Down with the Hierarchy: The 'H' in HNSW Stands for "Hubs"

Driven by recent breakthrough advances in neural representation learning, approximate near-neighbor (ANN) search over vector embeddings has emerged as a critical computational workload. With the introduction of the seminal Hierarchical Navigable Small World (HNSW) algorithm, graph-based indexes have established themseves as the overwhelmingly dominant paradigm for efficient and scalable ANN search. As the name suggests, HNSW searches a layered hierarchical graph to quickly identify neighborhoods of similar points to a given query vector. But is this hierarchy even necessary? A rigorous experimental analysis to answer this question would provide valuable insights into the nature of algorithm design for ANN search and motivate directions for future work in this increasingly crucial domain. To that end, we conduct an extensive benchmarking study covering more large-scale datasets than prior investigations of this question. We ultimately find that a flat graph retains all of the benefits of HNSW on high-dimensional datasets, with latency and recall performance essentially \emph{identical} to the original algorithm but with less memory overhead. Furthermore, we go a step further and study \emph{why} the hierarchy of HNSW provides no benefit in high dimensions, hypothesizing that navigable small world graphs contain a well-connected, frequently traversed ``highway" of hub nodes that maintain the same purported function as the hierarchical layers. We present compelling empirical evidence that the \emph{Hub Highway Hypothesis} holds for real datasets and investigate the mechanisms by which the highway forms. The implications of this hypothesis may also provide future research directions in developing enhancements to graph-based ANN search.

How to Train Data-Efficient LLMs

The training of large language models (LLMs) is expensive. In this paper, we study data-efficient approaches for pre-training LLMs, i.e., techniques that aim to optimize the Pareto frontier of model quality and training resource/data consumption. We seek to understand the tradeoffs associated with data selection routines based on (i) expensive-to-compute data-quality estimates, and (ii) maximization of coverage and diversity-based measures in the feature space. Our first technique, Ask-LLM, leverages the zero-shot reasoning capabilities of instruction-tuned LLMs to directly assess the quality of a training example. To target coverage, we propose Density sampling, which models the data distribution to select a diverse sample. In our comparison of 19 samplers, involving hundreds of evaluation tasks and pre-training runs, we find that Ask-LLM and Density are the best methods in their respective categories. Coverage sampling can recover the performance of the full data, while models trained on Ask-LLM data consistently outperform full-data training -- even when we reject 90% of the original dataset, while converging up to 70% faster.

Adaptive Sampling for Deep Learning via Efficient Nonparametric Proxies

Data sampling is an effective method to improve the training speed of neural networks, with recent results demonstrating that it can even break the neural scaling laws. These results critically rely on high-quality scores to estimate the importance of an input to the network. We observe that there are two dominant strategies: static sampling, where the scores are determined before training, and dynamic sampling, where the scores can depend on the model weights. Static algorithms are computationally inexpensive but less effective than their dynamic counterparts, which can cause end-to-end slowdown due to their need to explicitly compute losses. To address this problem, we propose a novel sampling distribution based on nonparametric kernel regression that learns an effective importance score as the neural network trains. However, nonparametric regression models are too computationally expensive to accelerate end-to-end training. Therefore, we develop an efficient sketch-based approximation to the Nadaraya-Watson estimator. Using recent techniques from high-dimensional statistics and randomized algorithms, we prove that our Nadaraya-Watson sketch approximates the estimator with exponential convergence guarantees. Our sampling algorithm outperforms the baseline in terms of wall-clock time and accuracy on four datasets.

CAPS: A Practical Partition Index for Filtered Similarity Search

With the surging popularity of approximate near-neighbor search (ANNS), driven by advances in neural representation learning, the ability to serve queries accompanied by a set of constraints has become an area of intense interest. While the community has recently proposed several algorithms for constrained ANNS, almost all of these methods focus on integration with graph-based indexes, the predominant class of algorithms achieving state-of-the-art performance in latency-recall tradeoffs. In this work, we take a different approach and focus on developing a constrained ANNS algorithm via space partitioning as opposed to graphs. To that end, we introduce Constrained Approximate Partitioned Search (CAPS), an index for ANNS with filters via space partitions that not only retains the benefits of a partition-based algorithm but also outperforms state-of-the-art graph-based constrained search techniques in recall-latency tradeoffs, with only 10% of the index size.

CARAMEL: A Succinct Read-Only Lookup Table via Compressed Static Functions

Lookup tables are a fundamental structure in many data processing and systems applications. Examples include tokenized text in NLP, quantized embedding collections in recommendation systems, integer sketches for streaming data, and hash-based string representations in genomics. With the increasing size of web-scale data, such applications often require compression techniques that support fast random $O(1)$ lookup of individual parameters directly on the compressed data (i.e. without blockwise decompression in RAM). While the community has proposd a number of succinct data structures that support queries over compressed representations, these approaches do not fully leverage the low-entropy structure prevalent in real-world workloads to reduce space. Inspired by recent advances in static function construction techniques, we propose a space-efficient representation of immutable key-value data, called CARAMEL, specifically designed for the case where the values are multi-sets. By carefully combining multiple compressed static functions, CARAMEL occupies space proportional to the data entropy with low memory overheads and minimal lookup costs. We demonstrate 1.25-16x compression on practical lookup tasks drawn from real-world systems, improving upon established techniques, including a production-grade read-only database widely used for development within Amazon.com.

Unified Embedding: Battle-Tested Feature Representations for Web-Scale ML Systems

Learning high-quality feature embeddings efficiently and effectively is critical for the performance of web-scale machine learning systems. A typical model ingests hundreds of features with vocabularies on the order of millions to billions of tokens. The standard approach is to represent each feature value as a d-dimensional embedding, introducing hundreds of billions of parameters for extremely high-cardinality features. This bottleneck has led to substantial progress in alternative embedding algorithms. Many of these methods, however, make the assumption that each feature uses an independent embedding table. This work introduces a simple yet highly effective framework, Feature Multiplexing, where one single representation space is used across many different categorical features. Our theoretical and empirical analysis reveals that multiplexed embeddings can be decomposed into components from each constituent feature, allowing models to distinguish between features. We show that multiplexed representations lead to Pareto-optimal parameter-accuracy tradeoffs for three public benchmark datasets. Further, we propose a highly practical approach called Unified Embedding with three major benefits: simplified feature configuration, strong adaptation to dynamic data distributions, and compatibility with modern hardware. Unified embedding gives significant improvements in offline and online metrics compared to highly competitive baselines across five web-scale search, ads, and recommender systems, where it serves billions of users across the world in industry-leading products.

BOLT: An Automated Deep Learning Framework for Training and Deploying Large-Scale Neural Networks on Commodity CPU Hardware

Efficient large-scale neural network training and inference on commodity CPU hardware is of immense practical significance in democratizing deep learning (DL) capabilities. Presently, the process of training massive models consisting of hundreds of millions to billions of parameters requires the extensive use of specialized hardware accelerators, such as GPUs, which are only accessible to a limited number of institutions with considerable financial resources. Moreover, there is often an alarming carbon footprint associated with training and deploying these models. In this paper, we address these challenges by introducing BOLT, a sparse deep learning library for training massive neural network models on standard CPU hardware. BOLT provides a flexible, high-level API for constructing models that will be familiar to users of existing popular DL frameworks. By automatically tuning specialized hyperparameters, BOLT also abstracts away the algorithmic details of sparse network training. We evaluate BOLT on a number of machine learning tasks drawn from recommendations, search, natural language processing, and personalization. We find that our proposed system achieves competitive performance with state-of-the-art techniques at a fraction of the cost and energy consumption and an order-of-magnitude faster inference time. BOLT has also been successfully deployed by multiple businesses to address critical problems, and we highlight one customer deployment case study in the field of e-commerce.

Efficient Inference via Universal LSH Kernel

Large machine learning models achieve unprecedented performance on various tasks and have evolved as the go-to technique. However, deploying these compute and memory hungry models on resource constraint environments poses new challenges. In this work, we propose mathematically provable Representer Sketch, a concise set of count arrays that can approximate the inference procedure with simple hashing computations and aggregations. Representer Sketch builds upon the popular Representer Theorem from kernel literature, hence the name, providing a generic fundamental alternative to the problem of efficient inference that goes beyond the popular approach such as quantization, iterative pruning and knowledge distillation. A neural network function is transformed to its weighted kernel density representation, which can be very efficiently estimated with our sketching algorithm. Empirically, we show that Representer Sketch achieves up to 114x reduction in storage requirement and 59x reduction in computation complexity without any drop in accuracy.

Density Sketches for Sampling and Estimation

We introduce Density sketches (DS): a succinct online summary of the data distribution. DS can accurately estimate point wise probability density. Interestingly, DS also provides a capability to sample unseen novel data from the underlying data distribution. Thus, analogous to popular generative models, DS allows us to succinctly replace the real-data in almost all machine learning pipelines with synthetic examples drawn from the same distribution as the original data. However, unlike generative models, which do not have any statistical guarantees, DS leads to theoretically sound asymptotically converging consistent estimators of the underlying density function. Density sketches also have many appealing properties making them ideal for large-scale distributed applications. DS construction is an online algorithm. The sketches are additive, i.e., the sum of two sketches is the sketch of the combined data. These properties allow data to be collected from distributed sources, compressed into a density sketch, efficiently transmitted in the sketch form to a central server, merged, and re-sampled into a synthetic database for modeling applications. Thus, density sketches can potentially revolutionize how we store, communicate, and distribute data.

Bloom Origami Assays: Practical Group Testing

We study the problem usually referred to as group testing in the context of COVID-19. Given n samples collected from patients, how should we select and test mixtures of samples to maximize information and minimize the number of tests? Group testing is a well-studied problem with several appealing solutions, but recent biological studies impose practical constraints for COVID-19 that are incompatible with traditional methods. Furthermore, existing methods use unnecessarily restrictive solutions, which were devised for settings with more memory and compute constraints than the problem at hand. This results in poor utility. In the new setting, we obtain strong solutions for small values of n using evolutionary strategies. We then develop a new method combining Bloom filters with belief propagation to scale to larger values of n (more than 100) with good empirical results. We also present a more accurate decoding algorithm that is tailored for specific COVID-19 settings. This work demonstrates the practical gap between dedicated algorithms and well-known generic solutions. Our efforts results in a new and practical multiplex method yielding strong empirical performance without mixing more than a chosen number of patients into the same probe. Finally, we briefly discuss adaptive methods, casting them into the framework of adaptive sub-modularity.