweiQxj", "reviewer": "Reviewer_fMku", "summary": "The paper introduces PECL, a contrastive learning framework for collaborative filtering recommendations. Instead of relying solely on conventional node-level graph augmentations, PECL proposes to use paths—specifically center and positive paths—as the basis for contrastive supervision. Two loss components are proposed: intra-path contrast, which encourages alignment between a target node and its intra-path neighbors, and inter-path contrast, which promotes consistency across semantically similar paths. To facilitate this, a time-aware path sampling strategy is developed. The model achieves strong improvements over state-of-the-art baselines.", "questions": "1. Could the authors report additional contrastive evaluation metrics?\n2. How does PECL compare to non-contrastive recommendation models with complex encoders?\n3. Have the authors considered learning time encodings jointly, rather than relying on fixed features?", "limitations": "yes", "rating": 6, "confidence": 5, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 4, "clarity": 4, "significance": 3, "originality": 4, "strengths_and_weaknesses": "Strengths\n1. This paper offers a compelling advancement in contrastive learning for recommendation. By using interaction paths instead of individual nodes as contrastive units, the model aligns more closely with the actual semantics of user-item interactions. This represents a meaningful shift in perspective and offers a new direction for future work in this area.\n2. The time-aware sampling mechanism is particularly thoughtful, aligning path selection with real-world behavioral patterns. This adds interpretability and practical relevance to the model, making it not only more effective but also more aligned with real-world data dynamics.\n3. The experimental results are robust and well-analyzed. PECL outperforms competitive baselines across all major metrics, and the performance gains on both datasets.\n4. The technical depth and clarity of the paper are its strengths. Despite the complexity of the proposed contrastive losses and sampling strategies, the methodology is described in a step-by-step, reproducible manner, supported by code, formulas, figures, and pseudocode in supplementary materials and appendix.\nWeaknesses:\n1. The experimental evaluation focuses solely on Recall and NDCG, but does not assess Hit Ratio or Precision, which are often discussed in recommender systems.\n2. Although several contrastive methods are compared, the performance gap between PECL and strong non-contrastive methods is not discussed in depth.\n3. The model incorporates timestamps in path sampling and encoding, but it does not explain why the temporal dynamics are fixed through sinusoidal functions.", "was_revised": true, "final_justification": "PECL has demonstrated SOTA performance. After reviewing the rebuttal and other reviewers' comments, I find that all my concerns have been addressed. I believe this paper can promote the development of this field, and thus  I am pleased to increase my score to 6(strong accept).", "rebuttal": "We thank reviewer for the constructive comments. We provide our feedbacks as follows.\n\nMain Comments:\n\nW1: The experimental evaluation focuses solely on Recall and NDCG, but does not assess Hit Ratio or Precision, which are often discussed in recommender systems.\n\nResponse: Thank you for this valuable suggestion. In response, we have conducted additional experiments using Hit Ratio (HR) and Precision as evaluation metrics. The results show that PECL maintains consistent performance advantages over all baselines on both ML-1M and Ciao, confirming that our improvements are robust across different evaluation criteria. We have also evaluated PECL on a new dataset (Amazon). The model achieves consistent gains under all four metrics (Recall, NDCG, HR, Precision), further validating its generalization ability. The results of new dataset are as follows: \n\nNGCF: Recall@10: 0.0813, Recall@20: 0.1257, NDCG@10: 0.0785, NDCG@20: 0.0913.\n\nSGL: Recall@10: 0.1135, Recall@20: 0.1501, NDCG@10: 0.1091, NDCG@20: 0.1256. \n\nLightGCN: Recall@10: 0.1084, Recall@20: 0.1528, NDCG@10: 0.1016, NDCG@20: 0.1183.\n\nSEPT: Recall@10: 0.1034, Recall@20: 0.1486, NDCG@10: 0.1013, NDCG@20: 0.1156.\n\nSelfCF: Recall@10: 0.1089, Recall@20: 0.1548, NDCG@10: 0.1054, NDCG@20: 0.1195.\n\nSimGCL: Recall@10: 0.1145, Recall@20: 0.1691, NDCG@10: 0.1013, NDCG@20: 0.1243.\n\nSCCF: Recall@10: 0.1029, Recall@20: 0.1494, NDCG@10: 0.1086, NDCG@20: 0.1208.\n\nPECL: Recall@10: 0.1231, Recall@20: 0.1808, NDCG@10: 0.1165, NDCG@20: 0.1343.\n\nNGCF: HR@10: 0.0813, HR@20: 0.1297, Precision@10: 0.0596, Precision @20: 0.0463.\n\nSGL: HR@10: 0.0969, HR@20: 0.1501, Precision@10: 0.0633, Precision @20: 0.0491. \n\nLightGCN: HR@10: 0.0936, HR@20: 0.1455, Precision@10: 0.0612, Precision @20: 0.0476.\n\nSEPT: HR@10: 0.0875, HR@20: 0.1392, Precision@10: 0.0605, Precision @20: 0.0459.\n\nSelfCF: HR@10: 0.0927, HR@20: 0.1554, Precision@10: 0.0637, Precision @20: 0.0451.\n\nSimGCL: HR@10: 0.0961, HR@20: 0.1565, Precision@10: 0.0683, Precision @20: 0.0493.\n\nSCCF: HR@10: 0.0921, HR@20: 0.1442, Precision@10: 0.0624, Precision @20: 0.0485.\n\nPECL: HR@10: 0.0989, HR@20: 0.1605, Precision@10: 0.0723, Precision @20: 0.0516.\n\nWe summarize the key findings as follows:\n\nPECL continues to consistently outperform all baselines in both HR and Precision across all evaluated datasets. The relative performance trend is highly consistent with that observed for Recall and NDCG, further validating the robustness and effectiveness of PECL.\n\nW2: Although several contrastive methods are compared, the performance gap between PECL and strong non-contrastive methods is not discussed in depth.\n\nResponse: Thank you for pointing this out. We agree that a more in-depth discussion comparing PECL with non-contrastive baselines would be valuable to highlight the practical advantages of our approach. In Table 1 of our experiments, we compare PECL with non-contrastive methods such as LightGCN, NGCF, and SelfCF. The results show that PECL outperforms these baselines by a clear margin. For example, on ML-1M:\n\nPECL achieves 0.4206 NDCG@10, compared to 0.3542 from LightGCN and 0.3629 from SelfCF.\nOn Recall@10, PECL reaches 0.1676, versus 0.1443 (LightGCN) and 0.1514 (SelfCF).\n\nThese gains can be attributed to several key enhancements in PECL beyond contrastive learning itself:\n\nPath-level modeling: PECL leverages intra- and inter-path structures, which allows it to capture richer, higher-order collaborative signals than point-wise methods. Temporal awareness: By encoding the order and timing of user-item interactions, PECL goes beyond static graph modeling. Multi-view supervision: Even compared to strong embedding-based models, the contrastive signals in PECL provide better generalization by regularizing embedding space geometry.\n\nW3: The model incorporates timestamps in path sampling and encoding, but it does not explain why the temporal dynamics are fixed through sinusoidal functions.\n\nResponse: We thank the reviewer for this sharp and meaningful question. Indeed, the choice of sinusoidal (non-learnable) temporal encoding warrants further clarification. We adopt sinusoidal functions (as used in Transformer’s positional encoding) for the following reasons:\nRelative Temporal Structure Awareness: Sinusoidal encoding allows the model to capture relative distances and ordering between timestamps through a fixed spectrum of periodic signals. This is particularly valuable in path-based modeling, where it is not only the timestamp itself but also how timestamps vary along the path that conveys semantic meaning. Parameter-Free and Stable: Unlike learnable time embeddings, sinusoidal encodings do not introduce additional parameters, which helps improve generalization, especially under sparse or noisy timestamp distributions (e.g., Ciao). They also retain consistency across unseen timestamps without requiring re-training. Alignment with Hermitian Encoding Scheme: Our path encoding involves Hermitian inner products on complex-valued representations, where sinusoidal encodings naturally fit as a way to rotate node embeddings in the complex plane, enabling consistent angular representation of temporal shifts.\n\nQ1: Could the authors report additional contrastive evaluation metrics?\n\nResponse: We thank the reviewer for this helpful suggestion. We have addressed this point in our response to W1, where we include additional evaluation metrics—including Hit Ratio and Precision. We also report results on a new dataset (Amazon) to further validate the effectiveness of PECL. All results are presented in the W1 response for clarity and completeness.\n\nQ2: How does PECL compare to non-contrastive recommendation models with complex encoders?\n\nResponse: We thank the reviewer for this important question. In our current evaluation, we compare PECL with popular non-contrastive models such as LightGCN, NGCF, and SelfCF, which represent the mainstream of efficient GNN-based recommendation models. These methods are widely used and serve as strong baselines in both academic and industrial settings. We acknowledge that there exist non-contrastive models with more complex encoders, including Graph Attention Networks (GAT), RNN-based session models, or Transformer-based sequential recommenders (e.g., SASRec, BERT4Rec). These models typically introduce significantly more parameters and computational overhead to capture sequential or structural patterns. In contrast, PECL is designed to be both lightweight and expressive, and achieves competitive or superior performance without relying on deep or heavy encoders. Its improvements stem from: Path-level contrastive learning, which provides global structural signals beyond local aggregation; Time-aware path sampling, which models user behavior dynamics more explicitly; Efficient implementation, as PECL builds upon LightGCN with minimal additional complexity during inference.\n\nQ3: Have the authors considered learning time encodings jointly, rather than relying on fixed features?\n\nResponse: We thank the reviewer for this thoughtful question. Indeed, using learnable time encodings is a promising alternative to fixed sinusoidal encodings, and we agree that it can potentially enhance temporal adaptability. In our current design, we adopt sinusoidal temporal encoding primarily because: It captures relative temporal patterns (e.g., time intervals and ordering) without introducing additional parameters; It ensures stable generalization to unseen timestamps, especially in sparse datasets where many time points appear only once; It integrates naturally with our Hermitian product path encoder, where time is treated as a phase component in the complex space. \n\nThat said, we recognize that jointly learning time representations could improve flexibility and allow the model to better adapt to dataset-specific temporal distributions. we have experimented with learnable time embeddings, where each timestamp is associated with a trainable vector that is optimized jointly with the rest of the model.\nHowever, in our preliminary experiments, we observed that learnable time embeddings did not yield better performance compared to the fixed sinusoidal encoding. In particular: On dense datasets like ML-1M, the difference was marginal; On sparse datasets like Ciao, the learnable time encoding led to unstable training and even performance degradation, likely due to insufficient exposure to many unique or rare timestamps; Moreover, learnable encodings introduce additional parameters and increase the risk of overfitting, especially when timestamp distributions are skewed.\nBy contrast, the sinusoidal encoding we adopted is parameter-free, captures relative temporal relationships inherently, and integrates naturally with our Hermitian path encoding scheme, where time acts as a phase component."}, {"review_id": "KTpVcnPyWO", "reviewer": "Reviewer_8aC1", "summary": "This work proposes a path-enhanced contrastive learning for graph-based recommendation. Specifically, the authors consider graph-related augmentations based on both intra-path and inter-path correlations for better representation learning. In experiments, the authors have conducted evaluations on two datasets and achieved better results compared the baselines. They also verify the effectiveness of their two CL strategies in ablation study.", "questions": "Refer to Weaknesses.", "limitations": "Yes", "rating": 4, "confidence": 4, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 2, "clarity": 2, "significance": 2, "originality": 2, "strengths_and_weaknesses": "### Strengths:\n\n1) The idea is sound and the writing is clear.\n2) The authors have conducted ablation study and parameter analysis to better understanding the effects of different components and parameters in their model.\n\n### Weaknesses:\n\n1) The major weakness of this work is the lack of sufficient related work that also concentrate on graph contrastive learning in recommendation. There are lots of GCL related works for recommendation and other fields [1-5], some of which also consider path-related information to build positive/negative samples in CL. The authors should (i) appropriately cite and introduce these related efforts, giving the detailed pros and cons of their proposed inter-/intra- CL compared to existing methods, and (ii) compare with recent good-performing GCL methods (at least better than the classical backbone lightGCN on the evaluation datasets to ensure the persuasiveness of the conclusion).\n2) Are the current baselines strong enough and were they properly trained? It is noticed that most of the compared baselines are proposed 2 years ago. The performance of SCCF (most recent baseline) is relatively poor (basically inferior to simGCL and even lightGCN), while simGCL and lightGCN are also comparable. The authors need to explain these unsatisfactory results of GCL baselines, and it is also recommended that the author release the codes and specific settings of essential baselines for reproducibility.\n3) Whether the performance differences mainly derive from the amount of augmentation samples rather than the specific augmentation methods? The authors could show the number of augmentation samples of different methods, as well as their real training costs.\n4) The current evaluations are mainly based on two datasets, and more datasets are required.\n5) Whether PECL w/o intra-path and inter-path CL equals LightGCN? If so, it seems that both intra-path and inter-path CL strategies have nearly 4-6% improvement in NDCG@10 in ML-1M, while other baselines’ CL strategies have far less advantages. More discussions are needed.\n\n\n### References:\n\n[1] Xu L, Liu Y, Xu T, et al. Graph augmentation empowered contrastive learning for recommendation[J]. ACM Transactions on Information Systems, 2025, 43(2): 1-27.\n\n[2] Huang J, Cao Q, Xie R, et al. Adversarial learning data augmentation for graph contrastive learning in recommendation[C]//International Conference on Database Systems for Advanced Applications. Cham: Springer Nature Switzerland, 2023: 373-388.\n\n[3] Zhang S, Chen L, Wang C, et al. Temporal graph contrastive learning for sequential recommendation[C]//Proceedings of the AAAI Conference on Artificial Intelligence. 2024, 38(8): 9359-9367.\n\n[4] Zhang W, Yang L, Song Z, et al. Mixed Supervised Graph Contrastive Learning for Recommendation[J]. arXiv preprint arXiv:2404.15954, 2024.\n\n[5] Sang L, Wang Y, Zhang Y, et al. Intent-guided Heterogeneous Graph Contrastive Learning for Recommendation[J]. IEEE Transactions on Knowledge and Data Engineering, 2025.", "was_revised": true, "final_justification": "I have read all reviews and the authors' rebuttal.\n\nMy original concerns mainly include (a) the insufficient related work, (b) the lack of recent strong GCL-related baselines, (c) the detailed baselines' settings and strange comparative results, (d) the lack of evaluation datasets (only two).\n\nThe author rebuttal has addressed most of my questions with additional experiments on two added baselines and one additional dataset. The discussions on the performance of models are also insightful. It is strongly suggested that these additional results and discussions should be included in the revision version. In conclusion, I will raise my voting to 4.", "rebuttal": "We thank reviewer for the constructive comments. We provide our feedbacks as follows.\n\nW1’s Response: We appreciate the opportunity to clarify the differences between our proposed Path-Enhanced Contrastive Learning (PECL) method and the related approaches you mentioned, and we will incorporate this clarification into our revised manuscript. Additionally, we have added two more recent state-of-the-art models [4],[5] for comparison.\n\nKey Differences:\nReference[1]: while Xu et al. primarily focuses on augmenting the graph structure, PECL introduces a dual contrastive learning mechanism that addresses the intra-path and inter-path relationships. This helps to bring target nodes closer to the relevant nodes along the interaction path, which has not been explicitly addressed in their work. PECL offers a more granular alignment between nodes within the same path (intra-path) and between different paths (inter-path), improving the model’s ability to capture complex collaborative signals.\nReference[2]: we focus on utilizing path-based augmentations rather than adversarial perturbations, which allows PECL to better preserve the structural information of the interaction graph. PECL captures more meaningful graph structures through its unique path-based sampling strategy, ensuring that the model focuses on the most relevant positive samples along the paths.\nReference[3] incorporates temporal information to contrast sequential patterns in recommendation tasks. PECL integrates temporal dynamics in the path encoding phase, allowing us to capture not only the structural relationships but also the temporal dependencies that are crucial for sequential recommendations. By combining path-aware contrastive learning with temporal context encoding, PECL can better model the evolving preferences of users and items over time, which is particularly useful for time-sensitive recommendations.\nReference[4]: PECL works with bipartite user-item graphs and specifically focuses on user-item interactions with path-based contrastive learning. It does not rely on heterogeneous graph structures but still captures complex relationships through path-aware learning. PECL achieves excellent performance in sparse data scenarios by leveraging path-based samples, whereas Sang et al. might be more specialized for heterogeneous graphs with richer node and edge types.\n\nNew Models:\nWe have added two more recent state-of-the-art models[4,5] for comparison:\n\nML-1M: \nIHGCL: Recall@10: 0.1601, Recall@20: 0.2565, NDCG@10: 0.4148, NDCG@20: 0.4006.\n\nGAIPSRec: Recall@10: 0.1582, Recall@20: 0.2514, NDCG@10: 0.4096, NDCG@20: 0.3985.\n\nCiao: \nIHGCL: Recall@10: 0.0476, Recall@20: 0.0691, NDCG@10: 0.0364, NDCG@20: 0.0450.\n\nGAIPSRec: Recall@10: 0.0481, Recall@20: 0.0728, NDCG@10: 0. 0382, NDCG@20: 0.0476.\n\nBoth methods demonstrate strong performance, not only outperforming the LightGCN model but also exhibiting competitive results compared to all original baseline methods. PECL consistently outperforms Sang et al.’s method in both Recall and NDCG metrics, demonstrating that PECL's path-enhanced contrastive learning is more effective in modeling user-item interaction patterns. PECL achieves significant improvements over Xiong et al.’s method in terms of Recall and NDCG, thanks to its dual contrastive mechanism that captures both local and global graph structures effectively. This highlights the advantage of our approach in handling sparse data and more complex collaborative signals.\n\nW2’s Response: We understand your concern regarding the relatively poor performance of SCCF, which was the most recent baseline included in our experiments. While SCCF is a promising approach that attempts to unify graph convolution and contrastive learning for collaborative filtering, its suboptimal performance in our experiments may stem from several factors: One of the key reasons for SCCF’s underperformance could be related to its graph augmentation strategy. The method applies a form of contrastive learning, but it does not generate sufficiently diverse or informative augmentations of the user-item interaction graph. As a result, SCCF might fail to fully exploit the graph structure, which is crucial in sparse recommendation settings. In addition, SCCF does not incorporate an explicit mechanism to contrast nodes along specific interaction paths, a design choice that may limit its ability to model high-order collaborative signals.\nSimGCL tends to achieve better performance than LightGCN in most cases.\nDue to the bad performance of SCCF, we have conducted experiments with two new, powerful baselines that further strengthen our evaluation(weakness1). Both demonstrate significantly better performance than the existing baselines, effectively addressing the reviewer's concerns.\n\nDue to space limitations, we are only able to report the hyperparameters of a subset of the best-performing baseline models for reproducibility in the rebuttal. We plan to include the full set of baseline configurations in a future version of the paper.\n\nML-1M’s best-performing model (IHGCL): ssl_lambda=0.05, intra_lambda=0.01, ib_lambda=0.001, mask_rate=0.3, remask_rate=0.6, epochs=200.\n\nCiao’s best-performing model (GAIPSRec): num_heads=8, patience=5, samples=20, num_paths_per_node=12, restart_prob=0.2.\n\nAmazon’s best-performing model (IHGCL): ssl_lambda=0.02, intra_lambda=0.001, ib_lambda=0.001, mask_rate=0, remask_rate=0.1, epochs=80.\n\nW3’s Response: The improved performance of PECL compared to other baselines is primarily driven by pulling the target node closer to its path nodes on the interaction path. To further emphasize this point:\nGAIPSRec, a newly added model for comparison(W1), has a similar number of augmentation samples to PECL, but PECL consistently outperforms GAIPSRec in Recall and NDCG metrics. This demonstrates that the path-based augmentation in PECL is more effective at leveraging the structure of the graph and generating high-quality samples that improve performance.\nSimilarly, SGL and IHGCL, which also incorporate a large number of augmentation samples, do not perform as well as PECL. \n\nRegarding the training costs, we understand the importance of considering the computational overhead when evaluating the performance of different models. To address this, we have conducted a detailed complexity analysis of our model in comparison to the baselines, which we have included in the supplementary material (Section A.5). The training costs associated with our model are detailed in the response to Reviewer Z83u’s Q1.\n\nW4’s Response: We have added a new dataset—Amazon[4] to our evaluation. The Amazon results are reported directly in this response for transparency. The experimental results are as follows: \n\nNGCF: R@10: 0.0813, R@20: 0.1257, N@10: 0.0785, N@20: 0.0913.\n\nSGL: R@10: 0.1135, R@20: 0.1501, N@10: 0.1091, N@20: 0.1256. \n\nLightGCN: R@10: 0.1084, R@20: 0.1528, N@10: 0.1016, N@20: 0.1183.\n\nSEPT: R@10: 0.1034, R@20: 0.1486, N@10: 0.1013, N@20: 0.1156.\n\nSelfCF: R@10: 0.1089, R@20: 0.1548, N@10: 0.1054, N@20: 0.1195.\n\nSimGCL: R@10: 0.1145, R@20: 0.1691, N@10: 0.1013, N@20: 0.1243.\n\nSCCF: R@10: 0.1029, R@20: 0.1494, N@10: 0.1086, N@20: 0.1208.\n\nGAIPSRec: R@10: 0.1129, R@20: 0.1664, N@10: 0.1105, N@20: 0.1240.\n\nIHGCL: R@10: 0.1193, R@20: 0.1764, N@10: 0.1132, N@20: 0.1309.\n\nPECL: R@10: 0.1231, R@20: 0.1808, N@10: 0.1165, N@20: 0.1343.\n\nThe experimental results on Amazon are consistent with our previous findings: PECL continues to outperform all baseline models across multiple metrics (Recall, NDCG, Hit Ratio, and Precision). This confirms that the proposed method is robust and generalizable across datasets with different characteristics (e.g., sparsity levels, interaction density, temporal resolution).\n\nW5’s Response: Yes, when both intra-path and inter-path contrastive learning components are removed, PECL reduces to LightGCN, which we also use as our backbone model.\nRegarding the magnitude of improvement, we would like to clarify that the 4–6% gain in NDCG@10 on ML-1M is specific to this single metric on a dense dataset. On other metrics such as Recall@10, HR@10, and Precision@10, as well as on sparser datasets like Ciao, the improvements from intra-path and inter-path contrastive learning are more moderate. Importantly, our experimental framework selects the best model checkpoint based on NDCG@10, which naturally emphasizes performance on this metric. The code was disclosed in the supplemental material and shared with reviewers. As a result, NDCG@10 tends to reflect the upper bound of performance gains, while other metrics may not exhibit the same relative increase. In addition, the larger relative gain on ML-1M NDCG@10 reflects the benefit of fine-grained temporal and structural alignment on a denser, timestamp-rich dataset. Therefore, while PECL’s contrastive components are indeed effective, we believe the gains are consistent but not disproportionate.\n\n[1] Xu L, Liu Y, Xu T, et al. Graph augmentation empowered contrastive learning for recommendation[J]. ACM Transactions on Information Systems, 2025, 43(2): 1-27.\n\n[2] Huang J, Cao Q, Xie R, et al. Adversarial learning data augmentation for graph contrastive learning in recommendation[C]//International Conference on Database Systems for Advanced Applications. Cham: Springer Nature Switzerland, 2023: 373-388.\n\n[3] Zhang S, Chen L, Wang C, et al. Temporal graph contrastive learning for sequential recommendation[C]//Proceedings of the AAAI Conference on Artificial Intelligence. 2024, 38(8): 9359-9367.\n\n[4] Sang L, Wang Y, Zhang Y, et al. Intent-guided Heterogeneous Graph Contrastive Learning for Recommendation[J]. IEEE Transactions on Knowledge and Data Engineering, 2025.\n\n[5] Xiong F, Sun H, Luo G, et al. Graph attention network with high-order neighbor information propagation for social recommendation[C]//IJCAI-24: Thirty-Third International Joint Conference on Artificial Intelligence. International Joint Conferences on Artificial Intelligence, 2024."}]

Author rebuttal:

Meta-review: Existing contrastive learning methods in collaborative filtering often inadvertently increase the distance between target nodes and their interaction path nodes, limiting recommendation effectiveness. To address this, the work proposes a Path Enhanced Contrastive Loss (PECL) model that incorporates both intra-path and inter-path contrastive learning, using a novel path sampling method for graph augmentation. Experimental results on real-world datasets demonstrate the effectiveness. All the reviewers agree to accept this work.
Decision: Accept (spotlight)