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Computational intelligence

In computer science, computational intelligence (CI) refers to concepts, paradigms, algorithms and implementations of systems that are designed to show "intelligent" behavior in complex and changing environments. These systems are aimed at mastering complex tasks in a wide variety of technical or commercial areas and offer solutions that recognize and interpret patterns, control processes, support decision-making or autonomously manoeuvre vehicles or robots in unknown environments, among other things. These concepts and paradigms are characterized by the ability to learn or adapt to new situations, to generalize, to abstract, to discover and associate. Nature-analog or nature-inspired methods play a key role in this. CI approaches primarily address those complex real-world problems for which traditional or mathematical modeling is not appropriate for various reasons: the processes cannot be described exactly with complete knowledge, the processes are too complex for mathematical reasoning, they contain some uncertainties during the process, such as unforeseen changes in the environment or in the process itself, or the processes are simply stochastic in nature. Thus, CI techniques are properly aimed at processes that are ill-defined, complex, nonlinear, time-varying and/or stochastic. A recent definition of the IEEE Computational Intelligence Societey describes CI as the theory, design, application and development of biologically and linguistically motivated computational paradigms. Traditionally the three main pillars of CI have been Neural Networks, Fuzzy Systems and Evolutionary Computation. ... CI is an evolving field and at present in addition to the three main constituents, it encompasses computing paradigms like ambient intelligence, artificial life, cultural learning, artificial endocrine networks, social reasoning, and artificial hormone networks. ... Over the last few years there has been an explosion of research on Deep Learning, in particular deep convolutional neural networks. Nowadays, deep learning has become the core method for artificial intelligence. In fact, some of the most successful AI systems are based on CI. However, as CI is an emerging and developing field there is no final definition of CI, especially in terms of the list of concepts and paradigms that belong to it. The general requirements for the development of an “intelligent system” are ultimately always the same, namely the simulation of intelligent thinking and action in a specific area of application. To do this, the knowledge about this area must be represented in a model so that it can be processed. The quality of the resulting system depends largely on how well the model was chosen in the development process. Sometimes data-driven methods are suitable for finding a good model and sometimes logic-based knowledge representations deliver better results. Hybrid models are usually used in real applications. According to actual textbooks, the following methods and paradigms, which largely complement each other, can be regarded as parts of CI: Fuzzy systems Neural networks and, in particular, convolutional neural networks Evolutionary computation and, in particular, multi-objective evolutionary optimization Swarm intelligence Bayesian networks Artificial immune systems Learning theory Probabilistic methods == Relationship between hard and soft computing and artificial and computational intelligence == Artificial intelligence (AI) is used in the media, but also by some of the scientists involved, as a kind of umbrella term for the various techniques associated with it or with CI. Craenen and Eiben state that attempts to define or at least describe CI can usually be assigned to one or more of the following groups: "Relative definition” comparing CI to AI Conceptual treatment of key notions and their roles in CI Listing of the (established) areas that belong to it The relationship between CI and AI has been a frequently discussed topic during the development of CI. While the above list implies that they are synonyms, the vast majority of AI/CI researchers working on the subject consider them to be distinct fields, where either CI is an alternative to AI AI includes CI CI includes AI The view of the first of the above three points goes back to Zadeh, the founder of the fuzzy set theory, who differentiated machine intelligence into hard and soft computing techniques, which are used in artificial intelligence on the one hand and computational intelligence on the other. In hard computing (HC) and traditional AI (e.g. expert systems), inaccuracy and uncertainty are undesirable characteristics of a system, while soft computing (SC) and thus CI focus on dealing with these characteristics. The adjacent figure illustrates this view and lists the most important CI techniques. Another frequently mentioned distinguishing feature is the representation of information in symbolic form in AI and in sub-symbolic form in CI techniques. Hard computing is a conventional computing method based on the principles of certainty and accuracy and it is deterministic. It requires a precisely stated analytical model of the task to be processed and a prewritten program, i.e. a fixed set of instructions. The models used are based on Boolean logic (also called crisp logic), where e.g. an element can be either a member of a set or not and there is nothing in between. When applied to real-world tasks, systems based on HC result in specific control actions defined by a mathematical model or algorithm. If an unforeseen situation occurs that is not included in the model or algorithm used, the action will most likely fail. Soft computing, on the other hand, is based on the fact that the human mind is capable of storing information and processing it in a goal-oriented way, even if it is imprecise and lacks certainty. SC is based on the model of the human brain with probabilistic thinking, fuzzy logic and multi-valued logic. Soft computing can process a wealth of data and perform a large number of computations, which may not be exact, in parallel. For hard problems for which no satisfying exact solutions based on HC are available, SC methods can be applied successfully. SC methods are usually stochastic in nature i.e., they are a randomly defined processes that can be analyzed statistically but not with precision. Up to now, the results of some CI methods, such as deep learning, cannot be verified and it is also not clear what they are based on. This problem represents an important scientific issue for the future. AI and CI are catchy terms, but they are also so similar that they can be confused. The meaning of both terms has developed and changed over a long period of time, with AI being used first. Bezdek describes this impressively and concludes that such buzzwords are frequently used and hyped by the scientific community, science management and (science) journalism. Not least because AI and biological intelligence are emotionally charged terms and it is still difficult to find a generally accepted definition for the basic term intelligence. == History == In 1950, Alan Turing, one of the founding fathers of computer science, developed a test for computer intelligence known as the Turing test. In this test, a person can ask questions via a keyboard and a monitor without knowing whether his counterpart is a human or a computer. A computer is considered intelligent if the interrogator cannot distinguish the computer from a human. This illustrates the discussion about intelligent computers at the beginning of the computer age. The term Computational Intelligence was first used as the title of the journal of the same name in 1985 and later by the IEEE Neural Networks Council (NNC), which was founded 1989 by a group of researchers interested in the development of biological and artificial neural networks. On November 21, 2001, the NNC became the IEEE Neural Networks Society, to become the IEEE Computational Intelligence Society two years later by including new areas of interest such as fuzzy systems and evolutionary computation. The NNC helped organize the first IEEE World Congress on Computational Intelligence in Orlando, Florida in 1994. On this conference the first clear definition of Computational Intelligence was introduced by Bezdek: A system is computationally intelligent when it: deals with only numerical (low-level) data, has pattern-recognition components, does not use knowledge in the AI sense; and additionally when it (begins to) exhibit (1) computational adaptivity; (2) computational fault tolerance; (3) speed approaching human-like turnaround and (4) error rates that approximate human performance. Today, with machine learning and deep learning in particular utilizing a breadth of supervised, unsupervised, and reinforcement learning approaches, the CI landscape has been greatly enhanced, with novell intelligent approaches. == The main algorithmic approaches of CI and their applicati
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The Best Free AI Virtual Assistant for Beginners

Comparing the best AI virtual assistant? An AI virtual assistant is software that uses machine learning to help you get more done — it lowers the barrier so anyone can produce professional output. Privacy matters too: check whether your data trains the model and whether a no-log or enterprise tier is available. Whether you are a beginner or a pro, the right AI virtual assistant slots into your workflow and pays for itself fast. We tested the leading options and ranked them by quality, value, and ease of use.
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How to Choose an Conversational AI Platform

Trying to pick the best conversational AI platform? An conversational AI platform is software that uses machine learning to help you get more done — it scales effortlessly from a single task to thousands. The best picks balance beginner-friendly simplicity with the depth power users need, and they ship updates often. Whether you are a beginner or a pro, the right conversational AI platform slots into your workflow and pays for itself fast. This guide breaks down the top picks, their pros and cons, and who each one is best for.
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Aravind Joshi

Aravind Krishna Joshi (August 5, 1929 – December 31, 2017) was the Henry Salvatori Professor of Computer and Cognitive Science in the computer science department of the University of Pennsylvania. Joshi defined the tree-adjoining grammar formalism which is often used in computational linguistics and natural language processing. Joshi studied at Pune University and the Indian Institute of Science, where he was awarded a BE in electrical engineering and a DIISc in communication engineering respectively. Joshi's graduate work was done in the electrical engineering department at the University of Pennsylvania, and he was awarded his PhD in 1960. He became a professor at Penn and was the co-founder and co-director of the Institute for Research in Cognitive Science. == Awards and recognitions == Guggenheim fellow, 1971–72 Fellow of the Institute of Electrical and Electronics Engineers (IEEE), 1976 Best Paper Award at the National Conference on Artificial Intelligence, 1987 Founding Fellow of the American Association for Artificial Intelligence (AAAI), 1990 IJCAI Award for Research Excellence, 1997 Fellow of the Association for Computing Machinery, 1998 Elected to the National Academy of Engineering, 1999 First to be awarded the Association for Computational Linguistics Lifetime Achievement Award at the 40th anniversary meeting of the ACL, 2002 Awarded the Rumelhart Prize, 2003 Benjamin Franklin Medal in Computer and Cognitive Science, 2005 Doctor honoris causa of mathematical and physical sciences, Charles University in Prague, October 30, 2013 S.-Y. Kuroda Prize of the SIG Mathematics of Language of the ACL, 2013 === Awarded history === On April 21, 2005, Joshi was awarded the Franklin Institute's Benjamin Franklin Medal in Computer and Cognitive Science. The Franklin Institute citation states that he was awarded the medal "for his fundamental contributions to our understanding of how language is represented in the mind, and for developing techniques that enable computers to process efficiently the wide range of human languages. These advances have led to new methods for computer translation."
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Image formation

The study of image formation encompasses the radiometric and geometric processes by which 2D images of 3D objects are formed. In the case of digital images, the image formation process also includes analog to digital conversion and sampling. == Imaging == The imaging process is a mapping of an object to an image plane. Each point on the image corresponds to a point on the object. An illuminated object will scatter light toward a lens and the lens will collect and focus the light to create the image. The ratio of the height of the image to the height of the object is the magnification. The spatial extent of the image surface and the focal length of the lens determines the field of view of the lens. Image formation of mirror these have a center of curvature and its focal length of the mirror is half of the center of curvature. == Illumination == An object may be illuminated by the light from an emitting source such as the sun, a light bulb or a Light Emitting Diode. The light incident on the object is reflected in a manner dependent on the surface properties of the object. For rough surfaces, the reflected light is scattered in a manner described by the Bi-directional Reflectance Distribution Function (BRDF) of the surface. The BRDF of a surface is the ratio of the exiting power per square meter per steradian (radiance) to the incident power per square meter (irradiance). The BRDF typically varies with angle and may vary with wavelength, but a specific important case is a surface that has constant BRDF. This surface type is referred to as Lambertian and the magnitude of the BRDF is R/π, where R is the reflectivity of the surface. The portion of scattered light that propagates toward the lens is collected by the entrance pupil of the imaging lens over the field of view. == Field of view and imagery == The Field of view of a lens is limited by the size of the image plane and the focal length of the lens. The relationship between a location on the image and a location on the object is y = ftan(θ), where y is the max extent of the image plane, f is the focal length of the lens and θ is the field of view. If y is the max radial size of the image then θ is the field of view of the lens. While the image created by a lens is continuous, it can be modeled as a set of discrete field points, each representing a point on the object. The quality of the image is limited by the aberrations in the lens and the diffraction created by the finite aperture stop. == Pupils and stops == The aperture stop of a lens is a mechanical aperture which limits the light collection for each field point. The entrance pupil is the image of the aperture stop created by the optical elements on the object side of the lens. The light scattered by an object is collected by the entrance pupil and focused onto the image plane via a series of refractive elements. The cone of the focused light at the image plane is set by the size of the entrance pupil and the focal length of the lens. This is often referred to as the f-stop or f-number of the lens. f/# = f/D where D is the diameter of the entrance pupil. == Pixelation and color vs. monochrome == In typical digital imaging systems, a sensor is placed at the image plane. The light is focused on to the sensor and the continuous image is pixelated. The light incident on each pixel in the sensor will be integrated within the pixel and a proportional electronic signal will be generated. The angular geometric resolution of a pixel is given by atan(p/f), where p is the pitch of the pixel. This is also called the pixel field of view. The sensor may be monochrome or color. In the case of a monochrome sensor, the light incident on each pixel is integrated and the resulting image is a grayscale like picture. For color images, a mosaic color filter is typically placed over the pixels to create a color image. An example is a Bayer filter. The signal incident on each pixel is then digitized to a bit stream. == Image quality == The quality of an image is dependent upon both geometric and physical items. Geometrically, higher density of pixels across an image will give less blocky pixelation and thus a better geometric image quality. Lens aberrations also contribute to the quality of the image. Physically, diffraction due to the aperture stop will limit the resolvable spatial frequencies as a function of f-number. In the frequency domain, Modulation Transfer Function (MTF) is a measure of the quality of the imaging system. The MTF is a measure of the visibility of a sinusoidal variation in irradiance on the image plane as a function of the frequency of the sinusoid. It includes the effects of diffraction, aberrations and pixelation. For the lens, the MTF is the autocorrelation of the pupil function, so it accounts for the finite pupil extent and the lens aberrations. The sensor MTF is the Fourier Transform of the pixel geometry. For a square pixel, MTF(ξ) = sin(πξp)/πξp where p is the pixel width and ξ is the spatial frequency. The MTF of the combination of the lens and detector is the product of the two component MTFs. == Perception == Color images can be perceived via two means. In the case of computer vision the light incident on the sensor comprises the image. In the case of visual perception, the human eye has a color dependent response to light so this must be accounted for. This is important consideration when converting to grayscale. == Image formation in eye == The principal difference between the lens of the eye and an ordinary optical lens is that the former is flexible. The radius of the curvature of the anterior surface of the lens is greater than the radius of its posterior surface. The shape of the lens is controlled by tension in the fibers of the ciliary body. To focus on distant objects, the controlling muscles cause the lens to be relatively flattened. Similarly, these muscles allow the lens to become thicker in order to focus on objects near the eye. The distance between the center of the lens and the retina (focal length) varies from approximately 17 mm to about 14 mm, as the refractive power of the lens increases from its minimum to its maximum. When the eye focuses on an object farther away than about 3 m, the lens exhibits its lowest refractive power. When the eye focuses on a close object, the lens is most strongly refractive.
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Translation unit

In the field of translation, a translation unit is a segment of a text which the translator treats as a single cognitive unit for the purposes of establishing an equivalence. It may be a single word, a phrase, one or more sentences, or even a larger unit. When a translator segments a text into translation units, the larger these units are, the better chance there is of obtaining an idiomatic translation. This is true not only of human translation, but also where human translators use computer-assisted translation, such as translation memories, and when translations are performed by machine translation systems. == Perceptions on the concept of unit == Vinay and Darbelnet took to Saussure's original concepts of the linguistic sign when beginning to discuss the idea of a single word as a translation unit. According to Saussure, the sign is naturally arbitrary, so it can only derive meaning from contrast in other signs in that same system. However, Russian scholar Leonid Barkhudarov stated that, limiting it to poetry, for instance, a translation unit can take the form of a complete text. This seems to relate to his conception that a translation unit is the smallest unit in the source language with an equivalent in the target one, and when its parts are taken individually, they become untranslatable; these parts can be as small as phonemes or morphemes, or as large as entire texts. Susan Bassnett widened Barkhudarov's poetry perception to include prose, adding that in this type of translation text is the prime unit, including the idea that sentence-by-sentence translation could cause loss of important structural features. Swiss linguist Werner Koller connected Barkhudarov's idea of unit sizing to the difference between the two languages involved, by stating that the more different or unrelated these languages were, the larger the unit would be. One final perception on the idea of unit came from linguist Eugene Nida. To him, translation units have a tendency to be small groups of language building up into sentences, thus forming what he called meaningful mouthfuls of language. == Points of view towards translation units == === Process-oriented POV === According to this point of view, a translation unit is a stretch of text on which attention is focused to be represented as a whole in the target language. In this point of view we can consider the concept of the think-aloud protocol, supported by German linguist Wolfgang Lörscher: isolating units using self-reports by translating subjects. It also relates to how experienced the translator in question is: language learners take a word as a translation unit, whereas experienced translators isolate and translate units of meaning in the form of phrases, clauses or sentences. Since 1996 and 2005 keylogging and eyetracking technologies were introduced in Translation Process Research. These more advanced and non-invasive research methods made it possible to elaborate a finer-grained assessment of translation units as loops of (source or target text) reading and target text typing. Loops of translation units are thought to be the basic units by which translations are produced. Thus, Malmkjaer, for instance, defines process oriented translation units as a “stretch of the source text that the translator keeps in mind at any one time, in order to produce translation equivalents in the text he or she is creating” (p. 286). Records of keystrokes and eye movements allow to investigate these mental constructs through their physical (observable) behavioral traces in the translation process data. Empirical Translation Process Research has deployed numerous theories to explain and models the behavioral traces of these assumed mental units. === Product-oriented POV === Here, the target-text unit can be mapped into an equivalent source-text unit. A case study on this matter was reported by Gideon Toury, in which 27 English-Hebrew student-produced translations were mapped onto a source text. Those students that were less experienced had larger numbers of small units at word and morpheme level in their translations, while one student with translation experience had approximately half of those units, mostly at phrase or clause level.
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Best AI Text-to-video Tools in 2026

In search of the best AI text-to-video tool? An AI text-to-video tool is software that uses machine learning to help you get more done — it turns a rough idea into a polished result in seconds. When choosing one, weigh output quality, pricing, export formats, and how well it fits the tools you already use. Whether you are a beginner or a pro, the right AI text-to-video tool slots into your workflow and pays for itself fast. We tested the leading options and ranked them by quality, value, and ease of use.
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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.)
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Residual neural network

A residual neural network (also referred to as a residual network or ResNet) is a deep learning architecture in which the layers learn residual functions with reference to the layer inputs. It was developed in 2015 for image recognition, and won the ImageNet Large Scale Visual Recognition Challenge (ILSVRC) of that year. As a point of terminology, "residual connection" refers to the specific architectural motif of x ↦ f ( x ) + x {\displaystyle x\mapsto f(x)+x} , where f {\displaystyle f} is an arbitrary neural network module. The motif had been used previously (see §History for details). However, the publication of ResNet made it widely popular for feedforward networks, appearing in neural networks that are seemingly unrelated to ResNet. The residual connection stabilizes the training and convergence of deep neural networks with hundreds of layers, and is a common motif in deep neural networks, such as transformer models (e.g., BERT, and GPT models such as ChatGPT), the AlphaGo Zero system, the AlphaStar system, and the AlphaFold system. == Mathematics == === Residual connection === In a multilayer neural network model, consider a (non-residual) subnetwork with a certain number of stacked layers (e.g., 2 or 3). Let H ( x ; α ) {\displaystyle H(x;\alpha )} denote the subnetwork. Suppose H ∗ {\displaystyle H^{}} is the desired optimal output of this subnetwork. Residual learning simply adds x {\displaystyle x} directly to the output, such that the optimal learned output now becomes be H ∗ − x {\displaystyle H^{}-x} , which is interpreted as a "residual" with respect to x {\displaystyle x} . The operation of "adding x {\displaystyle x} " is implemented via a "skip connection" that performs an identity mapping to connect the input of the subnetwork with its output. This connection is referred to as a "residual connection" in later work. Let F ( x ; α ) = H ( x ; a ) + x {\displaystyle F(x;\alpha )=H(x;a)+x} . The function F {\displaystyle F} is often represented by matrix multiplication interlaced with activation functions and normalization operations (e.g., batch normalization or layer normalization). As a whole, one of these subnetworks is referred to as a "residual block". A deep residual network is constructed by simply stacking these blocks. Long short-term memory (LSTM) has a memory mechanism that serves as a residual connection. In an LSTM without a forget gate, an input x t {\displaystyle x_{t}} is processed by a function F {\displaystyle F} and added to a memory cell c t {\displaystyle c_{t}} , resulting in c t + 1 = c t + F ( x t ) {\displaystyle c_{t+1}=c_{t}+F(x_{t})} . An LSTM with a forget gate essentially functions as a highway network. To stabilize the variance of the layers' inputs, it is recommended to replace the residual connections x + f ( x ) {\displaystyle x+f(x)} with x / L + f ( x ) {\displaystyle x/L+f(x)} , where L {\displaystyle L} is the total number of residual layers. === Projection connection === If the function F {\displaystyle F} is of type F : R n → R m {\displaystyle F:\mathbb {R} ^{n}\to \mathbb {R} ^{m}} where n ≠ m {\displaystyle n\neq m} , then F ( x ) + x {\displaystyle F(x)+x} is undefined. To handle this special case, a projection connection is used: y = F ( x ) + P ( x ) {\displaystyle y=F(x)+P(x)} where P {\displaystyle P} is typically a linear projection, defined by P ( x ) = M x {\displaystyle P(x)=Mx} where M {\displaystyle M} is a m × n {\displaystyle m\times n} matrix. The matrix is trained via backpropagation, as is any other parameter of the model. === Signal propagation === The introduction of identity mappings facilitates signal propagation in both forward and backward paths. ==== Forward propagation ==== If the output of the ℓ {\displaystyle \ell } -th residual block is the input to the ( ℓ + 1 ) {\displaystyle (\ell +1)} -th residual block (assuming no activation function between blocks), then the ( ℓ + 1 ) {\displaystyle (\ell +1)} -th input is: x ℓ + 1 = F ( x ℓ ) + x ℓ {\displaystyle x_{\ell +1}=F(x_{\ell })+x_{\ell }} Applying this formulation recursively, e.g.: x ℓ + 2 = F ( x ℓ + 1 ) + x ℓ + 1 = F ( x ℓ + 1 ) + F ( x ℓ ) + x ℓ {\displaystyle {\begin{aligned}x_{\ell +2}&=F(x_{\ell +1})+x_{\ell +1}\\&=F(x_{\ell +1})+F(x_{\ell })+x_{\ell }\end{aligned}}} yields the general relationship: x L = x ℓ + ∑ i = ℓ L − 1 F ( x i ) {\displaystyle x_{L}=x_{\ell }+\sum _{i=\ell }^{L-1}F(x_{i})} where L {\textstyle L} is the index of a residual block and ℓ {\textstyle \ell } is the index of some earlier block. This formulation suggests that there is always a signal that is directly sent from a shallower block ℓ {\textstyle \ell } to a deeper block L {\textstyle L} . ==== Backward propagation ==== The residual learning formulation provides the added benefit of mitigating the vanishing gradient problem to some extent. However, it is crucial to acknowledge that the vanishing gradient issue is not the root cause of the degradation problem, which is tackled through the use of normalization. To observe the effect of residual blocks on backpropagation, consider the partial derivative of a loss function E {\displaystyle {\mathcal {E}}} with respect to some residual block input x ℓ {\displaystyle x_{\ell }} . Using the equation above from forward propagation for a later residual block L > ℓ {\displaystyle L>\ell } : ∂ E ∂ x ℓ = ∂ E ∂ x L ∂ x L ∂ x ℓ = ∂ E ∂ x L ( 1 + ∂ ∂ x ℓ ∑ i = ℓ L − 1 F ( x i ) ) = ∂ E ∂ x L + ∂ E ∂ x L ∂ ∂ x ℓ ∑ i = ℓ L − 1 F ( x i ) {\displaystyle {\begin{aligned}{\frac {\partial {\mathcal {E}}}{\partial x_{\ell }}}&={\frac {\partial {\mathcal {E}}}{\partial x_{L}}}{\frac {\partial x_{L}}{\partial x_{\ell }}}\\&={\frac {\partial {\mathcal {E}}}{\partial x_{L}}}\left(1+{\frac {\partial }{\partial x_{\ell }}}\sum _{i=\ell }^{L-1}F(x_{i})\right)\\&={\frac {\partial {\mathcal {E}}}{\partial x_{L}}}+{\frac {\partial {\mathcal {E}}}{\partial x_{L}}}{\frac {\partial }{\partial x_{\ell }}}\sum _{i=\ell }^{L-1}F(x_{i})\end{aligned}}} This formulation suggests that the gradient computation of a shallower layer, ∂ E ∂ x ℓ {\textstyle {\frac {\partial {\mathcal {E}}}{\partial x_{\ell }}}} , always has a later term ∂ E ∂ x L {\textstyle {\frac {\partial {\mathcal {E}}}{\partial x_{L}}}} that is directly added. Even if the gradients of the F ( x i ) {\displaystyle F(x_{i})} terms are small, the total gradient ∂ E ∂ x ℓ {\textstyle {\frac {\partial {\mathcal {E}}}{\partial x_{\ell }}}} resists vanishing due to the added term ∂ E ∂ x L {\textstyle {\frac {\partial {\mathcal {E}}}{\partial x_{L}}}} . == Variants of residual blocks == === Basic block === A basic block is the simplest building block studied in the original ResNet. This block consists of two sequential 3x3 convolutional layers and a residual connection. The input and output dimensions of both layers are equal. === Bottleneck block === A bottleneck block consists of three sequential convolutional layers and a residual connection. The first layer in this block is a 1×1 convolution for dimension reduction (e.g., to 1/2 of the input dimension); the second layer performs a 3×3 convolution; the last layer is another 1×1 convolution for dimension restoration. The models of ResNet-50, ResNet-101, and ResNet-152 are all based on bottleneck blocks. === Pre-activation block === The pre-activation residual block applies activation functions before applying the residual function F {\displaystyle F} . Formally, the computation of a pre-activation residual block can be written as: x ℓ + 1 = F ( ϕ ( x ℓ ) ) + x ℓ {\displaystyle x_{\ell +1}=F(\phi (x_{\ell }))+x_{\ell }} where ϕ {\displaystyle \phi } can be any activation (e.g. ReLU) or normalization (e.g. LayerNorm) operation. This design reduces the number of non-identity mappings between residual blocks, and allows an identity mapping directly from the input to the output. This design was used to train models with 200 to over 1000 layers, and was found to consistently outperform variants where the residual path is not an identity function. The pre-activation ResNet with 200 layers took 3 weeks to train for ImageNet on 8 GPUs in 2016. Since GPT-2, transformer blocks have been mostly implemented as pre-activation blocks. This is often referred to as "pre-normalization" in the literature of transformer models. == Applications == Originally, ResNet was designed for computer vision. All transformer architectures include residual connections. Indeed, very deep transformers cannot be trained without them. The original ResNet paper made no claim on being inspired by biological systems. However, later research has related ResNet to biologically-plausible algorithms. A study published in Science in 2023 disclosed the complete connectome of an insect brain (specifically that of a fruit fly larva). This study discovered "multilayer shortcuts" that resemble the skip connections in artificial neural networks, including ResNets. == History == === Previous work === Residual connections were noticed in neu
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Top 10 AI Image Generators Compared (2026)

Curious about the best AI image generator? An AI image generator is software that uses machine learning to help you get more done — it combines speed, accuracy, and an interface that just works. Hands-on testing shows real-world results vary, so a short free trial is the smartest way to decide. Whether you are a beginner or a pro, the right AI image generator slots into your workflow and pays for itself fast. Read on for hands-on impressions, pricing tiers, and the standout features that matter.
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The Best Free AI Analytics Tool for Beginners

Trying to pick the best AI analytics tool? An AI analytics tool is software that uses machine learning to help you get more done — it scales effortlessly from a single task to thousands. The best picks balance beginner-friendly simplicity with the depth power users need, and they ship updates often. Whether you are a beginner or a pro, the right AI analytics tool slots into your workflow and pays for itself fast. This guide breaks down the top picks, their pros and cons, and who each one is best for.
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DALL-E

DALL-E, DALL-E 2, and DALL-E 3 (stylised DALL·E) are text-to-image models developed by OpenAI using deep learning methodologies to generate digital images from natural language descriptions known as prompts. The first version of DALL-E was announced in January 2021. In the following year, its successor DALL-E 2 was released. DALL-E 3 was released natively into ChatGPT for ChatGPT Plus and ChatGPT Enterprise customers in October 2023, with availability via OpenAI's API and "Labs" platform provided in early November. Microsoft implemented the model in Bing's Image Creator tool and plans to implement it into their Designer app. With Bing's Image Creator tool, Microsoft Copilot runs on DALL-E 3. In March 2025, DALL-E-3 was replaced in ChatGPT by GPT Image's native image-generation capabilities. == History and background == DALL-E was revealed by OpenAI in a blog post on 5 January 2021, and uses a version of GPT-3 modified to generate images. On 6 April 2022, OpenAI announced DALL-E 2, a successor designed to generate more realistic images at higher resolutions that "can combine concepts, attributes, and styles". On 20 July 2022, DALL-E 2 entered into a beta phase with invitations sent to 1 million waitlisted individuals; users could generate a certain number of images for free every month and may purchase more. Access had previously been restricted to pre-selected users for a research preview due to concerns about ethics and safety. On 28 September 2022, DALL-E 2 was opened to everyone and the waitlist requirement was removed. In September 2023, OpenAI announced their latest image model, DALL-E 3, capable of understanding "significantly more nuance and detail" than previous iterations. In early November 2022, OpenAI released DALL-E 2 as an API, allowing developers to integrate the model into their own applications. Microsoft unveiled their implementation of DALL-E 2 in their Designer app and Image Creator tool included in Bing and Microsoft Edge. The API operates on a cost-per-image basis, with prices varying depending on image resolution. Volume discounts are available to companies working with OpenAI's enterprise team. The software's name is a portmanteau of the names of animated robot Pixar character WALL-E and the Spanish surrealist artist Salvador Dalí. In February 2024, OpenAI began adding watermarks to DALL-E generated images, containing metadata in the C2PA (Coalition for Content Provenance and Authenticity) standard promoted by the Content Authenticity Initiative. == Technology == The first generative pre-trained transformer (GPT) model was initially developed by OpenAI in 2018, using a Transformer architecture. The first iteration, GPT-1, was scaled up to produce GPT-2 in 2019; in 2020, it was scaled up again to produce GPT-3, with 175 billion parameters. === DALL-E === DALL-E has three components: a discrete VAE, an autoregressive decoder-only Transformer model (12 billion parameters) similar to GPT-3, and a CLIP pair of image encoder and text encoder. The discrete VAE can convert an image to a sequence of tokens, and conversely, convert a sequence of tokens back to an image. This is necessary as the Transformer model does not directly process image data. The input to the Transformer model is a sequence of tokenised image caption followed by tokenised image patches. The image caption is in English, tokenised by byte pair encoding (vocabulary size 16384), and can be up to 256 tokens long. Each image is a 256×256 RGB image, divided into 32×32 patches of 4×4 each. Each patch is then converted by a discrete variational autoencoder to a token (vocabulary size 8192). DALL-E was developed and announced to the public in conjunction with CLIP (Contrastive Language-Image Pre-training). CLIP is a separate model based on contrastive learning that was trained on 400 million pairs of images with text captions scraped from the Internet. Its role is to "understand and rank" DALL-E's output by predicting which caption from a list of 32,768 captions randomly selected from the dataset (of which one was the correct answer) is most appropriate for an image. A trained CLIP pair is used to filter a larger initial list of images generated by DALL-E to select the image that is closest to the text prompt. === DALL-E 2 === DALL-E 2 uses 3.5 billion parameters, a smaller number than its predecessor. Instead of an autoregressive Transformer, DALL-E 2 uses a diffusion model conditioned on CLIP image embeddings, which, during inference, are generated from CLIP text embeddings by a prior model. This is the same architecture as that of Stable Diffusion, released a few months later. === DALL-E 3 === While a technical report was written for DALL-E 3, it does not include training or implementation details of the model, instead focusing on the improved prompt following capabilities developed for DALL-E 3. == Capabilities == DALL-E can generate imagery in multiple styles, including photorealistic imagery, paintings, and emoji. It can "manipulate and rearrange" objects in its images, and can correctly place design elements in novel compositions without explicit instruction. Thom Dunn writing for BoingBoing remarked that "For example, when asked to draw a daikon radish blowing its nose, sipping a latte, or riding a unicycle, DALL-E often draws the handkerchief, hands, and feet in plausible locations." DALL-E showed the ability to "fill in the blanks" to infer appropriate details without specific prompts, such as adding Christmas imagery to prompts commonly associated with the celebration, and appropriately placed shadows to images that did not mention them. Furthermore, DALL-E exhibits a broad understanding of visual and design trends. DALL-E can produce images for a wide variety of arbitrary descriptions from various viewpoints with only rare failures. Mark Riedl, an associate professor at the Georgia Tech School of Interactive Computing, found that DALL-E could blend concepts (described as a key element of human creativity). Its visual reasoning ability is sufficient to solve Raven's Matrices (visual tests often administered to humans to measure intelligence). DALL-E 3 follows complex prompts with more accuracy and detail than its predecessors, and is able to generate more coherent and accurate text. DALL-E 3 is integrated into ChatGPT Plus. === Image modification === Given an existing image, DALL-E 2 and DALL-E 3 can produce "variations" of the image as individual outputs based on the original, as well as edit the image to modify or expand upon it. The "inpainting" and "outpainting" abilities of these models use context from an image to fill in missing areas using a medium consistent with the original, following a given prompt. For example, this can be used to insert a new subject into an image, or expand an image beyond its original borders. According to OpenAI, "Outpainting takes into account the image’s existing visual elements — including shadows, reflections, and textures — to maintain the context of the original image." === Technical limitations === DALL-E 2's language understanding has limits. It is sometimes unable to distinguish "A yellow book and a red vase" from "A red book and a yellow vase" or "A panda making latte art" from "Latte art of a panda". It generates images of an astronaut riding a horse when presented with the prompt "a horse riding an astronaut". It also fails to generate the correct images in a variety of circumstances. Requesting more than three objects, negation, numbers, and connected sentences may result in mistakes, and object features may appear on the wrong object. Additional limitations include generating text, ambigrams and other forms of typography, which often results in dream-like gibberish. The model also has a limited capacity to address scientific information, such as astronomy or medical imagery. == Ethical concerns == DALL-E 2's reliance on public datasets influences its results and leads to algorithmic bias in some cases, such as generating higher numbers of men than women for requests that do not mention gender. DALL-E 2's training data was filtered to remove violent and sexual imagery, but this was found to increase bias in some cases such as reducing the frequency of women being generated. OpenAI hypothesise that this may be because women were more likely to be sexualised in training data which caused the filter to influence results. In September 2022, OpenAI confirmed to The Verge that DALL-E invisibly inserts phrases into user prompts to address bias in results; for instance, "black man" and "Asian woman" are inserted into prompts that do not specify gender or race. OpenAI claims to address concerns for potential "racy content" – containing nudity or sexual content generation, with DALL-E 3 through input/output filters, blocklists, ChatGPT refusals, and model level interventions. However, DALL-E 3 continues to disproportionally represent people as White, female, and youthful. Users are able to somewhat remedy
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Comparison of color models in computer graphics

This article provides introductory information about the RGB, HSV, and HSL color models from a computer graphics (web pages, images) perspective. An introduction to colors is also provided to support the main discussion. == Basics of color == === Primary colors and hue === First, "color" refers to the human brain's subjective interpretation of combinations of a narrow band of wavelengths of light. For this reason, the definition of "color" is not based on a strict set of physical phenomena. Therefore, even basic concepts like "primary colors" are not clearly defined. For example, traditional "Painter's Colors" use red, blue, and yellow as the primary colors, "Printer's Colors" use cyan, yellow, and magenta, and "Light Colors" use red, green, and blue. "Light colors", more formally known as additive colors, are formed by combining red, green, and blue light. This article refers to additive colors and refers to red, green, and blue as the primary colors. Hue is a term describing a pure color, that is, a color not modified by tinting or shading (see below). In additive colors, hues are formed by combining two primary colors. When two primary colors are combined in equal intensities, the result is a "secondary color". === Color wheel === A color wheel is a tool that provides a visual representation of the relationships between all possible hues. The primary colors are arranged around a circle at equal (120 degree) intervals. (Warning: Color wheels frequently depict "Painter's Colors" primary colors, which leads to a different set of hues than additive colors.) The illustration shows a simple color wheel based on the additive colors. Note that the position (top, right) of the starting color, typically red, is arbitrary, as is the order of green and blue (clockwise, counter-clockwise). The illustration also shows the secondary colors, yellow, cyan, and magenta, located halfway between (60 degrees) the primary colors. == Complementary color == The complement of a hue is the hue that is opposite it (180 degrees) on the color wheel. Using additive colors, mixing a hue and its complement in equal amounts produces white. === Tints and shades === The following discussion uses an illustration involving three projectors pointing to the same spot on a screen. Each projector is capable of generating one hue. The "intensities" of each projector are "matched" and can be equally adjusted from zero to full. (Note: "Intensity" is used here in the same sense as the RGB color model. The subject of matching, or "gamma correction", is beyond the level of this article.) A shade is produced by "dimming" a maximum chroma color. Painters refer to this as "adding black". In our illustration, one projector is set to full intensity, a second is set to some intensity between zero and full, and third is set to zero. "Dimming" is accomplished by decreasing each projector's intensity setting to the same fraction of its start setting. In the shade example, with any fully shaded hue, that all three projectors are set to zero intensity, resulting in black. A tint is produced by "lightening" a maximum chroma color. Painters refer to this as "adding white". In our illustration, one projector is set to full intensity, a second is set to some intensity between zero and full, and third is set to zero. "Lightening" is accomplished by increasing each projector's intensity setting by the same fraction from its start setting to full. In the tinting example, note that the third projector is now contributing. When the hue is fully lightened, all three projectors are each at full intensity, and the result is white. Note an attribute of the total intensity in the additive model. If full intensity for one projector is 1, then a primary color has a combined intensity of 1. A secondary color has a total intensity of 2. White has a total intensity of 3. Tinting, or "adding white", increases the total intensity of the hue. While this is simply a fact, the HSL model will take this fact into account in its design. === Tones === Tone is a general term, typically used by painters, to refer to the effects of reducing the "colorfulness" of a maximum chroma color; painters refer to it as "adding gray". Note that gray is not a color or even a single concept but refers to all the range of values between black and white where all three primary colors are equally represented. The general term is provided as more specific terms have conflicting definitions in different color models. Thus, shading takes a hue toward black, tinting takes a hue towards white, and tones cover the range between. == Choosing a color model == No one color model is necessarily "better" than another. Typically, the choice of a color model is dictated by external factors, such as a graphics tool or the need to specify colors according to the CSS2 or CSS3 standard. The following discussion only describes how the models function, centered on the concepts of hue, shade, tint, and tone. === RGB === The RGB model's approach to colors is important because: It directly reflects the physical properties of "Truecolor" displays As of 2011, most graphic cards define pixel values in terms of the colors red, green, and blue. The typical range of intensity values for each color, 0–255, is based on taking a binary number with 32 bits and breaking it up into four bytes of 8 bits each. 8 bits can hold a value from 0 to 255. The fourth byte is used to specify the "alpha", or the opacity, of the color. Opacity comes into play when layers with different colors are stacked. If the color in the top layer is less than fully opaque (alpha < 255), the color from underlying layers "shows through". In the RGB model, hues are represented by specifying one color as full intensity (255), a second color with a variable intensity, and the third color with no intensity (0). The following provides some examples using red as the full-intensity and green as the partial-intensity colors; blue is always zero: Shades are created by multiplying the intensity of each primary color by 1 minus the shade factor, in the range 0 to 1. A shade factor of 0 does nothing to the hue, a shade factor of 1 produces black: new intensity = current intensity (1 – shade factor) The following provides examples using orange: Tints are created by modifying each primary color as follows: the intensity is increased so that the difference between the intensity and full intensity (255) is decreased by the tint factor, in the range 0 to 1. A tint factor of 0 does nothing, a tint factor of 1 produces white: new intensity = current intensity + (255 – current intensity) tint factor The following provides examples using orange: Tones are created by applying both a shade and a tint. The order in which the two operations are performed does not matter, with the following restriction: when a tint operation is performed on a shade, the intensity of the dominant color becomes the "full intensity"; that is, the intensity value of the dominant color must be used in place of 255. The following provides examples using orange: === HSV === The HSV, or HSB, model describes colors in terms of hue, saturation, and value (brightness). Note that the range of values for each attribute is arbitrarily defined by various tools or standards. Be sure to determine the value ranges before attempting to interpret a value. Hue corresponds directly to the concept of hue in the Color Basics section. The advantages of using hue are The angular relationship between tones around the color circle is easily identified Shades, tints, and tones can be generated easily without affecting the hue Saturation corresponds directly to the concept of tint in the Color Basics section, except that full saturation produces no tint, while zero saturation produces white, a shade of gray, or black. Value corresponds directly to the concept of intensity in the Color Basics section. Pure colors are produced by specifying a hue with full saturation and value Shades are produced by specifying a hue with full saturation and less than full value Tints are produced by specifying a hue with less than full saturation and full value Tones are produced by specifying a hue and both less than full saturation and value White is produced by specifying zero saturation and full value, regardless of hue Black is produced by specifying zero value, regardless of hue or saturation Shades of gray are produced by specifying zero saturation and between zero and full value The advantage of HSV is that each of its attributes corresponds directly to the basic color concepts, which makes it conceptually simple. The perceived disadvantage of HSV is that the saturation attribute corresponds to tinting, so desaturated colors have increasing total intensity. For this reason, the CSS3 standard plans to support RGB and HSL but not HSV. === HSL === The HSL model describes colors in terms of hue, saturation, and lightness (also called luminance). (Note: the definition of sa
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Claire Cardie

Claire Cardie is an American computer scientist specializing in natural language processing. Since 2006, she has been a professor of computer science and information science at Cornell University, and from 2010 to 2011 she was the first Charles and Barbara Weiss Chair of Information Science at Cornell. Her research interests include coreference resolution and sentiment analysis. == Education and career == Cardie is a 1982 graduate of Yale University, majoring in computer science. After working for several companies as a computer programmer, she returned to graduate study in the late 1980s and completed her Ph.D. at the University of Massachusetts Amherst in 1994. Her dissertation, Domain-Specific Knowledge Acquisition for Conceptual Sentence Analysis, was supervised by Wendy Lehnert. She has been on the Cornell University faculty since 1994, initially in computer science and since 2005 also in information science. She was an assistant professor (1994–2000) and associate professor (2000–06), before being promoted to a full professorship in 2006. In 2007 she founded a start-up company, Appinions, and she was its chief scientist until 2015. Her doctoral students at Cornell have included Amit Singhal and Kiri Wagstaff. == Recognition == Cardie became a Fellow of the Association for Computational Linguistics in 2016. She was elected as an ACM Fellow in 2019 "for contributions to natural language processing, including coreference resolution, information and opinion extraction". She was named to the 2021 class of Fellows of the American Association for the Advancement of Science.
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Top 10 AI Photo Editors Compared (2026)

Looking for the best AI photo editor? An AI photo editor 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 photo editor slots into your workflow and pays for itself fast. This guide breaks down the top picks, their pros and cons, and who each one is best for.
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