In mathematical logic, basic fuzzy logic (or shortly BL), the logic of the continuous t-norms, is one of the t-norm fuzzy logics. It belongs to the broader class of substructural logics, or logics of residuated lattices; it extends the logic MTL of all left-continuous t-norms. == Syntax == === Language === The language of the propositional logic BL consists of countably many propositional variables and the following primitive logical connectives: Implication → {\displaystyle \rightarrow } (binary) Strong conjunction ⊗ {\displaystyle \otimes } (binary). The sign & is a more traditional notation for strong conjunction in the literature on fuzzy logic, while the notation ⊗ {\displaystyle \otimes } follows the tradition of substructural logics. Bottom ⊥ {\displaystyle \bot } (nullary — a propositional constant); 0 {\displaystyle 0} or 0 ¯ {\displaystyle {\overline {0}}} are common alternative signs and zero a common alternative name for the propositional constant (as the constants bottom and zero of substructural logics coincide in MTL). The following are the most common defined logical connectives: Weak conjunction ∧ {\displaystyle \wedge } (binary), also called lattice conjunction (as it is always realized by the lattice operation of meet in algebraic semantics). Unlike MTL and weaker substructural logics, weak conjunction is definable in BL as A ∧ B ≡ A ⊗ ( A → B ) {\displaystyle A\wedge B\equiv A\otimes (A\rightarrow B)} Negation ¬ {\displaystyle \neg } (unary), defined as ¬ A ≡ A → ⊥ {\displaystyle \neg A\equiv A\rightarrow \bot } Equivalence ↔ {\displaystyle \leftrightarrow } (binary), defined as A ↔ B ≡ ( A → B ) ∧ ( B → A ) {\displaystyle A\leftrightarrow B\equiv (A\rightarrow B)\wedge (B\rightarrow A)} As in MTL, the definition is equivalent to ( A → B ) ⊗ ( B → A ) . {\displaystyle (A\rightarrow B)\otimes (B\rightarrow A).} (Weak) disjunction ∨ {\displaystyle \vee } (binary), also called lattice disjunction (as it is always realized by the lattice operation of join in algebraic semantics), defined as A ∨ B ≡ ( ( A → B ) → B ) ∧ ( ( B → A ) → A ) {\displaystyle A\vee B\equiv ((A\rightarrow B)\rightarrow B)\wedge ((B\rightarrow A)\rightarrow A)} Top ⊤ {\displaystyle \top } (nullary), also called one and denoted by 1 {\displaystyle 1} or 1 ¯ {\displaystyle {\overline {1}}} (as the constants top and zero of substructural logics coincide in MTL), defined as ⊤ ≡ ⊥ → ⊥ {\displaystyle \top \equiv \bot \rightarrow \bot } Well-formed formulae of BL are defined as usual in propositional logics. In order to save parentheses, it is common to use the following order of precedence: Unary connectives (bind most closely) Binary connectives other than implication and equivalence Implication and equivalence (bind most loosely) === Axioms === A Hilbert-style deduction system for BL has been introduced by Petr Hájek (1998). Its single derivation rule is modus ponens: from A {\displaystyle A} and A → B {\displaystyle A\rightarrow B} derive B . {\displaystyle B.} The following are its axiom schemata: ( B L 1 ) : ( A → B ) → ( ( B → C ) → ( A → C ) ) ( B L 2 ) : A ⊗ B → A ( B L 3 ) : A ⊗ B → B ⊗ A ( B L 4 ) : A ⊗ ( A → B ) → B ⊗ ( B → A ) ( B L 5 a ) : ( A → ( B → C ) ) → ( A ⊗ B → C ) ( B L 5 b ) : ( A ⊗ B → C ) → ( A → ( B → C ) ) ( B L 6 ) : ( ( A → B ) → C ) → ( ( ( B → A ) → C ) → C ) ( B L 7 ) : ⊥ → A {\displaystyle {\begin{array}{ll}{\rm {(BL1)}}\colon &(A\rightarrow B)\rightarrow ((B\rightarrow C)\rightarrow (A\rightarrow C))\\{\rm {(BL2)}}\colon &A\otimes B\rightarrow A\\{\rm {(BL3)}}\colon &A\otimes B\rightarrow B\otimes A\\{\rm {(BL4)}}\colon &A\otimes (A\rightarrow B)\rightarrow B\otimes (B\rightarrow A)\\{\rm {(BL5a)}}\colon &(A\rightarrow (B\rightarrow C))\rightarrow (A\otimes B\rightarrow C)\\{\rm {(BL5b)}}\colon &(A\otimes B\rightarrow C)\rightarrow (A\rightarrow (B\rightarrow C))\\{\rm {(BL6)}}\colon &((A\rightarrow B)\rightarrow C)\rightarrow (((B\rightarrow A)\rightarrow C)\rightarrow C)\\{\rm {(BL7)}}\colon &\bot \rightarrow A\end{array}}} The axioms (BL2) and (BL3) of the original axiomatic system were shown to be redundant (Chvalovský, 2012) and (Cintula, 2005). All the other axioms were shown to be independent (Chvalovský, 2012). == Semantics == Like in other propositional t-norm fuzzy logics, algebraic semantics is predominantly used for BL, with three main classes of algebras with respect to which the logic is complete: General semantics, formed of all BL-algebras — that is, all algebras for which the logic is sound Linear semantics, formed of all linear BL-algebras — that is, all BL-algebras whose lattice order is linear Standard semantics, formed of all standard BL-algebras — that is, all BL-algebras whose lattice reduct is the real unit interval [0, 1] with the usual order; they are uniquely determined by the function that interprets strong conjunction, which can be any continuous t-norm.
Self-supervised learning
Self-supervised learning (SSL) is a paradigm in machine learning where a model is trained on a task using the data itself to generate supervisory signals, rather than relying on externally-provided labels. In the context of neural networks, self-supervised learning aims to leverage inherent structures or relationships within the input data to create meaningful training signals. SSL tasks are designed so that solving them requires capturing essential features or relationships in the data. The input data is typically augmented or transformed in a way that creates pairs of related samples, where one sample serves as the input, and the other is used to formulate the supervisory signal. This augmentation can involve introducing noise, cropping, rotation, or other transformations. Self-supervised learning more closely imitates the way humans learn to classify objects. During SSL, the model learns in two steps. First, the task is solved based on an auxiliary or pretext classification task using pseudo-labels, which help to initialize the model parameters. Next, the actual task is performed with supervised or unsupervised learning. Self-supervised learning has produced promising results in recent years, and has found practical application in fields such as audio processing, and is being used by Facebook and others for speech recognition. == Pseudo-labels == Pseudo-labels are automatically generated labels that a model assigns to unlabeled data based on its own predictions. They are widely used in self-supervised and semi-supervised learning, where ground-truth annotations are limited or unavailable. By treating predicted labels as surrogate ground truth, learning algorithms can make use of large quantities of unlabeled data in the training process. Pseudo-labeling also plays an important role in systems that must adapt to concept drift, where the statistical properties of the data change over time. In these scenarios, the model may detect that an incoming instance deviates from previously learned behavior. The system then generates a classification result for that instance, and this predicted class is used as a pseudo-label for updating or retraining model components that are becoming outdated. This approach enables continuous adaptation in dynamic environments without requiring manual annotation. In many adaptive learning pipelines, pseudo-labels are chosen when the classifier produces sufficiently confident predictions, reducing the risk of propagating errors. These pseudo-labeled instances are then incorporated into training to refresh or evolve the model's understanding of emerging data patterns, particularly when existing components show signs of “aging” due to drift or distributional shifts. This strategy reduces reliance on manual labeling while helping maintain long-term model performance. == Types == === Autoassociative self-supervised learning === Autoassociative self-supervised learning is a specific category of self-supervised learning where a neural network is trained to reproduce or reconstruct its own input data. In other words, the model is tasked with learning a representation of the data that captures its essential features or structure, allowing it to regenerate the original input. The term "autoassociative" comes from the fact that the model is essentially associating the input data with itself. This is often achieved using autoencoders, which are a type of neural network architecture used for representation learning. Autoencoders consist of an encoder network that maps the input data to a lower-dimensional representation (latent space), and a decoder network that reconstructs the input from this representation. The training process involves presenting the model with input data and requiring it to reconstruct the same data as closely as possible. The loss function used during training typically penalizes the difference between the original input and the reconstructed output (e.g. mean squared error). By minimizing this reconstruction error, the autoencoder learns a meaningful representation of the data in its latent space. === Contrastive self-supervised learning === For a binary classification task, training data can be divided into positive examples and negative examples. Positive examples are those that match the target. For example, if training a classifier to identify birds, the positive training data would include images that contain birds. Negative examples would be images that do not. Contrastive self-supervised learning uses both positive and negative examples. The loss function in contrastive learning is used to minimize the distance between positive sample pairs, while maximizing the distance between negative sample pairs. An early example uses a pair of 1-dimensional convolutional neural networks to process a pair of images and maximize their agreement. Contrastive Language-Image Pre-training (CLIP) allows joint pretraining of a text encoder and an image encoder, such that a matching image-text pair have image encoding vector and text encoding vector that span a small angle (having a large cosine similarity). InfoNCE (Noise-Contrastive Estimation) is a method to optimize two models jointly, based on Noise Contrastive Estimation (NCE). Given a set X = { x 1 , … x N } {\displaystyle X=\left\{x_{1},\ldots x_{N}\right\}} of N {\displaystyle N} random samples containing one positive sample from p ( x t + k ∣ c t ) {\displaystyle p\left(x_{t+k}\mid c_{t}\right)} and N − 1 {\displaystyle N-1} negative samples from the 'proposal' distribution p ( x t + k ) {\displaystyle p\left(x_{t+k}\right)} , it minimizes the following loss function: L N = − E X [ log f k ( x t + k , c t ) ∑ x j ∈ X f k ( x j , c t ) ] {\displaystyle {\mathcal {L}}_{\mathrm {N} }=-\mathbb {E} _{X}\left[\log {\frac {f_{k}\left(x_{t+k},c_{t}\right)}{\sum _{x_{j}\in X}f_{k}\left(x_{j},c_{t}\right)}}\right]} === Non-contrastive self-supervised learning === Non-contrastive self-supervised learning (NCSSL) uses only positive examples. Counterintuitively, NCSSL converges on a useful local minimum rather than reaching a trivial solution, with zero loss. For the example of binary classification, it would trivially learn to classify each example as positive. Effective NCSSL requires an extra predictor on the online side that does not back-propagate on the target side. === Joint-Embedding and Predictive Architectures === A major class of self-supervised learning moves beyond contrastive pairs, instead maximizing the agreement between views while preventing collapse through statistical constraints. Rooted in Deep Canonical Correlation Analysis (Deep CCA), this approach includes Joint-Embedding Architectures (JEA) like Barlow Twins and VICReg, which enforce covariance constraints to learn invariant representations without negative sampling. Deep Latent Variable Path Modelling (DLVPM) generalizes this to multimodal systems, using path models to enforce correlation and orthogonality across diverse data types. In 2022 Yann LeCun introduced Joint-Embedding Predictive Architectures (JEPA) as a step towards decision making, reasoning, and autonomous human intelligence in machines, including self-improvement through autonomous learning. Founded in representation learning, LeCun included the concept of a “world model” in JEPA which aims to enable machines to replicate human intellect by providing machines with a concept for the world in which they exist. Unlike autoencoders, JEPAs operate entirely in latent space, avoiding pixel-level noise to focus on semantic structure. Rather than just learning invariance, JEPAs learn by predicting masked latent representations from visible context. JEPA has been applied to domains such as image analysis, audio processing, and motion in images and video. == Comparison with other forms of machine learning == SSL belongs to supervised learning methods insofar as the goal is to generate a classified output from the input. At the same time, however, it does not require the explicit use of labeled input-output pairs. Instead, correlations, metadata embedded in the data, or domain knowledge present in the input are implicitly and autonomously extracted from the data. These supervisory signals, extracted from the data, can then be used for training. SSL is similar to unsupervised learning in that it does not require labels in the sample data. Unlike unsupervised learning, however, learning is not done using inherent data structures. Semi-supervised learning combines supervised and unsupervised learning, requiring only a small portion of the learning data be labeled. In transfer learning, a model designed for one task is reused on a different task. Training an autoencoder intrinsically constitutes a self-supervised process, because the output pattern needs to become an optimal reconstruction of the input pattern itself. However, in current jargon, the term 'self-supervised' often refers to tasks based on a pretext-task training setup
Douwe Kiela
Douwe Kiela is a Dutch-American research scientist and entrepreneur working in the field of artificial intelligence with a focus on machine learning and natural language processing. He is a research scientist director at Google DeepMind. He previously co-founded and served as CEO of Contextual AI, an enterprise software company that provides a platform for building grounded AI agents for enterprise knowledge bases. He previously led the research team at Meta AI that introduced the RAG approach in 2020, co-authoring the foundational paper "Retrieval-Augmented Generation for Knowledge-Intensive NLP Tasks." Kiela also served as Head of Research at Hugging Face and is an adjunct professor in Symbolic Systems at Stanford University. == Early life and education == Douwe Kiela was born in Amsterdam, Netherlands, in 1986. He earned a Bachelor of Science degree in Liberal Arts and Sciences from Utrecht University, with a double major in Cognitive Artificial Intelligence and Philosophy. He then obtained an MSc in logic (cum laude) from the University of Amsterdam's Institute for Logic, Language and Computation (ILLC). Kiela received an MPhil and PhD in Computer Science from the University of Cambridge, specializing in natural language processing and machine learning. == Career == === Facebook AI Research (Meta) === In 2016, Kiela joined Facebook AI Research (FAIR) as a postdoctoral researcher, later becoming a research scientist in New York. While at Meta, he co-authored papers in natural language processing, with a focus on multimodal and grounded language learning. His projects included creating a virtual assistant bot that could navigate tourists around a city and leading the development of Dynabench, an interactive benchmarking platform released in 2020 that used human feedback to test and improve language models. In 2020, Kiela led the Meta AI research team that introduced Retrieval-Augmented Generation (RAG), co-authoring the influential paper "Retrieval-Augmented Generation for Knowledge-Intensive NLP Tasks," alongside Patrick Lewis, Ethan Perez, and other researchers. The RAG framework transformed how large language models access and incorporate external information by allowing them to retrieve relevant context from external knowledge bases at query time, rather than relying solely on pre-trained data. This approach addressed key limitations such as hallucination, outdated information, and lack of source attribution. The RAG technique has since become widely adopted in enterprise AI applications and knowledge-intensive natural language processing tasks. === Hugging Face === After leaving Meta, Kiela served as Head of Research at Hugging Face. === Contextual AI === In 2023, Kiela co-founded Contextual AI with Amanpreet Singh, another former researcher at Facebook AI Research and Hugging Face. The Mountain View-based company develops a platform for building grounded AI agents for enterprises, focusing on applications in technology, semiconductor, logistics, finance, and media sectors. Contextual AI raised $20 million in seed funding in June 2023, led by Bain Capital Ventures. In August 2024, the company completed an $80 million Series A funding round led by Greycroft, with participation from Bezos Expeditions, NVentures (Nvidia), HSBC Ventures, and Snowflake Ventures, among others. In May 2026, Kiela joined Google DeepMind as part of a licensing agreement between Google and Contextual AI under which more than 20 Contextual AI researchers joined DeepMind. Following his departure, Jay Chen became interim CEO of Contextual AI. === Academic roles === Douwe Kiela serves as an adjunct professor in Symbolic Systems at Stanford University. In a 2023 interview with the Stanford Daily, he commented on the development of Alpaca, a low-cost instruction-finetuned model based on Meta's LLaMA, and emphasized the importance of open academic research in large language models.
Hideto Tomabechi
Hideto Tomabechi (苫米地 英人, Tomabechi Hideto; born 1959) is a Japanese cognitive scientist who is an adjunct fellow at Carnegie Mellon University and has had an executive role in several companies. == Early life and education == He grew up in Minato-ku, Tokyo. He graduated from Komaba Toho High School and then joined the University of Massachusetts Amherst. He received his first degree from Sophia University, then joined Mitsubishi Real Estate. Tomabechi was a Fulbright Scholar at Yale University and became member of Yale University Artificial Intelligence Research Center and Yale Cognitive Science Program. Hideto Tomabechi's research topic was: Cognition Models for Language Expressions and Computational Methods (Tomabechi Algorithm). Hideto Tomabechi received his Ph.D. in the field of computational linguistics from Carnegie Mellon University. His 1993 Ph.D. Thesis was entitled "Efficient Unification for Natural Language". == Career timeline == 1992-1998: Director, Justsystem Scientific Institute. 1998: CEO of Cognitive Research Laboratories Inc. 2007: Adjunct Fellow at the Cyber Security & Privacy Research Institute (CyLab) at Carnegie Mellon University. 2020: Visiting professor at Nano & Life Research Center, Waseda University. 2020: Chairman, Resilience Japan, LLC. 2022: Chairman of Japan Society for Foreign Policy. == Brain research == In 1993, Hideto Tomabechi became director of the Development Department. Later, Tomabechi became director of the JustSystems Basic Research Institute Tomabechi researched the basic functions of the human brain and mind. The purpose of brain and consciousness research were to develop the human machine interface. The main areas of research were altered states of consciousness, hypnosis, homeostasis, brain functions, and functions of the human mind in cyberspace. Dr. Tomabechi founded the Bechi Unit, the world's first virtual currency at JustSystems, based on Tomabech Algorithms. == Brainwashing == Tomabechi was the scientist who deprogrammed the leaders of the religious cult responsible for the terrorist attack in the Tokyo subway. The cult (Aum Shinrikyo) brainwashed its people and they carried out the attacks in an influenced state of consciousness.
Transfer-based machine translation
Transfer-based machine translation is a type of machine translation (MT). It is currently one of the most widely used methods of machine translation. In contrast to the simpler direct model of MT, transfer MT breaks translation into three steps: analysis of the source language text to determine its grammatical structure, transfer of the resulting structure to a structure suitable for generating text in the target language, and finally generation of this text. Transfer-based MT systems are thus capable of using knowledge of the source and target languages. == Design == Both transfer-based and interlingua-based machine translation have the same idea: to make a translation it is necessary to have an intermediate representation that captures the "meaning" of the original sentence in order to generate the correct translation. In interlingua-based MT this intermediate representation must be independent of the languages in question, whereas in transfer-based MT, it has some dependence on the language pair involved. The way in which transfer-based machine translation systems work varies substantially, but in general they follow the same pattern: they apply sets of linguistic rules which are defined as correspondences between the structure of the source language and that of the target language. The first stage involves analysing the input text for morphology and syntax (and sometimes semantics) to create an internal representation. The translation is generated from this representation using both bilingual dictionaries and grammatical rules. It is possible with this translation strategy to obtain fairly high quality translations, with accuracy in the region of 90% (although this is highly dependent on the language pair in question, for example the distance between the two). == Operation == In a rule-based machine translation system the original text is first analysed morphologically and syntactically in order to obtain a syntactic representation. This representation can then be refined to a more abstract level putting emphasis on the parts relevant for translation and ignoring other types of information. The transfer process then converts this final representation (still in the original language) to a representation of the same level of abstraction in the target language. These two representations are referred to as "intermediate" representations. From the target language representation, the stages are then applied in reverse. == Analysis and transformation == Various methods of analysis and transformation can be used before obtaining the final result. Along with these statistical approaches may be augmented generating hybrid systems. The methods which are chosen and the emphasis depends largely on the design of the system, however, most systems include at least the following stages: Morphological analysis. Surface forms of the input text are classified as to part-of-speech (e.g. noun, verb, etc.) and sub-category (number, gender, tense, etc.). All of the possible "analyses" for each surface form are typically made output at this stage, along with the lemma of the word. Lexical categorisation. In any given text some of the words may have more than one meaning, causing ambiguity in analysis. Lexical categorisation looks at the context of a word to try to determine the correct meaning in the context of the input. This can involve part-of-speech tagging and word sense disambiguation. Lexical transfer. This is basically dictionary translation; the source language lemma (perhaps with sense information) is looked up in a bilingual dictionary and the translation is chosen. Structural transfer. While the previous stages deal with words, this stage deals with larger constituents, for example phrases and chunks. Typical features of this stage include concordance of gender and number, and re-ordering of words or phrases. Morphological generation. From the output of the structural transfer stage, the target language surface forms are generated. == Transfer types == One of the main features of transfer-based machine translation systems is a phase that "transfers" an intermediate representation of the text in the original language to an intermediate representation of text in the target language. This can work at one of two levels of linguistic analysis, or somewhere in between. The levels are: Superficial transfer (or syntactic). This level is characterised by transferring "syntactic structures" between the source and target languages. It is suitable for languages in the same family or of the same type, for example in the Romance languages between Spanish, Catalan, French, Italian, etc. Deep transfer (or semantic). This level constructs a semantic representation that is dependent on the source language. This representation can consist of a series of structures which represent the meaning. In these transfer systems predicates are typically produced. The translation also typically requires structural transfer. This level is used to translate between more distantly related languages (e.g. Spanish-English or Spanish-Basque, etc.)
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.
How to Choose an AI Voice Assistant
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