Cong Fu

Xuan Zhang, Limei Wang, Jacob Helwig et al. · cambridge, mit

Advances in artificial intelligence (AI) are fueling a new paradigm of discoveries in natural sciences. Today, AI has started to advance natural sciences by improving, accelerating, and enabling our understanding of natural phenomena at a wide range of spatial and temporal scales, giving rise to a new area of research known as AI for science (AI4Science). Being an emerging research paradigm, AI4Science is unique in that it is an enormous and highly interdisciplinary area. Thus, a unified and technical treatment of this field is needed yet challenging. This work aims to provide a technically thorough account of a subarea of AI4Science; namely, AI for quantum, atomistic, and continuum systems. These areas aim at understanding the physical world from the subatomic (wavefunctions and electron density), atomic (molecules, proteins, materials, and interactions), to macro (fluids, climate, and subsurface) scales and form an important subarea of AI4Science. A unique advantage of focusing on these areas is that they largely share a common set of challenges, thereby allowing a unified and foundational treatment. A key common challenge is how to capture physics first principles, especially symmetries, in natural systems by deep learning methods. We provide an in-depth yet intuitive account of techniques to achieve equivariance to symmetry transformations. We also discuss other common technical challenges, including explainability, out-of-distribution generalization, knowledge transfer with foundation and large language models, and uncertainty quantification. To facilitate learning and education, we provide categorized lists of resources that we found to be useful. We strive to be thorough and unified and hope this initial effort may trigger more community interests and efforts to further advance AI4Science.

Jacob Helwig, Xuan Zhang, Cong Fu et al.

We consider solving partial differential equations (PDEs) with Fourier neural operators (FNOs), which operate in the frequency domain. Since the laws of physics do not depend on the coordinate system used to describe them, it is desirable to encode such symmetries in the neural operator architecture for better performance and easier learning. While encoding symmetries in the physical domain using group theory has been studied extensively, how to capture symmetries in the frequency domain is under-explored. In this work, we extend group convolutions to the frequency domain and design Fourier layers that are equivariant to rotations, translations, and reflections by leveraging the equivariance property of the Fourier transform. The resulting $G$-FNO architecture generalizes well across input resolutions and performs well in settings with varying levels of symmetry. Our code is publicly available as part of the AIRS library (https://github.com/divelab/AIRS).

Cong Fu, Xuan Zhang, Huixin Zhang et al.

Deep learning methods have been shown to be effective in representing ground-state wave functions of quantum many-body systems. Existing methods use convolutional neural networks (CNNs) for square lattices due to their image-like structures. For non-square lattices, existing method uses graph neural network (GNN) in which structure information is not precisely captured, thereby requiring additional hand-crafted sublattice encoding. In this work, we propose lattice convolutions in which a set of proposed operations are used to convert non-square lattices into grid-like augmented lattices on which regular convolution can be applied. Based on the proposed lattice convolutions, we design lattice convolutional networks (LCN) that use self-gating and attention mechanisms. Experimental results show that our method achieves performance on par or better than existing methods on spin 1/2 $J_1$-$J_2$ Heisenberg model over the square, honeycomb, triangular, and kagome lattices while without using hand-crafted encoding.

Yuxuan Zhu, Cong Fu, Yabo Ni et al.

Temporal distribution shift (TDS) erodes the long-term accuracy of recommender systems, yet industrial practice still relies on periodic incremental training, which struggles to capture both stable and transient patterns. Existing approaches such as invariant learning and self-supervised learning offer partial solutions but often suffer from unstable temporal generalization, representation collapse, or inefficient data utilization. To address these limitations, we propose ELBO$_\text{TDS}$, a probabilistic framework that integrates seamlessly into industry-scale incremental learning pipelines. First, we identify key shifting factors through statistical analysis of real-world production data and design a simple yet effective data augmentation strategy that resamples these time-varying factors to extend the training support. Second, to harness the benefits of this extended distribution while preventing representation collapse, we model the temporal recommendation scenario using a causal graph and derive a self-supervised variational objective, ELBO$_\text{TDS}$, grounded in the causal structure. Extensive experiments supported by both theoretical and empirical analysis demonstrate that our method achieves superior temporal generalization, yielding a 2.33\% uplift in GMV per user and has been successfully deployed in Shopee Product Search. Code is available at https://github.com/FuCongResearchSquad/ELBO4TDS.

Yu Liang, Zhongjin Zhang, Yuxuan Zhu et al.

Semantic ID (SID)-based recommendation is a promising paradigm for scaling sequential recommender systems, but existing methods largely follow a semantic-centric pipeline: item embeddings are learned from foundation models and discretized using generic quantization schemes. This design is misaligned with generative recommendation objectives: semantic embeddings are weakly coupled with collaborative prediction, and generic quantization is inefficient at reducing sequential uncertainty for autoregressive modeling. To address these, we propose ReSID, a recommendation-native, principled SID framework that rethinks representation learning and quantization from the perspective of information preservation and sequential predictability, without relying on LLMs. ReSID consists of two components: (i) Field-Aware Masked Auto-Encoding (FAMAE), which learns predictive-sufficient item representations from structured features, and (ii) Globally Aligned Orthogonal Quantization (GAOQ), which produces compact and predictable SID sequences by jointly reducing semantic ambiguity and prefix-conditional uncertainty. Theoretical analysis and extensive experiments across ten datasets show the effectiveness of ReSID. ReSID consistently outperforms strong sequential and SID-based generative baselines by an average of over 10%, while reducing tokenization cost by up to 122x. Code is available at https://github.com/FuCongResearchSquad/ReSID.

Keqiang Yan, Cong Fu, Xiaofeng Qian et al.

Crystal structures are characterized by atomic bases within a primitive unit cell that repeats along a regular lattice throughout 3D space. The periodic and infinite nature of crystals poses unique challenges for geometric graph representation learning. Specifically, constructing graphs that effectively capture the complete geometric information of crystals and handle chiral crystals remains an unsolved and challenging problem. In this paper, we introduce a novel approach that utilizes the periodic patterns of unit cells to establish the lattice-based representation for each atom, enabling efficient and expressive graph representations of crystals. Furthermore, we propose ComFormer, a SE(3) transformer designed specifically for crystalline materials. ComFormer includes two variants; namely, iComFormer that employs invariant geometric descriptors of Euclidean distances and angles, and eComFormer that utilizes equivariant vector representations. Experimental results demonstrate the state-of-the-art predictive accuracy of ComFormer variants on various tasks across three widely-used crystal benchmarks. Our code is publicly available as part of the AIRS library (https://github.com/divelab/AIRS).

Peter St. John, Dejun Lin, Polina Binder et al.

Artificial Intelligence models encoding biology and chemistry are opening new routes to high-throughput and high-quality in-silico drug development. However, their training increasingly relies on computational scale, with recent protein language models (pLM) training on hundreds of graphical processing units (GPUs). We introduce the BioNeMo Framework to facilitate the training of computational biology and chemistry AI models across hundreds of GPUs. Its modular design allows the integration of individual components, such as data loaders, into existing workflows and is open to community contributions. We detail technical features of the BioNeMo Framework through use cases such as pLM pre-training and fine-tuning. On 256 NVIDIA A100s, BioNeMo Framework trains a three billion parameter BERT-based pLM on over one trillion tokens in 4.2 days. The BioNeMo Framework is open-source and free for everyone to use.

Ye Chen, Wei Cai, Liangmin Wu et al.

We release and introduce the TigerBot family of large language models (LLMs), consisting of base and chat models, sized from 7, 13, 70 and 180 billion parameters. We develop our models embarking from Llama-2 and BLOOM, and push the boundary further in data, training algorithm, infrastructure, and application tools. Our models yield meaningful performance gain over SOTA open-source models, e.g., Llama-2, specifically 6% gain in English and 20% gain in Chinese. TigerBot model family also achieves leading performance in major academic and industrial benchmarks and leaderboards. We believe that TigerBot represents just a snapshot of lightning-fast progression in LLM open-source community. Therefore, we are thrilled to give back by publicly releasing our models and reporting our approach behind, with additional emphases on building SOTA LLMs in a democratized way and making LLMs of use in real-world applications.

Xuan Zhang, Jacob Helwig, Yuchao Lin et al.

We consider using deep neural networks to solve time-dependent partial differential equations (PDEs), where multi-scale processing is crucial for modeling complex, time-evolving dynamics. While the U-Net architecture with skip connections is commonly used by prior studies to enable multi-scale processing, our analysis shows that the need for features to evolve across layers results in temporally misaligned features in skip connections, which limits the model's performance. To address this limitation, we propose SineNet, consisting of multiple sequentially connected U-shaped network blocks, referred to as waves. In SineNet, high-resolution features are evolved progressively through multiple stages, thereby reducing the amount of misalignment within each stage. We furthermore analyze the role of skip connections in enabling both parallel and sequential processing of multi-scale information. Our method is rigorously tested on multiple PDE datasets, including the Navier-Stokes equations and shallow water equations, showcasing the advantages of our proposed approach over conventional U-Nets with a comparable parameter budget. We further demonstrate that increasing the number of waves in SineNet while maintaining the same number of parameters leads to a monotonically improved performance. The results highlight the effectiveness of SineNet and the potential of our approach in advancing the state-of-the-art in neural PDE solver design. Our code is available as part of AIRS (https://github.com/divelab/AIRS).

Cong Fu, Kun Wang, Jiahua Wu et al.

Modern e-commerce platforms rely heavily on modeling diverse user feedback to provide personalized services. Consequently, multi-task learning has become an integral part of their ranking systems. However, existing multi-task learning methods encounter two main challenges: some lack explicit modeling of task relationships, resulting in inferior performance, while others have limited applicability due to being computationally intensive, having scalability issues, or relying on strong assumptions. To address these limitations and better fit our real-world scenario, pre-rank in Shopee Search, we introduce in this paper ResFlow, a lightweight multi-task learning framework that enables efficient cross-task information sharing via residual connections between corresponding layers of task networks. Extensive experiments on datasets from various scenarios and modalities demonstrate its superior performance and adaptability over state-of-the-art methods. The online A/B tests in Shopee Search showcase its practical value in large-scale industrial applications, evidenced by a 1.29% increase in OPU (order-per-user) without additional system latency. ResFlow is now fully deployed in the pre-rank module of Shopee Search. To facilitate efficient online deployment, we propose a novel offline metric Weighted Recall@K, which aligns well with our online metric OPU, addressing the longstanding online-offline metric misalignment issue. Besides, we propose to fuse scores from the multiple tasks additively when ranking items, which outperforms traditional multiplicative fusion. The code is released at https://github.com/BrunoTruthAlliance/ResFlow

Ye Chen, Igor Couto, Wei Cai et al.

We introduce SoftTiger, a clinical large language model (CLaM) designed as a foundation model for healthcare workflows. The narrative and unstructured nature of clinical notes is a major obstacle for healthcare intelligentization. We address a critical problem of structuring clinical notes into clinical data, according to international interoperability standards. We collect and annotate data for three subtasks, namely, international patient summary, clinical impression and medical encounter. We then supervised fine-tuned a state-of-the-art LLM using public and credentialed clinical data. The training is orchestrated in a way that the target model can first support basic clinical tasks such as abbreviation expansion and temporal information extraction, and then learn to perform more complex downstream clinical tasks. Moreover, we address several modeling challenges in the healthcare context, e.g., extra long context window. Our blind pairwise evaluation shows that SoftTiger outperforms other popular open-source models and GPT-3.5, comparable to Gemini-pro, with a mild gap from GPT-4. We believe that LLMs may become a step-stone towards healthcare digitalization and democratization. Therefore, we publicly release SoftTiger models at scales of 13 billion and 70 billion parameters, as well as datasets and code for our innovative scalable evaluation, hopefully, making a significant contribution to the healthcare industry.

Xi Ru, Cong Fu, Zhongze Li et al.

Passivity indices have been widely adopted to derive distributed stability certificates for power systems. Nevertheless, conventional passivity indices remain scalar-valued even for multi-input-multi-output (MIMO) systems, which can introduce excessive conservatism and compromise analysis accuracy. To overcome these limitations, this paper extends the differential passivity index to a matrix-valued formulation that captures both channel-wise passivity properties and inter-channel coupling effects in MIMO subsystems. On this basis, semi-distributed and fully distributed stability criteria are developed for power systems with heterogeneous nonlinear devices. It is shown that system stability is guaranteed when the aggregate passivity excess of devices compensates for the passivity shortage imposed by the network. Furthermore, analytical passivity matrix expressions for typical power system components are derived, facilitating compositional stability analysis. Case studies on a three-bus system and a modified IEEE 118-bus system validate the effectiveness of the proposed framework.

Yuchao Lin, Cong Fu, Zachary Krueger et al.

$\rm{SO}(3)$-equivariant networks are the dominant models for machine learning interatomic potentials (MLIPs). The key operation of such networks is the Clebsch-Gordan (CG) tensor product, which is computationally expensive. To accelerate the computation, we develop tensor decomposition networks (TDNs) as a class of approximately equivariant networks in which CG tensor products are replaced by low-rank tensor decompositions, such as the CANDECOMP/PARAFAC (CP) decomposition. With the CP decomposition, we prove (i) a uniform bound on the induced error of $\rm{SO}(3)$-equivariance, and (ii) the universality of approximating any equivariant bilinear map. To further reduce the number of parameters, we propose path-weight sharing that ties all multiplicity-space weights across the $\mathcal{O}(L^3)$ CG paths into a single path without compromising equivariance, where $L$ is the maximum angular degree. The resulting layer acts as a plug-and-play replacement for tensor products in existing networks, and the computational complexity of tensor products is reduced from $\mathcal{O}(L^6)$ to $\mathcal{O}(L^4)$. We evaluate TDNs on PubChemQCR, a newly curated molecular relaxation dataset containing 105 million DFT-calculated snapshots. We also use existing datasets, including OC20, and OC22. Results show that TDNs achieve competitive performance with dramatic speedup in computations. Our code is publicly available as part of the AIRS library (\href{https://github.com/divelab/AIRS/tree/main/OpenMol/TDN}{https://github.com/divelab/AIRS/}).

Cong Fu, Keqiang Yan, Limei Wang et al.

Proteins are complex biomolecules that perform a variety of crucial functions within living organisms. Designing and generating novel proteins can pave the way for many future synthetic biology applications, including drug discovery. However, it remains a challenging computational task due to the large modeling space of protein structures. In this study, we propose a latent diffusion model that can reduce the complexity of protein modeling while flexibly capturing the distribution of natural protein structures in a condensed latent space. Specifically, we propose an equivariant protein autoencoder that embeds proteins into a latent space and then uses an equivariant diffusion model to learn the distribution of the latent protein representations. Experimental results demonstrate that our method can effectively generate novel protein backbone structures with high designability and efficiency. The code will be made publicly available at https://github.com/divelab/AIRS/tree/main/OpenProt/LatentDiff

Meng Liu, Cong Fu, Xuan Zhang et al.

Molecular property prediction is gaining increasing attention due to its diverse applications. One task of particular interests and importance is to predict quantum chemical properties without 3D equilibrium structures. This is practically favorable since obtaining 3D equilibrium structures requires extremely expensive calculations. In this work, we design a deep graph neural network to predict quantum properties by directly learning from 2D molecular graphs. In addition, we propose a 3D graph neural network to learn from low-cost conformer sets, which can be obtained with open-source tools using an affordable budget. We employ our methods to participate in the 2021 KDD Cup on OGB Large-Scale Challenge (OGB-LSC), which aims to predict the HOMO-LUMO energy gap of molecules. Final evaluation results reveal that we are one of the winners with a mean absolute error of 0.1235 on the holdout test set. Our implementation is available as part of the MoleculeX package (https://github.com/divelab/MoleculeX).

Meng Liu, Youzhi Luo, Limei Wang et al.

Although there exist several libraries for deep learning on graphs, they are aiming at implementing basic operations for graph deep learning. In the research community, implementing and benchmarking various advanced tasks are still painful and time-consuming with existing libraries. To facilitate graph deep learning research, we introduce DIG: Dive into Graphs, a turnkey library that provides a unified testbed for higher level, research-oriented graph deep learning tasks. Currently, we consider graph generation, self-supervised learning on graphs, explainability of graph neural networks, and deep learning on 3D graphs. For each direction, we provide unified implementations of data interfaces, common algorithms, and evaluation metrics. Altogether, DIG is an extensible, open-source, and turnkey library for researchers to develop new methods and effortlessly compare with common baselines using widely used datasets and evaluation metrics. Source code is available at https://github.com/divelab/DIG.

Cong Fu, Tong Chen, Meng Qu et al.

In recent years, there has been a surge of interests in interpretable graph reasoning methods. However, these models often suffer from limited performance when working on sparse and incomplete graphs, due to the lack of evidential paths that can reach target entities. Here we study open knowledge graph reasoning---a task that aims to reason for missing facts over a graph augmented by a background text corpus. A key challenge of the task is to filter out "irrelevant" facts extracted from corpus, in order to maintain an effective search space during path inference. We propose a novel reinforcement learning framework to train two collaborative agents jointly, i.e., a multi-hop graph reasoner and a fact extractor. The fact extraction agent generates fact triples from corpora to enrich the graph on the fly; while the reasoning agent provides feedback to the fact extractor and guides it towards promoting facts that are helpful for the interpretable reasoning. Experiments on two public datasets demonstrate the effectiveness of the proposed approach. Source code and datasets used in this paper can be downloaded at https://github.com/shanzhenren/CPL

Cong Fu, Changxu Wang, Deng Cai

Approximate Nearest Neighbor Search (ANNS) in high dimensional space is essential in database and information retrieval. Recently, there has been a surge of interest in exploring efficient graph-based indices for the ANNS problem. Among them, Navigating Spreading-out Graph (NSG) provides fine theoretical analysis and achieves state-of-the-art performance. However, we find there are several limitations with NSG: 1) NSG has no theoretical guarantee on nearest neighbor search when the query is not indexed in the database; 2) NSG is too sparse which harms the search performance. In addition, NSG suffers from high indexing complexity. To address the above problems, we propose the Satellite System Graphs (SSG) and a practical variant NSSG. Specifically, we propose a novel pruning strategy to produce SSGs from the complete graph. SSGs define a new family of MSNETs in which the out-edges of each node are distributed evenly in all directions. Each node in the graph builds effective connections to its neighborhood omnidirectionally, whereupon we derive SSG's excellent theoretical properties for both indexed and unindexed queries. We can adaptively adjust the sparsity of an SSG with a hyper-parameter to optimize the search performance. Further, NSSG is proposed to reduce the indexing complexity of the SSG for large-scale applications. Both theoretical and extensive experimental analyses are provided to demonstrate the strengths of the proposed approach over the existing representative algorithms. Our code has been released at https://github.com/ZJULearning/SSG.

Wenxiao Wang, Cong Fu, Jishun Guo et al.

Neural network compression empowers the effective yet unwieldy deep convolutional neural networks (CNN) to be deployed in resource-constrained scenarios. Most state-of-the-art approaches prune the model in filter-level according to the "importance" of filters. Despite their success, we notice they suffer from at least two of the following problems: 1) The redundancy among filters is not considered because the importance is evaluated independently. 2) Cross-layer filter comparison is unachievable since the importance is defined locally within each layer. Consequently, we must manually specify layer-wise pruning ratios. 3) They are prone to generate sub-optimal solutions because they neglect the inequality between reducing parameters and reducing computational cost. Reducing the same number of parameters in different positions in the network may reduce different computational cost. To address the above problems, we develop a novel algorithm named as COP (correlation-based pruning), which can detect the redundant filters efficiently. We enable the cross-layer filter comparison through global normalization. We add parameter-quantity and computational-cost regularization terms to the importance, which enables the users to customize the compression according to their preference (smaller or faster). Extensive experiments have shown COP outperforms the others significantly. The code is released at https://github.com/ZJULearning/COP.

Sunhao Dai, Jiakai Tang, Jiahua Wu et al.

Despite the growing interest in replicating the scaled success of large language models (LLMs) in industrial search and recommender systems, most existing industrial efforts remain limited to transplanting Transformer architectures, which bring only incremental improvements over strong Deep Learning Recommendation Models (DLRMs). From a first principle perspective, the breakthroughs of LLMs stem not only from their architectures but also from two complementary mechanisms: context engineering, which enriches raw input queries with contextual cues to better elicit model capabilities, and multi-step reasoning, which iteratively refines model outputs through intermediate reasoning paths. However, these two mechanisms and their potential to unlock substantial improvements remain largely underexplored in industrial ranking systems. In this paper, we propose OnePiece, a unified framework that seamlessly integrates LLM-style context engineering and reasoning into both retrieval and ranking models of industrial cascaded pipelines. OnePiece is built on a pure Transformer backbone and further introduces three key innovations: (1) structured context engineering, which augments interaction history with preference and scenario signals and unifies them into a structured tokenized input sequence for both retrieval and ranking; (2) block-wise latent reasoning, which equips the model with multi-step refinement of representations and scales reasoning bandwidth via block size; (3) progressive multi-task training, which leverages user feedback chains to effectively supervise reasoning steps during training. OnePiece has been deployed in the main personalized search scenario of Shopee and achieves consistent online gains across different key business metrics, including over $+2\%$ GMV/UU and a $+2.90\%$ increase in advertising revenue.

Lianhao Zhou, Hongyi Ling, Cong Fu et al.

Computing has long served as a cornerstone of scientific discovery. Recently, a paradigm shift has emerged with the rise of large language models (LLMs), introducing autonomous systems, referred to as agents, that accelerate discovery across varying levels of autonomy. These language agents provide a flexible and versatile framework that orchestrates interactions with human scientists, natural language, computer language and code, and physics. This paper presents our view and vision of LLM-based scientific agents and their growing role in transforming the scientific discovery lifecycle, from hypothesis discovery, experimental design and execution, to result analysis and refinement. We critically examine current methodologies, emphasizing key innovations, practical achievements, and outstanding limitations. Additionally, we identify open research challenges and outline promising directions for building more robust, generalizable, and adaptive scientific agents. Our analysis highlights the transformative potential of autonomous agents to accelerate scientific discovery across diverse domains.

Ye Chen, Dongdong Huang, Haoyun Xu et al.

We introduce the world's first clinical terminology for the Chinese healthcare community, namely MedCT, accompanied by a clinical foundation model MedBERT and an entity linking model MedLink. The MedCT system enables standardized and programmable representation of Chinese clinical data, successively stimulating the development of new medicines, treatment pathways, and better patient outcomes for the populous Chinese community. Moreover, the MedCT knowledge graph provides a principled mechanism to minimize the hallucination problem of large language models (LLMs), therefore achieving significant levels of accuracy and safety in LLM-based clinical applications. By leveraging the LLMs' emergent capabilities of generativeness and expressiveness, we were able to rapidly built a production-quality terminology system and deployed to real-world clinical field within three months, while classical terminologies like SNOMED CT have gone through more than twenty years development. Our experiments show that the MedCT system achieves state-of-the-art (SOTA) performance in semantic matching and entity linking tasks, not only for Chinese but also for English. We also conducted a longitudinal field experiment by applying MedCT and LLMs in a representative spectrum of clinical tasks, including electronic health record (EHR) auto-generation and medical document search for diagnostic decision making. Our study shows a multitude of values of MedCT for clinical workflows and patient outcomes, especially in the new genre of clinical LLM applications. We present our approach in sufficient engineering detail, such that implementing a clinical terminology for other non-English societies should be readily reproducible. We openly release our terminology, models and algorithms, along with real-world clinical datasets for the development.

Cong Fu, Yuchao Lin, Zachary Krueger et al.

Accurate molecular property predictions require 3D geometries, which are typically obtained using expensive methods such as density functional theory (DFT). Here, we attempt to obtain molecular geometries by relying solely on machine learning interatomic potential (MLIP) models. To this end, we first curate a large-scale molecular relaxation dataset comprising 3.5 million molecules and 300 million snapshots. Then MLIP foundation models are trained with supervised learning to predict energy and forces given 3D molecular structures. Once trained, we show that the foundation models can be used in different ways to obtain geometries either explicitly or implicitly. First, it can be used to obtain low-energy 3D geometries via geometry optimization, providing relaxed 3D geometries for downstream molecular property predictions. To mitigate potential biases and enhance downstream predictions, we introduce geometry fine-tuning based on the relaxed 3D geometries. Second, the foundation models can be directly fine-tuned for property prediction when ground truth 3D geometries are available. Our results demonstrate that MLIP foundation models trained on relaxation data can provide valuable molecular geometries that benefit property predictions.

Cong Fu, Chao Xiang, Changxu Wang et al.

Approximate nearest neighbor search (ANNS) is a fundamental problem in databases and data mining. A scalable ANNS algorithm should be both memory-efficient and fast. Some early graph-based approaches have shown attractive theoretical guarantees on search time complexity, but they all suffer from the problem of high indexing time complexity. Recently, some graph-based methods have been proposed to reduce indexing complexity by approximating the traditional graphs; these methods have achieved revolutionary performance on million-scale datasets. Yet, they still can not scale to billion-node databases. In this paper, to further improve the search-efficiency and scalability of graph-based methods, we start by introducing four aspects: (1) ensuring the connectivity of the graph; (2) lowering the average out-degree of the graph for fast traversal; (3) shortening the search path; and (4) reducing the index size. Then, we propose a novel graph structure called Monotonic Relative Neighborhood Graph (MRNG) which guarantees very low search complexity (close to logarithmic time). To further lower the indexing complexity and make it practical for billion-node ANNS problems, we propose a novel graph structure named Navigating Spreading-out Graph (NSG) by approximating the MRNG. The NSG takes the four aspects into account simultaneously. Extensive experiments show that NSG outperforms all the existing algorithms significantly. In addition, NSG shows superior performance in the E-commercial search scenario of Taobao (Alibaba Group) and has been integrated into their search engine at billion-node scale.

Cong Fu, Deng Cai

Approximate nearest neighbor (ANN) search is a fundamental problem in many areas of data mining, machine learning and computer vision. The performance of traditional hierarchical structure (tree) based methods decreases as the dimensionality of data grows, while hashing based methods usually lack efficiency in practice. Recently, the graph based methods have drawn considerable attention. The main idea is that \emph{a neighbor of a neighbor is also likely to be a neighbor}, which we refer as \emph{NN-expansion}. These methods construct a $k$-nearest neighbor ($k$NN) graph offline. And at online search stage, these methods find candidate neighbors of a query point in some way (\eg, random selection), and then check the neighbors of these candidate neighbors for closer ones iteratively. Despite some promising results, there are mainly two problems with these approaches: 1) These approaches tend to converge to local optima. 2) Constructing a $k$NN graph is time consuming. We find that these two problems can be nicely solved when we provide a good initialization for NN-expansion. In this paper, we propose EFANNA, an extremely fast approximate nearest neighbor search algorithm based on $k$NN Graph. Efanna nicely combines the advantages of hierarchical structure based methods and nearest-neighbor-graph based methods. Extensive experiments have shown that EFANNA outperforms the state-of-art algorithms both on approximate nearest neighbor search and approximate nearest neighbor graph construction. To the best of our knowledge, EFANNA is the fastest algorithm so far both on approximate nearest neighbor graph construction and approximate nearest neighbor search. A library EFANNA based on this research is released on Github.