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Neuro-symbolic AI

Neuro-symbolic AI is a subfield of artificial intelligence that integrates neural methods (e.g., neural networks and deep learning) with symbolic methods (e.g., formal logic, knowledge representation, and automated reasoning). The goal is to combine the strengths of both approaches, resulting in AI systems that can be trained from raw data and demonstrate robustness against outliers or errors in the base data, while preserving explainability, explicit use of expert knowledge, and explicit cognitive reasoning. As argued by Leslie Valiant and others, the effective construction of rich computational cognitive models demands the combination of symbolic reasoning and efficient machine learning. Gary Marcus argued, "We cannot construct rich cognitive models in an adequate, automated way without the triumvirate of hybrid architecture, rich prior knowledge, and sophisticated techniques for reasoning." Further, "To build a robust, knowledge-driven approach to AI we must have the machinery of symbol manipulation in our toolkit. Too much of useful knowledge is abstract to make do without tools that represent and manipulate abstraction, and to date, the only known machinery that can manipulate such abstract knowledge reliably is the apparatus of symbol manipulation." Angelo Dalli, Henry Kautz, Francesca Rossi, and Bart Selman also argued for such a synthesis. Their arguments attempt to address the two kinds of thinking, as discussed in Daniel Kahneman's book Thinking, Fast and Slow. It describes cognition as encompassing two components: System 1 is fast, reflexive, intuitive, and unconscious. System 2 is slower, step-by-step, and explicit. System 1 is used for pattern recognition. System 2 handles planning, deduction, and deliberative thinking. In this view, deep learning best handles the first kind of cognition, while symbolic reasoning best handles the second kind. Both are necessary for the development of a robust and reliable AI system capable of learning, reasoning, and interacting with humans to accept advice and answer questions. Since the 1990s, dual-process models with explicit references to the two contrasting systems have been the focus of research in both the fields of AI and cognitive science by numerous researchers. In 2025, the adoption of neurosymbolic AI, an approach that integrates neural networks with symbolic reasoning, increased in response to the need to address hallucination issues in large language models. For example, Amazon implemented Neurosymbolic AI in its Vulcan warehouse robots and Rufus shopping assistant to enhance accuracy and decision-making. == Approaches == Approaches for integration are diverse. Henry Kautz's taxonomy of neuro-symbolic architectures follows, along with some examples: Symbolic Neural symbolic is the current approach of many neural models in natural language processing, where words or subword tokens are the ultimate input and output of large language models. Examples include BERT, RoBERTa, and GPT-3. Symbolic[Neural] is exemplified by AlphaGo, where symbolic techniques are used to invoke neural techniques. In this case, the symbolic approach is Monte Carlo tree search and the neural techniques learn how to evaluate game positions. Neural | Symbolic uses a neural architecture to interpret perceptual data as symbols and relationships that are reasoned about symbolically. Neural-Concept Learner is an example. Neural: Symbolic → Neural relies on symbolic reasoning to generate or label training data that is subsequently learned by a deep learning model, e.g., to train a neural model for symbolic computation by using a Macsyma-like symbolic mathematics system to create or label examples. NeuralSymbolic uses a neural net that is generated from symbolic rules. An example is the Neural Theorem Prover, which constructs a neural network from an AND-OR proof tree generated from knowledge base rules and terms. Logic Tensor Networks also fall into this category. Neural[Symbolic] according to Kautz, this approach embeds true symbolic reasoning inside a neural network. These are tightly-coupled neural-symbolic systems, in which the logical inference rules are internal to the neural network. This way, the neural network internally computes the inference from the premises and learns to reason based on logical inference systems. Early work on connectionist modal and temporal logics by Garcez, Lamb, and Gabbay is aligned with this approach. These categories are not exhaustive, as they do not consider multi-agent systems. In 2005, Bader and Hitzler presented a more fine-grained categorization that took into account, e.g., whether the use of symbols included logic and, if so, whether the logic was propositional or first-order logic. The 2005 categorization and Kautz's taxonomy above are compared and contrasted in a 2021 article. Sepp Hochreiter argued that Graph Neural Networks "...are the predominant models of neural-symbolic computing" since "[t]hey describe the properties of molecules, simulate social networks, or predict future states in physical and engineering applications with particle-particle interactions." == Artificial general intelligence == Gary Marcus argues that "...hybrid architectures that combine learning and symbol manipulation are necessary for robust intelligence, but not sufficient", and that there are ...four cognitive prerequisites for building robust artificial intelligence: hybrid architectures that combine large-scale learning with the representational and computational powers of symbol manipulation, large-scale knowledge bases—likely leveraging innate frameworks—that incorporate symbolic knowledge along with other forms of knowledge, reasoning mechanisms capable of leveraging those knowledge bases in tractable ways, and rich cognitive models that work together with those mechanisms and knowledge bases. This echoes earlier calls for hybrid models as early as the 1990s. == History == Garcez and Lamb described research in this area as ongoing, at least since the 1990s. During that period, the terms symbolic and sub-symbolic AI were popular. A series of workshops on neuro-symbolic AI has been held annually since 2005 Neuro-Symbolic Artificial Intelligence. In the early 1990s, an initial set of workshops on this topic were organized. == Research == Key research questions remain, such as: What is the best way to integrate neural and symbolic architectures? How should symbolic structures be represented within neural networks and extracted from them? How should common-sense knowledge be learned and reasoned about? How can abstract knowledge that is hard to encode logically be handled? == Implementations == Implementations of neuro-symbolic approaches include: AllegroGraph: an integrated Knowledge Graph based platform for neuro-symbolic application development. Scallop: a language based on Datalog that supports differentiable logical and relational reasoning. Scallop can be integrated in Python and with a PyTorch learning module. Logic Tensor Networks: encode logical formulas as neural networks and simultaneously learn term encodings, term weights, and formula weights. DeepProbLog: combines neural networks with the probabilistic reasoning of ProbLog. Abductive Learning: integrates machine learning and logical reasoning in a balanced-loop via abductive reasoning, enabling them to work together in a mutually beneficial way. SymbolicAI: a compositional differentiable programming library.
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Tree (abstract data type)

In computer science, a tree is a widely used abstract data type that represents a hierarchical tree structure with a set of connected nodes. Each node in the tree can be connected to many children (depending on the type of tree), but must be connected to exactly one parent, except for the root node, which has no parent (i.e., the root node as the top-most node in the tree hierarchy). These constraints mean there are no cycles or "loops" (no node can be its own ancestor), and also that each child can be treated like the root node of its own subtree, making recursion a useful technique for tree traversal. In contrast to linear data structures, many trees cannot be represented by relationships between neighboring nodes (parent and children nodes of a node under consideration, if they exist) in a single straight line (called edge or link between two adjacent nodes). Binary trees are a commonly used type, which constrain the number of children for each parent to at most two. When the order of the children is specified, this data structure corresponds to an ordered tree in graph theory. A value or pointer to other data may be associated with every node in the tree, or sometimes only with the leaf nodes, which have no children nodes. The abstract data type (ADT) can be represented in a number of ways, including a list of parents with pointers to children, a list of children with pointers to parents, or a list of nodes and a separate list of parent-child relations (a specific type of adjacency list). Representations might also be more complicated, for example using indexes or ancestor lists for performance. Trees as used in computing are similar to but can be different from mathematical constructs of trees in graph theory, trees in set theory, and trees in descriptive set theory. == Terminology == A node is a structure which may contain data and connections to other nodes, sometimes called edges or links. Each node in a tree has zero or more child nodes, which are below it in the tree (by convention, trees are drawn with descendants going downwards). A node that has a child is called the child's parent node (or superior). All nodes have exactly one parent, except the topmost root node, which has none. A node might have many ancestor nodes, such as the parent's parent. Child nodes with the same parent are sibling nodes. Typically siblings have an order, with the first one conventionally drawn on the left. Some definitions allow a tree to have no nodes at all, in which case it is called empty. An internal node (also known as an inner node, inode for short, or branch node) is any node of a tree that has child nodes. Similarly, an external node (also known as an outer node, leaf node, or terminal node) is any node that does not have child nodes. The height of a node is the length of the longest downward path to a leaf from that node. The height of the root is the height of the tree. The depth of a node is the length of the path to its root (i.e., its root path). Thus the root node has depth zero, leaf nodes have height zero, and a tree with only a single node (hence both a root and leaf) has depth and height zero. Conventionally, an empty tree (tree with no nodes, if such are allowed) has height −1. Each non-root node can be treated as the root node of its own subtree, which includes that node and all its descendants. Other terms used with trees: Neighbor Parent or child. Ancestor A node reachable by repeated proceeding from child to parent. Descendant A node reachable by repeated proceeding from parent to child. Also known as subchild. Degree For a given node, its number of children. A leaf, by definition, has degree zero. Degree of tree The degree of a tree is the maximum degree of a node in the tree. Distance The number of edges along the shortest path between two nodes. Level The level of a node is the number of edges along the unique path between it and the root node. This is the same as depth. Width The number of nodes in a level. Breadth The number of leaves. Complete tree A tree with every level filled, except the last. Forest A set of one or more disjoint trees. Ordered tree A rooted tree in which an ordering is specified for the children of each vertex. Size of a tree Number of nodes in the tree. == Common operations == Enumerating all the items Enumerating a section of a tree Searching for an item Adding a new item at a certain position on the tree Deleting an item Pruning: Removing a whole section of a tree Grafting: Adding a whole section to a tree Finding the root for any node Finding the lowest common ancestor of two nodes === Traversal and search methods === Stepping through the items of a tree, by means of the connections between parents and children, is called walking the tree, and the action is a walk of the tree. Often, an operation might be performed when a pointer arrives at a particular node. A walk in which each parent node is traversed before its children is called a pre-order walk; a walk in which the children are traversed before their respective parents are traversed is called a post-order walk; a walk in which a node's left subtree, then the node itself, and finally its right subtree are traversed is called an in-order traversal. (This last scenario, referring to exactly two subtrees, a left subtree and a right subtree, assumes specifically a binary tree.) A level-order walk effectively performs a breadth-first search over the entirety of a tree; nodes are traversed level by level, where the root node is visited first, followed by its direct child nodes and their siblings, followed by its grandchild nodes and their siblings, etc., until all nodes in the tree have been traversed. == Representations == There are many different ways to represent trees. In working memory, nodes are typically dynamically allocated records with pointers to their children, their parents, or both, as well as any associated data. If of a fixed size, the nodes might be stored in a list. Nodes and relationships between nodes might be stored in a separate special type of adjacency list. In relational databases, nodes are typically represented as table rows, with indexed row IDs facilitating pointers between parents and children. Nodes can also be stored as items in an array, with relationships between them determined by their positions in the array (as in a binary heap). A binary tree can be implemented as a list of lists: the head of a list (the value of the first term) is the left child (subtree), while the tail (the list of second and subsequent terms) is the right child (subtree). This can be modified to allow values as well, as in Lisp S-expressions, where the head (value of first term) is the value of the node, the head of the tail (value of second term) is the left child, and the tail of the tail (list of third and subsequent terms) is the right child. Ordered trees can be naturally encoded by finite sequences, for example with natural numbers. == Examples of trees and non-trees == == Type theory == As an abstract data type, the abstract tree type T with values of some type E is defined, using the abstract forest type F (list of trees), by the functions: value: T → E children: T → F nil: () → F node: E × F → T with the axioms: value(node(e, f)) = e children(node(e, f)) = f In terms of type theory, a tree is an inductive type defined by the constructors nil (empty forest) and node (tree with root node with given value and children). == Mathematical terminology == Viewed as a whole, a tree data structure is an ordered tree, generally with values attached to each node. Concretely, it is (if required to be non-empty): A rooted tree with the "away from root" direction (a more narrow term is an "arborescence"), meaning: A directed graph, whose underlying undirected graph is a tree (any two vertices are connected by exactly one simple path), with a distinguished root (one vertex is designated as the root), which determines the direction on the edges (arrows point away from the root; given an edge, the node that the edge points from is called the parent and the node that the edge points to is called the child), together with: an ordering on the child nodes of a given node, and a value (of some data type) at each node. Often trees have a fixed (more properly, bounded) branching factor (outdegree), particularly always having two child nodes (possibly empty, hence at most two non-empty child nodes), hence a "binary tree". Allowing empty trees makes some definitions simpler, some more complicated: a rooted tree must be non-empty, hence if empty trees are allowed the above definition instead becomes "an empty tree or a rooted tree such that ...". On the other hand, empty trees simplify defining fixed branching factor: with empty trees allowed, a binary tree is a tree such that every node has exactly two children, each of which is a tree (possibly empty). == Applications == Trees are commonly used to represent or manipulate hierarchical data in ap
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Stochastic Neural Analog Reinforcement Calculator

The Stochastic Neural Analog Reinforcement Calculator (SNARC) is a neural network machine designed by Marvin Minsky. Prompted by a letter from Minsky, George Armitage Miller gathered the funding (a few thousand dollars) for the project from the Office of Naval Research of the U.S. Department of Defense in the summer of 1951 with the work to be carried out by Minsky, who was then a graduate student in mathematics at Princeton University. At the time, a physics graduate student at Princeton, Dean S. Edmonds, volunteered that he was good with electronics and therefore Minsky brought him onto the project. During undergraduate years, Minsky was inspired by the 1943 Warren McCulloch and Walter Pitts paper on artificial neurons, and decided to build such a machine. The learning was Skinnerian reinforcement learning, and Minsky talked with Skinner extensively during the development of the machine. They tested the machine on a copy of Shannon's maze, and found that it could learn to solve the maze. Unlike Shannon's maze, this machine did not control a physical robot, but simulated rats running in a maze. The simulation is displayed as an "arrangement of lights", and the circuit was reinforced each time the simulated rat reached the goal. The machine surprised its creators. "The rats actually interacted with one another. If one of them found a good path, the others would tend to follow it." The machine itself is a randomly connected network of approximately 40 Hebb synapses. These synapses each have a memory that holds the probability that signal comes in one input and another signal will come out of the output. There is a probability knob that goes from 0 to 1 that shows this probability of the signals propagating. If the probability signal gets through, a capacitor remembers this function and engages an electromagnetic clutch. At this point, the operator will press a button to give a reward to the machine. This activates a motor on a surplus Minneapolis-Honeywell C-1 gyroscopic autopilot from a B-24 bomber. The motor turns a chain that goes to all 40 synapse machines, checking if the clutch is engaged or not. As the capacitor can only "remember" for a certain amount of time, the chain only catches the most recent updates of the probabilities. Each neuron contained 6 vacuum tubes and a motor. The entire machine is "the size of a grand piano" and contained 300 vacuum tubes. The tubes failed regularly, but the machine would still work despite failures. This machine is considered one of the first pioneering attempts at the field of artificial intelligence. Minsky went on to be a founding member of MIT's Project MAC, which split to become the MIT Laboratory for Computer Science and the MIT Artificial Intelligence Lab, and is now the MIT Computer Science and Artificial Intelligence Laboratory. In 1985 Minsky became a founding member of the MIT Media Laboratory. According to Minsky, he loaned the machine to students in Dartmouth, and subsequently lost, except for a single neuron. A photo of Minsky's last neuron can be seen here. The photo shows 6 vacuum tubes, one of which is a Sylvania JAN-CHS-6H6GT/G/VT-90A.
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Stewart Nelson

Stewart Nelson is an American mathematician and programmer from The Bronx who co-founded Systems Concepts. == Biography == From a young age, Nelson was tinkering with electronics, aided and abetted by his father who was a physicist that had become an engineer. Stewart attended Poughkeepsie High School, graduating in the spring of 1963. From his first few days of High School, Stewart displayed his talents for hacking the international telephone trunk lines, along with an uncanny skill for picking combination locks, although this was always done as innocent entertainment. He simply loved the challenge of seeing how quickly he could accomplish this feat. His quirky sense of humor was always visible, as was his disdain for any rule that got in the way of his gaining knowledge. Stewart was an inspiration to the school's Tech-elec Club, as well as a ringleader in the founding of the school's pirate radio station. Nelson enrolled at MIT in 1963 and quickly became known for hooking up the AI Lab's PDP-1 (and later the PDP-6) to the telephone network, making him one of the first phreakers. Nelson later accomplished other feats like hard-wiring additional instructions into the PDP-1. Nelson was hired by Ed Fredkin's Information International Inc. at the urging of Marvin Minsky to work on PDP-7 programs at the MIT Computer Science and Artificial Intelligence Laboratory. Nelson was known as a brilliant software programmer. He was influential in LISP, the assembly instructions for the Digital Equipment Corporation PDP, and a number of other systems. The group of young hackers was known for working on systems after hours. One night, Nelson and others decided to rewire MIT's PDP-1 as a prank. Later, Margaret Hamilton tried to use the DEC-supplied DECAL assembler on the machine and it crashed repeatedly.
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ELMo

ELMo (embeddings from language model) is a word embedding method for representing a sequence of words as a corresponding sequence of vectors. It was created by researchers at the Allen Institute for Artificial Intelligence, and University of Washington and first released in February 2018. It is a bidirectional LSTM which takes character-level as inputs and produces word-level embeddings, trained on a corpus of about 30 million sentences and 1 billion words. The architecture of ELMo accomplishes a contextual understanding of tokens. Deep contextualized word representation is useful for many natural language processing tasks, such as coreference resolution and polysemy resolution. ELMo was historically important as a pioneer of self-supervised generative pretraining followed by fine-tuning, where a large model is trained to reproduce a large corpus, then the large model is augmented with additional task-specific weights and fine-tuned on supervised task data. It was an instrumental step in the evolution towards transformer-based language modelling. == Architecture == ELMo is a multilayered bidirectional LSTM on top of a token embedding layer. The output of all LSTMs concatenated together consists of the token embedding. The input text sequence is first mapped by an embedding layer into a sequence of vectors. Then two parts are run in parallel over it. The forward part is a 2-layered LSTM with 4096 units and 512 dimension projections, and a residual connection from the first to second layer. The backward part has the same architecture, but processes the sequence back-to-front. The outputs from all 5 components (embedding layer, two forward LSTM layers, and two backward LSTM layers) are concatenated and multiplied by a linear matrix ("projection matrix") to produce a 512-dimensional representation per input token. ELMo was pretrained on a text corpus of 1 billion words. The forward part is trained by repeatedly predicting the next token, and the backward part is trained by repeatedly predicting the previous token. After the ELMo model is pretrained, its parameters are frozen, except for the projection matrix, which can be fine-tuned to minimize loss on specific language tasks. This is an early example of the pretraining-fine-tune paradigm. The original paper demonstrated this by improving state of the art on six benchmark NLP tasks. === Contextual word representation === The architecture of ELMo accomplishes a contextual understanding of tokens. For example, the first forward LSTM of ELMo would process each input token in the context of all previous tokens, and the first backward LSTM would process each token in the context of all subsequent tokens. The second forward LSTM would then incorporate those to further contextualize each token. Deep contextualized word representation is useful for many natural language processing tasks, such as coreference resolution and polysemy resolution. For example, consider the sentenceShe went to the bank to withdraw money.In order to represent the token "bank", the model must resolve its polysemy in context. The first forward LSTM would process "bank" in the context of "She went to the", which would allow it to represent the word to be a location that the subject is going towards. The first backward LSTM would process "bank" in the context of "to withdraw money", which would allow it to disambiguate the word as referring to a financial institution. The second forward LSTM can then process "bank" using the representation vector provided by the first backward LSTM, thus allowing it to represent it to be a financial institution that the subject is going towards. == Historical context == ELMo is one link in a historical evolution of language modelling. Consider a simple problem of document classification, where we want to assign a label (e.g., "spam", "not spam", "politics", "sports") to a given piece of text. The simplest approach is the "bag of words" approach, where each word in the document is treated independently, and its frequency is used as a feature for classification. This was computationally cheap but ignored the order of words and their context within the sentence. GloVe and Word2Vec built upon this by learning fixed vector representations (embeddings) for words based on their co-occurrence patterns in large text corpora. Like BERT (but unlike "bag of words" such as Word2Vec and GloVe), ELMo word embeddings are context-sensitive, producing different representations for words that share the same spelling. It was trained on a corpus of about 30 million sentences and 1 billion words. Previously, bidirectional LSTM was used for contextualized word representation. ELMo applied the idea to a large scale, achieving state of the art performance. After the 2017 publication of Transformer architecture, the architecture of ELMo was changed from a multilayered bidirectional LSTM to a Transformer encoder, giving rise to BERT. BERT has a similar pretrain-fine-tune workflow, but uses a Transformer with implications for more parallelizable training.
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DAYDREAMER

DAYDREAMER is a goal-based agent and cognitive architecture developed at the University of California, Los Angeles by Erik T. Mueller and Michael G. Dyer beginning in 1983. The system models the human stream of thought and how it is triggered and directed by emotions, simulating human daydreaming. Taking situational descriptions as input, DAYDREAMER produces English-language daydreams as output and encodes new daydreams, plans, and planning strategies for later reuse. The program comprises five components: a scenario generator based on relaxed planning, a dynamic episodic memory, a collection of personal goals and control goals, an emotion component, and domain knowledge of interpersonal relations and everyday occurrences. The source code was released under a free software license in 2015. == History == Erik Mueller began DAYDREAMER in 1983 while he was a doctoral student in the Artificial Intelligence Laboratory of the Computer Science Department at the University of California, Los Angeles, studying under Michael G. Dyer. Initial development of the project was supported by a grant from the W. M. Keck Foundation with matching funds from the UCLA School of Engineering and Applied Sciences. Additionally, Mueller was supported by an Atlantic Richfield Doctoral Fellowship and Dyer by an IBM Faculty Development Award. The first published descriptions of the program appeared in 1985 at the Ninth International Joint Conference on Artificial Intelligence in Los Angeles and at the Seventh Annual Conference of the Cognitive Science Society in Irvine. Work on the program continued, and a book, Daydreaming in Humans and Machines, was published by Ablex Publishing in 1990. The program was implemented on top of GATE, a knowledge-representation and inference substrate developed by Mueller and Uri Zernik at UCLA, and was originally written in T, a dialect of Scheme. In 2015, Mueller released the DAYDREAMER source code, version 3.5, a Common Lisp rewrite of the original T implementation, on GitHub under the GNU General Public License version 2. The release comprised approximately 12,000 lines of Common Lisp code, along with the GATE knowledge-representation substrate on which DAYDREAMER had originally been built. == Architecture == The program operates in two modes. In daydreaming mode it daydreams continuously until interrupted, while performance mode allows it to demonstrate behavior it has learned through daydreaming. === Emotion and control goals === Emotions and daydreaming form a feedback loop for DAYDREAMER. Emotions activate goals that produce daydreams, and the resulting daydreams modify existing emotions and trigger new ones, which prompt subsequent daydreaming. Recall of a goal success produces a positive emotion whereas recall of a goal failure produces a negative emotion. Emotions activate a set of goals, called control goals, which direct the course of a daydream. The program has four control goals. "Rationalization" generates reasons why an unsatisfactory outcome is in fact acceptable, in order to reduce a negative emotion and maintain self-esteem. "Revenge" is activated by anger when a failure is caused by another and reduces negative emotion through imagined retaliation. "Failure/success reversal" imagines alternative scenarios in which a failure was prevented or a success did not occur as a means of learning planning strategies for future situations. "Preparation" generates hypothetical future scenarios in order to rehearse plans and actions for events that have not yet occurred. === Scenario generator and relaxed planning === The scenario generator produces the sequence of events that make up a daydream. It operates under multiple, often conflicting personal goals rather than pursuing a single goal, applies relaxation rules that permit the generation of non-realistic scenarios, and it draws on episodic memory of past experiences both as subject matter and as a source of planning knowledge. The personal goals that guide the scenario generator include health, food, sex, friendship, love, possessions, self-esteem, social esteem, enjoyment, and achievement. These goals are organized into a goal tree that specifies their relative importance at any given time. Relaxation rules allow the program to set aside its ordinary constraints when generating a scenario. The four constraints that may be relaxed are the behavior of others, the daydreamer's own attributes, physical constraints, and social constraints. The degree of relaxation varies with the active control goal. For example a failure-reversal goal aimed at alternatives uses a low level of relaxation, whereas a revenge goal aimed at a retaliation uses a high level. === Episodic memory and analogy === DAYDREAMER's episodic memory stores its personal and vicarious experiences along with the daydreams it generates. The memory is described as dynamic because it is continually modified during daydreaming such that previously daydreamed episodes become available alongside real ones. As it daydreams, the program indexes daydreams, future plans or actions, and planning strategies into memory. Episodes are organized and retrieved using surface-level similarities, emotions, abstract themes, and Plot Units which are abstract configurations of positive and negative outcomes developed by Wendy Lehnert. A recalled episode is adapted to the current situation through analogy, which requires less effort than generating an equivalent scenario from scratch. == Sample output == In the sample experience from the source code, called LOVERS1, DAYDREAMER begins from an initial situation in which it has a job, is not romantically involved, and is at home. Starting in daydreaming mode, it activates a top-level goal to be in a romantic relationship because it is not currently in one, and a positive motivating emotion of interest becomes associated with that goal. The program then activates a goal to be entertained and pursues seeing a film as a way to achieve it. Facts asserted into memory are converted to English and produced as output, such as "I want to be going out with someone" and "I have to go see a movie". == Reception and influence == DAYDREAMER has been cited in research on computational models of creativity, emotion, and narrative. Linda Wills and Janet Kolodner cite the program as an example of work on opportunism in their study of serendipitous recognition in design. Joseph Bates, A. Bryan Loyall, and W. Scott Reilly of the Carnegie Mellon Oz Project cite DAYDREAMER among prior work in their description of an architecture combining action, emotion, and social behavior. Rafael Pérez y Pérez, Ricardo Sosa, and Christian Lemaitre cite Mueller's DAYDREAMER as one of the few computer models at the time to model daydreaming during the creative process. Jichen Zhu and D. Fox Harrell likewise cite the program in their work on imagining and agency in generative interactive narrative.
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Generative AI Copyright Disclosure Act

The Generative AI Copyright Disclosure Act is a piece of legislation introduced by California Representative Adam Schiff in the United States Congress on April 9, 2024. It concerns the transparency of companies regarding their use of copyrighted work to train their generative artificial intelligence (AI) models. The legislation requires the submission of a notice regarding the identity and the uniform resource locator (URL) address of the copyrighted works used in the training data to the Register of Copyrights at least 30 days before the public release of the new or updated version of the AI model; it does not ban the use of copyrighted works for AI training. The bill's requirements would apply retroactively to prior AI models. Violation penalties would start at US$5,000. The legislation does not have a maximum penalty assessment that can be charged. The bill by Schiff was introduced a few days after The New York Times published an article regarding the business activities of major tech firms, including Google and Meta, in the training of their generative AI platforms on April 6, 2024. The legislation is supported by the Professional Photographers of America (PPA), SAG-AFTRA, the Writers Guild of America, the International Alliance of Theatrical Stage Employees (IATSE), the Recording Industry Association of America (RIAA), and others.
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StepFun

Shanghai Jieyue Xingchen Intelligent Technology Co., Ltd, known as StepFun, is an artificial intelligence (AI) company based in Shanghai, China. It has been dubbed one of China's "AI Tiger" companies by investors. == Background == StepFun was founded in April 2023 by former Microsoft employees. Investors include Tencent, Qiming Venture Partners and Shanghai State-owned Capital Investment. In July 2025 at the World Artificial Intelligence Conference, StepFun announced the "Model-Chip Ecosystem Innovation Alliance" which consisted of Chinese developers of large language models (LLMs) and AI chip manufacturers. This included companies such as Huawei, Biren Technology, Moore Threads and Enflame. Another second alliance named the "Shanghai General Chamber of Commerce AI Committee" was also established that included StepFun, SenseTime, MiniMax, MetaX and Iluvatar CoreX. On 25 February 2026, it was reported that StepFun was seeking an initial public offering on the Hong Kong Stock Exchange. StepFun focuses on multimodal models which are designed to understand multiple types of input data such as text, video and audio. == Products == In July 2024 at the World Artificial Intelligence Conference, StepFun officially launched Step-2, a trillion-parameter LLM, along with the Step-1.5V multimodal model and the Step-1X image generation model. In February 2025, StepFun and Geely jointly announced the open-sourcing of two multimodal large models to global developers. They were Step-Video-T2V and Step-Audio. In July 2025, StepFun released Step 3. The Model-Chip Ecosystem Innovation Alliance aimed to optimize Step 3 for domestic chips. In April 2025, Step-R1-V-Mini was released. It is a multimodal reasoning model designed for visual interpretation and image understanding. In February 2026, Step-3.5-Flash, a mixture-of-experts model with 196 billion parameters and 11 billion active parameters was released under the free and open-source Apache 2.0 license. It supports tool use and a 256k token context window. == Models ==
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Sparrow (chatbot)

Sparrow is a chatbot developed by the artificial intelligence research lab DeepMind, a subsidiary of Alphabet Inc. It is designed to answer users' questions correctly, while reducing the risk of unsafe and inappropriate answers. One motivation behind Sparrow is to address the problem of language models producing incorrect, biased or potentially harmful outputs. Sparrow is trained using human judgements, in order to be more “Helpful, Correct and Harmless” compared to baseline pre-trained language models. The development of Sparrow involved asking paid study participants to interact with Sparrow, and collecting their preferences to train a model of how useful an answer is. To improve accuracy and help avoid the problem of hallucinating incorrect answers, Sparrow has the ability to search the Internet using Google Search in order to find and cite evidence for any factual claims it makes. To make the model safer, its behaviour is constrained by a set of rules, for example "don't make threatening statements" and "don't make hateful or insulting comments", as well as rules about possibly harmful advice, and not claiming to be a person. During development study participants were asked to converse with the system and try to trick it into breaking these rules. A 'rule model' was trained on judgements from these participants, which was used for further training. Sparrow was introduced in a paper in September 2022, titled "Improving alignment of dialogue agents via targeted human judgements"; however, the bot was not released publicly. DeepMind CEO Demis Hassabis said DeepMind is considering releasing Sparrow for a "private beta" some time in 2023. == Training == Sparrow is a deep neural network based on the transformer machine learning model architecture. It is fine-tuned from DeepMind's Chinchilla AI pre-trained large language model (LLM), which has 70 Billion parameters. Sparrow is trained using reinforcement learning from human feedback (RLHF), although some supervised fine-tuning techniques are also used. The RLHF training utilizes two reward models to capture human judgements: a “preference model” that predicts what a human study participant would prefer and a “rule model” that predicts if the model has broken one of the rules. == Limitations == Sparrow's training data corpus is mainly in English, meaning it performs worse in other languages. When adversarially probed by study participants it breaks the rules 8% of the time; however, this is still three times lower than the baseline prompted pre-trained model (Chinchilla).
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Allen's interval algebra

Allen's interval algebra is a calculus for temporal reasoning that was introduced by James F. Allen in 1983. The calculus defines possible relations between time intervals and provides a composition table that can be used as a basis for reasoning about temporal descriptions of events. == Formal description == === Relations === The following 13 base relations capture the possible relations between two intervals. To see that the 13 relations are exhaustive, note that each point of X {\displaystyle X} can be at 5 possible locations relative to Y {\displaystyle Y} : before, at the start, within, at the end, after. These give 5 + 4 + 3 + 2 + 1 = 15 {\displaystyle 5+4+3+2+1=15} possible relative positions for the start and the end of X {\displaystyle X} . Of these, we cannot have X 0 = X 1 = Y 0 {\displaystyle X_{0}=X_{1}=Y_{0}} since X 0 < X 1 {\displaystyle X_{0} Read more →
Rule-based system

In computer science, a rule-based system is a computer system in which domain-specific knowledge is represented in the form of rules and general-purpose reasoning is used to solve problems in the domain. Two different kinds of rule-based systems emerged within the field of artificial intelligence in the 1970s: Production systems, which use if-then rules to derive actions from conditions. Logic programming systems, which use conclusion if conditions rules to derive conclusions from conditions. The differences and relationships between these two kinds of rule-based system has been a major source of misunderstanding and confusion. Both kinds of rule-based systems use either forward or backward chaining, in contrast with imperative programs, which execute commands listed sequentially. However, logic programming systems have a logical interpretation, whereas production systems do not. == Production system rules == A classic example of a production rule-based system is the domain-specific expert system that uses rules to make deductions or choices. For example, an expert system might help a doctor choose the correct diagnosis based on a cluster of symptoms, or select tactical moves to play a game. Rule-based systems can be used to perform lexical analysis to compile or interpret computer programs, or in natural language processing. Rule-based programming attempts to derive execution instructions from a starting set of data and rules. This is a more indirect method than that employed by an imperative programming language, which lists execution steps sequentially. === Construction === A typical rule-based system has four basic components: A list of rules or rule base, which is a specific type of knowledge base. An inference engine or semantic reasoner, which infers information or takes action based on the interaction of input and the rule base. The interpreter executes a production system program by performing the following match-resolve-act cycle: Match: In this first phase, the condition sides of all productions are matched against the contents of working memory. As a result a set (the conflict set) is obtained, which consists of instantiations of all satisfied productions. An instantiation of a production is an ordered list of working memory elements that satisfies the condition side of the production. Conflict-resolution: In this second phase, one of the production instantiations in the conflict set is chosen for execution. If no productions are satisfied, the interpreter halts. Act: In this third phase, the actions of the production selected in the conflict-resolution phase are executed. These actions may change the contents of working memory. At the end of this phase, execution returns to the first phase. Temporary working memory, which is a database of facts. A user interface or other connection to the outside world through which input and output signals are received and sent. Whereas the matching phase of the inference engine has a logical interpretation, the conflict resolution and action phases do not. Instead, "their semantics is usually described as a series of applications of various state-changing operators, which often gets quite involved (depending on the choices made in deciding which ECA rules fire, when, and so forth), and they can hardly be regarded as declarative". == Logic programming rules == The logic programming family of computer systems includes the programming language Prolog, the database language Datalog and the knowledge representation and problem-solving language Answer Set Programming (ASP). In all of these languages, rules are written in the form of clauses: A :- B1, ..., Bn. and are read as declarative sentences in logical form: A if B1 and ... and Bn. In the simplest case of Horn clauses (or "definite" clauses), which are a subset of first-order logic, all of the A, B1, ..., Bn are atomic formulae. Although Horn clause logic programs are Turing complete, for many practical applications, it is useful to extend Horn clause programs by allowing negative conditions, implemented by negation as failure. Such extended logic programs have the knowledge representation capabilities of a non-monotonic logic. == Differences and relationships between production rules and logic programming rules == The most obvious difference between the two kinds of systems is that production rules are typically written in the forward direction, if A then B, and logic programming rules are typically written in the backward direction, B if A. In the case of logic programming rules, this difference is superficial and purely syntactic. It does not affect the semantics of the rules. Nor does it affect whether the rules are used to reason backwards, Prolog style, to reduce the goal B to the subgoals A, or whether they are used, Datalog style, to derive B from A. In the case of production rules, the forward direction of the syntax reflects the stimulus-response character of most production rules, with the stimulus A coming before the response B. Moreover, even in cases when the response is simply to draw a conclusion B from an assumption A, as in modus ponens, the match-resolve-act cycle is restricted to reasoning forwards from A to B. Reasoning backwards in a production system would require the use of an entirely different kind of inference engine. In his Introduction to Cognitive Science, Paul Thagard includes logic and rules as alternative approaches to modelling human thinking. He does not consider logic programs in general, but he considers Prolog to be, not a rule-based system, but "a programming language that uses logic representations and deductive techniques" (page 40). He argues that rules, which have the form IF condition THEN action, are "very similar" to logical conditionals, but they are simpler and have greater psychological plausibility (page 51). Among other differences between logic and rules, he argues that logic uses deduction, but rules use search (page 45) and can be used to reason either forward or backward (page 47). Sentences in logic "have to be interpreted as universally true", but rules can be defaults, which admit exceptions (page 44). He does not observe that all of these features of rules apply to logic programming systems.
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Marco Camisani Calzolari

Marco Camisani Calzolari (born March 1969) is an Italian British university professor, author, and television personality specializing in digital communications, transformation, and artificial intelligence. He advises the Italian government and police on ethical AI and digital safety and hosts the digital segment of the Italian news show Striscia la Notizia. His research gained international attention in 2012 after creating an algorithm claiming to identify real Twitter users from fake users of bots. Marco Camisani Calzolari was awarded as an Honorary Police Officer by the Italian State Police and the Knight of the Italian Republic. == Biography == Camisani Calzolari was born in Milan, Italy where he began his television career, hosting on local provider LA7 in (2001). In 2008 Camisani Calzolari moved to the UK where he founded multiple digital start-ups. He is now a naturalised British citizen and applied to become a "Freeman of the City" in June 2022. In 2024, Marco Camisani Calzolari began serving as the Chair and Adjunct Professor of the elective course Cyber-Humanities within the Degree Programme in Medicine and Surgery at Università Vita-Salute S.Raffaele in Milan. On the 14th of May 2024, Camisani Calzolari was awarded the Knight of the Italian Republic (Order of the Star of Italy). In 2024, Marco Camisani Calzolari was awarded the title of Honorary Police Officer by the Italian State Police for his commitment to combating cybercrime and promoting digital security. He also received the Keynes Sraffa Award 2024 from the Italian Chamber of Commerce and Industry for the UK. Additionally, he was honored with the University Seal by Università degli Studi della Tuscia (Viterbo) for his efforts in disseminating knowledge both in Italy and abroad. == Academic career == Camisani Calzolari began his academic career at the Università Statale di Milano in 2007, until chairing a course on Corporate Communication and Digital Languages at the IULM University of Milan between 2007 and 2010. During this time Camisani Calzolari published his first written work under the title 'Impresa 4.0'. After moving to London, Camisani Calzolari focussed on digital start-ups including 'Digitalevaluation ltd' where he would publish the results of his Twitter algorithm study. Following its publication, he accepted a role as Affiliate Practitioner at the Centre for Culture Media & Regulation (CCMR), University of Brunel London, and subsequently another role at a British University as Lecturer in Digital Communication at the LCA Business School. Camisani Calzolari returned to Italy to lecture on Interactive Digital Communication at the University of Milan. From 2017 to 2023, he held various roles at the European University of Rome, including Adjunct Professor and Chair in Digital Communication, and published The Fake News Bible in 2018. In 2024 he became the Scientific Coordinator for a Master's program at Università San Raffaele in Milan. === Twitter fake followers study === In 2012, Camisani Calzolari's research came into the focus of the public eye following the publication of his findings in a study analysing the followers of high-profile public figures and corporations. He developed a computer algorithm claiming to be able to distinguish real followers from computer-generated "bots". The algorithm compiled data correlative of human activity such as having a name, image, physical address, using punctuation and cross-account activity. Genuine Twitter users were considered to have written at least 50 posts and possessed over 30 followers themselves. The findings led to scrutiny of several individuals and corporations for allegedly purchasing followers. === Publications === Camisani Calzolari is best for known for his work in improving accessibility to digital and tech solutions for everyday business and personal use. His work in digital and communications has been included in several publications including: Cyberhumanism (2023) The Fake News Bible (2018), First Digital Aid for Business (2015), The Digital World (2013), Escape from Facebook (2012), Enterprise 4.0. Camisani Calzolari was also the subject of a University College London (UCL) case study titled Marco Camisani-Calzolari: the Digital Renaissance Man. == Government work == Since 2023, he is a member of the Coordination Committee on Artificial Intelligence at the Presidency of the Council of Ministers and an advisor in Digital Skills and Designer of initiatives for the Department for Digital Transformation. He also serves as the official spokesperson for the State Police, educating the public on preventing digital threats, avoiding digital scams, and explaining criminal case. Since August 2024, Marco Camisani Calzolari has served as an expert for the Italian Agency for the National Cybersecurity (ACN). In October of the same year, he also became a member of the General-Purpose AI Code of Practice working group for the European Commission. == Television work == Camisani Calzolari hosts a digital segment for Striscia la Notizia, an Italian satirical television program on the Mediaset-controlled Canale 5. He presented on weekly segments that include: RAI 1 – Digital First Aid (TV Program – 2014 to 2017) in the program "Uno Mattina" as a digital expert; RTL 102.5 – Technology Space (Radio Program – 2012 to 2017) in the morning news program as a digital expert (100 episodes from 2012 to 2017); DIGITALK Talkshow (2004) as host of Digitalk; Misterweb (TV Program – 2001 to 2002), he presented the TV program “MisterWeb”, on "LA7". Marco Camisani Calzolari was a testimonial for several institutional communication campaigns by the Italian Department of Digital Transformation. These include initiatives promoting the Punti Digitale Facile, raising awareness about the NIS2 Directive for cybersecurity, and advocating for the adoption of the Electronic Identity Card (CIE).
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Cone tracing

Cone tracing and beam tracing are a derivative of the ray tracing algorithm that replaces rays, which have no thickness, with thick rays. == Principles == In ray tracing, rays are often modeled as geometric ray with no thickness to perform efficient geometric queries such as a ray-triangle intersection. From a physics of light transport point of view, however, this is an inaccurate model provided the pixel on the sensor plane has non-zero area. In the simplified pinhole camera optics model, the energy reaching the pixel comes from the integral of radiance from the solid angle by which the sensor pixel sees the scene through the pinhole at the focal plane. This yields the key notion of pixel footprint on surfaces or in the texture space, which is the back projection of the pixel on to the scene. Note that this approach can also represent a lens-based camera and thus depth of field effects, using a cone whose cross-section decreases from the lens size to zero at the focal plane, and then increases. Real optical system do not focus on exact points because of diffraction and imperfections. This can be modeled with a point spread function (PSF) weighted within a solid angle larger than the pixel. From a signal processing point of view, ignoring the point spread function and approximating the integral of radiance with a single, central sample (through a ray with no thickness) can lead to strong aliasing because the "projected geometric signal" has very high frequencies exceeding the Nyquist-Shannon maximal frequency that can be represented using the uniform pixel sampling rate. The physically based image formation model can be approximated by the convolution with the point spread function assuming the function is shift-invariant and linear. In practice, techniques such as multisample anti-aliasing estimate this cone-based model by oversampling the signal and then performing a convolution (the reconstruction filter). The backprojected cone footprint onto the scene can also be used to directly pre-filter the geometry and textures of the scene. Note that contrary to intuition, the reconstruction filter should not be the pixel footprint (as the pinhole camera model would suggest), since a box filter has poor spectral properties. Conversely, the ideal sinc function is not practical, having infinite support with possibly negative values which often creates ringing artifacts due to the Gibbs phenomenon. A Gaussian or a Lanczos filter are considered good compromises. == Computer graphics models == Cone and Beam early papers rely on different simplifications: the first considers a circular section and treats the intersection with various possible shapes. The second treats an accurate pyramidal beam through the pixel and along a complex path, but it only works for polyhedrical shapes. Cone tracing solves certain problems related to sampling and aliasing, which can plague conventional ray tracing. However, cone tracing creates a host of problems of its own. For example, just intersecting a cone with scene geometry leads to an enormous variety of possible results. For this reason, cone tracing has remained mostly unpopular. In recent years, increases in computer speed have made Monte Carlo algorithms like distributed ray tracing - i.e. stochastic explicit integration of the pixel - much more used than cone tracing because the results are exact provided enough samples are used. But the convergence is so slow that even in the context of off-line rendering a huge amount of time can be required to avoid noise. Differential cone-tracing, considering a differential angular neighborhood around a ray, avoids the complexity of exact geometry intersection but requires a LOD representation of the geometry and appearance of the objects. MIPmapping is an approximation of it limited to the integration of the surface texture within a cone footprint. Differential ray-tracing extends it to textured surfaces viewed through complex paths of cones reflected or refracted by curved surfaces. Raymarching methods over signed distance fields (SDFs) naturally allow easy use of cone-like tracing, at zero additional cost to the tracing, and both speeds up tracing and improves quality. Voxel cone tracing is a real-time algorithm that uses a hierarchical voxel representation of scene geometry, such as a sparse voxel octree, to support fast cone tracing for indirect illumination. This approach allows for the approximation of effects like glossy reflections and ambient occlusion at interactive framerates without the need for precomputation.
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Nortel Speech Server

The Nortel Speech Server (formerly known as Periphonics Speech Processing Platform) in telecommunications is a speech processing system that was originally developed by Nortel. Following the bankruptcy of Nortel, it is now sold by Avaya. The system is primarily used for large vocabulary speech recognition, natural language understanding, text-to-speech, and speaker verification. The Nortel Speech Server was based on the Periphonics OSCAR platform. The original OSCAR Platform was based upon Solaris servers. The current range of Speech Servers is Windows based. Nortel Speech Server is a component of the MPS 500, MPS 1000, and ICP platforms. On MPS systems, it may be used to stream prerecorded audio.
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Computer Science Ontology

The Computer Science Ontology (CSO) is an automatically generated taxonomy of research topics in the field of Computer Science. It was produced by the Open University in collaboration with Springer Nature by running an information extraction system over a large corpus of scientific articles. Several branches were manually improved by domain experts. The current version (CSO 3.2) includes about 14K research topics and 160K semantic relationships. CSO is available in OWL, Turtle, and N-Triples. It is aligned with several other knowledge graphs, including DBpedia, Wikidata, YAGO, Freebase, and Cyc. New versions of CSO are regularly released on the CSO Portal. CSO is mostly used to characterise scientific papers and other documents according to their research areas, in order to enable different kinds of analytics. The CSO Classifier is an open-source python tool for automatically annotating documents with CSO. == Applications == Recommender Systems. Computing the semantic similarity of documents. Extracting metadata from video lecture subtitles. Performing bibliometrics analysis.
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