In mathematics a radial basis function (RBF) is a real-valued function φ {\textstyle \varphi } whose value depends only on the distance between the input and some fixed point, either the origin, so that φ ( x ) = φ ^ ( ‖ x ‖ ) {\textstyle \varphi (\mathbf {x} )={\hat {\varphi }}(\left\|\mathbf {x} \right\|)} , or some other fixed point c {\textstyle \mathbf {c} } , called a center, so that φ ( x ) = φ ^ ( ‖ x − c ‖ ) {\textstyle \varphi (\mathbf {x} )={\hat {\varphi }}(\left\|\mathbf {x} -\mathbf {c} \right\|)} . Any function φ {\textstyle \varphi } that satisfies the property φ ( x ) = φ ^ ( ‖ x ‖ ) {\textstyle \varphi (\mathbf {x} )={\hat {\varphi }}(\left\|\mathbf {x} \right\|)} is a radial function. The distance is usually Euclidean distance, although other metrics are sometimes used. They are often used as a collection { φ k } k {\displaystyle \{\varphi _{k}\}_{k}} which forms a basis for some function space of interest, hence the name. Sums of radial basis functions are typically used to approximate given functions. This approximation process can also be interpreted as a simple kind of neural network; this was the context in which they were originally applied to machine learning, in work by David Broomhead and David Lowe in 1988, which stemmed from Michael J. D. Powell's seminal research from 1977. RBFs are also used as a kernel in support vector classification. The technique has proven effective and flexible enough that radial basis functions are now applied in a variety of engineering applications. == Definition == A radial function is a function φ : [ 0 , ∞ ) → R {\textstyle \varphi :[0,\infty )\to \mathbb {R} } . When paired with a norm ‖ ⋅ ‖ : V → [ 0 , ∞ ) {\textstyle \|\cdot \|:V\to [0,\infty )} on a vector space, a function of the form φ c = φ ( ‖ x − c ‖ ) {\textstyle \varphi _{\mathbf {c} }=\varphi (\|\mathbf {x} -\mathbf {c} \|)} is said to be a radial kernel centered at c ∈ V {\textstyle \mathbf {c} \in V} . A radial function and the associated radial kernels are said to be radial basis functions if, for any finite set of nodes { x k } k = 1 n ⊆ V {\displaystyle \{\mathbf {x} _{k}\}_{k=1}^{n}\subseteq V} , all of the following conditions are true: === Examples === Commonly used types of radial basis functions include (writing r = ‖ x − x i ‖ {\textstyle r=\left\|\mathbf {x} -\mathbf {x} _{i}\right\|} and using ε {\textstyle \varepsilon } to indicate a shape parameter that can be used to scale the input of the radial kernel): == Approximation == Radial basis functions are typically used to build up function approximations of the form where the approximating function y ( x ) {\textstyle y(\mathbf {x} )} is represented as a sum of N {\displaystyle N} radial basis functions, each associated with a different center x i {\textstyle \mathbf {x} _{i}} , and weighted by an appropriate coefficient w i . {\textstyle w_{i}.} The weights w i {\textstyle w_{i}} can be estimated using the matrix methods of linear least squares, because the approximating function is linear in the weights w i {\textstyle w_{i}} . Approximation schemes of this kind have been particularly used in time series prediction and control of nonlinear systems exhibiting sufficiently simple chaotic behaviour and 3D reconstruction in computer graphics (for example, hierarchical RBF and Pose Space Deformation). == RBF Network == The sum can also be interpreted as a rather simple single-layer type of artificial neural network called a radial basis function network, with the radial basis functions taking on the role of the activation functions of the network. It can be shown that any continuous function on a compact interval can in principle be interpolated with arbitrary accuracy by a sum of this form, if a sufficiently large number N {\textstyle N} of radial basis functions is used. The approximant y ( x ) {\textstyle y(\mathbf {x} )} is differentiable with respect to the weights w i {\textstyle w_{i}} . The weights could thus be learned using any of the standard iterative methods for neural networks. Using radial basis functions in this manner yields a reasonable interpolation approach provided that the fitting set has been chosen such that it covers the entire range systematically (equidistant data points are ideal). However, without a polynomial term that is orthogonal to the radial basis functions, estimates outside the fitting set tend to perform poorly. == RBFs for PDEs == Radial basis functions are used to approximate functions and so can be used to discretize and numerically solve Partial Differential Equations (PDEs). This was first done in 1990 by E. J. Kansa who developed the first RBF based numerical method. It is called the Kansa method and was used to solve the elliptic Poisson equation and the linear advection-diffusion equation. The function values at points x {\displaystyle \mathbf {x} } in the domain are approximated by the linear combination of RBFs: The derivatives are approximated as such: where N {\displaystyle N} are the number of points in the discretized domain, d {\displaystyle d} the dimension of the domain and λ {\displaystyle \lambda } the scalar coefficients that are unchanged by the differential operator. Different numerical methods based on Radial Basis Functions were developed thereafter. Some methods are the RBF-FD method, the RBF-QR method and the RBF-PUM method.
Google Gadgets
Google Gadgets are dynamic web content that can be embedded on a web page. They can be added to and interact strongly with Google's iGoogle personalized home page (discontinued in November 2013, although iGoogle Gadgets still work on other websites) and the Google Desktop (discontinued in September 2011) application, as well as Google Wave (also no longer supported by Google) and Google Sites. Webmasters can add and customize a gadget to their own business or personal web site, a process called "syndication". Gadgets are developed by Google and third-party developers using the Google Gadgets API, using basic web technologies such as XML and JavaScript. == Multi-user persistent - Wave Gadgets == With the advent of Google Wave (now Apache Wave), gadgets became able to have persistent storage and multi-user capabilities and better state management. Gadgets using Google Wave in this way were simply known as 'Wave Gadgets'. For instance, a game written using a Google Gadget could use Google Wave technology to record a list of users and high scores without having to worry about how to permanently store the scores on a hosted server. The use of Google Wave would give the gadget multi-user and permanent storage capabilities. For example, scores could be stored in a Google Wave hosted permanently by Google at no cost to the user. As of early 2013, Google Gadgets were deprecated in Google Spreadsheets. Shortly after, they were removed from all spreadsheets. == Technology == Google Gadgets are written in XML and can have HTML and JavaScript components, and were able to use Google Wave. Here is an example of a Hello World program written using Google Gadget technology. Google Gadgets API is a Google API which allows developers to create Google Gadgets easily.
Business process automation
Business process automation (BPA), also known as business automation, refers to the technology-enabled automation of business processes. == Development approaches == There are three main approaches to developing BPA: traditional business process automation involves developing BPA software in a programming language for integrating relevant applications in the digital ecosystem to execute a given process; robotic process automation uses software robots (also called agents, bots, or workers) to emulate human-computer interaction for executing a combination of processes, activities, transactions, and tasks in one or more unrelated software systems; hyperautomation (also called intelligent automation (IA), intelligent process automation (IPA), integrated automation platform (IAP), and cognitive automation (CA) combines business process automation, artificial intelligence (AI), and machine learning (ML) to discover, validate, and execute organizational processes automatically with no or minimal human intervention. == Deployment == BPA toolsets vary in capability. With the increasing adoption of artificial intelligence (AI), organizations are implementing AI-driven technologies that can process natural language, interpret unstructured datasets, and interact with users. These systems are designed to adapt to new types of problems with reduced reliance on human intervention. == Business process management implementation == A business process management system differs from BPA. However, it is possible to implement automation based on a BPM implementation. The methods to achieve this vary, from writing custom application code to using specialist BPA tools. == Robotic process automation == Robotic process automation (RPA) involves the deployment of attended or unattended software agents in an organization's environment. These software agents, or robots, are programmed to perform predefined structured and repetitive sets of business tasks or processes. Robotic process automation is designed to streamline workflows by delegating repetitive tasks to software agents, allowing human workers to focus on more complex and strategic activities. BPA providers typically focus on different industry sectors, but the underlying approach is generally similar in that they aim to provide the shortest route to automation by interacting with the user interface rather than modifying the application code or database behind it. == Use of artificial intelligence == Artificial intelligence software robots are used to handle unstructured data sets (like images, texts, audios) and are often deployed after implementing robotic process automation. They can, for instance, generate an automatic transcript from a video. The combination of automation and artificial intelligence (AI) enables autonomy for robots, along with the capability to perform cognitive tasks. At this stage, robots can learn and improve processes by analyzing and adapting them.
Inductive probability
Inductive probability attempts to give the probability of future events based on past events. It is the basis for inductive reasoning, and gives the mathematical basis for learning and the perception of patterns. It is a source of knowledge about the world. There are three sources of knowledge: inference, communication, and deduction. Communication relays information found using other methods. Deduction establishes new facts based on existing facts. Inference establishes new facts from data. Its basis is Bayes' theorem. Information describing the world is written in a language. For example, a simple mathematical language of propositions may be chosen. Sentences may be written down in this language as strings of characters. But in the computer it is possible to encode these sentences as strings of bits (1s and 0s). Then the language may be encoded so that the most commonly used sentences are the shortest. This internal language implicitly represents probabilities of statements. Occam's razor says the "simplest theory, consistent with the data is most likely to be correct". The "simplest theory" is interpreted as the representation of the theory written in this internal language. The theory with the shortest encoding in this internal language is most likely to be correct. == History == Probability and statistics was focused on probability distributions and tests of significance. Probability was formal, well defined, but limited in scope. In particular its application was limited to situations that could be defined as an experiment or trial, with a well defined population. Bayes's theorem is named after Rev. Thomas Bayes 1701–1761. Bayesian inference broadened the application of probability to many situations where a population was not well defined. But Bayes' theorem always depended on prior probabilities, to generate new probabilities. It was unclear where these prior probabilities should come from. Ray Solomonoff developed algorithmic probability which gave an explanation for what randomness is and how patterns in the data may be represented by computer programs, that give shorter representations of the data circa 1964. Chris Wallace and D. M. Boulton developed minimum message length circa 1968. Later Jorma Rissanen developed the minimum description length circa 1978. These methods allow information theory to be related to probability, in a way that can be compared to the application of Bayes' theorem, but which give a source and explanation for the role of prior probabilities. Marcus Hutter combined decision theory with the work of Ray Solomonoff and Andrey Kolmogorov to give a theory for the Pareto optimal behavior for an Intelligent agent, circa 1998. === Minimum description/message length === The program with the shortest length that matches the data is the most likely to predict future data. This is the thesis behind the minimum message length and minimum description length methods. At first sight Bayes' theorem appears different from the minimimum message/description length principle. At closer inspection it turns out to be the same. Bayes' theorem is about conditional probabilities, and states the probability that event B happens if firstly event A happens: P ( A ∧ B ) = P ( B ) ⋅ P ( A | B ) = P ( A ) ⋅ P ( B | A ) {\displaystyle P(A\land B)=P(B)\cdot P(A|B)=P(A)\cdot P(B|A)} becomes in terms of message length L, L ( A ∧ B ) = L ( B ) + L ( A | B ) = L ( A ) + L ( B | A ) . {\displaystyle L(A\land B)=L(B)+L(A|B)=L(A)+L(B|A).} This means that if all the information is given describing an event then the length of the information may be used to give the raw probability of the event. So if the information describing the occurrence of A is given, along with the information describing B given A, then all the information describing A and B has been given. ==== Overfitting ==== Overfitting occurs when the model matches the random noise and not the pattern in the data. For example, take the situation where a curve is fitted to a set of points. If a polynomial with many terms is fitted then it can more closely represent the data. Then the fit will be better, and the information needed to describe the deviations from the fitted curve will be smaller. Smaller information length means higher probability. However, the information needed to describe the curve must also be considered. The total information for a curve with many terms may be greater than for a curve with fewer terms, that has not as good a fit, but needs less information to describe the polynomial. === Inference based on program complexity === Solomonoff's theory of inductive inference is also inductive inference. A bit string x is observed. Then consider all programs that generate strings starting with x. Cast in the form of inductive inference, the programs are theories that imply the observation of the bit string x. The method used here to give probabilities for inductive inference is based on Solomonoff's theory of inductive inference. ==== Detecting patterns in the data ==== If all the bits are 1, then people infer that there is a bias in the coin and that it is more likely also that the next bit is 1 also. This is described as learning from, or detecting a pattern in the data. Such a pattern may be represented by a computer program. A short computer program may be written that produces a series of bits which are all 1. If the length of the program K is L ( K ) {\displaystyle L(K)} bits then its prior probability is, P ( K ) = 2 − L ( K ) {\displaystyle P(K)=2^{-L(K)}} The length of the shortest program that represents the string of bits is called the Kolmogorov complexity. Kolmogorov complexity is not computable. This is related to the halting problem. When searching for the shortest program some programs may go into an infinite loop. ==== Considering all theories ==== The Greek philosopher Epicurus is quoted as saying "If more than one theory is consistent with the observations, keep all theories". As in a crime novel all theories must be considered in determining the likely murderer, so with inductive probability all programs must be considered in determining the likely future bits arising from the stream of bits. Programs that are already longer than n have no predictive power. The raw (or prior) probability that the pattern of bits is random (has no pattern) is 2 − n {\displaystyle 2^{-n}} . Each program that produces the sequence of bits, but is shorter than the n is a theory/pattern about the bits with a probability of 2 − k {\displaystyle 2^{-k}} where k is the length of the program. The probability of receiving a sequence of bits y after receiving a series of bits x is then the conditional probability of receiving y given x, which is the probability of x with y appended, divided by the probability of x. ==== Universal priors ==== The programming language affects the predictions of the next bit in the string. The language acts as a prior probability. This is particularly a problem where the programming language codes for numbers and other data types. Intuitively we think that 0 and 1 are simple numbers, and that prime numbers are somehow more complex than numbers that may be composite. Using the Kolmogorov complexity gives an unbiased estimate (a universal prior) of the prior probability of a number. As a thought experiment an intelligent agent may be fitted with a data input device giving a series of numbers, after applying some transformation function to the raw numbers. Another agent might have the same input device with a different transformation function. The agents do not see or know about these transformation functions. Then there appears no rational basis for preferring one function over another. A universal prior insures that although two agents may have different initial probability distributions for the data input, the difference will be bounded by a constant. So universal priors do not eliminate an initial bias, but they reduce and limit it. Whenever we describe an event in a language, either using a natural language or other, the language has encoded in it our prior expectations. So some reliance on prior probabilities are inevitable. A problem arises where an intelligent agent's prior expectations interact with the environment to form a self reinforcing feed back loop. This is the problem of bias or prejudice. Universal priors reduce but do not eliminate this problem. === Universal artificial intelligence === The theory of universal artificial intelligence applies decision theory to inductive probabilities. The theory shows how the best actions to optimize a reward function may be chosen. The result is a theoretical model of intelligence. It is a fundamental theory of intelligence, which optimizes the agents behavior in, Exploring the environment; performing actions to get responses that broaden the agents knowledge. Competing or co-operating with another agent; games. Balancing short and long term rewards. In general no agent will always provi
Workplace impact of artificial intelligence
The impact of artificial intelligence on workers includes both applications to improve worker safety and health, and potential hazards that must be controlled. One potential application is using AI to eliminate hazards by removing humans from hazardous situations that involve risk of stress, overwork, or musculoskeletal injuries. Predictive analytics may also be used to identify conditions that may lead to hazards such as fatigue, repetitive strain injuries, or toxic substance exposure, leading to earlier interventions. Another is to streamline workplace safety and health workflows through automating repetitive tasks, enhancing safety training programs through virtual reality, or detecting and reporting near misses. When used in the workplace, AI also presents the possibility of new hazards. These may arise from machine learning techniques leading to unpredictable behavior and inscrutability in their decision-making, or from cybersecurity and information privacy issues. Many hazards of AI are psychosocial due to its potential to cause changes in work organization. These include increased monitoring leading to micromanagement, algorithms unintentionally or intentionally mimicking undesirable human biases, and assigning blame for machine errors to the human operator instead. AI may also lead to physical hazards in the form of human–robot collisions, and ergonomic risks of control interfaces and human–machine interactions. Hazard controls include cybersecurity and information privacy measures, communication and transparency with workers about data usage, and limitations on collaborative robots. From a workplace safety and health perspective, only "weak" or "narrow" AI that is tailored to a specific task is relevant, as there are many examples that are currently in use or expected to come into use in the near future. Certain digital technologies are predicted to result in job losses. Starting in the 2020s, the adoption of modern robotics has led to net employment growth. However, many businesses anticipate that automation, or employing robots would result in job losses in the future. This is especially true for companies in Central and Eastern Europe. Other digital technologies, such as platforms or big data, are projected to have a more neutral impact on employment. A large number of tech workers have been laid off starting in 2023; many such job cuts have been attributed to artificial intelligence. == Health and safety applications == In order for any potential AI health and safety application to be adopted, it requires acceptance by both managers and workers. For example, worker acceptance may be diminished by concerns about information privacy, or from a lack of trust and acceptance of the new technology, which may arise from inadequate transparency or training. Alternatively, managers may emphasize increases in economic productivity rather than gains in worker safety and health when implementing AI-based systems. === Eliminating hazardous tasks === AI may increase the scope of work tasks where a worker can be removed from a situation that carries risk. In a sense, while traditional automation can replace the functions of a worker's body with a robot, AI effectively replaces the functions of their brain with a computer. Hazards that can be avoided include stress, overwork, musculoskeletal injuries, and boredom. This can expand the range of affected job sectors into white-collar and service sector jobs such as in medicine, finance, and information technology. === Analytics to reduce risk === Machine learning is used for people analytics to make predictions about worker behavior to assist management decision-making, such as hiring and performance assessment. These could also be used to improve worker health. The analytics may be based on inputs such as online activities, monitoring of communications, location tracking, and voice analysis and body language analysis of filmed interviews. For example, sentiment analysis may be used to spot fatigue to prevent overwork. Decision support systems have a similar ability to be used to, for example, prevent industrial disasters or make disaster response more efficient. For manual material handling workers, predictive analytics and artificial intelligence may be used to reduce musculoskeletal injury. Traditional guidelines are based on statistical averages and are geared towards anthropometrically typical humans. The analysis of large amounts of data from wearable sensors may allow real-time, personalized calculation of ergonomic risk and fatigue management, as well as better analysis of the risk associated with specific job roles. Wearable sensors may also enable earlier intervention against exposure to toxic substances than is possible with area or breathing zone testing on a periodic basis. Furthermore, the large data sets generated could improve workplace health surveillance, risk assessment, and research. === Streamlining safety and health workflows === AI has also been used to attempt to make the workplace safety and health workflow more efficient. One example is coding of workers' compensation claims, which are submitted in a prose narrative form and must manually be assigned standardized codes. AI is being investigated to perform this task faster, more cheaply, and with fewer errors. == Hazards == There are several broad aspects of AI that may give rise to specific hazards. The risks depend on implementation rather than the mere presence of AI. Systems using sub-symbolic AI such as machine learning may behave unpredictably and are more prone to inscrutability in their decision-making. This is especially true if a situation is encountered that was not part of the AI's training dataset, and is exacerbated in environments that are less structured. Undesired behavior may also arise from flaws in the system's perception (arising either from within the software or from sensor degradation), knowledge representation and reasoning, or from software bugs. They may arise from improper training, such as a user applying the same algorithm to two problems that do not have the same requirements. Machine learning applied during the design phase may have different implications than that applied at runtime. Systems using symbolic AI are less prone to unpredictable behavior. The use of AI also increases cybersecurity risks relative to platforms that do not use AI, and information privacy concerns about collected data may pose a hazard to workers. === Psychosocial === Psychosocial hazards are those that arise from the way work is designed, organized, and managed, or its economic and social contexts, rather than arising from a physical substance or object. They cause not only psychiatric and psychological outcomes such as occupational burnout, anxiety disorders, and depression, but they can also cause physical injury or illness such as cardiovascular disease or musculoskeletal injury. Many hazards of AI are psychosocial in nature due to its potential to cause changes in work organization, in terms of increasing complexity and interaction between different organizational factors. However, psychosocial risks are often overlooked by designers of advanced manufacturing systems. Einola and Khoreva explore how different organizational groups perceive and interact with AI technologies. Their research shows that successful AI integration depends on human ownership and contextual understanding. They caution against blind technological optimism and stress the importance of tailoring AI use to specific workplace ecosystems. This perspective reinforces the need for inclusive design and transparent implementation strategies. ==== Changes in work practices ==== Over-reliance on AI tools may lead to deskilling of some professions. When AI becomes a substitute for traditional peer collaboration and mentorship, there is a risk of diminishing opportunities for interpersonal skill development and team-based learning. Increased monitoring may lead to micromanagement and thus to stress and anxiety. A perception of surveillance may also lead to stress. Controls for these include consultation with worker groups, extensive testing, and attention to introduced bias. Wearable sensors, activity trackers, and augmented reality may also lead to stress from micromanagement, both for assembly line workers and gig workers. Gig workers also lack the legal protections and rights of formal workers. Newell & Marabelli argue that AI alters power dynamics and employee autonomy, requiring a more nuanced understanding of its social and organizational implications. There is also the risk of people being forced to work at a robot's pace, or to monitor robot performance at nonstandard hours. A 2025 preprint paper based on users' interactions with the AI chatbot Microsoft Copilot identified forty jobs that the author's claimed had high overlaps with the capabilities of AI. Some media outlets used this paper to report on jobs becoming obsolete. Cri
Double descent
Double descent in statistics and machine learning is the phenomenon where a model's error rate on the test set initially decreases with the number of parameters, then peaks, then decreases again. This phenomenon has been considered surprising, as it contradicts assumptions about overfitting in classical machine learning. The increase usually occurs near the interpolation threshold, where the number of parameters is the same as the number of training data points (the model is just large enough to fit the training data). Or, more precisely, it is the maximum number of samples on which the model/training procedure achieves approximately on average 0 training error. == History == Early observations of what would later be called double descent in specific models date back to 1989. The term "double descent" was coined by Belkin et. al. in 2019, when the phenomenon gained popularity as a broader concept exhibited by many models. The latter development was prompted by a perceived contradiction between the conventional wisdom that too many parameters in the model result in a significant overfitting error (an extrapolation of the bias–variance tradeoff), and the empirical observations in the 2010s that some modern machine learning techniques tend to perform better with larger models. == Theoretical models == Double descent occurs in linear regression with isotropic Gaussian covariates and isotropic Gaussian noise. A model of double descent at the thermodynamic limit has been analyzed using the replica trick, and the result has been confirmed numerically. A number of works have suggested that double descent can be explained using the concept of effective dimension: While a network may have a large number of parameters, in practice only a subset of those parameters are relevant for generalization performance, as measured by the local Hessian curvature. This explanation is formalized through PAC-Bayes compression-based generalization bounds, which show that less complex models are expected to generalize better under a Solomonoff prior.
Timeline of artificial intelligence risks in global finance
The following article is a broad timeline of the course of events related to artificial intelligence risks in global finance. The AI boom has led to concerns including the existential risk from artificial intelligence, as the uptake on applications of artificial intelligence increases. By late 2025, global finance and artificial intelligence were "deeply intertwined". A June 2025 Menlo Ventures report raised concerns about the sustainability of future revenue and long-term profitability of AI, given the relatively low rate of consumer monetization. == 2017 == 30 NovemberThe New York Times said that new AI reports by McKinsey & Company, the National Bureau of Economic Research, and an AI Index created by university researchers, indicated an early AI boom. The Index built on a project—"The One Hundred Year Study on Artificial Intelligence" launched in 2014. == 2018 == 2018 was a year of incremental AI growth in finance. == 2022 == The release of ChatGPT by OpenAI became the catalyst for an artificial intelligence boom that continues to remake the global economy. According to a European Central Bank report, public interest in AI increased rapidly as evidenced with rising Google searches, AI jobs, models, patents, and innovations since late 2022. At that time Europe led the US in the size of its AI workforce. == 2023 == The regulatory body, the International Monetary Fund (IMF), published their report, "Generative Artificial Intelligence in Finance: Risk Considerations", drawing attention to oversight gaps and the need for regulations. The report explores the risks posed by using generative artificial intelligence (GenAI) systems in the financial sector including "broader risks to financial stability." == 2024 == January 12 In January 2024 Bloomberg's published its list of the "Magnificent Seven" Big Tech companies on the stock market based on their strength, size and market capitalization:Apple, Microsoft, Alphabet (Google), Amazon, Meta Platforms (Facebook), Nvidia, and Tesla. 21 June During the AI boom, Nvidia became the world's most valuable company, surpassing Microsoft, as its value increased to over US$4 trillion. In 2023 and 2024, the "Magnificent Seven" stocks were the primary drivers behind the increase in equity indexes, according to Reuters. == 2025 == === January === 23 January President Donald Trump's AI policy was announced calling for United States global leadership in artificial intelligence. The Economist noted that this politic shift in which the United States seeks "global dominance" in AI includes trimming regulations and assisting in expansion of infrastructure and increase in number of AI workers. Governments of Gulf nations were also investing trillions of dollars in AI. 27 January Against the backdrop of a tech war between China and the United States over AI dominance, within days of the launch of China's free DeepSeek App, it was the most downloaded app in the United States, rising to the first place in the Apple app store. President Trump responded immediately, saying this "sudden rise" should be a "wake-up" call to the United States, and called on US companies to be more competitive. === June === 26 June In their June 2025 report, Menlo Ventures estimated that only about 3% of consumers paid for artificial intelligence-related services, representing about $USD12 billion in annual spending. This is relatively low in contrast to the massive capital expenditure by AI infrastructure companies, which raises concerns about revenue sustainability and long-term profitability. === July === 23 July The Trump administration launched the US AI Action Plan, positioning the United States in a high-stakes technological race with China for global dominance in artificial intelligence, emphasizing that neither nation can afford to fall behind due to the exponential nature of AI advancement. The plan, a new government website and policy speech called for accelerated AI adoption across federal agencies, and a number of initiatives to make is easier for AI infrastructure expansion, and other measures to ensure American leadership in AI standards. Some leading experts warned that the administration failed to provide sufficient regulations and safeguards for AI safety. Concerns were raised about the negative impacts of cuts to research funding and tightened visa policies for scientists, potentially undermining public trust and America's ability to compete internationally. === September === 7 September The Economist cautioned that AI revenues are relatively modest compared to the high cost and investments in the creation of new data centers. Even Sam Altman, OpenAI CEO and one of the leading figures of the AI boom,, raised concerns about investors' outsized hopes for financial returns. At the same time, history has shown that new technologies, like railways and electricity, endured and spread after the initial hype faded. 12 September Economists warn that U.S. households' direct and indirect investments—mutual funds or retirement plans—in the stock market reached an unprecedented historically high level, now representing 45% of all financial assets, or about $USD51.2 trillion. Compared to the Dot-com bubble this represents a sharp increase in exposure. This makes U.S. households vulnerable to market downturns which in turn would result in decreasing consumer spending. U.S. household net worth rose to a record $176.3 trillion in the second quarter, an increase of $7.3 trillion since early 2025 and about $46 trillion higher than before the pandemic. Federal Reserve data attribute the surge primarily to gains in stock markets and housing values. However, the rise in wealth on paper coincided with increased household borrowing and growing government debt. 18 September Questions were being raised about how quickly the data centers, chips, servers, and GPUs assets of major AI companies will depreciate in value. Comparisons have been made to the Railway Mania in the aftermath of the stock market bubble where a valuable physical infrastructure remained standing, and the telecoms crash after the dot-com bubble which left fiber networks. 28 September There were warnings that record-high American stock ownership during the AI-fueled market boom is a red flag for systemic risk, as the current concentration in equities exceeds levels seen before the dot-com bubble burst in 2000, and could amplify the impact of any future stock market correction. === October === 3 October In 2025 alone, venture capitalists invested almost $USD200 billion in the artificial intelligence sector. 29 October Nvidia was the first company in the world to be valued at US$5 trillion, largely due to AI demand and strategic partnerships with leading technology and AI firms. Nvidia's increase in value was "meteoric". === November === 2 November Forbes reported that, since April, the 'Magnificent Seven' tech giants together contributed over 40% of the S&P 500's return, highlighting their outsized influence and the growing impact of AI on market valuations. CNN warned that while there is a current benefit to investors, with such a high concentration in the S&P 500, they are highly exposed to the fate of the Mag Seven. 2 November Globally there are 11,000 datacentres—huge campuses for AI infrastructure, including thousands of chips, GPUS, and servers. This represents a 500% increase over the last two decades. It is anticipated that $3USDtn more will be spent on increasing that number over the next two or three years. 5 November Concerns about the potential for a market bubble were raised as six of the AI-related Big Tech "Magnificent Seven"—that contribute to the AI boom—reported losing ground in the stock market. Global markets and artificial intelligence have become "deeply intertwined", according to a Reuters report. As of November 2025, more than 50% of the 20 largest S&P firms were deeply exposed to AI. In contrast, in 2000, the 20 S&P 500 firms represented 39% of its total value only 11 of these companies were exposed to the internet. If AI fails to deliver strong returns on their investments, these top S&P firms would be significantly impacted, according to the Economist. Analysts suggest that the AI market in 2025 may not behave like a traditional one, as investors are simultaneously aware of the risks and driven by the potential for outsized rewards. Leading AI labs may believe that the first company to achieve artificial general intelligence (AGI), when an AI system surpasses all human cognitive abilities and becomes capable of self-improvement—could dominate the future of technology and finance. While some have estimated that the potential value of such a breakthrough could be as high as $1.46 quadrillion, this figure is speculative and widely debated. 5 November Bloomberg described Nvidia's H100 Hopper-Blackwell AI chips as the "King of AI chips". Nvidia dominates the AI chip market with over 78% of the market share because of both speed and cost. According to B