AI App Gemini

AI App Gemini — independent reviews, comparisons, pricing and step-by-step guides on Aizhi.

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  Truth discovery

  Truth discovery (also known as truth finding) is the process of choosing the actual true value for a data item when different data sources provide conflicting information on it. Several algorithms have been proposed to tackle this problem, ranging from simple methods like majority voting to more complex ones able to estimate the trustworthiness of data sources. Truth discovery problems can be divided into two sub-classes: single-truth and multi-truth. In the first case only one true value is allowed for a data item (e.g birthday of a person, capital city of a country). While in the second case multiple true values are allowed (e.g. cast of a movie, authors of a book). Typically, truth discovery is the last step of a data integration pipeline, when the schemas of different data sources have been unified and the records referring to the same data item have been detected. == General principles == The abundance of data available on the web makes more and more probable to find that different sources provide (partially or completely) different values for the same data item. This, together with the fact that we are increasing our reliance on data to derive important decisions, motivates the need of developing good truth discovery algorithms. Many currently available methods rely on a voting strategy to define the true value of a data item. Nevertheless, recent studies, have shown that, if we rely only on majority voting, we could get wrong results even in 30% of the data items. The solution to this problem is to assess the trustworthiness of the sources and give more importance to votes coming from trusted sources. Ideally, supervised learning techniques could be exploited to assign a reliability score to sources after hand-crafted labeling of the provided values; unfortunately, this is not feasible since the number of needed labeled examples should be proportional to the number of sources, and in many applications the number of sources can be prohibitive. == Single-truth vs multi-truth discovery == Single-truth and multi-truth discovery are two very different problems. Single-truth discovery is characterized by the following properties: only one true value is allowed for each data item; different values provided for a given data item oppose to each other; values and sources can either be correct or erroneous. While in the multi-truth case the following properties hold: the truth is composed by a set of values; different values could provide a partial truth; claiming one value for a given data item does not imply opposing to all the other values; the number of true values for each data item is not known a priori. Multi-truth discovery has unique features that make the problem more complex and should be taken into consideration when developing truth-discovery solutions. The examples below point out the main differences of the two methods. Knowing that in both examples the truth is provided by source 1, in the single truth case (first table) we can say that sources 2 and 3 oppose to the truth and as a result provide wrong values. On the other hand, in the second case (second table), sources 2 and 3 are neither correct nor erroneous, they instead provide a subset of the true values and at the same time they do not oppose the truth. == Source trustworthiness == The vast majority of truth discovery methods are based on a voting approach: each source votes for a value of a certain data item and, at the end, the value with the highest vote is select as the true one. In the more sophisticated methods, votes do not have the same weight for all the data sources, more importance is indeed given to votes coming from trusted sources. Source trustworthiness usually is not known a priori but estimated with an iterative approach. At each step of the truth discovery algorithm the trustworthiness score of each data source is refined, improving the assessment of the true values that in turn leads to a better estimation of the trustworthiness of the sources. This process usually ends when all the values reach a convergence state. Source trustworthiness can be based on different metrics, such as accuracy of provided values, copying values from other sources and domain coverage. Detecting copying behaviors is very important, in fact, copy allows to spread false values easily making truth discovery very hard, since many sources would vote for the wrong values. Usually systems decrease the weight of votes associated to copied values or even don’t count them at all. == Single-truth methods == Most of the currently available truth discovery methods have been designed to work well only in the single-truth case. Below are reported some of the characteristics of the most relevant typologies of single-truth methods and how different systems model source trustworthiness. === Majority voting === Majority voting is the simplest method, the most popular value is selected as the true one. Majority voting is commonly used as a baseline when assessing the performances of more complex methods. === Web-link based === These methods estimate source trustworthiness exploiting a similar technique to the one used to measure authority of web pages based on web links. The vote assigned to a value is computed as the sum of the trustworthiness of the sources that provide that particular value, while the trustworthiness of a source is computed as the sum of the votes assigned to the values that the source provides. === Information-retrieval based === These methods estimate source trustworthiness using similarity measures typically used in information retrieval. Source trustworthiness is computed as the cosine similarity (or other similarity measures) between the set of values provided by the source and the set of values considered true (either selected in a probabilistic way or obtained from a ground truth). === Bayesian based === These methods use Bayesian inference to define the probability of a value being true conditioned on the values provided by all the sources. P ( v ∣ ψ ( o ) ) = P ( ψ ( o ) ∣ v ) ⋅ P ( v ) P ( ψ ( o ) ) {\displaystyle P(v\mid \psi (o))={\frac {P(\psi (o)\mid v)\cdot P(v)}{P(\psi (o))}}} where v {\displaystyle \textstyle v} is a value provided for a data item o {\displaystyle \textstyle o} and ψ ( o ) {\displaystyle \textstyle \psi (o)} is the set of the observed values provided by all the sources for that specific data item. The trustworthiness of a source is then computed based on the accuracy of the values that provides. Other more complex methods exploit Bayesian inference to detect copying behaviors and use these insights to better assess source trustworthiness. == Multi-truth methods == Due to its complexity, less attention has been devoted to the study of the multi-truth discovery Below are reported two typologies of multi-truth methods and their characteristics. === Bayesian based === These methods use Bayesian inference to define the probability of a group of values being true conditioned on the values provided by all the data sources. In this case, since there could be multiple true values for each data item, and sources can provide multiple values for a single data item, it is not possible to consider values individually. An alternative is to consider mappings and relations between set of provided values and sources providing them. The trustworthiness of a source is then computed based on the accuracy of the values that provides. More sophisticated methods also consider domain coverage and copying behaviors to better estimate source trustworthiness. === Probabilistic Graphical Models based === These methods use probabilistic graphical models to automatically define the set of true values of given data item and also to assess source quality without need of any supervision. == Applications == Many real-world applications can benefit from the use of truth discovery algorithms. Typical domains of application include: healthcare, crowd/social sensing, crowdsourcing aggregation, information extraction and knowledge base construction. Truth discovery algorithms could be also used to revolutionize the way in which web pages are ranked in search engines, going from current methods based on link analysis like PageRank, to procedures that rank web pages based on the accuracy of the information they provide.

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  Hierarchical Risk Parity

  Hierarchical Risk Parity (HRP) is an advanced investment portfolio optimization framework developed in 2016 by Marcos López de Prado at Guggenheim Partners and Cornell University. HRP is a probabilistic graph-based alternative to the prevailing mean-variance optimization (MVO) framework developed by Harry Markowitz in 1952, and for which he received the Nobel Prize in economic sciences. HRP algorithms apply discrete mathematics and machine learning techniques to create diversified and robust investment portfolios that outperform MVO methods out-of-sample. HRP aims to address the limitations of traditional portfolio construction methods, particularly when dealing with highly correlated assets. Following its publication, HRP has been implemented in numerous open-source libraries, and received multiple extensions. == Key features == HRP portfolios have been proposed as a robust alternative to traditional quadratic optimization methods, including the Critical Line Algorithm (CLA) of Markowitz. HRP addresses three central issues commonly associated with quadratic optimizers: numerical instability, excessive concentration in a small number of assets, and poor out-of-sample performance. HRP leverages techniques from graph theory and machine learning to construct diversified portfolios using only the information embedded in the covariance matrix. Unlike quadratic programming methods, HRP does not require the covariance matrix to be invertible. Consequently, HRP remains applicable even in cases where the covariance matrix is ill-conditioned or singular—conditions under which standard optimizers fail. Monte Carlo simulations indicate that HRP achieves lower out-of-sample variance than CLA, despite the fact that minimizing variance is the explicit optimization objective of CLA. Furthermore, HRP portfolios exhibit lower realized risk compared to those generated by traditional risk parity methodologies. Empirical backtests have demonstrated that HRP would have historically outperformed conventional portfolio construction techniques. Algorithms within the HRP framework are characterized by the following features: Machine Learning Approach: HRP employs hierarchical clustering, a machine learning technique, to group similar assets based on their correlations. This allows the algorithm to identify the underlying hierarchical structure of the portfolio, and avoid that errors spread through the entire network. Risk-Based Allocation: The algorithm allocates capital based on risk, ensuring that assets only compete with similar assets for representation in the portfolio. This approach leads to better diversification across different risk sources, while avoiding the instability associated with noisy returns estimates. Covariance Matrix Handling: Unlike traditional methods like Mean-Variance Optimization, HRP does not require inverting the covariance matrix. This makes it more stable and applicable to portfolios with a large number of assets, particularly when the covariance matrix's condition number is high. == The problem: Markowitz's Curse == Portfolio construction is perhaps the most recurrent financial problem. On a daily basis, investment managers must build portfolios that incorporate their views and forecasts on risks and returns. Despite the theoretical elegance of Markowitz's mean-variance framework, its practical implementation is hindered by several limitations that undermine the reliability of solutions derived from the Critical Line Algorithm (CLA). A principal concern is the high sensitivity of optimal portfolios to small perturbations in expected returns: even minor forecasting errors can result in significantly different allocations (Michaud, 1998). Given the inherent difficulty of producing accurate return forecasts, numerous researchers have advocated for approaches that forgo expected returns entirely and instead rely solely on the covariance structure of asset returns. This has given rise to risk-based allocation methods, among which risk parity is a widely cited example (Jurczenko, 2015). While eliminating return forecasts mitigates some instability, it does not eliminate it. Quadratic programming techniques employed in portfolio optimization require the inversion of a positive-definite covariance matrix, meaning all eigenvalues must be strictly positive. When the matrix is numerically ill-conditioned—that is, when the ratio of its largest to smallest eigenvalue (its condition number) is large—matrix inversion becomes unreliable and prone to significant numerical errors (Bailey and López de Prado, 2012). The condition number of a covariance, correlation, or any symmetric (and thus diagonalizable) matrix is defined as the absolute value of the ratio between its largest and smallest eigenvalues in modulus. The figure on the right presents the sorted eigenvalues of several correlation matrices; the condition number is represented by the ratio of the first to last eigenvalues in each sequence. A diagonal correlation matrix, which is equal to its own inverse, exhibits the minimum possible condition number. As the number of correlated (or multicollinear) assets in a portfolio increases, the condition number rises. At high levels, this leads to severe numerical instability, whereby slight modifications in any matrix entry may result in drastically different inverses. This phenomenon, often referred to as Markowitz’s curse, encapsulates the paradox wherein increased correlation among assets heightens the theoretical need for diversification, yet simultaneously increases the likelihood of unstable optimization outcomes. Consequently, the potential benefits of diversification are frequently overshadowed by estimation errors. These problems are exacerbated as the dimensionality of the covariance matrix increases. The estimation of each covariance term consumes degrees of freedom, and in general, a minimum of 1 2 N ( N + 1 ) {\displaystyle {\frac {1}{2}}N(N+1)} independent and identically distributed (IID) observations is required to estimate a non-singular covariance matrix of dimension N {\displaystyle N} . For example, constructing an invertible covariance matrix of dimension 50 necessitates at least five years of daily IID observations. However, empirical evidence suggests that the correlation structure of financial assets is highly unstable over such extended periods. These difficulties are highlighted by the observation that even naïve allocation strategies—such as equally weighted portfolios—have frequently outperformed both mean-variance and risk-based optimizations in out-of-sample tests (De Miguel et al., 2009). == The solution: Hierarchical Risk Parity == The HRP algorithm addresses Markowitz's curse in three steps: Hierarchical Clustering: Assets are grouped into clusters based on their correlations, forming a hierarchical tree structure. Quasi-Diagonalization: The correlation matrix is reordered based on the clustering results, revealing a block diagonal structure. Recursive Bisection: Weights are assigned to assets through a top-down approach, splitting the portfolio into smaller sub-portfolios and allocating capital based on inverse variance. === Step 1: Hierarchical clustering === Given a T × N {\displaystyle T\times N} matrix of asset returns X {\displaystyle X} , where each column represents a time series of returns for one of N {\displaystyle N} assets over T {\displaystyle T} time periods, a hierarchical clustering process can be used to construct a tree-based representation of asset relationships. First, we compute the N × N {\displaystyle N\times N} correlation matrix ρ = ρ i , j i , j = 1 . . . N {\displaystyle \rho ={\rho _{i,j}}\;{i,j=1\;...\;N}} , where ρ i , j = c o r r ( X i , X j ) {\displaystyle \rho _{i,j}=\mathrm {corr} (X_{i},X_{j})} . From this, a pairwise distance matrix D = d i , j {\displaystyle D={d_{i,j}}} is defined using the transformation: d i , j = 1 2 ( 1 − ρ i , j ) {\displaystyle d_{i,j}={\sqrt {{\frac {1}{2}}(1-\rho _{i,j})}}} This distance function defines a proper metric space, satisfying non-negativity, identity of indiscernibles, symmetry, and the triangle inequality. Next, a secondary distance matrix D ~ = d ~ i , j {\displaystyle {\tilde {D}}={{\tilde {d}}_{i,j}}} is computed, where each entry measures the Euclidean distance between the distance profiles of two assets: d ~ i , j = ∑ n = 1 N ( d n , i − d n , j ) 2 {\displaystyle {\tilde {d}}_{i,j}={\sqrt {\sum _{n=1}^{N}(d_{n,i}-d_{n,j})^{2}}}} While d i , j {\displaystyle d_{i,j}} reflects correlation-based proximity between two assets, d ~ i , j {\displaystyle {\tilde {d}}_{i,j}} quantifies dissimilarity across the entire system, as it depends on all pairwise distances. Hierarchical clustering proceeds by identifying the pair ( i , j ) {\displaystyle (i,j)} with the smallest value of d ~ i , j {\displaystyle {\tilde {d}}_{i,j}} (for i ≠ j {\displaystyle i\neq j} ), and forming a new cluster u [ 1 ] = ( i , j ) {\displaystyle u[1]=(i,j)} .

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  Highway network

  In machine learning, the Highway Network was the first working very deep feedforward neural network with hundreds of layers, much deeper than previous neural networks. It uses skip connections modulated by learned gating mechanisms to regulate information flow, inspired by long short-term memory (LSTM) recurrent neural networks. The advantage of the Highway Network over other deep learning architectures is its ability to overcome or partially prevent the vanishing gradient problem, thus improving its optimization. Gating mechanisms are used to facilitate information flow across the many layers ("information highways"). Highway Networks have found use in text sequence labeling and speech recognition tasks. In 2014, the state of the art was training deep neural networks with 20 to 30 layers. Stacking too many layers led to a steep reduction in training accuracy, known as the "degradation" problem. In 2015, two techniques were developed to train such networks: the Highway Network (published in May), and the residual neural network, or ResNet (December). ResNet behaves like an open-gated Highway Net. == Model == The model has two gates in addition to the H ( W H , x ) {\displaystyle H(W_{H},x)} gate: the transform gate T ( W T , x ) {\displaystyle T(W_{T},x)} and the carry gate C ( W C , x ) {\displaystyle C(W_{C},x)} . The latter two gates are non-linear transfer functions (specifically sigmoid by convention). The function H {\displaystyle H} can be any desired transfer function. The carry gate is defined as: C ( W C , x ) = 1 − T ( W T , x ) {\displaystyle C(W_{C},x)=1-T(W_{T},x)} while the transform gate is just a gate with a sigmoid transfer function. == Structure == The structure of a hidden layer in the Highway Network follows the equation: y = H ( x , W H ) ⋅ T ( x , W T ) + x ⋅ C ( x , W C ) = H ( x , W H ) ⋅ T ( x , W T ) + x ⋅ ( 1 − T ( x , W T ) ) {\displaystyle {\begin{aligned}y=H(x,W_{H})\cdot T(x,W_{T})+x\cdot C(x,W_{C})\\=H(x,W_{H})\cdot T(x,W_{T})+x\cdot (1-T(x,W_{T}))\end{aligned}}} == Related work == Sepp Hochreiter analyzed the vanishing gradient problem in 1991 and attributed to it the reason why deep learning did not work well. To overcome this problem, Long Short-Term Memory (LSTM) recurrent neural networks have residual connections with a weight of 1.0 in every LSTM cell (called the constant error carrousel) to compute y t + 1 = F ( x t ) + x t {\textstyle y_{t+1}=F(x_{t})+x_{t}} . During backpropagation through time, this becomes the residual formula y = F ( x ) + x {\textstyle y=F(x)+x} for feedforward neural networks. This enables training very deep recurrent neural networks with a very long time span t. A later LSTM version published in 2000 modulates the identity LSTM connections by so-called "forget gates" such that their weights are not fixed to 1.0 but can be learned. In experiments, the forget gates were initialized with positive bias weights, thus being opened, addressing the vanishing gradient problem. As long as the forget gates of the 2000 LSTM are open, it behaves like the 1997 LSTM. The Highway Network of May 2015 applies these principles to feedforward neural networks. It was reported to be "the first very deep feedforward network with hundreds of layers". It is like a 2000 LSTM with forget gates unfolded in time, while the later Residual Nets have no equivalent of forget gates and are like the unfolded original 1997 LSTM. If the skip connections in Highway Networks are "without gates," or if their gates are kept open (activation 1.0), they become Residual Networks. The residual connection is a special case of the "short-cut connection" or "skip connection" by Rosenblatt (1961) and Lang & Witbrock (1988) which has the form x ↦ F ( x ) + A x {\displaystyle x\mapsto F(x)+Ax} . Here the randomly initialized weight matrix A does not have to be the identity mapping. Every residual connection is a skip connection, but almost all skip connections are not residual connections. The original Highway Network paper not only introduced the basic principle for very deep feedforward networks, but also included experimental results with 20, 50, and 100 layers networks, and mentioned ongoing experiments with up to 900 layers. Networks with 50 or 100 layers had lower training error than their plain network counterparts, but no lower training error than their 20 layers counterpart (on the MNIST dataset, Figure 1 in ). No improvement on test accuracy was reported with networks deeper than 19 layers (on the CIFAR-10 dataset; Table 1 in ). The ResNet paper, however, provided strong experimental evidence of the benefits of going deeper than 20 layers. It argued that the identity mapping without modulation is crucial and mentioned that modulation in the skip connection can still lead to vanishing signals in forward and backward propagation (Section 3 in ). This is also why the forget gates of the 2000 LSTM were initially opened through positive bias weights: as long as the gates are open, it behaves like the 1997 LSTM. Similarly, a Highway Net whose gates are opened through strongly positive bias weights behaves like a ResNet. The skip connections used in modern neural networks (e.g., Transformers) are dominantly identity mappings.

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  Reciprocal human machine learning

  Reciprocal Human Machine Learning (RHML) is an interdisciplinary approach to designing human-AI interaction systems. RHML aims to enable continual learning between humans and machine learning models by having them learn from each other. This approach keeps the human expert "in the loop" to oversee and enhance machine learning performance and simultaneously support the human expert continue learning. == Background == RHML emerged in the context of the rise of big data analytics and artificial intelligence for intelligent tasks like sense-making and decision-making. As machine learning advanced to take on more roles, researchers realized fully autonomous systems had limitations and needed human guidance. RHML extends the concept of human-in-the-loop systems by promoting reciprocal learning. Humans learn from their interactions with machine learning models, staying up-to-date on evolving technology. The models also learn from human feedback and oversight. This amplification of learning on both sides is a key focus of RHML. The approach draws on theories of learning in dyads from education and psychology. It also builds on human-computer interaction and human-centered design principles. Implementing RHML requires developing specialized tools and interfaces tailored to the application == Applications == RHML has been explored across diverse domains including: Cybersecurity - Software to enable reciprocal learning between experts and AI models for social media threat detection. Organizational decision-making - RHML to structure collaboration between humans and AI systems. Workplace training - Using RHML for workers to learn from AI technologies on the job. Open science - Using human and AI collaboration to promote open science. Production and logistics - turning workers and intelligent machines into teammates. RHML maintains human oversight and control over AI systems, while enabling cutting-edge machine learning performance. This collaborative approach highlights the importance of keeping the human expert involved in the loop. An example of RHML in application is Free Spirit (AFSFCV), an open-source architecture first published in early 2025 as a whitepaper, proposing a visually structured approach to intent-based human–AI interaction.

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  Sparkles emoji

  The Sparkles emoji (U+2728 ✨ SPARKLES) is an emoji that has one large star surrounded by smaller stars. Originating from Japan to represent sparkles used in anime and manga, the sparkles are often used as emphasis in text by surrounding words or phrases with it. It is the third most-used emoji in the world on Twitter as of 2021. Since the early 2020s it has been used by major software companies to represent artificial intelligence, marketing the technology as "like magic". == Development == According to Emojipedia, the Sparkles emoji was first used by Japanese mobile operators SoftBank, Docomo and au in the late 1990s. The emoji was added to Unicode 6.0 in 2010 and Emoji 1.0 in 2015. On some platforms the Sparkles emoji has been multicoloured whilst on other platforms it has been one colour. Twitter and Microsoft's Sparkles have changed from being multicoloured to being a single colour. Samsung's version of the emoji previously had a night sky in the background. == Usage == === Interpersonal communication === The Sparkles emoji was originally meant to represent the usage of sparkles in Japanese anime and manga, where the sparkles are used to represent beauty, happiness or awe. The emoji has several meanings and depends upon context. Starting in the late 2010s, the emoji started being used to surround words or phrases to be used as emphasis, an example from the book Because Internet being "I would simply ✨pass away✨". It can also be used as sarcasm, irony or as a way to mock people. Without emoji this could be represented with tildes or asterisks, for example, "~tildes~" or "~asterisk plus tilde~" or "~~true sparkle exuberance~~". The sparkles emoji can be used to represent stars in text, be used to represent cleanliness or can be used to mean "orgasm" whilst sexting. In September 2021 the Sparkles emoji overtook the Pleading Face (🥺) emoji to become the third most-used emoji in the world according to Emojipedia, with approximately 1 per cent of all tweets containing the Sparkles emoji. === Artificial intelligence === In the early 2020s, the Sparkles emoji started being used as an icon to represent artificial intelligence (AI). Companies who use the emoji this way include Google, OpenAI, Samsung, Microsoft, Adobe, Spotify and Zoom. As of August 2024, seven of the top 10 software companies by market capitalisation use the Sparkles emojis with AI. OpenAI has different versions of the Sparkles for different versions of the models that ChatGPT uses. One explanation is that Sparkles is being used by these companies as a way to market AI as "magic". Marketing technology as "magic" has been used before AI, particularly by Apple. Another explanation given by designers and marketers choosing to use Sparkles to signify AI is simply that other platforms are doing it, making it familiar to users. Around 2024, some of these companies started removing two of the smaller stars from the emoji in their AI services and have kept the one large star, an example being Google's Gemini chatbot. In early 2024, the Nielsen Norman Group provided test subjects with the star in isolation and found that people did not associate the symbol with AI, but instead mostly with "optimisation" or "favourite or save an item".

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  Personoid

  Personoid is the concept coined by Stanisław Lem, a Polish science-fiction writer, in Non Serviam, from his book A Perfect Vacuum (1971). His personoids are an abstraction of functions of human mind and they live in computers; they do not need any human-like physical body. In cognitive and software modeling, personoid is a research approach to the development of intelligent autonomous agents. In frame of the IPK (Information, Preferences, Knowledge) architecture, it is a framework of abstract intelligent agent with a cognitive and structural intelligence. It can be seen as an essence of high intelligent entities. From the philosophical and systemics perspectives, personoid societies can also be seen as the carriers of a culture. According to N. Gessler, the personoids study can be a base for the research on artificial culture and culture evolution. == Personoids on TV and cinema == Welt am Draht (1973) The Thirteenth Floor (1999)

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  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

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  Dynamic epistemic logic

  Dynamic epistemic logic (DEL) is a logical framework dealing with knowledge and information change. Typically, DEL focuses on situations involving multiple agents and studies how their knowledge changes when events occur. These events can change factual properties of the actual world (they are called ontic events): for example a red card is painted in blue. They can also bring about changes of knowledge without changing factual properties of the world (they are called epistemic events): for example, a card is revealed publicly (or privately) to be red. Originally, DEL focused on epistemic events. Only some of the basic ideas are present in this entry of the original DEL framework; more details about DEL in general can be found in the references. Due to the nature of its object of study and its abstract approach, DEL is related and has applications to numerous research areas, such as computer science (artificial intelligence), philosophy (formal epistemology), economics (game theory) and cognitive science. In computer science, DEL is for example very much related to multi-agent systems, which are systems where multiple intelligent agents interact and exchange information. As a combination of dynamic logic and epistemic logic, dynamic epistemic logic is a young field of research. It really started in 1989 with Plaza's logic of public announcement. Independently, Gerbrandy and Groeneveld proposed a system dealing moreover with private announcement and that was inspired by the work of Veltman. Another system was proposed by van Ditmarsch whose main inspiration was the Cluedo game. But the most influential and original system was the system proposed by Baltag, Moss and Solecki. This system can deal with all the types of situations studied in the works above and its underlying methodology is conceptually grounded. This entry will present some of its basic ideas. Formally, DEL extends ordinary epistemic logic by the inclusion of event models to describe actions, and a product update operator that defines how epistemic models are updated as the consequence of executing actions described through event models. Epistemic logic will first be recalled. Then, actions and events will enter into the picture and we will introduce the DEL framework. == Epistemic logic == Epistemic logic is a modal logic dealing with the notions of knowledge and belief. As a logic, it is concerned with understanding the process of reasoning about knowledge and belief: which principles relating the notions of knowledge and belief are intuitively plausible? Like epistemology, it stems from the Greek word ϵ π ι σ τ η μ η {\displaystyle \epsilon \pi \iota \sigma \tau \eta \mu \eta } or ‘episteme’ meaning knowledge. Epistemology is nevertheless more concerned with analyzing the very nature and scope of knowledge, addressing questions such as “What is the definition of knowledge?” or “How is knowledge acquired?”. In fact, epistemic logic grew out of epistemology in the Middle Ages thanks to the efforts of Burley and Ockham. The formal work, based on modal logic, that inaugurated contemporary research into epistemic logic dates back only to 1962 and is due to Hintikka. It then sparked in the 1960s discussions about the principles of knowledge and belief and many axioms for these notions were proposed and discussed. For example, the interaction axioms K p → B p {\displaystyle Kp\rightarrow Bp} and B p → K B p {\displaystyle Bp\rightarrow KBp} are often considered to be intuitive principles: if an agent Knows p {\displaystyle p} then (s)he also Believes p {\displaystyle p} , or if an agent Believes p {\displaystyle p} , then (s)he Knows that (s)he Believes p {\displaystyle p} . More recently, these kinds of philosophical theories were taken up by researchers in economics, artificial intelligence and theoretical computer science where reasoning about knowledge is a central topic. Due to the new setting in which epistemic logic was used, new perspectives and new features such as computability issues were then added to the research agenda of epistemic logic. === Syntax === In the sequel, A G T S = { 1 , … , n } {\displaystyle AGTS=\{1,\ldots ,n\}} is a finite set whose elements are called agents and P R O P {\displaystyle PROP} is a set of propositional letters. The epistemic language is an extension of the basic multi-modal language of modal logic with a common knowledge operator C A {\displaystyle C_{A}} and a distributed knowledge operator D A {\displaystyle D_{A}} . Formally, the epistemic language L EL C {\displaystyle {\mathcal {L}}_{\textsf {EL}}^{C}} is defined inductively by the following grammar in BNF: L EL C : ϕ ::= p ∣ ¬ ϕ ∣ ( ϕ ∧ ϕ ) ∣ K j ϕ ∣ C A ϕ ∣ D A ϕ {\displaystyle {\mathcal {L}}_{\textsf {EL}}^{C}:\phi ~~::=~~p~\mid ~\neg \phi ~\mid ~(\phi \land \phi )~\mid ~K_{j}\phi ~\mid ~C_{A}\phi ~\mid ~D_{A}\phi } where p ∈ P R O P {\displaystyle p\in PROP} , j ∈ A G T S {\displaystyle j\in {AGTS}} and A ⊆ A G T S {\displaystyle A\subseteq {AGTS}} . The basic epistemic language L E L {\displaystyle {\mathcal {L}}_{EL}} is the language L E L C {\displaystyle {\mathcal {L}}_{EL}^{C}} without the common knowledge and distributed knowledge operators. The formula ⊥ {\displaystyle \bot } is an abbreviation for ¬ p ∧ p {\displaystyle \neg p\land p} (for a given p ∈ P R O P {\displaystyle p\in PROP} ), ⟨ K j ⟩ ϕ {\displaystyle \langle K_{j}\rangle \phi } is an abbreviation for ¬ K j ¬ ϕ {\displaystyle \neg K_{j}\neg \phi } , E A ϕ {\displaystyle E_{A}\phi } is an abbreviation for ⋀ j ∈ A K j ϕ {\displaystyle \bigwedge \limits _{j\in A}K_{j}\phi } and C ϕ {\displaystyle C\phi } an abbreviation for C A G T S ϕ {\displaystyle C_{AGTS}\phi } . Group notions: general, common and distributed knowledge. In a multi-agent setting there are three important epistemic concepts: general knowledge, distributed knowledge and common knowledge. The notion of common knowledge was first studied by Lewis in the context of conventions. It was then applied to distributed systems and to game theory, where it allows to express that the rationality of the players, the rules of the game and the set of players are commonly known. General knowledge. General knowledge of ϕ {\displaystyle \phi } means that everybody in the group of agents A G T S {\displaystyle {AGTS}} knows that ϕ {\displaystyle \phi } . Formally, this corresponds to the following formula: E ϕ := ⋀ j ∈ A G T S K j ϕ . {\displaystyle E\phi :={\underset {j\in {AGTS}}{\bigwedge }}K_{j}\phi .} Common knowledge. Common knowledge of ϕ {\displaystyle \phi } means that everybody knows ϕ {\displaystyle \phi } but also that everybody knows that everybody knows ϕ {\displaystyle \phi } , that everybody knows that everybody knows that everybody knows ϕ {\displaystyle \phi } , and so on ad infinitum. Formally, this corresponds to the following formula C ϕ := E ϕ ∧ E E ϕ ∧ E E E ϕ ∧ … {\displaystyle C\phi :=E\phi \land EE\phi \land EEE\phi \land \ldots } As we do not allow infinite conjunction the notion of common knowledge will have to be introduced as a primitive in our language. Before defining the language with this new operator, we are going to give an example introduced by Lewis that illustrates the difference between the notions of general knowledge and common knowledge. Lewis wanted to know what kind of knowledge is needed so that the statement p {\displaystyle p} : “every driver must drive on the right” be a convention among a group of agents. In other words, he wanted to know what kind of knowledge is needed so that everybody feels safe to drive on the right. Suppose there are only two agents i {\displaystyle i} and j {\displaystyle j} . Then everybody knowing p {\displaystyle p} (formally E p {\displaystyle Ep} ) is not enough. Indeed, it might still be possible that the agent i {\displaystyle i} considers possible that the agent j {\displaystyle j} does not know p {\displaystyle p} (formally ¬ K i K j p {\displaystyle \neg K_{i}K_{j}p} ). In that case the agent i {\displaystyle i} will not feel safe to drive on the right because he might consider that the agent j {\displaystyle j} , not knowing p {\displaystyle p} , could drive on the left. To avoid this problem, we could then assume that everybody knows that everybody knows that p {\displaystyle p} (formally E E p {\displaystyle EEp} ). This is again not enough to ensure that everybody feels safe to drive on the right. Indeed, it might still be possible that agent i {\displaystyle i} considers possible that agent j {\displaystyle j} considers possible that agent i {\displaystyle i} does not know p {\displaystyle p} (formally ¬ K i K j K i p {\displaystyle \neg K_{i}K_{j}K_{i}p} ). In that case and from i {\displaystyle i} ’s point of view, j {\displaystyle j} considers possible that i {\displaystyle i} , not knowing p {\displaystyle p} , will drive on the left. So from i {\displaystyle i} ’s point of view, j {\displaystyle j} might drive on the left as well (by the same argument as abov

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  Pharmacy automation

  Pharmacy automation involves the mechanical processes of handling and distributing medications. Any pharmacy task may be involved, including counting small objects (e.g., tablets, capsules); measuring and mixing powders and liquids for compounding; tracking and updating customer information in databases (e.g., personally identifiable information (PII), medical history, drug interaction risk detection); and inventory management. This article focuses on the changes that have taken place in the local, or community pharmacy since the 1960s. == History == Dispensing medications in a community pharmacy before the 1970s was a time-consuming operation. The pharmacist dispensed prescriptions in tablet or capsule form with a simple tray and spatula. Many new medications were developed by pharmaceutical manufacturers at an ever-increasing pace, and medications prices were rising steeply. A typical community pharmacist was working longer hours and often forced to hire staff to handle increased workloads which resulted in less time to focus on safety issues. These additional factors led to use of a machine to count medications. The original electronic portable digital tablet counting technology was invented in Manchester, England between 1967 and 1970 by the brothers John and Frank Kirby. I had the original idea of how the machine would work and it was my patent, but it was a joint effort getting it to work in a saleable form. It was 3 years of very hard work. I had originally studied heavy electrical engineering before changing over to Medical School and qualifying as a Medical Doctor in 1968. In fact I was Senior House (Casualty) Officer (A&E or ER) in 1970 at North Manchester General Hospital when I filed the patent. I must have been the only hospital doctor in Britain with an oscilloscope, a soldering iron and a drawing board in his room in the Doctors' Residence. The housekeepers were bemused by all the wires. Frank originally trained as a Banker but quit to take a job with a local electronics firm during the development. He died in 1987, a terrible loss. [Extract from personal communication received in March 2010 from John Kirby.] Frank and John Kirby and their associate Rodney Lester were pioneers in pharmacy automation and small-object counting technology. In 1967, the Kirbys invented a portable digital tablet counter to count tablets and capsules. With Lester they formed a limited company. In 1970, their invention was patented and put into production in Oldham, England. The tablet counter aided the pharmacy industry with time-consuming manual counting of drug prescriptions. A counting machine consistently counted medications accurately and quickly. This aspect of pharmacy automation was quickly adopted, and innovations emerged every decade to aid the pharmacy industry to deliver medications quickly, safely, and economically. Modern pharmacies have many new options to improve their workflow by using the new technology, and can choose intelligently from the many options available. === Chronology === On 1 January 1971 commercial production of the first portable digital tablet counters in the World began. John Kirby had filed U.K. Patent number GB1358378(A) on 8 September 1970 and U.S. patent number 3789194 on 9 August 1971. These early electronic counters were designed to help pharmacies replace the common (but often inaccurate) practice of counting medications by hand. In 1975, the digital technology was exported to America. In early 1980 a dedicated research, development and production facility was built in Oldham, England at a cost of £500,000. Between 1982 and 1983, two separate development facilities had been created. In America, overseen by Rodney Lester; and in England, overseen by the Kirby brothers. In 1987, Frank Kirby died. In 1989, John Kirby moved his UK facility to Devon, England. A simple to operate machine had been developed to accurately and quickly count prescription medications. Technology improvements soon resulted in a more compact model. The price of such equipment in 1980 was around £1,300. This substantial investment in new technology was a major financial consideration, but the pharmacy community considered the use of a counting machine as a superior method compared to hand-counting medications. These early devices became known as tablet counter, capsule counter, pill counter, or drug counter. The new counting technology replaced manual methods in many industries such as, vitamin and diet supplement manufacturing. Technicians needed a small, affordable device to count and bottle medications. In England and America, the 1980s and 1990s saw new the development of high-speed machines for counting and bottle filling, Like their pharmacy-based counterparts, these industrial units were designed to be fast and simple to operate, yet remain small and cost effective. In America, in the late 1990s/early 2000s a new type of tablet counter appeared. It was simple to use, compact, inexpensive, and had good counting accuracy. At the turn of the millennium technical advances allowed the design of counters with a software verification system. With an onboard computer, displaying photo images of medications to assist the pharmacist or pharmacy technician to verify that the correct medication was being dispensed. In addition, a database for storing all prescriptions that were counted on the device. Between September 2005 and May 2007, American Capital made a major financial investment in Kirby Lester, which then relocated to a larger facility to expand its research and development capabilities. This move added extra space for product research and development facility (R&D). It allowed the opportunity to develop new advanced technology products that met the pharmacy's needs for simple, accurate, and cost-effective ways to dispense prescriptions safely. Pictured here is an early American type of integrated counter and packaging device. This machine was a third generation step in the evolution of pharmacy automated devices. Later models held pre-counted containers of commonly-prescribed medications. == Global variations == In the EU member states legislation was introduced in 1998 which had a major effect on UK Pharmacy operations. It effectively prohibited the use of tablet counters for counting and dispensing bulk packaged tablets. Both usage and sales of the machines in the UK declined rapidly as a result of the introduction of blister packaging for medicines. == Current state of the industry == A tablet counter has become a standard in more than 30,000 sites in 35 countries (as of 2010) (including many non-pharmacy sites, such as manufacturing facilities that use a counting machine as a check for small items). During the 1990s through 2012, numerous new pharmacy automation products came to market. During this timeframe, counting technologies, robotics, workflow management software, and interactive voice recognition (IVR) systems for retail (both chain and independent), outpatient, government, and closed-door pharmacies (mail order and central fill) were all introduced. Additionally, the concept of scalability - of migrating from an entry-level product to the next level of automation (e.g., counting technology to robotics) - was introduced and subsequently launched a new product line in 1997. Pharmacists everywhere are making the switch to automation for its increased speed, greater accuracy, and better security. As the industry evolves and customer expectations grow, automation is becoming less of a luxury and more of a necessity. Especially for independent pharmacies, automation is now a means of keeping up with the competition of large chain pharmacies. == Technological changes and design improvements == Constant developments in technology make the dispensing of prescription medications safer, more accurate and more efficient. In America, in 2008, "next-generation" counting and verification systems were introduced. Based on the counting technology employed in preceding models, later machines included the ability to help the pharmacy operate more effectively. Equipped with a new computer interface to a pharmacy management system, with workflow and inventory software. It also included "checks and balances" to ensure the technician and pharmacist were dispensing the correct medication for each patient. This is something that is important to keep reported correctly when dealing with controlled substances like narcotics. This was a step forward to verify all 100% of prescriptions that were dispensed by pharmacy staff. In America, in 2009, further advanced counters were designed that included the ability to dispense hands-free – a feature that many operators had desired. This allowed pharmacies to automate their most commonly dispensed medications via calibrated cassettes. Thirty of a pharmacy's common medications would now be dispensed automatically. Another new model doubled that throughput via an enclosed robotic mechanism. Robo

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  Enterprise cognitive system

  Enterprise cognitive systems (ECS) are part of a broader shift in computing, from a programmatic to a probabilistic approach, called cognitive computing. An Enterprise Cognitive System makes a new class of complex decision support problems computable, where the business context is ambiguous, multi-faceted, and fast-evolving, and what to do in such a situation is usually assessed today by the business user. An ECS is designed to synthesize a business context and link it to the desired outcome. It recommends evidence-based actions to help the end-user achieve the desired outcome. It does so by finding past situations similar to the current situation, and extracting the repeated actions that best influence the desired outcome. While general-purpose cognitive systems can be used for different outputs, prescriptive, suggestive, instructive, or simply entertaining, an enterprise cognitive system is focused on action, not insight, to help in assessing what to do in a complex situation. == Key characteristics == ECS have to be: Adaptive: They must learn as information changes, and as goals and requirements evolve. They must resolve ambiguity and tolerate unpredictability. They must be engineered to feed on dynamic data in real time, or near real time. In the Enterprise, near-real time learning from data requires an agile information federation approach to ingest incremental data updates as they occur, and an unsupervised learning approach to ensure that new best practice is leveraged across the organization in a timely manner. Interactive: They must interact easily with users so that those users can define their needs comfortably. They may also interact with other processors, devices, and Cloud services, as well as with people. In the Enterprise, interactions are controlled via existing workflows and UIs. Therefore, embedding best practices directly into these existing interfaces, in the context of a specific step, is critical to ensure maximum end-user adoption. Iterative and stateful: They must aid in defining a problem by asking questions or finding additional source input if a problem statement is ambiguous or incomplete. They must “remember” previous interactions in a process and return information that is suitable for the specific application at that point in time. In the Enterprise, business context is often structured by a business process, and therefore sufficiently data-rich to make relevant recommendations without significant iterations from the end-user. A stateful memory of overall interactions across communication channels is critical for understanding of context, as a static profile will not capture intent and outcome potential the way behavior does. Contextual: They must understand, identify, and extract contextual elements such as meaning, syntax, time, location, appropriate domain, regulations, user's profile, process, task and goal. They may draw on multiple sources of information, including both structured and unstructured digital information, as well as sensory inputs (visual, gestural, auditory, or sensor-provided). In the Enterprise, Context is fragmented and must be aggregated across data types, sources, and locations. In most business environments, such data is captured in existing enterprise information systems, and the effort is linked to quickly source and unify such information. It is rare to have to directly process sensor, audio or visual data in real-time as direct input into the enterprise cognitive system. Instead, these data types are captured by Enterprise Applications and pre-processed into a binary or text format prior to consumption by the System. == Business applications powered by an ECS == Bottlenose – trends and brands monitoring Cybereason – security threat monitoring Dataminr – social media monitoring

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  Feature hashing

  In machine learning, feature hashing, also known as the hashing trick (by analogy to the kernel trick), is a fast and space-efficient way of vectorizing features, i.e. turning arbitrary features into indices in a vector or matrix. It works by applying a hash function to the features and using their hash values as indices directly (after a modulo operation), rather than looking the indices up in an associative array. In addition to its use for encoding non-numeric values, feature hashing can also be used for dimensionality reduction. This trick is often attributed to Weinberger et al. (2009), but there exists a much earlier description of this method published by John Moody in 1989. == Motivation == === Motivating example === In a typical document classification task, the input to the machine learning algorithm (both during learning and classification) is free text. From this, a bag of words (BOW) representation is constructed: the individual tokens are extracted and counted, and each distinct token in the training set defines a feature (independent variable) of each of the documents in both the training and test sets. Machine learning algorithms, however, are typically defined in terms of numerical vectors. Therefore, the bags of words for a set of documents is regarded as a term-document matrix where each row is a single document, and each column is a single feature/word; the entry i, j in such a matrix captures the frequency (or weight) of the j'th term of the vocabulary in document i. (An alternative convention swaps the rows and columns of the matrix, but this difference is immaterial.) Typically, these vectors are extremely sparse—according to Zipf's law. The common approach is to construct, at learning time or prior to that, a dictionary representation of the vocabulary of the training set, and use that to map words to indices. Hash tables and tries are common candidates for dictionary implementation. E.g., the three documents John likes to watch movies. Mary likes movies too. John also likes football. can be converted, using the dictionary to the term-document matrix ( John likes to watch movies Mary too also football 1 1 1 1 1 0 0 0 0 0 1 0 0 1 1 1 0 0 1 1 0 0 0 0 0 1 1 ) {\displaystyle {\begin{pmatrix}{\textrm {John}}&{\textrm {likes}}&{\textrm {to}}&{\textrm {watch}}&{\textrm {movies}}&{\textrm {Mary}}&{\textrm {too}}&{\textrm {also}}&{\textrm {football}}\\1&1&1&1&1&0&0&0&0\\0&1&0&0&1&1&1&0&0\\1&1&0&0&0&0&0&1&1\end{pmatrix}}} (Punctuation was removed, as is usual in document classification and clustering.) The problem with this process is that such dictionaries take up a large amount of storage space and grow in size as the training set grows. On the contrary, if the vocabulary is kept fixed and not increased with a growing training set, an adversary may try to invent new words or misspellings that are not in the stored vocabulary so as to circumvent a machine learned filter. To address this challenge, Yahoo! Research attempted to use feature hashing for their spam filters. Note that the hashing trick isn't limited to text classification and similar tasks at the document level, but can be applied to any problem that involves large (perhaps unbounded) numbers of features. === Mathematical motivation === Mathematically, a token is an element t {\displaystyle t} in a finite (or countably infinite) set T {\displaystyle T} . Suppose we only need to process a finite corpus, then we can put all tokens appearing in the corpus into T {\displaystyle T} , meaning that T {\displaystyle T} is finite. However, suppose we want to process all possible words made of the English letters, then T {\displaystyle T} is countably infinite. Most neural networks can only operate on real vector inputs, so we must construct a "dictionary" function ϕ : T → R n {\displaystyle \phi :T\to \mathbb {R} ^{n}} . When T {\displaystyle T} is finite, of size | T | = m ≤ n {\displaystyle |T|=m\leq n} , then we can use one-hot encoding to map it into R n {\displaystyle \mathbb {R} ^{n}} . First, arbitrarily enumerate T = { t 1 , t 2 , . . , t m } {\displaystyle T=\{t_{1},t_{2},..,t_{m}\}} , then define ϕ ( t i ) = e i {\displaystyle \phi (t_{i})=e_{i}} . In other words, we assign a unique index i {\displaystyle i} to each token, then map the token with index i {\displaystyle i} to the unit basis vector e i {\displaystyle e_{i}} . One-hot encoding is easy to interpret, but it requires one to maintain the arbitrary enumeration of T {\displaystyle T} . Given a token t ∈ T {\displaystyle t\in T} , to compute ϕ ( t ) {\displaystyle \phi (t)} , we must find out the index i {\displaystyle i} of the token t {\displaystyle t} . Thus, to implement ϕ {\displaystyle \phi } efficiently, we need a fast-to-compute bijection h : T → { 1 , . . . , m } {\displaystyle h:T\to \{1,...,m\}} , then we have ϕ ( t ) = e h ( t ) {\displaystyle \phi (t)=e_{h(t)}} . In fact, we can relax the requirement slightly: It suffices to have a fast-to-compute injection h : T → { 1 , . . . , n } {\displaystyle h:T\to \{1,...,n\}} , then use ϕ ( t ) = e h ( t ) {\displaystyle \phi (t)=e_{h(t)}} . In practice, there is no simple way to construct an efficient injection h : T → { 1 , . . . , n } {\displaystyle h:T\to \{1,...,n\}} . However, we do not need a strict injection, but only an approximate injection. That is, when t ≠ t ′ {\displaystyle t\neq t'} , we should probably have h ( t ) ≠ h ( t ′ ) {\displaystyle h(t)\neq h(t')} , so that probably ϕ ( t ) ≠ ϕ ( t ′ ) {\displaystyle \phi (t)\neq \phi (t')} . At this point, we have just specified that h {\displaystyle h} should be a hashing function. Thus we reach the idea of feature hashing. == Algorithms == === Feature hashing (Weinberger et al. 2009) === The basic feature hashing algorithm presented in (Weinberger et al. 2009) is defined as follows. First, one specifies two hash functions: the kernel hash h : T → { 1 , 2 , . . . , n } {\displaystyle h:T\to \{1,2,...,n\}} , and the sign hash ζ : T → { − 1 , + 1 } {\displaystyle \zeta :T\to \{-1,+1\}} . Next, one defines the feature hashing function: ϕ : T → R n , ϕ ( t ) = ζ ( t ) e h ( t ) {\displaystyle \phi :T\to \mathbb {R} ^{n},\quad \phi (t)=\zeta (t)e_{h(t)}} Finally, extend this feature hashing function to strings of tokens by ϕ : T ∗ → R n , ϕ ( t 1 , . . . , t k ) = ∑ j = 1 k ϕ ( t j ) {\displaystyle \phi :T^{}\to \mathbb {R} ^{n},\quad \phi (t_{1},...,t_{k})=\sum _{j=1}^{k}\phi (t_{j})} where T ∗ {\displaystyle T^{}} is the set of all finite strings consisting of tokens in T {\displaystyle T} . Equivalently, ϕ ( t 1 , . . . , t k ) = ∑ j = 1 k ζ ( t j ) e h ( t j ) = ∑ i = 1 n ( ∑ j : h ( t j ) = i ζ ( t j ) ) e i {\displaystyle \phi (t_{1},...,t_{k})=\sum _{j=1}^{k}\zeta (t_{j})e_{h(t_{j})}=\sum _{i=1}^{n}\left(\sum _{j:h(t_{j})=i}\zeta (t_{j})\right)e_{i}} ==== Geometric properties ==== We want to say something about the geometric property of ϕ {\displaystyle \phi } , but T {\displaystyle T} , by itself, is just a set of tokens, we cannot impose a geometric structure on it except the discrete topology, which is generated by the discrete metric. To make it nicer, we lift it to T → R T {\displaystyle T\to \mathbb {R} ^{T}} , and lift ϕ {\displaystyle \phi } from ϕ : T → R n {\displaystyle \phi :T\to \mathbb {R} ^{n}} to ϕ : R T → R n {\displaystyle \phi :\mathbb {R} ^{T}\to \mathbb {R} ^{n}} by linear extension: ϕ ( ( x t ) t ∈ T ) = ∑ t ∈ T x t ζ ( t ) e h ( t ) = ∑ i = 1 n ( ∑ t : h ( t ) = i x t ζ ( t ) ) e i {\displaystyle \phi ((x_{t})_{t\in T})=\sum _{t\in T}x_{t}\zeta (t)e_{h(t)}=\sum _{i=1}^{n}\left(\sum _{t:h(t)=i}x_{t}\zeta (t)\right)e_{i}} There is an infinite sum there, which must be handled at once. There are essentially only two ways to handle infinities. One may impose a metric, then take its completion, to allow well-behaved infinite sums, or one may demand that nothing is actually infinite, only potentially so. Here, we go for the potential-infinity way, by restricting R T {\displaystyle \mathbb {R} ^{T}} to contain only vectors with finite support: ∀ ( x t ) t ∈ T ∈ R T {\displaystyle \forall (x_{t})_{t\in T}\in \mathbb {R} ^{T}} , only finitely many entries of ( x t ) t ∈ T {\displaystyle (x_{t})_{t\in T}} are nonzero. Define an inner product on R T {\displaystyle \mathbb {R} ^{T}} in the obvious way: ⟨ e t , e t ′ ⟩ = { 1 , if t = t ′ , 0 , else. ⟨ x , x ′ ⟩ = ∑ t , t ′ ∈ T x t x t ′ ⟨ e t , e t ′ ⟩ {\displaystyle \langle e_{t},e_{t'}\rangle ={\begin{cases}1,{\text{ if }}t=t',\\0,{\text{ else.}}\end{cases}}\quad \langle x,x'\rangle =\sum _{t,t'\in T}x_{t}x_{t'}\langle e_{t},e_{t'}\rangle } As a side note, if T {\displaystyle T} is infinite, then the inner product space R T {\displaystyle \mathbb {R} ^{T}} is not complete. Taking its completion would get us to a Hilbert space, which allows well-behaved infinite sums. Now we have an inner product space, with enough structure to describe the geometry of the feature hashing function ϕ : R T → R n {\displaystyle \phi :\ma

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  Dataset shift

  Dataset shift is a phenomenon in machine learning and statistics in which the joint distribution of input variables and target labels is different in the training phase and the deployment or test phase (i.e., P t r a i n ( X , Y ) ≠ P t e s t ( X , Y ) {\displaystyle P_{train}(X,Y)\neq P_{test}(X,Y)} ). This happens when the statistical properties of data used to train a model are no longer representative of the data encountered in real-world use, often resulting in degraded predictive performance and diminished generalization ability. Dataset shift is a generic term for a number of particular types of distributional change. Covariate shift is when the distribution of the input features changes, but the conditional relationship between inputs and outputs remains constant . Prior probability shift (or label shift) happens when the distribution of target labels changes, but the conditional distribution of inputs given labels stays the same. Concept shift (also known as concept drift) is the change of the conditional relationship between inputs and outputs that renders previously learned patterns invalid over time. A key challenge for deploying machine learning systems is dataset shift, in particular in dynamic environments where the data distributions change over time. Detecting and mitigating such shifts is an active area of research, e.g., drift detection, domain adaptation, continual learning.

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  Roposo

  Roposo is an Indian video-sharing social media service, owned by Glance, a subsidiary of InMobi. Roposo provides a space where users can share posts related to different topics like food, comedy, music, poetry, fashion and travel. It is a platform where people express visually with homemade videos and photos. The app offers a TV-like browsing experience with user-generated content on its channels. Users can also use editing tools on the platform and upload their content. == History == Established in July 2014 under Relevant E-solutions Pvt. Ltd., Roposo is the brainchild of three IIT Delhi alumni – Mayank Bhangadia, Avinash Saxena, and Kaushal Shubhank. Under Bhangadia's leadership, the company pivoted from a fashion-based network into a short-form video platform with AI-powered moderation, and its journey was featured as a Harvard Business Publishing case study. In November 2019, Roposo was acquired by InMobi's Glance Digital Experience Pvt. Ltd.(the mobile content platform and part of the InMobi Group). When the Chinese-owned video-sharing app TikTok was banned on 30 June 2020, the app saw a huge spike in users with several TikTok users registering on Roposo. == Technology == The open platform has some features such as a TV-like browsing, different channels, a chat feature that lets buyers and sellers converse directly through the platform, and creation tools such as an option to add voice-over, music and GIF stickers for videos and photos.

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  AI-assisted software development

  AI-assisted software development is the use of artificial intelligence (AI) to augment software development. It uses large language models (LLMs), AI agents and other AI technologies to assist software developers. It helps in a range of tasks of the software development life cycle, from code generation to debugging, editing, testing, UI design, understanding the code, and documentation. Agentic coding denotes the use of AI agents for software development. == Technologies == === Source code generation === Large language models trained or fine-tuned on source-code corpora can generate source code from natural-language descriptions, comments, or docstrings. Research on code-generation systems often evaluates generated programs by functional correctness, such as whether the output passes automated test cases, rather than by syntax alone. Such tools can be features or extensions of integrated development environments (IDEs). === Intelligent code completion === AI agents using pre-trained and fine-tuned LLMs can predict and suggest code completions based on context. According to Husein, Aburajouh & Catal in a 2025 literature review in Computer Standards & Interfaces, "LLMs significantly enhance code completion performance across several programming languages and contexts, and their capability to predict relevant code snippets based on context and partial input boosts developer productivity substantially." === Testing, debugging, code review and analysis === AI is used to automatically generate test cases, identify potential bugs and security vulnerabilities, and suggest fixes. AI can also be used to perform static code analysis and suggest potential performance improvements. == Limitations == Both ownership of and responsibility for AI-generated code is disputed. According to a report from the German Federal Office for Information Security, the use of AI coding assistants without careful oversight from experienced developers can introduce both minor and major security vulnerabilities, and any potential gain in productivity should be weighed against the cost of additional quality control and security measures. According to Deloitte, outputs from AI-assisted software development must be validated through a combination of automated testing, static analysis tools and human review, creating a governance layer to improve quality and accountability. == Vibe coding ==

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  Computational humor

  Computational humor is a branch of computational linguistics and artificial intelligence which uses computers in humor research. It is a relatively new area, with the first dedicated conference organized in 1996. The first "computer model of a sense of humor" was suggested by Suslov as early as 1992. Investigation of the general scheme of the information processing show a possibility of a specific malfunction, conditioned by the necessity of a quick deletion from consciousness of a false version. This specific malfunction can be identified with a humorous effect on the psychological grounds; however, an essentially new ingredient, a role of timing, is added to a well known role of ambiguity. In biological systems, a sense of humour inevitably develops in the course of evolution, because its biological function consists in quickening the transmission of processed information into consciousness and in a more effective use of brain resources. A realization of this algorithm in neural networks explains naturally the mechanism of laughter: deletion of a false version corresponds to zeroing of some part of the neural network and excessive energy of neurons is thrown out to the motor cortex, arousing muscular contractions. Unfortunately, a practical realization of this algorithm needs extensive databases, whose creation in the automatic regime was suggested only recently . As a result, this magistral direction was not developed properly and subsequent investigations (see below) accepted somewhat specialized colouring. == Joke generators == === Pun generation === An approach to analysis of humor is classification of jokes. A further step is an attempt to generate jokes basing on the rules that underlie classification. Simple prototypes for computer pun generation were reported in the early 1990s, based on a natural language generator program, VINCI. Graeme Ritchie and Kim Binsted in their 1994 research paper described a computer program, JAPE, designed to generate question-answer-type puns from a general, i.e., non-humorous, lexicon. (The program name is an acronym for "Joke Analysis and Production Engine".) Some examples produced by JAPE are: Q: What is the difference between leaves and a car? A: One you brush and rake, the other you rush and brake. Q: What do you call a strange market? A: A bizarre bazaar. Since then the approach has been improved, and the latest report, dated 2007, describes the STANDUP joke generator, implemented in the Java programming language. The STANDUP generator was tested on children within the framework of analyzing its usability for language skills development for children with communication disabilities, e.g., because of cerebral palsy. (The project name is an acronym for "System To Augment Non-speakers' Dialog Using Puns" and an allusion to standup comedy.) Children responded to this "language playground" with enthusiasm, and showed marked improvement on certain types of language tests. The two young people, who used the system over a ten-week period, regaled their peers, staff, family and neighbors with jokes such as: "What do you call a spicy missile? A hot shot!" Their joy and enthusiasm at entertaining others was inspirational. === Other === Stock and Strapparava described a program to generate funny acronyms. == Joke recognition == A statistical machine learning algorithm to detect whether a sentence contained a "That's what she said" double entendre was developed by Kiddon and Brun (2011). There is an open-source Python implementation of Kiddon & Brun's TWSS system. A program to recognize knock-knock jokes was reported by Taylor and Mazlack. This kind of research is important in analysis of human–computer interaction. An application of machine learning techniques for the distinguishing of joke texts from non-jokes was described by Mihalcea and Strapparava (2006). Takizawa et al. (1996) reported on a heuristic program for detecting puns in the Japanese language. == Applications == A possible application for assistance in language acquisition is described in the section "Pun generation". Another envisioned use of joke generators is in cases of a steady supply of jokes where quantity is more important than quality. Another obvious, yet remote, direction is automated joke appreciation. It is known that humans interact with computers in ways similar to interacting with other humans that may be described in terms of personality, politeness, flattery, and in-group favoritism. Therefore, the role of humor in human–computer interaction is being investigated. In particular, humor generation in user interface to ease communications with computers was suggested. Craig McDonough implemented the Mnemonic Sentence Generator, which converts passwords into humorous sentences. Based on the incongruity theory of humor, it is suggested that the resulting meaningless but funny sentences are easier to remember. For example, the password AjQA3Jtv is converted into "Arafat joined Quayle's Ant, while TARAR Jeopardized thurmond's vase," an example chosen by combining politicians names with verbs and common nouns. == Related research == John Allen Paulos is known for his interest in mathematical foundations of humor. His book Mathematics and Humor: A Study of the Logic of Humor demonstrates structures common to humor and formal sciences (mathematics, linguistics) and develops a mathematical model of jokes based on catastrophe theory. Conversational systems which have been designed to take part in Turing test competitions generally have the ability to learn humorous anecdotes and jokes. Because many people regard humor as something particular to humans, its appearance in conversation can be quite useful in convincing a human interrogator that a hidden entity, which could be a machine or a human, is in fact a human.

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