Automate This

Automate This: How Algorithms Came to Rule Our World is a book written by Christopher Steiner and published by Penguin Group. == Book == Steiner begins his study of algorithms on Wall Street in the 1980s but also provides examples from other industries. For example, he explains the history of Pandora Radio and the use of algorithms in music identification. He expresses concern that such use of algorithms may lead to the homogenization of music over time. Steiner also discusses the algorithms that eLoyalty (now owned by Mattersight Corporation following divestiture of the technology) was created by dissecting 2 million speech patterns and can now identify a caller's personality style and direct the caller with a compatible customer support representative. Steiner's book shares both the warning and the opportunity that algorithms bring to just about every industry in the world, and the pros and cons of the societal impact of automation (e.g. impact on employment).

Contrastive Language-Image Pre-training

Contrastive Language-Image Pre-training (CLIP) is a technique for training a pair of neural network models, one for image understanding and one for text understanding, using a contrastive objective. This method has enabled broad applications across multiple domains, including cross-modal retrieval, text-to-image generation, and aesthetic ranking. == Algorithm == The CLIP method trains a pair of models contrastively. One model takes in a piece of text as input and outputs a single vector representing its semantic content. The other model takes in an image and similarly outputs a single vector representing its visual content. The models are trained so that the vectors corresponding to semantically similar text-image pairs are close together in the shared vector space, while those corresponding to dissimilar pairs are far apart. To train a pair of CLIP models, one would start by preparing a large dataset of image-caption pairs. During training, the models are presented with batches of N {\displaystyle N} image-caption pairs. Let the outputs from the text and image models be respectively v 1 , . . . , v N , w 1 , . . . , w N {\displaystyle v_{1},...,v_{N},w_{1},...,w_{N}} . Two vectors are considered "similar" if their dot product is large. The loss incurred on this batch is the multi-class N-pair loss, which is a symmetric cross-entropy loss over similarity scores: − 1 N ∑ i ln ⁡ e v i ⋅ w i / T ∑ j e v i ⋅ w j / T − 1 N ∑ j ln ⁡ e v j ⋅ w j / T ∑ i e v i ⋅ w j / T {\displaystyle -{\frac {1}{N}}\sum _{i}\ln {\frac {e^{v_{i}\cdot w_{i}/T}}{\sum _{j}e^{v_{i}\cdot w_{j}/T}}}-{\frac {1}{N}}\sum _{j}\ln {\frac {e^{v_{j}\cdot w_{j}/T}}{\sum _{i}e^{v_{i}\cdot w_{j}/T}}}} In essence, this loss function encourages the dot product between matching image and text vectors ( v i ⋅ w i {\displaystyle v_{i}\cdot w_{i}} ) to be high, while discouraging high dot products between non-matching pairs. The parameter T > 0 {\displaystyle T>0} is the temperature, which is parameterized in the original CLIP model as T = e − τ {\displaystyle T=e^{-\tau }} where τ ∈ R {\displaystyle \tau \in \mathbb {R} } is a learned parameter. Other loss functions are possible. For example, Sigmoid CLIP (SigLIP) proposes the following loss function: L = 1 N ∑ i , j ∈ 1 : N f ( ( 2 δ i , j − 1 ) ( e τ w i ⋅ v j + b ) ) {\displaystyle L={\frac {1}{N}}\sum _{i,j\in 1:N}f((2\delta _{i,j}-1)(e^{\tau }w_{i}\cdot v_{j}+b))} where f ( x ) = ln ⁡ ( 1 + e − x ) {\displaystyle f(x)=\ln(1+e^{-x})} is the negative log sigmoid loss, and the Dirac delta symbol δ i , j {\displaystyle \delta _{i,j}} is 1 if i = j {\displaystyle i=j} else 0. == CLIP models == While the original model was developed by OpenAI, subsequent models have been trained by other organizations as well. === Image model === The image encoding models used in CLIP are typically vision transformers (ViT). The naming convention for these models often reflects the specific ViT architecture used. For instance, "ViT-L/14" means a "vision transformer large" (compared to other models in the same series) with a patch size of 14, meaning that the image is divided into 14-by-14 pixel patches before being processed by the transformer. The size indicator ranges from B, L, H, G (base, large, huge, giant), in that order. Other than ViT, the image model is typically a convolutional neural network, such as ResNet (in the original series by OpenAI), or ConvNeXt (in the OpenCLIP model series by LAION). Since the output vectors of the image model and the text model must have exactly the same length, both the image model and the text model have fixed-length vector outputs, which in the original report is called "embedding dimension". For example, in the original OpenAI model, the ResNet models have embedding dimensions ranging from 512 to 1024, and for the ViTs, from 512 to 768. Its implementation of ViT was the same as the original one, with one modification: after position embeddings are added to the initial patch embeddings, there is a LayerNorm. Its implementation of ResNet was the same as the original one, with 3 modifications: In the start of the CNN (the "stem"), they used three stacked 3x3 convolutions instead of a single 7x7 convolution, as suggested by. There is an average pooling of stride 2 at the start of each downsampling convolutional layer (they called it rect-2 blur pooling according to the terminology of ). This has the effect of blurring images before downsampling, for antialiasing. The final convolutional layer is followed by a multiheaded attention pooling. ALIGN a model with similar capabilities, trained by researchers from Google used EfficientNet, a kind of convolutional neural network. === Text model === The text encoding models used in CLIP are typically Transformers. In the original OpenAI report, they reported using a Transformer (63M-parameter, 12-layer, 512-wide, 8 attention heads) with lower-cased byte pair encoding (BPE) with 49152 vocabulary size. Context length was capped at 76 for efficiency. Like GPT, it was decoder-only, with only causally-masked self-attention. Its architecture is the same as GPT-2. Like BERT, the text sequence is bracketed by two special tokens [SOS] and [EOS] ("start of sequence" and "end of sequence"). Take the activations of the highest layer of the transformer on the [EOS], apply LayerNorm, then a final linear map. This is the text encoding of the input sequence. The final linear map has output dimension equal to the embedding dimension of whatever image encoder it is paired with. These models all had context length 77 and vocabulary size 49408. ALIGN used BERT of various sizes. == Dataset == === WebImageText === The CLIP models released by OpenAI were trained on a dataset called "WebImageText" (WIT) containing 400 million pairs of images and their corresponding captions scraped from the internet. The total number of words in this dataset is similar in scale to the WebText dataset used for training GPT-2, which contains about 40 gigabytes of text data. The dataset contains 500,000 text-queries, with up to 20,000 (image, text) pairs per query. The text-queries were generated by starting with all words occurring at least 100 times in English Wikipedia, then extended by bigrams with high mutual information, names of all Wikipedia articles above a certain search volume, and WordNet synsets. The dataset is private and has not been released to the public, and there is no further information on it. ==== Data preprocessing ==== For the CLIP image models, the input images are preprocessed by first dividing each of the R, G, B values of an image by the maximum possible value, so that these values fall between 0 and 1, then subtracting by [0.48145466, 0.4578275, 0.40821073], and dividing by [0.26862954, 0.26130258, 0.27577711]. The rationale was that these are the mean and standard deviations of the images in the WebImageText dataset, so this preprocessing step roughly whitens the image tensor. These numbers slightly differ from the standard preprocessing for ImageNet, which uses [0.485, 0.456, 0.406] and [0.229, 0.224, 0.225]. If the input image does not have the same resolution as the native resolution (224×224 for all except ViT-L/14@336px, which has 336×336 resolution), then the input image is first scaled by bicubic interpolation, so that its shorter side is the same as the native resolution, then the central square of the image is cropped out. === Others === ALIGN used over one billion image-text pairs, obtained by extracting images and their alt-tags from online crawling. The method was described as similar to how the Conceptual Captions dataset was constructed, but instead of complex filtering, they only applied a frequency-based filtering. Later models trained by other organizations had published datasets. For example, LAION trained OpenCLIP with published datasets LAION-400M, LAION-2B, and DataComp-1B. == Training == In the original OpenAI CLIP report, they reported training 5 ResNet and 3 ViT (ViT-B/32, ViT-B/16, ViT-L/14). Each was trained for 32 epochs. The largest ResNet model took 18 days to train on 592 V100 GPUs. The largest ViT model took 12 days on 256 V100 GPUs. All ViT models were trained on 224×224 image resolution. The ViT-L/14 was then boosted to 336×336 resolution by FixRes, resulting in a model. They found this was the best-performing model. In the OpenCLIP series, the ViT-L/14 model was trained on 384 A100 GPUs on the LAION-2B dataset, for 160 epochs for a total of 32B samples seen. == Applications == === Cross-modal retrieval === CLIP's cross-modal retrieval enables the alignment of visual and textual data in a shared latent space, allowing users to retrieve images based on text descriptions and vice versa, without the need for explicit image annotations. In text-to-image retrieval, users input descriptive text, and CLIP retrieves images with matching embeddings. In image-to-text retrieval, images are used to find related text content. CLIP’s ability to connect vis

Region Based Convolutional Neural Networks

Region-based Convolutional Neural Networks (R-CNN) are a family of machine learning models for computer vision, and specifically object detection and localization. The original goal of R-CNN was to take an input image and produce a set of bounding boxes as output, where each bounding box contains an object and also the category (e.g. car or pedestrian) of the object. In general, R-CNN architectures perform selective search over feature maps outputted by a CNN. R-CNN has been extended to perform other computer vision tasks, such as: tracking objects from a drone-mounted camera, locating text in an image, and enabling object detection in Google Lens. Mask R-CNN is also one of seven tasks in the MLPerf Training Benchmark, which is a competition to speed up the training of neural networks. == History == The following covers some of the versions of R-CNN that have been developed. November 2013: R-CNN. April 2015: Fast R-CNN. June 2015: Faster R-CNN. March 2017: Mask R-CNN. December 2017: Cascade R-CNN is trained with increasing Intersection over Union (IoU, also known as the Jaccard index) thresholds, making each stage more selective against nearby false positives. June 2019: Mesh R-CNN adds the ability to generate a 3D mesh from a 2D image. == Architecture == For review articles see. === Selective search === Given an image (or an image-like feature map), selective search (also called Hierarchical Grouping) first segments the image by the algorithm in (Felzenszwalb and Huttenlocher, 2004), then performs the following: Input: (colour) image Output: Set of object location hypotheses L Segment image into initial regions R = {r1, ..., rn} using Felzenszwalb and Huttenlocher (2004) Initialise similarity set S = ∅ foreach Neighbouring region pair (ri, rj) do Calculate similarity s(ri, rj) S = S ∪ s(ri, rj) while S ≠ ∅ do Get highest similarity s(ri, rj) = max(S) Merge corresponding regions rt = ri ∪ rj Remove similarities regarding ri: S = S \ s(ri, r∗) Remove similarities regarding rj: S = S \ s(r∗, rj) Calculate similarity set St between rt and its neighbours S = S ∪ St R = R ∪ rt Extract object location boxes L from all regions in R === R-CNN === With R-CNN, prediction follows a two-step process. A preprocessing selective search step generates a large set of candidate objects (typically as many as 2000), known as regions of interest (ROI). These are forwarded to a CNN, which predicts an object class score and bounding box estimate, independently for each ROI. Importantly, the ROIs are heavily filtered to remove excess candidates. This is achieved using two mechanism. Filtering begins by removing ROIs assigned to the background category. This is a specialized category, which is scored by the CNN alongside other categories. An unfortunate reality is that remaining ROIs typically suffer from heavy duplication. Namely, multiple ROIs that cover same objects in the image are all assigned non-background categories. This is resolved by a heuristic non-maximum suppression (NMS) step. === Fast R-CNN === While the original R-CNN independently computed the neural network features on each of as many as two thousand regions of interest, Fast R-CNN runs the neural network once on the whole image. At the end of the network is a ROIPooling module, which slices out each ROI from the network's output tensor, reshapes it, and classifies it. As in the original R-CNN, the Fast R-CNN uses selective search to generate its region proposals. === Faster R-CNN === While Fast R-CNN used selective search to generate ROIs, Faster R-CNN integrates the ROI generation into the neural network itself. === Mask R-CNN === While previous versions of R-CNN focused on object detections, Mask R-CNN adds instance segmentation. Mask R-CNN also replaced ROIPooling with a new method called ROIAlign, which can represent fractions of a pixel.

Point distribution model

The point distribution model is a model for representing the mean geometry of a shape and some statistical modes of geometric variation inferred from a training set of shapes. == Background == The point distribution model concept has been developed by Cootes, Taylor et al. and became a standard in computer vision for the statistical study of shape and for segmentation of medical images where shape priors really help interpretation of noisy and low-contrasted pixels/voxels. The latter point leads to active shape models (ASM) and active appearance models (AAM). Point distribution models rely on landmark points. A landmark is an annotating point posed by an anatomist onto a given locus for every shape instance across the training set population. For instance, the same landmark will designate the tip of the index finger in a training set of 2D hands outlines. Principal component analysis (PCA), for instance, is a relevant tool for studying correlations of movement between groups of landmarks among the training set population. Typically, it might detect that all the landmarks located along the same finger move exactly together across the training set examples showing different finger spacing for a flat-posed hands collection. == Details == First, a set of training images are manually landmarked with enough corresponding landmarks to sufficiently approximate the geometry of the original shapes. These landmarks are aligned using the generalized procrustes analysis, which minimizes the least squared error between the points. k {\displaystyle k} aligned landmarks in two dimensions are given as X = ( x 1 , y 1 , … , x k , y k ) {\displaystyle \mathbf {X} =(x_{1},y_{1},\ldots ,x_{k},y_{k})} . It's important to note that each landmark i ∈ { 1 , … k } {\displaystyle i\in \lbrace 1,\ldots k\rbrace } should represent the same anatomical location. For example, landmark #3, ( x 3 , y 3 ) {\displaystyle (x_{3},y_{3})} might represent the tip of the ring finger across all training images. Now the shape outlines are reduced to sequences of k {\displaystyle k} landmarks, so that a given training shape is defined as the vector X ∈ R 2 k {\displaystyle \mathbf {X} \in \mathbb {R} ^{2k}} . Assuming the scattering is gaussian in this space, PCA is used to compute normalized eigenvectors and eigenvalues of the covariance matrix across all training shapes. The matrix of the top d {\displaystyle d} eigenvectors is given as P ∈ R 2 k × d {\displaystyle \mathbf {P} \in \mathbb {R} ^{2k\times d}} , and each eigenvector describes a principal mode of variation along the set. Finally, a linear combination of the eigenvectors is used to define a new shape X ′ {\displaystyle \mathbf {X} '} , mathematically defined as: X ′ = X ¯ + P b {\displaystyle \mathbf {X} '={\overline {\mathbf {X} }}+\mathbf {P} \mathbf {b} } where X ¯ {\displaystyle {\overline {\mathbf {X} }}} is defined as the mean shape across all training images, and b {\displaystyle \mathbf {b} } is a vector of scaling values for each principal component. Therefore, by modifying the variable b {\displaystyle \mathbf {b} } an infinite number of shapes can be defined. To ensure that the new shapes are all within the variation seen in the training set, it is common to only allow each element of b {\displaystyle \mathbf {b} } to be within ± {\displaystyle \pm } 3 standard deviations, where the standard deviation of a given principal component is defined as the square root of its corresponding eigenvalue. PDM's can be extended to any arbitrary number of dimensions, but are typically used in 2D image and 3D volume applications (where each landmark point is R 2 {\displaystyle \mathbb {R} ^{2}} or R 3 {\displaystyle \mathbb {R} ^{3}} ). == Discussion == An eigenvector, interpreted in euclidean space, can be seen as a sequence of k {\displaystyle k} euclidean vectors associated to corresponding landmark and designating a compound move for the whole shape. Global nonlinear variation is usually well handled provided nonlinear variation is kept to a reasonable level. Typically, a twisting nematode worm is used as an example in the teaching of kernel PCA-based methods. Due to the PCA properties: eigenvectors are mutually orthogonal, form a basis of the training set cloud in the shape space, and cross at the 0 in this space, which represents the mean shape. Also, PCA is a traditional way of fitting a closed ellipsoid to a Gaussian cloud of points (whatever their dimension): this suggests the concept of bounded variation. The idea behind PDMs is that eigenvectors can be linearly combined to create an infinity of new shape instances that will 'look like' the one in the training set. The coefficients are bounded alike the values of the corresponding eigenvalues, so as to ensure the generated 2n/3n-dimensional dot will remain into the hyper-ellipsoidal allowed domain—allowable shape domain (ASD).

AUTINDEX

AUTINDEX is a commercial text mining software package based on sophisticated linguistics. AUTINDEX, resulting from research in information extraction, is a product of the Institute of Applied Information Sciences (IAI) which is a non-profit institute that has been researching and developing language technology since its foundation in 1985. IAI is an institute affiliated to Saarland University in Saarbrücken, Germany. AUTINDEX is the result of a number of research projects funded by the EU (Project BINDEX), by Deutsche Forschungsgemeinschaft and the German Ministry for Economy. Amongst the latter there are the projects LinSearch, and WISSMER, see also the reference to IAI-Website. The basic functionality of AUTINDEX is the extraction of key words from a document to represent the semantics of the document. Ideally the system is integrated with a thesaurus that defines the standardised terms to be used for key word assignment. AUTINDEX is used in library applications (e.g. integrated in dandelon.com) as well as in high quality (expert) information systems, and in document management and content management environments. Together with AUTINDEX a number of additional software comes along such as an integration with Apache Solr / Lucene to provide a complete information retrieval environment, a classification and categorisation system on the basis of a machine learning software that assigns domains to the document, and a system for searching with semantically similar terms that are collected in so called tag clouds.

Something Big Is Happening

"Something Big Is Happening" is an essay by Matt Shumer, an AI entrepreneur, about the impact of artificial intelligence, published in February 2026, that has since been reportedly viewed more than 80 million times and widely discussed. Shumer noted that the technology has crossed an important threshold, where AI has become capable of creating self-improving systems. Referring to one the most recent AI models, he wrote: "It was making intelligent decisions. It had something that felt, for the first time, like judgment. Like taste." Speaking to CNBC's Power Lunch, Shumer said that his "core message" is "people in the workforce should start to use and experiment with AI tools so they can understand what’s coming". Even as the essay was widely shared and discussed, the essay also elicited criticism. Paulo Carvao, in an essay published by the Forbes Magazine stated that some of his advice is sound, but added: "It reads at times like a sales pitch. He urges readers to subscribe to the most advanced AI tools. He implies that those with access to premium models will outpace those without. He frames paid AI subscriptions as a form of insurance against obsolescence." Writing in The Guardian, Dan Milmo and Aisha Down mentioned Shumer as having a history of AI hype and stated, "He previously excited the internet by announcing the release of the world's "top open-source model", which it was not". Many workers in the technology sector criticized the article in blog posts shared on Hacker News; Edward Zitron commented that "while coding LLMs can test products, or scan/fix some bugs, this suggests they A) do this autonomously without human input, B) they do this correctly every time (or ever!)." In an article alluding to Shumer's original post, Ari Colaprete wrote "the LLM is fundamentally a writing machine, it does everything via text, and if you make it produce writing that exists purely to serve some sort of mechanical function, and you train it to succeed in that task, then it will tend to do so, even with vast intricacy."

Grammar induction

Grammar induction (or grammatical inference) is the process in machine learning of learning a formal grammar (usually as a collection of re-write rules or productions or alternatively as a finite-state machine or automaton of some kind) from a set of observations, thus constructing a model which accounts for the characteristics of the observed objects. More generally, grammatical inference is that branch of machine learning where the instance space consists of discrete combinatorial objects such as strings, trees and graphs. == Grammar classes == Grammatical inference has often been very focused on the problem of learning finite-state machines of various types (see the article Induction of regular languages for details on these approaches), since there have been efficient algorithms for this problem since the 1980s. Since the beginning of the century, these approaches have been extended to the problem of inference of context-free grammars and richer formalisms, such as multiple context-free grammars and parallel multiple context-free grammars. Other classes of grammars for which grammatical inference has been studied are combinatory categorial grammars, stochastic context-free grammars, contextual grammars and pattern languages. == Learning models == The simplest form of learning is where the learning algorithm merely receives a set of examples drawn from the language in question: the aim is to learn the language from examples of it (and, rarely, from counter-examples, that is, example that do not belong to the language). However, other learning models have been studied. One frequently studied alternative is the case where the learner can ask membership queries as in the exact query learning model or minimally adequate teacher model introduced by Angluin. == Methodologies == There is a wide variety of methods for grammatical inference. Two of the classic sources are Fu (1977) and Fu (1982). Duda, Hart & Stork (2001) also devote a brief section to the problem, and cite a number of references. The basic trial-and-error method they present is discussed below. For approaches to infer subclasses of regular languages in particular, see Induction of regular languages. A more recent textbook is de la Higuera (2010), which covers the theory of grammatical inference of regular languages and finite state automata. D'Ulizia, Ferri and Grifoni provide a survey that explores grammatical inference methods for natural languages. === Induction of probabilistic grammars === There are several methods for induction of probabilistic context-free grammars. === Grammatical inference by trial-and-error === The method proposed in Section 8.7 of Duda, Hart & Stork (2001) suggests successively guessing grammar rules (productions) and testing them against positive and negative observations. The rule set is expanded so as to be able to generate each positive example, but if a given rule set also generates a negative example, it must be discarded. This particular approach can be characterized as "hypothesis testing" and bears some similarity to Mitchel's version space algorithm. The Duda, Hart & Stork (2001) text provide a simple example which nicely illustrates the process, but the feasibility of such an unguided trial-and-error approach for more substantial problems is dubious. === Grammatical inference by genetic algorithms === Grammatical induction using evolutionary algorithms is the process of evolving a representation of the grammar of a target language through some evolutionary process. Formal grammars can easily be represented as tree structures of production rules that can be subjected to evolutionary operators. Algorithms of this sort stem from the genetic programming paradigm pioneered by John Koza. Other early work on simple formal languages used the binary string representation of genetic algorithms, but the inherently hierarchical structure of grammars couched in the EBNF language made trees a more flexible approach. Koza represented Lisp programs as trees. He was able to find analogues to the genetic operators within the standard set of tree operators. For example, swapping sub-trees is equivalent to the corresponding process of genetic crossover, where sub-strings of a genetic code are transplanted into an individual of the next generation. Fitness is measured by scoring the output from the functions of the Lisp code. Similar analogues between the tree structured lisp representation and the representation of grammars as trees, made the application of genetic programming techniques possible for grammar induction. In the case of grammar induction, the transplantation of sub-trees corresponds to the swapping of production rules that enable the parsing of phrases from some language. The fitness operator for the grammar is based upon some measure of how well it performed in parsing some group of sentences from the target language. In a tree representation of a grammar, a terminal symbol of a production rule corresponds to a leaf node of the tree. Its parent nodes corresponds to a non-terminal symbol (e.g. a noun phrase or a verb phrase) in the rule set. Ultimately, the root node might correspond to a sentence non-terminal. === Grammatical inference by greedy algorithms === Like all greedy algorithms, greedy grammar inference algorithms make, in iterative manner, decisions that seem to be the best at that stage. The decisions made usually deal with things like the creation of new rules, the removal of existing rules, the choice of a rule to be applied or the merging of some existing rules. Because there are several ways to define 'the stage' and 'the best', there are also several greedy grammar inference algorithms. These context-free grammar generating algorithms make the decision after every read symbol: Lempel-Ziv-Welch algorithm creates a context-free grammar in a deterministic way such that it is necessary to store only the start rule of the generated grammar. Sequitur and its modifications. These context-free grammar generating algorithms first read the whole given symbol-sequence and then start to make decisions: Byte pair encoding and its optimizations. === Distributional learning === A more recent approach is based on distributional learning. Algorithms using these approaches have been applied to learning context-free grammars and mildly context-sensitive languages and have been proven to be correct and efficient for large subclasses of these grammars. === Learning of pattern languages === Angluin defines a pattern to be "a string of constant symbols from Σ and variable symbols from a disjoint set". The language of such a pattern is the set of all its nonempty ground instances i.e. all strings resulting from consistent replacement of its variable symbols by nonempty strings of constant symbols. A pattern is called descriptive for a finite input set of strings if its language is minimal (with respect to set inclusion) among all pattern languages subsuming the input set. Angluin gives a polynomial algorithm to compute, for a given input string set, all descriptive patterns in one variable x. To this end, she builds an automaton representing all possibly relevant patterns; using sophisticated arguments about word lengths, which rely on x being the only variable, the state count can be drastically reduced. Erlebach et al. give a more efficient version of Angluin's pattern learning algorithm, as well as a parallelized version. Arimura et al. show that a language class obtained from limited unions of patterns can be learned in polynomial time. === Pattern theory === Pattern theory, formulated by Ulf Grenander, is a mathematical formalism to describe knowledge of the world as patterns. It differs from other approaches to artificial intelligence in that it does not begin by prescribing algorithms and machinery to recognize and classify patterns; rather, it prescribes a vocabulary to articulate and recast the pattern concepts in precise language. In addition to the new algebraic vocabulary, its statistical approach was novel in its aim to: Identify the hidden variables of a data set using real world data rather than artificial stimuli, which was commonplace at the time. Formulate prior distributions for hidden variables and models for the observed variables that form the vertices of a Gibbs-like graph. Study the randomness and variability of these graphs. Create the basic classes of stochastic models applied by listing the deformations of the patterns. Synthesize (sample) from the models, not just analyze signals with it. Broad in its mathematical coverage, pattern theory spans algebra and statistics, as well as local topological and global entropic properties. == Applications == The principle of grammar induction has been applied to other aspects of natural language processing, and has been applied (among many other problems) to semantic parsing, natural language understanding, example-based translation, language acquisition, grammar-based compre