Tree-structured Network Research Articles

A Tree-Structured Multitask Model Architectures Recommendation System.

Neural networks with branched architectures, namely, tree-structured models, have been employed to jointly tackle multiple vision tasks in the context of multitask learning (MTL). Such tree-structured networks typically start with a number of shared layers, after which different tasks branch out into their own sequence of layers. Hence, the major challenge is to determine where to branch out for each task given a backbone model to optimize for both task accuracy and computation efficiency. To address the challenge, this article proposes a recommendation system that, given a set of tasks and a convolutional neural network-based backbone model, automatically suggests tree-structured multitask architectures that could achieve a high task performance while meeting a user-specified computation budget without performing model training. Extensive evaluations on popular MTL benchmarks show that the recommended architectures could achieve competitive task accuracy and computation efficiency compared with state-of-the-art MTL methods. Our tree-structured multitask model recommender is open-sourced and available at https://github.com/zhanglijun95/TreeMTL.

Decentralized Generalized Approximate Message-Passing for Tree-Structured Networks

Decentralized Generalized Approximate Message-Passing for Tree-Structured Networks

Exploring the Scientific Mechanism of Tree Structure Network based on LiDAR Point Cloud Data

Abstract. To explore how trees optimize their structure, we developed a method based on Pareto optimality theory. This method consists of the following operations. Firstly, we utilize Quantitative Structure Models for Single Trees from Laser Scanner Data (TreeQSM) to extract tree structures from point clouds acquired through Light Detection and Ranging (LiDAR). Subsequently, we utilize a graph-theoretical model to characterize the natural tree structure networks and implement a greedy algorithm to generate Pareto optimal tree structure networks. Finally, based on the Pareto optimality theory, we explore whether tree structures are multi-objective optimized. This paper demonstrates that tree structures lie along the Pareto front between minimizing "transport distance" and minimizing "total length". The growth pattern of trees, which produces multi-objective optimized structures, is likely an intrinsic mechanism in the generation of tree structure networks. The location of tree structures along the Pareto front varies under different environmental conditions, reflecting their diverse survival strategies.

Scaling Up Pareto Optimization for Tree Structures with Affine Transformations: Evaluating Hybrid Floating Solar-Hydropower Systems in the Amazon

Sustainability challenges inherently involve the consideration of multiple competing objectives. The Pareto frontier – the set of all optimal solutions that cannot be improved with respect to one objective without negatively affecting another – is a crucial decision-making tool for navigating sustainability challenges as it highlights the inherent trade-offs among conflicting objectives. Our research is motivated by the strategic planning of hydropower in the Amazon basin, one of the earth’s largest and most biodiverse river systems, where the need to increase energy production coincides with the pressing requirement of minimizing detrimental environmental impacts. We investigate an innovative strategy that pairs hydropower with Floating Photovoltaic Solar Panels (FPV). We provide a new extended multi-tree network formulation, which enables the consideration of multiple dam configurations. To address the computational challenge of scaling up the Pareto optimization framework to tackle multiple objectives across the entire Amazon basin, we further enhance the state-of-the-art algorithm for Pareto frontiers in tree-structured networks with two improvements. We introduce affine transformations induced by the sub-frontiers to compute Pareto dominance and provide strategies for merging sub-trees, significantly increasing the pruning of dominated solutions. Our experiments demonstrate considerable speedups, in some cases by more than an order of magnitude, while maintaining optimality guarantees, thus allowing us to more effectively approximate the Pareto frontiers. Moreover, our findings suggest significant shifts towards higher energy values in the Pareto frontier when pairing hybrid hydropower with FPV solutions, potentially amplifying energy production while mitigating adverse impacts.

A hybrid modeling framework for generalizable and interpretable predictions of ICU mortality across multiple hospitals

The development of reliable mortality risk stratification models is an active research area in computational healthcare. Mortality risk stratification provides a standard to assist physicians in evaluating a patient’s condition or prognosis objectively. Particular interest lies in methods that are transparent to clinical interpretation and that retain predictive power once validated across diverse datasets they were not trained on. This study addresses the challenge of consolidating numerous ICD codes for predictive modeling of ICU mortality, employing a hybrid modeling approach that integrates mechanistic, clinical knowledge with mathematical and machine learning models . A tree-structured network connecting independent modules that carry clinical meaning is implemented for interpretability. Our training strategy utilizes graph-theoretic methods for data analysis, aiming to identify the functions of individual black-box modules within the tree-structured network by harnessing solutions from specific max-cut problems. The trained model is then validated on external datasets from different hospitals, demonstrating successful generalization capabilities, particularly in binary-feature datasets where label assessment involves extrapolation.

Autoencoding tree for city generation and applications

City modeling and generation have attracted an increased interest in various applications, including gaming, urban planning, and autonomous driving. Unlike previous works focused on the generation of single objects or indoor scenes, the huge volumes of spatial data in cities pose a challenge to the generative models. Furthermore, few publicly available 3D real-world city datasets also hinder the development of methods for city generation. In this paper, we first collect over 3,000,000 geo-referenced objects for the cities of New York, Zurich, Tokyo, Berlin, Boston, and several other large cities. Based on this dataset, we propose AETree, a tree-structured auto-encoder neural network, for city generation. Specifically, we first propose a novel Spatial-Geometric Distance (SGD) metric to measure the similarity between building layouts and then construct a binary tree over the raw geometric data of the building based on the SGD metric. Next, we present a tree-structured network whose encoder learns to extract and merge spatial information from the bottom-up iteratively. The resulting global representation is reversely decoded for reconstruction or generation. To address the issue of long-dependency as the level of the tree increases, a Long Short-Term Memory (LSTM) Cell is employed as a basic network element of the proposed AETree. Moreover, we introduce a novel metric, Overlapping Area Ratio (OAR), to quantitatively evaluate the generation results. Experiments on the collected dataset demonstrate that the proposed model outperforms baseline models, such as LayoutTransformer and LayoutVAE, in terms of key metrics. Specifically, the proposed model achieves a Jensen–Shannon Divergence (JSD) of 0.0033, compared to 0.0041 and 0.0061 for LayoutTransformer and LayoutVAE, respectively. Similarly, for the Overall Accuracy Rate (OAR), the proposed model scores 1.66, significantly better than 28.24 and 19.01 for the baseline models Furthermore, the latent features learned by AETree can serve downstream urban planning applications. Project webpage is available at https://ai4ce.github.io/RealCity3D.

Learning Conflict-Noticed Architecture for Multi-Task Learning

Multi-task learning has been widely used in many applications to enable more efficient learning by sharing part of the architecture across multiple tasks. However, a major challenge is the gradient conflict when optimizing the shared parameters, where the gradients of different tasks could have opposite directions. Directly averaging those gradients will impair the performance of some tasks and cause negative transfer. Different from most existing works that manipulate gradients to mitigate the gradient conflict, in this paper, we address this problem from the perspective of architecture learning and propose a Conflict-Noticed Architecture Learning (CoNAL) method to alleviate the gradient conflict by learning architectures. By introducing purely-specific modules specific to each task in the search space, the CoNAL method can automatically learn when to switch to purely-specific modules in the tree-structured network architectures when the gradient conflict occurs. To handle multi-task problems with a large number of tasks, we propose a progressive extension of the CoNAL method. Extensive experiments on computer vision, natural language processing, and reinforcement learning benchmarks demonstrate the effectiveness of the proposed methods.

SOME NETWORKS THAT ALLOW SPLASHES OF DYNAMIC FLOWS AND FINDING THE MAXIMUM SPLASH VALUE

This paper is devoted to dynamic network flows. A phenomenon called dynamic network flow splash is studied (splash is an exceeding of flow value over maximum feasible static flow for the same network). Parallel and tree-structured network topology classes are defined. Conditions for occurring network flow splash in the parallel and tree-structured networks are discovered. A formula for computing a value of maximum dynamic network flow splash is obtained. An algorithm for calculating the formula values is presented.

Urban 5G MmWave Networks: Line-of-Sight Probabilities and Optimal Site Locations

In this work, we implemented line-of-sight (LoS) ray tracing functionality to investigate problems in millimetre-wave propagation modelling and network planning in 3D city model environments. First, we validated an existing LoS propagation probability model expressed as an exponential rule with the link distance. By fitting ray tracing simulation results under different scenarios to the model, the relationships between key parameters in the model and factors including the building density and the transmitter height were qualitatively analysed. Next, we developed a network planning framework for a multi-hop outdoor urban network by formulating a mixed-integer linear programming problem which minimises the overall deployment cost through optimal site selection. Taking the sets of potential site locations and potential links as inputs, we selected a subset of the sites that comprise a tree-structured network that satisfies all the user demands at a minimum deployment cost. We also analysed the time required for solving this optimisation problem in order to provide a prediction of the execution time for larger-sized problems.

Blockchain Tree Powered Green Communication for Efficient and Sustainable Connected Autonomous Vehicles

Connected and Autonomous Vehicles (CAV) is a system of inter-connectivity and communication between smart automated vehicles. Blockchain has emerged as a technology focusing on data security with a decentralized architecture and has been successful to a very high degree. Unfortunately, this technology was not originally meant for low-power IoT devices and is very computationally expensive with high power requirements and a tendency to introduce delays. With the explosion of the Internet of Things (IoT) enabled autonomous vehicles, boosted further by the advent of smart cities, energy requirements have become an issue that can no longer be ignored. As a consequence, research into green technologies has been gaining popularity. With this area of focus, blockchain with its exponential power consumption levels is heavily flawed and thus presents itself as a prime candidate for improvement. In this paper, a framework is proposed to further evolve blockchain technology to integrate it with a semi-centralized data storage mechanism, while keeping network control decentralized. The proposed Blockchain Tree (BCT) approach entails a combination of a tree structure network composed of blockchains, based on a time-based upward data propagation mechanism that optimizes the architecture to reduce communication delay, cut down its high power consumption levels and ensure sustainability in the long run. As is evident in the comparative study, such a blockchain-based network structure offers drastic improvements in terms of speed, energy savings, storage and computation. The proposed model reduces the storage requirement of the blockchain by a factor of 0.17. The energy requirements and time complexity have been optimized by approximately 195% in the early stages of optimization. All the parameters get further optimized by orders of magnitude with more transactions and users.

Gated tree-structured RecurNN for Detecting Biomedical Event Trigger

It is critical to deeply mine semantic features for information extraction. Tree-structured model is a linguistically attractive option due to its linguistic representations of sentence syntactic structure. Tree-LSTM has been introduced to represent tree-structured network topologies for the syntactic properties. To alleviate the limitation of the Tree-LSTM, we work towards addressing the issue by developing gated mechanism variants for the tree-structured network. The gated mechanism is more complex and diverse for the tree-structured model. We apply Child-Sum Tree-LSTM and Child-Sum Tree-GRU for recognizing biomedical event triggers, and develop two new gated mechanism variants incorporating peephole connection and coupled mechanism into the tree-structured model. The experimental results showed the advantage of gated units. The Child-Sum Tree-LSTM achieved the best results among the gated tree-structured models, and the performance of variants is nearly the same as Child-Sum Tree-LSTM. However, Child-Sum Tree-GRU and Child-Sum Tree-coupled reach reduction in computation time.

Tree-structured data placement scheme with cluster-aided top-down transmission in erasure-coded distributed storage systems

In erasure-coded distributed storage systems, the rapid completion of data placement process is very critical to maintain system performance, where the process is defined as to insert coded blocks into a set of redundant storage nodes. However, the existing data placement schemes have some shortcomings, such as load imbalance and long transmission latency. To solve these problems, this paper proposes a tree-structured data placement scheme with cluster-aided top-down transmission, which improves the practicality and the efficiency of the data insertion. Specifically, the storage nodes are clustered by a location-based K-mean method at first, and then selecting a master node as the source node to encode file and distribute coded blocks in each cluster by designing a master node’s selection algorithm based on evolutionary game theory. Since multiple master nodes are used to receive data files from data core, the load imbalance problem caused by single node receiving data files is mitigated. In addition, to improve the data transmission efficiency, we construct a tree-structured network to organize the connections of the storage nodes in cluster, where the master node is the root node. Meanwhile, a data placement scheme with top-down transmission by combining an improved metaheuristic algorithm is proposed to manage the pipelined data transmission along the tree-structured network. Experimental results show that the proposed scheme can effectively improve the survive life of storage network and reduce the data insertion time. Furthermore, the proposed scheme has better performance than the optimal tree-structured scheme based on other optimization algorithms.

Path finding and guidance algorithms for autonomous mobile robots in a tree structure network

Considering an autonomous mobile robot that has to navigate indoor and outdoor from a certain point towards another certain point in a tree structure, the paper is giving a solution for finding the path and navigation. The mathematical model is proposed for a number nDP of departure/destination points (DP), a number nIP of intersection points (IP) and connections between them in a tree structure. Based on mathematical model, the problems solved and presented in this paper are i) to find a path from any departure point to any destination point, ii) to generate an algorithm for guidance of an autonomous robot to follow the path. Both algorithms were tested on Matlab Simulink® environment. An implementation of algorithms in a pseudocode is presented. The algorithms were adapted to be implemented on a microcontroller based board. The advantage of algorithms and implementation is simplicity. The outcome is less memory consumption and increased computing and execution speed.

Distributed Dual Coordinate Ascent in General Tree Networks and Communication Network Effect on Synchronous Machine Learning

Due to the big size of data and limited data storage volume of a single computer or a single server, data are often stored in a distributed manner. Thus, performing large-scale machine learning operations with the distributed datasets through communication networks is often required. In this paper, we study the convergence rate of the distributed dual coordinate ascent for distributed machine learning problems in a general tree-structured network. Since a tree network model can be understood as the generalization of a star network, our algorithm can be thought of as the generalization of the distributed dual coordinate ascent in a star network. We provide the convergence rate of the distributed dual coordinate ascent over a general tree network in a recursive manner and analyze the network effect on the convergence rate. Secondly, by considering network communication delays, we optimize the distributed dual coordinate ascent algorithm to maximize its convergence speed. From our analytical result, we can choose the optimal number of local iterations depending on the communication delay severity to achieve the fastest convergence speed. In numerical experiments, we consider machine learning scenarios over communication networks, where local workers cannot directly reach to a central node due to constraints in communication, and demonstrate that the usability of our distributed dual coordinate ascent algorithm in tree networks.

Decentralized Optimization Over Tree Graphs

This paper presents a decentralized algorithm for non-convex optimization over tree-structured networks. We assume that each node of this network can solve small-scale optimization problems and communicate approximate value functions with its neighbors based on a novel multi-sweep communication protocol. In contrast to existing parallelizable optimization algorithms for non-convex optimization, the nodes of the network are neither synchronized nor assign any central entity. None of the nodes needs to know the whole topology of the network, but all nodes know that the network is tree-structured. We discuss conditions under which locally quadratic convergence rates can be achieved. The method is illustrated by running the decentralized asynchronous multi-sweep protocol on a radial AC power network case study.

Dynamic linepack depletion models for natural gas pipeline networks

Given the critical role played by natural gas in providing electricity, heat, and other essential services, better models are needed to understand the dynamics of natural gas networks during extreme events. This paper aims at establishing appropriate and fast simulation models to capture the slow dynamics of linepack depletion for ideal isothermal natural gas pipeline networks. Instead of solving partial differential equations (PDE) on a large scale, three alternative implicit ordinary differential equation (ODE) simulation techniques are derived and discussed. The first one is commonly used in the literature with a slack node assumption. We show that the system of equations associated with this model is degenerate when flux injections are controlled (i.e. specified) at all nodes. To recover regularity under such a condition, two novel implicit ODE models are proposed with different techniques on boundary conditions. They are easy to derive and efficient to simulate by standard ODE solvers. More importantly, they present useful frameworks for analyzing how networks respond to system-wide mass flux imbalances. These techniques offer different alternatives for simulating system dynamics based on how sources and loads are chosen to be modeled, and they are all proven to be regular (non-degenerate) in tree-structured networks. These proposed techniques are all tested on the 20-node Belgium network. The simulation results show that the conventional model with the slack node assumption cannot effectively capture linepack depletion under long term system-wide mass flux imbalance, while the proposed models can characterize the network behavior until the linepack is completely depleted.

Deploying Virtual Network Functions With Non-Uniform Models in Tree-Structured Networks

Network Function Virtualization (NFV) has promoted the implementation of network functions from expensive hardwares to software middleboxes. These software middleboxes, also called Virtual Network Functions (VNFs), are executed on switch-connected servers. Efficiently deploying such VNFs on servers is challenging because the traffic rate of flows must be fully processed by their requested VNFs when they reach destinations, and the deployed positions of VNFs are restricted by the server capacity. In addition, each network function offers non-uniform VNF models (types) with different configurations of processing volumes and costs. This paper focuses on minimizing the total cost of deploying VNFs for providing a specific network function to all flows in tree-structured networks. First, we prove the NP-hardness of non-uniform VNF deployment in a tree topology and propose a dynamic programming based solution with a pseudo-polynomial time complexity. Then we narrow it down to three simplified cases by focusing on either uniform VNFs or the linear line topology. Specifically, three algorithms are introduced: an improved dynamic programming based algorithm for deploying uniform VNFs in a tree topology, a performance-guaranteed algorithm for deploying non-uniform VNFs in a linear line topology, and an optimal greedy algorithm for deploying uniform VNFs in a linear line topology. Additionally, we generalize our approach to a case of deploying a service chain, which consists of multiple network functions applied to flows in a specific order. We propose two solutions: one is optimal but time-consuming while another is heuristic but efficient. Extensive simulations are conducted to evaluate our algorithms.

Learning to Embed Sentences Using Attentive Recursive Trees

Sentence embedding is an effective feature representation for most deep learning-based NLP tasks. One prevailing line of methods is using recursive latent tree-structured networks to embed sentences with task-specific structures. However, existing models have no explicit mechanism to emphasize taskinformative words in the tree structure. To this end, we propose an Attentive Recursive Tree model (AR-Tree), where the words are dynamically located according to their importance in the task. Specifically, we construct the latent tree for a sentence in a proposed important-first strategy, and place more attentive words nearer to the root; thus, AR-Tree can inherently emphasize important words during the bottomup composition of the sentence embedding. We propose an end-to-end reinforced training strategy for AR-Tree, which is demonstrated to consistently outperform, or be at least comparable to, the state-of-the-art sentence embedding methods on three sentence understanding tasks.

A robust optimization approach to model supply and demand uncertainties in inventory systems

In this article, we simultaneously consider supply and demand uncertainties in a robust optimization (RO) framework. First, we apply the RO approach to a multi-period, single-station inventory problem where supply uncertainty is modeled by partial supply. Our main finding is that solving the robust counterpart is equivalent to solving a nominal problem with a modified deterministic demand sequence. In particular, in the stationary case the optimal robust policy follows the quasi-(s, S) form and the corresponding s and S levels are theoretically computable. Subsequently, the RO framework is extended to a multi-echelon case. We show that for a tree structure network, decomposition applies so that the optimal single-station robust policy remains valid for each echelon in the tree. We conduct extensive numerical studies to demonstrate the effectiveness of the proposed robust policies. Our results suggest that significant cost benefits can be realized by incorporating both supply and demand uncertainties.

Nash network formation among unmanned aerial vehicles

Multiple unmanned aerial vehicles (UAVs) are applicable to numerous civil and military scenarios, such as rescue, surveillance, inspection, mapping, and so on. In fact, there exists lifetime and distance restrictions in UAVs due to the limited energy and signal attenuation. Therefore, a distributed algorithm is proposed which makes use of cooperative communication to ensure reliable information transmission of UAVs in communication-limited environments. First, a system model is developed by jointly considering the achievable rate, delay and energy consumption, which constitute the utility function of UAVs. Then, in order to study the interactions among UAVs, we present a game framework which allows the UAVs making decision under the global topology. Via a hybrid of the pure-strategy and the mixed-strategy Nash network formation algorithm, a multi-hop tree structure network that connects the UAVs and the ground station is established. Based on our numerical simulation, it demonstrates that the UAVs can adapt to the changing environment. Finally, some comparisons are provided to illustrate the efficiency of the proposed algorithm.