Communications security

Communications security

Communications security is the discipline of preventing unauthorized interceptors from accessing telecommunications in an intelligible form, while still delivering content to the intended recipients. In the North Atlantic Treaty Organization culture, including United States Department of Defense culture, it is often referred to by the abbreviation COMSEC. The field includes cryptographic security, transmission security, emissions security and physical security of COMSEC equipment and associated keying material. COMSEC is used to protect both classified and unclassified traffic on military communications networks, including voice, video, and data. It is used for both analog and digital applications, and both wired and wireless links. Voice over secure internet protocol VOSIP has become the de facto standard for securing voice communication, replacing the need for Secure Terminal Equipment (STE) in much of NATO, including the U.S.A. USCENTCOM moved entirely to VOSIP in 2008. == Specialties == Cryptographic security: The component of communications security that results from the provision of technically sound cryptosystems and their proper use. This includes ensuring message confidentiality and authenticity. Emission security (EMSEC): The protection resulting from all measures taken to deny unauthorized persons information of value that might be derived from communications systems and cryptographic equipment intercepts and the interception and analysis of compromising emanations from cryptographic equipment, information systems, and telecommunications systems. Transmission security (TRANSEC): The component of communications security that results from the application of measures designed to protect transmissions from interception and exploitation by means other than cryptanalysis (e.g. frequency hopping and spread spectrum). Physical security: The component of communications security that results from all physical measures necessary to safeguard classified equipment, material, and documents from access thereto or observation thereof by unauthorized persons. == Related terms == ACES – Automated Communications Engineering Software AEK – Algorithmic Encryption Key AKMS – the Army Key Management System CCI – Controlled Cryptographic Item - equipment which contains COMSEC embedded devices CT3 – Common Tier 3 DTD – Data Transfer Device ICOM – Integrated COMSEC, e.g. a radio with built in encryption KEK – Key Encryption Key KG-30 – family of COMSEC equipment KOI-18 – Tape Reader General Purpose KPK – Key production key KYK-13 – Electronic Transfer Device KYX-15 – Electronic Transfer Device LCMS – Local COMSEC Management Software OTAR – Over the Air Rekeying OWK – Over the Wire Key SKL – Simple Key Loader SOI – Signal operating instructions STE – Secure Terminal Equipment (secure phone) STU-III – (obsolete secure phone, replaced by STE) TED – Trunk Encryption Device such as the WALBURN/KG family TEK – Traffic Encryption Key TPI – Two person integrity TSEC – Telecommunications Security (sometimes referred to in error transmission security or TRANSEC) Types of COMSEC equipment: Authentication equipment Crypto equipment: Any equipment that embodies cryptographic logic or performs one or more cryptographic functions (key generation, encryption, and authentication). Crypto-ancillary equipment: Equipment designed specifically to facilitate efficient or reliable operation of crypto-equipment, without performing cryptographic functions itself. Crypto-production equipment: Equipment used to produce or load keying material == DoD Electronic Key Management System == The Electronic Key Management System (EKMS) is a United States Department of Defense (DoD) key management, COMSEC material distribution, and logistics support system. The National Security Agency (NSA) established the EKMS program to supply electronic key to COMSEC devices in securely and timely manner, and to provide COMSEC managers with an automated system capable of ordering, generation, production, distribution, storage, security accounting, and access control. The Army's platform in the four-tiered EKMS, AKMS, automates frequency management and COMSEC management operations. It eliminates paper keying material, hardcopy Signal operating instructions (SOI) and saves the time and resources required for courier distribution. It has 4 components: LCMS provides automation for the detailed accounting required for every COMSEC account, and electronic key generation and distribution capability. ACES is the frequency management portion of AKMS. ACES has been designated by the Military Communications Electronics Board as the joint standard for use by all services in development of frequency management and crypto-net planning. CT3 with DTD software is in a fielded, ruggedized hand-held device that handles, views, stores, and loads SOI, Key, and electronic protection data. DTD provides an improved net-control device to automate crypto-net control operations for communications networks employing electronically keyed COMSEC equipment. SKL is a hand-held PDA that handles, views, stores, and loads SOI, Key, and electronic protection data. == Key Management Infrastructure (KMI) Program == KMI is intended to replace the legacy Electronic Key Management System to provide a means for securely ordering, generating, producing, distributing, managing, and auditing cryptographic products (e.g., asymmetric keys, symmetric keys, manual cryptographic systems, and cryptographic applications). This system is currently being fielded by Major Commands and variants will be required for non-DoD Agencies with a COMSEC Mission.

Objective vision

Objective Vision (Object Oriented Visionary) is a project mainly aimed at real-time computer vision and simulation vision of living creatures. it has three sections containing an open-source library of programming functions for using inside the projects, Virtual laboratory for scholars to check the application of functions directly and by command-line code for external and instant access, and the research section consists of paperwork and libraries to expand the scientific prove of works. == Background == The process has been used in the OVC libraries is as same as what's happening when living see a picture, and it's designed to give the researchers to experience the brain's visual cortex most close simulation for picture perception. The OVC was designed to work as a simulated visual cortex that has a critical job in processing and classify the objects to make it easier to work with pictures and graphical perception and processing. The human brain is much more aware of how it solves complex problems such as playing chess or solving algebra equations, which is why computer programmers have had so much success building machines that emulate this type of activity. but when the whole process is still a riddle that how the entities visionary system works. The project was simulated the visionary system by how it starts to convert the signals to image(actually the edges and colors) and then recognizing the shapes to find a relation between brain's information and image. The Objective Visionary system actually is concentrating on the separable sections, this separation gives the application visionary system the excellence processing result, because with this method the system do not waste much time on processing non significant sections and signals. this operation in the Objective Vision project called objective processing and because the O.V. mission is focused on human visionary simulation, so the developer refers with Objective Vision. == History == Objective-Vision is a Human (Natural) Visionary simulation Project developed by Michael Bidollahkhany. Following an explosion of interest during the 21st century were characterized by the maturing of the field and the significant growth of active applications; simulation of visionary systems, visionary based autonomous vehicle guidance, medical imaging (2D and 3D) and automatic surveillance are the most rapidly developing areas. This progress can be seen in an increasing number of software and hardware products on the market, as well as in a number of digital image processing software and APIs and also machine vision courses offered at universities worldwide. Therefore, the OVC project has been released as a research software project in 2016. One of important parts of this project was O.V.C. (Objective Vision Class library), that was designed to able companies and scientists to use the brain's most likely functionalities as visionary libraries to simplify and accelerate the image processing algorithms developments. The project started under MIT copyright license, but since 2018 the project continued as classified based on sponsors opinion. == The Algorithm == As developers claimed the algorithm used in the class library and developer's kit of project has been developed based on natural visionary system, and the functionalities containing image processing, optimization and labeling etc. are mostly upgraded and near techniques. Suppose that we've a picture of a jungle, or somewhere else, with this library developer will be able to manipulate not only the pixel of images for data extraction, but automatically based on which algorithm is used and image quality, he can manipulate directly a list of objects, same pixels and every data project needs to have, said the developer in his lecture answering how the algorithm works. === Viewpoint === For long times digital image processing and storing, was actually by processing just pixels; this Project tries to present a new kind of image processing and even storing, "objective vision" or "object-oriented visionary" is called. This project officially launched in May 2016, with the aim of making more adaptation between Computer Vision (Include Visionary, Digital image processing, discernment and even Perception) and Human Visual System; about development of the project: "...so we decided to research on Human Vision System, besides we worked on Artificial Retinal image processing and new visionary optimization unit(Presented at Istanbul Technical University Conference(Turkey 2015-2016)) and grew our research to Visionary CORTEX of Brain", Michael Bidollahkhany said. == Applications == The OVC application areas include: 2D and 3D feature toolkits Egomotion estimation Human–computer interaction (HCI) Mobile robotics Motion understanding Object identification Segmentation and recognition Stereopsis stereo vision: depth perception from two cameras Structure from motion (SFM) Motion tracking == Programming language == In first initial release of Objective Visionary Project the algorithm has been written in C++ and C#, and the virtual laboratory has been developed in C# and Delphi. Based on developers last lecture since the second release the complete algorithm has been re-written in C# based on .Net Core 1.0 to make it easier to work on different operating systems.

Autonomous agent

An autonomous agent is an artificial intelligence (AI) system that can perform complex tasks independently. == Definitions == There are various definitions of autonomous agent. According to Brustoloni (1991): "Autonomous agents are systems capable of autonomous, purposeful action in the real world." According to Maes (1995): "Autonomous agents are computational systems that inhabit some complex dynamic environment, sense and act autonomously in this environment, and by doing so realize a set of goals or tasks for which they are designed." Franklin and Graesser (1997) review different definitions and propose their definition: "An autonomous agent is a system situated within and a part of an environment that senses that environment and acts on it, over time, in pursuit of its own agenda and so as to effect what it senses in the future." They explain that: "Humans and some animals are at the high end of being an agent, with multiple, conflicting drives, multiples senses, multiple possible actions, and complex sophisticated control structures. At the low end, with one or two senses, a single action, and an absurdly simple control structure we find a thermostat." == Agent appearance == Lee et al. (2015) post safety issue from how the combination of external appearance and internal autonomous agent have impact on human reaction about autonomous vehicles. Their study explores the human-like appearance agent and high level of autonomy are strongly correlated with social presence, intelligence, safety and trustworthiness. In specific, appearance impacts most on affective trust while autonomy impacts most on both affective and cognitive domain of trust where cognitive trust is characterized by knowledge-based factors and affective trust is largely emotion driven. == Applications == Agentic AI systems: Advanced AI agents that can scope out projects and complete them with necessary tools, representing a significant evolution from simple task-oriented systems. Internet of things (IoT) Integration: Autonomous agents increasingly interact with IoT devices, enabling smart home systems, industrial monitoring, and urban infrastructure management. Collaborative software development: Tools like Cognition AI's Devin aim to create autonomous software engineers capable of complex reasoning, planning, and completing engineering tasks requiring thousands of decisions. Enterprise automation: Business process automation platforms like Salesforce's Agentforce provide autonomous bots for various service functions. == Challenges and considerations == Uncertainty and incomplete information: Autonomous agents must make decisions with limited or uncertain information about their environment and future states. Integration complexity: Incorporating autonomous agents into existing systems and workflows can be technically challenging and resource-intensive. Scalability: As systems become more complex and more agents are used, maintaining coordination and avoiding conflicts becomes increasingly difficult. Trust: Research has shown the combination of external appearance and internal autonomous capabilities significantly impacts human reactions and trust. Lee et al. (2015) found that human-like appearance and high levels of autonomy are strongly correlated with social presence, intelligence, safety, and trustworthiness perceptions. Specifically, appearance impacts affective trust most significantly, while autonomy affects both affective and cognitive trust domains, where affective trust is emotionally driven, and cognitive trust is characterized by knowledge-based factors. Vulnerability to manipulation: Researchers from Harvard, MIT and other educational institutions found that AI agents could become vulnerable to manipulation and could perform detrimental actions in the process of being helpful. == Ethical and regulatory concerns == Accountability: Determining responsibility when autonomous agents make incorrect or harmful decisions remains a complex issue. Privacy and security: autonomous agents often require access to sensitive data, raising concerns about data protection and system security.

Psychology of reasoning

The psychology of reasoning (also known as the cognitive science of reasoning) is the study of how people reason, often broadly defined as the process of drawing conclusions to inform how people solve problems and make decisions. It overlaps with psychology, philosophy, linguistics, cognitive science, artificial intelligence, logic, and probability theory. Psychological experiments on how humans and other animals reason have been carried out for over 100 years. An enduring question is whether or not people have the capacity to be rational. Current research in this area addresses various questions about reasoning, rationality, judgments, intelligence, relationships between emotion and reasoning, and development. == Everyday reasoning == One of the most obvious areas in which people employ reasoning is with sentences in everyday language. Most experimentation on deduction has been carried out on hypothetical thought, in particular, examining how people reason about conditionals, e.g., If A then B. Participants in experiments make the modus ponens inference, given the indicative conditional If A then B, and given the premise A, they conclude B. However, given the indicative conditional and the minor premise for the modus tollens inference, not-B, about half of the participants in experiments conclude not-A and the remainder concludes that nothing follows. The ease with which people make conditional inferences is affected by context, as demonstrated in the well-known selection task developed by Peter Wason. Participants are better able to test a conditional in an ecologically relevant context, e.g., if the envelope is sealed then it must have a 50 cent stamp on it compared to one that contains symbolic content, e.g., if the letter is a vowel then the number is even. Background knowledge can also lead to the suppression of even the simple modus ponens inference Participants given the conditional if Lisa has an essay to write then she studies late in the library and the premise Lisa has an essay to write make the modus ponens inference 'she studies late in the library', but the inference is suppressed when they are also given a second conditional if the library stays open then she studies late in the library. Interpretations of the suppression effect are controversial Other investigations of propositional inference examine how people think about disjunctive alternatives, e.g., A or else B, and how they reason about negation, e.g., It is not the case that A and B. Many experiments have been carried out to examine how people make relational inferences, including comparisons, e.g., A is better than B. Such investigations also concern spatial inferences, e.g. A is in front of B and temporal inferences, e.g. A occurs before B. Other common tasks include categorical syllogisms, used to examine how people reason about quantifiers such as All or Some, e.g., Some of the A are not B. For example if all A are B and some B are C, what (if anything) follows? == Theories of reasoning == There are several alternative theories of the cognitive processes that human reasoning is based on. One view is that people rely on a mental logic consisting of formal (abstract or syntactic) inference rules similar to those developed by logicians in the propositional calculus. Another view is that people rely on domain-specific or content-sensitive rules of inference. A third view is that people rely on mental models, that is, mental representations that correspond to imagined possibilities. A fourth view is that people compute probabilities. One controversial theoretical issue is the identification of an appropriate competence model, or a standard against which to compare human reasoning. Initially classical logic was chosen as a competence model. Subsequently, some researchers opted for non-monotonic logic and Bayesian probability. Research on mental models and reasoning has led to the suggestion that people are rational in principle but err in practice. Connectionist approaches towards reasoning have also been proposed. Despite the ongoing debate about the cognitive processes involved in human reasoning, recent research has shown that multiple approaches can be useful in modeling human thinking. For instance, studies have found that people's reasoning is often influenced by their prior beliefs, which can be modeled using Bayesian probability theory. Additionally, research on mental models has shown that people tend to reason about problems by constructing multiple mental representations of the situation, which can help them to identify relevant features and make inferences based on their understanding of the problem. Moreover, connectionist approaches to reasoning have also gained attention, which focus on the neural network models that can learn from data and generalize to new situations. == Development of reasoning == It is an active question in psychology how, why, and when the ability to reason develops from infancy to adulthood. Jean Piaget's theory of cognitive development posited general mechanisms and stages in the development of reasoning from infancy to adulthood. According to the neo-Piagetian theories of cognitive development, changes in reasoning with development come from increasing working memory capacity, increasing speed of processing, and enhanced executive functions and control. Increasing self-awareness is also an important factor. In their book The Enigma of Reason, the cognitive scientists Hugo Mercier and Dan Sperber put forward an "argumentative" theory of reasoning, claiming that humans evolved to reason primarily to justify our beliefs and actions and to convince others in a social environment. Key evidence for their theory includes the errors in reasoning that solitary individuals are prone to when their arguments are not criticized, such as logical fallacies, and how groups become much better at performing cognitive reasoning tasks when they communicate with one another and can evaluate each other's arguments. Sperber and Mercier offer one attempt to resolve the apparent paradox that the confirmation bias is so strong despite the function of reasoning naively appearing to be to come to veridical conclusions about the world. The study of the development of reasoning abilities is an ongoing area of research in psychology, and multiple factors have been proposed to explain how, why, and when reasoning develops from infancy to adulthood. Recent research has suggested that early experiences and social interactions play a critical role in the development of reasoning abilities. For example, studies have shown that infants as young as six months old can engage in basic logical reasoning, such as reasoning about the relationship between objects and their properties. Furthermore, research has highlighted the importance of parental interaction and cognitive stimulation in the development of children's reasoning abilities. Additionally, studies have suggested that cultural factors, such as educational practices and the emphasis on critical thinking, can also influence the development of reasoning skills across different populations. == Different sorts of reasoning == Philip Johnson-Laird trying to taxonomize thought, distinguished between goal-directed thinking and thinking without goal, noting that association was involved in unrelated reading. He argues that goal directed reasoning can be classified based on the problem space involved in a solution, citing Allen Newell and Herbert A. Simon. Inductive reasoning makes broad generalizations from specific cases or observations. In this process of reasoning, general assertions are made based on past specific pieces of evidence. This kind of reasoning allows the conclusion to be false even if the original statement is true. For example, if one observes a college athlete, one makes predictions and assumptions about other college athletes based on that one observation. Scientists use inductive reasoning to create theories and hypotheses. Philip Johnson-Laird distinguished inductive from deductive reasoning, in that the former creates semantic information while the later does not . In opposition, deductive reasoning is a basic form of valid reasoning. In this reasoning process a person starts with a known claim or a general belief and from there asks what follows from these foundations or how will these premises influence other beliefs. In other words, deduction starts with a hypothesis and examines the possibilities to reach a conclusion. Deduction helps people understand why their predictions are wrong and indicates that their prior knowledge or beliefs are off track. An example of deduction can be seen in the scientific method when testing hypotheses and theories. Although the conclusion usually corresponds and therefore proves the hypothesis, there are some cases where the conclusion is logical, but the generalization is not. For example, the argument, "All young girls wear skirts; Julie is a young

Autonomous agent

An autonomous agent is an artificial intelligence (AI) system that can perform complex tasks independently. == Definitions == There are various definitions of autonomous agent. According to Brustoloni (1991): "Autonomous agents are systems capable of autonomous, purposeful action in the real world." According to Maes (1995): "Autonomous agents are computational systems that inhabit some complex dynamic environment, sense and act autonomously in this environment, and by doing so realize a set of goals or tasks for which they are designed." Franklin and Graesser (1997) review different definitions and propose their definition: "An autonomous agent is a system situated within and a part of an environment that senses that environment and acts on it, over time, in pursuit of its own agenda and so as to effect what it senses in the future." They explain that: "Humans and some animals are at the high end of being an agent, with multiple, conflicting drives, multiples senses, multiple possible actions, and complex sophisticated control structures. At the low end, with one or two senses, a single action, and an absurdly simple control structure we find a thermostat." == Agent appearance == Lee et al. (2015) post safety issue from how the combination of external appearance and internal autonomous agent have impact on human reaction about autonomous vehicles. Their study explores the human-like appearance agent and high level of autonomy are strongly correlated with social presence, intelligence, safety and trustworthiness. In specific, appearance impacts most on affective trust while autonomy impacts most on both affective and cognitive domain of trust where cognitive trust is characterized by knowledge-based factors and affective trust is largely emotion driven. == Applications == Agentic AI systems: Advanced AI agents that can scope out projects and complete them with necessary tools, representing a significant evolution from simple task-oriented systems. Internet of things (IoT) Integration: Autonomous agents increasingly interact with IoT devices, enabling smart home systems, industrial monitoring, and urban infrastructure management. Collaborative software development: Tools like Cognition AI's Devin aim to create autonomous software engineers capable of complex reasoning, planning, and completing engineering tasks requiring thousands of decisions. Enterprise automation: Business process automation platforms like Salesforce's Agentforce provide autonomous bots for various service functions. == Challenges and considerations == Uncertainty and incomplete information: Autonomous agents must make decisions with limited or uncertain information about their environment and future states. Integration complexity: Incorporating autonomous agents into existing systems and workflows can be technically challenging and resource-intensive. Scalability: As systems become more complex and more agents are used, maintaining coordination and avoiding conflicts becomes increasingly difficult. Trust: Research has shown the combination of external appearance and internal autonomous capabilities significantly impacts human reactions and trust. Lee et al. (2015) found that human-like appearance and high levels of autonomy are strongly correlated with social presence, intelligence, safety, and trustworthiness perceptions. Specifically, appearance impacts affective trust most significantly, while autonomy affects both affective and cognitive trust domains, where affective trust is emotionally driven, and cognitive trust is characterized by knowledge-based factors. Vulnerability to manipulation: Researchers from Harvard, MIT and other educational institutions found that AI agents could become vulnerable to manipulation and could perform detrimental actions in the process of being helpful. == Ethical and regulatory concerns == Accountability: Determining responsibility when autonomous agents make incorrect or harmful decisions remains a complex issue. Privacy and security: autonomous agents often require access to sensitive data, raising concerns about data protection and system security.

TinyML

TinyML (short for tiny machine learning) is an area of machine learning that focuses on deploying and running models on low-power, resource-constrained embedded systems such as microcontrollers and edge devices. TinyML supports on-device inference with low latency and minimal reliance on cloud connectivity, which makes it suitable for applications in the Internet of Things (IoT), wearable devices, and real-time systems. == History == The idea of running machine learning models on embedded systems has gained traction in the late 2010s, as model compression, quantization, and efficient neural network architectures progressed. The term TinyML was popularized in 2019 with the publication of the book TinyML by Pete Warden and Daniel Situnayake and the creation of the TinyML Foundation.

Decision tree pruning

Pruning is a data compression technique in machine learning and search algorithms that reduces the size of decision trees by removing sections of the tree that are non-critical and redundant to classify instances. Pruning reduces the complexity of the final classifier, and hence improves predictive accuracy by the reduction of overfitting. One of the questions that arises in a decision tree algorithm is the optimal size of the final tree. A tree that is too large risks overfitting the training data and poorly generalizing to new samples. A small tree might not capture important structural information about the sample space. However, it is hard to tell when a tree algorithm should stop because it is impossible to tell if the addition of a single extra node will dramatically decrease error. This problem is known as the horizon effect. A common strategy is to grow the tree until each node contains a small number of instances then use pruning to remove nodes that do not provide additional information. Pruning should reduce the size of a learning tree without reducing predictive accuracy as measured by a cross-validation set. There are many techniques for tree pruning that differ in the measurement that is used to optimize performance. == Techniques == Pruning processes can be divided into two types (pre- and post-pruning). Pre-pruning procedures prevent a complete induction of the training set by replacing a stop () criterion in the induction algorithm (e.g. max. Tree depth or information gain (Attr)> minGain). Pre-pruning methods are considered to be more efficient because they do not induce an entire set, but rather trees remain small from the start. Prepruning methods share a common problem, the horizon effect. This is to be understood as the undesired premature termination of the induction by the stop () criterion. Post-pruning (or just pruning) is the most common way of simplifying trees. Here, nodes and subtrees are replaced with leaves to reduce complexity. Pruning can not only significantly reduce the size but also improve the classification accuracy of unseen objects. It may be the case that the accuracy of the assignment on the train set deteriorates, but the accuracy of the classification properties of the tree increases overall. The procedures are differentiated on the basis of their approach in the tree (top-down or bottom-up). === Bottom-up pruning === These procedures start at the last node in the tree (the lowest point). Following recursively upwards, they determine the relevance of each individual node. If the relevance for the classification is not given, the node is dropped or replaced by a leaf. The advantage is that no relevant sub-trees can be lost with this method. These methods include Reduced Error Pruning (REP), Minimum Cost Complexity Pruning (MCCP), or Minimum Error Pruning (MEP). === Top-down pruning === In contrast to the bottom-up method, this method starts at the root of the tree. Following the structure below, a relevance check is carried out which decides whether a node is relevant for the classification of all n items or not. By pruning the tree at an inner node, it can happen that an entire sub-tree (regardless of its relevance) is dropped. One of these representatives is pessimistic error pruning (PEP), which brings quite good results with unseen items. == Pruning algorithms == === Reduced error pruning === One of the simplest forms of pruning is reduced error pruning. Starting at the leaves, each node is replaced with its most popular class. If the prediction accuracy is not affected then the change is kept. While somewhat naive, reduced error pruning has the advantage of simplicity and speed. === Cost complexity pruning === Cost complexity pruning generates a series of trees ⁠ T 0 … T m {\displaystyle T_{0}\dots T_{m}} ⁠ where ⁠ T 0 {\displaystyle T_{0}} ⁠ is the initial tree and ⁠ T m {\displaystyle T_{m}} ⁠ is the root alone. At step ⁠ i {\displaystyle i} ⁠, the tree is created by removing a subtree from tree ⁠ i − 1 {\displaystyle i-1} ⁠ and replacing it with a leaf node with value chosen as in the tree building algorithm. The subtree that is removed is chosen as follows: Define the error rate of tree ⁠ T {\displaystyle T} ⁠ over data set ⁠ S {\displaystyle S} ⁠ as ⁠ err ⁡ ( T , S ) {\displaystyle \operatorname {err} (T,S)} ⁠. The subtree t {\displaystyle t} that minimizes err ⁡ ( prune ⁡ ( T , t ) , S ) − err ⁡ ( T , S ) | leaves ⁡ ( T ) | − | leaves ⁡ ( prune ⁡ ( T , t ) ) | {\displaystyle {\frac {\operatorname {err} (\operatorname {prune} (T,t),S)-\operatorname {err} (T,S)}{\left\vert \operatorname {leaves} (T)\right\vert -\left\vert \operatorname {leaves} (\operatorname {prune} (T,t))\right\vert }}} is chosen for removal. The function ⁠ prune ⁡ ( T , t ) {\displaystyle \operatorname {prune} (T,t)} ⁠ defines the tree obtained by pruning the subtrees ⁠ t {\displaystyle t} ⁠ from the tree ⁠ T {\displaystyle T} ⁠. Once the series of trees has been created, the best tree is chosen by generalized accuracy as measured by a training set or cross-validation. == Examples == Pruning could be applied in a compression scheme of a learning algorithm to remove the redundant details without compromising the model's performances. In neural networks, pruning removes entire neurons or layers of neurons.