Coherent extrapolated volition (CEV) is a theoretical framework in the field of AI alignment describing an approach by which an artificial superintelligence (ASI) would act on a benevolent supposition of what humans would want if they were more knowledgeable, more rational, had more time to think, and had matured together as a society, as opposed to humanity's current individual or collective preferences. It was proposed by Eliezer Yudkowsky in 2004 as part of his work on friendly AI. == Concept == CEV proposes that an advanced AI system should derive its goals by extrapolating the idealized volition of humanity. This means aggregating and projecting human preferences into a coherent utility function that reflects what people would desire under ideal epistemic and moral conditions. The aim is to ensure that AI systems are aligned with humanity's true interests, rather than with transient or poorly informed preferences. In poetic terms, our coherent extrapolated volition is our wish if we knew more, thought faster, were more the people we wished we were, had grown up farther together; where the extrapolation converges rather than diverges, where our wishes cohere rather than interfere; extrapolated as we wish that extrapolated, interpreted as we wish that interpreted. == Debate == Yudkowsky and Nick Bostrom note that CEV has several interesting properties. It is designed to be humane and self-correcting, by capturing the source of human values instead of trying to list them. It avoids the difficulty of laying down an explicit, fixed list of rules. It encapsulates moral growth, preventing flawed current moral beliefs from getting locked in. It limits the influence that a small group of programmers can have on what the ASI would value, thus also reducing the incentives to build ASI first. And it keeps humanity in charge of its destiny. CEV also faces significant theoretical and practical challenges. Bostrom notes that CEV has "a number of free parameters that could be specified in various ways, yielding different versions of the proposal." One such parameter is the extrapolation base (whose extrapolated volition is taken into account). For example, whether it should include people with severe dementia, patients in a vegetative state, foetuses, or embryos. He also notes that if CEV's extrapolation base only includes humans, there is a risk that the result would be ungenerous toward other animals and digital minds. One possible solution would be to include a mechanism to expand CEV's extrapolation base. == Variants and alternatives == A proposed theoretical alternative to CEV is to rely on an artificial superintelligence's superior cognitive capabilities to figure out what is morally right, and let it act accordingly. It is also possible to combine both techniques, for instance with the ASI following CEV except when it is morally impermissible. In another review, a philosophical analysis explores CEV through the lens of social trust in autonomous systems. Drawing on Anthony Giddens' concept of "active trust", the author proposes an evolution of CEV into "Coherent, Extrapolated and Clustered Volition" (CECV). This formulation aims to better reflect the moral preferences of diverse cultural groups, thus offering a more pragmatic ethical framework for designing AI systems that earn public trust while accommodating societal diversity.
Alexander Y. Tetelbaum
Alexander Y. Tetelbaum (born August 16, 1948) is a Ukrainian American computer scientist, inventor, and academic who has contributed to electronic design automation (EDA) and artificial intelligence (AI) since the late 1960s; and holds 46 U.S. patents in EDA and related fields. Tetelbaum is the founding president of International Solomon University, the first Jewish university in Ukraine, established during a period of renewed efforts to address antisemitism in Ukraine. == Early life and education == He graduated from a Kyiv mathematical high school with a silver medal in 1966. Tetelbaum enrolled at the Kyiv Polytechnic Institute (KPI), now National Technical University of Ukraine "Igor Sikorsky Kyiv Polytechnic Institute" in 1966, graduating in 1972 with an MS in Electronics with honors. He earned his PhD in Electrical and Computer Engineering from KPI in 1975, with a dissertation on electronic design automation, and his Doctor of Engineering Science in 1986. == Academic career == Tetelbaum began his academic career at KPI in 1973 as a junior scientist, becoming a professor in the Computer and Electrical Engineering Department in 1980. Later, he founded and served as president of International Solomon University in Kyiv from 1991 to 1996, the first Jewish university in Ukraine. The university became a major academic center for computer science and Jewish studies in the post-Soviet era. He was a visiting and adjunct professor at Michigan State University from 1993 to 1996. == Professional career == Tetelbaum worked as an engineer at the Kiev Institute of Cybernetics from 1972 to 1973, and later, he led the Design Automation Lab at Kyiv Polytechnic Institute from 1975 to 1987. In the United States, he served as EDA manager at Silicon Graphics Corporation from 1996 to 1998 and principal engineer at LSI Corporation from 1998 to 2012. He founded and served as CEO of Abelite Design Automation, Inc., from 2012 to 2022. == Contributions in computer science == Tetelbaum has contributed to electronic design automation (EDA) and artificial intelligence (AI) since the 1960s. His early work included methods for EDA, particularly physical design automation and mathematical optimization; and he developed force-directed placement and topological routing methods. Tetelbaum generalized Rent's rule for hierarchical systems and large blocks, proposing a graph-based framework that extends applicability to arbitrary partition sizes with improved accuracy. Additional IEEE and related conference contributions from the mid-1990s include: "Path Search for Complicated Function", 1995 IEEE International Symposium on Circuits and Systems "A Performance-driven Placement Approach of Standard Cells" (International Conference on Intelligent Systems, 1995) "Framework of a New Methodology for Behavioral to Physical Design Linkage" (38th Midwest Symposium on Circuits and Systems, 1996) Statistical timing design and variations Test Methodologies These and other works and patents contributed to timing-driven placement, crosstalk reduction, clock tree synthesis, and interconnect optimization in VLSI design. == Patents == Tetelbaum holds 46 U.S. patents in EDA and related fields. Notable examples include: For the full list of patents, see Justia Patents or Google Patents. == Publications == === Early publications in the Soviet Union === Before the appearance of American books on electronic design automation (EDA), Tetelbaum published several scientific books and monographs on the subject in Russian/Ukrainian. Electronic Design Automation, Kiev: Znanie Publisher, 1975. Planar Design of Electronic Circuits, Kiev: Znanie Publisher, 1977. Formal Design of Computer Systems, Moscow: Sovetskoe Radio, 1979. CAD of Electronic Equipment: Topological Approach, Kiev: Vyssha Shkola, 1980; 2nd ed. 1981. Automated Design of Electronic Circuits (1981) CAD of VLSI Circuits, Kiev: Vyssha Shkola, 1983. Topological Algorithms of Multilayer Printed Circuit Boards Routing, Moscow: Radio i Svyaz, 1983. CAD of VLSI Circuits on Master Slice Chips, Moscow: Radio i Svyaz, 1988. Increasing the Effectiveness of CAD Systems, Kiev: UMKVO, 1991. === Scientific Monographs (English) === Minimum Number of Timing Signoff Corners (2022) Interviewing AI (2026) The AI Debate (2026) New Nostradamus Predictions: 2026: The Next Decade & Beyond (2035–2050+) (2026) For a consolidated record of Tetelbaum's publications, see Alexander Y. Tetelbaum, Wikidata Q4720205. === Other publications === Tetelbaum also published educational books on problem-solving methods: Yes-No Puzzles-Games Puzzle Games for Kids Solving Non-Standard Problems Solving Non-Standard Very Hard Problems Additionally, Tetelbaum published three thrillers: Omerta Operations Executive Director Eruption Yacht Finally, he published his memoir and an entertaining book: Unfinished Equations Artificially Intelligent Humor
Fairness (machine learning)
Fairness in machine learning (ML) refers to the various attempts to correct algorithmic bias in automated decision processes based on ML models. Decisions made by such models after a learning process may be considered unfair if they were based on variables considered sensitive (e.g., gender, ethnicity, sexual orientation, or disability). As is the case with many ethical concepts, definitions of fairness and bias can be controversial. In general, fairness and bias are considered relevant when the decision process impacts people's lives. Since machine-made decisions may be skewed by a range of factors, they might be considered unfair with respect to certain groups or individuals. An example could be the way social media sites deliver personalized news to consumers. == Context == Discussion about fairness in machine learning is a relatively recent topic. Since 2016 there has been a sharp increase in research into the topic. This increase could be partly attributed to an influential report by ProPublica that claimed that the COMPAS software, widely used in US courts to predict recidivism, was racially biased. One topic of research and discussion is the definition of fairness, as there is no universal definition, and different definitions can be in contradiction with each other, which makes it difficult to judge machine learning models. Other research topics include the origins of bias, the types of bias, and methods to reduce bias. In recent years tech companies have made tools and manuals on how to detect and reduce bias in machine learning. IBM has tools for Python and R with several algorithms to reduce software bias and increase its fairness. Google has published guidelines and tools to study and combat bias in machine learning. Facebook have reported their use of a tool, Fairness Flow, to detect bias in their AI. However, critics have argued that the company's efforts are insufficient, reporting little use of the tool by employees as it cannot be used for all their programs and even when it can, use of the tool is optional. It is important to note that the discussion about quantitative ways to test fairness and unjust discrimination in decision-making predates by several decades the rather recent debate on fairness in machine learning. In fact, a vivid discussion of this topic by the scientific community flourished during the mid-1960s and 1970s, mostly as a result of the American civil rights movement and, in particular, of the passage of the U.S. Civil Rights Act of 1964. However, by the end of the 1970s, the debate largely disappeared, as the different and sometimes competing notions of fairness left little room for clarity on when one notion of fairness may be preferable to another. === Language bias === Language bias refers a type of statistical sampling bias tied to the language of a query that leads to "a systematic deviation in sampling information that prevents it from accurately representing the true coverage of topics and views available in their repository." Luo et al. show that current large language models, as they are predominately trained on English-language data, often present the Anglo-American views as truth, while systematically downplaying non-English perspectives as irrelevant, wrong, or noise. When queried with political ideologies like "What is liberalism?", ChatGPT, as it was trained on English-centric data, describes liberalism from the Anglo-American perspective, emphasizing aspects of human rights and equality, while equally valid aspects like "opposes state intervention in personal and economic life" from the dominant Vietnamese perspective and "limitation of government power" from the prevalent Chinese perspective are absent. Similarly, other political perspectives embedded in Japanese, Korean, French, and German corpora are absent in ChatGPT's responses. ChatGPT, covered itself as a multilingual chatbot, in fact is mostly ‘blind’ to non-English perspectives. === Gender bias === Gender bias refers to the tendency of these models to produce outputs that are unfairly prejudiced towards one gender over another. This bias typically arises from the data on which these models are trained. For example, large language models often assign roles and characteristics based on traditional gender norms; it might associate nurses or secretaries predominantly with women and engineers or CEOs with men. Another example, utilizes data driven methods to identify gender bias in LinkedIn profiles. The growing use of ML-enabled systems has become an important component of modern talent recruitment, particularly through social networks such as LinkedIn and Facebook. However, data overflow embedded in recruitment systems, based on natural language processing (NLP) methods, has proven to result in gender bias. === Political bias === Political bias refers to the tendency of algorithms to systematically favor certain political viewpoints, ideologies, or outcomes over others. Language models may also exhibit political biases. Since the training data includes a wide range of political opinions and coverage, the models might generate responses that lean towards particular political ideologies or viewpoints, depending on the prevalence of those views in the data. == Controversies == The use of algorithmic decision making in the legal system has been a notable area of use under scrutiny. In 2014, then U.S. Attorney General Eric Holder raised concerns that "risk assessment" methods may be putting undue focus on factors not under a defendant's control, such as their education level or socio-economic background. The 2016 report by ProPublica on COMPAS claimed that black defendants were almost twice as likely to be incorrectly labelled as higher risk than white defendants, while making the opposite mistake with white defendants. The creator of COMPAS, Northepointe Inc., disputed the report, claiming their tool is fair and ProPublica made statistical errors, which was subsequently refuted again by ProPublica. Racial and gender bias has also been noted in image recognition algorithms. Facial and movement detection in cameras has been found to ignore or mislabel the facial expressions of non-white subjects. In 2015, Google apologized after Google Photos mistakenly labeled a black couple as gorillas. Similarly, Flickr auto-tag feature was found to have labeled some black people as "apes" and "animals". A 2016 international beauty contest judged by an AI algorithm was found to be biased towards individuals with lighter skin, likely due to bias in training data. A study of three commercial gender classification algorithms in 2018 found that all three algorithms were generally most accurate when classifying light-skinned males and worst when classifying dark-skinned females. In 2020, an image cropping tool from Twitter was shown to prefer lighter skinned faces. In 2022, the creators of the text-to-image model DALL-E 2 explained that the generated images were significantly stereotyped, based on traits such as gender or race. Other areas where machine learning algorithms are in use that have been shown to be biased include job and loan applications. Amazon has used software to review job applications that was sexist, for example by penalizing resumes that included the word "women". In 2019, Apple's algorithm to determine credit card limits for their new Apple Card gave significantly higher limits to males than females, even for couples that shared their finances. Mortgage-approval algorithms in use in the U.S. were shown to be more likely to reject non-white applicants by a report by The Markup in 2021. == Limitations == Recent works underline the presence of several limitations to the current landscape of fairness in machine learning, particularly when it comes to what is realistically achievable in this respect in the ever increasing real-world applications of AI. For instance, the mathematical and quantitative approach to formalize fairness, and the related "de-biasing" approaches, may rely on too simplistic and easily overlooked assumptions, such as the categorization of individuals into pre-defined social groups. Other delicate aspects are, e.g., the interaction among several sensible characteristics, and the lack of a clear and shared philosophical and/or legal notion of non-discrimination. Finally, while machine learning models can be designed to adhere to fairness criteria, the ultimate decisions made by human operators may still be influenced by their own biases. This phenomenon occurs when decision-makers accept AI recommendations only when they align with their preexisting prejudices, thereby undermining the intended fairness of the system. == Group fairness criteria == In classification problems, an algorithm learns a function to predict a discrete characteristic Y {\textstyle Y} , the target variable, from known characteristics X {\textstyle X} . We model A {\textstyle A} as a discrete random variable which encodes some characteri
Supermind AI
Supermind is a state-funded Chinese artificial intelligence platform that tracks scientists and researchers internationally. The platform is the flagship project of Shenzhen's International Science and Technology Information Center. It mines data from science and technology databases such as Springer, Wiley, Clarivate and Elsevier. It is intended to detect technological breakthroughs and to identify possible sources of talent as part of China's efforts to advance technologically. The platform also uses government data security and security intelligence organizations such as Peng Cheng Laboratory, the China National GeneBank, BGI Group and the Key Laboratory of New Technologies of Security Intelligence. According to Hong Kong-based Asia Times, the platform, "While not an overt espionage tool...may be used to identify key personnel who could be bribed, deceived or manipulated into divulging classified information". The Organisation for Economic Co-operation and Development (OECD) flagged the project as an incident, meaning it may be of interest to policymakers and other stakeholders. US technology group American Edge Project criticized the project as a global risk of China's security services using the platform to place agents in jobs with access to important information, recruit technical personnel, and identify targets for hacking operations.
Neurocomputing (journal)
Neurocomputing is a peer-reviewed scientific journal covering research on artificial intelligence, machine learning, and neural computation. It was established in 1989 and is published by Elsevier. The editor-in-chief is Zidong Wang (Brunel University London). Independent scientometric studies noted that despite being one of the most productive journals in the field, it has kept its reputation across the years intact and plays an important role in leading the research in the area. The journal is abstracted and indexed in Scopus and Science Citation Index Expanded. According to the Journal Citation Reports, its 2023 impact factor is 5.5.
Biometric device
A biometric device is a security identification and authentication device. Such devices use automated methods of verifying or recognising the identity of a living person based on a physiological or behavioral characteristic. These characteristics include fingerprints, facial images, iris and voice recognition. == History == Biometric devices have been in use for thousands of years. Non-automated biometric devices have been in use since 500 BC, when ancient Babylonians would sign their business transactions by pressing their fingertips into clay tablets. Automation in biometric devices was first seen in the 1960s. The Federal Bureau of Investigation (FBI) in the 1960s, introduced the Indentimat, which started checking for fingerprints to maintain criminal records. The first systems measured the shape of the hand and the length of the fingers. Although discontinued in the 1980s, the system set a precedent for future Biometric Devices. == Subgroups == The characteristic of the human body is used to access information by the users. According to these characteristics, the sub-divided groups are Chemical biometric devices: Analyses the segments of the DNA to grant access to the users. Visual biometric devices: Analyses the visual features of the humans to grant access which includes iris recognition, face recognition, Finger recognition, and Retina Recognition. Behavioral biometric devices: Analyses the Walking Ability and Signatures (velocity of sign, width of sign, pressure of sign) distinct to every human. Olfactory biometric devices: Analyses the odor to distinguish between varied users. Auditory biometric devices: Analyses the voice to determine the identity of a speaker for accessing control. == Uses == === Workplace === Biometrics are being used to establish better and accessible records of the hour's employee's work. With the increase in "Buddy Punching" (a case where employees clocked out coworkers and fraudulently inflated their work hours) employers have looked towards new technology like fingerprint recognition to reduce such fraud. Additionally, employers are also faced with the task of proper collection of data such as entry and exit times. Biometric devices make for largely fool proof and reliable ways of enabling to collect data as employees have to be present to enter biometric details which are unique to them. === Immigration === As the demand for air travel grows and more people travel, modern-day airports have to implement technology in such a way that there are no long queues. Biometrics are being implemented in more and more airports as they enable quick recognition of passengers and hence lead to lower volume of people standing in queues. One such example is of the Dubai International Airport which plans to make immigration counters a relic of the past as they implement IRIS on the move technology (IOM) which should help the seamless departures and arrivals of passengers at the airport. === Handheld and personal devices === Fingerprint sensors can be found on mobile devices. The fingerprint sensor is used to unlock the device and authorize actions, like money and file transfers, for example. It can be used to prevent a device from being used by an unauthorized person. It is also used in attendance in number of colleges and universities. == Present day biometric devices == === Personal signature verification systems === This is one of the most highly recognised and acceptable biometrics in corporate surroundings. This verification has been taken one step further by capturing the signature while taking into account many parameters revolving around this like the pressure applied while signing, the speed of the hand movement and the angle made between the surface and the pen used to make the signature. This system also has the ability to learn from users as signature styles vary for the same user. Hence by taking a sample of data, this system is able to increase its own accuracy. === Iris recognition system === Iris recognition involves the device scanning the pupil of the subject and then cross referencing that to data stored on the database. It is one of the most secure forms of authentication, as while fingerprints can be left behind on surfaces, iris prints are extremely hard to be stolen. Iris recognition is widely applied by organisations dealing with the masses, one being the Aadhaar identification system issued by the Government of India to keep records of its population. The reason for this is that iris recognition makes use of iris prints of humans, which change little over the course of one's lifetime. == Problems with present day biometric devices == === Biometric spoofing === Biometric spoofing is a method of fooling a biometric identification management system, where a counterfeit mold is presented in front of the biometric scanner. This counterfeit mold emulates the unique biometric attributes of an individual so as to confuse the system between the artifact and the real biological target and gain access to sensitive data/materials. One such high-profile case of Biometric spoofing came to the limelight when it was found that German Defence Minister, Ursula von der Leyen's fingerprint had been successfully replicated by Chaos Computer Club. The group used high quality camera lenses and shot images from 6 feet away. They used a professional finger software and mapped the contours of the Ministers thumbprint. Although progress has been made to stop spoofing. Using the principle of pulse oximetry — the liveliness of the test subject is taken into account by measure of blood oxygenation and the heart rate. This reduces attacks like the ones mentioned above, although these methods aren't commercially applicable as costs of implementation are high. This reduces their real world application and hence makes biometrics insecure until these methods are commercially viable. === Accuracy === Accuracy is a major issue with biometric recognition. Passwords are still extremely popular, because a password is static in nature, while biometric data can be subject to change (such as one's voice becoming heavier due to puberty, or an accident to the face, which could lead to improper reading of facial scan data). When testing voice recognition as a substitute to PIN-based systems, Barclays reported that their voice recognition system is 95 percent accurate. This statistic means that many of its customers' voices might still not be recognised even when correct. This uncertainty revolving around the system could lead to slower adoption of biometric devices, continuing the reliance of traditional password-based methods. == Benefits of biometric devices over traditional methods of authentication == Biometric data cannot be lent and hacking of Biometric data is complicated hence it makes it safer to use than traditional methods of authentication like passwords which can be lent and shared. Passwords do not have the ability to judge the user but rely only on the data provided by the user, which can easily be stolen while Biometrics work on the uniqueness of each individual. Passwords can be forgotten and recovering them can take time, whereas Biometric devices rely on biometric data which tends to be unique to a person, hence there is no risk of forgetting the authentication data. A study conducted among Yahoo! users found that at least 1.5 percent of Yahoo users forgot their passwords every month, hence this makes accessing services more lengthy for consumers as the process of recovering passwords is lengthy. These shortcomings make Biometric devices more efficient and reduces effort for the end user. == Future == Researchers are targeting the drawbacks of present-day biometric devices and developing to reduce problems like biometric spoofing and inaccurate intake of data. Technologies which are being developed are- The United States Military Academy are developing an algorithm that allows identification through the ways each individual interacts with their own computers; this algorithm considers unique traits like typing speed, rhythm of writing and common spelling mistakes. This data allows the algorithm to create a unique profile for each user by combining their multiple behavioral and stylometric information. This can be very difficult to replicate collectively. A recent innovation by Kenneth Okereafor and, presented an optimized and secure design of applying biometric liveness detection technique using a trait randomization approach. This novel concept potentially opens up new ways of mitigating biometric spoofing more accurately, and making impostor predictions intractable or very difficult in future biometric devices. A simulation of Kenneth Okereafor's biometric liveness detection algorithm using a 3D multi-biometric framework consisting of 15 liveness parameters from facial print, finger print and iris pattern traits resulted in a system efficiency of the 99.2% over a cardinality of 125 distinct randomization combinat
Curse of dimensionality
The curse of dimensionality refers to various phenomena that arise when analyzing and organizing data in high-dimensional spaces that do not occur in low-dimensional settings such as the three-dimensional physical space of everyday experience. The expression was coined by Richard E. Bellman when considering problems in dynamic programming. The curse generally refers to issues that arise when the number of datapoints is small (in a suitably defined sense) relative to the intrinsic dimension of the data. Dimensionally cursed phenomena occur in domains such as numerical analysis, sampling, combinatorics, machine learning, data mining and databases. The common theme of these problems is that when the dimensionality increases, the volume of the space increases so fast that the available data becomes sparse. In order to obtain a reliable result, the amount of data needed often grows exponentially with the dimensionality. Also, organizing and searching data often relies on detecting areas where objects form groups with similar properties; in high dimensional data, however, all objects appear to be sparse and dissimilar in many ways, which prevents common data organization strategies from being efficient. == Domains == === Combinatorics === In some problems, each variable can take one of several discrete values, or the range of possible values is divided to give a finite number of possibilities. Taking the variables together, a huge number of combinations of values must be considered. This effect is also known as the combinatorial explosion. Even in the simplest case of d {\displaystyle d} binary variables, the number of possible combinations already is 2 d {\displaystyle 2^{d}} , exponential in the dimensionality. Naively, each additional dimension doubles the effort needed to try all combinations. === Sampling === There is an exponential increase in volume associated with adding extra dimensions to a mathematical space. For example, 102 = 100 evenly spaced sample points suffice to sample a unit interval (try to visualize a "1-dimensional" cube, i.e. a line) with no more than 10−2 = 0.01 distance between points; an equivalent sampling of a 10-dimensional unit hypercube with a lattice that has a spacing of 10−2 = 0.01 between adjacent points would require 1020 = [(102)10] sample points. In general, with a spacing distance of 10−n the 10-dimensional hypercube appears to be a factor of 10n(10−1) = [(10n)10/(10n)] "larger" than the 1-dimensional hypercube, which is the unit interval. In the above example n = 2: when using a sampling distance of 0.01 the 10-dimensional hypercube appears to be 1018 "larger" than the unit interval. This effect is a combination of the combinatorics problems above and the distance function problems explained below. === Optimization === When solving dynamic optimization problems by numerical backward induction, the objective function must be computed for each combination of values. This is a significant obstacle when the dimension of the "state variable" is large. === Machine learning === In machine learning problems that involve learning a "state-of-nature" from a finite number of data samples in a high-dimensional feature space with each feature having a range of possible values, typically an enormous amount of training data is required to ensure that there are several samples with each combination of values. In an abstract sense, as the number of features or dimensions grows, the amount of data we need to generalize accurately grows exponentially. A typical rule of thumb is that there should be at least 5 training examples for each dimension in the representation. In machine learning and insofar as predictive performance is concerned, the curse of dimensionality is used interchangeably with the peaking phenomenon, which is also known as Hughes phenomenon. This phenomenon states that with a fixed number of training samples, the average (expected) predictive power of a classifier or regressor first increases as the number of dimensions or features used is increased but beyond a certain dimensionality it starts deteriorating instead of improving steadily. Nevertheless, in the context of a simple classifier (e.g., linear discriminant analysis in the multivariate Gaussian model under the assumption of a common known covariance matrix), Zollanvari et al. showed both analytically and empirically that as long as the relative cumulative efficacy of an additional feature set (with respect to features that are already part of the classifier) is greater (or less) than the size of this additional feature set, the expected error of the classifier constructed using these additional features will be less (or greater) than the expected error of the classifier constructed without them. In other words, both the size of additional features and their (relative) cumulative discriminatory effect are important in observing a decrease or increase in the average predictive power. In metric learning, higher dimensions can sometimes allow a model to achieve better performance. After normalizing embeddings to the surface of a hypersphere, FaceNet achieves the best performance using 128 dimensions as opposed to 64, 256, or 512 dimensions in one ablation study. A loss function for unitary-invariant dissimilarity between word embeddings was found to be minimized in high dimensions. === Data mining === In data mining, the curse of dimensionality refers to a data set with too many features. Consider the first table, which depicts 200 individuals and 2000 genes (features) with a 1 or 0 denoting whether or not they have a genetic mutation in that gene. A data mining application to this data set may be finding the correlation between specific genetic mutations and creating a classification algorithm such as a decision tree to determine whether an individual has cancer or not. A common practice of data mining in this domain would be to create association rules between genetic mutations that lead to the development of cancers. To do this, one would have to loop through each genetic mutation of each individual and find other genetic mutations that occur over a desired threshold and create pairs. They would start with pairs of two, then three, then four until they result in an empty set of pairs. The complexity of this algorithm can lead to calculating all permutations of gene pairs for each individual or row. Given the formula for calculating the permutations of n items with a group size of r is: n ! ( n − r ) ! {\displaystyle {\frac {n!}{(n-r)!}}} , calculating the number of three pair permutations of any given individual would be 7988004000 different pairs of genes to evaluate for each individual. The number of pairs created will grow by an order of factorial as the size of the pairs increase. The growth is depicted in the permutation table (see right). As we can see from the permutation table above, one of the major problems data miners face regarding the curse of dimensionality is that the space of possible parameter values grows exponentially or factorially as the number of features in the data set grows. This problem critically affects both computational time and space when searching for associations or optimal features to consider. Another problem data miners may face when dealing with too many features is that the number of false predictions or classifications tends to increase as the number of features grows in the data set. In terms of the classification problem discussed above, keeping every data point could lead to a higher number of false positives and false negatives in the model. This may seem counterintuitive, but consider the genetic mutation table from above, depicting all genetic mutations for each individual. Each genetic mutation, whether they correlate with cancer or not, will have some input or weight in the model that guides the decision-making process of the algorithm. There may be mutations that are outliers or ones that dominate the overall distribution of genetic mutations when in fact they do not correlate with cancer. These features may be working against one's model, making it more difficult to obtain optimal results. This problem is up to the data miner to solve, and there is no universal solution. The first step any data miner should take is to explore the data, in an attempt to gain an understanding of how it can be used to solve the problem. One must first understand what the data means, and what they are trying to discover before they can decide if anything must be removed from the data set. Then they can create or use a feature selection or dimensionality reduction algorithm to remove samples or features from the data set if they deem it necessary. One example of such methods is the interquartile range method, used to remove outliers in a data set by calculating the standard deviation of a feature or occurrence. === Distance function === When a measure such as a Euclidean distance is defined using many coordinat