AI For Business Georgia Tech — independent reviews, comparisons, pricing and step-by-step guides on Aizhi.
Chroma or ChromaDB is open-source data infrastructure tailored to applications with large language models. Its headquarters are in San Francisco. In April 2023, it raised 18 million US dollars as seed funding. ChromaDB has been used in academic studies on artificial intelligence, particularly as part of the tech stack for retrieval-augmented generation.
Read more →
Curious about the best AI customer-support bot? An AI customer-support bot is software that uses machine learning to help you get more done — it combines speed, accuracy, and an interface that just works. Hands-on testing shows real-world results vary, so a short free trial is the smartest way to decide. Whether you are a beginner or a pro, the right AI customer-support bot 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.
Read more →
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
Read more →
Trying to pick the best AI marketing tool? An AI marketing tool 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 marketing tool 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.
Read more →
Amália is a Portuguese large language model (LLM) announced in November 2024 by the Portuguese Prime-Minister Luís Montenegro. Its final version is expected to be launched in 2026. It is being developed by Center for Responsible AI (Centro para a AI Responsável) and by the research centers of NOVA School of Science and Technology and Instituto Superior Técnico. == History == In 2024 it was announced that the Portuguese Agency for Administrative Modernization (Agência para a Modernização Administrativa) transpose this LLM to Portuguese Public Administration. According to Paulo Dimas (CEO of the Center for Responsible AI) the three fundamental points of this LLM project are the linguistic variant (European Portuguese), cultural representation and data protection. In April 2025 it was announced that Amália had entered beta phase with an improved version being expected to be launched in September 2025. The beta version released in September is available only to the Public Administration, but the website launched in October reiterates the final version will be an open model.
Read more →
Looking for the best AI code-review tool? An AI code-review tool is software that uses machine learning to help you get more done — it can save you hours every week by automating repetitive work. Most options offer a generous free tier, with paid plans unlocking higher limits, faster processing, and team features. Whether you are a beginner or a pro, the right AI code-review tool slots into your workflow and pays for itself fast. Read on for hands-on impressions, pricing tiers, and the standout features that matter.
Read more →
In computer science, in particular in formal language theory, a quotient automaton can be obtained from a given nondeterministic finite automaton by joining some of its states. The quotient recognizes a superset of the given automaton; in some cases, handled by the Myhill–Nerode theorem, both languages are equal. == Formal definition == A (nondeterministic) finite automaton is a quintuple A = ⟨Σ, S, s0, δ, Sf⟩, where: Σ is the input alphabet (a finite, non-empty set of symbols), S is a finite, non-empty set of states, s0 is the initial state, an element of S, δ is the state-transition relation: δ ⊆ S × Σ × S, and Sf is the set of final states, a (possibly empty) subset of S. A string a1...an ∈ Σ is recognized by A if there exist states s1, ..., sn ∈ S such that ⟨si-1,ai,si⟩ ∈ δ for i=1,...,n, and sn ∈ Sf. The set of all strings recognized by A is called the language recognized by A; it is denoted as L(A). For an equivalence relation ≈ on the set S of A’s states, the quotient automaton A/≈ = ⟨Σ, S/≈, [s0], δ/≈, Sf/≈⟩ is defined by the input alphabet Σ being the same as that of A, the state set S/≈ being the set of all equivalence classes of states from S, the start state [s0] being the equivalence class of A’s start state, the state-transition relation δ/≈ being defined by δ/≈([s],a,[t]) if δ(s,a,t) for some s ∈ [s] and t ∈ [t], and the set of final states Sf/≈ being the set of all equivalence classes of final states from Sf. The process of computing A/≈ is also called factoring A by ≈. == Example == For example, the automaton A shown in the first row of the table is formally defined by ΣA = {0,1}, SA = {a,b,c,d}, sA0 = a, δA = { ⟨a,1,b⟩, ⟨b,0,c⟩, ⟨c,0,d⟩ }, and SAf = { b,c,d }. It recognizes the finite set of strings { 1, 10, 100 }; this set can also be denoted by the regular expression "1+10+100". The relation (≈) = { ⟨a,a⟩, ⟨a,b⟩, ⟨b,a⟩, ⟨b,b⟩, ⟨c,c⟩, ⟨c,d⟩, ⟨d,c⟩, ⟨d,d⟩ }, more briefly denoted as a≈b,c≈d, is an equivalence relation on the set {a,b,c,d} of automaton A’s states. Building the quotient of A by that relation results in automaton C in the third table row; it is formally defined by ΣC = {0,1}, SC = {a,c}, sC0 = a, δC = { ⟨a,1,a⟩, ⟨a,0,c⟩, ⟨c,0,c⟩ }, and SCf = { a,c }. It recognizes the finite set of all strings composed of arbitrarily many 1s, followed by arbitrarily many 0s, i.e. { ε, 1, 10, 100, 1000, ..., 11, 110, 1100, 11000, ..., 111, ... }; this set can also be denoted by the regular expression "10". Informally, C can be thought of resulting from A by glueing state a onto state b, and glueing state c onto state d. The table shows some more quotient relations, such as B = A/a≈b, and D = C/a≈c. == Properties == For every automaton A and every equivalence relation ≈ on its states set, L(A/≈) is a superset of (or equal to) L(A). Given a finite automaton A over some alphabet Σ, an equivalence relation ≈ can be defined on Σ by x ≈ y if ∀ z ∈ Σ: xz ∈ L(A) ↔ yz ∈ L(A). By the Myhill–Nerode theorem, A/≈ is a deterministic automaton that recognizes the same language as A. As a consequence, the quotient of A by every refinement of ≈ also recognizes the same language as A.
Read more →
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
Read more →
In natural language processing, a sentence embedding is a representation of a sentence as a vector of numbers which encodes meaningful semantic information. State of the art embeddings are based on the learned hidden layer representation of dedicated sentence transformer models. BERT pioneered an approach involving the use of a dedicated [CLS] token prepended to the beginning of each sentence inputted into the model; the final hidden state vector of this token encodes information about the sentence and can be fine-tuned for use in sentence classification tasks. In practice however, BERT's sentence embedding with the [CLS] token achieves poor performance, often worse than simply averaging non-contextual word embeddings. SBERT later achieved superior sentence embedding performance by fine tuning BERT's [CLS] token embeddings through the usage of a siamese neural network architecture on the SNLI dataset. Other approaches are loosely based on the idea of distributional semantics applied to sentences. Skip-Thought trains an encoder-decoder structure for the task of neighboring sentences predictions; this has been shown to achieve worse performance than approaches such as InferSent or SBERT. An alternative direction is to aggregate word embeddings, such as those returned by Word2vec, into sentence embeddings. The most straightforward approach is to simply compute the average of word vectors, known as continuous bag-of-words (CBOW). However, more elaborate solutions based on word vector quantization have also been proposed. One such approach is the vector of locally aggregated word embeddings (VLAWE), which demonstrated performance improvements in downstream text classification tasks. == Applications == In recent years, sentence embedding has seen a growing level of interest due to its applications in natural language queryable knowledge bases through the usage of vector indexing for semantic search. LangChain for instance utilizes sentence transformers for purposes of indexing documents. In particular, an indexing is generated by generating embeddings for chunks of documents and storing (document chunk, embedding) tuples. Then given a query in natural language, the embedding for the query can be generated. A top k similarity search algorithm is then used between the query embedding and the document chunk embeddings to retrieve the most relevant document chunks as context information for question answering tasks. This approach is also known formally as retrieval-augmented generation. Though not as predominant as BERTScore, sentence embeddings are commonly used for sentence similarity evaluation which sees common use for the task of optimizing a Large language model's generation parameters is often performed via comparing candidate sentences against reference sentences. By using the cosine-similarity of the sentence embeddings of candidate and reference sentences as the evaluation function, a grid-search algorithm can be utilized to automate hyperparameter optimization. == Evaluation == A way of testing sentence encodings is to apply them on Sentences Involving Compositional Knowledge (SICK) corpus for both entailment (SICK-E) and relatedness (SICK-R). In the best results are obtained using a BiLSTM network trained on the Stanford Natural Language Inference (SNLI) Corpus. The Pearson correlation coefficient for SICK-R is 0.885 and the result for SICK-E is 86.3. A slight improvement over previous scores is presented in: SICK-R: 0.888 and SICK-E: 87.8 using a concatenation of bidirectional Gated recurrent unit.
Read more →
Looking for the best AI resume builder? An AI resume builder is software that uses machine learning to help you get more done — it can save you hours every week by automating repetitive work. Most options offer a generous free tier, with paid plans unlocking higher limits, faster processing, and team features. Whether you are a beginner or a pro, the right AI resume builder slots into your workflow and pays for itself fast. Read on for hands-on impressions, pricing tiers, and the standout features that matter.
Read more →
In electrical engineering, statistical computing and bioinformatics, the Baum–Welch algorithm is a special case of the expectation–maximization algorithm used to find the unknown parameters of a hidden Markov model (HMM). It makes use of the forward-backward algorithm to compute the statistics for the expectation step. The Baum–Welch algorithm, the primary method for inference in hidden Markov models, is numerically unstable due to its recursive calculation of joint probabilities. As the number of variables grows, these joint probabilities become increasingly small, leading to the forward recursions rapidly approaching values below machine precision. == History == The Baum–Welch algorithm was named after its inventors Leonard E. Baum and Lloyd R. Welch. The algorithm and the Hidden Markov models were first described in a series of articles by Baum and his peers at the IDA Center for Communications Research, Princeton in the late 1960s and early 1970s. One of the first major applications of HMMs was to the field of speech processing. In the 1980s, HMMs were emerging as a useful tool in the analysis of biological systems and information, and in particular genetic information. They have since become an important tool in the probabilistic modeling of genomic sequences. == Description == A hidden Markov model describes the joint probability of a collection of "hidden" and observed discrete random variables. It relies on the assumption that the i-th hidden variable given the (i − 1)-th hidden variable is independent of previous hidden variables, and the current observation variables depend only on the current hidden state. The Baum–Welch algorithm uses the well known EM algorithm to find the maximum likelihood estimate of the parameters of a hidden Markov model given a set of observed feature vectors. Let X t {\displaystyle X_{t}} be a discrete hidden random variable with N {\displaystyle N} possible values (i.e. We assume there are N {\displaystyle N} states in total). We assume the P ( X t ∣ X t − 1 ) {\displaystyle P(X_{t}\mid X_{t-1})} is independent of time t {\displaystyle t} , which leads to the definition of the time-independent stochastic transition matrix A = { a i j } = P ( X t = j ∣ X t − 1 = i ) . {\displaystyle A=\{a_{ij}\}=P(X_{t}=j\mid X_{t-1}=i).} The initial state distribution (i.e. when t = 1 {\displaystyle t=1} ) is given by π i = P ( X 1 = i ) . {\displaystyle \pi _{i}=P(X_{1}=i).} The observation variables Y t {\displaystyle Y_{t}} can take one of K {\displaystyle K} possible values. We also assume the observation given the "hidden" state is time independent. The probability of a certain observation y i {\displaystyle y_{i}} at time t {\displaystyle t} for state X t = j {\displaystyle X_{t}=j} is given by b j ( y i ) = P ( Y t = y i ∣ X t = j ) . {\displaystyle b_{j}(y_{i})=P(Y_{t}=y_{i}\mid X_{t}=j).} Taking into account all the possible values of Y t {\displaystyle Y_{t}} and X t {\displaystyle X_{t}} , we obtain the N × K {\displaystyle N\times K} matrix B = { b j ( y i ) } {\displaystyle B=\{b_{j}(y_{i})\}} where b j {\displaystyle b_{j}} belongs to all the possible states and y i {\displaystyle y_{i}} belongs to all the observations. An observation sequence is given by Y = ( Y 1 = y 1 , Y 2 = y 2 , … , Y T = y T ) {\displaystyle Y=(Y_{1}=y_{1},Y_{2}=y_{2},\ldots ,Y_{T}=y_{T})} . Thus we can describe a hidden Markov chain by θ = ( A , B , π ) {\displaystyle \theta =(A,B,\pi )} . The Baum–Welch algorithm finds a local maximum for θ ∗ = a r g m a x θ P ( Y ∣ θ ) {\displaystyle \theta ^{}=\operatorname {arg\,max} _{\theta }P(Y\mid \theta )} (i.e. the HMM parameters θ {\displaystyle \theta } that maximize the probability of the observation). === Algorithm === Set θ = ( A , B , π ) {\displaystyle \theta =(A,B,\pi )} with random initial conditions. They can also be set using prior information about the parameters if it is available; this can speed up the algorithm and also steer it toward the desired local maximum. ==== Forward procedure ==== Let α i ( t ) = P ( Y 1 = y 1 , … , Y t = y t , X t = i ∣ θ ) {\displaystyle \alpha _{i}(t)=P(Y_{1}=y_{1},\ldots ,Y_{t}=y_{t},X_{t}=i\mid \theta )} , the probability of seeing the observations y 1 , y 2 , … , y t {\displaystyle y_{1},y_{2},\ldots ,y_{t}} and being in state i {\displaystyle i} at time t {\displaystyle t} . This is found recursively: α i ( 1 ) = π i b i ( y 1 ) , {\displaystyle \alpha _{i}(1)=\pi _{i}b_{i}(y_{1}),} α i ( t + 1 ) = b i ( y t + 1 ) ∑ j = 1 N α j ( t ) a j i . {\displaystyle \alpha _{i}(t+1)=b_{i}(y_{t+1})\sum _{j=1}^{N}\alpha _{j}(t)a_{ji}.} Since this series converges exponentially to zero, the algorithm will numerically underflow for longer sequences. However, this can be avoided in a slightly modified algorithm by scaling α {\displaystyle \alpha } in the forward and β {\displaystyle \beta } in the backward procedure below. ==== Backward procedure ==== Let β i ( t ) = P ( Y t + 1 = y t + 1 , … , Y T = y T ∣ X t = i , θ ) {\displaystyle \beta _{i}(t)=P(Y_{t+1}=y_{t+1},\ldots ,Y_{T}=y_{T}\mid X_{t}=i,\theta )} that is the probability of the ending partial sequence y t + 1 , … , y T {\displaystyle y_{t+1},\ldots ,y_{T}} given starting state i {\displaystyle i} at time t {\displaystyle t} . We calculate β i ( t ) {\displaystyle \beta _{i}(t)} as, β i ( T ) = 1 , {\displaystyle \beta _{i}(T)=1,} β i ( t ) = ∑ j = 1 N β j ( t + 1 ) a i j b j ( y t + 1 ) . {\displaystyle \beta _{i}(t)=\sum _{j=1}^{N}\beta _{j}(t+1)a_{ij}b_{j}(y_{t+1}).} ==== Update ==== We can now calculate the temporary variables, according to Bayes' theorem: γ i ( t ) = P ( X t = i ∣ Y , θ ) = P ( X t = i , Y ∣ θ ) P ( Y ∣ θ ) = α i ( t ) β i ( t ) ∑ j = 1 N α j ( t ) β j ( t ) , {\displaystyle \gamma _{i}(t)=P(X_{t}=i\mid Y,\theta )={\frac {P(X_{t}=i,Y\mid \theta )}{P(Y\mid \theta )}}={\frac {\alpha _{i}(t)\beta _{i}(t)}{\sum _{j=1}^{N}\alpha _{j}(t)\beta _{j}(t)}},} which is the probability of being in state i {\displaystyle i} at time t {\displaystyle t} given the observed sequence Y {\displaystyle Y} and the parameters θ {\displaystyle \theta } ξ i j ( t ) = P ( X t = i , X t + 1 = j ∣ Y , θ ) = P ( X t = i , X t + 1 = j , Y ∣ θ ) P ( Y ∣ θ ) = α i ( t ) a i j β j ( t + 1 ) b j ( y t + 1 ) ∑ k = 1 N ∑ w = 1 N α k ( t ) a k w β w ( t + 1 ) b w ( y t + 1 ) , {\displaystyle \xi _{ij}(t)=P(X_{t}=i,X_{t+1}=j\mid Y,\theta )={\frac {P(X_{t}=i,X_{t+1}=j,Y\mid \theta )}{P(Y\mid \theta )}}={\frac {\alpha _{i}(t)a_{ij}\beta _{j}(t+1)b_{j}(y_{t+1})}{\sum _{k=1}^{N}\sum _{w=1}^{N}\alpha _{k}(t)a_{kw}\beta _{w}(t+1)b_{w}(y_{t+1})}},} which is the probability of being in state i {\displaystyle i} and j {\displaystyle j} at times t {\displaystyle t} and t + 1 {\displaystyle t+1} respectively given the observed sequence Y {\displaystyle Y} and parameters θ {\displaystyle \theta } . The denominators of γ i ( t ) {\displaystyle \gamma _{i}(t)} and ξ i j ( t ) {\displaystyle \xi _{ij}(t)} are the same ; they represent the probability of making the observation Y {\displaystyle Y} given the parameters θ {\displaystyle \theta } . The parameters of the hidden Markov model θ {\displaystyle \theta } can now be updated: π i ∗ = γ i ( 1 ) , {\displaystyle \pi _{i}^{}=\gamma _{i}(1),} which is the expected frequency spent in state i {\displaystyle i} at time 1 {\displaystyle 1} . a i j ∗ = ∑ t = 1 T − 1 ξ i j ( t ) ∑ t = 1 T − 1 γ i ( t ) , {\displaystyle a_{ij}^{}={\frac {\sum _{t=1}^{T-1}\xi _{ij}(t)}{\sum _{t=1}^{T-1}\gamma _{i}(t)}},} which is the expected number of transitions from state i to state j compared to the expected total number of transitions starting in state i, including from state i to itself. The number of transitions starting in state i is equivalent to the number of times state i is observed in the sequence from t = 1 to t = T − 1. b i ∗ ( v k ) = ∑ t = 1 T 1 y t = v k γ i ( t ) ∑ t = 1 T γ i ( t ) , {\displaystyle b_{i}^{}(v_{k})={\frac {\sum _{t=1}^{T}1_{y_{t}=v_{k}}\gamma _{i}(t)}{\sum _{t=1}^{T}\gamma _{i}(t)}},} where 1 y t = v k = { 1 if y t = v k , 0 otherwise {\displaystyle 1_{y_{t}=v_{k}}={\begin{cases}1&{\text{if }}y_{t}=v_{k},\\0&{\text{otherwise}}\end{cases}}} is an indicator function, and b i ∗ ( v k ) {\displaystyle b_{i}^{}(v_{k})} is the expected number of times the output observations have been equal to v k {\displaystyle v_{k}} while in state i {\displaystyle i} over the expected total number of times in state i {\displaystyle i} . These steps are now repeated iteratively until a desired level of convergence. Note: It is possible to over-fit a particular data set. That is, P ( Y ∣ θ final ) > P ( Y ∣ θ true ) {\displaystyle P(Y\mid \theta _{\text{final}})>P(Y\mid \theta _{\text{true}})} . The algorithm also does not guarantee a global maximum. ==== Multiple sequences ==== The algorithm described thus far assumes a single observed sequence Y = y 1 , … , y T {\displaystyle Y=y_{1},\ldots ,y_{T}} . However, in many situations, there are several sequences observed: Y 1 ,
Read more →
Lillian Lee is a computer scientist whose research involves natural language processing, sentiment analysis, and computational social science. She is a professor of computer science and information science at Cornell University, and co-editor-in-chief of the journal Transactions of the Association for Computational Linguistics. == Education == Lee graduated from Cornell University in 1993 with an undergraduate degree in math and science. She completed her Ph.D. at Harvard University in 1997. Her dissertation, Similarity-Based Approaches to Natural Language Processing, was supervised by Stuart M. Shieber. == Career == Lee has been a member of the Cornell faculty since 1997. == Recognition == Lee has been a fellow of the Association for the Advancement of Artificial Intelligence since 2013, and of the Association for Computational Linguistics since 2017. Lee was elected as an ACM Fellow in 2018 for "contributions to natural language processing, sentiment analysis, and computational social science".
Read more →
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.
Read more →
Comparing the best AI avatar generator? An AI avatar generator is software that uses machine learning to help you get more done — it lowers the barrier so anyone can produce professional output. Privacy matters too: check whether your data trains the model and whether a no-log or enterprise tier is available. Whether you are a beginner or a pro, the right AI avatar generator slots into your workflow and pays for itself fast. We tested the leading options and ranked them by quality, value, and ease of use.
Read more →
Mark Thomas Gerard Keane (Irish: Marcus Ó Cathain, born 3 July 1961, Dublin, Ireland) is a cognitive scientist and author of several books on human cognition and artificial intelligence, including Cognitive Psychology: A Student's Handbook (8 editions, with Michael Eysenck), Advances in the Psychology of Thinking (1992, with Ken Gilhooly), Novice Programming Environments (1992/2018, with Marc Eisenstadt and Tim Rajan), Advances in Case-Based Reasoning (1995, with J-P Haton and Michel Manago)., Case-Based Reasoning: Research & Development (2022, with N Wiratunga). == Education == Keane received a B.A. in Psychology from University College Dublin in 1982. He then received a Ph.D. from Trinity College Dublin in 1987. He then moved to postdoctoral positions in Queen Mary University of London and the Open University. == Academic career == He was a Lecturer in Psychology at Cardiff University. He became a lecturer in Computer Science at Trinity College Dublin in 1990, and became a fellow in 1994. Keane moved to become Chair of Computer Science at University College Dublin in 1998. In 2006, he was seconded to Science Foundation Ireland as Director of ICT, overseeing on a $700m research investment. He advised the Irish Government on its 3.7B euro Strategy for Science, Technology & Innovation (SSTI). From 2006 to 2007, he was Director General of Science Foundation Ireland before returning to University College Dublin where he was appointed VP of Innovation & Partnerships (2007-2009). Keane's research has been split between cognitive science and computer science. His cognitive science research has been in analogy, metaphor, conceptual combination and similarity. His computer science research has been in natural language processing, machine learning, case-based reasoning, text analytics and explainable artificial intelligence. He has been a PI in the Science Foundation Ireland funded Insight Centre for Data Analytics working on digital journalism and digital humanities. More recently, he was deputy director of the VistaMilk SFI Research Centre that is exploring precision agriculture in the dairy sector.
Read more →