Namkyeong Lee

LG
h-index20
22papers
563citations
Novelty55%
AI Score49

22 Papers

CVNov 28, 2022Code
Heterogeneous Graph Learning for Multi-modal Medical Data Analysis

Sein Kim, Namkyeong Lee, Junseok Lee et al.

Routine clinical visits of a patient produce not only image data, but also non-image data containing clinical information regarding the patient, i.e., medical data is multi-modal in nature. Such heterogeneous modalities offer different and complementary perspectives on the same patient, resulting in more accurate clinical decisions when they are properly combined. However, despite its significance, how to effectively fuse the multi-modal medical data into a unified framework has received relatively little attention. In this paper, we propose an effective graph-based framework called HetMed (Heterogeneous Graph Learning for Multi-modal Medical Data Analysis) for fusing the multi-modal medical data. Specifically, we construct a multiplex network that incorporates multiple types of non-image features of patients to capture the complex relationship between patients in a systematic way, which leads to more accurate clinical decisions. Extensive experiments on various real-world datasets demonstrate the superiority and practicality of HetMed. The source code for HetMed is available at https://github.com/Sein-Kim/Multimodal-Medical.

MNApr 29, 2023Code
Conditional Graph Information Bottleneck for Molecular Relational Learning

Namkyeong Lee, Dongmin Hyun, Gyoung S. Na et al.

Molecular relational learning, whose goal is to learn the interaction behavior between molecular pairs, got a surge of interest in molecular sciences due to its wide range of applications. Recently, graph neural networks have recently shown great success in molecular relational learning by modeling a molecule as a graph structure, and considering atom-level interactions between two molecules. Despite their success, existing molecular relational learning methods tend to overlook the nature of chemistry, i.e., a chemical compound is composed of multiple substructures such as functional groups that cause distinctive chemical reactions. In this work, we propose a novel relational learning framework, called CGIB, that predicts the interaction behavior between a pair of graphs by detecting core subgraphs therein. The main idea is, given a pair of graphs, to find a subgraph from a graph that contains the minimal sufficient information regarding the task at hand conditioned on the paired graph based on the principle of conditional graph information bottleneck. We argue that our proposed method mimics the nature of chemical reactions, i.e., the core substructure of a molecule varies depending on which other molecule it interacts with. Extensive experiments on various tasks with real-world datasets demonstrate the superiority of CGIB over state-of-the-art baselines. Our code is available at https://github.com/Namkyeong/CGIB.

LGAug 21, 2022Code
Relational Self-Supervised Learning on Graphs

Namkyeong Lee, Dongmin Hyun, Junseok Lee et al.

Over the past few years, graph representation learning (GRL) has been a powerful strategy for analyzing graph-structured data. Recently, GRL methods have shown promising results by adopting self-supervised learning methods developed for learning representations of images. Despite their success, existing GRL methods tend to overlook an inherent distinction between images and graphs, i.e., images are assumed to be independently and identically distributed, whereas graphs exhibit relational information among data instances, i.e., nodes. To fully benefit from the relational information inherent in the graph-structured data, we propose a novel GRL method, called RGRL, that learns from the relational information generated from the graph itself. RGRL learns node representations such that the relationship among nodes is invariant to augmentations, i.e., augmentation-invariant relationship, which allows the node representations to vary as long as the relationship among the nodes is preserved. By considering the relationship among nodes in both global and local perspectives, RGRL overcomes limitations of previous contrastive and non-contrastive methods, and achieves the best of both worlds. Extensive experiments on fourteen benchmark datasets over various downstream tasks demonstrate the superiority of RGRL over state-of-the-art baselines. The source code for RGRL is available at https://github.com/Namkyeong/RGRL.

LGApr 4, 2022Code
GraFN: Semi-Supervised Node Classification on Graph with Few Labels via Non-Parametric Distribution Assignment

Junseok Lee, Yunhak Oh, Yeonjun In et al.

Despite the success of Graph Neural Networks (GNNs) on various applications, GNNs encounter significant performance degradation when the amount of supervision signals, i.e., number of labeled nodes, is limited, which is expected as GNNs are trained solely based on the supervision obtained from the labeled nodes. On the other hand,recent self-supervised learning paradigm aims to train GNNs by solving pretext tasks that do not require any labeled nodes, and it has shown to even outperform GNNs trained with few labeled nodes. However, a major drawback of self-supervised methods is that they fall short of learning class discriminative node representations since no labeled information is utilized during training. To this end, we propose a novel semi-supervised method for graphs, GraFN, that leverages few labeled nodes to ensure nodes that belong to the same class to be grouped together, thereby achieving the best of both worlds of semi-supervised and self-supervised methods. Specifically, GraFN randomly samples support nodes from labeled nodes and anchor nodes from the entire graph. Then, it minimizes the difference between two predicted class distributions that are non-parametrically assigned by anchor-supports similarity from two differently augmented graphs. We experimentally show that GraFN surpasses both the semi-supervised and self-supervised methods in terms of node classification on real-world graphs. The source code for GraFN is available at https://github.com/Junseok0207/GraFN.

MTRL-SCINov 17, 2023Code
Compositional Representation of Polymorphic Crystalline Materials

Namkyeong Lee, Heewoong Noh, Gyoung S. Na et al.

Machine learning (ML) has seen promising developments in materials science, yet its efficacy largely depends on detailed crystal structural data, which are often complex and hard to obtain, limiting their applicability in real-world material synthesis processes. An alternative, using compositional descriptors, offers a simpler approach by indicating the elemental ratios of compounds without detailed structural insights. However, accurately representing materials solely with compositional descriptors presents challenges due to polymorphism, where a single composition can correspond to various structural arrangements, creating ambiguities in its representation. To this end, we introduce PCRL, a novel approach that employs probabilistic modeling of composition to capture the diverse polymorphs from available structural information. Extensive evaluations on sixteen datasets demonstrate the effectiveness of PCRL in learning compositional representation, and our analysis highlights its potential applicability of PCRL in material discovery. The source code for PCRL is available at https://github.com/Namkyeong/PCRL.

IRJun 1, 2023Code
Task Relation-aware Continual User Representation Learning

Sein Kim, Namkyeong Lee, Donghyun Kim et al.

User modeling, which learns to represent users into a low-dimensional representation space based on their past behaviors, got a surge of interest from the industry for providing personalized services to users. Previous efforts in user modeling mainly focus on learning a task-specific user representation that is designed for a single task. However, since learning task-specific user representations for every task is infeasible, recent studies introduce the concept of universal user representation, which is a more generalized representation of a user that is relevant to a variety of tasks. Despite their effectiveness, existing approaches for learning universal user representations are impractical in real-world applications due to the data requirement, catastrophic forgetting and the limited learning capability for continually added tasks. In this paper, we propose a novel continual user representation learning method, called TERACON, whose learning capability is not limited as the number of learned tasks increases while capturing the relationship between the tasks. The main idea is to introduce an embedding for each task, i.e., task embedding, which is utilized to generate task-specific soft masks that not only allow the entire model parameters to be updated until the end of training sequence, but also facilitate the relationship between the tasks to be captured. Moreover, we introduce a novel knowledge retention module with pseudo-labeling strategy that successfully alleviates the long-standing problem of continual learning, i.e., catastrophic forgetting. Extensive experiments on public and proprietary real-world datasets demonstrate the superiority and practicality of TERACON. Our code is available at https://github.com/Sein-Kim/TERACON.

LGMar 13, 2023Code
Predicting Density of States via Multi-modal Transformer

Namkyeong Lee, Heewoong Noh, Sungwon Kim et al.

The density of states (DOS) is a spectral property of materials, which provides fundamental insights on various characteristics of materials. In this paper, we propose a model to predict the DOS by reflecting the nature of DOS: DOS determines the general distribution of states as a function of energy. Specifically, we integrate the heterogeneous information obtained from the crystal structure and the energies via multi-modal transformer, thereby modeling the complex relationships between the atoms in the crystal structure, and various energy levels. Extensive experiments on two types of DOS, i.e., Phonon DOS and Electron DOS, with various real-world scenarios demonstrate the superiority of DOSTransformer. The source code for DOSTransformer is available at https://github.com/HeewoongNoh/DOSTransformer.

MTRL-SCIOct 24, 2023Code
Density of States Prediction of Crystalline Materials via Prompt-guided Multi-Modal Transformer

Namkyeong Lee, Heewoong Noh, Sungwon Kim et al.

The density of states (DOS) is a spectral property of crystalline materials, which provides fundamental insights into various characteristics of the materials. While previous works mainly focus on obtaining high-quality representations of crystalline materials for DOS prediction, we focus on predicting the DOS from the obtained representations by reflecting the nature of DOS: DOS determines the general distribution of states as a function of energy. That is, DOS is not solely determined by the crystalline material but also by the energy levels, which has been neglected in previous works. In this paper, we propose to integrate heterogeneous information obtained from the crystalline materials and the energies via a multi-modal transformer, thereby modeling the complex relationships between the atoms in the crystalline materials and various energy levels for DOS prediction. Moreover, we propose to utilize prompts to guide the model to learn the crystal structural system-specific interactions between crystalline materials and energies. Extensive experiments on two types of DOS, i.e., Phonon DOS and Electron DOS, with various real-world scenarios demonstrate the superiority of DOSTransformer. The source code for DOSTransformer is available at https://github.com/HeewoongNoh/DOSTransformer.

AIJul 12, 2024Code
Vision Language Model is NOT All You Need: Augmentation Strategies for Molecule Language Models

Namkyeong Lee, Siddhartha Laghuvarapu, Chanyoung Park et al.

Recently, there has been a growing interest among researchers in understanding molecules and their textual descriptions through molecule language models (MoLM). However, despite some early promising developments, the advancement of MoLM still trails significantly behind that of vision language models (VLM). This is because unique challenges exist apart from VLM in the field of MoLM due to 1) a limited amount of molecule-text paired data and 2) missing expertise that occurred due to the specialized areas of focus among the experts. To this end, we propose AMOLE, which 1) augments molecule-text pairs with structural similarity preserving loss, and 2) transfers the expertise between the molecules. Specifically, AMOLE enriches molecule-text pairs by sharing descriptions among structurally similar molecules with a novel structural similarity preserving loss. Moreover, we propose an expertise reconstruction loss to transfer knowledge from molecules that have extensive expertise to those with less expertise. Extensive experiments on various downstream tasks demonstrate the superiority of AMOLE in comprehending molecules and their descriptions, highlighting its potential for application in real-world drug discovery. The source code for AMOLE is available at https://github.com/Namkyeong/AMOLE.

LGSep 22, 2024
Protein-Mamba: Biological Mamba Models for Protein Function Prediction

Bohao Xu, Yingzhou Lu, Yoshitaka Inoue et al.

Protein function prediction is a pivotal task in drug discovery, significantly impacting the development of effective and safe therapeutics. Traditional machine learning models often struggle with the complexity and variability inherent in predicting protein functions, necessitating more sophisticated approaches. In this work, we introduce Protein-Mamba, a novel two-stage model that leverages both self-supervised learning and fine-tuning to improve protein function prediction. The pre-training stage allows the model to capture general chemical structures and relationships from large, unlabeled datasets, while the fine-tuning stage refines these insights using specific labeled datasets, resulting in superior prediction performance. Our extensive experiments demonstrate that Protein-Mamba achieves competitive performance, compared with a couple of state-of-the-art methods across a range of protein function datasets. This model's ability to effectively utilize both unlabeled and labeled data highlights the potential of self-supervised learning in advancing protein function prediction and offers a promising direction for future research in drug discovery.

LGJul 27, 2024
Debiased Graph Poisoning Attack via Contrastive Surrogate Objective

Kanghoon Yoon, Yeonjun In, Namkyeong Lee et al.

Graph neural networks (GNN) are vulnerable to adversarial attacks, which aim to degrade the performance of GNNs through imperceptible changes on the graph. However, we find that in fact the prevalent meta-gradient-based attacks, which utilizes the gradient of the loss w.r.t the adjacency matrix, are biased towards training nodes. That is, their meta-gradient is determined by a training procedure of the surrogate model, which is solely trained on the training nodes. This bias manifests as an uneven perturbation, connecting two nodes when at least one of them is a labeled node, i.e., training node, while it is unlikely to connect two unlabeled nodes. However, these biased attack approaches are sub-optimal as they do not consider flipping edges between two unlabeled nodes at all. This means that they miss the potential attacked edges between unlabeled nodes that significantly alter the representation of a node. In this paper, we investigate the meta-gradients to uncover the root cause of the uneven perturbations of existing attacks. Based on our analysis, we propose a Meta-gradient-based attack method using contrastive surrogate objective (Metacon), which alleviates the bias in meta-gradient using a new surrogate loss. We conduct extensive experiments to show that Metacon outperforms existing meta gradient-based attack methods through benchmark datasets, while showing that alleviating the bias towards training nodes is effective in attacking the graph structure.

LGFeb 22, 2025Code
RAG-Enhanced Collaborative LLM Agents for Drug Discovery

Namkyeong Lee, Edward De Brouwer, Ehsan Hajiramezanali et al.

Recent advances in large language models (LLMs) have shown great potential to accelerate drug discovery. However, the specialized nature of biochemical data often necessitates costly domain-specific fine-tuning, posing major challenges. First, it hinders the application of more flexible general-purpose LLMs for cutting-edge drug discovery tasks. More importantly, it limits the rapid integration of the vast amounts of scientific data continuously generated through experiments and research. Compounding these challenges is the fact that real-world scientific questions are typically complex and open-ended, requiring reasoning beyond pattern matching or static knowledge retrieval.To address these challenges, we propose CLADD, a retrieval-augmented generation (RAG)-empowered agentic system tailored to drug discovery tasks. Through the collaboration of multiple LLM agents, CLADD dynamically retrieves information from biomedical knowledge bases, contextualizes query molecules, and integrates relevant evidence to generate responses - all without the need for domain-specific fine-tuning. Crucially, we tackle key obstacles in applying RAG workflows to biochemical data, including data heterogeneity, ambiguity, and multi-source integration. We demonstrate the flexibility and effectiveness of this framework across a variety of drug discovery tasks, showing that it outperforms general-purpose and domain-specific LLMs as well as traditional deep learning approaches. Our code is publicly available at https://github.com/Genentech/CLADD.

LGMar 6, 2025Code
Subgraph Federated Learning for Local Generalization

Sungwon Kim, Yoonho Lee, Yunhak Oh et al.

Federated Learning (FL) on graphs enables collaborative model training to enhance performance without compromising the privacy of each client. However, existing methods often overlook the mutable nature of graph data, which frequently introduces new nodes and leads to shifts in label distribution. Since they focus solely on performing well on each client's local data, they are prone to overfitting to their local distributions (i.e., local overfitting), which hinders their ability to generalize to unseen data with diverse label distributions. In contrast, our proposed method, FedLoG, effectively tackles this issue by mitigating local overfitting. Our model generates global synthetic data by condensing the reliable information from each class representation and its structural information across clients. Using these synthetic data as a training set, we alleviate the local overfitting problem by adaptively generalizing the absent knowledge within each local dataset. This enhances the generalization capabilities of local models, enabling them to handle unseen data effectively. Our model outperforms baselines in our proposed experimental settings, which are designed to measure generalization power to unseen data in practical scenarios. Our code is available at https://github.com/sung-won-kim/FedLoG

LGOct 28, 2024Code
Retrieval-Retro: Retrieval-based Inorganic Retrosynthesis with Expert Knowledge

Heewoong Noh, Namkyeong Lee, Gyoung S. Na et al.

While inorganic retrosynthesis planning is essential in the field of chemical science, the application of machine learning in this area has been notably less explored compared to organic retrosynthesis planning. In this paper, we propose Retrieval-Retro for inorganic retrosynthesis planning, which implicitly extracts the precursor information of reference materials that are retrieved from the knowledge base regarding domain expertise in the field. Specifically, instead of directly employing the precursor information of reference materials, we propose implicitly extracting it with various attention layers, which enables the model to learn novel synthesis recipes more effectively. Moreover, during retrieval, we consider the thermodynamic relationship between target material and precursors, which is essential domain expertise in identifying the most probable precursor set among various options. Extensive experiments demonstrate the superiority of Retrieval-Retro in retrosynthesis planning, especially in discovering novel synthesis recipes, which is crucial for materials discovery. The source code for Retrieval-Retro is available at https://github.com/HeewoongNoh/Retrieval-Retro.

LGMay 28, 2025Code
Global Context-aware Representation Learning for Spatially Resolved Transcriptomics

Yunhak Oh, Junseok Lee, Yeongmin Kim et al.

Spatially Resolved Transcriptomics (SRT) is a cutting-edge technique that captures the spatial context of cells within tissues, enabling the study of complex biological networks. Recent graph-based methods leverage both gene expression and spatial information to identify relevant spatial domains. However, these approaches fall short in obtaining meaningful spot representations, especially for spots near spatial domain boundaries, as they heavily emphasize adjacent spots that have minimal feature differences from an anchor node. To address this, we propose Spotscape, a novel framework that introduces the Similarity Telescope module to capture global relationships between multiple spots. Additionally, we propose a similarity scaling strategy to regulate the distances between intra- and inter-slice spots, facilitating effective multi-slice integration. Extensive experiments demonstrate the superiority of Spotscape in various downstream tasks, including single-slice and multi-slice scenarios. Our code is available at the following link: https: //github.com/yunhak0/Spotscape.

LGDec 4, 2024Code
3D Interaction Geometric Pre-training for Molecular Relational Learning

Namkyeong Lee, Yunhak Oh, Heewoong Noh et al.

Molecular Relational Learning (MRL) is a rapidly growing field that focuses on understanding the interaction dynamics between molecules, which is crucial for applications ranging from catalyst engineering to drug discovery. Despite recent progress, earlier MRL approaches are limited to using only the 2D topological structure of molecules, as obtaining the 3D interaction geometry remains prohibitively expensive. This paper introduces a novel 3D geometric pre-training strategy for MRL (3DMRL) that incorporates a 3D virtual interaction environment, overcoming the limitations of costly traditional quantum mechanical calculation methods. With the constructed 3D virtual interaction environment, 3DMRL trains 2D MRL model to learn the global and local 3D geometric information of molecular interaction. Extensive experiments on various tasks using real-world datasets, including out-of-distribution and extrapolation scenarios, demonstrate the effectiveness of 3DMRL, showing up to a 24.93% improvement in performance across 40 tasks. Our code is publicly available at https://github.com/Namkyeong/3DMRL.

LGMay 30, 2023Code
Task-Equivariant Graph Few-shot Learning

Sungwon Kim, Junseok Lee, Namkyeong Lee et al.

Although Graph Neural Networks (GNNs) have been successful in node classification tasks, their performance heavily relies on the availability of a sufficient number of labeled nodes per class. In real-world situations, not all classes have many labeled nodes and there may be instances where the model needs to classify new classes, making manual labeling difficult. To solve this problem, it is important for GNNs to be able to classify nodes with a limited number of labeled nodes, known as few-shot node classification. Previous episodic meta-learning based methods have demonstrated success in few-shot node classification, but our findings suggest that optimal performance can only be achieved with a substantial amount of diverse training meta-tasks. To address this challenge of meta-learning based few-shot learning (FSL), we propose a new approach, the Task-Equivariant Graph few-shot learning (TEG) framework. Our TEG framework enables the model to learn transferable task-adaptation strategies using a limited number of training meta-tasks, allowing it to acquire meta-knowledge for a wide range of meta-tasks. By incorporating equivariant neural networks, TEG can utilize their strong generalization abilities to learn highly adaptable task-specific strategies. As a result, TEG achieves state-of-the-art performance with limited training meta-tasks. Our experiments on various benchmark datasets demonstrate TEG's superiority in terms of accuracy and generalization ability, even when using minimal meta-training data, highlighting the effectiveness of our proposed approach in addressing the challenges of meta-learning based few-shot node classification. Our code is available at the following link: https://github.com/sung-won-kim/TEG

LGMay 29, 2023Code
Shift-Robust Molecular Relational Learning with Causal Substructure

Namkyeong Lee, Kanghoon Yoon, Gyoung S. Na et al.

Recently, molecular relational learning, whose goal is to predict the interaction behavior between molecular pairs, got a surge of interest in molecular sciences due to its wide range of applications. In this work, we propose CMRL that is robust to the distributional shift in molecular relational learning by detecting the core substructure that is causally related to chemical reactions. To do so, we first assume a causal relationship based on the domain knowledge of molecular sciences and construct a structural causal model (SCM) that reveals the relationship between variables. Based on the SCM, we introduce a novel conditional intervention framework whose intervention is conditioned on the paired molecule. With the conditional intervention framework, our model successfully learns from the causal substructure and alleviates the confounding effect of shortcut substructures that are spuriously correlated to chemical reactions. Extensive experiments on various tasks with real-world and synthetic datasets demonstrate the superiority of CMRL over state-of-the-art baseline models. Our code is available at https://github.com/Namkyeong/CMRL.

LGDec 5, 2021Code
Augmentation-Free Self-Supervised Learning on Graphs

Namkyeong Lee, Junseok Lee, Chanyoung Park

Inspired by the recent success of self-supervised methods applied on images, self-supervised learning on graph structured data has seen rapid growth especially centered on augmentation-based contrastive methods. However, we argue that without carefully designed augmentation techniques, augmentations on graphs may behave arbitrarily in that the underlying semantics of graphs can drastically change. As a consequence, the performance of existing augmentation-based methods is highly dependent on the choice of augmentation scheme, i.e., hyperparameters associated with augmentations. In this paper, we propose a novel augmentation-free self-supervised learning framework for graphs, named AFGRL. Specifically, we generate an alternative view of a graph by discovering nodes that share the local structural information and the global semantics with the graph. Extensive experiments towards various node-level tasks, i.e., node classification, clustering, and similarity search on various real-world datasets demonstrate the superiority of AFGRL. The source code for AFGRL is available at https://github.com/Namkyeong/AFGRL.

AIApr 11, 2025
MedRep: Medical Concept Representation for General Electronic Health Record Foundation Models

Junmo Kim, Namkyeong Lee, Jiwon Kim et al.

Electronic health record (EHR) foundation models have been an area ripe for exploration with their improved performance in various medical tasks. Despite the rapid advances, there exists a fundamental limitation: Processing unseen medical codes out of vocabulary. This problem limits the generalizability of EHR foundation models and the integration of models trained with different vocabularies. To alleviate this problem, we propose a set of novel medical concept representations (MedRep) for EHR foundation models based on the observational medical outcome partnership (OMOP) common data model (CDM). For concept representation learning, we enrich the information of each concept with a minimal definition through large language model (LLM) prompts and complement the text-based representations through the graph ontology of OMOP vocabulary. Our approach outperforms the vanilla EHR foundation model and the model with a previously introduced medical code tokenizer in diverse prediction tasks. We also demonstrate the generalizability of MedRep through external validation.

AIAug 22, 2025
IR-Agent: Expert-Inspired LLM Agents for Structure Elucidation from Infrared Spectra

Heewoong Noh, Namkyeong Lee, Gyoung S. Na et al.

Spectral analysis provides crucial clues for the elucidation of unknown materials. Among various techniques, infrared spectroscopy (IR) plays an important role in laboratory settings due to its high accessibility and low cost. However, existing approaches often fail to reflect expert analytical processes and lack flexibility in incorporating diverse types of chemical knowledge, which is essential in real-world analytical scenarios. In this paper, we propose IR-Agent, a novel multi-agent framework for molecular structure elucidation from IR spectra. The framework is designed to emulate expert-driven IR analysis procedures and is inherently extensible. Each agent specializes in a specific aspect of IR interpretation, and their complementary roles enable integrated reasoning, thereby improving the overall accuracy of structure elucidation. Through extensive experiments, we demonstrate that IR-Agent not only improves baseline performance on experimental IR spectra but also shows strong adaptability to various forms of chemical information.

CVMay 27, 2025
Thickness-aware E(3)-Equivariant 3D Mesh Neural Networks

Sungwon Kim, Namkyeong Lee, Yunyoung Doh et al.

Mesh-based 3D static analysis methods have recently emerged as efficient alternatives to traditional computational numerical solvers, significantly reducing computational costs and runtime for various physics-based analyses. However, these methods primarily focus on surface topology and geometry, often overlooking the inherent thickness of real-world 3D objects, which exhibits high correlations and similar behavior between opposing surfaces. This limitation arises from the disconnected nature of these surfaces and the absence of internal edge connections within the mesh. In this work, we propose a novel framework, the Thickness-aware E(3)-Equivariant 3D Mesh Neural Network (T-EMNN), that effectively integrates the thickness of 3D objects while maintaining the computational efficiency of surface meshes. Additionally, we introduce data-driven coordinates that encode spatial information while preserving E(3)-equivariance or invariance properties, ensuring consistent and robust analysis. Evaluations on a real-world industrial dataset demonstrate the superior performance of T-EMNN in accurately predicting node-level 3D deformations, effectively capturing thickness effects while maintaining computational efficiency.