Title: Learning-Augmented Streaming Algorithms for Correlation Clustering
Venue: NeurIPS 2025
Accepted: yes
Keywords: Correlation Clustering

graph streaming algorithms

learning-augmented algorithms
Abstract: We study streaming algorithms for Correlation Clustering. Given a graph as an arbitrary-order stream of edges, with each edge labeled as positive or negative, the goal is to partition the vertices into disjoint clusters, such that the number of disagreements is minimized. In this paper, we give the first learning-augmented streaming algorithms for the problem on both complete and general graphs, improving the best-known space-approximation tradeoffs. Based on the works of Cambus et al. (SODA'24) and Ahn et al. (ICML'15), our algorithms use the predictions of pairwise distances between vertices provided by a predictor. For complete graphs, our algorithm achieves a better-than-$3$ approximation under good prediction quality, while using $\tilde{O}(n)$ total space. For general graphs, our algorithm achieves an $O(\log |E^-|)$ approximation under good prediction quality using $\tilde{O}(n)$ total space, improving the best-known non-learning algorithm in terms of space efficiency. Experimental results on synthetic and real-world datasets demonstrate the superiority of our proposed algorithms over their non-learning counterparts.


Peer reviews:
{"IS_META_REVIEW": false, "comments": "SUMMARY:\nThis paper tackles the problem of correlation clustering in the streaming setting (both insertion-only and dynamic streams) and proposes to augment classical streaming algorithms with predictions to improve performance. In correlation clustering, we receive a stream of edges (each labeled positive or negative) of a graph and aim to partition the vertices into clusters to minimize disagreements (positive edges across clusters plus negative edges within clusters). The authors introduce the first learning-augmented streaming algorithms for this problem. Their algorithms assume access to a predictor that provides pairwise “dissimilarity” scores between vertices (intended to estimate whether two vertices should be separated or not in the optimal clustering). Using these predictions, the paper’s algorithms achieve an approximation ratio better than 3 for clustering on complete graphs, which is the first time an approximation factor below 3 has been attained in the single-pass dynamic streaming model. For general (not necessarily complete) graphs, the paper presents a streaming algorithm that attains an $O(\\beta \\log |E^-|)$ approximation (here $|E^-|$ is the number of negative edges and $\\beta$ measures prediction error) using only $\\tilde O(n)$ space, improving the memory usage over the prior $O(|E^-|)$ space bound without predictions. The methods build upon and simplify prior techniques (notably the Pivot-based algorithms by Ahn et al. 2015 and Cambus et al. 2024) by incorporating predicted pairwise distances into the clustering decisions. The paper includes experiments on synthetic and real datasets, which indicate that the proposed learning-augmented algorithms outperform baseline streaming algorithms that do not use predictions.\n\nSTRENGTHS AND WEAKNESSES:\nQuality: \n\nS1 - The paper appears to be technically solid, providing rigorous theoretical results alongside empirical validation. The algorithms are described with clear theoretical guarantees: for complete graphs, the algorithm achieves an expected $(\\min{2.06\\beta, 3}+\\epsilon)$-approximation using $\\tilde O(n)$ space, and for general graphs an $O(\\beta \\log |E^-|)$-approximation with similar space usage. These results improve upon the best-known streaming trade-offs (e.g., beating the previous $3+\\epsilon$ approximation barrier in dynamic streams). The proofs build on established methods (Pivot algorithm and LP-based rounding) and adapt them to incorporate prediction errors, which is intellectually sound. The experimental section is a notable strength: by demonstrating performance gains on real and synthetic data, the authors bolster confidence that the theoretical improvements translate into practice. The paper’s claims are well-supported by the analysis. \n\nW1 - The reliance on an oracle predictor is a major weakness. The theory assumes a “$\\beta$-level” predictor which may be non-trivial to obtain in practice. While this assumption is clearly stated and the algorithm is robust to predictor error, it does mean the quality of results hinges on an external learning component. The paper could further discuss how one might train or derive such a predictor in real-world scenarios.\n\n\nClarity:\n\nS2 - The paper is well-written and organized, making a complex theoretical contribution accessible. The introduction clearly defines the correlation clustering problem and the streaming models, with helpful context on prior results and their limitations. Key concepts like the $\\beta$-level predictor are explained intuitively (the predictor’s quality $\\beta$ indicates how close the predicted clustering is to optimal), and the paper provides pointers to formal definitions in the text. The algorithms and theoretical results are presented with appropriate theorem statements and proofs.\n\nW2 - One area for improvement in clarity could be a more explicit discussion on practical usage of the predictor (perhaps a short example of how a predictor might be learned or an intuitive illustration of its inputs/outputs)\n\nSignificance:\n\n\nS3 - The contributions of this paper are significant, especially within the streaming and approximation algorithms community. Correlation clustering is a fundamental ML problem with many applications (e.g. community detection and image segmentation), and the streaming setting is increasingly relevant for large-scale data. Prior to this work, achieving better than a 3-approximation in a single-pass dynamic stream was an open challenge – this paper provides the first result to surpass that barrier by leveraging predictions. Moreover, the algorithm for general graphs significantly reduces memory requirements: it removes the dependence on storing all negative edges ($|E^-|$) by using predictions, which can be extremely beneficial when the graph is dense. In practical terms, if a reasonable predictor is available, one can now cluster streaming data with higher accuracy or using less memory than before. The paper also connects two areas (streaming algorithms and learning augmentation), demonstrating how machine learning predictions can be used to overcome traditional worst-case barriers.\n\nW3 - One caveat on significance is that the improvements are conditional on predictor quality. If no reliable predictor exists, the method falls back to the known 3-approximation and offers no worst-case gain. Thus, the result is very meaningful assuming the predictor can be trained or provided. Additionally, while the paper simplifies implementation compared to a state-of-the-art 1.847-approx algorithm, the achieved approximation (≈2.06) is still higher than 1.847. There remains a gap to close if one hopes to reach near-optimal clustering in streaming.\n\nOriginality:\n\n\nS4 - The idea of learning-augmented algorithms is a relatively recent trend, and this paper applies it in a novel way to the correlation clustering problem. To the best of my knowledge, there were no prior streaming algorithms for correlation clustering that incorporate predictions, so this represents a fresh contribution. The authors build on known techniques (like the Pivot algorithm by Ailon et al. and its streaming variants) but innovate by integrating a prediction oracle into the clustering process.\n\nW4 - One could argue that the paper’s techniques are incremental in the sense that they extend existing algorithms with an oracle rather than inventing a completely new clustering method. The core idea is largely based on existing approaches, and the main theoretical results are derived from previous work, which limits the paper’s novelty. However, I acknowledge that making this extension successful and theoretically analyzable is non-trivial.\n\nQUESTIONS:\n1. The theoretical model assumes an oracle predictor with a known $\\beta$-level of quality. How do the authors envision obtaining such a predictor in practice? For instance, could it be trained on smaller samples or past instances of similar clustering problems, and how sensitive is the algorithm’s performance to mis-specification of $\\beta$? \n\n2. The paper mentions the $1.847$-approximation insertion-only streaming algorithm by Cohen-Addad et al. (STOC 2024), noting that the new approach is much simpler and works in the dynamic setting. Could the authors elaborate on the performance gap here? For example, if we restrict to insertion-only streams, does the learning-augmented algorithm attain a similar 2.06 approximation, or could it be improved further? A brief discussion on whether the learning-augmented approach might close the gap to $1.847$ in insertion-only scenarios (or why that might be difficult) would be insightful.\n\n3. The general graph result uses an adapted $\\beta$-level predictor. Is this essentially the same notion of predictor quality as in complete graphs, or does it require a different adaptation (e.g., predicting distances in a sparsified graph or dealing with multicut structure)? It would be helpful if the paper clarified what adjustments are needed for the predictor in general graphs and whether obtaining such an adapted predictor is harder or easier than in the complete graph case.\n\n4. In practice, do the authors observe any memory overhead due to the learning-augmented approach (like needing to store predictor information)? If the space usage was tightened or if less space is available, how would the algorithm degrade?\n\n5. Limited Novelty - The algorithm is essentially formed by the truncation during the stream and the post-processing part. For the streaming phase, the idea is mainly from CKLPU [SODA’24] (cf. CM [NeurIPS’23]), and I do not see anything that is substantially novel. Am I understanding it correctly, or am I missing something? Also, the approximation factor is somewhat weak; to outperform the pivot-based approximation, there has to be a value of $\\beta$ where you need predictions with very high quality, correct?\n\nLIMITATIONS:\nThe paper does acknowledge its limitations. The authors clearly state all necessary assumptions (e.g., the need for an oracle predictor and its quality parameter $\\beta$) and ensure the reader understands in which scenarios the theoretical guarantees hold. They also empirically test robustness by varying parameters like dataset size to see how the algorithm copes. The limitations I see are the following\n\n1. The focus on correlation clustering on cliques is primarily a theoretical problem. Existing streaming algorithms already offer better guarantees for this specific case.\n\n2. The novelty is somewhat limited, as the algorithm builds upon existing techniques and incorporates a learning component which does not mean that the novelty is significant. I again acknowledge that coming up with mathematical proofs and making the proof go through is not trivial.\n\n3. Unnatural Oracle: This is a significant drawback in the paper. The ML oracle used by the algorithm seems somewhat artificial, and its practical implementation may be challenging. On a very high-level intuition, the way I see it is \"Suppose we assume that we can predict similarities that could be used to obtain a good approximation of the optimal solution, then we have an approximation algorithm of that quality.\" Is my understanding correct? If yes, then the significance of the result is somewhat limited and seems heavily dependent on that assumption.\n\nRegarding societal impacts, the paper does not flag any negative consequences of this research, which seems reasonable given the theoretical nature of the work.", "TITLE": "Official Review", "RECOMMENDATION": 4, "REVIEWER_CONFIDENCE": 4, "CLARITY": 4, "IMPACT": 3, "ORIGINALITY": 2, "DATE": "2025-06-05"}

{"IS_META_REVIEW": false, "comments": "SUMMARY:\nThis paper studied learning-augmented correlation clustering in data streams for complete and general graphs. The goal is to cluster vertices of a graph arriving in a stream to minimize disagreements—positive edges that cross clusters and negative edges that fall within them.\n\nThe most commonly-studied version of the problem uses complete graphs, meaning that there are ${n \\choose 2}$ edges in the graph, and each edge is annotated with either $(-)$ or $(+)$ labels. A more complicated version is on general graphs, in which we will lose the ability to ‘infer’ $(-)$ edges from the set of $(+)$ edges. In the offline setting, there are separations between the two cases: we could achieve 1.437-approximation in polynomial time for complete graphs, but we cannot obtain any $O(1)$-approximation for the version with general graphs under plausible complexity assumptions. \n\nThis paper studied semi-streaming algorithms for the paper in the presence of a learning-augmented oracle. The oracle in the paper predicts distances between vertex pairs. Ideally, if the predictions are always correct, the optimal solution will pay costs for negative edges with $(1-d_{u,v})$ and positive edges with $d_{u,v}$. The algorithm uses a parameter $\\beta$ to represent a multiplicative approximation of $\\text{OPT}$ for the cost induced by the above solution.\n\nThe main results of the paper are: $i).$ for the complete graph setting, an algorithm that achieves $(min{2.06β,3}+0.1)$-approximation in $O(n \\text{polylog}(n))$ space; and $ii).$ for the general graph setting, an algorithm that achieves $O(\\beta\\log{|E^-|})$-approximation in $O(n \\text{polylog}(n))$ space. All of these algorithms run in polynomial time for post-processing. \n\nThe paper further conducted some experiments, showing that the algorithm for complete graphs has competitive experimental performances. In particular, for synthetic dataset, the proposed algorithm has a competitive performance with algorithms based on agreement decompositions (which is known to be very good for experiments); for real-world datasets, the proposed algorithm outperforms other benchmarks.\n\nSTRENGTHS AND WEAKNESSES:\nMy general opinion for this paper is supportive. The paper studied an important problem with learning-augmented oracles. It is nice to see that the learning-augmented oracle could work for both complete and general graphs. Learning-augmented algorithms are growing popular in the recent two years (e.g., by BDSW [APPROX’24]; CDGLP [NeurIPS’24]; MRTV [ITCS'25]), and although I have some reservations about whether the oracle prediction used in this paper is ‘natural’, it is good to see such addition to the literature.\n\nThe paper is also well-written, and despite the rapid developments of the literature in correlation clustering recently, the paper still did a decent job to emphasize the significance of their results.\n\nOn the flip side, I have the following main criticisms:\n- Whether the oracle prediction used in this paper is ‘natural’: this is somehow subjective, and it is definitely not the most natural oracle one would come up with. The motivation of the oracle seems highly related to the metric LP used by CMSY [STOC’15]. In other words, somehow the model is designed to be tailored to the techniques the authors had in mind. This does not look natural to me.\n- Most of the techniques used in this paper follow from existing work. For instance, in the algorithm for complete graphs, despite a rather involved description and analysis of the TRUNCATEDPIVOT algorithm, the analysis really follows from CKLPU [SODA’24]. The PAIRWISEDISS algorithm, together with the ball-growing algorithm for general graphs, does need some white-box adaptation of existing algorithms. However, these adaptations also do not seem to have much technical novelty.\n\nOverall, I think despite the criticism, the merits of the paper still outweigh the flaws. I think much of my opinion was influenced by the fact that the paper contains algorithms for both complete and general-case correlation clustering and the landscape of the literature (which considers learning-augmented graph algorithms more practical now).\n\nQUESTIONS:\nSome questions were asked in the weakness part of the paper. One additional comment: please make sure that the discussion in Table 1 is for the polynomial-time case only. If one only cares about the space complexity, as in the ‘theory aspect’ of streaming algorithms, you can simply store a cut sparsifier, enumerate all possible clusters (this takes $n^n$ time), and output the one with the smallest cost. This gives us a $(1+\\varepsilon)$-approximation in semi-streaming space, although it is a very impractical algorithm. One of the main contributions of Assadi,  Khanna, and Putterman [STOC’25] is to show the approximation can be done in *polynomial time*.\n\nLIMITATIONS:\nThis work mostly concerns the theoretical foundation of ML, and I do not see any immediate negative societal impacts.", "TITLE": "Official Review", "RECOMMENDATION": 5, "REVIEWER_CONFIDENCE": 3, "CLARITY": 4, "IMPACT": 3, "ORIGINALITY": 3, "DATE": "2025-07-02"}

{"IS_META_REVIEW": false, "comments": "SUMMARY:\nThe paper studies the correlation cclustering problem in the streaming setting and proposes a new learning augmented algorithm for this problem. More specifically, given a $\\beta$-level predictor, the algorithm can achieve an improved $(\\min(2.06\\beta, 3) + \\epsilon)$-approximation in the complete graph case and an improved space in the general graph setting. Here the prediction information we want to get from the predictor is roughly about the pairwise distance on the graph (but more complicated, formally). Finally, the paper also presents an empirical evaluation on both synthetic and real-world datasetss, which demonstrates the advantage of the proposed algorithm.\n\nSTRENGTHS AND WEAKNESSES:\nStrengths:\n\n- The technical contribution of this paper is solid. The paper gives a rigorous analysis (which is based on two previous theoretical papers) to show that, given a good predictor, there are better algorithms for the correlation clustering problem in both complete graph and general graph setting.\n\n- The paper gives a somewhat detailed experiments section that suggests the advantage of the proposed algorithms.\n\n- The organization of the paper is clear.\n\nWeaknesses:\n\n- I agree it is natural to consider predicting the pair-wise distance in a graph. But the formal definition of the $\\beta$-level predictor is a bit artificial to me and it is not very clear to me whether this guarantee is easy to achieve in practice. Also, to get a better approximation ratio, the $\\beta$ needs to be small (< 1.5).\n\n- The algorithms proposed in this paper seem to be largely based on the previous purely theoretical work. From a technical perspective, the new algorithms are not super surprise to me (but I agree the theoretical work of this paper is solid).\n\nQUESTIONS:\nFor the binary classifier in the experiment. What is the split of the training and test data (like, is the experiment setting similar to the setting where we use part of the dataset for training and run the evaluation on the remaining part)?\n\nLIMITATIONS:\nN/A", "TITLE": "Official Review", "RECOMMENDATION": 4, "REVIEWER_CONFIDENCE": 3, "CLARITY": 3, "IMPACT": 3, "ORIGINALITY": 2, "DATE": "2025-07-03"}

{"IS_META_REVIEW": false, "comments": "SUMMARY:\nThe authors study streaming algorithms for Correlation Clustering, which use the predictions of pairwise distances between vertices provided by a predictor. Experimental results on synthetic and real-world datasets demonstrate the superiority. Experimental results on synthetic and real-world datasets demonstrate  the superiority of the proposed algorithms over their non-learning counterparts.\n\nSTRENGTHS AND WEAKNESSES:\nStrengths:\n\n1. The article has certain theoretical analysis and a clear explanation of the essence of the algorithm;\n\n2. The proposed method is relatively novel.\n\n3. The paper introduces an innovative idea that provides valuable insights into newly designed components, which could significantly benefit researchers in related fields.\n\nWeaknesses:\n\n1. I suggest that the author further enrich the experiments to verify the advantages of the model.\n\n2. The organizational structure of the article needs to be further optimized, including some background knowledge and related work additions\n\n3. The limitations are not discussed in the paper. This would be beneficial as it would present suggestions for future research that addresses the limitations of this work.\n\n4. A more in-depth discussion of computational complexity, runtime, and performance under hardware limitations is needed to better assess the practicality of the method.\n\nQUESTIONS:\n1. The limitations are not discussed in the paper. This would be beneficial as it would present suggestions for future research that addresses the limitations of this work.\n\n2. A more in-depth discussion of computational complexity, runtime, and performance under hardware limitations is needed to better assess the practicality of the method.\n\nLIMITATIONS:\n1. I suggest that the author further enrich the experiments to verify the advantages of the model.\n\n2. The organizational structure of the article needs to be further optimized, including some background knowledge and related work additions", "TITLE": "Official Review", "RECOMMENDATION": 4, "REVIEWER_CONFIDENCE": 2, "CLARITY": 3, "IMPACT": 3, "ORIGINALITY": 3, "DATE": "2025-07-04"}