Too Good To Go is a service with a mobile application that connects customers to restaurants and stores that have surplus unsold food. The service covers major European cities, and in October 2020 started operations in North America. As part of the initiatives taken on the International Day of Awareness of Food Loss and Waste to reduce food loss and waste, the app is suggested alongside OLIO among many others. In 2023 Too Good To Go was the fastest-growing sustainable food app startup by number of downloads. As of August 2023, it claimed 164,000 businesses, serving 62 million users, have saved 155 million bags of food. As of March 2023, it claimed to have saved over 200 million meals. == History == The company was created in 2015 in Denmark by Thomas Bjørn Momsen, Klaus Bagge Pedersen, Adam Sigbrand and Brian Christensen. In 2017, Mette Lykke (co-founder of Endomondo) joined as CEO. In February 2019, the company raised an additional 6 million euros in a new round of investment. In August 2019, Too Good To Go was re-launched in Austria. In September 2019, Too Good To Go acquired the Spanish startup weSAVEeat and merged it into its own brand. In November 2019, the offer of Too Good To Go extended to plants through a partnership with the French retail plants company Jardiland. In December 2019, Too Good To Go partnered with the French grocery retail stores Intermarché, and donated 60K euros to the French charity Restaurants du Cœur. In October 2021, Bonnie Wright teamed up with Too Good To Go to drive the initiative to reduce food waste. == Corporate affairs == The key trends for the Danish entity Too Good To Go ApS are (as of the financial year ending December 31): == International expansion == As of March 2026 the company serves the European countries Austria, Belgium, Czechia, Denmark, the Faroe Islands, France, Germany, Ireland, Italy, the Netherlands, Norway, Poland, Portugal, Spain, Sweden, Switzerland, the United Kingdom. Outside of Europe the service is available in Australia, Canada, Japan, New Zealand and the United States. == Purpose == The purpose of Too Good To Go is to reduce food waste worldwide. It developed a mobile application that connects restaurants and stores that have unsold, surplus food, with customers who can then buy whatever food the outlet considers surplus to requirements—without being able to choose—at a much lower price than normal. The food on the app is priced at one-third its original price. The company claims this reduces the waste of food that would otherwise be discarded; food waste is a global problem that affects the environment. In three years active, the app reached more than 9.5 million users. As of 2022, more than 57.7 million users and 154,000 establishments have signed up, and 139 million meals have been collected. In 2019, the company had 350 employees in Europe. As of June 2023 the company was estimated to have 1,289 employees. == Use == Food outlets must notify the TGTG company about what they have available on each day, stating what sort of food they have (baked foods, meals, produce, vegan food), and the price for a 'surprise bag', whose contents they determine; the user cannot choose, but the original prices will be three or more times the TGTG price. Notification is made early based upon the quantity predicted to be left over, not at the end of a selling period. Users must register to use the service. A mobile phone with an Internet connection running Android or iOS is needed. The user runs the TGTG app, which lists outlets available within a chosen distance and time range. The customer can then order and pay for a 'surprise bag'. The supplier can cancel an order at any time if the expected surplus is not available—the purchaser is notified by text message—and the purchaser can cancel with two hours' notice. The phone must be taken to the food supplier in a specified pickup time window, often 30 or 60 minutes long, and the transaction is finalised by swiping the app—connected to the Internet—to confirm collection.
Imieliński–Lipski algebra
In database theory, Imieliński–Lipski algebra is an extension of relational algebra onto tables with different types of null values. It is used to operate on relations with incomplete information. Imieliński–Lipski algebras are defined to satisfy precise conditions for semantically meaningful extension of the usual relational operators, such as projection, selection, union, and join, from operators on relations to operators on relations with various kinds of "null values". These conditions require that the system be safe in the sense that no incorrect conclusion is derivable by using a specified subset F of the relational operators; and that it be complete in the sense that all valid conclusions expressible by relational expressions using operators in F are in fact derivable in this system. For example, it is well known that the three-valued logic approach to deal with null values, supported treatment of nulls values by SQL is not complete, see Ullman book. To show this, let T be: Take SQL query Q SQL query Q will return empty set (no results) under 3-valued semantics currently adopted by all variants of SQL. This is the case because in SQL, NULL is never equal to any constant – in this case, neither to “Spring” nor “Fall” nor “Winter” (if there is Winter semester in this school). NULL='Spring' will evaluate to MAYBE and so will NULL='Fall'. The disjunction MAYBE OR MAYBE evaluates to MAYBE (not TRUE). Thus Igor will not be part of the answer (and of course neither will Rohit). But Igor should be returned as the answer. Indeed, regardless what semester Igor took the Networks class (no matter what was the unknown value of NULL), the selection condition will be true. This “Igor” will be missed by SQL and the SQL answer would be incomplete according to completeness requirements specified in Tomasz Imieliński, Witold Lipski, 'Incomplete Information in Relational Databases'. It is also argued there that 3-valued logic (TRUE, FALSE, MAYBE) can never provide guarantee of complete answer for tables with incomplete information. Three algebras which satisfy conditions of safety and completeness are defined as Imielinski–Lipski algebras: the Codd-Tables algebra, the V-tables algebra and the Conditional tables (C-tables) algebra. == Codd-tables algebra == Codd-tables algebra is based on the usual Codd's single NULL values. The table T above is an example of Codd-table. Codd-table algebra supports projection and positive selections only. It is also demonstrated in [IL84 that it is not possible to correctly extend more relational operators over Codd-Tables. For example, such basic operation as join is not extendable over Codd-tables. It is not possible to define selections with Boolean conditions involving negation and preserve completeness. For example, queries like the above query Q cannot be supported. In order to be able to extend more relational operators, more expressive form of null value representation is needed in tables which are called V-table. == V-tables algebra == V-tables algebra is based on many different ("marked") null values or variables allowed to appear in a table. V-tables allow to show that a value may be unknown but the same for different tuples. For example, in the table below Gaurav and Igor order the same (but unknown) beer in two unknown bars (which may, or may not be different – but remain unknown). Gaurav and Jane frequent the same unknown bar (Y1). Thus, instead one NULL value, we use indexed variables, or Skolem constants . V-tables algebra is shown to correctly support projection, positive selection (with no negation occurring in the selection condition), union, and renaming of attributes, which allows for processing arbitrary conjunctive queries. A very desirable property enjoyed by the V-table algebra is that all relational operators on tables are performed in exactly the same way as in the case of the usual relations. === Conditional tables (c-tables) algebra === Example of conditional table (c-table) is shown below. It has additional column “con” which is a Boolean condition involving variables, null values – same as in V-tables. over the following table c-table Conditional tables algebra, mainly of theoretical interest, supports projection, selection, union, join, and renaming. Under closed-world assumption, it can also handle the operator of difference, thus it can support all relational operators. == History == Imieliński–Lipski algebras were introduced by Tomasz Imieliński and Witold Lipski Jr. in Incomplete Information in Relational Databases.
Topological deep learning
Topological deep learning (TDL) is a research field that extends deep learning to handle complex, non-Euclidean data structures. Traditional deep learning models, such as convolutional neural networks (CNNs) and recurrent neural networks (RNNs), excel in processing data on regular grids and sequences. However, scientific and real-world data often exhibit more intricate data domains encountered in scientific computations, including point clouds, meshes, time series, scalar fields graphs, or general topological spaces like simplicial complexes and CW complexes. TDL addresses this by incorporating topological concepts to process data with higher-order relationships, such as interactions among multiple entities and complex hierarchies. This approach leverages structures like simplicial complexes and hypergraphs to capture global dependencies and qualitative spatial properties, offering a more nuanced representation of data. TDL also encompasses methods from computational and algebraic topology that permit studying properties of neural networks and their training process, such as their predictive performance or generalization properties. The mathematical foundations of TDL are algebraic topology, differential topology, and geometric topology. Therefore, TDL can be generalized for data on differentiable manifolds, knots, links, tangles, curves, etc. == History and motivation == Traditional techniques from deep learning often operate under the assumption that a dataset is residing in a highly-structured space (like images, where convolutional neural networks exhibit outstanding performance over alternative methods) or a Euclidean space. The prevalence of new types of data, in particular graphs, meshes, and molecules, resulted in the development of new techniques, culminating in the field of geometric deep learning, which originally proposed a signal-processing perspective for treating such data types. While originally confined to graphs, where connectivity is defined based on nodes and edges, follow-up work extended concepts to a larger variety of data types, including simplicial complexes and CW complexes, with recent work proposing a unified perspective of message-passing on general combinatorial complexes. An independent perspective on different types of data originated from topological data analysis, which proposed a new framework for describing structural information of data, i.e., their "shape," that is inherently aware of multiple scales in data, ranging from local information to global information. While at first restricted to smaller datasets, subsequent work developed new descriptors that efficiently summarized topological information of datasets to make them available for traditional machine-learning techniques, such as support vector machines or random forests. Such descriptors ranged from new techniques for feature engineering over new ways of providing suitable coordinates for topological descriptors, or the creation of more efficient dissimilarity measures. Contemporary research in this field is largely concerned with either integrating information about the underlying data topology into existing deep-learning models or obtaining novel ways of training on topological domains. == Learning on topological spaces == One of the core concepts in topological deep learning is considering the domain upon which this data is defined and supported. In case of Euclidean data, such as images, this domain is a grid, upon which the pixel value of the image is supported. In a more general setting this domain might be a topological domain. Studying and developing deep learning models that are supported ln topological domains constitute the essence of topological deep learning. Next, we introduce the most common topological domains that are encountered in a deep learning setting. These domains include, but not limited to, graphs, simplicial complexes, cell complexes, combinatorial complexes and hypergraphs. Given a finite set S of abstract entities, a neighborhood function N {\displaystyle {\mathcal {N}}} on S is an assignment that attach to every point x {\displaystyle x} in S a subset of S or a relation. Such a function can be induced by equipping S with an auxiliary structure. Edges provide one way of defining relations among the entities of S. More specifically, edges in a graph allow one to define the notion of neighborhood using, for instance, the one hop neighborhood notion. Edges however, limited in their modeling capacity as they can only be used to model binary relations among entities of S since every edge is connected typically to two entities. In many applications, it is desirable to permit relations that incorporate more than two entities. The idea of using relations that involve more than two entities is central to topological domains. Such higher-order relations allow for a broader range of neighborhood functions to be defined on S to capture multi-way interactions among entities of S. Next we review the main properties, advantages, and disadvantages of some commonly studied topological domains in the context of deep learning, including (abstract) simplicial complexes, regular cell complexes, hypergraphs, and combinatorial complexes. ==== Comparisons among topological domains ==== Each of the enumerated topological domains has its own characteristics, advantages, and limitations: Simplicial complexes Simplest form of higher-order domains. Extensions of graph-based models. Admit hierarchical structures, making them suitable for various applications. Hodge theory can be naturally defined on simplicial complexes. Require relations to be subsets of larger relations, imposing constraints on the structure. Cell Complexes Generalize simplicial complexes. Provide more flexibility in defining higher-order relations. Each cell in a cell complex is homeomorphic to an open ball, attached together via attaching maps. Boundary cells of each cell in a cell complex are also cells in the complex. Represented combinatorially via incidence matrices. Hypergraphs Allow arbitrary set-type relations among entities. Relations are not imposed by other relations, providing more flexibility. Do not explicitly encode the dimension of cells or relations. Useful when relations in the data do not adhere to constraints imposed by other models like simplicial and cell complexes. Combinatorial Complexes : Generalize and bridge the gaps between simplicial complexes, cell complexes, and hypergraphs. Allow for hierarchical structures and set-type relations. Combine features of other complexes while providing more flexibility in modeling relations. Can be represented combinatorially, similar to cell complexes. ==== Hierarchical structure and set-type relations ==== The properties of simplicial complexes, cell complexes, and hypergraphs give rise to two main features of relations on higher-order domains, namely hierarchies of relations and set-type relations. ===== Rank function ===== A rank function on a higher-order domain X is an order-preserving function rk: X → Z, where rk(x) attaches a non-negative integer value to each relation x in X, preserving set inclusion in X. Cell and simplicial complexes are common examples of higher-order domains equipped with rank functions and therefore with hierarchies of relations. ===== Set-type relations ===== Relations in a higher-order domain are called set-type relations if the existence of a relation is not implied by another relation in the domain. Hypergraphs constitute examples of higher-order domains equipped with set-type relations. Given the modeling limitations of simplicial complexes, cell complexes, and hypergraphs, we develop the combinatorial complex, a higher-order domain that features both hierarchies of relations and set-type relations. The learning tasks in TDL can be broadly classified into three categories: Cell classification: Predict targets for each cell in a complex. Examples include triangular mesh segmentation, where the task is to predict the class of each face or edge in a given mesh. Complex classification: Predict targets for an entire complex. For example, predict the class of each input mesh. Cell prediction: Predict properties of cell-cell interactions in a complex, and in some cases, predict whether a cell exists in the complex. An example is the prediction of linkages among entities in hyperedges of a hypergraph. In practice, to perform the aforementioned tasks, deep learning models designed for specific topological spaces must be constructed and implemented. These models, known as topological neural networks, are tailored to operate effectively within these spaces. === Topological neural networks === Central to TDL are topological neural networks (TNNs), specialized architectures designed to operate on data structured in topological domains. Unlike traditional neural networks tailored for grid-like structures, TNNs are adept at handling more intricate data representations, such as graphs
Natural language processing
Natural language processing (NLP) is the processing of natural language information by a computer. NLP is a subfield of computer science and is closely associated with artificial intelligence. NLP is also related to information retrieval, knowledge representation, computational linguistics, and linguistics more broadly. Major processing tasks in an NLP system include: speech recognition, text classification, natural language understanding, and natural language generation. == History == Natural language processing has its roots in the 1950s. Already in 1950, Alan Turing published an article titled "Computing Machinery and Intelligence," which proposed what is now called the Turing test as a criterion of intelligence, though at the time that was not articulated as a problem separate from artificial intelligence. The proposed test includes a task that involves the automated interpretation and generation of natural language. === Symbolic NLP (1950s – early 1990s) === The premise of symbolic NLP is often illustrated using John Searle's Chinese room thought experiment: Given a collection of rules (e.g., a Chinese phrasebook, with questions and matching answers), the computer emulates natural language understanding (or other NLP tasks) by applying those rules to the data it confronts. 1950s: The Georgetown experiment in 1954 involved fully automatic translation of more than sixty Russian sentences into English. The authors claimed that within three or five years, machine translation would be a solved problem. However, real progress was much slower, and after the ALPAC report in 1966, which found that ten years of research had failed to fulfill the expectations, funding for machine translation was dramatically reduced. Little further research in machine translation was conducted in America (though some research continued elsewhere, such as Japan and Europe) until the late 1980s when the first statistical machine translation systems were developed. 1960s: Some notably successful natural language processing systems developed in the 1960s were SHRDLU, a natural language system working in restricted "blocks worlds" with restricted vocabularies, and ELIZA, a simulation of Rogerian psychotherapy, written by Joseph Weizenbaum between 1964 and 1966. Despite using minimal information about human thought or emotion, ELIZA was able to produce interactions that appeared human-like. When the "patient" exceeded the very small knowledge base, ELIZA might provide a generic response, for example, responding to "My head hurts" with "Why do you say your head hurts?". Ross Quillian's successful work on natural language was demonstrated with a vocabulary of only twenty words, because that was all that would fit in a computer memory at the time. 1970s: During the 1970s, many programmers began to write "conceptual ontologies", which structured real-world information into computer-understandable data. Examples are MARGIE (Schank, 1975), SAM (Cullingford, 1978), PAM (Wilensky, 1978), TaleSpin (Meehan, 1976), QUALM (Lehnert, 1977), Politics (Carbonell, 1979), and Plot Units (Lehnert 1981). During this time, the first chatterbots were written (e.g., PARRY). 1980s: The 1980s and early 1990s mark the heyday of symbolic methods in NLP. Focus areas of the time included research on rule-based parsing (e.g., the development of HPSG as a computational operationalization of generative grammar), morphology (e.g., two-level morphology), semantics (e.g., Lesk algorithm), reference (e.g., within Centering Theory) and other areas of natural language understanding (e.g., in the Rhetorical Structure Theory). Other lines of research were continued, e.g., the development of chatterbots with Racter and Jabberwacky. An important development (that eventually led to the statistical turn in the 1990s) was the rising importance of quantitative evaluation in this period. === Statistical NLP (1990s–present) === Up until the 1980s, most natural language processing systems were based on complex sets of hand-written rules. Starting in the late 1980s, however, there was a revolution in natural language processing with the introduction of machine learning algorithms for language processing. This shift was influenced by increasing computational power (see Moore's law) and a decline in the dominance of Chomskyan linguistic theories (e.g. transformational grammar), whose theoretical underpinnings discouraged the sort of corpus linguistics that underlies the machine-learning approach to language processing. 1990s: Many of the notable early successes in statistical methods in NLP occurred in the field of machine translation, due especially to work at IBM Research, such as IBM alignment models. These systems were able to take advantage of existing multilingual textual corpora that had been produced by the Parliament of Canada and the European Union as a result of laws calling for the translation of all governmental proceedings into all official languages of the corresponding systems of government. However, many systems relied on corpora that were specifically developed for the tasks they were designed to perform. This reliance has been a major limitation to their broader effectiveness and continues to affect similar systems. Consequently, significant research has focused on methods for learning effectively from limited amounts of data. 2000s: With the growth of the web, increasing amounts of raw (unannotated) language data have become available since the mid-1990s. Research has thus increasingly focused on unsupervised and semi-supervised learning algorithms. Such algorithms can learn from data that has not been hand-annotated with the desired answers or using a combination of annotated and non-annotated data. Generally, this task is much more difficult than supervised learning, and typically produces less accurate results for a given amount of input data. However, large quantities of non-annotated data are available (including, among other things, the entire content of the World Wide Web), which can often make up for the worse efficiency if the algorithm used has a low enough time complexity to be practical. 2003: word n-gram model, at the time the best statistical algorithm, is outperformed by a multi-layer perceptron (with a single hidden layer and context length of several words, trained on up to 14 million words, by Bengio et al.) 2010: Tomáš Mikolov (then a PhD student at Brno University of Technology) with co-authors applied a simple recurrent neural network with a single hidden layer to language modeling, and in the following years he went on to develop Word2vec. In the 2010s, representation learning and deep neural network-style (featuring many hidden layers) machine learning methods became widespread in natural language processing. This shift gained momentum due to results showing that such techniques can achieve state-of-the-art results in many natural language tasks, e.g., in language modeling and parsing. This is increasingly important in medicine and healthcare, where NLP helps analyze notes and text in electronic health records that would otherwise be inaccessible for study when seeking to improve care or protect patient privacy. == Approaches: Symbolic, statistical, neural networks == Symbolic approach, i.e., the hand-coding of a set of rules for manipulating symbols, coupled with a dictionary lookup, was historically the first approach used both by AI in general and by NLP in particular: such as by writing grammars or devising heuristic rules for stemming. Machine learning approaches, which include both statistical and neural networks, on the other hand, have many advantages over the symbolic approach: both statistical and neural network methods tend to focus more on the most common cases extracted from a corpus of texts, whereas the rule-based approach needs to provide rules for both rare and common cases equally. language models, produced by either statistical or neural networks methods, are more robust to both unfamiliar (e.g. containing words or structures that have not been seen before) and erroneous input (e.g. with misspelled words or words accidentally omitted) in comparison to the rule-based systems, which are also more costly to produce. the larger such a (probabilistic) language model is, the more accurate it becomes, in contrast to rule-based systems that can gain accuracy only by increasing the amount and complexity of the rules leading to intractability problems. Rule-based systems are commonly used: when the amount of training data is insufficient to successfully apply machine learning methods, e.g., for the machine translation of low-resource languages such as provided by the Apertium system, for preprocessing in NLP pipelines, e.g., tokenization, or for post-processing and transforming the output of NLP pipelines, e.g., for knowledge extraction from syntactic parses. === Statistical approach === In the late 1980s and mid-1990s, the statistical approach ended a peri
Contextual AI
Contextual AI is an enterprise software company based in Mountain View, California. It develops a platform for building specialized Retrieval-Augmented Generation (RAG) agents for enterprise use. The company was founded in 2023 by Douwe Kiela and Amanpreet Singh, both former AI researchers at Facebook AI Research (FAIR) and Hugging Face. Douwe Kiela previously led the Meta research team that introduced the Retrieval-Augmented Generation (RAG) approach in 2020. Contextual AI focuses on enterprise generative AI applications using RAG 2.0 technology, with deployments primarily in the technology, banking, finance and media sectors. == History == In June 2023, Contextual AI announced it had raised $20 million in a seed funding round led by Bain Capital Ventures (BCV), with participation from Lightspeed Venture Partners, Greycroft, SV Angel, and several angel investors. In August 2024, the company raised $80 million in a Series A funding round led by Greycroft, with participation from previous investors including Bain Capital Ventures, Lightspeed, and Conviction Partners. The round also included new backers such as Bezos Expeditions, NVentures (Nvidia), HSBC Ventures, and Snowflake Ventures. == Features == Retrieval-Augmented Generation (RAG) is an artificial intelligence framework that integrates information retrieval with text generation to improve the performance of large language models (LLMs) on complex, knowledge-intensive tasks. It was introduced in 2020 by researchers at Meta AI, including Douwe Kiela, Patrick Lewis and others, in their paper Retrieval-Augmented Generation for Knowledge-Intensive NLP Tasks. RAG enables language models to access and incorporate external information, such as proprietary databases or real-time web content, at query time, instead of relying solely on pre-trained, internal, static knowledge. This architecture addresses common limitations of standard LLMs, including hallucination, outdated information, and lack of attribution to source materials. RAG systems retrieve relevant context through a variety of techniques - including vector search, keyword search, text-to-SQL - and feeds this context into the language model to generate responses. The approach improves factual accuracy, supports domain-specific customization, enables citation of sources, and allows for more updated information without retraining the model itself. General Availability. In January 2025, Contextual AI announced the general availability of its enterprise platform for building specialized RAG agents. Early adopters included Qualcomm, which used the platform for their Customer Engineering team needs. Grounded Language Model. In March 2025, the company introduced a Grounded Language Model (GLM) for factual accuracy in enterprise AI applications. Reranker. In March 2025, Contextual AI released an instruction-following reranker that allows users to influence the ranking of retrieved documents through natural language instructions, such as prioritizing recent files, specific formats, or content from designated sources. == Applications == Contextual AI's platform has been adopted across a range of industries, including finance, technology, media and professional services. Clients include Fortune 500 companies such as Qualcomm and HSBC.
List of security assessment tools
This is a list of available software and hardware tools that are designed for or are particularly suited to various kinds of security assessment and security testing. == Operating systems and tool suites == Several operating systems and tool suites provide bundles of tools useful for various types of security assessment. === Operating system distributions === Kali Linux (formerly BackTrack), a penetration-test-focused Linux distribution based on Debian Pentoo, a penetration-test-focused Linux distribution based on Gentoo ParrotOS, a Linux distro focused on penetration testing, forensics, and online anonymity. == Tools ==
Inception (deep learning architecture)
Inception is a family of convolutional neural network (CNN) for computer vision, introduced by researchers at Google in 2014 as GoogLeNet (later renamed Inception v1). The series was historically important as an early CNN that separates the stem (data ingest), body (data processing), and head (prediction), an architectural design that persists in all modern CNN. == Version history == === Inception v1 === In 2014, a team at Google developed the GoogLeNet architecture, an instance of which won the ImageNet Large-Scale Visual Recognition Challenge 2014 (ILSVRC14). The name came from the LeNet of 1998, since both LeNet and GoogLeNet are CNNs. They also called it "Inception" after a "we need to go deeper" internet meme, a phrase from Inception (2010) the film. Because later, more versions were released, the original Inception architecture was renamed again as "Inception v1". The models and the code were released under Apache 2.0 license on GitHub. The Inception v1 architecture is a deep CNN composed of 22 layers. Most of these layers were "Inception modules". The original paper stated that Inception modules are a "logical culmination" of Network in Network and (Arora et al, 2014). Since Inception v1 is deep, it suffered from the vanishing gradient problem. The team solved it by using two "auxiliary classifiers", which are linear-softmax classifiers inserted at 1/3-deep and 2/3-deep within the network, and the loss function is a weighted sum of all three: L = 0.3 L a u x , 1 + 0.3 L a u x , 2 + L r e a l {\displaystyle L=0.3L_{aux,1}+0.3L_{aux,2}+L_{real}} These were removed after training was complete. This was later solved by the ResNet architecture. The architecture consists of three parts stacked on top of one another: The stem (data ingestion): The first few convolutional layers perform data preprocessing to downscale images to a smaller size. The body (data processing): The next many Inception modules perform the bulk of data processing. The head (prediction): The final fully-connected layer and softmax produces a probability distribution for image classification. This structure is used in most modern CNN architectures. === Inception v2 === Inception v2 was released in 2015, in a paper that is more famous for proposing batch normalization. It had 13.6 million parameters. It improves on Inception v1 by adding batch normalization, and removing dropout and local response normalization which they found became unnecessary when batch normalization is used. === Inception v3 === Inception v3 was released in 2016. It improves on Inception v2 by using factorized convolutions. As an example, a single 5×5 convolution can be factored into 3×3 stacked on top of another 3×3. Both has a receptive field of size 5×5. The 5×5 convolution kernel has 25 parameters, compared to just 18 in the factorized version. Thus, the 5×5 convolution is strictly more powerful than the factorized version. However, this power is not necessarily needed. Empirically, the research team found that factorized convolutions help. It also uses a form of dimension-reduction by concatenating the output from a convolutional layer and a pooling layer. As an example, a tensor of size 35 × 35 × 320 {\displaystyle 35\times 35\times 320} can be downscaled by a convolution with stride 2 to 17 × 17 × 320 {\displaystyle 17\times 17\times 320} , and by maxpooling with pool size 2 × 2 {\displaystyle 2\times 2} to 17 × 17 × 320 {\displaystyle 17\times 17\times 320} . These are then concatenated to 17 × 17 × 640 {\displaystyle 17\times 17\times 640} . Other than this, it also removed the lowest auxiliary classifier during training. They found that the auxiliary head worked as a form of regularization. They also proposed label-smoothing regularization in classification. For an image with label c {\displaystyle c} , instead of making the model to predict the probability distribution δ c = ( 0 , 0 , … , 0 , 1 ⏟ c -th entry , 0 , … , 0 ) {\displaystyle \delta _{c}=(0,0,\dots ,0,\underbrace {1} _{c{\text{-th entry}}},0,\dots ,0)} , they made the model predict the smoothed distribution ( 1 − ϵ ) δ c + ϵ / K {\displaystyle (1-\epsilon )\delta _{c}+\epsilon /K} where K {\displaystyle K} is the total number of classes. === Inception v4 === In 2017, the team released Inception v4, Inception ResNet v1, and Inception ResNet v2. Inception v4 is an incremental update with even more factorized convolutions, and other complications that were empirically found to improve benchmarks. Inception ResNet v1 and v2 are both modifications of Inception v4, where residual connections are added to each Inception module, inspired by the ResNet architecture. === Xception === Xception ("Extreme Inception") was published in 2017. It is a linear stack of depthwise separable convolution layers with residual connections. The design was proposed on the hypothesis that in a CNN, the cross-channels correlations and spatial correlations in the feature maps can be entirely decoupled. Training each network took 3 days on 60 K80 GPUs, or approximately 0.5 petaFLOP-days.