AI Writing Tools

Explore the best AI Writing Tools — independent reviews, comparisons, pricing and step-by-step how-to guides, curated by Aizhi.

Hierarchical navigable small world

Hierarchical navigable small world (HNSW) is an algorithm for approximate nearest neighbor search. It is used to find items that are similar to a query item in a large collection, without comparing the query with every item one by one. The algorithm is commonly used for searching vector data. In these systems, an item such as a document, image, song, or user profile is represented by a list of numbers called a vector. Items with similar vectors are treated as similar according to the model that produced the vectors. HNSW provides a way to search these vectors quickly, especially in large datasets. HNSW stores vectors in a graph. Each vector is a node, and links connect it to some nearby vectors. The graph has several layers: upper layers contain fewer nodes and act like a rough map, while the bottom layer contains all nodes and gives a more detailed view. A search starts in an upper layer, follows links toward nodes that are closer to the query, and then repeats the process in lower layers until it finds a set of likely nearest neighbors. == Background == The nearest neighbor search problem asks which items in a dataset are closest to a query item. A direct search can compare the query with every item in the dataset, but this becomes slow when the dataset is large. Exact search methods based on spatial trees, such as the k-d tree and R-tree, can also become less effective for high-dimensional data, a problem often associated with the curse of dimensionality. Approximate nearest neighbor methods trade some exactness for speed or lower resource use. Instead of always guaranteeing the exact closest item, they try to return close items quickly. Other approximate methods include locality-sensitive hashing and product quantization. HNSW builds on research into small-world networks and navigable graphs. In a small-world graph, most nodes can be reached from other nodes through a short chain of links. In a navigable graph, a search procedure can use local information to move toward a target. Jon Kleinberg's work on navigation in small-world networks is an important example of this research area. Later work studied ways to add links that make graphs easier to navigate greedily. The HNSW algorithm extends earlier navigable small world methods for similarity search by adding a hierarchy of graph layers. This hierarchy helps the algorithm find a good region of the graph before doing a more detailed search in the bottom layer. == Algorithm == HNSW is based on a proximity graph. In this graph, nearby vectors are connected by edges. The algorithm uses these edges to move through the dataset, rather than scanning every vector. The graph is hierarchical. Every vector appears in the bottom layer. Some vectors are also placed in higher layers, with fewer vectors appearing as the layers go upward. The upper layers allow long-range movement across the dataset, while the lower layers allow a more detailed search near promising candidates. A typical search proceeds as follows: The search begins from an entry point in the highest layer. At each step, the algorithm looks at neighboring nodes and moves to a neighbor that is closer to the query. When it cannot find a closer neighbor in that layer, it moves down to the next layer. In the bottom layer, it explores a wider set of candidate nodes and returns the nearest candidates found. This search strategy is often described as greedy navigation. The algorithm repeatedly chooses locally better nodes, using the graph structure to approach the query point. == Construction and parameters == The HNSW graph is built incrementally. When a new vector is inserted, the algorithm assigns it a maximum layer, searches for nearby existing nodes, and connects the new node to selected neighbors in each layer where it appears. Implementations usually expose parameters that control the trade-off between speed, accuracy, memory use, and construction time. A higher number of graph connections can improve recall but requires more memory. A larger search candidate list can improve accuracy but makes queries slower. A larger construction candidate list can improve the quality of the graph but makes index building slower. Because HNSW is approximate, its results are not always identical to a full exact search. Its practical performance depends on the dataset, distance measure, implementation, and parameter settings. Benchmarking studies have found HNSW-based libraries to be strong performers among approximate nearest neighbor methods, although worst-case performance can differ from performance on common benchmark datasets. == Use in vector search systems == HNSW is used as an index in systems that store and search high-dimensional vectors. These systems include vector databases, search engines, and database extensions. Typical uses include semantic search, recommender systems, image similarity search, and retrieval-augmented generation. Several software projects implement or support HNSW. Libraries include hnswlib, which is associated with the original HNSW authors, and FAISS. Database and search systems that document HNSW support include Apache Lucene, Chroma, ClickHouse, DuckDB, MariaDB, Milvus, pgvector, Qdrant, and Redis.
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Additive smoothing

In statistics, additive smoothing, also called Laplace smoothing or Lidstone smoothing, is a technique used to smooth count data, eliminating issues caused by certain values having 0 occurrences. Given a set of observation counts x = ⟨ x 1 , x 2 , … , x d ⟩ {\displaystyle \mathbf {x} =\langle x_{1},x_{2},\ldots ,x_{d}\rangle } from a d {\displaystyle d} -dimensional multinomial distribution with N {\displaystyle N} trials, a "smoothed" version of the counts gives the estimator θ ^ i = x i + α N + α d ( i = 1 , … , d ) , {\displaystyle {\hat {\theta }}_{i}={\frac {x_{i}+\alpha }{N+\alpha d}}\qquad (i=1,\ldots ,d),} where the smoothed count x ^ i = N θ ^ i {\displaystyle {\hat {x}}_{i}=N{\hat {\theta }}_{i}} , and the "pseudocount" α > 0 is a smoothing parameter, with α = 0 corresponding to no smoothing (this parameter is explained in § Pseudocount below). Additive smoothing is a type of shrinkage estimator, as the resulting estimate will be between the empirical probability (relative frequency) x i / N {\displaystyle x_{i}/N} and the uniform probability 1 / d . {\displaystyle 1/d.} Common choices for α are 0 (no smoothing), +1⁄2 (the Jeffreys prior), or 1 (Laplace's rule of succession), but the parameter may also be set empirically based on the observed data. From a Bayesian point of view, this corresponds to the expected value of the posterior distribution, using a symmetric Dirichlet distribution with parameter α as a prior distribution. In the special case where the number of categories is 2, this is equivalent to using a beta distribution as the conjugate prior for the parameters of the binomial distribution. == History == Laplace came up with this smoothing technique when he tried to estimate the chance that the sun will rise tomorrow. His rationale was that even given a large sample of days with the rising sun, we still can not be completely sure that the sun will still rise tomorrow (known as the sunrise problem). == Pseudocount == A pseudocount is an amount (not generally an integer, despite its name) added to the number of observed cases in order to change the expected probability in a model of those data, when not known to be zero. It is so named because, roughly speaking, a pseudo-count of value α {\displaystyle \alpha } weighs into the posterior distribution similarly to each category having an additional count of α {\displaystyle \alpha } . If the number of occurrences of each item i {\displaystyle i} is x i {\displaystyle x_{i}} out of N {\displaystyle N} samples, the empirical probability of event i {\displaystyle i} is p i , empirical = x i N , {\displaystyle p_{i,{\text{empirical}}}={\frac {x_{i}}{N}},} but the posterior probability when additively smoothed is p i , α -smoothed = x i + α N + α d , {\displaystyle p_{i,\alpha {\text{-smoothed}}}={\frac {x_{i}+\alpha }{N+\alpha d}},} as if to increase each count x i {\displaystyle x_{i}} by α {\displaystyle \alpha } a priori. Depending on the prior knowledge, which is sometimes a subjective value, a pseudocount may have any non-negative finite value. It may only be zero (or the possibility ignored) if impossible by definition, such as the possibility of a decimal digit of π being a letter, or a physical possibility that would be rejected and so not counted, such as a computer printing a letter when a valid program for π is run, or excluded and not counted because of no interest, such as if only interested in the zeros and ones. Generally, there is also a possibility that no value may be computable or observable in a finite time (see the halting problem). But at least one possibility must have a non-zero pseudocount, otherwise no prediction could be computed before the first observation. The relative values of pseudocounts represent the relative prior expected probabilities of their possibilities. The sum of the pseudocounts, which may be very large, represents the estimated weight of the prior knowledge compared with all the actual observations (one for each) when determining the expected probability. In any observed data set or sample there is the possibility, especially with low-probability events and with small data sets, of a possible event not occurring. Its observed frequency is therefore zero, apparently implying a probability of zero. This oversimplification is inaccurate and often unhelpful, particularly in probability-based machine learning techniques such as artificial neural networks and hidden Markov models. By artificially adjusting the probability of rare (but not impossible) events so those probabilities are not exactly zero, zero-frequency problems are avoided. Also see Cromwell's rule. === Choice of pseudocount === ==== Weakly informative prior ==== One common approach is to add 1 to each observed number of events, including the zero-count possibilities. This is sometimes called Laplace's rule of succession. This approach is equivalent to assuming a uniform prior distribution over the probabilities for each possible event (spanning the simplex where each probability is between 0 and 1, and they all sum to 1). Using the Jeffreys prior approach, a pseudocount of one half should be added to each possible outcome. Pseudocounts should be set to one or one-half only when there is no prior knowledge at all – see the principle of indifference. However, given appropriate prior knowledge, the sum should be adjusted in proportion to the expectation that the prior probabilities should be considered correct, despite evidence to the contrary – see further analysis. Higher values are appropriate inasmuch as there is prior knowledge of the true values (for a mint-condition coin, say); lower values inasmuch as there is prior knowledge that there is probable bias, but of unknown degree (for a bent coin, say). ==== Frequentist interval ==== One way to motivate pseudocounts, particularly for binomial data, is via a formula for the midpoint of an interval estimate, particularly a binomial proportion confidence interval. The best-known is due to Edwin Bidwell Wilson, in Wilson (1927): the midpoint of the Wilson score interval corresponding to ⁠ z {\displaystyle z} ⁠ standard deviations on either side is n S + z n + 2 z {\displaystyle {\frac {n_{S}+z}{n+2z}}} Taking z = 2 {\displaystyle z=2} standard deviations to approximate a 95% confidence interval (⁠ z ≈ 1.96 {\displaystyle z\approx 1.96} ⁠) yields pseudocount of 2 for each outcome, so 4 in total, colloquially known as the "plus four rule": n S + 2 n + 4 {\displaystyle {\frac {n_{S}+2}{n+4}}} This is also the midpoint of the Agresti–Coull interval (Agresti & Coull 1998). ==== Known incidence rates ==== Often the bias of an unknown trial population is tested against a control population with known parameters (incidence rates) μ = ⟨ μ 1 , μ 2 , … , μ d ⟩ . {\displaystyle {\boldsymbol {\mu }}=\langle \mu _{1},\mu _{2},\ldots ,\mu _{d}\rangle .} In this case the uniform probability 1 / d {\displaystyle 1/d} should be replaced by the known incidence rate of the control population μ i {\displaystyle \mu _{i}} to calculate the smoothed estimator: θ ^ i = x i + μ i α d N + α d ( i = 1 , … , d ) . {\displaystyle {\hat {\theta }}_{i}={\frac {x_{i}+\mu _{i}\alpha d}{N+\alpha d}}\qquad (i=1,\ldots ,d).} As a consistency check, if the empirical estimator happens to equal the incidence rate, i.e. μ i = x i / N , {\displaystyle \mu _{i}=x_{i}/N,} the smoothed estimator is independent of α {\displaystyle \alpha } and also equals the incidence rate. == Applications == === Classification === Additive smoothing is commonly a component of naive Bayes classifiers. === Statistical language modelling === In a bag of words model of natural language processing and information retrieval, the data consists of the number of occurrences of each word in a document. Additive smoothing allows the assignment of non-zero probabilities to words which do not occur in the sample. Studies have shown that additive smoothing is more effective than other probability smoothing methods in several retrieval tasks such as language-model-based pseudo-relevance feedback and recommender systems.
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AI Website Builders: Free vs Paid (2026)

Looking for the best AI website builder? An AI website 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 website builder 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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Top 10 AI Copywriting Tools Compared (2026)

In search of the best AI copywriting tool? An AI copywriting tool 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 copywriting tool 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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Multimedia database

A Multimedia database (MMDB) is a collection of related for multimedia data. The multimedia data include one or more primary media data types such as text, images, graphic objects (including drawings, sketches and illustrations) animation sequences, audio and video. A Multimedia Database Management System (MMDBMS) is a framework that manages different types of data potentially represented in a wide diversity of formats on a wide array of media sources. It provides support for multimedia data types, and facilitate for creation, storage, access, query and control of a multimedia database. == Contents of MMDB == A Multimedia Database (MMDB) hosts one or more multimedia data types (i.e. text, images, graphic objects, audio, video, animation sequences). These data types are broadly categorized into three classes: Static media (time-independent: image and graphic object). Dynamic media (time-dependent: audio, video and animation). Dimensional media(3D game and computer aided drafting programs). === Comparison of multimedia data types === Additionally, a Multimedia Database (MMDB) needs to manage additional information pertaining to the actual multimedia data. The information is about the following: Media data: the actual data representing an object. Media format data: information about the format of the media data after it goes through the acquisition, processing, and encoding phases. Media keyword data: the keyword descriptions, usually relating to the generation of the media data. Media feature data: content dependent data such as contain information about the distribution of colours, the kinds of textures and the different shapes present in an image. The last three types are called metadata as they describe several different aspects of the media data. The media keyword data and media feature data are used as indices for searching purpose. The media format data is used to present the retrieved information. == Requirements of Multimedia databases == Like the traditional databases, Multimedia databases should address the following requirements: Integration Data items do not need to be duplicated for different programs invocations Data independence Separate the database and the management from the application programs Concurrency control Allows concurrent transactions Persistence Data objects can be saved and re-used by different transactions and program invocations Privacy Access and authorization control Integrity control Ensures database consistency between transactions Recovery Failures of transactions should not affect the persistent data storage Query support Allows easy querying of multimedia data Multimedia databases should have the ability to uniformly query data (media data, textual data) represented in different formats and have the ability to simultaneously query different media sources and conduct classical database operations across them. (Query support) They should have the ability to retrieve media objects from a local storage device in a good manner. (Storage support) They should have the ability to take the response generated by a query and develop a presentation of that response in terms of audio-visual media and have the ability to deliver this presentation. (Presentation and delivery support) == Issues and challenges == Multimedia data consists of a variety of media formats or file representations including TIFF, BMP, PPT, IVUE, FPX, JPEG, MPEG, AVI, MID, WAV, DOC, GIF, EPS, PNG, etc. Because of restrictions on the conversion from one format to the other, the use of the data in a specific format has been limited as well. Usually, the data size of multimedia is large such as video; therefore, multimedia data often require a large storage. Multimedia database consume a lot of processing time, as well as bandwidth. Some multimedia data types such as video, audio, and animation sequences have temporal requirements that have implications on their storage, manipulation and presentation, but images, video and graphics data have special constraints in terms of their content. == Application areas == Examples of multimedia database application areas: Digital Libraries News-on-Demand Video-on-Demand Music database Geographic Information Systems (GIS) Telemedicine
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Sepp Hochreiter

Josef "Sepp" Hochreiter (born 14 February 1967) is a German computer scientist. Since 2018 he has led the Institute for Machine Learning at the Johannes Kepler University of Linz after having led the Institute of Bioinformatics from 2006 to 2018. In 2017 he became the head of the Linz Institute of Technology (LIT) AI Lab. Hochreiter is also a founding director of the Institute of Advanced Research in Artificial Intelligence (IARAI). Previously, he was at Technische Universität Berlin, at University of Colorado Boulder, and at the Technical University of Munich. He is a chair of the Critical Assessment of Massive Data Analysis (CAMDA) conference. Hochreiter has made contributions in the fields of machine learning, deep learning and bioinformatics, most notably the development of the long short-term memory (LSTM) neural network architecture, but also in meta-learning, reinforcement learning and biclustering with application to bioinformatics data. == Scientific career == === Long short-term memory (LSTM) === Hochreiter developed the long short-term memory (LSTM) neural network architecture in his diploma thesis in 1991 leading to the main publication in 1997. LSTM overcomes the problem of numerical instability in training recurrent neural networks (RNNs) that prevents them from learning from long sequences (vanishing or exploding gradient). In 2007, Hochreiter and others successfully applied LSTM with an optimized architecture to very fast protein homology detection without requiring a sequence alignment. LSTM networks have also been used in Google Voice for transcription and search, and in the Google Allo chat app for generating response suggestion with low latency. === Other machine learning contributions === Beyond LSTM, Hochreiter has developed "Flat Minimum Search" to increase the generalization of neural networks and introduced rectified factor networks (RFNs) for sparse coding which have been applied in bioinformatics and genetics. Hochreiter introduced modern Hopfield networks with continuous states and applied them to the task of immune repertoire classification. Hochreiter worked with Jürgen Schmidhuber in the field of reinforcement learning on actor-critic systems that learn by "backpropagation through a model". Hochreiter has been involved in the development of factor analysis methods with application to bioinformatics, including FABIA for biclustering, HapFABIA for detecting short segments of identity by descent and FARMS for preprocessing and summarizing high-density oligonucleotide DNA microarrays to analyze RNA gene expression. In 2006, Hochreiter and others proposed an extension of the support vector machine (SVM), the "Potential Support Vector Machine" (PSVM), which can be applied to non-square kernel matrices and can be used with kernels that are not positive definite. Hochreiter and his collaborators have applied PSVM to feature selection, including gene selection for microarray data. == Awards == Hochreiter was awarded the IEEE CIS Neural Networks Pioneer Prize in 2021 for his work on LSTM.
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Restricted Boltzmann machine

A restricted Boltzmann machine (RBM) (also called a restricted Sherrington–Kirkpatrick model with external field or restricted stochastic Ising–Lenz–Little model) is a generative stochastic artificial neural network that can learn a probability distribution over its set of inputs. RBMs were initially proposed under the name Harmonium by Paul Smolensky in 1986, and rose to prominence after Geoffrey Hinton and collaborators used fast learning algorithms for them in the mid-2000s. RBMs have found applications in dimensionality reduction, classification, collaborative filtering, feature learning, topic modelling, immunology, and even many‑body quantum mechanics. They can be trained in either supervised or unsupervised ways, depending on the task. As their name implies, RBMs are a variant of Boltzmann machines, with the restriction that their neurons must form a bipartite graph: a pair of nodes from each of the two groups of units (commonly referred to as the "visible" and "hidden" units respectively) may have a symmetric connection between them; and there are no connections between nodes within a group. By contrast, "unrestricted" Boltzmann machines may have connections between hidden units. This restriction allows for more efficient training algorithms than are available for the general class of Boltzmann machines, in particular the gradient-based contrastive divergence algorithm. Restricted Boltzmann machines can also be used in deep learning networks. In particular, deep belief networks can be formed by "stacking" RBMs and optionally fine-tuning the resulting deep network with gradient descent and backpropagation. == Structure == The standard type of RBM has binary-valued (Boolean) hidden and visible units, and consists of a matrix of weights W {\displaystyle W} of size m × n {\displaystyle m\times n} . Each weight element ( w i , j ) {\displaystyle (w_{i,j})} of the matrix is associated with the connection between the visible (input) unit v i {\displaystyle v_{i}} and the hidden unit h j {\displaystyle h_{j}} . In addition, there are bias weights (offsets) a i {\displaystyle a_{i}} for v i {\displaystyle v_{i}} and b j {\displaystyle b_{j}} for h j {\displaystyle h_{j}} . Given the weights and biases, the energy of a configuration (pair of Boolean vectors) (v,h) is defined as E ( v , h ) = − ∑ i a i v i − ∑ j b j h j − ∑ i ∑ j v i w i , j h j {\displaystyle E(v,h)=-\sum _{i}a_{i}v_{i}-\sum _{j}b_{j}h_{j}-\sum _{i}\sum _{j}v_{i}w_{i,j}h_{j}} or, in matrix notation, E ( v , h ) = − a T v − b T h − v T W h . {\displaystyle E(v,h)=-a^{\mathrm {T} }v-b^{\mathrm {T} }h-v^{\mathrm {T} }Wh.} This energy function is analogous to that of a Hopfield network. As with general Boltzmann machines, the joint probability distribution for the visible and hidden vectors is defined in terms of the energy function as follows, P ( v , h ) = 1 Z e − E ( v , h ) {\displaystyle P(v,h)={\frac {1}{Z}}e^{-E(v,h)}} where Z {\displaystyle Z} is a partition function defined as the sum of e − E ( v , h ) {\displaystyle e^{-E(v,h)}} over all possible configurations, which can be interpreted as a normalizing constant to ensure that the probabilities sum to 1. The marginal probability of a visible vector is the sum of P ( v , h ) {\displaystyle P(v,h)} over all possible hidden layer configurations, P ( v ) = 1 Z ∑ { h } e − E ( v , h ) {\displaystyle P(v)={\frac {1}{Z}}\sum _{\{h\}}e^{-E(v,h)}} , and vice versa. Since the underlying graph structure of the RBM is bipartite (meaning there are no intra-layer connections), the hidden unit activations are mutually independent given the visible unit activations. Conversely, the visible unit activations are mutually independent given the hidden unit activations. That is, for m visible units and n hidden units, the conditional probability of a configuration of the visible units v, given a configuration of the hidden units h, is P ( v | h ) = ∏ i = 1 m P ( v i | h ) {\displaystyle P(v|h)=\prod _{i=1}^{m}P(v_{i}|h)} . Conversely, the conditional probability of h given v is P ( h | v ) = ∏ j = 1 n P ( h j | v ) {\displaystyle P(h|v)=\prod _{j=1}^{n}P(h_{j}|v)} . The individual activation probabilities are given by P ( h j = 1 | v ) = σ ( b j + ∑ i = 1 m w i , j v i ) {\displaystyle P(h_{j}=1|v)=\sigma \left(b_{j}+\sum _{i=1}^{m}w_{i,j}v_{i}\right)} and P ( v i = 1 | h ) = σ ( a i + ∑ j = 1 n w i , j h j ) {\displaystyle \,P(v_{i}=1|h)=\sigma \left(a_{i}+\sum _{j=1}^{n}w_{i,j}h_{j}\right)} where σ {\displaystyle \sigma } denotes the logistic sigmoid. The visible units of Restricted Boltzmann Machine can be multinomial, although the hidden units are Bernoulli. In this case, the logistic function for visible units is replaced by the softmax function P ( v i k = 1 | h ) = exp ⁡ ( a i k + Σ j W i j k h j ) Σ k ′ = 1 K exp ⁡ ( a i k ′ + Σ j W i j k ′ h j ) {\displaystyle P(v_{i}^{k}=1|h)={\frac {\exp(a_{i}^{k}+\Sigma _{j}W_{ij}^{k}h_{j})}{\Sigma _{k'=1}^{K}\exp(a_{i}^{k'}+\Sigma _{j}W_{ij}^{k'}h_{j})}}} where K is the number of discrete values that the visible values have. They are applied in topic modeling, and recommender systems. === Relation to other models === Restricted Boltzmann machines are a special case of Boltzmann machines and Markov random fields. The graphical model of RBMs corresponds to that of factor analysis. == Training algorithm == Restricted Boltzmann machines are trained to maximize the product of probabilities assigned to some training set V {\displaystyle V} (a matrix, each row of which is treated as a visible vector v {\displaystyle v} ), arg ⁡ max W ∏ v ∈ V P ( v ) {\displaystyle \arg \max _{W}\prod _{v\in V}P(v)} or equivalently, to maximize the expected log probability of a training sample v {\displaystyle v} selected randomly from V {\displaystyle V} : arg ⁡ max W E [ log ⁡ P ( v ) ] {\displaystyle \arg \max _{W}\mathbb {E} \left[\log P(v)\right]} The algorithm most often used to train RBMs, that is, to optimize the weight matrix W {\displaystyle W} , is the contrastive divergence (CD) algorithm due to Hinton, originally developed to train PoE (product of experts) models. The algorithm performs Gibbs sampling and is used inside a gradient descent procedure (similar to the way backpropagation is used inside such a procedure when training feedforward neural nets) to compute weight update. The basic, single-step contrastive divergence (CD-1) procedure for a single sample can be summarized as follows: Take a training sample v, compute the probabilities of the hidden units and sample a hidden activation vector h from this probability distribution. Compute the outer product of v and h and call this the positive gradient. From h, sample a reconstruction v' of the visible units, then resample the hidden activations h' from this. (Gibbs sampling step) Compute the outer product of v' and h' and call this the negative gradient. Let the update to the weight matrix W {\displaystyle W} be the positive gradient minus the negative gradient, times some learning rate: Δ W = ϵ ( v h T − v ′ h ′ T ) {\displaystyle \Delta W=\epsilon (vh^{\mathsf {T}}-v'h'^{\mathsf {T}})} . Update the biases a and b analogously: Δ a = ϵ ( v − v ′ ) {\displaystyle \Delta a=\epsilon (v-v')} , Δ b = ϵ ( h − h ′ ) {\displaystyle \Delta b=\epsilon (h-h')} . A Practical Guide to Training RBMs written by Hinton can be found on his homepage. == Stacked Restricted Boltzmann Machine == The difference between the Stacked Restricted Boltzmann Machines and RBM is that RBM has lateral connections within a layer that are prohibited to make analysis tractable. On the other hand, the Stacked Boltzmann consists of a combination of an unsupervised three-layer network with symmetric weights and a supervised fine-tuned top layer for recognizing three classes. The usage of Stacked Boltzmann is to understand Natural languages, retrieve documents, image generation, and classification. These functions are trained with unsupervised pre-training and/or supervised fine-tuning. Unlike the undirected symmetric top layer, with a two-way unsymmetric layer for connection for RBM. The restricted Boltzmann's connection is three-layers with asymmetric weights, and two networks are combined into one. Stacked Boltzmann does share similarities with RBM, the neuron for Stacked Boltzmann is a stochastic binary Hopfield neuron, which is the same as the Restricted Boltzmann Machine. The energy from both Restricted Boltzmann and RBM is given by Gibb's probability measure: E = − 1 2 ∑ i , j w i j s i s j + ∑ i θ i s i {\displaystyle E=-{\frac {1}{2}}\sum _{i,j}{w_{ij}{s_{i}}{s_{j}}}+\sum _{i}{\theta _{i}}{s_{i}}} . The training process of Restricted Boltzmann is similar to RBM. Restricted Boltzmann train one layer at a time and approximate equilibrium state with a 3-segment pass, not performing back propagation. Restricted Boltzmann uses both supervised and unsupervised on different RBM for pre-training for classification and recognition. The training uses contrastive divergence with
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Danqi Chen

Danqi Chen (Chinese: 陈丹琦; pinyin: Chén Dānqí, IPA: [ʈ͡ʂʰə̌n tan t͡ɕʰǐ]; born in Changsha, China) is a Chinese computer scientist and assistant professor at Princeton University specializing in the AI field of natural language processing (NLP). In 2019, she joined the Princeton NLP group, alongside Sanjeev Arora, Christiane Fellbaum, and Karthik Narasimhan. She was previously a visiting scientist at Facebook AI Research (FAIR). She earned her Ph.D. at Stanford University and her BS from Tsinghua University. Chen is the author of Neural Reading Comprehension and Beyond, a dissertation on using artificial intelligence to access knowledge in ordinary and structured documents. She is the author or co-author of a number of journal articles, including Reading Wikipedia to Answer Open-Domain Questions. Google's SyntaxNet is based on algorithms developed by Danqi Chen and Christopher Manning at Stanford. Her primary research interests are in text understanding and knowledge representation and reasoning. She won a gold medal at the 2008 International Informatics Olympiad. She is known among friends as CDQ. A well known algorithm in competitive programming, CDQ Divide and Conquer, is named after this acronym. She is married to Huacheng Yu, an assistant professor in theoretical computer science at Princeton University.
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Vero (app)

Vero (stylized as VERO) is a social media platform and mobile app company. Vero markets itself as a social network free from advertisements, data mining and algorithms. == History == The app was founded by French-Lebanese billionaire Ayman Hariri who is the son of former Lebanese prime minister Rafic Hariri. The name is taken from the Italian word for true. The app launched officially in 2015 as an alternative to Facebook and their popular photo-blogging app Instagram. Within weeks of its release the app surged in popularity although users expressed mixed reports with some feeling confused about how the app worked. Cosplayers were early to adopt the app as their photo-sharing platform of choice, favouring the app's pinch and zoom magnification feature over Instagram's zoom feature. Other creative communities soon followed, and the app became popular with niche groups of makeup artists, tattoo artists, and skateboarders. In March 2018, Vero's popularity surged, partly helped by an exodus from Facebook and Instagram following the Cambridge Analytica data scandal. In the wake of the scandal, Vero devised an advertising campaign aimed at defected Facebook and Instagram users, hoping the app's policies and privacy settings would assuage concerns over sharing personal information on the internet. Within the space of one week, the app went from being a small service, akin to Ello or Peach, to being the most downloaded app in eighteen countries. In December 2020, Vero released its most significant update to date, Vero 2.0 which introduced new features including voice and video calls, game and app posts and bookmarks, and refinements to the UI. In October 2021, Vero introduced their Desktop app (beta) with multiple post options and a re-sizable multi-column feed. == Concept and funding == Vero's content feed resembles Instagram's although users can share a wider variety of content and the app has a chronological content feed whereas Facebook and Instagram's feeds are algorithm based. Vero's business plan is also distinct from similar social media apps. Whereas its competitors such as Facebook or Instagram make money from in-app advertising revenue and the sale of user data, Vero's business plan was to invite the first one million users to use the app for free then charge any subsequent users a subscription fee. The app was entirely funded by its founder and generated additional revenues by charging affiliate fees when someone buys a product they find on Vero. == Awards == Vero was recognized at the 2021 Webbys, being named as an Honoree in the Best Visual Design - Aesthetic Category. == Controversies == === Privacy === Vero has faced some criticism over the wording of their manifesto, in particular, the statement "Vero only collects the data we believe is necessary to provide users with a great experience and to ensure the security of their accounts." Because this policy does not explicitly state that the app will not sell data on to third parties some users fear that the need to monetise the app through data might prove too tempting. Users have also complained about not being able to delete their accounts. While this was never the case, the option was hidden deep in the app's settings. === Russian involvement === Although Vero remains transparent about the app's Russian development team, they have been caught up in concerns about Russian interference on social media platforms. The app's founder Ayman Hariri was quick to dismiss the remarks as xenophobic and defend the nationality of his employees, stating in an interview with Time Magazine; "At the end of the day, where people are from is really not how anybody should judge anyone". === Criticism of the app's founder === Until 2013, Vero's founder Ayman Harari was deputy CEO and chairman of Saudi Oger, the Saudi Arabian construction company which collapsed in 2017, mired by controversies over the welfare and treatment of their employees. However, Hariri is quick to point out that he divested from the firm in 2014 and the worker's rights violations occurred after he had left the company.
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Barney Pell

Barney Pell (born March 18, 1968) is an American entrepreneur, angel investor and computer scientist. He was co-founder and CEO of Powerset, a pioneering natural language search startup, search strategist and architect for Microsoft's Bing search engine, a pioneer in the field of general game playing in artificial intelligence, and the architect of the first intelligent agent to fly onboard and control a spacecraft. He was co-founder, Vice Chairman and Chief Strategy Officer of Moon Express; co-founder and chairman of LocoMobi; and Associate Founder of Singularity University. == Career == === Education === Pell received his Bachelor of Science degree in symbolic systems from Stanford University in 1989, where he graduated Phi Beta Kappa and was a National Merit Scholar. Pell earned a PhD in computer science from Cambridge University in 1993, supervised by Stephen Pulman, where he was a Marshall Scholar. === Research === Pell's research is focused on basic problems in the study of intelligence, computer game playing, machine learning, natural language processing, autonomous robotics, and web search. Barney Pell has published over 30 technical papers on topics related to information retrieval, knowledge management, machine learning, artificial intelligence, and scheduling systems. In computer game playing and machine learning, he was a pioneer in the field of General Game Playing, and created programs to generate the rules of chess-like games and programs to play individual games directly from the rules without human assistance. He also did early work on machine learning in the game of Go and on an architecture for pragmatic reasoning for bidding in the game of Bridge. In natural language processing, he was a scientist in the Artificial Intelligence Center at SRI International, where he worked on the Core Language Engine. Barney Pell was the Technical Area Manager of the Collaborative and Assistant Systems area within the Computational Sciences Division (now the Intelligent Systems Division) at NASA Ames Research Center, where he oversaw a staff of 80 scientists working on information retrieval, search, knowledge management, machine learning, semantic technology, human centered systems, collaboration technology, adaptive user interfaces, human robot interaction, and other areas of artificial intelligence. From 1993 to 1998, Barney Pell worked as a Principal Investigator and Senior Computer Scientist at NASA Ames, where he conducted advanced research and development of autonomous control software for NASA's deep space missions. He was the Architect for the Deep Space One Remote Agent Experiment and the Project Lead for the Executive component of the Remote Agent Experiment, the first intelligent agent to fly onboard and control a spacecraft. === Business === Pell is an entrepreneur who has founded or co-founded several business ventures, including Powerset, Moon Express, and LocoMobi. He was the founder and CEO of Powerset, a San Francisco startup company that built a search engine based on natural language processing technology originally developed at XEROX PARC. On May 11, 2008, the company unveiled a tool for searching a fixed subset of Wikipedia using conversational phrases rather than keywords. On July 1, 2008, Microsoft signed an agreement to acquire Powerset for an estimated $100 million. Powerset became a part of Microsoft's search engine, Bing. From 2008 until August 2011, Pell served as Partner, Search Strategist, and Evangelist for Microsoft's search engine, Bing and as Head of Bing's Local and Mobile Search teams. Prior to joining Powerset, Pell was an Entrepreneur-in-Residence at Mayfield Fund, a venture capital firm in Silicon Valley. Pell is also a founder of Moon Express, Inc., a U.S. company awarded a $10M commercial lunar contract by NASA and a competitor in the Google Lunar X PRIZE. Pell was also co-founder and chairman of LocoMobi, Inc., a U.S. company developing mobile, software and hardware technology solutions for the parking industry. LocoMobi was winner of the Tie50 Award in 2014. Pell is also an associate founder of Singularity University and a Machine Learning Fellow at the Creative Destruction Lab at the Rotman School of Management From 1998 to 2000, Pell served as chief strategist and vice president of business development at StockMaster.com (acquired by Red Herring in March, 2000). From 2000 to 2002, Pell was Chief Strategist and Vice President of Business Development for Whizbang Labs. Pell has been an angel investor and advisor to numerous startup companies, including Pulse.io (acquired by Google), Aardvark (acquired by Google), Appjet (acquired by Google), Jibe Mobile (acquired by Google), Movity (acquired by Trulia), QuestBridge, BrandYourself, CrowdFlower (acquired by Appen), and LinkedIn. === Views and predictions === Pell has expressed views and predictions regarding technological advancements in coming years. He believes that humans will soon have "brain-machine interfaces that will let people interact with each other as if they had 'hangouts' in their mind." Pell predicts these interfaces to become available within 20 to 30 years. Pell also predicts advancements in bodily augmentation, such as "even-better-than-human prosthetics and high-quality tissue engineering within 10 years." Pell believes that with advancements in space exploration technology the moon will soon be a commercially viable resource for material such as platinum and water. == Awards and recognition == In 1986, Pell was awarded a National Merit Scholarship. In 1989, Pell was awarded a Marshall Scholarship. In 1989, Pell was elected Phi Beta Kappa. In 1997, Pell was part of the team award a NASA Software of the Year Award for the Deep Space 1 Remote Agent.
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Project Bergamot

Project Bergamot is a joint project between several European universities and Mozilla for the development of machine translation software based on artificial neural networks, which is intended for local execution on end-user devices. The software library that was created and the associated language models were made available to the general public as Free Software. Execution requires a x86 CPU with SSE4.1 instruction set extensions. In 2022, Devin Coldewey of TechCrunch judged the translation quality to be "more than adequate", but considered Firefox Translations to be not yet fully mature. == Usage == Mozilla used the Bergamot Translator to expand its web browser Firefox with a feature for translating web pages, which was previously considered an important gap in Firefox' feature set. It is often compared to the much older corresponding feature in Google Chrome, which utilizes a cloud-based background service. In contrast, Firefox Translations does not require any data to leave the user's computer, resulting in advantages in terms of data protection, availability and possibly response times. There is just the installation of a new language model that needs to take place the first time a new language is encountered. Greater independence from large technology companies and their interests is also mentioned as an important advantage. Mozilla thus strengthened its position as an alternative software vendor with a particular focus on data protection and security. Mozilla followed up with the similar feature of speech recognition for spoken user input, based on whisperfile. On the other hand, slow translation times have been observed, especially on older devices. Also, Firefox Translations initially supported far fewer language pairs than other major translation services and is only gradually adding new models. On that matter, the training pipeline is also made available to interested parties to enable the creation of missing language models. TranslateLocally is a Firefox-independent translation software based on the Bergamot Translator. It is also available as an (Electron-based) standalone application or as an extension for Chromium-based web browsers. == History == Mozilla had already tried to get a (cloud-based) web content translation feature into Firefox a few years before Project Bergamot, but had failed because of the financial challenge. Microsoft had already delivered offline capabilities for its translation software in 2018. Google soon followed suit, Apple two years later. The software is based on the free translation framework Marian, which the University of Edinburgh had previously developed in cooperation with Microsoft, and is itself based on the Nematus toolkit that was presented in 2017. Under the leadership of the University of Edinburgh, a development consortium was formed with the Mozilla Corporation and the additional European universities of Prague, Sheffield and Tartu. In 2018, it was able to get 3 million euros of funding from the EU's Horizon 2020 programme. Firefox Translations was initially provided as an add-on. A first functional demonstration prototype was presented in October 2019. Beta version 117 had the feature integrated directly into the browser, the official release was in version 118 from September 2023. Both the add-on module and as part of Firefox, the code and the models are subject to the version 2 of the Mozilla Public License. Since 2022, the EU-funded HPLT project creates new language models. It involves additional partners, including the universities of Helsinki, Turku, Oslo and other partners from Spain, Norway and the Czech Republic.
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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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Standard test image

A standard test image is a digital image file used across different institutions to test image processing and image compression algorithms. By using the same standard test images, different labs are able to compare results, both visually and quantitatively. The images are in many cases chosen to represent natural or typical images that a class of processing techniques would need to deal with. Other test images are chosen because they present a range of challenges to image reconstruction algorithms, such as the reproduction of fine detail and textures, sharp transitions and edges, and uniform regions. == Historical origins == Test images as transmission system calibration material probably date back to the original Paris to Lyon pantelegraph link. Analogue fax equipment (and photographic equipment for the printing trade) were the largest user groups of the standardized image for calibration technology until the coming of television and digital image transmission systems. == Common test image resolutions == The standard resolution of the images is usually 512×512 or 720×576. Most of these images are available as TIFF files from the University of Southern California's Signal and Image Processing Institute. Kodak has released 768×512 images, available as PNGs, that was originally on Photo CD with higher resolution, that are widely used for comparing image compression techniques.
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Top 10 AI Code-review Tools Compared (2026)

In search of the best AI code-review tool? An AI code-review tool 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 code-review tool 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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Arthur Zimek

Arthur Zimek is a professor in data mining, data science and machine learning at the University of Southern Denmark in Odense, Denmark. He graduated from LMU Munich in Germany, where he worked with Prof. Hans-Peter Kriegel. His dissertation on "Correlation Clustering" was awarded the "SIGKDD Doctoral Dissertation Award 2009 Runner-up" by the Association for Computing Machinery. He is well known for his work on outlier detection, density-based clustering, correlation clustering, and the curse of dimensionality. He is one of the founders and core developers of the open-source ELKI data mining framework.
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