arXiv subjects

Edo Liberty

Publications and source records attributed to Edo Liberty.

At least 19 recordsLinked to original sources

arXiv2026

VQ-bench: A Composable Vector Quantization Framework

Vector quantization is an old problem but has recently become central to AI infrastructure. It is therefore experiencing a surge of renewed engineering and research activity. This paper provides a unified framework for developing and benchmarking new quantization algorithms. We describe 7 common conceptual quantization primitives and show how to compose them arbitrarily. We then re-express 25 common quantizers as pipelines of these primitives. Finally, we publish VQ-bench as open-source to be extended further and make reproducible benchmarks publicly available.

cs.AI↗

arXiv2026

Nearly Optimal Attention Coresets

We consider the problem of estimating the Attention mechanism in small space, and prove the existence of coresets for it of nearly optimal size. Specifically, we show that for any set of unit-norm keys and values $(K,V)$ in $\mathbb{R}^d$, there exists a subset $(K',V')$ of size at most $O({\sqrt{d} e^{\rho+o(\rho)}/\varepsilon})$ such that \[ \left\| \operatorname{Attn}(q,K,V)- \operatorname{Attn}(q,K',V') \right\| \le \varepsilon \] simultaneously for all queries whose norm is bounded by $\rho$. This outperforms the best known results for this problem. We also offer an improved lower bound showing that $\varepsilon$-coresets must have size $\Omega({\sqrt{d} e^{\rho}/\epsilon})$.

cs.DS↗

arXiv2025

SIGIR 2025 -- LiveRAG Challenge Report

The LiveRAG Challenge at SIGIR 2025, held between March and May 2025, provided a competitive platform for advancing Retrieval-Augmented Generation (RAG) technologies. Participants from academia and industry were invited to develop a RAG-based question-answering system using a fixed corpus (Fineweb-10BT) and a common open-source LLM (Falcon3-10B-Instruct). The goal was to facilitate challenging comparisons of retrieval and prompting strategies. During the Live Challenge Day, 70 teams from 27 different countries provided answers and supportive information to 500 unseen questions within a strict two-hour time window. Evaluation was conducted in two stages: first an automated LLM-as-a-judge approach was used to compute correctness and faithfulness score, then a manual review of top ranked submissions was conducted. The finalists were announced on June 12, 2025, with prizes awarded during the LiveRAG Workshop at SIGIR 2025 in Padua, Italy.

cs.CL↗

arXiv2024

Results of the Big ANN: NeurIPS'23 competition

The 2023 Big ANN Challenge, held at NeurIPS 2023, focused on advancing the state-of-the-art in indexing data structures and search algorithms for practical variants of Approximate Nearest Neighbor (ANN) search that reflect the growing complexity and diversity of workloads. Unlike prior challenges that emphasized scaling up classical ANN search ~\cite{DBLP:conf/nips/SimhadriWADBBCH21}, this competition addressed filtered search, out-of-distribution data, sparse and streaming variants of ANNS. Participants developed and submitted innovative solutions that were evaluated on new standard datasets with constrained computational resources. The results showcased significant improvements in search accuracy and efficiency over industry-standard baselines, with notable contributions from both academic and industrial teams. This paper summarizes the competition tracks, datasets, evaluation metrics, and the innovative approaches of the top-performing submissions, providing insights into the current advancements and future directions in the field of approximate nearest neighbor search.

cs.IR↗

arXiv2023

Bridging Dense and Sparse Maximum Inner Product Search

Maximum inner product search (MIPS) over dense and sparse vectors have progressed independently in a bifurcated literature for decades; the latter is better known as top-$k$ retrieval in Information Retrieval. This duality exists because sparse and dense vectors serve different end goals. That is despite the fact that they are manifestations of the same mathematical problem. In this work, we ask if algorithms for dense vectors could be applied effectively to sparse vectors, particularly those that violate the assumptions underlying top-$k$ retrieval methods. We study IVF-based retrieval where vectors are partitioned into clusters and only a fraction of clusters are searched during retrieval. We conduct a comprehensive analysis of dimensionality reduction for sparse vectors, and examine standard and spherical KMeans for partitioning. Our experiments demonstrate that IVF serves as an efficient solution for sparse MIPS. As byproducts, we identify two research opportunities and demonstrate their potential. First, we cast the IVF paradigm as a dynamic pruning technique and turn that insight into a novel organization of the inverted index for approximate MIPS for general sparse vectors. Second, we offer a unified regime for MIPS over vectors that have dense and sparse subspaces, and show its robustness to query distributions.

cs.IR↗

arXiv2023

An Approximate Algorithm for Maximum Inner Product Search over Streaming Sparse Vectors

Maximum Inner Product Search or top-k retrieval on sparse vectors is well-understood in information retrieval, with a number of mature algorithms that solve it exactly. However, all existing algorithms are tailored to text and frequency-based similarity measures. To achieve optimal memory footprint and query latency, they rely on the near stationarity of documents and on laws governing natural languages. We consider, instead, a setup in which collections are streaming -- necessitating dynamic indexing -- and where indexing and retrieval must work with arbitrarily distributed real-valued vectors. As we show, existing algorithms are no longer competitive in this setup, even against naive solutions. We investigate this gap and present a novel approximate solution, called Sinnamon, that can efficiently retrieve the top-k results for sparse real valued vectors drawn from arbitrary distributions. Notably, Sinnamon offers levers to trade-off memory consumption, latency, and accuracy, making the algorithm suitable for constrained applications and systems. We give theoretical results on the error introduced by the approximate nature of the algorithm, and present an empirical evaluation of its performance on two hardware platforms and synthetic and real-valued datasets. We conclude by laying out concrete directions for future research on this general top-k retrieval problem over sparse vectors.

cs.IR↗

arXiv2022

Even Simpler Deterministic Matrix Sketching

This paper provides a one-line proof of Frequent Directions (FD) for sketching streams of matrices. The simpler proof arises from sketching the covariance of the stream of matrices rather than the stream itself.

cs.DS↗

arXiv2021

Projective Clustering Product Quantization

This paper suggests the use of projective clustering based product quantization for improving nearest neighbor and max-inner-product vector search (MIPS) algorithms. We provide anisotropic and quantized variants of projective clustering which outperform previous clustering methods used for this problem such as ScaNN. We show that even with comparable running time complexity, in terms of lookup-multiply-adds, projective clustering produces more quantization centers resulting in more accurate dot-product estimates. We provide thorough experimentation to support our claims.

cs.DS↗

arXiv2020

Relative Error Streaming Quantiles

Estimating ranks, quantiles, and distributions over streaming data is a central task in data analysis and monitoring. Given a stream of $n$ items from a data universe equipped with a total order, the task is to compute a sketch (data structure) of size polylogarithmic in $n$. Given the sketch and a query item $y$, one should be able to approximate its rank in the stream, i.e., the number of stream elements smaller than or equal to $y$. Most works to date focused on additive $\varepsilon n$ error approximation, culminating in the KLL sketch that achieved optimal asymptotic behavior. This paper investigates multiplicative $(1\pm\varepsilon)$-error approximations to the rank. Practical motivation for multiplicative error stems from demands to understand the tails of distributions, and hence for sketches to be more accurate near extreme values. The most space-efficient algorithms due to prior work store either $O(\log(\varepsilon^2 n)/\varepsilon^2)$ or $O(\log^3(\varepsilon n)/\varepsilon)$ universe items. We present a randomized sketch storing $O(\log^{1.5}(\varepsilon n)/\varepsilon)$ items that can $(1\pm\varepsilon)$-approximate the rank of each universe item with high constant probability; this space bound is within an $O(\sqrt{\log(\varepsilon n)})$ factor of optimal. Our algorithm does not require prior knowledge of the stream length and is fully mergeable, rendering it suitable for parallel and distributed computing environments.

cs.DS↗

arXiv2019

Streaming Quantiles Algorithms with Small Space and Update Time

Approximating quantiles and distributions over streaming data has been studied for roughly two decades now. Recently, Karnin, Lang, and Liberty proposed the first asymptotically optimal algorithm for doing so. This manuscript complements their theoretical result by providing a practical variants of their algorithm with improved constants. For a given sketch size, our techniques provably reduce the upper bound on the sketch error by a factor of two. These improvements are verified experimentally. Our modified quantile sketch improves the latency as well by reducing the worst case update time from $O(1/\varepsilon)$ down to $O(\log (1/\varepsilon))$. We also suggest two algorithms for weighted item streams which offer improved asymptotic update times compared to naïve extensions. Finally, we provide a specialized data structure for these sketches which reduces both their memory footprints and update times.

cs.DS↗

arXiv2019

Asymmetric Random Projections

Random projections (RP) are a popular tool for reducing dimensionality while preserving local geometry. In many applications the data set to be projected is given to us in advance, yet the current RP techniques do not make use of information about the data. In this paper, we provide a computationally light way to extract statistics from the data that allows designing a data dependent RP with superior performance compared to data-oblivious RP. We tackle scenarios such as matrix multiplication and linear regression/classification in which we wish to estimate inner products between pairs of vectors from two possibly different sources. Our technique takes advantage of the difference between the sources and is provably superior to oblivious RPs. Additionally, we provide extensive experiments comparing RPs with our approach showing significant performance lifts in fast matrix multiplication, regression and classification problems.

cs.LG↗

arXiv2019

Discrepancy, Coresets, and Sketches in Machine Learning

This paper defines the notion of class discrepancy for families of functions. It shows that low discrepancy classes admit small offline and streaming coresets. We provide general techniques for bounding the class discrepancy of machine learning problems. As corollaries of the general technique we bound the discrepancy (and therefore coreset complexity) of logistic regression, sigmoid activation loss, matrix covariance, kernel density and any analytic function of the dot product or the squared distance. Our results prove the existence of epsilon-approximation O(sqrt{d}/epsilon) sized coresets for the above problems. This resolves the long-standing open problem regarding the coreset complexity of Gaussian kernel density estimation. We provide two more related but independent results. First, an exponential improvement of the widely used merge-and-reduce trick which gives improved streaming sketches for any low discrepancy problem. Second, an extremely simple deterministic algorithm for finding low discrepancy sequences (and therefore coresets) for any positive semi-definite kernel. This paper establishes some explicit connections between class discrepancy, coreset complexity, learnability, and streaming algorithms.

cs.LG↗

arXiv2019

ProxQuant: Quantized Neural Networks via Proximal Operators

To make deep neural networks feasible in resource-constrained environments (such as mobile devices), it is beneficial to quantize models by using low-precision weights. One common technique for quantizing neural networks is the straight-through gradient method, which enables back-propagation through the quantization mapping. Despite its empirical success, little is understood about why the straight-through gradient method works. Building upon a novel observation that the straight-through gradient method is in fact identical to the well-known Nesterov's dual-averaging algorithm on a quantization constrained optimization problem, we propose a more principled alternative approach, called ProxQuant, that formulates quantized network training as a regularized learning problem instead and optimizes it via the prox-gradient method. ProxQuant does back-propagation on the underlying full-precision vector and applies an efficient prox-operator in between stochastic gradient steps to encourage quantizedness. For quantizing ResNets and LSTMs, ProxQuant outperforms state-of-the-art results on binary quantization and is on par with state-of-the-art on multi-bit quantization. For binary quantization, our analysis shows both theoretically and experimentally that ProxQuant is more stable than the straight-through gradient method (i.e. BinaryConnect), challenging the indispensability of the straight-through gradient method and providing a powerful alternative.

cs.LG↗

arXiv2017

A High-Performance Algorithm for Identifying Frequent Items in Data Streams

Estimating frequencies of items over data streams is a common building block in streaming data measurement and analysis. Misra and Gries introduced their seminal algorithm for the problem in 1982, and the problem has since been revisited many times due its practicality and applicability. We describe a highly optimized version of Misra and Gries' algorithm that is suitable for deployment in industrial settings. Our code is made public via an open source library called DataSketches that is already used by several companies and production systems. Our algorithm improves on two theoretical and practical aspects of prior work. First, it handles weighted updates in amortized constant time, a common requirement in practice. Second, it uses a simple and fast method for merging summaries that asymptotically improves on prior work even for unweighted streams. We describe experiments confirming that our algorithms are more efficient than prior proposals.

cs.DS↗

arXiv2016

A Short Proof for Gap Independence of Simultaneous Iteration

This note provides a very short proof of a spectral gap independent property of the simultaneous iterations algorithm for finding the top singular space of a matrix. See Rokhlin-Szlam-Tygert-2009, Halko-Martinsson-Tropp-2011 and Musco-Musco-2015. The proof is terse but completely self contained and should be accessible to the linear algebra savvy reader.

math.NA↗

arXiv2016

Optimal Quantile Approximation in Streams

This paper resolves one of the longest standing basic problems in the streaming computational model. Namely, optimal construction of quantile sketches. An $\varepsilon$ approximate quantile sketch receives a stream of items $x_1,\ldots,x_n$ and allows one to approximate the rank of any query up to additive error $\varepsilon n$ with probability at least $1-δ$. The rank of a query $x$ is the number of stream items such that $x_i \le x$. The minimal sketch size required for this task is trivially at least $1/\varepsilon$. Felber and Ostrovsky obtain a $O((1/\varepsilon)\log(1/\varepsilon))$ space sketch for a fixed $δ$. To date, no better upper or lower bounds were known even for randomly permuted streams or for approximating a specific quantile, e.g.,\ the median. This paper obtains an $O((1/\varepsilon)\log \log (1/δ))$ space sketch and a matching lower bound. This resolves the open problem and proves a qualitative gap between randomized and deterministic quantile sketching. One of our contributions is a novel representation and modification of the widely used merge-and-reduce construction. This subtle modification allows for an analysis which is both tight and extremely simple. Similar techniques should be useful for improving other sketching objectives and geometric coreset constructions.

cs.DS↗

arXiv2016

Space Lower Bounds for Itemset Frequency Sketches

Given a database, computing the fraction of rows that contain a query itemset or determining whether this fraction is above some threshold are fundamental operations in data mining. A uniform sample of rows is a good sketch of the database in the sense that all sufficiently frequent itemsets and their approximate frequencies are recoverable from the sample, and the sketch size is independent of the number of rows in the original database. For many seemingly similar problems there are better sketching algorithms than uniform sampling. In this paper we show that for itemset frequency sketching this is not the case. That is, we prove that there exist classes of databases for which uniform sampling is a space optimal sketch for approximate itemset frequency analysis, up to constant or iterated-logarithmic factors.

cs.DS↗

arXiv2016

Efficient Frequent Directions Algorithm for Sparse Matrices

This paper describes Sparse Frequent Directions, a variant of Frequent Directions for sketching sparse matrices. It resembles the original algorithm in many ways: both receive the rows of an input matrix $A^{n \times d}$ one by one in the streaming setting and compute a small sketch $B \in R^{\ell \times d}$. Both share the same strong (provably optimal) asymptotic guarantees with respect to the space-accuracy tradeoff in the streaming setting. However, unlike Frequent Directions which runs in $O(nd\ell)$ time regardless of the sparsity of the input matrix $A$, Sparse Frequent Directions runs in $\tilde{O} (nnz(A)\ell + n\ell^2)$ time. Our analysis loosens the dependence on computing the Singular Value Decomposition (SVD) as a black box within the Frequent Directions algorithm. Our bounds require recent results on the properties of fast approximate SVD computations. Finally, we empirically demonstrate that these asymptotic improvements are practical and significant on real and synthetic data.

cs.DS↗