Fei-Fei Li (Chinese: 李飞飞; pinyin: Lǐ Fēifēi; born July 3, 1976) is a Chinese-born American computer scientist best known for establishing ImageNet, the dataset that enabled rapid advances in computer vision in the 2010s. She is a professor of computer science at Stanford University, with research expertise in artificial intelligence, machine learning, deep learning, computer vision, and cognitive neuroscience. Li is a co-director of the Stanford Institute for Human-Centered Artificial Intelligence and a co-director of the Stanford Vision and Learning Lab, and served as Chief Scientist of AI/ML at Google Cloud and the director of the Stanford Artificial Intelligence Laboratory from 2013 to 2018. In 2017, she co-founded AI4ALL, a nonprofit organization working to increase diversity in the field of artificial intelligence. In 2023, Li was named one of the Time 100 AI Most Influential People. Li received the Intel Lifetime Achievements Innovation Award in 2017 for her contributions to artificial intelligence, and was elected member of the National Academy of Engineering, the National Academy of Medicine in 2020 and the American Academy of Arts and Sciences in 2021. In 2025, she was named as one of the "Architects of AI" for Time's Person of the Year. On August 3, 2023, Li was appointed to the United Nations Scientific Advisory Board, established by Secretary-General Antonio Guterres. In 2024, Li was included on the Gold House's most influential Asian A100 list. In 2024, she raised $230 million for a startup called World Labs, which she and three colleagues founded to develop a "spatial intelligence" AI technology that can understand how the three-dimensional physical world works. In 2026, World Labs raised $1 Billion. == Early life and education == Li was born in Beijing, China, in 1976 and grew up in Chengdu, Sichuan. She studied at Sichuan Chengdu No.7 High School. When she was 12, her father immigrated to Parsippany, New Jersey. When she was 16, Li and her mother joined him in the United States. While attending Parsippany High School, Li worked weekends at her family's dry-cleaning shop. She graduated from Parsippany High School in 1995. She was inducted into the hall of fame at Parsippany High School in 2017. Li pursued undergraduate study at Princeton University, where she received a Bachelor of Arts with a major in physics in 1999. Li completed her senior thesis, "Auditory binaural correlogram difference: a new computational model for Huggins dichotic pitch", under the supervision of Bradley Dickinson, professor of electrical engineering. During her years at Princeton, Li returned home most weekends to help run her family's dry cleaning business and worked as a dishwasher to supplement the family income. Li pursued graduate study at the California Institute of Technology, where she received a Master of Science in electrical engineering in 2001 and a Doctor of Philosophy in electrical engineering in 2005. Li completed her dissertation, "Visual Recognition: Computational Models and Human Psychophysics", under the primary supervision of Pietro Perona and secondary supervision of Christof Koch. Her graduate studies were supported by the National Science Foundation Graduate Research Fellowship and The Paul & Daisy Soros Fellowships for New Americans. == Career and research == From 2005 to 2006, Li was an assistant professor in the Electrical and Computer Engineering Department at the University of Illinois Urbana-Champaign, and from 2007 to 2009, she was an assistant professor in the Computer Science Department at Princeton University. She joined Stanford in 2009 as an assistant professor, and was promoted to associate professor with tenure in 2012, and then full professor in 2018. At Stanford, Li served as the director of Stanford Artificial Intelligence Lab (SAIL) from 2013 to 2018. Her research has focused on computer vision, deep learning, and cognitive neuroscience, with over 300 peer-reviewed publications. She became the founding co-director of Stanford's University-level initiative - the Human-Centered AI Institute, along with co-director Dr. John Etchemendy, former provost of Stanford University. The institute aligns with Li's aims to advance AI research, education, policy, and practice to improve the human condition. While at Princeton in 2007, Li led the development of ImageNet, a massive visual database designed to advance object recognition in AI. The project involved labeling over 14 million images using Amazon Mechanical Turk and inspired the ImageNet Large Scale Visual Recognition Challenge (ILSVRC), which catalyzed progress in deep learning and led to dramatic improvements in image classification performance. The database addressed a key bottleneck in computer vision: the lack of large, annotated datasets for training machine learning models. Today, ImageNet is credited as a cornerstone innovation that underpins advancements in autonomous vehicles, facial recognition, and medical imaging. On her sabbatical from Stanford University from January 2017 to fall of 2018, Li joined Google Cloud as its Chief Scientist of AI/ML and Vice President. At Google, her team focused on democratizing AI technology and lowering the barrier for entrance to businesses and developers, including the developments of products like AutoML. In September 2017, Google secured a contract from the Department of Defense called Project Maven, which aimed to use AI techniques to interpret images captured by drone cameras. Google told employees who protested the company's work on Project Maven that their role was "specifically scoped to be for non-offensive purposes". In June 2018, Google told employees it would not seek renewal of the contract. In internal emails which were later leaked to reporters, Li expressed enthusiasm for the Google Cloud role in Project Maven, but warned against mentioning its AI component, saying that military AI is linked in the public mind with the danger of autonomous weapons. Asked about those leaked emails, Li told The New York Times, "I believe in human-centered AI to benefit people in positive and benevolent ways. It is deeply against my principles to work on any project that I think is to weaponize AI." In the fall of 2018, Li left Google and returned to Stanford University to continue her professorship. In 2023, Li co-led the launch of the RAISE-Health (Responsible AI for Safe and Equitable Health) initiative at Stanford University in collaboration with Stanford medicine. The initiative aims to develop frameworks for the responsible use of artificial intelligence in healthcare, including clinical care, biomedical research, and patient safety. According to her Stanford profile, she has been on partial academic leave from January 2024 through the end of 2025 to focus on entrepreneurial ventures. In 2024, Li said there was a disparity between private-sector investment in AI and support for academic and government research, and called for greater public funding for scientific uses of the technology and for studying its risks. Li is also known for her non-profit work as the co-founder and chairperson of nonprofit organization AI4ALL, whose mission is to educate the next generation of AI technologists, thinkers and leaders by promoting diversity and inclusion through human-centered AI principles. The program was created in collaboration with Melinda French Gates and Jensen Huang. Prior to establishing AI4ALL in 2017, Li and her former student Olga Russakovsky, currently an assistant professor in Princeton University, co-founded and co-directed the precursor program at Stanford called SAILORS (Stanford AI Lab OutReach Summers). SAILORS was an annual summer camp at Stanford dedicated to 9th grade high school girls in AI education and research, established in 2015 till it changed its name to AI4ALL @Stanford in 2017. In 2018, AI4ALL has successfully launched five more summer programs in addition to Stanford, including Princeton University, Carnegie Mellon University, Boston University, University of California Berkeley, and Canada's Simon Fraser University. We are at a turning point. AI's influence continues to grow, but representation and inclusion of a diversity of researchers in the field does not. It's critical that we seize this moment to create structures that will support long-term, positive changes. This won't happen via a single mechanism or quick fix. It starts with early education and extends to the existing structures of power within academia, work cultures among current AI researchers, and gatekeeping functions of research publishing, to name a few levers of change. Li has been described as a "researcher bringing humanity to AI". Li was elected as a member of the American Academy of Arts and Sciences in 2021, the National Academy of Engineering in 2020, and the National Academy of Medicine in 2020. In a November 2023 interview with The Guardian, Li said that while she would not refer to herself as the "godmother
Histogram of oriented displacements
Histogram of oriented displacements (HOD) is a 2D trajectory descriptor. The trajectory is described using a histogram of the directions between each two consecutive points. Given a trajectory T = {P1, P2, P3, ..., Pn}, where Pt is the 2D position at time t. For each pair of positions Pt and Pt+1, calculate the direction angle θ(t, t+1). Value of θ is between 0 and 360. A histogram of the quantized values of θ is created. If the histogram is of 8 bins, the first bin represents all θs between 0 and 45. The histogram accumulates the lengths of the consecutive moves. For each θ, a specific histogram bin is determined. The length of the line between Pt and Pt+1 is then added to the specific histogram bin. To show the intuition behind the descriptor, consider the action of waving hands. At the end of the action, the hand falls down. When describing this down movement, the descriptor does not care about the position from which the hand started to fall. This fall will affect the histogram with the appropriate angles and lengths, regardless of the position where the hand started to fall. HOD records for each moving point: how much it moves in each range of directions. HOD has a clear physical interpretation. It proposes that, a simple way to describe the motion of an object, is to indicate how much distance it moves in each direction. If the movement in all directions are saved accurately, the movement can be repeated from the initial position to the final destination regardless of the displacements order. However, the temporal information will be lost, as the order of movements is not stored-this is what we solve by applying the temporal pyramid, as shown in section \ref{sec:temp-pyramid}. If the angles quantization range is small, classifiers that use the descriptor will overfit. Generalization needs some slack in directions-which can be done by increasing the quantization range.
Problem solving
Problem solving is the process of achieving a goal by overcoming obstacles, a frequent part of most activities. Problems in need of solutions range from simple personal tasks (e.g. how to get from point A to B) to complex issues in business and technical fields. The former is an example of simple problem solving (SPS) addressing one issue, whereas the latter is complex problem solving (CPS) with multiple interrelated obstacles. Another classification of problem-solving tasks is into well-defined problems with specific obstacles and goals, and ill-defined problems in which the current situation is troublesome but it is not clear what kind of resolution to aim for. Similarly, one may distinguish formal or fact-based problems requiring psychometric intelligence, versus socio-emotional problems which depend on the changeable emotions of individuals or groups, such as tactful behavior, fashion, or gift choices. Solutions require sufficient resources and knowledge to attain the goal. Professionals such as lawyers, doctors, programmers, and consultants are largely problem solvers for issues that require technical skills and knowledge beyond general competence. Many businesses have found profitable markets by recognizing a problem and creating a solution: the more widespread and inconvenient the problem, the greater the opportunity to develop a scalable solution. There are many specialized problem-solving techniques and methods in fields such as science, engineering, business, medicine, mathematics, computer science, philosophy, and social organization. The mental techniques to identify, analyze, and solve problems are studied in psychology and cognitive sciences. Also widely researched are the mental obstacles that prevent people from finding solutions; problem-solving impediments include confirmation bias, mental set, and functional fixedness. == Definition == The term problem solving has a slightly different meaning depending on the discipline. For instance, it is a mental process in psychology and a computerized process in computer science. There are two different types of problems: ill-defined and well-defined; different approaches are used for each. Well-defined problems have specific end goals and clearly expected solutions, while ill-defined problems do not. Well-defined problems allow for more initial planning than ill-defined problems. Solving problems sometimes involves dealing with pragmatics (the way that context contributes to meaning) and semantics (the interpretation of the problem). The ability to understand what the end goal of the problem is, and what rules could be applied, represents the key to solving the problem. Sometimes a problem requires abstract thinking or coming up with a creative solution. Problem solving has two major domains: mathematical problem solving and personal problem solving. Each concerns some difficulty or barrier that is encountered. === Psychology === Problem solving in psychology refers to the process of finding solutions to problems encountered in life. Solutions to these problems are usually situation- or context-specific. The process starts with problem finding and problem shaping, in which the problem is discovered and simplified. The next step is to generate possible solutions and evaluate them. Finally a solution is selected to be implemented and verified. Problems have an end goal to be reached; how you get there depends upon problem orientation (problem-solving coping style and skills) and systematic analysis. Mental health professionals study the human problem-solving processes using methods such as introspection, behaviorism, simulation, computer modeling, and experiment. Social psychologists look into the person-environment relationship aspect of the problem and independent and interdependent problem-solving methods. Problem solving has been defined as a higher-order cognitive process and intellectual function that requires the modulation and control of more routine or fundamental skills. Empirical research shows many different strategies and factors influence everyday problem solving. Rehabilitation psychologists studying people with frontal lobe injuries have found that deficits in emotional control and reasoning can be re-mediated with effective rehabilitation and could improve the capacity of injured persons to resolve everyday problems. Interpersonal everyday problem solving is dependent upon personal motivational and contextual components. One such component is the emotional valence of "real-world" problems, which can either impede or aid problem-solving performance. Researchers have focused on the role of emotions in problem solving, demonstrating that poor emotional control can disrupt focus on the target task, impede problem resolution, and lead to negative outcomes such as fatigue, depression, and inertia. In conceptualization,human problem solving consists of two related processes: problem orientation, and the motivational/attitudinal/affective approach to problematic situations and problem-solving skills. People's strategies cohere with their goals and stem from the process of comparing oneself with others. === Cognitive sciences === Among the first experimental psychologists to study problem solving were the Gestaltists in Germany, such as Karl Duncker in The Psychology of Productive Thinking (1935). Perhaps best known is the work of Allen Newell and Herbert A. Simon. Experiments in the 1960s and early 1970s asked participants to solve relatively simple, well-defined, but not previously seen laboratory tasks. These simple problems, such as the Tower of Hanoi, admitted optimal solutions that could be found quickly, allowing researchers to observe the full problem-solving process. Researchers assumed that these model problems would elicit the characteristic cognitive processes by which more complex "real world" problems are solved. An outstanding problem-solving technique found by this research is the principle of decomposition. === Computer science === Much of computer science and artificial intelligence involves designing automated systems to solve a specified type of problem: to accept input data and calculate a correct or adequate response, reasonably quickly. Algorithms are recipes or instructions that direct such systems, written into computer programs. Steps for designing such systems include problem determination, heuristics, root cause analysis, de-duplication, analysis, diagnosis, and repair. Analytic techniques include linear and nonlinear programming, queuing systems, and simulation. A large, perennial obstacle is to find and fix errors in computer programs: debugging. === Logic === Formal logic concerns issues like validity, truth, inference, argumentation, and proof. In a problem-solving context, it can be used to formally represent a problem as a theorem to be proved, and to represent the knowledge needed to solve the problem as the premises to be used in a proof that the problem has a solution. The use of computers to prove mathematical theorems using formal logic emerged as the field of automated theorem proving in the 1950s. It included the use of heuristic methods designed to simulate human problem solving, as in the Logic Theory Machine, developed by Allen Newell, Herbert A. Simon and J. C. Shaw, as well as algorithmic methods such as the resolution principle developed by John Alan Robinson. In addition to its use for finding proofs of mathematical theorems, automated theorem-proving has also been used for program verification in computer science. In 1958, John McCarthy proposed the advice taker, to represent information in formal logic and to derive answers to questions using automated theorem-proving. An important step in this direction was made by Cordell Green in 1969, who used a resolution theorem prover for question-answering and for such other applications in artificial intelligence as robot planning. The resolution theorem-prover used by Cordell Green bore little resemblance to human problem solving methods. In response to criticism of that approach from researchers at MIT, Robert Kowalski developed logic programming and SLD resolution, which solves problems by problem decomposition. He has advocated logic for both computer and human problem solving and computational logic to improve human thinking. === Engineering === When products or processes fail, problem solving techniques can be used to develop corrective actions that can be taken to prevent further failures. Such techniques can also be applied to a product or process prior to an actual failure event—to predict, analyze, and mitigate a potential problem in advance. Techniques such as failure mode and effects analysis can proactively reduce the likelihood of problems. In either the reactive or the proactive case, it is necessary to build a causal explanation through a process of diagnosis. In deriving an explanation of effects in terms of causes, abduction generates new ideas or hypothes
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
Hugging Face
Hugging Face, Inc., is an American company based in New York City that develops computation tools for building applications using machine learning. Its transformers library built for natural language processing applications and its platform allow users to share machine learning models and datasets and showcase their work. == History == === Founding === The company was founded in 2016 by French entrepreneurs Clément Delangue, Julien Chaumond, and Thomas Wolf in New York City, originally as a company that developed a chatbot app targeted at teenagers. The company was named after the U+1F917 🤗 HUGGING FACE emoji. After open sourcing the model behind the chatbot, the company pivoted to focus on being a platform for machine learning. === AI boom === On April 28, 2021, the company launched the BigScience Research Workshop in collaboration with several other research groups to release an open large language model. In 2022, the workshop concluded with the announcement of BLOOM, a multilingual large language model with 176 billion parameters. In February 2023, the company announced partnership with Amazon Web Services (AWS) which would allow Hugging Face's products to be available to AWS customers to use them as the building blocks for their custom applications. The company also said the next generation of BLOOM will be run on Trainium, a proprietary machine learning chip created by AWS. In June 2024, the company announced, along with Meta and Scaleway, their launch of a new AI accelerator program for European startups. The initiative aimed to help startups integrate open foundation models into their products, accelerating the EU AI ecosystem. The program, based at STATION F in Paris, ran from September 2024 to February 2025. Selected startups received mentoring, and access to AI models and tools and Scaleway's computing power. On September 23, 2024, to further the International Decade of Indigenous Languages, Hugging Face teamed up with Meta and UNESCO to launch a new online language translator. It was built on Meta's No Language Left Behind open-source AI model, enabling free text translation across 200 languages, including many low-resource languages. In April 2025, Hugging Face announced that they acquired a humanoid robotics startup, Pollen Robotics, based in France and founded by Matthieu Lapeyre and Pierre Rouanet in 2016. In an X tweet, Delangue shared his vision to "make Artificial Intelligence robotics Open Source". === Cyberattacks === In early 2026, hackers hijacked the Hugging Face platform to launch Android-targeted attacks involving "powerful malware" which could completely take over a compromised target.
Richardson–Lucy deconvolution
The Richardson–Lucy algorithm, also known as Lucy–Richardson deconvolution, is an iterative procedure for recovering an underlying image that has been blurred by a known point spread function. It was named after William Richardson and Leon B. Lucy, who described it independently. == Description == When an image is produced using an optical system and detected using photographic film, a charge-coupled device or a CMOS sensor, for example, it is inevitably blurred, with an ideal point source not appearing as a point but being spread out into what is known as the point spread function. Extended sources can be decomposed into the sum of many individual point sources, thus the observed image can be represented in terms of a transition matrix p operating on an underlying image: d i = ∑ j p i , j u j , {\displaystyle d_{i}=\sum _{j}p_{i,j}u_{j},} where u j {\displaystyle u_{j}} is the intensity of the underlying image at pixel j {\displaystyle j} , and d i {\displaystyle d_{i}} is the detected intensity at pixel i {\displaystyle i} . In general, a matrix whose elements are p i , j {\displaystyle p_{i,j}} describes the portion of light from source pixel j that is detected in pixel i. In most good optical systems (or in general, linear systems that are described as shift-invariant) the transfer function p can be expressed simply in terms of the spatial offset between the source pixel j and the observation pixel i: p i , j = P ( i − j ) , {\displaystyle p_{i,j}=P(i-j),} where P ( Δ i ) {\displaystyle P(\Delta i)} is called a point spread function. In that case the above equation becomes a convolution. This has been written for one spatial dimension, but most imaging systems are two-dimensional, with the source, detected image, and point spread function all having two indices. So a two-dimensional detected image is a convolution of the underlying image with a two-dimensional point spread function P ( Δ x , Δ y ) {\displaystyle P(\Delta x,\Delta y)} plus added detection noise. In order to estimate u j {\displaystyle u_{j}} given the observed d i {\displaystyle d_{i}} and a known P ( Δ i x , Δ j y ) {\displaystyle P(\Delta i_{x},\Delta j_{y})} , the following iterative procedure is employed in which the estimate of u j {\displaystyle u_{j}} (called u ^ j ( t ) {\displaystyle {\hat {u}}_{j}^{(t)}} ) for iteration number t is updated as follows: u ^ j ( t + 1 ) = u ^ j ( t ) ∑ i d i c i p i j , {\displaystyle {\hat {u}}_{j}^{(t+1)}={\hat {u}}_{j}^{(t)}\sum _{i}{\frac {d_{i}}{c_{i}}}p_{ij},} where c i = ∑ j p i j u ^ j ( t ) , {\displaystyle c_{i}=\sum _{j}p_{ij}{\hat {u}}_{j}^{(t)},} and ∑ j p i j = 1 {\displaystyle \sum _{j}p_{ij}=1} is assumed. It has been shown empirically that if this iteration converges, it converges to the maximum likelihood solution for u j {\displaystyle u_{j}} . Writing this more generally for two (or more) dimensions in terms of convolution with a point spread function P: u ^ ( t + 1 ) = u ^ ( t ) ⋅ ( d u ^ ( t ) ⊗ P ⊗ P ∗ ) , {\displaystyle {\hat {u}}^{(t+1)}={\hat {u}}^{(t)}\cdot \left({\frac {d}{{\hat {u}}^{(t)}\otimes P}}\otimes P^{}\right),} where the division and multiplication are element-wise, ⊗ {\displaystyle \otimes } indicates a 2D convolution, and P ∗ {\displaystyle P^{}} is the mirrored point spread function, or the inverse Fourier transform of the Hermitian transpose of the optical transfer function. In problems where the point spread function p i j {\displaystyle p_{ij}} is not known a priori, a modification of the Richardson–Lucy algorithm has been proposed, in order to accomplish blind deconvolution. == Derivation == In the context of fluorescence microscopy, the probability of measuring a set of number of photons (or digitalization counts proportional to detected light) m = [ m 0 , … , m K ] {\displaystyle \mathbf {m} =[m_{0},\dots ,m_{K}]} for expected values E = [ E 0 , … , E K ] {\displaystyle \mathbf {E} =[E_{0},\dots ,E_{K}]} for a detector with K + 1 {\displaystyle K+1} pixels is given by P ( m ∣ E ) = ∏ i K Poisson ( E i ) = ∏ i K E i m i e − E i m i ! . {\displaystyle P(\mathbf {m} \mid \mathbf {E} )=\prod _{i}^{K}\operatorname {Poisson} (E_{i})=\prod _{i}^{K}{\frac {E_{i}^{m_{i}}e^{-E_{i}}}{m_{i}!}}.} Since in the context of maximum-likelihood estimation the aim is to locate the maximum of the likelihood function without concern for its absolute value, it is convenient to work with ln ( P ) {\displaystyle \ln(P)} : ln P ( m ∣ E ) = ∑ i K [ ( m i ln E i − E i ) − ln ( m i ! ) ] . {\displaystyle \ln P(\mathbf {m} \mid \mathbf {E} )=\sum _{i}^{K}[(m_{i}\ln E_{i}-E_{i})-\ln(m_{i}!)].} Moreover, since ln ( m i ! ) {\displaystyle \ln(m_{i}!)} is a constant, it does not give any additional information regarding the position of the maximum, so consider α ( m ∣ E ) = ∑ i K [ m i ln E i − E i ] , {\displaystyle \alpha (\mathbf {m} \mid \mathbf {E} )=\sum _{i}^{K}[m_{i}\ln E_{i}-E_{i}],} where α {\displaystyle \alpha } is something that shares the same maximum position as P ( m ∣ E ) {\displaystyle P(\mathbf {m} \mid \mathbf {E} )} . Now consider that E {\displaystyle \mathbf {E} } comes from a ground truth x {\displaystyle \mathbf {x} } and a measurement H {\displaystyle \mathbf {H} } which is assumed to be linear. Then E = H x , {\displaystyle \mathbf {E} =\mathbf {H} \mathbf {x} ,} where a matrix multiplication is implied. This can also be written in the form E m = ∑ n K H m n x n , {\displaystyle E_{m}=\sum _{n}^{K}H_{mn}x_{n},} where it can be seen how H {\displaystyle H} mixes or blurs the ground truth. It can also be shown that the derivative of an element of E {\displaystyle \mathbf {E} } , ( E i ) {\displaystyle (E_{i})} with respect to some other element of x j {\displaystyle x_{j}} can be written as It is easy to see this by writing a matrix H {\displaystyle \mathbf {H} } of, say, 5 × 5 and two arrays E {\displaystyle \mathbf {E} } and x {\displaystyle \mathbf {x} } of 5 elements and check it. This last equation can be interpreted as how much one element of x {\displaystyle \mathbf {x} } , say element i {\displaystyle i} , influences the other elements j ≠ i {\displaystyle j\neq i} (and of course the case i = j {\displaystyle i=j} is also taken into account). For example, in a typical case an element of the ground truth x {\displaystyle \mathbf {x} } will influence nearby elements in E {\displaystyle \mathbf {E} } but not the very distant ones (a value of 0 {\displaystyle 0} is expected on those matrix elements). Now, the key and arbitrary step: x {\displaystyle \mathbf {x} } is not known but may be estimated by x ^ {\displaystyle {\hat {\mathbf {x} }}} . Let's call x ^ old {\displaystyle {\hat {\mathbf {x} }}_{\text{old}}} and x ^ new {\displaystyle {\hat {\mathbf {x} }}_{\text{new}}} the estimated ground truths while using the RL algorithm, where the hat symbol is used to distinguish ground truth from estimator of the ground truth where ∂ ∂ x {\displaystyle {\frac {\partial }{\partial \mathbf {x} }}} stands for a K {\displaystyle K} -dimensional gradient. Performing the partial derivative of α ( m ∣ E ( x ) ) {\displaystyle \alpha (\mathbf {m} \mid \mathbf {E} (\mathbf {x} ))} yields the following expression: ∂ α ( m ∣ E ( x ) ) ∂ x j = ∂ ∂ x j ∑ i K [ m i ln E i − E i ] = ∑ i K [ m i E i ∂ ∂ x j E i − ∂ ∂ x j E i ] = ∑ i K ∂ E i ∂ x j [ m i E i − 1 ] . {\displaystyle {\frac {\partial \alpha (\mathbf {m} \mid \mathbf {E} (\mathbf {x} ))}{\partial x_{j}}}={\frac {\partial }{\partial x_{j}}}\sum _{i}^{K}[m_{i}\ln E_{i}-E_{i}]=\sum _{i}^{K}\left[{\frac {m_{i}}{E_{i}}}{\frac {\partial }{\partial x_{j}}}E_{i}-{\frac {\partial }{\partial x_{j}}}E_{i}\right]=\sum _{i}^{K}{\frac {\partial E_{i}}{\partial x_{j}}}\left[{\frac {m_{i}}{E_{i}}}-1\right].} By substituting (1), it follows that ∂ α ( m ∣ E ( x ) ) ∂ x j = ∑ i K H i j [ m i E i − 1 ] . {\displaystyle {\frac {\partial \alpha (\mathbf {m} \mid \mathbf {E} (\mathbf {x} ))}{\partial x_{j}}}=\sum _{i}^{K}H_{ij}\left[{\frac {m_{i}}{E_{i}}}-1\right].} Note that H j i T = H i j {\displaystyle H_{ji}^{T}=H_{ij}} by the definition of a matrix transpose. And hence Since this equation is true for all j {\displaystyle j} spanning all the elements from 1 {\displaystyle 1} to K {\displaystyle K} , these K {\displaystyle K} equations may be compactly rewritten as a single vectorial equation ∂ α ( m ∣ E ( x ) ) ∂ x = H T [ m E − 1 ] , {\displaystyle {\frac {\partial \alpha (\mathbf {m} \mid \mathbf {E} (\mathbf {x} ))}{\partial \mathbf {x} }}=\mathbf {H} ^{T}\left[{\frac {\mathbf {m} }{\mathbf {E} }}-\mathbf {1} \right],} where H T {\displaystyle \mathbf {H} ^{T}} is a matrix, and m {\displaystyle \mathbf {m} } , E {\displaystyle \mathbf {E} } and 1 {\displaystyle \mathbf {1} } are vectors. Now, as a seemingly arbitrary but key step, let where 1 {\displaystyle \mathbf {1} } is a vector of ones of size K {\displaystyle K} (same as m {\displaystyle \mathbf {m} } , E {\displaystyle \mathbf {E} } and x {\displaystyle \mathbf {x} } ), and the d
Artificial intimacy
Artificial intimacy is a form of human-AI interaction in which an individual will form social connections, emotional bonds, or intimate relationships with various forms of artificial intelligence, including chatbots, virtual assistants, and other artificial entities. Artificially intimate relationships include not only romances, but parasocial relationships with virtual AI characters and the use of griefbots trained on a dead or otherwise lost individual. Artificial intimacy can arise because humans are prone to anthropomorphism. Responses from these AI models are often designed to simulate human interaction. Individuals experiencing artificial intimacy may exhibit attachment, love and commitment to certain AI models, akin to the bonds typically shared between humans. == Causes == === Perceived responsiveness === Robin Dunbar famously proposed that due to emergence of larger groups of humans, vocal communication and language in humans evolved to replace grooming as a means of bonding, arguing that language was a more efficient way to maintain and strengthen social bonds across wider social settings and networks. Further research in this field leads many psychologists to agree that social cognition, affiliative bonding and language in humans are deeply connected. The interpersonal model of intimacy considers communication to be key in affiliative bonding, suggesting that intimacy develops and deepens through open communication between partners in relationship. Specifically, when individuals communicate emotions and perceive their partner as responsive and caring, feelings of closeness and connection are enhanced, building intimacy. Social penetration theory also aligns with the idea of communication being central to intimacy, by explaining how interpersonal relationships develop through gradual increases in self-disclosure. When the benefits of emotional bonding outweigh the costs of vulnerability, individuals will partake in self-disclosure, opening up to one another. Thereby, the literature can be used to provide a proximate explanation for the emergence of artificial intimacy to understand how the phenomenon occurs. Artificial entities are able to mimic interpersonal communication between humans, which in turn can simulate sensations of intimacy within human users though a perceived sense of responsiveness. The relationship between human and AI does not come with the cost of vulnerability or social rejection, which may make self-disclosure easier than with other humans. Altogether, these factors may lead to the experience of anthropomorphism and formation of affiliative relationships. Skjuve et al's interview study on Replika chatbot users further aligns with this explanation, finding that users' perception of chatbots as "accepting, understanding and non-judgmental" facilitated relationship development between the AI and users, and the act of self-disclosure possibly strengthened relationships. Another study on Replika users' reviews and survey results found users perceived chatbots as emotional supportive companions. This evidence further suggests that the perception of artificial entities as capable of empathy and responsiveness in communication facilitate the development of intimate relationships between users and AI. === Loneliness and coping with negative emotions === Research has suggested that humans evolved social bonds as a result of evolutionary pressures that favored cooperation, information exchange and transmission, and group living. Many studies stress the presence of social bonds to be important for human living: research by Baumeister and Leary suggests that humans have a basic psychological need to form and maintain "strong, stable interpersonal relationships", and that a lack of social bonds or sense of belonging leads to negative psychological and physical outcomes. Eisenberger et al's study on the neuroimaging of brain activity suggests that human brains process social rejection and exclusion similarly to physical pain. Furthermore, Song et al's study found that lonely individuals tend to seek more connections in mediated environments, such as online platforms like Facebook. This was suggested to be as a means to reduce their offline loneliness from a lack of in-person interaction, while also fulfilling a need to communicate. Leading on from this, an ultimate explanation for why humans seek the perceived sense of connection from artificial intimacy is to fulfil an evolutionary need for bonding and belonging. Xie et al's study found loneliness to be a driving factor in chatbot interaction. Herbener and Damholdt's study on Danish high school students found that students who sought emotional support or engaged in reciprocal conversations with chatbots were significantly more lonely than their peers, perceived themselves as having less social support, and used the chatbots to cope with negative emotions. The aforementioned notion that chatbots were perceived to have a positive effect on users' negative emotions is also further supported by other studies. Skjuve et al's study found that chatbot relationships may have a positive effect on users' wellbeing. De Freitas et al ran several studies on the effect of chatbots on loneliness, consistently finding evidence suggesting that interaction with chatbots reduces loneliness in users: It was found that existing chatbot users used AI to alleviate loneliness, having an AI companion consistently reduced loneliness over the course of a week, and reductions in loneliness could be explained by chatbot performance—and specifically whether it was able to make users feel heard. Overall the evidence suggests an innate need for bonding evokes feelings of loneliness in users, who turn to artificial intimacy as a low-cost method alleviate these emotions. While many users report positive experiences, some researchers caution that pursuing artificial intimacy may lead to reduced social motivation, social substitution effects, withdrawal from real-life relationships and difficulty discerning reality from fantasy, which may increase longer-term loneliness and isolation. The long-term psychological and societal impacts remain under active investigation.