In the field of machine learning, the universal approximation theorems (UATs) state that neural networks with a certain structure can, in principle, approximate any continuous function to any desired degree of accuracy. These theorems provide a mathematical justification for using neural networks, assuring researchers that a sufficiently large or deep network can model the complex, non-linear relationships often found in real-world data. The best-known version of the theorem applies to feedforward networks with a single hidden layer. It states that if the layer's activation function is non-polynomial (which is true for common choices like the sigmoid function or ReLU), then the network can act as a "universal approximator." Universality is achieved by increasing the number of neurons in the hidden layer, making the network "wider." Other versions of the theorem show that universality can also be achieved by keeping the network's width fixed but increasing its number of layers, making it "deeper." These are existence theorems. They guarantee that a network with the right structure exists, but they do not provide a method for finding the network's parameters (training it), nor do they specify exactly how large the network must be for a given function. Finding a suitable network remains a practical challenge that is typically addressed with optimization algorithms like backpropagation. == Setup == Artificial neural networks are combinations of multiple simple mathematical functions that implement more complicated functions from (typically) real-valued vectors to real-valued vectors. The spaces of multivariate functions that can be implemented by a network are determined by the structure of the network, the set of simple functions, and its multiplicative parameters. A great deal of theoretical work has gone into characterizing these function spaces. Most universal approximation theorems are in one of two classes. The first quantifies the approximation capabilities of neural networks with an arbitrary number of artificial neurons ("arbitrary width" case) and the second focuses on the case with an arbitrary number of hidden layers, each containing a limited number of artificial neurons ("arbitrary depth" case). In addition to these two classes, there are also universal approximation theorems for neural networks with bounded number of hidden layers and a limited number of neurons in each layer ("bounded depth and bounded width" case). == History == === Arbitrary width === The first results concerned the arbitrary width case. Ken-ichi Funahashi (May 1989) showed that Rumelhart–Hinton–Williams type backpropagation networks possess universal approximation capability with a class of sigmoidal activation functions, extending the result to multi-output mappings as well. Kurt Hornik, Maxwell Stinchcombe, and Halbert White (July 1989) showed that multilayer feed-forward networks with as few as one hidden layer are universal approximators, provided that the activation function satisfies certain conditions. George Cybenko (December 1989) independently established a related result for sigmoid activation functions using functional-analytic methods. Hornik also showed in 1991 that it is not the specific choice of the activation function but rather the multilayer feed-forward architecture itself that gives neural networks the potential of being universal approximators. Moshe Leshno et al in 1993 and later Allan Pinkus in 1999 showed that the universal approximation property is equivalent to having a nonpolynomial activation function. === Arbitrary depth === The arbitrary depth case was also studied by a number of authors such as Gustaf Gripenberg in 2003, Dmitry Yarotsky, Zhou Lu et al in 2017, Boris Hanin and Mark Sellke in 2018 who focused on neural networks with ReLU activation function. In 2020, Patrick Kidger and Terry Lyons extended those results to neural networks with general activation functions such, e.g. tanh or GeLU. One special case of arbitrary depth is that each composition component comes from a finite set of mappings. In 2024, Cai constructed a finite set of mappings, named a vocabulary, such that any continuous function can be approximated by compositing a sequence from the vocabulary. This is similar to the concept of compositionality in linguistics, which is the idea that a finite vocabulary of basic elements can be combined via grammar to express an infinite range of meanings. === Bounded depth and bounded width === The bounded depth and bounded width case was first studied by Maiorov and Pinkus in 1999. They showed that there exists an analytic sigmoidal activation function such that two hidden layer neural networks with bounded number of units in hidden layers are universal approximators. In 2018, Guliyev and Ismailov constructed a smooth sigmoidal activation function providing universal approximation property for two hidden layer feedforward neural networks with fewer units in hidden layers. In 2018, they also constructed single hidden layer networks with bounded width that are still universal approximators for univariate functions. However, this does not apply for multivariable functions. In 2022, Shen et al. obtained precise quantitative information on the depth and width required to approximate a target function by deep and wide ReLU neural networks. === Quantitative bounds === The question of minimal possible width for universality was first studied in 2021, Park et al obtained the minimum width required for the universal approximation of Lp functions using feed-forward neural networks with ReLU as activation functions. Similar results that can be directly applied to residual neural networks were also obtained in the same year by Paulo Tabuada and Bahman Gharesifard using control-theoretic arguments. In 2023, Cai obtained the optimal minimum width bound for the universal approximation. For the arbitrary depth case, Leonie Papon and Anastasis Kratsios derived explicit depth estimates depending on the regularity of the target function and of the activation function. === Kolmogorov network === The Kolmogorov–Arnold representation theorem is similar in spirit. Indeed, certain neural network families can directly apply the Kolmogorov–Arnold theorem to yield a universal approximation theorem. Robert Hecht-Nielsen showed that a three-layer neural network can approximate any continuous multivariate function. This was extended to the discontinuous case by Vugar Ismailov. In 2024, Ziming Liu and co-authors showed a practical application. === Reservoir computing and quantum reservoir computing === In reservoir computing a sparse recurrent neural network with fixed weights equipped of fading memory and echo state property is followed by a trainable output layer. Its universality has been demonstrated separately for what concerns networks of rate neurons and spiking neurons, respectively. In 2024, the framework has been generalized and extended to quantum reservoirs where the reservoir is based on qubits defined over Hilbert spaces. === Variants === Variants include discontinuous activation functions, noncompact domains, certifiable networks, random neural networks, and alternative network architectures and topologies. The universal approximation property of width-bounded networks has been studied as a dual of classical universal approximation results on depth-bounded networks. For input dimension d x {\displaystyle d_{x}} and output dimension d y {\displaystyle d_{y}} the minimum width required for the universal approximation of the Lp functions is exactly m a x { d x + 1 , d y } {\displaystyle max\{d_{x}+1,d_{y}\}} (for a ReLU network). More generally this also holds if both ReLU and a threshold activation function are used. Universal function approximation on graphs (or rather on graph isomorphism classes) by popular graph convolutional neural networks (GCNs or GNNs) can be made as discriminative as the Weisfeiler–Leman graph isomorphism test. In 2020, a universal approximation theorem result was established by Brüel-Gabrielsson, showing that graph representation with certain injective properties is sufficient for universal function approximation on bounded graphs and restricted universal function approximation on unbounded graphs, with an accompanying O ( | V | ⋅ | E | ) {\displaystyle {\mathcal {O}}(\left|V\right|\cdot \left|E\right|)} -runtime method that performed at state of the art on a collection of benchmarks (where V {\displaystyle V} and E {\displaystyle E} are the sets of nodes and edges of the graph respectively). There are also a variety of results between non-Euclidean spaces and other commonly used architectures and, more generally, algorithmically generated sets of functions, such as the convolutional neural network (CNN) architecture, radial basis functions, or neural networks with specific properties. == Arbitrary-width case == A universal approximation theorem formally states that a family of neural network funct
AIOps
AIOps (Artificial Intelligence for IT Operations) refers to the use of artificial intelligence, machine learning, and big data analytics to automate and enhance data center management. It helps organizations manage complex IT environments by detecting, diagnosing, and resolving issues more efficiently than traditional methods. == History == AIOps was first defined by Gartner in 2016, combining "artificial intelligence" and "IT operations" to describe the application of AI and machine learning to enhance IT operations. This concept was introduced to address the increasing complexity and data volume in IT environments, aiming to automate processes such as event correlation, anomaly detection, and causality determination. == Definition == AIOps refers to multi-layered, complex technology platforms that enhance and automate IT operations by using machine learning and analytics to analyze the large amounts of data collected from various DevOps devices and tools, automatically identifying and responding to issues in real-time. AIOps represents a shift from isolated IT data to aggregated observational data (e.g., job logs and monitoring systems) and interaction data (such as ticketing, events, or incident records) within a big data platform. AIOps applies machine learning and analytics to this data, resulting in continuous visibility that, when combined with automation, can lead to ongoing improvements. AIOps connects three IT disciplines (automation, service management, and performance management) to achieve continuous visibility and improvement. This new approach in modern, accelerated, and hyper-scaled IT environments leverages advances in machine learning and big data to overcome previous limitations. == Components == AIOps includes, but is not limited to, the following processes and techniques: Anomaly Detection Log Analysis Root Cause Analysis Cohort Analysis Event Correlation Predictive Analytics Hardware Failure Prediction Automated Remediation Performance Prediction Incident Management Causality Determination Queue Management Resource Scheduling and Optimization Predictive Capacity Management Resource Allocation Service Quality Monitoring Deployment and Integration Testing System Configuration Auto-diagnosis and Problem Localization Efficient ML Training and Inferencing Using LLMs for Cloud Ops Auto Service Healing Data Center Management Customer Support Security and Privacy in Cloud Operations == Comparison with DevOps == AIOps is increasingly compared with DevOps in terms of impact on operational efficiency. While DevOps focuses on collaboration between development and operations teams to accelerate software delivery, AIOps integrates artificial intelligence to enhance monitoring, automation, and predictive capabilities. Various industry analyses have explored the similarities and differences between the two approaches, including discussions on how organizations can combine them to improve incident management and resource optimization. == Results == AI optimizes IT operations in five ways: First, intelligent monitoring powered by AI helps identify potential issues before they cause outages, improving metrics like Mean Time to Detect (MTTD) by 15-20%. Second, performance data analysis and insights enable quick decision-making by ingesting and analyzing large data sets in real time. Third, AI-driven automated infrastructure optimization efficiently allocates resources and thereby reducing cloud costs. Fourth, enhanced IT service management reduces critical incidents by over 50% through AI-driven end-to-end service management. Lastly, intelligent task automation accelerates problem resolution and automates remedial actions with minimal human intervention. In 2025, Atera Networks was identified as a leader in AIOps by the software review platform G2. == AIOps vs. MLOps == AIOps tools use big data analytics, machine learning algorithms, and predictive analytics to detect anomalies, correlate events, and provide proactive insights. This automation reduces the burden on IT teams, allowing them to focus on strategic tasks rather than routine operational issues. AIOps is widely used by IT operations teams, DevOps, network administrators, and IT service management (ITSM) teams to enhance visibility and enable quicker incident resolution in hybrid cloud environments, data centers, and other IT infrastructures. In contrast to MLOps (Machine Learning Operations), which focuses on the lifecycle management and operational aspects of machine learning models, AIOps focuses on optimizing IT operations using a variety of analytics and AI-driven techniques. While both disciplines rely on AI and data-driven methods, AIOps primarily targets IT operations, whereas MLOps is concerned with the deployment, monitoring, and maintenance of ML models. == Conferences == There are several conferences that are specific to AIOps: AIOps Summit AI Dev Summit IBM Think conference
AI Mode
AI Mode is a search feature used within Google Search. In March 2025, Google introduced an experimental "AI Mode" within its search platform, enabling users to input complex, multi-part queries and receive comprehensive, AI-generated responses. This feature uses Google's Gemini model, which enhances the system's reasoning capabilities and supports multimodal inputs, including text, images, and voice. Users need to be signed in to be able to use the image generation features. Initially, AI Mode was available to Google One AI Premium subscribers in the United States, who could access it through the Search Labs platform. This phased rollout allowed Google to gather user feedback and refine the feature before a broader release.
INDIAai
INDIAai is a web portal launched by the Government of India on 07 March 2024 for artificial intelligence-related developments in India. It is known as the National AI Portal of India, which was jointly started by the Ministry of Electronics and Information Technology (MeitY), the National e-Governance Division (NeGD) and the National Association of Software and Service Companies (NASSCOM) with support from the Department of School Education and Literacy (DoSE&L) and Ministry of Human Resource Development. == History == The portal was launched on 30 May 2020, by Ravi Shankar Prasad, the Union Minister for Electronics and IT, Law and Justice and Communications, on the first anniversary of the second tenure of Prime Minister Narendra Modi-led government. A national program for the youth, 'Responsible AI for Youth', was also launched on the same day. As of 2022, the website was visited by more than 4.5 lakh users with 1.2 million page views. It has 1151 articles on artificial intelligence, 701 news stories, 98 reports, 95 case studies and 213 videos on its portal. It maintains a database on AI ecosystem of India featuring 121 government initiatives and 281 startups. In May 2022, INDIAai released a book titled 'AI for Everyone' that covers the basics of AI. Cabinet chaired by the Prime Minister Narendra Modi has approved the comprehensive national-level IndiaAI mission with a budget outlay of Rs.10,371.92 crore. The Mission will be implemented by ‘IndiaAI’ Independent Business Division (IBD) under Digital India Corporation (DIC). == Objective and features == It aims to function as a one-stop portal for all AI-related development in India. The platform publishes resources such as articles, news, interviews, and investment funding news and events for AI startups, AI companies, and educational firms related to artificial intelligence in India. It also distributes documents, case studies, and research reports. Additionally, the platform provides education and employment opportunities related to AI. It offers AI courses, both free and paid.
Automated machine learning
Automated machine learning (AutoML) is the process of automating the tasks of applying machine learning to real-world problems. It is the combination of automation and ML. AutoML potentially includes every stage from beginning with a raw dataset to building a machine learning model ready for deployment. AutoML was proposed as an artificial intelligence-based solution to the growing challenge of applying machine learning. The high degree of automation in AutoML aims to allow non-experts to make use of machine learning models and techniques without requiring them to become experts in machine learning. Automating the process of applying machine learning end-to-end additionally offers the advantages of producing simpler solutions, faster creation of those solutions, and models that often outperform hand-designed models. Common techniques used in AutoML include hyperparameter optimization, meta-learning and neural architecture search. == Comparison to the standard approach == In a typical machine learning application, practitioners have a set of input data points to be used for training. The raw data may not be in a form that all algorithms can be applied to. To make the data amenable for machine learning, an expert may have to apply appropriate data pre-processing, feature engineering, feature extraction, and feature selection methods. After these steps, practitioners must then perform algorithm selection and hyperparameter optimization to maximize the predictive performance of their model. If deep learning is used, the architecture of the neural network must also be chosen manually by the machine learning expert. Each of these steps may be challenging, resulting in significant hurdles to using machine learning. AutoML aims to simplify these steps for non-experts, and to make it easier for them to use machine learning techniques correctly and effectively. AutoML plays an important role within the broader approach of automating data science, which also includes challenging tasks such as data engineering, data exploration and model interpretation and prediction. == Targets of automation == Automated machine learning can target various stages of the machine learning process. Steps to automate are: Data preparation and ingestion (from raw data and miscellaneous formats) Column type detection; e.g., Boolean, discrete numerical, continuous numerical, or text Column intent detection; e.g., target/label, stratification field, numerical feature, categorical text feature, or free text feature Task detection; e.g., binary classification, regression, clustering, or ranking Feature engineering Feature selection Feature extraction Meta-learning and transfer learning Detection and handling of skewed data and/or missing values Model selection - choosing which machine learning algorithm to use, often including multiple competing software implementations Ensembling - a form of consensus where using multiple models often gives better results than any single model Hyperparameter optimization of the learning algorithm and featurization Neural architecture search Pipeline selection under time, memory, and complexity constraints Selection of evaluation metrics and validation procedures Problem checking Leakage detection Misconfiguration detection Analysis of obtained results Creating user interfaces and visualizations == Challenges and Limitations == There are a number of key challenges being tackled around automated machine learning. A big issue surrounding the field is referred to as "development as a cottage industry". This phrase refers to the issue in machine learning where development relies on manual decisions and biases of experts. This is contrasted to the goal of machine learning which is to create systems that can learn and improve from their own usage and analysis of the data. Basically, it's the struggle between how much experts should get involved in the learning of the systems versus how much freedom they should be giving the machines. However, experts and developers must help create and guide these machines to prepare them for their own learning. To create this system, it requires labor intensive work with knowledge of machine learning algorithms and system design. Additionally, other challenges include meta-learning and computational resource allocation.
Imo.im
imo.im is a proprietary audio/video calling and instant messaging software service. It allows sending music, video, PDFs and other files, along with various free stickers. It supports encrypted group video and voice calls with up to 20 participants. According to its developer, the service possesses over 200 million users and over 50 million messages per day are sent through it. == History == The product was created as a web-based application in 2005 for accessing multiple chat platforms, including Facebook Messenger, Google Talk, Yahoo! Messenger, and Skype chat. It was developed by Pagebites, which is a subsidiary of Singularity IM, Inc. and required a subscriber's phone number to verify the users' account. In March 2014, support for all third-party messaging networks ended. In January 2018, the app reached 500 million installs. imo.im has implemented end-to-end encryption for its chats and calls, ensuring that the conversations remain private between the sender and receiver.
Artificial intelligence in hiring
Artificial intelligence can be used to automate aspects of the job recruitment process. Advances in artificial intelligence, such as the advent of machine learning and the growth of big data, enable AI to be utilized to recruit, screen, and predict the success of applicants. Proponents of artificial intelligence in hiring claim it reduces bias, assists with finding qualified candidates, and frees up human resource workers' time for other tasks, while opponents worry that AI perpetuates inequalities in the workplace and will eliminate jobs. Despite the potential benefits, the ethical implications of AI in hiring remain a subject of debate, with concerns about algorithmic transparency, accountability, and the need for ongoing oversight to ensure fair and unbiased decision-making throughout the recruitment process. == Background == It is common for companies to use AI to automate aspects of their hiring process, especially the hospitality, finance, and tech industries. == Uses == === Screeners === Screeners are tests that allow companies to sift through a large applicant pool and extract applicants that have desirable features. What factors are used to screen applicants is a concern to ethicists and civil rights activists. A screener that favors people who have similar characteristics to those already employed at a company may perpetuate inequalities. For example, if a company that is predominantly white and male uses its employees' data to train its screener it may accidentally create a screening process that favors white, male applicants. The automation of screeners also has the potential to reduce biases. Biases against applicants with African American sounding names have been shown in multiple studies. An AI screener has the potential to limit human bias and error in the hiring process, allowing more minority applicants to be successful. === Recruitment === Recruitment involves the identification of potential applicants and the marketing of positions. AI is commonly utilized in the recruitment process because it can help boost the number of qualified applicants for positions. Companies are able to use AI to target their marketing to applicants who are likely to be good fits for a position. This often involves the use of social media sites advertising tools, which rely on AI. Facebook allows advertisers to target ads based on demographics, location, interests, behavior, and connections. Facebook also allows companies to target a "look-a-like" audience, that is the company supplies Facebook with a data set, typically the company's current employees, and Facebook will target the ad to profiles that are similar to the profiles in the data set. Additionally, job sites like Indeed, Glassdoor, and ZipRecruiter target job listings to applicants that have certain characteristics employers are looking for. Targeted advertising has many advantages for companies trying to recruit such being a more efficient use of resources, reaching a desired audience, and boosting qualified applicants. This has helped make it a mainstay in modern hiring. Who receives a targeted ad can be controversial. In hiring, the implications of targeted ads have to do with who is able to find out about and then apply to a position. Most targeted ad algorithms are proprietary information. Some platforms, like Facebook and Google, allow users to see why they were shown a specific ad, but users who do not receive the ad likely never know of its existence and also have no way of knowing why they were not shown the ad. === Interviews === Chatbots were one of the first applications of AI and are commonly used in the hiring process. Interviewees interact with chatbots to answer interview questions, and an analysis of their responses can be generated by AI. HireVue has created technology that analyzes interviewees' responses and gestures during recorded video interviews. Over 12 million interviewees have been screened by the more than 700 companies that utilize the service. == Controversies == Artificial intelligence in hiring confers many benefits, but it also has some challenges that have concerned experts. AI is only as good as the data it is using. Biases can inadvertently be baked into the data used in AI. Often companies will use data from their employees to decide what people to recruit or hire. This can perpetuate bias and lead to more homogenous workforces. Facebook Ads was an example of a platform that created such controversy for allowing business owners to specify what type of employee they are looking for. For example, job advertisements for nursing and teach could be set such that only women of a specific age group would see the advertisements. Facebook Ads has since then removed this function from its platform, citing the potential problems with the function in perpetuating biases and stereotypes against minorities. The growing use of Artificial Intelligence-enabled hiring systems has become an important component of modern talent hiring, particularly through social networks such as LinkedIn and Facebook. However, data overflow embedded in the hiring systems, based on Natural Language Processing (NLP) methods, may result in unconscious gender bias. Utilizing data driven methods may mitigate some bias generated from these systems It can also be hard to quantify what makes a good employee. This poses a challenge for training AI to predict which employees will be best. Commonly used metrics like performance reviews can be subjective and have been shown to favor white employees over black employees and men over women. Another challenge is the limited amount of available data. Employers only collect certain details about candidates during the initial stages of the hiring process. This requires AI to make determinations about candidates with very limited information to go off of. Additionally, many employers do not hire employees frequently and so have limited firm specific data to go off. To combat this, many firms will use algorithms and data from other firms in their industry. AI's reliance on applicant and current employees personal data raises privacy issues. These issues effect both the applicants and current employees, but also may have implications for third parties who are linked through social media to applicants or current employees. For example, a sweep of someone's social media will also show their friends and people they have tagged in photos or posts. == AI and the future of hiring == Artificial intelligence along with other technological advances such as improvements in robotics have placed 47% of jobs at risk of being eliminated in the near future. In 2016 the founder of the World Economic Forum, Klaus Schwab, called AI and related technology the "Fourth Industrial Revolution". According to some scholars, however, the transformative impact of AI on labor has been overstated. The "no-real-change" theory holds that an IT revolution has already occurred, but that the benefits of implementing new technologies does not outweigh the costs associated with adopting them. This theory claims that the result of the IT revolution is thus much less impactful than had originally been forecasted. Other scholars refute this theory claiming that AI has already led to significant job loss for unskilled labor and that it will eliminate middle skill and high skill jobs in the future. This position is based around the idea that AI is not yet a technology of general use and that any potential 4th industrial revolution has not fully occurred. A third theory holds that the effect of AI and other technological advances is too complicated to yet be understood. This theory is centered around the idea that while AI will likely eliminate jobs in the short term it will also likely increase the demand for other jobs. The question then becomes will the new jobs be accessible to people and will they emerge near when jobs are eliminated. == AI use in hiring for candidates == Job seekers now commonly encounter AI-driven tools at multiple stages, including automated resume parsing, video interview analysis, chatbots for frequently asked questions, and real‑time application updates. Some candidates also employ AI career agents, designed to optimize job searches, tailor applications, and interface with hiring teams. A 2025 Australian study found that AI-driven video interviews exhibited transcription error rates of up to 22% for non‑native speakers and those with speech-related disabilities, raising concerns of discrimination. A 2017 study in the Journal of Sociology found persistent gender and racial disparities in AI screening tools, even when fairness interventions are applied. Industry observers describe a growing “AI arms race” in recruitment, where both employers and candidates increasingly rely on automated agents. Employers use recruiting systems to source and filter applicants, while candidates deploy AI agents to prepare and submit applications. == Regulations == The Artifici