Large Language Models (LLMs) hold promise in automating data analysis tasks, yet open-source models face significant limitations in these kinds of reasoning-intensive scenarios. In this work, we investigate strategies to enhance the data analysis capabilities of open-source LLMs. By curating a seed dataset of diverse, realistic scenarios, we evaluate models across three dimensions: data understanding, code generation, and strategic planning. Our analysis reveals three key findings: (1) Strategic planning quality serves as the primary determinant of model performance; (2) Interaction design and task complexity significantly influence reasoning capabilities; (3) Data quality demonstrates a greater impact than diversity in achieving optimal performance. We leverage these insights to develop a data synthesis methodology, demonstrating significant improvements in open-source LLMs' analytical reasoning capabilities.

Slow-thinking Large Language Models (LLMs) have demonstrated strong reasoning capabilities but often suffer from severe hallucinations due to an inability to recognize their knowledge boundaries.Existing Reinforcement Learning (RL) approaches typically rely on outcomeoriented rewards, which can inadvertently reinforce fabricated reasoning paths when the final answer is correct.To address this, we propose Knowledge-enhanced RL, KnowRL, a framework that integrates factual supervision directly into the reasoning process.By decomposing the chain of thought into atomic facts and verifying them against the corresponding ground-truth knowledge, KnowRL performs fine-grained checks to encourage models to reason faithfully.Crucially, this processoriented supervision teaches the model to identify its knowledge boundaries, learning to say "I don't know" instead of fabricating answers when information is missing.Experimental results demonstrate that KnowRL effectively mitigates hallucinations-reducing the Incorrect Rate on SimpleQA by 20.3% for distillationbased slow-thinking models while maintaining strong performance on complex reasoning benchmarks like GPQA and AIME 2025.Furthermore, our method shows robust transferability to out-of-distribution tasks, indicating that the model learns a generalizable verification behavior 1 .

Jintian Zhang, Yuqi Zhu, Mengshu Sun, Yujie Luo, Shuofei Qiao, Lun Du, Da Zheng, Huajun Chen, Ningyu Zhang. Proceedings of the 2025 Conference on Empirical Methods in Natural Language Processing. 2025.

Ensuring high-quality recommendations for newly onboarded users requires the continuous retraining of Deep Learning Recommendation Models (DLRMs) with freshly generated data. To serve the online DLRM retraining, existing solutions use hundreds of CPU computing nodes designated for input preprocessing, causing significant power consumption that surpasses even the power usage of GPU trainers.

Relational graph neural networks (RGNNs) are graph neural networks with dedicated structures for modeling the different types of nodes and edges in heterogeneous graphs. While RGNNs have been increasingly adopted in many real-world applications due to their versatility and accuracy, they pose performance and system design challenges: inherent memory-intensive computation patterns, the gap between the programming interface and kernel APIs, and heavy programming effort required to optimize kernels caused by their coupling with data layout and heterogeneity. To systematically address these challenges, we propose Hector, a novel two-level intermediate representation and its code generator framework that (a) captures the key properties of RGNN models, and opportunities to reduce memory accesses in inter-operator scheduling and materialization, (b) generates code with flexible data access schemes to eliminate redundant data copies, and (c) decouples model semantics, data layout, and operators-specific optimizations from each other to reduce programming effort. By building on one general matrix multiply (GEMM) template and a node/edge traversal template, Hector achieves up to 9.9× speed-up in inference and 43.7× speed-up in training compared with the state-of-the-art public systems on select models, RGCN, RGAT and HGT, when running heterogeneous graphs provided by Deep Graph Library (DGL) and Open Graph Benchmark (OGB). In addition, Hector does not trigger any out-of-memory (OOM) exception in these tests. We also propose linear operator reordering and compact materialization to further accelerate the system by up to 3.8×. As an indicator of the reduction of programming effort, Hector takes in 51 lines of code expressing the three models and generates a total of 8K lines of CUDA and C++ code. Through profiling, we found that higher memory efficiency allows Hector to accommodate larger input and therefore attain higher throughput in forward propagation, while backward propagation is bound by latency introduced by atomic updates and outer products.

This paper introduces OrthoReg, a simple yet effective Graph-regularized MLP model for semi-supervised node representation learning. We first demonstrate, through empirical observations and theoretical analysis, that node embeddings learned from conventional GR-MLPs suffer from the over-correlation issue. This issue arises when a few dominant singular values overwhelm the embedding space, leading to the limited expressive power of the learned node representations. To mitigate this problem, we propose a novel GR-MLP model called OrthoReg. By incorporating a soft regularization loss on the correlation matrix of node embeddings, OrthoReg explicitly encourages orthogonal node representations, effectively avoiding over-correlated representations. Compared to the currently popular GNN models, our OrthoReg possesses two distinct advantages: 1) Much faster inference speed, particularly for large-scale graphs. 2) Significantly superior performance in inductive cold-start settings. Experiments on semi-supervised node classification tasks, together with the extensive ablation studies, have demonstrated the effectiveness of the proposed designs.

Given a node-attributed graph, and a graph task (link prediction or node classification), can we tell if a graph neural network (GNN) will perform well? More specifically, do the graph structure and the node features carry enough usable information for the task? Our goals are (1) to develop a fast tool to measure how much information is in the graph structure and in the node features, and (2) to exploit the information to solve the task, if there is enough. We propose NetInfoF, a framework including NetInfoF_Probe and NetInfoF_Act, for the measurement and the exploitation of network usable information (NUI), respectively. Given a graph data, NetInfoF_Probe measures NUI without any model training, and NetInfoF_Act solves link prediction and node classification, while two modules share the same backbone. In summary, NetInfoF has following notable advantages: (a) General, handling both link prediction and node classification; (b) Principled, with theoretical guarantee and closed-form solution; (c) Effective, thanks to the proposed adjustment to node similarity; (d) Scalable, scaling linearly with the input size. In our carefully designed synthetic datasets, NetInfoF correctly identifies the ground truth of NUI and is the only method being robust to all graph scenarios. Applied on real-world datasets, NetInfoF wins in 11 out of 12 times on link prediction compared to general GNN baselines.

Graph machine learning (GML) is effective in many business applications. However, making GML easy to use and applicable to industry applications with massive datasets remain challenging. We developed GraphStorm, which provides an end-to-end solution for scalable graph construction, graph model training and inference. GraphStorm has the following desirable properties: (a) Easy to use: it can perform graph construction and model training and inference with just a single command; (b) Expert-friendly: GraphStorm contains many advanced GML modeling techniques to handle complex graph data and improve model performance; (c) Scalable: every component in GraphStorm can operate on graphs with billions of nodes and can scale model training and inference to different hardware without changing any code. GraphStorm has been used and deployed for over a dozen billion-scale industry applications after its release in May 2023. It is open-sourced in Github: https://github.com/awslabs/graphstorm.

This article aims to unify spatial dependency and temporal dependency in a non-Euclidean space while capturing the inner spatial-temporal dependencies for traffic data. For spatial-temporal attribute entities with topological structure, the space-time is consecutive and unified while each node's current status is influenced by its neighbors' past states over variant periods of each neighbor. Most spatial-temporal neural networks for traffic forecasting study spatial dependency and temporal correlation separately in processing, gravely impaired the spatial-temporal integrity, and ignore the fact that the neighbors' temporal dependency period for a node can be delayed and dynamic. To model this actual condition, we propose TraverseNet, a novel spatial-temporal graph neural network, viewing space and time as an inseparable whole, to mine spatial-temporal graphs while exploiting the evolving spatial-temporal dependencies for each node via message traverse mechanisms. Experiments with ablation and parameter studies have validated the effectiveness of the proposed TraverseNet, and the detailed implementation can be found from https://github.com/nnzhan/TraverseNet.

Model pre-training on large text corpora has been demonstrated effective for various downstream applications in the NLP domain. In the graph mining domain, a similar analogy can be drawn for pre-training graph models on large graphs in the hope of benefiting downstream graph applications, which has also been explored by several recent studies. However, no existing study has ever investigated the pre-training of text plus graph models on large heterogeneous graphs with abundant textual information (a.k.a. large graph corpora) and then fine-tuning the model on different related downstream applications with different graph schemas. To address this problem, we propose a framework of graph-aware language model pre-training (GaLM) on a large graph corpus, which incorporates large language models and graph neural networks, and a variety of fine-tuning methods on downstream applications. We conduct extensive experiments on Amazon's real internal datasets and large public datasets. Comprehensive empirical results and in-depth analysis demonstrate the effectiveness of our proposed methods along with lessons learned.

Applying Graph Neural Networks (GNNs) to real-world problems is challenging for machine learning (ML) practitioners due to two major obstacles. The first hurdle is the high barrier to learn programming GNNs from scratch. The second challenge lies in overcoming engineering difficulties when scaling GNN models for large graphs at an industry-level. To address these challenges, GraphStorm, an open-source framework, offers a solution by providing an easy-to-use user interface and an end-to-end GNN training/inference pipeline that seamlessly handles extremely large graphs in a distributed manner This tutorial aims to provide participants with a comprehensive understanding of GraphStorm, including its design principles, target users, and use cases, through presentations. The hands-on sections will enable attendees to walk through four practical GraphStorm use cases that can assist them in leveraging GNNs to address real-world business problems.

Jointly utilizing multiple GPUs to train graph neural networks (GNNs) is crucial for handling large graphs and achieving high efficiency. However, we find that existing systems suffer from high communication costs and low GPU utilization due to improper data layout and training procedures. Thus, we propose a system dubbed Distributed Sampling and Pipelining (DSP) for multi-GPU GNN training. DSP adopts a tailored data layout to utilize the fast NVLink connections among the GPUs, which stores the graph topology and popular node features in GPU memory. For efficient graph sampling with multiple GPUs, we introduce a collective sampling primitive (CSP), which pushes the sampling tasks to data to reduce communication. We also design a producer-consumer-based pipeline, which allows tasks from different mini-batches to run congruently to improve GPU utilization. We compare DSP with state-of-the-art GNN training frameworks, and the results show that DSP consistently outperforms the baselines under different datasets, GNN models and GPU counts. The speedup of DSP can be up to 26x and is over 2x in most cases.

Graph learning is becoming increasingly popular due to its superior performance in tackling many grand challenges. While quantization is widely used to accelerate Graph Neural Network (GNN) computation, quantized training faces remarkable roadblocks. Current quantized GNN training systems often experience longer training time than their full-precision counterparts for two reasons: (i) addressing the quantization accuracy challenge leads to excessive overhead, and (ii) the optimization potential exposed by quantization is not adequately leveraged. This paper introduces Tango which re-thinks quantization challenges and opportunities for graph neural network training on GPUs with three contributions: Firstly, we introduce efficient rules to maintain accuracy during quantized GNN training. Secondly, we design and implement quantization-aware primitives and inter-primitive optimizations to speed up GNN training. Finally, we integrate Tango with the popular Deep Graph Library (DGL) system and demonstrate its superior performance over the state-of-the-art approaches on various GNN models and datasets.

Memory-based Temporal Graph Neural Networks are powerful tools in dynamic graph representation learning and have demonstrated superior performance in many real-world applications. However, their node memory favors smaller batch sizes to capture more dependencies in graph events and needs to be maintained synchronously across all trainers. As a result, existing frameworks suffer from accuracy loss when scaling to multiple GPUs. Even worse, the tremendous overhead of synchronizing the node memory makes it impractical to deploy the solution in GPU clusters. In this work, we propose DistTGL --- an efficient and scalable solution to train memory-based TGNNs on distributed GPU clusters. DistTGL has three improvements over existing solutions: an enhanced TGNN model, a novel training algorithm, and an optimized system. In experiments, DistTGL achieves near-linear convergence speedup, outperforming the state-of-the-art single-machine method by 14.5% in accuracy and 10.17× in training throughput.

Transparency and accountability have become major concerns for black-box machine learning (ML) models. Proper explanations for the model behavior increase model transparency and help researchers develop more accountable models. Graph neural networks (GNN) have recently shown superior performance in many graph ML problems than traditional methods, and explaining them has attracted increased interest. However, GNN explanation for link prediction (LP) is lacking in the literature. LP is an essential GNN task and corresponds to web applications like recommendation and sponsored search on web. Given existing GNN explanation methods only address node/graph-level tasks, we propose Path-based GNN Explanation for heterogeneous Link prediction (PaGE-Link) that generates explanations with connection interpretability, enjoys model scalability, and handles graph heterogeneity. Qualitatively, PaGE-Link can generate explanations as paths connecting a node pair, which naturally captures connections between the two nodes and easily transfer to human-interpretable explanations. Quantitatively, explanations generated by PaGE-Link improve AUC for recommendation on citation and user-item graphs by 9 - 35% and are chosen as better by 78.79% of responses in human evaluation.

This paper describes a new method for representing embedding tables of graph neural networks (GNNs) more compactly via tensor-train (TT) decomposition. We consider the scenario where (a) the graph data that lack node features, thereby requiring the learning of embeddings during training; and (b) we wish to exploit GPU platforms, where smaller tables are needed to reduce host-to-GPU communication even for large-memory GPUs. The use of TT enables a compact parameterization of the embedding, rendering it small enough to fit entirely on modern GPUs even for massive graphs. When combined with judicious schemes for initialization and hierarchical graph partitioning, this approach can reduce the size of node embedding vectors by 1,659 times to 81,362 times on large publicly available benchmark datasets, achieving comparable or better accuracy and significant speedups on multi-GPU systems. In some cases, our model without explicit node features on input can even match the accuracy of models that use node features.

Graph neural networks (GNN) have shown great success in learn- ing from graph-structured data. They are widely used in various applications, such as recommendation, fraud detection, and search. In these domains, the graphs are typically large and heterogeneous, containing many millions or billions of vertices and edges of different types. To tackle this challenge, we develop DistDGLv2, a system that extends DistDGL for training GNNs on massive heterogeneous graphs in a mini-batch fashion, using distributed hybrid CPU/GPU training. DistDGLv2 places graph data in distributed CPU memory and performs mini-batch computation in GPUs. For ease of use, DistDGLv2 adopts API compatible with Deep Graph Library (DGL)'s mini-batch training and heterogeneous graph API, which enables distributed training with almost no code modification. To ensure model accuracy, DistDGLv2 follows a synchronous training approach and allows ego-networks forming mini-batches to include non-local vertices. To ensure data locality and load balancing, DistDGLv2 partitions heterogeneous graphs by using a multi-level partitioning algorithm with min-edge cut and multiple balancing constraints. DistDGLv2 deploys an asynchronous mini- batch generation pipeline that makes computation and data access asynchronous to fully utilize all hardware (CPU, GPU, network, PCIe). We demonstrate DistDGLv2 on various GNN workloads. Our results show that DistDGLv2 achieves 2 - 3x speedup over DistDGL and 18× speedup over Euler. It takes only 5 - 10 seconds to complete an epoch on graphs with hundreds of millions of vertices on a cluster with 64 GPUs.

Many real world graphs contain time domain information. Temporal Graph Neural Networks capture temporal information as well as structural and contextual information in the generated dynamic node embeddings. Researchers have shown that these embeddings achieve state-of-the-art performance in many different tasks. In this work, we propose TGL, a unified framework for large-scale offline Temporal Graph Neural Network training where users can compose various Temporal Graph Neural Networks with simple configuration files. TGL comprises five main components, a temporal sampler, a mailbox, a node memory module, a memory updater, and a message passing engine. We design a Temporal-CSR data structure and a parallel sampler to efficiently sample temporal neighbors to form training mini-batches. We propose a novel random chunk scheduling technique that mitigates the problem of obsolete node memory when training with a large batch size. To address the limitations of current TGNNs only being evaluated on small-scale datasets, we introduce two large-scale real-world datasets with 0.2 and 1.3 billion temporal edges. We evaluate the performance of TGL on four small-scale datasets with a single GPU and the two large datasets with multiple GPUs for both link prediction and node classification tasks. We compare TGL with the open-sourced code of five methods and show that TGL achieves similar or better accuracy with an average of 13X speedup. Our temporal parallel sampler achieves an average of 173X speedup on a multi-core CPU compared with the baselines. On a 4-GPU machine, TGL can train one epoch of more than one billion temporal edges within 1-10 hours. To the best of our knowledge, this is the first work that proposes a general framework for large-scale Temporal Graph Neural Networks training on multiple GPUs.

Graph convolutional network (GCN) based approaches have achieved significant progress for solving complex, graph-structured problems. GCNs incorporate the graph structure information and the node (or edge) features through message passing and computes ‘deep’ node representations. Despite significant progress in the field, designing GCN architectures for heterogeneous graphs still remains an open challenge. Due to the schema of a heterogeneous graph, useful information may reside multiple hops away. A key question is how to perform message passing to incorporate information of neighbors multiple hops away while avoiding the well-known over-smoothing problem in GCNs. To address this question, we propose our GCN framework Deep Heterogeneous Graph Convolutional Network (DHGCN), which takes advantage of the schema of a heterogeneous graph and uses a hierarchical approach to effectively utilize information many hops away. It first computes representations of the target nodes based on their schema-derived ego-network (SEN). It then links the nodes of the same type with various pre-defined metapaths and performs message passing along these links to compute final node representations. Our design choices naturally capture the way a heterogeneous graph is generated from the schema. The experimental results on real and synthetic datasets corroborate the design choice and illustrate the performance gains relative to competing alternatives.

Graph neural networks (GNNs) are powerful tools for learning from graph data and are widely used in various applications such as social network recommendation, fraud detection, and graph search. The graphs in these applications are typically large, usually containing hundreds of millions of nodes. Training GNN models on such large graphs efficiently remains a big challenge. Despite a number of sampling-based methods have been proposed to enable mini-batch training on large graphs, these methods have not been proved to work on truly industry-scale graphs, which require GPUs or mixed CPU-GPU training. The state-of-the-art sampling-based methods are usually not optimized for these real-world hardware setups, in which data movement between CPUs and GPUs is a bottleneck. To address this issue, we propose Global Neighborhood Sampling that aims at training GNNs on giant graphs specifically for mixed CPU-GPU training. The algorithm samples a global cache of nodes periodically for all mini-batches and stores them in GPUs. This global cache allows in-GPU importance sampling of mini-batches, which drastically reduces the number of nodes in a mini-batch, especially in the input layer, to reduce data copy between CPU and GPU and mini-batch computation without compromising the training convergence rate or model accuracy. We provide a highly efficient implementation of this method and show that our implementation outperforms an efficient node-wise neighbor sampling baseline by a factor of 2× ~ 4× on giant graphs. It outperforms an efficient implementation of LADIES with small layers by a factor of 2× ~ 14× while achieving much higher accuracy than LADIES. We also theoretically analyze the proposed algorithm and show that with cached node data of a proper size, it enjoys a comparable convergence rate as the underlying node-wise sampling method.

Graph representation learning has made major strides over the past decade.However, in many relational domains, the input data are not suited for simple graph representations as the relationships between entities go beyond pairwise interactions.In such cases, the relationships in the data are better represented as hyperedges (set of entities) of a non-uniform hypergraph.While there have been works on principled methods for learning representations of nodes of a hypergraph, these approaches are limited in their applicability to tasks on non-uniform hypergraphs (hyperedges with different cardinalities).In this work, we exploit the incidence structure to develop a hypergraph neural network to learn provably expressive representations of variable sized hyperedges which preserve local-isomorphism in the line graph of the hypergraph, while also being invariant to permutations of its constituent vertices.Specifically, for a given vertex set, we propose frameworks for (1) hyperedge classification and (2) variable sized expansion of partially observed hyperedges which captures the higher order interactions among vertices and hyperedges.We evaluate performance on multiple real-world hypergraph datasets and demonstrate consistent, significant improvement in accuracy, over state-of-the-art models.

Learning from graph and relational data plays a major role in many applications including social network analysis, marketing, e-commerce, information retrieval, knowledge modeling, medical and biological sciences, engineering, and others. Recently, Graph Neural Networks (GNNs) have emerged as a promising new learning framework capable of bringing the power of deep representation learning to graph and relational data. This ever-growing body of research has shown that GNNs achieve state-of-the-art performance for problems such as link prediction, fraud detection, target-ligand binding activity prediction, knowledge-graph completion, and product recommendations. In practice, many of the real-world graphs are very large. It is urgent to have scalable solutions to train GNN on large graphs efficiently.

Learning from graph and relational data plays a major role in many applications including social network analysis, marketing, e-commerce, information retrieval, knowledge modeling, medical and biological sciences, engineering, and others. In the last few years, Graph Neural Networks (GNNs) have emerged as a promising new supervised learning framework capable of bringing the power of deep representation learning to graph and relational data. This ever-growing body of research has shown that GNNs achieve state-of-the-art performance for problems such as link prediction, fraud detection, target-ligand binding activity prediction, knowledge-graph completion, and product recommendations. In practice, many of the real-world graphs are very large. It is urgent to have scalable solutions to train GNN on large graphs efficiently.

Graph neural networks (GNNs) are gaining popularity as a promising approach to machine learning on graphs. Unlike traditional graph workloads where each vertex/edge is associated with a scalar, GNNs attach a feature tensor to each vertex/edge. This additional feature dimension, along with consequently more complex vertex- and edge-wise computations, has enormous implications on locality and parallelism, which existing graph processing systems fail to exploit. This paper proposes FeatGraph to accelerate GNN workloads by co-optimizing graph traversal and feature dimension computation. FeatGraph provides a flexible programming interface to express diverse GNN models by composing coarse-grained sparse templates with fine-grained user-defined functions (UDFs) on each vertex/edge. FeatGraph incorporates optimizations for graph traversal into the sparse templates and allows users to specify optimizations for UDFs with a feature dimension schedule (FDS). FeatGraph speeds up end-to-end GNN training and inference by up to 32× on CPU and 7× on GPU.

Knowledge graphs have emerged as a key abstraction for organizing information in diverse domains and their embeddings are increasingly used to harness their information in various information retrieval and machine learning tasks. However, the ever growing size of knowledge graphs requires computationally efficient algorithms capable of scaling to graphs with millions of nodes and billions of edges. This paper presents DGL-KE, an open-source package to efficiently compute knowledge graph embeddings. DGL-KE introduces various novel optimizations that accelerate training on knowledge graphs with millions of nodes and billions of edges using multi-processing, multi-GPU, and distributed parallelism. These optimizations are designed to increase data locality, reduce communication overhead, overlap computations with memory accesses, and achieve high operation efficiency. Experiments on knowledge graphs consisting of over 86M nodes and 338M edges show that DGL-KE can compute embeddings in 100 minutes on an EC2 instance with 8 GPUs and 30 minutes on an EC2 cluster with 4 machines with 48 cores/machine. These results represent a 2× ~ 5× speedup over the best competing approaches. DGL-KE is available on https://github.com/awslabs/dgl-ke.

Knowledge graph (e.g. Freebase, YAGO) is a multi-relational graph representing rich factual information among entities of various types. Entity alignment is the key step towards knowledge graph integration from multiple sources. It aims to identify entities across different knowledge graphs that refer to the same real world entity. However, current entity alignment systems overlook the sparsity of different knowledge graphs and can not align multi-type entities by one single model. In this paper, we present a Collective Graph neural network for Multi-type entity Alignment, called CG-MuAlign. Different from previous work, CG-MuAlign jointly aligns multiple types of entities, collectively leverages the neighborhood information and generalizes to unlabeled entity types. Specifically, we propose novel collective aggregation function tailored for this task, that (1) relieves the incompleteness of knowledge graphs via both cross-graph and self attentions, (2) scales up efficiently with mini-batch training paradigm and effective neighborhood sampling strategy. We conduct experiments on real world knowledge graphs with millions of entities and observe the superior performance beyond existing methods. In addition, the running time of our approach is much less than the current state-of-the-art deep learning methods.

R is one of the most popular programming languages for statistics and machine learning, but it is slow and unable to scale to large datasets. The general approach for having an efficient algorithm in R is to implement it in C or FORTRAN and provide an R wrapper. FlashR accelerates and scales existing R code by parallelizing a large number of matrix functions in the R base package and scaling them beyond memory capacity with solid-state drives (SSDs). FlashR performs memory hierarchy aware execution to speed up parallelized R code by (i) evaluating matrix operations lazily, (ii) performing all operations in a DAG in a single execution and with only one pass over data to increase the ratio of computation to I/O, (iii) performing two levels of matrix partitioning and reordering computation on matrix partitions to reduce data movement in the memory hierarchy. We evaluate FlashR on various machine learning and statistics algorithms on inputs of up to four billion data points. Despite the huge performance gap between SSDs and RAM, FlashR on SSDs closely tracks the performance of FlashR in memory for many algorithms. The R implementations in FlashR outperforms H2O and Spark MLlib by a factor of 3 -- 20.

k-means is one of the most influential and utilized machine learning algorithms. Its computation limits the performance and scalability of many statistical analysis and machine learning tasks. We rethink and optimize k-means in terms of modern NUMA architectures to develop a novel parallelization scheme that delays and minimizes synchronization barriers. The k-means NUMA Optimized Routine knor) library has (i) in-memory knori), (ii) distributed memory (knord), and (ii) semi-external memory (\textsf{knors}) modules that radically improve the performance of k-means for varying memory and hardware budgets. knori boosts performance for single machine datasets by an order of magnitude or more. \textsf{knors} improves the scalability of k-means on a memory budget using SSDs. knors scales to billions of points on a single machine, using a fraction of the resources that distributed in-memory systems require. knord retains knori's performance characteristics, while scaling in-memory through distributed computation in the cloud. knor modifies Elkan's triangle inequality pruning algorithm such that we utilize it on billion-point datasets without the significant memory overhead of the original algorithm. We demonstrate knor outperforms distributed commercial products like H2O, Turi (formerly Dato, GraphLab) and Spark's MLlib by more than an order of magnitude for datasets of 107 to 109 points.

Sparse matrix multiplication is traditionally performed in memory and scales to large matrices using the distributed memory of multiple nodes. In contrast, we scale sparse matrix multiplication beyond memory capacity by implementing sparse matrix dense matrix multiplication (SpMM) in a semi-external memory (SEM) fashion; i.e., we keep the sparse matrix on commodity SSDs and dense matrices in memory. Our SEM-SpMM incorporates many in-memory optimizations for large power-law graphs. It outperforms the in-memory implementations of Trilinos and Intel MKL and scales to billion-node graphs, far beyond the limitations of memory. Furthermore, on a single large parallel machine, our SEM-SpMM operates as fast as the distributed implementations of Trilinos using five times as much processing power. We also run our implementation in memory (IM-SpMM) to quantify the overhead of keeping data on SSDs. SEM-SpMM achieves almost 100 percent performance of IM-SpMM on graphs when the dense matrix has more than four columns; it achieves at least 65 percent performance of IM-SpMM on all inputs. We apply our SpMM to three important data analysis tasks-PageRank, eigensolving, and non-negative matrix factorization-and show that our SEM implementations significantly advance the state of the art.

We describe a storage system that removes I/O bottlenecks to achieve more than one million IOPS based on a user-space file abstraction for arrays of commodity SSDs. The file abstraction refactors I/O scheduling and placement for extreme parallelism and non-uniform memory and I/O. The system includes a set-associative, parallel page cache in the user space. We redesign page caching to eliminate CPU overhead and lock-contention in non-uniform memory architecture machines. We evaluate our design on a 32 core NUMA machine with four, eight-core processors. Experiments show that our design delivers 1.23 million 512-byte read IOPS. The page cache realizes the scalable IOPS of Linux asynchronous I/O (AIO) and increases user-perceived I/O performance linearly with cache hit rates. The parallel, set-associative cache matches the cache hit rates of the global Linux page cache under real workloads.