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

Transcendence Book 10: The Ultimate "Why?"

Authors:
(1) Li Siyao, S-Lab, Nanyang Technological University;
(2) Tianpei Gu, Lexica and Work completed at UCLA;
(3) Weiye Xiao, Southeast University;
(4) Henghui Ding, S-Lab, Nanyang Technological University;
(5) Ziwei Liu, S-Lab, Nanyang Technological University;
(6) Chen Change Loy, S-Lab, Nanyang Technological University and a Corresponding Author. Table of Links Abstract and 1. Introduction Related Work
Mixamo Line Art Dataset
Our Approach
Experiment
Conclusion and References 5. Experiment Evaluation Metric. Following [16, 5], we adopt the chamfer distance (CD) as the evaluation metric, which has been initially introduced to measure the similarity between two point clouds. Formally, CD is computed as: 5.1. Comparison to Existing Methods As shown in Table 2, our AnimeInbet favorably outperforms all compared methods on both the validation set and the test set of MixamoLine240. On the validation set, our approach achieves an average CD value of 11.53, representing a significant improvement over the best-performing compared method, FILM, with over 30% enhancement. Upon closer inspection, the advantage of AnimeInbet becomes more pronounced as the frame gap increases (0.98, 5.72 and 9.47 for gaps of 1, 5, and 9, respectively), indicating that our method is more robust in handling larger motions. On the test set, our method maintains its lead over the other compared methods, with improvements of 0.70 (20%), 5.25 (29%), and 10.30 (31%) from the best-performing compared method FILM for the frame gaps of 1, 5, and 9, respectively. Given that both the characters and actions in the test set are new, our method’s superiority on the test set provides more convincing evidence of its advantages over the existing frame interpolation methods. To illustrate the advantages of our method, we present several inbetweening results in Figure 8. We arranged these examples in increasing levels of difficulty from top to bottom. When the motion is simple, compared methods can interpolate a relatively complete shape of the main body of the drawing. However, they tend to produce strong blurring (RIFE) or disappearance (VFIformer, EISAI, and FILM) of noticeable moving compositions (indicated by red arrows). In contrast, our method maintains a concise line structure in these key areas. When the input frames involve the whole body’s movement within large magnitudes, the intermediate frames predicted by the compared methods become indistinguishable and patchy, rendering the results invalid for further use. However, our AnimeInbet method can still preserve the general shape in the correct positions, even with a partial loss of details, which can be easily fixed with minor manual effort. User Study. To further evaluate the visual performance of our methods, we conduct a user study among 36 participants. For each participant, we randomly show 60 pairs, each composed of a result of AnimeInbet and that of a compared method, and ask the participant to select the better. To allow participants to take temporal consistency into the decision, we display these results in GIF formats formed by triplets of input frames and the inbetweened one. The winning rates of our method are shown in Figure 9, where AnimeInbet wins over 92% versus the compared methods. Notably, for “gap = 5” and “gap = 9” slots, the winning rates of our methods are close to 100% with smaller deviations than “gap = 1”, suggesting the advantages of our method on cases within large motions. 5.2. Ablation Study Embedding Features. To investigate the effectiveness of the three types of embeddings mentioned in Section 4.1, we trained several variants by removing the corresponding modules. As shown in Table 3, for each variant, we list the matching accuracy for all vertices (“Acc.”), the accuracy for non-occluded vertices (“Valid Acc.”) and the final CD values of inbetweening on the validation set (gap = 5). If removing the positional embedding EP , the “Valid Acc.” and the CD value drop 15.83% and 0.74, respectively; while the lacking of topological embedding ET lowers “Valid Acc.” by 5.66% and worsens CD by 0.43, which reveals the importance of these two components. Repositioning Propagation and Visibility Mask. We demonstrate the contribution of repositioning propagation (prepos. prop.) and visibility mask (vis. mask) both quantitatively and qualitatively. As shown in Table 4, without repositioning propagation, the CD value will be sharply worsened by 12.50 (112%), while the lacking of visibility mask will also make a drop of 1.69 (15%). An example is shown in Figure 10, where “w/o. repos. prop.” appears within many messy lines due to undefined positions for those unmatched vertices, while “w/o. vis. mask” shows some redundant segments (red box) after repositioning; the complete AnimeInbet can resolve these issues and produce a clean yet complete result. Geometrizor. As shown in Table 2, the quantitative metrics of AnimeInbet-VS are generally worse by around 0.6 compared to AnimeInbet. This is because VirtualSketcher [15] does not vectorize the line arts as precisely as the ground truth labels (average vertex number 587 vs 1,351). As shown in Figure 10, the curves in “AnimeInbet-VS” become sharper and lose some details, which decreases the quality of the inbetweened frame. Using a more accurate geometrizer would lead to higher quality inbetweening results for raster image inputs. Data Influence. As mentioned in Section 3, we created a validation set composed of 20 sequences of unseen characters but seen actions, 20 of unseen actions but seen characters and 4 of unseen both to explore the influence on data. Our experiment finds that whether the characters or the actions are seen does not fundamentally influence the inbetweening quality, while the motion magnitude is the key factor. As shown in Table 5, the CD value of unseen characters is 14.70, which is over 47% worse than that of unseen both due to larger vertex shifts (44.59 vs 29.62), while the difference between the CD values of unseen actions and unseen both is around 10% under similar occlusion rates and shifts. This paper is available on arxiv under CC BY-NC-SA 4.0 DEED license. Authors: (1) Li Siyao, S-Lab, Nanyang Technological University; (2) Tianpei Gu, Lexica and Work completed at UCLA; (3) Weiye Xiao, Southeast University; (4) Henghui Ding, S-Lab, Nanyang Technological University; (5) Ziwei Liu, S-Lab, Nanyang Technological University; (6) Chen Change Loy, S-Lab, Nanyang Technological University and a Corresponding Author. Authors: Authors: (1) Li Siyao, S-Lab, Nanyang Technological University; (2) Tianpei Gu, Lexica and Work completed at UCLA; (3) Weiye Xiao, Southeast University; (4) Henghui Ding, S-Lab, Nanyang Technological University; (5) Ziwei Liu, S-Lab, Nanyang Technological University; (6) Chen Change Loy, S-Lab, Nanyang Technological University and a Corresponding Author. Table of Links Abstract and 1. Introduction Abstract and 1. Introduction Related Work Mixamo Line Art Dataset Our Approach Experiment Conclusion and References Related Work Related Work Mixamo Line Art Dataset Mixamo Line Art Dataset Our Approach Our Approach Experiment Experiment Conclusion and References Conclusion and References 5. Experiment Evaluation Metric. Following [16, 5], we adopt the chamfer distance (CD) as the evaluation metric, which has been initially introduced to measure the similarity between two point clouds. Formally, CD is computed as: Evaluation Metric. 5.1. Comparison to Existing Methods As shown in Table 2, our AnimeInbet favorably outperforms all compared methods on both the validation set and the test set of MixamoLine240. On the validation set, our approach achieves an average CD value of 11.53, representing a significant improvement over the best-performing compared method, FILM, with over 30% enhancement. Upon closer inspection, the advantage of AnimeInbet becomes more pronounced as the frame gap increases (0.98, 5.72 and 9.47 for gaps of 1, 5, and 9, respectively), indicating that our method is more robust in handling larger motions. On the test set, our method maintains its lead over the other compared methods, with improvements of 0.70 (20%), 5.25 (29%), and 10.30 (31%) from the best-performing compared method FILM for the frame gaps of 1, 5, and 9, respectively. Given that both the characters and actions in the test set are new, our method’s superiority on the test set provides more convincing evidence of its advantages over the existing frame interpolation methods. AnimeInbet To illustrate the advantages of our method, we present several inbetweening results in Figure 8. We arranged these examples in increasing levels of difficulty from top to bottom. When the motion is simple, compared methods can interpolate a relatively complete shape of the main body of the drawing. However, they tend to produce strong blurring (RIFE) or disappearance (VFIformer, EISAI, and FILM) of noticeable moving compositions (indicated by red arrows). In contrast, our method maintains a concise line structure in these key areas. When the input frames involve the whole body’s movement within large magnitudes, the intermediate frames predicted by the compared methods become indistinguishable and patchy, rendering the results invalid for further use. However, our AnimeInbet method can still preserve the general shape in the correct positions, even with a partial loss of details, which can be easily fixed with minor manual effort. AnimeInbet User Study. To further evaluate the visual performance of our methods, we conduct a user study among 36 participants. For each participant, we randomly show 60 pairs, each composed of a result of AnimeInbet and that of a compared method, and ask the participant to select the better. To allow participants to take temporal consistency into the decision, we display these results in GIF formats formed by triplets of input frames and the inbetweened one. The winning rates of our method are shown in Figure 9, where AnimeInbet wins over 92% versus the compared methods. Notably, for “gap = 5” and “gap = 9” slots, the winning rates of our methods are close to 100% with smaller deviations than “gap = 1”, suggesting the advantages of our method on cases within large motions. User Study. 5.2. Ablation Study Embedding Features. To investigate the effectiveness of the three types of embeddings mentioned in Section 4.1, we trained several variants by removing the corresponding modules. As shown in Table 3, for each variant, we list the matching accuracy for all vertices (“Acc.”), the accuracy for non-occluded vertices (“Valid Acc.”) and the final CD values of inbetweening on the validation set (gap = 5). If removing the positional embedding EP , the “Valid Acc.” and the CD value drop 15.83% and 0.74, respectively; while the lacking of topological embedding ET lowers “Valid Acc.” by 5.66% and worsens CD by 0.43, which reveals the importance of these two components. Repositioning Propagation and Visibility Mask. We demonstrate the contribution of repositioning propagation (prepos. prop.) and visibility mask (vis. mask) both quantitatively and qualitatively. As shown in Table 4, without repositioning propagation, the CD value will be sharply worsened by 12.50 (112%), while the lacking of visibility mask will also make a drop of 1.69 (15%). An example is shown in Figure 10, where “w/o. repos. prop.” appears within many messy lines due to undefined positions for those unmatched vertices, while “w/o. vis. mask” shows some redundant segments (red box) after repositioning; the complete AnimeInbet can resolve these issues and produce a clean yet complete result. Repositioning Propagation and Visibility Mask. Geometrizor . As shown in Table 2, the quantitative metrics of AnimeInbet-VS are generally worse by around 0.6 compared to AnimeInbet . This is because VirtualSketcher [15] does not vectorize the line arts as precisely as the ground truth labels (average vertex number 587 vs 1,351). As shown in Figure 10, the curves in “ AnimeInbet-VS ” become sharper and lose some details, which decreases the quality of the inbetweened frame. Using a more accurate geometrizer would lead to higher quality inbetweening results for raster image inputs. Geometrizor AnimeInbet-VS AnimeInbet VirtualSketcher AnimeInbet-VS Data Influence. As mentioned in Section 3, we created a validation set composed of 20 sequences of unseen characters but seen actions, 20 of unseen actions but seen characters and 4 of unseen both to explore the influence on data. Our experiment finds that whether the characters or the actions are seen does not fundamentally influence the inbetweening quality, while the motion magnitude is the key factor. As shown in Table 5, the CD value of unseen characters is 14.70, which is over 47% worse than that of unseen both due to larger vertex shifts (44.59 vs 29.62), while the difference between the CD values of unseen actions and unseen both is around 10% under similar occlusion rates and shifts. Data Influence. This paper is available on arxiv under CC BY-NC-SA 4.0 DEED license. This paper is available on arxiv under CC BY-NC-SA 4.0 DEED license. available on arxiv

Deep Geometrized Cartoon Line Inbetweening: Experiment

Authors:
(1) Li Siyao, S-Lab, Nanyang Technological University;
(2) Tianpei Gu, Lexica and Work completed at UCLA;
(3) Weiye Xiao, Southeast University;
(4) Henghui Ding, S-Lab, Nanyang Technological University;
(5) Ziwei Liu, S-Lab, Nanyang Technological University;
(6) Chen Change Loy, S-Lab, Nanyang Technological University and a Corresponding Author. Table of Links Abstract and 1. Introduction Related Work
Mixamo Line Art Dataset
Our Approach
Experiment
Conclusion and References 4. Our Approach Geometrizing Line Drawings. The process of creating artwork has become largely digital, allowing for direct export in vectorized format. However, for line drawings that only appear in raster images, there are various commercial software and open-source research projects available [40, 36, 15, 12] that can be used to convert the raster images into the required vectorized input format. We will ablate the performance of line vectorization in our experiments. 4.1. Vertex Geometric Embedding Discriminative features for each vertex are desired to achieve accurate graph matching. Line graphs are different from general graphs as the spatial position of endpoint vertices, in addition to the topology of connections, determines the geometric shape of the line. The geometric graph embedding for line art is hence designed to comprise three parts: 1) image contextual embedding, 2) positional embedding, and 3) topological embedding, as shown in Figure 6. 4.2. Vertex Correspondence Transformer We use geometric features F0 and F1 to establish a vertexwise correspondence between G0 and G1. Specifically, we compute a correlation matrix between vertex features and identify the matching pair as those with the highest value across both the row and the column of the matrix. Prior to this step, we apply a Transformer that aggregates the mutual consistency both intra- and inter-graph. Mutual Aggregation. Following [24, 31], we employ a cascade of alternating self- and cross-attention layers to aggregate the vertex feature. In a self-attention layer, all queries, keys and values are derived from the single source feature, 4.3. Repositioning Propagation 4.4. Visibility Prediction and Graph Fusion 4.5. Learning This paper is available on arxiv under CC BY-NC-SA 4.0 DEED license. Authors: (1) Li Siyao, S-Lab, Nanyang Technological University; (2) Tianpei Gu, Lexica and Work completed at UCLA; (3) Weiye Xiao, Southeast University; (4) Henghui Ding, S-Lab, Nanyang Technological University; (5) Ziwei Liu, S-Lab, Nanyang Technological University; (6) Chen Change Loy, S-Lab, Nanyang Technological University and a Corresponding Author. Authors: Authors: (1) Li Siyao, S-Lab, Nanyang Technological University; (2) Tianpei Gu, Lexica and Work completed at UCLA; (3) Weiye Xiao, Southeast University; (4) Henghui Ding, S-Lab, Nanyang Technological University; (5) Ziwei Liu, S-Lab, Nanyang Technological University; (6) Chen Change Loy, S-Lab, Nanyang Technological University and a Corresponding Author. Table of Links Abstract and 1. Introduction Abstract and 1. Introduction Related Work Mixamo Line Art Dataset Our Approach Experiment Conclusion and References Related Work Related Work Mixamo Line Art Dataset Mixamo Line Art Dataset Our Approach Our Approach Experiment Experiment Conclusion and References Conclusion and References 4. Our Approach Geometrizing Line Drawings. The process of creating artwork has become largely digital, allowing for direct export in vectorized format. However, for line drawings that only appear in raster images, there are various commercial software and open-source research projects available [40, 36, 15, 12] that can be used to convert the raster images into the required vectorized input format. We will ablate the performance of line vectorization in our experiments. Geometrizing Line Drawings. 4.1. Vertex Geometric Embedding Discriminative features for each vertex are desired to achieve accurate graph matching. Line graphs are different from general graphs as the spatial position of endpoint vertices, in addition to the topology of connections, determines the geometric shape of the line. The geometric graph embedding for line art is hence designed to comprise three parts: 1) image contextual embedding , 2) positional embedding , and 3) topological embedding , as shown in Figure 6. 1) image contextual embedding 2) positional embedding 3) topological embedding 4.2. Vertex Correspondence Transformer We use geometric features F0 and F1 to establish a vertexwise correspondence between G0 and G1. Specifically, we compute a correlation matrix between vertex features and identify the matching pair as those with the highest value across both the row and the column of the matrix. Prior to this step, we apply a Transformer that aggregates the mutual consistency both intra- and inter-graph. Mutual Aggregation. Following [24, 31], we employ a cascade of alternating self- and cross-attention layers to aggregate the vertex feature. In a self-attention layer, all queries, keys and values are derived from the single source feature, Mutual Aggregation. 4.3. Repositioning Propagation 4.4. Visibility Prediction and Graph Fusion 4.5. Learning This paper is available on arxiv under CC BY-NC-SA 4.0 DEED license. This paper is available on arxiv under CC BY-NC-SA 4.0 DEED license. available on arxiv

Deep Geometrized Cartoon Line Inbetweening: Our Approach

Authors:
(1) Li Siyao, S-Lab, Nanyang Technological University;
(2) Tianpei Gu, Lexica and Work completed at UCLA;
(3) Weiye Xiao, Southeast University;
(4) Henghui Ding, S-Lab, Nanyang Technological University;
(5) Ziwei Liu, S-Lab, Nanyang Technological University;
(6) Chen Change Loy, S-Lab, Nanyang Technological University and a Corresponding Author. Table of Links Abstract and 1. Introduction Related Work
Mixamo Line Art Dataset
Our Approach
Experiment
Conclusion and References 3. Mixamo Line Art Dataset To facilitate training and evaluation of geometrized line inbetweening, we develop a large-scale dataset, named MixamoLine240, which consists of 240 sequences of consecutive line drawing frames, with 100 sequences for training and 140 for validation and testing. To obtain this vast amount of cartoon line data, we utilize a “Cel-shading” technique, i.e., to use computer graphics software (Blender in this work) to render 3D resources into an anime-style appearance that mimics the hand-drawn artistry. Unlike previous works [25, 29] that only provide raster images, MixamoLine240 also provides ground-truth geometrization labels for each frame, which include the coordinates of a group of vertices (V ) and the connection topology (T). Additionally, we assign an index number (R[i]) to each 2D endpoint (V [i]) that refers to a unique vertex in the 3D mesh of the character, as illustrated in Figure 3, which can be further used to deduce the vertex level correspondence. Specifically, given two frames I0 and I1 in a sequence, the 3D reference IDs reveal the vertex correspondence {(i, j)} for those vertices i in I0 and j in I1 having R0[i] = R1[j], while the rest unmatched vertices are marked as occluded. This strategy allows us to produce correspondence pairs with arbitrary frame gaps to flexibly adjust the input frame rate during training. Next, we discuss the construction and challenges inherent in the data. Data Construction. In Blender, the mesh structure of a 3D character remains stable, i.e., the number of 3D vertex and the edge topology keep constant, when moving without additional subdivision modifier. We employ this property to achieve consistent line art rendering and accurate annotations for geometrization and vertex matching. As shown in Figure 3, the original 3D mesh contains all the necessary line segments required to represent the character in line art. During rendering, the visible outline from the camera’s perspective is selected based on the material boundary and the object’s edge. This process ensures that every line segment in the resulting raster image corresponds to an edge in the original mesh. The 2D endpoints of each line segment are simply the relevant 3D vertices projected onto the camera plane, referenced by the unique and consistent index of the corresponding 3D vertex. Meanwhile, since the 3D mesh naturally defines the vertex connections, the topology of the 2D lines can be transferred from the selective edges used for rendering. To prevent any topological ambiguity that may be caused by overlapped vertices in 3D space, we merge the endpoints that are within a Euclidean distance of 0.1 in the projected 2D space. This enables us to obtain both the raster line drawings and the accurate labels of each frame. To create a diverse dataset, we used the open-source 3D material library Mixamo [1] and selected 20 characters and 20 actions, as shown in Figure 4. Each action has an average of 191 frames. We combined 10 characters and 10 actions to render 100 sequences, with a total of 19,930 frames as the training set. We then used the remaining 10 characters and 10 actions to render an 18,230-frame test set, ensuring that the training and testing partitions are exclusive. We also created a 44-sequence validation set, consisting of 20 unseen characters, 20 unseen actions, and 4 with both unseen character and action. To create this set, we combined the test characters “Swat”and “Warrok” and actions “sword slash” and “hip hop” with the training characters and actions. The validation set contains 11,102 frames and was also rendered at 1080p resolution with a frame rate of 60 fps. To ensure consistency across all frames, we cropped and resized each frame to a unified 720 × 720 character-centered image. Challenges. Table 1 summarizes the statistics that reflect the difficulty of the line inbetweening task under various input frame rates. With an increase in frame gaps, the inbetweening task becomes more challenging with larger motion magnitudes and higher occlusion percentages. For instance, when the frame gap is 9, the input frame rate becomes 6 fps, and the average vertex shift is 62.8 pixels. The mean value of the maximum vertex shift in a frame (“Avg. max vtx shift”) reaches 192.3 pixels, which is 27% of the image width. Additionally, nearly half of the vertices are unmatched in such cases, making line inbetweening a tough problem. Furthermore, the image composition of the test set is more complex than that of the training set. A training frame has an average of 1,256 vertices and 1,753 edges, while a test frame has an average of 1,512 vertices and 2,099 edges since the test set has more complex characters such as “Maw”. This paper is available on arxiv under CC BY-NC-SA 4.0 DEED license. Authors: (1) Li Siyao, S-Lab, Nanyang Technological University; (2) Tianpei Gu, Lexica and Work completed at UCLA; (3) Weiye Xiao, Southeast University; (4) Henghui Ding, S-Lab, Nanyang Technological University; (5) Ziwei Liu, S-Lab, Nanyang Technological University; (6) Chen Change Loy, S-Lab, Nanyang Technological University and a Corresponding Author. Authors: Authors: (1) Li Siyao, S-Lab, Nanyang Technological University; (2) Tianpei Gu, Lexica and Work completed at UCLA; (3) Weiye Xiao, Southeast University; (4) Henghui Ding, S-Lab, Nanyang Technological University; (5) Ziwei Liu, S-Lab, Nanyang Technological University; (6) Chen Change Loy, S-Lab, Nanyang Technological University and a Corresponding Author. Table of Links Abstract and 1. Introduction Abstract and 1. Introduction Related Work Mixamo Line Art Dataset Our Approach Experiment Conclusion and References Related Work Related Work Mixamo Line Art Dataset Mixamo Line Art Dataset Our Approach Our Approach Experiment Experiment Conclusion and References Conclusion and References 3. Mixamo Line Art Dataset To facilitate training and evaluation of geometrized line inbetweening, we develop a large-scale dataset, named MixamoLine240, which consists of 240 sequences of consecutive line drawing frames, with 100 sequences for training and 140 for validation and testing. To obtain this vast amount of cartoon line data, we utilize a “Cel-shading” technique, i.e., to use computer graphics software (Blender in this work) to render 3D resources into an anime-style appearance that mimics the hand-drawn artistry. Unlike previous works [25, 29] that only provide raster images, MixamoLine240 also provides ground-truth geometrization labels for each frame, which include the coordinates of a group of vertices (V ) and the connection topology (T). Additionally, we assign an index number (R[i]) to each 2D endpoint (V [i]) that refers to a unique vertex in the 3D mesh of the character, as illustrated in Figure 3, which can be further used to deduce the vertex level correspondence. Specifically, given two frames I0 and I1 in a sequence, the 3D reference IDs reveal the vertex correspondence {(i, j)} for those vertices i in I0 and j in I1 having R0[i] = R1[j], while the rest unmatched vertices are marked as occluded. This strategy allows us to produce correspondence pairs with arbitrary frame gaps to flexibly adjust the input frame rate during training. Next, we discuss the construction and challenges inherent in the data. Data Construction. In Blender, the mesh structure of a 3D character remains stable, i.e., the number of 3D vertex and the edge topology keep constant, when moving without additional subdivision modifier. We employ this property to achieve consistent line art rendering and accurate annotations for geometrization and vertex matching. As shown in Figure 3, the original 3D mesh contains all the necessary line segments required to represent the character in line art. During rendering, the visible outline from the camera’s perspective is selected based on the material boundary and the object’s edge. This process ensures that every line segment in the resulting raster image corresponds to an edge in the original mesh. The 2D endpoints of each line segment are simply the relevant 3D vertices projected onto the camera plane, referenced by the unique and consistent index of the corresponding 3D vertex. Meanwhile, since the 3D mesh naturally defines the vertex connections, the topology of the 2D lines can be transferred from the selective edges used for rendering. To prevent any topological ambiguity that may be caused by overlapped vertices in 3D space, we merge the endpoints that are within a Euclidean distance of 0.1 in the projected 2D space. This enables us to obtain both the raster line drawings and the accurate labels of each frame. Data Construction. To create a diverse dataset, we used the open-source 3D material library Mixamo [1] and selected 20 characters and 20 actions, as shown in Figure 4. Each action has an average of 191 frames. We combined 10 characters and 10 actions to render 100 sequences, with a total of 19,930 frames as the training set. We then used the remaining 10 characters and 10 actions to render an 18,230-frame test set, ensuring that the training and testing partitions are exclusive. We also created a 44-sequence validation set, consisting of 20 unseen characters, 20 unseen actions, and 4 with both unseen character and action. To create this set, we combined the test characters “Swat”and “Warrok” and actions “sword slash” and “hip hop” with the training characters and actions. The validation set contains 11,102 frames and was also rendered at 1080p resolution with a frame rate of 60 fps. To ensure consistency across all frames, we cropped and resized each frame to a unified 720 × 720 character-centered image. Challenges. Table 1 summarizes the statistics that reflect the difficulty of the line inbetweening task under various input frame rates. With an increase in frame gaps, the inbetweening task becomes more challenging with larger motion magnitudes and higher occlusion percentages. For instance, when the frame gap is 9, the input frame rate becomes 6 fps, and the average vertex shift is 62.8 pixels. The mean value of the maximum vertex shift in a frame (“Avg. max vtx shift”) reaches 192.3 pixels, which is 27% of the image width. Additionally, nearly half of the vertices are unmatched in such cases, making line inbetweening a tough problem. Furthermore, the image composition of the test set is more complex than that of the training set. A training frame has an average of 1,256 vertices and 1,753 edges, while a test frame has an average of 1,512 vertices and 2,099 edges since the test set has more complex characters such as “Maw”. Challenges. This paper is available on arxiv under CC BY-NC-SA 4.0 DEED license. This paper is available on arxiv under CC BY-NC-SA 4.0 DEED license. available on arxiv

Deep Geometrized Cartoon Line Inbetweening: Mixamo Line Art Dataset

NeRF Editing and Inpainting Techniques: Conclusion and References

It sounds like science fiction, but with all the hype around AI, the danger of ‘kidnapping’ is worth talking about. It goes like this - companies who can afford to build their own internal LLMs throw all of their valuable IP (intellectual property, covering everything from trade secret designs to marketing campaigns and product strategies) into the model for it to generate relevant responses. Essentially, while it’s still a non-sentient AI model, it’s also a repository of all the most valuable information the company has. This makes it a fantastic target for a criminal attacker, or even an unethical competitor. If it can be poisoned to generate bad responses, cloned to give the attacker more insider knowledge than they know what to do with, or even somehow locked down for ransom, then it can do a huge amount of damage to the company. Companies struggle to secure their systems, with regular headlines showing large enterprises being breached. An LLM model, containing everything about the company, is going to quickly become a favoured target for virtual ‘kidnapping.’ Whether it’s a case of adapting ransomware to encrypt models, exfiltrating them and destroying the local copy, or subverting them into an insider threat (say, if the LLM has been integrated with the company’s invoicing and finance systems without effective human oversight), the potential for harm is dramatic. Making it worse, the value of these models will come from their availability and accessibility within the company. If no one can use them, they’re nothing but a resource sink. They must be used effectively to have value, and that means they must be accessible. How do we match the need for availability with the need for security on these systems? Is Software Security Enough? Maybe software-defined networks could be a solution? The problem is that any software solution is inherently vulnerable to compromise. And if we’re talking about an LLM which has been integrated with administrative systems (this is already being done, the ethics and risks of this are a whole article in themselves - maybe a book), then it would be simplicity itself for a malicious party to prompt the AI to create a way in for further attacks. Software solutions, and classic devices such as firewalls and data diodes, definitely have a place in a secure AI system design, but something with so much value to a company justifies a much more absolute approach. If we go old-school, what we’d talk about as the last resort for any attack is pulling the plug. Ultimately, unless an attacker can change the laws of physics (or is sitting inside the data centre, which is unlikely) unplugging the network is pretty unbeatable. The problem is that unplugging and reconnecting the network takes time - making a phone call to your network engineer to plug it in or out every time you want to send an authorised prompt doesn’t seem a great option. The Goldilock FireBreak I recently came across a security device which impressed me, which doesn’t happen often these days. It wasn’t because of its brand new quantum dark web AI firewall technology, as so many vendors advertise these days. Instead it was because it’s a company which has taken a very old idea, thought about it, and brought it bang up to date in a way that opens up a lot of possibilities for secure network topologies. The approach is simple, and pretty unbeatable (obviously nothing is 100% secure, but the attack vectors against a physical disconnect are vanishingly sparse). Essentially the FireBreak (as opposed to firewall, of course) unplugs the network cable on command - or plugs it back in. It’s not quite having someone on-call in the data centre to manipulate cables on demand, but that’s an easy way to think about it - except the person can plug or unplug the cables in a fraction of a second in response to prompts from any method you choose. Often management networks are separated only by a firewall, whereas FireBreak itself has a control plane completely out-of-band from the network. I can easily imagine tying together FireBreak with your ticketing system to only physically connect the management planes during defined change windows, making them unavailable even to the most privileged attacker without going through a documented process. “Operating in a so-called ‘post-breach era’, the security industry seems resigned to the idea that cyber-attacks are a matter of ‘when’ and not ‘if’. At Goldilock, we wanted to find a way to empower individuals and organisations to take more accountability and control over what happens to their data. Our flagship product, FireBreak, was born out of this idea. Its hardware-based approach enables users to physically segment all digital assets, from LLMs to entire networks, remotely, instantly and without using the internet. This allows users to physically connect and disconnect when required, from wherever they are in the world, hiding any assets from view and enhancing their existing depth of defence, including against AI, which is essentially just a type of software. Ultimately, we want people to rethink what needs to be kept online and see a move away from the "always-on" model that can leave sensitive data exposed. Because any data kept online is at risk of being breached. With more and more companies training their own LLM models in-house, a new realm of security considerations needs to be made. Network segmentation should be part of a holistic cybersecurity strategy that keeps bad actors out and ensures they can be stopped in their tracks if they do breach external parameters." -- Tony Hasek, CEO and Co-Founder of Goldilock So how does this help with the LLM kidnappings? LLM models are big. No one is going to clone one in seconds. They can also be used asynchronously - they don’t depend on a constant connection to generate a response to a prompt and could easily reconnect and send it when finished instead of working in an interactive session. There is no need for a user to have an active session to the LLM while they’re generating a prompt. There’s no need for them to have an active connection while they’re waiting for the response to be generated. Connecting only for the fraction of a second needed to send a prompt or receive the response is one, very effective, way to minimise the exposure time to threats. This disconnect/reconnect happens too quickly for humans to be aware of any delay, and LLMs have very few use cases which are time critical on the level of microseconds. It’s not the only layer of security to apply, and there are many other ways it can be applied, but it’s definitely one worth thinking about. It sounds like science fiction, but with all the hype around AI, the danger of ‘kidnapping’ is worth talking about. It goes like this - companies who can afford to build their own internal LLMs throw all of their valuable IP (intellectual property, covering everything from trade secret designs to marketing campaigns and product strategies) into the model for it to generate relevant responses. Essentially, while it’s still a non-sentient AI model, it’s also a repository of all the most valuable information the company has. This makes it a fantastic target for a criminal attacker, or even an unethical competitor. If it can be poisoned to generate bad responses, cloned to give the attacker more insider knowledge than they know what to do with, or even somehow locked down for ransom, then it can do a huge amount of damage to the company. Companies struggle to secure their systems, with regular headlines showing large enterprises being breached. An LLM model, containing everything about the company, is going to quickly become a favoured target for virtual ‘kidnapping.’ Whether it’s a case of adapting ransomware to encrypt models, exfiltrating them and destroying the local copy, or subverting them into an insider threat (say, if the LLM has been integrated with the company’s invoicing and finance systems without effective human oversight), the potential for harm is dramatic. Making it worse, the value of these models will come from their availability and accessibility within the company. If no one can use them, they’re nothing but a resource sink. They must be used effectively to have value, and that means they must be accessible. How do we match the need for availability with the need for security on these systems? Is Software Security Enough? Maybe software-defined networks could be a solution? The problem is that any software solution is inherently vulnerable to compromise. And if we’re talking about an LLM which has been integrated with administrative systems (this is already being done, the ethics and risks of this are a whole article in themselves - maybe a book), then it would be simplicity itself for a malicious party to prompt the AI to create a way in for further attacks. Software solutions, and classic devices such as firewalls and data diodes, definitely have a place in a secure AI system design, but something with so much value to a company justifies a much more absolute approach. If we go old-school, what we’d talk about as the last resort for any attack is pulling the plug. Ultimately, unless an attacker can change the laws of physics (or is sitting inside the data centre, which is unlikely) unplugging the network is pretty unbeatable. The problem is that unplugging and reconnecting the network takes time - making a phone call to your network engineer to plug it in or out every time you want to send an authorised prompt doesn’t seem a great option. The Goldilock FireBreak I recently came across a security device which impressed me, which doesn’t happen often these days. It wasn’t because of its brand new quantum dark web AI firewall technology, as so many vendors advertise these days. Instead it was because it’s a company which has taken a very old idea, thought about it, and brought it bang up to date in a way that opens up a lot of possibilities for secure network topologies. The approach is simple, and pretty unbeatable (obviously nothing is 100% secure, but the attack vectors against a physical disconnect are vanishingly sparse). Essentially the FireBreak (as opposed to firewall, of course) unplugs the network cable on command - or plugs it back in. It’s not quite having someone on-call in the data centre to manipulate cables on demand, but that’s an easy way to think about it - except the person can plug or unplug the cables in a fraction of a second in response to prompts from any method you choose. FireBreak Often management networks are separated only by a firewall, whereas FireBreak itself has a control plane completely out-of-band from the network. I can easily imagine tying together FireBreak with your ticketing system to only physically connect the management planes during defined change windows, making them unavailable even to the most privileged attacker without going through a documented process. “Operating in a so-called ‘post-breach era’, the security industry seems resigned to the idea that cyber-attacks are a matter of ‘when’ and not ‘if’. At Goldilock, we wanted to find a way to empower individuals and organisations to take more accountability and control over what happens to their data. Our flagship product, FireBreak, was born out of this idea. Its hardware-based approach enables users to physically segment all digital assets, from LLMs to entire networks, remotely, instantly and without using the internet. “Operating in a so-called ‘post-breach era’, the security industry seems resigned to the idea that cyber-attacks are a matter of ‘ when’ and not ‘ if’ . At Goldilock, we wanted to find a way to empower individuals and organisations to take more accountability and control over what happens to their data. Our flagship product, FireBreak, was born out of this idea. Its hardware-based approach enables users to physically segment all digital assets, from LLMs to entire networks, remotely, instantly and without using the internet. when’ if’ This allows users to physically connect and disconnect when required, from wherever they are in the world, hiding any assets from view and enhancing their existing depth of defence, including against AI, which is essentially just a type of software. This allows users to physically connect and disconnect when required, from wherever they are in the world, hiding any assets from view and enhancing their existing depth of defence, including against AI, which is essentially just a type of software. Ultimately, we want people to rethink what needs to be kept online and see a move away from the "always-on" model that can leave sensitive data exposed. Because any data kept online is at risk of being breached. With more and more companies training their own LLM models in-house, a new realm of security considerations needs to be made. Network segmentation should be part of a holistic cybersecurity strategy that keeps bad actors out and ensures they can be stopped in their tracks if they do breach external parameters." Ultimately, we want people to rethink what needs to be kept online and see a move away from the "always-on" model that can leave sensitive data exposed. Because any data kept online is at risk of being breached. With more and more companies training their own LLM models in-house, a new realm of security considerations needs to be made. Network segmentation should be part of a holistic cybersecurity strategy that keeps bad actors out and ensures they can be stopped in their tracks if they do breach external parameters." -- Tony Hasek, CEO and Co-Founder of Goldilock -- Tony Hasek, CEO and Co-Founder of Goldilock So how does this help with the LLM kidnappings? LLM models are big. No one is going to clone one in seconds. They can also be used asynchronously - they don’t depend on a constant connection to generate a response to a prompt and could easily reconnect and send it when finished instead of working in an interactive session. There is no need for a user to have an active session to the LLM while they’re generating a prompt. There’s no need for them to have an active connection while they’re waiting for the response to be generated. Connecting only for the fraction of a second needed to send a prompt or receive the response is one, very effective, way to minimise the exposure time to threats. This disconnect/reconnect happens too quickly for humans to be aware of any delay, and LLMs have very few use cases which are time critical on the level of microseconds. It’s not the only layer of security to apply, and there are many other ways it can be applied, but it’s definitely one worth thinking about.

Lock Up Your LLMs: Pulling the Plug

আপনার LLMs লক আপ করুন: প্লাগ টানা

Sperren Sie Ihre LLMs: Den Stecker ziehen

Bloquee sus LLM: desconecte

Verrouillez vos LLM : débranchez-vous

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Yüksek Lisans Derecelerinizi Kilitleyin: Fişi Çekmek

Khóa LLM của bạn: Rút phích cắm

锁定你的法学硕士 (LLM)：拔掉插头

Author:
(1) Attila Losonczi. Table of Links Abstract and 1 Introduction 1.1 Basic notions and notations 1.2 Basic definitions from [7] and [8] 2 Generalized integral 2.1 Multiplication on [0, +∞) × [−∞, +∞] 2.2 Measurability 2.3 The integral of functions taking values in [0, +∞) × [0, +∞) 3 Applications 4 References Abstract We go on to widen the scope of the previously defined Hausdorff-integral in the sense that we extend it to functions taking values in [0, +∞) × [0, +∞). In all our intentions, we follow the same attitude that we had in our previous investigations, i.e. we work in the realm of Hausdorff dimension and measure. 1 Introduction This paper can be considered as a continuation of the papers [7] and [8]. For original intentions, aims and motivation, we suggest that the reader should consult to [7] and [8]. In [7] we defined the Hausdorff-integral on R for real functions, then in [8] we generalized it for real functions on so-called h-measure spaces and found connection between the two integral notions. We can go on generalizing and define the integral of functions whose values are taken from [0, +∞)×[0, +∞) and are defined on h-measure spaces. Our applications will be based on the integral of such functions. The new integral has the usual properties, e.g. it is a linear functional (homogeneous and additive), monotone, it provides an h-measure, etc. However this generalization of the integral has some flaws. It is not true anymore that if fn → f, (0, 0) ≤ fn ≤ fn+1 (n ∈ N), then (H)R K fn dµ → (H)R K f dµ. It is a consequence of the fact that the topological space [0, +∞) × [0, +∞] is not separable. It is not true either that every measurable function is a limit of simple functions, therefore in some of the proofs, different, more sophisticated methods have to be applied. The structure of the paper is the following. First, we define a multiplication in [0, +∞)×[−∞, +∞], as it is essential for the integral. Afterwards, we define the new integral for simple functions (some call them step functions) and analyze its properties. In the next step, we extend the integral for nonnegative measurable functions and again we derive its properties. In many of the cases, our proofs follow the usual arguments however we always have to listen to the slight but in some cases important differences. Finally, we present some applications which are sophisticated deficiency measurements. This paper is available on arxiv under CC BY-NC-ND 4.0 DEED license. Author: (1) Attila Losonczi. Author: Author: (1) Attila Losonczi. Table of Links Abstract and 1 Introduction Abstract and 1 Introduction 1.1 Basic notions and notations 1.1 Basic notions and notations 1.2 Basic definitions from [7] and [8] 1.2 Basic definitions from [7] and [8] 2 Generalized integral 2.1 Multiplication on [0, +∞) × [−∞, +∞] 2.1 Multiplication on [0, +∞) × [−∞, +∞] 2.2 Measurability 2.2 Measurability 2.3 The integral of functions taking values in [0, +∞) × [0, +∞) 2.3 The integral of functions taking values in [0, +∞) × [0, +∞) 3 Applications 3 Applications 4 References 4 References Abstract We go on to widen the scope of the previously defined Hausdorff-integral in the sense that we extend it to functions taking values in [0, +∞) × [0, +∞). In all our intentions, we follow the same attitude that we had in our previous investigations, i.e. we work in the realm of Hausdorff dimension and measure. 1 Introduction This paper can be considered as a continuation of the papers [7] and [8]. For original intentions, aims and motivation, we suggest that the reader should consult to [7] and [8]. In [7] we defined the Hausdorff-integral on R for real functions, then in [8] we generalized it for real functions on so-called h-measure spaces and found connection between the two integral notions. We can go on generalizing and define the integral of functions whose values are taken from [0, +∞)×[0, +∞) and are defined on h-measure spaces. Our applications will be based on the integral of such functions. The new integral has the usual properties, e.g. it is a linear functional (homogeneous and additive), monotone, it provides an h-measure, etc. However this generalization of the integral has some flaws. It is not true anymore that if fn → f, (0, 0) ≤ fn ≤ fn+1 (n ∈ N), then (H)R K fn dµ → (H)R K f dµ. It is a consequence of the fact that the topological space [0, +∞) × [0, +∞] is not separable. It is not true either that every measurable function is a limit of simple functions, therefore in some of the proofs, different, more sophisticated methods have to be applied. The structure of the paper is the following. First, we define a multiplication in [0, +∞)×[−∞, +∞], as it is essential for the integral. Afterwards, we define the new integral for simple functions (some call them step functions) and analyze its properties. In the next step, we extend the integral for nonnegative measurable functions and again we derive its properties. In many of the cases, our proofs follow the usual arguments however we always have to listen to the slight but in some cases important differences. Finally, we present some applications which are sophisticated deficiency measurements. This paper is available on arxiv under CC BY-NC-ND 4.0 DEED license. This paper is available on arxiv under CC BY-NC-ND 4.0 DEED license. available on arxiv

Generalized Hausdorff Integral and Its Applications: Abstract and Introduction

Breaking Down Organizational Barriers to Accelerate Software Development

সফ্টওয়্যার বিকাশকে ত্বরান্বিত করতে সাংগঠনিক বাধাগুলি ভেঙে ফেলা

Abbau organisatorischer Barrieren zur Beschleunigung der Softwareentwicklung

Derribar barreras organizacionales para acelerar el desarrollo de software

Supprimer les barrières organisationnelles pour accélérer le développement de logiciels

सॉफ्टवेयर विकास में तेजी लाने के लिए संगठनात्मक बाधाओं को तोड़ना

組織的障壁を打破しソフトウェア開発を加速する

조직의 장벽을 허물어 소프트웨어 개발 가속화

Quebrando barreiras organizacionais para acelerar o desenvolvimento de software

Разрушение организационных барьеров для ускорения разработки программного обеспечения

Yazılım Geliştirmeyi Hızlandırmak için Organizasyonel Engelleri Yıkmak

Phá vỡ các rào cản tổ chức để tăng tốc phát triển phần mềm

打破组织障碍，加速软件开发

Load Balancing For High Performance Computing
Using Quantum Annealing: Conclusions and Outlook

Real-Time Data Processing with Kafka Streams: Simplifying Stream Processing Applications

Machine Learning Enhanced Characterization of Labyrinthine Structures in Bi-doped Films

Authors:
(1) Agustin Moreno;
(2) Francesco Ruscelli. Table of Links Abstract
Introduction
Preliminaries
The B-signature
GIT sequence: low dimensions
GIT sequence: arbitrary dimension
Appendix A. Stability, the Krein–Moser theorem, and refinements and References Abstract We address the general problem of studying linear stability and bifurcations of periodic orbits for Hamiltonian systems of arbitrary degrees of freedom. We study the topology of the GIT sequence introduced by the first author and Urs frauenfelder in [FM], in arbitrary dimension. In particular, we note that the combinatorics encoding the linear stability of periodic orbits is governed by a quotient of the associahedron. Our approach gives a topological/combinatorial proof of the classical Krein–Moser theorem, and refines it for the case of symmetric orbits. This paper is available on arxiv under CC BY-NC-SA 4.0 DEED license. Authors: (1) Agustin Moreno; (2) Francesco Ruscelli. Authors: Authors: (1) Agustin Moreno; (2) Francesco Ruscelli. Table of Links Abstract Introduction Preliminaries The B-signature GIT sequence: low dimensions GIT sequence: arbitrary dimension Appendix A. Stability, the Krein–Moser theorem, and refinements and References Abstract Abstract Introduction Introduction Preliminaries Preliminaries The B-signature The B-signature GIT sequence: low dimensions GIT sequence: low dimensions GIT sequence: arbitrary dimension GIT sequence: arbitrary dimension Appendix A. Stability, the Krein–Moser theorem, and refinements and References Appendix A. Stability, the Krein–Moser theorem, and refinements and References Abstract We address the general problem of studying linear stability and bifurcations of periodic orbits for Hamiltonian systems of arbitrary degrees of freedom. We study the topology of the GIT sequence introduced by the first author and Urs frauenfelder in [FM], in arbitrary dimension. In particular, we note that the combinatorics encoding the linear stability of periodic orbits is governed by a quotient of the associahedron. Our approach gives a topological/combinatorial proof of the classical Krein–Moser theorem, and refines it for the case of symmetric orbits. This paper is available on arxiv under CC BY-NC-SA 4.0 DEED license. This paper is available on arxiv under CC BY-NC-SA 4.0 DEED license. available on arxiv

Addressing the General Problem of Studying Linear Stability and Bifurcations of Periodic Orbits

রৈখিক স্থিতিশীলতা এবং পর্যায়ক্রমিক কক্ষপথের বিভাজন অধ্যয়নের সাধারণ সমস্যা সমাধান করা

Behandlung des allgemeinen Problems der Untersuchung linearer Stabilität und Bifurkationen periodischer Bahnen

Abordar el problema general del estudio de la estabilidad lineal y las bifurcaciones de órbitas periódicas

Aborder le problème général de l'étude de la stabilité linéaire et des bifurcations des orbites périodiques

आवर्त कक्षाओं के रैखिक स्थायित्व और द्विभाजन के अध्ययन की सामान्य समस्या का समाधान

周期軌道の線形安定性と分岐を研究する一般的な問題への取り組み

선형 안정성과 주기 궤도 분기 연구의 일반적인 문제 해결

Resolvendo o problema geral do estudo da estabilidade linear e bifurcações de órbitas periódicas

К общей проблеме исследования линейной устойчивости и бифуркаций периодических орбит

Periyodik Yörüngelerin Doğrusal Kararlılığı ve Çatallanmalarının İncelenmesine İlişkin Genel Sorunun Ele Alınması

Giải quyết vấn đề chung của việc nghiên cứu sự ổn định tuyến tính và sự phân nhánh của quỹ đạo định kỳ

解决研究周期轨道的线性稳定性和分岔的一般问题

Assessing VASP Solvency For Cryptoassets: Measuring VASPs Cryptoasset Holdings

Author:
(1) Yuki Koto Table of Links Abstract and Intro
Genus-zero Gromov-Witten Theory
Toric Bundles
Lagrangian cones of Toric bundles
Mirror theorem for a product of projectives bundles
Mirror Theorem for Toric Bundles
Appendix A. Equivariant Fourier Transformation and References Appendix A. Equivariant Fourier transformation Note that this is a straightforward generalization of [20, Conjecture 1.7]. References Dan Abramovich, Tom Graber, and Angelo Vistoli, Gromov-Witten theory of Deligne-Mumford stacks, Amer. J. Math. 130 (2008), no. 5, 1337–1398.


M. F. Atiyah and R. Bott, The moment map and equivariant cohomology, Topology 23 (1984), no. 1, 1–28.


K. Behrend, Gromov-Witten invariants in algebraic geometry, Invent. Math. 127 (1997), no. 3, 601–617.


Nicole Berline and Mich`ele Vergne, Classes caract´eristiques ´equivariantes. Formule de localisation en cohomologie ´equivariante, C. R. Acad. Sci. Paris S´er. I Math. 295 (1982), no. 9, 539–541.


Jeff Brown, Gromov-Witten invariants of toric fibrations, Int. Math. Res. Not. IMRN (2014), no. 19, 5437–5482.


Charles Cadman, Using stacks to impose tangency conditions on curves, Amer. J. Math. 129 (2007), no. 2, 405–427.


Tom Coates, Alessio Corti, Hiroshi Iritani, and Hsian-Hua Tseng, Computing genus-zero twisted GromovWitten invariants, Duke Math. J. 147 (2009), no. 3, 377–438.


_________, A mirror theorem for toric stacks, Compos. Math. 151 (2015), no. 10, 1878–1912.


Tom Coates and Alexander Givental, Quantum Riemann-Roch, Lefschetz and Serre, Ann. of Math. (2) 165 (2007), no. 1, 15–53.


Artur Elezi, A mirror conjecture for projective bundles, Int. Math. Res. Not. (2005), no. 55, 3445–3458.


Honglu Fan and Yuan-Pin Lee, On Gromov-Witten theory of projective bundles, Michigan Math. J. 69 (2020), no. 1, 153–178.


William Fulton, Intersection theory, second ed., Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge. A Series of Modern Surveys in Mathematics [Results in Mathematics and Related Areas. 3rd Series. A Series of Modern Surveys in Mathematics], vol. 2, Springer-Verlag, Berlin, 1998.


Alexander Givental, A mirror theorem for toric complete intersections, Topological field theory, primitive forms and related topics (Kyoto, 1996), Progr. Math., vol. 160, Birkh¨auser Boston, Boston, MA, 1998, pp. 141–175.


Alexander B. Givental, Symplectic geometry of Frobenius structures, Frobenius manifolds, Aspects Math., vol. E36, Friedr. Vieweg, Wiesbaden, 2004, pp. 91–112.


T. Graber and R. Pandharipande, Localization of virtual classes, Invent. Math. 135 (1999), no. 2, 487–518.


Tam´as Hausel and Bernd Sturmfels, Toric hyperK¨ahler varieties, Doc. Math. 7 (2002), 495–534.


Hiroshi Iritani, An integral structure in quantum cohomology and mirror symmetry for toric orbifolds, Adv. Math. 222 (2009), no. 3, 1016–1079.


_________, Quantum cohomology and periods, Ann. Inst. Fourier (Grenoble) 61 (2011), no. 7, 2909–2958.


_________, Shift operators and toric mirror theorem, Geom. Topol. 21 (2017), no. 1, 315–343.


Hiroshi Iritani, Quantum cohomology of blowups, 2023.


Hiroshi Iritani and Yuki Koto, Quantum cohomology of projective bundles, 2023, arXiv:2307.03696 [math.AG].


Hiroshi Iritani and Fumihiko Sanda, private communication.


Yunfeng Jiang, Hsian-Hua Tseng, and Fenglong You, The quantum orbifold cohomology of toric stack bundles, Lett. Math. Phys. 107 (2017), no. 3, 439–465.


Bumsig Kim, Andrew Kresch, and Tony Pantev, Functoriality in intersection theory and a conjecture of Cox, Katz, and Lee, J. Pure Appl. Algebra 179 (2003), no. 1-2, 127–136.


Chiu-Chu Melissa Liu, Localization in Gromov-Witten theory and orbifold Gromov-Witten theory, Handbook of moduli. Vol. II, Adv. Lect. Math. (ALM), vol. 25, Int. Press, Somerville, MA, 2013, pp. 353–425.


Rahul Pandharipande, Rational curves on hypersurfaces (after A. Givental), no. 252, 1998, S´eminaire Bourbaki. Vol. 1997/98, pp. Exp. No. 848, 5, 307–340.


Constantin Teleman, Gauge theory and mirror symmetry, Proceedings of the International Congress of Mathematicians—Seoul 2014. Vol. II, Kyung Moon Sa, Seoul, 2014, pp. 1309–1332.


Valentin Tonita, Twisted orbifold Gromov-Witten invariants, Nagoya Math. J. 213 (2014), 141–187.


Angelo Vistoli, Intersection theory on algebraic stacks and on their moduli spaces, Invent. Math. 97 (1989), no. 3, 613–670. This paper is available on arxiv under CC 4.0 license. Author: (1) Yuki Koto Author: Author: (1) Yuki Koto Table of Links Abstract and Intro Genus-zero Gromov-Witten Theory Toric Bundles Lagrangian cones of Toric bundles Mirror theorem for a product of projectives bundles Mirror Theorem for Toric Bundles Appendix A. Equivariant Fourier Transformation and References Abstract and Intro Abstract and Intro Genus-zero Gromov-Witten Theory Genus-zero Gromov-Witten Theory Toric Bundles Toric Bundles Lagrangian cones of Toric bundles Lagrangian cones of Toric bundles Mirror theorem for a product of projectives bundles Mirror theorem for a product of projectives bundles Mirror Theorem for Toric Bundles Mirror Theorem for Toric Bundles Appendix A. Equivariant Fourier Transformation and References Appendix A. Equivariant Fourier Transformation and References Appendix A. Equivariant Fourier transformation Note that this is a straightforward generalization of [20, Conjecture 1.7]. References Dan Abramovich, Tom Graber, and Angelo Vistoli, Gromov-Witten theory of Deligne-Mumford stacks, Amer. J. Math. 130 (2008), no. 5, 1337–1398. M. F. Atiyah and R. Bott, The moment map and equivariant cohomology, Topology 23 (1984), no. 1, 1–28. K. Behrend, Gromov-Witten invariants in algebraic geometry, Invent. Math. 127 (1997), no. 3, 601–617. Nicole Berline and Mich`ele Vergne, Classes caract´eristiques ´equivariantes. Formule de localisation en cohomologie ´equivariante, C. R. Acad. Sci. Paris S´er. I Math. 295 (1982), no. 9, 539–541. Jeff Brown, Gromov-Witten invariants of toric fibrations, Int. Math. Res. Not. IMRN (2014), no. 19, 5437–5482. Charles Cadman, Using stacks to impose tangency conditions on curves, Amer. J. Math. 129 (2007), no. 2, 405–427. Tom Coates, Alessio Corti, Hiroshi Iritani, and Hsian-Hua Tseng, Computing genus-zero twisted GromovWitten invariants, Duke Math. J. 147 (2009), no. 3, 377–438. _________, A mirror theorem for toric stacks, Compos. Math. 151 (2015), no. 10, 1878–1912. Tom Coates and Alexander Givental, Quantum Riemann-Roch, Lefschetz and Serre, Ann. of Math. (2) 165 (2007), no. 1, 15–53. Artur Elezi, A mirror conjecture for projective bundles, Int. Math. Res. Not. (2005), no. 55, 3445–3458. Honglu Fan and Yuan-Pin Lee, On Gromov-Witten theory of projective bundles, Michigan Math. J. 69 (2020), no. 1, 153–178. William Fulton, Intersection theory, second ed., Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge. A Series of Modern Surveys in Mathematics [Results in Mathematics and Related Areas. 3rd Series. A Series of Modern Surveys in Mathematics], vol. 2, Springer-Verlag, Berlin, 1998. Alexander Givental, A mirror theorem for toric complete intersections, Topological field theory, primitive forms and related topics (Kyoto, 1996), Progr. Math., vol. 160, Birkh¨auser Boston, Boston, MA, 1998, pp. 141–175. Alexander B. Givental, Symplectic geometry of Frobenius structures, Frobenius manifolds, Aspects Math., vol. E36, Friedr. Vieweg, Wiesbaden, 2004, pp. 91–112. T. Graber and R. Pandharipande, Localization of virtual classes, Invent. Math. 135 (1999), no. 2, 487–518. Tam´as Hausel and Bernd Sturmfels, Toric hyperK¨ahler varieties, Doc. Math. 7 (2002), 495–534. Hiroshi Iritani, An integral structure in quantum cohomology and mirror symmetry for toric orbifolds, Adv. Math. 222 (2009), no. 3, 1016–1079. _________, Quantum cohomology and periods, Ann. Inst. Fourier (Grenoble) 61 (2011), no. 7, 2909–2958. _________, Shift operators and toric mirror theorem, Geom. Topol. 21 (2017), no. 1, 315–343. Hiroshi Iritani, Quantum cohomology of blowups, 2023. Hiroshi Iritani and Yuki Koto, Quantum cohomology of projective bundles, 2023, arXiv:2307.03696 [math.AG]. Hiroshi Iritani and Fumihiko Sanda, private communication. Yunfeng Jiang, Hsian-Hua Tseng, and Fenglong You, The quantum orbifold cohomology of toric stack bundles, Lett. Math. Phys. 107 (2017), no. 3, 439–465. Bumsig Kim, Andrew Kresch, and Tony Pantev, Functoriality in intersection theory and a conjecture of Cox, Katz, and Lee, J. Pure Appl. Algebra 179 (2003), no. 1-2, 127–136. Chiu-Chu Melissa Liu, Localization in Gromov-Witten theory and orbifold Gromov-Witten theory, Handbook of moduli. Vol. II, Adv. Lect. Math. (ALM), vol. 25, Int. Press, Somerville, MA, 2013, pp. 353–425. Rahul Pandharipande, Rational curves on hypersurfaces (after A. Givental), no. 252, 1998, S´eminaire Bourbaki. Vol. 1997/98, pp. Exp. No. 848, 5, 307–340. Constantin Teleman, Gauge theory and mirror symmetry, Proceedings of the International Congress of Mathematicians—Seoul 2014. Vol. II, Kyung Moon Sa, Seoul, 2014, pp. 1309–1332. Valentin Tonita, Twisted orbifold Gromov-Witten invariants, Nagoya Math. J. 213 (2014), 141–187. Angelo Vistoli, Intersection theory on algebraic stacks and on their moduli spaces, Invent. Math. 97 (1989), no. 3, 613–670. Dan Abramovich, Tom Graber, and Angelo Vistoli, Gromov-Witten theory of Deligne-Mumford stacks, Amer. J. Math. 130 (2008), no. 5, 1337–1398. Dan Abramovich, Tom Graber, and Angelo Vistoli, Gromov-Witten theory of Deligne-Mumford stacks, Amer. J. Math. 130 (2008), no. 5, 1337–1398. M. F. Atiyah and R. Bott, The moment map and equivariant cohomology, Topology 23 (1984), no. 1, 1–28. M. F. Atiyah and R. Bott, The moment map and equivariant cohomology, Topology 23 (1984), no. 1, 1–28. K. Behrend, Gromov-Witten invariants in algebraic geometry, Invent. Math. 127 (1997), no. 3, 601–617. K. Behrend, Gromov-Witten invariants in algebraic geometry, Invent. Math. 127 (1997), no. 3, 601–617. Nicole Berline and Mich`ele Vergne, Classes caract´eristiques ´equivariantes. Formule de localisation en cohomologie ´equivariante, C. R. Acad. Sci. Paris S´er. I Math. 295 (1982), no. 9, 539–541. Nicole Berline and Mich`ele Vergne, Classes caract´eristiques ´equivariantes. Formule de localisation en cohomologie ´equivariante, C. R. Acad. Sci. Paris S´er. I Math. 295 (1982), no. 9, 539–541. Jeff Brown, Gromov-Witten invariants of toric fibrations, Int. Math. Res. Not. IMRN (2014), no. 19, 5437–5482. Jeff Brown, Gromov-Witten invariants of toric fibrations, Int. Math. Res. Not. IMRN (2014), no. 19, 5437–5482. Charles Cadman, Using stacks to impose tangency conditions on curves, Amer. J. Math. 129 (2007), no. 2, 405–427. Charles Cadman, Using stacks to impose tangency conditions on curves, Amer. J. Math. 129 (2007), no. 2, 405–427. Tom Coates, Alessio Corti, Hiroshi Iritani, and Hsian-Hua Tseng, Computing genus-zero twisted GromovWitten invariants, Duke Math. J. 147 (2009), no. 3, 377–438. Tom Coates, Alessio Corti, Hiroshi Iritani, and Hsian-Hua Tseng, Computing genus-zero twisted GromovWitten invariants, Duke Math. J. 147 (2009), no. 3, 377–438. _________, A mirror theorem for toric stacks, Compos. Math. 151 (2015), no. 10, 1878–1912. _________ , A mirror theorem for toric stacks, Compos. Math. 151 (2015), no. 10, 1878–1912. _________ Tom Coates and Alexander Givental, Quantum Riemann-Roch, Lefschetz and Serre, Ann. of Math. (2) 165 (2007), no. 1, 15–53. Tom Coates and Alexander Givental, Quantum Riemann-Roch, Lefschetz and Serre, Ann. of Math. (2) 165 (2007), no. 1, 15–53. Artur Elezi, A mirror conjecture for projective bundles, Int. Math. Res. Not. (2005), no. 55, 3445–3458. Artur Elezi, A mirror conjecture for projective bundles, Int. Math. Res. Not. (2005), no. 55, 3445–3458. Honglu Fan and Yuan-Pin Lee, On Gromov-Witten theory of projective bundles, Michigan Math. J. 69 (2020), no. 1, 153–178. Honglu Fan and Yuan-Pin Lee, On Gromov-Witten theory of projective bundles, Michigan Math. J. 69 (2020), no. 1, 153–178. William Fulton, Intersection theory, second ed., Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge. A Series of Modern Surveys in Mathematics [Results in Mathematics and Related Areas. 3rd Series. A Series of Modern Surveys in Mathematics], vol. 2, Springer-Verlag, Berlin, 1998. William Fulton, Intersection theory, second ed., Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge. A Series of Modern Surveys in Mathematics [Results in Mathematics and Related Areas. 3rd Series. A Series of Modern Surveys in Mathematics], vol. 2, Springer-Verlag, Berlin, 1998. Alexander Givental, A mirror theorem for toric complete intersections, Topological field theory, primitive forms and related topics (Kyoto, 1996), Progr. Math., vol. 160, Birkh¨auser Boston, Boston, MA, 1998, pp. 141–175. Alexander Givental, A mirror theorem for toric complete intersections, Topological field theory, primitive forms and related topics (Kyoto, 1996), Progr. Math., vol. 160, Birkh¨auser Boston, Boston, MA, 1998, pp. 141–175. Alexander B. Givental, Symplectic geometry of Frobenius structures, Frobenius manifolds, Aspects Math., vol. E36, Friedr. Vieweg, Wiesbaden, 2004, pp. 91–112. Alexander B. Givental, Symplectic geometry of Frobenius structures, Frobenius manifolds, Aspects Math., vol. E36, Friedr. Vieweg, Wiesbaden, 2004, pp. 91–112. T. Graber and R. Pandharipande, Localization of virtual classes, Invent. Math. 135 (1999), no. 2, 487–518. T. Graber and R. Pandharipande, Localization of virtual classes, Invent. Math. 135 (1999), no. 2, 487–518. Tam´as Hausel and Bernd Sturmfels, Toric hyperK¨ahler varieties, Doc. Math. 7 (2002), 495–534. Tam´as Hausel and Bernd Sturmfels, Toric hyperK¨ahler varieties, Doc. Math. 7 (2002), 495–534. Hiroshi Iritani, An integral structure in quantum cohomology and mirror symmetry for toric orbifolds, Adv. Math. 222 (2009), no. 3, 1016–1079. Hiroshi Iritani, An integral structure in quantum cohomology and mirror symmetry for toric orbifolds, Adv. Math. 222 (2009), no. 3, 1016–1079. _________, Quantum cohomology and periods, Ann. Inst. Fourier (Grenoble) 61 (2011), no. 7, 2909–2958. _________ , Quantum cohomology and periods, Ann. Inst. Fourier (Grenoble) 61 (2011), no. 7, 2909–2958. _________ _________, Shift operators and toric mirror theorem, Geom. Topol. 21 (2017), no. 1, 315–343. _________ , Shift operators and toric mirror theorem, Geom. Topol. 21 (2017), no. 1, 315–343. _________ Hiroshi Iritani, Quantum cohomology of blowups, 2023. Hiroshi Iritani, Quantum cohomology of blowups, 2023. Hiroshi Iritani and Yuki Koto, Quantum cohomology of projective bundles, 2023, arXiv:2307.03696 [math.AG]. 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