Jiyan Yang

Shali Jiang, Hua Zheng, Boyang Liu et al.

Knowledge distillation (KD) transfers a single scalar prediction from a large foundation model (FM) to compact vertical models (VMs), suffering from diminishing transfer ratio -- the fraction of FM improvement captured by the VM -- as a single scalar cannot convey the rich intermediate knowledge that larger FMs learn. To address this bottleneck, we propose LoopFM (Learning frOm HistOrical ReP*resentations of FM), a framework that opens a high-bandwidth transfer channel by structuring FM intermediate embeddings as input features (e.g., user history sequence) for downstream VMs, without requiring real-time FM inference at serving and architectural coupling between FM and VM. We provide a theoretical framework for LoopFM with a gain decomposition and transfer-ratio analysis. On three public benchmarks, LoopFM demonstrates strong AUC improvements (e.g., 6\%+ on TaobaoAd) and complementary knowledge transfer capability with KD. On industrial-scale systems (billions of examples, trillion-parameter FMs), LoopFM approximately doubles the knowledge transfer ratio on top of KD, delivering a +0.5\% conversion improvement in Y1H1, and a +1.03\% and +1.22\% conversion improvement from two individual launches respectively in Y1H2.

Buyun Zhang, Liang Luo, Xi Liu et al.

Learning feature interactions is important to the model performance of online advertising services. As a result, extensive efforts have been devoted to designing effective architectures to learn feature interactions. However, we observe that the practical performance of those designs can vary from dataset to dataset, even when the order of interactions claimed to be captured is the same. That indicates different designs may have different advantages and the interactions captured by them have non-overlapping information. Motivated by this observation, we propose DHEN - a deep and hierarchical ensemble architecture that can leverage strengths of heterogeneous interaction modules and learn a hierarchy of the interactions under different orders. To overcome the challenge brought by DHEN's deeper and multi-layer structure in training, we propose a novel co-designed training system that can further improve the training efficiency of DHEN. Experiments of DHEN on large-scale dataset from CTR prediction tasks attained 0.27\% improvement on the Normalized Entropy (NE) of prediction and 1.2x better training throughput than state-of-the-art baseline, demonstrating their effectiveness in practice.

Xuewei Wang, Qiang Jin, Shengyu Huang et al.

Dividing ads ranking system into retrieval, early, and final stages is a common practice in large scale ads recommendation to balance the efficiency and accuracy. The early stage ranking often uses efficient models to generate candidates out of a set of retrieved ads. The candidates are then fed into a more computationally intensive but accurate final stage ranking system to produce the final ads recommendation. As the early and final stage ranking use different features and model architectures because of system constraints, a serious ranking consistency issue arises where the early stage has a low ads recall, i.e., top ads in the final stage are ranked low in the early stage. In order to pass better ads from the early to the final stage ranking, we propose a multi-task learning framework for early stage ranking to capture multiple final stage ranking components (i.e. ads clicks and ads quality events) and their task relations. With our multi-task learning framework, we can not only achieve serving cost saving from the model consolidation, but also improve the ads recall and ranking consistency. In the online A/B testing, our framework achieves significantly higher click-through rate (CTR), conversion rate (CVR), total value and better ads-quality (e.g. reduced ads cross-out rate) in a large scale industrial ads ranking system.

Wei Wen, Kuang-Hung Liu, Igor Fedorov et al.

Neural Architecture Search (NAS) has demonstrated its efficacy in computer vision and potential for ranking systems. However, prior work focused on academic problems, which are evaluated at small scale under well-controlled fixed baselines. In industry system, such as ranking system in Meta, it is unclear whether NAS algorithms from the literature can outperform production baselines because of: (1) scale - Meta ranking systems serve billions of users, (2) strong baselines - the baselines are production models optimized by hundreds to thousands of world-class engineers for years since the rise of deep learning, (3) dynamic baselines - engineers may have established new and stronger baselines during NAS search, and (4) efficiency - the search pipeline must yield results quickly in alignment with the productionization life cycle. In this paper, we present Rankitect, a NAS software framework for ranking systems at Meta. Rankitect seeks to build brand new architectures by composing low level building blocks from scratch. Rankitect implements and improves state-of-the-art (SOTA) NAS methods for comprehensive and fair comparison under the same search space, including sampling-based NAS, one-shot NAS, and Differentiable NAS (DNAS). We evaluate Rankitect by comparing to multiple production ranking models at Meta. We find that Rankitect can discover new models from scratch achieving competitive tradeoff between Normalized Entropy loss and FLOPs. When utilizing search space designed by engineers, Rankitect can generate better models than engineers, achieving positive offline evaluation and online A/B test at Meta scale.

Hang Yin, Kuang-Hung Liu, Mengying Sun et al.

Web-scale ranking systems at Meta serving billions of users is complex. Improving ranking models is essential but engineering heavy. Automated Machine Learning (AutoML) can release engineers from labor intensive work of tuning ranking models; however, it is unknown if AutoML is efficient enough to meet tight production timeline in real-world and, at the same time, bring additional improvements to the strong baselines. Moreover, to achieve higher ranking performance, there is an ever-increasing demand to scale up ranking models to even larger capacity, which imposes more challenges on the efficiency. The large scale of models and tight production schedule requires AutoML to outperform human baselines by only using a small number of model evaluation trials (around 100). We presents a sampling-based AutoML method, focusing on neural architecture search and hyperparameter optimization, addressing these challenges in Meta-scale production when building large capacity models. Our approach efficiently handles large-scale data demands. It leverages a lightweight predictor-based searcher and reinforcement learning to explore vast search spaces, significantly reducing the number of model evaluations. Through experiments in large capacity modeling for CTR and CVR applications, we show that our method achieves outstanding Return on Investment (ROI) versus human tuned baselines, with up to 0.09% Normalized Entropy (NE) loss reduction or $25\%$ Query per Second (QPS) increase by only sampling one hundred models on average from a curated search space. The proposed AutoML method has already made real-world impact where a discovered Instagram CTR model with up to -0.36% NE gain (over existing production baseline) was selected for large-scale online A/B test and show statistically significant gain. These production results proved AutoML efficacy and accelerated its adoption in ranking systems at Meta.

Dongqi Fu, Kaushik Rangadurai, Haiyu Lu et al.

The increase in data volume, computational resources, and model parameters during training has led to the development of numerous large-scale industrial retrieval models for recommendation tasks. However, effectively and efficiently deploying these large-scale foundational retrieval models remains a critical challenge that has not been fully addressed. Common quick-win solutions for deploying these massive models include relying on offline computations (such as cached user dictionaries) or distilling large models into smaller ones. Yet, both approaches fall short of fully leveraging the representational and inference capabilities of foundational models. In this paper, we explore whether it is possible to learn a hierarchical organization over the memory of foundational retrieval models. Such a hierarchical structure would enable more efficient search by reducing retrieval costs while preserving exactness. To achieve this, we propose jointly learning a hierarchical index using cross-attention and residual quantization for large-scale retrieval models. We also present its real-world deployment at Meta, supporting daily advertisement recommendations for billions of Facebook and Instagram users. Interestingly, we discovered that the intermediate nodes in the learned index correspond to a small set of high-quality data. Fine-tuning the model on this set further improves inference performance, and concretize the concept of "test-time training" within the recommendation system domain. We demonstrate these findings using both internal and public datasets with strong baseline comparisons and hope they contribute to the community's efforts in developing the next generation of foundational retrieval models.

Bojian Hou, Xiaolong Liu, Xiaoyi Liu et al.

Deriving predictable scaling laws that govern the relationship between model performance and computational investment is crucial for designing and allocating resources in massive-scale recommendation systems. While such laws are established for large language models, they remain challenging for recommendation systems, especially those processing both user history and context features. We identify poor scaling efficiency as the main barrier to predictable power-law scaling, stemming from inefficient modules with low Model FLOPs Utilization (MFU) and suboptimal resource allocation. We introduce Kunlun, a scalable architecture that systematically improves model efficiency and resource allocation. Our low-level optimizations include Generalized Dot-Product Attention (GDPA), Hierarchical Seed Pooling (HSP), and Sliding Window Attention. Our high-level innovations feature Computation Skip (CompSkip) and Event-level Personalization. These advances increase MFU from 17% to 37% on NVIDIA B200 GPUs and double scaling efficiency over state-of-the-art methods. Kunlun is now deployed in major Meta Ads models, delivering significant production impact.

Zhiyao Zhang, Zhuqing Liu, Xin Zhang et al.

As machine learning (ML) applications grow increasingly complex in recent years, modern ML frameworks often need to address multiple potentially conflicting objectives with coupled decision variables across different layers. This creates a compelling need for multi-objective bilevel learning (MOBL). So far, however, the field of MOBL remains in its infancy and many important problems remain under-explored. This motivates us to fill this gap and systematically investigate the theoretical and algorithmic foundation of MOBL. Specifically, we consider MOBL problems with multiple conflicting objectives guided by preferences at the upper-level subproblem, where part of the inputs depend on the optimal solution of the lower-level subproblem. Our goal is to develop efficient MOBL optimization algorithms to (1) identify a preference-guided Pareto-stationary solution with low oracle complexity; and (2) enable systematic Pareto front exploration. To this end, we propose a unifying algorithmic framework called weighted-Chebyshev multi-hyper-gradient-descent (WC-MHGD) for both deterministic and stochastic settings with finite-time Pareto-stationarity convergence rate guarantees, which not only implies low oracle complexity but also induces systematic Pareto front exploration. We further conduct extensive experiments to confirm our theoretical results.

Kaushik Rangadurai, Siyang Yuan, Minhui Huang et al.

Retrieval, the initial stage of a recommendation system, is tasked with down-selecting items from a pool of tens of millions of candidates to a few thousands. Embedding Based Retrieval (EBR) has been a typical choice for this problem, addressing the computational demands of deep neural networks across vast item corpora. EBR utilizes Two Tower or Siamese Networks to learn representations for users and items, and employ Approximate Nearest Neighbor (ANN) search to efficiently retrieve relevant items. Despite its popularity in industry, EBR faces limitations. The Two Tower architecture, relying on a single dot product interaction, struggles to capture complex data distributions due to limited capability in learning expressive interactions between users and items. Additionally, ANN index building and representation learning for user and item are often separate, leading to inconsistencies exacerbated by representation (e.g. continuous online training) and item drift (e.g. items expired and new items added). In this paper, we introduce the Hierarchical Structured Neural Network (HSNN), an efficient deep neural network model to learn intricate user and item interactions beyond the commonly used dot product in retrieval tasks, achieving sublinear computational costs relative to corpus size. A Modular Neural Network (MoNN) is designed to maintain high expressiveness for interaction learning while ensuring efficiency. A mixture of MoNNs operate on a hierarchical item index to achieve extensive computation sharing, enabling it to scale up to large corpus size. MoNN and the hierarchical index are jointly learnt to continuously adapt to distribution shifts in both user interests and item distributions. HSNN achieves substantial improvement in offline evaluation compared to prevailing methods.

Wei Wen, Quanyu Zhu, Weiwei Chu et al.

Scaling up deep learning models has been proven effective to improve intelligence of machine learning (ML) models, especially for industry recommendation models and large language models. The co-design of large distributed ML systems and algorithms (to maximize training performance) plays a pivotal role for its success. As it scales, the number of co-design hyper-parameters grows rapidly which brings challenges to feasibly find the optimal setup for system performance maximization. In this paper, we propose CubicML which uses ML to automatically optimize training performance of large distributed ML systems. In CubicML, we use an ML model as a proxy to predict the training performance for search efficiency and performance modeling flexibility. We proved that CubicML can effectively optimize training speed of in-house ads recommendation models with 73 billion parameters and large language models up to 405 billion parameters at Meta.

Carolina Zheng, Minhui Huang, Dmitrii Pedchenko et al.

The exponential growth of online content has posed significant challenges to ID-based models in industrial recommendation systems, ranging from extremely high cardinality and dynamically growing ID space, to highly skewed engagement distributions, to prediction instability as a result of natural id life cycles (e.g, the birth of new IDs and retirement of old IDs). To address these issues, many systems rely on random hashing to handle the id space and control the corresponding model parameters (i.e embedding table). However, this approach introduces data pollution from multiple ids sharing the same embedding, leading to degraded model performance and embedding representation instability. This paper examines these challenges and introduces Semantic ID prefix ngram, a novel token parameterization technique that significantly improves the performance of the original Semantic ID. Semantic ID prefix ngram creates semantically meaningful collisions by hierarchically clustering items based on their content embeddings, as opposed to random assignments. Through extensive experimentation, we demonstrate that Semantic ID prefix ngram not only addresses embedding instability but also significantly improves tail id modeling, reduces overfitting, and mitigates representation shifts. We further highlight the advantages of Semantic ID prefix ngram in attention-based models that contextualize user histories, showing substantial performance improvements. We also report our experience of integrating Semantic ID into Meta production Ads Ranking system, leading to notable performance gains and enhanced prediction stability in live deployments.

Mingfu Liang, Xi Liu, Rong Jin et al.

Ads recommendation is a prominent service of online advertising systems and has been actively studied. Recent studies indicate that scaling-up and advanced design of the recommendation model can bring significant performance improvement. However, with a larger model scale, such prior studies have a significantly increasing gap from industry as they often neglect two fundamental challenges in industrial-scale applications. First, training and inference budgets are restricted for the model to be served, exceeding which may incur latency and impair user experience. Second, large-volume data arrive in a streaming mode with data distributions dynamically shifting, as new users/ads join and existing users/ads leave the system. We propose the External Large Foundation Model (ExFM) framework to address the overlooked challenges. Specifically, we develop external distillation and a data augmentation system (DAS) to control the computational cost of training/inference while maintaining high performance. We design the teacher in a way like a foundation model (FM) that can serve multiple students as vertical models (VMs) to amortize its building cost. We propose Auxiliary Head and Student Adapter to mitigate the data distribution gap between FM and VMs caused by the streaming data issue. Comprehensive experiments on internal industrial-scale applications and public datasets demonstrate significant performance gain by ExFM.

Xiaolong Liu, Zhichen Zeng, Xiaoyi Liu et al.

Recent advances in foundation models have established scaling laws that enable the development of larger models to achieve enhanced performance, motivating extensive research into large-scale recommendation models. However, simply increasing the model size in recommendation systems, even with large amounts of data, does not always result in the expected performance improvements. In this paper, we propose a novel framework, Collaborative Ensemble Training Network (CETNet), to leverage multiple distinct models, each with its own embedding table, to capture unique feature interaction patterns. Unlike naive model scaling, our approach emphasizes diversity and collaboration through collaborative learning, where models iteratively refine their predictions. To dynamically balance contributions from each model, we introduce a confidence-based fusion mechanism using general softmax, where model confidence is computed via negation entropy. This design ensures that more confident models have a greater influence on the final prediction while benefiting from the complementary strengths of other models. We validate our framework on three public datasets (AmazonElectronics, TaobaoAds, and KuaiVideo) as well as a large-scale industrial dataset from Meta, demonstrating its superior performance over individual models and state-of-the-art baselines. Additionally, we conduct further experiments on the Criteo and Avazu datasets to compare our method with the multi-embedding paradigm. Our results show that our framework achieves comparable or better performance with smaller embedding sizes, offering a scalable and efficient solution for CTR prediction tasks.

Huixue Zhou, Hengrui Gu, Xi Liu et al.

The deployment of Large Language Models (LLMs) in recommender systems for predicting Click-Through Rates (CTR) necessitates a delicate balance between computational efficiency and predictive accuracy. This paper presents an optimization framework that combines Retrieval-Augmented Generation (RAG) with an innovative multi-head early exit architecture to concurrently enhance both aspects. By integrating Graph Convolutional Networks (GCNs) as efficient retrieval mechanisms, we are able to significantly reduce data retrieval times while maintaining high model performance. The early exit strategy employed allows for dynamic termination of model inference, utilizing real-time predictive confidence assessments across multiple heads. This not only quickens the responsiveness of LLMs but also upholds or improves their accuracy, making it ideal for real-time application scenarios. Our experiments demonstrate how this architecture effectively decreases computation time without sacrificing the accuracy needed for reliable recommendation delivery, establishing a new standard for efficient, real-time LLM deployment in commercial systems.

Zhichen Zeng, Mengyue Hang, Xiaolong Liu et al.

Deep models have driven significant advances in click-through rate (CTR) prediction. While vertical scaling via layer stacking improves model expressiveness, the layer-by-layer sequential computation poses challenges to efficient scaling. Conversely, horizontal scaling through Mixture of Experts (MoE) achieves efficient scaling by activating a small subset of experts in parallel, but flat MoE layers may struggle to capture the hierarchical structure inherent in recommendation tasks. To push the Return-On-Investment (ROI) boundary, we explore the complementary strengths of both directions and propose HiLoMoE, a hierarchical LoRA MoE framework that enables holistic scaling in a parameter-efficient manner. Specifically, HiLoMoE employs lightweight rank-1 experts for parameter-efficient horizontal scaling, and stacks multiple MoE layers with hierarchical routing to enable combinatorially diverse expert compositions. Unlike conventional stacking, HiLoMoE routes based on prior layer scores rather than outputs, allowing all layers to execute in parallel. A principled three-stage training framework ensures stable optimization and expert diversity. Experiments on four public datasets show that HiLoMoE achieving better performance-efficiency tradeoff, achieving an average AUC improvement of 0.20\% in AUC and 18.5\% reduction in FLOPs compared to the non-MoE baseline.

Xin Zhang, Quanyu Zhu, Liangbei Xu et al.

The increasing complexity of deep learning recommendation models (DLRM) has led to a growing need for large-scale distributed systems that can efficiently train vast amounts of data. In DLRM, the sparse embedding table is a crucial component for managing sparse categorical features. Typically, these tables in industrial DLRMs contain trillions of parameters, necessitating model parallelism strategies to address memory constraints. However, as training systems expand with massive GPUs, the traditional fully parallelism strategies for embedding table post significant scalability challenges, including imbalance and straggler issues, intensive lookup communication, and heavy embedding activation memory. To overcome these limitations, we propose a novel two-dimensional sparse parallelism approach. Rather than fully sharding tables across all GPUs, our solution introduces data parallelism on top of model parallelism. This enables efficient all-to-all communication and reduces peak memory consumption. Additionally, we have developed the momentum-scaled row-wise AdaGrad algorithm to mitigate performance losses associated with the shift in training paradigms. Our extensive experiments demonstrate that the proposed approach significantly enhances training efficiency while maintaining model performance parity. It achieves nearly linear training speed scaling up to 4K GPUs, setting a new state-of-the-art benchmark for recommendation model training.

Zhichen Zeng, Xiaolong Liu, Mengyue Hang et al.

Click-through rate (CTR) prediction, which predicts the probability of a user clicking an ad, is a fundamental task in recommender systems. The emergence of heterogeneous information, such as user profile and behavior sequences, depicts user interests from different aspects. A mutually beneficial integration of heterogeneous information is the cornerstone towards the success of CTR prediction. However, most of the existing methods suffer from two fundamental limitations, including (1) insufficient inter-mode interaction due to the unidirectional information flow between modes, and (2) aggressive information aggregation caused by early summarization, resulting in excessive information loss. To address the above limitations, we propose a novel module named InterFormer to learn heterogeneous information interaction in an interleaving style. To achieve better interaction learning, InterFormer enables bidirectional information flow for mutually beneficial learning across different modes. To avoid aggressive information aggregation, we retain complete information in each data mode and use a separate bridging arch for effective information selection and summarization. Our proposed InterFormer achieves state-of-the-art performance on three public datasets and a large-scale industrial dataset.

Dheevatsa Mudigere, Yuchen Hao, Jianyu Huang et al.

Deep learning recommendation models (DLRMs) are used across many business-critical services at Facebook and are the single largest AI application in terms of infrastructure demand in its data-centers. In this paper we discuss the SW/HW co-designed solution for high-performance distributed training of large-scale DLRMs. We introduce a high-performance scalable software stack based on PyTorch and pair it with the new evolution of Zion platform, namely ZionEX. We demonstrate the capability to train very large DLRMs with up to 12 Trillion parameters and show that we can attain 40X speedup in terms of time to solution over previous systems. We achieve this by (i) designing the ZionEX platform with dedicated scale-out network, provisioned with high bandwidth, optimal topology and efficient transport (ii) implementing an optimized PyTorch-based training stack supporting both model and data parallelism (iii) developing sharding algorithms capable of hierarchical partitioning of the embedding tables along row, column dimensions and load balancing them across multiple workers; (iv) adding high-performance core operators while retaining flexibility to support optimizers with fully deterministic updates (v) leveraging reduced precision communications, multi-level memory hierarchy (HBM+DDR+SSD) and pipelining. Furthermore, we develop and briefly comment on distributed data ingestion and other supporting services that are required for the robust and efficient end-to-end training in production environments.

Kiwan Maeng, Shivam Bharuka, Isabel Gao et al.

The paper proposes and optimizes a partial recovery training system, CPR, for recommendation models. CPR relaxes the consistency requirement by enabling non-failed nodes to proceed without loading checkpoints when a node fails during training, improving failure-related overheads. The paper is the first to the extent of our knowledge to perform a data-driven, in-depth analysis of applying partial recovery to recommendation models and identified a trade-off between accuracy and performance. Motivated by the analysis, we present CPR, a partial recovery training system that can reduce the training time and maintain the desired level of model accuracy by (1) estimating the benefit of partial recovery, (2) selecting an appropriate checkpoint saving interval, and (3) prioritizing to save updates of more frequently accessed parameters. Two variants of CPR, CPR-MFU and CPR-SSU, reduce the checkpoint-related overhead from 8.2-8.5% to 0.53-0.68% compared to full recovery, on a configuration emulating the failure pattern and overhead of a production-scale cluster. While reducing overhead significantly, CPR achieves model quality on par with the more expensive full recovery scheme, training the state-of-the-art recommendation model using Criteo's Ads CTR dataset. Our preliminary results also suggest that CPR can speed up training on a real production-scale cluster, without notably degrading the accuracy.

Mao Ye, Dhruv Choudhary, Jiecao Yu et al.

Large scale deep learning provides a tremendous opportunity to improve the quality of content recommendation systems by employing both wider and deeper models, but this comes at great infrastructural cost and carbon footprint in modern data centers. Pruning is an effective technique that reduces both memory and compute demand for model inference. However, pruning for online recommendation systems is challenging due to the continuous data distribution shift (a.k.a non-stationary data). Although incremental training on the full model is able to adapt to the non-stationary data, directly applying it on the pruned model leads to accuracy loss. This is because the sparsity pattern after pruning requires adjustment to learn new patterns. To the best of our knowledge, this is the first work to provide in-depth analysis and discussion of applying pruning to online recommendation systems with non-stationary data distribution. Overall, this work makes the following contributions: 1) We present an adaptive dense to sparse paradigm equipped with a novel pruning algorithm for pruning a large scale recommendation system with non-stationary data distribution; 2) We design the pruning algorithm to automatically learn the sparsity across layers to avoid repeating hand-tuning, which is critical for pruning the heterogeneous architectures of recommendation systems trained with non-stationary data.

Qingquan Song, Dehua Cheng, Hanning Zhou et al.

Click-Through Rate (CTR) prediction is one of the most important machine learning tasks in recommender systems, driving personalized experience for billions of consumers. Neural architecture search (NAS), as an emerging field, has demonstrated its capabilities in discovering powerful neural network architectures, which motivates us to explore its potential for CTR predictions. Due to 1) diverse unstructured feature interactions, 2) heterogeneous feature space, and 3) high data volume and intrinsic data randomness, it is challenging to construct, search, and compare different architectures effectively for recommendation models. To address these challenges, we propose an automated interaction architecture discovering framework for CTR prediction named AutoCTR. Via modularizing simple yet representative interactions as virtual building blocks and wiring them into a space of direct acyclic graphs, AutoCTR performs evolutionary architecture exploration with learning-to-rank guidance at the architecture level and achieves acceleration using low-fidelity model. Empirical analysis demonstrates the effectiveness of AutoCTR on different datasets comparing to human-crafted architectures. The discovered architecture also enjoys generalizability and transferability among different datasets.

Qinqing Zheng, Bor-Yiing Su, Jiyan Yang et al.

Recommendation systems are often trained with a tremendous amount of data, and distributed training is the workhorse to shorten the training time. While the training throughput can be increased by simply adding more workers, it is also increasingly challenging to preserve the model quality. In this paper, we present \shadowsync, a distributed framework specifically tailored to modern scale recommendation system training. In contrast to previous works where synchronization happens as part of the training process, \shadowsync separates the synchronization from training and runs it in the background. Such isolation significantly reduces the synchronization overhead and increases the synchronization frequency, so that we are able to obtain both high throughput and excellent model quality when training at scale. The superiority of our procedure is confirmed by experiments on training deep neural networks for click-through-rate prediction tasks. Our framework is capable to express data parallelism and/or model parallelism, generic to host various types of synchronization algorithms, and readily applicable to large scale problems in other areas.

Hui Guan, Andrey Malevich, Jiyan Yang et al.

Continuous representations have been widely adopted in recommender systems where a large number of entities are represented using embedding vectors. As the cardinality of the entities increases, the embedding components can easily contain millions of parameters and become the bottleneck in both storage and inference due to large memory consumption. This work focuses on post-training 4-bit quantization on the continuous embeddings. We propose row-wise uniform quantization with greedy search and codebook-based quantization that consistently outperforms state-of-the-art quantization approaches on reducing accuracy degradation. We deploy our uniform quantization technique on a production model in Facebook and demonstrate that it can reduce the model size to only 13.89% of the single-precision version while the model quality stays neutral.

Antonio Ginart, Maxim Naumov, Dheevatsa Mudigere et al.

Embedding representations power machine intelligence in many applications, including recommendation systems, but they are space intensive -- potentially occupying hundreds of gigabytes in large-scale settings. To help manage this outsized memory consumption, we explore mixed dimension embeddings, an embedding layer architecture in which a particular embedding vector's dimension scales with its query frequency. Through theoretical analysis and systematic experiments, we demonstrate that using mixed dimensions can drastically reduce the memory usage, while maintaining and even improving the ML performance. Empirically, we show that the proposed mixed dimension layers improve accuracy by 0.1% using half as many parameters or maintain it using 16X fewer parameters for click-through rate prediction task on the Criteo Kaggle dataset.

Hao-Jun Michael Shi, Dheevatsa Mudigere, Maxim Naumov et al.

Modern deep learning-based recommendation systems exploit hundreds to thousands of different categorical features, each with millions of different categories ranging from clicks to posts. To respect the natural diversity within the categorical data, embeddings map each category to a unique dense representation within an embedded space. Since each categorical feature could take on as many as tens of millions of different possible categories, the embedding tables form the primary memory bottleneck during both training and inference. We propose a novel approach for reducing the embedding size in an end-to-end fashion by exploiting complementary partitions of the category set to produce a unique embedding vector for each category without explicit definition. By storing multiple smaller embedding tables based on each complementary partition and combining embeddings from each table, we define a unique embedding for each category at smaller memory cost. This approach may be interpreted as using a specific fixed codebook to ensure uniqueness of each category's representation. Our experimental results demonstrate the effectiveness of our approach over the hashing trick for reducing the size of the embedding tables in terms of model loss and accuracy, while retaining a similar reduction in the number of parameters.

Dhiraj Kalamkar, Dheevatsa Mudigere, Naveen Mellempudi et al.

This paper presents the first comprehensive empirical study demonstrating the efficacy of the Brain Floating Point (BFLOAT16) half-precision format for Deep Learning training across image classification, speech recognition, language modeling, generative networks and industrial recommendation systems. BFLOAT16 is attractive for Deep Learning training for two reasons: the range of values it can represent is the same as that of IEEE 754 floating-point format (FP32) and conversion to/from FP32 is simple. Maintaining the same range as FP32 is important to ensure that no hyper-parameter tuning is required for convergence; e.g., IEEE 754 compliant half-precision floating point (FP16) requires hyper-parameter tuning. In this paper, we discuss the flow of tensors and various key operations in mixed precision training, and delve into details of operations, such as the rounding modes for converting FP32 tensors to BFLOAT16. We have implemented a method to emulate BFLOAT16 operations in Tensorflow, Caffe2, IntelCaffe, and Neon for our experiments. Our results show that deep learning training using BFLOAT16 tensors achieves the same state-of-the-art (SOTA) results across domains as FP32 tensors in the same number of iterations and with no changes to hyper-parameters.

Peng Xu, Jiyan Yang, Farbod Roosta-Khorasani et al.

We consider the problem of finding the minimizer of a convex function $F: \mathbb R^d \rightarrow \mathbb R$ of the form $F(w) := \sum_{i=1}^n f_i(w) + R(w)$ where a low-rank factorization of $\nabla^2 f_i(w)$ is readily available. We consider the regime where $n \gg d$. As second-order methods prove to be effective in finding the minimizer to a high-precision, in this work, we propose randomized Newton-type algorithms that exploit \textit{non-uniform} sub-sampling of $\{\nabla^2 f_i(w)\}_{i=1}^{n}$, as well as inexact updates, as means to reduce the computational complexity. Two non-uniform sampling distributions based on {\it block norm squares} and {\it block partial leverage scores} are considered in order to capture important terms among $\{\nabla^2 f_i(w)\}_{i=1}^{n}$. We show that at each iteration non-uniformly sampling at most $\mathcal O(d \log d)$ terms from $\{\nabla^2 f_i(w)\}_{i=1}^{n}$ is sufficient to achieve a linear-quadratic convergence rate in $w$ when a suitable initial point is provided. In addition, we show that our algorithms achieve a lower computational complexity and exhibit more robustness and better dependence on problem specific quantities, such as the condition number, compared to similar existing methods, especially the ones based on uniform sampling. Finally, we empirically demonstrate that our methods are at least twice as fast as Newton's methods with ridge logistic regression on several real datasets.

Jiyan Yang, Alex Gittens

Recent years have demonstrated that using random feature maps can significantly decrease the training and testing times of kernel-based algorithms without significantly lowering their accuracy. Regrettably, because random features are target-agnostic, typically thousands of such features are necessary to achieve acceptable accuracies. In this work, we consider the problem of learning a small number of explicit polynomial features. Our approach, named Tensor Machines, finds a parsimonious set of features by optimizing over the hypothesis class introduced by Kar and Karnick for random feature maps in a target-specific manner. Exploiting a natural connection between polynomials and tensors, we provide bounds on the generalization error of Tensor Machines. Empirically, Tensor Machines behave favorably on several real-world datasets compared to other state-of-the-art techniques for learning polynomial features, and deliver significantly more parsimonious models.

Jiyan Yang, Yin-Lam Chow, Christopher Ré et al.

In recent years, stochastic gradient descent (SGD) methods and randomized linear algebra (RLA) algorithms have been applied to many large-scale problems in machine learning and data analysis. We aim to bridge the gap between these two methods in solving constrained overdetermined linear regression problems---e.g., $\ell_2$ and $\ell_1$ regression problems. We propose a hybrid algorithm named pwSGD that uses RLA techniques for preconditioning and constructing an importance sampling distribution, and then performs an SGD-like iterative process with weighted sampling on the preconditioned system. We prove that pwSGD inherits faster convergence rates that only depend on the lower dimension of the linear system, while maintaining low computation complexity. Particularly, when solving $\ell_1$ regression with size $n$ by $d$, pwSGD returns an approximate solution with $ε$ relative error in the objective value in $\mathcal{O}(\log n \cdot \text{nnz}(A) + \text{poly}(d)/ε^2)$ time. This complexity is uniformly better than that of RLA methods in terms of both $ε$ and $d$ when the problem is unconstrained. For $\ell_2$ regression, pwSGD returns an approximate solution with $ε$ relative error in the objective value and the solution vector measured in prediction norm in $\mathcal{O}(\log n \cdot \text{nnz}(A) + \text{poly}(d) \log(1/ε) /ε)$ time. We also provide lower bounds on the coreset complexity for more general regression problems, indicating that still new ideas will be needed to extend similar RLA preconditioning ideas to weighted SGD algorithms for more general regression problems. Finally, the effectiveness of such algorithms is illustrated numerically on both synthetic and real datasets.

Jiyan Yang, Xiangrui Meng, Michael W. Mahoney

In this era of large-scale data, distributed systems built on top of clusters of commodity hardware provide cheap and reliable storage and scalable processing of massive data. Here, we review recent work on developing and implementing randomized matrix algorithms in large-scale parallel and distributed environments. Randomized algorithms for matrix problems have received a great deal of attention in recent years, thus far typically either in theory or in machine learning applications or with implementations on a single machine. Our main focus is on the underlying theory and practical implementation of random projection and random sampling algorithms for very large very overdetermined (i.e., overconstrained) $\ell_1$ and $\ell_2$ regression problems. Randomization can be used in one of two related ways: either to construct sub-sampled problems that can be solved, exactly or approximately, with traditional numerical methods; or to construct preconditioned versions of the original full problem that are easier to solve with traditional iterative algorithms. Theoretical results demonstrate that in near input-sparsity time and with only a few passes through the data one can obtain very strong relative-error approximate solutions, with high probability. Empirical results highlight the importance of various trade-offs (e.g., between the time to construct an embedding and the conditioning quality of the embedding, between the relative importance of computation versus communication, etc.) and demonstrate that $\ell_1$ and $\ell_2$ regression problems can be solved to low, medium, or high precision in existing distributed systems on up to terabyte-sized data.

Haim Avron, Vikas Sindhwani, Jiyan Yang et al.

We consider the problem of improving the efficiency of randomized Fourier feature maps to accelerate training and testing speed of kernel methods on large datasets. These approximate feature maps arise as Monte Carlo approximations to integral representations of shift-invariant kernel functions (e.g., Gaussian kernel). In this paper, we propose to use Quasi-Monte Carlo (QMC) approximations instead, where the relevant integrands are evaluated on a low-discrepancy sequence of points as opposed to random point sets as in the Monte Carlo approach. We derive a new discrepancy measure called box discrepancy based on theoretical characterizations of the integration error with respect to a given sequence. We then propose to learn QMC sequences adapted to our setting based on explicit box discrepancy minimization. Our theoretical analyses are complemented with empirical results that demonstrate the effectiveness of classical and adaptive QMC techniques for this problem.

Jiyan Yang, Xiangrui Meng, Michael W. Mahoney

Quantile regression is a method to estimate the quantiles of the conditional distribution of a response variable, and as such it permits a much more accurate portrayal of the relationship between the response variable and observed covariates than methods such as Least-squares or Least Absolute Deviations regression. It can be expressed as a linear program, and, with appropriate preprocessing, interior-point methods can be used to find a solution for moderately large problems. Dealing with very large problems, \emph(e.g.), involving data up to and beyond the terabyte regime, remains a challenge. Here, we present a randomized algorithm that runs in nearly linear time in the size of the input and that, with constant probability, computes a $(1+ε)$ approximate solution to an arbitrary quantile regression problem. As a key step, our algorithm computes a low-distortion subspace-preserving embedding with respect to the loss function of quantile regression. Our empirical evaluation illustrates that our algorithm is competitive with the best previous work on small to medium-sized problems, and that in addition it can be implemented in MapReduce-like environments and applied to terabyte-sized problems.