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
Rabbit r1
The Rabbit r1 is an artificial intelligence personal assistant device developed by the American technology startup Rabbit Inc and co-designed by Teenage Engineering. It was announced at the 2024 Consumer Electronics Show as a handheld device intended to perform digital tasks through voice commands, touch interaction, and web-based AI agents. The r1 was marketed around Rabbit's concept of a "large action model" (LAM), which the company described as software able to operate websites and services on behalf of users. The device runs rabbitOS, an operating system based on the Android Open Source Project. Its services have included AI search, image recognition, voice interaction, music playback, rideshare and food-ordering integrations, and later experimental web-agent features such as LAM Playground and teach mode. Initial reviews were largely negative, with reviewers criticizing the device's limited functionality, bugs, and unclear advantages over a smartphone. Critics also questioned Rabbit's claims after the r1 software was shown to run on an Android phone. Rabbit continued to issue software updates after launch, including rabbitOS 2 in September 2025, which introduced a redesigned card-based interface, gesture navigation, and a "creations" feature for generating small software tools and experiences on the device. Rabbit Inc was founded by Jesse Lyu Cheng. == Hardware == Display: A 2.88-inch touchscreen for interactive user input. Input: push-to-talk button to activate voice commands; scroll wheel; Gyroscope; Magnetometer; Accelerometer; GPS. Camera: 8 MP single camera, with a resolution of 3264x2448, allowing for the connected external AI to use computer vision. Audio: Equipped with a speaker and dual microphones for audio interaction. Connectivity: Supports Wi-Fi and cellular connections via a SIM card slot to access internet services. Processor: Runs on a 2.3GHz MediaTek Helio P35 processor. Memory: Contains 4GB of RAM for operational tasks. Storage: Offers 128GB of internal storage for data. Ports: Utilizes a USB-C port for charging and data connections. == Software == The Rabbit r1 runs rabbitOS, which is based on the Android Open Source Project (AOSP), specifically Android 13. Rabbit founder Jesse Lyu described rabbitOS as a "very bespoke AOSP" after reports that the r1's software could be run on a conventional Android phone. Rabbit described the r1 as using a large action model (LAM), a type of AI agent intended to perform tasks across software interfaces rather than only answer questions. At launch, the device supported a limited set of services, including AI search, vision features, music playback, and some third-party integrations. Perplexity.ai was one of the AI services used to answer user queries. In 2024, Rabbit released several software updates that added features and attempted to address early criticism of the device. In July 2024, the company launched "beta rabbit", an advanced search and conversation mode for more complex queries. In October 2024, it released LAM Playground, a web-based agent feature intended to let the r1 operate websites on behalf of users. Reviewers found the feature experimental; Android Authority reported that it could perform some navigation tasks but struggled with CAPTCHAs, loops, and unintended behavior. In November 2024, Rabbit introduced a beta "teach mode", which allowed users to demonstrate web-based tasks in the Rabbithole web portal and later ask the r1 to repeat them. The company described teach mode as experimental, and The Verge noted that Rabbit warned users that results could be unpredictable and that CAPTCHA-protected sites could cause problems. Rabbit released rabbitOS 2 in September 2025. The update redesigned the interface around a card-based layout, added additional touchscreen gestures, and introduced "creations", a feature that lets users generate simple software tools, games, and interfaces through natural-language prompts. Coverage of the update described it as a major software overhaul rather than new hardware. == Reception == === Funding === Rabbit raised $20 million in funding from Khosla Ventures, Synergis Capital and Kakao Investment in October 2023. The company announced an additional $10 million in funding in December 2023. === Sales === Following its announcement at the 2024 Consumer Electronics Show, 130,000 units were sold. On August 13, 2024, Rabbit announced that sales of r1 had expanded to the entire European Union (except Malta) and United Kingdom. On August 21, 2024, sales of r1 expanded to Singapore. === Reviews === The r1 was met with strong criticism immediately after Rabbit began shipping the device. Some reviews questioned what the device was able to do that a smartphone could not, while comparing it to the similar Humane Ai Pin. YouTuber Marques Brownlee called the device "barely reviewable". Android Authority's Mishaal Rahman managed to install Rabbit r1's software on a Pixel 6a smartphone, after a tipster shared an APK file. The Verge echoed the claims made by Rahman. In response, Lyu published statements confirming its use of Android, but denying that the r1 is an Android app. Mashable called its Vision features impressive, but said that "these praise-worthy features are overshadowed by buggy performance". Ars Technica wrote a blog post claiming "the company is blocking access from bootleg APKs". TechCrunch gave a slightly more positive review, calling the device a "fun peep at a possible future", but could not "advise anyone to buy one now." Shortly after the launch of r1, Rabbit began a weekly cadence of software updates to address much of the criticism from the early reviews, including "battery and GPS performance, time zone selection, and more". Digital Trends said the Magic Camera feature "takes the most mundane, ordinary, and badly composed photos and makes something fun and eye-catching from them." Mashable said the "beta rabbit" feature "makes Rabbit R1 more conversational and intelligent". Later coverage noted that Rabbit continued to update the r1 after its poorly received launch. The Verge reported in September 2024 that about 5,000 of roughly 100,000 purchasers were using the device at any given moment, citing Lyu, and described the product as having launched before it was ready. In 2025, coverage of rabbitOS 2 described the update as an attempt to reset the device's software experience after the criticism of its original release. == Controversies == === GAMA project === Rabbit Inc has garnered attention due to allegations surrounding its funding and the company's past projects. The company came under scrutiny when Stephen Findeisen, known as Coffeezilla on YouTube, published a video in May 2024, alleging that Rabbit Incorporation was "built on a scam". Rabbit Incorporation, initially named Cyber Manufacturing Co, rebranded just two months before launching the Rabbit R1. The company, under its former name, raised $6 million in November 2021 for a project called GAMA, described as a "Next Generation NFT Project." Jesse Lyu, the CEO of Rabbit Incorporation, referred to GAMA as a "fun little project." Coffeezilla, who investigates influencer scams, highlighted old Clubhouse recordings of Jesse Lyu discussing the GAMA project. In these recordings, Lyu emphasized the substantial funding behind GAMA and its potential to be a revolutionary, carbon-negative cryptocurrency. Coffeezilla questioned the whereabouts of the funds raised for GAMA, estimating that approximately $1 million in refunds to investors remained unresolved. He suggested that the rebranding to Rabbit Incorporation and the shift to developing the Rabbit R1 were attempts to divert from the GAMA project's issues. In response to Coffeezilla's inquiries, Rabbit Incorporation stated that the $6 million raised was used for the GAMA project. The company said that NFTs cannot be refunded unless the owner agrees to "burn" them on the blockchain. Rabbit Incorporation also said that the GAMA project was open-sourced and returned to the community, aligning with community feedback. They also mentioned that efforts to buy back NFTs were made to counteract malicious trading and maintain market stability. === Security === In June 2024, Engadget reported that the Rabbitude team, a community reverse engineering project, had gained access to the r1's codebase revealing that r1's software contained several hardcoded API keys in its code for ElevenLabs, Microsoft Azure, Yelp, and Google Maps, potentially allowing unauthorized access to r1 responses, including those containing the users' personal information. For a short time, Rabbit immediately began revoking and rotating those secrets and confirmed that the code was leaked by an employee who had "been terminated and remains under investigation". In July 2024, the company revealed that all user chats and device pairing data were logged on the r1 with no ability to delete them. This meant that lost or stolen devices could be used to extract user
KataGo
KataGo is a free and open-source computer Go program, capable of defeating top-level human players. First released on 27 February 2019, it is developed by David Wu, who also developed the Arimaa playing program bot_Sharp which defeated three top human players to win the Arimaa AI Challenge in 2015. KataGo's first release was trained by David Wu using resources provided by his employer Jane Street Capital, but it is now trained by a distributed effort. Members of the computer Go community provide computing resources by running the client, which generates self-play games and rating games, and submits them to a server. The self-play games are used to train newer networks and the rating games to evaluate the networks' relative strengths. KataGo supports the Go Text Protocol, with various extensions, thus making it compatible with popular GUIs such as Lizzie. As an alternative, it also implements a custom "analysis engine" protocol, which is used by the KaTrain GUI, among others. KataGo is widely used by strong human go players, including the South Korean national team, for training purposes. KataGo is also used as the default analysis engine in the online Go website AI Sensei, as well as OGS (the Online Go Server). == Technology == Based on techniques used by DeepMind's AlphaGo Zero, KataGo implements Monte Carlo tree search with a convolutional neural network providing position evaluation and policy guidance. Compared to AlphaGo, KataGo introduces many refinements that enable it to learn faster and play more strongly. Notable features of KataGo that are absent in many other Go-playing programs include score estimation; support for small boards, rectangular boards, and large boards; arbitrary values of komi and handicaps; and the ability to use various Go rulesets and adjust its play and evaluation for the small differences between them. === Network === The network used in KataGo are ResNets with pre-activation. While AlphaGo Zero has only game board history as input features (as it was designed as a general architecture for board games, subsequently becoming AlphaZero), the input to the network contains additional features designed by hand specifically for playing Go. These features include liberties, komi parity, pass-alive, and ladders. The trunk is essentially the same as in AlphaGo Zero, but with global pooling layers added to allow the network to be conditioned on global context such as ko fights. This is similar to the Squeeze-and-Excitation Network. The network has two heads: a policy head and a value head. The policy and value heads are mostly the same as in AlphaGo Zero, but both heads have auxiliary subheads to provide auxiliary loss signal for faster training: Policy head: predicts policy for the current player's move this turn, and the opponent player's move in the next turn. A policy Each is a logit array of size 19 × 19 + 1 {\displaystyle 19\times 19+1} , representing the logit of making a move in one of the points, plus the logit of passing. Value head: predicts game outcome, expected score difference, expected board ownership, etc. The network is described in detail in Appendix A of the report. The code base switched from using TensorFlow to PyTorch in version 1.12. === Training === Let its trunk have b {\displaystyle b} residual blocks and c {\displaystyle c} channels. During its first training run, multiple networks were trained with increasing ( b , c ) {\displaystyle (b,c)} . It took 19 days using a maximum of 28 Nvidia V100 GPUs at 4.2 million games. After the first training run, training became a distributed project run by volunteers, with increasing network sizes. As of August 2024, it has reached b28c512 (28 blocks, 512 channels). == Adversarial attacks == In 2022, KataGo was used as the target for adversarial attack research, designed to demonstrate the "surprising failure modes" of AI systems. The researchers were able to trick KataGo into ending the game prematurely. Adversarial training improves defense against adversarial attacks, though not perfectly.
Linear belief function
Linear belief functions are an extension of the Dempster–Shafer theory of belief functions to the case when variables of interest are continuous. Examples of such variables include financial asset prices, portfolio performance, and other antecedent and consequent variables. The theory was originally proposed by Arthur P. Dempster in the context of Kalman Filters and later was elaborated, refined, and applied to knowledge representation in artificial intelligence and decision making in finance and accounting by Liping Liu. == Concept == A linear belief function intends to represent our belief regarding the location of the true value as follows: We are certain that the truth is on a so-called certainty hyperplane but we do not know its exact location; along some dimensions of the certainty hyperplane, we believe the true value could be anywhere from –∞ to +∞ and the probability of being at a particular location is described by a normal distribution; along other dimensions, our knowledge is vacuous, i.e., the true value is somewhere from –∞ to +∞ but the associated probability is unknown. A belief function in general is defined by a mass function over a class of focal elements, which may have nonempty intersections. A linear belief function is a special type of belief function in the sense that its focal elements are exclusive, parallel sub-hyperplanes over the certainty hyperplane and its mass function is a normal distribution across the sub-hyperplanes. Based on the above geometrical description, Shafer and Liu propose two mathematical representations of a LBF: a wide-sense inner product and a linear functional in the variable space, and as their duals over a hyperplane in the sample space. Monney proposes still another structure called Gaussian hints. Although these representations are mathematically neat, they tend to be unsuitable for knowledge representation in expert systems. == Knowledge representation == A linear belief function can represent both logical and probabilistic knowledge for three types of variables: deterministic such as an observable or controllable, random whose distribution is normal, and vacuous on which no knowledge bears. Logical knowledge is represented by linear equations, or geometrically, a certainty hyperplane. Probabilistic knowledge is represented by a normal distribution across all parallel focal elements. In general, assume X is a vector of multiple normal variables with mean μ and covariance Σ. Then, the multivariate normal distribution can be equivalently represented as a moment matrix: M ( X ) = ( μ Σ ) . {\displaystyle M(X)=\left({\begin{array}{{20}c}\mu \\\Sigma \end{array}}\right).} If the distribution is non-degenerate, i.e., Σ has a full rank and its inverse exists, the moment matrix can be fully swept: M ( X → ) = ( μ Σ − 1 − Σ − 1 ) {\displaystyle M({\vec {X}})=\left({\begin{array}{{20}c}\mu \Sigma ^{-1}\\-\Sigma ^{-1}\end{array}}\right)} Except for normalization constant, the above equation completely determines the normal density function for X. Therefore, M ( X → ) {\displaystyle M({\vec {X}})} represents the probability distribution of X in the potential form. These two simple matrices allow us to represent three special cases of linear belief functions. First, for an ordinary normal probability distribution M(X) represents it. Second, suppose one makes a direct observation on X and obtains a value μ. In this case, since there is no uncertainty, both variance and covariance vanish, i.e., Σ = 0. Thus, a direct observation can be represented as: M ( X ) = ( μ 0 ) {\displaystyle M(X)=\left({\begin{array}{{20}c}\mu \\0\end{array}}\right)} Third, suppose one is completely ignorant about X. This is a very thorny case in Bayesian statistics since the density function does not exist. By using the fully swept moment matrix, we represent the vacuous linear belief functions as a zero matrix in the swept form follows: M ( X → ) = [ 0 0 ] {\displaystyle M({\vec {X}})=\left[{\begin{array}{{20}c}0\\0\end{array}}\right]} One way to understand the representation is to imagine complete ignorance as the limiting case when the variance of X approaches to ∞, where one can show that Σ−1 = 0 and hence M ( X → ) {\displaystyle M({\vec {X}})} vanishes. However, the above equation is not the same as an improper prior or normal distribution with infinite variance. In fact, it does not correspond to any unique probability distribution. For this reason, a better way is to understand the vacuous linear belief functions as the neutral element for combination (see later). To represent the remaining three special cases, we need the concept of partial sweeping. Unlike a full sweeping, a partial sweeping is a transformation on a subset of variables. Suppose X and Y are two vectors of normal variables with the joint moment matrix: M ( X , Y ) = [ μ 1 Σ 11 Σ 21 μ 2 Σ 12 Σ 22 ] {\displaystyle M(X,Y)=\left[{\begin{array}{{20}c}{\begin{array}{{20}c}\mu _{1}\\\Sigma _{11}\\\Sigma _{21}\end{array}}&{\begin{array}{{20}c}\mu _{2}\\\Sigma _{12}\\\Sigma _{22}\end{array}}\end{array}}\right]} Then M(X, Y) may be partially swept. For example, we can define the partial sweeping on X as follows: M ( X → , Y ) = [ μ 1 ( Σ 11 ) − 1 − ( Σ 11 ) − 1 Σ 21 ( Σ 11 ) − 1 μ 2 − μ 1 ( Σ 11 ) − 1 Σ 12 ( Σ 11 ) − 1 Σ 12 Σ 22 − Σ 21 ( Σ 11 ) − 1 Σ 12 ] {\displaystyle M({\vec {X}},Y)=\left[{\begin{array}{{20}c}{\begin{array}{{20}c}\mu _{1}(\Sigma _{11})^{-1}\\-(\Sigma _{11})^{-1}\\\Sigma _{21}(\Sigma _{11})^{-1}\end{array}}&{\begin{array}{{20}c}\mu _{2}-\mu _{1}(\Sigma _{11})^{-1}\Sigma _{12}\\(\Sigma _{11})^{-1}\Sigma _{12}\\\Sigma _{22}-\Sigma _{21}(\Sigma _{11})^{-1}\Sigma _{12}\end{array}}\end{array}}\right]} If X is one-dimensional, a partial sweeping replaces the variance of X by its negative inverse and multiplies the inverse with other elements. If X is multidimensional, the operation involves the inverse of the covariance matrix of X and other multiplications. A swept matrix obtained from a partial sweeping on a subset of variables can be equivalently obtained by a sequence of partial sweepings on each individual variable in the subset and the order of the sequence does not matter. Similarly, a fully swept matrix is the result of partial sweepings on all variables. We can make two observations. First, after the partial sweeping on X, the mean vector and covariance matrix of X are respectively μ 1 ( Σ 11 ) − 1 {\displaystyle \mu _{1}(\Sigma _{11})^{-1}} and − ( Σ 11 ) − 1 {\displaystyle -(\Sigma _{11})^{-1}} , which are the same as that of a full sweeping of the marginal moment matrix of X. Thus, the elements corresponding to X in the above partial sweeping equation represent the marginal distribution of X in potential form. Second, according to statistics, μ 2 − μ 1 ( Σ 11 ) − 1 Σ 12 {\displaystyle \mu _{2}-\mu _{1}(\Sigma _{11})^{-1}\Sigma _{12}} is the conditional mean of Y given X = 0; Σ 22 − Σ 21 ( Σ 11 ) − 1 Σ 12 {\displaystyle \Sigma _{22}-\Sigma _{21}(\Sigma _{11})^{-1}\Sigma _{12}} is the conditional covariance matrix of Y given X = 0; and ( Σ 11 ) − 1 Σ 12 {\displaystyle (\Sigma _{11})^{-1}\Sigma _{12}} is the slope of the regression model of Y on X. Therefore, the elements corresponding to Y indices and the intersection of X and Y in M ( X → , Y ) {\displaystyle M({\vec {X}},Y)} represents the conditional distribution of Y given X = 0. These semantics render the partial sweeping operation a useful method for manipulating multivariate normal distributions. They also form the basis of the moment matrix representations for the three remaining important cases of linear belief functions, including proper belief functions, linear equations, and linear regression models. === Proper linear belief functions === For variables X and Y, assume there exists a piece of evidence justifying a normal distribution for variables Y while bearing no opinions for variables X. Also, assume that X and Y are not perfectly linearly related, i.e., their correlation is less than 1. This case involves a mix of an ordinary normal distribution for Y and a vacuous belief function for X. Thus, we represent it using a partially swept matrix as follows: M ( X → , Y ) = [ 0 0 0 μ 2 0 Σ 22 ] {\displaystyle M({\vec {X}},Y)=\left[{\begin{array}{{20}c}{\begin{array}{{20}c}0\\0\\0\end{array}}&{\begin{array}{{20}c}\mu _{2}\\0\\\Sigma _{22}\\\end{array}}\end{array}}\right]} This is how we could understand the representation. Since we are ignorant on X, we use its swept form and set μ 1 ( Σ 11 ) − 1 = 0 {\displaystyle \mu _{1}(\Sigma _{11})^{-1}=0} and − ( Σ 11 ) − 1 = 0 {\displaystyle -(\Sigma _{11})^{-1}=0} . Since the correlation between X and Y is less than 1, the regression coefficient of X on Y approaches to 0 when the variance of X approaches to ∞. Therefore, ( Σ 11 ) − 1 Σ 12 = 0 {\displaystyle (\Sigma _{11})^{-1}\Sigma _{12}=0} . Similarly, one can prove that μ 1 ( Σ 11 ) − 1 Σ 12 = 0 {\displaystyle \mu _{1}(\Sigma _{11})^{-1}\Sigma _{12}=0} and Σ 21 ( Σ 11 ) −
Lisp machine
Lisp machines are general-purpose computers designed to efficiently run Lisp as their main software and programming language, usually via hardware support. They are an example of a high-level language computer architecture. In a sense, they were the first commercial single-user workstations. Despite being modest in number (perhaps 7,000 units total as of 1988) Lisp machines commercially pioneered some now-commonplace technologies, including networking innovations such as Chaosnet, and effective garbage collection. Several firms built and sold Lisp machines in the 1980s: Symbolics (3600, 3640, XL1200, MacIvory, and other models), Lisp Machines Incorporated (LMI Lambda), Texas Instruments (Explorer, MicroExplorer), and Xerox (Interlisp-D workstations). The operating systems were written in Lisp Machine Lisp, Interlisp (Xerox), and later partly in Common Lisp. == History == === Historical context === Artificial intelligence (AI) computer programs of the 1960s and 1970s intrinsically required what was then considered a huge amount of computer power, as measured in processor time and memory space. The power requirements of AI research were exacerbated by the Lisp symbolic programming language, when commercial hardware was designed and optimized for assembly- and Fortran-like programming languages. At first, the cost of such computer hardware meant that it had to be shared among many users. As integrated circuit technology shrank the size and cost of computers in the 1960s and early 1970s, and the memory needs of AI programs began to exceed the address space of the most common research computer, the Digital Equipment Corporation (DEC) PDP-10, researchers considered a new approach: a computer designed specifically to develop and run large artificial intelligence programs, and tailored to the semantics of the Lisp language. To provide consistent performance for interactive programs, these machines would often not be shared, but would be dedicated to a single user at a time. === Initial development === In 1973, Richard Greenblatt and Thomas Knight, programmers at Massachusetts Institute of Technology (MIT) Artificial Intelligence Laboratory (AI Lab), began what would become the MIT Lisp Machine Project when they first began building a computer hardwired to run certain basic Lisp operations, rather than run them in software, in a 24-bit tagged architecture. The machine also did incremental (or Arena) garbage collection. More specifically, since Lisp variables are typed at runtime rather than compile time, a simple addition of two variables could take five times as long on conventional hardware, due to test and branch instructions. Lisp Machines ran the tests in parallel with the more conventional single instruction additions. If the simultaneous tests failed, then the result was discarded and recomputed; this meant in many cases a speed increase by several factors. This simultaneous checking approach was used as well in testing the bounds of arrays when referenced, and other memory management necessities (not merely garbage collection or arrays). Type checking was further improved and automated when the conventional byte word of 32 bits was lengthened to 36 bits for Symbolics 3600-model Lisp machines and eventually to 40 bits or more (usually, the excess bits not accounted for by the following were used for error-correcting codes). The first group of extra bits were used to hold type data, making the machine a tagged architecture, and the remaining bits were used to implement compressed data representation (CDR) coding (wherein the usual linked list elements are compressed to occupy roughly half the space), aiding garbage collection by reportedly an order of magnitude. A further improvement was two microcode instructions which specifically supported Lisp functions, reducing the cost of calling a function to as little as 20 clock cycles, in some Symbolics implementations. The first machine was called the CONS machine (named after the list construction operator cons in Lisp). Often it was affectionately referred to as the Knight machine, perhaps since Knight wrote his master's thesis on the subject; it was extremely well received. It was subsequently improved into a version called CADR (a pun; in Lisp, the cadr function, which returns the second item of a list, is pronounced /ˈkeɪ.dəɹ/ or /ˈkɑ.dəɹ/, as some pronounce the word "cadre") which was based on essentially the same architecture. About 25 of what were essentially prototype CADRs were sold within and without MIT for ~$50,000; it quickly became the favorite machine for hacking – many of the most favored software tools were quickly ported to it (e.g. Emacs was ported from ITS in 1975). It was so well received at an AI conference held at MIT in 1978 that Defense Advanced Research Projects Agency (DARPA) began funding its development. === Commercializing MIT Lisp machine technology === In 1979, Russell Noftsker, being convinced that Lisp machines had a bright commercial future due to the strength of the Lisp language and the enabling factor of hardware acceleration, proposed to Greenblatt that they commercialize the technology. In a counter-intuitive move for an AI Lab hacker, Greenblatt acquiesced, hoping perhaps that he could recreate the informal and productive atmosphere of the Lab in a real business. These ideas and goals were considerably different from those of Noftsker. The two negotiated at length, but neither would compromise. As the proposed firm could succeed only with the full and undivided assistance of the AI Lab hackers as a group, Noftsker and Greenblatt decided that the fate of the enterprise was up to them, and so the choice should be left to the hackers. The ensuing discussions of the choice divided the lab into two factions. In February 1979, matters came to a head. The hackers sided with Noftsker, believing that a commercial venture-fund-backed firm had a better chance of surviving and commercializing Lisp machines than Greenblatt's proposed self-sustaining start-up. Greenblatt lost the battle. It was at this juncture that Symbolics, Noftsker's enterprise, slowly came together. While Noftsker was paying his staff a salary, he had no building or any equipment for the hackers to work on. He bargained with Patrick Winston that, in exchange for allowing Symbolics' staff to keep working out of MIT, Symbolics would let MIT use internally and freely all the software Symbolics developed. A consultant from CDC, who was trying to put together a natural language computer application with a group of West-coast programmers, came to Greenblatt, seeking a Lisp machine for his group to work with, about eight months after the disastrous conference with Noftsker. Greenblatt had decided to start his own rival Lisp machine firm, but he had done nothing. The consultant, Alexander Jacobson, decided that the only way Greenblatt was going to start the firm and build the Lisp machines that Jacobson desperately needed was if Jacobson pushed and otherwise helped Greenblatt launch the firm. Jacobson pulled together business plans, a board, a partner for Greenblatt (one F. Stephen Wyle). The newfound firm was named LISP Machine, Inc. (LMI), and was funded by CDC orders, via Jacobson. Around this time Symbolics (Noftsker's firm) began operating. It had been hindered by Noftsker's promise to give Greenblatt a year's head start, and by severe delays in procuring venture capital. Symbolics still had the major advantage that while 3 or 4 of the AI Lab hackers had gone to work for Greenblatt, 14 other hackers had signed onto Symbolics. Two AI Lab people were not hired by either: Richard Stallman and Marvin Minsky. Stallman, however, blamed Symbolics for the decline of the hacker community that had centered around the AI lab. For two years, from 1982 to the end of 1983, Stallman worked by himself to clone the output of the Symbolics programmers, with the aim of preventing them from gaining a monopoly on the lab's computers. Regardless, after a series of internal battles, Symbolics did get off the ground in 1980/1981, selling the CADR as the LM-2, while Lisp Machines, Inc. sold it as the LMI-CADR. Symbolics did not intend to produce many LM-2s, since the 3600 family of Lisp machines was supposed to ship quickly, but the 3600s were repeatedly delayed, and Symbolics ended up producing ~100 LM-2s, each of which sold for $70,000. Both firms developed second-generation products based on the CADR: the Symbolics 3600 and the LMI-LAMBDA (of which LMI managed to sell ~200). The 3600, which shipped a year late, expanded on the CADR by widening the machine word to 36-bits, expanding the address space to 28-bits, and adding hardware to accelerate certain common functions that were implemented in microcode on the CADR. The LMI-LAMBDA, which came out a year after the 3600, in 1983, was compatible with the CADR (it could run CADR microcode), but hardware differences existed. Texas Instruments (TI) joined the fray whe
Thunderspy
Thunderspy is a type of security vulnerability, based on the Intel Thunderbolt 3 port, first reported publicly on 10 May 2020, that can result in an evil maid (i.e., attacker of an unattended device) attack gaining full access to a computer's information in about five minutes, and may affect millions of Apple, Linux and Windows computers, as well as any computers manufactured before 2019, and some after that. According to Björn Ruytenberg, the discoverer of the vulnerability, "All the evil maid needs to do is unscrew the backplate, attach a device momentarily, reprogram the firmware, reattach the backplate, and the evil maid gets full access to the laptop. All of this can be done in under five minutes." The malicious firmware is used to clone device identities which makes classical DMA attack possible. == History == The Thunderspy security vulnerabilities were first publicly reported by Björn Ruytenberg of Eindhoven University of Technology in the Netherlands on 10 May 2020. Thunderspy is similar to Thunderclap, another security vulnerability, reported in 2019, that also involves access to computer files through the Thunderbolt port. == Impact == The security vulnerability affects millions of Apple, Linux and Windows computers, as well as all computers manufactured before 2019, and some after that. However, this impact is restricted mainly to how precise a bad actor would have to be to execute the attack. Physical access to a machine with a vulnerable Thunderbolt controller is necessary, as well as a writable ROM chip for the Thunderbolt controller's firmware. Additionally, part of Thunderspy, specifically the portion involving re-writing the firmware of the controller, requires the device to be in sleep, or at least in some sort of powered-on state, to be effective. Machines that force power-off when the case is open may assist in resisting this attack to the extent that the feature (switch) itself resists tampering. Due to the nature of attacks that require extended physical access to hardware, it's unlikely the attack will affect users outside of a business or government environment. == Mitigation == The researchers claim there is no easy software solution, and may only be mitigated by disabling the Thunderbolt port altogether. However, the impacts of this attack (reading kernel level memory without the machine needing to be powered off) are largely mitigated by anti-intrusion features provided by many business machines. Intel claims enabling such features would substantially restrict the effectiveness of the attack. Microsoft's official security recommendations recommend disabling sleep mode while using BitLocker. Using hibernation in place of sleep mode turns the device off, mitigating potential risks of attack on encrypted data.
Linear belief function
Linear belief functions are an extension of the Dempster–Shafer theory of belief functions to the case when variables of interest are continuous. Examples of such variables include financial asset prices, portfolio performance, and other antecedent and consequent variables. The theory was originally proposed by Arthur P. Dempster in the context of Kalman Filters and later was elaborated, refined, and applied to knowledge representation in artificial intelligence and decision making in finance and accounting by Liping Liu. == Concept == A linear belief function intends to represent our belief regarding the location of the true value as follows: We are certain that the truth is on a so-called certainty hyperplane but we do not know its exact location; along some dimensions of the certainty hyperplane, we believe the true value could be anywhere from –∞ to +∞ and the probability of being at a particular location is described by a normal distribution; along other dimensions, our knowledge is vacuous, i.e., the true value is somewhere from –∞ to +∞ but the associated probability is unknown. A belief function in general is defined by a mass function over a class of focal elements, which may have nonempty intersections. A linear belief function is a special type of belief function in the sense that its focal elements are exclusive, parallel sub-hyperplanes over the certainty hyperplane and its mass function is a normal distribution across the sub-hyperplanes. Based on the above geometrical description, Shafer and Liu propose two mathematical representations of a LBF: a wide-sense inner product and a linear functional in the variable space, and as their duals over a hyperplane in the sample space. Monney proposes still another structure called Gaussian hints. Although these representations are mathematically neat, they tend to be unsuitable for knowledge representation in expert systems. == Knowledge representation == A linear belief function can represent both logical and probabilistic knowledge for three types of variables: deterministic such as an observable or controllable, random whose distribution is normal, and vacuous on which no knowledge bears. Logical knowledge is represented by linear equations, or geometrically, a certainty hyperplane. Probabilistic knowledge is represented by a normal distribution across all parallel focal elements. In general, assume X is a vector of multiple normal variables with mean μ and covariance Σ. Then, the multivariate normal distribution can be equivalently represented as a moment matrix: M ( X ) = ( μ Σ ) . {\displaystyle M(X)=\left({\begin{array}{{20}c}\mu \\\Sigma \end{array}}\right).} If the distribution is non-degenerate, i.e., Σ has a full rank and its inverse exists, the moment matrix can be fully swept: M ( X → ) = ( μ Σ − 1 − Σ − 1 ) {\displaystyle M({\vec {X}})=\left({\begin{array}{{20}c}\mu \Sigma ^{-1}\\-\Sigma ^{-1}\end{array}}\right)} Except for normalization constant, the above equation completely determines the normal density function for X. Therefore, M ( X → ) {\displaystyle M({\vec {X}})} represents the probability distribution of X in the potential form. These two simple matrices allow us to represent three special cases of linear belief functions. First, for an ordinary normal probability distribution M(X) represents it. Second, suppose one makes a direct observation on X and obtains a value μ. In this case, since there is no uncertainty, both variance and covariance vanish, i.e., Σ = 0. Thus, a direct observation can be represented as: M ( X ) = ( μ 0 ) {\displaystyle M(X)=\left({\begin{array}{{20}c}\mu \\0\end{array}}\right)} Third, suppose one is completely ignorant about X. This is a very thorny case in Bayesian statistics since the density function does not exist. By using the fully swept moment matrix, we represent the vacuous linear belief functions as a zero matrix in the swept form follows: M ( X → ) = [ 0 0 ] {\displaystyle M({\vec {X}})=\left[{\begin{array}{{20}c}0\\0\end{array}}\right]} One way to understand the representation is to imagine complete ignorance as the limiting case when the variance of X approaches to ∞, where one can show that Σ−1 = 0 and hence M ( X → ) {\displaystyle M({\vec {X}})} vanishes. However, the above equation is not the same as an improper prior or normal distribution with infinite variance. In fact, it does not correspond to any unique probability distribution. For this reason, a better way is to understand the vacuous linear belief functions as the neutral element for combination (see later). To represent the remaining three special cases, we need the concept of partial sweeping. Unlike a full sweeping, a partial sweeping is a transformation on a subset of variables. Suppose X and Y are two vectors of normal variables with the joint moment matrix: M ( X , Y ) = [ μ 1 Σ 11 Σ 21 μ 2 Σ 12 Σ 22 ] {\displaystyle M(X,Y)=\left[{\begin{array}{{20}c}{\begin{array}{{20}c}\mu _{1}\\\Sigma _{11}\\\Sigma _{21}\end{array}}&{\begin{array}{{20}c}\mu _{2}\\\Sigma _{12}\\\Sigma _{22}\end{array}}\end{array}}\right]} Then M(X, Y) may be partially swept. For example, we can define the partial sweeping on X as follows: M ( X → , Y ) = [ μ 1 ( Σ 11 ) − 1 − ( Σ 11 ) − 1 Σ 21 ( Σ 11 ) − 1 μ 2 − μ 1 ( Σ 11 ) − 1 Σ 12 ( Σ 11 ) − 1 Σ 12 Σ 22 − Σ 21 ( Σ 11 ) − 1 Σ 12 ] {\displaystyle M({\vec {X}},Y)=\left[{\begin{array}{{20}c}{\begin{array}{{20}c}\mu _{1}(\Sigma _{11})^{-1}\\-(\Sigma _{11})^{-1}\\\Sigma _{21}(\Sigma _{11})^{-1}\end{array}}&{\begin{array}{{20}c}\mu _{2}-\mu _{1}(\Sigma _{11})^{-1}\Sigma _{12}\\(\Sigma _{11})^{-1}\Sigma _{12}\\\Sigma _{22}-\Sigma _{21}(\Sigma _{11})^{-1}\Sigma _{12}\end{array}}\end{array}}\right]} If X is one-dimensional, a partial sweeping replaces the variance of X by its negative inverse and multiplies the inverse with other elements. If X is multidimensional, the operation involves the inverse of the covariance matrix of X and other multiplications. A swept matrix obtained from a partial sweeping on a subset of variables can be equivalently obtained by a sequence of partial sweepings on each individual variable in the subset and the order of the sequence does not matter. Similarly, a fully swept matrix is the result of partial sweepings on all variables. We can make two observations. First, after the partial sweeping on X, the mean vector and covariance matrix of X are respectively μ 1 ( Σ 11 ) − 1 {\displaystyle \mu _{1}(\Sigma _{11})^{-1}} and − ( Σ 11 ) − 1 {\displaystyle -(\Sigma _{11})^{-1}} , which are the same as that of a full sweeping of the marginal moment matrix of X. Thus, the elements corresponding to X in the above partial sweeping equation represent the marginal distribution of X in potential form. Second, according to statistics, μ 2 − μ 1 ( Σ 11 ) − 1 Σ 12 {\displaystyle \mu _{2}-\mu _{1}(\Sigma _{11})^{-1}\Sigma _{12}} is the conditional mean of Y given X = 0; Σ 22 − Σ 21 ( Σ 11 ) − 1 Σ 12 {\displaystyle \Sigma _{22}-\Sigma _{21}(\Sigma _{11})^{-1}\Sigma _{12}} is the conditional covariance matrix of Y given X = 0; and ( Σ 11 ) − 1 Σ 12 {\displaystyle (\Sigma _{11})^{-1}\Sigma _{12}} is the slope of the regression model of Y on X. Therefore, the elements corresponding to Y indices and the intersection of X and Y in M ( X → , Y ) {\displaystyle M({\vec {X}},Y)} represents the conditional distribution of Y given X = 0. These semantics render the partial sweeping operation a useful method for manipulating multivariate normal distributions. They also form the basis of the moment matrix representations for the three remaining important cases of linear belief functions, including proper belief functions, linear equations, and linear regression models. === Proper linear belief functions === For variables X and Y, assume there exists a piece of evidence justifying a normal distribution for variables Y while bearing no opinions for variables X. Also, assume that X and Y are not perfectly linearly related, i.e., their correlation is less than 1. This case involves a mix of an ordinary normal distribution for Y and a vacuous belief function for X. Thus, we represent it using a partially swept matrix as follows: M ( X → , Y ) = [ 0 0 0 μ 2 0 Σ 22 ] {\displaystyle M({\vec {X}},Y)=\left[{\begin{array}{{20}c}{\begin{array}{{20}c}0\\0\\0\end{array}}&{\begin{array}{{20}c}\mu _{2}\\0\\\Sigma _{22}\\\end{array}}\end{array}}\right]} This is how we could understand the representation. Since we are ignorant on X, we use its swept form and set μ 1 ( Σ 11 ) − 1 = 0 {\displaystyle \mu _{1}(\Sigma _{11})^{-1}=0} and − ( Σ 11 ) − 1 = 0 {\displaystyle -(\Sigma _{11})^{-1}=0} . Since the correlation between X and Y is less than 1, the regression coefficient of X on Y approaches to 0 when the variance of X approaches to ∞. Therefore, ( Σ 11 ) − 1 Σ 12 = 0 {\displaystyle (\Sigma _{11})^{-1}\Sigma _{12}=0} . Similarly, one can prove that μ 1 ( Σ 11 ) − 1 Σ 12 = 0 {\displaystyle \mu _{1}(\Sigma _{11})^{-1}\Sigma _{12}=0} and Σ 21 ( Σ 11 ) −