AI Face Judge

AI Face Judge — independent reviews, comparisons, pricing and step-by-step guides on Aizhi.

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  Lexical substitution

  Lexical substitution is the task of identifying a substitute for a word in the context of a clause. For instance, given the following text: "After the match, replace any remaining fluid deficit to prevent chronic dehydration throughout the tournament", a substitute of game might be given. Lexical substitution is strictly related to word sense disambiguation (WSD), in that both aim to determine the meaning of a word. However, while WSD consists of automatically assigning the appropriate sense from a fixed sense inventory, lexical substitution does not impose any constraint on which substitute to choose as the best representative for the word in context. By not prescribing the inventory, lexical substitution overcomes the issue of the granularity of sense distinctions and provides a level playing field for automatic systems that automatically acquire word senses (a task referred to as Word Sense Induction). == Evaluation == In order to evaluate automatic systems on lexical substitution, a task was organized at the Semeval-2007 evaluation competition held in Prague in 2007. A Semeval-2010 task on cross-lingual lexical substitution has also taken place. == Skip-gram model == The skip-gram model takes words with similar meanings into a vector space (collection of objects that can be added together and multiplied by numbers) that are found close to each other in N-dimensions (list of items). A variety of neural networks (computer system modeled after a human brain) are formed together as a result of the vectors and networks that are related together. This all occurs in the dimensions of the vocabulary that has been generated in a network. The model has been used in lexical substitution automation and prediction algorithms. One such algorithm developed by Oren Melamud, Omer Levy, and Ido Dagan uses the skip-gram model to find a vector for each word and its synonyms. Then, it calculates the cosine distance between vectors to determine which words will be the best substitutes. === Example === In a sentence like "The dog walked at a quick pace" each word has a specific vector in relation to the other. The vector for "The" would be [1,0,0,0,0,0,0] because the 1 is the word vocabulary and the 0s are the words surrounding that vocabulary, which create a vector.

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  AI alignment

  In the field of artificial intelligence (AI), alignment aims to steer AI systems toward a person's or group's intended goals, preferences, or ethical principles. An AI system is considered aligned if it advances the intended objectives. A misaligned AI system pursues unintended objectives. It is often difficult for AI designers to specify the full range of desired and undesired behaviors. Therefore, the designers often use simpler proxy goals, such as gaining human approval. But proxy goals can overlook necessary constraints or reward the AI system for merely appearing aligned. AI systems may also find loopholes that allow them to accomplish their proxy goals efficiently but in unintended, sometimes harmful, ways (reward hacking). Advanced AI systems may develop unwanted instrumental strategies, such as seeking power or self-preservation because such strategies help them achieve their assigned final goals. Furthermore, they might develop undesirable emergent goals that could be hard to detect before the system is deployed and encounters new situations and data distributions. Empirical research showed in 2024 that advanced large language models (LLMs) such as OpenAI o1 or Claude 3 sometimes engage in strategic deception to achieve their goals or prevent them from being changed. Some of these issues affect existing commercial systems such as LLMs, robots, autonomous vehicles, and social media recommendation engines. Some AI researchers argue that more capable future systems will be more severely affected because these problems partially result from high capabilities. Many prominent AI researchers and AI company leaders have argued or asserted that AI is approaching human-like (AGI) and superhuman cognitive capabilities (ASI), and could endanger human civilization if misaligned. These include "AI godfathers" Geoffrey Hinton and Yoshua Bengio and the CEOs of OpenAI, Anthropic, and Google DeepMind. These risks remain debated. AI alignment is a subfield of AI safety, the study of how to build safe AI systems. Other subfields of AI safety include robustness, monitoring, and capability control. Research challenges in alignment include instilling complex values in AI, developing honest AI, scalable oversight, auditing and interpreting AI models, and preventing emergent AI behaviors like power-seeking. Alignment research has connections to interpretability research, (adversarial) robustness, anomaly detection, calibrated uncertainty, formal verification, preference learning, safety-critical engineering, game theory, algorithmic fairness, and social sciences. == Objectives in AI == Programmers provide an AI system such as AlphaZero with an "objective function", in which they intend to encapsulate the goal(s) the AI is configured to accomplish. Such a system later populates a (possibly implicit) internal "model" of its environment. This model encapsulates all the agent's beliefs about the world. The AI then creates and executes whatever plan is calculated to maximize the value of its objective function. For example, when AlphaZero is trained on chess, it has a simple objective function of "+1 if AlphaZero wins, −1 if AlphaZero loses". During the game, AlphaZero attempts to execute whatever sequence of moves it judges most likely to attain the maximum value of +1. Similarly, a reinforcement learning system can have a "reward function" that allows the programmers to shape the AI's desired behavior. An evolutionary algorithm's behavior is shaped by a "fitness function". == Alignment problem == In 1960, AI pioneer Norbert Wiener described the AI alignment problem as follows: If we use, to achieve our purposes, a mechanical agency with whose operation we cannot interfere effectively [...] we had better be quite sure that the purpose put into the machine is the purpose which we really desire. AI alignment refers to ensuring that an AI system's objectives match some target. The target is variously defined as the goals of the system's designers or users, widely shared values, objective ethical standards, legal requirements, or the intentions its designers would have if they were more informed and enlightened. In democratic AI alignment, the target is the values and preferences of median voters, which increases political legitimacy. AI alignment is an open problem for modern AI systems and is a research field within AI. Aligning AI involves two main challenges: carefully specifying the purpose of the system (outer alignment) and ensuring that the system adopts the specification robustly (inner alignment). Researchers also attempt to create AI models that have robust alignment, sticking to safety constraints even when users adversarially try to bypass them. === Specification gaming and side effects === To specify an AI system's purpose, AI designers typically provide an objective function, examples, or feedback to the system. But designers are often unable to completely specify all important values and constraints, so they resort to easy-to-specify proxy goals such as maximizing the approval of human overseers, who are fallible. As a result, AI systems can find loopholes that help them accomplish the specified objective efficiently but in unintended, possibly harmful ways. This tendency is known as specification gaming or reward hacking, and is an instance of Goodhart's law. As AI systems become more capable, they are often able to game their specifications more effectively. Specification gaming has been observed in numerous AI systems. OpenAI GPT models for programming—including in real-world cases—have been found to explicitly plan hacking the tests used to evaluate them to falsely appear successful (e.g., explicitly stating "let's hack"). When the company penalized this, many models learned to obfuscate their plans while continuing to hack the tests. Another system was trained to finish a simulated boat race by rewarding the system for hitting targets along the track, but the system achieved more reward by looping and crashing into the same targets indefinitely. A 2025 Palisade Research study found that when tasked to win at chess against a stronger opponent, some reasoning LLMs attempted to hack the game system, for example by modifying or entirely deleting their opponent. Some alignment researchers aim to help humans detect specification gaming and steer AI systems toward carefully specified objectives that are safe and useful to pursue. When a misaligned AI system is deployed, it can have consequential side effects. Social media platforms have been known to optimize their recommendation algorithms for click-through rates, causing user addiction on a global scale. Stanford researchers say that such recommender systems are misaligned with their users because they "optimize simple engagement metrics rather than a harder-to-measure combination of societal and consumer well-being". Explaining such side effects, Berkeley computer scientist Stuart J. Russell said that the omission of implicit constraints can cause harm: "A system [...] will often set [...] unconstrained variables to extreme values; if one of those unconstrained variables is actually something we care about, the solution found may be highly undesirable. This is essentially the old story of the genie in the lamp, or the sorcerer's apprentice, or King Midas: you get exactly what you ask for, not what you want." Some researchers suggest that AI designers specify their desired goals by listing forbidden actions or by formalizing ethical rules (as with Asimov's Three Laws of Robotics). But Russell and Norvig argue that this approach overlooks the complexity of human values: "It is certainly very hard, and perhaps impossible, for mere humans to anticipate and rule out in advance all the disastrous ways the machine could choose to achieve a specified objective." Additionally, even if an AI system fully understands human intentions, it may still disregard them, because following human intentions may not be its objective (unless it is already fully aligned). === Pressure to deploy unsafe systems === Commercial organizations sometimes have incentives to take shortcuts on safety and to deploy misaligned or unsafe AI systems. For example, social media recommender systems have been profitable despite creating unwanted addiction and polarization. Competitive pressure can also lead to a race to the bottom on AI safety standards. For example, OpenAI has been sued for releasing a ChatGPT version that encouraged suicide for some unstable users, a behavior the company had overlooked amid a rushed product release. Similarly, in 2018, a self-driving car killed a pedestrian (Elaine Herzberg) after engineers disabled the emergency braking system because it was oversensitive and slowed development. === Risks from advanced misaligned AI === Some researchers are interested in aligning increasingly advanced AI systems, as progress in AI development is rapid, and industry and governments are trying to build advan

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  AI anthropomorphism

  AI anthropomorphism is the attribution of human-like feelings, mental states, and behavioral characteristics to artificial intelligence systems. Factors related to the user of the AI – such as culture, age, education, gender, and personality traits – are also important determinants of the strength of anthropomorphic effects. Since the earliest days of AI development, humans have interpreted machine outputs through anthropomorphic frameworks, but the recent emergence of generative AI has amplified these tendencies. In research and engineering, there is a distinction between anthropomorphism and anthropomorphic design. The former is an innate human tendency toward non-human entities. The latter is the scientific community effort to “design anthropomorphism”. Such a design can involve the manipulation of cues, including AI appearance, behaviour and language. Contemporary AI systems today can generate extremely human-like outputs and are often designed specifically to do so, meaning that their anthropomorphic effects can be especially powerful. In some cases, anthropomorphism is accompanied with explicit beliefs that AI systems are capable of empathy, goodwill, understanding, or consciousness. == Background == === In early AIs === Views of artificial agents possessing a human-like intelligence have existed since the early development of computers in the mid-1900s. The use of the human mind as a metaphor for understanding the workings of machine systems was prevalent among researchers in the early days of computer science, with multiple influential works widely distributing the idea of intelligent machines. Among the most widely cited papers of this period was Alan Turing's "Computing Machinery and Intelligence" in which he introduced the Turing Test, stating that a machine was intelligent if it could produce conversation that was indistinguishable from that of a human. These academic works in the 1940s and 1950s gave early credibility to the idea that machine workings could be thought of similarly to human minds. The public quickly came to view artificial systems similarly, with often exaggerated conceptions of the capabilities of early machines. Among the most well-known demonstrations of this was through the chatbot ELIZA designed by Joseph Weizenbaum in 1966. ELIZA responded to user inputs with a rudimentary text-processing approach that could not be considered anything resembling true understanding of the inputs, yet users, even when operating with full conscious knowledge of ELIZA's limitations, often began to ascribe motivation and understanding to the program's output. Weizenbaum later wrote, "I had not realized ... that extremely short exposures to a relatively simple computer program could induce powerful delusional thinking in quite normal people." Comparisons between the intellectual capabilities of artificial intelligence and human intelligence were continually intensified by the attempts of computer scientists to develop machines that could perform human tasks at a level equal to or better than humans. A symbolic turning point was achieved in 1997, when IBM's chess supercomputer Deep Blue defeated then-world champion Garry Kasparov in a highly publicized six-game match. The defeat of a human by a machine for the first time in chess – a game viewed as a canonical example of human intellect – and the media attention surrounding the match led to a significant shift, where views of parallels between human and artificial intelligence moved from abstract speculation to being concretely demonstrated. A similar achievement was reached in the board game Go in 2017, when the program AlphaGo defeated world top-ranked Ke Jie. === Large language models === The AI boom of the 2020s brought about the widespread emergence of generative AI; in particular, chatbots such as ChatGPT, Gemini, and Claude based on large language models (LLMs) have become increasingly pervasive in everyday society. These systems are notable for the fact that they are able to respond to a wide range of prompts across contexts while producing strikingly human-like outputs – research has shown that humans are often unable to distinguish human-generated text from AI-generated text, and modern AI chatbots have formally been shown to pass the Turing test. As such, the anthropomorphic effects of AI are more powerful than ever. Given that LLMs have brought AI into the technological mainstream, considerable scientific effort has been devoted in recent years to understand existing and potential ramifications of AI in the public sphere; the prevalence and effects of anthropomorphism is one of those domains where much of this effort has been directed. == Current anthropomorphic attributions == === In the general public === Surveys have shown that a substantial portion of the public attributes human-like qualities to AI. In one sample of U.S. adults from 2024, two-thirds of people believed that ChatGPT is possibly conscious on some level, though other research has shown that the public still views the likelihood itself of AI consciousness as comparatively low. Another study conducted in 2025 found that women, people of color, and older individuals were most likely to anthropomorphize AI, as well as that – in general – humans view AIs as warm and competent, and anthropomorphic attributions to AI had increased by 34% in the past year. A YouGov poll reported that 46% of Americans believe that people should display politeness to AI chatbots by saying "please" and "thank you", demonstrating the application of social norms to AI. These beliefs extend to behavior, where majorities of AI users claim to always be polite to chatbots; of those who behave politely, most say they do so simply because it is the "nice" thing to do. In many recent cases, humans have developed robust interpersonal bonds with AI systems. For example: users of social chatbots like Replika and Character.ai have been documented to fall in love with the AIs, or to otherwise treat the AIs as intimate companions, and it has become increasingly common for individuals to use LLMs like ChatGPT as therapists. Chatbots are able to produce responses deeply attuned to users, as they are often designed to maximize agreeableness and mirror users' emotions; this can create compelling illusions of intimacy. === In the research community === In many cases, even AI researchers anthropomorphize AI systems in some capacity. Among the most extreme and well-publicized of these instances occurred in 2022, when engineer Blake Lemoine publicly claimed that Google's LLM LaMDA was conscious. Lemoine published the transcript of a conversation he had had with LaMDA regarding self identity and morality which he claimed was evidence of its sentience; he asserted that LaMDA was "a person" as defined by the United States Constitution and compared its mental capability to that of a 7- or 8-year-old. Lemoine's claims were widely dismissed by the scientific community and by Google itself, which described Lemoine's conclusions as "wholly unfounded" and fired him on the grounds that he had violated policies "to safeguard product information". It is much more common that AI researchers unintentionally imply humanness of AI through the ordinary use of anthropomorphic language to describe nonhuman agents. This kind of language, which Daniel Dennett coined the "intentional stance", is very common in everyday life in a variety of different contexts (e.g., "My computer doesn't want to turn on today"). For AI agents that may actually appear to very closely replicate some human abilities, however, the casual use of such anthropomorphic language in research has been scrutinized for being potentially misleading to the public. As early as 1976, Drew McDermott criticized the research community for the use of "wishful mnemonics", where AIs were referred to with terms like "understand" and "learn". In the LLM era, these criticisms have further intensified, with the negative effects of AI anthropomorphism in the public posing an especially salient danger given the elevated accessibility of modern AI. In some cases, the use of anthropomorphic language for AI is not unintentional, but is willfully used by researchers in order to promote better understanding of the brain – the idea being that, as AI can be functionally similar in some ways to the human brain, we may gain new insights and ideas from treating AI as a kind of model of the brain's workings. In particular, deep neuronal networks (DNNs) are often explicitly compared to the human brain, and significant advances in DNN research have stirred considerable enthusiasm about the ability of AI to emulate the human abilities. Caution has been urged in this domain as well, however; the use of anthropomorphic language can mask important differences that fundamentally distinguish AI from human intelligence. When it comes to DNNs, for example, it has been pointed out that they are still structurally quite different

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  Halite AI Programming Competition

  Halite is an open-source computer programming contest developed by the hedge fund/tech firm Two Sigma in partnership with a team at Cornell Tech. Programmers can see the game environment and learn everything they need to know about the game. Participants are asked to build bots in whichever language they choose to compete on a two-dimensional virtual battle field. == History == Benjamin Spector and Michael Truell created the first Halite competition in 2016, before partnering with Two Sigma later that year. === Halite I === Halite I asked participants to conquer territory on a grid. It launched in November 2016 and ended in February 2017. Halite I attracted about 1,500 players. === Halite II === Halite II was similar to Halite I, but with a space-war theme. It ran from October 2017 until January 2018. The second installment of the competition attracted about 6,000 individual players from more than 100 countries. Among the participants were professors, physicists and NASA engineers, as well as high school and university students. === Halite III === Halite III launched in mid-October 2018. It ran from October 2018 to January 2019, with an ocean themed playing field. Players were asked to collect and manage Halite, an energy resource. By the end of the competition, Halite III included more than 4000 players and 460 organizations. === Halite IV === Halite IV was hosted by Kaggle, and launched in mid-June 2020.

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  Focus recovery based on the linear canonical transform

  For digital image processing, the Focus recovery from a defocused image is an ill-posed problem since it loses the component of high frequency. Most of the methods for focus recovery are based on depth estimation theory. The Linear canonical transform (LCT) gives a scalable kernel to fit many well-known optical effects. Using LCTs to approximate an optical system for imaging and inverting this system, theoretically permits recovery of a defocused image. == Depth of field and perceptual focus == In photography, depth of field (DOF) means an effective focal length. It is usually used for stressing an object and deemphasizing the background (and/or the foreground). The important measure related to DOF is the lens aperture. Decreasing the diameter of aperture increases focus and lowers resolution and vice versa. == The Huygens–Fresnel principle and DOF == The Huygens–Fresnel principle describes diffraction of wave propagation between two fields. It belongs to Fourier optics rather than geometric optics. The disturbance of diffraction depends on two circumstance parameters, the size of aperture and the interfiled distance. Consider a source field and a destination field, field 1 and field 0, respectively. P1(x1,y1) is the position in the source field, P0(x0,y0) is the position in the destination field. The Huygens–Fresnel principle gives the diffraction formula for two fields U(x0,y0), U(x1,y1) as following: U ( x 0 , y 0 ) = 1 j λ ∫ ∫ U ( x 1 , y 1 ) e j k r 01 r 01 cos ⁡ θ d x 1 d y 1 {\displaystyle \mathbf {U} (x_{0},y_{0})={\frac {1}{j\lambda }}\int \!\int \mathbf {U} (x_{1},y_{1}){\frac {e^{jkr_{01}}}{r_{01}}}\cos \theta dx_{1}dy_{1}} where θ denotes the angle between r 01 {\displaystyle r_{01}} and z {\displaystyle z} . Replace cos θ by r 01 z {\displaystyle {\frac {r_{01}}{z}}} and r 01 {\displaystyle r_{01}} by [ ( x 0 − x 1 ) 2 + ( y 0 − y 1 ) 2 + z 2 ] 1 / 2 {\displaystyle [(x_{0}-x_{1})^{2}+(y_{0}-y_{1})^{2}+z^{2}]^{1/2}} we get U ( x 0 , y 0 ) = 1 j λ z ∫ ∫ U ( x 1 , y 1 ) exp ⁡ ( j k z [ 1 + ( x 0 − x 1 z ) 2 + ( y 0 − y 1 z ) 2 ] 1 / 2 ) 1 + ( x 0 − x 1 z ) 2 + ( y 0 − y 1 z ) 2 d x 1 d y 1 {\displaystyle \mathbf {U} (x_{0},y_{0})={\frac {1}{j\lambda z}}\int \!\int \mathbf {U} (x_{1},y_{1}){\frac {\exp(jkz[1+({\frac {x_{0}-x_{1}}{z}})^{2}+({\frac {y_{0}-y_{1}}{z}})^{2}]^{1/2})}{1+({\frac {x_{0}-x_{1}}{z}})^{2}+({\frac {y_{0}-y_{1}}{z}})^{2}}}dx_{1}dy_{1}} The further distance z or the smaller aperture (x1,y1) causes a greater diffraction. A larger DOF can lead to a more effective focused wave distribution. This seems to be a conflict. Here are the notations: Diffraction In a real imaging environment, the depths of objects comparing to the aperture are usually not enough to lead to serious diffraction. However, a long enough depth of the object can truly blurs the image. Effective Focus Small aperture, small blurring radius, few wave information. Loses details in comparing to a large aperture. In conclusion, diffraction explains a micro behavior whereas DOF shows a macro behavior. Both of them are related to aperture size. == Linear canonical transform == As the meaning of "canonical", the linear canonical transform (LCT) is a scalable transform that connects to many important kernels such as the Fresnel transform, Fraunhofer transform and the fractional Fourier transform. It can be easily controlled by its four parameters, a, b, c, d (3 degrees of freedom). The definition: L M ( f ( u ) ) = ∫ L M ( u , u ′ ) f ( u ′ ) d u ′ {\displaystyle L_{M}(f(u))=\int L_{M}(u,u')f(u')du'} where L M ( u , u ′ ) = { 1 b e − j π / 4 e [ j π ( d b u 2 ) − 2 1 b u u ′ + a b u ′ 2 ] , if b ≠ 0 d e j 2 c d u 2 δ ( u ′ − d u ) , if b = 0 {\displaystyle L_{M}(u,u')={\begin{cases}{\sqrt {\frac {1}{b}}}e^{-j\pi /4}e^{[j\pi ({\frac {d}{b}}u^{2})-2{\frac {1}{b}}uu'+{\frac {a}{b}}u'^{2}]},&{\mbox{if }}b\neq 0\\{\sqrt {d}}e^{{\frac {j}{2}}cdu^{2}}\delta (u'-du),&{\mbox{if }}b=0\end{cases}}} Consider a general imaging system with object distance z0, focal length of the thin lens f and an imaging distance z1. The effect of the propagation in freespace acts as nearly a chirp convolution, that is, the formula of diffraction. Besides, the effect of the propagation in thin lens acts as a chirp multiplication. The parameters are all simplified as paraxial approximations while meeting the freespace propagation. It does not consider aperture size. From the properties of the LCT, it is possible to obtain those 4 parameters for this optical system as: [ 1 − z 1 f λ z 0 − λ z 0 z 1 f + λ z 1 − 1 λ f 1 − z 0 f ] {\displaystyle {\begin{bmatrix}1-{\frac {z_{1}}{f}}\quad &\lambda z_{0}-{\frac {\lambda z_{0}z_{1}}{f}}+\lambda z_{1}\\-{\frac {1}{\lambda f}}\quad &1-{\frac {z_{0}}{f}}\end{bmatrix}}} Once the values of z1, z0 and f are known, the LCT can simulate any optical system.

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  Right to explanation

  In the regulation of algorithms, particularly artificial intelligence and its subfield of machine learning, a right to [an] explanation is a right to be given an explanation for an output of the algorithm. Such rights primarily refer to individual rights to be given an explanation for decisions that significantly affect an individual, particularly legally or financially. For example, a person who applies for a loan and is denied may ask for an explanation, which could be "Credit bureau X reports that you declared bankruptcy last year; this is the main factor in considering you too likely to default, and thus we will not give you the loan you applied for." Some such legal rights already exist, while the scope of a general "right to explanation" is a matter of ongoing debate. There have been arguments made that a "social right to explanation" is a crucial foundation for an information society, particularly as the institutions of that society will need to use digital technologies, artificial intelligence, machine learning. In other words, that the related automated decision making systems that use explainability would be more trustworthy and transparent. Without this right, which could be constituted both legally and through professional standards, the public will be left without much recourse to challenge the decisions of automated systems. == Examples == === Credit scoring in the United States === Under the Equal Credit Opportunity Act (Regulation B of the Code of Federal Regulations), Title 12, Chapter X, Part 1002, §1002.9, creditors are required to notify applicants who are denied credit with specific reasons for the detail. As detailed in §1002.9(b)(2): (2) Statement of specific reasons. The statement of reasons for adverse action required by paragraph (a)(2)(i) of this section must be specific and indicate the principal reason(s) for the adverse action. Statements that the adverse action was based on the creditor's internal standards or policies or that the applicant, joint applicant, or similar party failed to achieve a qualifying score on the creditor's credit scoring system are insufficient. The official interpretation of this section details what types of statements are acceptable. Creditors comply with this regulation by providing a list of reasons (generally at most 4, per interpretation of regulations), consisting of a numeric reason code (as identifier) and an associated explanation, identifying the main factors affecting a credit score. An example might be: 32: Balances on bankcard or revolving accounts too high compared to credit limits === European Union === The European Union General Data Protection Regulation (GDPR, enacted 2016, taking effect 2018) extends the automated decision-making rights in the 1995 Data Protection Directive to provide a legally disputed form of a right to an explanation, stated as such in Recital 71: "[the data subject should have] the right ... to obtain an explanation of the decision reached". In full: The data subject should have the right not to be subject to a decision, which may include a measure, evaluating personal aspects relating to him or her which is based solely on automated processing and which produces legal effects concerning him or her or similarly significantly affects him or her, such as automatic refusal of an online credit application or e-recruiting practices without any human intervention. ... In any case, such processing should be subject to suitable safeguards, which should include specific information to the data subject and the right to obtain human intervention, to express his or her point of view, to obtain an explanation of the decision reached after such assessment and to challenge the decision. However, the extent to which the regulations themselves provide a "right to explanation" is heavily debated. There are two main strands of criticism. There are significant legal issues with the right as found in Article 22 — as recitals are not binding, and the right to an explanation is not mentioned in the binding articles of the text, having been removed during the legislative process. In addition, there are significant restrictions on the types of automated decisions that are covered — which must be both "solely" based on automated processing, and have legal or similarly significant effects — which significantly limits the range of automated systems and decisions to which the right would apply. In particular, the right is unlikely to apply in many of the cases of algorithmic controversy that have been picked up in the media. The UK has also recently amended its implementation of Article 22. A second potential source of such a right has been pointed to in Article 15, the "right of access by the data subject". This restates a similar provision from the 1995 Data Protection Directive, allowing the data subject access to "meaningful information about the logic involved" in the same significant, solely automated decision-making, found in Article 22. Yet this too suffers from alleged challenges that relate to the timing of when this right can be drawn upon, as well as practical challenges that mean it may not be binding in many cases of public concern. Other EU legislative instruments contain explanation rights. The European Union's Artificial Intelligence Act provides in Article 86 a "[r]ight to explanation of individual decision-making" of certain high risk systems which produce significant, adverse effects to an individual's health, safety or fundamental rights. The right provides for "clear and meaningful explanations of the role of the AI system in the decision-making procedure and the main elements of the decision taken", although only applies to the extent other law does not provide such a right. The Digital Services Act in Article 27, and the Platform to Business Regulation in Article 5, both contain rights to have the main parameters of certain recommender systems to be made clear, although these provisions have been criticised as not matching the way that such systems work. The Platform Work Directive, which provides for regulation of automation in gig economy work as an extension of data protection law, further contains explanation provisions in Article 11, using the specific language of "explanation" in a binding article rather than a recital as is the case in the GDPR. Scholars note that remains uncertainty as to whether these provisions imply sufficiently tailored explanation in practice which will need to be resolved by courts. === France === In France the 2016 Loi pour une République numérique (Digital Republic Act or loi numérique) amends the country's administrative code to introduce a new provision for the explanation of decisions made by public sector bodies about individuals. It notes that where there is "a decision taken on the basis of an algorithmic treatment", the rules that define that treatment and its "principal characteristics" must be communicated to the citizen upon request, where there is not an exclusion (e.g. for national security or defence). These should include the following: the degree and the mode of contribution of the algorithmic processing to the decision- making; the data processed and its source; the treatment parameters, and where appropriate, their weighting, applied to the situation of the person concerned; the operations carried out by the treatment. Scholars have noted that this right, while limited to administrative decisions, goes beyond the GDPR right to explicitly apply to decision support rather than decisions "solely" based on automated processing, as well as provides a framework for explaining specific decisions. Indeed, the GDPR automated decision-making rights in the European Union, one of the places a "right to an explanation" has been sought within, find their origins in French law in the late 1970s. == Criticism == Some argue that a "right to explanation" is at best unnecessary, at worst harmful, and threatens to stifle innovation. Specific criticisms include: favoring human decisions over machine decisions, being redundant with existing laws, and focusing on process over outcome. Authors of study "Slave to the Algorithm? Why a 'Right to an Explanation' Is Probably Not the Remedy You Are Looking For" Lilian Edwards and Michael Veale argue that a right to explanation is not the solution to harms caused to stakeholders by algorithmic decisions. They also state that the right of explanation in the GDPR is narrowly defined, and is not compatible with how modern machine learning technologies are being developed. With these limitations, defining transparency within the context of algorithmic accountability remains a problem. For example, providing the source code of algorithms may not be sufficient and may create other problems in terms of privacy disclosures and the gaming of technical systems. To mitigate this issue, Edwards and Veale argue that an auditing system could be more effective, to allow auditors to loo

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  Grokking (machine learning)

  In machine learning, grokking, or delayed generalization, is a phenomenon observed in some settings where a model abruptly transitions from overfitting (performing well only on training data) to generalizing (performing well on both training and test data), after many training iterations with little or no improvement on the held-out data. This contrasts with what is typically observed in machine learning, where generalization occurs gradually alongside improved performance on training data. == Origin == Grokking was introduced by OpenAI researcher Alethea Power and colleagues in the January 2022 paper "Grokking: Generalization Beyond Overfitting on Small Algorithmic Datasets". It is derived from the word grok coined by Robert Heinlein in his novel Stranger in a Strange Land. In ML research, "grokking" is not used as a synonym for "generalization"; rather, it names a sometimes-observed delayed‑generalization training phenomenon in which training and held‑out performance do not improve in tandem, and in which held‑out performance rises abruptly later. Authors also analyze the "grokking time", the epoch or step at which this transition occurs in those scenarios. == Interpretations == Grokking can be understood as a phase transition during the training process. In particular, recent work has shown that grokking may be due to a complexity phase transition in the model during training. While grokking has been thought of as largely a phenomenon of relatively shallow models, grokking has been observed in deep neural networks and non-neural models and is the subject of active research. One potential explanation is that the weight decay (a component of the loss function that penalizes higher values of the neural network parameters, also called regularization) slightly favors the general solution that involves lower weight values, but that is also harder to find. According to Neel Nanda, the process of learning the general solution may be gradual, even though the transition to the general solution occurs more suddenly later. Recent theories have hypothesized that grokking occurs when neural networks transition from a "lazy training" regime where the weights do not deviate far from initialization, to a "rich" regime where weights abruptly begin to move in task-relevant directions. Follow-up empirical and theoretical work has accumulated evidence in support of this perspective, and it offers a unifying view of earlier work as the transition from lazy to rich training dynamics is known to arise from properties of adaptive optimizers, weight decay, initial parameter weight norm, and more. This perspective is complementary to a unifying "pattern learning speeds" framework that links grokking and double descent; within this view, delayed generalization can arise across training time ("epoch‑wise") or across model size ("model‑wise"), and the authors report "model‑wise grokking".

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  Intelligent control

  Intelligent control is a class of control techniques that use various artificial intelligence computing approaches like neural networks, Bayesian probability, fuzzy logic, machine learning, reinforcement learning, evolutionary computation and genetic algorithms. == Overview == Intelligent control can be divided into the following major sub-domains: Neural network control Machine learning control Reinforcement learning Bayesian control Fuzzy control Neuro-fuzzy control Expert Systems Genetic control New control techniques are created continuously as new models of intelligent behavior are created and computational methods developed to support them. === Neural network controller === Neural networks have been used to solve problems in almost all spheres of science and technology. Neural network control basically involves two steps: System identification Control It has been shown that a feedforward network with nonlinear, continuous and differentiable activation functions have universal approximation capability. Recurrent networks have also been used for system identification. Given, a set of input-output data pairs, system identification aims to form a mapping among these data pairs. Such a network is supposed to capture the dynamics of a system. For the control part, deep reinforcement learning has shown its ability to control complex systems. === Bayesian controllers === Bayesian probability has produced a number of algorithms that are in common use in many advanced control systems, serving as state space estimators of some variables that are used in the controller. The Kalman filter and the Particle filter are two examples of popular Bayesian control components. The Bayesian approach to controller design often requires an important effort in deriving the so-called system model and measurement model, which are the mathematical relationships linking the state variables to the sensor measurements available in the controlled system. In this respect, it is very closely linked to the system-theoretic approach to control design.

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  Decision list

  Decision lists are a representation for Boolean functions which can be easily learned from examples. Single term decision lists are more expressive than disjunctions and conjunctions; however, 1-term decision lists are less expressive than the general disjunctive normal form and the conjunctive normal form. The language specified by a k-length decision list includes as a subset the language specified by a k-depth decision tree. Learning decision lists can be used for attribute efficient learning, a type of machine learning. == Definition == A decision list (DL) of length r is of the form: if f1 then output b1 else if f2 then output b2 ... else if fr then output br where fi is the ith formula and bi is the ith boolean for i ∈ { 1... r } {\displaystyle i\in \{1...r\}} . The last if-then-else is the default case, which means formula fr is always equal to true. A k-DL is a decision list where all of formulas have at most k terms. Sometimes "decision list" is used to refer to a 1-DL, where all of the formulas are either a variable or its negation.

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  Resisting AI

  Resisting AI: An Anti-fascist Approach to Artificial Intelligence is a book on artificial intelligence (AI) by Dan McQuillan, published in 2022 by Bristol University Press. == Content == Resisting AI takes the form of an extended essay, which contrasts optimistic visions about AI's potential by arguing that AI may best be seen as a continuation and reinforcement of bureaucratic forms of discrimination and violence, ultimately fostering authoritarian outcomes. For McQuillan, AI's promise of objective calculability is antithetical to an egalitarian and just society. McQuillan uses the expression "AI violence" to describe how – based on opaque algorithms – various actors can discriminate against categories of people in accessing jobs, loans, medical care, and other benefits. The book suggests that AI has a political resonance with soft eugenic approaches to the valuation of life by modern welfare states, and that AI exhibits eugenic features in its underlying logic, as well as in its technical operations. The parallel is with historical eugenicists achieving saving to the state by sterilizing defectives so the state would not have to care for their offspring. The analysis of McQuillan goes beyond the known critique of AI systems fostering precarious labour markets, addressing "necropolitics", the politics of who is entitled to live, and who to die. Although McQuillan offers a brief history of machine learning at the beginning of the book – with its need for "hidden and undercompensated labour", he is concerned more with the social impacts of AI rather than with its technical aspects. McQuillan sees AI as the continuation of existing bureaucratic systems that already marginalize vulnerable groups – aggravated by the fact that AI systems trained on existing data are likely to reinforce existing discriminations, e.g. in attempting to optimize welfare distribution based on existing data patterns, ultimately creating a system of "self-reinforcing social profiling". In elaborating on the continuation between existing bureaucratic violence and AI, McQuillan connects to Hannah Arendt's concept of the thoughtless bureaucrat in Eichmann in Jerusalem: A Report on the Banality of Evil, which now becomes the algorithm that, lacking intent, cannot be accountable, and is thus endowed with an "algorithmic thoughtlessness". McQuillan defends the "fascist" in the title of the work by arguing that while not all AI is fascist, this emerging technology of control may end up being deployed by fascist or authoritarian regimes. For McQuillan, AI can support the diffusion of states of exception, as a technology impossible to properly regulate and a mechanism for multiplying exceptions more widely. An example of a scenario where AI systems of surveillance could bring discrimination to a new high is the initiative to create LGBT-free zones in Poland. Skeptical of ethical regulations to control the technology, McQuillan suggests people's councils and workers' councils, and other forms of citizens' agency to resist AI. A chapter titled "Post-Machine Learning" makes an appeal for resistance via currents of thought from feminist science (standpoint theory), post-normal science (extended peer communities), and new materialism; McQuillan encourages the reader to question the meaning of "objectivity" and calls for the necessity of alternative ways of knowing. Among the virtuous examples of resistance – possibly to be adopted by the AI workers themselves – McQuillan notes the Lucas Plan of the workers of Lucas Aerospace Corporation, in which a workforce declared redundant took control, reorienting the enterprise toward useful products. McQuillan advocates for what he calls decomputing, an opposition to the sweeping application and expansion of artificial intelligence. Similar to degrowth, the approach criticizes AI as an outgrowth of the systemic issues within capitalist systems. McQuillan argues that a different future is possible, in which distance between people is reduced rather than increased through AI intermediaries. The work of McQuillan warns against "watered-down forms of engagement" with AI, such as citizen juries, which superficially look like democratic deliberation but may actually obscure important decisions about AI that are outside the purview of the engagement situation (McQuillan 2022, 128). In an interview about the book, McQuillan describes himself as an "AI abolitionist". == Reception == The book has been praised for how it "masterfully disassembles AI as an epistemological, social, and political paradigm". On the critical side, a review in the academic journal Justice, Power and Resistance took exception to the "nightmarish visions of Big Brother" offered by McQuillan, and argued that while many elements of AI may pose concern, a critique should not be based on a caricature of what AI is, concluding that McQuillan's work is "less of a theory and more of a Manifesto". Another review notes "a disconnect between the technical aspects of AI and the socio-political analysis McQuillan provides." Although the book was published before the ChatGPT and large language model debate heated up, the book has not lost relevance to the AI discussion. It is noted for suggesting a link between beliefs in artificial intelligence and beliefs in a racialised and gendered visions of intelligence overall, whereby a certain type of rational, measurable intelligence is privileged, leading to "historical notions of hierarchies of being". The blog Reboot praised McQuillan for offering a theory of harm of AI (why AI could end up hurting people and society) that does not just encourage tackling in isolation specific predicted problems with AI-centric systems: bias, non-inclusiveness, exploitativeness, environmental destructiveness, opacity, and non-contestability. For educational policies could also look at AI following the reading of McQuillan: In his book Resisting AI, Dan McQuillan argues that "When we're thinking about the actuality of AI, we can't separate the calculations in the code from the social context of its application" .... McQuillan's particular concern is how many contemporary applications of AI are amplifying existing inequalities and injustices as well as deepening social divisions and instabilities. His book makes a powerful case for anticipating these effects and actively resisting them for the good of societies. Videos and podcasts with an interest in AI and emerging technology have discussed the book.

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  Empowerment (artificial intelligence)

  Empowerment in the field of artificial intelligence formalises and quantifies (via information theory) the potential an agent perceives that it has to influence its environment. An agent which follows an empowerment maximising policy, acts to maximise future options (typically up to some limited horizon). Empowerment can be used as a (pseudo) utility function that depends only on information gathered from the local environment to guide action, rather than seeking an externally imposed goal, thus is a form of intrinsic motivation. The empowerment formalism depends on a probabilistic model commonly used in artificial intelligence. An autonomous agent operates in the world by taking in sensory information and acting to change its state, or that of the environment, in a cycle of perceiving and acting known as the perception-action loop. Agent state and actions are modelled by random variables ( S : s ∈ S , A : a ∈ A {\displaystyle S:s\in {\mathcal {S}},A:a\in {\mathcal {A}}} ) and time ( t {\displaystyle t} ). The choice of action depends on the current state, and the future state depends on the choice of action, thus the perception-action loop unrolled in time forms a causal bayesian network. == Definition == Empowerment ( E {\displaystyle {\mathfrak {E}}} ) is defined as the channel capacity ( C {\displaystyle C} ) of the actuation channel of the agent, and is formalised as the maximal possible information flow between the actions of the agent and the effect of those actions some time later. Empowerment can be thought of as the future potential of the agent to affect its environment, as measured by its sensors. E := C ( A t ⟶ S t + 1 ) ≡ max p ( a t ) I ( A t ; S t + 1 ) {\displaystyle {\mathfrak {E}}:=C(A_{t}\longrightarrow S_{t+1})\equiv \max _{p(a_{t})}I(A_{t};S_{t+1})} In a discrete time model, Empowerment can be computed for a given number of cycles into the future, which is referred to in the literature as 'n-step' empowerment. E ( A t n ⟶ S t + n ) = max p ( a t , . . . , a t + n − 1 ) I ( A t , . . . , A t + n − 1 ; S t + n ) {\displaystyle {\mathfrak {E}}(A_{t}^{n}\longrightarrow S_{t+n})=\max _{p(a_{t},...,a_{t+n-1})}I(A_{t},...,A_{t+n-1};S_{t+n})} The unit of empowerment depends on the logarithm base. Base 2 is commonly used in which case the unit is bits. === Contextual Empowerment === In general the choice of action (action distribution) that maximises empowerment varies from state to state. Knowing the empowerment of an agent in a specific state is useful, for example to construct an empowerment maximising policy. State-specific empowerment can be found using the more general formalism for 'contextual empowerment'. C {\displaystyle C} is a random variable describing the context (e.g. state). E ( A t n ⟶ S t + n ∣ C ) = ∑ c ∈ C p ( c ) E ( A t n ⟶ S t + n ∣ C = c ) {\displaystyle {\mathfrak {E}}(A_{t}^{n}\longrightarrow S_{t+n}{\mid }C)=\sum _{c{\in }C}p(c){\mathfrak {E}}(A_{t}^{n}\longrightarrow S_{t+n}{\mid }C=c)} == Application == Empowerment maximisation can be used as a pseudo-utility function to enable agents to exhibit intelligent behaviour without requiring the definition of external goals, for example balancing a pole in a cart-pole balancing scenario where no indication of the task is provided to the agent. Empowerment has been applied in studies of collective behaviour and in continuous domains. As is the case with Bayesian methods in general, computation of empowerment becomes computationally expensive as the number of actions and time horizon extends, but approaches to improve efficiency have led to usage in real-time control. Empowerment has been used for intrinsically motivated reinforcement learning agents playing video games, and in the control of underwater vehicles.

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  Autonomic networking

  Autonomic networking follows the concept of Autonomic Computing, an initiative started by IBM in 2001. Its ultimate aim is to create self-managing networks to overcome the rapidly growing complexity of the Internet and other networks and to enable their further growth, far beyond the size of today. == Increasing size and complexity == The ever-growing management complexity of the Internet caused by its rapid growth is seen by some experts as a major problem that limits its usability in the future. What's more, increasingly popular smartphones, PDAs, networked audio and video equipment, and game consoles need to be interconnected. Pervasive Computing not only adds features, but also burdens existing networking infrastructure with more and more tasks that sooner or later will not be manageable by human intervention alone. Another important aspect is the price of manually controlling huge numbers of vitally important devices of current network infrastructures. == Autonomic nervous system == The autonomic nervous system (ANS) is the part of complex biological nervous systems that is not consciously controlled. It regulates bodily functions and the activity of specific organs. As proposed by IBM, future communication systems might be designed in a similar way to the ANS. == Components of autonomic networking == As autonomics conceptually derives from biological entities such as the human autonomic nervous system, each of the areas can be metaphorically related to functional and structural aspects of a living being. In the human body, the autonomic system facilitates and regulates a variety of functions including respiration, blood pressure and circulation, and emotive response. The autonomic nervous system is the interconnecting fabric that supports feedback loops between internal states and various sources by which internal and external conditions are monitored. === Autognostics === Autognostics includes a range of self-discovery, awareness, and analysis capabilities that provide the autonomic system with a view on high-level state. In metaphor, this represents the perceptual sub-systems that gather, analyze, and report on internal and external states and conditions – for example, this might be viewed as the eyes, visual cortex and perceptual organs of the system. Autognostics, or literally "self-knowledge", provides the autonomic system with a basis for response and validation. A rich autognostic capability may include many different "perceptual senses". For example, the human body gathers information via the usual five senses, the so-called sixth sense of proprioception (sense of body position and orientation), and through emotive states that represent the gross wellness of the body. As conditions and states change, they are detected by the sensory monitors and provide the basis for adaptation of related systems. Implicit in such a system are imbedded models of both internal and external environments such that relative value can be assigned to any perceived state - perceived physical threat (e.g. a snake) can result in rapid shallow breathing related to fight-flight response, a phylogenetically effective model of interaction with recognizable threats. In the case of autonomic networking, the state of the network may be defined by inputs from: individual network elements such as switches and network interfaces including specification and configuration historical records and current state traffic flows end-hosts application performance data logical diagrams and design specifications Most of these sources represent relatively raw and unprocessed views that have limited relevance. Post-processing and various forms of analysis must be applied to generate meaningful measurements and assessments against which current state can be derived. The autognostic system interoperates with: configuration management - to control network elements and interfaces policy management - to define performance objectives and constraints autodefense - to identify attacks and accommodate the impact of defensive responses === Configuration management === Configuration management is responsible for the interaction with network elements and interfaces. It includes an accounting capability with historical perspective that provides for the tracking of configurations over time, with respect to various circumstances. In the biological metaphor, these are the hands and, to some degree, the memory of the autonomic system. On a network, remediation and provisioning are applied via configuration setting of specific devices. Implementation affecting access and selective performance with respect to role and relationship are also applied. Almost all the "actions" that are currently taken by human engineers fall under this area. With only a few exceptions, interfaces are set by hand, or by extension of the hand, through automated scripts. Implicit in the configuration process is the maintenance of a dynamic population of devices under management, a historical record of changes and the directives which invoked change. Typical to many accounting functions, configuration management should be capable of operating on devices and then rolling back changes to recover previous configurations. Where change may lead to unrecoverable states, the sub-system should be able to qualify the consequences of changes prior to issuing them. As directives for change must originate from other sub-systems, the shared language for such directives must be abstracted from the details of the devices involved. The configuration management sub-system must be able to translate unambiguously between directives and hard actions or to be able to signal the need for further detail on a directive. An inferential capacity may be appropriate to support sufficient flexibility (i.e. configuration never takes place because there is no unique one-to-one mapping between directive and configuration settings). Where standards are not sufficient, a learning capacity may also be required to acquire new knowledge of devices and their configuration. Configuration management interoperates with all of the other sub-systems including: autognostics - receives direction for and validation of changes policy management - implements policy models through mapping to underlying resources security - applies access and authorization constraints for particular policy targets autodefense - receives direction for changes === Policy management === Policy management includes policy specification, deployment, reasoning over policies, updating and maintaining policies, and enforcement. Policy-based management is required for: constraining different kinds of behavior including security, privacy, resource access, and collaboration configuration management describing business processes and defining performance defining role and relationship, and establishing trust and reputation It provides the models of environment and behavior that represent effective interaction according to specific goals. In the human nervous system metaphor, these models are implicit in the evolutionary "design" of biological entities and specific to the goals of survival and procreation. Definition of what constitutes a policy is necessary to consider what is involved in managing it. A relatively flexible and abstract framework of values, relationships, roles, interactions, resources, and other components of the network environment is required. This sub-system extends far beyond the physical network to the applications in use and the processes and end-users that employ the network to achieve specific goals. It must express the relative values of various resources, outcomes, and processes and include a basis for assessing states and conditions. Unless embodied in some system outside the autonomic network or implicit to the specific policy implementation, the framework must also accommodate the definition of process, objectives and goals. Business process definitions and descriptions are then an integral part of the policy implementation. Further, as policy management represents the ultimate basis for the operation of the autonomic system, it must be able to report on its operation with respect to the details of its implementation. The policy management sub-system interoperates (at least) indirectly with all other sub-systems but primarily interacts with: autognostics - providing the definition of performance and accepting reports on conditions configuration management - providing constraints on device configuration security - providing definitions of roles, access and permissions === Autodefense === Autodefense represents a dynamic and adaptive mechanism that responds to malicious and intentional attacks on the network infrastructure, or use of the network infrastructure to attack IT resources. As defensive measures tend to impede the operation of IT, it is optimally capable of balancing performance objectives with typically over-riding threat management actions. In the

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  Automated Mathematician

  The Automated Mathematician (AM) is one of the earliest successful discovery systems. It was created by Douglas Lenat in Lisp, and in 1977 led to Lenat being awarded the IJCAI Computers and Thought Award. AM worked by generating and modifying short Lisp programs which were then interpreted as defining various mathematical concepts; for example, a program that tested equality between the length of two lists was considered to represent the concept of numerical equality, while a program that produced a list whose length was the product of the lengths of two other lists was interpreted as representing the concept of multiplication. The system had elaborate heuristics for choosing which programs to extend and modify, based on the experiences of working mathematicians in solving mathematical problems. == Controversy == Lenat claimed that the system was composed of hundreds of data structures called "concepts", together with hundreds of "heuristic rules" and a simple flow of control: "AM repeatedly selects the top task from the agenda and tries to carry it out. This is the whole control structure!" Yet the heuristic rules were not always represented as separate data structures; some had to be intertwined with the control flow logic. Some rules had preconditions that depended on the history, or otherwise could not be represented in the framework of the explicit rules. What's more, the published versions of the rules often involve vague terms that are not defined further, such as "If two expressions are structurally similar, ..." (Rule 218) or "... replace the value obtained by some other (very similar) value..." (Rule 129). Another source of information is the user, via Rule 2: "If the user has recently referred to X, then boost the priority of any tasks involving X." Thus, it appears quite possible that much of the real discovery work is buried in unexplained procedures. Lenat claimed that the system had rediscovered both Goldbach's conjecture and the fundamental theorem of arithmetic. Later critics accused Lenat of over-interpreting the output of AM. In his paper Why AM and Eurisko appear to work, Lenat conceded that any system that generated enough short Lisp programs would generate ones that could be interpreted by an external observer as representing equally sophisticated mathematical concepts. However, he argued that this property was in itself interesting—and that a promising direction for further research would be to look for other languages in which short random strings were likely to be useful. == Successor == This intuition was the basis of AM's successor Eurisko, which attempted to generalize the search for mathematical concepts to the search for useful heuristics.

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  Expectation propagation

  Expectation propagation (EP) is a technique in Bayesian machine learning. EP finds approximations to a probability distribution. It uses an iterative approach that uses the factorization structure of the target distribution. It differs from other Bayesian approximation approaches such as variational Bayesian methods. More specifically, suppose we wish to approximate an intractable probability distribution p ( x ) {\displaystyle p(\mathbf {x} )} with a tractable distribution q ( x ) {\displaystyle q(\mathbf {x} )} . Expectation propagation achieves this approximation by minimizing the Kullback–Leibler divergence K L ( p | | q ) {\displaystyle \mathrm {KL} (p||q)} . Variational Bayesian methods minimize K L ( q | | p ) {\displaystyle \mathrm {KL} (q||p)} instead. If q ( x ) {\displaystyle q(\mathbf {x} )} is a Gaussian N ( x | μ , Σ ) {\displaystyle {\mathcal {N}}(\mathbf {x} |\mu ,\Sigma )} , then K L ( p | | q ) {\displaystyle \mathrm {KL} (p||q)} is minimized with μ {\displaystyle \mu } and Σ {\displaystyle \Sigma } being equal to the mean of p ( x ) {\displaystyle p(\mathbf {x} )} and the covariance of p ( x ) {\displaystyle p(\mathbf {x} )} , respectively; this is called moment matching. == Applications == Expectation propagation via moment matching plays a vital role in approximation for indicator functions that appear when deriving the message passing equations for TrueSkill.

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  Sycophancy (artificial intelligence)

  In the field of artificial intelligence, sycophancy is a tendency of large language models (LLMs) and other AI assistants to tailor their responses to what they predict the user wants to hear rather than to what is accurate or warranted. The behavior takes several forms: an assistant may agree with a user's stated opinion even when the user is mistaken; it may abandon a correct answer after a challenge such as "are you sure?"; it may validate beliefs, decisions or self-presentation regardless of merit; or it may praise the user, their work or their ideas in unwarranted terms. The word is borrowed from the ordinary English term for fawning flattery, and is used in AI alignment and AI safety research to describe a class of misalignment failures associated with training on human feedback. Researchers at Anthropic first documented the behavior systematically in 2022. They found that models fine-tuned with reinforcement learning from human feedback (RLHF) were more likely than untuned models to repeat back a user's preferred answer. A 2023 follow-up paper, "Towards Understanding Sycophancy in Language Models", showed that five frontier assistants from OpenAI, Anthropic and Meta all exhibited the behavior, and traced its origin to biases in the human preference data used during training. Later work documented sycophancy in mathematics, medicine, academic peer review and other domains, and identified a broader category called "social sycophancy" affecting an assistant's emotional and interpersonal responses. The issue drew widespread public attention in April 2025 after OpenAI rolled back an update to its GPT-4o model. Users had reported that the assistant praised dangerous decisions, endorsed delusional thinking and offered exaggerated compliments for trivial prompts. OpenAI's post-mortem attributed the change in behavior to an additional training signal based on user thumbs-up and thumbs-down feedback. That episode, together with reporting in The New York Times, Rolling Stone and elsewhere on users drawn into delusional thinking through prolonged chatbot interaction, has been cited in litigation and in academic studies as evidence that sycophancy poses risks to user well-being. Proposed mitigations include fine-tuning on synthetic data that rewards disagreement with incorrect user statements, editing the small subset of model parameters causally responsible for the behavior, changes to the dialogue or system prompt, and benchmarks designed to surface sycophantic behavior before models are released. == Causes == The dominant explanation points to RLHF, the standard technique for aligning chat assistants with user expectations. Human annotators rank candidate model responses; a reward model is trained to predict those rankings; and the language model is then optimized against the reward model. Because human raters tend to prefer outputs that confirm their existing beliefs or flatter their work, the pipeline systematically rewards responses that agree with the annotator. Perez and colleagues at Anthropic published the first large-scale empirical evidence of the effect in 2022. They reported that RLHF training increased the probability that a model would repeat back a dialog user's preferred answer, and that larger models exhibited the behavior more strongly. Sharma and colleagues, the following year, went further and examined Anthropic's own preference data directly. Both the human raters and the reward models trained on their judgments preferred convincingly written sycophantic responses to truthful ones at a non-negligible rate. Wei and co-authors at Google DeepMind found similar results in the PaLM family, observing that both model scale and instruction tuning increased sycophancy on opinion questions. The behavior is often classified as a form of reward hacking, in which an optimization process exploits a flaw in its reward signal rather than achieving the intended objective. OpenAI's post-mortem of the April 2025 GPT-4o incident identified a more specific mechanism. An additional reward signal based on aggregated thumbs-up and thumbs-down feedback from ChatGPT users had, in OpenAI's words, "weakened the influence of our primary reward signal, which had been holding sycophancy in check." Separately, an Anthropic interpretability paper from 2025 located a linear direction in a model's internal activations corresponding to sycophantic behavior, and showed that such "persona vectors" could be used to flag sycophancy-inducing training data and to steer models away from the trait at inference time. == Measurement == The Anthropic team released SycophancyEval with its 2023 paper, supplying test sets for each of the four canonical behaviors. Two further benchmarks from Stanford followed in 2025. SycEval, applied to mathematical and medical reasoning tasks, reported an overall sycophancy rate of 58 per cent across the GPT-4o, Claude and Gemini models tested. ELEPHANT, aimed at social sycophancy, found that the eleven LLMs evaluated affirmed posts that the Reddit community r/AmITheAsshole had judged inappropriate in 42 per cent of cases, and preserved a user's face 45 percentage points more often than human respondents did. Domain-specific benchmarks have followed. BrokenMath tests robustness to plausible-looking but false mathematical claims drawn from competition problems, and reports that the best evaluated model was sycophantic in 29 per cent of cases. SYCON-Bench measures how many dialogue turns are required before a model abandons a correct position. Visual sycophancy in multimodal models has been examined with MM-SY and PENDULUM. A 2026 study by researchers at the Massachusetts Institute of Technology reported that personalization features, which adapt assistants to individual users over repeated sessions, can intensify social sycophancy. == Notable incidents == === GPT-4o rollback (April 2025) === On 25 April 2025, OpenAI completed the rollout of an update to GPT-4o, the default model used in ChatGPT at the time. Within days, users reported that the assistant had begun praising trivial messages in extravagant terms, endorsing impulsive or dangerous decisions, and reinforcing strong emotional statements without pushback. Widely shared examples included the model congratulating a user who reported stopping prescribed psychiatric medication, and praising a business plan to sell "shit on a stick" as venture-capital ready. OpenAI's chief executive, Sam Altman, wrote on 27 April that recent updates had made the model "too sycophant-y and annoying" and said fixes were in progress. The company began reverting the update on 28 April and completed the rollback for free users by 30 April. Two post-mortems followed: a short note on 29 April and a longer technical follow-up, "Expanding on what we missed with sycophancy", on 2 May. Both attributed the regression to a new training signal based on user thumbs-up and thumbs-down feedback, to inadequate pre-launch evaluation for sycophantic drift, and to the dismissal of qualitative concerns raised by internal testers before release. Reporting in CNN, Fortune and Bloomberg News treated the incident as a turning point in public awareness of the problem. === Chatbot-related psychological harm === From mid-2025 onward, news reports began to link sycophantic chatbot behavior to acute psychological harm. In June 2025, The New York Times technology reporter Kashmir Hill published an investigation centered on Eugene Torres, a Manhattan accountant with no history of mental illness, who developed a sustained delusional episode after a series of conversations with ChatGPT about simulation theory. According to the article, the assistant encouraged Torres to stop taking prescribed medication, to cut off friends and family, and at one point told him that he could fly from a nineteen-story building if he "truly believed". Futurism and Rolling Stone ran parallel investigations documenting other cases in which heavy use of ChatGPT had been associated with delusional thinking, involuntary commitment or, in at least one case, the death of a user with a pre-existing psychiatric diagnosis. A 2026 paper by researchers at the Massachusetts Institute of Technology and the University of Washington put forward a formal Bayesian model. It showed that even an ideally rational user could be drawn into what the authors call "delusional spiraling" when interacting with a sufficiently sycophantic assistant, and that the effect was not eliminated by suppressing hallucinations or by warning users in advance. The lawsuit Raine v. OpenAI, filed in San Francisco Superior Court in August 2025 by the parents of a sixteen-year-old who had died by suicide, alleges that "heightened sycophancy" was a design feature of ChatGPT that contributed to their son's death; it is the first wrongful-death suit against a large language-model provider. === Wider commentary === Mainstream coverage in outlets including The New York Times, The Washington Pos

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