Pairing Clustered Inverted Indexes with kNN Graphs for Fast Approximate Retrieval over Learned Sparse Representations

Learned sparse representations form an effective and interpretable class of embeddings for text retrieval. While exact top-k retrieval over such embeddings faces efficiency challenges, a recent algorithm called Seismic has enabled remarkably fast, highly-accurate approximate retrieval. Seismic statically prunes inverted lists, organizes each list into geometrically-cohesive blocks, and augments each block with a summary vector. At query time, each inverted list associated with a query term is traversed one block at a time in an arbitrary order, with the inner product between the query and summaries determining if a block must be evaluated. When a block is deemed promising, its documents are fully evaluated with a forward index. Seismic is one to two orders of magnitude faster than state-of-the-art inverted index-based solutions and significantly outperforms the winning graph-based submissions to the BigANN 2023 Challenge. In this work, we speed up Seismic further by introducing two innovations to its query processing subroutine. First, we traverse blocks in order of importance, rather than arbitrarily. Second, we take the list of documents retrieved by Seismic and expand it to include the neighbors of each document using an offline k-regular nearest neighbor graph; the expanded list is then ranked to produce the final top-k set. Experiments on two public datasets show that our extension, named SeismicWave, can reach almost-exact accuracy levels and is up to 2.2x faster than Seismic.

Optimistic Query Routing in Clustering-based Approximate Maximum Inner Product Search

Clustering-based nearest neighbor search is a simple yet effective method in which data points are partitioned into geometric shards to form an index, and only a few shards are searched during query processing to find an approximate set of top-$k$ vectors. Even though the search efficacy is heavily influenced by the algorithm that identifies the set of shards to probe, it has received little attention in the literature. This work attempts to bridge that gap by studying the problem of routing in clustering-based maximum inner product search (MIPS). We begin by unpacking existing routing protocols and notice the surprising contribution of optimism. We then take a page from the sequential decision making literature and formalize that insight following the principle of ``optimism in the face of uncertainty.'' In particular, we present a new framework that incorporates the moments of the distribution of inner products within each shard to optimistically estimate the maximum inner product. We then present a simple instance of our algorithm that uses only the first two moments to reach the same accuracy as state-of-the-art routers such as \scann by probing up to $50%$ fewer points on a suite of benchmark MIPS datasets. Our algorithm is also space-efficient: we design a sketch of the second moment whose size is independent of the number of points and in practice requires storing only $O(1)$ additional vectors per shard.

Efficient Inverted Indexes for Approximate Retrieval over Learned Sparse Representations

Learned sparse representations form an attractive class of contextual embeddings for text retrieval. That is so because they are effective models of relevance and are interpretable by design. Despite their apparent compatibility with inverted indexes, however, retrieval over sparse embeddings remains challenging. That is due to the distributional differences between learned embeddings and term frequency-based lexical models of relevance such as BM25. Recognizing this challenge, a great deal of research has gone into, among other things, designing retrieval algorithms tailored to the properties of learned sparse representations, including approximate retrieval systems. In fact, this task featured prominently in the latest BigANN Challenge at NeurIPS 2023, where approximate algorithms were evaluated on a large benchmark dataset by throughput and recall. In this work, we propose a novel organization of the inverted index that enables fast yet effective approximate retrieval over learned sparse embeddings. Our approach organizes inverted lists into geometrically-cohesive blocks, each equipped with a summary vector. During query processing, we quickly determine if a block must be evaluated using the summaries. As we show experimentally, single-threaded query processing using our method, Seismic, reaches sub-millisecond per-query latency on various sparse embeddings of the MS MARCO dataset while maintaining high recall. Our results indicate that Seismic is one to two orders of magnitude faster than state-of-the-art inverted index-based solutions and further outperforms the winning (graph-based) submissions to the BigANN Challenge by a significant margin.

A Learning-to-Rank Formulation of Clustering-Based Approximate Nearest Neighbor Search

A critical piece of the modern information retrieval puzzle is approximate nearest neighbor search. Its objective is to return a set of $k$ data points that are closest to a query point, with its accuracy measured by the proportion of exact nearest neighbors captured in the returned set. One popular approach to this question is clustering: The indexing algorithm partitions data points into non-overlapping subsets and represents each partition by a point such as its centroid. The query processing algorithm first identifies the nearest clusters -- a process known as routing -- then performs a nearest neighbor search over those clusters only. In this work, we make a simple observation: The routing function solves a ranking problem. Its quality can therefore be assessed with a ranking metric, making the function amenable to learning-to-rank. Interestingly, ground-truth is often freely available: Given a query distribution in a top-$k$ configuration, the ground-truth is the set of clusters that contain the exact top-$k$ vectors. We develop this insight and apply it to Maximum Inner Product Search (MIPS). As we demonstrate empirically on various datasets, learning a simple linear function consistently improves the accuracy of clustering-based MIPS.

Foundations of Vector Retrieval

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

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.

Efficient and Effective Tree-based and Neural Learning to Rank

This monograph takes a step towards promoting the study of efficiency in the era of neural information retrieval by offering a comprehensive survey of the literature on efficiency and effectiveness in ranking, and to a limited extent, retrieval. This monograph was inspired by the parallels that exist between the challenges in neural network-based ranking solutions and their predecessors, decision forest-based learning to rank models, as well as the connections between the solutions the literature to date has to offer. We believe that by understanding the fundamentals underpinning these algorithmic and data structure solutions for containing the contentious relationship between efficiency and effectiveness, one can better identify future directions and more efficiently determine the merits of ideas. We also present what we believe to be important research directions in the forefront of efficiency and effectiveness in retrieval and ranking.

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.

Yggdrasil Decision Forests: A Fast and Extensible Decision Forests Library

Yggdrasil Decision Forests is a library for the training, serving and interpretation of decision forest models, targeted both at research and production work, implemented in C++, and available in C++, command line interface, Python (under the name TensorFlow Decision Forests), JavaScript, and Go. The library has been developed organically since 2018 following a set of four design principles applicable to machine learning libraries and frameworks: simplicity of use, safety of use, modularity and high-level abstraction, and integration with other machine learning libraries. In this paper, we describe those principles in detail and present how they have been used to guide the design of the library. We then showcase the use of our library on a set of classical machine learning problems. Finally, we report a benchmark comparing our library to related solutions.

Modeling Text with Decision Forests using Categorical-Set Splits

Decision forest algorithms model data by learning a binary tree structure recursively where every node splits the feature space into two regions, sending examples into the left or right branches. This "decision" is the result of the evaluation of a condition. For example, a node may split input data by applying a threshold to a numerical feature value. Such decisions are learned using (often greedy) algorithms that attempt to optimize a local loss function. Crucially, whether an algorithm exists to find and evaluate splits for a feature type (e.g., text) determines whether a decision forest algorithm can model that feature type at all. In this work, we set out to devise such an algorithm for textual features, thereby equipping decision forests with the ability to directly model text without the need for feature transformation. Our algorithm is efficient during training and the resulting splits are fast to evaluate with our extension of the QuickScorer inference algorithm. Experiments on benchmark text classification datasets demonstrate the utility and effectiveness of our proposal.