A world model in artificial intelligence is a machine learning system that builds an internal representation of an environment. The model predicts how that environment changes over time in response to actions. Researchers design world models to help agents plan, reason, and act without constant real-world trial and error. World models differ from systems that merely classify or generate outputs. They simulate dynamics such as physics, object interactions, and causality. Early ideas date to the 1990s. Modern versions power robots, autonomous driving, and interactive video generation. == History == Jürgen Schmidhuber introduced the term world model in machine learning in 1990. He proposed recurrent neural networks that predict future states from observations and use those predictions to train agents. David Ha and Schmidhuber revived the concept in a 2018 paper. Their agents learned to drive virtual cars and play video games inside self-generated simulations. Yann LeCun advanced the idea in a 2022 position paper titled "A Path Towards Autonomous Machine Intelligence". He argued that intelligence requires predictive models of the world rather than pure pattern matching. LeCun proposed the joint embedding predictive architecture (JEPA) as a practical foundation. LeCun and collaborators developed several JEPA variants. V-JEPA 2 reached state-of-the-art performance on video understanding and physical reasoning at the time. It supports zero-shot robot control in unfamiliar environments. Introduced in March 2026, LeWorldModel trains stably end-to-end from raw pixels and uses two loss terms and avoids hand-crafted heuristics. LeCun founded Advanced Machine Intelligence Labs in 2026 to further develop world models. Google DeepMind introduced Genie in 2024. The model learned interactive environments from unlabeled internet videos. Genie 2 followed in late 2024 and added three-dimensional generation. The Genie series set benchmarks for general-purpose simulation. Genie 3 was introduced in August 2025. It produces photorealistic, real-time interactive worlds from text prompts which are displayed at 24 frames per second and explored in real time with text or image prompts. The model supports persistent three-dimensional worlds and real-time interaction. Waymo adopted Genie 3 in February 2026 and used it to create a specialized world model for autonomous driving simulation, called the Waymo World Model. It produces synchronized camera and lidar outputs and creates edge cases that real robotaxis rarely encounter. The edge cases were reported to be unusual by PCMag. General Intuition announced a $133.7 million seed round. World Labs raised $1 billion. AMI raised $1.03 billion. In April 2026, Alibaba announced Happy Oyster, its world model designed for real-time and “flowy” world model. It includes a directing mode for world building based on text and image prompts and a wandering mode for exploring the resulting world. It can generate 3-minute in-world video clips. Also in April, World Labs, co-founded by Li Fei Fei, unveiled Spark 2.0, an open-source 3D Gaussian splatting rendering engine that targets smartphone-class devices. In June 2026, Nvidia released Cosmos 3, a family of open-weight models. It combines previously independent physical reasoning, world simulation, and action generation. Cosmos 3 integrates can process and generate text, image, video, audio, and action sequences. The model employs a Mixture-of-Transformers" (MoT) approach. An autoregressive (AR) transformer handles reasoning and next-token prediction, while a diffusion transformer (DT) does multimodal generation. Encoders (ViT for vision, VAE for visual/audio, and domain-specific for actions) and generate a shared representation space using 3D multi-dimensional rotary position embedding (mRoPE) for spatial and temporal information. The family includes Cosmos3-Nano (16B parameters) for workstations; Cosmos3-Super (64B parameters) for research. == Architecture == World models process raw sensory data such as video frames or lidar scans. They compress this input into compact latent representations. The system then predicts future representations rather than pixel-by-pixel reconstructions. Many modern world models use joint embedding predictive architecture (JEPA). An encoder turns observations into embeddings. A predictor estimates one or a suite of embeddings from the current one and an action. In some cases a critic chooses one embedding as the best result. A regularizer keeps embeddings well-behaved. The model trains by minimizing prediction error in embedding space. This approach avoids the high cost of generating every detail. Some architectures add explicit components. A fast reactive path handles immediate responses. A slower deliberative path performs longer-horizon planning. Video prediction accuracy or robot success rates are key metrics, but do not always predict real-world performance. Generative world models such as Genie 3 combine these with a simulator. They accept text prompts or layouts and output consistent video, lidar, or three-dimensional scenes. World models often train with self-supervised learning. They use large unlabeled datasets of video or robot interactions. Self-supervised learning can speed learning. Reinforcement learning can fine-tune a model for specific tasks. == Applications == World models support robot learning. Agents train inside simulations and transfer skills to the physical world. This reduces the need for dangerous or expensive real-world trials. Autonomous vehicles use world models to test rare events. Waymo's system simulates tornadoes or unusual pedestrian behavior. Companies train planners without putting vehicles on public roads. Interactive entertainment benefits from world models. Genie 3 lets users generate playable environments from simple descriptions. Game studios prototype levels faster. Scientific simulation gains from these models. Researchers model physical systems or biological processes at scale. Planners in logistics or urban design test strategies inside accurate digital twins. == Comparison with large language models == Both world models and large language models (LLMs) use inferencing on their inputs to make predictions. LLMs operate on textual inputs. They predict the next token in text sequences. They excel at language-oriented tasks such as translation or summarization. However, they lack understanding of physics. World models operate on sensor inputs such as pixels. They predict state changes in that data in latent space. This design supports planning and causal reasoning. LLMs generate fluent text but often fail at consistent physical predictions. Their architecture employs transformers with refinements such as mixture of experts. World models divide an inferencing task into work performed by encoders, predictors, simulators, and other pieces. They typically handle multimodal inputs such as video, lidar, radar, and audio, guided by textual prompting. LLMs power chatbots and code assistants. World models drive embodied agents that act in dynamic environments, such as autonomous driving. The two may be combined in hybrid systems. For example, a LLM handles instructions, while a world model manages low-level control. World model proponents such as LeCun claim that because LLMs are trained only on text, they have no ability to predict anything beyond text, such as real-world events. == Benchmarks == World model benchmarks test physical understanding, long-term consistency, planning, and generalization from sensor data. Meta introduced three benchmarks for V-JEPA 2. IntPhys 2 measures a model's ability to detect physics violations. It presents pairs of videos that diverge when one breaks physical rules. Humans score near 100% accuracy. V-JEPA 2 achieves little better than random chance on many conditions. Minimal Video Pairs (MVPBench) tests physical understanding through multiple-choice questions based on short video clips. It probes object interactions and causality. Something-Something tests action recognition. Epic-Kitchens-100 tests human action anticipation. DeepMind benchmark: Interactive evaluation measures consistency over minutes of interaction, memory of off-screen objects, and response to user actions or text prompts. Waymo benchmark: Output generation quality: Metrics include realism, controllability (via text prompts), and usefulness for training planners in simulated worlds. However, pixel reconstruction error rate with episodic rewards often fails. Other: Epic-Kitchens-100 (often measured with Recall@5) Ego4D 50 Salads, Breakfast, etc. Potential benchmarks: Zero-shot transfer to robots Long-horizon planning Implausible prediction rate
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Perusall
Perusall is a social web annotation tool intended for use by students at schools and universities. It allows users to annotate the margins of a text in a virtual group setting that is similar to social media—with upvoting, emojis, chat functionality, and notification. It also includes automatic AI grading. == History == Perusall began as a research project at Harvard University. It later became an educational product for students and teachers. As of 2024, Perusall states more than 5 million students have used the tool at over 5,000 educational institutions in 112 countries." == Functionality == Perusall integrates with learning management systems such as Moodle, Canvas and Blackboard to aid with collaborative annotation. The tool supports annotation of a range of media including text, images, equations, videos, PDFs and snapshots of webpages.
Learnable function class
In statistical learning theory, a learnable function class is a set of functions for which an algorithm can be devised to asymptotically minimize the expected risk, uniformly over all probability distributions. The concept of learnable classes are closely related to regularization in machine learning, and provides large sample justifications for certain learning algorithms. == Definition == === Background === Let Ω = X × Y = { ( x , y ) } {\displaystyle \Omega ={\mathcal {X}}\times {\mathcal {Y}}=\{(x,y)\}} be the sample space, where y {\displaystyle y} are the labels and x {\displaystyle x} are the covariates (predictors). F = { f : X ↦ Y } {\displaystyle {\mathcal {F}}=\{f:{\mathcal {X}}\mapsto {\mathcal {Y}}\}} is a collection of mappings (functions) under consideration to link x {\displaystyle x} to y {\displaystyle y} . L : Y × Y ↦ R {\displaystyle L:{\mathcal {Y}}\times {\mathcal {Y}}\mapsto \mathbb {R} } is a pre-given loss function (usually non-negative). Given a probability distribution P ( x , y ) {\displaystyle P(x,y)} on Ω {\displaystyle \Omega } , define the expected risk I P ( f ) {\displaystyle I_{P}(f)} to be: I P ( f ) = ∫ L ( f ( x ) , y ) d P ( x , y ) {\displaystyle I_{P}(f)=\int L(f(x),y)dP(x,y)} The general goal in statistical learning is to find the function in F {\displaystyle {\mathcal {F}}} that minimizes the expected risk. That is, to find solutions to the following problem: f ^ = arg min f ∈ F I P ( f ) {\displaystyle {\hat {f}}=\arg \min _{f\in {\mathcal {F}}}I_{P}(f)} But in practice the distribution P {\displaystyle P} is unknown, and any learning task can only be based on finite samples. Thus we seek instead to find an algorithm that asymptotically minimizes the empirical risk, i.e., to find a sequence of functions { f ^ n } n = 1 ∞ {\displaystyle \{{\hat {f}}_{n}\}_{n=1}^{\infty }} that satisfies lim n → ∞ P ( I P ( f ^ n ) − inf f ∈ F I P ( f ) > ϵ ) = 0 {\displaystyle \lim _{n\rightarrow \infty }\mathbb {P} (I_{P}({\hat {f}}_{n})-\inf _{f\in {\mathcal {F}}}I_{P}(f)>\epsilon )=0} One usual algorithm to find such a sequence is through empirical risk minimization. === Learnable function class === We can make the condition given in the above equation stronger by requiring that the convergence is uniform for all probability distributions. That is: The intuition behind the more strict requirement is as such: the rate at which sequence { f ^ n } {\displaystyle \{{\hat {f}}_{n}\}} converges to the minimizer of the expected risk can be very different for different P ( x , y ) {\displaystyle P(x,y)} . Because in real world the true distribution P {\displaystyle P} is always unknown, we would want to select a sequence that performs well under all cases. However, by the no free lunch theorem, such a sequence that satisfies (1) does not exist if F {\displaystyle {\mathcal {F}}} is too complex. This means we need to be careful and not allow too "many" functions in F {\displaystyle {\mathcal {F}}} if we want (1) to be a meaningful requirement. Specifically, function classes that ensure the existence of a sequence { f ^ n } {\displaystyle \{{\hat {f}}_{n}\}} that satisfies (1) are known as learnable classes. It is worth noting that at least for supervised classification and regression problems, if a function class is learnable, then the empirical risk minimization automatically satisfies (1). Thus in these settings not only do we know that the problem posed by (1) is solvable, we also immediately have an algorithm that gives the solution. == Interpretations == If the true relationship between y {\displaystyle y} and x {\displaystyle x} is y ∼ f ∗ ( x ) {\displaystyle y\sim f^{}(x)} , then by selecting the appropriate loss function, f ∗ {\displaystyle f^{}} can always be expressed as the minimizer of the expected loss across all possible functions. That is, f ∗ = arg min f ∈ F ∗ I P ( f ) {\displaystyle f^{}=\arg \min _{f\in {\mathcal {F}}^{}}I_{P}(f)} Here we let F ∗ {\displaystyle {\mathcal {F}}^{}} be the collection of all possible functions mapping X {\displaystyle {\mathcal {X}}} onto Y {\displaystyle {\mathcal {Y}}} . f ∗ {\displaystyle f^{}} can be interpreted as the actual data generating mechanism. However, the no free lunch theorem tells us that in practice, with finite samples we cannot hope to search for the expected risk minimizer over F ∗ {\displaystyle {\mathcal {F}}^{}} . Thus we often consider a subset of F ∗ {\displaystyle {\mathcal {F}}^{}} , F {\displaystyle {\mathcal {F}}} , to carry out searches on. By doing so, we risk that f ∗ {\displaystyle f^{}} might not be an element of F {\displaystyle {\mathcal {F}}} . This tradeoff can be mathematically expressed as In the above decomposition, part ( b ) {\displaystyle (b)} does not depend on the data and is non-stochastic. It describes how far away our assumptions ( F {\displaystyle {\mathcal {F}}} ) are from the truth ( F ∗ {\displaystyle {\mathcal {F}}^{}} ). ( b ) {\displaystyle (b)} will be strictly greater than 0 if we make assumptions that are too strong ( F {\displaystyle {\mathcal {F}}} too small). On the other hand, failing to put enough restrictions on F {\displaystyle {\mathcal {F}}} will cause it to be not learnable, and part ( a ) {\displaystyle (a)} will not stochastically converge to 0. This is the well-known overfitting problem in statistics and machine learning literature. == Example: Tikhonov regularization == A good example where learnable classes are used is the so-called Tikhonov regularization in reproducing kernel Hilbert space (RKHS). Specifically, let F ∗ {\displaystyle {\mathcal {F^{}}}} be an RKHS, and | | ⋅ | | 2 {\displaystyle ||\cdot ||_{2}} be the norm on F ∗ {\displaystyle {\mathcal {F^{}}}} given by its inner product. It is shown in that F = { f : | | f | | 2 ≤ γ } {\displaystyle {\mathcal {F}}=\{f:||f||_{2}\leq \gamma \}} is a learnable class for any finite, positive γ {\displaystyle \gamma } . The empirical minimization algorithm to the dual form of this problem is arg min f ∈ F ∗ { ∑ i = 1 n L ( f ( x i ) , y i ) + λ | | f | | 2 } {\displaystyle \arg \min _{f\in {\mathcal {F}}^{}}\left\{\sum _{i=1}^{n}L(f(x_{i}),y_{i})+\lambda ||f||_{2}\right\}} This was first introduced by Tikhonov to solve ill-posed problems. Many statistical learning algorithms can be expressed in such a form (for example, the well-known ridge regression). The tradeoff between ( a ) {\displaystyle (a)} and ( b ) {\displaystyle (b)} in (2) is geometrically more intuitive with Tikhonov regularization in RKHS. We can consider a sequence of { F γ } {\displaystyle \{{\mathcal {F}}_{\gamma }\}} , which are essentially balls in F ∗ {\displaystyle {\mathcal {F^{}}}} with centers at 0. As γ {\displaystyle \gamma } gets larger, F γ {\displaystyle {\mathcal {F}}_{\gamma }} gets closer to the entire space, and ( b ) {\displaystyle (b)} is likely to become smaller. However we will also suffer smaller convergence rates in ( a ) {\displaystyle (a)} . The way to choose an optimal γ {\displaystyle \gamma } in finite sample settings is usually through cross-validation. == Relationship to empirical process theory == Part ( a ) {\displaystyle (a)} in (2) is closely linked to empirical process theory in statistics, where the empirical risk { ∑ i = 1 n L ( y i , f ( x i ) ) , f ∈ F } {\displaystyle \{\sum _{i=1}^{n}L(y_{i},f(x_{i})),f\in {\mathcal {F}}\}} are known as empirical processes. In this field, the function class F {\displaystyle {\mathcal {F}}} that satisfies the stochastic convergence are known as uniform Glivenko–Cantelli classes. It has been shown that under certain regularity conditions, learnable classes and uniformly Glivenko-Cantelli classes are equivalent. Interplay between ( a ) {\displaystyle (a)} and ( b ) {\displaystyle (b)} in statistics literature is often known as the bias-variance tradeoff. However, note that in the authors gave an example of stochastic convex optimization for General Setting of Learning where learnability is not equivalent with uniform convergence.
Symbolic artificial intelligence
In artificial intelligence, symbolic artificial intelligence (also known as classical artificial intelligence or logic-based artificial intelligence) is the term for the collection of all methods in artificial intelligence research that are based on high-level symbolic (human-readable) representations of problems, logic, and search. Symbolic AI used tools such as logic programming, production rules, semantic nets and frames, and it developed applications such as knowledge-based systems (in particular, expert systems), symbolic mathematics, automated theorem provers, ontologies, the semantic web, and automated planning and scheduling systems. The Symbolic AI paradigm led to important ideas in search, symbolic programming languages, agents, multi-agent systems, the semantic web, and the strengths and limitations of formal knowledge and reasoning systems. Symbolic AI was the dominant paradigm of AI research from the mid-1950s until the mid-1990s. Researchers in the 1960s and the 1970s were convinced that symbolic approaches would eventually succeed in creating a machine with artificial general intelligence and considered this the ultimate goal of their field. An early boom, with early successes such as the Logic Theorist and Samuel's Checkers Playing Program, led to unrealistic expectations and promises and was followed by the first AI Winter as funding dried up. A second boom (1969–1986) occurred with the rise of expert systems, their promise of capturing corporate expertise, and an enthusiastic corporate embrace. That boom, and some early successes, e.g., with XCON at DEC, was followed again by later disappointment. Problems with difficulties in knowledge acquisition, maintaining large knowledge bases, and brittleness in handling out-of-domain problems arose. Another, second, AI Winter (1988–2011) followed. Subsequently, AI researchers focused on addressing underlying problems in handling uncertainty and in knowledge acquisition. Uncertainty was addressed with formal methods such as hidden Markov models, Bayesian reasoning, and statistical relational learning. Symbolic machine learning addressed the knowledge acquisition problem with contributions including Version Space, Valiant's PAC learning, Quinlan's ID3 decision-tree learning, case-based learning, and inductive logic programming to learn relations. Neural networks, a subsymbolic approach, had been pursued from early days and reemerged strongly in 2012. Early examples are Rosenblatt's perceptron learning work, the backpropagation work of Rumelhart, Hinton and Williams, and work in convolutional neural networks by LeCun et al. in 1989. However, neural networks were not viewed as successful until about 2012: "Until Big Data became commonplace, the general consensus in the Al community was that the so-called neural-network approach was hopeless. Systems just didn't work that well, compared to other methods. ... A revolution came in 2012, when a number of people, including a team of researchers working with Hinton, worked out a way to use the power of GPUs to enormously increase the power of neural networks." Over the next several years, deep learning had spectacular success in handling vision, speech recognition, speech synthesis, image generation, and machine translation, though symbolic approaches continue to be useful in a few domains such as computer algebra systems and proof assistants. == History == A short history of symbolic AI to the present day follows below. Time periods and titles are drawn from Henry Kautz's 2020 AAAI Robert S. Engelmore Memorial Lecture and the longer Wikipedia article on the History of AI, with dates and titles differing slightly for increased clarity. === The first AI summer: irrational exuberance, 1948–1966 === Success at early attempts in AI occurred in three main areas: artificial neural networks, knowledge representation, and heuristic search, contributing to high expectations. This section summarizes Kautz's reprise of early AI history. ==== Approaches inspired by human or animal cognition or behavior ==== Cybernetic approaches attempted to replicate the feedback loops between animals and their environments. A robotic turtle, with sensors, motors for driving and steering, and seven vacuum tubes for control, based on a preprogrammed neural net, was built as early as 1948. This work can be seen as an early precursor to later work in neural networks, reinforcement learning, and situated robotics. An important early symbolic AI program was the Logic theorist, written by Allen Newell, Herbert Simon and Cliff Shaw in 1955–56, as it was able to prove 38 elementary theorems from Whitehead and Russell's Principia Mathematica. Newell, Simon, and Shaw later generalized this work to create a domain-independent problem solver, GPS (General Problem Solver). GPS solved problems represented with formal operators via state-space search using means-ends analysis. During the 1960s, symbolic approaches achieved great success at simulating intelligent behavior in structured environments such as game-playing, symbolic mathematics, and theorem-proving. AI research was concentrated in four institutions in the 1960s: Carnegie Mellon University, Stanford, MIT and (later) University of Edinburgh. Each one developed its own style of research. Earlier approaches based on cybernetics or artificial neural networks were abandoned or pushed into the background. Herbert Simon and Allen Newell studied human problem-solving skills and attempted to formalize them, and their work laid the foundations of the field of artificial intelligence, as well as cognitive science, operations research and management science. Their research team used the results of psychological experiments to develop programs that simulated the techniques that people used to solve problems. This tradition, centered at Carnegie Mellon University would eventually culminate in the development of the Soar architecture in the middle 1980s. ==== Heuristic search ==== In addition to the highly specialized domain-specific kinds of knowledge that we will see later used in expert systems, early symbolic AI researchers discovered another more general application of knowledge. These were called heuristics, rules of thumb that guide a search in promising directions: "How can non-enumerative search be practical when the underlying problem is exponentially hard? The approach advocated by Simon and Newell is to employ heuristics: fast algorithms that may fail on some inputs or output suboptimal solutions." Another important advance was to find a way to apply these heuristics that guarantees a solution will be found, if there is one, not withstanding the occasional fallibility of heuristics: "The A algorithm provided a general frame for complete and optimal heuristically guided search. A is used as a subroutine within practically every AI algorithm today but is still no magic bullet; its guarantee of completeness is bought at the cost of worst-case exponential time. ==== Early work on knowledge representation and reasoning ==== Early work covered both applications of formal reasoning emphasizing first-order logic, along with attempts to handle common-sense reasoning in a less formal manner. ===== Modeling formal reasoning with logic: the "neats" ===== Unlike Simon and Newell, John McCarthy felt that machines did not need to simulate the exact mechanisms of human thought, but could instead try to find the essence of abstract reasoning and problem-solving with logic, regardless of whether people used the same algorithms. His laboratory at Stanford (SAIL) focused on using formal logic to solve a wide variety of problems, including knowledge representation, planning and learning. Logic was also the focus of the work at the University of Edinburgh and elsewhere in Europe which led to the development of the programming language Prolog and the science of logic programming. ===== Modeling implicit common-sense knowledge with frames and scripts: the "scruffies" ===== Researchers at MIT (such as Marvin Minsky and Seymour Papert) found that solving difficult problems in vision and natural language processing required ad hoc solutions—they argued that no simple and general principle (like logic) would capture all the aspects of intelligent behavior. Roger Schank described their "anti-logic" approaches as "scruffy" (as opposed to the "neat" paradigms at CMU and Stanford). Commonsense knowledge bases (such as Doug Lenat's Cyc) are an example of "scruffy" AI, since they must be built by hand, one complicated concept at a time. === The first AI winter: crushed dreams, 1967–1977 === The first AI winter was a shock: During the first AI summer, many people thought that machine intelligence could be achieved in just a few years. The Defense Advance Research Projects Agency (DARPA) launched programs to support AI research to use AI to solve problems of national security; in particular, to automate the translation of Russian to English for inte
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Decision list
Decision lists are a representation for Boolean functions which can be easily learned from examples. Single term decision lists are more expressive than disjunctions and conjunctions; however, 1-term decision lists are less expressive than the general disjunctive normal form and the conjunctive normal form. The language specified by a k-length decision list includes as a subset the language specified by a k-depth decision tree. Learning decision lists can be used for attribute efficient learning, a type of machine learning. == Definition == A decision list (DL) of length r is of the form: if f1 then output b1 else if f2 then output b2 ... else if fr then output br where fi is the ith formula and bi is the ith boolean for i ∈ { 1... r } {\displaystyle i\in \{1...r\}} . The last if-then-else is the default case, which means formula fr is always equal to true. A k-DL is a decision list where all of formulas have at most k terms. Sometimes "decision list" is used to refer to a 1-DL, where all of the formulas are either a variable or its negation.