Knowledge Atlas Technology Joint Stock Co., Ltd., branded internationally as Z.ai, is a Chinese technology company specializing in artificial intelligence (AI). The company was formerly known as Zhipu AI outside China until its rebranding in 2025. Z.ai's flagship product is the GLM (General Language Model) family of large language models, which the company has released under the free and open-source MIT License since July 2025. As of 2024, it is one of China's "AI tiger" companies by investors and considered to be the third-largest LLM market player in China's AI industry according to the International Data Corporation. In January 2025, the United States Commerce Department blacklisted the company in its Entity List due to national security concerns. == History == Founded in 2019, the startup company began from Tsinghua University and was later spun out as an independent company. Researchers published an Association for Computational Linguistics conference paper in May 2022 introducing the GLM (General Language Model) training algorithm, which uses an "autoregressive blank infilling" strategy that creates cloze tests by randomly removing segments of input text and trains the model to autoregressively regenerate the removed text. In 2023, it raised 2.5 billion yuan (approx. 350 million in USD) from Alibaba Group and Tencent, along with Meituan, Ant Group, Xiaomi, and HongShan. In March 2024, Zhipu AI announced it was developing a Sora-like technology to achieve artificial general intelligence (AGI). In May 2024, the Saudi Arabian finance firm Prosperity7 Ventures, LLC participated in a USD $400 million financing round for Zhipu AI with a valuation of approximately 3 billion USD. In July 2024, they debuted the Ying text-to-video model. Zhipu released GLM-4-Plus in August 2024. In October 2024, Zhipu released GLM-4-Voice, an end-to-end speech large language model that can adjust its tone or dialect. Zhipu disclosed in April 2025 that it had started preparing for its initial public offering (IPO) and released two models under the free and open-source MIT License. In May 2025, the company sealed a 61.28 million yuan deal from the Chinese government for city projects in Hangzhou. In July 2025, Zhipu AI released GLM-4.5 and GLM-4.5 Air, their next generation language models, and the company rebranded itself as Z.ai internationally. In August 2025, Z.ai announced that their GLM models are compatible with Huawei's Ascend processors. On August 11, 2025, Z.ai released a new vision-language model (VLM) with a total of 106B parameters, GLM-4.5V. In late September 2025, the company released GLM-4.6 using China's domestic chips such as those from Cambricon Technologies. Z.ai released GLM-4.6V and GLM-4.7 in December 2025. That same year, the company changed its official name to Knowledge Atlas Technology JSC Ltd. On 8 January 2026, Z.ai held its IPO on the Hong Kong Stock Exchange to become a listed company. It is considered to be China's first major LLM company that went through an IPO. On February 11, 2026, Z.ai released GLM-5. In late February 2026, Z.ai's shares fell by 23%, and had a shortage of compute resources, leading to user complaints and Z.ai issuing a public call for support. Z.ai also restricted new user signups. In late March, 2026, Z.ai released the GLM-5.1 model to subscription users. On April 8th, 2026, Z.ai released GLM-5.1 as open-source. The same day, Z.ai increased its API prices by 10%, but maintained a lower price than its United States competitor Anthropic's Opus 4.6 model. On release, the company's share price increased 11.5%. == Description == Z.ai provides the following products and services: General Language Model (commonly abbreviated as GLM; formerly known as ChatGLM), a series of pre-trained dialogue models initially developed by Zhipu AI and Tsinghua KEG in 2023. GLM 4.5, released in July 2025 by Z.ai, can run on eight NVIDIA H20 chips. The release of GLM-4.6 in late September 2025 marked the first integration of FP8 and Int4 quantization on Cambricon chips. It also supports native FP8 on Moore Threads GPUs. Ying, a text-to-video model that generates image and text prompts into a six-second video clip for around 30 seconds. AutoGLM, an AI agent application that uses voice commands to complete tasks within a smartphone. The app can analyze complex tasks such as ordering an item from a nearby store and repeating an order based from the user's shopping history. AMiner, created by Jie Tang (co-founder of Z.ai) in March 2006, now owned by Z.ai. Z.ai has offices in the Middle East, United Kingdom, Singapore, and Malaysia, along with innovation center projects across Southeast Asia (2025). In January 2025, the United States Commerce Department added the company to its Entity List, citing national security concerns. == Models ==
List of performance analysis tools
This is a list of performance analysis tools for use in software development. == General purpose, language independent == The following tools work based on log files that can be generated from various systems. time (Unix) - can be used to determine the run time of a program, separately counting user time vs. system time, and CPU time vs. clock time. timem (Unix) - can be used to determine the wall-clock time, CPU time, and CPU utilization similar to time (Unix) but supports numerous extensions. Supports reporting peak resident set size, major and minor page faults, priority and voluntary context switches via getrusage. Supports sampling procfs on supporting systems to report metrics such as page-based resident set size, virtual memory size, read-bytes, and write-bytes, etc. Supports collecting hardware counters when built with PAPI support. == Multiple languages == The following tools work for multiple languages or binaries. == C and C++ == Arm MAP, a performance profiler supporting Linux platforms. AppDynamics, an application performance management service for C/C++ applications via SDK. AQtime Pro, a performance profiler and memory allocation debugger that can be integrated into Microsoft Visual Studio, and Embarcadero RAD Studio, or can run as a stand-alone application. IBM Rational Purify was a memory debugger allowing performance analysis. Instruments (bundled with Xcode) is used to profile an executable's memory allocations, time usage, filesystem activity, GPU activity etc. Intel Parallel Studio contains Intel VTune Amplifier, which tunes both serial and parallel programs. It also includes Intel Advisor and Intel Inspector. Intel Advisor optimizes vectorization (use of SIMD instructions) and prototypes threading implementations. Intel Inspector detects and debugs races, deadlocks and memory errors. Parasoft Insure++ provides a graphical tool that displays and animates memory allocations in real time to expose memory blowout, fragmentation, overuse, bottlenecks and leaks. Visual Studio Team System Profiler, commercial profiler by Microsoft. == Java == inspectIT is an open-source application performance management (APM) service for monitoring and analyzing software applications, available under the Apache License, Version 2.0 (ALv2). JConsole is the profiler which comes with the Java Development Kit JProfiler JRockit Mission Control, a profiler with low overhead. Netbeans Profiler, a profiler integrated into the NetBeans IDE (internally uses jvisualvm profiler) Plumbr, Java application performance monitoring with automated root cause detection. Links memory leaks, GC inefficiency, slow database and external web service calls, locked threads, and other performance problems to the line in source code that causes them. OverOps, Continuous reliability for the modern software supply chain, automatically detect and deliver root cause automation for all errors. VisualVM is a visual tool integrating several commandline JDK tools and lightweight profiling capabilities. It is bundled with the Java Development Kit since version 6, update 7. == JavaScript == The Firefox web browser's developer tools contain a Performance tool, which gives insight into JavaScript performance of a website. Microsoft Visual Studio AJAX Profiling Extensions is a free profiling tool for JavaScript by Microsoft Research. == .NET == CLR Profiler is a free memory profiler provided by Microsoft for CLR applications. GlowCode is a performance and memory profiler for .NET applications using C# and other .NET languages. It identifies time-intensive functions and detects memory leaks and errors in native, managed and mixed Windows x64 and x86 applications. Visual Studio == PHP == BlackFire.io Dbg Xdebug is a PHP extension which provides debugging and profiling capabilities.
Anna Ridler
Anna Ridler (born 1985) is an artist who works with machine learning, handmade archives and moving image. She builds her own datasets to expose the labour and ideology embedded in the systems that organise knowledge. Her work is held in the permanent collections of the Whitney Museum of American Art, the Victoria and Albert Museum, M+ and ZKM Center for Art and Media Karlsruhe, and has been exhibited widely at cultural institutions including Tate Modern, Barbican Centre, Centre Pompidou, The Photographers' Gallery, Taipei Fine Arts Museum, MIT Museum, Kunsthaus Graz, ZKM Center for Art and Media Karlsruhe and Ars Electronica. == Biography == Born in London in 1985, Ridler spent her childhood raised between Atlanta, Georgia and the United Kingdom. She obtained a Bachelor of Arts in English Literature and Language from Oxford University in 2007 and a Master of Arts in Information Experience Design from the Royal College of Art in 2017. == Art practice == Ridler's practice uses technology, and in particular machine learning, to investigate how naming, classification and financial speculation determine what can be seen and what is erased. A core element of Ridler's work lies in the creation of handmade data sets through a laborious process of selecting and classifying images and text. By creating her own data sets, Ridler is able to uncover and expose underlying themes and concepts while also inverting the usual process of scraping pre-classified images found in large databases on the Internet. She began working with machine learning as an artistic material in 2017, at a moment when the technology required building every dataset by hand; that constraint became the foundation of the practice. Her interests are in drawing, machine learning, data collection, storytelling and technology. == Work == Some of Ridler's most notable works to date fall within her ‘tulip series’ which explores the hysteria around tulip mania and compares it to the speculation and bubbles surrounding cryptocurrencies. The series is expressed in three forms: a photographic dataset in Myriad (Tulips), 2018; two iterations of machine generated videos in Mosaic Virus (2018) and Mosaic Virus (2019); and a website with an accompanied functioning decentralized application in Bloemenveiling (2019). === Myriad (Tulips) (2018) === I wanted to draw together ideas around capitalism, value, and the tangible and intangible nature of speculation, and collapse from two very different yet surprisingly similar moments in history. Myriad (Tulips) (2018) is an installation of ten thousand hand-labeled photographs forming a dataset of unique tulips. The ten thousand, or myriad of, photographs were taken by Ridler over the course of three months, roughly the length of a tulip season, spent in Utrecht. Each photograph is carefully affixed one by one with magnets to a specially painted black wall in a laborious process to form a seemingly precise grid. Myriad (Tulips) (2018) has been exhibited in AI: More than Human, Barbican Centre, London, UK (May 16 - August 26, 2019); Error—The Art of Imperfection, Ars Electronica Export, Berlin, Germany (November 17, 2018 – March 3, 2019); Peer to Peer, Shanghai Centre of Photography, Shanghai, China (December 8 - February 9, 2020). The work was featured in Bloomberg, It’s Nice That, and Hyperallergic. For Myriad (Tulips), Ridler was nominated for a Beazley Design of the Year award for her presentation of an alternative perspective on how to engage with artificial intelligence; demonstrating a departure from ownership and control of major corporations to a more personalized process of constructing and conceptualizing from the ground-up. === Mosaic Virus (2018, 2019) === Mosaic Virus (2018) is a single screen video installation displaying a grid of continually evolving tulips in bloom. For Mosaic Virus (2019) Ridler used three screens. The appearance of the tulips is controlled by artificial intelligence using fluctuations in the price of bitcoin. The stripes on the tulips' petals reflect the value of the cryptocurrency. Ridler draws parallels with the tulip mania of the 17th century; representing the hysteria and speculation around crypto-currencies. The work takes its name from the mosaic virus which caused stripes in tulip petals, subsequently increasing their desirability and leading to speculative prices. Ridler trained a general adversarial network (GAN) on the set of ten thousand photographs of individual tulips from her work Myriad (Tulips). She used a technique called spectral normalization to improve the output. The work was exhibited in Error—The Art of Imperfection, Ars Electronica Export, Berlin, Germany (November 17, 2018 – March 3, 2019). === Bloemenveiling (2019) === Bloemenveiling (2019) is an auction of artificial-intelligence-generated tulips on the blockchain in the form of a functioning decentralized application: http://bloemenveiling.bid. Ridler collaborated with senior research scientist at DeepMind, David Pfau to investigate whether blockchain could be used as a means of finding poetic substance within it. The piece interrogates the way technology drives human desire and economic dynamics by creating artificial scarcity. In the work, short moving image pieces of tulips created by generative adversarial networks are sold at auction using smart contracts on the Ethereum network. Each time a tulip is sold, thousands of computers around the world all work to verify the transaction, checking each other's work against each other. While the artificial intelligence behind the moving image pieces has the potential to generate infinite flowers, the enormous distributed network is used, at great environmental cost, to introduce scarcity to an otherwise limitless resource. Bloemenveiling was exhibited in Entangled Realities, HEK Basel, Basel, Switzerland in 2019. == Solo exhibitions == Anna Ridler, Circadian Bloom, ZKM Center for Art and Media, Karlsruhe, (2023) Anna Ridler, Time Blooms, Buk Seoul Museum of Art, Seoul, (2025) Anna Ridler, Trace Remains, Galerie Nagel Draxler, Cologne, (2026) Anna Ridler, Laws of Ordered Form, The Photographers' Gallery, London (2020); The Abstraction of Nature, Aksioma, Ljubljana (2020) == Awards and recognition == European Union EMAP Fellow (2018) DARE Art Prize (2018–2019) Featured in Thames & Hudson, Digital Art (1960s–Now) Featured in British Art: The Last 15 Years ABS Digital Artist of the Year (2025)
Smartglasses
Smartglasses or smart glasses are eye or head-worn wearable computers. Many smartglasses include displays that add information alongside or to what the wearer sees. Alternatively, smartglasses are sometimes defined as glasses that are able to change their optical properties, such as smart sunglasses that are programmed to change tint by electronic means. Alternatively, smartglasses are sometimes defined as glasses that include headphone functionality. A pair of smartglasses can be considered an augmented reality device if it performs pose tracking. Superimposing information onto a field of view is achieved through an optical head-mounted display (OHMD) or embedded wireless glasses with transparent heads-up display (HUD) or augmented reality (AR) overlay. These systems have the capability to reflect projected digital images as well as allowing the user to see through it or see better with it. While early models can perform basic tasks, such as serving as a front end display for a remote system, as in the case of smartglasses utilizing cellular technology or Wi-Fi, modern smart glasses are effectively wearable computers which can run self-contained mobile apps. Some are handsfree and can communicate with the Internet via natural language voice commands, while others use touch buttons. Like other computers, smartglasses may collect information from internal or external sensors. It may control or retrieve data from other instruments or computers. In most cases, it supports wireless technologies like Bluetooth, Wi-Fi, and GPS. A small number of models run a mobile operating system and function as portable media players to send audio and video files to the user via a Bluetooth or WiFi headset. Some smartglasses models also feature full lifelogging and activity tracker capability. Smartglasses devices may also have features found on a smartphone. Some have activity tracker functionality features (also known as "fitness tracker") as seen in some GPS watches. == Features and applications == As with other lifelogging and activity tracking devices, the GPS tracking unit and digital camera of some smartglasses can be used to record historical data. For example, after the completion of a workout, data can be uploaded into a computer or online to create a log of exercise activities for analysis. Some smart watches can serve as full GPS navigation devices, displaying maps and current coordinates. Users can "mark" their current location and then edit the entry's name and coordinates, which enables navigation to those new coordinates. Although some smartglasses models manufactured in the 21st century are completely functional as standalone products, most manufacturers recommend or even require that consumers purchase mobile phone handsets that run the same operating system so that the two devices can be synchronized for additional and enhanced functionality. The smartglasses can work as an extension, for head-up display (HUD) or remote control of the phone and alert the user to communication data such as calls, SMS messages, emails, and calendar invites. === Security applications === Smart glasses could be used as a body camera. In 2018, Chinese police in Zhengzhou and Beijing were using smart glasses to take photos which are compared against a government database using facial recognition to identify suspects, retrieve an address, and track people moving beyond their home areas. === Sport applications === Smart glasses are used in sports like cycling, running, skiing, golf, tennis, or sailing, giving athletes real-time, heads-up data without looking down at the screen of a watch or smartphone. In 2025, Meta has announced a new partnership with sports eyewear brand Oakley. === Healthcare applications === Several proofs of concept for Google Glasses have been proposed in healthcare. In July 2013, Lucien Engelen started research on the usability and impact of Google Glass in health care. Engelen, who is based at Singularity University and in Europe at Radboud University Medical Center, is participating in the Glass Explorer program. Key findings of Engelen's research included: The quality of pictures and video are usable for healthcare education, reference, and remote consultation. The camera needs to be tilted to different angle for most of the operative procedures Tele-consultation is possible—depending on the available bandwidth—during operative procedures. A stabilizer should be added to the video function to prevent choppy transmission when a surgeon looks to screens or colleagues. Battery life can be easily extended with the use of an external battery. Controlling the device and/or programs from another device is needed for some features because of a sterile environment. Text-to-speech ("Take a Note" to Evernote) exhibited a correction rate of 60 percent, without the addition of a medical thesaurus. A protocol or checklist displayed on the screen of Google Glass can be helpful during procedures. Dr. Phil Haslam and Dr. Sebastian Mafeld demonstrated the first concept for Google Glass in the field of interventional radiology. They demonstrated the manner in which the concept of Google Glass could assist a liver biopsy and fistulaplasty, and the pair stated that Google Glass has the potential to improve patient safety, operator comfort, and procedure efficiency in the field of interventional radiology. In June 2013, surgeon Dr. Rafael Grossmann was the first person to integrate Google Glass into the operating theater, when he wore the device during a PEG (percutaneous endoscopic gastrostomy) procedure. In August 2013, Google Glass was also used at Wexner Medical Center at Ohio State University. Surgeon Dr. Christopher Kaeding used Google Glass to consult with a colleague in a distant part of Columbus, Ohio. A group of students at The Ohio State University College of Medicine also observed the operation on their laptop computers. Following the procedure, Kaeding stated, "To be honest, once we got into the surgery, I often forgot the device was there. It just seemed very intuitive and fit seamlessly." 16 November 2013, in Santiago de Chile, the maxillofacial team led by Dr.gn Antonio Marino conducted the first orthognathic surgery assisted with Google Glass in Latin America, interacting with them and working with simultaneous three-dimensional navigation. The surgical team was interviewed by ADN radio. In January 2014, Indian Orthopedic Surgeon Selene G. Parekh conducted the foot and ankle surgery using Google Glass in Jaipur, which was broadcast live on Google website via the internet. The surgery was held during a three-day annual Indo-US conference attended by a team of experts from the US and co-organized by Ashish Sharma. Sharma said Google Glass allows looking at an X-Ray or MRI without taking the eye off of the patient and allows a doctor to communicate with a patient's family or friends during a procedure. In Australia, during January 2014, Melbourne tech startup Small World Social collaborated with the Australian Breastfeeding Association to create the first hands-free breastfeeding Google Glass application for new mothers. The application, named Google Glass Breastfeeding app trial, allows mothers to nurse their baby while viewing instructions about common breastfeeding issues (latching on, posture etc.) or call a lactation consultant via a secure Google Hangout, who can view the issue through the mother's Google Glass camera. The trial was successfully concluded in Melbourne in April 2014, and 100% of participants were breastfeeding confidently. == Display types == Various techniques have existed for see-through HMDs. Most of these techniques can be summarized into two main families: "Curved Mirror" (or Curved Combiner) based and "Waveguide" or "Light-guide" based. The mirror technique has been used in EyeTaps, by Meta in their Meta 1, by Vuzix in their Star 1200 product, by Olympus, and by Laster Technologies. Various waveguide techniques have existed for some time. These techniques include diffraction optics, holographic optics, polarized optics, reflective optics, and projection: Diffractive waveguide – slanted diffraction grating elements (nanometric 10E-9). Nokia technique now licensed to Vuzix. Holographic waveguide – 3 holographic optical elements (HOE) sandwiched together (RGB). Used by Sony and Konica Minolta. Reflective waveguide – A thick light guide with single semi-reflective mirror is used by Epson in their Moverio product. A curved light guide with partial-reflective segmented mirror array to out-couple the light is used by tooz technologies GmbH. Virtual retinal display (VRD) – Also known as a retinal scan display (RSD) or retinal projector (RP), is a display technology that draws a raster display (like a television) directly onto the retina of the eye - developed by MicroVision, Inc. OLED microdisplays for near-eye applications (outdoor optical equipment, night vision glasses, ocular equipment for medical devices, augme
Model collapse
Model collapse, also known by other names such as "AI inbreeding", "AI cannibalism", "Habsburg AI", and "model autophagy disorder" or "MAD" is a phenomenon noted in artificial intelligence studies, where machine learning models gradually degrade due to errors coming from uncurated synthetic data, or due to training on the outputs of another model such as prior versions of itself. It is unclear to what extent the phenomenon threatens the long-term development of such models, and some techniques have been proposed to mitigate the effect. == Characteristics == Shumailov et al. coined the term to describe two specific stages to the degradation of machine learning models: early model collapse and late model collapse: In early model collapse, the model begins losing information about the tails of the distribution – mostly affecting minority data. Later work highlighted that early model collapse is hard to notice, since overall performance may appear to improve, while the model loses performance on minority data. In late model collapse, the model loses a significant proportion of its performance, confusing concepts and losing most of its variance. == Mechanism == Using synthetic data as training data can lead to issues with the quality and reliability of the trained model. Model collapse occurs for three main reasons: functional approximation errors sampling errors learning errors Importantly, it happens in even the simplest of models, where not all of the error sources are present. In more complex models the errors often compound, leading to faster collapse. == Disagreement over real-world impact == Some researchers and commentators on model collapse warn that the phenomenon could fundamentally threaten future generative AI development: As AI-generated data is shared on the Internet, it will inevitably end up in future training datasets, which are often crawled from the Internet. If training on "slop" (large quantities of unlabeled synthetic data) inevitably leads to model collapse, this could therefore pose a difficult problem. However, recently, other researchers have disagreed with this argument, showing that if synthetic data accumulates alongside human-generated data, model collapse is avoided. The researchers argue that data accumulating over time is a more realistic description of reality than deleting all existing data every year, and that the real-world impact of model collapse may not be as catastrophic as feared. An alternative branch of the literature investigates the use of machine learning detectors and watermarking to identify model generated data and filter it out. == Mathematical models of the phenomenon == === 1D Gaussian model === In 2024, a first attempt has been made at illustrating collapse for the simplest possible model — a single dimensional normal distribution fit using unbiased estimators of mean and variance, computed on samples from the previous generation. To make this more precise, we say that original data follows a normal distribution X 0 ∼ N ( μ , σ 2 ) {\displaystyle X^{0}\sim {\mathcal {N}}(\mu ,\sigma ^{2})} , and we possess M 0 {\displaystyle M_{0}} samples X j 0 {\displaystyle X_{j}^{0}} for j ∈ { 1 , … , M 0 } {\displaystyle j\in {\{\,1,\dots ,M_{0}\,{}\}}} . Denoting a general sample X j i {\displaystyle X_{j}^{i}} as sample j ∈ { 1 , … , M i } {\displaystyle j\in {\{\,1,\dots ,M_{i}\,{}\}}} at generation i {\displaystyle i} , then the next generation model is estimated using the sample mean and variance: μ i + 1 = 1 M i ∑ j X j i ; σ i + 1 2 = 1 M i − 1 ∑ j ( X j i − μ i + 1 ) 2 . {\displaystyle \mu _{i+1}={\frac {1}{M_{i}}}\sum _{j}X_{j}^{i};\quad \sigma _{i+1}^{2}={\frac {1}{M_{i}-1}}\sum _{j}(X_{j}^{i}-\mu _{i+1})^{2}.} Leading to a conditionally normal next generation model X j i + 1 | μ i + 1 , σ i + 1 ∼ N ( μ i + 1 , σ i + 1 2 ) {\displaystyle X_{j}^{i+1}|\mu _{i+1},\;\sigma _{i+1}\sim {\mathcal {N}}(\mu _{i+1},\sigma _{i+1}^{2})} . In theory, this is enough to calculate the full distribution of X j i {\displaystyle X_{j}^{i}} . However, even after the first generation, the full distribution is no longer normal: It follows a variance-gamma distribution. To continue the analysis, instead of writing the probability density function at each generation, it is possible to explicitly construct them in terms of independent random variables using Cochran's theorem. To be precise, μ 1 {\displaystyle \mu _{1}} and σ 1 {\displaystyle \sigma _{1}} are independent, with μ 1 ∼ N ( μ , σ 2 M 0 ) {\displaystyle \mu _{1}\sim {\mathcal {N}}\left(\mu ,{\frac {\sigma ^{2}}{M_{0}}}\right)} and ( M 0 − 1 ) σ 1 2 ∼ σ 2 Γ ( M 0 − 1 2 , 1 2 ) {\displaystyle (M_{0}-1)\,\sigma _{1}^{2}\sim \sigma ^{2}\,\Gamma \left({\frac {M_{0}-1}{2}},{\frac {1}{2}}\right)} , following a Gamma distribution. Denoting with Z {\displaystyle Z} Gaussian random variables distributed according to N ( 0 , 1 ) {\displaystyle {\mathcal {N}}(0,1)} and with S i {\displaystyle S^{i}} random variables distributed with 1 M i − 1 − 1 Γ ( M i − 1 − 1 2 , 1 2 ) {\displaystyle {\frac {1}{M_{i-1}-1}}\Gamma \left({\frac {M_{i-1}-1}{2}},{\frac {1}{2}}\right)} , it turns out to be possible to write samples at each generation as X j 0 = μ + σ Z j 0 , {\textstyle X_{j}^{0}=\mu +\sigma Z_{j}^{0},} X j 1 = μ + σ M 0 Z 1 + σ S 1 Z j 1 , {\textstyle X_{j}^{1}=\mu +{\frac {\sigma }{\sqrt {M_{0}}}}Z^{1}+\sigma {\sqrt {S^{1}}}Z_{j}^{1},} and more generally X j n = μ + σ M 0 Z 1 + σ M 1 S 1 Z 2 + ⋯ + σ M n − 1 S 1 × ⋯ × S n − 1 Z n + σ S 1 × ⋯ × S n Z j n . {\displaystyle X_{j}^{n}=\mu +{\frac {\sigma }{\sqrt {M_{0}}}}Z^{1}+{\frac {\sigma }{\sqrt {M_{1}}}}{\sqrt {S^{1}}}Z^{2}+\dots +{\frac {\sigma }{\sqrt {M_{n-1}}}}{\sqrt {S^{1}\times \dots \times S^{n-1}}}Z^{n}+\sigma {\sqrt {S^{1}\times \dots \times S^{n}}}Z_{j}^{n}.} Note, that these are not joint distributions, as Z n {\displaystyle Z^{n}} and S n {\displaystyle S^{n}} depend directly on Z j n − 1 {\displaystyle Z_{j}^{n-1}} , but when considering X j n {\displaystyle X_{j}^{n}} on its own the formula above provides all the information about the full distribution. To analyse the model collapse, we can first calculate variance and mean of samples at generation n {\displaystyle n} . This would tell us what kind of distributions we expect to arrive at after n {\displaystyle n} generations. It is possible to find its exact value in closed form, but the mean and variance of the square root of gamma distribution are expressed in terms of gamma functions, making the result quite clunky. Following, it is possible to expand all results to second order in each of 1 / M i {\displaystyle 1/M_{i}} , assuming each sample size to be large. It is then possible to show that 1 σ 2 Var ( X j n ) = 1 M 0 + 1 M 1 + ⋯ + 1 M n − 1 + 1 + O ( M i − 2 ) . {\displaystyle {\frac {1}{\sigma ^{2}}}\operatorname {Var} (X_{j}^{n})={\frac {1}{M_{0}}}+{\frac {1}{M_{1}}}+\dots +{\frac {1}{M_{n-1}}}+1+{\mathcal {O}}\left(M_{i}^{-2}\right).} And if all sample sizes M i = M {\displaystyle M_{i}=M} are constant, this diverges linearly as n → ∞ {\displaystyle n\to \infty } : Var ( X j n ) = σ 2 ( 1 + n M ) ; E ( X j n ) = μ . {\displaystyle \operatorname {Var} (X_{j}^{n})=\sigma ^{2}\left(1+{\frac {n}{M}}\right);\quad \mathbb {E} (X_{j}^{n})=\mu .} This is the same scaling as for a single dimensional Gaussian random walk. However, divergence of the variance of X j n {\displaystyle X_{j}^{n}} does not directly provide any information about the corresponding estimates of μ n + 1 {\displaystyle \mu _{n+1}} and σ n + 1 {\displaystyle \sigma _{n+1}} , particularly how different they are from the original μ {\displaystyle \mu } and σ {\displaystyle \sigma } . It turns out to be possible to calculate the distance between the true distribution and the approximated distribution at step n + 1 {\displaystyle n+1} , using the Wasserstein-2 distance (which is also sometimes referred to as risk): E [ W 2 2 ( N ( μ , σ 2 ) , N ( μ n + 1 , σ n + 1 2 ) ) ] = 3 2 σ 2 ( 1 M 0 + 1 M 1 + ⋯ + 1 M n ) + O ( M i − 2 ) , {\displaystyle \mathbb {E} \left[\mathbb {W} _{2}^{2}\left({\mathcal {N}}(\mu ,\sigma ^{2}),{\mathcal {N}}(\mu _{n+1},\sigma _{n+1}^{2})\right)\right]={\frac {3}{2}}\sigma ^{2}\left({\frac {1}{M_{0}}}+{\frac {1}{M_{1}}}+\dots +{\frac {1}{M_{n}}}\right)+{\mathcal {O}}\left(M_{i}^{-2}\right),} Var [ W 2 2 ( N ( μ , σ 2 ) , N ( μ n + 1 , σ n + 1 2 ) ) ] = 1 2 σ 4 ( 3 M 0 2 + 3 M 1 2 + ⋯ + 3 M n 2 + ∑ i ≠ j 4 M i M j ) + O ( M i − 3 ) . {\displaystyle \operatorname {Var} \left[\mathbb {W} _{2}^{2}\left({\mathcal {N}}(\mu ,\sigma ^{2}),{\mathcal {N}}(\mu _{n+1},\sigma _{n+1}^{2})\right)\right]={\frac {1}{2}}\sigma ^{4}\left({\frac {3}{M_{0}^{2}}}+{\frac {3}{M_{1}^{2}}}+\dots +{\frac {3}{M_{n}^{2}}}+\sum _{i\neq j}{\frac {4}{M_{i}M_{j}}}\right)+{\mathcal {O}}\left(M_{i}^{-3}\right).} This directly shows why model collapse occurs in this simple model. Due to errors from re-sampling the approximated distribution, each generation ends up corresponding to a
Halite AI Programming Competition
Halite is an open-source computer programming contest developed by the hedge fund/tech firm Two Sigma in partnership with a team at Cornell Tech. Programmers can see the game environment and learn everything they need to know about the game. Participants are asked to build bots in whichever language they choose to compete on a two-dimensional virtual battle field. == History == Benjamin Spector and Michael Truell created the first Halite competition in 2016, before partnering with Two Sigma later that year. === Halite I === Halite I asked participants to conquer territory on a grid. It launched in November 2016 and ended in February 2017. Halite I attracted about 1,500 players. === Halite II === Halite II was similar to Halite I, but with a space-war theme. It ran from October 2017 until January 2018. The second installment of the competition attracted about 6,000 individual players from more than 100 countries. Among the participants were professors, physicists and NASA engineers, as well as high school and university students. === Halite III === Halite III launched in mid-October 2018. It ran from October 2018 to January 2019, with an ocean themed playing field. Players were asked to collect and manage Halite, an energy resource. By the end of the competition, Halite III included more than 4000 players and 460 organizations. === Halite IV === Halite IV was hosted by Kaggle, and launched in mid-June 2020.
SmartAction
SmartAction Company LLC is a U.S.-based software company that develops artificial intelligence–driven virtual agents for customer service applications, including voice-based interactive voice response (IVR) systems, chat, and SMS. The company was founded in 2009 by inventor and entrepreneur Peter Voss and is headquartered in Fort Worth, Texas. == History == In 2001, Peter Voss founded Adaptive AI, Inc., a research and development company focused on artificial intelligence concepts. In 2009, Voss founded SmartAction Company, LLC to commercialize customer-service automation software derived from this work. The company’s initial products focused on automating inbound and outbound calls for contact center environments. In November 2022, Kyle Johnson was appointed chief executive officer, succeeding Gary Davis, who had served as CEO since 2020. In 2024, SmartAction was acquired by Capacity, an AI-powered customer support automation company based in St. Louis, Missouri. == Technology == SmartAction develops cloud-based voice automation software that integrates speech recognition and natural language processing to support automated customer interactions in contact center environments. The platform supports automated handling of common customer service tasks and is designed to integrate with enterprise systems.