In the context of artificial neural networks, the rectifier or ReLU (rectified linear unit) activation function is an activation function defined as the non-negative part of its argument, i.e., the ramp function: ReLU ( x ) = x + = max ( 0 , x ) = x + | x | 2 = { x if x > 0 , 0 x ≤ 0 {\displaystyle \operatorname {ReLU} (x)=x^{+}=\max(0,x)={\frac {x+|x|}{2}}={\begin{cases}x&{\text{if }}x>0,\\0&x\leq 0\end{cases}}} where x {\displaystyle x} is the input to a neuron. This is analogous to half-wave rectification in electrical engineering. ReLU is one of the most popular activation functions for artificial neural networks, and finds application in computer vision and speech recognition using deep neural nets and computational neuroscience. == History == The ReLU was first used by Alston Householder in 1941 as a mathematical abstraction of biological neural networks. Kunihiko Fukushima in 1969 used ReLU in the context of visual feature extraction in hierarchical neural networks. In 1998, Gregory Woodbury demonstrated that the rectified linear function could account for a broad range of emergent properties in the visual cortex. His work showed that a single unified model could drive the joint development of refined retinotopic maps, ocular dominance columns, and orientation selectivity. By utilizing the rectifier's "cutoff" property, Woodbury achieved a close quantitative fit to biological data, matching the spatial periodicities and topographic refinement patterns observed in macaque and cat cortical maps. Furthermore, he extended this framework to adult plasticity, accurately replicating the spatial and temporal dynamics of lesion-induced cortical reorganization. This research established that the rectified linear response was a necessary mechanism for the stable self-organisation and maintenance of complex, multi-feature neural maps. In 2000, Hahnloser et al. argued that ReLU approximates the biological relationship between neural firing rates and input current, in addition to enabling recurrent neural network dynamics to stabilise under weaker criteria. Prior to 2010, most activation functions used were the logistic sigmoid (which is inspired by probability theory; see logistic regression) and its more numerically efficient counterpart, the hyperbolic tangent. Around 2010, the use of ReLU became common again. Jarrett et al. (2009) noted that rectification by either absolute or ReLU (which they called "positive part") was critical for object recognition in convolutional neural networks (CNNs), specifically because it allows average pooling without neighboring filter outputs cancelling each other out. They hypothesized that the use of sigmoid or tanh was responsible for poor performance in previous CNNs. Nair and Hinton (2010) made a theoretical argument that the softplus activation function should be used, in that the softplus function numerically approximates the sum of an exponential number of linear models that share parameters. They then proposed ReLU as a good approximation to it. Specifically, they began by considering a single binary neuron in a Boltzmann machine that takes x {\displaystyle x} as input, and produces 1 as output with probability σ ( x ) = 1 1 + e − x {\displaystyle \sigma (x)={\frac {1}{1+e^{-x}}}} . They then considered extending its range of output by making infinitely many copies of it X 1 , X 2 , X 3 , … {\displaystyle X_{1},X_{2},X_{3},\dots } , that all take the same input, offset by an amount 0.5 , 1.5 , 2.5 , … {\displaystyle 0.5,1.5,2.5,\dots } , then their outputs are added together as ∑ i = 1 ∞ X i {\displaystyle \sum _{i=1}^{\infty }X_{i}} . They then demonstrated that ∑ i = 1 ∞ X i {\displaystyle \sum _{i=1}^{\infty }X_{i}} is approximately equal to N ( log ( 1 + e x ) , σ ( x ) ) {\displaystyle {\mathcal {N}}(\log(1+e^{x}),\sigma (x))} , which is also approximately equal to ReLU ( N ( x , σ ( x ) ) ) {\displaystyle \operatorname {ReLU} ({\mathcal {N}}(x,\sigma (x)))} , where N {\displaystyle {\mathcal {N}}} stands for the gaussian distribution. They also argued for another reason for using ReLU: that it allows "intensity equivariance" in image recognition. That is, multiplying input image by a constant k {\displaystyle k} multiplies the output also. In contrast, this is false for other activation functions like sigmoid or tanh. They found that ReLU activation allowed good empirical performance in restricted Boltzmann machines. Glorot et al (2011) argued that ReLU has the following advantages over sigmoid or tanh: ReLU is more similar to biological neurons' responses in their main operating regime. ReLU avoids vanishing gradients. ReLU is cheaper to compute. ReLU creates sparse representation naturally, because many hidden units output exactly zero for a given input. They also found empirically that deep networks trained with ReLU can achieve strong performance without unsupervised pre-training, especially on large, purely supervised tasks. In 2017, the rectified linear function became a central component of the transformer architecture introduced in the Vaswani et al paper "Attention Is All You Need". Within every transformer layer, ReLU is utilized in the position-wise feed-forward networks (FFN), defined by Equation 2 of their paper: FFN ( x ) = max ( 0 , x W 1 + b 1 ) W 2 + b 2 {\displaystyle \operatorname {FFN} (x)=\max(0,xW_{1}+b_{1})W_{2}+b_{2}} This equation is foundational to the model's capacity; while the attention mechanism determines the relationships between tokens, the ReLU-based FFN performs the majority of the numerical computation and houses the bulk of the model's parameters. The efficiency and scalability of this rectified framework triggered a global technological revolution, enabling the development of Large Language Models that have had a profound economic impact. The industrial response to this architecture—including the massive expansion of AI-specific hardware and the birth of the generative AI sector—has positioned the Transformer as a cornerstone of 21st-century infrastructure. During the post 2017 period of rapid AI advancement, the rectified linear unit function has been key to achieving increased model performance and scaling due to the fact that it zeros out responses that are immaterial for a given stimuli, preventing them from accumulating in massive scale models. It is the complete silencing of the parts of the model found to be stimuli-irrelevant during learning that allows for scaling. As the stimuli-irrelevant proportion of the model becomes more massive, these highly numerous connections within the model would inevitably accumulate during scaling no matter how small each individual response is. Therefore, the rectified linear unit function, with its absolute zeroing property, enabled the scaling to hundred billion parameter models and beyond. Early Transformer scaling giants like GPT-3 (2020) and Falcon-180B (2023) relied on the rectified linear unit function explicitly, while successors such as GPT-4 (2023) and Llama 3 (2024) utilized smoother variants like GELU or SwiGLU. These variants were used to improve training stability while fundamentally preserving the rectified principle of zeroing low responses. At the centre of modern artificial intelligence ReLU and its variants maintain absolute zero response across the bulk of the model at any one time, while maintaining approximately linear reponses for stimuli-relevant connections enabling high performance on each specific cognitive task. This feature of activation sparsity has been critical for massive scaling and performance gains of AI models right up to the present day. == Advantages == Advantages of ReLU include: Sparse activation: for example, in a randomly initialized network, only about 50% of hidden units are activated (i.e. have a non-zero output). Better gradient propagation: fewer vanishing gradient problems compared to sigmoidal activation functions that saturate in both directions. Efficiency: only requires comparison and addition. Scale-invariant (homogeneous, or "intensity equivariance"): max ( 0 , a x ) = a max ( 0 , x ) for a ≥ 0 {\displaystyle \max(0,ax)=a\max(0,x){\text{ for }}a\geq 0} . == Potential problems == Possible downsides can include: Non-differentiability at zero (however, it is differentiable anywhere else, and the value of the derivative at zero can be chosen to be 0 or 1 arbitrarily). Not zero-centered: ReLU outputs are always non-negative. This can make it harder for the network to learn during backpropagation, because gradient updates tend to push weights in one direction (positive or negative). Batch normalization can help address this. ReLU is unbounded. Redundancy of the parametrization: Because ReLU is scale-invariant, the network computes the exact same function by scaling the weights and biases in front of a ReLU activation by k {\displaystyle k} , and the weights after by 1 / k {\displaystyle 1/k} . Dying ReLU: ReLU neurons can sometimes be pushed into states
Grammar checker
A grammar checker, in computing terms, is a program, or part of a program, that attempts to verify written text for grammatical correctness. Grammar checkers are most often implemented as a feature of a larger program, such as a word processor, but are also available as a stand-alone application that can be activated from within programs that work with editable text. The implementation of a grammar checker makes use of natural language processing. == History == The earliest "grammar checkers" were programs that checked for punctuation and style inconsistencies, rather than a complete range of possible grammatical errors. The first system was called Writer's Workbench, and was a set of writing tools included with Unix systems as far back as the 1970s. The whole Writer's Workbench package included several separate tools to check for various writing problems. The "diction" tool checked for wordy, trite, clichéd or misused phrases in a text. The tool would output a list of questionable phrases and provide suggestions for improving the writing. The "style" tool analyzed the writing style of a given text. It performed a number of readability tests on the text and output the results, and gave some statistical information about the sentences of the text. Aspen Software of Albuquerque, New Mexico released the earliest version of a diction and style checker for personal computers, Grammatik, in 1981. Grammatik was first available for a Radio Shack - TRS-80, and soon had versions for CP/M and the IBM PC. Reference Software International of San Francisco, California, acquired Grammatik in 1985. Development of Grammatik continued, and it became an actual grammar checker that could detect writing errors beyond simple style checking. Other early diction and style checking programs included Punctuation & Style, Correct Grammar, RightWriter and PowerEdit. While all the earliest programs started as simple diction and style checkers, all eventually added various levels of language processing, and developed some level of true grammar checking capability. Until 1992, grammar checkers were sold as add-on programs. There were a large number of different word processing programs available at that time, with WordPerfect and Microsoft Word the top two in market share. In 1992, Microsoft decided to add grammar checking as a feature of Word, and licensed CorrecText, a grammar checker from Houghton Mifflin that had not yet been marketed as a standalone product. WordPerfect answered Microsoft's move by acquiring Reference Software, and the direct descendant of Grammatik is still included with WordPerfect. As of 2019, grammar checkers are built into systems like Google Docs, browser extensions like Grammarly and Qordoba, desktop applications like Ginger, free and open-source software like LanguageTool, and text editor plugins like those available from WebSpellChecker Software. == Technical issues == The earliest writing style programs checked for wordy, trite, clichéd, or misused phrases in a text. This process was based on simple pattern matching. The heart of the program was a list of many hundreds or thousands of phrases that are considered poor writing by many experts. The list of questionable phrases included alternative wording for each phrase. The checking program would simply break text into sentences, check for any matches in the phrase dictionary, flag suspect phrases and show an alternative. These programs could also perform some mechanical checks. For example, they would typically flag doubled words, doubled punctuation, some capitalization errors, and other simple mechanical mistakes. True grammar checking is more complex. While a programming language has a very specific syntax and grammar, this is not so for natural languages. One can write a somewhat complete formal grammar for a natural language, but there are usually so many exceptions in real usage that a formal grammar is of minimal help in writing a grammar checker. One of the most important parts of a natural language grammar checker is a dictionary of all the words in the language, along with the part of speech of each word. The fact that a natural word may be used as any one of several parts of speech (such as "free" being used as an adjective, adverb, noun, or verb) greatly increases the complexity of any grammar checker. A grammar checker will find each sentence in a text, look up each word in the dictionary, and then attempt to parse the sentence into a form that matches a grammar. Using various rules, the program can then detect various errors, such as agreement in tense, number, word order, and so on. It is also possible to detect some stylistic problems with the text. For example, some popular style guides such as The Elements of Style deprecate excessive use of the passive voice. Grammar checkers may attempt to identify passive sentences and suggest an active-voice alternative. The software elements required for grammar checking are closely related to some of the development issues that need to be addressed for speech recognition software. In voice recognition, parsing can be used to help predict which word is most likely intended, based on part of speech and position in the sentence. In grammar checking, the parsing is used to detect words that fail to follow accepted grammar usage. Recently, research has focused on developing algorithms which can recognize grammar errors based on the context of the surrounding words. == Criticism == Grammar checkers are considered a type of foreign language writing aid which non-native speakers can use to proofread their writings as such programs endeavor to identify syntactical errors. However, as with other computerized writing aids such as spell checkers, popular grammar checkers are often criticized when they fail to spot errors and incorrectly flag correct text as erroneous. The linguist Geoffrey K. Pullum argued in 2007 that they were generally so inaccurate as to do more harm than good: "for the most part, accepting the advice of a computer grammar checker on your prose will make it much worse, sometimes hilariously incoherent."
Airfair
AirFair was a mobile travel application that checks flights, and shows whether a traveler is owed compensation. == History == AirFair was developed in 2016 by Allay Logic Ltd; a Newcastle-based tech-company. == Services == AirFair offered a free flight check to see if compensation is owed. The app could indicate how much the person is owed within minutes whether the flight was delayed, cancelled or the traveler is refused boarding.
ChatGPT
ChatGPT is a generative artificial intelligence chatbot developed by OpenAI. Originally released in November 2022, the product uses large language models—specifically generative pre-trained transformers (GPTs)—to generate text, speech, and images in response to user prompts. ChatGPT accelerated the AI boom, an ongoing period marked by rapid investment and public attention toward the field of artificial intelligence (AI). OpenAI operates the service on a freemium model. Users can interact with ChatGPT through text, audio, and image prompts. ChatGPT was quickly adopted, reaching 100 million monthly active users two months after its release and 900 million weekly active users in February 2026. It has been lauded for its potential to transform numerous professional fields, and has instigated public debate about the nature of creativity and the future of knowledge work. The chatbot has also been criticized for its limitations and potential for unethical use. It can generate plausible-sounding but incorrect or nonsensical answers, known as hallucinations. Biases in its training data have been reflected in its responses. The chatbot can facilitate academic dishonesty, generate misinformation, and create malicious code. The ethics of its development, particularly the use of copyrighted content as training data, have also drawn controversy. == Features == ChatGPT is a chatbot and AI assistant built on large language model (LLM) technology. It is designed to generate human-like text and can carry out a wide variety of tasks. These include, among many others, writing and debugging computer programs, composing music, scripts, fairy tales, and essays, answering questions (sometimes at a level exceeding that of an average human test-taker), and generating business concepts. ChatGPT is frequently used for translation and summarization tasks, and can simulate interactive environments such as a Linux terminal, a multi-user chat room, or simple text-based games such as tic-tac-toe. Users interact with ChatGPT through conversations which consist of text, audio, and image inputs and outputs. The user's inputs to these conversations are referred to as prompts. An optional "Memory" feature allows users to tell ChatGPT to memorize specific information. Another option allows ChatGPT to recall old conversations. GPT-based moderation classifiers are used to reduce the risk of harmful outputs being presented to users. In March 2023, OpenAI added support for plugins for ChatGPT. This includes both plugins made by OpenAI, such as web browsing and code interpretation, and external plugins from developers such as Expedia, OpenTable, and Zapier. From October to December 2024, ChatGPT Search was deployed. It allows ChatGPT to search the web in an attempt to make more accurate and up-to-date responses. It increased OpenAI's direct competition with major search engines. OpenAI allows businesses to tailor how their content appears in the ChatGPT Search results and influence what sources are used. In December 2024, OpenAI launched a new feature allowing users to call ChatGPT with a telephone for up to 15 minutes per month for free. In September 2025, OpenAI added a feature called Pulse, which generates a daily analysis of a user's chats and connected apps such as Gmail and Google Calendar. In October 2025, OpenAI launched ChatGPT Atlas, a browser integrating the ChatGPT assistant directly into web navigation, to compete with existing browsers such as Google Chrome. It has an additional feature called "agentic mode" that allows it to take online actions for the user. === Paid tier === ChatGPT was initially free to the public and remains free in a limited capacity. In February 2023, OpenAI launched a premium service, ChatGPT Plus, that costs US$20 per month. What was offered on the paid plan versus the free tier changed as OpenAI has continued to update ChatGPT, and a Pro tier at $200/mo was introduced in December 2024. The Pro launch coincided with the release of the o1 model. In August 2025, ChatGPT Go was offered in India for ₹399 per month. The plan has higher limits than the free version. === Mobile apps === In May-July 2023, OpenAI began offering ChatGPT iOS and Android apps. ChatGPT can also power Android's assistant. An app for Windows launched on the Microsoft Store on October 15, 2024. === Languages === OpenAI met Icelandic President Guðni Th. Jóhannesson in 2022. In 2023, OpenAI worked with a team of 40 Icelandic volunteers to fine-tune ChatGPT's Icelandic conversation skills as a part of Iceland's attempts to preserve the Icelandic language. ChatGPT (based on GPT-4) was better able to translate Japanese to English when compared to Bing, Bard, and DeepL Translator in 2023. In December 2023, the Albanian government decided to use ChatGPT for the rapid translation of European Union documents and the analysis of required changes needed for Albania's accession to the EU. Several studies have shown that ChatGPT can outperform Google Translate in some mainstream translation tasks. However, as of 2024, no machine translation services match human expert performance. In August 2024, a representative of the Asia Pacific wing of OpenAI made a visit to Taiwan, during which a demonstration of ChatGPT's Chinese abilities was made. ChatGPT's Mandarin Chinese abilities were lauded, but the ability of the AI to produce content in Mandarin Chinese in a Taiwanese accent was found to be "less than ideal" due to differences between mainland Mandarin Chinese and Taiwanese Mandarin. === GPT Store === In November 2023, OpenAI released GPT Builder, a tool allowing users to customize ChatGPT's behavior for a specific use case. The customized systems are referred to as GPTs. In January 2024, OpenAI launched the GPT Store, a marketplace for GPTs. At launch, OpenAI included more than 3 million GPTs created by GPT Builder users in the GPT Store. === ChatGPT Apps === In September 2025, OpenAI added support for Model Context Protocol (MCP) to ChatGPT apps. When enabled in developer mode, this allows for improved third-party access to ChatGPT tools and servers. === Deep Research === In February 2025, OpenAI released Deep Research, a feature that generates reports based on extensive web searches. It was initially based on the reasoning model o3 and took 5 to 30 minutes per report. === Images === In October 2023, OpenAI's image generation model DALL-E 3 was integrated into ChatGPT. The integration used ChatGPT to write prompts for DALL-E guided by conversations with users. In March 2025, OpenAI updated ChatGPT to generate images using GPT Image instead of DALL-E. One of the most significant improvements was in the generation of text within images, which is especially useful for branded content. However, this ability is noticeably worse in non-Latin alphabets. The model can also generate new images based on existing ones provided in the prompt. These images are generated with C2PA metadata, which can be used to verify that they are AI-generated. OpenAI has emplaced additional safeguards to prevent what the company deems to be harmful image generation. === Agents === In 2025, OpenAI added several features to make ChatGPT more agentic (capable of autonomously performing longer tasks). In January, Operator was released. It was capable of autonomously performing tasks through web browser interactions, including filling forms, placing online orders, scheduling appointments, and other browser-based tasks. It was controlling a software environment inside a virtual machine with limited internet connectivity and with safety restrictions. It struggled with complex user interfaces. In May 2025, OpenAI introduced an agent for coding named Codex. It is capable of writing software, answering codebase questions, running tests, and proposing pull requests. It is based on a fine-tuned version of OpenAI o3. It has two versions, one running in a virtual machine in the cloud, and one where the agent runs in the cloud, but performs actions on a local machine connected via API. In July 2025, OpenAI released ChatGPT agent, an AI agent that can perform multi-step tasks. Like Operator, it controls a virtual computer. It also inherits from Deep Research's ability to gather and summarize significant volumes of information. The user can interrupt tasks or provide additional instructions as needed. In September 2025, OpenAI partnered with Stripe, Inc. to release Agentic Commerce Protocol, enabling purchases through ChatGPT. At launch, the feature was limited to purchases on Etsy from US users with a payment method linked to their OpenAI account. OpenAI takes an undisclosed cut from the merchant's payment. === ChatGPT Health === On January 7, 2026, OpenAI introduced a feature called "ChatGPT Health", whereby ChatGPT can discuss the user's health in a way that is separate from other chats. The feature is not available for users in the United Kingdom, Switzerland, or the European Economic Area, and is available on a waitli
Legendre moment
In mathematics, Legendre moments are a type of image moment and are achieved by using the Legendre polynomial. Legendre moments are used in areas of image processing including: pattern and object recognition, image indexing, line fitting, feature extraction, edge detection, and texture analysis. Legendre moments have been studied as a means to reduce image moment calculation complexity by limiting the amount of information redundancy through approximation. == Legendre moments == Source: With order of m + n, and object intensity function f(x,y): L m n = ( 2 m + 1 ) ( 2 n + 1 ) 4 ∫ − 1 1 ∫ − 1 1 P m ( x ) P n ( y ) f ( x , y ) d x d y {\displaystyle L_{mn}={\frac {(2m+1)(2n+1)}{4}}\int \limits _{-1}^{1}\int \limits _{-1}^{1}P_{m}(x)P_{n}(y)f(x,y)\,dx\,dy} where m,n = 1, 2, 3, ...∞ with the nth-order Legendre polynomials being: P n ( x ) = ∑ k = 0 n a k , n x k = ( − 1 ) n 2 n n ! ( d d x ) [ ( 1 − x 2 ) n ] {\displaystyle P_{n}(x)=\sum _{k=0}^{n}a_{k,n}x^{k}={\frac {(-1)^{n}}{2^{n}n!}}\left({\frac {d}{dx}}\right)[(1-x^{2})^{n}]} which can also be written: P n ( x ) = ∑ k = 0 D ( n ) ( − 1 ) k ( 2 n − 2 k ) ! 2 n k ! ( n − k ) ! ( n − 2 k ) ! x n − 2 k = ( 2 n ) ! 2 n ( n ! ) 2 x n − ( 2 n − 2 ) ! 2 n 1 ! ( n − 1 ) ! ( n − 2 ) ! x n − 2 + ⋯ {\displaystyle {\begin{aligned}P_{n}(x)&=\sum _{k=0}^{D(n)}(-1)^{k}{\frac {(2n-2k)!}{2^{n}k!(n-k)!(n-2k)!}}x^{n-2k}\\[5pt]&={\frac {(2n)!}{2^{n}(n!)^{2}}}x^{n}-{\frac {(2n-2)!}{2^{n}1!(n-1)!(n-2)!}}x^{n-2}+\cdots \end{aligned}}} where D(n) = floor(n/2). The set of Legendre polynomials {Pn(x)} form an orthogonal set on the interval [−1,1]: ∫ − 1 1 P n ( x ) P m ( x ) d x = 2 2 n + 1 δ n m {\displaystyle \int _{-1}^{1}P_{n}(x)P_{m}(x)\,dx={\frac {2}{2n+1}}\delta _{nm}} A recurrence relation can be used to compute the Legendre polynomial: ( n + 1 ) P n + 1 ( x ) − ( 2 n + 1 ) x P n ( x ) + n P n − 1 ( x ) = 0 {\displaystyle (n+1)P_{n+1}(x)-(2n+1)xP_{n}(x)+nP_{n-1}(x)=0} f(x,y) can be written as an infinite series expansion in terms of Legendre polynomials [−1 ≤ x,y ≤ 1.]: f ( x , y ) = ∑ m = 0 ∞ ∑ n = 0 ∞ λ m n P m ( x ) P n ( y ) {\displaystyle f(x,y)=\sum _{m=0}^{\infty }\sum _{n=0}^{\infty }\lambda _{mn}P_{m}(x)P_{n}(y)}
Color reproduction
Color reproduction is an aspect of color science concerned with producing light spectra that evoke a desired color, either through additive (light emitting) or subtractive (surface color) models. It converts physical correlates of color perception (CIE 1931 XYZ color space tristimulus values and related quantities) into light spectra that can be experienced by observers. In this way, it is the opposite of colorimetry. It is concerned with the faithful reproduction of a color in one medium, with a color in another, so it is a central concept in color management and relies heavily on color calibration. For example, food packaging must be able to faithfully reproduce the colors of the foods therein in order to appeal to a customer. This involves proper color calibration of at least four devices: Lighting, which must have a high color rendering index and not give a color cast to the object. Camera, which measures the reflected spectrum of the object and converts to a trichromatic color space (e.g. RGB). Screen, which reproduces color so a designer can proof the captured image and make color corrections as necessary. Printer, which reproduces the final color on paper.
Chinchilla (language model)
Chinchilla is a family of large language models (LLMs) developed by the research team at Google DeepMind, presented in March 2022. == Models == It is named "chinchilla" because it is a further development over a previous model family named Gopher. Both model families were trained in order to investigate the scaling laws of large language models. It claimed to outperform GPT-3. It considerably simplifies downstream utilization because it requires much less computer power for inference and fine-tuning. Based on the training of previously employed language models, it has been determined that if one doubles the model size, one must also have twice the number of training tokens. This hypothesis has been used to train Chinchilla by DeepMind. Similar to Gopher in terms of cost, Chinchilla has 70B parameters and four times as much data. Chinchilla has an average accuracy of 67.5% on the Measuring Massive Multitask Language Understanding (MMLU) benchmark, which is 7% higher than Gopher's performance. Chinchilla was still in the testing phase as of January 12, 2023. Chinchilla contributes to developing an effective training paradigm for large autoregressive language models with limited compute resources. The Chinchilla team recommends that the number of training tokens is twice for every model size doubling, meaning that using larger, higher-quality training datasets can lead to better results on downstream tasks. It has been used for the Flamingo vision-language model. == Architecture == Both the Gopher family and Chinchilla family are families of transformer models. In particular, they are essentially the same as GPT-2, with different sizes and minor modifications. Gopher family uses RMSNorm instead of LayerNorm; relative positional encoding rather than absolute positional encoding. The Chinchilla family is the same as the Gopher family, but trained with AdamW instead of Adam optimizer. The Gopher family contains six models of increasing size, from 44 million parameters to 280 billion parameters. They refer to the largest one as "Gopher" by default. Similar naming conventions apply for the Chinchilla family. Table 1 of shows the entire Gopher family: Table 4 of compares the 70-billion-parameter Chinchilla with Gopher 280B.