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Dabbler is natural media drawing software for beginners. It was initially developed by Fractal Design Corporation. It is a simplified version of Fractal Design Painter, and included multimedia tutorials and a fullscreen interface. Dabbler was released as "Art Dabbler" after the MetaCreations merger, and rights were eventually transferred to Corel. Dabbler operating systems are Mac OS and Microsoft Windows.
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Human–AI interaction is a developing field of research and a sub-field of human–computer interaction (HCI). HCI is a field of research that explores the interactions between humans and computer-based technology, focusing on design implementation, user experience, and psychological factors. With the proliferation of artificial intelligence (AI), there has developed a sub-section of HCI research dedicated specifically to artificial intelligence and how people interact with and are impacted by it. This is human–AI interaction, abbreviated either as HAX or HAII. == Introduction == Artificial intelligence (AI), in general, has fluid definitions and varied research applications, but in brief can be applied to mechanizing tasks that would require human intelligence to complete. AI are tools designed to replicate the human abilities of navigating uncertainty, active learning, and processing information in different contexts. Within the context of HCI and HAX research, artificial intelligence can be broken into two sub-fields, natural language processing (NLP) and computer vision (CV). AI technologies notably include machine-learning, deep-learning and neural networks, and large-language models (LLMs). As a new and rapidly developing technology, AI is changing how computers work and therefore changing how humans interact with computers. Unlike the traditional human-computer interaction, where a human directs a machine, human-AI interaction is characterized by a more collaborative relationship between the computer program (the AI) and the human user, as AI is perceived as an active agent rather than a tool. This changing dynamic creates new questions and necessitates new research methods that are not present in traditional HCI research. According to a scoping review on the state of the discipline, the HAX field comprises research on the "design, development, and evaluation of AI systems" and encompasses the themes of human-AI collaboration, human-AI competition, human-AI conflict, and human-AI symbiosis. == Design == Machine learning and artificial intelligence have been used for decades in targeted advertising and to recommend content in social media. Ethical Guidelines (Framework for ethical AI development) == User Experience (UX) == This section should handle research on how users interact with tools. What techniques do they use, do they develop habits, what types of programs and devices are they using to access these tools, what do they use these tools to do exactly. === Cognitive Frameworks in AI Tool Users === AI has been viewed with various expectations, attributions, and often misconceptions. Many people exclusively understand AI as the LLM chatbots they interact with, like ChatGPT or Claude, or other generative AI programs. [Insert section: discuss how people interact with these specific AI tools as a connection to the following paragraphs] Most fundamentally, humans have a mental model of understanding AI's reasoning and motivation for its decision recommendations, and building a holistic and precise mental model of AI helps people create prompts to receive more valuable responses from AI. However, these mental models are not whole because people can only gain more information about AI through their limited interaction with it; more interaction with AI builds a better mental model that a person may build to produce better prompt outcomes. Research on human-AI interaction has emphasized that users develop mental models of AI systems and revise those models through repeated use, feedback, and explanation, while design research has stressed the importance of communicating capabilities and limitations early and supporting trust calibration through explanation and correction. In a 2025 SSRN working paper, John DeVadoss proposed "Hypothetico-Deductive Interaction" (HDI), a framework that describes human-AI interaction as a mutual process of conjecture and refutation in which users test assumptions about an AI system's capabilities while the system infers and updates assumptions about user goals through its responses and clarifying questions. DeVadoss argued that this framing helps explain prompt iteration, weak capability awareness, and trust miscalibration, and suggested design responses such as clearer communication of uncertainty, easier correction, actionable explanations, and safer failure modes. == Research themes == === Human-AI collaboration === Human-AI collaboration occurs when the human and AI supervise the task on the same level and extent to achieve the same goal. Some collaboration occurs in the form of augmenting human capability. AI may help human ability in analysis and decision-making through providing and weighing a volume of information, and learning to defer to the human decision when it recognizes its unreliability. It is especially beneficial when the human can detect a task that AI can be trusted to make few errors so that there is not a lot of excessive checking process required on the human's end. Some findings show signs of human-AI augmentation, or human–AI symbiosis, in which AI enhances human ability in a way that co-working on a task with AI produces better outcomes than a human working alone. For example: the quality and speed of customer service tasks increase when a human agent collaborates with AI, training on specific models allows AI to improve diagnoses in clinical settings, and AI with human-intervention can improve creativity of artwork while fully AI-generated haikus were rated negatively. Human-AI synergy, a concept in which human-AI collaboration would produce more optimal outcomes than either human or AI working alone could explain why AI does not always help with performance. Some AI features and development may accelerate human-AI synergy, while others may stagnate it. For example, when AI updates for better performance, it sometimes worsens the team performance with human and AI by reducing the compatibility with the new model and the mental model a user has developed on the previous version. Research has found that AI often supports human capabilities in the form of human-AI augmentation and not human-AI synergy, potentially because people rely too much on AI and stop thinking on their own. Prompting people to actively engage in analysis and think when to follow AI recommendations reduces their over-reliance, especially for individuals with higher need for cognition. === Human-AI competition === Robots and computers have substituted routine tasks historically completed by humans, but agentic AI has made it possible to also replace cognitive tasks including taking phone calls for appointments and driving a car. At the point of 2016, research has estimated that 45% of paid activities could be replaced by AI by 2030. Perceived autonomy of robots is known to increase people's negative attitude toward them, and worry about the technology taking over leads people to reject it. There has been a consistent tendency of algorithm aversion in which people prefer human advice over AI advice. However, people are not always able to tell apart tasks completed by AI or other humans. See AI takeover for more information. It is also notable that this sentiment is more prominent in the Western cultures as Westerners tend to show less positive views about AI compared to East Asians. == Research on the psychological impacts of AI == === Perception on others who use AI === As much as people perceive and make judgment about AI itself, they also form impressions of themselves and others who use AI. In the workplace, employees who disclose the use of AI in their tasks are more likely to receive feedback that they are not as hardworking as those who are in the same job who receive non-AI help to complete the same tasks. AI use disclosure diminishes the perceived legitimacy in the employee's task and decision making which ultimately leads observers to distrust people who use AI. Although these negative effects of AI use disclosure are weakened by the observers who use AI frequently themselves, the effect is still not attenuated by the observers' positive attitude towards AI. === Bias, AI, and human === Although AI provides a wide range of information and suggestions to its users, AI itself is not free of biases and stereotypes, and it does not always help people reduce their cognitive errors and biases. People are prone to such errors by failing to see other potential ideas and cases that are not listed by AI responses and committing to a decision suggested by AI that directly contradicts the correct information and directions that they are already aware of. Gender bias is also reflected as the female gendering of AI technologies which conceptualizes females as a helpful assistant. == Emotional connection with AI == Human-AI interaction has been theorized in the context of interpersonal relationships mainly in social psychology, communications and media studies, and as a technology interface through the lens of hu
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The Artificial Inventor Project (AIP) is a global legal initiative headed by Professor Ryan Abbott dedicated to pursuing intellectual property (IP) rights for inventions and creative works generated autonomously by artificial intelligence (AI) systems without traditional human inventorship or authorship. The project coordinates a series of pro bono test cases worldwide, aiming to prompt law reform and public debate on how IP law should accommodate non-human creators. == History == In 2019, AIP filed patent applications in multiple jurisdictions, including the United States, United Kingdom, European Patent Office, Australia, Switzerland, and South Africa, naming the AI system DABUS (Device for the Autonomous Bootstrapping of Unified Sentience), created by Stephen Thaler, as the inventor. The aim was to challenge legal norms that require inventors to be natural persons and highlight pressing policy questions about AI-generated innovation and IP regimes. == Legal proceedings by jurisdiction == === Australia === In July 2021, a Federal Court of Australia judge (Beach J) ruled that AI can be considered an inventor under the Patents Act 1990, ordering IP Australia to reinstate the relevant patent. However, the full court then overturned this ruling on appeal and denied further review. === European Patent Office === The EPO Board of Appeal determined in 2022 that only a human inventor may be named, rendering DABUS‑based applications unacceptable. === South Africa === In 2021, a patent was granted listing DABUS as the inventor. As South Africa’s procedural system does not involve substantive inventorship review, the grant proceeded on formal grounds alone. === Switzerland === On 26 June 2025, the Swiss Federal Administrative Court ruled that artificial intelligence systems such as DABUS cannot be listed as inventors on patent applications. The court upheld the existing practice of the Swiss Federal Institute of Intellectual Property (IPI), affirming that only natural persons may be recognized as inventors under Swiss patent law. === United Kingdom === In December 2023, the UK Supreme Court unanimously held that AI systems cannot be legally recognized as inventors, affirming that "an inventor must be a person" under current British law. === United States === In Thaler v. Hirshfeld (2021), a U.S. federal court agreed with the USPTO that inventors must be natural persons, rejecting the DABUS application and setting a precedent consistent with existing statute and administrative policy. == Criticism and impact == The project has fueled substantial discourse. Critics caution that allowing AI inventorship may complicate notions of accountability and ownership. Proponents argue that legal recognition must evolve to avoid disincentivizing innovation produced by AI and to maintain honesty about the true source of invention.
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.ai is the Internet country code top-level domain (ccTLD) for Anguilla, a British Overseas Territory in the Caribbean. It is administered by the government of Anguilla. It is a popular domain hack with companies and projects related to the artificial intelligence industry (AI). Google's ad targeting treats .ai as a generic top-level domain (gTLD) because "users and website owners frequently see [the domain] as being more generic than country-targeted." In 2021, Google Search analyst Gary Illyes announced that ".ai" had been added to Google’s list of generic country-code top-level domains, meaning that Google would no longer infer Anguilla-specific targeting from the ccTLD. Identity Digital began managing the domain as of January 2025. == Second and third level registrations == Registrations within off.ai, com.ai, net.ai, and org.ai are available worldwide without restriction. From 15 September 2009, second level registrations within .ai are available to everyone worldwide. == Registration == The minimum registration term allowed for .ai domains is 2 through 10 years for registration and renewal, and a 2-year renewal for domain transfer. Identity Digital is the authority in charge of managing this extension. Registrations began on 16 February 1995. The limits on the number of characters used for the domain name are, at a minimum, from 1 to 3, depending on the registrar, and always at most 63 characters. The character set supported for .ai domain names includes A–Z, a–z, 0–9, and hyphen. As of November 2022, .ai domains cannot accommodate IDN characters. There are no requirements for registering a domain, including local and foreign residents. A .ai domain can be suspended or revoked, if the domain is involved in illegal activity such as violating trademarks or copyrights. Usage must not violate the laws of Anguilla. Anguilla uses the UDRP. Filing a UDRP challenge requires using one of the ICANN Approved Dispute Resolution Service Providers. If the domain is with an ICANN accredited registrar, they should work with the arbitrator. Usually this means either doing nothing or transferring a domain. .ai domains are transferable to any desired registrars as the registration of domain is done maintaining EPP. There used to be a whois.ai-based platform of expired domains in which those could be procured and auctioned every ten days through a standard online process. The last auctions of such kind closed there in December 2024; the platform had been scheduled for shutdown on 30 June 2025, but remained online in the months following that date. == Valuation == Domains cost depends on the registrar, with yearly fees ranging from US$140 (the base fee, as established by Anguilla) to $200. As of July 2025, the highest-valued .ai domain is an undisclosed one sold on 8 November 2023, on Escrow.com, for US$1,500,000—months after an initial $300,000 sale to the same buyer. Among the publicly disclosed ones, the most valued, fin.ai, was sold for $1,000,000 in March 2025. On 16 December 2017, the .ai registry started supporting the Extensible Provisioning Protocol (EPP) and migrated all of its domains onto an EPP system. Consequently, many registrars are allowed to sell .ai domains. Since that date, the .ai ccTLD has also been popular with artificial intelligence companies and organisations. Though such trends are primarily seen among new AI based companies or startups, many established AI and Tech companies preferred not to opt for .ai domains. For example, DeepMind has its domain retained at .com; Meta has redirected its facebook.ai domain to ai.meta.com. == Impact on Anguilla's economy == The registration fees earned from the .ai domains go to the treasury of the Government of Anguilla. As per a 2018 New York Times report, the total revenue generated out of selling .ai domains was $2.9 million. In 2023, Anguilla's government made about US$32 million from fees collected for registering .ai domains; that amounted to over 10% of gross domestic product for the territory. "In the years before the real breakthrough of AI, revenue from .ai domains made up less than 1% of our state income, by 2025 it will be around 47%," explained Jose Vanterpool, Minister of Infrastructure and Communications (MICUHITES), in an interview with BBC. The high 90% renewal rate of .ai domains and the 2025 renewal wave of domains registered in 2023 are driving another surge in state revenues, according to Domaintechnik.
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In representation learning, knowledge graph embedding (KGE), also called knowledge representation learning (KRL), or multi-relation learning, is a machine learning task of learning a low-dimensional representation of a knowledge graph's entities and relations while preserving their semantic meaning. Leveraging their embedded representation, knowledge graphs can be used for various applications such as link prediction, triple classification, entity recognition, clustering, and relation extraction. == Definition == A knowledge graph G = { E , R , F } {\displaystyle {\mathcal {G}}=\{E,R,F\}} is a collection of entities E {\displaystyle E} , relations R {\displaystyle R} , and facts F {\displaystyle F} . A fact is a triple ( h , r , t ) ∈ F {\displaystyle (h,r,t)\in F} that denotes a link r ∈ R {\displaystyle r\in R} between the head h ∈ E {\displaystyle h\in E} and the tail t ∈ E {\displaystyle t\in E} of the triple. Another notation that is often used in the literature to represent a triple (or fact) is ⟨ head , relation , tail ⟩ {\displaystyle \langle {\text{head}},{\text{relation}},{\text{tail}}\rangle } . This notation is called the Resource Description Framework (RDF). A knowledge graph represents the knowledge related to a specific domain; leveraging this structured representation, it is possible to infer a piece of new knowledge from it after some refinement steps. However, nowadays, people have to deal with the sparsity of data and the computational inefficiency to use them in a real-world application. The embedding of a knowledge graph is a function that translates each entity and each relation into a vector of a given dimension d {\displaystyle d} , called embedding dimension. It is even possible to embed the entities and relations with different dimensions. The embedding vectors can then be used for other tasks. A knowledge graph embedding is characterized by four aspects: Representation space: The low-dimensional space in which the entities and relations are represented. Scoring function: A measure of the goodness of a triple-embedded representation. Encoding models: The modality in which the embedded representation of the entities and relations interact with each other. Additional information: Any additional information coming from the knowledge graph that can enrich the embedded representation. Usually, an ad hoc scoring function is integrated into the general scoring function for each additional piece of information. == Embedding procedure == All algorithms for creating a knowledge graph embedding follow the same approach. First, the embedding vectors are initialized to random values. Then, they are iteratively optimized using a training set of triples. In each iteration, a batch of size b {\displaystyle b} triples is sampled from the training set, and a triple from it is sampled and corrupted—i.e., a triple that does not represent a true fact in the knowledge graph. The corruption of a triple involves substituting the head or the tail (or both) of the triple with another entity that makes the fact false. The original triple and the corrupted triple are added in the training batch, and then the embeddings are updated, optimizing a scoring function. Iteration stops when a stop condition is reached. Usually, the stop condition depends on the overfitting of the training set. At the end, the learned embeddings should have extracted semantic meaning from the training triples and should correctly predict unseen true facts in the knowledge graph. === Pseudocode === The following is the pseudocode for the general embedding procedure. algorithm Compute entity and relation embeddings input: The training set S = { ( h , r , t ) } {\displaystyle S=\{(h,r,t)\}} , entity set E {\displaystyle E} , relation set R {\displaystyle R} , embedding dimension k {\displaystyle k} output: Entity and relation embeddings initialization: the entities e {\displaystyle e} and relations r {\displaystyle r} embeddings (vectors) are randomly initialized while stop condition do S b a t c h ← s a m p l e ( S , b ) {\displaystyle S_{batch}\leftarrow sample(S,b)} // Sample a batch from the training set for each ( h , r , t ) {\displaystyle (h,r,t)} in S b a t c h {\displaystyle S_{batch}} do ( h ′ , r , t ′ ) ← s a m p l e ( S ′ ) {\displaystyle (h',r,t')\leftarrow sample(S')} // Sample a corrupted fact T b a t c h ← T b a t c h ∪ { ( ( h , r , t ) , ( h ′ , r , t ′ ) ) } {\displaystyle T_{batch}\leftarrow T_{batch}\cup \{((h,r,t),(h',r,t'))\}} end for Update embeddings by minimizing the loss function end while == Performance indicators == These indexes are often used to measure the embedding quality of a model. The simplicity of the indexes makes them very suitable for evaluating the performance of an embedding algorithm even on a large scale. Given Q {\displaystyle {\ce {Q}}} as the set of all ranked predictions of a model, it is possible to define three different performance indexes: Hits@K, MR, and MRR. === Hits@K === Hits@K or in short, H@K, is a performance index that measures the probability to find the correct prediction in the first top K model predictions. Usually, it is used k = 10 {\displaystyle k=10} . Hits@K reflects the accuracy of an embedding model to predict the relation between two given triples correctly. Hits@K = | { q ∈ Q : q < k } | | Q | ∈ [ 0 , 1 ] {\displaystyle ={\frac {|\{q\in Q:q
In statistics and machine learning, leakage (also known as data leakage or target leakage) refers to the use of information during model training that would not be available at prediction time. This results in overly optimistic performance estimates, as the model appears to perform better during evaluation than it actually would in a production environment. Leakage is often subtle and indirect, making it difficult to detect and eliminate. It can lead a statistician or modeler to select a suboptimal model, which may be outperformed by a leakage-free alternative. == Leakage modes == Leakage can occur at multiple stages of the machine learning workflow. Broadly, its sources can be divided into two categories: those arising from features and those arising from training examples. === Feature leakage === Feature or column-wise leakage is caused by the inclusion of columns which are one of the following: a duplicate label, a proxy for the label, or the label itself. These features, known as anachronisms, will not be available when the model is used for predictions, and result in leakage if included when the model is trained. For example, including a "MonthlySalary" column when predicting "YearlySalary"; or "MinutesLate" when predicting "IsLate". === Training example leakage === Row-wise leakage is caused by improper sharing of information between rows of data. Types of row-wise leakage include: Premature featurization; leaking from premature featurization before Cross-validation/Train/Test split (must fit MinMax/ngrams/etc on only the train split, then transform the test set) Duplicate rows between train/validation/test (for example, oversampling a dataset to pad its size before splitting; or, different rotations/augmentations of a single image; bootstrap sampling before splitting; or duplicating rows to up sample the minority class) Non-independent and identically distributed random (non-IID) data Time leakage (for example, splitting a time-series dataset randomly instead of newer data in test set using a train/test split or rolling-origin cross-validation) Group leakage—not including a grouping split column (for example, Andrew Ng's group had 100k x-rays of 30k patients, meaning ~3 images per patient. The paper used random splitting instead of ensuring that all images of a patient were in the same split. Hence the model partially memorized the patients instead of learning to recognize pneumonia in chest x-rays.) A 2023 review found data leakage to be "a widespread failure mode in machine-learning (ML)-based science", having affected at least 294 academic publications across 17 disciplines, and causing a potential reproducibility crisis. == Detection == Data leakage in machine learning can be detected through various methods, focusing on performance analysis, feature examination, data auditing, and model behavior analysis. Performance-wise, unusually high accuracy or significant discrepancies between training and test results often indicate leakage. Inconsistent cross-validation outcomes may also signal issues. Feature examination involves scrutinizing feature importance rankings and ensuring temporal integrity in time series data. A thorough audit of the data pipeline is crucial, reviewing pre-processing steps, feature engineering, and data splitting processes. Detecting duplicate entries across dataset splits is also important. For language models, the Min-K% method can detect the presence of data in a pretraining dataset. It presents a sentence suspected to be present in the pretraining dataset, and computes the log-likelihood of each token, then compute the average of the lowest K of these. If this exceeds a threshold, then the sentence is likely present. This method is improved by comparing against a baseline of the mean and variance. Analyzing model behavior can reveal leakage. Models relying heavily on counter-intuitive features or showing unexpected prediction patterns warrant investigation. Performance degradation over time when tested on new data may suggest earlier inflated metrics due to leakage. Advanced techniques include backward feature elimination, where suspicious features are temporarily removed to observe performance changes. Using a separate hold-out dataset for final validation before deployment is advisable.
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Concurrent MetateM is a multi-agent language in which each agent is programmed using a set of (augmented) temporal logic specifications of the behaviour it should exhibit. These specifications are executed directly to generate the behaviour of the agent. As a result, there is no risk of invalidating the logic as with systems where logical specification must first be translated to a lower-level implementation. The root of the MetateM concept is Gabbay's separation theorem; any arbitrary temporal logic formula can be rewritten in a logically equivalent past → future form. Execution proceeds by a process of continually matching rules against a history, and firing those rules when antecedents are satisfied. Any instantiated future-time consequents become commitments which must subsequently be satisfied, iteratively generating a model for the formula made up of the program rules. == Temporal Connectives == The Temporal Connectives of Concurrent MetateM can divided into two categories, as follows: Strict past time connectives: '●' (weak last), '◎' (strong last), '◆' (was), '■' (heretofore), 'S' (since), and 'Z' (zince, or weak since). Present and future time connectives: '◯' (next), '◇' (sometime), '□' (always), 'U' (until), and 'W' (unless). The connectives {◎,●,◆,■,◯,◇,□} are unary; the remainder are binary. === Strict past time connectives === ==== Weak last ==== ●ρ is satisfied now if ρ was true in the previous time. If ●ρ is interpreted at the beginning of time, it is satisfied despite there being no actual previous time. Hence "weak" last. ==== Strong last ==== ◎ρ is satisfied now if ρ was true in the previous time. If ◎ρ is interpreted at the beginning of time, it is not satisfied because there is no actual previous time. Hence "strong" last. ==== Was ==== ◆ρ is satisfied now if ρ was true in any previous moment in time. ==== Heretofore ==== ■ρ is satisfied now if ρ was true in every previous moment in time. ==== Since ==== ρSψ is satisfied now if ψ is true at any previous moment and ρ is true at every moment after that moment. ==== Zince, or weak since ==== ρZψ is satisfied now if (ψ is true at any previous moment and ρ is true at every moment after that moment) OR ψ has not happened in the past. === Present and future time connectives === ==== Next ==== ◯ρ is satisfied now if ρ is true in the next moment in time. ==== Sometime ==== ◇ρ is satisfied now if ρ is true now or in any future moment in time. ==== Always ==== □ρ is satisfied now if ρ is true now and in every future moment in time. ==== Until ==== ρUψ is satisfied now if ψ is true at any future moment and ρ is true at every moment prior. ==== Unless ==== ρWψ is satisfied now if (ψ is true at any future moment and ρ is true at every moment prior) OR ψ does not happen in the future.
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Kolmogorov–Arnold Networks (KANs) are a type of artificial neural network architecture inspired by the Kolmogorov–Arnold representation theorem, also known as the superposition theorem. Unlike traditional multilayer perceptrons (MLPs), which rely on fixed activation functions and linear weights, KANs replace each weight with a learnable univariate function, often represented using splines. == History == KANs (Kolmogorov–Arnold Networks) were proposed by Liu et al. (2024) as a generalization of the Kolmogorov–Arnold representation theorem (KART), aiming to outperform MLPs in small-scale AI and scientific tasks. Before KANs, numerous studies explored KART's connections to neural networks or used it as a basis for designing new network architectures. In the 1980s and 1990s, early research applied KART to neural network design. Kůrková et al. (1992), Hecht-Nielsen (1987), and Nees (1994) established theoretical foundations for multilayer networks based on KART. Igelnik et al. (2003) introduced the Kolmogorov Spline Network using cubic splines to model complex functions. Sprecher (1996, 1997) introduced numerical methods for building network layers, while Nakamura et al. (1993) created activation functions with guaranteed approximation accuracy. These works linked KART's theoretical potential with practical neural network implementation. KART has also been used in other computational and theoretical fields. Coppejans (2004) developed nonparametric regression estimators using B-splines, Bryant (2008) applied it to high-dimensional image tasks, Liu (2015) investigated theoretical applications in optimal transport and image encryption, and more recently, Polar and Poluektov (2021) used Urysohn operators for efficient KART construction, while Fakhoury et al. (2022) introduced ExSpliNet, integrating KART with probabilistic trees and multivariate B-splines for improved function approximation. == Architecture == KANs are based on the Kolmogorov–Arnold representation theorem, which was linked to the 13th Hilbert problem. Given x = ( x 1 , x 2 , … , x n ) {\displaystyle x=(x_{1},x_{2},\dots ,x_{n})} consisting of n variables, a multivariate continuous function f ( x ) {\displaystyle f(x)} can be represented as: f ( x ) = f ( x 1 , … , x n ) = ∑ q = 1 2 n + 1 Φ q ( ∑ p = 1 n φ q , p ( x p ) ) {\displaystyle f(x)=f(x_{1},\dots ,x_{n})=\sum _{q=1}^{2n+1}\Phi _{q}\left(\sum _{p=1}^{n}\varphi _{q,p}(x_{p})\right)} (1) This formulation contains two nested summations: an outer and an inner sum. The outer sum ∑ q = 1 2 n + 1 {\displaystyle \sum _{q=1}^{2n+1}} aggregates 2 n + 1 {\displaystyle 2n+1} terms, each involving a function Φ q : R → R {\displaystyle \Phi _{q}:\mathbb {R} \to \mathbb {R} } . The inner sum ∑ p = 1 n {\displaystyle \sum _{p=1}^{n}} computes n terms for each q, where each term φ q , p : [ 0 , 1 ] → R {\displaystyle \varphi _{q,p}:[0,1]\to \mathbb {R} } is a continuous function of the single variable x p {\displaystyle x_{p}} . The inner continuous functions φ q , p {\displaystyle \varphi _{q,p}} are universal, independent of f {\displaystyle f} , while the outer functions Φ q {\displaystyle \Phi _{q}} depend on the specific function f {\displaystyle f} being represented. The representation (1) holds for all multivariate functions f {\displaystyle f} as proved in . If f {\displaystyle f} is continuous, then the outer functions Φ q {\displaystyle \Phi _{q}} are continuous; if f {\displaystyle f} is discontinuous, then the corresponding Φ q {\displaystyle \Phi _{q}} are generally discontinuous, while the inner functions φ q , p {\displaystyle \varphi _{q,p}} remain the same universal functions. Liu et al. proposed the name KAN. A general KAN network consisting of L layers takes x to generate the output as: K A N ( x ) = ( Φ L − 1 ∘ Φ L − 2 ∘ ⋯ ∘ Φ 1 ∘ Φ 0 ) x {\displaystyle \mathrm {KAN} (x)=(\Phi ^{L-1}\circ \Phi ^{L-2}\circ \cdots \circ \Phi ^{1}\circ \Phi ^{0})x} (3) Here, Φ l {\displaystyle \Phi ^{l}} is the function matrix of the l-th KAN layer or a set of pre-activations. Let i denote the neuron of the l-th layer and j the neuron of the (l+1)-th layer. The activation function φ j , i l {\displaystyle \varphi _{j,i}^{l}} connects (l, i) to (l+1, j): φ j , i l , l = 0 , … , L − 1 , i = 1 , … , n l , j = 1 , … , n l + 1 {\displaystyle \varphi _{j,i}^{l},\quad l=0,\dots ,L-1,\;i=1,\dots ,n_{l},\;j=1,\dots ,n_{l+1}} (4) where nl is the number of nodes of the l-th layer. Thus, the function matrix Φ l {\displaystyle \Phi ^{l}} can be represented as an n l + 1 × n l {\displaystyle n_{l+1}\times n_{l}} matrix of activations: x l + 1 = ( φ 1 , 1 l ( ⋅ ) φ 1 , 2 l ( ⋅ ) ⋯ φ 1 , n l l ( ⋅ ) φ 2 , 1 l ( ⋅ ) φ 2 , 2 l ( ⋅ ) ⋯ φ 2 , n l l ( ⋅ ) ⋮ ⋮ ⋱ ⋮ φ n l + 1 , 1 l ( ⋅ ) φ n l + 1 , 2 l ( ⋅ ) ⋯ φ n l + 1 , n l l ( ⋅ ) ) x l {\displaystyle x^{l+1}={\begin{pmatrix}\varphi _{1,1}^{l}(\cdot )&\varphi _{1,2}^{l}(\cdot )&\cdots &\varphi _{1,n_{l}}^{l}(\cdot )\\\varphi _{2,1}^{l}(\cdot )&\varphi _{2,2}^{l}(\cdot )&\cdots &\varphi _{2,n_{l}}^{l}(\cdot )\\\vdots &\vdots &\ddots &\vdots \\\varphi _{n_{l+1},1}^{l}(\cdot )&\varphi _{n_{l+1},2}^{l}(\cdot )&\cdots &\varphi _{n_{l+1},n_{l}}^{l}(\cdot )\end{pmatrix}}x^{l}} == Implementations == To make the KAN layers optimizable, the inner function is formed by the combination of spline and basic functions as the formula: φ ( x ) = w b b ( x ) + w s spline ( x ) {\displaystyle \varphi (x)=w_{b}\,b(x)+w_{s}\,{\text{spline}}(x)} where b ( x ) {\displaystyle b(x)} is the basic function, usually defined as s i l u ( x ) = x / ( 1 + e x ) {\displaystyle silu(x)=x/(1+e^{x})} and w b {\displaystyle w_{b}} is the base weight matrix. Also, w s {\displaystyle w_{s}} is the spline weight matrix and spline ( x ) {\displaystyle {\text{spline}}(x)} is the spline function. The spline function can be a sum of B-splines. spline ( x ) = ∑ i c i B i ( x ) {\displaystyle {\text{spline}}(x)=\sum _{i}c_{i}B_{i}(x)} Many studies suggested to use other polynomial and curve functions instead of B-spline to create new KAN variants. == Functions used == The choice of functional basis strongly influences the performance of KANs. Common function families include: B-splines: Provide locality, smoothness, and interpretability; they are the most widely used in current implementations. RBFs (include Gaussian RBFs): Capture localized features in data and are effective in approximating functions with non-linear or clustered structures. Chebyshev polynomials: Offer efficient approximation with minimized error in the maximum norm, making them useful for stable function representation. Rational function: Useful for approximating functions with singularities or sharp variations, as they can model asymptotic behavior better than polynomials. Fourier series: Capture periodic patterns effectively and are particularly useful in domains such as physics-informed machine learning. Wavelet functions (DoG, Mexican hat, Morlet, and Shannon): Used for feature extraction as they can capture both high-frequency and low-frequency data components. Piecewise linear functions: Provide efficient approximation for multivariate functions in KANs. == Usage == In some modern neural architectures like convolutional neural networks (CNNs), recurrent neural networks (RNNs), and Transformers, KANs are typically used as drop-in substitutes for MLP layers. Despite KANs' general-purpose design, researchers have created and used them for a number of tasks: Scientific machine learning (SciML): Function fitting, partial differential equations (PDEs) and physical/mathematical laws. Continual learning: KANs better preserve previously learned information during incremental updates, avoiding catastrophic forgetting due to the locality of spline adjustments. Graph neural networks: Extensions such as Kolmogorov–Arnold Graph Neural Networks (KA-GNNs) integrate KAN modules into message-passing architectures, showing improvements in molecular property prediction tasks. Sensor data processing: Kolmogorov–Arnold Networks (KANs) have recently been applied to sensor data processing due to their ability to model complex nonlinear relationships with relatively few parameters and improved interpretability compared to conventional multilayer perceptrons. Applications include industrial soft sensors, biomedical signal analysis, remote sensing, and environmental monitoring systems. == Drawbacks == KANs can be computationally intensive and require a large number of parameters due to their use of polynomial functions to capture data.
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The Journal of Machine Learning Research is a peer-reviewed open access scientific journal covering machine learning. It was established in 2000 and the first editor-in-chief was Leslie Kaelbling. The current editors-in-chief are Francis Bach (Inria) and David Blei (Columbia University). == History == The journal was established as an open-access alternative to the journal Machine Learning. In 2001, forty editorial board members of Machine Learning resigned, saying that in the era of the Internet, it was detrimental for researchers to continue publishing their papers in expensive journals with pay-access archives. The open access model employed by the Journal of Machine Learning Research allows authors to publish articles for free and retain copyright, while archives are freely available online. Print editions of the journal were published by MIT Press until 2004 and by Microtome Publishing thereafter. From its inception, the journal received no revenue from the print edition and paid no subvention to MIT Press or Microtome Publishing. In response to the prohibitive costs of arranging workshop and conference proceedings publication with traditional academic publishing companies, the journal launched a proceedings publication arm in 2007 and now publishes proceedings for several leading machine learning conferences, including the International Conference on Machine Learning, COLT, AISTATS, and workshops held at the Conference on Neural Information Processing Systems.
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Spatial embedding is one of feature learning techniques used in spatial analysis where points, lines, polygons or other spatial data types. representing geographic locations are mapped to vectors of real numbers. Conceptually it involves a mathematical embedding from a space with many dimensions per geographic object to a continuous vector space with a much lower dimension. Such embedding methods allow complex spatial data to be used in neural networks and have been shown to improve performance in spatial analysis tasks == Embedded data types == Geographic data can take many forms: text, images, graphs, trajectories, polygons. Depending on the task, there may be a need to combine multimodal data from different sources. The next section describes examples of different types of data and their uses. === Text === Geolocated posts on social media can be used to acquire a library of documents bound to a given place that can be later transformed to embedded vectors using word embedding techniques. === Image === Satellites and aircraft collect digital spatial data acquired from remotely sensed images which can be used in machine learning. They are sometimes hard to analyse using basic image analysis methods and convolutional neural networks can be used to acquire an embedding of images bound to a given geographical object or a region. === Point === A single point of interest (POI) can be assigned multiple features that can be used in machine learning. These could be demographic, transportation, meteorological, or economic data, for example. When embedding single points, it is common to consider the entire set of available points as nodes in a graph. === Line / multiline === Among other things, motion trajectories are represented as lines (multilines). Individual trajectories are embedded taking into account travel time, distances and also features of points visited along the way. Embedding of trajectories allows to improve performance of such tasks as clustering and also categorization. === Polygon === The geographic areas analyzed in machine learning are defined by both administrative boundaries and top-down division into grids of regular shapes such as rectangles, for example. Both types are represented as polygons and, like points, can be assigned different demographic, transportation, or economic features. A polygon can also have features related to the size of the area or shape it represents. === Graph === An example domain where graph representation is used is the street layout in a city, where vertices can be intersections and edges can be roads. The vertices can also be destination points like public transport stops or important points in the city, and the edges represent the flow between them. Embedding graphs or single vertices allows to improve accuracy of analysis methods in which the treated geographical domain can be represented as a network. == Usage == POI recommendation - generating personalized point of interest recommendations based on user preferences. Next/future location prediction - prediction of the next location a person will go to based on their historical trajectory. Zone functions classification - based on different mobility of people or POI distribution a function of a given area in a city can be predicted. Crime prediction - estimation of crime rate in different regions of a city. Local event detection - studying spatio-temporal changes in embeddings can provide valuable information in detection of local event occurring in specific location. Regional mobility popularity prediction - analysis of mobility can show patterns in popularity of different regions in a city. Shape matching - finding a similar shape of given polygon, for example finding building with the same shape as input building. Travel time estimation - predicting estimated travel time given current traffic conditions and special occurring events. Time estimation for on-demand food delivery - estimation of delivery time when placing an order through the website. == Temporal aspect == Some of the data analyzed has a timestamp associated with it. In some cases of data analysis this information is omitted and in others it is used to divide the set into groups. The most common division is the separation of weekdays from weekends or division into hours of the day. This is particularly important in the analysis of mobility data, because the characteristics of mobility during the week and at different times of the day are very different from each other. Another area in which time division into, for example, individual months can be used is in the analysis of tourism of a given region. In order to take such a split into account, embedding methods treat the time stamp specifically or separate versions of the model are developed for different subgroups of the analyzed set.
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In machine learning, embedding is a representation learning technique that maps complex, high-dimensional data into a lower-dimensional vector space of numerical vectors. == Technique == It also denotes the resulting representation, where meaningful patterns or relationships are preserved. As a technique, it learns these vectors from data like words, images, or user interactions, differing from manually designed methods such as one-hot encoding. This process reduces complexity and captures key features without needing prior knowledge of the domain. == Similarity == In natural language processing, words or concepts may be represented as feature vectors, where similar concepts are mapped to nearby vectors. The resulting embeddings vary by type, including word embeddings for text (e.g., Word2Vec), image embeddings for visual data, and knowledge graph embeddings for knowledge graphs, each tailored to tasks like NLP, computer vision, or recommendation systems. This dual role enhances model efficiency and accuracy by automating feature extraction and revealing latent similarities across diverse applications. To measure the distance between two embeddings, a similarity measure can be used to find the overall similarity of the concepts represented by the embeddings. If the vectors are normalized to have a magnitude of 1, then the similarity measures are proportional to cos ( θ a b ) {\displaystyle \cos \left(\theta _{ab}\right)} . The cosine similarity disregards the magnitude of the vector when determining similarity, so it is less biased towards training data that appears very frequently. The dot product includes the magnitude inherently, so it will tend to value more popular data. Generally, for high-dimensional vector spaces, vectors tend to converge in distance, so Euclidean distance becomes less reliable for large embedding vectors.
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Inferential Theory of Learning (ITL) is an area of machine learning which describes inferential processes performed by learning agents. ITL has been continuously developed by Ryszard S. Michalski, starting in the 1980s. The first known publication of ITL was in 1983. In the ITL learning process is viewed as a search (inference) through hypotheses space guided by a specific goal. The results of learning need to be stored. Stored information will later be used by the learner for future inferences. Inferences are split into multiple categories including conclusive, deduction, and induction. In order for an inference to be considered complete it was required that all categories must be taken into account. This is how the ITL varies from other machine learning theories like Computational Learning Theory and Statistical Learning Theory; which both use singular forms of inference. == Usage == The most relevant published usage of ITL was in scientific journal published in 2012 and used ITL as a way to describe how agent-based learning works. According to the journal "The Inferential Theory of Learning (ITL) provides an elegant way of describing learning processes by agents".
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Cloud-Based Secure File Transfer is a managed or hosted file transfer service that provides cloud storage that can be accessed via SSH File Transfer Protocol (SFTP). These services allow secure, reliable file transfers while offering the scalability, redundancy, and high availability of cloud infrastructure. == Technical overview == The evolution of file transfer protocols began with File Transfer Protocol (FTP) and SSH File Transfer Protocol (SFTP). SFTP offered enhanced security through the use of SSH (Secure Shell) encryption, which addressed many of the security concerns associated with traditional FTP. Over time, as businesses increasingly adopted cloud infrastructure, the demand for services that integrate secure file transfer with cloud storage led to the rise of Cloud-Based Secure File Transfer services. These services combine the benefits of secure, encrypted file transfer with the scalability and flexibility of cloud-based storage systems. Traditional on-premises SFTP typically involves setting up and managing physical or virtual servers to handle file transfers. In contrast, Cloud-Based Secure File Transfer utilizes managed cloud infrastructure, such as AWS EC2, Azure VMs, or Google Cloud, to automate scaling, ensure redundancy, and provide high availability. These cloud environments can be configured to automatically scale with demand, enabling businesses to handle large volumes of data transfers without the need for extensive physical hardware. == Features == Scalability and availability: Cloud-Based Secure File Transfer services are inherently scalable, with features like load balancing, multi-region deployments, and auto-scaling groups that adjust resources in response to traffic spikes. This ensures that the system can handle varying workloads and provides continuous availability, even during high-demand periods. Cost-effectiveness: By eliminating the need for physical infrastructure and reducing ongoing server maintenance costs, Cloud-Based Secure File Transfer services offer significant cost savings compared to traditional on-premises services. Cloud providers typically offer pay-as-you-go pricing models, where users only pay for the resources they use, further optimizing costs. Security and compliance: Cloud-Based Secure File Transfer products offer strong security measures, including end-to-end encryption, key management, detailed logging, and auditing. These services are often compliant with industry regulations such as HIPAA (Health Insurance Portability and Accountability Act), GDPR (General Data Protection Regulation), and SOC 2 (System and Organization Controls), ensuring that data transfers meet necessary security and privacy standards. == Cloud-Based Secure File Transfer providers == == Uses == Cloud-Based Secure File Transfer is used across various industries to securely transfer sensitive data and integrate into business workflows. In healthcare, Cloud-Based Secure File Transfer is essential for securely transferring electronic Protected Health Information (ePHI), ensuring compliance with regulations like HIPAA. In financial institutions, it is used to protect sensitive financial data during transfer, maintaining privacy and security. Data analytics also benefits from Cloud-Based Secure File Transfer, offering a secure and efficient method for transferring large datasets between systems or partners. Technically, Cloud-Based Secure File Transfer is often integrated into enterprise workflows through automated file transfers, using scripting or APIs. It also plays a key role in cloud backup and disaster recovery, ensuring that files are securely transferred and stored in cloud environments, which supports business continuity. However, businesses must address certain implementation challenges. Despite its secure design, Cloud-Based Secure File Transfer is not immune to risks such as misconfigured SSH keys, improper access control, or inadequate encryption. Regular security audits and careful configuration management are necessary to minimize the risk of data breaches. Additionally, integrating Cloud-Based Secure File Transfer with legacy systems can present challenges, such as incompatible APIs or outdated authentication methods. == Comparisons with related technologies == Cloud-Based Secure File Transfer differs from traditional SFTP primarily in its deployment and management model. Traditional SFTP services are typically hosted on-premises or on virtual servers, requiring manual configuration, ongoing infrastructure maintenance, and security management by in-house IT teams. In contrast, Cloud-Based Secure File Transfer is offered as a Software-as-a-Service (SaaS) service, reducing infrastructure overhead by eliminating the need for dedicated hardware or virtual machines. This model simplifies management through centralized web-based interfaces, automated updates, and built-in scalability. While Cloud-Based Secure File Transfer is focused on providing secure file transfers over the SFTP protocol, Managed File Transfer (MFT) platforms generally support a broader range of protocols, including FTP, FTPS, HTTP/S, and AS2. MFT services often include advanced features such as end-to-end encryption, extensive automation, compliance reporting, and integration with enterprise systems. Cloud-Based Secure File Transfer services may offer some of these features but are typically more lightweight and streamlined, targeting organizations seeking a secure and scalable alternative to traditional SFTP without the full suite of MFT capabilities. As such, Cloud-Based Secure File Transfer can be seen as a specialized subset within the broader managed file transfer ecosystem.
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GOLOG is a high-level logic programming language for the specification and execution of complex actions in dynamical domains. It is based on the situation calculus. It is a first-order logical language for reasoning about action and change. GOLOG was developed at the University of Toronto. == History == The concept of situation calculus on which the GOLOG programming language is based was first proposed by John McCarthy in 1963. == Description == A GOLOG interpreter automatically maintains a direct characterization of the dynamic world being modeled, on the basis of user supplied axioms about preconditions, effects of actions and the initial state of the world. This allows the application to reason about the condition of the world and consider the impacts of different potential actions before focusing on a specific action. Golog is a logic programming language and is very different from conventional programming languages. A procedural programming language like C defines the execution of statements in advance. The programmer creates a subroutine which consists of statements, and the computer executes each statement in a linear order. In contrast, fifth-generation programming languages like Golog work with an abstract model with which the interpreter can generate the sequence of actions. The source code defines the problem and it is up to the solver to find the next action. This approach can facilitate the management of complex problems from the domain of robotics. A Golog program defines the state space in which the agent is allowed to operate. A path in the symbolic domain is found with state space search. To speed up the process, Golog programs are realized as hierarchical task networks. Apart from the original Golog language, there are some extensions available. The ConGolog language provides concurrency and interrupts. Other dialects like IndiGolog and Readylog were created for real time applications in which sensor readings are updated on the fly. == Uses == Golog has been used to model the behavior of autonomous agents. In addition to a logic-based action formalism for describing the environment and the effects of basic actions, they enable the construction of complex actions using typical programming language constructs. It is also used for applications in high level control of robots and industrial processes, virtual agents, discrete event simulation etc. It can be also used to develop Belief Desire Intention-style agent systems. == Planning and scripting == In contrast to the Planning Domain Definition Language, Golog supports planning and scripting as well. Planning means that a goal state in the world model is defined, and the solver brings a logical system into this state. Behavior scripting implements reactive procedures, which are running as a computer program. For example, suppose the idea is to authoring a story. The user defines what should be true at the end of the plot. A solver gets started and applies possible actions to the current situation until the goal state is reached. The specification of a goal state and the possible actions are realized in the logical world model. In contrast, a hardwired reactive behavior doesn't need a solver but the action sequence is provided in a scripting language. The Golog interpreter, which is written in Prolog, executes the script and this will bring the story into the goal state.
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Histogram of oriented displacements (HOD) is a 2D trajectory descriptor. The trajectory is described using a histogram of the directions between each two consecutive points. Given a trajectory T = {P1, P2, P3, ..., Pn}, where Pt is the 2D position at time t. For each pair of positions Pt and Pt+1, calculate the direction angle θ(t, t+1). Value of θ is between 0 and 360. A histogram of the quantized values of θ is created. If the histogram is of 8 bins, the first bin represents all θs between 0 and 45. The histogram accumulates the lengths of the consecutive moves. For each θ, a specific histogram bin is determined. The length of the line between Pt and Pt+1 is then added to the specific histogram bin. To show the intuition behind the descriptor, consider the action of waving hands. At the end of the action, the hand falls down. When describing this down movement, the descriptor does not care about the position from which the hand started to fall. This fall will affect the histogram with the appropriate angles and lengths, regardless of the position where the hand started to fall. HOD records for each moving point: how much it moves in each range of directions. HOD has a clear physical interpretation. It proposes that, a simple way to describe the motion of an object, is to indicate how much distance it moves in each direction. If the movement in all directions are saved accurately, the movement can be repeated from the initial position to the final destination regardless of the displacements order. However, the temporal information will be lost, as the order of movements is not stored-this is what we solve by applying the temporal pyramid, as shown in section \ref{sec:temp-pyramid}. If the angles quantization range is small, classifiers that use the descriptor will overfit. Generalization needs some slack in directions-which can be done by increasing the quantization range.
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