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Knowledge graph embedding
In representation learning, knowledge graph embedding (KGE), also called knowledge representation learning (KRL), or multi-relation learning, is a machine learning task of learning a low-dimensional representation of a knowledge graph's entities and relations while preserving their semantic meaning. Leveraging their embedded representation, knowledge graphs can be used for various applications such as link prediction, triple classification, entity recognition, clustering, and relation extraction. == Definition == A knowledge graph G = { E , R , F } {\displaystyle {\mathcal {G}}=\{E,R,F\}} is a collection of entities E {\displaystyle E} , relations R {\displaystyle R} , and facts F {\displaystyle F} . A fact is a triple ( h , r , t ) ∈ F {\displaystyle (h,r,t)\in F} that denotes a link r ∈ R {\displaystyle r\in R} between the head h ∈ E {\displaystyle h\in E} and the tail t ∈ E {\displaystyle t\in E} of the triple. Another notation that is often used in the literature to represent a triple (or fact) is ⟨ head , relation , tail ⟩ {\displaystyle \langle {\text{head}},{\text{relation}},{\text{tail}}\rangle } . This notation is called the Resource Description Framework (RDF). A knowledge graph represents the knowledge related to a specific domain; leveraging this structured representation, it is possible to infer a piece of new knowledge from it after some refinement steps. However, nowadays, people have to deal with the sparsity of data and the computational inefficiency to use them in a real-world application. The embedding of a knowledge graph is a function that translates each entity and each relation into a vector of a given dimension d {\displaystyle d} , called embedding dimension. It is even possible to embed the entities and relations with different dimensions. The embedding vectors can then be used for other tasks. A knowledge graph embedding is characterized by four aspects: Representation space: The low-dimensional space in which the entities and relations are represented. Scoring function: A measure of the goodness of a triple-embedded representation. Encoding models: The modality in which the embedded representation of the entities and relations interact with each other. Additional information: Any additional information coming from the knowledge graph that can enrich the embedded representation. Usually, an ad hoc scoring function is integrated into the general scoring function for each additional piece of information. == Embedding procedure == All algorithms for creating a knowledge graph embedding follow the same approach. First, the embedding vectors are initialized to random values. Then, they are iteratively optimized using a training set of triples. In each iteration, a batch of size b {\displaystyle b} triples is sampled from the training set, and a triple from it is sampled and corrupted—i.e., a triple that does not represent a true fact in the knowledge graph. The corruption of a triple involves substituting the head or the tail (or both) of the triple with another entity that makes the fact false. The original triple and the corrupted triple are added in the training batch, and then the embeddings are updated, optimizing a scoring function. Iteration stops when a stop condition is reached. Usually, the stop condition depends on the overfitting of the training set. At the end, the learned embeddings should have extracted semantic meaning from the training triples and should correctly predict unseen true facts in the knowledge graph. === Pseudocode === The following is the pseudocode for the general embedding procedure. algorithm Compute entity and relation embeddings input: The training set S = { ( h , r , t ) } {\displaystyle S=\{(h,r,t)\}} , entity set E {\displaystyle E} , relation set R {\displaystyle R} , embedding dimension k {\displaystyle k} output: Entity and relation embeddings initialization: the entities e {\displaystyle e} and relations r {\displaystyle r} embeddings (vectors) are randomly initialized while stop condition do S b a t c h ← s a m p l e ( S , b ) {\displaystyle S_{batch}\leftarrow sample(S,b)} // Sample a batch from the training set for each ( h , r , t ) {\displaystyle (h,r,t)} in S b a t c h {\displaystyle S_{batch}} do ( h ′ , r , t ′ ) ← s a m p l e ( S ′ ) {\displaystyle (h',r,t')\leftarrow sample(S')} // Sample a corrupted fact T b a t c h ← T b a t c h ∪ { ( ( h , r , t ) , ( h ′ , r , t ′ ) ) } {\displaystyle T_{batch}\leftarrow T_{batch}\cup \{((h,r,t),(h',r,t'))\}} end for Update embeddings by minimizing the loss function end while == Performance indicators == These indexes are often used to measure the embedding quality of a model. The simplicity of the indexes makes them very suitable for evaluating the performance of an embedding algorithm even on a large scale. Given Q {\displaystyle {\ce {Q}}} as the set of all ranked predictions of a model, it is possible to define three different performance indexes: Hits@K, MR, and MRR. === Hits@K === Hits@K or in short, H@K, is a performance index that measures the probability to find the correct prediction in the first top K model predictions. Usually, it is used k = 10 {\displaystyle k=10} . Hits@K reflects the accuracy of an embedding model to predict the relation between two given triples correctly. Hits@K = | { q ∈ Q : q < k } | | Q | ∈ [ 0 , 1 ] {\displaystyle ={\frac {|\{q\in Q:q GNOWSYS (Gnowledge Networking and Organizing system) is a specification for a generic distributed network based memory/knowledge management. It is developed as an application for developing and maintaining semantic web content. It is written in Python. It is implemented as a Django app. The GNOWSYS project was launched by Nagarjuna G. in 2001, while he was working at Homi Bhabha Centre for Science Education (HBCSE). The memory of GNOWSYS is designed as a node-oriented space. A node is described by other nodes to which it has links. The nodes are organized and processed according to a complex data structure called the neighborhood. == Applications == The application can be used for web-based knowledge representation and content management projects, for developing structured knowledge bases, as a collaborative authoring tool, suitable for making electronic glossaries, dictionaries and encyclopedias, for managing large web sites or links, developing an online catalogue for a library of any thing including books, to make ontologies, classifying and networking any objects, etc. This tool is also intended to be used for an on-line tutoring system with dependency management between various concepts or software packages. For example, the dependency relations between Debian packages have been represented by the gnowledge portal Archived 2018-05-14 at the Wayback Machine. == Component Classes == The kernel is designed to provide support to persistently store highly granular nodes of knowledge representation like terms, predicates and very complex propositional systems like arguments, rules, axiomatic systems, loosely held paragraphs, and more complex structured and consistent compositions. All the component classes in GNOWSYS are classified according to complexity into three groups, where the first two groups are used to express all possible well formed formulae permissible in a first order logic. === Terms === ‘Object’, ‘Object Type’ for declarative knowledge, ‘Event’, ‘Event Type’, for temporal objects, and ‘Meta Types’ for expressing upper ontology. The objects in this group are essentially any thing about which the knowledge engineer intends to express and store in the knowledge base, i.e., they are the objects of discourse. The instances of these component classes can be stored with or without expressing ‘instance of’ or ‘sub-class of’ relations among them. === Predicates === This group consists of ‘Relation’, and ‘Relation Type’ for expressing declarative knowledge, and ‘Function’ and ‘Function Type’ for expressing procedural knowledge. This group is to express qualitative and quantitative relations among the various instances stored in the knowledge base. While instantiating the predicates can be characterized by their logical properties of relations, quantifiers and cardinality as monadic predicates of these predicate objects. === Structures === ‘System’, ‘Encapsulated Class’, ‘Program’, and ‘Process’, are other base classes for complex structures, which can be combined iteratively to produce more complex systems. The component class ‘System’ is to store in the knowledge base a set of propositions composed into ontologies, axiomatic systems, complex systems like say a human body, an artifact like a vehicle etc., with or without consistency check. An ‘Encapsulated Class’ is to com- pose declarative and behavioural objects in a flexible way to build classes. A ‘Program’ is not only to store the logic of any complete program or a component class, composed from the already available behavioural instances in the knowledge base with built-in connectives (conditions, and loops), but also execute them as web services. A ‘Process’ is to structure temporal objects with sequence, concurrency, synchronous or asynchronous specifications. Every node in the database keeps the neighbourhood information, such as its super-class, sub-class, instance-of, and other relations, in which the object has a role, in the form of predicates. This feature makes computation of drawing graphs and inferences, on the one hand, and dependency and navigation paths on the other hand very easy. All the data and metadata is indexed in a central catalogue making query and locating resources efficient. Andrej Karpathy (born 23 October 1986) is a Slovak-Canadian AI researcher, who co-founded and formerly worked at OpenAI, where he specialized in deep learning and computer vision. He also worked as the director of artificial intelligence and Autopilot Vision at Tesla, and in 2024 he founded Eureka Labs, an AI education platform. In 2026 he joined Anthropic as part of the pretraining team. == Education and early life == Karpathy was born in Bratislava, Czechoslovakia (now Slovakia), and moved with his family to Toronto when he was 15. He completed his Computer Science and Physics bachelor's degrees at University of Toronto in 2009 and his master's degree at University of British Columbia in 2011, where he worked on physically simulated figures (for example, a simulated runner or a simulated person in a crowd) with his adviser Michiel van de Panne. In 2006, Karpathy began posting videos on YouTube on his channel, badmephisto. He garnered fame by posting Rubik's cube tutorials which have been used by famous speedcubers such as Feliks Zemdegs. The channel has over 9 million views as of June 2025. Karpathy received a PhD from Stanford University in 2015 under the supervision of Fei-Fei Li, focusing on the intersection of natural language processing and computer vision, and deep learning models suited for this task. == Career and research == He authored and was the primary instructor of the first deep learning course at Stanford, CS 231n: Convolutional Neural Networks for Visual Recognition. The course became one of the largest classes at Stanford, growing from 150 students in 2015 to 750 in 2017. Karpathy is a founding member of the artificial intelligence research group OpenAI, where he was a research scientist from 2015 to 2017. In June 2017 he became Tesla's director of artificial intelligence and reported to Elon Musk. He was named one of MIT Technology Review's Innovators Under 35 for 2020. After taking a several-months-long sabbatical from Tesla, he announced he was leaving the company in July 2022. As of February 2023, he makes YouTube videos on how to create artificial neural networks. On February 9, 2023, Karpathy announced he was returning to OpenAI. A year later on February 13, 2024, an OpenAI spokesperson confirmed that Karpathy had left OpenAI. In the same year, he was named one of Time Magazine's 100 Most Influential People in AI. On July 16, 2024, Karpathy announced on his X account that he started a new AI education company called Eureka Labs. Their first product was the AI course, LLM101n. He also has a broader educational effort, the "Zero to Hero" series on LLM fundamentals. The company also advocates for AI teaching assistants, a concept which has been criticized due to data privacy concerns and the removal of personal connection between teacher and student. In February 2025, Karpathy coined the term vibe coding to describe how AI tools allow hobbyists to construct apps and websites just by typing prompts. On May 19, 2026, he announced that he joined Anthropic via a statement on X, while the company stated that he will be leading a team for research in pretraining. Leabra stands for local, error-driven and associative, biologically realistic algorithm. It is a model of learning which is a balance between Hebbian and error-driven learning with other network-derived characteristics. This model is used to mathematically predict outcomes based on inputs and previous learning influences. Leabra is heavily influenced by and contributes to neural network designs and models, including emergent. == Background == It is the default algorithm in emergent (successor of PDP++) when making a new project, and is extensively used in various simulations. Hebbian learning is performed using conditional principal components analysis (CPCA) algorithm with correction factor for sparse expected activity levels. Error-driven learning is performed using GeneRec, which is a generalization of the recirculation algorithm, and approximates Almeida–Pineda recurrent backpropagation. The symmetric, midpoint version of GeneRec is used, which is equivalent to the contrastive Hebbian learning algorithm (CHL). See O'Reilly (1996; Neural Computation) for more details. The activation function is a point-neuron approximation with both discrete spiking and continuous rate-code output. Layer or unit-group level inhibition can be computed directly using a k-winners-take-all (KWTA) function, producing sparse distributed representations. A feedforward and feedback (FFFB) form of inhibition has now replaced the KWTA form of inhibition. FFFB inhibition can be efficiently implemented by using the average excitatory input and activity levels in a given layer. The net input is computed as an average, not a sum, over connections, based on normalized, sigmoidally transformed weight values, which are subject to scaling on a connection-group level to alter relative contributions. Automatic scaling is performed to compensate for differences in expected activity level in the different projections. Documentation about this algorithm can be found in the book "Computational Explorations in Cognitive Neuroscience: Understanding the Mind by Simulating the Brain" published by MIT press. and in the Emergent Documentation Archived 2009-04-16 at the Wayback Machine == Overview of the leabra algorithm == The pseudocode for Leabra is given here, showing exactly how the pieces of the algorithm described in more detail in the subsequent sections fit together. Iterate over minus and plus phases of settling for each event. o At start of settling, for all units: - Initialize all state variables (activation, v_m, etc.). - Apply external patterns (clamp input in minus, input & output in plus). - Compute net input scaling terms (constants, computed here so network can be dynamically altered). - Optimization: compute net input once from all static activations (e.g., hard-clamped external inputs). o During each cycle of settling, for all non-clamped units: - Compute excitatory netinput (g_e(t), aka eta_j or net) -- sender-based optimization by ignoring inactives. - Compute kWTA inhibition for each layer, based on g_i^Q: Sort units into two groups based on g_i^Q: top k and remaining k+1 -> n. If basic, find k and k+1th highest If avg-based, compute avg of 1 -> k & k+1 -> n. Set inhibitory conductance g_i from g^Q_k and g^Q_k+1 - Compute point-neuron activation combining excitatory input and inhibition o After settling, for all units, record final settling activations as either minus or plus phase (y^-_j or y^+_j). After both phases update the weights (based on linear current weight values), for all connections: o Compute error-driven weight changes with CHL with soft weight bounding o Compute Hebbian weight changes with CPCA from plus-phase activations o Compute net weight change as weighted sum of error-driven and Hebbian o Increment the weights according to net weight change. == Implementations == Emergent Archived 2015-10-03 at the Wayback Machine is the original implementation of Leabra; its most recent implementation is written in Go. It was written chiefly by Dr. O'Reilly, but professional software engineers were recently hired to improve the existing codebase. This is the fastest implementation, suitable for constructing large networks. Although emergent has a graphical user interface, it is very complex and has a steep learning curve. If you want to understand the algorithm in detail, it will be easier to read non-optimized code. For this purpose, check out the MATLAB version. There is also an R version available, that can be easily installed via install.packages("leabRa") in R and has a short introduction to how the package is used. The MATLAB and R versions are not suited for constructing very large networks, but they can be installed quickly and (with some programming background) are easy to use. Furthermore, they can also be adapted easily. == Special algorithms == Temporal differences and general dopamine modulation. Temporal differences (TD) is widely used as a model of midbrain dopaminergic firing. Primary value learned value (PVLV). PVLV simulates behavioral and neural data on Pavlovian conditioning and the midbrain dopaminergic neurons that fire in proportion to unexpected rewards (an alternative to TD). Prefrontal cortex basal ganglia working memory (PBWM). PBWM uses PVLV to train prefrontal cortex working memory updating system, based on the biology of the prefrontal cortex and basal ganglia. Cozi is a family organization website and mobile app designed to streamline household management. It offers shared calendars, to-do lists, shopping lists, and messaging tools, allowing multiple users to coordinate under one account. Founded in 2005 by former Microsoft employees, Cozi has evolved through acquisitions and now operates under OurFamilyWizard. The app is available in both free and premium versions on iOS, Android, and desktop platforms. == History == Cozi was founded in 2005 by Robbie Cape and Jan Miksovsky, two former Microsoft employees who sought to simplify family logistics with technology. The company's first product, Cozi Central, was released on September 25, 2006, and included a family calendar, shopping lists, family messaging and a photo collage screensaver. The company is based in Seattle, Washington. Cozi has both a freemium version, and a paid version called Cozi Gold. Cozi Gold's additional features include Cozi Contacts, a birthday tracker, more reminders, mobile month view, and change notifications. The software can be used on desktop or mobile applications for iOS and Android. On June 5, 2011, Cozi set a Guinness World Record for the longest line of ducks in a row. The line stretched for one mile and was made up of 17,782 rubber ducks. Cozi was acquired by Time Inc. in 2014. After the Meredith Corporation acquired Time in 2018, Cozi was moved into the Parents Network division. On May 4, 2022, Cozi was acquired by OurFamilyWizard of Minneapolis, Minnesota, reporting more than 20 million registered users. CuckooChess is an advanced free and open-source chess engine under the GNU General Public License written in Java by Peter Österlund. CuckooChess provides an own GUI, and optionally supports the Universal Chess Interface protocol for the use with external GUIs such as Arena. An Android port is available, where its GUI is also based on Peter Österlund's Stockfish port dubbed DroidFish. The program uses the Chess Cases chess font, created by Matthieu Leschemelle. The name CuckooChess comes due that the transposition table is based on Cuckoo hashing. Android app based chess gaming app Droidfish employs both CuckooChess and Stockfish chess engines. Similarly, Kickstarter funded AI based virtual reality chess game Square Off also uses CuckooChess engine. It has an ELO rating of 2583 (as of July 2018) and a rank of 135‑137 in the Computer Chess Rating List.GNOWSYS
Andrej Karpathy
Leabra
Cozi
CuckooChess