Tixologi

tixologi

The choice of a suitable network topology is critical for effective and stable multiplayer. We'll talk about the pros and cons of the main network topologies for real-time multiplayer: P2P, authoritative servers, relay servers, and more. Greetings again everyone, I'm Dmitrii Ivashchenko, Lead Software Engineer at MY.GAMES. Our article series on the landscape of Unity realtime multiplayer in 2023 continues — and today's topic concerns the main network topologies for realtime multiplayer. Network Topology The key factor in ensuring the effective and stable operation of a multiplayer game is the choice of a suitable network architecture, or topology. This decision affects both the way data is transmitted and processed in the game, as well as performance and resource consumption. Let's look at some possible models. P2P (Peer-to-Peer) P2P, or peer-to-peer architecture, is a model in which each player connects to every other player and exchanges data about game state and events. In “pure” P2P, there is no single "host". Instead, each client is responsible for managing its own game character (or units) while receiving updates about events from each of the other clients. Advantages of P2P: No need to develop or maintain dedicated servers. Clients create direct connections with each other, providing the most direct connection (which usually, but not always, corresponds to a low ping). Disadvantages of P2P: The absence of a single authoritative host makes cheat detection significantly more difficult. This also makes compensation for delays less effective. Additionally, a "desynchronization" of clients is possible, leading to differences in game state between them. Each client creates multiple outgoing connections and accepts incoming connections, so each client has to deal with firewall settings and port forwarding. Authoritative servers In this model, one of the nodes of the game network (this is usually initially selected or based on network connection features) becomes the "authoritative server", controlling the game state and processing all game events. The other nodes (clients) send their actions to this server and receive updated game state from it. Server-client with the authoritative dedicated game server (DSG) In a client-server architecture with an authoritative dedicated game server, all clients connect to a single game server. The dedicated game server (DGS) runs the game engine and is the source of the game's final state. It receives updates from connected clients, incorporates them into its game state, and sends the resulting state to each client. MMORPGs and other games with persistent online worlds also fall into this category. In such cases, DGS also includes databases that store data about the persistent world. Advantages of DGS: The game server is "authoritative": it has the final say on whether events created by clients are valid or not. This allows for a wide range of delay compensation mechanisms and fraud prevention, as well as eliminating synchronization issues, as the server overrides the state of clients. Disadvantages of DGS: It is necessary to develop and manage a dedicated game server, and doing this has certain costs associated with it. Leveraging a client-server architecture with an authoritative dedicated game server is one of the most common approaches in large multiplayer games and provides a high degree of control over the state of the game and combating fraud. Server-client with authoritative client-host In a client-server architecture with an authoritative client-host, instead of using a dedicated game server to maintain authoritative game state, it's possible to use one of the client machines as a server. This client becomes a client-host; simultaneously the host of the game session as well as a participant in the game. Advantages of client-host: Client-host has advantages as a dedicated game server but without the additional cost of running one. Disadvantages of client-host: The host machine must perform additional calculations to simultaneously perform host and client functions. Locally connected clients have much lower connection latency to the host compared to other clients, which can create a competitive advantage (known as "host advantage"). The client-server architecture with an authoritative client-host allows players to independently organize multiplayer sessions without the need to connect to a dedicated game server. However, it's necessary to consider the load on the host machine and potential issues with "host advantage". Relay server In architecture with a relay/matchmaking server for finding opponents, the server exists to facilitate connections and data transmission between clients, but does not actively participate in the game. Although a dedicated server is still required because it does not need to run a game engine, creation and management of this can be relatively inexpensive. Moreover, most P2P games can easily switch to using a relay server, since the network code only differs in the way clients connect to each other. : Advantages of relay servers Since an external server is used, clients only need to establish outgoing connections, so they don't need to configure port forwarding or firewalls. : Disadvantages of relay servers Relay severs have the same drawbacks as P2P, but the delay is higher because the connections are no longer direct. The operation of a relay server still requires certain costs, although they are lower than those of a dedicated game server. The relay/server architecture for finding opponents provides a simple and inexpensive solution for ensuring connections and data transmission between clients. It avoids problems related to port forwarding and firewalls, but it may have some delay due to the intermediate server. Here's an example of the class in C# that uses TCP to listen for incoming client connections and then add them to a list of active clients. The server then asynchronously handles each client connection by reading data and forwarding it to all connected clients: RelayServer public class RelayServer
{
    private TcpListener _listener;
    private List<TcpClient> _clients = new List<TcpClient>();

    public async Task StartAsync(int port)
    {
        _listener = new TcpListener(IPAddress.Any, port);
        _listener.Start();
        Console.WriteLine($"Server started on port {port}");

        while (true)
        {
            TcpClient client = await _listener.AcceptTcpClientAsync();
            _clients.Add(client);

            Task.Run(() => HandleClientAsync(client));
        }
    }
} The code below represents the function , which is responsible for processing each connected client in asynchronous mode. HandleClientAsync First, the function creates a buffer for reading data and obtains a stream for reading and writing data. Next, in an infinite loop, the function asynchronously reads data from the stream. If no data is received (i.e. the client disconnected), the function removes the client from the list and stops processing. Otherwise, the received data is converted to a string and sent to all connected clients: private async Task HandleClientAsync(TcpClient client)
{
    byte[] buffer = new byte[1024];
    NetworkStream stream = client.GetStream();

    while (true)
    {
        int bytesRead = await stream.ReadAsync(buffer, 0, buffer.Length);

        if (bytesRead == 0)
        {
            _clients.Remove(client);
            return;
        }

        string message = Encoding.UTF8.GetString(buffer, 0, bytesRead);
        BroadcastMessage(message);
    }
} To send the received message to all connected clients, we will need the function : BroadcastMessage private void BroadcastMessage(string message)
{
    foreach (var client in _clients)
    {
        NetworkStream stream = client.GetStream();
        byte[] buffer = Encoding.UTF8.GetBytes(message);
        stream.Write(buffer, 0, buffer.Length);
    }
} The function takes a message as a string, iterates through the list of connected clients, and for each of them converts the message to bytes and writes it to the corresponding network connection stream. This way, the message is successfully transmitted to all clients. Conclusion In this article, we discussed the main network topologies for real-time multiplayer games — including P2P, authoritative server, and relay server. Each topology has its advantages and disadvantages, such as direct connections and low ping in P2P, and effective cheat detection and fraud prevention in authoritative server; relay server provides a simple and inexpensive solution for ensuring connections and data transmission between clients. Choosing the right topology is crucial for ensuring a smooth gaming experience in real-time multiplayer games. But this decision also concerns infrastructure cost and project scalability. In the next article, we will consider the main patterns of network architecture in different game genres.

Unity Realtime Multiplayer, Part 6: Game Network Topologies

Topological sorting refers to the linear ordering of vertices in a graph such that for every directed edge , of vertex to , always comes before . ab a b a, b Above is an image showing a directed acyclic graph (edge 0 and edge 1 are directed at edge 2, edge 2 is directed at edge 3 and edge 3 is directed at edge 4). from: https://generalducky.github.io/DAG/ : For the image above, there are two possible topological sort orders for this graph which would be: 1, 0, 2, 3, 4 or 0, 1, 2, 3, 4 . Example of topological sorting would be: task scheduling (what task should proceed before the order), pre-requisite problems (what course or problems should be solved in order to solve an higher problem) — (adapted from ) Typical applications geekforgeeks Our approach to solving this problem would involve using the . let’s get down to business already 😊 depth-first search First, we would create a module, import from rust’s standard library into our module, and define a ( ) struct name it , which defines what our graph would like: Graph hashMap Directed Acyclic Graph DAG DAG Graph { std::collections::HashMap; { graph: <HashMap< , < >>,
  }
} mod use //import hashmap from std lib pub struct DAG // define the DAG struct Option u8 Vec u8 Next, we will define a method on the struct call it that will create a graph from the argument passed into it. 1. The method accepts an argument which is a vector of tuples containing values. 2. Creates a hashMap ( ) that would contain the edges and vectors in our graph. 3. Loops through the argument and populates the with the information on the graph 4. Move the into the struct, wrapping it in theOption type as defined on the struct with it’s key as . 5. and then calls the method. DAG new new graph_info u8 adjacency_map graph_info adjacency_map adjacency_map Graph graph get_topological_order Graph { std::collections::HashMap; {
    graph: <HashMap< , < >>,
  } DAG { (graph_info: <( , )>) -> < > { adjacency_map: HashMap< , < >> = HashMap::new(); value graph_info { source_vertex = & adjacency_list.entry(value. ).or_insert( []);
                source_vertex.push(value. );
            } the_graph = DAG {
                graph: (adjacency_map),
            }; the_graph.get_topological_order();
        }
} mod use pub struct DAG Option u8 Vec u8 impl pub fn new Vec u8 u8 Vec u8 let mut u8 Vec u8 for in let mut 0 vec! 1 let Some return The method basically stores the order of the graph in a stack ( 1. Create a stack (in this case, we would use a vector but only use it as a stack) data-structure called , a vector of values. 2. Loop through the keys to get the order using the method. 3. Once the order is obtained, we would reverse the stack. get_topological_order LIFO i.e last in, first out). stack u8 graph get_order std::collections::HashMap; {
    graph: <HashMap< , < >>,
  } DAG { (graph_info: <( , )>) -> < > {...} (& ) -> < > { source_nodes = .graph.as_ref().unwrap().keys(); stack: < > = []; node source_nodes { .get_order(node, & stack);
            }
            stack.reverse(); ( , stack); stack;
        }
} use pub struct DAG Option u8 Vec u8 impl pub fn new Vec u8 u8 Vec u8 pub fn get_topological_order self Vec u8 let self let mut Vec u8 vec! for in self mut println! "THE STACK!! {:?}" return The method accepts the Using the node (current key) passed to it, the method gets all the values of such key, which are edges that this edge points to and does the same of all of such edges points to. Adding them to the stack. if such node does not point anywhere and has not been visited, i.e. it is not on the stack., it is pushed into the stack. get_order node (current key, borrowed u8 value), stack(mutable vector of u8 values) . get_order Graph { std::collections::HashMap; {
    graph: <HashMap< , < >>,
  } DAG { (graph_info: <( , )>) -> < > {...} (& )-> < > {
            ...
            stack.reverse(); ( , stack); stack;
        } (& , node: & , stack: & < >) { receiving_nodes = .graph.as_ref().unwrap().get(node); receiving_nodes != { value receiving_nodes.unwrap() { .get_order(value, stack);
                    }
                } !stack.contains(node) {
                    stack.push(*node);
                }
        }
} mod use pub struct DAG Option u8 Vec u8 impl pub fn new Vec u8 u8 Vec u8 pub fn get_topological_order self Vec u8 println! "THE STACK!! {:?}" return pub fn get_order self u8 mut Vec u8 let self if None for in self if The result of our function should be one of the two vectors here: [1, 0, 2, 3, 4] or [0, 1, 2, 3, 4] . If we passed the argument as: vec![(0, 2), (1, 2), (2, 3), (3, 4)] () { Graphs; Graphs::DAG::new( [( , ), ( , ), ( , ), ( , )]);
} Graphs { std::collections::HashMap; {
        graph: <HashMap< , < >>>,
    } DAG { (graph_info: <( , )>) -> < > { adjacency_list: HashMap< , < >> = HashMap::new(); graph = graph_info.get( ..); value graph.unwrap() { source_vertex = & adjacency_list.entry(value. ).or_insert( []);
                source_vertex.push(value. );
            } the_graph = DAG {
                graph: (adjacency_list),
            }; the_graph.get_topological_order();
        } (& ) -> < > { source_nodes = .graph.as_ref().unwrap().keys(); stack: < > = []; node source_nodes { .get_order(node, & stack); }
            stack.reverse(); ( , stack); stack;
        } (& , node: & , stack: & < >) { receiving_nodes = .graph.as_ref().unwrap().get(node); receiving_nodes != { value receiving_nodes.unwrap() { .get_order(value, stack);
                }
            } !stack.contains(node) {
                stack.push(*node);
            } }
    }
} pub fn execute use // Graphs::DAG::new(vec![(4, 3), (1, 2), (4, 1), (3, 1)]); // Graphs::DAG::new(vec![(1, 2), (1, 4), (2, 3), (2, 4), (4, 3), (4, 5)]); vec! 0 2 1 2 2 3 3 4 mod use pub struct DAG Option u8 Vec u8 impl pub fn new Vec u8 u8 Vec u8 // DirectedGraph { graph: None } let mut u8 Vec u8 let 0 for in let mut 0 vec! 1 let Some return pub fn get_topological_order self Vec u8 let self let mut Vec u8 vec! // let mut visited: HashMap<u8, bool> = HashMap::new(); for in // if visited.get(node) == None { self mut // } println! "THE STACK!! {:?}" return pub fn get_order self u8 mut Vec u8 let self // if visited.get(node) == None { if None for in self if // } Going a step forward to test our output: () { Graphs; result = Graphs::DAG::new( [( , ), ( , ), ( , ), ( , )]); ( , result);
} Graphs { std::collections::HashMap; {
        graph: <HashMap< , < >>>,
    } DAG { (graph_info: <( , )>) -> < > { adjacency_list: HashMap< , < >> = HashMap::new(); graph = graph_info.get( ..); value graph.unwrap() { source_vertex = & adjacency_list.entry(value. ).or_insert( []);
                source_vertex.push(value. );
            } the_graph = DAG {
                graph: (adjacency_list),
            }; the_graph.get_topological_order();
        } (& ) -> < > { source_nodes = .graph.as_ref().unwrap().keys(); stack: < > = []; node source_nodes { .get_order(node, & stack); }
            stack.reverse(); ( , stack); stack;
        } (& , node: & , stack: & < >) { receiving_nodes = .graph.as_ref().unwrap().get(node); receiving_nodes != { value receiving_nodes.unwrap() { .get_order(value, stack);
                }
            } !stack.contains(node) {
                stack.push(*node);
            } }
    }
} test { super::Graphs; () { result = Graphs::DAG::new( [( , ), ( , ), ( , ), ( , )]); (result.pop(), ( )); (result.pop(), ( )); (result.pop(), ( ));
    }
} pub fn execute use // Graphs::DAG::new(vec![(4, 3), (1, 2), (4, 1), (3, 1)]); // Graphs::DAG::new(vec![(1, 2), (1, 4), (2, 3), (2, 4), (4, 3), (4, 5)]); let vec! 0 2 1 2 2 3 3 4 println! "THE RESULT >>>  {:?}" mod use pub struct DAG Option u8 Vec u8 impl pub fn new Vec u8 u8 Vec u8 // DirectedGraph { graph: None } let mut u8 Vec u8 let 0 for in let mut 0 vec! 1 let Some return pub fn get_topological_order self Vec u8 let self let mut Vec u8 vec! // let mut visited: HashMap<u8, bool> = HashMap::new(); for in // if visited.get(node) == None { self mut // } println! "THE STACK!! {:?}" return pub fn get_order self u8 mut Vec u8 let self // if visited.get(node) == None { if None for in self if // } #[cfg(test)] mod use #[test] fn test_topological_order let mut vec! 0 2 1 2 2 3 3 4 assert_eq! Some 4 assert_eq! Some 3 assert_eq! Some 2 find me on twitter [ @tolumide ] and github: [ tolumide-ng ]

Topological Sorting of a Directed Acyclic Graph in Rust Using DFS

In previous posts [ ] [ ] we briefly introduced our message oriented protocol IAP which is an integral part of project. In this post, we`ll share a little bit more lightweight technical information about currently supported IAP message exchange patterns and network topologies. 1 2 Nanosai.com Before we start, it is important to know that at we are all about helping developers build intelligent distributed systems via the ecosystem we are developing. This ecosystem will for example enable developers to access advanced distributed systems services provided by or third party services plugged into our distributed infrastructure as shown in the diagram below. Nanosai.com Nanosai.com IAP Design Goals Good communication is key for distributed systems to work smoothly as nodes need to be able to communicate properly with each other internally and also often externally depending on whether the system needs to access third parties or be exposed to third parties. We designed IAP from ground up with following intentions; To be a viable replacement/supplement to HTTP, FTP, SNMP, ODBC, RPC etc. To be faster and more compact than HTTP/JSON. To support more message flows and thus more use cases than HTTP. More plug and play than HTTP. Able to be layered on top of both TCP and UDP. Support both synchronous and asynchronous communication. IAP Core Concepts Before proceeding to the IAP message patterns, it is worth revising the core concepts behind IAP. IAP comes with a basic message format which is used across many different use cases and all IAP messages are encoded using our binary data format . ION Additionally, IAP was designed to be versatile and so enables developers to define different semantic protocols on top of the basic message format. The basic message format contains a set of fields that are pretty much always used in network communication. Semantic protocols can extend this message format and add protocol specific fields that are needed for a particular use case. Supported Message Exchange Patterns The message exchange patterns above are the ones that we have decided to support first because they cover many use cases. Supported Network Topologies The network topologies above are the ones that we have decided to support first because they cover many use cases. Finally, please download our free eBook authored by our CTO . Our open source Java toolkit Grid Ops (including IAP) is available on . If you would like to receive beta invite for our hosted infrastructure services when we launch, please here Github Subscribe here. Posted by Bambordé Baldé , Co — Founder.

IAP Message Exchange Patterns & Network Topologies

Topology of a neural network refers to the way the Neurons are connected, and it is an important factor in network functioning and learning. A common topology in unsupervised learning is a direct mapping of inputs to a collection of units that represents categories (e.g., Self-organizing maps). — Springer In our previous post we learned about the components that form a neural network: Input Nodes Neurons Output Nodes as well that those elements will be organized in the following layers: Input Layer Hidden Layers Output Layer However, it still not very clear what the process for organizing and connecting those neural networks is; how do we determine how many hidden layers we need to create? How do we connect those neurons to the inputs, outputs and to each other? How do we know how many output nodes we need to create? How to organize our Neural Network What we need is a way to represent how neurons are connected in order to form a network, a . The topology of a neural network plays an essential role in its function and performance. Neural Network Topology An important thing to notice is that can be used to learn the same set of data, and they are even likely to produce similar results; and as such there is not ‘best’ topology for a single neural network; that being said topology can greatly impact the amount of time required for a neural network to learn data as well its accuracy when classifying new data. multiple topologies One a approach to topology selection is to simply make it a trial and error process, where we manually tweak the Neural network by modifying things like the number of , and so on. Taking this approach would limit us greatly as there are many possible permutations even for a ; to complicate matters even further, Neural networks are not limited to the relatively simple layout we have seen before, to mention a few: hidden layers connections between nodes, simple neural network Feed-Forward Feed-forward Recurrent Long Short Term Memory Jordan Elman Hopfield So outside of very simple applications, known problems or learning exercises is not a viable option, in order to find the ideal topology we have to let our neural network to learn the topology from the training data as well. The goal is to find a topology for our neural network that * manual topology selection minimizes the the error on new data. * One of most novel approaches for this objective is the use of genetic programming. Genetic Programming and Neuro Evolution Genetic algorithms are based on the evolutionary principles of the , and ; a genetic algorithm will approach a particular problem by generating a large number of potential solutions and finding the solutions with the best . natural selection mutation survival of the fittest fitness score Without going too deep into the weeds, a is a method to measure how close was the solution to known result or to a expected metric; in the case of a neural network where we have training data that we can use as reference point. fitness score The Genetic algorithm will tweak and mutate our neural network generation after generation until the desired fitness score is achieved or until we reach the maximum number of iterations. Disclaimer: The above is a oversimplified description of how genetic algorithms work I highly recommend, for an amazing breakdown of the subject, even if you are not into Erlang the author makes a terrific job on breaking down the concepts and introduction genetic algorithms. The Handbook of Neuroevolution through Erlang Summary I’m important that we understand how topology, that is the of our neural networks can impact their effectiveness; there are many existing types of artificial neural networks some best suited to particular tasks of applications, and is important to familiarize ourselves with the most common types. number of layers and how they are connect Additional, in order to find the optimal topology one can use in order to try to evolve the topology for a given application. Genetic algorithms ‘perfect’ There is still a lot more to learn and go, but feel free to if you find any factual errors or if you think something . leave a comment needs more clarification This article was originally posted on my own site .

Neural Networks Without a PhD: Topologies

Running Cisco pyATS on Windows 11 Really Helped Me Brush Up My Python Fundamentals

How K-SIF and SIF Revolutionize Anomaly Detection in Complex Datasets

Authors:
(1) Guillaume Staerman, INRIA, CEA, Univ. Paris-Saclay, France;
(2) Marta Campi, CERIAH, Institut de l’Audition, Institut Pasteur, France;
(3) Gareth W. Peters, Department of Statistics & Applied Probability, University of California Santa Barbara, USA. Table of Links Abstract and 1. Introduction 2. Background & Preliminaries 2.1. Functional Isolation Forest 2.2. The Signature Method 3. Signature Isolation Forest Method 4. Numerical Experiments 4.1. Parameters Sensitivity Analysis 4.2. Advantages of (K-)SIF over FIF 4.3. Real-data Anomaly Detection Benchmark 5. Discussion & Conclusion, Impact Statements, and References Appendix A. Additional Information About the Signature B. K-SIF and SIF Algorithms C. Additional Numerical Experiments 2.2. The Signature Method The signature of a path is a sequence of iterated integrals that captures important information about the path’s geometric and topological features (Lyons et al., 2007; Fermanian, 2021). Furthermore, the signature of X is defined as the infinite collection of coordinate signature One may refer to Lee and Oberhauser (2023) for an account of the untruncated kernel signature. See also Section A in the Appendix for further details about the signature and its properties. This paper is available on arxiv under CC BY 4.0 DEED license. Authors: (1) Guillaume Staerman, INRIA, CEA, Univ. Paris-Saclay, France; (2) Marta Campi, CERIAH, Institut de l’Audition, Institut Pasteur, France; (3) Gareth W. Peters, Department of Statistics & Applied Probability, University of California Santa Barbara, USA. Authors: Authors: (1) Guillaume Staerman, INRIA, CEA, Univ. Paris-Saclay, France; (2) Marta Campi, CERIAH, Institut de l’Audition, Institut Pasteur, France; (3) Gareth W. Peters, Department of Statistics & Applied Probability, University of California Santa Barbara, USA. Table of Links Abstract and 1. Introduction Abstract and 1. Introduction 2. Background & Preliminaries 2. Background & Preliminaries 2.1. Functional Isolation Forest 2.1. Functional Isolation Forest 2.2. The Signature Method 2.2. The Signature Method 3. Signature Isolation Forest Method 3. Signature Isolation Forest Method 4. Numerical Experiments 4. Numerical Experiments 4.1. Parameters Sensitivity Analysis 4.1. Parameters Sensitivity Analysis 4.2. Advantages of (K-)SIF over FIF 4.2. Advantages of (K-)SIF over FIF 4.3. Real-data Anomaly Detection Benchmark 4.3. Real-data Anomaly Detection Benchmark 5. Discussion & Conclusion, Impact Statements, and References 5. Discussion & Conclusion, Impact Statements, and References Appendix A. Additional Information About the Signature A. Additional Information About the Signature B. K-SIF and SIF Algorithms B. K-SIF and SIF Algorithms C. Additional Numerical Experiments C. Additional Numerical Experiments 2.2. The Signature Method The signature of a path is a sequence of iterated integrals that captures important information about the path’s geometric and topological features (Lyons et al., 2007; Fermanian, 2021). Furthermore, the signature of X is defined as the infinite collection of coordinate signature Furthermore, the signature of X is defined as the infinite collection of coordinate signature X One may refer to Lee and Oberhauser (2023) for an account of the untruncated kernel signature. See also Section A in the Appendix for further details about the signature and its properties. This paper is available on arxiv under CC BY 4.0 DEED license. This paper is available on arxiv under CC BY 4.0 DEED license. available on arxiv

Unveiling Path Signatures: A Key to Geometric Insights in Data

Onthulling van padhandtekeninge: 'n Sleutel tot meetkundige insigte in data

Descubriendo las firmas de trayectoria: una clave para obtener información geométrica en los datos

Revelación de sinaturas de camiños: unha clave para coñecer os datos xeométricos

Mengungkap Tanda Jalur: Kunci Wawasan Geometris dalam Data

パスシグネチャの解明: データの幾何学的洞察への鍵

Жол қолтаңбаларын ашу: деректердегі геометриялық түсініктердің кілті

경로 서명 공개: 데이터에서 기하학적 통찰력의 열쇠

Famoahana sonia lalana: lakile ho an'ny fahitana geometrika amin'ny angona

د لارې لاسلیکونه افشا کول: په ډیټا کې د جیومیټریک بصیرت لپاره کلیدي

Kuzarura Nzira Masiginicha: Kiyi yeGeometric Insights muData

Zbulimi i nënshkrimeve të rrugës: Një çelës për njohuritë gjeometrike në të dhëna

راستے کے دستخطوں کی نقاب کشائی: ڈیٹا میں جیومیٹرک بصیرت کی کلید

What is the Signature Isolation Forest? 

The Trick That Agentic Frameworks Pulled On Us

El truco que nos hicieron los frameworks de gestión de agentes

O truco que nos tiraron os frameworks axentes

A trükk, amelyet az ügynöki keretek rántottak ránk

エージェントフレームワークが私たちに仕掛けたトリック

Triks, ko mūs pamudināja aģentu sistēmas

Trucul pe care ni l-au tras de cadrele agentice

නියෝජිත රාමු අප වෙත ඇදී ගිය උපක්‍රමය

Mashtrimi që Kornizat Agjentike na tërhoqën

Ҳилае, ки чаҳорчӯбаи агентӣ ба мо кашид

Agentic Framework'ün Bize Yaptığı Hile

Трюк, який Agentic Frameworks застосував до нас

Thủ thuật mà các khuôn khổ Agentic đã áp dụng với chúng ta

Authors:
(1) Junwei Su, Department of Computer Science, the University of Hong Kong and jwsu@cs.hku.hk;
(2) Chuan Wu, Department of Computer Science, the University of Hong Kong and cwu@cs.hku.hk. Table of Links Abstract and 1 Introduction 2 Related Work 3 Framework 4 Main Results 5 A Case Study on Shortest-Path Distance 6 Conclusion and Discussion, and References 7 Proof of Theorem 1 8 Proof of Theorem 2 9 Procedure for Solving Eq. (6) 10 Additional Experiments Details and Results 11 Other Potential Applications Abstract Many computer vision and machine learning problems are modelled as learning tasks on graphs, where graph neural networks (GNNs) have emerged as a dominant tool for learning representations of graphstructured data. A key feature of GNNs is their use of graph structures as input, enabling them to exploit the graphs’ inherent topological properties—known as the topology awareness of GNNs. Despite the empirical successes of GNNs, the influence of topology awareness on generalization performance remains unexplored, particularly for node-level tasks that diverge from the assumption of data being independent and identically distributed (I.I.D.). The precise definition and characterization of the topology awareness of GNNs, especially concerning different topological features, are still unclear. This paper introduces a comprehensive framework to characterize the topology awareness of GNNs across any topological feature. Using this framework, we investigate the effects of topology awareness on GNN generalization performance. Contrary to the prevailing belief that enhancing the topology awareness of GNNs is always advantageous, our analysis reveals a critical insight: improving the topology awareness of GNNs may inadvertently lead to unfair generalization across structural groups, which might not be desired in some scenarios. Additionally, we conduct a case study using the intrinsic graph metric, the shortest-path distance, on various benchmark datasets. The empirical results of this case study confirm our theoretical insights. Moreover, we demonstrate the practical applicability of our framework by using it to tackle the cold start problem in graph active learning. 1 Introduction Many problems in computer vision and machine learning are modeled as learning tasks on graphs. For example, in semantic segmentation, graphs model the relationships between different image regions, enhancing accuracy and context-aware segmentation. Graph neural networks (GNNs) have emerged as a dominant class of machine learning models specifically designed for learning representations of graph-structured data. They have demonstrated considerable success in addressing a wide range of graph-related problems in various domains such as chemistry [10], biology [37], social networking [6, 22], scene graph generation [46, 51] and visual relationship detection [24,43,49]. A defining characteristic of GNNs is their use of a spatial approach through message passing on the graph structure for feature aggregation. This enables GNNs to preserve structural information or dependencies (referred to as topology awareness) from the underlying graph structure, allowing them to be highly effective in tasks such as node classification. Fig. 1 illustrates the overall learning process of GNNs. Despite their practicality and potential, there remains a lack of theoretical understanding about GNNs, particularly in the semi-supervised node classification setting where the dependencies among the data differ significantly from other machine learning models [25]. In this setting, the goal is to leverage relations, as captured by the graph structure, among the data and a small set of labelled nodes to predict labels for the remaining nodes. Most of the existing theoretical studies of GNNs have focused on the connection between the message-passing mechanism of GNNs and the Weisfeiler-Lehman isomorphism test [19], aiming to understand the ability of GNNs to differentiate different graph structures in the learned representations, known as the expressive power of GNNs. Inspired by the expressiveness studies, it is commonly believed that increasing topology awareness is universally beneficial and many studies focus on enabling GNNs to preserve more structural properties in the learned representation [29, 33, 48]. However, as GNNs become more reliant on and sensitive (aware) of graph structure as input, they may exhibit different generalization performances towards certain structural subgroups (distinct data subsets grouped by structural similarity to the training set) within the data. The quantification of GNN generalization across distinct structural subgroups is termed structural subgroup generalization [25]. Such considerations are vital in GNN application and development. For instance, within protein-protein interaction networks, these structural subgroups could represent different molecular complexes, influencing the accuracy of interaction predictions. Similarly, understanding how the topology awareness of GNNs influences generalization is essential when devising sampling strategies for training. The extent to which the generalization performance of GNNs is influenced by specific structural features of graph data is critical in deciding the composition of training datasets. Despite its importance, an understanding of the relationship between the topology awareness of GNNs and its structural subgroup generalization is still lacking. Furthermore, characterizing the topology awareness of GNNs poses a challenge, especially considering that different domains and tasks may prioritize distinct structural aspects. Therefore, a versatile framework is needed to assess the topology awareness of GNNs in relation to various structures. To address this gap, in this paper, we propose a novel framework based on approximate metric embedding to study the relationship between structural subgroup generalization and topology awareness of GNNs in the context of semisupervised node classification. The proposed framework allows for the investigation of the structural subgroup generalization of GNNs with respect to different structural subgroups. More concretely, the main contributions of this work are summarized as follows. 1. We propose a novel, structure-agnostic framework using approximate metric embedding to examine the interplay between GNNs’ structural subgroup generalization and topology awareness. This framework is versatile, accommodating various structural measures like shortest-path distance, and requires only the corresponding structural measure. Its simplicity in estimating key factors makes it applicable and generalizable to a wide range of scenarios. 2. Through formal analysis within our framework, we establish a clear link between GNN topology awareness and their generalization performance (Theorem 1). We also demonstrate that while enhanced topology awareness boosts GNN expressiveness, it can result in uneven generalization performance, favouring subgroups more structurally similar to the training set (Theorem 2). Such structural property can be harmful (causing unfairness issues) or useful (informing design decisions) depending on the scenario. This challenges the prevailing belief that increased topology awareness universally benefits GNNs [29, 33, 48], emphasizing the importance of considering the relationship between topology awareness and generalization performance. 3. We validate our framework through a case study on shortest-path distance, highlighting its practicality and relevance. The results corroborate our theoretical findings, showing that GNNs with heightened awareness of shortestpath distances excel in classifying vertex groups closer to the training set. Moreover, we demonstrate how our findings can be applied to mitigate the cold start problem in graph active learning [11,15], highlighting the practical implications of our framework and results. This paper is available on arxiv under CC BY 4.0 DEED license. Authors: (1) Junwei Su, Department of Computer Science, the University of Hong Kong and jwsu@cs.hku.hk; (2) Chuan Wu, Department of Computer Science, the University of Hong Kong and cwu@cs.hku.hk. Authors: Authors: (1) Junwei Su, Department of Computer Science, the University of Hong Kong and jwsu@cs.hku.hk; (2) Chuan Wu, Department of Computer Science, the University of Hong Kong and cwu@cs.hku.hk. Table of Links Abstract and 1 Introduction Abstract and 1 Introduction 2 Related Work 2 Related Work 3 Framework 3 Framework 4 Main Results 4 Main Results 5 A Case Study on Shortest-Path Distance 5 A Case Study on Shortest-Path Distance 6 Conclusion and Discussion, and References 6 Conclusion and Discussion, and References 7 Proof of Theorem 1 7 Proof of Theorem 1 8 Proof of Theorem 2 8 Proof of Theorem 2 9 Procedure for Solving Eq. (6) 9 Procedure for Solving Eq. (6) 10 Additional Experiments Details and Results 10 Additional Experiments Details and Results 11 Other Potential Applications 11 Other Potential Applications Abstract Many computer vision and machine learning problems are modelled as learning tasks on graphs, where graph neural networks (GNNs) have emerged as a dominant tool for learning representations of graphstructured data. A key feature of GNNs is their use of graph structures as input, enabling them to exploit the graphs’ inherent topological properties—known as the topology awareness of GNNs. Despite the empirical successes of GNNs, the influence of topology awareness on generalization performance remains unexplored, particularly for node-level tasks that diverge from the assumption of data being independent and identically distributed (I.I.D.). The precise definition and characterization of the topology awareness of GNNs, especially concerning different topological features, are still unclear. This paper introduces a comprehensive framework to characterize the topology awareness of GNNs across any topological feature. Using this framework, we investigate the effects of topology awareness on GNN generalization performance. Contrary to the prevailing belief that enhancing the topology awareness of GNNs is always advantageous, our analysis reveals a critical insight: improving the topology awareness of GNNs may inadvertently lead to unfair generalization across structural groups, which might not be desired in some scenarios. Additionally, we conduct a case study using the intrinsic graph metric, the shortest-path distance, on various benchmark datasets. The empirical results of this case study confirm our theoretical insights. Moreover, we demonstrate the practical applicability of our framework by using it to tackle the cold start problem in graph active learning. 1 Introduction Many problems in computer vision and machine learning are modeled as learning tasks on graphs. For example, in semantic segmentation, graphs model the relationships between different image regions, enhancing accuracy and context-aware segmentation. Graph neural networks (GNNs) have emerged as a dominant class of machine learning models specifically designed for learning representations of graph-structured data. They have demonstrated considerable success in addressing a wide range of graph-related problems in various domains such as chemistry [10], biology [37], social networking [6, 22], scene graph generation [46, 51] and visual relationship detection [24,43,49]. A defining characteristic of GNNs is their use of a spatial approach through message passing on the graph structure for feature aggregation. This enables GNNs to preserve structural information or dependencies (referred to as topology awareness) from the underlying graph structure, allowing them to be highly effective in tasks such as node classification. Fig. 1 illustrates the overall learning process of GNNs. Despite their practicality and potential, there remains a lack of theoretical understanding about GNNs, particularly in the semi-supervised node classification setting where the dependencies among the data differ significantly from other machine learning models [25]. In this setting, the goal is to leverage relations, as captured by the graph structure, among the data and a small set of labelled nodes to predict labels for the remaining nodes. Most of the existing theoretical studies of GNNs have focused on the connection between the message-passing mechanism of GNNs and the Weisfeiler-Lehman isomorphism test [19], aiming to understand the ability of GNNs to differentiate different graph structures in the learned representations, known as the expressive power of GNNs. Inspired by the expressiveness studies, it is commonly believed that increasing topology awareness is universally beneficial and many studies focus on enabling GNNs to preserve more structural properties in the learned representation [29, 33, 48]. However, as GNNs become more reliant on and sensitive (aware) of graph structure as input, they may exhibit different generalization performances towards certain structural subgroups (distinct data subsets grouped by structural similarity to the training set) within the data. The quantification of GNN generalization across distinct structural subgroups is termed structural subgroup generalization [25]. Such considerations are vital in GNN application and development. For instance, within protein-protein interaction networks, these structural subgroups could represent different molecular complexes, influencing the accuracy of interaction predictions. Similarly, understanding how the topology awareness of GNNs influences generalization is essential when devising sampling strategies for training. The extent to which the generalization performance of GNNs is influenced by specific structural features of graph data is critical in deciding the composition of training datasets. Despite its importance, an understanding of the relationship between the topology awareness of GNNs and its structural subgroup generalization is still lacking. Furthermore, characterizing the topology awareness of GNNs poses a challenge, especially considering that different domains and tasks may prioritize distinct structural aspects. Therefore, a versatile framework is needed to assess the topology awareness of GNNs in relation to various structures. To address this gap, in this paper, we propose a novel framework based on approximate metric embedding to study the relationship between structural subgroup generalization and topology awareness of GNNs in the context of semisupervised node classification. The proposed framework allows for the investigation of the structural subgroup generalization of GNNs with respect to different structural subgroups. More concretely, the main contributions of this work are summarized as follows. 1. We propose a novel, structure-agnostic framework using approximate metric embedding to examine the interplay between GNNs’ structural subgroup generalization and topology awareness. This framework is versatile, accommodating various structural measures like shortest-path distance, and requires only the corresponding structural measure. Its simplicity in estimating key factors makes it applicable and generalizable to a wide range of scenarios. 2. Through formal analysis within our framework, we establish a clear link between GNN topology awareness and their generalization performance (Theorem 1). We also demonstrate that while enhanced topology awareness boosts GNN expressiveness, it can result in uneven generalization performance, favouring subgroups more structurally similar to the training set (Theorem 2). Such structural property can be harmful (causing unfairness issues) or useful (informing design decisions) depending on the scenario. This challenges the prevailing belief that increased topology awareness universally benefits GNNs [29, 33, 48], emphasizing the importance of considering the relationship between topology awareness and generalization performance. 3. We validate our framework through a case study on shortest-path distance, highlighting its practicality and relevance. The results corroborate our theoretical findings, showing that GNNs with heightened awareness of shortestpath distances excel in classifying vertex groups closer to the training set. Moreover, we demonstrate how our findings can be applied to mitigate the cold start problem in graph active learning [11,15], highlighting the practical implications of our framework and results. This paper is available on arxiv under CC BY 4.0 DEED license. This paper is available on arxiv under CC BY 4.0 DEED license. available on arxiv

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