The Public Services Network (PSN) is a UK government's high-performance network, which helps public sector organisations work together, reduce duplication and share resources. It unified the provision of network infrastructure across the United Kingdom public sector into an interconnected "network of networks" to increase efficiency and reduce overall public expenditure. It is now a legacy network and public sector organisations are being migrated to using services on the public internet. == Origins == The Public Services Network (PSN) was launched officially as part of the Transformational Government Strategy commencing in 2005, under the original name of the Public Sector Network. Prior to this, some parts of local government had already successfully implemented the concept. The Hampshire Public Services Network (HPSN) was the first PSN, launched in 1999, followed closely by Kent County Councils partnerships with the KPSN. The HPSN, encompassing all of the borough, district and unitary councils, with the County Council, as well as the Fire Services, the Isle of Wight Council and 540 schools. National PSN technical and architecture compliance criteria were established from 2007, by GDS working with local government leaders from Socitm (the Society of Information Technology Management) on the National CIO Council and the Local CIO Council. The PSN's aim was to bring public services organisations with a common interest onto a single, coherent and standards-based ‘network of networks’. This would create influence, economies of scale and a commonality of standards for secure and easy inter-connection between public service organisations. The original concept of a network of networks strategy was based upon the work already undertaken in local government and recognition of Communities of Interest (COI) within the Criminal Justice Sector during work by the Office for Criminal Justice Reform (OCJR) between 2005 and 2007 to enable data sharing across business units. In this context a COI was defined as groups of Government departments and external partners who in combination provided services within a specific area of operation and used the same data, with a similar risk profile, shared risk appetite and common governance framework. Historically each group member had implemented their own networks and standards of operation in isolation with little or no consideration as to how services and data may be shared and resulting in increased costs of operation. The Network of Networks strategy proposed within OCJR recommended the creation of specific networks based upon these Communities of Interest which were joined together through data interchange gateways supporting common standards. Under this approach networks would be arranged by data type and business functions such as Criminal Justice, Health and Social Care, Defence and Intelligence or Public Finance rather than solely on established departmental boundaries. Within a COI, trust relationships and data interchange are readily supported, enabling data sharing without a need to cross network boundaries and providing benefits of scale without the challenges and compromises intrinsic to homogeneous cross sector networks. Data is made available without a need to transport it between organisations and control is retained by the data originator. In early 2007 a group of UK Government department CTOs in conjunction with the Office for Government Commerce Buying Solutions (OGC BS) established the vision for a single commonly provided, procured and managed public sector voice and data network infrastructure to replace the multitude of separately procured and managed networks serving various segments of the UK public sector; Education, Health, Central Government, Local Government etc. In 2008 an Industry Working Group was established to document the objectives and requirements more clearly. Their report set out the architectural and commercial principles as well as anticipated security, service management, governance and transition arrangements. == Architecture == The PSN comprises a core network, the Government Conveyancing Network or GCN provided by GCN Service Providers or GCNSPs. The GCN interconnects multiple operator networks, termed Direct Network Service Providers or DNSPs. Subscriber organisations contract to a connection from a local participating DNSP, connect via that to GCN and hence onwards to other interconnected networks and services. The GCN network is entirely based on IPv4 and MPLS and the GCNSPs are not currently mandated to provide IPv6, though they should have a roadmap to implementing it if and when required. == Commercial framework == In 2010 Virgin Media Business, BT, Cable & Wireless and Global Crossing signed Deeds of Undertaking (DoU) and subsequently achieved accreditation for providing GCN and IP VPN services. In March 2012, BT, Cable & Wireless, Capita Business Services, Eircom, Fujitsu, Kcom, Level 3, Logicalis, MDNX, Thales, Updata and Virgin Media Business were successful bidders for the initial two-year PSN Connectivity framework. In June 2012, 29 companies were confirmed as suppliers of ICT services to the UK public sector under the Government's PSN Services framework contract. Apart from most of the previous suppliers, additional companies also included 2e2, Airwave Solutions, Azzurri Communications, Cassidian, CSC Computer Sciences, Computacenter, Daisy Communications, Easynet Global Services, EE, Freedom Communications, Icom Holdings, NextiraOne, PageOne Communications, Phoenix IT Group, Siemens Communications, Specialist Computer Centres, Telefónica, telent Technology Services, Uniworld Communications and Vodafone. == Governance == The PSN is managed within the Cabinet Office where it is part of the Government Digital Service. == Early implementations == There were already notable initiatives in progress in county council areas, demonstrating public sector network integration in both the Hampshire HPSN2 network and in Kent's community network. Project Pathway was established as a pilot linking these two county-wide networks, with Virgin Media Business and Global Crossing the subscriber and GCN network elements. Staffordshire County Council was the first council in England to establish a PSN that included the county's NHS Health partners. Other county councils have since followed the leads of these councils. == Transition == Centrally procured public sector networks are expected to migrate across to the PSN framework as they reach the end of their contract terms, either through an interim framework or directly. The Government Secure Intranet (GSi) contracts expired in September 2011, running on to 12 February 2012 and were replaced by the transitional Government Secure Intranet Convergence Framework (GCF). The Managed Telephony Service (MTS) contract expired on 31 December 2011 and was replaced by the Managed Telephony Convergence Framework (MTCF). == Future plan == In a blog post published on 20 January 2017, Government Digital Service announced that the Technology Leaders Network (TLN) had agreed that government was starting a journey away from the PSN. This was because using the Internet was considered suitable for the vast majority of the work that the public sector does. The blog post confirmed that the 'move was not going to happen immediately' and stated that 'there's quite a bit of work to do across the public sector to prepare for the changes'. It also stated that it was too early for a full timeline to be provided, although all PSN-connected organisations would be updated as the process evolved. The blog post confirmed that organisations that need to access services that are only available on the PSN would still need to connect to it for the time being and continue to meet its assurance requirements. In a blog post published on 16 March 2017, Government Digital Service (GDS) set out its plans for PSN assurance. The blog post confirmed that the PSN compliance process wasn't 'going anywhere, certainly for a while yet'. It explained that the TLN agreed that – as one of the only recognised, externally accredited, cross-government common assurance standards – it 'needs to live on far beyond the end of the physical PSN network'. Government Digital Service, along with the National Cyber Security Centre (NCSC) and the Cyber and Government Security Directorate, are now looking at ways to expand and reframe PSN compliance in a new context that, while retaining the assurance principles that are the basis of the existing process, will aim to improve the process. A GDS blog post titled 'The road to closing down the PSN' published on 8 September 2020 describes how the public sector will migrate away from the PSN. The Cabinet Office has set up a programme called Future Networks for Government (FN4G) to help organisations move away from the PSN.
Slopaganda
Slopaganda is a portmanteau of "AI slop" and "propaganda", referring to AI-generated content designed to manipulate beliefs, emotions, and political decision-making at scale. The term is credited to Michał Klincewicz, an assistant professor in the Department of Computational Cognitive Science at Tilburg University, in 2025. == Definition == Slopaganda is distinguished from traditional propaganda by three features: scale, scope, and speed. Generative AI makes it possible to produce large volumes of content quickly and at low cost, allows for highly personalised and targeted messaging to specific sub-audiences, and leverages the hyper-connectivity of social networks to accelerate dissemination beyond what conventional media could achieve. Unlike traditional propaganda, which delivers a uniform message to all recipients, slopaganda can be micro-targeted — tailored to individuals based on estimated prior beliefs to reinforce political biases or emotional associations. The authors note that it need not aim at literal deception: much slopaganda is expressive rather than truth-apt, designed to create emotional associations rather than false factual beliefs. == Relation to AI slop == Slopaganda is a subset of AI slop — low-quality, mass-produced AI-generated content — distinguished by intent. Where AI slop may be produced indifferently for commercial or engagement-farming purposes, slopaganda is deployed with a deliberate political or ideological goal. == Notable examples == Examples discussed by the term's originators include Donald Trump's prolific use of AI in Truth Social posts and Iranian Lego-themed music videos. AI-generated videos posted by the White House mixing real military footage with clips from films and video games; and deepfake audio imitating political candidates during the 2024 US presidential campaign have also been given the label slopaganda.
Isabelle Guyon
Isabelle Guyon (French pronunciation: [izabɛl ɡɥijɔ̃]; born August 15, 1961) is a French-born researcher in machine learning known for her work on support-vector machines, artificial neural networks and bioinformatics. She is a Chair Professor at the University of Paris-Saclay. Guyon serves as the Director of Research at Google DeepMind since October 2022. She is considered to be a pioneer in the field, with her contribution to the support-vector machines with Vladimir Vapnik and Bernhard Boser. == Biography == After graduating from the French engineering school ESPCI Paris in 1985, she joined the group of Gerard Dreyfus at the Université Pierre-et-Marie-Curie to do a PhD on neural networks architectures and training. Guyon defended her thesis in 1988 and was hired the year after at AT&T Bell Laboratories, first as a post-doc, then as a group leader. She worked at Bell Labs for six years, where she explored several research areas, from neural networks to pattern recognition and computational learning theory, with application to handwriting recognition. She collaborated with Yann LeCun, Léon Bottou, Vladimir Vapnik, Corinna Cortes, Yoshua Bengio, Patrice Simard, and met her future husband, Bernhard Boser. In 1996, Guyon left Bell Labs and raised her children at Berkeley, California. In Berkeley, she created her own machine learning consulting company, Clopinet. She became interested in medical applications, and used her previous work to classify the genes responsible for different types of cancers. Since 2003, Guyon has organized many challenges in data science, in order to stimulate research in this field. She founded ChaLearn in 2011, a non-profit organization aimed at creating machine learning challenges open to everyone. She was Program Chair of NeurIPS 2016 and became General Chair of NeurIPS in 2017. She is also Action Editor for the Journal of Machine Learning Research and Series Editor for Series: Challenges in Machine Learning. She is a member of the European Laboratory for Learning and Intelligent Systems. In 2016, Guyon came back to France to take the Chair Professorship in Big data between the University of Paris-Saclay and INRIA. She works in TAU (TAckling the Underspecified), a research collaboration of the Laboratoire de recherche en informatique. Together with Bernhard Schölkopf and Vladimir Vapnik, she received in 2020 the BBVA Foundation Frontiers of Knowledge Awards for her work in machine learning. == Scientific work == Guyon has worked in many subfields of machine learning, including neural networks, support-vector machines, feature selection and applications of machine learning to biology. === Support-vector machines === Among her most notable contributions, Guyon co-invented support-vector machines (SVM) in 1992, with Bernhard Boser and Vladimir Vapnik. SVM is a supervised machine learning algorithm, comparable to neural networks or decision trees, which has quickly become a classical technique in machine learning. SVMs have especially contributed to the popularization of kernel methods. === Neural networks === During her years at Bell Labs, Guyon took part of numerous projects involving neural networks. In particular, she wrote some of the first papers on the use of neural network for handwriting recognition using the MNIST database. She is also a co-inventor of the siamese neural networks, a neural network architecture used to learn similarities, with applications to signature, face or object recognition. === Machine learning for biology === Guyon is the author of many publications at the intersection of biology (cancer research and genomics) and artificial intelligence. She has notably introduced the use of support-vector machines to detect cancer using genes. === Machine learning challenges === Through her non-profit organization ChaLearn, Guyon has organized and directed challenges open to everyone in order to solve open problems in machine learning, including computer vision, neurosciences, particle physics, feature selection, causality and automated machine learning. Most of the challenges organized by ChaLearn have resulted in publications. Among the most cited ones are: Guyon et al., Result analysis of the NIPS 2003 feature selection challenge, Advances in neural information processing systems, 2005, link Escalera et al., ChaLearn Looking at People Challenge 2014: Dataset and Results, Computer Vision - ECCV 2014 Workshops, Springer International Publishing, 2014, link Guyon et al., A brief Review of the ChaLearn AutoML Challenge, JMLR: Workshop and Conference Proceedings 64:21-30, 2016, link Adam-Bourdario et al., The Higgs boson machine learning challenge, JMLR: Workshop and Conference Proceedings 42:19-55, 2015, link == Private life == She is married to Bernhard Boser, a professor at UC Berkeley. She has twins and one daughter, all three of whom have completed a science degree. Guyon has three citizenships: French by birth, Swiss by marriage and American by naturalization. == Awards and honors == Nomination at the French Academy of technologies (2024) Recipient of the BBVA Foundation Frontiers of Knowledge Awards (2020) American Medical Informatics Association Fellow (2011) == Publications == Bernhard Boser, Isabelle Guyon and Vladmir Vapnik, A training algorithm for optimal margin classifiers, Proceedings of the fifth annual workshop on Computational learning theory, 1992, doi:10.1145/130385.130401 Jane Bromley, Isabelle Guyon, Yann LeCun, Eduard Säckinger and Roopak Shah, Signature verification using a" siamese" time delay neural network, Advances in Neural Information Processing Systems, 1994. Isabelle Guyon and André Elisseeff, An introduction to variable and feature selection, Journal of Machine Learning Research, 2003. Isabelle Guyon, Jason Weston, Stephen Barnhill and Vladimir Vapnik, Gene selection for cancer classification using support vector machines, Machine Learning, Kluwer Academic Publishers, 2002, doi:10.1023/A:1012487302797
Top 10 AI Bug Finders Compared (2026)
Trying to pick the best AI bug finder? An AI bug finder is software that uses machine learning to help you get more done — it scales effortlessly from a single task to thousands. The best picks balance beginner-friendly simplicity with the depth power users need, and they ship updates often. Whether you are a beginner or a pro, the right AI bug finder slots into your workflow and pays for itself fast. This guide breaks down the top picks, their pros and cons, and who each one is best for.
Hapax legomenon
In corpus linguistics, a hapax legomenon ( also or ; pl. hapax legomena; sometimes abbreviated to hapax, plural hapaxes) is a word or an expression that occurs only once within a context: either in the written record of an entire language, in the works of an author, or in a single text. The term is also sometimes used to describe a word that occurs in just one of an author's works but more than once in that particular work. Hapax legomenon is a transliteration of Greek ἅπαξ λεγόμενον, meaning "said once". The related terms dis legomenon, tris legomenon, and tetrakis legomenon respectively (, , ) refer to double, triple, or quadruple occurrences, but are far less commonly used. Hapax legomena are quite common, as predicted by Zipf's law, which states that the frequency of any word in a corpus is inversely proportional to its rank in the frequency table. For large corpora, about 40% to 60% of the words are hapax legomena, and another 10% to 15% are dis legomena. Thus, in the Brown Corpus of American English, about half of the 50,000 distinct words are hapax legomena within that corpus. Hapax legomenon refers to the appearance of a word or an expression in a body of text, not to either its origin or its prevalence in speech. It thus differs from a nonce word, which may never be recorded, may find currency and may be widely recorded, or may appear several times in the work which coins it, and so on. == Significance == Hapax legomena in ancient texts are usually difficult to decipher, since it is easier to infer meaning from multiple contexts than from just one. For example, many of the remaining undeciphered Mayan glyphs are hapax legomena, and Biblical (particularly Hebrew; see § Hebrew) hapax legomena sometimes pose problems in translation. Hapax legomena also pose challenges in natural language processing. Some scholars consider Hapax legomena useful in determining the authorship of written works. P. N. Harrison, in The Problem of the Pastoral Epistles (1921) made hapax legomena popular among Bible scholars, when he argued that there are considerably more of them in the three Pastoral Epistles than in other Pauline Epistles. He argued that the number of hapax legomena in a putative author's corpus indicates his or her vocabulary and is characteristic of the author as an individual. Harrison's theory has faded in significance due to a number of problems raised by other scholars. For example, in 1896, W. P. Workman found the following numbers of hapax legomena in each Pauline Epistle: At first glance, the last three totals (for the Pastoral Epistles) are not out of line with the others. To take account of the varying length of the epistles, Workman also calculated the average number of hapax legomena per page of the Greek text, which ranged from 3.6 to 13, as summarized in the diagram on the right. Although the Pastoral Epistles have more hapax legomena per page, Workman found the differences to be moderate in comparison to the variation among other Epistles. This was reinforced when Workman looked at several plays by Shakespeare, which showed similar variations (from 3.4 to 10.4 per page of Irving's one-volume edition), as summarized in the second diagram on the right. Apart from author identity, there are several other factors that can explain the number of hapax legomena in a work: text length: this directly affects the expected number and percentage of hapax legomena; the brevity of the Pastoral Epistles also makes any statistical analysis problematic. text topic: if the author writes on different subjects, of course many subject-specific words will occur only in limited contexts. text audience: if the author is writing to a peer rather than a student, or their spouse rather than their employer, again quite different vocabulary will appear. time: over the course of years, both the language and an author's knowledge and use of language will change. In the particular case of the Pastoral Epistles, all of these variables are quite different from those in the rest of the Pauline corpus, and hapax legomena are no longer widely accepted as strong indicators of authorship; those who reject Pauline authorship of the Pastorals rely on other arguments. There are also subjective questions over whether two forms amount to "the same word": dog vs. dogs, clue vs. clueless, sign vs. signature; many other gray cases also arise. The Jewish Encyclopedia points out that, although there are 1,500 hapaxes in the Hebrew Bible, only about 400 are not obviously related to other attested word forms. A final difficulty with the use of hapax legomena for authorship determination is that there is considerable variation among works known to be by a single author, and disparate authors often show similar values. In other words, hapax legomena are not a reliable indicator. Authorship studies now usually use a wide range of measures to look for patterns rather than relying upon single measurements. == Computer science == In the fields of computational linguistics and natural language processing (NLP), esp. corpus linguistics and machine-learned NLP, it is common to disregard hapax legomena (and sometimes other infrequent words), as they are likely to have little value for computational techniques. This disregard has the added benefit of significantly reducing the memory use of an application, since, by Zipf's law, many words are hapax legomena. == Examples == The following are some examples of hapax legomena in languages or corpora. === Arabic === In the Qurʾān: The proper nouns Iram (Q 89:7, Iram of the Pillars), Bābil (Q 2:102, Babylon), Bakka(t) (Q 3:96, Bakkah), Jibt (Q 4:51), Ramaḍān (Q 2:185, Ramadan), ar-Rūm (Q 30:2, Byzantine Empire), Tasnīm (Q 83:27), Qurayš (Q 106:1, Quraysh), Majūs (Q 22:17, Magian/Zoroastrian), Mārūt (Q 2:102, Harut and Marut), Makka(t) (Q 48:24, Mecca), Nasr (Q 71:23), (Ḏū) an-Nūn (Q 21:87) and Hārūt (Q 2:102, Harut and Marut) occur only once. zanjabīl (زَنْجَبِيل – ginger) is a Qurʾānic hapax (Q 76:17). zamharīr (زَمْهَرِيرًۭ) is a Qurʾānic hapax (Q 76:13), usually glossed as referring to extreme cold. The epitheton ornans aṣ-ṣamad (الصَّمَد – the One besought) is a Qurʾānic hapax (Q 112:2). ṭūd (طُودْ - mountain) is a Qurʾānic hapax (Q 26:63). === Chinese and Japanese === Classical Chinese and Japanese literature contains many Chinese characters that feature only once in the corpus, and their meaning and pronunciation has often been lost. Known in Japanese as kogo (孤語), literally "lonely characters", these can be considered a type of hapax legomenon. For example, the Classic of Poetry (c. 1000 BC) uses the character 篪 exactly once in the verse 「伯氏吹塤, 仲氏吹篪」, and it was only through the discovery of a description by Guo Pu (276–324 AD) that the character could be associated with a specific type of ancient flute. === English === It is fairly common for authors to "coin" new words to convey a particular meaning or for the sake of entertainment, without any suggestion that they are "proper" words. For example, P.G. Wodehouse and Lewis Carroll frequently coined novel words. Indexy, below, appears to be an example of this. Flother, as a synonym for snowflake, is a hapax legomenon of written English found in a manuscript entitled The XI Pains of Hell (c. 1275). Honorificabilitudinitatibus is a hapax legomenon of Shakespeare's works, coming from Erasmus' Adagia Indexy, in Bram Stoker's Dracula, used as an adjective to describe a situational state with no other further use in the language: "If that man had been an ordinary lunatic I would have taken my chance of trusting him; but he seems so mixed up with the Count in an indexy kind of way that I am afraid of doing anything wrong by helping his fads." Manticratic, meaning "of the rule by the Prophet's family or clan", was apparently invented by T. E. Lawrence and appears once in Seven Pillars of Wisdom. Nortelrye, a word for "education", occurs only once in Chaucer's The Reeve's Tale. Sassigassity, perhaps with the meaning of "audacity", occurs only once in Dickens's short story "A Christmas Tree". Slæpwerigne, "sleep-weary", occurs exactly once in the Old English corpus, in the Exeter Book. There is debate over whether it means "weary with sleep" or "weary for sleep". === German === The name of the 9th-century poem Muspilli is a back-formation from "muspille", Old High German hapax legomenon of unclear meaning only found in this text (see Muspilli § Etymology for discussion). === Ancient Greek === According to classical scholar Clyde Pharr, "the Iliad has 1,097 hapax legomena, while the Odyssey has 868". Others have defined the term differently, however, and count as few as 303 in the Iliad and 191 in the Odyssey. panaōrios (παναώριος), ancient Greek for "very untimely", is one of many words that occur only once in the Iliad. The Greek New Testament contains 686 local hapax legomena, which are sometimes called "New Testament hapaxes". 62 of these occur in 1 Peter and 54 occur in 2 Peter
Highway network
In machine learning, the Highway Network was the first working very deep feedforward neural network with hundreds of layers, much deeper than previous neural networks. It uses skip connections modulated by learned gating mechanisms to regulate information flow, inspired by long short-term memory (LSTM) recurrent neural networks. The advantage of the Highway Network over other deep learning architectures is its ability to overcome or partially prevent the vanishing gradient problem, thus improving its optimization. Gating mechanisms are used to facilitate information flow across the many layers ("information highways"). Highway Networks have found use in text sequence labeling and speech recognition tasks. In 2014, the state of the art was training deep neural networks with 20 to 30 layers. Stacking too many layers led to a steep reduction in training accuracy, known as the "degradation" problem. In 2015, two techniques were developed to train such networks: the Highway Network (published in May), and the residual neural network, or ResNet (December). ResNet behaves like an open-gated Highway Net. == Model == The model has two gates in addition to the H ( W H , x ) {\displaystyle H(W_{H},x)} gate: the transform gate T ( W T , x ) {\displaystyle T(W_{T},x)} and the carry gate C ( W C , x ) {\displaystyle C(W_{C},x)} . The latter two gates are non-linear transfer functions (specifically sigmoid by convention). The function H {\displaystyle H} can be any desired transfer function. The carry gate is defined as: C ( W C , x ) = 1 − T ( W T , x ) {\displaystyle C(W_{C},x)=1-T(W_{T},x)} while the transform gate is just a gate with a sigmoid transfer function. == Structure == The structure of a hidden layer in the Highway Network follows the equation: y = H ( x , W H ) ⋅ T ( x , W T ) + x ⋅ C ( x , W C ) = H ( x , W H ) ⋅ T ( x , W T ) + x ⋅ ( 1 − T ( x , W T ) ) {\displaystyle {\begin{aligned}y=H(x,W_{H})\cdot T(x,W_{T})+x\cdot C(x,W_{C})\\=H(x,W_{H})\cdot T(x,W_{T})+x\cdot (1-T(x,W_{T}))\end{aligned}}} == Related work == Sepp Hochreiter analyzed the vanishing gradient problem in 1991 and attributed to it the reason why deep learning did not work well. To overcome this problem, Long Short-Term Memory (LSTM) recurrent neural networks have residual connections with a weight of 1.0 in every LSTM cell (called the constant error carrousel) to compute y t + 1 = F ( x t ) + x t {\textstyle y_{t+1}=F(x_{t})+x_{t}} . During backpropagation through time, this becomes the residual formula y = F ( x ) + x {\textstyle y=F(x)+x} for feedforward neural networks. This enables training very deep recurrent neural networks with a very long time span t. A later LSTM version published in 2000 modulates the identity LSTM connections by so-called "forget gates" such that their weights are not fixed to 1.0 but can be learned. In experiments, the forget gates were initialized with positive bias weights, thus being opened, addressing the vanishing gradient problem. As long as the forget gates of the 2000 LSTM are open, it behaves like the 1997 LSTM. The Highway Network of May 2015 applies these principles to feedforward neural networks. It was reported to be "the first very deep feedforward network with hundreds of layers". It is like a 2000 LSTM with forget gates unfolded in time, while the later Residual Nets have no equivalent of forget gates and are like the unfolded original 1997 LSTM. If the skip connections in Highway Networks are "without gates," or if their gates are kept open (activation 1.0), they become Residual Networks. The residual connection is a special case of the "short-cut connection" or "skip connection" by Rosenblatt (1961) and Lang & Witbrock (1988) which has the form x ↦ F ( x ) + A x {\displaystyle x\mapsto F(x)+Ax} . Here the randomly initialized weight matrix A does not have to be the identity mapping. Every residual connection is a skip connection, but almost all skip connections are not residual connections. The original Highway Network paper not only introduced the basic principle for very deep feedforward networks, but also included experimental results with 20, 50, and 100 layers networks, and mentioned ongoing experiments with up to 900 layers. Networks with 50 or 100 layers had lower training error than their plain network counterparts, but no lower training error than their 20 layers counterpart (on the MNIST dataset, Figure 1 in ). No improvement on test accuracy was reported with networks deeper than 19 layers (on the CIFAR-10 dataset; Table 1 in ). The ResNet paper, however, provided strong experimental evidence of the benefits of going deeper than 20 layers. It argued that the identity mapping without modulation is crucial and mentioned that modulation in the skip connection can still lead to vanishing signals in forward and backward propagation (Section 3 in ). This is also why the forget gates of the 2000 LSTM were initially opened through positive bias weights: as long as the gates are open, it behaves like the 1997 LSTM. Similarly, a Highway Net whose gates are opened through strongly positive bias weights behaves like a ResNet. The skip connections used in modern neural networks (e.g., Transformers) are dominantly identity mappings.
Levenshtein automaton
In computer science, a Levenshtein automaton for a string w and a number n is a finite-state automaton that can recognize the set of all strings whose Levenshtein distance from w is at most n. That is, a string x is in the formal language recognized by the Levenshtein automaton if and only if x can be transformed into w by at most n single-character insertions, deletions, and substitutions. == Applications == Levenshtein automata may be used for spelling correction, by finding words in a given dictionary that are close to a misspelled word. In this application, once a word is identified as being misspelled, its Levenshtein automaton may be constructed, and then applied to all of the words in the dictionary to determine which ones are close to the misspelled word. If the dictionary is stored in compressed form as a trie, the time for this algorithm (after the automaton has been constructed) is proportional to the number of nodes in the trie, significantly faster than using dynamic programming to compute the Levenshtein distance separately for each dictionary word. It is also possible to find words in a regular language, rather than a finite dictionary, that are close to a given target word, by computing the Levenshtein automaton for the word, and then using a Cartesian product construction to combine it with an automaton for the regular language, giving an automaton for the intersection language. Alternatively, rather than using the product construction, both the Levenshtein automaton and the automaton for the given regular language may be traversed simultaneously using a backtracking algorithm. Levenshtein automata are used in Lucene for full-text searches that can return relevant documents even if the query is misspelled. == Construction == For any fixed constant n, the Levenshtein automaton for w and n may be constructed in time O(|w|). Mitankin studies a variant of this construction called the universal Levenshtein automaton, determined only by a numeric parameter n, that can recognize pairs of words (encoded in a certain way by bitvectors) that are within Levenshtein distance n of each other. Touzet proposed an effective algorithm to build this automaton. Yet a third finite automaton construction of Levenshtein (or Damerau–Levenshtein) distance are the Levenshtein transducers of Hassan et al., who show finite state transducers implementing edit distance one, then compose these to implement edit distances up to some constant.