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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.

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.

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 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.

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.

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.

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.

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 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, Go, and Google Sheets (under the name Simple ML for Sheets). 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.

We study hybrid search in text retrieval where lexical and semantic search are fused together with the intuition that the two are complementary in how they model relevance. In particular, we examine fusion by a convex combination (CC) of lexical and semantic scores, as well as the Reciprocal Rank Fusion (RRF) method, and identify their advantages and potential pitfalls. Contrary to existing studies, we find RRF to be sensitive to its parameters; that the learning of a CC fusion is generally agnostic to the choice of score normalization; that CC outperforms RRF in in-domain and out-of-domain settings; and finally, that CC is sample efficient, requiring only a small set of training examples to tune its only parameter to a target domain.

Decision forest algorithms typically model data by learning a binary tree structure recursively where every node splits the feature space into two sub-regions, sending examples into the left or right branch as a result. In axis-aligned decision forests, the "decision" to route an input example is the result of the evaluation of a condition on a single dimension in the feature space. Such conditions are learned using efficient, often greedy algorithms that optimize a local loss function. For example, a node's condition may be a threshold function applied to a numerical feature, and its parameter may be learned by sweeping over the set of values available at that node and choosing a threshold that maximizes some measure of purity. Crucially, whether an algorithm exists to learn and evaluate conditions for a feature type determines whether a decision forest algorithm can model that feature type at all. For example, decision forests today cannot consume textual features directly -- such features must be transformed to summary statistics instead. In this work, we set out to bridge that gap. We define a condition that is specific to categorical-set features -- defined as an unordered set of categorical variables -- and present an algorithm to learn it, thereby equipping decision forests with the ability to directly model text, albeit without preserving sequential order. Our algorithm is efficient during training and the resulting conditions 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.

Axis-aligned decision forests have long been the leading class of machine learning algorithms for modeling tabular data. In many applications of machine learning such as learning-to-rank, decision forests deliver remarkable performance. They also possess other coveted characteristics such as interpretability. Despite their widespread use and rich history, decision forests to date fail to consume raw structured data such as text, or learn effective representations for them, a factor behind the success of deep neural networks in recent years. While there exist methods that construct smoothed decision forests to achieve representation learning, the resulting models are decision forests in name only: They are no longer axis-aligned, use stochastic decisions, or are not interpretable. Furthermore, none of the existing methods are appropriate for problems that require a Transfer Learning treatment. In this work, we present a novel but intuitive proposal to achieve representation learning for decision forests without imposing new restrictions or necessitating structural changes. Our model is simply a decision forest, possibly trained using any forest learning algorithm, atop a deep neural network. By approximating the gradients of the decision forest through input perturbation, a purely analytical procedure, the decision forest directs the neural network to learn or fine-tune representations. Our framework has the advantage that it is applicable to any arbitrary decision forest and that it allows the use of arbitrary deep neural networks for representation learning. We demonstrate the feasibility and effectiveness of our proposal through experiments on synthetic and benchmark classification datasets.

Listwise learning-to-rank methods form a powerful class of ranking algorithms that are widely adopted in applications such as information retrieval. These algorithms learn to rank a set of items by optimizing a loss that is a function of the entire set -- as a surrogate to a typically non-differentiable ranking metric. Despite their empirical success, existing listwise methods are based on heuristics and remain theoretically ill-understood. In particular, none of the empirically successful loss functions are related to ranking metrics. In this work, we propose a cross entropy-based learning-to-rank loss function that is theoretically sound, is a convex bound on NDCG -- a popular ranking metric -- and is consistent with NDCG under learning scenarios common in information retrieval. Furthermore, empirical evaluation of an implementation of the proposed method with gradient boosting machines on benchmark learning-to-rank datasets demonstrates the superiority of our proposed formulation over existing algorithms in quality and robustness.

Learning-to-Rank deals with maximizing the utility of a list of examples presented to the user, with items of higher relevance being prioritized. It has several practical applications such as large-scale search, recommender systems, document summarization and question answering. While there is widespread support for classification and regression based learning, support for learning-to-rank in deep learning has been limited. We propose TensorFlow Ranking, the first open source library for solving large-scale ranking problems in a deep learning framework. It is highly configurable and provides easy-to-use APIs to support different scoring mechanisms, loss functions and evaluation metrics in the learning-to-rank setting. Our library is developed on top of TensorFlow and can thus fully leverage the advantages of this platform. For example, it is highly scalable, both in training and in inference, and can be used to learn ranking models over massive amounts of user activity data, which can include heterogeneous dense and sparse features. We empirically demonstrate the effectiveness of our library in learning ranking functions for large-scale search and recommendation applications in Gmail and Google Drive. We also show that ranking models built using our model scale well for distributed training, without significant impact on metrics. The proposed library is available to the open source community, with the hope that it facilitates further academic research and industrial applications in the field of learning-to-rank., Comment: KDD 2019

While in a classification or a regression setting a label or a value is assigned to each individual document, in a ranking setting we determine the relevance ordering of the entire input document list. This difference leads to the notion of relative relevance between documents in ranking. The majority of the existing learning-to-rank algorithms model such relativity at the loss level using pairwise or listwise loss functions. However, they are restricted to univariate scoring functions, i.e., the relevance score of a document is computed based on the document itself, regardless of other documents in the list. To overcome this limitation, we propose a new framework for multivariate scoring functions, in which the relevance score of a document is determined jointly by multiple documents in the list. We refer to this framework as GSFs -- groupwise scoring functions. We learn GSFs with a deep neural network architecture, and demonstrate that several representative learning-to-rank algorithms can be modeled as special cases in our framework. We conduct evaluation using click logs from one of the largest commercial email search engines, as well as a public benchmark dataset. In both cases, GSFs lead to significant performance improvements, especially in the presence of sparse textual features.