Web intelligence is the area of scientific research and development that explores the roles and makes use of artificial intelligence and information technology for new products, services and frameworks that are empowered by the World Wide Web. The term was coined in a paper written by Ning Zhong, Jiming Liu Yao and Y.Y. Ohsuga in the Computer Software and Applications Conference in 2000. == Research == The research about the web intelligence covers many fields – including data mining (in particular web mining), information retrieval, pattern recognition, predictive analytics, the semantic web, web data warehousing – typically with a focus on web personalization and adaptive websites.
AI Background Removers: Free vs Paid (2026)
Looking for the best AI background remover? An AI background remover is software that uses machine learning to help you get more done — it can save you hours every week by automating repetitive work. Most options offer a generous free tier, with paid plans unlocking higher limits, faster processing, and team features. Whether you are a beginner or a pro, the right AI background remover slots into your workflow and pays for itself fast. Read on for hands-on impressions, pricing tiers, and the standout features that matter.
Dynamic epistemic logic
Dynamic epistemic logic (DEL) is a logical framework dealing with knowledge and information change. Typically, DEL focuses on situations involving multiple agents and studies how their knowledge changes when events occur. These events can change factual properties of the actual world (they are called ontic events): for example a red card is painted in blue. They can also bring about changes of knowledge without changing factual properties of the world (they are called epistemic events): for example, a card is revealed publicly (or privately) to be red. Originally, DEL focused on epistemic events. Only some of the basic ideas are present in this entry of the original DEL framework; more details about DEL in general can be found in the references. Due to the nature of its object of study and its abstract approach, DEL is related and has applications to numerous research areas, such as computer science (artificial intelligence), philosophy (formal epistemology), economics (game theory) and cognitive science. In computer science, DEL is for example very much related to multi-agent systems, which are systems where multiple intelligent agents interact and exchange information. As a combination of dynamic logic and epistemic logic, dynamic epistemic logic is a young field of research. It really started in 1989 with Plaza's logic of public announcement. Independently, Gerbrandy and Groeneveld proposed a system dealing moreover with private announcement and that was inspired by the work of Veltman. Another system was proposed by van Ditmarsch whose main inspiration was the Cluedo game. But the most influential and original system was the system proposed by Baltag, Moss and Solecki. This system can deal with all the types of situations studied in the works above and its underlying methodology is conceptually grounded. This entry will present some of its basic ideas. Formally, DEL extends ordinary epistemic logic by the inclusion of event models to describe actions, and a product update operator that defines how epistemic models are updated as the consequence of executing actions described through event models. Epistemic logic will first be recalled. Then, actions and events will enter into the picture and we will introduce the DEL framework. == Epistemic logic == Epistemic logic is a modal logic dealing with the notions of knowledge and belief. As a logic, it is concerned with understanding the process of reasoning about knowledge and belief: which principles relating the notions of knowledge and belief are intuitively plausible? Like epistemology, it stems from the Greek word ϵ π ι σ τ η μ η {\displaystyle \epsilon \pi \iota \sigma \tau \eta \mu \eta } or ‘episteme’ meaning knowledge. Epistemology is nevertheless more concerned with analyzing the very nature and scope of knowledge, addressing questions such as “What is the definition of knowledge?” or “How is knowledge acquired?”. In fact, epistemic logic grew out of epistemology in the Middle Ages thanks to the efforts of Burley and Ockham. The formal work, based on modal logic, that inaugurated contemporary research into epistemic logic dates back only to 1962 and is due to Hintikka. It then sparked in the 1960s discussions about the principles of knowledge and belief and many axioms for these notions were proposed and discussed. For example, the interaction axioms K p → B p {\displaystyle Kp\rightarrow Bp} and B p → K B p {\displaystyle Bp\rightarrow KBp} are often considered to be intuitive principles: if an agent Knows p {\displaystyle p} then (s)he also Believes p {\displaystyle p} , or if an agent Believes p {\displaystyle p} , then (s)he Knows that (s)he Believes p {\displaystyle p} . More recently, these kinds of philosophical theories were taken up by researchers in economics, artificial intelligence and theoretical computer science where reasoning about knowledge is a central topic. Due to the new setting in which epistemic logic was used, new perspectives and new features such as computability issues were then added to the research agenda of epistemic logic. === Syntax === In the sequel, A G T S = { 1 , … , n } {\displaystyle AGTS=\{1,\ldots ,n\}} is a finite set whose elements are called agents and P R O P {\displaystyle PROP} is a set of propositional letters. The epistemic language is an extension of the basic multi-modal language of modal logic with a common knowledge operator C A {\displaystyle C_{A}} and a distributed knowledge operator D A {\displaystyle D_{A}} . Formally, the epistemic language L EL C {\displaystyle {\mathcal {L}}_{\textsf {EL}}^{C}} is defined inductively by the following grammar in BNF: L EL C : ϕ ::= p ∣ ¬ ϕ ∣ ( ϕ ∧ ϕ ) ∣ K j ϕ ∣ C A ϕ ∣ D A ϕ {\displaystyle {\mathcal {L}}_{\textsf {EL}}^{C}:\phi ~~::=~~p~\mid ~\neg \phi ~\mid ~(\phi \land \phi )~\mid ~K_{j}\phi ~\mid ~C_{A}\phi ~\mid ~D_{A}\phi } where p ∈ P R O P {\displaystyle p\in PROP} , j ∈ A G T S {\displaystyle j\in {AGTS}} and A ⊆ A G T S {\displaystyle A\subseteq {AGTS}} . The basic epistemic language L E L {\displaystyle {\mathcal {L}}_{EL}} is the language L E L C {\displaystyle {\mathcal {L}}_{EL}^{C}} without the common knowledge and distributed knowledge operators. The formula ⊥ {\displaystyle \bot } is an abbreviation for ¬ p ∧ p {\displaystyle \neg p\land p} (for a given p ∈ P R O P {\displaystyle p\in PROP} ), ⟨ K j ⟩ ϕ {\displaystyle \langle K_{j}\rangle \phi } is an abbreviation for ¬ K j ¬ ϕ {\displaystyle \neg K_{j}\neg \phi } , E A ϕ {\displaystyle E_{A}\phi } is an abbreviation for ⋀ j ∈ A K j ϕ {\displaystyle \bigwedge \limits _{j\in A}K_{j}\phi } and C ϕ {\displaystyle C\phi } an abbreviation for C A G T S ϕ {\displaystyle C_{AGTS}\phi } . Group notions: general, common and distributed knowledge. In a multi-agent setting there are three important epistemic concepts: general knowledge, distributed knowledge and common knowledge. The notion of common knowledge was first studied by Lewis in the context of conventions. It was then applied to distributed systems and to game theory, where it allows to express that the rationality of the players, the rules of the game and the set of players are commonly known. General knowledge. General knowledge of ϕ {\displaystyle \phi } means that everybody in the group of agents A G T S {\displaystyle {AGTS}} knows that ϕ {\displaystyle \phi } . Formally, this corresponds to the following formula: E ϕ := ⋀ j ∈ A G T S K j ϕ . {\displaystyle E\phi :={\underset {j\in {AGTS}}{\bigwedge }}K_{j}\phi .} Common knowledge. Common knowledge of ϕ {\displaystyle \phi } means that everybody knows ϕ {\displaystyle \phi } but also that everybody knows that everybody knows ϕ {\displaystyle \phi } , that everybody knows that everybody knows that everybody knows ϕ {\displaystyle \phi } , and so on ad infinitum. Formally, this corresponds to the following formula C ϕ := E ϕ ∧ E E ϕ ∧ E E E ϕ ∧ … {\displaystyle C\phi :=E\phi \land EE\phi \land EEE\phi \land \ldots } As we do not allow infinite conjunction the notion of common knowledge will have to be introduced as a primitive in our language. Before defining the language with this new operator, we are going to give an example introduced by Lewis that illustrates the difference between the notions of general knowledge and common knowledge. Lewis wanted to know what kind of knowledge is needed so that the statement p {\displaystyle p} : “every driver must drive on the right” be a convention among a group of agents. In other words, he wanted to know what kind of knowledge is needed so that everybody feels safe to drive on the right. Suppose there are only two agents i {\displaystyle i} and j {\displaystyle j} . Then everybody knowing p {\displaystyle p} (formally E p {\displaystyle Ep} ) is not enough. Indeed, it might still be possible that the agent i {\displaystyle i} considers possible that the agent j {\displaystyle j} does not know p {\displaystyle p} (formally ¬ K i K j p {\displaystyle \neg K_{i}K_{j}p} ). In that case the agent i {\displaystyle i} will not feel safe to drive on the right because he might consider that the agent j {\displaystyle j} , not knowing p {\displaystyle p} , could drive on the left. To avoid this problem, we could then assume that everybody knows that everybody knows that p {\displaystyle p} (formally E E p {\displaystyle EEp} ). This is again not enough to ensure that everybody feels safe to drive on the right. Indeed, it might still be possible that agent i {\displaystyle i} considers possible that agent j {\displaystyle j} considers possible that agent i {\displaystyle i} does not know p {\displaystyle p} (formally ¬ K i K j K i p {\displaystyle \neg K_{i}K_{j}K_{i}p} ). In that case and from i {\displaystyle i} ’s point of view, j {\displaystyle j} considers possible that i {\displaystyle i} , not knowing p {\displaystyle p} , will drive on the left. So from i {\displaystyle i} ’s point of view, j {\displaystyle j} might drive on the left as well (by the same argument as abov
Progress in artificial intelligence
Progress in artificial intelligence (AI) refers to the advances, milestones, and breakthroughs that have been achieved in the field of artificial intelligence over time. AI is a branch of computer science that aims to create machines and systems capable of performing tasks that typically require human intelligence. AI applications have been used in a wide range of fields including medical diagnosis, finance, robotics, law, video games, agriculture, and scientific discovery. The society as a whole is looking for artificial intelligence to be on a key factor in the upcming years because of its potential. However, many AI applications are not perceived as AI: "A lot of cutting-edge AI has filtered into general applications, often without being called AI because once something becomes useful enough and common enough it's not labeled AI anymore." "Many thousands of AI applications are deeply embedded in the infrastructure of every industry." In the late 1990s and early 2000s, AI technology became widely used as elements of larger systems, but the field was rarely credited for these successes at the time. Kaplan and Haenlein structure artificial intelligence along three evolutionary stages: Artificial narrow intelligence – AI capable only of specific tasks; Artificial general intelligence – AI with ability in several areas, and able to autonomously solve problems they were never even designed for; Artificial superintelligence – AI capable of general tasks, including scientific creativity, social skills, and general wisdom. To allow comparison with human performance, artificial intelligence can be evaluated on constrained and well-defined problems. Such tests have been termed subject-matter expert Turing tests. Also, smaller problems provide more achievable goals and there are an ever-increasing number of positive results. In 2023, humans still substantially outperformed both GPT-4 and other models tested on the ConceptARC benchmark. Those models scored 60% on most, and 77% on one category, while humans scored 91% on all and 97% on one category. However, later research in 2025 showed that human-generated output grids were only accurate 73% of the time, while AI models available that year managed to score above 77%. == History == Increasing, promoting or constraining AI progress has often be done via controlling or increasing the amount of compute. == Current performance in specific areas == There are many useful abilities that can be described as showing some form of intelligence. This gives better insight into the comparative success of artificial intelligence in different areas. AI, like electricity or the steam engine, is a general-purpose technology. There is no consensus on how to characterize which tasks AI tends to excel at. Some versions of Moravec's paradox observe that humans are more likely to outperform machines in areas such as physical dexterity that have been the direct target of natural selection. While projects such as AlphaZero have succeeded in generating their own knowledge from scratch, many other machine learning projects require large training datasets. Researcher Andrew Ng has suggested, as a "highly imperfect rule of thumb", that "almost anything a typical human can do with less than one second of mental thought, we can probably now or in the near future automate using AI." Games provide a high-profile benchmark for assessing rates of progress; many games have a large professional player base and a well-established competitive rating system. AlphaGo brought the era of classical board-game benchmarks to a close when Artificial Intelligence proved their competitive edge over humans in 2016. Deep Mind's AlphaGo AI software program defeated the world's best professional Go Player Lee Sedol. Games of imperfect knowledge provide new challenges to AI in the area of game theory; the most prominent milestone in this area was brought to a close by Libratus' poker victory in 2017. E-sports continue to provide additional benchmarks; Facebook AI, Deepmind, and others have engaged with the popular StarCraft franchise of videogames. Broad classes of outcome for an AI test may be given as: optimal: it is not possible to perform better (note: some of these entries were solved by humans) super-human: performs better than all humans high-human: performs better than most humans par-human: performs similarly to most humans sub-human: performs worse than most humans === Optimal === Tic-tac-toe Connect Four: 1988 Checkers (aka 8x8 draughts): Weakly solved (2007) Rubik's Cube: Mostly solved (2010) Heads-up limit hold'em poker: Statistically optimal in the sense that "a human lifetime of play is not sufficient to establish with statistical significance that the strategy is not an exact solution" (2015) === Super-human === Othello (aka reversi): c. 1997 Scrabble: 2006 Backgammon: c. 1995–2002 Chess: Supercomputer (c. 1997); Personal computer (c. 2006); Mobile phone (c. 2009); Computer defeats human + computer (c. 2017) Jeopardy!: Question answering, although the machine did not use speech recognition (2011) Arimaa: 2015 Shogi: c. 2017 Go: 2017 Heads-up no-limit hold'em poker: 2017 Six-player no-limit hold'em poker: 2019 Gran Turismo Sport: 2022 === High-human === Crosswords: c. 2012 Freeciv: 2016 Dota 2: 2018 Bridge card-playing: According to a 2009 review, "the best programs are attaining expert status as (bridge) card players", excluding bidding. StarCraft II: 2019 Mahjong: 2019 Stratego: 2022 No-Press Diplomacy: 2022 Hanabi: 2022 Natural language processing === Par-human === Optical character recognition for ISO 1073-1:1976 and similar special characters. Classification of images Handwriting recognition Facial recognition Visual question answering SQuAD 2.0 English reading-comprehension benchmark (2019) SuperGLUE English-language understanding benchmark (2020) Some school science exams (2019) Some tasks based on Raven's Progressive Matrices Many Atari 2600 games (2015) === Sub-human === Optical character recognition for printed text (nearing par-human for Latin-script typewritten text) Object recognition Various robotics tasks that may require advances in robot hardware as well as AI, including: Stable bipedal locomotion: Bipedal robots can walk, but are less stable than human walkers (as of 2017) Humanoid soccer Speech recognition: "nearly equal to human performance" (2017) Explainability. Current medical systems can diagnose certain medical conditions well, but cannot explain to users why they made the diagnosis. Many tests of fluid intelligence (2020) Bongard visual cognition problems, such as the Bongard-LOGO benchmark (2020) Visual Commonsense Reasoning (VCR) benchmark (as of 2020) Stock market prediction: Financial data collection and processing using Machine Learning algorithms Angry Birds video game, as of 2020 Various tasks that are difficult to solve without contextual knowledge, including: Translation Word-sense disambiguation == Proposed tests of artificial intelligence == In his famous Turing test, Alan Turing picked language, the defining feature of human beings, for its basis. The Turing test is now considered too exploitable to be a meaningful benchmark. The Feigenbaum test, proposed by the inventor of expert systems, tests a machine's knowledge and expertise about a specific subject. A paper by Jim Gray of Microsoft in 2003 suggested extending the Turing test to speech understanding, speaking and recognizing objects and behavior. Proposed "universal intelligence" tests aim to compare how well machines, humans, and even non-human animals perform on problem sets that are generic as possible. At an extreme, the test suite can contain every possible problem, weighted by Kolmogorov complexity; however, these problem sets tend to be dominated by impoverished pattern-matching exercises where a tuned AI can easily exceed human performance levels. == Exams == According to OpenAI, in 2023 GPT-4 achieved high scores on several standardized and professional examinations, including around the 90th percentile on the Uniform Bar Exam, the 89th percentile on the mathematics section of the SAT, the 93rd percentile on SAT Reading and Writing, the 54th percentile on the analytical writing section of the GRE, the 88th percentile on GRE quantitative reasoning, and the 99th percentile on GRE verbal reasoning. OpenAI also reported that GPT-4 scored in the 99th to 100th percentile on the 2020 USA Biology Olympiad semifinal exam and earned top scores on several AP exams. Independent researchers found in 2023 that ChatGPT based on GPT-3.5 performed "at or near the passing threshold" on all three parts of the United States Medical Licensing Examination (USMLE), suggesting that large language models could reach passing-level performance on some medical knowledge assessments even without domain-specific fine-tuning. GPT-3.5 was also reported to attain a low but passing grade on examinations for four law school courses at the University of Minnes
Kolmogorov–Arnold Networks
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.
AI Writing Assistants Reviews: What Actually Works in 2026
Looking for the best AI writing assistant? An AI writing assistant is software that uses machine learning to help you get more done — it can save you hours every week by automating repetitive work. Most options offer a generous free tier, with paid plans unlocking higher limits, faster processing, and team features. Whether you are a beginner or a pro, the right AI writing assistant slots into your workflow and pays for itself fast. Read on for hands-on impressions, pricing tiers, and the standout features that matter.
AI Mode
AI Mode is a search feature used within Google Search. In March 2025, Google introduced an experimental "AI Mode" within its search platform, enabling users to input complex, multi-part queries and receive comprehensive, AI-generated responses. This feature uses Google's Gemini model, which enhances the system's reasoning capabilities and supports multimodal inputs, including text, images, and voice. Users need to be signed in to be able to use the image generation features. Initially, AI Mode was available to Google One AI Premium subscribers in the United States, who could access it through the Search Labs platform. This phased rollout allowed Google to gather user feedback and refine the feature before a broader release.