Daily Papers

Scaling up Large Language Model(LLM) training involves fitting a tremendous amount of training parameters across a limited number of workers. However, methods like ZeRO-3 that drastically reduce GPU memory pressure often incur heavy communication to ensure global synchronization and consistency. Established efforts such as ZeRO++ use secondary partitions to avoid inter-node communications, given that intra-node GPU-GPU transfer generally has more bandwidth and lower latency than inter-node connections. However, as more capable infrastructure like Frontier, equipped with AMD GPUs, emerged with impressive computing capability, there is a need for investigations on the hardware topology and to develop targeted strategies to improve training efficiency. In this work, we propose a collection of communication and optimization strategies for ZeRO++ to reduce communication costs and improve memory utilization. In this paper, we propose a 3-level hierarchical partitioning specifically for the current Top-1 supercomputing cluster, Frontier, which aims at leveraging various bandwidths across layers of communications (GCD-GCD, GPU-GPU, and inter-node) to reduce communication overhead. For a 20B GPT model, we observe a 1.71x increase in TFLOPS per GPU when compared with ZeRO++ up to 384 GCDs and a scaling efficiency of 0.94 for up to 384 GCDs. To the best of our knowledge, our work is also the first effort to efficiently optimize LLM workloads on Frontier AMD GPUs.

Large Language Models (LLMs) have emerged as powerful tools for Text-to-SQL tasks, exhibiting remarkable reasoning capabilities. Different from tasks such as math word problems and commonsense reasoning, SQL solutions have a relatively fixed pattern. This facilitates the investigation of whether LLMs can benefit from categorical thinking, mirroring how humans acquire knowledge through inductive reasoning based on comparable examples. In this study, we propose that employing query group partitioning allows LLMs to focus on learning the thought processes specific to a single problem type, consequently enhancing their reasoning abilities across diverse difficulty levels and problem categories. Our experiments reveal that multiple advanced LLMs, when equipped with PTD-SQL, can either surpass or match previous state-of-the-art (SOTA) methods on the Spider and BIRD datasets. Intriguingly, models with varying initial performances have exhibited significant improvements, mainly at the boundary of their capabilities after targeted drilling, suggesting a parallel with human progress. Code is available at https://github.com/lrlbbzl/PTD-SQL.

This paper focuses on the EmoWoz dataset, an extension of MultiWOZ that provides emotion labels for the dialogues. MultiWOZ was partitioned initially for another purpose, resulting in a distributional shift when considering the new purpose of emotion recognition. The emotion tags in EmoWoz are highly imbalanced and unevenly distributed across the partitions, which causes sub-optimal performance and poor comparison of models. We propose a stratified sampling scheme based on emotion tags to address this issue, improve the dataset's distribution, and reduce dataset shift. We also introduce a special technique to handle conversation (sequential) data with many emotional tags. Using our proposed sampling method, models built upon EmoWoz can perform better, making it a more reliable resource for training conversational agents with emotional intelligence. We recommend that future researchers use this new partitioning to ensure consistent and accurate performance evaluations.

Clustering is a NP-hard problem. Thus, no optimal algorithm exists, heuristics are applied to cluster the data. Heuristics can be very resource-intensive, if not applied properly. For substantially large data sets computational efficiencies can be achieved by reducing the input space if a minimal loss of information can be achieved. Clustering algorithms, in general, face two common problems: 1) these converge to different settings with different initial conditions and; 2) the number of clusters has to be arbitrarily decided beforehand. This problem has become critical in the realm of big data. Recently, clustering algorithms have emerged which can speedup computations using parallel processing over the grid but face the aforementioned problems. Goals: Our goals are to find methods to cluster data which: 1) guarantee convergence to the same settings irrespective of the initial conditions; 2) eliminate the need to establish the number of clusters beforehand, and 3) can be applied to cluster large datasets. Methods: We introduce a method that combines probabilistic and combinatorial clustering methods to produce repeatable and compact clusters that are not sensitive to initial conditions. This method harnesses the power of k-means (a combinatorial clustering method) to cluster/partition very large dimensional datasets and uses the Gaussian Mixture Model (a probabilistic clustering method) to validate the k-means partitions. Results: We show that this method produces very compact clusters that are not sensitive to initial conditions. This method can be used to identify the most 'separable' set in a dataset which increases the 'clusterability' of a dataset. This method also eliminates the need to specify the number of clusters in advance.

Design flows use graph partitioning both as a precursor to place and route for single devices, and to divide netlists or task graphs among multiple devices. Partitioners have accommodated FPGA heterogeneity via multi-resource constraints, but have not yet exploited the corresponding ability to implement some computations in multiple ways (e.g., LUTs vs. DSP blocks), which could enable a superior solution. This paper introduces multi-personality graph partitioning, which incorporates aspects of resource mapping into partitioning. We present a modified multi-level KLFM partitioning algorithm that also performs heterogeneous resource mapping for nodes with multiple potential implementations (multiple personalities). We evaluate several variants of our multi-personality FPGA circuit partitioner using 21 circuits and benchmark graphs, and show that dynamic resource mapping improves cut size on average by 27% over static mapping for these circuits. We further show that it improves deviation from target resource utilizations by 50% over post-partitioning resource mapping.

Accurately determining salient regions of an image is challenging when labeled data is scarce. DINO-based self-supervised approaches have recently leveraged meaningful image semantics captured by patch-wise features for locating foreground objects. Recent methods have also incorporated intuitive priors and demonstrated value in unsupervised methods for object partitioning. In this paper, we propose SEMPART, which jointly infers coarse and fine bi-partitions over an image's DINO-based semantic graph. Furthermore, SEMPART preserves fine boundary details using graph-driven regularization and successfully distills the coarse mask semantics into the fine mask. Our salient object detection and single object localization findings suggest that SEMPART produces high-quality masks rapidly without additional post-processing and benefits from co-optimizing the coarse and fine branches.

Polygonal meshes are ubiquitous, but have only played a relatively minor role in the deep learning revolution. State-of-the-art neural generative models for 3D shapes learn implicit functions and generate meshes via expensive iso-surfacing. We overcome these challenges by employing a classical spatial data structure from computer graphics, Binary Space Partitioning (BSP), to facilitate 3D learning. The core operation of BSP involves recursive subdivision of 3D space to obtain convex sets. By exploiting this property, we devise BSP-Net, a network that learns to represent a 3D shape via convex decomposition without supervision. The network is trained to reconstruct a shape using a set of convexes obtained from a BSP-tree built over a set of planes, where the planes and convexes are both defined by learned network weights. BSP-Net directly outputs polygonal meshes from the inferred convexes. The generated meshes are watertight, compact (i.e., low-poly), and well suited to represent sharp geometry. We show that the reconstruction quality by BSP-Net is competitive with those from state-of-the-art methods while using much fewer primitives. We also explore variations to BSP-Net including using a more generic decoder for reconstruction, more general primitives than planes, as well as training a generative model with variational auto-encoders. Code is available at https://github.com/czq142857/BSP-NET-original.

Quantum algorithms are usually described as monolithic circuits, becoming large at modest input size. Near-term quantum architectures can only manage a small number of qubits. We develop an automated method to distribute quantum circuits over multiple agents, minimising quantum communication between them. We reduce the problem to hypergraph partitioning and then solve it with state-of-the-art optimisers. This makes our approach useful in practice, unlike previous methods. Our implementation is evaluated on five quantum circuits of practical relevance.

Large Language Models (LLMs) have demonstrated impressive performance across various downstream tasks. When training these models, there is a growing inclination to process more tokens on larger training scales but with relatively smaller model sizes. Zero Redundancy Optimizer (ZeRO), although effective in conventional training environments, grapples with scaling challenges when confronted with this emerging paradigm. To this end, we propose a novel LLM training framework AMSP, which undertakes a granular partitioning of model states, encompassing parameters (P), gradient (G), and optimizer states (OS). Specifically, AMSP(1) builds a unified partitioning space, enabling independent partitioning strategies for P, G, and OS; (2) incorporates a scale-aware partitioner to autonomously search for optimal partitioning strategies: (3) designs a dedicated communication optimizer to ensure proficient management of data placement discrepancies arising from diverse partitioning strategies. Our evaluations show that AMSP achieves up to 90.3% scaling efficiency across 1024 GPUs.

Scaling Transformers to longer sequence lengths has been a major problem in the last several years, promising to improve performance in language modeling and high-resolution image understanding, as well as to unlock new applications in code, audio, and video generation. The attention layer is the main bottleneck in scaling to longer sequences, as its runtime and memory increase quadratically in the sequence length. FlashAttention exploits the asymmetric GPU memory hierarchy to bring significant memory saving (linear instead of quadratic) and runtime speedup (2-4times compared to optimized baselines), with no approximation. However, FlashAttention is still not nearly as fast as optimized matrix-multiply (GEMM) operations, reaching only 25-40\% of the theoretical maximum FLOPs/s. We observe that the inefficiency is due to suboptimal work partitioning between different thread blocks and warps on the GPU, causing either low-occupancy or unnecessary shared memory reads/writes. We propose FlashAttention-2, with better work partitioning to address these issues. In particular, we (1) tweak the algorithm to reduce the number of non-matmul FLOPs (2) parallelize the attention computation, even for a single head, across different thread blocks to increase occupancy, and (3) within each thread block, distribute the work between warps to reduce communication through shared memory. These yield around 2times speedup compared to FlashAttention, reaching 50-73\% of the theoretical maximum FLOPs/s on A100 and getting close to the efficiency of GEMM operations. We empirically validate that when used end-to-end to train GPT-style models, FlashAttention-2 reaches training speed of up to 225 TFLOPs/s per A100 GPU (72\% model FLOPs utilization).

We present GSPMD, an automatic, compiler-based parallelization system for common machine learning computations. It allows users to write programs in the same way as for a single device, then give hints through a few annotations on how to distribute tensors, based on which GSPMD will parallelize the computation. Its representation of partitioning is simple yet general, allowing it to express different or mixed paradigms of parallelism on a wide variety of models. GSPMD infers the partitioning for every operator based on limited user annotations, making it convenient to scale existing single-device programs. It solves several technical challenges for production usage, allowing GSPMD to achieve 50% to 62% compute utilization on up to 2048 Cloud TPUv3 cores for models with up to one trillion parameters.

Clustering is an unsupervised learning problem that aims to partition unlabelled data points into groups with similar features. Traditional clustering algorithms provide limited insight into the groups they find as their main focus is accuracy and not the interpretability of the group assignments. This has spurred a recent line of work on explainable machine learning for clustering. In this paper we focus on the cluster description problem where, given a dataset and its partition into clusters, the task is to explain the clusters. We introduce a new approach to explain clusters by constructing polyhedra around each cluster while minimizing either the complexity of the resulting polyhedra or the number of features used in the description. We formulate the cluster description problem as an integer program and present a column generation approach to search over an exponential number of candidate half-spaces that can be used to build the polyhedra. To deal with large datasets, we introduce a novel grouping scheme that first forms smaller groups of data points and then builds the polyhedra around the grouped data, a strategy which out-performs simply sub-sampling data. Compared to state of the art cluster description algorithms, our approach is able to achieve competitive interpretability with improved description accuracy.

Pairwise clustering, in general, partitions a set of items via a known similarity function. In our treatment, clustering is modeled as a transductive prediction problem. Thus rather than beginning with a known similarity function, the function instead is hidden and the learner only receives a random sample consisting of a subset of the pairwise similarities. An additional set of pairwise side-information may be given to the learner, which then determines the inductive bias of our algorithms. We measure performance not based on the recovery of the hidden similarity function, but instead on how well we classify each item. We give tight bounds on the number of misclassifications. We provide two algorithms. The first algorithm SACA is a simple agglomerative clustering algorithm which runs in near linear time, and which serves as a baseline for our analyses. Whereas the second algorithm, RGCA, enables the incorporation of side-information which may lead to improved bounds at the cost of a longer running time.

Clustering has been a major research topic in the field of machine learning, one to which Deep Learning has recently been applied with significant success. However, an aspect of clustering that is not addressed by existing deep clustering methods, is that of efficiently producing multiple, diverse partitionings for a given dataset. This is particularly important, as a diverse set of base clusterings are necessary for consensus clustering, which has been found to produce better and more robust results than relying on a single clustering. To address this gap, we propose DivClust, a diversity controlling loss that can be incorporated into existing deep clustering frameworks to produce multiple clusterings with the desired degree of diversity. We conduct experiments with multiple datasets and deep clustering frameworks and show that: a) our method effectively controls diversity across frameworks and datasets with very small additional computational cost, b) the sets of clusterings learned by DivClust include solutions that significantly outperform single-clustering baselines, and c) using an off-the-shelf consensus clustering algorithm, DivClust produces consensus clustering solutions that consistently outperform single-clustering baselines, effectively improving the performance of the base deep clustering framework.

Many clustering schemes are defined by optimizing an objective function defined on the partitions of the underlying set of a finite metric space. In this paper, we construct a framework for studying what happens when we instead impose various structural conditions on the clustering schemes, under the general heading of functoriality. Functoriality refers to the idea that one should be able to compare the results of clustering algorithms as one varies the data set, for example by adding points or by applying functions to it. We show that within this framework, one can prove a theorems analogous to one of J. Kleinberg, in which for example one obtains an existence and uniqueness theorem instead of a non-existence result. We obtain a full classification of all clustering schemes satisfying a condition we refer to as excisiveness. The classification can be changed by varying the notion of maps of finite metric spaces. The conditions occur naturally when one considers clustering as the statistical version of the geometric notion of connected components. By varying the degree of functoriality that one requires from the schemes it is possible to construct richer families of clustering schemes that exhibit sensitivity to density.

The notion of shortcut partition, introduced recently by Chang, Conroy, Le, Milenkovi\'c, Solomon, and Than [CCLMST23], is a new type of graph partition into low-diameter clusters. Roughly speaking, the shortcut partition guarantees that for every two vertices u and v in the graph, there exists a path between u and v that intersects only a few clusters. They proved that any planar graph admits a shortcut partition and gave several applications, including a construction of tree cover for arbitrary planar graphs with stretch 1+varepsilon and O(1) many trees for any fixed varepsilon in (0,1). However, the construction heavily exploits planarity in multiple steps, and is thus inherently limited to planar graphs. In this work, we breach the "planarity barrier" to construct a shortcut partition for K_r-minor-free graphs for any r. To this end, we take a completely different approach -- our key contribution is a novel deterministic variant of the cop decomposition in minor-free graphs [And86, AGG14]. Our shortcut partition for K_r-minor-free graphs yields several direct applications. Most notably, we construct the first optimal distance oracle for K_r-minor-free graphs, with 1+varepsilon stretch, linear space, and constant query time for any fixed varepsilon in (0,1). The previous best distance oracle [AG06] uses O(nlog n) space and O(log n) query time, and its construction relies on Robertson-Seymour structural theorem and other sophisticated tools. We also obtain the first tree cover of O(1) size for minor-free graphs with stretch 1+varepsilon, while the previous best (1+varepsilon)-tree cover has size O(log^2 n) [BFN19].

Clustering is a fundamental building block of modern statistical analysis pipelines. Fair clustering has seen much attention from the machine learning community in recent years. We are some of the first to study fairness in the context of hierarchical clustering, after the results of Ahmadian et al. from NeurIPS in 2020. We evaluate our results using Dasgupta's cost function, perhaps one of the most prevalent theoretical metrics for hierarchical clustering evaluation. Our work vastly improves the previous O(n^{5/6}polylog(n)) fair approximation for cost to a near polylogarithmic O(n^delta polylog(n)) fair approximation for any constant deltain(0,1). This result establishes a cost-fairness tradeoff and extends to broader fairness constraints than the previous work. We also show how to alter existing hierarchical clusterings to guarantee fairness and cluster balance across any level in the hierarchy.

We consider the problem of constructing small coresets for k-Median in Euclidean spaces. Given a large set of data points Psubset R^d, a coreset is a much smaller set Ssubset R^d, so that the k-Median costs of any k centers w.r.t. P and S are close. Existing literature mainly focuses on the high-dimension case and there has been great success in obtaining dimension-independent bounds, whereas the case for small d is largely unexplored. Considering many applications of Euclidean clustering algorithms are in small dimensions and the lack of systematic studies in the current literature, this paper investigates coresets for k-Median in small dimensions. For small d, a natural question is whether existing near-optimal dimension-independent bounds can be significantly improved. We provide affirmative answers to this question for a range of parameters. Moreover, new lower bound results are also proved, which are the highest for small d. In particular, we completely settle the coreset size bound for 1-d k-Median (up to log factors). Interestingly, our results imply a strong separation between 1-d 1-Median and 1-d 2-Median. As far as we know, this is the first such separation between k=1 and k=2 in any dimension.

This paper discusses about a sorting algorithm which uses the concept of buckets where each bucket represents a certain number of digits. A two dimensional data structure is used where one dimension represents buckets i. e; number of digits and each bucket's corresponding dimensions represents the input numbers that belong to that bucket. Each bucket is then individually sorted. Since every preceding bucket elements will always be smaller than the succeeding buckets no comparison between them is required. By doing this we can significantly reduced the time complexity of any sorting algorithm used to sort the given set of inputs.

Efficient performance estimation of architectures drawn from large search spaces is essential to Neural Architecture Search. One-Shot methods tackle this challenge by training one supernet to approximate the performance of every architecture in the search space via weight-sharing, thereby drastically reducing the search cost. However, due to coupled optimization between child architectures caused by weight-sharing, One-Shot supernet's performance estimation could be inaccurate, leading to degraded search outcomes. To address this issue, Few-Shot NAS reduces the level of weight-sharing by splitting the One-Shot supernet into multiple separated sub-supernets via edge-wise (layer-wise) exhaustive partitioning. Since each partition of the supernet is not equally important, it necessitates the design of a more effective splitting criterion. In this work, we propose a gradient matching score (GM) that leverages gradient information at the shared weight for making informed splitting decisions. Intuitively, gradients from different child models can be used to identify whether they agree on how to update the shared modules, and subsequently to decide if they should share the same weight. Compared with exhaustive partitioning, the proposed criterion significantly reduces the branching factor per edge. This allows us to split more edges (layers) for a given budget, resulting in substantially improved performance as NAS search spaces usually include dozens of edges (layers). Extensive empirical evaluations of the proposed method on a wide range of search spaces (NASBench-201, DARTS, MobileNet Space), datasets (cifar10, cifar100, ImageNet) and search algorithms (DARTS, SNAS, RSPS, ProxylessNAS, OFA) demonstrate that it significantly outperforms its Few-Shot counterparts while surpassing previous comparable methods in terms of the accuracy of derived architectures.

Hierarchical clustering of networks consists in finding a tree of communities, such that lower levels of the hierarchy reveal finer-grained community structures. There are two main classes of algorithms tackling this problem. Divisive (top-down) algorithms recursively partition the nodes into two communities, until a stopping rule indicates that no further split is needed. In contrast, agglomerative (bottom-up) algorithms first identify the smallest community structure and then repeatedly merge the communities using a linkage method. In this article, we establish theoretical guarantees for the recovery of the hierarchical tree and community structure of a Hierarchical Stochastic Block Model by a bottom-up algorithm. We also establish that this bottom-up algorithm attains the information-theoretic threshold for exact recovery at intermediate levels of the hierarchy. Notably, these recovery conditions are less restrictive compared to those existing for top-down algorithms. This shows that bottom-up algorithms extend the feasible region for achieving exact recovery at intermediate levels. Numerical experiments on both synthetic and real data sets confirm the superiority of bottom-up algorithms over top-down algorithms. We also observe that top-down algorithms can produce dendrograms with inversions. These findings contribute to a better understanding of hierarchical clustering techniques and their applications in network analysis.

Data sharding, a technique for partitioning and distributing data among multiple servers or nodes, offers enhancements in the scalability, performance, and fault tolerance of extensive distributed systems. Nonetheless, this strategy introduces novel challenges, including load balancing among shards, management of node failures and data loss, and adaptation to evolving data and workload patterns. This paper proposes an innovative approach to tackle these challenges by empowering self-healing nodes with adaptive data sharding. Leveraging concepts such as self-replication, fractal regeneration, sentient data sharding, and symbiotic node clusters, our approach establishes a dynamic and resilient data sharding scheme capable of addressing diverse scenarios and meeting varied requirements. Implementation and evaluation of our approach involve a prototype system simulating a large-scale distributed database across various data sharding scenarios. Comparative analyses against existing data sharding techniques highlight the superior scalability, performance, fault tolerance, and adaptability of our approach. Additionally, the paper delves into potential applications and limitations, providing insights into the future research directions that can further advance this innovative approach.

Federated Learning (FL) is a machine learning paradigm that safeguards privacy by retaining client data on edge devices. However, optimizing FL in practice can be challenging due to the diverse and heterogeneous nature of the learning system. Though recent research has focused on improving the optimization of FL when distribution shifts occur among clients, ensuring global performance when multiple types of distribution shifts occur simultaneously among clients -- such as feature distribution shift, label distribution shift, and concept shift -- remain under-explored. In this paper, we identify the learning challenges posed by the simultaneous occurrence of diverse distribution shifts and propose a clustering principle to overcome these challenges. Through our research, we find that existing methods fail to address the clustering principle. Therefore, we propose a novel clustering algorithm framework, dubbed as FedRC, which adheres to our proposed clustering principle by incorporating a bi-level optimization problem and a novel objective function. Extensive experiments demonstrate that FedRC significantly outperforms other SOTA cluster-based FL methods. Our code is available at https://github.com/LINs-lab/FedRC.

Self-supervised features are the cornerstone of modern machine learning systems. They are typically pre-trained on data collections whose construction and curation typically require extensive human effort. This manual process has some limitations similar to those encountered in supervised learning, e.g., the crowd-sourced selection of data is costly and time-consuming, preventing scaling the dataset size. In this work, we consider the problem of automatic curation of high-quality datasets for self-supervised pre-training. We posit that such datasets should be large, diverse and balanced, and propose a clustering-based approach for building ones satisfying all these criteria. Our method involves successive and hierarchical applications of k-means on a large and diverse data repository to obtain clusters that distribute uniformly among data concepts, followed by a hierarchical, balanced sampling step from these clusters. Extensive experiments on three different data domains including web-based images, satellite images and text show that features trained on our automatically curated datasets outperform those trained on uncurated data while being on par or better than ones trained on manually curated data.

Compartmentalization effectively prevents initial corruption from turning into a successful attack. This paper presents O2C, a pioneering system designed to enforce OS kernel compartmentalization on the fly. It not only provides immediate remediation for sudden threats but also maintains consistent system availability through the enforcement process. O2C is empowered by the newest advancements of the eBPF ecosystem which allows to instrument eBPF programs that perform enforcement actions into the kernel at runtime. O2C takes the lead in embedding a machine learning model into eBPF programs, addressing unique challenges in on-the-fly compartmentalization. Our comprehensive evaluation shows that O2C effectively confines damage within the compartment. Further, we validate that decision tree is optimally suited for O2C owing to its advantages in processing tabular data, its explainable nature, and its compliance with the eBPF ecosystem. Last but not least, O2C is lightweight, showing negligible overhead and excellent sacalability system-wide.

Single-stage neural combinatorial optimization solvers have achieved near-optimal results on various small-scale combinatorial optimization (CO) problems without requiring expert knowledge. However, these solvers exhibit significant performance degradation when applied to large-scale CO problems. Recently, two-stage neural methods motivated by divide-and-conquer strategies have shown efficiency in addressing large-scale CO problems. Nevertheless, the performance of these methods highly relies on problem-specific heuristics in either the dividing or the conquering procedure, which limits their applicability to general CO problems. Moreover, these methods employ separate training schemes and ignore the interdependencies between the dividing and conquering strategies, often leading to sub-optimal solutions. To tackle these drawbacks, this article develops a unified neural divide-and-conquer framework (i.e., UDC) for solving general large-scale CO problems. UDC offers a Divide-Conquer-Reunion (DCR) training method to eliminate the negative impact of a sub-optimal dividing policy. Employing a high-efficiency Graph Neural Network (GNN) for global instance dividing and a fixed-length sub-path solver for conquering divided sub-problems, the proposed UDC framework demonstrates extensive applicability, achieving superior performance in 10 representative large-scale CO problems. The code is available at https://github.com/CIAM-Group/NCO_code/tree/main/single_objective/UDC-Large-scale-CO-master.

We consider the problem of graph matching, or learning vertex correspondence, between two correlated stochastic block models (SBMs). The graph matching problem arises in various fields, including computer vision, natural language processing and bioinformatics, and in particular, matching graphs with inherent community structure has significance related to de-anonymization of correlated social networks. Compared to the correlated Erdos-Renyi (ER) model, where various efficient algorithms have been developed, among which a few algorithms have been proven to achieve the exact matching with constant edge correlation, no low-order polynomial algorithm has been known to achieve exact matching for the correlated SBMs with constant correlation. In this work, we propose an efficient algorithm for matching graphs with community structure, based on the comparison between partition trees rooted from each vertex, by extending the idea of Mao et al. (2021) to graphs with communities. The partition tree divides the large neighborhoods of each vertex into disjoint subsets using their edge statistics to different communities. Our algorithm is the first low-order polynomial-time algorithm achieving exact matching between two correlated SBMs with high probability in dense graphs.

We introduce a novel neural network-based algorithm to compute optimal transport (OT) plans for general cost functionals. In contrast to common Euclidean costs, i.e., ell^1 or ell^2, such functionals provide more flexibility and allow using auxiliary information, such as class labels, to construct the required transport map. Existing methods for general costs are discrete and have limitations in practice, i.e. they do not provide an out-of-sample estimation. We address the challenge of designing a continuous OT approach for general costs that generalizes to new data points in high-dimensional spaces, such as images. Additionally, we provide the theoretical error analysis for our recovered transport plans. As an application, we construct a cost functional to map data distributions while preserving the class-wise structure.

This paper studies the fair range clustering problem in which the data points are from different demographic groups and the goal is to pick k centers with the minimum clustering cost such that each group is at least minimally represented in the centers set and no group dominates the centers set. More precisely, given a set of n points in a metric space (P,d) where each point belongs to one of the ell different demographics (i.e., P = P_1 uplus P_2 uplus cdots uplus P_ell) and a set of ell intervals [alpha_1, beta_1], cdots, [alpha_ell, beta_ell] on desired number of centers from each group, the goal is to pick a set of k centers C with minimum ell_p-clustering cost (i.e., (sum_{vin P} d(v,C)^p)^{1/p}) such that for each group iin ell, |Ccap P_i| in [alpha_i, beta_i]. In particular, the fair range ell_p-clustering captures fair range k-center, k-median and k-means as its special cases. In this work, we provide efficient constant factor approximation algorithms for fair range ell_p-clustering for all values of pin [1,infty).

Planning the layout of bicycle-sharing stations is a complex process, especially in cities where bicycle sharing systems are just being implemented. Urban planners often have to make a lot of estimates based on both publicly available data and privately provided data from the administration and then use the Location-Allocation model popular in the field. Many municipalities in smaller cities may have difficulty hiring specialists to carry out such planning. This thesis proposes a new solution to streamline and facilitate the process of such planning by using spatial embedding methods. Based only on publicly available data from OpenStreetMap, and station layouts from 34 cities in Europe, a method has been developed to divide cities into micro-regions using the Uber H3 discrete global grid system and to indicate regions where it is worth placing a station based on existing systems in different cities using transfer learning. The result of the work is a mechanism to support planners in their decision making when planning a station layout with a choice of reference cities.

A new pre-exascale computer cluster has been designed to foster scientific progress and competitive innovation across European research systems, it is called LEONARDO. This paper describes the general architecture of the system and focuses on the technologies adopted for its GPU-accelerated partition. High density processing elements, fast data movement capabilities and mature software stack collections allow the machine to run intensive workloads in a flexible and scalable way. Scientific applications from traditional High Performance Computing (HPC) as well as emerging Artificial Intelligence (AI) domains can benefit from this large apparatus in terms of time and energy to solution.

In this paper, we introduce a novel graph-based method to classify the regions with similar climate in a local area. We refer our proposed method as Graph Partition Based Method (GPBM). Our proposed method attempts to overcome the shortcomings of the current state-of-the-art methods in the literature. It has no limit on the number of variables that can be used and also preserves the nature of climate data. To illustrate the capability of our proposed algorithm, we benchmark its performance with other state-of-the-art climate classification techniques. The climate data is collected from 24 synoptic stations in Fars province in southern Iran. The data includes seven climate variables stored as time series from 1951 to 2017. Our results exhibit that our proposed method performs a more realistic climate classification with less computational time. It can save more information during the climate classification process and is therefore efficient in further data analysis. Furthermore, using our method, we can introduce seasonal graphs to better investigate seasonal climate changes. To the best of our knowledge, our proposed method is the first graph-based climate classification system.

In this paper, we introduce the MoisesDB dataset for musical source separation. It consists of 240 tracks from 45 artists, covering twelve musical genres. For each song, we provide its individual audio sources, organized in a two-level hierarchical taxonomy of stems. This will facilitate building and evaluating fine-grained source separation systems that go beyond the limitation of using four stems (drums, bass, other, and vocals) due to lack of data. To facilitate the adoption of this dataset, we publish an easy-to-use Python library to download, process and use MoisesDB. Alongside a thorough documentation and analysis of the dataset contents, this work provides baseline results for open-source separation models for varying separation granularities (four, five, and six stems), and discuss their results.

We consider the problem of fairly allocating a sequence of indivisible items that arrive online in an arbitrary order to a group of n agents with additive normalized valuation functions. We consider both the allocation of goods and chores and propose algorithms for approximating maximin share (MMS) allocations. When agents have identical valuation functions the problem coincides with the semi-online machine covering problem (when items are goods) and load balancing problem (when items are chores), for both of which optimal competitive ratios have been achieved. In this paper, we consider the case when agents have general additive valuation functions. For the allocation of goods, we show that no competitive algorithm exists even when there are only three agents and propose an optimal 0.5-competitive algorithm for the case of two agents. For the allocation of chores, we propose a (2-1/n)-competitive algorithm for n>=3 agents and a square root of 2 (approximately 1.414)-competitive algorithm for two agents. Additionally, we show that no algorithm can do better than 15/11 (approximately 1.364)-competitive for two agents.

Clustering non-Euclidean data is difficult, and one of the most used algorithms besides hierarchical clustering is the popular algorithm Partitioning Around Medoids (PAM), also simply referred to as k-medoids clustering. In Euclidean geometry the mean-as used in k-means-is a good estimator for the cluster center, but this does not exist for arbitrary dissimilarities. PAM uses the medoid instead, the object with the smallest dissimilarity to all others in the cluster. This notion of centrality can be used with any (dis-)similarity, and thus is of high relevance to many domains and applications. A key issue with PAM is its high run time cost. We propose modifications to the PAM algorithm that achieve an O(k)-fold speedup in the second ("SWAP") phase of the algorithm, but will still find the same results as the original PAM algorithm. If we relax the choice of swaps performed (while retaining comparable quality), we can further accelerate the algorithm by eagerly performing additional swaps in each iteration. With the substantially faster SWAP, we can now explore faster initialization strategies, because (i) the classic ("BUILD") initialization now becomes the bottleneck, and (ii) our swap is fast enough to compensate for worse starting conditions. We also show how the CLARA and CLARANS algorithms benefit from the proposed modifications. While we do not study the parallelization of our approach in this work, it can easily be combined with earlier approaches to use PAM and CLARA on big data (some of which use PAM as a subroutine, hence can immediately benefit from these improvements), where the performance with high k becomes increasingly important. In experiments on real data with k=100,200, we observed a 458x respectively 1191x speedup compared to the original PAM SWAP algorithm, making PAM applicable to larger data sets, and in particular to higher k.

Clustering is a widely used unsupervised learning technique involving an intensive discrete optimization problem. Associative Memory models or AMs are differentiable neural networks defining a recursive dynamical system, which have been integrated with various deep learning architectures. We uncover a novel connection between the AM dynamics and the inherent discrete assignment necessary in clustering to propose a novel unconstrained continuous relaxation of the discrete clustering problem, enabling end-to-end differentiable clustering with AM, dubbed ClAM. Leveraging the pattern completion ability of AMs, we further develop a novel self-supervised clustering loss. Our evaluations on varied datasets demonstrate that ClAM benefits from the self-supervision, and significantly improves upon both the traditional Lloyd's k-means algorithm, and more recent continuous clustering relaxations (by upto 60% in terms of the Silhouette Coefficient).

Graph measures that express closeness or distance between nodes can be employed for graph nodes clustering using metric clustering algorithms. There are numerous measures applicable to this task, and which one performs better is an open question. We study the performance of 25 graph measures on generated graphs with different parameters. While usually measure comparisons are limited to general measure ranking on a particular dataset, we aim to explore the performance of various measures depending on graph features. Using an LFR graph generator, we create a dataset of 11780 graphs covering the whole LFR parameter space. For each graph, we assess the quality of clustering with k-means algorithm for each considered measure. Based on this, we determine the best measure for each area of the parameter space. We find that the parameter space consists of distinct zones where one particular measure is the best. We analyze the geometry of the resulting zones and describe it with simple criteria. Given particular graph parameters, this allows us to recommend a particular measure to use for clustering.

A spanning tree T of graph G is a rho-approximate universal Steiner tree (UST) for root vertex r if, for any subset of vertices S containing r, the cost of the minimal subgraph of T connecting S is within a rho factor of the minimum cost tree connecting S in G. Busch et al. (FOCS 2012) showed that every graph admits 2^{O(log n)}-approximate USTs by showing that USTs are equivalent to strong sparse partition hierarchies (up to poly-logs). Further, they posed poly-logarithmic USTs and strong sparse partition hierarchies as open questions. We settle these open questions by giving polynomial-time algorithms for computing both O(log ^ 7 n)-approximate USTs and poly-logarithmic strong sparse partition hierarchies. For graphs with constant doubling dimension or constant pathwidth we improve this to O(log n)-approximate USTs and O(1) strong sparse partition hierarchies. Our doubling dimension result is tight up to second order terms. We reduce the existence of these objects to the previously studied cluster aggregation problem and what we call dangling nets.

Fair division considers the allocation of scarce resources among agents in such a way that every agent gets a fair share. It is a fundamental problem in society and has received significant attention and rapid developments from the game theory and artificial intelligence communities in recent years. The majority of the fair division literature can be divided along at least two orthogonal directions: goods versus chores, and divisible versus indivisible resources. In this survey, besides describing the state of the art, we outline a number of interesting open questions and future directions in three mixed fair division settings: (i) indivisible goods and chores, (ii) divisible and indivisible goods (mixed goods), and (iii) indivisible goods with subsidy which can be viewed like a divisible good.

The input space of a neural network with ReLU-like activations is partitioned into multiple linear regions, each corresponding to a specific activation pattern of the included ReLU-like activations. We demonstrate that this partition exhibits the following encoding properties across a variety of deep learning models: (1) {\it determinism}: almost every linear region contains at most one training example. We can therefore represent almost every training example by a unique activation pattern, which is parameterized by a {\it neural code}; and (2) {\it categorization}: according to the neural code, simple algorithms, such as K-Means, K-NN, and logistic regression, can achieve fairly good performance on both training and test data. These encoding properties surprisingly suggest that {\it normal neural networks well-trained for classification behave as hash encoders without any extra efforts.} In addition, the encoding properties exhibit variability in different scenarios. {Further experiments demonstrate that {\it model size}, {\it training time}, {\it training sample size}, {\it regularization}, and {\it label noise} contribute in shaping the encoding properties, while the impacts of the first three are dominant.} We then define an {\it activation hash phase chart} to represent the space expanded by {model size}, training time, training sample size, and the encoding properties, which is divided into three canonical regions: {\it under-expressive regime}, {\it critically-expressive regime}, and {\it sufficiently-expressive regime}. The source code package is available at https://github.com/LeavesLei/activation-code.

Combining several (sample approximations of) distributions, which we term sub-posteriors, into a single distribution proportional to their product, is a common challenge. Occurring, for instance, in distributed 'big data' problems, or when working under multi-party privacy constraints. Many existing approaches resort to approximating the individual sub-posteriors for practical necessity, then find either an analytical approximation or sample approximation of the resulting (product-pooled) posterior. The quality of the posterior approximation for these approaches is poor when the sub-posteriors fall out-with a narrow range of distributional form, such as being approximately Gaussian. Recently, a Fusion approach has been proposed which finds an exact Monte Carlo approximation of the posterior, circumventing the drawbacks of approximate approaches. Unfortunately, existing Fusion approaches have a number of computational limitations, particularly when unifying a large number of sub-posteriors. In this paper, we generalise the theory underpinning existing Fusion approaches, and embed the resulting methodology within a recursive divide-and-conquer sequential Monte Carlo paradigm. This ultimately leads to a competitive Fusion approach, which is robust to increasing numbers of sub-posteriors.

We propose a graph clustering formulation based on multicut (a.k.a. weighted correlation clustering) on the complete graph. Our formulation does not need specification of the graph topology as in the original sparse formulation of multicut, making our approach simpler and potentially better performing. In contrast to unweighted correlation clustering we allow for a more expressive weighted cost structure. In dense multicut, the clustering objective is given in a factorized form as inner products of node feature vectors. This allows for an efficient formulation and inference in contrast to multicut/weighted correlation clustering, which has at least quadratic representation and computation complexity when working on the complete graph. We show how to rewrite classical greedy algorithms for multicut in our dense setting and how to modify them for greater efficiency and solution quality. In particular, our algorithms scale to graphs with tens of thousands of nodes. Empirical evidence on instance segmentation on Cityscapes and clustering of ImageNet datasets shows the merits of our approach.

Clustering is a class of unsupervised learning methods that has been extensively applied and studied in computer vision. Little work has been done to adapt it to the end-to-end training of visual features on large scale datasets. In this work, we present DeepCluster, a clustering method that jointly learns the parameters of a neural network and the cluster assignments of the resulting features. DeepCluster iteratively groups the features with a standard clustering algorithm, k-means, and uses the subsequent assignments as supervision to update the weights of the network. We apply DeepCluster to the unsupervised training of convolutional neural networks on large datasets like ImageNet and YFCC100M. The resulting model outperforms the current state of the art by a significant margin on all the standard benchmarks.

We introduce Compartmentalized Diffusion Models (CDM), a method to train different diffusion models (or prompts) on distinct data sources and arbitrarily compose them at inference time. The individual models can be trained in isolation, at different times, and on different distributions and domains and can be later composed to achieve performance comparable to a paragon model trained on all data simultaneously. Furthermore, each model only contains information about the subset of the data it was exposed to during training, enabling several forms of training data protection. In particular, CDMs are the first method to enable both selective forgetting and continual learning for large-scale diffusion models, as well as allowing serving customized models based on the user's access rights. CDMs also allow determining the importance of a subset of the data in generating particular samples.

Reasoning models have demonstrated remarkable progress in solving complex and logic-intensive tasks by generating extended Chain-of-Thoughts (CoTs) prior to arriving at a final answer. Yet, the emergence of this "slow-thinking" paradigm, with numerous tokens generated in sequence, inevitably introduces substantial computational overhead. To this end, it highlights an urgent need for effective acceleration. This survey aims to provide a comprehensive overview of recent advances in efficient reasoning. It categorizes existing works into three key directions: (1) shorter - compressing lengthy CoTs into concise yet effective reasoning chains; (2) smaller - developing compact language models with strong reasoning capabilities through techniques such as knowledge distillation, other model compression techniques, and reinforcement learning; and (3) faster - designing efficient decoding strategies to accelerate inference. A curated collection of papers discussed in this survey is available in our GitHub repository.

Enterprise data lakes often suffer from substantial amounts of duplicate and redundant data, with data volumes ranging from terabytes to petabytes. This leads to both increased storage costs and unnecessarily high maintenance costs for these datasets. In this work, we focus on identifying and reducing redundancy in enterprise data lakes by addressing the problem of 'dataset containment'. To the best of our knowledge, this is one of the first works that addresses table-level containment at a large scale. We propose R2D2: a three-step hierarchical pipeline that efficiently identifies almost all instances of containment by progressively reducing the search space in the data lake. It first builds (i) a schema containment graph, followed by (ii) statistical min-max pruning, and finally, (iii) content level pruning. We further propose minimizing the total storage and access costs by optimally identifying redundant datasets that can be deleted (and reconstructed on demand) while respecting latency constraints. We implement our system on Azure Databricks clusters using Apache Spark for enterprise data stored in ADLS Gen2, and on AWS clusters for open-source data. In contrast to existing modified baselines that are inaccurate or take several days to run, our pipeline can process an enterprise customer data lake at the TB scale in approximately 5 hours with high accuracy. We present theoretical results as well as extensive empirical validation on both enterprise (scale of TBs) and open-source datasets (scale of MBs - GBs), which showcase the effectiveness of our pipeline.

While dataset condensation effectively enhances training efficiency, its application in on-device scenarios brings unique challenges. 1) Due to the fluctuating computational resources of these devices, there's a demand for a flexible dataset size that diverges from a predefined size. 2) The limited computational power on devices often prevents additional condensation operations. These two challenges connect to the "subset degradation problem" in traditional dataset condensation: a subset from a larger condensed dataset is often unrepresentative compared to directly condensing the whole dataset to that smaller size. In this paper, we propose Multisize Dataset Condensation (MDC) by compressing N condensation processes into a single condensation process to obtain datasets with multiple sizes. Specifically, we introduce an "adaptive subset loss" on top of the basic condensation loss to mitigate the "subset degradation problem". Our MDC method offers several benefits: 1) No additional condensation process is required; 2) reduced storage requirement by reusing condensed images. Experiments validate our findings on networks including ConvNet, ResNet and DenseNet, and datasets including SVHN, CIFAR-10, CIFAR-100 and ImageNet. For example, we achieved 6.40% average accuracy gains on condensing CIFAR-10 to ten images per class. Code is available at: https://github.com/he-y/Multisize-Dataset-Condensation.

Video applications and analytics are routinely projected as a stressing and significant service of the Nationwide Public Safety Broadband Network. As part of a NIST PSCR funded effort, the New Jersey Office of Homeland Security and Preparedness and MIT Lincoln Laboratory have been developing a computer vision dataset of operational and representative public safety scenarios. The scale and scope of this dataset necessitates a hierarchical organization approach for efficient compute and storage. We overview architectural considerations using the Lincoln Laboratory Supercomputing Cluster as a test architecture. We then describe how we intelligently organized the dataset across LLSC and evaluated it with large scale imagery inference across terabytes of data.

Model order reduction has been extensively studied over the last two decades. Projection-based methods such as the Proper Orthogonal Decomposition and the Reduced Basis Method enjoy the important advantages of Galerkin methods in the derivation of the reduced problem, but are limited to linear data compression for which the reduced solution is sought as a linear combination of spatial modes. Nonlinear data compression must be used when the solution manifold is not embedded in a low-dimensional subspace. Early methods involve piecewise linear data compression, by constructing a dictionary of reduced-order models tailored to a partition of the solution manifold. In this work, we introduce the concept of optimal partition of the solution manifold in terms of normalized Kolmogorov widths, and prove that the optimal partitions can be found by means of a representative-based clustering algorithm using the sine dissimilarity measure on the solution manifold.

Vector databases have emerged as key enablers for bridging intelligent applications with unstructured data, providing generic search and management support for embedding vectors extracted from the raw unstructured data. As multiple data users can share the same database infrastructure, multi-tenancy support for vector databases is increasingly desirable. This hinges on an efficient filtered search operation, i.e., only querying the vectors accessible to a particular tenant. Multi-tenancy in vector databases is currently achieved by building either a single, shared index among all tenants, or a per-tenant index. The former optimizes for memory efficiency at the expense of search performance, while the latter does the opposite. Instead, this paper presents Curator, an in-memory vector index design tailored for multi-tenant queries that simultaneously achieves the two conflicting goals, low memory overhead and high performance for queries, vector insertion, and deletion. Curator indexes each tenant's vectors with a tenant-specific clustering tree and encodes these trees compactly as sub-trees of a shared clustering tree. Each tenant's clustering tree adapts dynamically to its unique vector distribution, while maintaining a low per-tenant memory footprint. Our evaluation, based on two widely used data sets, confirms that Curator delivers search performance on par with per-tenant indexing, while maintaining memory consumption at the same level as metadata filtering on a single, shared index.

Driven by advances in recording technology, large-scale high-dimensional datasets have emerged across many scientific disciplines. Especially in biology, clustering is often used to gain insights into the structure of such datasets, for instance to understand the organization of different cell types. However, clustering is known to scale poorly to high dimensions, even though the exact impact of dimensionality is unclear as current benchmark datasets are mostly two-dimensional. Here we propose MNIST-Nd, a set of synthetic datasets that share a key property of real-world datasets, namely that individual samples are noisy and clusters do not perfectly separate. MNIST-Nd is obtained by training mixture variational autoencoders with 2 to 64 latent dimensions on MNIST, resulting in six datasets with comparable structure but varying dimensionality. It thus offers the chance to disentangle the impact of dimensionality on clustering. Preliminary common clustering algorithm benchmarks on MNIST-Nd suggest that Leiden is the most robust for growing dimensions.

We study the problem of fairly allocating indivisible goods among a set of agents. Our focus is on the existence of allocations that give each agent their maximin fair share--the value they are guaranteed if they divide the goods into as many bundles as there are agents, and receive their lowest valued bundle. An MMS allocation is one where every agent receives at least their maximin fair share. We examine the existence of such allocations when agents have cost utilities. In this setting, each item has an associated cost, and an agent's valuation for an item is the cost of the item if it is useful to them, and zero otherwise. Our main results indicate that cost utilities are a promising restriction for achieving MMS. We show that for the case of three agents with cost utilities, an MMS allocation always exists. We also show that when preferences are restricted slightly further--to what we call laminar set approvals--we can guarantee MMS allocations for any number of agents. Finally, we explore if it is possible to guarantee each agent their maximin fair share while using a strategyproof mechanism.

The k-means++ seeding algorithm (Arthur & Vassilvitskii, 2007) is widely used in practice for the k-means clustering problem where the goal is to cluster a dataset X subset R ^d into k clusters. The popularity of this algorithm is due to its simplicity and provable guarantee of being O(log k) competitive with the optimal solution in expectation. However, its running time is O(|X|kd), making it expensive for large datasets. In this work, we present a simple and effective rejection sampling based approach for speeding up k-means++. Our first method runs in time O(nnz (X) + beta k^2d) while still being O(log k ) competitive in expectation. Here, beta is a parameter which is the ratio of the variance of the dataset to the optimal k-means cost in expectation and O hides logarithmic factors in k and |X|. Our second method presents a new trade-off between computational cost and solution quality. It incurs an additional scale-invariant factor of k^{-Omega( m/beta)} Var (X) in addition to the O(log k) guarantee of k-means++ improving upon a result of (Bachem et al, 2016a) who get an additional factor of m^{-1}Var(X) while still running in time O(nnz(X) + mk^2d). We perform extensive empirical evaluations to validate our theoretical results and to show the effectiveness of our approach on real datasets.

High-precision modeling of systems is one of the main areas of industrial data analysis. Models of systems, their digital twins, are used to predict their behavior under various conditions. We have developed several models of a storage system using machine learning-based generative models. The system consists of several components: hard disk drive (HDD) and solid-state drive (SSD) storage pools with different RAID schemes and cache. Each storage component is represented by a probabilistic model that describes the probability distribution of the component performance in terms of IOPS and latency, depending on their configuration and external data load parameters. The results of the experiments demonstrate the errors of 4-10 % for IOPS and 3-16 % for latency predictions depending on the components and models of the system. The predictions show up to 0.99 Pearson correlation with Little's law, which can be used for unsupervised reliability checks of the models. In addition, we present novel data sets that can be used for benchmarking regression algorithms, conditional generative models, and uncertainty estimation methods in machine learning.

In this work, we define a diffusion-based generative model capable of both music synthesis and source separation by learning the score of the joint probability density of sources sharing a context. Alongside the classic total inference tasks (i.e., generating a mixture, separating the sources), we also introduce and experiment on the partial generation task of source imputation, where we generate a subset of the sources given the others (e.g., play a piano track that goes well with the drums). Additionally, we introduce a novel inference method for the separation task based on Dirac likelihood functions. We train our model on Slakh2100, a standard dataset for musical source separation, provide qualitative results in the generation settings, and showcase competitive quantitative results in the source separation setting. Our method is the first example of a single model that can handle both generation and separation tasks, thus representing a step toward general audio models.