As part of the Gaza war, the Israel Defense Forces (IDF) have used artificial intelligence to rapidly and automatically perform much of the process of determining what to bomb. Israel has greatly expanded the bombing of the Gaza Strip, which in previous wars had been limited by the Israeli Air Force running out of targets. These tools include the Gospel, an AI which automatically reviews surveillance data looking for buildings, equipment and people thought to belong to the enemy, and upon finding them, recommends bombing targets to a human analyst who may then decide whether to pass it along to the field. Another is Lavender, an "AI-powered database" which lists tens of thousands of Palestinian men linked by AI to Hamas or Palestinian Islamic Jihad, and which is also used for target recommendation. Critics have argued the use of these AI tools puts civilians at risk, blurs accountability, and results in militarily disproportionate violence in violation of international humanitarian law. == The Gospel == Israel uses an AI system dubbed "Habsora", "the Gospel", to determine which targets the Israeli Air Force would bomb. It automatically provides a targeting recommendation to a human analyst, who decides whether to pass it along to soldiers in the field. The recommendations can be anything from individual fighters, rocket launchers, Hamas command posts, to private homes of suspected Hamas or Islamic Jihad members. AI can process military intelligence far faster than humans. Retired Lt Gen. Aviv Kohavi, head of the IDF until 2023, stated that the system could produce 100 bombing targets in Gaza a day, with real-time recommendations which ones to attack, where human analysts might produce 50 a year. A lecturer interviewed by NPR estimated these figures as 50–100 targets in 300 days for 20 intelligence officers, and 200 targets within 10–12 days for the Gospel. === Technological background === The Gospel uses machine learning, where an AI is tasked with identifying commonalities in vast amounts of data (e.g. scans of cancerous tissue, photos of a facial expression, surveillance of Hamas members identified by human analysts), then looking for those commonalities in new material. What information the Gospel uses is not known, but it is thought to combine surveillance data from diverse sources in enormous amounts. Recommendations are based on pattern-matching. A person with enough similarities to other people labeled as enemy combatants may be labelled a combatant themselves. Regarding the suitability of AIs for the task, NPR cited Heidy Khlaaf, engineering director of AI Assurance at the technology security firm Trail of Bits, as saying "AI algorithms are notoriously flawed with high error rates observed across applications that require precision, accuracy, and safety." Bianca Baggiarini, lecturer at the Australian National University's Strategic and Defence Studies Centre wrote AIs are "more effective in predictable environments where concepts are objective, reasonably stable, and internally consistent." She contrasted this with telling the difference between a combatant and non-combatant, which even humans frequently can't do. Khlaaf went on to point out that such a system's decisions depend entirely on the data it's trained on, and are not based on reasoning, factual evidence or causation, but solely on statistical probability. === Operation === The IAF ran out of targets to strike in the 2014 war and 2021 crisis. In an interview on France 24, investigative journalist Yuval Abraham of +972 Magazine stated that to maintain military pressure, and due to political pressure to continue the war, the military would bomb the same places twice. Since then, the integration of AI tools has significantly sped up the selection of targets. In early November, the IDF stated more than 12,000 targets in Gaza had been identified by the target administration division that uses the Gospel. NPR wrote on December 14 that it was unclear how many targets from the Gospel had been acted upon, but that the Israeli military said it was currently striking as many as 250 targets a day. The bombing, too, has intensified to what the December 14 article called an astonishing pace: the Israeli military stated at the time it had struck more than 22,000 targets inside Gaza, at a daily rate more than double that of the 2021 conflict, more than 3,500 of them since the collapse of the truce on December 1. Early in the offensive the head of the Air Force stated his forces only struck military targets, but added: "We are not being surgical." Once a recommendation is accepted, another AI, Fire Factory, cuts assembling the attack down from hours to minutes by calculating munition loads, prioritizing and assigning targets to aircraft and drones, and proposing a schedule, according to a pre-war Bloomberg article that described such AI tools as tailored for a military confrontation and proxy war with Iran. One change that The Guardian noted is that since senior Hamas leaders disappear into tunnels at the start of an offensive, systems such as the Gospel have allowed the IDF to locate and attack a much larger pool of more junior Hamas operatives. It cited an official who worked on targeting decisions in previous Gaza operations as saying that while the homes of junior Hamas members had previously not been targeted for bombing, the official believes the houses of suspected Hamas operatives were now targeted regardless of rank. In the France 24 interview, Abraham, of +972 Magazine, characterized this as enabling the systematization of dropping a 2000 lb bomb into a home to kill one person and everybody around them, something that had previously been done to a very small group of senior Hamas leaders. NPR cited a report by +972 Magazine and its sister publication Local Call as asserting the system is being used to manufacture targets so that Israeli military forces can continue to bombard Gaza at an enormous rate, punishing the general Palestinian population. NPR noted it had not verified this; it was unclear how many targets are being generated by AI alone, but there had been a substantial increase in targeting, with an enormous civilian toll. In principle, the combination of a computer's speed to identify opportunities and a human's judgment to evaluate them can enable more precise attacks and fewer civilian casualties. Israeli military and media have emphasized this capacity to minimize harm to non-combatants. Richard Moyes, researcher and head of the NGO Article 36, pointed to "the widespread flattening of an urban area with heavy explosive weapons" to question these claims, while Lucy Suchman, professor emeritus at Lancaster University, described the bombing as "aimed at maximum devastation of the Gaza Strip". The Guardian wrote that when a strike was authorized on private homes of those identified as Hamas or Islamic Jihad operatives, target researchers knew in advance the expected number of civilians killed, each target had a file containing a collateral damage score stipulating how many civilians were likely to be killed in a strike, and according to a senior Israeli military source, operatives use a "very accurate" measurement of the rate of civilians evacuating a building shortly before a strike. "We use an algorithm to evaluate how many civilians are remaining. It gives us a green, yellow, red, like a traffic signal." ==== 2021 use ==== Kohavi compared the target division using the Gospel to a machine and stated that once the machine was activated in the war of May 2021, it generated 100 targets a day, with half of them being attacked, in contrast with 50 targets in Gaza per year beforehand. Approximately 200 targets came from the Gospel out of the 1,500 targets Israel struck in Gaza in the war, including both static and moving targets according to the military. The Jewish Institute for National Security of America's after action report identified an issue, stating the system had data on what was a target, but lacked data on what wasn't. The system depends entirely on training data, and intel that human analysts had examined and deemed didn't constitute a target had been discarded, risking bias. The vice president expressed his hopes this had since been rectified. === Organization === The Gospel is used by the military's target administration division (or Directorate of Targets or Targeting Directorate), which was formed in 2019 in the IDF's intelligence directorate to address the air force running out of targets to bomb, and which Kohavi described as "powered by AI capabilities" and including hundreds of officers of soldiers. In addition to its wartime role, The Guardian wrote it'd helped the IDF build a database of between 30,000 and 40,000 suspected militants in recent years, and that systems such as the Gospel had played a critical role in building lists of individuals authorized to be assassinated. The Gospel was developed by Unit 8200 of the Israeli Intelligence C
STIT logic
STIT logic (from seeing to it that) is a family of modal and branching-time logics for reasoning about agency and choice. A typical STIT operator has the form [ i s t i t : φ ] {\displaystyle [i\ {\mathsf {stit}}:\varphi ]} , usually read as "agent i {\displaystyle i} sees to it that φ {\displaystyle \varphi } ", and is interpreted in models where agents choose between alternative possible futures. STIT logics are used in action theory, deontic logic, epistemic logic, and the theory of intelligent agents to formalise notions such as "could have done otherwise", responsibility, joint action, and strategic ability in an indeterministic world. == Etymology == The acronym STIT comes from the English phrase "seeing to it that", introduced in influential work by Nuel Belnap and Michael Perloff on the logical analysis of agentive expressions. In this tradition, "to see to it that φ {\displaystyle \varphi } " is treated as a primitive agency operator, rather than being reduced to ordinary modal necessity. == History == Modern STIT logic arose in the 1980s in the context of branching-time semantics and formal theories of agency. Belnap and Perloff's article "Seeing to it that: A canonical form for agentives" introduced the idea of treating expressions of the form "agent i sees to it that φ" as a primitive modal operator, and analysed such sentences using a branching tree of moments and histories. This approach was further developed in a series of papers on indeterminism and agency and provided the conceptual core for later STIT formalisms. In the 1990s the basic formal systems of STIT logic were worked out. Horty and Belnap's influential paper on the deliberative STIT operator distinguished between a "Chellas" STIT that merely records the result of an agent's present choice and a "deliberative" STIT that requires the agent's choice to make a difference, and connected STIT with issues of action, omission, ability and obligation. Around the same time, Ming Xu proved completeness and decidability results for basic STIT systems, including a single-agent logic with Kripke-style semantics and axiomatizations for multi-agent deliberative STIT, thereby establishing STIT as a well-behaved normal modal framework. This early work was systematised in Belnap, Perloff and Xu's monograph Facing the Future: Agents and Choices in Our Indeterminist World, which presents a general branching-time semantics for individual and group STIT operators, discusses independence-of-agents conditions and articulates the metaphysical picture of an indeterministic "tree" of moments. At roughly the same time, Horty's book Agency and Deontic Logic developed deontic STIT logics in which obligations are tied to agents' available choices rather than to static states of affairs, and used the resulting systems to analyse "ought implies can", contrary-to-duty obligations and deontic paradoxes. These works helped to position STIT at the intersection of action theory, temporal logic and deontic logic. From the late 1990s and 2000s onward, STIT logics were combined with epistemic, temporal and strategic modalities. Broersen introduced complete STIT logics for knowledge and action and deontic-epistemic STIT systems that distinguish different modes of mens rea, with applications to responsibility and the specification of multi-agent systems. Work on group and coalitional agency investigated axiomatisations and complexity results for group STIT logics, and related STIT-based analyses of agency to coalition logic and alternating-time temporal logic (ATL) by exhibiting formal embeddings between the frameworks. Explicit temporal operators were added to STIT in so-called temporal STIT logics. Lorini proposed a temporal STIT with "next" and "until" operators along histories and showed how it can be applied to normative reasoning about ongoing behaviour and commitments. Ciuni and Lorini compared different semantics for temporal STIT, clarifying the relationships between branching-time, game-based and epistemic approaches, while Boudou and Lorini gave a semantics for temporal STIT based on concurrent game structures, thus strengthening links with standard models of multi-agent interaction used for ATL and strategy logic. In parallel, complexity-theoretic work by Balbiani, Herzig and Troquard and by Schwarzentruber and co-authors investigated the satisfiability and model-checking problems for various STIT fragments, showing for instance that many expressive group STIT logics are undecidable or of high computational complexity. In the 2010s, STIT ideas were combined with justification logic, imagination operators and refined deontic notions. Justification STIT logics, developed by Olkhovikov and others, merge explicit justifications with STIT-style agency so that producing a proof can itself be treated as an action that brings about knowledge, and they come with completeness and decidability results. Olkhovikov and Wansing introduced STIT imagination logics, together with axiomatic systems and tableau calculi, to model acts of voluntary imagining and their role in doxastic control. Other authors have proposed STIT-based logics of responsibility, blameworthiness and intentionality for use in philosophical and AI settings. Xu's survey article "Combinations of STIT with Ought and Know" (2015) reviews many of these developments and emphasises the interplay between deontic and epistemic STIT logics. Current research on STIT focuses on proof theory, automated reasoning and richer expressive resources. Lyon and van Berkel, building on earlier work on labelled calculi for STIT, have developed cut-free sequent systems and proof-search algorithms that yield syntactic decision procedures for a range of deontic and non-deontic multi-agent STIT logics and support applications such as duty checking and compliance checking in autonomous systems. Sawasaki has proposed first-order cstit-based STIT logics that can distinguish de re and de dicto readings of agency statements and has proved strong completeness results for Hilbert systems over finite models, moving the STIT programme beyond the purely propositional level. Further work investigates interpreted-system and computationally grounded semantics for STIT and its extensions in order to model the behaviour of autonomous agents in multi-agent settings, and proposes STIT-based semantics for epistemic notions based on patterns of information disclosure in interactive systems. == Branching-time semantics == STIT logics are usually interpreted over branching-time models. A standard STIT frame consists of: a non-empty set of moments T {\displaystyle T} , partially ordered by < {\displaystyle <} so that ( T , < ) {\displaystyle (T,<)} forms a tree (every pair of moments with a common predecessor has a greatest lower bound); a set of histories, each history being a maximal linearly ordered subset of T {\displaystyle T} ; a non-empty set of agents A g {\displaystyle Ag} ; for each agent i ∈ A g {\displaystyle i\in Ag} and moment m {\displaystyle m} , a choice function c h o i c e i m {\displaystyle {\mathsf {choice}}_{i}^{m}} that partitions the set of histories passing through m {\displaystyle m} into choice cells. The idea is that a moment represents a time at which choices are made, and histories represent complete possible future courses of events. At each moment, each agent's choice corresponds to selecting one of the available cells of histories determined by their choice function. Formulas are evaluated at pairs ( m , h ) {\displaystyle (m,h)} of a moment and a history through that moment (sometimes written m / h {\displaystyle m/h} ). A valuation assigns truth-values to atomic propositions at such indices; Boolean connectives are interpreted pointwise as in Kripke-style modal logic. == Chellas and deliberative STIT operators == Several STIT operators have been distinguished in the literature. A common approach uses two closely related operators, often called Chellas STIT and deliberative STIT. Let H m {\displaystyle H_{m}} be the set of histories passing through a moment m {\displaystyle m} , and write H m {\displaystyle H_{m}} ⟦ φ ⟧ m = { h ∈ H m ∣ M , m / h ⊨ φ } {\displaystyle {\text{⟦}}\varphi {\text{⟧}}_{m}=\{h\in H_{m}\mid M,m/h\models \varphi \}} for the set of histories at m {\displaystyle m} where φ {\displaystyle \varphi } holds. The Chellas STIT operator, often written [ i c s t i t : φ ] {\displaystyle [i\ {\mathsf {cstit}}:\varphi ]} , is given by M , m / h ⊨ [ i c s t i t : φ ] iff c h o i c e i m ( h ) ⊆ ⟦ φ ⟧ m . {\displaystyle M,m/h\models [i\ {\mathsf {cstit}}:\varphi ]\quad {\text{iff}}\quad {\mathsf {choice}}_{i}^{m}(h)\subseteq {\text{⟦}}\varphi {\text{⟧}}_{m}.} Intuitively, agent i {\displaystyle i} sees to it that φ {\displaystyle \varphi } if φ {\displaystyle \varphi } holds at all histories compatible with their present choice. The deliberative STIT operator, [ i d s t i t : φ ] {\displaystyle [i\ {\mathsf {dstit}}:\varphi ]} , adds
LightGBM
LightGBM, short for Light Gradient-Boosting Machine, is a free and open-source distributed gradient-boosting framework for machine learning, originally developed by Microsoft. It is based on decision tree algorithms and used for ranking, classification and other machine learning tasks. The development focus is on performance and scalability. == Overview == The LightGBM framework supports different algorithms including GBT, GBDT, GBRT, GBM, MART and RF. LightGBM has many of XGBoost's advantages, including sparse optimization, parallel training, multiple loss functions, regularization, bagging, and early stopping. A major difference between the two lies in the construction of trees. LightGBM does not grow a tree level-wise — row by row — as most other implementations do. Instead it grows trees leaf-wise. It will choose the leaf with max delta loss to grow. Besides, LightGBM does not use the widely used sorted-based decision tree learning algorithm, which searches the best split point on sorted feature values, as XGBoost or other implementations do. Instead, LightGBM implements a highly optimized histogram-based decision tree learning algorithm, which yields great advantages on both efficiency and memory consumption. The LightGBM algorithm utilizes two novel techniques called Gradient-Based One-Side Sampling (GOSS) and Exclusive Feature Bundling (EFB) which allow the algorithm to run faster while maintaining a high level of accuracy. LightGBM works on Linux, Windows, and macOS and supports C++, Python, R, and C#. The source code is licensed under MIT License and available on GitHub. == Gradient-based one-side sampling == When using gradient descent, one thinks about the space of possible configurations of the model as a valley, in which the lowest part of the valley is the model which most closely fits the data. In this metaphor, one walks in different directions to learn how much lower the valley becomes. Typically, in gradient descent, one uses the whole set of data to calculate the valley's slopes. However, this commonly used method assumes that every data point is equally informative. By contrast, Gradient-Based One-Side Sampling (GOSS), a method first developed for gradient-boosted decision trees, does not rely on the assumption that all data are equally informative. Instead, it treats data points with smaller gradients (shallower slopes) as less informative by randomly dropping them. This is intended to filter out data which may have been influenced by noise, allowing the model to more accurately model the underlying relationships in the data. == Exclusive feature bundling == Exclusive feature bundling (EFB) is a near-lossless method to reduce the number of effective features. In a sparse feature space many features are nearly exclusive, implying they rarely take nonzero values simultaneously. One-hot encoded features are a perfect example of exclusive features. EFB bundles these features, reducing dimensionality to improve efficiency while maintaining a high level of accuracy. The bundle of exclusive features into a single feature is called an exclusive feature bundle.
Comet (browser)
Comet is an AI-powered web browser based on Chromium. It was released by Perplexity AI for Microsoft Windows and macOS on July 9, 2025, for Android on November 20, 2025, and for iOS on March 18, 2026. Initial access to the browser was limited to users subscribed to Perplexity's most expensive tier, with broader availability expected over time. The browser was released for free download in October 2025. == Features == Comet is integrated with Perplexity's AI-assisted search engine. The browser features an assistant which enables users to perform a variety of tasks such as generating article summaries, sending emails, or buying products. == Security concerns == Researchers at LayerX Security identified a malicious attack vector which they call CometJacking. The exploit could possibly exfiltrate a user's personal sensitive data to a remote server controlled by the attacker. LayerX attempted to responsibly disclose their findings to Comet's developer Perplexity AI in August 2025. Perplexity responded that they saw no security impact and marked the disclosure as not applicable.
Vilém Flusser
Vilém Flusser (May 12, 1920 – November 27, 1991) was a Czech-born Brazilian philosopher, writer and journalist, best known for his contributions to media studies, communication theory, and the philosophy of language. He lived for a long period in São Paulo (where he became a Brazilian citizen) and later in France, and his works are written in many different languages. His early work was marked by discussion of the thought of Martin Heidegger, and by the influence of existentialism and phenomenology. Phenomenology would play a major role in the transition to the later phase of his work, in which he turned his attention to the philosophy of communication and of artistic production. He contributed to the dichotomy logic theory through history: the period of image worship, and period of text worship, with deviations consequently into idolatry and "textolatry". == Life == Flusser was born in 1920 in Prague, Czechoslovakia into a family of Jewish intellectuals. His father, Gustav Flusser, studied mathematics and physics (under Albert Einstein among others). Vilém attended German and Czech primary schools and later a German grammar school. In 1938, Flusser started to study philosophy at the Juridical Faculty of the Charles University in Prague. In 1939, shortly after the Nazi occupation, Flusser emigrated to London (with Edith Barth, his later wife, and her parents) to continue his studies for one term at the London School of Economics and Political Science. Vilém Flusser lost all of his family in the German concentration camps: his father died in Buchenwald in 1940; his grandparents, his mother and his sister were brought to Theresienstadt and later to Auschwitz where they were killed. The next year, he emigrated to Brazil, living both in São Paulo and Rio de Janeiro. He started working at a Czech import/export company and then at Stabivolt, a manufacturer of radios and transistors. In 1960 he started to collaborate with the Brazilian Institute of Philosophy (IBF) in São Paulo and published in the Revista Brasileira de Filosofia; by these means he seriously approached the Brazilian intellectual community. Flusser had as his friend and closest interlocutor the Brazilian philosopher Vicente Ferreira da Silva. Flusser and Vicente Ferreira da Silva met in São Paulo in the 1960s and began a close intellectual dialogue that continued until Ferreira da Silva's death in 1963. Flusser wrote several essays on Ferreira da Silva's work and that Ferreira da Silva's concept of "Fundamental ontology” had a significant impact on Flusser's understanding of the nature of reality. During the 60s Flusser published and taught at several schools in São Paulo, being Lecturer for Philosophy of Science at the Escola Politécnica of the University of São Paulo and Professor of Philosophy of Communication at the Escola Dramática and the Escola Superior de Cinema in São Paulo. He also participated actively in the arts, collaborating with the Bienal de São Paulo, among other cultural events. Beginning in the 1950s he taught philosophy and worked as a journalist, before publishing his first book Língua e realidade (Language and Reality) in 1963. In 1972 he decided to leave Brazil. Some say it was because it was becoming difficult to publish because of the military regime. Others dispute this reason, since his work on communication and language did not threaten the military. In 1970, when a reform took place at the University of São Paulo by the Brazilian military government, all Lecturers of Philosophy (members of the Department of Philosophy) were dismissed. Flusser, who taught at the Engineering School (Escola Politécnica), had to leave the university as well. In 1972 he and his wife Edith settled temporarily in Merano (Tyrol). Further short stays in various European countries followed until they moved to Robion in southern France in 1981, where they remained until Flusser's death in 1991. To the end of his life, he was quite active writing and giving lectures around media theory and working with new topics (Philosophy of Photography, Technical Images, etc.). He died in 1991 in a car accident near the Czech–German border, while trying to visit his native city, Prague, to give a lecture. Vilém Flusser is the cousin of David Flusser. == Philosophy == Flusser's essays are short, provocative and lucid, with a resemblance to the style of journalistic articles. Critics have noted he is less a 'systematic' thinker than a 'dialogic' one, purposefully eclectic and provocative (Cubitt 2004). However, his early books, written in the 1960s, primarily in Portuguese, and published in Brazil, have a slightly different style. Flusser's writings relate to each other, however, which means that he intensively works over certain topics and dissects them into a number of brief essays. His main topics of interest were: epistemology, ethics, aesthetics, ontology, language philosophy, semiotics, philosophy of science, the history of Western culture, the philosophy of religion, the history of symbolic language, technology, writing, the technical image, photography, migration, media and literature, and, especially in his later years, the philosophy of communication and of artistic production. His writings reflect his wandering life: although the majority of his work was written in German and Portuguese, he also wrote in English and French, with scarce translation to other languages. Because Flusser's writings in different languages are dispersed in the form of books, articles or sections of books, his work as a media philosopher and cultural theorist is only now becoming more widely known. The first book by Flusser to be published in English was Towards a Philosophy of Photography in 1984 by the then new journal European Photography, which was his own translation of the work. The Shape of Things, was published in London in 1999 and was followed by a new translation of Towards a Philosophy of Photography. Flusser's archives have been held by the Academy of Media Arts in Cologne and are currently housed at the Berlin University of the Arts. === Philosophy of photography === Writing about photography in the 1970s and 80s, in the face of the early worldwide impact of computer technologies, Flusser argued that the photograph was the first in a number of technical image forms to have fundamentally changed the way in which the world is seen. Historically, the importance of photography had been that it introduced nothing less than a new epoch: 'The invention of photography constitutes a break in history that can only be understood in comparison to that other historical break constituted by the invention of linear writing.' Whereas ideas might previously have been interpreted in terms of their written form, photography heralded new forms of perceptual experience and knowledge. As Flusser Archive Supervisor Claudia Becker describes, "For Flusser, photography is not only a reproductive imaging technology, it is a dominant cultural technique through which reality is constituted and understood". In this context, Flusser argued that photographs have to be understood in strict separation from 'pre-technical image forms'. For example, he contrasted them to paintings which he described as images that can be sensibly 'decoded', because the viewer is able to interpret what he or she sees as more or less direct signs of what the painter intended. By contrast, even though photography produces images that seem to be 'faithful reproductions' of objects and events they cannot be so directly 'decoded'. The crux of this difference stems, for Flusser, from the fact that photographs are produced through the operations of an apparatus. And the photographic apparatus operates in ways that are not immediately known or shaped by its operator. For example, he described the act of photographing as follows: The photographer's gesture as the search for a viewpoint onto a scene takes place within the possibilities offered by the apparatus. The photographer moves within specific categories of space and time regarding the scene: proximity and distance, bird- and worm's-eye views, frontal- and side-views, short or long exposures, etc. The Gestalt of space–time surrounding the scene is prefigured for the photographer by the categories of his camera. These categories are an a priori for him. He must 'decide' within them: he must press the trigger. Roughly put, the person using a camera might think that they are operating its controls to produce a picture that shows the world the way they want it to be seen, but it is the pre-programmed character of the camera that sets the parameters of this act and it is the apparatus that shapes the meaning of the resulting image. Given the central role of photography to almost all aspects of contemporary life, the programmed character of the photographic apparatus shapes the experience of looking at and interpreting photographs as well as most of the cultural contexts in which we do so. Flusse
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 REEM is a prototype humanoid robot built by PAL Robotics in Spain. It is a 1.70 m high humanoid robot with 22 degrees of freedom, with a mobile base with wheels, allowing it to move at 4 km/hour. The upper part of the robot consists of a torso with a touch screen, two motorized arms, which give it a high degree of expression, and a head, which is also motorized. REEM-A and REEM-B are the first and second prototypes of humanoid robots created by PAL Robotics. REEM-B can recognize, grasp and lift objects and walk by itself, avoiding obstacles through simultaneous localization and mapping. The robot accepts voice commands and can recognize faces. == Specifications ==REEM