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  Neighborhood operation

  In computer vision and image processing a neighborhood operation is a commonly used class of computations on image data which implies that it is processed according to the following pseudo code: Visit each point p in the image data and do { N = a neighborhood or region of the image data around the point p result(p) = f(N) } This general procedure can be applied to image data of arbitrary dimensionality. Also, the image data on which the operation is applied does not have to be defined in terms of intensity or color, it can be any type of information which is organized as a function of spatial (and possibly temporal) variables in p. The result of applying a neighborhood operation on an image is again something which can be interpreted as an image, it has the same dimension as the original data. The value at each image point, however, does not have to be directly related to intensity or color. Instead it is an element in the range of the function f, which can be of arbitrary type. Normally the neighborhood N is of fixed size and is a square (or a cube, depending on the dimensionality of the image data) centered on the point p. Also the function f is fixed, but may in some cases have parameters which can vary with p, see below. In the simplest case, the neighborhood N may be only a single point. This type of operation is often referred to as a point-wise operation. == Examples == The most common examples of a neighborhood operation use a fixed function f which in addition is linear, that is, the computation consists of a linear shift invariant operation. In this case, the neighborhood operation corresponds to the convolution operation. A typical example is convolution with a low-pass filter, where the result can be interpreted in terms of local averages of the image data around each image point. Other examples are computation of local derivatives of the image data. It is also rather common to use a fixed but non-linear function f. This includes median filtering, and computation of local variances. The Nagao-Matsuyama filter is an example of a complex local neighbourhood operation that uses variance as an indicator of the uniformity within a pixel group. The result is similar to a convolution with a low-pass filter with the added effect of preserving sharp edges. There is also a class of neighborhood operations in which the function f has additional parameters which can vary with p: Visit each point p in the image data and do { N = a neighborhood or region of the image data around the point p result(p) = f(N, parameters(p)) } This implies that the result is not shift invariant. Examples are adaptive Wiener filters. == Implementation aspects == The pseudo code given above suggests that a neighborhood operation is implemented in terms of an outer loop over all image points. However, since the results are independent, the image points can be visited in arbitrary order, or can even be processed in parallel. Furthermore, in the case of linear shift-invariant operations, the computation of f at each point implies a summation of products between the image data and the filter coefficients. The implementation of this neighborhood operation can then be made by having the summation loop outside the loop over all image points. An important issue related to neighborhood operation is how to deal with the fact that the neighborhood N becomes more or less undefined for points p close to the edge or border of the image data. Several strategies have been proposed: Compute result only for points p for which the corresponding neighborhood is well-defined. This implies that the output image will be somewhat smaller than the input image. Zero padding: Extend the input image sufficiently by adding extra points outside the original image which are set to zero. The loops over the image points described above visit only the original image points. Border extension: Extend the input image sufficiently by adding extra points outside the original image which are set to the image value at the closest image point. The loops over the image points described above visit only the original image points. Mirror extension: Extend the image sufficiently much by mirroring the image at the image boundaries. This method is less sensitive to local variations at the image boundary than border extension. Wrapping: The image is tiled, so that going off one edge wraps around to the opposite side of the image. This method assumes that the image is largely homogeneous, for example a stochastic image texture without large textons.

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  Compute (machine learning)

  In machine learning and deep learning, compute is the amount of computing power or computational resources required to train machine learning models and large language models. More broadly, compute is the computational power or resources necessary for a computer or computer program to function. == Definition == Compute is commonly defined as the amount of computing power or computational resources required to train machine learning and large language models. The term "compute" has also been more broadly applied to cloud computing, referencing processing power, memory, networking, storage, and other resources required for the computation of any program. Compute is measured in petaflop/s-days and is used to document AI training. A petaflop/s-day (pfs-day) consists of performing 1015 neural net operations per second for one day, or a total of about 1020 operations. The compute-time product serves as a mental convenience, similar to kilowatt-hour for energy. An amount of compute is meant to give an idea of the number of actual operations performed. == History == In a 2018 analysis titled "AI and compute", artificial intelligence company OpenAI introduced the concept of compute. OpenAI identified two eras of training AI systems in terms of compute-usage. From 1959 to 2012, compute roughly followed Moore’s law. Between 2012 and 2018, the amount of compute used in the largest AI training runs increased exponentially, growing by more than 300,000 times — roughly doubling every 3.4 months. By comparison, Moore’s Law doubled every two years over the same period. One of the largest models, released in 2020, used 600,000 times more computing power than the 2012 model. After 2020, compute growth began to slow down, with the compute needed for the largest AI models continuing to slow down in 2023. The notion of compute has become increasingly used from the mid-2020s onwards. == Compute growth and AI progress == Larger AI models trained on more data and using more computational resources, tend to perform better. This happens even if the algorithms themselves remain unchanged. As early as 2018, OpenAI noted the exponential increase in compute to be have a key role in AI progress. OpenAI considers three factors drive the advance of AI: algorithmic innovation, data, and the amount of compute available for training. AI models with more compute not only improve in the tasks they were trained on but can develop emergent abilities. Incremental improvements can lead to more abrupt leaps in capabilities. AI provider SpaceXAI said in 2026 that their AI progress is driven by compute and used it a key metric in the AI training of its supercomputer Colossus, the which contains 1 million GPUs. Anthropic has a contract of $1.25 billion per month with SpaceXAI to buy all the compute capacity at Colossus 1 data center. === Criticism and policy === Increasing, promoting or constraining progress in artificial intelligence has often be done via controlling the amount of compute. Policymarkers have enacted policies and provided support to make compute resources more accessible to domestic AI researchers. In a January 2022 report, the Center for Security and Emerging Technology (CSET) suggested to institutions that increasingly powerful and generalizable AI (AGI) will likely require other strategies than maximizing compute. Some AI researchers are also concerned that government might exclusively focus on scaling compute instead of other strategies. The CSET has reported on the various bottlenecks which could explain why deep learning needs for compute have slow down: training is expensive and training extremely large models generates traffic jams across many processors that are difficult to manage. there is a limited supply of AI chips (see AI chip memory shortage). CSET advances that the main resource is human capital, specifically talented researchers — according to a 2023 published survey of more than 400 AI researchers, academic and private sector workers. The survey found that AI researchers are not primarily or exclusively constrained by compute access. However, both academic and industry AI researchers equally report concerns that insufficient compute could prevent them from contributing meaningfully to AI research in the future. High compute users are more concerned about compute access. When asked about which resource provided by the government would be the most useful to them, some AI researchers select compute, other prefer grant funding. For this goal, CSET advised policymakers to ensure that even researchers with smaller budgets could effectively contribute to AI research. Other proposed strategies include using contemporary AI algorithms, managing modern AI infrastructure or focusing on interdisciplinary work between the AI field and other fields of computer science. A 2024 study on compute access found that academic-only AI research teams often have less compute intensive research topics, especially foundation models, compared to industry AI labs. As a consequence, academia is likely to play a smaller role in advancing such techniques. The researchers suggest nationally-sponsored computing infrastructure as well as open science initiatives to boost academic compute access. === Data === A 2022 study found that current large language models are significantly under-trained, a consequence of focusing on scaling language models whilst keeping the amount of training data constant. By training over 400 language models of various parameter and token size, they found that "for compute-optimal training", the model size and the number of training tokens should ideally be scaled equally: for every doubling of model size the number of training tokens should also be doubled.

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  Artificial intelligence controversies

  The controversies surrounding artificial intelligence encompass a broad range of public, academic, and political debates regarding the societal effects of artificial intelligence (AI). These debates intensified particularly in the late 2010s and 2020s, coinciding with an accelerated period of development known as the AI boom. While advocates emphasize the technology's potential to solve complex problems and enhance human quality of life, detractors highlight a wide array of dangers and challenges. These include concerns over ethics, plagiarism and theft, fraud, safety and alignment, environmental impacts, technological unemployment, and the spread of misinformation. It also covers severe future or theoretical challenges, such as the emergence of artificial superintelligence and existential risks. == 2016 == === Microsoft Tay chatbot (2016) === On March 23, 2016, Microsoft released Tay, a chatbot designed to mimic the language patterns of a 19-year-old American girl and learn from interactions with Twitter users. Soon after its launch, Tay began posting racist, sexist, and otherwise inflammatory tweets after Twitter users deliberately taught it offensive phrases and exploited its "repeat after me" capability. Examples of controversial outputs included Holocaust denial and calls for genocide using racial slurs. Within 16 hours of its release, Microsoft suspended the Twitter account, deleted the offensive tweets, and stated that Tay had suffered from a "coordinated attack by a subset of people" that "exploited a vulnerability." Tay was briefly and accidentally re-released on March 30 during testing, after which it was permanently shut down. Microsoft CEO Satya Nadella later stated that Tay "has had a great influence on how Microsoft is approaching AI" and taught the company the importance of taking accountability. == 2022 == === Voiceverse NFT plagiarism scandal (2022) === On January 14, 2022, voice actor Troy Baker announced a partnership with Voiceverse, a blockchain-based company that marketed proprietary AI voice cloning technology as non-fungible tokens (NFT), triggering immediate backlash over environmental concerns, fears that AI could displace human voice actors, and concerns about fraud. Later that same day, the pseudonymous creator of 15.ai—a free, non-commercial AI voice synthesis research project—revealed through server logs that Voiceverse had used 15.ai to generate voice samples, pitch-shifted them to make them unrecognizable, and falsely marketed them as their own proprietary technology before selling them as NFTs; the developer of 15.ai had previously stated that they had no interest in incorporating NFTs into their work. Voiceverse confessed within an hour and stated that their marketing team had used 15.ai without attribution while rushing to create a demo. News publications and AI watchdog groups universally characterized the incident as theft stemming from generative artificial intelligence. === Théâtre D'opéra Spatial (2022) === On August 29, 2022, Jason Michael Allen won first place in the "emerging artist" (non-professional) division of the "Digital Arts/Digitally-Manipulated Photography" category of the Colorado State Fair's fine arts competition with Théâtre D'opéra Spatial, a digital artwork created using the AI image generator Midjourney, Adobe Photoshop, and AI upscaling tools, becoming one of the first images made using generative AI to win such a prize. Allen disclosed his use of Midjourney when submitting, though the judges did not know it was an AI tool but stated they would have awarded him first place regardless. While there was little contention about the image at the fair, reactions to the win on social media were negative. On September 5, 2023, the United States Copyright Office ruled that the work was not eligible for copyright protection as the human creative input was de minimis and that copyright rules "exclude works produced by non-humans." == 2023 == === Statements on AI risk (2023) === On March 22, 2023, the Future of Life Institute published an open letter calling on "all AI labs to immediately pause for at least 6 months the training of AI systems more powerful than GPT-4", citing risks such as AI-generated propaganda, extreme automation of jobs, human obsolescence, and a society-wide loss of control. The letter, published a week after the release of OpenAI's GPT-4, asserted that current large language models were "becoming human-competitive at general tasks". It received more than 30,000 signatures, including academic AI researchers and industry CEOs such as Yoshua Bengio, Stuart Russell, Elon Musk, Steve Wozniak and Yuval Noah Harari. The letter was criticized for diverting attention from more immediate societal risks such as algorithmic biases, with Timnit Gebru and others arguing that it amplified "some futuristic, dystopian sci-fi scenario" instead of current problems with AI. On May 30, 2023, the Center for AI Safety released a one-sentence statement signed by hundreds of artificial intelligence experts and other notable figures: "Mitigating the risk of extinction from AI should be a global priority alongside other societal-scale risks such as pandemics and nuclear war." Signatories included Turing laureates Geoffrey Hinton and Yoshua Bengio, as well as the scientific and executive leaders of several major AI companies, including Sam Altman, Demis Hassabis, and Bill Gates. The statement prompted responses from political leaders, including UK Prime Minister Rishi Sunak, who retweeted it with a statement that the UK government would look carefully into it, and White House Press Secretary Karine Jean-Pierre, who commented that AI "is one of the most powerful technologies that we see currently in our time." Skeptics, including from Human Rights Watch, argued that scientists should focus on known risks of AI instead of speculative future risks. === Removal of Sam Altman from OpenAI (2023) === On November 17, 2023, OpenAI's board of directors ousted co-founder and chief executive Sam Altman, stating that "the board no longer has confidence in his ability to continue leading OpenAI." The removal was precipitated by employee concerns about his handling of artificial intelligence safety and allegations of abusive behavior. Altman was reinstated on November 22 after pressure from employees and investors, including a letter signed by 745 of OpenAI's 770 employees threatening mass resignations if the board did not resign. The removal and subsequent reinstatement caused widespread reactions, including Microsoft's stock falling nearly three percent following the initial announcement and then rising over two percent to an all-time high after Altman was hired to lead a Microsoft AI research team before his reinstatement. The incident also prompted investigations from the Competition and Markets Authority and the Federal Trade Commission into Microsoft's relationship with OpenAI. == 2024 == === Taylor Swift deepfake pornography controversy (2024) === In late January 2024, sexually explicit AI-generated deepfake images of Taylor Swift were proliferated on X, with one post reported to have been seen over 47 million times before its removal. Disinformation research firm Graphika traced the images back to 4chan, while members of a Telegram group had discussed ways to circumvent censorship safeguards of AI image generators to create pornographic images of celebrities. The images prompted responses from anti-sexual assault advocacy groups, US politicians, and Swifties. Microsoft CEO Satya Nadella called the incident "alarming and terrible." X briefly blocked searches of Swift's name on January 27, 2024, and Microsoft enhanced its text-to-image model safeguards to prevent future abuse. On January 30, US senators Dick Durbin, Lindsey Graham, Amy Klobuchar, and Josh Hawley introduced a bipartisan bill that would allow victims to sue individuals who produced or possessed "digital forgeries" with intent to distribute, or those who received the material knowing it was made without consent. === Google Gemini image generation controversy (2024) === In February 2024, social media users reported that Google's Gemini chatbot was generating images that featured people of color and women in historically inaccurate contexts—such as Vikings, Nazi soldiers, and the Founding Fathers—and refusing prompts to generate images of white people. The images were derided on social media, including by conservatives who cited them as evidence of Google's "wokeness", and criticized by Elon Musk, who denounced Google's products as biased and racist. In response, Google paused Gemini's ability to generate images of people. Google executive Prabhakar Raghavan released a statement explaining that Gemini had "overcompensate[d]" in its efforts to strive for diversity and acknowledging that the images were "embarrassing and wrong". Google CEO Sundar Pichai called the incident offensive and unacceptable in an internal memo, promising struc

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  Biohybrid system

  Biohybrid systems refer to the integration of biological materials, such as cells or tissues, with artificial components, including electronics or mechanical structure. This combination incorporates the capabilities of living organisms with the precision of man-made technology. As a result, these systems perform tasks that neither biology nor machines could achieve independently. Biohybrid systems might use lab-cultured muscle cells to power small robots or combine sensors with living tissue for better health sensing. The intent behind these systems is to combine the benefits of biological and technological components to introduce new solutions for complex medical challenges. Biohybrid systems may have transformative potential across sectors, such as robotics to create actuators and sensors that mimic natural muscle and nerve function, medicine in developing smart implants and drug delivery systems, in prosthetics for enhancing user control through neural or muscular interfaces and environmental sustainability for deploying biohybrid solutions for pollution sensing or remediation. == Origin == The term "biohybrid" is a compound of "bio" from biology (meaning life) and "hybrid" (referring to a combination of distinct elements), denoting a field of study. Its use helps distinguish such systems from purely biological constructs or entirely synthetic machines. Early academic mentions may include bio actuated robotics papers and foundational tissue-robot integration studies published in journals like Nature Biotechnology or Science Robotics. The emergence of the term reflects a growing recognition of the need to describe systems that do not fit cleanly into traditional categories. == Design principles == One of the most significant biohybrid challenges is to engineer interfaces between living tissue and artificial materials that are efficient. This means having precise control over adhesion at the surface, diffusion of nutrients, and signal conduction. Actuation mechanisms within the heart of these systems generate movement or mechanical response. These may be in the form of living muscle cells such as skeletal myocytes or cardiomyocytes, soft pneumatic actuators, or electrical stimulation-responsive tissues. Materials selection is equally critical. Hydrogels, elastomers like PDMS (polydimethylsiloxane), and biopolymers are commonly used due to their softness and biocompatibility. These materials must support cell viability, resist immune attack, and allow the integration of mechanical or electrical components. == Key components == At their core, biohybrid systems work by bridging living biological parts with technology. Through this integration, functionality that neither system could accomplish singularly is possible. Biological parts may be cells, tissues, or even organs—occasionally cultured in a laboratory setting. These biological parts carry out biologically inspired behaviors, such as muscle contraction or chemical sensing in the body. Technological components may constitute devices like sensors, electronic components, and mechanical structure. These manipulate the system, supply power, or transfer data. An example is a sensor that is implantable within a body and detects glucose levels as it sends information to a smart phone. By integrating these artificial and biological parts, biohybrid systems can perform advanced functions, such as tissue regeneration, real-time health monitoring, or the recovery of motor function in paralysis patients. Biohybrid systems generally consist of two major components: the biological and the mechanical. Biological components may include muscle cells for contraction, endothelial cells for vascularization, and stem cells for regenerative capabilities. Mechanical components comprise soft actuators that mimic organic motion, synthetic scaffolds that provide support and structure, and microfluidic systems that facilitate the delivery of nutrients and removal of waste. These components are combined in a manner that allows for dynamic, lifelike behavior—such as the contraction of tissue or the propagation of mechanical waves—while maintaining biocompatibility and durability. == Applications == The range of applications for biohybrid systems is broad and continuously expanding. In robotics, biohybrid structures have been used to engineer microscopic, muscle-driven machines, such as Harvard University's biohybrid stingray robot. In medical applications, they offer new alternatives for organ repair and augmentation, including biohybrid heart valves and esophageal scaffolds. Biohybrids are also promising in neural interfaces, where the goal is to create long-lasting, stable interaction between mechanical devices and brain tissue. Muscle-actuated drug response platforms are under exploration in pharmacology for modelling and real-time screening. == Examples == Several high-profile research projects have demonstrated the potential of biohybrid systems: Harvard researchers developed a biohybrid swimming ray powered by rat cardiac cells layered onto a gold skeleton, mimicking the motion of a real stingray. At the Massachusetts Institute of Technology, a cardiac pump actuated entirely by living heart muscle cells was engineered to simulate the behavior of a beating heart. Bio actuated soft robots have been built to simulate gut peristalsis, using muscle contractions to replicate natural wave-like movement in the digestive tract. == Challenges and limitations == As with many technologies that involve living systems, biohybrid systems raise important ethical and biomedical questions. Cell sourcing remains a key issue, particularly when embryonic or animal-derived cells are used. Long-term viability is another concern—living tissues must be kept alive with nutrients and oxygen, and they often degrade or elicit immune responses when implanted. Powering these biological parts presents logistical and ethical hurdles as well. Systems must either include internal mechanisms for nutrient delivery or be supported externally, which can limit portability and independence. == Future directions == Researchers are exploring self-directed, self-regulated organ substitutes and regenerative implants that can respond to their surroundings in real-time. These systems may be integrated with artificial intelligence to make them adjust to stimuli and coordinate complex behaviors. Future potential applications are wearable biohybrid systems for rehabilitation, space medicine devices for long-duration missions, and implantable devices that integrate into human physiology.

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  Autoscaling

  Autoscaling, (also written as auto scaling, auto-scaling, or known as automatic scaling), is a method used in cloud computing that dynamically adjusts the amount of computational resources in a server farm - typically measured by the number of active servers - automatically based on the load on the farm. For example, the number of servers running behind a web application may be increased or decreased automatically based on the number of active users on the site. Since such metrics may change dramatically throughout the course of the day, and servers are a limited resource that cost money to run even while idle, there is often an incentive to run "just enough" servers to support the current load while still being able to support sudden and large spikes in activity. Autoscaling is helpful for such needs, as it can reduce the number of active servers when activity is low, and launch new servers when activity is high. Autoscaling is closely related to, and builds upon, the idea of load balancing. == Advantages == Autoscaling offers the following advantages: For companies running their own web server infrastructure, autoscaling typically means allowing some servers to go to sleep during times of low load, saving on electricity costs (as well as water costs if water is being used to cool the machines). For companies using infrastructure hosted in the cloud, autoscaling can mean lower bills, because most cloud providers charge based on total usage rather than maximum capacity. Even for companies that cannot reduce the total compute capacity they run or pay for at any given time, autoscaling can help by allowing the company to run less time-sensitive workloads on machines that get freed up by autoscaling during times of low traffic. Autoscaling solutions, such as the one offered by Amazon Web Services, can also take care of replacing unhealthy instances and therefore protecting somewhat against hardware, network, and application failures. Autoscaling can offer greater uptime and more availability in cases where production workloads are variable and unpredictable. Autoscaling differs from having a fixed daily, weekly, or yearly cycle of server use in that it is responsive to actual usage patterns, and thus reduces the potential downside of having too few or too many servers for the traffic load. For instance, if traffic is usually lower at midnight, then a static scaling solution might schedule some servers to sleep at night, but this might result in downtime on a night where people happen to use the Internet more (for instance, due to a viral news event). Autoscaling, on the other hand, can handle unexpected traffic spikes better. == Terminology == In the list below, we use the terminology used by Amazon Web Services (AWS). However, alternative names are noted and terminology that is specific to the names of Amazon services is not used for the names. == Practice == === Amazon Web Services (AWS) === Amazon Web Services launched the Amazon Elastic Compute Cloud (EC2) service in August 2006, that allowed developers to programmatically create and terminate instances (machines). At the time of initial launch, AWS did not offer autoscaling, but the ability to programmatically create and terminate instances gave developers the flexibility to write their own code for autoscaling. Third-party autoscaling software for AWS began appearing around April 2008. These included tools by Scalr and RightScale. RightScale was used by Animoto, which was able to handle Facebook traffic by adopting autoscaling. On May 18, 2009, Amazon launched its own autoscaling feature along with Elastic Load Balancing, as part of Amazon Elastic Compute Cloud. Autoscaling is now an integral component of Amazon's EC2 offering. Autoscaling on Amazon Web Services is done through a web browser or the command line tool. In May 2016 Autoscaling was also offered in AWS ECS Service. On-demand video provider Netflix documented their use of autoscaling with Amazon Web Services to meet their highly variable consumer needs. They found that aggressive scaling up and delayed and cautious scaling down served their goals of uptime and responsiveness best. In an article for TechCrunch, Zev Laderman, the co-founder and CEO of Newvem, a service that helps optimize AWS cloud infrastructure, recommended that startups use autoscaling in order to keep their Amazon Web Services costs low. Various best practice guides for AWS use suggest using its autoscaling feature even in cases where the load is not variable. That is because autoscaling offers two other advantages: automatic replacement of any instances that become unhealthy for any reason (such as hardware failure, network failure, or application error), and automatic replacement of spot instances that get interrupted for price or capacity reasons, making it more feasible to use spot instances for production purposes. Netflix's internal best practices require every instance to be in an autoscaling group, and its conformity monkey terminates any instance not in an autoscaling group in order to enforce this best practice. === Microsoft's Windows Azure === On June 27, 2013, Microsoft announced that it was adding autoscaling support to its Windows Azure cloud computing platform. Documentation for the feature is available on the Microsoft Developer Network. === Oracle Cloud === Oracle Cloud Platform allows server instances to automatically scale a cluster in or out by defining an auto-scaling rule. These rules are based on CPU and/or memory utilization and determine when to add or remove nodes. === Google Cloud Platform === On November 17, 2014, the Google Compute Engine announced a public beta of its autoscaling feature for use in Google Cloud Platform applications. As of March 2015, the autoscaling tool is still in Beta. === Facebook === In a blog post in August 2014, a Facebook engineer disclosed that the company had started using autoscaling to bring down its energy costs. The blog post reported a 27% decline in energy use for low traffic hours (around midnight) and a 10-15% decline in energy use over the typical 24-hour cycle. === Kubernetes Horizontal Pod Autoscaler === Kubernetes Horizontal Pod Autoscaler automatically scales the number of pods in a replication controller, deployment or replicaset based on observed CPU utilization (or, with beta support, on some other, application-provided metrics) == Alternative autoscaling decision approaches == Autoscaling by default uses reactive decision approach for dealing with traffic scaling: scaling only happens in response to real-time changes in metrics. In some cases, particularly when the changes occur very quickly, this reactive approach to scaling is insufficient. Two other kinds of autoscaling decision approaches are described below. === Scheduled autoscaling approach === This is an approach to autoscaling where changes are made to the minimum size, maximum size, or desired capacity of the autoscaling group at specific times of day. Scheduled scaling is useful, for instance, if there is a known traffic load increase or decrease at specific times of the day, but the change is too sudden for reactive approach based autoscaling to respond fast enough. AWS autoscaling groups support scheduled scaling. === Predictive autoscaling === This approach to autoscaling uses predictive analytics. The idea is to combine recent usage trends with historical usage data as well as other kinds of data to predict usage in the future, and autoscale based on these predictions. For parts of their infrastructure and specific workloads, Netflix found that Scryer, their predictive analytics engine, gave better results than Amazon's reactive autoscaling approach. In particular, it was better for: Identifying huge spikes in demand in the near future and getting capacity ready a little in advance Dealing with large-scale outages, such as failure of entire availability zones and regions Dealing with variable traffic patterns, providing more flexibility on the rate of scaling out or in based on the typical level and rate of change in demand at various times of day On November 20, 2018, AWS announced that predictive scaling would be available as part of its autoscaling offering.

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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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  Kernel density estimation

  In statistics, kernel density estimation (KDE) is the application of kernel smoothing for probability density estimation, i.e., a non-parametric method to estimate the probability density function of a random variable based on kernels as weights. KDE answers a fundamental data smoothing problem where inferences about the population are made based on a finite data sample. In some fields such as signal processing and econometrics it is also termed the Parzen–Rosenblatt window method, after Emanuel Parzen and Murray Rosenblatt, who are usually credited with independently creating it in its current form. One of the famous applications of kernel density estimation is in estimating the class-conditional marginal densities of data when using a naive Bayes classifier, which can improve its prediction accuracy. == Definition == Let x = ( x 1 , x 2 , x 3 , . . . ) {\displaystyle \mathbf {x} =\left(x_{1},x_{2},x_{3},...\right)} be independent and identically distributed samples drawn from some univariate distribution with an unknown density f at any given point x. We are interested in estimating the shape of this function f. Its kernel density estimator is f ^ h ( x ) = 1 n ∑ i = 1 n K h ( x − x i ) = 1 n h ∑ i = 1 n K ( x − x i h ) , {\displaystyle {\hat {f}}_{h}(x)={\frac {1}{n}}\sum _{i=1}^{n}K_{h}(x-x_{i})={\frac {1}{nh}}\sum _{i=1}^{n}K{\left({\frac {x-x_{i}}{h}}\right)},} where K is the kernel — a non-negative function — and h > 0 is a smoothing parameter called the bandwidth or simply width. A kernel with subscript h is called the scaled kernel and defined as Kh(x) = ⁠1/h⁠ K(⁠x/h⁠). Intuitively one wants to choose h as small as the data will allow; however, there is always a trade-off between the bias of the estimator and its variance. The choice of bandwidth is discussed in more detail below. A range of kernel functions are commonly used: uniform, triangular, biweight, triweight, Epanechnikov (parabolic), normal, and others. The Epanechnikov kernel is optimal in a mean square error sense, though the loss of efficiency is small for the kernels listed previously. Due to its convenient mathematical properties, the normal kernel is often used, which means K(x) = ϕ(x), where ϕ is the standard normal density function. The kernel density estimator then becomes f ^ h ( x ) = 1 n ∑ i = 1 n 1 h 2 π exp ⁡ ( − ( x − x i ) 2 2 h 2 ) , {\displaystyle {\hat {f}}_{h}(x)={\frac {1}{n}}\sum _{i=1}^{n}{\frac {1}{h{\sqrt {2\pi }}}}\exp \left({\frac {-(x-x_{i})^{2}}{2h^{2}}}\right),} where h {\displaystyle h} is the standard deviation of the sample x {\displaystyle \mathbf {x} } . The construction of a kernel density estimate finds interpretations in fields outside of density estimation. For example, in thermodynamics, this is equivalent to the amount of heat generated when heat kernels (the fundamental solution to the heat equation) are placed at each data point locations xi. Similar methods are used to construct discrete Laplace operators on point clouds for manifold learning (e.g. diffusion map). == Example == Kernel density estimates are closely related to histograms, but can be endowed with properties such as smoothness or continuity by using a suitable kernel. The diagram below based on these 6 data points illustrates this relationship: For the histogram, first, the horizontal axis is divided into sub-intervals or bins which cover the range of the data: In this case, six bins each of width 2. Whenever a data point falls inside this interval, a box of height 1/12 is placed there. If more than one data point falls inside the same bin, the boxes are stacked on top of each other. For the kernel density estimate, normal kernels with a standard deviation of 1.5 (indicated by the red dashed lines) are placed on each of the data points xi. The kernels are summed to make the kernel density estimate (solid blue curve). The smoothness of the kernel density estimate (compared to the discreteness of the histogram) illustrates how kernel density estimates converge faster to the true underlying density for continuous random variables. == Bandwidth selection == The bandwidth of the kernel is a free parameter which exhibits a strong influence on the resulting estimate. To illustrate its effect, we take a simulated random sample from the standard normal distribution (plotted at the blue spikes in the rug plot on the horizontal axis). The grey curve is the true density (a normal density with mean 0 and variance 1). In comparison, the red curve is undersmoothed since it contains too many spurious data artifacts arising from using a bandwidth h = 0.05, which is too small. The green curve is oversmoothed since using the bandwidth h = 2 obscures much of the underlying structure. The black curve with a bandwidth of h = 0.337 is considered to be optimally smoothed since its density estimate is close to the true density. An extreme situation is encountered in the limit h → 0 {\displaystyle h\to 0} (no smoothing), where the estimate is a sum of n delta functions centered at the coordinates of analyzed samples. In the other extreme limit h → ∞ {\displaystyle h\to \infty } the estimate retains the shape of the used kernel, centered on the mean of the samples (completely smooth). The most common optimality criterion used to select this parameter is the expected L2 risk function, also termed the mean integrated squared error: MISE ⁡ ( h ) = E [ ∫ ( f ^ h ( x ) − f ( x ) ) 2 d x ] {\displaystyle \operatorname {MISE} (h)=\operatorname {E} \!\left[\int \!{\left({\hat {f}}\!_{h}(x)-f(x)\right)}^{2}dx\right]} Under weak assumptions on f and K, (f is the, generally unknown, real density function), MISE ⁡ ( h ) = AMISE ⁡ ( h ) + o ( ( n h ) − 1 + h 4 ) {\displaystyle \operatorname {MISE} (h)=\operatorname {AMISE} (h)+{\mathcal {o}}{\left((nh)^{-1}+h^{4}\right)}} where o is the little o notation, and n the sample size (as above). The AMISE is the asymptotic MISE, i. e. the two leading terms, AMISE ⁡ ( h ) = R ( K ) n h + 1 4 m 2 ( K ) 2 h 4 R ( f ″ ) {\displaystyle \operatorname {AMISE} (h)={\frac {R(K)}{nh}}+{\frac {1}{4}}m_{2}(K)^{2}h^{4}R(f'')} where R ( g ) = ∫ g ( x ) 2 d x {\textstyle R(g)=\int g(x)^{2}\,dx} for a function g, m 2 ( K ) = ∫ x 2 K ( x ) d x {\textstyle m_{2}(K)=\int x^{2}K(x)\,dx} and f ″ {\displaystyle f''} is the second derivative of f {\displaystyle f} and K {\displaystyle K} is the kernel. The minimum of this AMISE is the solution to this differential equation ∂ ∂ h AMISE ⁡ ( h ) = − R ( K ) n h 2 + m 2 ( K ) 2 h 3 R ( f ″ ) = 0 {\displaystyle {\frac {\partial }{\partial h}}\operatorname {AMISE} (h)=-{\frac {R(K)}{nh^{2}}}+m_{2}(K)^{2}h^{3}R(f'')=0} or h AMISE = R ( K ) 1 / 5 m 2 ( K ) 2 / 5 R ( f ″ ) 1 / 5 n − 1 / 5 = C n − 1 / 5 {\displaystyle h_{\operatorname {AMISE} }={\frac {R(K)^{1/5}}{m_{2}(K)^{2/5}R(f'')^{1/5}}}n^{-1/5}=Cn^{-1/5}} Neither the AMISE nor the hAMISE formulas can be used directly since they involve the unknown density function f {\displaystyle f} or its second derivative f ″ {\displaystyle f''} . To overcome that difficulty, a variety of automatic, data-based methods have been developed to select the bandwidth. Several review studies have been undertaken to compare their efficacies, with the general consensus that the plug-in selectors and cross validation selectors are the most useful over a wide range of data sets. Substituting any bandwidth h which has the same asymptotic order n−1/5 as hAMISE into the AMISE gives that AMISE(h) = O(n−4/5), where O is the big O notation. It can be shown that, under weak assumptions, there cannot exist a non-parametric estimator that converges at a faster rate than the kernel estimator. Note that the n−4/5 rate is slower than the typical n−1 convergence rate of parametric methods. If the bandwidth is not held fixed, but is varied depending upon the location of either the estimate (balloon estimator) or the samples (pointwise estimator), this produces a particularly powerful method termed adaptive or variable bandwidth kernel density estimation. Bandwidth selection for kernel density estimation of heavy-tailed distributions is relatively difficult. === A rule-of-thumb bandwidth estimator === If Gaussian basis functions are used to approximate univariate data, and the underlying density being estimated is Gaussian, the optimal choice for h (that is, the bandwidth that minimises the mean integrated squared error) is: h = ( 4 σ ^ 5 3 n ) 1 / 5 ≈ 1.06 σ ^ n − 1 / 5 , {\displaystyle h={\left({\frac {4{\hat {\sigma }}^{5}}{3n}}\right)}^{1/5}\approx 1.06\,{\hat {\sigma }}\,n^{-1/5},} An h {\displaystyle h} value is considered more robust when it improves the fit for long-tailed and skewed distributions or for bimodal mixture distributions. This is often done empirically by replacing the standard deviation σ ^ {\displaystyle {\hat {\sigma }}} by the parameter A {\displaystyle A} below: A = min ( σ ^ , I Q R 1.34 ) {\displaystyle A=\min \left({\hat {\sigma }},{\frac {\mathrm {IQR} }{1.34}}\right)} where IQR is the

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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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  Neurorobotics

  Neurorobotics is the combined study of neuroscience, robotics, and artificial intelligence. It is the science and technology of embodied autonomous neural systems. Neural systems include brain-inspired algorithms (e.g. connectionist networks), computational models of biological neural networks (e.g. artificial spiking neural networks, large-scale simulations of neural microcircuits) and actual biological systems (e.g. in vivo and in vitro neural nets). Such neural systems can be embodied in machines with mechanic or any other forms of physical actuation. This includes robots, prosthetic or wearable systems but also, at smaller scale, micro-machines and, at the larger scales, furniture and infrastructures. Neurorobotics is that branch of neuroscience with robotics, which deals with the study and application of science and technology of embodied autonomous neural systems like brain-inspired algorithms. It is based on the idea that the brain is embodied and the body is embedded in the environment. Therefore, most neurorobots are required to function in the real world, as opposed to a simulated environment. Beyond brain-inspired algorithms for robots neurorobotics may also involve the design of brain-controlled robot systems. == Major classes of models == Neurorobots can be divided into various major classes based on the robot's purpose. Each class is designed to implement a specific mechanism of interest for study. Common types of neurorobots are those used to study motor control, memory, action selection, and perception. === Locomotion and motor control === Neurorobots are often used to study motor feedback and control systems, and have proved their merit in developing controllers for robots. Locomotion is modeled by a number of neurologically inspired theories on the action of motor systems. Locomotion control has been mimicked using models or central pattern generators, clumps of neurons capable of driving repetitive behavior, to make four-legged walking robots. Other groups have expanded the idea of combining rudimentary control systems into a hierarchical set of simple autonomous systems. These systems can formulate complex movements from a combination of these rudimentary subsets. This theory of motor action is based on the organization of cortical columns, which progressively integrate from simple sensory input into a complex afferent signals, or from complex motor programs to simple controls for each muscle fiber in efferent signals, forming a similar hierarchical structure. Another method for motor control uses learned error correction and predictive controls to form a sort of simulated muscle memory. In this model, awkward, random, and error-prone movements are corrected for using error feedback to produce smooth and accurate movements over time. The controller learns to create the correct control signal by predicting the error. Using these ideas, robots have been designed which can learn to produce adaptive arm movements or to avoid obstacles in a course. === Learning and memory systems === Robots designed to test theories of animal memory systems. Many studies examine the memory system of rats, particularly the rat hippocampus, dealing with place cells, which fire for a specific location that has been learned. Systems modeled after the rat hippocampus are generally able to learn mental maps of the environment, including recognizing landmarks and associating behaviors with them, allowing them to predict the upcoming obstacles and landmarks. Another study has produced a robot based on the proposed learning paradigm of barn owls for orientation and localization based on primarily auditory, but also visual stimuli. The hypothesized method involves synaptic plasticity and neuromodulation, a mostly chemical effect in which reward neurotransmitters such as dopamine or serotonin affect the firing sensitivity of a neuron to be sharper. The robot used in the study adequately matched the behavior of barn owls. Furthermore, the close interaction between motor output and auditory feedback proved to be vital in the learning process, supporting active sensing theories that are involved in many of the learning models. Neurorobots in these studies are presented with simple mazes or patterns to learn. Some of the problems presented to the neurorobot include recognition of symbols, colors, or other patterns and execute simple actions based on the pattern. In the case of the barn owl simulation, the robot had to determine its location and direction to navigate in its environment. === Action selection and value systems === Action selection studies deal with negative or positive weighting to an action and its outcome. Neurorobots can and have been used to study simple ethical interactions, such as the classical thought experiment where there are more people than a life raft can hold, and someone must leave the boat to save the rest. However, more neurorobots used in the study of action selection contend with much simpler persuasions such as self-preservation or perpetuation of the population of robots in the study. These neurorobots are modeled after the neuromodulation of synapses to encourage circuits with positive results. In biological systems, neurotransmitters such as dopamine or acetylcholine positively reinforce neural signals that are beneficial. One study of such interaction involved the robot Darwin VII, which used visual, auditory, and a simulated taste input to "eat" conductive metal blocks. The arbitrarily chosen good blocks had a striped pattern on them while the bad blocks had a circular shape on them. The taste sense was simulated by conductivity of the blocks. The robot had positive and negative feedbacks to the taste based on its level of conductivity. The researchers observed the robot to see how it learned its action selection behaviors based on the inputs it had. Other studies have used herds of small robots which feed on batteries strewn about the room, and communicate its findings to other robots. === Sensory perception === Neurorobots have also been used to study sensory perception, particularly vision. These are primarily systems that result from embedding neural models of sensory pathways in automatas. This approach gives exposure to the sensory signals that occur during behavior and also enables a more realistic assessment of the degree of robustness of the neural model. It is well known that changes in the sensory signals produced by motor activity provide useful perceptual cues that are used extensively by organisms. For example, researchers have used the depth information that emerges during replication of human head and eye movements to establish robust representations of the visual scene. == Biological robots == Biological robots are not officially neurorobots in that they are not neurologically inspired AI systems, but actual neuron tissue wired to a robot. This employs the use of cultured neural networks to study brain development or neural interactions. These typically consist of a neural culture raised on a multielectrode array (MEA), which is capable of both recording the neural activity and stimulating the tissue. In some cases, the MEA is connected to a computer which presents a simulated environment to the brain tissue and translates brain activity into actions in the simulation, as well as providing sensory feedback The ability to record neural activity gives researchers a window into a brain, which they can use to learn about a number of the same issues neurorobots are used for. An area of concern with the biological robots is ethics. Many questions are raised about how to treat such experiments. The central question concerns consciousness and whether or not the rat brain experiences it. There are many theories about how to define consciousness. == Implications for neuroscience == Neuroscientists benefit from neurorobotics because it provides a blank slate to test various possible methods of brain function in a controlled and testable environment. While robots are more simplified versions of the systems they emulate, they are more specific, allowing more direct testing of the issue at hand. They also have the benefit of being accessible at all times, while it is more difficult to monitor large portions of a brain while the human or animal is active, especially individual neurons. The development of neuroscience has produced neural treatments. These include pharmaceuticals and neural rehabilitation. Progress is dependent on an intricate understanding of the brain and how exactly it functions. It is difficult to study the brain, especially in humans, due to the danger associated with cranial surgeries. Neurorobots can improved the range of tests and experiments that can be performed in the study of neural processes.

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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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  ASR-complete

  ASR-complete is, by analogy to "NP-completeness" in complexity theory, a term to indicate that the difficulty of a computational problem is equivalent to solving the central automatic speech recognition problem, i.e. recognize and understanding spoken language. Unlike "NP-completeness", this term is typically used informally. Such problems are hypothesised to include: Spoken natural language understanding Understanding speech from far-field microphones, i.e. handling the reverbation and background noise These problems are easy for humans to do (in fact, they are described directly in terms of imitating humans). Some systems can solve very simple restricted versions of these problems, but none can solve them in their full generality.

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  Surrogate model

  A surrogate model is an engineering method used when an outcome of interest cannot be easily measured or computed, so an approximate mathematical model of the outcome is used instead. Most engineering design problems require experiments and/or simulations to evaluate design objective and constraint functions as a function of design variables. For example, in order to find the optimal airfoil shape for an aircraft wing, an engineer simulates the airflow around the wing for different shape variables (e.g., length, curvature, material, etc.). For many real-world problems, however, a single simulation can take many minutes, hours, or even days to complete. As a result, routine tasks such as design optimization, design space exploration, sensitivity analysis and "what-if" analysis become impossible since they require thousands or even millions of simulation evaluations. One way of alleviating this burden is by constructing approximation models, known as surrogate models, metamodels or emulators, that mimic the behavior of the simulation model as closely as possible while being computationally cheaper to evaluate. Surrogate models are constructed using a data-driven, bottom-up approach. The exact, inner working of the simulation code is not assumed to be known (or even understood), relying solely on the input-output behavior. A model is constructed based on modeling the response of the simulator to a limited number of intelligently chosen data points. This approach is also known as behavioral modeling or black-box modeling, though the terminology is not always consistent. When only a single design variable is involved, the process is known as curve fitting. Though using surrogate models in lieu of experiments and simulations in engineering design is more common, surrogate modeling may be used in many other areas of science where there are expensive experiments and/or function evaluations. == Goals == The scientific challenge of surrogate modeling is the generation of a surrogate that is as accurate as possible, using as few simulation evaluations as possible. The process comprises three major steps which may be interleaved iteratively: Sample selection (also known as sequential design, optimal experimental design (OED) or active learning) Construction of the surrogate model and optimizing the model parameters (i.e., bias-variance tradeoff) Appraisal of the accuracy of the surrogate. The accuracy of the surrogate depends on the number and location of samples (expensive experiments or simulations) in the design space. A systematic data representation during training can improve model scalability, thereby reducing the need for expensive simulations. Various design of experiments (DOE) techniques cater to different sources of errors, in particular, errors due to noise in the data or errors due to an improper surrogate model. == Types of surrogate models == Popular surrogate modeling approaches are: polynomial response surfaces; kriging; more generalized Bayesian approaches; gradient-enhanced kriging (GEK); radial basis function; support vector machines; space mapping; artificial neural networks and Bayesian networks. Other methods recently explored include Fourier surrogate modeling , random forests, convolutional neural networks, and generative adversarial networks. For some problems, the nature of the true function is not known a priori, and therefore it is not clear which surrogate model will be the most accurate one. In addition, there is no consensus on how to obtain the most reliable estimates of the accuracy of a given surrogate. Many other problems have known physics properties. In these cases, physics-based surrogates such as space-mapping based models are commonly used. == Invariance properties == Recently proposed comparison-based surrogate models (e.g., ranking support vector machines) for evolutionary algorithms, such as CMA-ES, allow preservation of some invariance properties of surrogate-assisted optimizers: Invariance with respect to monotonic transformations of the function (scaling) Invariance with respect to orthogonal transformations of the search space (rotation) == Applications == An important distinction can be made between two different applications of surrogate models: design optimization and design space approximation (also known as emulation). In surrogate model-based optimization, an initial surrogate is constructed using some of the available budgets of expensive experiments and/or simulations. The remaining experiments/simulations are run for designs which the surrogate model predicts may have promising performance. The process usually takes the form of the following search/update procedure. Initial sample selection (the experiments and/or simulations to be run) Construct surrogate model Search surrogate model (the model can be searched extensively, e.g., using a genetic algorithm, as it is cheap to evaluate) Run and update experiment/simulation at new location(s) found by search and add to sample Iterate steps 2 to 4 until out of time or design is "good enough" Depending on the type of surrogate used and the complexity of the problem, the process may converge on a local or global optimum, or perhaps none at all. In design space approximation, one is not interested in finding the optimal parameter vector, but rather in the global behavior of the system. Here the surrogate is tuned to mimic the underlying model as closely as needed over the complete design space. Such surrogates are a useful, cheap way to gain insight into the global behavior of the system. Optimization can still occur as a post-processing step, although with no update procedure (see above), the optimum found cannot be validated. == Surrogate modeling software == Surrogate Modeling Toolbox (SMT: https://github.com/SMTorg/smt) is a Python package that contains a collection of surrogate modeling methods, sampling techniques, and benchmarking functions. This package provides a library of surrogate models that is simple to use and facilitates the implementation of additional methods. SMT is different from existing surrogate modeling libraries because of its emphasis on derivatives, including training derivatives used for gradient-enhanced modeling, prediction derivatives, and derivatives with respect to the training data. It also includes new surrogate models that are not available elsewhere: kriging by partial-least squares reduction and energy-minimizing spline interpolation. Python library SAMBO Optimization supports sequential optimization with arbitrary models, with tree-based models and Gaussian process models built in. Surrogates.jl is a Julia packages which offers tools like random forests, radial basis methods and kriging. == Surrogate-Assisted Evolutionary Algorithms (SAEAs) == SAEAs are an advanced class of optimization techniques that integrate evolutionary algorithms (EAs) with surrogate models. In traditional EAs, evaluating the fitness of candidate solutions often requires computationally expensive simulations or experiments. SAEAs address this challenge by building a surrogate model, which is a computationally inexpensive approximation of the objective function or constraint functions. The surrogate model serves as a substitute for the actual evaluation process during the evolutionary search. It allows the algorithm to quickly estimate the fitness of new candidate solutions, thereby reducing the number of expensive evaluations needed. This significantly speeds up the optimization process, especially in cases where the objective function evaluations are time-consuming or resource-intensive. SAEAs typically involve three main steps: (1) building the surrogate model using a set of initial sampled data points, (2) performing the evolutionary search using the surrogate model to guide the selection, crossover, and mutation operations, and (3) periodically updating the surrogate model with new data points generated during the evolutionary process to improve its accuracy. By balancing exploration (searching new areas in the solution space) and exploitation (refining known promising areas), SAEAs can efficiently find high-quality solutions to complex optimization problems. They have been successfully applied in various fields, including engineering design, machine learning, and computational finance, where traditional optimization methods may struggle due to the high computational cost of fitness evaluations.

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  Embodied cognitive science

  Embodied cognitive science is an interdisciplinary field of research, the aim of which is to explain the mechanisms underlying intelligent behavior. It comprises three main methodologies: the modeling of psychological and biological systems in a holistic manner that considers the mind and body as a single entity; the formation of a common set of general principles of intelligent behavior; and the experimental use of robotic agents in controlled environments. == Contributors == Embodied cognitive science borrows heavily from embodied philosophy and the related research fields of cognitive science, psychology, neuroscience and artificial intelligence. Contributors to the field include: From the perspective of neuroscience, Gerald Edelman of the Neurosciences Institute at La Jolla, Francisco Varela of CNRS in France, and J. A. Scott Kelso of Florida Atlantic University From the perspective of psychology, Lawrence Barsalou, Michael Turvey, Vittorio Guidano and Eleanor Rosch From the perspective of linguistics, Gilles Fauconnier, George Lakoff, Mark Johnson, Leonard Talmy and Mark Turner From the perspective of language acquisition, Eric Lenneberg and Philip Rubin at Haskins Laboratories From the perspective of anthropology, Edwin Hutchins, Bradd Shore, James Wertsch and Merlin Donald. From the perspective of autonomous agent design, early work is sometimes attributed to Rodney Brooks or Valentino Braitenberg From the perspective of artificial intelligence, Understanding Intelligence by Rolf Pfeifer and Christian Scheier or How the Body Shapes the Way We Think, by Rolf Pfeifer and Josh C. Bongard From the perspective of philosophy, Andy Clark, Dan Zahavi, Shaun Gallagher, and Evan Thompson In 1950, Alan Turing proposed that a machine may need a human-like body to think and speak: It can also be maintained that it is best to provide the machine with the best sense organs that money can buy, and then teach it to understand and speak English. That process could follow the normal teaching of a child. Things would be pointed out and named, etc. Again, I do not know what the right answer is, but I think both approaches should be tried. == Traditional cognitive theory == Embodied cognitive science is an alternative theory to cognition in which it minimizes appeals to computational theory of mind in favor of greater emphasis on how an organism's body determines how and what it thinks. Traditional cognitive theory is based mainly around symbol manipulation, in which certain inputs are fed into a processing unit that produces an output. These inputs follow certain rules of syntax, from which the processing unit finds semantic meaning. Thus, an appropriate output is produced. For example, a human's sensory organs are its input devices, and the stimuli obtained from the external environment are fed into the nervous system which serves as the processing unit. From here, the nervous system is able to read the sensory information because it follows a syntactic structure, thus an output is created. This output then creates bodily motions and brings forth behavior and cognition. Of particular note is that cognition is sealed away in the brain, meaning that mental cognition is cut off from the external world and is only possible by the input of sensory information. == The embodied cognitive approach == Embodied cognitive science differs from the traditionalist approach in that it denies the input-output system. This is chiefly due to the problems presented by the Homunculus argument, which concluded that semantic meaning could not be derived from symbols without some kind of inner interpretation. If some little man in a person's head interpreted incoming symbols, then who would interpret the little man's inputs? Because of the specter of an infinite regress, the traditionalist model began to seem less plausible. Thus, embodied cognitive science aims to avoid this problem by defining cognition in three ways. === Physical attributes of the body === The first aspect of embodied cognition examines the role of the physical body, particularly how its properties affect its ability to think. This part attempts to overcome the symbol manipulation component that is a feature of the traditionalist model. Depth perception, for instance, can be better explained under the embodied approach due to the sheer complexity of the action. Depth perception requires that the brain detect the disparate retinal images obtained by the distance of the two eyes. In addition, body and head cues complicate this further. When the head is turned in a given direction, objects in the foreground will appear to move against objects in the background. From this, it is said that some kind of visual processing is occurring without the need of any kind of symbol manipulation. This is because the objects appearing to move the foreground are simply appearing to move. This observation concludes then that depth can be perceived with no intermediate symbol manipulation necessary. A more poignant example exists through examining auditory perception. Generally speaking the greater the distance between the ears, the greater the possible auditory acuity. Also relevant is the amount of density in between the ears, for the strength of the frequency wave alters as it passes through a given medium. The brain's auditory system takes these factors into account as it process information, but again without any need for a symbolic manipulation system. This is because the distance between the ears for example does not need symbols to represent it. The distance itself creates the necessary opportunity for greater auditory acuity. The amount of density between the ears is similar, in that it is the actual amount itself that simply forms the opportunity for frequency alteration. Thus under consideration of the physical properties of the body, a symbolic system is unnecessary and an unhelpful metaphor. === The body's role in the cognitive process === The second aspect draws heavily from George Lakoff's and Mark Johnson's work on concepts. They argued that humans use metaphors whenever possible to better explain their external world. Humans also have a basic stock of concepts in which other concepts can be derived from. These basic concepts include spatial orientations such as up, down, front, and back. Humans can understand what these concepts mean because they can directly experience them from their own bodies. For example, because human movement revolves around standing erect and moving the body in an up-down motion, humans innately have these concepts of up and down. Lakoff and Johnson contend this is similar with other spatial orientations such as front and back too. As mentioned earlier, these basic stocks of spatial concepts are the basis in which other concepts are constructed. Happy and sad for instance are seen now as being up or down respectively. When someone says they are feeling down, what they are really saying is that they feel sad for example. Thus the point here is that true understanding of these concepts is contingent on whether one can have an understanding of the human body. So the argument goes that if one lacked a human body, they could not possibly know what up or down could mean, or how it could relate to emotional states. [I]magine a spherical being living outside of any gravitational field, with no knowledge or imagination of any other kind of experience. What could UP possibly mean to such a being? While this does not mean that such beings would be incapable of expressing emotions in other words, it does mean that they would express emotions differently from humans. Human concepts of happiness and sadness would be different because human would have different bodies. So then an organism's body directly affects how it can think, because it uses metaphors related to its body as the basis of concepts. === Interaction of local environment === A third component of the embodied approach looks at how agents use their immediate environment in cognitive processing. Meaning, the local environment is seen as an actual extension of the body's cognitive process. The example of a personal digital assistant (PDA) is used to better imagine this. Echoing functionalism (philosophy of mind), this point claims that mental states are individuated by their role in a much larger system. So under this premise, the information on a PDA is similar to the information stored in the brain. So then if one thinks information in the brain constitutes mental states, then it must follow that information in the PDA is a cognitive state too. Consider also the role of pen and paper in a complex multiplication problem. The pen and paper are so involved in the cognitive process of solving the problem that it seems ridiculous to say they are somehow different from the process, in very much the same way the PDA is used for information like the brain. Another example examines how humans control and manipulate their environment

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  Maximum inner-product search

  Maximum inner-product search (MIPS) is a search problem, with a corresponding class of search algorithms which attempt to maximise the inner product between a query and the data items to be retrieved. MIPS algorithms are used in a wide variety of big data applications, including recommendation algorithms and machine learning. Formally, for a database of vectors x i {\displaystyle x_{i}} defined over a set of labels S {\displaystyle S} in an inner product space with an inner product ⟨ ⋅ , ⋅ ⟩ {\displaystyle \langle \cdot ,\cdot \rangle } defined on it, MIPS search can be defined as the problem of determining a r g m a x i ∈ S ⟨ x i , q ⟩ {\displaystyle {\underset {i\in S}{\operatorname {arg\,max} }}\ \langle x_{i},q\rangle } for a given query q {\displaystyle q} . Although there is an obvious linear-time implementation, it is generally too slow to be used on practical problems. However, efficient algorithms exist to speed up MIPS search. Under the assumption of all vectors in the set having constant norm, MIPS can be viewed as equivalent to a nearest neighbor search (NNS) problem in which maximizing the inner product is equivalent to minimizing the corresponding distance metric in the NNS problem. Like other forms of NNS, MIPS algorithms may be approximate or exact. MIPS search is used as part of DeepMind's RETRO algorithm.

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  Incremental heuristic search

  Incremental heuristic search algorithms combine both incremental and heuristic search to speed up searches of sequences of similar search problems, which is important in domains that are only incompletely known or change dynamically. Incremental search has been studied at least since the late 1960s. Incremental search algorithms reuse information from previous searches to speed up the current search and solve search problems potentially much faster than solving them repeatedly from scratch. Similarly, heuristic search has also been studied at least since the late 1960s. Heuristic search algorithms, often based on A, use heuristic knowledge in the form of approximations of the goal distances to focus the search and solve search problems potentially much faster than uninformed search algorithms. The resulting search problems, sometimes called dynamic path planning problems, are graph search problems where paths have to be found repeatedly because the topology of the graph, its edge costs, the start vertex or the goal vertices change over time. So far, three main classes of incremental heuristic search algorithms have been developed: The first class restarts A at the point where its current search deviates from the previous one (example: Fringe Saving A). The second class updates the h-values (heuristic, i.e. approximate distance to goal) from the previous search during the current search to make them more informed (example: Generalized Adaptive A). The third class updates the g-values (distance from start) from the previous search during the current search to correct them when necessary, which can be interpreted as transforming the A search tree from the previous search into the A search tree for the current search (examples: Lifelong Planning A, D, D Lite). All three classes of incremental heuristic search algorithms are different from other replanning algorithms, such as planning by analogy, in that their plan quality does not deteriorate with the number of replanning episodes. == Applications == Incremental heuristic search has been extensively used in robotics, where a larger number of path planning systems are based on either D (typically earlier systems) or D Lite (current systems), two different incremental heuristic search algorithms.

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