Daily Papers

Most methods for Personalized PageRank (PPR) precompute and store all accurate PPR vectors, and at query time, return the ones of interest directly. However, the storage and computation of all accurate PPR vectors can be prohibitive for large graphs, especially in caching them in memory for real-time online querying. In this paper, we propose a distributed framework that strikes a better balance between offline indexing and online querying. The offline indexing attains a fingerprint of the PPR vector of each vertex by performing billions of "short" random walks in parallel across a cluster of machines. We prove that our indexing method has an exponential convergence, achieving the same precision with previous methods using a much smaller number of random walks. At query time, the new PPR vector is composed by a linear combination of related fingerprints, in a highly efficient vertex-centric decomposition manner. Interestingly, the resulting PPR vector is much more accurate than its offline counterpart because it actually uses more random walks in its estimation. More importantly, we show that such decomposition for a batch of queries can be very efficiently processed using a shared decomposition. Our implementation, PowerWalk, takes advantage of advanced distributed graph engines and it outperforms the state-of-the-art algorithms by orders of magnitude. Particularly, it responses to tens of thousands of queries on graphs with billions of edges in just a few seconds.

This work proposes a novel framework based on nested evolving set processes to accelerate Personalized PageRank (PPR) computation. At each stage of the process, we employ a localized inexact proximal point iteration to solve a simplified linear system. We show that the time complexity of such localized methods is upper bounded by min{mathcal{O}(R^2/ε^2), mathcal{O}(m)} to obtain an ε-approximation of the PPR vector, where m denotes the number of edges in the graph and R is a constant defined via nested evolving set processes. Furthermore, the algorithms induced by our framework require solving only mathcal{O}(1/sqrtα) such linear systems, where α is the damping factor. When 1/ε^2ll m, this implies the existence of an algorithm that computes an epsilon -approximation of the PPR vector with an overall time complexity of mathcal{O}left(R^2 / (sqrtαε^2)right), independent of the underlying graph size. Our result resolves an open conjecture from existing literature. Experimental results on real-world graphs validate the efficiency of our methods, demonstrating significant convergence in the early stages.

Given the damping factor α and precision tolerance ε, andersen2006local introduced Approximate Personalized PageRank (APPR), the de facto local method for approximating the PPR vector, with runtime bounded by Θ(1/(αε)) independent of the graph size. Recently, fountoulakis2022open asked whether faster local algorithms could be developed using O(1/(sqrtαε)) operations. By noticing that APPR is a local variant of Gauss-Seidel, this paper explores the question of whether standard iterative solvers can be effectively localized. We propose to use the locally evolving set process, a novel framework to characterize the algorithm locality, and demonstrate that many standard solvers can be effectively localized. Let operatorname{vol}{ (S_t)} and overlineγ_{t} be the running average of volume and the residual ratio of active nodes textstyle S_{t} during the process. We show operatorname{vol}{ (S_t)}/overlineγ_{t} leq 1/ε and prove APPR admits a new runtime bound O(operatorname{vol}(S_t)/(αoverlineγ_{t})) mirroring the actual performance. Furthermore, when the geometric mean of residual reduction is Θ(sqrtα), then there exists c in (0,2) such that the local Chebyshev method has runtime O(operatorname{vol}(S_{t})/(sqrtα(2-c))) without the monotonicity assumption. Numerical results confirm the efficiency of this novel framework and show up to a hundredfold speedup over corresponding standard solvers on real-world graphs.

Graph-augmented retrieval combines dense similarity with graph-based relevance signals such as Personalized PageRank (PPR), but these scores have different distributions and are not directly comparable. We study this as a score calibration problem for heterogeneous retrieval fusion in multi-hop question answering. Our method, PhaseGraph, maps vector and graph scores to a common unit-free scale using percentile-rank normalization (PIT) before fusion, enabling stable combination without discarding magnitude information. Across MuSiQue and 2WikiMultiHopQA, calibrated fusion improves held-out last-hop retrieval on HippoRAG2-style benchmarks: LastHop@5 increases from 75.1% to 76.5% on MuSiQue (8W/1L, p=0.039) and from 51.7% to 53.6% on 2WikiMultiHopQA (11W/2L, p=0.023), both on independent held-out test splits. A theory-driven ablation shows that percentile-based calibration is directionally more robust than min-max normalization on both tune and test splits (1W/6L, p=0.125), while Boltzmann weighting performs comparably to linear fusion after calibration (0W/3L, p=0.25). These results suggest that score commensuration is a robust design choice, and the exact post-calibration operator appears to matter less on these benchmarks.

Recent advances in Retrieval-Augmented Generation (RAG) have shifted from simple vector similarity to structure-aware approaches like HippoRAG, which leverage Knowledge Graphs (KGs) and Personalized PageRank (PPR) to capture multi-hop dependencies. However, these methods suffer from a "Static Graph Fallacy": they rely on fixed transition probabilities determined during indexing. This rigidity ignores the query-dependent nature of edge relevance, causing semantic drift where random walks are diverted into high-degree "hub" nodes before reaching critical downstream evidence. Consequently, models often achieve high partial recall but fail to retrieve the complete evidence chain required for multi-hop queries. To address this, we propose CatRAG, Context-Aware Traversal for robust RAG, a framework that builds on the HippoRAG 2 architecture and transforms the static KG into a query-adaptive navigation structure. We introduce a multi-faceted framework to steer the random walk: (1) Symbolic Anchoring, which injects weak entity constraints to regularize the random walk; (2) Query-Aware Dynamic Edge Weighting, which dynamically modulates graph structure, to prune irrelevant paths while amplifying those aligned with the query's intent; and (3) Key-Fact Passage Weight Enhancement, a cost-efficient bias that structurally anchors the random walk to likely evidence. Experiments across four multi-hop benchmarks demonstrate that CatRAG consistently outperforms state of the art baselines. Our analysis reveals that while standard Recall metrics show modest gains, CatRAG achieves substantial improvements in reasoning completeness, the capacity to recover the entire evidence path without gaps. These results reveal that our approach effectively bridges the gap between retrieving partial context and enabling fully grounded reasoning. Resources are available at https://github.com/kwunhang/CatRAG.

Personalized PageRank (PPR) has enormous applications, such as link prediction and recommendation systems for social networks, which often require the fully PPR to be known. Besides, most of real-life graphs are edge-weighted, e.g., the interaction between users on the Facebook network. However, it is computationally difficult to compute the fully PPR, especially on large graphs, not to mention that most existing approaches do not consider the weights of edges. In particular, the existing approach cannot handle graphs with billion edges on a moderate-size cluster. To address this problem, this paper presents a novel study on the computation of fully edge-weighted PPR on large graphs using the distributed computing framework. Specifically, we employ the Monte Carlo approximation that performs a large number of random walks from each node of the graph, and exploits the parallel pipeline framework to reduce the overall running time of the fully PPR. Based on that, we develop several optimization techniques which (i) alleviate the issue of large nodes that could explode the memory space, (ii) pre-compute short walks for small nodes that largely speedup the computation of random walks, and (iii) optimize the amount of random walks to compute in each pipeline that significantly reduces the overhead. With extensive experiments on a variety of real-life graph datasets, we demonstrate that our solution is several orders of magnitude faster than the state-of-the-arts, and meanwhile, largely outperforms the baseline algorithms in terms of accuracy.

Many machine learning algorithms require the input to be represented as a fixed-length feature vector. When it comes to texts, one of the most common fixed-length features is bag-of-words. Despite their popularity, bag-of-words features have two major weaknesses: they lose the ordering of the words and they also ignore semantics of the words. For example, "powerful," "strong" and "Paris" are equally distant. In this paper, we propose Paragraph Vector, an unsupervised algorithm that learns fixed-length feature representations from variable-length pieces of texts, such as sentences, paragraphs, and documents. Our algorithm represents each document by a dense vector which is trained to predict words in the document. Its construction gives our algorithm the potential to overcome the weaknesses of bag-of-words models. Empirical results show that Paragraph Vectors outperform bag-of-words models as well as other techniques for text representations. Finally, we achieve new state-of-the-art results on several text classification and sentiment analysis tasks.

We introduce pVR, a topological machine learning framework for alignment-free genomic sequence classification that combines p-adic numbers with topological data analysis. Each DNA sequence is encoded along two complementary axes: a p-adic distance on k-mer prefixes, which captures hierarchical positional structure, and a compositional L_1 distance on k-mer frequencies, which captures local sequence content. The two distances jointly parameterise a bi-filtered Vietoris--Rips complex, and per-sequence topological summaries from this bi-filtration serve as features for standard machine learning classifiers. We establish theoretical guarantees for the construction: stability under metric perturbations and invariance to the choice of prime, alongside a result that explains why a single p-adic axis is topologically uninformative and why the bi-filtration recovers nontrivial homology. On twelve genomic benchmarks (28 to 500 sequences, 3 to 7 classes), pVR outperforms four established alignment-free baselines on three of six low-sample datasets, with gains of up to 21 percentage points; it underperforms only on a SARS-CoV-2 variant benchmark whose point-mutation divergence violates the hierarchical assumption, and all methods saturate in the large-sample regime. pVR also outperforms zero-shot frozen embeddings from the 500M-parameter Nucleotide Transformer v2 by 6.7 to 11.4 percentage points on three low-sample benchmarks. The pVR codebase is publicly available at https://github.com/MAHI-Group/pVR.

Vectors are universal mathematical objects that can represent text, images, speech, or a mix of these data modalities. That happens regardless of whether data is represented by hand-crafted features or learnt embeddings. Collect a large enough quantity of such vectors and the question of retrieval becomes urgently relevant: Finding vectors that are more similar to a query vector. This monograph is concerned with the question above and covers fundamental concepts along with advanced data structures and algorithms for vector retrieval. In doing so, it recaps this fascinating topic and lowers barriers of entry into this rich area of research.

Given a K-vertex simplex in a d-dimensional space, suppose we measure n points on the simplex with noise (hence, some of the observed points fall outside the simplex). Vertex hunting is the problem of estimating the K vertices of the simplex. A popular vertex hunting algorithm is successive projection algorithm (SPA). However, SPA is observed to perform unsatisfactorily under strong noise or outliers. We propose pseudo-point SPA (pp-SPA). It uses a projection step and a denoise step to generate pseudo-points and feed them into SPA for vertex hunting. We derive error bounds for pp-SPA, leveraging on extreme value theory of (possibly) high-dimensional random vectors. The results suggest that pp-SPA has faster rates and better numerical performances than SPA. Our analysis includes an improved non-asymptotic bound for the original SPA, which is of independent interest.

Large Language Models (LLMs) increasingly rely on external tools such as search engines to solve complex agentic tasks that require reasoning and external knowledge retrieval. Recently, reinforcement learning with verifiable rewards (RLVR) has demonstrated its effectiveness in advancing capabilities of LLMs by rewarding the final answers via outcome rewards. While straightforward to supervise, outcome rewards only provide sparse signals and delayed feedback, which limits their effectiveness on long trajectories. Process rewards address this by evaluating intermediate steps, providing fine-grained supervision and encouraging grounded problem solving. However, it is notoriously hard to annotate step-wise labels, especially in non-verifiable process without "golden" answers. Furthermore, step-wise judgment requires the balance between local quality with contribution to the final outcome, as optimizing towards higher process reward may not always align with better final outcomes. To address the above challenges, we introduce Principle Process Reward (PPR), an RL approach that unifies principled step-level assessment and outcome verification. We train a principle-based reward model to improve the transparency and reliability of process evaluation, and further introduce a Reward Normalization (ReNorm) strategy to calibrate outcome and process rewards. Experiment results show that PPR achieves state-of-the-art performance across a wide range of benchmarks, demonstrating its impressive robustness and generalization. Our code and model collection is available in this link.

Document layout analysis is a critical preprocessing step in document intelligence, enabling the detection and localization of structural elements such as titles, text blocks, tables, and formulas. Despite its importance, existing layout detection models face significant challenges in generalizing across diverse document types, handling complex layouts, and achieving real-time performance for large-scale data processing. To address these limitations, we present PP-DocLayout, which achieves high precision and efficiency in recognizing 23 types of layout regions across diverse document formats. To meet different needs, we offer three models of varying scales. PP-DocLayout-L is a high-precision model based on the RT-DETR-L detector, achieving 90.4% mAP@0.5 and an end-to-end inference time of 13.4 ms per page on a T4 GPU. PP-DocLayout-M is a balanced model, offering 75.2% mAP@0.5 with an inference time of 12.7 ms per page on a T4 GPU. PP-DocLayout-S is a high-efficiency model designed for resource-constrained environments and real-time applications, with an inference time of 8.1 ms per page on a T4 GPU and 14.5 ms on a CPU. This work not only advances the state of the art in document layout analysis but also provides a robust solution for constructing high-quality training data, enabling advancements in document intelligence and multimodal AI systems. Code and models are available at https://github.com/PaddlePaddle/PaddleX .