Iterative Viterbi decoding is an algorithm that spots the subsequence S of an observation O = {o1, ..., on} having the highest average probability (i.e., probability scaled by the length of S) of being generated by a given hidden Markov model M with m states. The algorithm uses a modified Viterbi algorithm as an internal step. The scaled probability measure was first proposed by John S. Bridle. An early algorithm to solve this problem, sliding window, was proposed by Jay G. Wilpon et al., 1989, with constant cost T = mn2/2. A faster algorithm consists of an iteration of calls to the Viterbi algorithm, reestimating a filler score until convergence. == The algorithm == A basic (non-optimized) version, finding the sequence s with the smallest normalized distance from some subsequence of t is: // input is placed in observation s[1..n], template t[1..m], // and [[distance matrix]] d[1..n,1..m] // remaining elements in matrices are solely for internal computations (int, int, int) AverageSubmatchDistance(char s[0..(n+1)], char t[0..(m+1)], int d[1..n,0..(m+1)]) { // score, subsequence start, subsequence end declare int e, B, E t'[0] := t'[m+1] := s'[0] := s'[n+1] := 'e' e := random() do e' := e for i := 1 to n do d'[i,0] := d'[i,m+1] := e (e, B, E) := ViterbiDistance(s', t', d') e := e/(E-B+1) until (e == e') return (e, B, E) } The ViterbiDistance() procedure returns the tuple (e, B, E), i.e., the Viterbi score "e" for the match of t and the selected entry (B) and exit (E) points from it. "B" and "E" have to be recorded using a simple modification to Viterbi. A modification that can be applied to CYK tables, proposed by Antoine Rozenknop, consists in subtracting e from all elements of the initial matrix d.
SPL notation
SPL (Sentence Plan Language) is an abstract notation representing the semantics of a sentence in natural language. In a classical Natural Language Generation (NLG) workflow, an initial text plan (hierarchically or sequentially organized factoids, often modelled in accordance with Rhetorical Structure Theory) is transformed by a sentence planner (generator) component to a sequence of sentence plans modelled in a Sentence Plan Language. A surface generator can be used to transform the SPL notation into natural language sentences. Probably the most widely used SPL language used today (2022) is AMR (Abstract Meaning Representation, see there for further references), but is owes parts of its popularity to its application to NLP problems other than NLG, e.g., machine translation and semantic parsing.
Multi-agent reinforcement learning
Multi-agent reinforcement learning (MARL) is a sub-field of reinforcement learning. It focuses on studying the behavior of multiple learning agents that coexist in a shared environment. Each agent is motivated by its own rewards, and does actions to advance its own interests; in some environments these interests are opposed to the interests of other agents, resulting in complex group dynamics. Multi-agent reinforcement learning is closely related to game theory and especially repeated games, as well as multi-agent systems. Its study combines the pursuit of finding ideal algorithms that maximize rewards with a more sociological set of concepts. While research in single-agent reinforcement learning is concerned with finding the algorithm that gets the biggest number of points for one agent, research in multi-agent reinforcement learning evaluates and quantifies social metrics, such as cooperation, reciprocity, equity, social influence, language and discrimination. == Definition == Similarly to single-agent reinforcement learning, multi-agent reinforcement learning is modeled as some form of a Markov decision process (MDP). Fix a set of agents I = { 1 , . . . , N } {\displaystyle I=\{1,...,N\}} . We then define: A set S {\displaystyle S} of environment states. One set A i {\displaystyle {\mathcal {A}}_{i}} of actions for each of the agents i ∈ I = { 1 , … , N } {\displaystyle i\in I=\{1,\dots ,N\}} . P a → ( s , s ′ ) = Pr ( s t + 1 = s ′ ∣ s t = s , a → t = a → ) {\displaystyle P_{\vec {a}}(s,s')=\Pr(s_{t+1}=s'\mid s_{t}=s,{\vec {a}}_{t}={\vec {a}})} is the probability of transition (at time t {\displaystyle t} ) from state s {\displaystyle s} to state s ′ {\displaystyle s'} under joint action a → {\displaystyle {\vec {a}}} . R → a → ( s , s ′ ) {\displaystyle {\vec {R}}_{\vec {a}}(s,s')} is the immediate joint reward after the transition from s {\displaystyle s} to s ′ {\displaystyle s'} with joint action a → {\displaystyle {\vec {a}}} . In settings with perfect information, such as the games of chess and Go, the MDP would be fully observable. In settings with imperfect information, especially in real-world applications like self-driving cars, each agent would access an observation that only has part of the information about the current state. In the partially observable setting, the core model is the partially observable stochastic game in the general case, and the decentralized POMDP in the cooperative case. == Cooperation vs. competition == When multiple agents are acting in a shared environment their interests might be aligned or misaligned. MARL allows exploring all the different alignments and how they affect the agents' behavior: In pure competition settings, the agents' rewards are exactly opposite to each other, and therefore they are playing against each other. Pure cooperation settings are the other extreme, in which agents get the exact same rewards, and therefore they are playing with each other. Mixed-sum settings cover all the games that combine elements of both cooperation and competition. === Pure competition settings === When two agents are playing a zero-sum game, they are in pure competition with each other. Many traditional games such as chess and Go fall under this category, as do two-player variants of video games like StarCraft. Because each agent can only win at the expense of the other agent, many complexities are stripped away. There is no prospect of communication or social dilemmas, as neither agent is incentivized to take actions that benefit its opponent. The Deep Blue and AlphaGo projects demonstrate how to optimize the performance of agents in pure competition settings. One complexity that is not stripped away in pure competition settings is autocurricula. As the agents' policy is improved using self-play, multiple layers of learning may occur. === Pure cooperation settings === MARL is used to explore how separate agents with identical interests can communicate and work together. Pure cooperation settings are explored in recreational cooperative games such as Overcooked, as well as real-world scenarios in robotics. In pure cooperation settings all the agents get identical rewards, which means that social dilemmas do not occur. In pure cooperation settings, oftentimes there are an arbitrary number of coordination strategies, and agents converge to specific "conventions" when coordinating with each other. The notion of conventions has been studied in language and also alluded to in more general multi-agent collaborative tasks. === Mixed-sum settings === Most real-world scenarios involving multiple agents have elements of both cooperation and competition. For example, when multiple self-driving cars are planning their respective paths, each of them has interests that are diverging but not exclusive: Each car is minimizing the amount of time it's taking to reach its destination, but all cars have the shared interest of avoiding a traffic collision. Zero-sum settings with three or more agents often exhibit similar properties to mixed-sum settings, since each pair of agents might have a non-zero utility sum between them. Mixed-sum settings can be explored using classic matrix games such as prisoner's dilemma, more complex sequential social dilemmas, and recreational games such as Among Us, Diplomacy and StarCraft II. Mixed-sum settings can give rise to communication and social dilemmas. == Social dilemmas == As in game theory, much of the research in MARL revolves around social dilemmas, such as prisoner's dilemma, chicken and stag hunt. While game theory research might focus on Nash equilibria and what an ideal policy for an agent would be, MARL research focuses on how the agents would learn these ideal policies using a trial-and-error process. The reinforcement learning algorithms that are used to train the agents are maximizing the agent's own reward; the conflict between the needs of the agents and the needs of the group is a subject of active research. Various techniques have been explored in order to induce cooperation in agents: Modifying the environment rules, adding intrinsic rewards, and more. === Sequential social dilemmas === Social dilemmas like prisoner's dilemma, chicken and stag hunt are "matrix games". Each agent takes only one action from a choice of two possible actions, and a simple 2x2 matrix is used to describe the reward that each agent will get, given the actions that each agent took. In humans and other living creatures, social dilemmas tend to be more complex. Agents take multiple actions over time, and the distinction between cooperating and defecting is not as clear cut as in matrix games. The concept of a sequential social dilemma (SSD) was introduced in 2017 as an attempt to model that complexity. There is ongoing research into defining different kinds of SSDs and showing cooperative behavior in the agents that act in them. == Autocurricula == An autocurriculum (plural: autocurricula) is a reinforcement learning concept that's salient in multi-agent experiments. As agents improve their performance, they change their environment; this change in the environment affects themselves and the other agents. The feedback loop results in several distinct phases of learning, each depending on the previous one. The stacked layers of learning are called an autocurriculum. Autocurricula are especially apparent in adversarial settings, where each group of agents is racing to counter the current strategy of the opposing group. The Hide and Seek game is an accessible example of an autocurriculum occurring in an adversarial setting. In this experiment, a team of seekers is competing against a team of hiders. Whenever one of the teams learns a new strategy, the opposing team adapts its strategy to give the best possible counter. When the hiders learn to use boxes to build a shelter, the seekers respond by learning to use a ramp to break into that shelter. The hiders respond by locking the ramps, making them unavailable for the seekers to use. The seekers then respond by "box surfing", exploiting a glitch in the game to penetrate the shelter. Each "level" of learning is an emergent phenomenon, with the previous level as its premise. This results in a stack of behaviors, each dependent on its predecessor. Autocurricula in reinforcement learning experiments are compared to the stages of the evolution of life on Earth and the development of human culture. A major stage in evolution happened 2-3 billion years ago, when photosynthesizing life forms started to produce massive amounts of oxygen, changing the balance of gases in the atmosphere. In the next stages of evolution, oxygen-breathing life forms evolved, eventually leading up to land mammals and human beings. These later stages could only happen after the photosynthesis stage made oxygen widely available. Similarly, human culture could not have gone through the Industrial Revolution in the 18th century without the resources and insights gaine
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
LanguageWare
LanguageWare is a natural language processing (NLP) technology developed by IBM, which allows applications to process natural language text. It comprises a set of Java libraries that provide a range of NLP functions: language identification, text segmentation/tokenization, normalization, entity and relationship extraction, and semantic analysis and disambiguation. The analysis engine uses a finite-state machine approach at multiple levels, which aids its performance characteristics while maintaining a reasonably small footprint. The behaviour of the system is driven by a set of configurable lexico-semantic resources which describe the characteristics and domain of the processed language. A default set of resources comes as part of LanguageWare and these describe the native language characteristics, such as morphology, and the basic vocabulary for the language. Supplemental resources have been created that capture additional vocabularies, terminologies, rules and grammars, which may be generic to the language or specific to one or more domains. A set of Eclipse-based customization tooling, LanguageWare Resource Workbench, is available on IBM's alphaWorks site, and allows domain knowledge to be compiled into these resources and thereby incorporated into the analysis process. LanguageWare can be deployed as a set of UIMA-compliant annotators, Eclipse plug-ins or Web Services.
Materialized view
In computing, a materialized view is a database object that contains the results of a query. For example, it may be a local copy of data located remotely, or may be a subset of the rows and/or columns of a table or join result, or may be a summary using an aggregate function. The process of setting up a materialized view is sometimes called materialization. This is a form of caching the results of a query, similar to memoization of the value of a function in functional languages, and it is sometimes described as a form of precomputation. As with other forms of precomputation, database users typically use materialized views for performance reasons, i.e. as a form of optimization. Materialized views that store data based on remote tables were also known as snapshots (deprecated Oracle terminology). In any database management system following the relational model, a view is a virtual table representing the result of a database query. Whenever a query or an update addresses an ordinary view's virtual table, the DBMS converts these into queries or updates against the underlying base tables. A materialized view takes a different approach: the query result is cached as a concrete ("materialized") table (rather than a view as such) that may be updated from the original base tables from time to time. This enables much more efficient access, at the cost of extra storage and of some data being potentially out-of-date. Materialized views find use especially in data warehousing scenarios, where frequent queries of the actual base tables can be expensive. In a materialized view, indexes can be built on any column. In contrast, in a normal view, it's typically only possible to exploit indexes on columns that come directly from (or have a mapping to) indexed columns in the base tables; often this functionality is not offered at all. == Implementations == === Oracle === Materialized views were implemented first by the Oracle Database: the Query rewrite feature was added from version 8i. Example syntax to create a materialized view in Oracle: === PostgreSQL === In PostgreSQL, version 9.3 and newer natively support materialized views. In version 9.3, a materialized view is not auto-refreshed, and is populated only at time of creation (unless WITH NO DATA is used). It may be refreshed later manually using REFRESH MATERIALIZED VIEW. In version 9.4, the refresh may be concurrent with selects on the materialized view if CONCURRENTLY is used. Example syntax to create a materialized view in PostgreSQL: === SQL Server === Microsoft SQL Server differs from other RDBMS by the way of implementing materialized view via a concept known as "Indexed Views". The main difference is that such views do not require a refresh because they are in fact always synchronized to the original data of the tables that compound the view. To achieve this, it is necessary that the lines of origin and destination are "deterministic" in their mapping, which limits the types of possible queries to do this. This mechanism has been realised since the 2000 version of SQL Server. Example syntax to create a materialized view in SQL Server: === Stream processing frameworks === Apache Kafka (since v0.10.2), Apache Spark (since v2.0), Apache Flink, Kinetica DB, Materialize, RisingWave, and Epsio all support materialized views on streams of data. === Others === Materialized views are also supported in Sybase SQL Anywhere. In IBM Db2, they are called "materialized query tables". ClickHouse supports materialized views that automatically refresh on merges. MySQL doesn't support materialized views natively, but workarounds can be implemented by using triggers or stored procedures or by using the open-source application Flexviews. Materialized views can be implemented in Amazon DynamoDB using data modification events captured by DynamoDB Streams. Google announced in 8 April 2020 the availability of materialized views for BigQuery as a beta release.
1 Second Everyday
1 Second Everyday (1SE) is an application developed by Cesar Kuriyama. The application allows the user to record one second of video every day and then chronologically edits (mashes) them together into a single film. It is compatible with iOS and Android. The idea of the application was developed by Kuriyama's 1 Second Everyday — Age 30 video. The application was launched in January 2013. 1 Second Everyday played a part in the plot of Chef and also became the inspiration for the 2014 short animated clip Feast. == Background == === Kuriyama's video === In February 2011, when Cesar Kuriyama turned 30, after saving money, he quit his job in an advertising firm and took a year off to travel. During this time, he started working on a project he called 1 Second Everyday. As part of the project, every day he recorded one second of video – something that was supposed to help him remember that day. He started the project because he was frustrated with his memory. He planned to stockpile the 365 one-second clips into one film to serve as a memento of his year. While working on the project Kuriyama realized that recording one second every day impacted the decisions he made in a positive way. After a year he made a 365-second clip out of his recordings. The video called 1 Second Everyday – Age 30, went viral. According to Kuriyama, he was initially inspired to take a year off from work by a TED talk given by Stefan Sagmeister called "The Power of Time Off." Kuriyama also delivered a TED talk about 1 Second Everyday in 2012 at TED 2012 in Long Beach California. === Kickstarter campaign === After completing his own video, Kuriyama decided to develop an application that would allow the users to record one second every day and compile their own videos. He developed a prototype of the application and then in 2012, he launched a Kickstarter campaign to raise funds for completing the application. The campaign became one of the most backed app campaigns in the history of Kickstarter. It was backed by 11,281 backers who pledged a total of $56,959 on an initial goal of $20,000. Following the completion of the Kickstarter campaign, he partnered with an application design studio in Brooklyn to develop the application. 1 Second Everyday was released two weeks after the completion of its Kickstarter campaign. == Application == The application was released for iOS on 10 January 2013. An Android-compatible version of the application was developed later. Using it, the user can record the videos in the application or they can select one second portions from their libraries. 1 Second Everyday dates every snippet. The user can also set alarms to remember to record their daily video. In order to compile a video, the user selects the seconds they want and the application creates a compilation video. The user can keep multiple timelines. It also allows users to post directly on social networks. The main interface in 1 Second Everyday is a calendar, which shows the user which days have snippets and which they can still fill in. In the beginning, 1 Second Everyday restricted the recording to one second. However, the developers later released Super Seconds, which allowed users to record an additional half a second video. In 2014, 1 Second Everyday Crowds was launched, which is an area in the application featuring compilations of second clips from different users. == In the media == The Kickstarter campaign of 1 Second Everyday was featured in Entrepreneur's 3 Innovative Tech Startups on Kickstarter Right Now in 2012. The application was featured in The New York Times, The Washington Post, Gawker and other media outlets. By the end of the launch day, it was in Top 10 Free Apps on App Store. It was also selected as the App of the Week on GeekWire in 2013. Several other one-second compilation videos were also posted on the Internet after Kuriyama's video gained media attention. Sam Cornwell, an English photographer documented his son Indigo's growth using a montage of one-second iPhone clips. He shot these clips every single day from the moment of birth right up to the baby's first birthday. According to Cornwell, he was inspired by Kuriyama's project. The video of Cornwell's son gained considerable media attention after it was posted on YouTube. Save the Children also made a video commercial based on a similar format that showed a British girl oblivious of the Syrian war end up being a refugee. 1SE was a finalist for the Fast Company Innovation by Design Award in 2015, but lost to Google Maps. In 2015, Google Android created a gallery, Leap Second 2015, with the help of Droga5 and Kuriyama. The gallery showcased how people around the world enjoyed the one extra second of their lives. Through the 1 Second Everyday app available at Google Play, people were able to submit their extra second, which were then vetted and added to the gallery. The viewers were able to view other celebratory seconds from around the world as well as searching for them using different hashtags.