In artificial intelligence, apprenticeship learning (or learning from demonstration or imitation learning) is the process of learning by observing an expert. It can be viewed as a form of supervised learning, where the training dataset consists of task executions by a demonstration teacher. == Mapping function approach == Mapping methods try to mimic the expert by forming a direct mapping either from states to actions, or from states to reward values. For example, in 2002 researchers used such an approach to teach an AIBO robot basic soccer skills. === Inverse reinforcement learning approach === Inverse reinforcement learning (IRL) is the process of deriving a reward function from observed behavior. While ordinary "reinforcement learning" involves using rewards and punishments to learn behavior, in IRL the direction is reversed, and a robot observes a person's behavior to figure out what goal that behavior seems to be trying to achieve. The IRL problem can be defined as: Given 1) measurements of an agent's behaviour over time, in a variety of circumstances; 2) measurements of the sensory inputs to that agent; 3) a model of the physical environment (including the agent's body): Determine the reward function that the agent is optimizing. IRL researcher Stuart J. Russell proposes that IRL might be used to observe humans and attempt to codify their complex "ethical values", in an effort to create "ethical robots" that might someday know "not to cook your cat" without needing to be explicitly told. The scenario can be modeled as a "cooperative inverse reinforcement learning game", where a "person" player and a "robot" player cooperate to secure the person's implicit goals, despite these goals not being explicitly known by either the person nor the robot. In 2017, OpenAI and DeepMind applied deep learning to the cooperative inverse reinforcement learning in simple domains such as Atari games and straightforward robot tasks such as backflips. The human role was limited to answering queries from the robot as to which of two different actions were preferred. The researchers found evidence that the techniques may be economically scalable to modern systems. Apprenticeship via inverse reinforcement learning (AIRP) was developed by in 2004 Pieter Abbeel, Professor in Berkeley's EECS department, and Andrew Ng, Associate Professor in Stanford University's Computer Science Department. AIRP deals with "Markov decision process where we are not explicitly given a reward function, but where instead we can observe an expert demonstrating the task that we want to learn to perform". AIRP has been used to model reward functions of highly dynamic scenarios where there is no obvious reward function intuitively. Take the task of driving for example, there are many different objectives working simultaneously - such as maintaining safe following distance, a good speed, not changing lanes too often, etc. This task, may seem easy at first glance, but a trivial reward function may not converge to the policy wanted. One domain where AIRP has been used extensively is helicopter control. While simple trajectories can be intuitively derived, complicated tasks like aerobatics for shows has been successful. These include aerobatic maneuvers like - in-place flips, in-place rolls, loops, hurricanes and even auto-rotation landings. This work was developed by Pieter Abbeel, Adam Coates, and Andrew Ng - "Autonomous Helicopter Aerobatics through Apprenticeship Learning" === System model approach === System models try to mimic the expert by modeling world dynamics. == Plan approach == The system learns rules to associate preconditions and postconditions with each action. In one 1994 demonstration, a humanoid learns a generalized plan from only two demonstrations of a repetitive ball collection task. == Example == Learning from demonstration is often explained from a perspective that the working Robot-control-system is available and the human-demonstrator is using it. And indeed, if the software works, the Human operator takes the robot-arm, makes a move with it, and the robot will reproduce the action later. For example, he teaches the robot-arm how to put a cup under a coffeemaker and press the start-button. In the replay phase, the robot is imitating this behavior 1:1. But that is not how the system works internally; it is only what the audience can observe. In reality, Learning from demonstration is much more complex. One of the first works on learning by robot apprentices (anthropomorphic robots learning by imitation) was Adrian Stoica's PhD thesis in 1995. In 1997, robotics expert Stefan Schaal was working on the Sarcos robot-arm. The goal was simple: solve the pendulum swingup task. The robot itself can execute a movement, and as a result, the pendulum is moving. The problem is, that it is unclear what actions will result into which movement. It is an Optimal control-problem which can be described with mathematical formulas but is hard to solve. The idea from Schaal was, not to use a Brute-force solver but record the movements of a human-demonstration. The angle of the pendulum is logged over three seconds at the y-axis. This results into a diagram which produces a pattern. In computer animation, the principle is called spline animation. That means, on the x-axis the time is given, for example 0.5 seconds, 1.0 seconds, 1.5 seconds, while on the y-axis is the variable given. In most cases it's the position of an object. In the inverted pendulum it is the angle. The overall task consists of two parts: recording the angle over time and reproducing the recorded motion. The reproducing step is surprisingly simple. As an input we know, in which time step which angle the pendulum must have. Bringing the system to a state is called “Tracking control” or PID control. That means, we have a trajectory over time, and must find control actions to map the system to this trajectory. Other authors call the principle “steering behavior”, because the aim is to bring a robot to a given line.
Virtual intelligence
Virtual intelligence (VI) is the term given to artificial intelligence that exists within a virtual world. Many virtual worlds have options for persistent avatars that provide information, training, role-playing, and social interactions. The immersion in virtual worlds provides a platform for VI beyond the traditional paradigm of past user interfaces (UIs). What Alan Turing established as a benchmark for telling the difference between human and computerized intelligence was devoid of visual influences. With today's VI bots, virtual intelligence has evolved past the constraints of past testing into a new level of the machine's ability to demonstrate intelligence. The immersive features of these environments provide nonverbal elements that affect the realism provided by virtually intelligent agents. Virtual intelligence is the intersection of these two technologies: Virtual environments: Immersive 3D spaces provide for collaboration, simulations, and role-playing interactions for training. Many of these virtual environments are currently being used for government and academic projects, including Second Life, VastPark, Olive, OpenSim, Outerra, Oracle's Open Wonderland, Duke University's Open Cobalt, and many others. Some of the commercial virtual worlds are also taking this technology into new directions, including the high-definition virtual world Blue Mars. Artificial intelligence (AI): AI is a branch of computer science that aims to create intelligent machines capable of performing tasks that typically require human intelligence. VI is a type of AI that operates within virtual environments to simulate human-like interactions and responses. == Applications == Cutlass Bomb Disposal Robot: Northrop Grumman developed a virtual training opportunity because of the prohibitive real-world cost and dangers associated with bomb disposal. By replicating a complicated system without having to learn advanced code, the virtual robot has no risk of damage, trainee safety hazards, or accessibility constraints. MyCyberTwin: NASA is among the companies that have used the MyCyberTwin AI technologies. They used it for the Phoenix rover in the virtual world Second Life. Their MyCyberTwin used a programmed profile to relay information about what the Phoenix rover was doing and its purpose. Second China: The University of Florida developed the "Second China" project as an immersive training experience for learning how to interact with the culture and language in a foreign country. Students are immersed in an environment that provides role-playing challenges coupled with language and cultural sensitivities magnified during country-level diplomatic missions or during times of potential conflict or regional destabilization. The virtual training provides participants with opportunities to access information, take part in guided learning scenarios, communicate, collaborate, and role-play. While China was the country for the prototype, this model can be modified for use with any culture to help better understand social and cultural interactions and see how other people think and what their actions imply. Duke School of Nursing Training Simulation: Extreme Reality developed virtual training to test critical thinking with a nurse performing trained procedures to identify critical data to make decisions and performing the correct steps for intervention. Bots are programmed to respond to the nurse's actions as the patient with their conditions improving if the nurse performs the correct actions.
SpreeAI
SpreeAI (stylized as SPREEAI) is an American fashion technology company headquartered in Incline Village, Nevada that develops artificial intelligence software for the apparel and retail industries, including photorealistic virtual try-on, AI-powered sizing recommendations, and digital model generation. Founded in 2022 by John Imah and Bob Davidson, the company achieved unicorn status in 2025 following a Series B round led by Davidson Group that valued the company at approximately US$1.5 billion. TechCrunch identified SpreeAI as one of the more than 100 new tech unicorns minted in 2025. Its board of directors includes supermodel Naomi Campbell and hospitality executive Larry Ruvo. == History == SpreeAI was founded in 2022 by John Imah and Bob Davidson with a focus on artificial intelligence applications in fashion retail. By 2024, the company had raised approximately US$60 million in venture funding. In May 2025, SpreeAI announced a Series B round led by Davidson Group; reporting at the time placed the company's valuation at approximately US$1.5 billion, making it one of a small number of fashion-technology companies to reach unicorn status. In January 2026, TechCrunch listed SpreeAI among the more than 100 new tech unicorns minted in 2025. == Technology == SpreeAI develops a suite of artificial intelligence tools for the apparel industry. Its consumer-facing platform allows shoppers to upload a single photograph or select a digital model and then visualize clothing items on that figure with photorealistic rendering, while a complementary sizing engine generates fit recommendations intended to reduce returns. The platform is designed for integration with online retailers so that shoppers can preview garments before purchase. The company has stated that its models were developed in part through research collaborations with the Massachusetts Institute of Technology and Carnegie Mellon University. == Leadership and board == John Imah, a Nigerian-American technology executive who previously held roles at Samsung, Twitch, Meta Platforms, and Snap Inc., is co-founder and chief executive officer. Co-founder Bob Davidson, through Davidson Group, led the company's Series B financing. The company's board of directors includes supermodel Naomi Campbell, who joined in 2024, and Las Vegas hospitality executive Larry Ruvo. == Partnerships == SpreeAI has formed partnerships across both academia and the fashion industry. Council of Fashion Designers of America (CFDA). In 2025, SpreeAI entered a partnership with the CFDA to support American designers and brands with AI-driven tools; the CFDA described SpreeAI as "a fashion technology leader delivering innovative solutions to help designers and brands thrive." Massachusetts Institute of Technology and Carnegie Mellon University. The company has cited ongoing research and talent collaborations with both institutions. Sergio Hudson and Kai Collective. In 2025, SpreeAI made what WWD described as its Met Gala debut through a custom collaboration with designer Sergio Hudson and Nigerian-British label Kai Collective; the collaboration paired Hudson's couture with SpreeAI's virtual try-on platform. == Recognition == In 2025, TechCrunch named SpreeAI among the new tech unicorns of the year. In 2025, SpreeAI was named an honoree in Inc.'s Best in Business awards, and CEO John Imah was included on Inc.'s list of 40 business leaders who "propelled their organizations to success." In 2025, Imah was named to the Observer's AI Power Index, a list of 100 leaders shaping the future of artificial intelligence. In 2025, Imah was included in AfroTech's Future 50, recognizing Black innovators in technology. SpreeAI and Imah have been the subject of profile coverage in The Washington Post, Rolling Stone UK, WWD, Vogue UA, L'Officiel Arabia, GQ South Africa, and Inc..
Fuzzy differential inclusion
Fuzzy differential inclusion is the extension of differential inclusion to fuzzy sets introduced by Lotfi A. Zadeh. x ′ ( t ) ∈ [ f ( t , x ( t ) ) ] α {\displaystyle x'(t)\in [f(t,x(t))]^{\alpha }} with x ( 0 ) ∈ [ x 0 ] α {\displaystyle x(0)\in [x_{0}]^{\alpha }} Suppose f ( t , x ( t ) ) {\displaystyle f(t,x(t))} is a fuzzy valued continuous function on Euclidean space. Then it is the collection of all normal, upper semi-continuous, convex, compactly supported fuzzy subsets of R n {\displaystyle \mathbb {R} ^{n}} . == Second order differential == The second order differential is x ″ ( t ) ∈ [ k x ] α {\displaystyle x''(t)\in [kx]^{\alpha }} where k ∈ [ K ] α {\displaystyle k\in [K]^{\alpha }} , K {\displaystyle K} is trapezoidal fuzzy number ( − 1 , − 1 / 2 , 0 , 1 / 2 ) {\displaystyle (-1,-1/2,0,1/2)} , and x 0 {\displaystyle x_{0}} is a trianglular fuzzy number (-1,0,1). == Applications == Fuzzy differential inclusion (FDI) has applications in Cybernetics Artificial intelligence, Neural network, Medical imaging Robotics Atmospheric dispersion modeling Weather forecasting Cyclone Pattern recognition Population biology
Conceptual dependency theory
Conceptual dependency theory is a model of natural language understanding used in artificial intelligence systems. Roger Schank at Stanford University introduced the model in 1969, in the early days of artificial intelligence. This model was extensively used by Schank's students at Yale University such as Robert Wilensky, Wendy Lehnert, and Janet Kolodner. Schank developed the model to represent knowledge for natural language input into computers. Partly influenced by the work of Sydney Lamb, his goal was to make the meaning independent of the words used in the input, i.e. two sentences identical in meaning would have a single representation. The system was also intended to draw logical inferences. The model uses the following basic representational tokens: real world objects, each with some attributes. real world actions, each with attributes times locations A set of conceptual transitions then act on this representation, e.g. an ATRANS is used to represent a transfer such as "give" or "take" while a PTRANS is used to act on locations such as "move" or "go". An MTRANS represents mental acts such as "tell", etc. A sentence such as "John gave a book to Mary" is then represented as the action of an ATRANS on two real world objects, John and Mary.
Geo-replication
Geo-replication systems are designed to provide improved availability and disaster tolerance by using geographically distributed data centers. This is intended to improve the response time for applications such as web portals. Geo-replication can be achieved using software, hardware or a combination of the two. == Software == Geo-replication software is a network performance-enhancing technology that is designed to provide improved access to portal or intranet content for users at the most remote parts of large organizations. It is based on the principle of storing complete replicas of portal content on local servers, and then keeping the content on those servers up-to-date using heavily compressed data updates. === Portal acceleration === Geo-replication technologies are used to provide replication of the content of portals, intranets, web applications, content and data between servers, across wide area networks WAN to allow users at remote sites to access central content at LAN speeds. Geo-replication software can improve the performance of data networks that suffer limited bandwidth, latency and periodic disconnection. Terabytes of data can be replicated over a wide area network, giving remote sites faster access to web applications. Geo-replication software uses a combination of data compression and content caching technologies. differencing technologies can also be employed to reduce the volume of data that has to be transmitted to keep portal content accurate across all servers. This update compression can reduce the load that portal traffic places on networks, and improve the response time of a portal. === Portal replication === Remote users of web portals and collaboration environments will frequently experience network bandwidth and latency problems which will slow down their experience of opening and closing files, and otherwise interacting with the portal. Geo-replication technology is deployed to accelerate the remote end user portal performance to be equivalent to that experienced by users locally accessing the portal in the central office. === Differencing engine technologies === To deliver this reduction in the size of the required data updates across a portal, geo-replication systems often use differencing engine technologies. These systems are able to difference the content of each portal server right down to the byte level. This knowledge of the content that is already on each server enables the system to rebuild any changes to the content on one server, across each of the other servers in the deployment from content already hosted on those other servers. This type of differencing system ensures that no content, at the byte level, is ever sent to a server twice. === Offline portal replication on laptops === Geo-replication systems are often extended to deliver local replication beyond the server and down to the laptop used by a single user. Server to laptop replication enables mobile users to have access to a local replica of their business portal on a standard laptop. This technology may be employed to provide in the field access to portal content by, for example, sales forces and combat forces. == Geo-replication systems ==
Riffusion
Riffusion is a neural network, designed by Seth Forsgren and Hayk Martiros, that generates music using images of sound rather than audio. The resulting music has been described as "de otro mundo" (otherworldly), although unlikely to replace man-made music. The model was made available on December 15, 2022, with the code also freely available on GitHub. The first version of Riffusion was created as a fine-tuning of Stable Diffusion, an existing open-source model for generating images from text prompts, on spectrograms, resulting in a model which used text prompts to generate image files which could then be put through an inverse Fourier transform and converted into audio files. While these files were only several seconds long, the model could also use latent space between outputs to interpolate different files together (using the img2img capabilities of SD). It was one of many models derived from Stable Diffusion. In December 2022, Mubert similarly used Stable Diffusion to turn descriptive text into music loops. In January 2023, Google published a paper on their own text-to-music generator called MusicLM. Forsgren and Martiros formed a startup, also called Riffusion, and raised $4 million in venture capital funding in October 2023.