AI Email Corrector

AI Email Corrector — independent reviews, comparisons, pricing and step-by-step guides on Aizhi.

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  Moving object detection

  Moving object detection is a technique used in computer vision and image processing. Multiple consecutive frames from a video are compared by various methods to determine if any moving object is detected. Moving objects detection has been used for wide range of applications like video surveillance, activity recognition, road condition monitoring, airport safety, monitoring of protection along marine border, etc. == Definition == Moving object detection is to recognize the physical movement of an object in a given place or region. By acting segmentation among moving objects and stationary area or region, the moving objects' motion can be tracked and thus analyzed later. To achieve this, consider a video is a structure built upon single frames, moving object detection is to find the foreground moving target(s), either in each video frame or only when the moving target shows the first appearance in the video. == Traditional methods == Among all the traditional moving object detection methods, we could categorize them into four major approaches: Background subtraction, Frame differencing, Temporal Differencing, and Optical Flow. === Frame differencing === Instead of using traditional approach, to use image subtraction operator by subtracting second and images afterwards, the frame differencing method makes comparisons between two successive frames to detect moving targets. === Temporal differencing === The temporal differencing method identifies the moving object by applying pixel-wise difference method with two or three consecutive frames.

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  Best AI Customer-support Bots in 2026

  In search of the best AI customer-support bot? An AI customer-support bot is software that uses machine learning to help you get more done — it turns a rough idea into a polished result in seconds. When choosing one, weigh output quality, pricing, export formats, and how well it fits the tools you already use. Whether you are a beginner or a pro, the right AI customer-support bot slots into your workflow and pays for itself fast. Below we compare features, pricing, and real output so you can choose with confidence.

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  Timnit Gebru

  Timnit W. Gebru (Amharic and Tigrinya: ትምኒት ገብሩ; 1982/1983) is an Eritrean Ethiopian-born computer scientist who works in the fields of artificial intelligence (AI), algorithmic bias and data mining. She is a co-founder of Black in AI, an advocacy group that has pushed for more Black roles in AI development and research. She is the founder of the Distributed Artificial Intelligence Research Institute (DAIR). In December 2020, public controversy erupted over the circumstances surrounding Gebru's departure from Google, where she was technical co-lead of the Ethical Artificial Intelligence Team. Gebru had coauthored a paper on the risks of large language models (LLMs) acting as stochastic parrots, and submitted it for publication. According to Jeff Dean, head of Google AI, the paper was submitted without waiting for Google's internal review, which then asserted that it ignored too much relevant research. Google management requested that Gebru either withdraw the paper or remove the names of all the authors employed by Google. Gebru requested the identity and feedback of every reviewer, and stated that if Google refused, she would talk to her manager about "a last date". Google terminated her employment immediately, stating that they were accepting her resignation. Gebru maintained that she had not formally offered to resign, and only threatened to. Gebru has been widely recognized for her expertise in the ethics of artificial intelligence. She was named one of the World's 50 Greatest Leaders by Fortune and one of Nature's ten people who shaped science in 2021, and in 2022, one of Time's most influential people. == Early life and education == Gebru was raised in Addis Ababa, Ethiopia. Her father, an electrical engineer with a Doctor of Philosophy (PhD), died when she was five years old, and she was raised by her mother, an economist. Both her parents are from Eritrea. When Gebru was 15, during the Eritrean–Ethiopian War, she fled Ethiopia after some of her family were deported to Eritrea and compelled to fight in the war. She was initially denied a U.S. visa and briefly lived in Ireland, but she eventually received political asylum in the U.S., an experience she said was "miserable". Gebru settled in Somerville, Massachusetts to attend high school, where she says she immediately started to experience racial discrimination, with some teachers refusing to allow her to take certain Advanced Placement courses, despite being a high-achiever. After she completed high school, an encounter with the police set Gebru on a course toward a focus on ethics in technology. A friend of hers, a Black woman, was assaulted in a bar, and Gebru called the police to report it. She says that instead of filing the assault report, her friend was arrested and remanded to a cell. Gebru called it a pivotal moment and a "blatant example of systemic racism." In 2001, Gebru was accepted at Stanford University. There, she earned her Bachelor of Science and Master of Science degrees in electrical engineering and her PhD in computer vision in 2017. Gebru was advised during her PhD program by Fei-Fei Li. During the 2008 United States presidential election, Gebru canvassed in support of Barack Obama. Gebru presented her doctoral research at the 2017 LDV Capital Vision Summit competition, where computer vision scientists present their work to members of industry and venture capitalists. Gebru won the competition, starting a series of collaborations with other entrepreneurs and investors. Both during her PhD program in 2016 and in 2018, Gebru returned to Ethiopia with Jelani Nelson's programming campaign, AddisCoder. While working on her PhD, Gebru authored a paper that was never published about her concern over the future of AI. She wrote of the dangers of the lack of diversity in the field, centered on her experiences with the police and on a ProPublica investigation into predictive policing, which revealed a projection of human biases in machine learning. In the paper, she scathed the "boy's club culture", reflecting on her experiences at conference gatherings of drunken male attendees sexually harassing her, and criticized the hero worship of the field's celebrities. == Career == === 2004–2013: Software development at Apple === Gebru joined Apple as an intern while at Stanford, working in their hardware division making circuitry for audio components, and was offered a full-time position the following year. Of her work as an audio engineer, her manager told Wired she was "fearless", and well-liked by her colleagues. During her tenure at Apple, Gebru became more interested in building software, namely computer vision that could detect human figures. She went on to develop signal processing algorithms for the first iPad. At the time, she said she did not consider the potential use for surveillance, saying "I just found it technically interesting." Long after leaving the company, during the #AppleToo movement in the summer of 2021, which was led by Apple engineer Cher Scarlett, who consulted with Gebru, Gebru revealed she experienced "so many egregious things" and "always wondered how they manage[d] to get out of the spotlight." She said that accountability at Apple was long overdue, and warned they could not continue to fly under the radar for much longer. Gebru also criticized the way the media covers Apple and other tech giants, saying that the press helps shield such companies from public scrutiny. === 2013–2017: Research at Stanford and Microsoft === In 2013, Gebru joined Fei-Fei Li's lab at Stanford, where she combined deep learning with Google Street View to estimate the demographics of United States neighbourhoods, showing that socioeconomic attributes such as voting patterns, income, race, and education can be inferred from observations of cars. In 2015, Gebru attended the field's top conference, Neural Information Processing Systems (NIPS), in Montreal, Canada. Out of 3,700 attendees, she noted she was one of only a few Black researchers. When she attended again the following year, she kept a tally and noted that there were only five Black men and that she was the only Black woman out of 8,500 delegates. Together with her colleague Rediet Abebe, Gebru founded Black in AI, a community of Black researchers working in artificial intelligence that aims to increase the presence, visibility, and well-being of Black professionals and leaders within the field. In the summer of 2017, Gebru joined Microsoft as a postdoctoral researcher in the Fairness, Accountability, Transparency, and Ethics in AI (FATE) lab. In 2017, Gebru spoke at the Fairness and Transparency conference, where MIT Technology Review interviewed her about biases that exist in AI systems and how adding diversity in AI teams can fix that issue. In her interview with Jackie Snow, Snow asked Gebru, "How does the lack of diversity distort artificial intelligence and specifically computer vision?" and Gebru pointed out that there are biases that exist in the software developers. While at Microsoft, Gebru co-authored a research paper called Gender Shades, which became the namesake of a project of a broader Massachusetts Institute of Technology project led by co-author Joy Buolamwini. The pair investigated facial recognition software, finding that in one particular implementation Black women were 35% less likely to be recognized than White men. === 2018–2020: Artificial intelligence ethics at Google === Gebru joined Google in 2018, where she co-led a team on the ethics of artificial intelligence with Margaret Mitchell. She studied the implications of artificial intelligence, looking to improve the ability of technology to do social good. In 2019, Gebru and other artificial intelligence researchers "signed a letter calling on Amazon to stop selling its facial-recognition technology to law enforcement agencies because it is biased against women and people of color", citing a study that was conducted by MIT researchers showing that Amazon's facial recognition system had more trouble identifying darker-skinned females than any other technology company's facial recognition software. In a New York Times interview, Gebru has further expressed that she believes facial recognition is too dangerous to be used for law enforcement and security purposes at present. === Exit from Google === In 2020 Gebru and five co-authors wrote a paper titled "On the Dangers of Stochastic Parrots: Can Language Models Be Too Big? 🦜". The paper examined risks of very large language models, including their environmental footprint, financial costs, the inscrutability of large models, the potential for LLMs to display prejudice against certain groups, the inability of LLMs to understand the language they process, and the use of LLMs to spread disinformation. In December 2020, her employment with Google ended after Google management asked her to either withdraw the paper before publication, or remove the names of all the Google employees from

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  Trie

  In computer science, a trie (, ), also known as a digital tree or prefix tree, is a specialized search tree data structure used to store and retrieve strings from a dictionary or set. Unlike a binary search tree, nodes in a trie do not store their associated key. Instead, each node's position within the trie determines its associated key, with the connections between nodes defined by individual characters rather than the entire key. Tries are particularly effective for tasks such as autocomplete, spell checking, and IP routing, offering advantages over hash tables due to their prefix-based organization and lack of hash collisions. Every child node shares a common prefix with its parent node, and the root node represents the empty string. While basic trie implementations can be memory-intensive, various optimization techniques such as compression and bitwise representations have been developed to improve their efficiency. A notable optimization is the radix tree, which provides more efficient prefix-based storage. While tries store character strings, they can be adapted to work with any ordered sequence of elements, such as permutations of digits or shapes. A notable variant is the bitwise trie, which uses individual bits from fixed-length binary data (such as integers or memory addresses) as keys. == History, etymology, and pronunciation == The idea of a trie for representing a set of strings was first abstractly described by Axel Thue in 1912. Tries were first described in a computer context by René de la Briandais in 1959. The idea was independently described in 1960 by Edward Fredkin, who coined the term trie, pronouncing it (as "tree"), after the middle syllable of retrieval. However, other authors pronounce it (as "try"), in an attempt to distinguish it verbally from "tree". == Overview == Tries are a form of string-indexed look-up data structure, which is used to store a dictionary list of words that can be searched on in a manner that allows for efficient generation of completion lists. A prefix trie is an ordered tree data structure used in the representation of a set of strings over a finite alphabet set, which allows efficient storage of words with common prefixes. Tries can be efficacious on string-searching algorithms such as predictive text, approximate string matching, and spell checking in comparison to binary search trees. A trie can be seen as a tree-shaped deterministic finite automaton. == Operations == Tries support various operations: insertion, deletion, and lookup of a string key. Tries are composed of nodes that contain links, which either point to other suffix child nodes or null. As for every tree, each node except the root is pointed to by only one other node, called its parent. Each node contains as many links as the number of characters in the applicable alphabet (although tries tend to have a substantial number of null links). In some cases, the alphabet used is simply that of the character encoding—resulting in, for example, a size of 128 in the case of ASCII. The null links within the children of a node emphasize the following characteristics: Characters and string keys are implicitly stored in the trie, and include a character sentinel value indicating string termination. Each node contains one possible link to a prefix of strong keys of the set. A basic structure type of nodes in the trie is as follows: Node {\displaystyle {\text{Node}}} may contain an optional Value {\displaystyle {\text{Value}}} , which is associated with the key that corresponds to the node. === Searching === Searching for a value in a trie is guided by the characters in the search string key, as each node in the trie contains a corresponding link to each possible character in the given string. Thus, following the string within the trie yields the associated value for the given string key. A null link during the search indicates the inexistence of the key. The following pseudocode implements the search procedure for a given string key in a rooted trie x. In the above pseudocode, x and key correspond to the pointer of the trie's root node and the string key, respectively. The search operation takes O ( m ) {\displaystyle O(m)} time, where m {\displaystyle m} is the size of the string parameter key. In a balanced binary search tree, on the other hand, it takes O ( m log ⁡ n ) {\displaystyle O(m\log n)} time, in the worst case, since key needs to be compared with O ( log ⁡ n ) {\displaystyle O(\log n)} other keys and each comparison takes O ( m ) {\displaystyle O(m)} time, in the worst case. The trie occupies less space, in comparison with a binary search tree, in the case of a large number of short strings, since nodes share common initial string subsequences and store the keys implicitly. === Insertion === Insertion into a trie is guided by using the character sets as indexes to the children array until the last character of the string key is reached. Each node in the trie corresponds to one call of the radix sorting routine, as the trie structure reflects the execution pattern of the top-down radix sort. If null links are encountered before reaching the last character of the string key, new nodes are created. The input value is assigned to the value of the last node traversed, which is the node that corresponds to the key. === Deletion === Deletion of a key–value pair from a trie involves finding the node corresponding to the key, setting its value to null, and recursively removing nodes that have no children. The procedure begins by examining key; an empty string indicates arrival at the node corresponding to the (original) key, in which case its value is set to null. If the node, then, has null value and no children, it is removed from the trie by returning null; otherwise, the node is kept by returning the node itself. == Replacing other data structures == === Replacement for hash tables === A trie can be used to replace a hash table, over which it has the following advantages: Searching for a node with an associated key of size m {\displaystyle m} has the complexity of O ( m ) {\displaystyle O(m)} , whereas an imperfect hash function may have numerous colliding keys, and the worst-case lookup speed of such a table would be O ( N ) {\displaystyle O(N)} , where N {\displaystyle N} denotes the total number of nodes within the table. Tries do not need a hash function for the operation, unlike a hash table; there are also no collisions of different keys in a trie. Within a trie, keys can be efficiently sorted lexicographically. However, tries are less efficient than a hash table when the data is directly accessed on a secondary storage device such as a hard disk drive that has higher random access time than the main memory. == Implementation strategies == Tries can be represented in several ways, corresponding to different trade-offs between memory use and speed of the operations. Using a vector of pointers for representing a trie consumes enormous space; however, memory space can be reduced at the expense of running time if a singly linked list is used for each node vector, as most entries of the vector contains nil {\displaystyle {\text{nil}}} . Techniques such as alphabet reduction may reduce the large space requirements by reinterpreting the original string as a longer string over a smaller alphabet. For example, a string of n bytes can alternatively be regarded as a string of 2n four-bit units. This can reduce memory usage by a factor of eight; but lookups need to visit twice as many nodes in the worst case. Another technique includes storing a vector of 256 ASCII pointers as a bitmap of 256 bits representing ASCII alphabet, which reduces the size of individual nodes dramatically. === Bitwise tries === Bitwise tries are used to address the enormous space requirement for the trie nodes in a naive simple pointer vector implementations. Each character in the string key set is represented via individual bits, which are used to traverse the trie over a string key. The implementations for these types of trie use vectorized CPU instructions to find the first set bit in a fixed-length key input (e.g. GCC's __builtin_clz() intrinsic function). Accordingly, the set bit is used to index the first item, or child node, in the 32- or 64-entry based bitwise tree. Search then proceeds by testing each subsequent bit in the key. This procedure is also cache-local and highly parallelizable due to register independency, and thus performant on out-of-order execution CPUs. === Compressed tries === Radix tree, also known as a compressed trie, is a space-optimized variant of a trie in which any node with only one child gets merged with its parent; elimination of branches of the nodes with a single child results in better metrics in both space and time. This works best when the trie remains static and set of keys stored are very sparse within their representation space. One more approach for static tries is to "pack" the trie by storing disjoint

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  FMLLR

  In signal processing, Feature space Maximum Likelihood Linear Regression (fMLLR) is a global feature transform that are typically applied in a speaker adaptive way, where fMLLR transforms acoustic features to speaker adapted features by a multiplication operation with a transformation matrix. In some literature, fMLLR is also known as the Constrained Maximum Likelihood Linear Regression (cMLLR). == Overview == fMLLR transformations are trained in a maximum likelihood sense on adaptation data. These transformations may be estimated in many ways, but only maximum likelihood (ML) estimation is considered in fMLLR. The fMLLR transformation is trained on a particular set of adaptation data, such that it maximizes the likelihood of that adaptation data given a current model-set. This technique is a widely used approach for speaker adaptation in HMM-based speech recognition. Later research also shows that fMLLR is an excellent acoustic feature for DNN/HMM hybrid speech recognition models. The advantage of fMLLR includes the following: the adaptation process can be performed within a pre-processing phase, and is independent of the ASR training and decoding process. this type of adapted feature can be applied to deep neural networks (DNN) to replace traditionally used mel-spectrogram in end-to-end speech recognition models. fMLLR's speaker adaptation process leads to a significant performance boost for ASR models, hence outperforming other transform or features like MFCCs (Mel-Frequency Cepstral Coefficients) and FBANKs (Filter bank) coefficients. fMLLR features can be efficiently realized with speech toolkits like Kaldi. Major problem and disadvantage of fMLLR: when the amount of adaptation data is limited, the transformation matrices tends to easily overfit the given data. == Computing fMLLR transform == Feature transform of fMLLR can be easily computed with the open source speech tool Kaldi, the Kaldi script uses the standard estimation scheme described in Appendix B of the original paper, in particular the section Appendix B.1 "Direct method over rows". In the Kaldi formulation, fMLLR is an affine feature transform of the form x {\displaystyle x} → A {\displaystyle A} x {\displaystyle x} + b {\displaystyle +b} , which can be written in the form x {\displaystyle x} →W x ^ {\displaystyle {\hat {x}}} , where x ^ {\displaystyle {\hat {x}}} = [ x 1 ] {\displaystyle {\begin{bmatrix}x\\1\end{bmatrix}}} is the acoustic feature x {\displaystyle x} with a 1 appended. Note that this differs from some of the literature where the 1 comes first as x ^ {\displaystyle {\hat {x}}} = [ 1 x ] {\displaystyle {\begin{bmatrix}1\\x\end{bmatrix}}} . The sufficient statistics stored are: K = ∑ t , j , m γ j , m ( t ) Σ j m − 1 μ j m x ( t ) + {\displaystyle K=\sum _{t,j,m}\gamma _{j,m}(t)\textstyle \Sigma _{jm}^{-1}\mu _{jm}x(t)^{+}\displaystyle } where Σ j m − 1 {\displaystyle \textstyle \Sigma _{jm}^{-1}\displaystyle } is the inverse co-variance matrix. And for 0 ≤ i ≤ D {\displaystyle 0\leq i\leq D} where D {\displaystyle D} is the feature dimension: G ( i ) = ∑ t , j , m γ j , m ( t ) ( 1 σ j , m 2 ( i ) ) x ( t ) + x ( t ) + T {\displaystyle G^{(i)}=\sum _{t,j,m}\gamma _{j,m}(t)\left({\frac {1}{\sigma _{j,m}^{2}(i)}}\right)x(t)^{+}x(t)^{+T}\displaystyle } For a thorough review that explains fMLLR and the commonly used estimation techniques, see the original paper "Maximum likelihood linear transformations for HMM-based speech recognition ". Note that the Kaldi script that performs the feature transforms of fMLLR differs with by using a column of the inverse in place of the cofactor row. In other words, the factor of the determinant is ignored, as it does not affect the transform result and can causes potential danger of numerical underflow or overflow. == Comparing with other features or transforms == Experiment result shows that by using the fMLLR feature in speech recognition, constant improvement is gained over other acoustic features on various commonly used benchmark datasets (TIMIT, LibriSpeech, etc). In particular, fMLLR features outperform MFCCs and FBANKs coefficients, which is mainly due to the speaker adaptation process that fMLLR performs. In, phoneme error rate (PER, %) is reported for the test set of TIMIT with various neural architectures: As expected, fMLLR features outperform MFCCs and FBANKs coefficients despite the use of different model architecture. Where MLP (multi-layer perceptron) serves as a simple baseline, on the other hand RNN, LSTM, and GRU are all well known recurrent models. The Li-GRU architecture is based on a single gate and thus saves 33% of the computations over a standard GRU model, Li-GRU thus effectively address the gradient vanishing problem of recurrent models. As a result, the best performance is obtained with the Li-GRU model on fMLLR features. == Extract fMLLR features with Kaldi == fMLLR can be extracted as reported in the s5 recipe of Kaldi. Kaldi scripts can certainly extract fMLLR features on different dataset, below are the basic example steps to extract fMLLR features from the open source speech corpora Librispeech. Note that the instructions below are for the subsets train-clean-100,train-clean-360,dev-clean, and test-clean, but they can be easily extended to support the other sets dev-other, test-other, and train-other-500. These instruction are based on the codes provided in this GitHub repository, which contains Kaldi recipes on the LibriSpeech corpora to execute the fMLLR feature extraction process, replace the files under $KALDI_ROOT/egs/librispeech/s5/ with the files in the repository. Install Kaldi. Install Kaldiio. If running on a single machine, change the following lines in $KALDI_ROOT/egs/librispeech/s5/cmd.sh to replace queue.pl to run.pl: Change the data path in run.sh to your LibriSpeech data path, the directory LibriSpeech/ should be under that path. For example: Install flac with: sudo apt-get install flac Run the Kaldi recipe run.sh for LibriSpeech at least until Stage 13 (included), for simplicity you can use the modified run.sh. Copy exp/tri4b/trans. files into exp/tri4b/decode_tgsmall_train_clean_/ with the following command: Compute the fMLLR features by running the following script, the script can also be downloaded here: Compute alignments using: Apply CMVN and dump the fMLLR features to new .ark files, the script can also be downloaded here: Use the Python script to convert Kaldi generated .ark features to .npy for your own dataloader, an example Python script is provided:

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  Best AI Analytics Tools in 2026

  Curious about the best AI analytics tool? An AI analytics tool 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 analytics 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.

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  Interacting particle system

  In probability theory, an interacting particle system (IPS) is a stochastic process ( X ( t ) ) t ∈ R + {\displaystyle (X(t))_{t\in \mathbb {R} ^{+}}} on some configuration space Ω = S G {\displaystyle \Omega =S^{G}} given by a site space, a countably-infinite-order graph G {\displaystyle G} and a local state space, a compact metric space S {\displaystyle S} . More precisely IPS are continuous-time Markov jump processes describing the collective behavior of stochastically interacting components. IPS are the continuous-time analogue of stochastic cellular automata. Among the main examples are the voter model, the contact process, the asymmetric simple exclusion process (ASEP), the Glauber dynamics and in particular the stochastic Ising model. IPS are usually defined via their Markov generator giving rise to a unique Markov process using Markov semigroups and the Hille-Yosida theorem. The generator again is given via so-called transition rates c Λ ( η , ξ ) > 0 {\displaystyle c_{\Lambda }(\eta ,\xi )>0} where Λ ⊂ G {\displaystyle \Lambda \subset G} is a finite set of sites and η , ξ ∈ Ω {\displaystyle \eta ,\xi \in \Omega } with η i = ξ i {\displaystyle \eta _{i}=\xi _{i}} for all i ∉ Λ {\displaystyle i\notin \Lambda } . The rates describe exponential waiting times of the process to jump from configuration η {\displaystyle \eta } into configuration ξ {\displaystyle \xi } . More generally the transition rates are given in form of a finite measure c Λ ( η , d ξ ) {\displaystyle c_{\Lambda }(\eta ,d\xi )} on S Λ {\displaystyle S^{\Lambda }} . The generator L {\displaystyle L} of an IPS has the following form. First, the domain of L {\displaystyle L} is a subset of the space of "observables", that is, the set of real valued continuous functions on the configuration space Ω {\displaystyle \Omega } . Then for any observable f {\displaystyle f} in the domain of L {\displaystyle L} , one has L f ( η ) = ∑ Λ ∫ ξ : ξ Λ c = η Λ c c Λ ( η , d ξ ) [ f ( ξ ) − f ( η ) ] {\displaystyle Lf(\eta )=\sum _{\Lambda }\int _{\xi :\xi _{\Lambda ^{c}}=\eta _{\Lambda ^{c}}}c_{\Lambda }(\eta ,d\xi )[f(\xi )-f(\eta )]} . For example, for the stochastic Ising model we have G = Z d {\displaystyle G=\mathbb {Z} ^{d}} , S = { − 1 , + 1 } {\displaystyle S=\{-1,+1\}} , c Λ = 0 {\displaystyle c_{\Lambda }=0} if Λ ≠ { i } {\displaystyle \Lambda \neq \{i\}} for some i ∈ G {\displaystyle i\in G} and c i ( η , η i ) = exp ⁡ [ − β ∑ j : | j − i | = 1 η i η j ] {\displaystyle c_{i}(\eta ,\eta ^{i})=\exp[-\beta \sum _{j:|j-i|=1}\eta _{i}\eta _{j}]} where η i {\displaystyle \eta ^{i}} is the configuration equal to η {\displaystyle \eta } except it is flipped at site i {\displaystyle i} . β {\displaystyle \beta } is a new parameter modeling the inverse temperature. == The Voter model == The voter model (usually in continuous time, but there are discrete versions as well) is a process similar to the contact process. In this process η ( x ) {\displaystyle \eta (x)} is taken to represent a voter's attitude on a particular topic. Voters reconsider their opinions at times distributed according to independent exponential random variables (this gives a Poisson process locally – note that there are in general infinitely many voters so no global Poisson process can be used). At times of reconsideration, a voter chooses one neighbor uniformly from amongst all neighbors and takes that neighbor's opinion. One can generalize the process by allowing the picking of neighbors to be something other than uniform. === Discrete time process === In the discrete time voter model in one dimension, ξ t ( x ) : Z → { 0 , 1 } {\displaystyle \xi _{t}(x):\mathbb {Z} \to \{0,1\}} represents the state of particle x {\displaystyle x} at time t {\displaystyle t} . Informally each individual is arranged on a line and can "see" other individuals that are within a radius, r {\displaystyle r} . If more than a certain proportion, θ {\displaystyle \theta } of these people disagree then the individual changes her attitude, otherwise she keeps it the same. Durrett and Steif (1993) and Steif (1994) show that for large radii there is a critical value θ c {\displaystyle \theta _{c}} such that if θ > θ c {\displaystyle \theta >\theta _{c}} most individuals never change, and for θ ∈ ( 1 / 2 , θ c ) {\displaystyle \theta \in (1/2,\theta _{c})} in the limit most sites agree. (Both of these results assume the probability of ξ 0 ( x ) = 1 {\displaystyle \xi _{0}(x)=1} is one half.) This process has a natural generalization to more dimensions, some results for this are discussed in Durrett and Steif (1993). === Continuous time process === The continuous time process is similar in that it imagines each individual has a belief at a time and changes it based on the attitudes of its neighbors. The process is described informally by Liggett (1985, 226), "Periodically (i.e., at independent exponential times), an individual reassesses his view in a rather simple way: he chooses a 'friend' at random with certain probabilities and adopts his position." A model was constructed with this interpretation by Holley and Liggett (1975). This process is equivalent to a process first suggested by Clifford and Sudbury (1973) where animals are in conflict over territory and are equally matched. A site is selected to be invaded by a neighbor at a given time.

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  Maike Osborne

  Maike Osborne (born Michael Osborne, 1982) is an Australian academic and scientist who serves as a professor of machine learning at University of Oxford in the Machine Learning Research Group in the Department of Engineering Science. In 2016 she co-founded Mind Foundry, an artificial intelligence company, along with fellow professor Stephen Roberts. == Education == She has a BEng in Mechanical Engineering and a BSc in both Pure Mathematics and Physics from the University of Western Australia. She has a PhD in Machine Learning from the University of Oxford. == Career == Osborne has contributed to over 100 publications, and her work has received over 24,000 citations with an h-index of 46 according to Google Scholar. and has acted as principal or co-investigator for £10.6M of research funding. Her career has focused in particular on Bayesian approaches to AI and machine learning, named after the famous British statistician Thomas Bayes. Osborne's work has contributed to Probabilistic numerics, with Osborne co-authoring the first textbook on the subject. In 2013, Osborne co-authored a paper alongside Swedish-German economist Carl Benedikt Frey called "The Future of Employment: How Susceptible are Jobs to Computerisation?". The paper has received over 13,000 citations and extensive media coverage. In 2023 Osborne gave oral evidence to the UK House of Commons Science and Technology Committee on the subject of the "Governance of Artificial Intelligence". Her testimony received significant coverage around her warnings of the threat of "rogue AI". == Honors == She is also an Official Fellow of Exeter College, and St Peter's College, Oxford, a Fellow of the ELLIS society, and a Faculty Member of the Oxford-Man Institute of Quantitative Finance. She joined the Oxford Martin School as Lead Researcher on the Oxford Martin Programme on Technology and Employment in 2015. She is a Director of the EPSRC Centre for Doctoral Training in Autonomous Intelligent Machines and Systems.

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  1.58-bit large language model

  A 1.58-bit large language model (also known as a ternary LLM) is a type of large language model (LLM) designed to be computationally efficient. It achieves this by using weights that are restricted to only three values: -1, 0, and +1. This restriction significantly reduces the model's memory footprint and allows for faster processing, as computationally expensive multiplication operations can be replaced with lower-cost additions. This contrasts with traditional models that use 16-bit floating-point numbers (FP16 or BF16) for their weights. Studies have shown that for models up to several billion parameters, the performance of 1.58-bit LLMs on various tasks is comparable to their full-precision counterparts. This approach could enable powerful AI to run on less specialized and lower-power hardware. The name "1.58-bit" comes from the fact that a system with three states contains log 2 ⁡ 3 ≈ 1.58 {\displaystyle \log _{2}3\approx 1.58} bits of information. These models are sometimes also referred to as 1-bit LLMs in research papers, although this term can also refer to true binary models (with weights of -1 and +1). == BitNet == In 2024, Ma et al., researchers at Microsoft, declared that their 1.58-bit model, BitNet b1.58 is comparable in performance to the 16-bit Llama 2 and opens the era of 1-bit LLM. BitNet creators did not use the post-training quantization of weights but instead relied on the new BitLinear transform that replaced the nn.Linear layer of the traditional transformer design. In 2025, Microsoft researchers had released an open-weights and open inference code model BitNet b1.58 2B4T demonstrating performance competitive with the full precision models at 2B parameters and 4T training tokens. == Post-training quantization == BitNet derives its performance from being trained natively in 1.58 bit instead of being quantized from a full-precision model after training. Still, training is an expensive process and it would be desirable to be able to somehow convert an existing model to 1.58 bits. In 2024, HuggingFace reported a way to gradually ramp up the 1.58-bit quantization in fine-tuning an existing model down to 1.58 bits. == Critique == Some researchers point out that the scaling laws of large language models favor the low-bit weights only in case of undertrained models. As the number of training tokens increases, the deficiencies of low-bit quantization surface.

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  Aravind Joshi

  Aravind Krishna Joshi (August 5, 1929 – December 31, 2017) was the Henry Salvatori Professor of Computer and Cognitive Science in the computer science department of the University of Pennsylvania. Joshi defined the tree-adjoining grammar formalism which is often used in computational linguistics and natural language processing. Joshi studied at Pune University and the Indian Institute of Science, where he was awarded a BE in electrical engineering and a DIISc in communication engineering respectively. Joshi's graduate work was done in the electrical engineering department at the University of Pennsylvania, and he was awarded his PhD in 1960. He became a professor at Penn and was the co-founder and co-director of the Institute for Research in Cognitive Science. == Awards and recognitions == Guggenheim fellow, 1971–72 Fellow of the Institute of Electrical and Electronics Engineers (IEEE), 1976 Best Paper Award at the National Conference on Artificial Intelligence, 1987 Founding Fellow of the American Association for Artificial Intelligence (AAAI), 1990 IJCAI Award for Research Excellence, 1997 Fellow of the Association for Computing Machinery, 1998 Elected to the National Academy of Engineering, 1999 First to be awarded the Association for Computational Linguistics Lifetime Achievement Award at the 40th anniversary meeting of the ACL, 2002 Awarded the Rumelhart Prize, 2003 Benjamin Franklin Medal in Computer and Cognitive Science, 2005 Doctor honoris causa of mathematical and physical sciences, Charles University in Prague, October 30, 2013 S.-Y. Kuroda Prize of the SIG Mathematics of Language of the ACL, 2013 === Awarded history === On April 21, 2005, Joshi was awarded the Franklin Institute's Benjamin Franklin Medal in Computer and Cognitive Science. The Franklin Institute citation states that he was awarded the medal "for his fundamental contributions to our understanding of how language is represented in the mind, and for developing techniques that enable computers to process efficiently the wide range of human languages. These advances have led to new methods for computer translation."

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  Top 10 AI Subtitle Generators Compared (2026)

  Curious about the best AI subtitle generator? An AI subtitle generator 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 subtitle generator slots into your workflow and pays for itself fast. Read on for hands-on impressions, pricing tiers, and the standout features that matter.

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  Karsten Borgwardt

  Karsten Borgwardt (born 1980) is a German computer scientist and biologist specializing in machine learning and computational biology. Since February 2023, he has been a director at the Max Planck Institute of Biochemistry in Martinsried, Germany, where he leads the Department of Machine Learning and Systems Biology. == Education and career == Borgwardt was born in Kaiserslautern. He obtained a Diplom (equivalent to a master’s degree) in computer science from LMU Munich in 2004 and a Master of Science in biology from the University of Oxford in 2003. In 2007, he obtained his PhD from LMU Munich in computer science. Following a postdoctoral position at the University of Cambridge, he became a research group leader for machine learning and computational biology at the Max Planck Institute for Biological Cybernetics and the former Max Planck Institute for Developmental Biology in Tübingen in 2008. In 2011, Borgwardt was appointed professor of data mining in the life sciences at the University of Tübingen. In 2014, he joined ETH Zurich as an associate professor in the Department of Biosystems Science and Engineering (D-BSSE) and was promoted to full professor in 2017. During his tenure at ETH Zurich, he coordinated significant research programs, including two Marie Curie Innovative Training Networks and the Personalized Swiss Sepsis Study, focusing on the prediction of sepsis using machine learning. In 2023, he was appointed as Scientific Member of the Max Planck Society and as Director at the Max Planck Institute of Biochemistry in Martinsried. == Research contributions == Borgwardt’s research integrates big data analysis with biomedical research. He develops novel machine learning algorithms to detect patterns and statistical dependencies in large biological and medical datasets. His work aims to enable the automatic generation of new knowledge from big data and to understand the relationship between the function of biological systems and their molecular properties, which is fundamental for personalized medicine. == Awards and honors == During his studies, he was a scholar of the Stiftung Maximilianeum, and the Bavarian Foundation for the Promotion of the Gifted. Borgwardt received scholarships from the Studienstiftung des deutschen Volkes in 2002 and 2007. His PhD dissertation received the Heinz Schwärtzel Dissertation Award for Foundations of Computer Science in 2007. As a professor in Tübingen, he was awarded the Alfried-Krupp-Förderpreis for Young Professors in 2013. In 2015, he received an SNSF Starting Grant. In 2014, 2015 and 2016, he was listed in “Top 40 under 40” in Germany rankings selected by Capital magazine. In 2018, Borgwardt was named among “25 individuals who have the potential to shape the next 25 years” by Focus magazine. In 2023, Borgwardt received an honorary professorship from LMU Munich by the Faculty of Chemistry and Pharmacy. Publications from Borgwardt's group have received the Outstanding Student Paper Award in NIPS in 2009, the SIB Graduate Paper Award in 2020 and SIB Remarkable Output Awards in 2020 and 2021 from the Swiss Institute of Bioinformatics (SIB). == Selected publications == Weisfeiler-Lehman Graph Kernels (’‘Journal of Machine Learning Research’’, 2011): Introduced an efficient graph kernel based on the Weisfeiler-Lehman algorithm. “Direct antimicrobial resistance prediction from clinical MALDI-TOF mass spectra using machine learning” (’‘Nature Medicine’’, 2022): showcased the feasibility of predicting antimicrobial resistance from readily collected mass spectrometry data in the hospital. The new method is able to identify antibiotic resistance 24 hours earlier than previous methods.

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  Reverse correlation technique

  The reverse correlation technique is a data driven study method used primarily in psychological and neurophysiological research. This method earned its name from its origins in neurophysiology, where cross-correlations between white noise stimuli and sparsely occurring neuronal spikes could be computed quicker when only computing it for segments preceding the spikes. The term has since been adopted in psychological experiments that usually do not analyze the temporal dimension, but also present noise to human participants. In contrast to the original meaning, the term is here thought to reflect that the standard psychological practice of presenting stimuli of defined categories to the participants is "reversed": Instead, the participant's mental representations of categories are estimated from interactions of the presented noise and the behavioral responses. It is used to create composite pictures of individual and/or group mental representations of various items (e.g. faces, bodies, and the self) that depict characteristics of said items (e.g. trustworthiness and self-body image). This technique is helpful when evaluating the mental representations of those with and without mental illnesses. == Terms == This technique utilizes spike-triggered average to explain what areas of signal and noise in an image are valuable for the given research question. Signal is information used to produce objects of value that help explain and connect the world around us. Noise is commonly referred to as unwanted signal that obscures the information that the signal is trying to present. Most importantly for reverse correlation studies, noise is randomly varying information. To determine the areas of importance using reverse correlation, noise is applied to a base image and then evaluated by observers. A base image is any image void of noise that relates to the research question. A base image that has noise superimposed on top is the stimuli that is presented to and evaluated by participants. Each time a new set of stimuli is presented to a participant, this is known as a trial. After a participant has responded to hundreds to thousands of trials, a researcher is ready to create a classification image. A classification image (abbreviated as "CI" in some studies) is a single image that represents the average noise patterns in the images selected by participants. A classification image can also be computed for groups by averaging the individuals’ classification images. These classification images are what researchers use to interpret the data and draw conclusions. As a whole, the reverse correlation method is a process that results in a composite image (from an individual or group) that can be used to estimate and interpret mental representations. == Basic study layout == The reverse correlation method is typically executed as an in-lab computer experiment. This method follows four broad steps. Each of the following steps are described in greater detail below. After creating a research question and determining that the reverse correlation method is the most suitable technique to answer the question, a researcher must (1) design randomly varying stimuli. After the stimuli have been prepared, a researcher should (2) collect data from participants who will see and respond to approximately 300 -1,000 trials. Each trial will either consist of one or two images (side by side) derived from the same base image with noise superimposed on top. Participant responses will depend on the chosen study design; if a researcher presents only one image at a time, participants rate the image on a 4pt scale, but when two images are shown, the participant is asked to choose which best aligns with the given category (e.g. choose the image that looks the most aggressive). Once all of the data is collected, the researcher will (3) compute classification images for each participant and using those images compute group classification images. Finally, with the classification images available, the researcher will (4) evaluate the images and draw conclusions about their results. === Step 1: making stimuli === When designing the stimuli for a reverse correlation study, the two primary factors that one should consider are (1) the base image and (2) the noise that will be used. While not all bases are images per se, the majority are and for this reason the base is typically referred to as a base image. The base image should represent whatever the research question is addressing. For example, if you are interested in peoples’ mental representations of Chinese people, it would not make sense to use a base image of a Spanish or Caucasian person. Again, if you are interested in the mental representations of male vocal patterns, it would make the most sense to use a base vocal pattern that has been produced by a male. Having a base is important because it provides a kind of anchor for participants to work from. When there is no base image, the number of trials that are required increases dramatically, thus making it harder to collect data. While there are studies that have excluded a base image, (e.g. the S study), for more elaborate and nuanced research questions, it is important to have a base image that is a fair representation of what participants are being asked to categorize. Photographs of faces are generally the most popular base image. Although the reverse correlation method is capable of investigating a wide variety of research questions, the most common application of the method is for evaluating faces on a single trait. Reverse correlation studies that address evaluations of the face are sometimes referred to as being a face space reverse correlation model (FSRCM). Thankfully, there are existing databases for face images of varying demographics and emotion that work well as base images. The reverse correlation method can also be used to help researchers identify what areas of an image (e.g. the areas on the face) have diagnostic value. In order to identify these areas of value, researchers start by minimizing the space a participant can pull information from. By imposing a “mask” on an image (e.g. blur an image while leaving random areas un-blurred), this reduces the information individuals might see, and forces them to focus on certain areas. Then, if/when participants are able to correctly identify an image with a trait repeatedly, we can draw conclusions about what areas have diagnostic value. While faces and visual stimuli are the most popular, this is not the only stimuli that can be used in a reverse correlation study. This method was originally designed for auditory stimuli which allows researchers to investigate how perceivers interpret auditory information and create trait based attributions to different sound patterns. For example, by segmenting a vocal recording of a single word (total sound time 426 ms) into six segments (71 ms each), and varying each segment's pitch using Gaussian distributions, researchers were able to uncover what vocal patterns people associated with certain traits. Specifically, this study investigated how listeners rated sound clips of the word “really” as sounding more interrogative (i.e. like the more common reverse correlation studies this study had participants listen to two sound clips per trial, choose which fit the category the best, and then created an average of the pitch contours). Beyond face and auditory perception, research utilizing the reverse correlation method has expanded to investigate how individuals see three-dimensional objects in images with noise (but no signal). After selecting your base image, regardless of what the image is, it is helpful to apply a Gaussian blur to smooth noise in the image. While noise will be applied later, it is helpful to reduce existing noise in the photo before applying your chosen noise. There are three primary choices when it comes to noise: white noise, sine-wave noise, and Gabor noise. The latter two of these constrain the configurations that the noise can have, and because of this white noise is usually the most commonly used. Regardless of the type of noise that is chosen, it is crucial that the noise randomly varies. === Step 2: data collection === Once the stimuli for the study has been developed, the researcher must make a few decisions before actually collecting the data. The researcher must come to a conclusion on how many stimuli will be presented at a time and how many trials the participants will see. In terms of stimuli presentation, a researcher can choose from either a 2-Image Forced Choice (2IFC) or a 4-Alternative Forced Choice (4AFC). The 2IFC presents two images at once (side by side) and requires participants to choose between the two on a specified category (e.g. which image looks the most like a male). Typically the noise from the left image is the mathematical inverse of the noise from the right image. This method was developed to better answer questions that could n

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  Aslı Çelikyılmaz

  Aslı Çelikyılmaz is an engineer specializing in natural language processing, and particularly in natural language generation for software agents with advanced reasoning and real-world modeling capabilities. Educated in Turkey and Canada, she works in the US as senior research lead at Fundamentals AI Research, Meta. She also holds an affiliate faculty position in computer science at the University of Washington, and is co-editor-in-chief of the journal Transactions of the Association for Computational Linguistics. == Education and career == Çelikyılmaz is a 1997 graduate of Istanbul Technical University, where she studied industrial engineering. After a 2002 master's degree in computer and information science from Seneca Polytechnic in Toronto, and a second master's degree in information science from the University of Toronto in 2005, she completed a Ph.D. in information science at the University of Toronto in 2008. She worked as a postdoctoral researcher in California, at the University of California, Berkeley, from 2008 to 2010. In 2010 she joined Microsoft in Sunnyvale, California, where she became a senior scientist and later a senior principal researcher in Redmond, Washington. She added her affiliation with the University of Washington in 2018, and moved to Meta in Seattle in 2021. == Recognition == Çelikyılmaz was named to the 2026 class of IEEE Fellows, "for contributions to conversational systems and language generation".

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  AI Essay Writers: Free vs Paid (2026)

  Looking for the best AI essay writer? An AI essay writer 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 essay writer slots into your workflow and pays for itself fast. Read on for hands-on impressions, pricing tiers, and the standout features that matter.

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