AI Coding Quality

AI Coding Quality — independent reviews, comparisons, pricing and step-by-step guides on Aizhi.

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  Perplexity AI

  Perplexity AI, Inc., or simply Perplexity, is an American privately held software company offering a web search engine that processes user queries and synthesizes responses. Perplexity products use large language models and incorporate real-time web search capabilities, providing responses based on current Internet content, citing sources used. Its real-time search engine is called Sonar and is based on Meta's Llama model. A free public version is available, while a paid Pro subscription offers access to more advanced language models and additional features. Perplexity AI, Inc., was founded in August 2022 by Aravind Srinivas, Denis Yarats, Johnny Ho, and Andy Konwinski. As of September 2025, the company was valued at US$20 billion. Perplexity AI has attracted legal scrutiny over allegations of copyright infringement, unauthorized content use, and trademark issues from several major media organizations, including the BBC, Dow Jones, and The New York Times. According to separate analyses by Wired and later Cloudflare, Perplexity uses undisclosed web crawlers with spoofed user-agent strings to scrape the content of websites which prohibit, or explicitly block, web scraping. == History == In August 2022, Perplexity AI, Inc., was founded by Aravind Srinivas, Denis Yarats, Johnny Ho, and Andy Konwinski, engineers with backgrounds in back-end systems, artificial intelligence (AI) and machine learning. It launched its main search engine on December 7, 2022, and has since released a Google Chrome extension and apps for iOS and Android. In February 2023, Perplexity reported two million unique visitors. By April 2024, Perplexity had raised $165 million in funding, valuing the company at over $1 billion. As of June 2025, Perplexity closed a $500 million round of funding that elevated its valuation to $14 billion. Investors in Perplexity AI have included Jeff Bezos, Tobias Lütke, Nat Friedman, Nvidia, and Databricks. Perplexity has also received funding from 1789 Capital, a venture capital firm notable for its association with Donald Trump Jr. During Bloomberg’s Tech Summit 2025, Srinivas shared that the company processed 780 million queries in May 2025, experiencing more than 20% month-over-month growth, processing around 30 million queries daily. In July 2024, Perplexity announced the launch of a new publishers' program to share advertising revenue with partners. On January 18, 2025, the day before the impending U.S. ban on the social media app TikTok, Perplexity submitted a proposal for a merger with TikTok US. On August 12, 2025, Perplexity made a bid to buy Chrome from Google for $34.5 billion. Perplexity stated that the sale could remedy anti-trust litigation against Google, in which a judge was considering compelling the sale of Chrome. In December 2025, Cristiano Ronaldo took an undisclosed stake in Perplexity AI and entered a global brand partnership with the company. === Business Strategy and Finance (2026) === As of early 2026, Perplexity AI reached a valuation of $21.21 billion following its Series E-6 funding round. The company's Annual Recurring Revenue (ARR) grew from $80 million in late 2024 to an estimated $200 million by February 2026. In January 2026, the company entered into a three-year, $750 million commitment with Microsoft Azure to secure the GPU capacity required for its advanced "Deep Research" and "Model Council" features. In February 2026, Perplexity transitioned to a subscription-first model by discontinuing its AI-integrated advertising strategy. Leadership stated the move was intended to preserve user trust in the "answer engine," prioritizing objective results over ad revenue. The company also introduced the "Model Council" feature on February 5, 2026, which allows users to compare outputs from multiple large language models, such as GPT-5.2 and Claude 4.6, simultaneously. To expand its user base, Perplexity began offering a free year of Pro access to students, U.S. Military Veterans, and government employees. == Products and services == === Search engine web portal === Perplexity’s primary offering is an online information retrieval system (search engine) that uses large language models to generate responses to user queries by searching and summarizing web-based content. Perplexity offers a feature known as Perplexity Pages that generates structured summaries and report-like content from user queries by aggregating cited sources. Perplexity is available without charge or registration to Web users, a freemium model. === Perplexity Pro === Perplexity Pro is a subscription tier, a more capable paid "enterprise" service, including stronger security and data protection and additional tools, including the ability to search uploaded documents alongside web content and access to a programmatic application programming interface (API). It allows the user to select between backend models such as GPT-5.4, Claude 4.6 and Gemini 3.1 Pro. The company has also developed its own models, Sonar (based on Llama 3.3) and R1 1776 (based on DeepSeek R1). === Internal Knowledge Search === Internal Knowledge Search enables Pro and Enterprise Pro users to simultaneously search across web content and internal documents. Users can upload and search through Excel, Word, PDF, and other common file formats. Enterprise Pro users can upload and index up to 500 files. === Search API === Perplexity's Search API provides AI developers with programmatic access to the company's search infrastructure. The September 2025 release includes a software development kit, an open-source evaluation framework called search_evals, and documentation detailing the API's design and optimization. === Shopping hub === Perplexity's Shopping Hub is an online shopping platform that provides AI-generated product recommendations, and enables users to purchase products directly through Perplexity's interface. It was launched in November 2024 with backing by Amazon and Nvidia. === Finance === In October 2024, Perplexity AI introduced new finance-related features, including looking up stock prices and company earnings data. The tool provides real-time stock quotes and price tracking, industry peer comparisons and basic financial analysis tools. The platform sources its financial data from Financial Modeling Prep. === Assistant === In January 2025, Perplexity launched the Perplexity Assistant, an AI-powered tool designed to enhance the functionality of its search engine. It can perform tasks across multiple apps, such as hailing a ride or searching for a song, and can maintain context across actions. The assistant is also multi-modal, meaning it can use a phone's camera to provide answers about the user's surroundings or on-screen content. Perplexity has acknowledged that the assistant is still in development and may not always function as expected. For instance, certain features, such as summarizing unread emails or upcoming calendar events, require users to enable a workaround based on notifications. === Comet === In July 2025, Perplexity launched Comet, an AI browser based on Chromium. Initially, access to the browser was limited to users subscribed to the most expensive subscription tier. The browser was later released for free download in October 2025. A key feature is integration of the Perplexity search engine, which can perform a variety of tasks such as generating article summaries, describing an image, conducting research about a topic and composing emails. === Truth Social chatbot === Perplexity has been contracted to produce a chatbot for Donald Trump's social media platform Truth Social. == Leadership == Aravind Srinivas is the CEO and co-founder of Perplexity AI. He previously held research positions at OpenAI, Google DeepMind, and other AI research institutions focusing on machine learning and artificial intelligence. In a March 2026 All-In episode, Srinivas said the incoming AI-related layoffs were "glorious future" to "look forward", as it freed people from jobs they didn't like and gave them opportunities to pursue entrepreneurship. == Controversies == === Copyright and trademark infringement allegations === In June 2024, Forbes publicly criticized Perplexity for using their content. According to Forbes, Perplexity published a story largely copied from a proprietary Forbes article without mentioning or prominently citing Forbes. In response, Srinivas said that the feature had some "rough edges" and accepted feedback but maintained that Perplexity only "aggregates" rather than plagiarizes information. In October 2024, The New York Times sent a cease-and-desist notice to Perplexity to stop accessing and using NYT content, claiming that Perplexity is violating its copyright by scraping data from its website. In June 2024, Dow Jones and New York Post filed a lawsuit against Perplexity, alleging copyright infringement. The lawsuit also alleged that Perplexity harmed their brand by attributing hallucinated quotes, for example on F-16 jets for Ukraine, to artic

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  Is an AI Text-to-image Tool Worth It in 2026?

  Trying to pick the best AI text-to-image tool? An AI text-to-image tool is software that uses machine learning to help you get more done — it scales effortlessly from a single task to thousands. The best picks balance beginner-friendly simplicity with the depth power users need, and they ship updates often. Whether you are a beginner or a pro, the right AI text-to-image tool slots into your workflow and pays for itself fast. Read on for hands-on impressions, pricing tiers, and the standout features that matter.

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  Best AI Content Generators in 2026

  Trying to pick the best AI content generator? An AI content generator is software that uses machine learning to help you get more done — it scales effortlessly from a single task to thousands. The best picks balance beginner-friendly simplicity with the depth power users need, and they ship updates often. Whether you are a beginner or a pro, the right AI content generator slots into your workflow and pays for itself fast. This guide breaks down the top picks, their pros and cons, and who each one is best for.

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  Büchi automaton

  In computer science and automata theory, a deterministic Büchi automaton is a theoretical machine which either accepts or rejects infinite inputs. Such a machine has a set of states and a transition function, which determines which state the machine should move to from its current state when it reads the next input character. Some states are accepting states and one state is the start state. The machine accepts an input if and only if it will pass through an accepting state infinitely many times as it reads the input. A non-deterministic Büchi automaton, later referred to just as a Büchi automaton, has a transition function which may have multiple outputs, leading to many possible paths for the same input; it accepts an infinite input if and only if some possible path is accepting. Deterministic and non-deterministic Büchi automata generalize deterministic finite automata and nondeterministic finite automata to infinite inputs. Each are types of ω-automata. Büchi automata recognize the ω-regular languages, the infinite word version of regular languages. They are named after the Swiss mathematician Julius Richard Büchi, who invented them in 1962. Büchi automata are often used in model checking as an automata-theoretic version of a formula in linear temporal logic. == Formal definition == Formally, a deterministic Büchi automaton is a tuple A = ( Q , Σ , δ , q 0 , F ) {\textstyle A=(Q,\Sigma ,\delta ,q_{0},\mathbf {F} )} that consists of the following components: Q {\textstyle Q} is a finite set. The elements of Q {\textstyle Q} are called the states of A {\textstyle A} . Σ {\textstyle \Sigma } is a finite set called the alphabet of A {\textstyle A} . δ : Q × Σ → Q {\textstyle \delta \colon Q\times \Sigma \to Q} is a function, called the transition function of A {\textstyle A} . q 0 {\textstyle q_{0}} is an element of Q {\textstyle Q} , called the initial state of A {\textstyle A} . F ⊆ Q {\textstyle \mathbf {F} \subseteq Q} is the acceptance condition. A run i _ = i 0 i 1 i 2 ⋯ ∈ Σ ω {\displaystyle {\underline {i}}=i_{0}i_{1}i_{2}\cdots \in \Sigma ^{\omega }} is an infinite string of inputs of A {\displaystyle A} . By calling δ {\displaystyle \delta } recursively, we can extend it to a function δ ω : Σ ω → Q ω {\displaystyle \delta ^{\omega }:\Sigma ^{\omega }\to Q^{\omega }} . A state q ∈ Q {\displaystyle q\in Q} is said to occur infinitely often for a run i _ {\displaystyle {\underline {i}}} when the set { n ∈ N ∣ δ ω ( i _ ) n = q } {\displaystyle \{n\in \mathbb {N} \mid \delta ^{\omega }({\underline {i}})_{n}=q\}} is infinite. Let I n f ( i _ ) {\displaystyle \mathrm {Inf} ({\underline {i}})} be the set of states occurring infinitely often for i _ {\displaystyle {\underline {i}}} . The language of A {\displaystyle A} is then the set of runs of A {\displaystyle A} in which at least one of the infinitely-often occurring states is in F {\textstyle \mathbf {F} } ; in symbols: L ( A ) = { i _ ∈ Σ ω ∣ I n f ( i _ ) ∩ F ≠ ∅ } . {\displaystyle L(A)=\{{\underline {i}}\in \Sigma ^{\omega }\mid \mathrm {Inf} ({\underline {i}})\cap \mathbf {F} \neq \varnothing \}.} In a (non-deterministic) Büchi automaton, the transition function δ {\textstyle \delta } is replaced with a transition relation Δ {\textstyle \Delta } that returns a set of states, and the single initial state q 0 {\textstyle q_{0}} is replaced by a set I {\textstyle I} of initial states. Generally, the term Büchi automaton without qualifier refers to non-deterministic Büchi automata. For more comprehensive formalism see also ω-automaton. == Closure properties == The set of Büchi automata is closed under the following operations. Let A = ( Q A , Σ , Δ A , I A , F A ) {\displaystyle A=(Q_{A},\Sigma ,\Delta _{A},I_{A},{F}_{A})} and B = ( Q B , Σ , Δ B , I B , F B ) {\displaystyle B=(Q_{B},\Sigma ,\Delta _{B},I_{B},{F}_{B})} be Büchi automata and C = ( Q C , Σ , Δ C , I C , F C ) {\displaystyle C=(Q_{C},\Sigma ,\Delta _{C},I_{C},{F}_{C})} be a finite automaton. Union: There is a Büchi automaton that recognizes the language L ( A ) ∪ L ( B ) . {\displaystyle L(A)\cup L(B).} Proof: If we assume, w.l.o.g., Q A ∩ Q B {\displaystyle Q_{A}\cap Q_{B}} is empty then L ( A ) ∪ L ( B ) {\displaystyle L(A)\cup L(B)} is recognized by the Büchi automaton ( Q A ∪ Q B , Σ ∪ Σ , Δ A ∪ Δ B , I A ∪ I B , F A ∪ F B ) . {\displaystyle (Q_{A}\cup Q_{B},\Sigma \cup \Sigma ,\Delta _{A}\cup \Delta _{B},I_{A}\cup I_{B},{F}_{A}\cup {F}_{B}).} Intersection: There is a Büchi automaton that recognizes the language L ( A ) ∩ L ( B ) . {\displaystyle L(A)\cap L(B).} Proof: The Büchi automaton A ′ = ( Q ′ , Σ , Δ ′ , I ′ , F ′ ) {\displaystyle A'=(Q',\Sigma ,\Delta ',I',F')} recognizes L ( A ) ∩ L ( B ) , {\displaystyle L(A)\cap L(B),} where Q ′ = Q A × Q B × { 1 , 2 } {\displaystyle Q'=Q_{A}\times Q_{B}\times \{1,2\}} Δ ′ = Δ 1 ∪ Δ 2 {\displaystyle \Delta '=\Delta _{1}\cup \Delta _{2}} Δ 1 = { ( ( q A , q B , 1 ) , a , ( q A ′ , q B ′ , i ) ) | ( q A , a , q A ′ ) ∈ Δ A and ( q B , a , q B ′ ) ∈ Δ B and if q A ∈ F A then i = 2 else i = 1 } {\displaystyle \Delta _{1}=\{((q_{A},q_{B},1),a,(q'_{A},q'_{B},i))|(q_{A},a,q'_{A})\in \Delta _{A}{\text{ and }}(q_{B},a,q'_{B})\in \Delta _{B}{\text{ and if }}q_{A}\in F_{A}{\text{ then }}i=2{\text{ else }}i=1\}} Δ 2 = { ( ( q A , q B , 2 ) , a , ( q A ′ , q B ′ , i ) ) | ( q A , a , q A ′ ) ∈ Δ A and ( q B , a , q B ′ ) ∈ Δ B and if q B ∈ F B then i = 1 else i = 2 } {\displaystyle \Delta _{2}=\{((q_{A},q_{B},2),a,(q'_{A},q'_{B},i))|(q_{A},a,q'_{A})\in \Delta _{A}{\text{ and }}(q_{B},a,q'_{B})\in \Delta _{B}{\text{ and if }}q_{B}\in F_{B}{\text{ then }}i=1{\text{ else }}i=2\}} I ′ = I A × I B × { 1 } {\displaystyle I'=I_{A}\times I_{B}\times \{1\}} F ′ = { ( q A , q B , 2 ) | q B ∈ F B } {\displaystyle F'=\{(q_{A},q_{B},2)|q_{B}\in F_{B}\}} By construction, r ′ = ( q A 0 , q B 0 , i 0 ) , ( q A 1 , q B 1 , i 1 ) , … {\displaystyle r'=(q_{A}^{0},q_{B}^{0},i^{0}),(q_{A}^{1},q_{B}^{1},i^{1}),\dots } is a run of automaton A' on input word w {\textstyle w} if r A = q A 0 , q A 1 , … {\displaystyle r_{A}=q_{A}^{0},q_{A}^{1},\dots } is run of A {\textstyle A} on w {\textstyle w} and r B = q B 0 , q B 1 , … {\displaystyle r_{B}=q_{B}^{0},q_{B}^{1},\dots } is run of B {\textstyle B} on w {\textstyle w} . r A {\textstyle r_{A}} is accepting and r B {\textstyle r_{B}} is accepting if r ′ {\textstyle r'} is concatenation of an infinite series of finite segments of 1-states (states with third component 1) and 2-states (states with third component 2) alternatively. There is such a series of segments of r ′ {\textstyle r'} if r ′ {\textstyle r'} is accepted by A ′ {\textstyle A'} . Concatenation: There is a Büchi automaton that recognizes the language L ( C ) ⋅ L ( A ) . {\displaystyle L(C)\cdot L(A).} Proof: If we assume, w.l.o.g., Q C ∩ Q A {\displaystyle Q_{C}\cap Q_{A}} is empty then the Büchi automaton A ′ = ( Q C ∪ Q A , Σ , Δ ′ , I ′ , F A ) {\displaystyle A'=(Q_{C}\cup Q_{A},\Sigma ,\Delta ',I',F_{A})} recognizes L ( C ) ⋅ L ( A ) {\displaystyle L(C)\cdot L(A)} , where Δ ′ = Δ A ∪ Δ C ∪ { ( q , a , q ′ ) | q ′ ∈ I A and ∃ f ∈ F C . ( q , a , f ) ∈ Δ C } {\displaystyle \Delta '=\Delta _{A}\cup \Delta _{C}\cup \{(q,a,q')|q'\in I_{A}{\text{ and }}\exists f\in F_{C}.(q,a,f)\in \Delta _{C}\}} if I C ∩ F C is empty then I ′ = I C otherwise I ′ = I C ∪ I A {\displaystyle {\text{ if }}I_{C}\cap F_{C}{\text{ is empty then }}I'=I_{C}{\text{ otherwise }}I'=I_{C}\cup I_{A}} ω-closure: If L ( C ) {\displaystyle L(C)} does not contain the empty word then there is a Büchi automaton that recognizes the language L ( C ) ω . {\displaystyle L(C)^{\omega }.} Proof: The Büchi automaton that recognizes L ( C ) ω {\displaystyle L(C)^{\omega }} is constructed in two stages. First, we construct a finite automaton A ′ {\textstyle A'} such that A ′ {\textstyle A'} also recognizes L ( C ) {\displaystyle L(C)} but there are no incoming transitions to initial states of A ′ {\textstyle A'} . So, A ′ = ( Q C ∪ { q new } , Σ , Δ ′ , { q new } , F C ) , {\displaystyle A'=(Q_{C}\cup \{q_{\text{new}}\},\Sigma ,\Delta ',\{q_{\text{new}}\},F_{C}),} where Δ ′ = Δ C ∪ { ( q new , a , q ′ ) | ∃ q ∈ I C . ( q , a , q ′ ) ∈ Δ C } . {\displaystyle \Delta '=\Delta _{C}\cup \{(q_{\text{new}},a,q')|\exists q\in I_{C}.(q,a,q')\in \Delta _{C}\}.} Note that L ( C ) = L ( A ′ ) {\displaystyle L(C)=L(A')} because L ( C ) {\displaystyle L(C)} does not contain the empty string. Second, we will construct the Büchi automaton A ″ {\textstyle A''} that recognize L ( C ) ω {\displaystyle L(C)^{\omega }} by adding a loop back to the initial state of A ′ {\textstyle A'} . So, A ″ = ( Q C ∪ { q new } , Σ , Δ ″ , { q new } , { q new } ) {\displaystyle A''=(Q_{C}\cup \{q_{\text{new}}\},\Sigma ,\Delta '',\{q_{\text{new}}\},\{q_{\text{new}}\})} , where Δ ″ = Δ ′ ∪ { ( q , a , q new ) | ∃ q ′ ∈ F C . ( q , a , q ′ ) ∈ Δ ′ } . {\displaystyle \Delta ''=\Delta '\cup \{(q,a,q_{\text{new}})|\exists q'\in F_{C}.(q,a,q')\in \Delta '\}.} Complementation:

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  The Drivers Cooperative

  The Drivers Cooperative or Co-Op Ride is an American ridesharing company and mobile app that is a workers cooperative, owned collectively by the drivers. The cooperative launched in May 2021 in New York City, with the first 2,500 drivers issued their ownership certificates in a media event. The cooperative was co-founded by Grenadan immigrant and for hire vehicle driver Ken Lewis, labor organizer Erik Forman, and former Uber executive Alissa Orlando. Mohammad Hossen is the first member of the drivers' advisory board, which they plan to expand democratically as more drivers are onboarded. Other staff include software and industry veterans and in addition to co-founder Lewis, there are other drivers in management roles such as ex-driver and organizer David Alexis. The Co-Op Ride app is on the iOS and Android platforms and is built on Google Maps, Stripe, and Waze. By July, the app had been downloaded by 30,000 users and the number of drivers increased to 3,400, and by August there were 40,000 users. The cooperative is owned by the drivers themselves, and takes 15% from each ride for business overhead costs, as opposed to the 25% to 40% ride hail apps like Uber or Lyft take per ride. While being ultimately owned by the driver members, not by investors, the cooperative began with seed money from the Minnesota-based Community Development Financial Institution Shared Capital Cooperative, the local Lower East Side People's Federal Credit Union, and welcomed individual donations via crowdfunding in the form of revenue sharing debt on Wefunder. Each driver is a member of the cooperative and owns one share of the company and one vote in business and leadership decisions. In addition to a larger percentage of the fees per ride driven, each driver as a part-owner will also receive a share of the company's profits after loans and other expenses are paid, in the form of weighted dividends. The drivers use their own cars. The cooperative vets its owner-members further than what is already performed by the New York City Taxi and Limousine Commission (TLC), and gives a fixed price when a car is ordered and does not engage in surge pricing. The TLC imposed a minimum payrate for mobile app ridesharing companies operating in New York city in 2018. In 2021 that is $1.26 per mile which Uber and Lyft do not pay above; the cooperative pays a minimum mileage of $1.64. The cooperative intends to be able to set aside 10% of profits to community foundations and other non-profits and community organizations. The cooperative has engaged in advocacy around a policy agenda voted on by its members. Legislation to achieve this policy goal was introduced by State Senator Julia Salazar and Assemblymember Jessica González-Rojas, with the support of a coalition led by The Drivers Cooperative, United Auto Workers Region 9 and 9A, Sunrise Movement, New York Lawyers for the Public Interest, and New York Communities for Change.

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  Markov information source

  In mathematics, a Markov information source, or simply, a Markov source, is an information source whose underlying dynamics are given by a stationary finite Markov chain. == Formal definition == An information source is a sequence of random variables ranging over a finite alphabet Γ {\displaystyle \Gamma } , having a stationary distribution. A Markov information source is then a (stationary) Markov chain M {\displaystyle M} , together with a function f : S → Γ {\displaystyle f:S\to \Gamma } that maps states S {\displaystyle S} in the Markov chain to letters in the alphabet Γ {\displaystyle \Gamma } . A unifilar Markov source is a Markov source for which the values f ( s k ) {\displaystyle f(s_{k})} are distinct whenever each of the states s k {\displaystyle s_{k}} are reachable, in one step, from a common prior state. Unifilar sources are notable in that many of their properties are far more easily analyzed, as compared to the general case. == Applications == Markov sources are commonly used in communication theory, as a model of a transmitter. Markov sources also occur in natural language processing, where they are used to represent hidden meaning in a text. Given the output of a Markov source, whose underlying Markov chain is unknown, the task of solving for the underlying chain is undertaken by the techniques of hidden Markov models, such as the Viterbi algorithm.

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  Alberto Broggi

  Alberto Broggi is General Manager at VisLab srl (spinoff of the University of Parma acquired by Silicon-Valley company Ambarella Inc. in June 2015) and a professor of Computer Engineering at the University of Parma in Italy. == Research in computer vision, hardware, and AV == Broggi's research activities started in 1991–1994. His group together with the Dipartimento di Elettronica, Politecnico di Torino, Italy, built their own hardware architecture (named PAPRICA, for PArallel PRocessor for Image Checking and Analysis, based on 256 single-bit processing elements working in SIMD fashion) and installed it on board of a mobile laboratory (Mob-Lab) to develop and test some initial concepts in the field of intelligent vehicles. In 1996, Broggi's group worked to develop a real vehicle prototype (named ARGO, a Lancia Thema passenger car which was equipped with vision sensors, processing systems, and vehicle actuators) and developed the necessary software and hardware that made it able to drive autonomously on standard roads. Broggi's research group (called VisLab from then on) gathered all their findings in a book, which was then also translated in Chinese. When Broggi was with the University of Pavia, his research was extended and applied to extreme conditions (automatic driving on snow and ice): in 2001, VisLab led the research effort of providing a vehicle (RAS, Robot Antartico di Superficie) with sensing capabilities so that it was able to automatically follow the vehicle in front. In 2010 Broggi's group embarked on driving 4 vehicles autonomously from Italy to China with no human intervention. This challenge is called VIAC, for VisLab Intercontinental Autonomous Challenge . Soon after this, Broggi was awarded a second ERC grant (Proof of concept) to industrialize some of the results obtained and successfully tested on the VIAC vehicles. On July 12, 2013, VisLab tested the BRAiVE vehicle in downtown Parma, negotiating two-way narrow rural roads, pedestrian crossings, traffic lights, artificial bumps, pedestrian areas, and tight roundabouts. The vehicle traveled from Parma University Campus up to Piazza della Pilotta (downtown Parma): a 20 minutes run in a real environment, together with real traffic at 11am on a working day, that required absolutely no human intervention. Part of this test was driven with nobody in the driver seat, for the first time ever on public roads.

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  Isolation forest

  Isolation forest is an unsupervised learning algorithm for anomaly detection that works on the principle of isolating anomalies, instead of the most common techniques of profiling normal points. In statistics, an anomaly (a.k.a. outlier) is an observation or event that deviates so much from other events to arouse suspicion it was generated by a different mean. For example, the graph in Fig.1 represents ingress traffic to a web server, expressed as the number of requests in 3-hours intervals, for a period of one month. It is quite evident by simply looking at the picture that some points (marked with a red circle) are unusually high, to the point of inducing suspect that the web server might have been under attack at that time. On the other hand, the flat segment indicated by the red arrow also seems unusual and might possibly be a sign that the server was down during that time period. Anomalies in a big dataset may follow very complicated patterns, which are difficult to detect "by eye" in the great majority of cases. This is the reason why the field of anomaly detection is well suited for the application of machine learning techniques. The most common techniques employed for anomaly detection are based on the construction of a profile of what is "normal": anomalies are reported as those instances in the dataset that do not conform to the normal profile. Isolation Forest uses a different approach: instead of trying to build a model of normal instances, it explicitly isolates anomalous points in the dataset. The main advantage of this approach is the possibility of exploiting sampling techniques to an extent that is not allowed to the profile-based methods, creating a very fast algorithm with a low memory demand. == History == The Isolation Forest (iForest) algorithm was initially proposed by Fei Tony Liu, Kai Ming Ting and Zhi-Hua Zhou in 2008. The authors took advantage of two quantitative properties of anomalous data points in a sample, that is: they are the minority consisting of fewer instances and they have attribute-values that are very different from those of normal instances Since anomalies are typically few and very different from the other points in the sample, they must be easier to "isolate" compared to normal points. On the basis of this principle, Isolation Forest builds an ensemble of "Isolation Trees" (iTrees) for the data set and marks as anomalies the points that have short average path lengths on the iTrees. In a later paper, published in 2012 the same authors described a set of experiments to prove that iForest: has a low linear time complexity and a small memory requirement is able to deal with high dimensional data with irrelevant attributes can be trained with or without anomalies in the training set can provide detection results with different levels of granularity without re-training In 2013 Zhiguo Ding and Minrui Fei proposed a framework based on iForest to resolve the problem of detecting anomalies in streaming data. More application of iForest to streaming data are described in papers by Swee Chuan Tan et al., G. A. Susto et al. and Yu Weng et al. One of the main problems of the application of iForest to anomaly detection was not with the model itself, but rather in the way the "anomaly score" was computed. This problem was highlighted by Sahand Hariri, Matias Carrasco Kind and Robert J. Brunner in a 2018 paper, wherein they proposed an improved iForest model named Extended Isolation Forest (EIF). In the same paper the authors describe the improvements made to the original model and how they are able to enhance the consistency and reliability of the anomaly score produced for a given data point. == Algorithm == At the basis of the Isolation Forest algorithm there is the tendency of anomalous instances in a dataset to be easier to separate from the rest of the sample (isolate), compared to normal points. In order to isolate a data point the algorithm recursively generates partitions on the sample by randomly selecting an attribute and then randomly selecting a split value for the attribute, between the minimum and maximum values allowed for that attribute. An example of random partitioning in a 2D dataset of normally distributed points is given in Fig. 2 for a non-anomalous point and Fig. 3 for a point that's more likely to be an anomaly. It is apparent from the pictures how anomalies require fewer random partitions to be isolated, compared to normal points. From a mathematical point of view, recursive partitioning can be represented by a tree structure named Isolation Tree, while the number of partitions required to isolate a point can be interpreted as the length of the path, within the tree, to reach a terminating node starting from the root. For example, the path length of point xi in Fig. 2 is greater than the path length of xj in Fig. 3. More formally, let X = { x1, ..., xn } be a set of d-dimensional points and X' ⊂ X a subset of X. An Isolation Tree (iTree) is defined as a data structure with the following properties: for each node T in the Tree, T is either an external-node with no child, or an internal-node with one "test" and exactly two daughter nodes (Tl, Tr) a test at node T consists of an attribute q and a split value p such that the test q < p determines the traversal of a data point to either Tl or Tr. In order to build an iTree, the algorithm recursively divides X' by randomly selecting an attribute q and a split value p, until either (i) the node has only one instance or (ii) all data at the node have the same values. When the iTree is fully grown, each point in X is isolated at one of the external nodes. Intuitively, the anomalous points are those (easier to isolate, hence) with the smaller path length in the tree, where the path length h(xi) of point x i ∈ X {\displaystyle x_{i}\in X} is defined as the number of edges xi traverses from the root node to get to an external node. A probabilistic explanation of iTree is provided in the iForest original paper. == Properties of Isolation Forest == Sub-sampling: since iForest does not need to isolate all of normal instances, it can frequently ignore the big majority of the training sample. As a consequence, iForest works very well when the sampling size is kept small, a property that is in contrast with the great majority of existing methods, where large sampling size is usually desirable. Swamping: when normal instances are too close to anomalies, the number of partitions required to separate anomalies increases, a phenomena known as swamping, which makes it more difficult for iForest to discriminate between anomalies and normal points. One of the main reasons for swamping is the presence of too many data for the purpose of anomaly detection, which implies one possible solution to the problem is sub-sampling. Since iForest respond very well to sub-sampling in terms of performance, the reduction of the number of points in the sample is also a good way to reduce the effect of swamping. Masking: when the number of anomalies is high it is possible that some of those aggregate in a dense and large cluster, making it more difficult to separate the single anomalies and, in turn, to detect such points as anomalous. Similarly to swamping, this phenomena (known as "masking") is also more likely when the number of points in the sample is big, and can be alleviated through sub-sampling. High Dimensional Data: one of the main limitation to standard, distance-based methods is their inefficiency in dealing with high dimensional datasets:. The main reason for that is, in a high dimensional space every point is equally sparse, so using a distance-based measure of separation is pretty ineffective. Unfortunately, high-dimensional data also affects the detection performance of iForest, but the performance can be vastly improved by adding a features selection test like Kurtosis to reduce the dimensionality of the sample space. Normal Instances Only: iForest performs well even if the training set does not contain any anomalous point, the reason being that iForest describes data distributions in such a way that high values of the path length h(xi) correspond to the presence of data points. As a consequence, the presence of anomalies is pretty irrelevant to iForest's detection performance. == Anomaly Detection with Isolation Forest == Anomaly detection with Isolation Forest is a process composed of two main stages: in the first stage, a training dataset is used to build iTrees as described in previous sections. in the second stage, each instance in test set is passed through the iTrees build in the previous stage, and a proper "anomaly score" is assigned to the instance using the algorithm described below Once all the instances in the test set have been assigned an anomaly score, it is possible to mark as "anomaly" any point whose score is greater than a predefined threshold, which depends on the domain the analysis is being applied to. === Anomaly Score === Th

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  Computer-aided lean management

  Computer-aided lean management, in business management, is a methodology of developing and using software-controlled, lean systems integration. Its goal is to drive innovation towards cost and cycle-time savings. It attempts to create an efficient use of capital and resources through the development and use of one integrated system model to run a business's planning, engineering, design, maintenance, and operations. == Overview == Computer-Aided Lean Management (CALM) is a management philosophy that uses software to reduce risk and inefficiencies. CALM acts on uncertainties and business inefficiencies to increase profitability through the use of computational decision-making tools that enable opportunities for additional value creation. It is based on the application of software to enable continuous improvement through an Integrated System Model (ISM) of the business’s physical assets, business processes, and machine learning. This integration of software applications using lean principles was developed in the aerospace industry and has migrated to the energy industry. The creation of an ISM removes the barriers posed by the silos or stovepipes inherent in the departmentalization of most companies. Integration enables lean uses of information for the creation of actionable knowledge. CALM strives to create such a lean management approach to running the company through the rigors of software enforcement. From this software enforcement comes clear policy and procedures that are adhered to, activity-based costing, measurement of effectiveness, and the capability of using advanced algorithms for dramatic improvements in optimization of resources. CALM creates business capabilities through software to enable technology application, streamlining of processes, and a lean organizational structure. The methodology is based on a common sense approach for running a business, by measuring actions taken and using those measurements to design more efficient processes. == History == CALM was inspired by lean processes and techniques that were already dominant management technologies with a wide diversity of applications and successes. Motorola and General Electric had been known for the concepts of Six Sigma; Boeing had been managing mass (using modular and flexible assembly options), and Toyota combined elements of these methodologies to create the Toyota Production System. Boeing then took the Toyota model and added computer-aided enforcement of lean methodologies throughout the manufacturing process. One of the major sources for CALM's outgrowth was integrated definition (IDEF) modeling in aerospace manufacturing that was pioneered by the U.S. Air Force in the 1970s. IDEF is a methodology designed to model the end-to-end decisions, actions, and activities of an organization or system so that costs, performance, and cycle times can be optimized. IDEF methods have been adapted for wider use in automotive, aerospace, pharmaceuticals, and software development industries. IDEF methods serve as a starting point to understand lean management through semantic data modeling. The IDEF process begins by mapping the existing functions of an enterprise, creating a graphical model, or road map, that shows what controls each important function, who performs it, what resources are required for carrying it out, what it produces, how much it costs, and what relationships it has to other functions of the organization. IDEF simulations have been found to be efficient at streamlining and modernizing both companies and governmental agencies. Perhaps the best-developed evolution of the IDEF model beyond Toyota was at Boeing. Their project life-cycle process has grown into a rigorous software system that links people, tasks, tools, materials, and the environmental impact of any newly planned project, before any building is allowed to begin. Routinely, more than half of the time for any given project is spent building the precedence diagrams, or three-dimensional process maps, integrating with outside suppliers, and designing the implementation plan–all on the computer. Once real activity is initiated, an action tracker is used to monitor inputs and outputs versus the schedule and delivery metrics in real time throughout the organization. When the execution of a new airplane design begins, it is so well organized that it consistently cuts both costs and build time in half for each successive generation of airframe. Boeing created a complex lean management process called 'define and control airplane configuration/manufacturing resource management' (DCAC/MRM). The process was built with the help of the operations research and computer sciences departments of the University of Pittsburgh. The manufacture of the Boeing 777 was ultimately a success, and it became the precursor to succeeding generations of CALM at Boeing. The methodology of CALM has recently been applied to field orientated infrastructure based businesses with highly interdependent systems, such as electric utilities where a smart grid concept is being researched and developed. The management of infrastructure-based industries like oil, gas, electricity, water, transportation, and renewables requires massive investments in interdependent, physical infrastructure, as well as simultaneous attention to disparate market forces. In infrastructure businesses that manage field assets, uncertainty is the biggest impediment to profitability, rather than the maintenance of efficient supply chains or the management of factory assembly lines. These businesses are dominated by risk from uncertainties such as weather, market variations, transportation disruptions, government actions, logistic difficulties, geology, and asset reliability. CALM has been applied to deal with these types of infrastructure based challenges.

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  AI Sales Assistants: Free vs Paid (2026)

  Trying to pick the best AI sales assistant? An AI sales assistant is software that uses machine learning to help you get more done — it scales effortlessly from a single task to thousands. The best picks balance beginner-friendly simplicity with the depth power users need, and they ship updates often. Whether you are a beginner or a pro, the right AI sales assistant slots into your workflow and pays for itself fast. Read on for hands-on impressions, pricing tiers, and the standout features that matter.

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  Adobe Enhanced Speech

  Adobe Enhanced Speech is an online artificial intelligence software tool by Adobe that aims to significantly improve the quality of recorded speech that may be badly muffled, reverberated, full of artifacts, tinny, etc. and convert it to a studio-grade, professional level, regardless of the initial input's clarity. Users may upload mp3 or wav files up to an hour long and a gigabyte in size to the site to convert them relatively quickly, then being free to listen to the converted version, toggle back-and-forth and alternate between it and the original as it plays, and download it. Currently in beta and free to the public, it has been used in the restoration of old movies and the creation of professional-quality podcasts, narrations, etc. by those without sufficient microphones. Although the model still has some current limitations, such as not being compatible with singing and occasional issues with excessively muffled source audio resulting in a light lisp in the improved version, it is otherwise noted as incredibly effective and efficient in its purpose. Utilizing advanced machine learning algorithms to distinguish between speech and background sounds, it enhances the quality of the speech by filtering out the noise and artifacts, adjusting the pitch and volume levels, and normalizing the audio. This is accomplished by the network having been trained on a large dataset of speech samples from a diverse range of sources and then being fine-tuned to optimize the output.

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  Indic OCR

  Indic OCR refers to the process of converting text images written in Indic scripts into e-text using Optical character recognition (OCR) techniques. Broadly, it can also refer to the OCR systems of Brahmic scripts for languages of South Asia and Southeast Asia, not just the scripts of the Indian subcontinent, which are all written in an abugida-based writing system. OCR for Latin characters is still not 100% accurate but a relatively high degree of accuracy in conversion has been able to be achieved. Such accuracy has not yet been able to be achieved for Indic scripts using OCR. This is due in part to the writing systems of Indic languages as well as a lack of standard representation, encoding, and support among operating systems and keyboards. The Centre for Development of Advanced Computing (C-DAC) and Technology Development for Indian Languages, the premier R&D organisation of the Ministry of Electronics and Information Technology (also known as MeitY) of India have carried out many projects relating to OCR. Their projects include OCR for Malayalam, Odia, Punjabi, Telugu and Devanagari script. == Properties of Indian writing systems == There are 22 officially recognised languages in India. Of these, Hindi, Bengali and Punjabi are the most widely spoken Indo-Aryan languages and are also the fourth, seventh and tenth most widely spoken languages in the world respectively. Two or more languages can be written with same script. For example, Devanagari is used to write Hindi, Marathi, Rajasthani, Sanskrit, Bhojpuri and others, while Eastern Nagari is used to write Bengali, Assamese, Manipuri and others. Apart from basic characters as consonants and vowels, most Indic languages combine 2 or more basic characters to form compound characters. The shape of a compound character is more complex than the constituent basic characters. Some Indo-Aryan languages (including Hindi and Punjabi) have a horizontal line over the characters, while other languages (including Gujarati) and Dravidian languages (Malayalam, Kannada, Tamil, and Telugu) do not. These are some of the main challenges for creating a single OCR for all Indic languages. Indic OCR also generally includes support for recently invented scripts in India like Ol Chiki, Warang Citi, Mundari Bani, etc. which are mainly created for writing Munda languages of Austroasiatic family. The concept of upper/lower case is absent in Indic scripts. Apart from Urdu, Sindhi, Kashmiri and Thaana, all other Indic languages are written from left to right. == Examples == SanskritOCR - OCR software for Sanskrit, Hindi and other Indo-Aryan languages based on the Devanagari script. Sanskrit OCR is developed by a Sanskrit scholar from Germany - Dr. Oliver Hellwig of Department for Languages and Cultures of Southern Asia, Freie Universität Berlin. The official website is in German. The interface of earlier versions of the software was also in German, but later versions have an English interface too. E-aksharayan - Optical character recognition engine for Indian languages Chitrankan - This technology was developed by ISI, Kolkata, and transferred to C-DAC. It processes printed Hindi text from a scanner or from an image. Indic OCR models for Tesseract (software) == OCR in use == OCR has been used for Wikisource and other projects.

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  Algorithmic inference

  Algorithmic inference gathers new developments in the statistical inference methods made feasible by the powerful computing devices widely available to any data analyst. Cornerstones in this field are computational learning theory, granular computing, bioinformatics, and, long ago, structural probability (Fraser 1966). The main focus is on the algorithms which compute statistics rooting the study of a random phenomenon, along with the amount of data they must feed on to produce reliable results. This shifts the interest of mathematicians from the study of the distribution laws to the functional properties of the statistics, and the interest of computer scientists from the algorithms for processing data to the information they process. == The Fisher parametric inference problem == Concerning the identification of the parameters of a distribution law, the mature reader may recall lengthy disputes in the mid 20th century about the interpretation of their variability in terms of fiducial distribution (Fisher 1956), structural probabilities (Fraser 1966), priors/posteriors (Ramsey 1925), and so on. From an epistemology viewpoint, this entailed a companion dispute as to the nature of probability: is it a physical feature of phenomena to be described through random variables or a way of synthesizing data about a phenomenon? Opting for the latter, Fisher defines a fiducial distribution law of parameters of a given random variable that he deduces from a sample of its specifications. With this law he computes, for instance "the probability that μ (mean of a Gaussian variable – omeur note) is less than any assigned value, or the probability that it lies between any assigned values, or, in short, its probability distribution, in the light of the sample observed". == The classic solution == Fisher fought hard to defend the difference and superiority of his notion of parameter distribution in comparison to analogous notions, such as Bayes' posterior distribution, Fraser's constructive probability and Neyman's confidence intervals. For half a century, Neyman's confidence intervals won out for all practical purposes, crediting the phenomenological nature of probability. With this perspective, when you deal with a Gaussian variable, its mean μ is fixed by the physical features of the phenomenon you are observing, where the observations are random operators, hence the observed values are specifications of a random sample. Because of their randomness, you may compute from the sample specific intervals containing the fixed μ with a given probability that you denote confidence. === Example === Let X be a Gaussian variable with parameters μ {\displaystyle \mu } and σ 2 {\displaystyle \sigma ^{2}} and { X 1 , … , X m } {\displaystyle \{X_{1},\ldots ,X_{m}\}} a sample drawn from it. Working with statistics S μ = ∑ i = 1 m X i {\displaystyle S_{\mu }=\sum _{i=1}^{m}X_{i}} and S σ 2 = ∑ i = 1 m ( X i − X ¯ ) 2 , where X ¯ = S μ m {\displaystyle S_{\sigma ^{2}}=\sum _{i=1}^{m}(X_{i}-{\overline {X}})^{2},{\text{ where }}{\overline {X}}={\frac {S_{\mu }}{m}}} is the sample mean, we recognize that T = S μ − m μ S σ 2 m − 1 m = X ¯ − μ S σ 2 / ( m ( m − 1 ) ) {\displaystyle T={\frac {S_{\mu }-m\mu }{\sqrt {S_{\sigma ^{2}}}}}{\sqrt {\frac {m-1}{m}}}={\frac {{\overline {X}}-\mu }{\sqrt {S_{\sigma ^{2}}/(m(m-1))}}}} follows a Student's t distribution (Wilks 1962) with parameter (degrees of freedom) m − 1, so that f T ( t ) = Γ ( m / 2 ) Γ ( ( m − 1 ) / 2 ) 1 π ( m − 1 ) ( 1 + t 2 m − 1 ) m / 2 . {\displaystyle f_{T}(t)={\frac {\Gamma (m/2)}{\Gamma ((m-1)/2)}}{\frac {1}{\sqrt {\pi (m-1)}}}\left(1+{\frac {t^{2}}{m-1}}\right)^{m/2}.} Gauging T between two quantiles and inverting its expression as a function of μ {\displaystyle \mu } you obtain confidence intervals for μ {\displaystyle \mu } . With the sample specification: x = { 7.14 , 6.3 , 3.9 , 6.46 , 0.2 , 2.94 , 4.14 , 4.69 , 6.02 , 1.58 } {\displaystyle \mathbf {x} =\{7.14,6.3,3.9,6.46,0.2,2.94,4.14,4.69,6.02,1.58\}} having size m = 10, you compute the statistics s μ = 43.37 {\displaystyle s_{\mu }=43.37} and s σ 2 = 46.07 {\displaystyle s_{\sigma ^{2}}=46.07} , and obtain a 0.90 confidence interval for μ {\displaystyle \mu } with extremes (3.03, 5.65). == Inferring functions with the help of a computer == From a modeling perspective the entire dispute looks like a chicken-egg dilemma: either fixed data by first and probability distribution of their properties as a consequence, or fixed properties by first and probability distribution of the observed data as a corollary. The classic solution has one benefit and one drawback. The former was appreciated particularly back when people still did computations with sheet and pencil. Per se, the task of computing a Neyman confidence interval for the fixed parameter θ is hard: you do not know θ, but you look for disposing around it an interval with a possibly very low probability of failing. The analytical solution is allowed for a very limited number of theoretical cases. Vice versa a large variety of instances may be quickly solved in an approximate way via the central limit theorem in terms of confidence interval around a Gaussian distribution – that's the benefit. The drawback is that the central limit theorem is applicable when the sample size is sufficiently large. Therefore, it is less and less applicable with the sample involved in modern inference instances. The fault is not in the sample size on its own part. Rather, this size is not sufficiently large because of the complexity of the inference problem. With the availability of large computing facilities, scientists refocused from isolated parameters inference to complex functions inference, i.e. re sets of highly nested parameters identifying functions. In these cases we speak about learning of functions (in terms for instance of regression, neuro-fuzzy system or computational learning) on the basis of highly informative samples. A first effect of having a complex structure linking data is the reduction of the number of sample degrees of freedom, i.e. the burning of a part of sample points, so that the effective sample size to be considered in the central limit theorem is too small. Focusing on the sample size ensuring a limited learning error with a given confidence level, the consequence is that the lower bound on this size grows with complexity indices such as VC dimension or detail of a class to which the function we want to learn belongs. === Example === A sample of 1,000 independent bits is enough to ensure an absolute error of at most 0.081 on the estimation of the parameter p of the underlying Bernoulli variable with a confidence of at least 0.99. The same size cannot guarantee a threshold less than 0.088 with the same confidence 0.99 when the error is identified with the probability that a 20-year-old man living in New York does not fit the ranges of height, weight and waistline observed on 1,000 Big Apple inhabitants. The accuracy shortage occurs because both the VC dimension and the detail of the class of parallelepipeds, among which the one observed from the 1,000 inhabitants' ranges falls, are equal to 6. == The general inversion problem solving the Fisher question == With insufficiently large samples, the approach: fixed sample – random properties suggests inference procedures in three steps: === Definition === For a random variable and a sample drawn from it a compatible distribution is a distribution having the same sampling mechanism M X = ( Z , g θ ) {\displaystyle {\mathcal {M}}_{X}=(Z,g_{\boldsymbol {\theta }})} of X with a value θ {\displaystyle {\boldsymbol {\theta }}} of the random parameter Θ {\displaystyle \mathbf {\Theta } } derived from a master equation rooted on a well-behaved statistic s. === Example === You may find the distribution law of the Pareto parameters A and K as an implementation example of the population bootstrap method as in the figure on the left. Implementing the twisting argument method, you get the distribution law F M ( μ ) {\displaystyle F_{M}(\mu )} of the mean M of a Gaussian variable X on the basis of the statistic s M = ∑ i = 1 m x i {\textstyle s_{M}=\sum _{i=1}^{m}x_{i}} when Σ 2 {\displaystyle \Sigma ^{2}} is known to be equal to σ 2 {\displaystyle \sigma ^{2}} (Apolloni, Malchiodi & Gaito 2006). Its expression is: F M ( μ ) = Φ ( m μ − s M σ m ) , {\displaystyle F_{M}(\mu )=\Phi {\left({\frac {m\mu -s_{M}}{\sigma {\sqrt {m}}}}\right)},} shown in the figure on the right, where Φ {\displaystyle \Phi } is the cumulative distribution function of a standard normal distribution. Computing a confidence interval for M given its distribution function is straightforward: we need only find two quantiles (for instance δ / 2 {\displaystyle \delta /2} and 1 − δ / 2 {\displaystyle 1-\delta /2} quantiles in case we are interested in a confidence interval of level δ symmetric in the tail's probabilities) as indicated on the left in the diagram showing the behavior of

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  Structured prediction

  Structured prediction or structured output learning is an umbrella term for supervised machine learning techniques that involves predicting structured objects, rather than discrete or real values. Similar to commonly used supervised learning techniques, structured prediction models are typically trained by means of observed data in which the predicted value is compared to the ground truth, and this is used to adjust the model parameters. Due to the complexity of the model and the interrelations of predicted variables, the processes of model training and inference are often computationally infeasible, so approximate inference and learning methods are used. == Applications == An example application is the problem of translating a natural language sentence into a syntactic representation such as a parse tree. This can be seen as a structured prediction problem in which the structured output domain is the set of all possible parse trees. Structured prediction is used in a wide variety of domains including bioinformatics, natural language processing (NLP), speech recognition, and computer vision. === Example: sequence tagging === Sequence tagging is a class of problems prevalent in NLP in which input data are often sequential, for instance sentences of text. The sequence tagging problem appears in several guises, such as part-of-speech tagging (POS tagging) and named entity recognition. In POS tagging, for example, each word in a sequence must be 'tagged' with a class label representing the type of word: The main challenge of this problem is to resolve ambiguity: in the above example, the words "sentence" and "tagged" in English can also be verbs. While this problem can be solved by simply performing classification of individual tokens, this approach does not take into account the empirical fact that tags do not occur independently; instead, each tag displays a strong conditional dependence on the tag of the previous word. This fact can be exploited in a sequence model such as a hidden Markov model or conditional random field that predicts the entire tag sequence for a sentence (rather than just individual tags) via the Viterbi algorithm. == Techniques == Probabilistic graphical models form a large class of structured prediction models. In particular, Bayesian networks and random fields are popular. Other algorithms and models for structured prediction include inductive logic programming, case-based reasoning, structured SVMs, Markov logic networks, Probabilistic Soft Logic, and constrained conditional models. The main techniques are: Conditional random fields Structured support vector machines Structured k-nearest neighbours Recurrent neural networks, in particular Elman networks Transformers. === Structured perceptron === One of the easiest ways to understand algorithms for general structured prediction is the structured perceptron by Collins. This algorithm combines the perceptron algorithm for learning linear classifiers with an inference algorithm (classically the Viterbi algorithm when used on sequence data) and can be described abstractly as follows: First, define a function ϕ ( x , y ) {\displaystyle \phi (x,y)} that maps a training sample x {\displaystyle x} and a candidate prediction y {\displaystyle y} to a vector of length n {\displaystyle n} ( x {\displaystyle x} and y {\displaystyle y} may have any structure; n {\displaystyle n} is problem-dependent, but must be fixed for each model). Let G E N {\displaystyle GEN} be a function that generates candidate predictions. Then: Let w {\displaystyle w} be a weight vector of length n {\displaystyle n} For a predetermined number of iterations: For each sample x {\displaystyle x} in the training set with true output t {\displaystyle t} : Make a prediction y ^ {\displaystyle {\hat {y}}} : y ^ = a r g m a x { y ∈ G E N ( x ) } ( w T , ϕ ( x , y ) ) {\displaystyle {\hat {y}}={\operatorname {arg\,max} }\,\{y\in GEN(x)\}\,(w^{T},\phi (x,y))} Update w {\displaystyle w} (from y ^ {\displaystyle {\hat {y}}} towards t {\displaystyle t} ): w = w + c ( − ϕ ( x , y ^ ) + ϕ ( x , t ) ) {\displaystyle w=w+c(-\phi (x,{\hat {y}})+\phi (x,t))} , where c {\displaystyle c} is the learning rate. In practice, finding the argmax over G E N ( x ) {\displaystyle {GEN}({x})} is done using an algorithm such as Viterbi or a max-sum, rather than an exhaustive search through an exponentially large set of candidates. The idea of learning is similar to that for multiclass perceptrons.

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  Datacap

  Datacap (an IBM Company), a privately owned company, manufactures and sells computer software, and services. Datacap's first product, Paper Keyboard, was a "forms processing" product and shipped in 1989. In August 2010, IBM announced that it had acquired Datacap for an undisclosed amount. == Overview == Datacap sells products through a value-added distribution network worldwide. The software is classified as "enterprise software", meaning that it requires trained professionals to install and configure. Although the Company has focused on providing solutions for scanning paper documents, most recently Company materials have emphasized customer requirements to handle electronic documents ("eDocs"), documents being received into an organization electronically (usually email). Datacap claims that its software is unique because of the rules engine ("Rulerunner") used for processing inbound documents, including performing the image processing (deskew, noise removal, etc.), optical character recognition (OCR), intelligent character recognition (ICR), validations, and export-release formatting of extracted data to target ERP and line of business application.

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