Embedding-based Retrieval Models (ERMs) have emerged as a promising framework for large-scale text retrieval problems due to powerful large language models. Nevertheless, fine-tuning ERMs to reach state-of-the-art results can be expensive due to the extreme scale of data as well as the complexity of multi-stages pipelines (e.g., pre-training, fine-tuning, distillation). In this work, we propose the PEFA framework, namely ParamEter-Free Adapters, for fast tuning of ERMs without any backward pass in the optimization. At index building stage, PEFA equips the ERM with a non-parametric k-nearest neighbor (kNN) component. At inference stage, PEFA performs a convex combination of two scoring functions, one from the ERM and the other from the kNN. Based on the neighborhood definition, PEFA framework induces two realizations, namely PEFA-XL (i.e., extra large) using double ANN indices and PEFA-XS (i.e., extra small) using a single ANN index. Empirically, PEFA achieves significant improvement on two retrieval applications. For document retrieval, regarding Recall@100 metric, PEFA improves not only pre-trained ERMs on Trivia-QA by an average of 13.2%, but also fine-tuned ERMs on NQ-320K by an average of 5.5%, respectively. For product search, PEFA improves the Recall@100 of the fine-tuned ERMs by an average of 5.3% and 14.5%, for PEFA-XS and PEFA-XL, respectively. Our code is available at https://github.com/amzn/pecos/tree/mainline/examples/pefa-wsdm24.

Entity disambiguation is one of the most important natural language tasks to identify entities behind ambiguous surface mentions within a knowledge base. Although many recent studies apply deep learning to achieve decent results, they need exhausting pre-training and mediocre recall in the retrieval stage. In this paper, we propose a novel framework, eXtreme Multi-label Ranking for Entity Disambiguation (XMRED), to address this challenge. An efficient zero-shot entity retriever with auxiliary data is first pre-trained to recall relevant entities based on linear models. Specifically, the retrieval process can be considered as an extreme multi-label ranking (XMR) task. Entities are first clustered at different scales to form a label tree, thereby learning multi-scale entity retrievers over the label tree with high recall. Moreover, XMRED applies deep cross-encoder as a re-ranker to achieve high precision based on high-quality candidates. Extensive experimental results based on the AIDA-CoNLL benchmark and five zero-shot testing datasets demonstrate that XMRED obtains 98% and over 95% recall scores for in-domain and zero-shot datasets with top-10 retrieved entities. With a deep cross-encoder as the re-ranker, XMRED further outperforms the previous state-of-the-art by 1.74% in In-KB micro-F1 scores on average with a significant improvement on the training efficiency from days to 3.48 hours. In addition, XMRED also beats the state-of-the-art for page-level document retrieval by 2.38% in accuracy and 1.90% in recall@5.

The semantic matching problem in product search seeks to retrieve all semantically relevant products given a user query. Recent studies have shown that extreme multi-label classification~(XMC) model enjoys both low inference latency and high recall in real-world scenarios. These XMC semantic matching models adopt TF-IDF vectorizers to extract query text features and use mainly sparse matrices for the model weights. However, limited availability of libraries for efficient parallel sparse modules may lead to tediously long model building time when the problem scales to hundreds of millions of labels. This incurs significant hardware cost and renders the semantic model stale even before it is deployed. In this paper, we investigate and accelerate the model building procedures in a tree-based XMC model. On a real-world semantic matching task with 100M labels, our enhancements achieve over 10 times acceleration (from 3.1 days to 6.7 hours) while reducing hardware cost by 25%.

Uncertainty quantification is one of the most crucial tasks to obtain trustworthy and reliable machine learning models for decision making. However, most research in this domain has only focused on problems with small label spaces and ignored eXtreme Multi-label Classification (XMC), which is an essential task in the era of big data for web-scale machine learning applications. Moreover, enormous label spaces could also lead to noisy retrieval results and intractable computational challenges for uncertainty quantification. In this paper, we aim to investigate general uncertainty quantification approaches for tree-based XMC models with a probabilistic ensemble-based framework. In particular, we analyze label-level and instance-level uncertainty in XMC, and propose a general approximation framework based on beam search to efficiently estimate the uncertainty with a theoretical guarantee under long-tail XMC predictions. Empirical studies on six large-scale real-world datasets show that our framework not only outperforms single models in predictive performance, but also can serve as strong uncertainty-based baselines for label misclassification and out-of-distribution detection, with significant speedup. Besides, our framework can further yield better state-of-the-art results based on deep XMC models with uncertainty quantification.

Approximate K-Nearest Neighbor Search (AKNNS) has now become ubiquitous in modern applications, such as a fast search procedure with two-tower deep learning models. Graph-based methods for AKNNS in particular have received great attention due to their superior performance. These methods rely on greedy graph search to traverse the data points as embedding vectors in a database. Under this greedy search scheme, we make a key observation: many distance computations do not influence search updates so that these computations can be approximated without hurting performance. As a result, we propose FINGER, a fast inference method for efficient graph search in AKNNS. FINGER approximates the distance function by estimating angles between neighboring residual vectors. The approximated distance can be used to bypass unnecessary computations for faster searches. Empirically, when it comes to speeding up the inference of HNSW, which is one of the most popular graph-based AKNNS methods, FINGER significantly outperforms existing acceleration approaches and conventional libraries by 20 to 60 across different benchmark datasets.

Different from traditional machine learning tasks and benchmarks, real-world problems are usually accompanied by enormous output spaces, from hundred thousands of diseases in medical diagnosis, to millions of items and billions of websites in product and web search engines. Unfortunately, conventional machine learning tools and libraries are incapable of efficiently and accurately tackling large-scale output spaces. To address this issue, PECOS (Prediction for Enormous and Correlated Output Spaces) [11] is a state-of-the-art and open-sourced machine learning library1, which not only provides high-level and user-friendly interfaces of both linear and deep learning models, but also supplies considerable flexibility for solving diverse machine learning problems. Specifically, PECOS eases complicated semantic indexing for organizing enormous output spaces, thereby efficiently training models and deriving predictions by magnitude orders on correlated output labels. As a powerful and useful framework, PECOS has already been adopted in various real- world large-scale products like semantic search in Amazon [1], as well as achieved state-of-the-art on public extreme multi-label classification (XMC) benchmarks [2, 11, 12 ] and various downstream applications [3, 7, 9].

In the era of big data, eXtreme Multi-label Classification (XMC) has already become one of the most essential research tasks to deal with enormous label spaces in machine learning applications. Instead of assessing every individual label, most XMC methods rely on label trees or filters to derive short ranked label lists as prediction, thereby reducing computational overhead. Specifically, existing studies obtain ranked label lists with a fixed length for prediction and evaluation. However, these predictions are unreasonable since data points have varied numbers of relevant labels. The greatly small and large list lengths in evaluation, such as [email protected] and [email protected], can also lead to the ignorance of other relevant labels or the tolerance of many irrelevant labels. In this paper, we aim to provide reasonable prediction for extreme multi-label classification with dynamic numbers of predicted labels. In particular, we propose a novel framework, Model-Agnostic List Truncation with Ordinal Regression (MALTOR), to leverage the ranking properties and truncate long ranked label lists for better accuracy. Extensive experiments conducted on six large-scale real-world benchmark datasets demonstrate that MALTOR significantly outperforms statistical baseline methods and conventional ranked list truncation methods in ad-hoc retrieval with both linear and deep XMC models. The results of an ablation study also shows the effectiveness of each individual component in our proposed MALTOR.

Tree-based models underpin many modern semantic search engines and recommender systems due to their sub-linear inference times. In industrial applications, these models operate at extreme scales, where every bit of performance is critical. Memory constraints at extreme scales also require that models be sparse, hence tree-based models are often back-ended by sparse matrix algebra routines. However, there are currently no sparse matrix techniques specifically designed for the sparsity structure one encounters in tree-based models for extreme multi-label ranking/classification (XMR/XMC) problems. To address this issue, we present the masked sparse chunk multiplication (MSCM) technique, a sparse matrix technique specifically tailored to XMR trees. MSCM is easy to implement, embarrassingly parallelizable, and offers a significant performance boost to any existing tree inference pipeline at no cost. We perform a comprehensive study of MSCM applied to several different sparse inference schemes and benchmark our methods on a general purpose extreme multi-label ranking framework. We observe that MSCM gives consistently dramatic speedups across both the online and batch inference settings, single- and multi-threaded settings, and on many different tree models and datasets. To demonstrate its utility in industrial applications, we apply MSCM to an enterprise-scale semantic product search problem with 100 million products and achieve sub-millisecond latency of 0.88 ms per query on a single thread — an 8x reduction in latency over vanilla inference techniques. The MSCM technique requires absolutely no sacrifices to model accuracy as it gives exactly the same results as standard sparse matrix techniques. Therefore, we believe that MSCM will enable users of XMR trees to save a substantial amount of compute resources in their inference pipelines at very little cost. Our code is publicly available at https://github.com/amzn/pecos , as well as our complete benchmarks and code for reproduction at https://github.com/UniqueUpToPermutation/pecos/tree/benchmark.

We consider the problem of semantic matching in product search: given a customer query, retrieve all semantically related products from a huge catalog of size 100 million, or more. Because of large catalog spaces and real-time latency constraints, semantic matching algorithms not only desire high recall but also need to have low latency. Conventional lexical matching approaches (e.g., Okapi-BM25) exploit inverted indices to achieve fast inference time, but fail to capture behavioral signals between queries and products. In contrast, embedding-based models learn semantic representations from customer behavior data, but the performance is often limited by shallow neural encoders due to latency constraints. Semantic product search can be viewed as an eXtreme Multi-label Classification (XMC) problem, where customer queries are input instances and products are output labels. In this paper, we aim to improve semantic product search by using tree-based XMC models where inference time complexity is logarithmic in the number of products. We consider hierarchical linear models with n-gram features for fast real-time inference. Quantitatively, our method maintains a low latency of 1.25 milliseconds per query and achieves a 65% improvement of [email protected] (60.9% v.s. 36.8%) over a competing embedding-based DSSM model. Our model is robust to weight pruning with varying thresholds, which can flexibly meet different system requirements for online deployments. Qualitatively, our method can retrieve products that are complementary to existing product search system and add diversity to the match set.

We consider the extreme multi-label text classification (XMC) problem: given an input text, return the most relevant labels from a large label collection. For example, the input text could be a product description on Amazon.com and the labels could be product categories. XMC is an important yet challenging problem in the NLP community. Recently, deep pretrained transformer models have achieved state-of-the-art performance on many NLP tasks including sentence classification, albeit with small label sets. However, naively applying deep transformer models to the XMC problem leads to sub-optimal performance due to the large output space and the label sparsity issue. In this paper, we propose X-Transformer, the first scalable approach to fine-tuning deep transformer models for the XMC problem. The proposed method achieves new state-of-the-art results on four XMC benchmark datasets. In particular, on a Wiki dataset with around 0.5 million labels, the [email protected] of X-Transformer is 77.28%, a substantial improvement over state-of-the-art XMC approaches Parabel (linear) and AttentionXML (neural), which achieve 68.70% and 76.95% [email protected], respectively. We further apply X-Transformer to a product2query dataset from Amazon and gained 10.7% relative improvement on [email protected] over Parabel.

Many recommender systems have only implicit user feedback. The two possible ratings are positive and negative, but only part of positive entries are observed. One-class matrix factorization (MF) is a popular approach for such scenarios by treating some missing entries as negative. Two major ways to select negative entries are by sub-sampling a set with similar size to that of observed positive entries or by including all missing entries as negative. They are referred to as “subsampled” and “full” approaches in this work, respectively. Currently detailed comparisons between these two selection schemes on large-scale data are still lacking. One important reason is that the “full” approach leads to a hard optimization problem after treating all missing entries as negative. In this paper, we successfully develop efficient optimization techniques to solve this challenging problem so that the “full” approach becomes practically viable. We then compare in detail the two approaches “subsampled” and “full” for selecting negative entries. Results show that the “full” approach of including much more missing entries as negative yields better results.

Learning meaningful topic models with massive document collections which contain millions of documents and billions of tokens is challenging because of two reasons. First, one needs to deal with a large number of topics (typically on the order of thousands). Second, one needs a scalable and efficient way of distributing the computation across multiple machines. In this paper, we present a novel algorithm F+Nomad LDA which simultaneously tackles both these problems. In order to handle large number of topics we use an appropriately modified Fenwick tree. This data structure allows us to sample from a multinomial distribution over T items in O(log T) time. Moreover, when topic counts change the data structure can be updated in O(log T) time. In order to distribute the computation across multiple processors, we present a novel asynchronous framework inspired by the Nomad algorithm of Yun et al, 2014. We show that F+Nomad LDA significantly outperforms recent state-of-the-art topic modeling approaches on massive problems which involve millions of documents, billions of words, and thousands of topics.

We develop an efficient parallel distributed algorithm for matrix completion, named NOMAD (Non-locking, stOchastic Multi-machine algorithm for Asynchronous and Decentralized matrix completion). NOMAD is a decentralized algorithm with non-blocking communication between processors. One of the key features of NOMAD is that the ownership of a variable is asynchronously transferred between processors in a decentralized fashion. As a consequence it is a lock-free parallel algorithm. In spite of being asynchronous, the variable updates of NOMAD are serializable, that is, there is an equivalent update ordering in a serial implementation. NOMAD outperforms synchronous algorithms which require explicit bulk synchronization after every iteration: our extensive empirical evaluation shows that not only does our algorithm perform well in distributed setting on commodity hardware, but also outperforms state-of-the-art algorithms on a HPC cluster both in multi-core and distributed memory settings.

Matrix factorization, when the matrix has missing values, has become one of the leading techniques for recommender systems. To handle web-scale datasets with millions of users and billions of ratings, scalability becomes an important issue. Alternating Least Squares (ALS) and Stochastic Gradient Descent (SGD) are two popular approaches to compute matrix factorization. There has been a recent flurry of activity to parallelize these algorithms. However, due to the cubic time complexity in the target rank, ALS is not scalable to large-scale datasets. On the other hand, SGD conducts efficient updates but usually suffers from slow convergence that is sensitive to the parameters. Coordinate descent, a classical optimization approach, has been used for many other large-scale problems, but its application to matrix factorization for recommender systems has not been explored thoroughly. In this paper, we show that coordinate descent based methods have a more efficient update rule compared to ALS, and are faster and have more stable convergence than SGD. We study different update sequences and propose the CCD++ algorithm, which updatesrank-one factors one by one. In addition, CCD++ can be easily parallelized on both multi-core and distributed systems. We empirically show that CCD++ is much faster than ALS and SGD in both settings. As an example, on a synthetic dataset with 2 billion ratings, CCD++ is 4 times faster than both SGD and ALS using a distributed system with 20 machines.

Recent advances in linear classification have shown that for applications such as document classification, the training process can be extremely efficient. However, most of the existing training methods are designed by assuming that data can be stored in the computer memory. These methods cannot be easily applied to data larger than the memory capacity due to the random access to the disk. We propose and analyze a block minimization framework for data larger than the memory size. At each step a block of data is loaded from the disk and handled by certain learning methods. We investigate two implementations of the proposed framework for primal and dual SVMs, respectively. Because data cannot fit in memory, many design considerations are very different from those for traditional algorithms. We discuss and compare with existing approaches that are able to handle data larger than memory. Experiments using data sets 20 times larger than the memory demonstrate the effectiveness of the proposed method.

Recent advances in linear classification have shown that for applications such as document classification, the training can be extremely efficient. However, most of the existing training methods are designed by assuming that data can be stored in the computer memory. These methods cannot be easily applied to data larger than the memory capacity due to the random access to the disk. We propose and analyze a block minimization framework for data larger than the memory size. At each step a block of data is loaded from the disk and handled by certain learning methods. We investigate two implementations of the proposed framework for primal and dual SVMs, respectively. As data cannot fit in memory, many design considerations are very different from those for traditional algorithms. Experiments using data sets 20 times larger than the memory demonstrate the effectiveness of the proposed method.