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  Language-Theoretic Security

  Language-theoretic security, or LangSec, is an approach to software security that focuses on input handling, complexity, and program design as strategies to improve the verifiability of computer programs. It was introduced in 2005 by Robert J. Hansen and Meredith L. Patterson at BlackHat and in 2011 by Len Sassaman and Patterson. It aims to create a formal description of which software is likely to have security vulnerabilities of particular classes, and why. It considers programs to have an inherent parser component, whether or not explicit, composed of that part of the program which operates on external input before that input is fully parsed. A central hypothesis of language-theoretic security is that vulnerabilities in software increase according to the computational power of the notional input-accepting automaton equivalent to this parser, using the definitions of automata theory. The lower bound on this computational power is the input language complexity of the program. The extent to which reducing this complexity is possible is a function of the specification of the communication protocol or file format the program takes as input. == Parsing as a security mechanism == The behaviour of a program is defined with reference to its expected input. Unexpected input being used by a program is a factor in numerous security bugs, including the so-called Android master key vulnerability (CVE-2013-4787), because accepting unexpected input renders the program's specification ambiguous. In that instance, the unexpected ambiguity came in the form of a ZIP file with duplicate filenames. If a program fully parses its input and only acts on input that unambiguously meets the specification, it follows that the program will avoid these types of vulnerabilities. This is an intentional inversion of the Postel principle. Accepting only unambiguous and valid input is a more formal requirement than input validation or sanitization, and narrows the number of possible but unanticipated program states that can be induced in an application via user input. Conversely, failure to do this is associated with security vulnerabilities. Input sanitization in particular is held to be an inadequate approach to avoiding malicious input because it inherently ignores context-sensitive properties of the input; it can therefore result in paradoxical effects, such as sanitization code activating otherwise inert cross-site scripting payloads in browsers. === Parser differentials === If the language of accepted program input is sufficiently simple, it is possible to verify that two implementations parse the same input language consistently. This is advantageous because it shows no parser differential exists between the two implementations. The requisite level of simplicity is theoretically that for which there is a solution to the equivalence problem. If the two parsers involved in CVE-2013-4787 were equivalent - that is, if they rendered the same output state given the same input state - the vulnerability could not have existed. One strategy for doing this is to publish machine-readable specifications of a format or protocol, and then use a parser generator to generate the parser code. An example of a parser generator built for this purpose is DaeDaLus. The combination of Lex with any of GNU Bison, ANTLR, or Yacc also accomplishes this. However, many parser generators allow the mixing of general purpose code with the parsing definitions, which weakens the guarantees provided by parsing. === Analysis of injection attacks === Injection attacks are generally the result of differences between the serializer (or "unparser") and the corresponding parser at a layer boundary in a system; therefore, they are a special case of parser differentials. In a SQL injection attack, for example, an attacker is able to cause the application with which they are interacting to serialize a SQL query that has different semantics than intended. In the simplest case where the payload ends a string and adds new code, the payload has crossed the code-data boundary in SQL. In language-theoretic security, this is treated as a bug in the serializer of the SQL query, which should instead be written in a way that constrains its possible outputs to those within the scope of the intended query. === Parser combinators === If a parser generator is not used, it is still possible to avoid implementation bugs by using parser combinator such as Nom to implement the parser code. This has the drawback of relying on a programmer correctly translating the specification into the language of the parser generator library, though this task is still less error-prone than hand-coding a parser. == Input format complexity == Complexity in computer programs is associated with security vulnerabilities. Within the domain of language-theoretic security, complexity is described with reference to the computational power of the abstract machine necessary to implement the program, or more particularly, to implement the parser for its input language. This complexity describes whether it is possible to show that there is no unintended or undesired functionality in the program which might be exploitable by an attacker. To be bounded in complexity, the program's input must be well-defined both in terms of form and of semantics. === Weird machines === A weird machine is a model of computation in a program that exists in parallel with, but is distinct from, the intended abstract model of computation in that program. Some classes of weird machine arise from the multi-layered nature of computer programs, or the context in which the programs run; others result from the unanticipated functionality a program has due to its complexity or to software bugs. The more complex the computation model of a program, the more likely it is to implement a weird machine. Depending on context, the weird machine may or may not be concretely useful for an attacker. Since the space of weird machines in the context of some program is the universe of all possible states that are not within the program's intended states, many exploited states including remote code execution and injection attacks belong to the domain of weird machines. A reduction in weird machines is therefore a likely correlate with reduced program vulnerability. === SafeDocs project === SafeDocs is a DARPA project undertaken in 2018 to take existing file formats, create safer subsets of them, and develop programming tools to work for the safer formats. The initial test case for this was PDF. The purpose of creating safer subsets in this case is to lower the minimum bound on parser complexity so that it becomes possible to create tools that will generate correct, normative parsers for them. == Relation to programming languages == The analytic framework of language-theoretic security assumes programs to be virtual machines that execute their input. A document that is read by an application is in this sense a form of machine code, in a generalization of the data as code idea, following the automata theory description of parsers. === Type-safe programming languages === Parsing input and serializing output are operations that consume one data type and emit another. A programming language can therefore check that data is correctly parsed and contains the expected structure by checking data types, and correct serializing (or unparsing) can be implemented as operations on the data types that are relevant to the program's output. This approach can be used to show that the recognizer and unparser patterns have been implemented. It is also possible to implement type checking across a distributed system to enforce parsing and unparsing of the expected structures and to verify that the assumptions made in designing the compositional properties of a distributed system have been followed. === Memory-safe programming languages === In the general case, spatial memory correctness is undecidable. If any proof of spatial memory correctness is to be made, it is therefore necessary to bound the complexity of the code. Interpreted languages such as Java and Python effectively accomplish this via runtime bounds checking, and frameworks for runtime bounds checking also exist for C. The effect of these strategies for spatial memory correctness are to create a halt state in place of a spatial memory correctness violation; therefore, it can be shown that the program will not violate spatial memory correctness, but in exchange, it cannot be shown in the general case that programs will not have runtime bounds checking exceptions. Some programming languages, such as Rust, accomplish this using borrow checking. The borrow checker acts to assure spatial memory correctness by compile-time reference counting. Code for which spatial memory correctness cannot be shown to not be violated therefore does not compile, inherently limiting the complexity of the spatial memory correctness of the program to what is decidable. Thi

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  Behavior informatics

  Behavior informatics (BI) is the informatics of behaviors so as to obtain behavior intelligence and behavior insights. BI is a research method combining science and technology, specifically in the area of engineering. The purpose of BI includes analysis of current behaviors as well as the inference of future possible behaviors. This occurs through pattern recognition. Different from applied behavior analysis from the psychological perspective, BI builds computational theories, systems and tools to qualitatively and quantitatively model, represent, analyze, and manage behaviors of individuals, groups and/or organizations. BI is built on classic study of behavioral science, including behavior modeling, applied behavior analysis, behavior analysis, behavioral economics, and organizational behavior. Typical BI tasks consist of individual and group behavior formation, representation, computational modeling, analysis, learning, simulation, and understanding of behavior impact, utility, non-occurring behaviors, etc. for behavior intervention and management. The Behavior Informatics approach to data utilizes cognitive as well as behavioral data. By combining the data, BI has the potential to effectively illustrate the big picture when it comes to behavioral decisions and patterns. One of the goals of BI is also to be able to study human behavior while eliminating issues like self-report bias. This creates more reliable and valid information for research studies. == Behavior == From an Informatics perspective, a behavior consists of three key elements: actors (behavioral subjects and objects), operations (actions, activities) and interactions (relationships), and their properties. A behavior can be represented as a behavior vector, all behaviors of an actor or an actor group can be represented as behavior sequences and multi-dimensional behavior matrix. The following table explains some of the elements of behavior. Behavior Informatics takes into account behavior when analyzing business patterns and intelligence. The inclusion of behavior in these analyses provides prominent information on social and driving factors of patterns. == Applications == Behavior Informatics is being used in a variety of settings, including but not limited to health care management, telecommunications, marketing, and security. Behavior Informatics provides a manner in which to analyze and organize the many aspects that go into a person's health care needs and decisions. When it comes to business models, behavior informatics may be utilized for a similar role. Organizations implement behavior informatics to enhance business structure and regime, where it helps moderate ideal business decisions and situations.

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  Hidden layer

  In artificial neural networks, a hidden layer is a layer of artificial neurons that is neither an input layer nor an output layer. The simplest examples appear in multilayer perceptrons (MLP), as illustrated in the diagram. An MLP without any hidden layer is essentially just a linear model. With hidden layers and activation functions, however, nonlinearity is introduced into the model. In typical machine learning practice, the weights and biases are initialized, then iteratively updated during training via backpropagation.

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  Human-in-the-loop

  Human-in-the-loop (HITL) is used in multiple contexts. It can be defined as a model requiring human interaction. HITL is associated with modeling and simulation (M&S) in the live, virtual, and constructive taxonomy. HITL, along with the related human-on-the-loop, are also used in relation to lethal autonomous weapons. Further, HITL is used in the context of machine learning.It is also used in conversational AI to manage complex interactions that require human empathy. == Machine learning == In machine learning, HITL is used in the sense of humans aiding the computer in making the correct decisions in building a model. HITL improves machine learning over random sampling by selecting the most critical data needed to refine the model. == Simulation == In simulation, HITL models may conform to human factors requirements as in the case of a mockup. In this type of simulation, a human is always part of the simulation and consequently influences the outcome in such a way that is difficult if not impossible to reproduce exactly. HITL also readily allows for the identification of problems and requirements that may not be easily identified by other means of simulation. HITL is often referred to as an interactive simulation, which is a special kind of physical simulation in which physical simulations include human operators, such as in a flight or a driving simulator. === Benefits === Human-in-the-loop allows the user to change the outcome of an event or process. The immersion effectively contributes to a positive transfer of acquired skills into the real world. This can be demonstrated by trainees utilizing flight simulators in preparation to become pilots. HITL also allows for the acquisition of knowledge regarding how a new process may affect a particular event. Utilizing HITL allows participants to interact with realistic models and attempt to perform as they would in an actual scenario. HITL simulations bring to the surface issues that would not otherwise be apparent until after a new process has been deployed. A real-world example of HITL simulation as an evaluation tool is its usage by the Federal Aviation Administration (FAA) to allow air traffic controllers to test new automation procedures by directing the activities of simulated air traffic while monitoring the effect of the newly implemented procedures. As with most processes, there is always the possibility of human error, which can only be reproduced using HITL simulation. Although much can be done to automate systems, humans typically still need to take the information provided by a system to determine the next course of action based on their judgment and experience. Intelligent systems can only go so far in certain circumstances to automate a process; only humans in the simulation can accurately judge the final design. Tabletop simulation may be useful in the very early stages of project development for the purpose of collecting data to set broad parameters, but the important decisions require human-in-the-loop simulation. HITL reflects scenarios where human input remains essential despite advances in automation. === Within the virtual simulation taxonomy === Virtual simulations inject HITL in a central role by exercising motor control skills (e.g. flying an airplane), decision making skills (e.g. committing fire control resources to action), or communication skills (e.g. as members of a C4I team). === Examples === Flight simulators Driving simulators Marine simulators Video games Supply chain management simulators Digital puppetry === Misconceptions === Although human-in-the-loop simulation can include a computer simulation in the form of a synthetic environment, computer simulation is not necessarily a form of human-in-the-loop simulation, and is often considered as human-out-of-the loop simulation. In this particular case, a computer model’s behavior is modified according to a set of initial parameters. The results of the model differ from the results stemming from a true human-in-the-loop simulation because the results can easily be replicated time and time again, by simply providing identical parameters. == Weapons == === Taxonomy === Three classifications of the degree of human control of autonomous weapon systems were laid out by Bonnie Docherty in a 2012 Human Rights Watch report. human-in-the-loop: a human must instigate the action of the weapon (in other words not fully autonomous) human-on-the-loop: a human may abort an action human-out-of-the-loop: no human action is involved === Positive human action === In discussions of autonomous weapons and nuclear command and control, the phrase positive human action has been used alongside "human-in-the-loop" to emphasize that a human operator must affirmatively authorize the use of force. Descriptions of the United States Navy's Aegis Combat System have used the phrase in characterizing a requirement for affirmative human action to initiate live firing. A survey of autonomous weapons systems described the Aegis "Auto SM" mode as one in which "the system fully develops the engagement process however engagement requires positive human action". The phrase entered United States federal law in the National Defense Authorization Act for Fiscal Year 2025, which stipulates that artificial intelligence systems not compromise "the principle of requiring positive human actions in execution of decisions by the President with respect to the employment of nuclear weapons".

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  ByLock

  ByLock was a smartphone application that allowed users to communicate via a private, encrypted connection. It was launched in March 2014 on Google Play, Apple App Store The app was downloaded over 600,000 times from its launch in April 2014 until March 2016, when it was permanently shut down. The Turkish National Intelligence Organization (Turkish: Millî İstihbarat Teşkilatı, MİT) stated that the app was downloaded mainly in Turkey and the users were “Fetullahist Terror Organisation (FETÖ) which was formerly known as “Gülen movement” members. == Gülen Movement controversy == In Turkey, possession of the app is deemed evidence of membership in the Gülen Movement, which was allegedly connected to the failed Turkish coup d'état attempt in July 2016. Users of ByLock were deemed terrorists in Turkish courts. According to Deutsche Welle, of the 215,000 former ByLock users, an estimated 23,000 have been detained by Turkish authorities. Some believe that the MİT and other Turkish authorities manipulated the ByLock database in order to arrest suspected members of the Gülen Movement. Tuncay Beşikçi, a computer forensic expert in Turkey, emphasized that "the demands to investigate and analyze ByLock data from independent institutions are refused by the Turkish courts. But it is not normal". Tuncay Beşikçi believes that this application is precisely one of the channels for Gülen molecules to communicate and can also monitor the activities of other members of the organization. He also stated that the developers behind the Mor Beyin app, deliberately set a plan in motion that would put thousands of innocent people in prison as a cover for the Gülen movement. In December 2017, Turkish authorities revealed that almost half the people who had been prosecuted for having ByLock on their smartphones would have their legal cases reviewed, as they could have been redirected to the app without their knowledge. Following the failed coup attempt on 15 July 2016, the use of the ByLock messaging application by members of the Gülen Movement was the sole evidence in investigations and prosecutions to justify arrests and convictions for "membership in an armed terrorist organization." However, these decisions have been considered human rights violations by the European Court of Human Rights (ECHR), the United Nations Human Rights Committee, and the UN Working Group on Arbitrary Detention. Some of the relevant decisions include the following: === Decisions of the European Court of Human Rights === On 20 July 2021, in the case of Tekin Akgün v. Turkey, the European Court of Human Rights (ECHR) ruled that the use of the ByLock messaging application, unless supported by other evidence, does not create a reasonable suspicion of a crime. Based on this reasoning, the court found that the detention order violated Article 5 of the European Convention on Human Rights, which protects the right to liberty and security. In the Yüksel Yalçınkaya v. Turkey decision on 26 September 2023, the European Court of Human Rights (ECHR) examined an appeal against a conviction based on the use of ByLock. The Court ruled that the failure to provide an opportunity to challenge the authenticity of the ByLock data violated the right to a fair trial (Article 6 of the ECHR). The Court also stated that the mere use of ByLock could not be considered sufficient evidence for membership in an armed terrorist organization. It further noted that local courts had established an automatic presumption of guilt based solely on ByLock use, creating a broad and unpredictable interpretation of the law, making it nearly impossible for the accused to exonerate themselves. Therefore, the Court concluded that the conviction based on the use of ByLock violated the principle of no punishment without law (Article 7 of the ECHR). On 22 July 2025, in the Demirhan and 238 Others case, the European Court of Human Rights (ECHR) consolidated the applications of 239 individuals who had been convicted of "membership in an armed terrorist organization" based on their use of ByLock, as determined by 239 separate courts in Turkey. The Court ruled that the convictions violated the right to a fair trial under Article 6 and the principle of no punishment without law under Article 7 of the European Convention on Human Rights (ECHR). The ruling stated that the Turkish courts' "categorical approach" to the use of ByLock lacked legal foundation. In this context, it was emphasized that anyone who had used ByLock could not be convicted of membership in an armed terrorist organization based solely on this reasoning. The ruling also stated that, due to the large number of similar applications, the issue was "systemic in nature" and it called for a national solution to be developed by Turkey. While the Court did not order compensation for the 239 applicants, it emphasized that reopening the trial to ensure the enforcement of the violation ruling was the most appropriate remedy. This ruling, which confirms the violation finding in the Yüksel Yalçınkaya case of 26 September 2023, is considered a continuation of the ECHR's case law concerning trials based on ByLock evidence. === Decisions of the United Nations Human Rights Committee and Working Group === In the İsmet Özçelik and Turgay Karaman v. Turkey decision, dated 28 May 2019 (Application No. 2980/2017), the UN Human Rights Committee ruled that the use of ByLock and allegations of depositing money into Bank Asya could not justify the applicants' arrests. In the Mestan Yayman v. Turkey decision (Opinion No. 42/2018 – 21 August 2018) by the UN Human Rights Council Working Group on Arbitrary Detention, it was stated that using a public messaging application like ByLock cannot be considered criminal evidence, and that the use of such an application falls under the scope of freedom of thought and expression. The dozens of decisions later issued by the UN Human Rights Council Working Group are of the same nature.

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  Meta-Labeling

  Meta-labeling, also known as corrective AI, is a machine learning (ML) technique utilized in quantitative finance to enhance the performance of investment and trading strategies, developed in 2017 by Marcos López de Prado at Guggenheim Partners and Cornell University. The core idea is to separate the decision of trade direction (side) from the decision of trade sizing, addressing the inefficiencies of simultaneously learning both side and size predictions. The side decision involves forecasting market movements (long, short, neutral), while the size decision focuses on risk management and profitability. It serves as a secondary decision-making layer that evaluates the signals generated by a primary predictive model. By assessing the confidence and likely profitability of those signals, meta-labeling allows investors and algorithms to dynamically size positions and suppress false positives. == Motivation == Meta-labeling is designed to improve precision without sacrificing recall. As noted by López de Prado, attempting to model both the direction and the magnitude of a trade using a single algorithm can result in poor generalization. By separating these tasks, meta-labeling enables greater flexibility and robustness: Enhances control over capital allocation. Reduces overfitting by limiting model complexity. Allows the use of interpretability tools and tailored thresholds to manage risk. Enables dynamic trade suppression in unfavorable regimes. == Applications == Meta-labeling has been applied in a variety of financial ML contexts, including: Algorithmic trading: Filtering and sizing trades to reduce false positives. Portfolio optimization: Scaling exposure across multiple signals with differing confidence levels. Risk management: Dynamically disabling strategies in adverse market conditions. Model validation: Interpreting when and why a model may be underperforming due to regime shifts. == General architecture == Meta-labeling decouples two core components of systematic trading strategies: directional prediction and position sizing. The process involves training a primary model to generate trade signals (e.g., buy, sell, or hold) and then training a secondary model to determine whether each signal is likely to lead to a profitable trade. The second model outputs a probability that is interpreted as the confidence in the forecast, which can be used to adjust the position size or to filter out unreliable trades. Meta-labeling is typically implemented as a three-stage process: Primary model (M1): Predicts the direction or label of a financial outcome using features such as market prices, returns, or volatility indicators. A typical output is directional, e.g., Y ∈ {−1,0,1}, representing short, neutral, or long positions. Secondary model (M2): A binary classifier trained to predict whether the primary model's prediction will be profitable. The target variable is a binary meta-label F ∈ { 0 , 1 } {\displaystyle F\in \{0,1\}} . Inputs can include features used in the primary model, performance diagnostics, or market regime data. Position sizing algorithm (M3): Translates the output probability of the secondary model into a position size. Higher confidence scores result in larger allocations, while lower confidence leads to reduced or zero exposure. === Stage 1: Forecasting side === Primary model architecture Figure 1 Figure 1 presents the architecture of a primary model. It focuses on forecasting the side of the trade. Following the example, this model (M1) takes in input data – such as open-high-low-close data and determines the side of the position to take: a negative number is a short position, and positive number is a long position, the range is set between −1 and 1 (the closer it is to −1 or 1, the stronger the models conviction is). When training the model, the labels are −1 and 1, based on the direction of forward returns for some predefined investment horizon. The researcher may decide to apply a recall check (τ: "Tau") by setting a minimum threshold that the initial output needs to be to qualify of a short or long position (if the threshold is not met, no side forecast is predicted, leading to closing of any open positions), this leads to the primary model output which is one of three possible side forecasts: −1, 0, or 1. The primary model also generates evaluation data which can be used by the secondary model, to improve performance of size forecasts. Some examples of evaluation data include rolling accuracy, F1, recall, precision, and AUC scores. === Stage 2: Filtering out false positives === General meta-labeling architecture Figure 2 Next comes the phase of filtering out false positives, by applying a secondary machine learning model (M2), which is a binary classifier trained to determine if the trade will be profitable or not. The model takes as input four general groupings of data: General input data which is predictive of a false positive. For example the last 30 days rolling volatility of the underlying asset. Evaluation data. Market state and regime data, one may find that macro economic data or clustering the market into regimes may help as specific trading strategies are known to perform better in particular regimes. Example: momentum based strategies perform best in periods with low volatility and strong directional moves. Primary models initial input which is a value between −1 and 1. This highlights the strength of the primary models conviction. The output of the model is a value between −1 and 1 (if using a Tanh function) which will indicate the strength of the conviction that a short or long position is profitable, or it could simply be between 0 and 1 (using a sigmoid function) if one only wanted to know if it made money or not. This output allows filtering out trades that are likely to lead to losses. One could stop at this point or use the outputs of the secondary model as inputs to a position sizing algorithm (M3) which could further enhance strategy performance metrics by translating the output probability of the secondary model into a position size. Higher confidence scores result in larger allocations, while lower confidence leads to reduced or zero exposure. === Stage 3: Optimizing position sizes === ==== Position sizing methods (M3) ==== Various algorithms have been proposed for transforming predicted probabilities into trade sizes: All-or-nothing: Allocate 100% of capital if the probability exceeds a predefined threshold (e.g., 0.5); otherwise, do not trade. Model confidence: Use the probability score directly as the fraction of capital allocated. Linear scaling: Rescale the model's probabilities using min-max normalization based on the training data. Normal CDF (NCDF): Use a normal cumulative distribution function applied to a z-statistic derived from the predicted probability. Empirical CDF (ECDF): Rank probabilities based on their percentile in the training data to ensure relative allocation. Sigmoid Optimal Position Sizing (SOPS): Applies a smooth non-linear sigmoid transformation optimized to maximize risk-adjusted returns (Sharpe ratio). ==== Model calibration ==== Each machine learning algorithm used in meta-labeling tends to produce outputs with different characteristic distributions; for example, some are approximately normally distributed, whereas others exhibit a pronounced U-shape, concentrating probabilities near the extremes. Due to these varying distributions, simply summing the outputs of different models can inadvertently lead to uneven weighting of signals, biasing trade decisions. To address this, model calibration techniques are essential to adjust the predicted probabilities towards frequentist probabilities, ensuring that model outputs reflect true likelihoods more accurately. Two common calibration techniques are: Platt scaling (Sigmoid scaling): Suitable for correcting S-shaped calibration plots typically produced by models such as support vector machines (SVMs). Isotonic regression: Fits a non-decreasing step function to probabilities and is effective particularly with larger datasets, though it can sometimes lead to overfitting. Transforming predictions to frequentist probabilities is crucial as it provides probabilistic outputs that are directly interpretable as the actual likelihood of an event occurring. Such calibration significantly enhances the effectiveness of fixed position sizing methods, reducing maximum drawdowns and increasing risk-adjusted returns. However, calibration has less impact on position sizing methods that directly estimate parameters from the training data, such as ECDF and SOPS, suggesting that calibration is a critical step mainly for fixed methods that rely heavily on raw model outputs. =

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  Neurocomputing (journal)

  Neurocomputing is a peer-reviewed scientific journal covering research on artificial intelligence, machine learning, and neural computation. It was established in 1989 and is published by Elsevier. The editor-in-chief is Zidong Wang (Brunel University London). Independent scientometric studies noted that despite being one of the most productive journals in the field, it has kept its reputation across the years intact and plays an important role in leading the research in the area. The journal is abstracted and indexed in Scopus and Science Citation Index Expanded. According to the Journal Citation Reports, its 2023 impact factor is 5.5.

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  Admissible heuristic

  In computer science, specifically in algorithms related to pathfinding, a heuristic function is said to be admissible if it never overestimates the cost of reaching the goal, i.e. the cost it estimates to reach the goal is not higher than the lowest possible cost from the current point in the path. In other words, it should act as a lower bound. It is related to the concept of consistent heuristics. While all consistent heuristics are admissible, not all admissible heuristics are consistent. == Search algorithms == An admissible heuristic is used to estimate the cost of reaching the goal state in an informed search algorithm. In order for a heuristic to be admissible to the search problem, the estimated cost must always be lower than or equal to the actual cost of reaching the goal state. The search algorithm uses the admissible heuristic to find an estimated optimal path to the goal state from the current node. For example, in A search the evaluation function (where n {\displaystyle n} is the current node) is: f ( n ) = g ( n ) + h ( n ) {\displaystyle f(n)=g(n)+h(n)} where f ( n ) {\displaystyle f(n)} = the evaluation function. g ( n ) {\displaystyle g(n)} = the cost from the start node to the current node h ( n ) {\displaystyle h(n)} = estimated cost from current node to goal. h ( n ) {\displaystyle h(n)} is calculated using the heuristic function. With a non-admissible heuristic, the A algorithm could overlook the optimal solution to a search problem due to an overestimation in f ( n ) {\displaystyle f(n)} . == Formulation == n {\displaystyle n} is a node h {\displaystyle h} is a heuristic h ( n ) {\displaystyle h(n)} is cost indicated by h {\displaystyle h} to reach a goal from n {\displaystyle n} h ∗ ( n ) {\displaystyle h^{}(n)} is the optimal cost to reach a goal from n {\displaystyle n} h ( n ) {\displaystyle h(n)} is admissible if, ∀ n {\displaystyle \forall n} h ( n ) ≤ h ∗ ( n ) {\displaystyle h(n)\leq h^{}(n)} == Construction == An admissible heuristic can be derived from a relaxed version of the problem, or by information from pattern databases that store exact solutions to subproblems of the problem, or by using inductive learning methods. == Examples == Two different examples of admissible heuristics apply to the fifteen puzzle problem: Hamming distance Manhattan distance The Hamming distance is the total number of misplaced tiles. It is clear that this heuristic is admissible since the total number of moves to order the tiles correctly is at least the number of misplaced tiles (each tile not in place must be moved at least once). The cost (number of moves) to the goal (an ordered puzzle) is at least the Hamming distance of the puzzle. The Manhattan distance of a puzzle is defined as: h ( n ) = ∑ all tiles d i s t a n c e ( tile, correct position ) {\displaystyle h(n)=\sum _{\text{all tiles}}{\mathit {distance}}({\text{tile, correct position}})} Consider the puzzle below in which the player wishes to move each tile such that the numbers are ordered. The Manhattan distance is an admissible heuristic in this case because every tile will have to be moved at least the number of spots in between itself and its correct position. The subscripts show the Manhattan distance for each tile. The total Manhattan distance for the shown puzzle is: h ( n ) = 3 + 1 + 0 + 1 + 2 + 3 + 3 + 4 + 3 + 2 + 4 + 4 + 4 + 1 + 1 = 36 {\displaystyle h(n)=3+1+0+1+2+3+3+4+3+2+4+4+4+1+1=36} == Optimality proof == If an admissible heuristic is used in an algorithm that, per iteration, progresses only the path of lowest evaluation (current cost + heuristic) of several candidate paths, terminates the moment its exploration reaches the goal and, crucially, closes all optimal paths before terminating (something that's possible with A search algorithm if special care isn't taken), then this algorithm can only terminate on an optimal path. To see why, consider the following proof by contradiction: Assume such an algorithm managed to terminate on a path T with a true cost Ttrue greater than the optimal path S with true cost Strue. This means that before terminating, the evaluated cost of T was less than or equal to the evaluated cost of S (or else S would have been picked). Denote these evaluated costs Teval and Seval respectively. The above can be summarized as follows, Strue < Ttrue Teval ≤ Seval If our heuristic is admissible it follows that at this penultimate step Teval = Ttrue because any increase on the true cost by the heuristic on T would be inadmissible and the heuristic cannot be negative. On the other hand, an admissible heuristic would require that Seval ≤ Strue which combined with the above inequalities gives us Teval < Ttrue and more specifically Teval ≠ Ttrue. As Teval and Ttrue cannot be both equal and unequal our assumption must have been false and so it must be impossible to terminate on a more costly than optimal path. As an example, let us say we have costs as follows:(the cost above/below a node is the heuristic, the cost at an edge is the actual cost) 0 10 0 100 0 START ---- O ----- GOAL | | 0| |100 | | O ------- O ------ O 100 1 100 1 100 So clearly we would start off visiting the top middle node, since the expected total cost, i.e. f ( n ) {\displaystyle f(n)} , is 10 + 0 = 10 {\displaystyle 10+0=10} . Then the goal would be a candidate, with f ( n ) {\displaystyle f(n)} equal to 10 + 100 + 0 = 110 {\displaystyle 10+100+0=110} . Then we would clearly pick the bottom nodes one after the other, followed by the updated goal, since they all have f ( n ) {\displaystyle f(n)} lower than the f ( n ) {\displaystyle f(n)} of the current goal, i.e. their f ( n ) {\displaystyle f(n)} is 100 , 101 , 102 , 102 {\displaystyle 100,101,102,102} . So even though the goal was a candidate, we could not pick it because there were still better paths out there. This way, an admissible heuristic can ensure optimality. However, note that although an admissible heuristic can guarantee final optimality, it is not necessarily efficient.

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  World model (artificial intelligence)

  A world model in artificial intelligence is a machine learning system that builds an internal representation of an environment. The model predicts how that environment changes over time in response to actions. Researchers design world models to help agents plan, reason, and act without constant real-world trial and error. World models differ from systems that merely classify or generate outputs. They simulate dynamics such as physics, object interactions, and causality. Early ideas date to the 1990s. Modern versions power robots, autonomous driving, and interactive video generation. == History == Jürgen Schmidhuber introduced the term world model in machine learning in 1990. He proposed recurrent neural networks that predict future states from observations and use those predictions to train agents. David Ha and Schmidhuber revived the concept in a 2018 paper. Their agents learned to drive virtual cars and play video games inside self-generated simulations. Yann LeCun advanced the idea in a 2022 position paper titled "A Path Towards Autonomous Machine Intelligence". He argued that intelligence requires predictive models of the world rather than pure pattern matching. LeCun proposed the joint embedding predictive architecture (JEPA) as a practical foundation. LeCun and collaborators developed several JEPA variants. V-JEPA 2 reached state-of-the-art performance on video understanding and physical reasoning at the time. It supports zero-shot robot control in unfamiliar environments. Introduced in March 2026, LeWorldModel trains stably end-to-end from raw pixels and uses two loss terms and avoids hand-crafted heuristics. LeCun founded Advanced Machine Intelligence Labs in 2026 to further develop world models. Google DeepMind introduced Genie in 2024. The model learned interactive environments from unlabeled internet videos. Genie 2 followed in late 2024 and added three-dimensional generation. The Genie series set benchmarks for general-purpose simulation. Genie 3 was introduced in August 2025. It produces photorealistic, real-time interactive worlds from text prompts which are displayed at 24 frames per second and explored in real time with text or image prompts. The model supports persistent three-dimensional worlds and real-time interaction. Waymo adopted Genie 3 in February 2026 and used it to create a specialized world model for autonomous driving simulation, called the Waymo World Model. It produces synchronized camera and lidar outputs and creates edge cases that real robotaxis rarely encounter. The edge cases were reported to be unusual by PCMag. General Intuition announced a $133.7 million seed round. World Labs raised $1 billion. AMI raised $1.03 billion. In April 2026, Alibaba announced Happy Oyster, its world model designed for real-time and “flowy” world model. It includes a directing mode for world building based on text and image prompts and a wandering mode for exploring the resulting world. It can generate 3-minute in-world video clips. Also in April, World Labs, co-founded by Li Fei Fei, unveiled Spark 2.0, an open-source 3D Gaussian splatting rendering engine that targets smartphone-class devices. In June 2026, Nvidia released Cosmos 3, a family of open-weight models. It combines previously independent physical reasoning, world simulation, and action generation. Cosmos 3 integrates can process and generate text, image, video, audio, and action sequences. The model employs a Mixture-of-Transformers" (MoT) approach. An autoregressive (AR) transformer handles reasoning and next-token prediction, while a diffusion transformer (DT) does multimodal generation. Encoders (ViT for vision, VAE for visual/audio, and domain-specific for actions) and generate a shared representation space using 3D multi-dimensional rotary position embedding (mRoPE) for spatial and temporal information. The family includes Cosmos3-Nano (16B parameters) for workstations; Cosmos3-Super (64B parameters) for research. == Architecture == World models process raw sensory data such as video frames or lidar scans. They compress this input into compact latent representations. The system then predicts future representations rather than pixel-by-pixel reconstructions. Many modern world models use joint embedding predictive architecture (JEPA). An encoder turns observations into embeddings. A predictor estimates one or a suite of embeddings from the current one and an action. In some cases a critic chooses one embedding as the best result. A regularizer keeps embeddings well-behaved. The model trains by minimizing prediction error in embedding space. This approach avoids the high cost of generating every detail. Some architectures add explicit components. A fast reactive path handles immediate responses. A slower deliberative path performs longer-horizon planning. Video prediction accuracy or robot success rates are key metrics, but do not always predict real-world performance. Generative world models such as Genie 3 combine these with a simulator. They accept text prompts or layouts and output consistent video, lidar, or three-dimensional scenes. World models often train with self-supervised learning. They use large unlabeled datasets of video or robot interactions. Self-supervised learning can speed learning. Reinforcement learning can fine-tune a model for specific tasks. == Applications == World models support robot learning. Agents train inside simulations and transfer skills to the physical world. This reduces the need for dangerous or expensive real-world trials. Autonomous vehicles use world models to test rare events. Waymo's system simulates tornadoes or unusual pedestrian behavior. Companies train planners without putting vehicles on public roads. Interactive entertainment benefits from world models. Genie 3 lets users generate playable environments from simple descriptions. Game studios prototype levels faster. Scientific simulation gains from these models. Researchers model physical systems or biological processes at scale. Planners in logistics or urban design test strategies inside accurate digital twins. == Comparison with large language models == Both world models and large language models (LLMs) use inferencing on their inputs to make predictions. LLMs operate on textual inputs. They predict the next token in text sequences. They excel at language-oriented tasks such as translation or summarization. However, they lack understanding of physics. World models operate on sensor inputs such as pixels. They predict state changes in that data in latent space. This design supports planning and causal reasoning. LLMs generate fluent text but often fail at consistent physical predictions. Their architecture employs transformers with refinements such as mixture of experts. World models divide an inferencing task into work performed by encoders, predictors, simulators, and other pieces. They typically handle multimodal inputs such as video, lidar, radar, and audio, guided by textual prompting. LLMs power chatbots and code assistants. World models drive embodied agents that act in dynamic environments, such as autonomous driving. The two may be combined in hybrid systems. For example, a LLM handles instructions, while a world model manages low-level control. World model proponents such as LeCun claim that because LLMs are trained only on text, they have no ability to predict anything beyond text, such as real-world events. == Benchmarks == World model benchmarks test physical understanding, long-term consistency, planning, and generalization from sensor data. Meta introduced three benchmarks for V-JEPA 2. IntPhys 2 measures a model's ability to detect physics violations. It presents pairs of videos that diverge when one breaks physical rules. Humans score near 100% accuracy. V-JEPA 2 achieves little better than random chance on many conditions. Minimal Video Pairs (MVPBench) tests physical understanding through multiple-choice questions based on short video clips. It probes object interactions and causality. Something-Something tests action recognition. Epic-Kitchens-100 tests human action anticipation. DeepMind benchmark: Interactive evaluation measures consistency over minutes of interaction, memory of off-screen objects, and response to user actions or text prompts. Waymo benchmark: Output generation quality: Metrics include realism, controllability (via text prompts), and usefulness for training planners in simulated worlds. However, pixel reconstruction error rate with episodic rewards often fails. Other: Epic-Kitchens-100 (often measured with Recall@5) Ego4D 50 Salads, Breakfast, etc. Potential benchmarks: Zero-shot transfer to robots Long-horizon planning Implausible prediction rate

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  Personality computing

  Personality computing is a research field related to artificial intelligence and personality psychology that studies personality by means of computational techniques from different sources, including text, multimedia, and social networks. == Overview == Personality computing addresses three main problems involving personality: automatic personality recognition, perception, and synthesis. Automatic personality recognition is the inference of the personality type of target individuals from their digital footprint. Automatic personality perception is the inference of the personality attributed by an observer to a target individual based on some observable behavior. Automatic personality synthesis is the generation of the style or behaviour of artificial personalities in Avatars and virtual agents. Self-assessed personality tests or observer ratings are always exploited as the ground truth for testing and validating the performance of artificial intelligence algorithms for the automatic prediction of personality types. There is a wide variety of personality tests, such as the Myers Briggs Type Indicator (MBTI) or the MMPI, but the most used are tests based on the Five Factor Model such as the Revised NEO Personality Inventory. Personality computing can be considered as an extension or complement of Affective computing, where the former focuses on personality traits and the latter on affective states. A further extension of the two fields is Character Computing which combines various character states and traits including but not limited to personality and affect. == History == Personality computing began around 2005 with the pioneering research in personality recognition by Shlomo Argamon and later by François Mairesse. These works showed that personality traits could be inferred with reasonable accuracy from text, such as blogs, self-presentations, and email addresses. In 2008, the concept of "portable personality" for the distributed management of personality profiles has been developed. A few years later, research began in personality recognition and perception from multimodal and social signals, such as recorded meetings and voice calls. In the 2010s, the research focused mainly on personality recognition and perception from social media, helped by the first workshops organized by Fabio Celli. In particular personality was extracted from Facebook, Twitter and Instagram. In the same years, automatic personality synthesis helped improve the coherence of simulated behavior in virtual agents. Scientific works by Michal Kosinski demonstrated the validity of Personality Computing from different digital footprints, in particular from user preferences such as Facebook page likes, showed that machines can recognize personality better than humans and raised a warning against Cambridge Analytica and misuse of this kind of technology. == Applications == Personality computing techniques, in particular personality recognition and perception, have applications in Social media marketing, where they can help reducing the cost of advertising campaigns through psychological targeting.

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  Actor-critic algorithm

  The actor-critic algorithm (AC) is a family of reinforcement learning (RL) algorithms that combine policy-based RL algorithms such as policy gradient methods, and value-based RL algorithms such as value iteration, Q-learning, SARSA, and TD learning. An AC algorithm consists of two main components: an "actor" that determines which actions to take according to a policy function, and a "critic" that evaluates those actions according to a value function. Some AC algorithms are on-policy, some are off-policy. Some apply to either continuous or discrete action spaces. Some work in both cases. == Overview == The actor-critic methods can be understood as an improvement over pure policy gradient methods like REINFORCE via introducing a baseline. === Actor === The actor uses a policy function π ( a | s ) {\displaystyle \pi (a|s)} , while the critic estimates either the value function V ( s ) {\displaystyle V(s)} , the action-value Q-function Q ( s , a ) , {\displaystyle Q(s,a),} the advantage function A ( s , a ) {\displaystyle A(s,a)} , or any combination thereof. The actor is a parameterized function π θ {\displaystyle \pi _{\theta }} , where θ {\displaystyle \theta } are the parameters of the actor. The actor takes as argument the state of the environment s {\displaystyle s} and produces a probability distribution π θ ( ⋅ | s ) {\displaystyle \pi _{\theta }(\cdot |s)} . If the action space is discrete, then ∑ a π θ ( a | s ) = 1 {\displaystyle \sum _{a}\pi _{\theta }(a|s)=1} . If the action space is continuous, then ∫ a π θ ( a | s ) d a = 1 {\displaystyle \int _{a}\pi _{\theta }(a|s)da=1} . The goal of policy optimization is to improve the actor. That is, to find some θ {\displaystyle \theta } that maximizes the expected episodic reward J ( θ ) {\displaystyle J(\theta )} : J ( θ ) = E π θ [ ∑ t = 0 T γ t r t ] {\displaystyle J(\theta )=\mathbb {E} _{\pi _{\theta }}\left[\sum _{t=0}^{T}\gamma ^{t}r_{t}\right]} where γ {\displaystyle \gamma } is the discount factor, r t {\displaystyle r_{t}} is the reward at step t {\displaystyle t} , and T {\displaystyle T} is the time-horizon (which can be infinite). The goal of policy gradient method is to optimize J ( θ ) {\displaystyle J(\theta )} by gradient ascent on the policy gradient ∇ J ( θ ) {\displaystyle \nabla J(\theta )} . As detailed on the policy gradient method page, there are many unbiased estimators of the policy gradient: ∇ θ J ( θ ) = E π θ [ ∑ 0 ≤ j ≤ T ∇ θ ln ⁡ π θ ( A j | S j ) ⋅ Ψ j | S 0 = s 0 ] {\displaystyle \nabla _{\theta }J(\theta )=\mathbb {E} _{\pi _{\theta }}\left[\sum _{0\leq j\leq T}\nabla _{\theta }\ln \pi _{\theta }(A_{j}|S_{j})\cdot \Psi _{j}{\Big |}S_{0}=s_{0}\right]} where Ψ j {\textstyle \Psi _{j}} is a linear sum of the following: ∑ 0 ≤ i ≤ T ( γ i R i ) {\textstyle \sum _{0\leq i\leq T}(\gamma ^{i}R_{i})} . γ j ∑ j ≤ i ≤ T ( γ i − j R i ) {\textstyle \gamma ^{j}\sum _{j\leq i\leq T}(\gamma ^{i-j}R_{i})} : the REINFORCE algorithm. γ j ∑ j ≤ i ≤ T ( γ i − j R i ) − b ( S j ) {\textstyle \gamma ^{j}\sum _{j\leq i\leq T}(\gamma ^{i-j}R_{i})-b(S_{j})} : the REINFORCE with baseline algorithm. Here b {\displaystyle b} is an arbitrary function. γ j ( R j + γ V π θ ( S j + 1 ) − V π θ ( S j ) ) {\textstyle \gamma ^{j}\left(R_{j}+\gamma V^{\pi _{\theta }}(S_{j+1})-V^{\pi _{\theta }}(S_{j})\right)} : TD(1) learning. γ j Q π θ ( S j , A j ) {\textstyle \gamma ^{j}Q^{\pi _{\theta }}(S_{j},A_{j})} . γ j A π θ ( S j , A j ) {\textstyle \gamma ^{j}A^{\pi _{\theta }}(S_{j},A_{j})} : Advantage Actor-Critic (A2C). γ j ( R j + γ R j + 1 + γ 2 V π θ ( S j + 2 ) − V π θ ( S j ) ) {\textstyle \gamma ^{j}\left(R_{j}+\gamma R_{j+1}+\gamma ^{2}V^{\pi _{\theta }}(S_{j+2})-V^{\pi _{\theta }}(S_{j})\right)} : TD(2) learning. γ j ( ∑ k = 0 n − 1 γ k R j + k + γ n V π θ ( S j + n ) − V π θ ( S j ) ) {\textstyle \gamma ^{j}\left(\sum _{k=0}^{n-1}\gamma ^{k}R_{j+k}+\gamma ^{n}V^{\pi _{\theta }}(S_{j+n})-V^{\pi _{\theta }}(S_{j})\right)} : TD(n) learning. γ j ∑ n = 1 ∞ λ n − 1 1 − λ ⋅ ( ∑ k = 0 n − 1 γ k R j + k + γ n V π θ ( S j + n ) − V π θ ( S j ) ) {\textstyle \gamma ^{j}\sum _{n=1}^{\infty }{\frac {\lambda ^{n-1}}{1-\lambda }}\cdot \left(\sum _{k=0}^{n-1}\gamma ^{k}R_{j+k}+\gamma ^{n}V^{\pi _{\theta }}(S_{j+n})-V^{\pi _{\theta }}(S_{j})\right)} : TD(λ) learning, also known as GAE (generalized advantage estimate). This is obtained by an exponentially decaying sum of the TD(n) learning terms. === Critic === In the unbiased estimators given above, certain functions such as V π θ , Q π θ , A π θ {\displaystyle V^{\pi _{\theta }},Q^{\pi _{\theta }},A^{\pi _{\theta }}} appear. These are approximated by the critic. Since these functions all depend on the actor, the critic must learn alongside the actor. The critic is learned by value-based RL algorithms. For example, if the critic is estimating the state-value function V π θ ( s ) {\displaystyle V^{\pi _{\theta }}(s)} , then it can be learned by any value function approximation method. Let the critic be a function approximator V ϕ ( s ) {\displaystyle V_{\phi }(s)} with parameters ϕ {\displaystyle \phi } . The simplest example is TD(1) learning, which trains the critic to minimize the TD(1) error: δ i = R i + γ V ϕ ( S i + 1 ) − V ϕ ( S i ) {\displaystyle \delta _{i}=R_{i}+\gamma V_{\phi }(S_{i+1})-V_{\phi }(S_{i})} The critic parameters are updated by gradient descent on the squared TD error: ϕ ← ϕ − α ∇ ϕ ( δ i ) 2 = ϕ + α δ i ∇ ϕ V ϕ ( S i ) {\displaystyle \phi \leftarrow \phi -\alpha \nabla _{\phi }(\delta _{i})^{2}=\phi +\alpha \delta _{i}\nabla _{\phi }V_{\phi }(S_{i})} where α {\displaystyle \alpha } is the learning rate. Note that the gradient is taken with respect to the ϕ {\displaystyle \phi } in V ϕ ( S i ) {\displaystyle V_{\phi }(S_{i})} only, since the ϕ {\displaystyle \phi } in γ V ϕ ( S i + 1 ) {\displaystyle \gamma V_{\phi }(S_{i+1})} constitutes a moving target, and the gradient is not taken with respect to that. This is a common source of error in implementations that use automatic differentiation, and requires "stopping the gradient" at that point. Similarly, if the critic is estimating the action-value function Q π θ {\displaystyle Q^{\pi _{\theta }}} , then it can be learned by Q-learning or SARSA. In SARSA, the critic maintains an estimate of the Q-function, parameterized by ϕ {\displaystyle \phi } , denoted as Q ϕ ( s , a ) {\displaystyle Q_{\phi }(s,a)} . The temporal difference error is then calculated as δ i = R i + γ Q θ ( S i + 1 , A i + 1 ) − Q θ ( S i , A i ) {\displaystyle \delta _{i}=R_{i}+\gamma Q_{\theta }(S_{i+1},A_{i+1})-Q_{\theta }(S_{i},A_{i})} . The critic is then updated by θ ← θ + α δ i ∇ θ Q θ ( S i , A i ) {\displaystyle \theta \leftarrow \theta +\alpha \delta _{i}\nabla _{\theta }Q_{\theta }(S_{i},A_{i})} The advantage critic can be trained by training both a Q-function Q ϕ ( s , a ) {\displaystyle Q_{\phi }(s,a)} and a state-value function V ϕ ( s ) {\displaystyle V_{\phi }(s)} , then let A ϕ ( s , a ) = Q ϕ ( s , a ) − V ϕ ( s ) {\displaystyle A_{\phi }(s,a)=Q_{\phi }(s,a)-V_{\phi }(s)} . Although, it is more common to train just a state-value function V ϕ ( s ) {\displaystyle V_{\phi }(s)} , then estimate the advantage by A ϕ ( S i , A i ) ≈ ∑ j ∈ 0 : n − 1 γ j R i + j + γ n V ϕ ( S i + n ) − V ϕ ( S i ) {\displaystyle A_{\phi }(S_{i},A_{i})\approx \sum _{j\in 0:n-1}\gamma ^{j}R_{i+j}+\gamma ^{n}V_{\phi }(S_{i+n})-V_{\phi }(S_{i})} Here, n {\displaystyle n} is a positive integer. The higher n {\displaystyle n} is, the more lower is the bias in the advantage estimation, but at the price of higher variance. The Generalized Advantage Estimation (GAE) introduces a hyperparameter λ {\displaystyle \lambda } that smoothly interpolates between Monte Carlo returns ( λ = 1 {\displaystyle \lambda =1} , high variance, no bias) and 1-step TD learning ( λ = 0 {\displaystyle \lambda =0} , low variance, high bias). This hyperparameter can be adjusted to pick the optimal bias-variance trade-off in advantage estimation. It uses an exponentially decaying average of n-step returns with λ {\displaystyle \lambda } being the decay strength. == Variants == Asynchronous Advantage Actor-Critic (A3C): Parallel and asynchronous version of A2C. Soft Actor-Critic (SAC): Incorporates entropy maximization for improved exploration. Deep Deterministic Policy Gradient (DDPG): Specialized for continuous action spaces.

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  PagedAttention

  PagedAttention is an attention algorithm for efficient serving of large language models (LLMs). It was introduced in 2023 by Woosuk Kwon and colleagues in the paper Efficient Memory Management for Large Language Model Serving with PagedAttention, alongside the vLLM serving engine. The method stores the key–value cache used during autoregressive decoding in fixed-size blocks that can be mapped to non-contiguous physical memory, borrowing ideas from virtual memory, paging, and operating system design. == Background == In transformer inference, the key–value cache grows with sequence length and the number of concurrent requests. Kwon et al. argued that earlier serving systems typically reserved contiguous cache regions in advance, which caused reserved space, internal fragmentation, and external fragmentation. In their experiments, the paper reported that the effective memory utilization of previous systems could fall as low as 20.4%. == Description == PagedAttention partitions the cache of each sequence into fixed-size KV blocks. A request's cache is represented as a sequence of logical blocks, while a block table maps those logical blocks to physical GPU-memory blocks. As a result, neighboring logical blocks do not need to be contiguous in physical memory, and new blocks can be allocated on demand as generation proceeds. The design also makes it easier to share cache state across related decoding paths. In vLLM, physical blocks can be reference-counted and shared among requests or branches, with block-granularity copy-on-write used when a shared block must be modified. The original paper applied this design to parallel sampling, beam search, and prompts with shared prefixes. == Mathematical formulation == For a query token i {\displaystyle i} in causal self-attention, the standard attention output can be written as a i j = exp ⁡ ( q i ⊤ k j / d ) ∑ t = 1 i exp ⁡ ( q i ⊤ k t / d ) , o i = ∑ j = 1 i a i j v j {\displaystyle a_{ij}={\frac {\exp(\mathbf {q} _{i}^{\top }\mathbf {k} _{j}/{\sqrt {d}})}{\sum _{t=1}^{i}\exp(\mathbf {q} _{i}^{\top }\mathbf {k} _{t}/{\sqrt {d}})}},\;\mathbf {o} _{i}=\sum _{j=1}^{i}a_{ij}\mathbf {v} _{j}} where q i {\displaystyle \mathbf {q} _{i}} , k j {\displaystyle \mathbf {k} _{j}} , and v j {\displaystyle \mathbf {v} _{j}} are the query, key, and value vectors, and d {\displaystyle d} is the attention dimension. If the cache is partitioned into blocks of size B {\displaystyle B} , the key and value blocks may be written as K j = ( k ( j − 1 ) B + 1 , … , k j B ) , V j = ( v ( j − 1 ) B + 1 , … , v j B ) {\displaystyle \mathbf {K} _{j}=(\mathbf {k} _{(j-1)B+1},\ldots ,\mathbf {k} _{jB}),\;\mathbf {V} _{j}=(\mathbf {v} _{(j-1)B+1},\ldots ,\mathbf {v} _{jB})} PagedAttention then performs the computation blockwise: A i j = exp ⁡ ( q i ⊤ K j / d ) ∑ t = 1 ⌈ i / B ⌉ exp ⁡ ( q i ⊤ K t / d ) , o i = ∑ j = 1 ⌈ i / B ⌉ V j A i j ⊤ {\displaystyle \mathbf {A} _{ij}={\frac {\exp(\mathbf {q} _{i}^{\top }\mathbf {K} _{j}/{\sqrt {d}})}{\sum _{t=1}^{\lceil i/B\rceil }\exp(\mathbf {q} _{i}^{\top }\mathbf {K} _{t}/{\sqrt {d}})}},\;\mathbf {o} _{i}=\sum _{j=1}^{\lceil i/B\rceil }\mathbf {V} _{j}\mathbf {A} _{ij}^{\top }} where A i j {\displaystyle \mathbf {A} _{ij}} is the vector of attention scores for the j {\displaystyle j} -th KV block. In the formulation given by Kwon et al., this preserves the causal attention calculation while allowing the key and value blocks to reside in non-contiguous physical memory. == Performance and use == The vLLM paper reported that, on its evaluated workloads, the use of PagedAttention and the associated memory-management design improved serving throughput by 2–4× over the compared baselines, including FasterTransformer and Orca, while preserving model outputs. In experiments on OPT-13B with the Alpaca trace, the paper also reported memory savings of 6.1–9.8% for parallel sampling and 37.6–55.2% for beam search through KV-block sharing. A 2024 survey of LLM serving systems described PagedAttention as having become an industry norm in LLM serving frameworks, citing support in TGI, vLLM, and TensorRT-LLM. == Limitations and alternatives == Subsequent work has described trade-offs in the approach. The 2025 vAttention paper argued that PagedAttention requires attention kernels to be rewritten to support paging and increases software complexity, portability issues, redundancy, and execution overhead, proposing instead a memory manager that keeps the cache contiguous in virtual memory while relying on demand paging for physical allocation. === vAttention === Unlike PagedAttention, vAttention does not introduce a different attention rule; it retains the standard attention computation Attention ⁡ ( q i , K , V ) = softmax ⁡ ( q i K ⊤ s c a l e ) V . {\displaystyle \operatorname {Attention} (q_{i},K,V)=\operatorname {softmax} \left({\frac {q_{i}K^{\top }}{\mathrm {scale} }}\right)V.} In the notation of Prabhu et al., the key and value tensors for a request seen so far are K , V ∈ R L ′ × ( H × D ) {\displaystyle K,V\in \mathbb {R} ^{L'\times (H\times D)}} , where L ′ {\displaystyle L'} is the context length seen so far, H {\displaystyle H} is the number of KV heads on a worker, and D {\displaystyle D} is the dimension of each KV head. In systems prior to PagedAttention, the K cache (or V cache) at each layer of a worker is typically allocated as a 4D tensor of shape [ B , L , H , D ] , {\displaystyle [B,L,H,D],} where B {\displaystyle B} is batch size and L {\displaystyle L} is the maximum context length supported by the model. vAttention preserves this contiguous virtual-memory view while deferring physical-memory allocation to runtime. A serving framework maintains separate K and V tensors for each layer, so vAttention reserves 2 N {\displaystyle 2N} virtual-memory buffers on a worker, where N {\displaystyle N} is the number of layers managed by that worker. The maximum size of one virtual-memory buffer is B S = B × S , {\displaystyle BS=B\times S,} where S {\displaystyle S} is the maximum size of a single request's per-layer K cache (or V cache) on a worker. The paper defines S = L × H × D × P , {\displaystyle S=L\times H\times D\times P,} where P {\displaystyle P} is the number of bytes needed to store one element. In this formulation, vAttention keeps the KV cache contiguous in virtual memory and relies on demand paging for physical allocation, rather than modifying the attention kernel to operate over non-contiguous KV-cache blocks.

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  Clara.io

  Clara.io is web-based freemium 3D computer graphics software developed by Exocortex, a Canadian software company. The free or "Basic" component of their freemium offering, however, places severe restrictions, such as on saving models and importing texture maps, which are undisclosed in the company's own descriptions of their plans.vf TMN == History == Clara.io was announced in July 2013, and first presented as part of the official SIGGRAPH 2013 program later that month. By November 2013, when the open beta period started, Clara.io had 14,000 registered users. Clara.io claimed to have 26,000 registered users in January 2014, which grew to 85,000 by December 2014. Clara.io was permanently shut down on December 31, 2022, but the site is currently still partially functional to logged-in users. == Features == Polygonal modeling Constructive solid geometry Key frame animation Skeletal animation Hierarchical scene graph Texture mapping Photorealistic rendering (streaming cloud rendering using V-Ray Cloud) Scene publishing via HTML iframe embedding FBX, Collada, OBJ, STL and Three.js import/export Collaborative real-time editing Revision control (versioning & history) Scripting, Plugins & REST APIs 3D model library Unlisted and Private scenes (paid subscriptions only). == Technology == Clara.io is developed using HTML5, JavaScript, WebGL and Three.js. Clara.io does not rely on any browser plugins and thus runs on any platform that has a modern standards compliant browser. == Screenshots ==

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  Wetware (brain)

  Wetware is a term drawn from the computer-related idea of hardware or software, but applied to biological life forms. == Usage == The prefix "wet" is a reference to the water found in living creatures. Wetware is used to describe the elements equivalent to hardware and software found in a person, especially the central nervous system (CNS) and the human mind. The term wetware finds use in works of fiction, in scholarly publications and in popularizations. The "hardware" component of wetware concerns the bioelectric and biochemical properties of the CNS, specifically the brain. If the sequence of impulses traveling across the various neurons are thought of symbolically as software, then the physical neurons would be the hardware. The amalgamated interaction of this software and hardware is manifested through continuously changing physical connections, and chemical and electrical influences that spread across the body. The process by which the mind and brain interact to produce the collection of experiences that we define as self-awareness is in question. == History == Although the exact definition has shifted over time, the term Wetware and its fundamental reference to "the physical mind" has been around at least since the mid-1950s. Mostly used in relatively obscure articles and papers, it was not until the heyday of cyberpunk, however, that the term found broad adoption. Among the first uses of the term in popular culture was the Bruce Sterling novel Schismatrix (1985) and the Michael Swanwick novel Vacuum Flowers (1987). Rudy Rucker references the term in a number of books, including one entitled Wetware (1988): ... all sparks and tastes and tangles, all its stimulus/response patterns – the whole bio-cybernetic software of mind. Rucker did not use the word to simply mean a brain, nor in the human-resources sense of employees. He used wetware to stand for the data found in any biological system, analogous perhaps to the firmware that is found in a ROM chip. In Rucker's sense, a seed, a plant graft, an embryo, or a biological virus are all wetware. DNA, the immune system, and the evolved neural architecture of the brain are further examples of wetware in this sense. Rucker describes his conception in a 1992 compendium The Mondo 2000 User's Guide to the New Edge, which he quotes in a 2007 blog entry. Early cyber-guru Arthur Kroker used the term in his blog. With the term getting traction in trendsetting publications, it became a buzzword in the early 1990s. In 1991, Dutch media theorist Geert Lovink organized the Wetware Convention in Amsterdam, which was supposed to be an antidote to the "out-of-body" experiments conducted in high-tech laboratories, such as experiments in virtual reality. Timothy Leary, in an appendix to Info-Psychology originally written in 1975–76 and published in 1989, used the term wetware, writing that "psychedelic neuro-transmitters were the hot new technology for booting-up the 'wetware' of the brain". Another common reference is: "Wetware has 7 plus or minus 2 temporary registers." The numerical allusion is to a classic 1957 article by George A. Miller, The magical number 7 plus or minus two: some limits in our capacity for processing information, which later gave way to Miller's law.

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  Description logic

  Description logics (DL) are a family of formal knowledge representation languages. Many DLs are more expressive than propositional logic but less expressive than first-order logic. In contrast to the latter, the core reasoning problems for DLs are (usually) decidable, and efficient decision procedures have been designed and implemented for these problems. There are general, spatial, temporal, spatiotemporal, and fuzzy description logics, and each description logic features a different balance between expressive power and reasoning complexity by supporting different sets of mathematical constructors. DLs are used in artificial intelligence to describe and reason about the relevant concepts of an application domain (known as terminological knowledge). It is of particular importance in providing a logical formalism for ontologies and the Semantic Web: the Web Ontology Language (OWL) and its profiles are based on DLs. A major area of application of DLs and OWL is in biomedical informatics, where they assist in the codification of biomedical knowledge. DLs and OWL are also applied in other domains, including defense, climate modeling, and large-scale industrial knowledge graphs. == Introduction == A DL models concepts, roles and individuals, and their relationships. The fundamental modeling concept of a DL is the axiom—a logical statement relating roles and/or concepts. This is a key difference from the frames paradigm where a frame specification declares and completely defines a class. == Nomenclature == === Terminology compared to FOL and OWL === The description logic community uses different terminology than the first-order logic (FOL) community for operationally equivalent notions; some examples are given below. The Web Ontology Language (OWL) uses again a different terminology, also given in the table below. === Naming convention === There are many varieties of description logics and there is an informal naming convention, roughly describing the operators allowed. The expressivity is encoded in the label for a logic starting with one of the following basic logics: Followed by any of the following extensions: ==== Exceptions ==== Some canonical DLs that do not exactly fit this convention are: ==== Examples ==== As an example, A L C {\displaystyle {\mathcal {ALC}}} is a centrally important description logic from which comparisons with other varieties can be made. A L C {\displaystyle {\mathcal {ALC}}} is simply A L {\displaystyle {\mathcal {AL}}} with complement of any concept allowed, not just atomic concepts. A L C {\displaystyle {\mathcal {ALC}}} is used instead of the equivalent A L U E {\displaystyle {\mathcal {ALUE}}} . A further example, the description logic S H I Q {\displaystyle {\mathcal {SHIQ}}} is the logic A L C {\displaystyle {\mathcal {ALC}}} plus extended cardinality restrictions, and transitive and inverse roles. The naming conventions aren't purely systematic so that the logic A L C O I N {\displaystyle {\mathcal {ALCOIN}}} might be referred to as A L C N I O {\displaystyle {\mathcal {ALCNIO}}} and other abbreviations are also made where possible. The Protégé ontology editor supports S H O I N ( D ) {\displaystyle {\mathcal {SHOIN}}^{\mathcal {(D)}}} . Three major biomedical informatics terminology bases, SNOMED CT, GALEN, and GO, are expressible in E L {\displaystyle {\mathcal {EL}}} (with additional role properties). OWL 2 provides the expressiveness of S R O I Q ( D ) {\displaystyle {\mathcal {SROIQ}}^{\mathcal {(D)}}} , OWL-DL is based on S H O I N ( D ) {\displaystyle {\mathcal {SHOIN}}^{\mathcal {(D)}}} , and for OWL-Lite it is S H I F ( D ) {\displaystyle {\mathcal {SHIF}}^{\mathcal {(D)}}} . == History == Description logic was given its current name in the 1980s. Previous to this it was called (chronologically): terminological systems, and concept languages. === Knowledge representation === Frames and semantic networks lack formal (logic-based) semantics. DL was first introduced into knowledge representation (KR) systems to overcome this deficiency. The first DL-based KR system was KL-ONE (by Ronald J. Brachman and Schmolze, 1985). During the '80s other DL-based systems using structural subsumption algorithms were developed including KRYPTON (1983), LOOM (1987), BACK (1988), K-REP (1991) and CLASSIC (1991). This approach featured DL with limited expressiveness but relatively efficient (polynomial time) reasoning. In the early '90s, the introduction of a new tableau based algorithm paradigm allowed efficient reasoning on more expressive DL. DL-based systems using these algorithms — such as KRIS (1991) — show acceptable reasoning performance on typical inference problems even though the worst case complexity is no longer polynomial. From the mid '90s, reasoners were created with good practical performance on very expressive DL with high worst case complexity. Examples from this period include FaCT, RACER (2001), CEL (2005), and KAON 2 (2005). DL reasoners, such as FaCT, FaCT++, RACER, DLP and Pellet, implement the method of analytic tableaux. KAON2 is implemented by algorithms which reduce a SHIQ(D) knowledge base to a disjunctive datalog program. === Semantic web === The DARPA Agent Markup Language (DAML) and Ontology Inference Layer (OIL) ontology languages for the Semantic Web can be viewed as syntactic variants of DL. In particular, the formal semantics and reasoning in OIL use the S H I Q {\displaystyle {\mathcal {SHIQ}}} DL. The DAML+OIL DL was developed as a submission to—and formed the starting point of—the World Wide Web Consortium (W3C) Web Ontology Working Group. In 2004, the Web Ontology Working Group completed its work by issuing the OWL recommendation. The design of OWL is based on the S H {\displaystyle {\mathcal {SH}}} family of DL with OWL DL and OWL Lite based on S H O I N ( D ) {\displaystyle {\mathcal {SHOIN}}^{\mathcal {(D)}}} and S H I F ( D ) {\displaystyle {\mathcal {SHIF}}^{\mathcal {(D)}}} respectively. The W3C OWL Working Group began work in 2007 on a refinement of - and extension to - OWL. In 2009, this was completed by the issuance of the OWL2 recommendation. OWL2 is based on the description logic S R O I Q ( D ) {\displaystyle {\mathcal {SROIQ}}^{\mathcal {(D)}}} . Practical experience demonstrated that OWL DL lacked several key features necessary to model complex domains. == Modeling == === TBox vs Abox === In DL, a distinction is drawn between the so-called TBox (terminological box) and the ABox (assertional box). In general, the TBox contains sentences describing concept hierarchies (i.e., relations between concepts) while the ABox contains ground sentences stating where in the hierarchy, individuals belong (i.e., relations between individuals and concepts). For example, the statement: belongs in the TBox, while the statement: belongs in the ABox. Note that the TBox/ABox distinction is not significant, in the same sense that the two "kinds" of sentences are not treated differently in first-order logic (which subsumes most DL). When translated into first-order logic, a subsumption axiom like (1) is simply a conditional restriction to unary predicates (concepts) with only variables appearing in it. Clearly, a sentence of this form is not privileged or special over sentences in which only constants ("grounded" values) appear like (2). === Motivation for having Tbox and Abox === So why was the distinction introduced? The primary reason is that the separation can be useful when describing and formulating decision-procedures for various DL. For example, a reasoner might process the TBox and ABox separately, in part because certain key inference problems are tied to one but not the other one ('classification' is related to the TBox, 'instance checking' to the ABox). Another example is that the complexity of the TBox can greatly affect the performance of a given decision-procedure for a certain DL, independently of the ABox. Thus, it is useful to have a way to talk about that specific part of the knowledge base. The secondary reason is that the distinction can make sense from the knowledge base modeler's perspective. It is plausible to distinguish between our conception of terms/concepts in the world (class axioms in the TBox) and particular manifestations of those terms/concepts (instance assertions in the ABox). In the above example: when the hierarchy within a company is the same in every branch but the assignment to employees is different in every department (because there are other people working there), it makes sense to reuse the TBox for different branches that do not use the same ABox. There are two features of description logic that are not shared by most other data description formalisms: DL does not make the unique name assumption (UNA) or the closed-world assumption (CWA). Not having UNA means that two concepts with different names may be allowed by some inference to be shown to be equivalent. Not having CWA, or rather having the open world assumption (OWA) means that

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