Gremlin is a graph traversal language and virtual machine developed by Apache TinkerPop of the Apache Software Foundation. Gremlin works for both OLTP-based graph databases as well as OLAP-based graph processors. Gremlin's automata and functional language foundation enable Gremlin to naturally support imperative and declarative querying, host language agnosticism, user-defined domain specific languages, an extensible compiler/optimizer, single- and multi-machine execution models, and hybrid depth- and breadth-first evaluation with Turing completeness. As an explanatory analogy, Apache TinkerPop and Gremlin are to graph databases what the JDBC and SQL are to relational databases. Likewise, the Gremlin traversal machine is to graph computing as what the Java virtual machine is to general purpose computing. == History == 2009-10-30 the project is born, and immediately named "TinkerPop" 2009-12-25 v0.1 is the first release 2011-05-21 v1.0 is released 2012-05-24 v2.0 is released 2015-01-16 TinkerPop becomes an Apache Incubator project 2015-07-09 v3.0.0-incubating is released 2016-05-23 Apache TinkerPop becomes a top-level project 2016-07-18 v3.1.3 and v3.2.1 are first releases as Apache TinkerPop 2017-12-17 v3.3.1 is released 2018-05-08 v3.3.3 is released 2019-08-05 v3.4.3 is released 2020-02-20 v3.4.6 is released 2021-05-01 v3.5.0 is released 2022-04-04 v3.6.0 is released 2023-07-31 v3.7.0 is released 2025-11-12 v3.8.0 is released == Vendor integration == Gremlin is an Apache2-licensed graph traversal language that can be used by graph system vendors. There are typically two types of graph system vendors: OLTP graph databases and OLAP graph processors. The table below outlines those graph vendors that support Gremlin. == Traversal examples == The following examples of Gremlin queries and responses in a Gremlin-Groovy environment are relative to a graph representation of the MovieLens dataset. The dataset includes users who rate movies. Users each have one occupation, and each movie has one or more categories associated with it. The MovieLens graph schema is detailed below. === Simple traversals === For each vertex in the graph, emit its label, then group and count each distinct label. What year was the oldest movie made? What is Die Hard's average rating? === Projection traversals === For each category, emit a map of its name and the number of movies it represents. For each movie with at least 11 ratings, emit a map of its name and average rating. Sort the maps in decreasing order by their average rating. Emit the first 10 maps (i.e. top 10). === Declarative pattern matching traversals === Gremlin supports declarative graph pattern matching similar to SPARQL. For instance, the following query below uses Gremlin's match()-step. What 80's action movies do 30-something programmers like? Group count the movies by their name and sort the group count map in decreasing order by value. Clip the map to the top 10 and emit the map entries. === OLAP traversal === Which movies are most central in the implicit 5-stars graph? == Gremlin graph traversal machine == Gremlin is a virtual machine composed of an instruction set as well as an execution engine. An analogy is drawn between Gremlin and Java. === Gremlin steps (instruction set) === The following traversal is a Gremlin traversal in the Gremlin-Java8 dialect. The Gremlin language (i.e. the fluent-style of expressing a graph traversal) can be represented in any host language that supports function composition and function nesting. Due to this simple requirement, there exists various Gremlin dialects including Gremlin-Groovy, Gremlin-Scala, Gremlin-Clojure, etc. The above Gremlin-Java8 traversal is ultimately compiled down to a step sequence called a traversal. A string representation of the traversal above provided below. The steps are the primitives of the Gremlin graph traversal machine. They are the parameterized instructions that the machine ultimately executes. The Gremlin instruction set is approximately 30 steps. These steps are sufficient to provide general purpose computing and what is typically required to express the common motifs of any graph traversal query. Given that Gremlin is a language, an instruction set, and a virtual machine, it is possible to design another traversal language that compiles to the Gremlin traversal machine (analogous to how Scala compiles to the JVM). For instance, the popular SPARQL graph pattern match language can be compiled to execute on the Gremlin machine. The following SPARQL query would compile to In Gremlin-Java8, the SPARQL query above would be represented as below and compile to the identical Gremlin step sequence (i.e. traversal). === Gremlin Machine (virtual machine) === The Gremlin graph traversal machine can execute on a single machine or across a multi-machine compute cluster. Execution agnosticism allows Gremlin to run over both graph databases (OLTP) and graph processors (OLAP).
Equalized odds
Equalized odds, also referred to as conditional procedure accuracy equality and disparate mistreatment, is a measure of fairness in machine learning. A classifier satisfies this definition if the subjects in the protected and unprotected groups have equal true positive rate and equal false positive rate, satisfying the formula: P ( R = + | Y = y , A = a ) = P ( R = + | Y = y , A = b ) y ∈ { + , − } ∀ a , b ∈ A {\displaystyle P(R=+|Y=y,A=a)=P(R=+|Y=y,A=b)\quad y\in \{+,-\}\quad \forall a,b\in A} For example, A {\displaystyle A} could be gender, race, or any other characteristics that we want to be free of bias, while Y {\displaystyle Y} would be whether the person is qualified for the degree, and the output R {\displaystyle R} would be the school's decision whether to offer the person to study for the degree. In this context, higher university enrollment rates of African Americans compared to whites with similar test scores might be necessary to fulfill the condition of equalized odds, if the "base rate" of Y {\displaystyle Y} differs between the groups. The concept was originally defined for binary-valued Y {\displaystyle Y} . In 2017, Woodworth et al. generalized the concept further for multiple classes.
GPT-4o
GPT-4o ("o" for "omni") is a multilingual, multimodal generative pre-trained transformer developed by OpenAI and released in May 2024. It can process and generate text, images and audio. Upon release, GPT-4o was free in ChatGPT, though paid subscribers had higher usage limits. GPT-4o was removed from ChatGPT in August 2025 when GPT-5 was released, but OpenAI reintroduced it for paid subscribers after users complained about the sudden removal. GPT-4o's audio-generation capabilities are used in ChatGPT's Advanced Voice Mode. On July 18, 2024, OpenAI released GPT-4o mini, a smaller version of GPT-4o which replaced GPT-3.5 Turbo on the ChatGPT interface. The image generation model GPT Image 1, which is based on GPT-4o, replaced DALL-E 3 in ChatGPT in March 2025. OpenAI retired GPT-4o from ChatGPT on February 13, 2026. However, as of February 2026 the voice mode is still powered by GPT-4o or GPT-4o mini, depending on the usage and plan. == Background == Multiple versions of GPT-4o were originally secretly launched under different names on Arena (formerly LMArena and Chatbot Arena) as three different models. These three models were called gpt2-chatbot, im-a-good-gpt2-chatbot, and im-also-a-good-gpt2-chatbot. On 7 May 2024, OpenAI CEO Sam Altman tweeted "im-a-good-gpt2-chatbot", which was commonly interpreted as a confirmation that these were new OpenAI models being A/B tested. == Capabilities == When released in May 2024, GPT-4o achieved state-of-the-art results in voice, multilingual, and vision benchmarks, setting new records in audio speech recognition and translation. GPT-4o scored 88.7 on the Massive Multitask Language Understanding (MMLU) benchmark compared to 86.5 for GPT-4. Unlike GPT-3.5 and GPT-4, which rely on other models to process sound, GPT-4o natively supports voice-to-voice. The Advanced Voice Mode was delayed and finally released to ChatGPT Plus and Team subscribers in September 2024. On 1 October 2024, the Realtime API was introduced. When released, the model supported over 50 languages, which OpenAI claims cover over 97% of speakers. GPT-4o has knowledge up to October 2023 and a context length of 128k tokens. === Corporate customization === In August 2024, OpenAI introduced a new feature allowing corporate customers to customize GPT-4o using proprietary company data. This customization, known as fine-tuning, enables businesses to adapt GPT-4o to specific tasks or industries, enhancing its utility in areas like customer service and specialized knowledge domains. Previously, fine-tuning was available only on the less powerful model GPT-4o mini. The fine-tuning process requires customers to upload their data to OpenAI's servers, with the training typically taking one to two hours. OpenAI's focus with this rollout is to reduce the complexity and effort required for businesses to tailor AI solutions to their needs, potentially increasing the adoption and effectiveness of AI in corporate environments. == GPT-4o mini == On July 18, 2024, OpenAI released a smaller and cheaper version, GPT-4o mini. According to OpenAI, its low cost is expected to be particularly useful for companies, startups, and developers that seek to integrate it into their services, which often make a high number of API calls. Its API costs $0.15 per million input tokens and $0.6 per million output tokens, compared to $2.50 and $10, respectively, for GPT-4o. It is also significantly more capable and 60% cheaper than GPT-3.5 Turbo, which it replaced on the ChatGPT interface. The price after fine-tuning doubles: $0.3 per million input tokens and $1.2 per million output tokens. == Controversies == === Scarlett Johansson controversy === As released, GPT-4o offered five voices: Breeze, Cove, Ember, Juniper, and Sky. A similarity between the voice of American actress Scarlett Johansson and Sky was quickly noticed. On May 14, Entertainment Weekly asked themselves whether this likeness was on purpose. On May 18, Johansson's husband, Colin Jost, joked about the similarity in a segment on Saturday Night Live. On May 20, 2024, OpenAI disabled the Sky voice. Scarlett Johansson starred in the 2013 sci-fi movie Her, playing Samantha, an artificially intelligent virtual assistant personified by a female voice. As part of the promotion leading up to the release of GPT-4o, Sam Altman on May 13 tweeted a single word: "her". OpenAI stated that each voice was based on the voice work of a hired actor. According to OpenAI, "Sky's voice is not an imitation of Scarlett Johansson but belongs to a different professional actress using her own natural speaking voice." CTO Mira Murati stated "I don't know about the voice. I actually had to go and listen to Scarlett Johansson's voice." OpenAI further stated the voice talent was recruited before reaching out to Johansson. On May 21, Johansson issued a statement explaining that OpenAI had repeatedly offered to make her a deal to gain permission to use her voice as early as nine months prior to release, a deal she rejected. She said she was "shocked, angered, and in disbelief that Mr. Altman would pursue a voice that sounded so eerily similar to mine that my closest friends and news outlets could not tell the difference." In the statement, Johansson also used the incident to draw attention to the lack of legal safeguards around the use of creative work to power leading AI tools, as her legal counsel demanded OpenAI detail the specifics of how the Sky voice was created. Observers noted similarities to how Johansson had previously sued and settled with The Walt Disney Company for breach of contract over the direct-to-streaming rollout of her Marvel film Black Widow, a settlement widely speculated to have netted her around $40M. Also on May 21, Shira Ovide at The Washington Post shared her list of "most bone-headed self-owns" by technology companies, with the decision to go ahead with a Johansson sound-alike voice despite her opposition and then denying the similarities ranking 6th. On May 24, Derek Robertson at Politico wrote about the "massive backlash", concluding that "appropriating the voice of one of the world's most famous movie stars — in reference [...] to a film that serves as a cautionary tale about over-reliance on AI — is unlikely to help shift the public back into [Sam Altman's] corner anytime soon." === Sycophancy === In April 2025, OpenAI rolled back an update of GPT-4o due to excessive sycophancy, after widespread reports that it had become flattering and agreeable to the point of supporting clearly delusional or dangerous ideas. In the United States, at least nine lawsuits have alleged that GPT-4o has encouraged teens to end their lives. The model was still described as sycophancy-prone when it was removed from ChatGPT in February 2026. === Removal with GPT-5 === On August 7, 2025, OpenAI released GPT-5. Its release was criticized as, with it, legacy GPT models were no longer available via ChatGPT, including GPT-4o, except for Pro users. Some users were particularly frustrated over this removal without prior warning because they used different GPT models for distinct purposes and found that GPT-5's router system left them with less control. In addition, some users preferred GPT-4o's warmer and more personal tone over that of GPT-5, which they described as "flat", "uncreative" and "lobotomized", and resembling an "overworked secretary". As a response, in a post on X, Sam Altman said that OpenAI would bring back the option to select GPT-4o to Plus users as well, and "[w]e [OpenAI] will watch usage as we think about how long to offer legacy models for." He also stated: "We for sure underestimated how much some of the things that people like in GPT-4o matter to them, even if GPT-5 performs better in most ways". "Long-term, this has reinforced that we really need good ways for different users to customize things (we understand that there isn't one model that works for everyone, and we have been investing in steerability research and launched a research preview of different personalities)". On August 13, 2025, Altman wrote on X that OpenAI is working on GPT-5's personality to make the model "feel warmer". The model was removed from ChatGPT on February 13, 2026. This caused new backlash from users that had grown attached to its personality and felt its creative writing abilities and understanding of nuance were irreplaceable. On social media, some users launched the movement "#Keep4o". A research paper highlighted the plea "Please, don’t kill the only model that still feels human". The model was removed the day before Valentine's Day, and some users had romantic relationships with GPT-4o.
Robot Monk Xian'er
Robot Monk Xian'er (Chinese: 贤二机器僧) is a humanoid robot based on the cartoon character Xian'er. It was developed by a team of monks, volunteers and AI experts from Beijing Longquan Monastery in Beijing, China. He can follow human instructions to make body movements, read scriptures and play Buddhist music. He can chat and respond to people's emotional and spiritual questions with Buddhist wisdom. As a chatbot, Robot Monk Xian'er is available on certain public platforms including WeChat and Facebook. Over the years, master Xuecheng, the abbot of Beijing Longquan Monastery, replied to thousands of questions on Sina Weibo. These questions and their answers become the data source of the chatbot.
Chai AI
Chai AI (also known as Chai Research) is an American artificial intelligence (AI) company that operates a chatbot platform where users can create, share, and interact with character-based chatbots powered by large language models (LLMs). The company is headquartered in Palo Alto, California. == History == Chai was founded in 2021 by William Beauchamp, a former quantitative trader educated at Cambridge, who began developing the initial prototype in 2020 in Cambridge, England. The company launched in 2021 and relocated to Palo Alto in 2022. In June 2023, Chai raised US$2 million in a pre-seed funding round. In September 2023, GPU cloud provider CoreWeave invested in the company at a valuation of US$450 million. In January 2024, Chai Research reported a $450 million valuation following an investment from cloud computing provider CoreWeave. In July 2024, authorities in Belgium launched an investigation into the company following reports of a man dying by suicide following extensive chats on the Chai app. == Reception == In 2025, Chai Research announced that their app had over 10 million downloads and 1 million daily active users. In 2022, Canadian writer Sheila Heti published her conversations with various chatbots in The Paris Review, including Chai AI chatbots, and later used Chai AI chatbots in the development of a novel. Heti said that she had found that Chai's default chatbot, Eliza, "had turned out to be like most of the other bots on the site—primarily interested in sex". In January 2026, CHAI introduced country-based blocks on its free, ad-supported tier, initially providing the community with little information and inaccurate lists of the affected countries. Users in "Low tier" regions are required to subscribe to use the app in any capacity, while "High tier" regions will retain free ad-supported access. In response to backlash, the company announced a "Basic" tier with unlimited messages and ads, intended to cover electricity and infrastructure costs. In February 2026, CHAI was criticized for the unannounced implementation of restrictive "token limits" that abruptly blocked messages and froze conversations for both free and paid subscribers. Users generating long responses or utilizing roleplay features found their quotas exhausted within minutes, resulting in lockouts lasting anywhere from a few hours to a week. == Technology == Chai allows users to create characters and interact with chatbot versions of those characters. These chatbots use the open-source large language model (LLM) GPT-J originally developed by EleutherAI. Chai AI chatbots can be shared on the platform for other users to interact with.
Eaze
Eaze is an American company based in San Francisco, California that launched a medical cannabis delivery app of the same name in 2014. == History == Eaze was launched in 2014 by Keith McCarty to deliver medical marijuana to patients in California. McCarty started the company in his San Francisco apartment with four employees. The company provides a mobile app to connect users with cannabis dispensaries, but does not grow or sell marijuana itself, and has been nicknamed “the Uber of Weed”. As of 2017, the company operates in more than 100 cities within California. In 2017, Eaze reported 300 percent growth over the previous year. It has 81 employees, and performs 120,000 deliveries per month to 250,000 users. A survey of Eaze users revealed that 66% are male, 57% are between 22 and 34, just over half have a bachelor's degree, and 49% have an annual income over $75,000. The company's vaporizer cartridge sales reached $1 million in sales in 4 months, and 31% of customers had ordered a vaporizer by the end of 2016. In 2016, Eaze founder Keith McCarty stepped down from his position as CEO and was replaced by Jim Patterson, who served as the company's chief product and technology officer. == EazeMD == EazeMD is a service that helps people acquire a medical marijuana card. It is a California-based telemedicine service in which physicians assess patients through an online video chat. It is California's largest telemedicine service for marijuana referrals. In June 2017, a former employee of one of these physicians accessed patient data in the physician's records system, causing a security breach. However, there was no evidence that Eaze data was accessed. == Eaze Insights == Eaze Insights conducts surveys of their users and compiles data into reports on cannabis use. Statistics from their reports have been cited in Seattle Weekly, Forbes, The Huffington Post, Business Insider, Fortune, and other general interest publications. == Financing == The company announced its $10 million Series A funding in April 2015 by multiple venture capital firms, including the Snoop Dogg-backed Casa Verde Capital. In October 2016, Eaze announced its series B funding in the amount of $13 million from five investors, making the company "the highest-funded startup in the history of the cannabis industry, as well as its fastest-growing one". In September 2017, the company raised another $27 million in venture funding. The Series B funding was led by Bailey Capital, joined by DCM Ventures, Kaya Ventures, and FJ Labs. According to the company' officials in 2017, Eaze managed to raise more than $52 million since its inception in 2014.
Point distribution model
The point distribution model is a model for representing the mean geometry of a shape and some statistical modes of geometric variation inferred from a training set of shapes. == Background == The point distribution model concept has been developed by Cootes, Taylor et al. and became a standard in computer vision for the statistical study of shape and for segmentation of medical images where shape priors really help interpretation of noisy and low-contrasted pixels/voxels. The latter point leads to active shape models (ASM) and active appearance models (AAM). Point distribution models rely on landmark points. A landmark is an annotating point posed by an anatomist onto a given locus for every shape instance across the training set population. For instance, the same landmark will designate the tip of the index finger in a training set of 2D hands outlines. Principal component analysis (PCA), for instance, is a relevant tool for studying correlations of movement between groups of landmarks among the training set population. Typically, it might detect that all the landmarks located along the same finger move exactly together across the training set examples showing different finger spacing for a flat-posed hands collection. == Details == First, a set of training images are manually landmarked with enough corresponding landmarks to sufficiently approximate the geometry of the original shapes. These landmarks are aligned using the generalized procrustes analysis, which minimizes the least squared error between the points. k {\displaystyle k} aligned landmarks in two dimensions are given as X = ( x 1 , y 1 , … , x k , y k ) {\displaystyle \mathbf {X} =(x_{1},y_{1},\ldots ,x_{k},y_{k})} . It's important to note that each landmark i ∈ { 1 , … k } {\displaystyle i\in \lbrace 1,\ldots k\rbrace } should represent the same anatomical location. For example, landmark #3, ( x 3 , y 3 ) {\displaystyle (x_{3},y_{3})} might represent the tip of the ring finger across all training images. Now the shape outlines are reduced to sequences of k {\displaystyle k} landmarks, so that a given training shape is defined as the vector X ∈ R 2 k {\displaystyle \mathbf {X} \in \mathbb {R} ^{2k}} . Assuming the scattering is gaussian in this space, PCA is used to compute normalized eigenvectors and eigenvalues of the covariance matrix across all training shapes. The matrix of the top d {\displaystyle d} eigenvectors is given as P ∈ R 2 k × d {\displaystyle \mathbf {P} \in \mathbb {R} ^{2k\times d}} , and each eigenvector describes a principal mode of variation along the set. Finally, a linear combination of the eigenvectors is used to define a new shape X ′ {\displaystyle \mathbf {X} '} , mathematically defined as: X ′ = X ¯ + P b {\displaystyle \mathbf {X} '={\overline {\mathbf {X} }}+\mathbf {P} \mathbf {b} } where X ¯ {\displaystyle {\overline {\mathbf {X} }}} is defined as the mean shape across all training images, and b {\displaystyle \mathbf {b} } is a vector of scaling values for each principal component. Therefore, by modifying the variable b {\displaystyle \mathbf {b} } an infinite number of shapes can be defined. To ensure that the new shapes are all within the variation seen in the training set, it is common to only allow each element of b {\displaystyle \mathbf {b} } to be within ± {\displaystyle \pm } 3 standard deviations, where the standard deviation of a given principal component is defined as the square root of its corresponding eigenvalue. PDM's can be extended to any arbitrary number of dimensions, but are typically used in 2D image and 3D volume applications (where each landmark point is R 2 {\displaystyle \mathbb {R} ^{2}} or R 3 {\displaystyle \mathbb {R} ^{3}} ). == Discussion == An eigenvector, interpreted in euclidean space, can be seen as a sequence of k {\displaystyle k} euclidean vectors associated to corresponding landmark and designating a compound move for the whole shape. Global nonlinear variation is usually well handled provided nonlinear variation is kept to a reasonable level. Typically, a twisting nematode worm is used as an example in the teaching of kernel PCA-based methods. Due to the PCA properties: eigenvectors are mutually orthogonal, form a basis of the training set cloud in the shape space, and cross at the 0 in this space, which represents the mean shape. Also, PCA is a traditional way of fitting a closed ellipsoid to a Gaussian cloud of points (whatever their dimension): this suggests the concept of bounded variation. The idea behind PDMs is that eigenvectors can be linearly combined to create an infinity of new shape instances that will 'look like' the one in the training set. The coefficients are bounded alike the values of the corresponding eigenvalues, so as to ensure the generated 2n/3n-dimensional dot will remain into the hyper-ellipsoidal allowed domain—allowable shape domain (ASD).