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LanguageWare

LanguageWare is a natural language processing (NLP) technology developed by IBM, which allows applications to process natural language text. It comprises a set of Java libraries that provide a range of NLP functions: language identification, text segmentation/tokenization, normalization, entity and relationship extraction, and semantic analysis and disambiguation. The analysis engine uses a finite-state machine approach at multiple levels, which aids its performance characteristics while maintaining a reasonably small footprint. The behaviour of the system is driven by a set of configurable lexico-semantic resources which describe the characteristics and domain of the processed language. A default set of resources comes as part of LanguageWare and these describe the native language characteristics, such as morphology, and the basic vocabulary for the language. Supplemental resources have been created that capture additional vocabularies, terminologies, rules and grammars, which may be generic to the language or specific to one or more domains. A set of Eclipse-based customization tooling, LanguageWare Resource Workbench, is available on IBM's alphaWorks site, and allows domain knowledge to be compiled into these resources and thereby incorporated into the analysis process. LanguageWare can be deployed as a set of UIMA-compliant annotators, Eclipse plug-ins or Web Services.
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Bag-of-words model

The bag-of-words (BoW) model is a model of text which uses an unordered collection (a "bag") of words. It is used in natural language processing and information retrieval (IR). It disregards word order (and thus most of syntax or grammar) but captures multiplicity. The bag-of-words model is commonly used in methods of document classification where, for example, the (frequency of) occurrence of each word is used as a feature for training a classifier. It has also been used for computer vision. An early reference to "bag of words" in a linguistic context can be found in Zellig Harris's 1954 article on Distributional Structure. == Definition == The following models a text document using bag-of-words. Here are two simple text documents: Based on these two text documents, a list is constructed as follows for each document: Representing each bag-of-words as a JSON object, and attributing to the respective JavaScript variable: Each key is the word, and each value is the number of occurrences of that word in the given text document. The order of elements is free, so, for example {"too":1,"Mary":1,"movies":2,"John":1,"watch":1,"likes":2,"to":1} is also equivalent to BoW1. It is also what we expect from a strict JSON object representation. Note: if another document is like a union of these two, its JavaScript representation will be: So, as we see in the bag algebra, the "union" of two documents in the bags-of-words representation is, formally, the disjoint union, summing the multiplicities of each element. === Word order === The BoW representation of a text removes all word ordering. For example, the BoW representation of "man bites dog" and "dog bites man" are the same, so any algorithm that operates with a BoW representation of text must treat them in the same way. Despite this lack of syntax or grammar, BoW representation is fast and may be sufficient for simple tasks that do not require word order. For instance, for document classification, if the words "stocks" "trade" "investors" appears multiple times, then the text is likely a financial report, even though it would be insufficient to distinguish between Yesterday, investors were rallying, but today, they are retreating.andYesterday, investors were retreating, but today, they are rallying.and so the BoW representation would be insufficient to determine the detailed meaning of the document. == Implementations == Implementations of the bag-of-words model might involve using frequencies of words in a document to represent its contents. The frequencies can be "normalized" by the inverse of document frequency, or tf–idf. Additionally, for the specific purpose of classification, supervised alternatives have been developed to account for the class label of a document. Lastly, binary (presence/absence or 1/0) weighting is used in place of frequencies for some problems (e.g., this option is implemented in the WEKA machine learning software system). == Hashing trick == A common alternative to using dictionaries is the hashing trick, where words are mapped directly to indices with a hash function. When using a hash function, no memory is required to store a dictionary. In practice, hashing simplifies the implementation of bag-of-words models and improves scalability. Collisions can occur when two words are hashed to the same index, but this happens infrequently and may function as a form of regularization.
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Token maxxing

Token Maxxing or Token Maxing is a metric used in an attempt to track productivity in the workplace especially for those using Artificial Intelligence (AI) based services. AI services charge for each token which represent units of effort expended by an AI service to solve a problem. Some believe that token consumption equates to productivity and thus can be used as a metric to monitor an employee's work. Supporters believe that higher token usage indicates higher productivity and higher utilization of powerful AI services. This also suggests that those not consuming enough tokens may be less productive and underutilizing powerful AI services. This belief might lead to an environment that incentivizes higher token usage to predict increased productivity. Critics of token maxxing as a metric claim that prudent workers will maximize any metric that management wants increased to gain a workplace advantage. For example: Engineers in the tech industries pressed to consume as many tokens as possible might run several AI agents in tandem, enter longer input prompts, or automate their tasks to maximize their token consumption. To management, this higher token usage may indicate potential productivity, but in reality may cause additional token costs, worker burnout, or actually create more bloated code of lower quality. Another claim is AI service companies potentially benefit from such an emphasis on token consumption and actively encourage the trend. Some developers have publicly advocated the practice. Developer Sigrid Jin, who said he used 50 billion tokens in a single year, has argued that maximizing token consumption is the best way to understand the value of AI, advising others to spend as much on AI usage as they pay in rent to obtain a return on investment. == See Also == Goodhart's law Perverse incentive Jevons Paradox
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Machine unlearning

Machine unlearning is a branch of machine learning focused on removing specific undesired element, such as private data, wrong or manipulated training data, outdated information, copyrighted material, harmful content, dangerous abilities, or misinformation, without needing to rebuild models from the ground up. Large language models, like the ones powering ChatGPT, may be asked not just to remove specific elements but also to unlearn a "concept," "fact," or "knowledge," which aren't easily linked to specific examples. New terms such as "model editing," "concept editing," and "knowledge unlearning" have emerged to describe this process. == History == Early research efforts were largely motivated by Article 17 of the GDPR, the European Union's privacy regulation commonly known as the "right to be forgotten" (RTBF), introduced in 2014. The GDPR did not anticipate that the development of large language models would make data erasure a complex task. This issue has since led to research on "machine unlearning," with a growing focus on removing copyrighted material, harmful content, dangerous capabilities, and misinformation. Just as early experiences in humans shape later ones, some concepts are more fundamental and harder to unlearn. A piece of knowledge may be so deeply embedded in the model's knowledge graph that unlearning it could cause internal contradictions, requiring adjustments to other parts of the graph to resolve them. Researchers have now also started studying unlearning in the context of removing incorrect or adversarially manipulated training data such as systematically biased labels or poisoning attacks. == Motivations == At present, machine unlearning is motivated by a growing range of concerns that extend well beyond the field's original focus on data privacy. A widely used taxonomy in the literature distinguishes two high-level categories of motivation. Access revocation covers cases where a data subject or rights holder requests the removal of data they own or control. This is most commonly associated with RTBF established by the European Union's General Data Protection Regulation (GDPR) and analogous legislation such as the California Consumer Privacy Act (CCPA). These regulations grant individuals the legal right to request erasure of their personal data from any system that has processed it, including models that were trained on it. Access revocation also encompasses the removal of copyrighted or pay-walled content that was incorporated into training corpora without the necessary licenses, a concern that has become prominent with the widespread use of largely web-scraped pre-training datasets. Model correction covers cases where the model exhibits undesirable behavior arising from the training data, regardless of any individual's request. This includes: Removal of toxic, biased, or unsafe outputs introduced by harmful content in the training set Correction of stale or factually incorrect associations, such as outdated knowledge encoded in a deployed model Removal of dangerous capabilities, such as detailed knowledge of the synthesis of chemical or biological agents Correction of the influence of data poisoning or adversarial attacks that have corrupted model behavior This second category has been formalized as corrective machine unlearning, which frames unlearning as a post-training mechanism for repairing the effects of bad or harmful training data. It is closely related to the AI safety literature, where data filtering alone has been found insufficient to prevent hazardous knowledge from being encoded in model weights, motivating unlearning as a complementary risk mitigation strategy. A further distinction has been drawn in the literature between removal {eliminating the influence of specific training data on model parameters) and suppression (preventing the model from generating specific outputs regardless of how that knowledge is encoded). These two goals are not equivalent: removing training data does not guarantee meaningful output suppression, and suppressing outputs does not constitute removal of the underlying training data's influence. == SISA Training == SISA is a training strategy consisting of four mechanisms designed to make machine unlearning more efficient by structuring how models are trained and updated. Its goal is to allow a system to remove the influence of specific data points without retraining an entire model from scratch. By reorganizing training data and workflows, SISA reduces the computational burden of unlearning requests. Sharding divides the training dataset into multiple disjoint subsets, or shards. Each shard is used to train a separate model instance. This ensures that a single data point affects only one shard, so unlearning it requires updating only the corresponding shard rather than the full model. Isolation refers to training each shard independently, with nothing shared across shards during the training process. This separation prevents cross-contamination between shards, ensuring that forgetting data in one shard does not require adjustments to any others. Slicing breaks the data within each shard into sequential slices and stores model states after each slice is trained on. When an unlearning request targets a piece of data, the system can roll back to the checkpoint before the point was seen and retrain only from that slice forward. This reduces retraining time even within a shard. Aggregation occurs at inference, when the model is queried. It combines the outputs of each shard to determine the output of the overall model. This is often through majority voting or averaging. This allows SISA-trained systems to behave like a single model despite being composed of multiple shard-level models. Together, these mechanisms enable machine learning systems to forget specific data points with far lower computational cost than full retraining. The trade-off is that sharding and slicing can lead to reduced model accuracy, worse generalization, and increased storage requirements for the intermediate checkpoints. This can be tolerable based on the needs of the individual or organization to comply with "right to be forgotten" or efficiently recover from backdoor attacks. == Algorithms == Machine unlearning algorithms are broadly categorized into exact and approximate methods, reflecting a fundamental trade-off between formal guarantees and computational tractability. === Exact Unlearning === Exact unlearning methods produce a model that is statistically indistinguishable from one retrained from scratch on the dataset with the forget data removed. The canonical framework for exact unlearning is SISA Training (Sharded, Isolated, Sliced, and Aggregated), introduced by Bourtoule et al. (2021). SISA partitions the training dataset into disjoint shards and trains a separate sub-model on each. At inference time, predictions are aggregated across sub-models. When an unlearning request is received, only the sub-model corresponding to the shard containing the target data requires retraining, reducing computational overhead proportionally to the number of shards. Exact methods provide the strongest guarantees but become prohibitively expensive for large pre-trained neural networks and are generally limited to settings where training can be structured in advance. === Approximate Unlearning === Approximate unlearning methods seek to produce a model whose behavior is sufficiently close to an exactly unlearned model without the cost of full retraining. These methods dominate practical applications. Common approaches include: Gradient Ascent: The model is fine-tuned by maximizing the loss on the forget set, directly degrading its performance on targeted data. This is the most direct approach but risks destabilizing performance on retained data. Random Labelling: The model is fine-tuned on the forget set using randomly shuffled labels, confusing its associations with the targeted data while producing a less aggressive weight shift than pure gradient ascent. Gradient Difference: Combines gradient ascent on the forget set with simultaneous gradient descent on the retain set, using the retain objective as a regularizer to preserve general model utility. KL Divergence Regularization: Minimizes the KL divergence between the outputs of the unlearned model and the original model on the retain set, anchoring behavior on data the model should remember. Weight Pruning and Fine-tuning: Parameters with the smallest L1-norm are pruned — targeting weights most weakly associated with general knowledge and potentially most associated with the forget set — followed by fine-tuning on the retain set to restore utility. Layer Reset and Fine-tuning: The first or last k layers are re-initialized to random weights and the model is subsequently fine-tuned on the retain set. This is a coarse but computationally simple approach. Selective Synaptic Dampening: Uses influence functions to estimate the effect of individual trainin
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Image texture

An image texture is the small-scale structure perceived on an image, based on the spatial arrangement of color or intensities. It can be quantified by a set of metrics calculated in image processing. Image texture metrics give us information about the whole image or selected regions. Image textures can be artificially created or found in natural scenes captured in an image. Image textures are one way that can be used to help in segmentation or classification of images. For more accurate segmentation the most useful features are spatial frequency and an average grey level. To analyze an image texture in computer graphics, there are two ways to approach the issue: structured approach and statistical approach. == Structured approach == A structured approach sees an image texture as a set of primitive texels in some regular or repeated pattern. This works well when analyzing artificial textures. To obtain a structured description a characterization of the spatial relationship of the texels is gathered by using Voronoi tessellation of the texels. == Statistical approach == A statistical approach sees an image texture as a quantitative measure of the arrangement of intensities in a region. In general this approach is easier to compute and is more widely used, since natural textures are made of patterns of irregular subelements. === Edge detection === The use of edge detection is to determine the number of edge pixels in a specified region, helps determine a characteristic of texture complexity. After edges have been found the direction of the edges can also be applied as a characteristic of texture and can be useful in determining patterns in the texture. These directions can be represented as an average or in a histogram. Consider a region with N pixels. the gradient-based edge detector is applied to this region by producing two outputs for each pixel p: the gradient magnitude Mag(p) and the gradient direction Dir(p). The edgeness per unit area can be defined by F e d g e n e s s = | { p | M a g ( p ) > T } | N {\displaystyle F_{edgeness}={\frac {|\{p|Mag(p)>T\}|}{N}}} for some threshold T. To include orientation with edgeness histograms for both gradient magnitude and gradient direction can be used. Hmag(R) denotes the normalized histogram of gradient magnitudes of region R, and Hdir(R) denotes the normalized histogram of gradient orientations of region R. Both are normalized according to the size NR Then F m a g , d i r = ( H m a g ( R ) , H d i r ( R ) ) {\displaystyle F_{mag,dir}=(H_{mag}(R),H_{dir}(R))} is a quantitative texture description of region R. === Co-occurrence matrices === The co-occurrence matrix captures numerical features of a texture using spatial relations of similar gray tones. Numerical features computed from the co-occurrence matrix can be used to represent, compare, and classify textures. The following are a subset of standard features derivable from a normalized co-occurrence matrix: A n g u l a r 2 n d M o m e n t = ∑ i ∑ j p [ i , j ] 2 C o n t r a s t = ∑ i = 1 N g ∑ j = 1 N g n 2 p [ i , j ] , where | i − j | = n C o r r e l a t i o n = ∑ i = 1 N g ∑ j = 1 N g ( i j ) p [ i , j ] − μ x μ y σ x σ y E n t r o p y = − ∑ i ∑ j p [ i , j ] l n ( p [ i , j ] ) {\displaystyle {\begin{aligned}Angular{\text{ }}2nd{\text{ }}Moment&=\sum _{i}\sum _{j}p[i,j]^{2}\\Contrast&=\sum _{i=1}^{Ng}\sum _{j=1}^{Ng}n^{2}p[i,j]{\text{, where }}|i-j|=n\\Correlation&={\frac {\sum _{i=1}^{Ng}\sum _{j=1}^{Ng}(ij)p[i,j]-\mu _{x}\mu _{y}}{\sigma _{x}\sigma _{y}}}\\Entropy&=-\sum _{i}\sum _{j}p[i,j]ln(p[i,j])\\\end{aligned}}} where p [ i , j ] {\displaystyle p[i,j]} is the [ i , j ] {\displaystyle [i,j]} th entry in a gray-tone spatial dependence matrix, and Ng is the number of distinct gray-levels in the quantized image. One negative aspect of the co-occurrence matrix is that the extracted features do not necessarily correspond to visual perception. It is used in dentistry for the objective evaluation of lesions [DOI: 10.1155/2020/8831161], treatment efficacy [DOI: 10.3390/ma13163614; DOI: 10.11607/jomi.5686; DOI: 10.3390/ma13173854; DOI: 10.3390/ma13132935] and bone reconstruction during healing [DOI: 10.5114/aoms.2013.33557; DOI: 10.1259/dmfr/22185098; EID: 2-s2.0-81455161223; DOI: 10.3390/ma13163649]. === Laws texture energy measures === Another approach is to use local masks to detect various types of texture features. Laws originally used four vectors representing texture features to create sixteen 2D masks from the outer products of the pairs of vectors. The four vectors and relevant features were as follows: L5 = [ +1 +4 6 +4 +1 ] (Level) E5 = [ -1 -2 0 +2 +1 ] (Edge) S5 = [ -1 0 2 0 -1 ] (Spot) R5 = [ +1 -4 6 -4 +1 ] (Ripple) To these 4, a fifth is sometimes added: W5 = [ -1 +2 0 -2 +1 ] (Wave) From Laws' 4 vectors, 16 5x5 "energy maps" are then filtered down to 9 in order to remove certain symmetric pairs. For instance, L5E5 measures vertical edge content and E5L5 measures horizontal edge content. The average of these two measures is the "edginess" of the content. The resulting 9 maps used by Laws are as follows: L5E5/E5L5 L5R5/R5L5 E5S5/S5E5 S5S5 R5R5 L5S5/S5L5 E5E5 E5R5/R5E5 S5R5/R5S5 Running each of these nine maps over an image to create a new image of the value of the origin ([2,2]) results in 9 "energy maps," or conceptually an image with each pixel associated with a vector of 9 texture attributes. === Autocorrelation and power spectrum === The autocorrelation function of an image can be used to detect repetitive patterns of textures. == Texture segmentation == The use of image texture can be used as a description for regions into segments. There are two main types of segmentation based on image texture, region based and boundary based. Though image texture is not a perfect measure for segmentation it is used along with other measures, such as color, that helps solve segmenting in image. === Region based === Attempts to group or cluster pixels based on texture properties. === Boundary based === Attempts to group or cluster pixels based on edges between pixels that come from different texture properties.
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Neuro-symbolic AI

Neuro-symbolic AI is a subfield of artificial intelligence that integrates neural methods (e.g., neural networks and deep learning) with symbolic methods (e.g., formal logic, knowledge representation, and automated reasoning). The goal is to combine the strengths of both approaches, resulting in AI systems that can be trained from raw data and demonstrate robustness against outliers or errors in the base data, while preserving explainability, explicit use of expert knowledge, and explicit cognitive reasoning. As argued by Leslie Valiant and others, the effective construction of rich computational cognitive models demands the combination of symbolic reasoning and efficient machine learning. Gary Marcus argued, "We cannot construct rich cognitive models in an adequate, automated way without the triumvirate of hybrid architecture, rich prior knowledge, and sophisticated techniques for reasoning." Further, "To build a robust, knowledge-driven approach to AI we must have the machinery of symbol manipulation in our toolkit. Too much of useful knowledge is abstract to make do without tools that represent and manipulate abstraction, and to date, the only known machinery that can manipulate such abstract knowledge reliably is the apparatus of symbol manipulation." Angelo Dalli, Henry Kautz, Francesca Rossi, and Bart Selman also argued for such a synthesis. Their arguments attempt to address the two kinds of thinking, as discussed in Daniel Kahneman's book Thinking, Fast and Slow. It describes cognition as encompassing two components: System 1 is fast, reflexive, intuitive, and unconscious. System 2 is slower, step-by-step, and explicit. System 1 is used for pattern recognition. System 2 handles planning, deduction, and deliberative thinking. In this view, deep learning best handles the first kind of cognition, while symbolic reasoning best handles the second kind. Both are necessary for the development of a robust and reliable AI system capable of learning, reasoning, and interacting with humans to accept advice and answer questions. Since the 1990s, dual-process models with explicit references to the two contrasting systems have been the focus of research in both the fields of AI and cognitive science by numerous researchers. In 2025, the adoption of neurosymbolic AI, an approach that integrates neural networks with symbolic reasoning, increased in response to the need to address hallucination issues in large language models. For example, Amazon implemented Neurosymbolic AI in its Vulcan warehouse robots and Rufus shopping assistant to enhance accuracy and decision-making. == Approaches == Approaches for integration are diverse. Henry Kautz's taxonomy of neuro-symbolic architectures follows, along with some examples: Symbolic Neural symbolic is the current approach of many neural models in natural language processing, where words or subword tokens are the ultimate input and output of large language models. Examples include BERT, RoBERTa, and GPT-3. Symbolic[Neural] is exemplified by AlphaGo, where symbolic techniques are used to invoke neural techniques. In this case, the symbolic approach is Monte Carlo tree search and the neural techniques learn how to evaluate game positions. Neural | Symbolic uses a neural architecture to interpret perceptual data as symbols and relationships that are reasoned about symbolically. Neural-Concept Learner is an example. Neural: Symbolic → Neural relies on symbolic reasoning to generate or label training data that is subsequently learned by a deep learning model, e.g., to train a neural model for symbolic computation by using a Macsyma-like symbolic mathematics system to create or label examples. NeuralSymbolic uses a neural net that is generated from symbolic rules. An example is the Neural Theorem Prover, which constructs a neural network from an AND-OR proof tree generated from knowledge base rules and terms. Logic Tensor Networks also fall into this category. Neural[Symbolic] according to Kautz, this approach embeds true symbolic reasoning inside a neural network. These are tightly-coupled neural-symbolic systems, in which the logical inference rules are internal to the neural network. This way, the neural network internally computes the inference from the premises and learns to reason based on logical inference systems. Early work on connectionist modal and temporal logics by Garcez, Lamb, and Gabbay is aligned with this approach. These categories are not exhaustive, as they do not consider multi-agent systems. In 2005, Bader and Hitzler presented a more fine-grained categorization that took into account, e.g., whether the use of symbols included logic and, if so, whether the logic was propositional or first-order logic. The 2005 categorization and Kautz's taxonomy above are compared and contrasted in a 2021 article. Sepp Hochreiter argued that Graph Neural Networks "...are the predominant models of neural-symbolic computing" since "[t]hey describe the properties of molecules, simulate social networks, or predict future states in physical and engineering applications with particle-particle interactions." == Artificial general intelligence == Gary Marcus argues that "...hybrid architectures that combine learning and symbol manipulation are necessary for robust intelligence, but not sufficient", and that there are ...four cognitive prerequisites for building robust artificial intelligence: hybrid architectures that combine large-scale learning with the representational and computational powers of symbol manipulation, large-scale knowledge bases—likely leveraging innate frameworks—that incorporate symbolic knowledge along with other forms of knowledge, reasoning mechanisms capable of leveraging those knowledge bases in tractable ways, and rich cognitive models that work together with those mechanisms and knowledge bases. This echoes earlier calls for hybrid models as early as the 1990s. == History == Garcez and Lamb described research in this area as ongoing, at least since the 1990s. During that period, the terms symbolic and sub-symbolic AI were popular. A series of workshops on neuro-symbolic AI has been held annually since 2005 Neuro-Symbolic Artificial Intelligence. In the early 1990s, an initial set of workshops on this topic were organized. == Research == Key research questions remain, such as: What is the best way to integrate neural and symbolic architectures? How should symbolic structures be represented within neural networks and extracted from them? How should common-sense knowledge be learned and reasoned about? How can abstract knowledge that is hard to encode logically be handled? == Implementations == Implementations of neuro-symbolic approaches include: AllegroGraph: an integrated Knowledge Graph based platform for neuro-symbolic application development. Scallop: a language based on Datalog that supports differentiable logical and relational reasoning. Scallop can be integrated in Python and with a PyTorch learning module. Logic Tensor Networks: encode logical formulas as neural networks and simultaneously learn term encodings, term weights, and formula weights. DeepProbLog: combines neural networks with the probabilistic reasoning of ProbLog. Abductive Learning: integrates machine learning and logical reasoning in a balanced-loop via abductive reasoning, enabling them to work together in a mutually beneficial way. SymbolicAI: a compositional differentiable programming library.
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Manifold hypothesis

The manifold hypothesis posits that many high-dimensional data sets that occur in the real world actually lie along low-dimensional latent manifolds inside that high-dimensional space. As a consequence of the manifold hypothesis, many data sets that appear to initially require many variables to describe, can actually be described by a comparatively small number of variables, linked to the local coordinate system of the underlying manifold. It is suggested that this principle underpins the effectiveness of machine learning algorithms in describing high-dimensional data sets by considering a few common features. The manifold hypothesis is related to the effectiveness of nonlinear dimensionality reduction techniques in machine learning. Many techniques of dimensional reduction make the assumption that data lies along a low-dimensional submanifold, such as manifold sculpting, manifold alignment, and manifold regularization. The major implications of this hypothesis is that Machine learning models only have to fit relatively simple, low-dimensional, highly structured subspaces within their potential input space (latent manifolds). Within one of these manifolds, it's always possible to interpolate between two inputs, that is to say, morph one into another via a continuous path along which all points fall on the manifold. The ability to interpolate between samples is the key to generalization in deep learning. == The information geometry of statistical manifolds == An empirically-motivated approach to the manifold hypothesis focuses on its correspondence with an effective theory for manifold learning under the assumption that robust machine learning requires encoding the dataset of interest using methods for data compression. This perspective gradually emerged using the tools of information geometry thanks to the coordinated effort of scientists working on the efficient coding hypothesis, predictive coding and variational Bayesian methods. The argument for reasoning about the information geometry on the latent space of distributions rests upon the existence and uniqueness of the Fisher information metric. In this general setting, we are trying to find a stochastic embedding of a statistical manifold. From the perspective of dynamical systems, in the big data regime this manifold generally exhibits certain properties such as homeostasis: We can sample large amounts of data from the underlying generative process. Machine Learning experiments are reproducible, so the statistics of the generating process exhibit stationarity. In a sense made precise by theoretical neuroscientists working on the free energy principle, the statistical manifold in question possesses a Markov blanket.
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Belief–desire–intention model

For popular psychology, the belief–desire–intention (BDI) model of human practical reasoning was developed by Michael Bratman as a way of explaining future-directed intention. BDI is fundamentally reliant on folk psychology (the 'theory theory'), which is the notion that our mental models of the world are theories. It was used as a basis for developing the belief–desire–intention software model. == Applications == BDI was part of the inspiration behind the BDI software architecture, which Bratman was also involved in developing. Here, the notion of intention was seen as a way of limiting time spent on deliberating about what to do, by eliminating choices inconsistent with current intentions. BDI has also aroused some interest in psychology. BDI formed the basis for a computational model of childlike reasoning CRIBB.
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Fillrate

In computer graphics, a video card's pixel fillrate refers to the number of pixels that can be rendered on the screen and written to video memory in one second. Pixel fillrates are given in megapixels per second or in gigapixels per second (in the case of newer cards), and are obtained by multiplying the number of render output units (ROPs) by the clock frequency of the graphics processing unit (GPU) of a video card. A similar concept, texture fillrate, refers to the number of texture map elements (texels) the GPU can map to pixels in one second. Texture fillrate is obtained by multiplying the number of texture mapping units (TMUs) by the clock frequency of the GPU. Texture fillrates are given in mega or gigatexels per second. However, there is no full agreement on how to calculate and report fillrates. Another possible method is to multiply the number of pixel pipelines by the GPU's clock frequency. The results of these multiplications correspond to a theoretical number. The actual fillrate depends on many other factors. In the past, the fillrate has been used as an indicator of performance by video card manufacturers such as ATI and NVIDIA, however, the importance of the fillrate as a measurement of performance has declined as the bottleneck in graphics applications has shifted. For example, today, the number and speed of unified shader processing units has gained attention. Although fillrate doesn't provide a substantial bottleneck in games, it can still provide a bottleneck for certain parts of the game, for example applying a gaussian blur can be bottlenecked by fillrate. Scene complexity can be increased by overdrawing, which happens when an object is drawn to the frame buffer, and another object (such as a wall) is then drawn on top of it, covering it up. The time spent drawing the first object is thus wasted because it is not visible. When a sequence of scenes is extremely complex (many pixels have to be drawn for each scene), the frame rate for the sequence may drop. When designing graphics intensive applications, one can determine whether the application is fillrate-limited (or shader limited) by seeing if the frame rate increases dramatically when the application runs at a lower resolution or in a smaller window. Although this is not a full-proof method, modern videogame engines can dynamically reduce the level-of-detail required and thereby reducing fillrate-limited applications. The best way to find fillrate bottlenecks is to use GPU vendor software like NVIDIA Nsight Graphics, AMD Radeon GPU Profile and the Intel Graphics Performance Analyzers.
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Hyperparameter optimization

In machine learning, hyperparameter optimization or tuning is the problem of choosing a set of optimal hyperparameters for a learning algorithm. A hyperparameter is a parameter whose value is used to control the learning process, which must be configured before the process starts. Hyperparameter optimization determines the set of hyperparameters that yields an optimal model which minimizes a predefined loss function on a given data set. The objective function takes a set of hyperparameters and returns the associated loss. Cross-validation is often used to estimate this generalization performance, and therefore choose the set of values for hyperparameters that maximize it. == Approaches == === Grid search === The traditional method for hyperparameter optimization has been grid search, or a parameter sweep, which is simply an exhaustive searching through a manually specified subset of the hyperparameter space of a learning algorithm. A grid search algorithm must be guided by some performance metric, typically measured by cross-validation on the training set or evaluation on a hold-out validation set. Since the parameter space of a machine learner may include real-valued or unbounded value spaces for certain parameters, manually set bounds and discretization may be necessary before applying grid search. For example, a typical soft-margin SVM classifier equipped with an RBF kernel has at least two hyperparameters that need to be tuned for good performance on unseen data: a regularization constant C and a kernel hyperparameter γ. Both parameters are continuous, so to perform grid search, one selects a finite set of "reasonable" values for each, say C ∈ { 10 , 100 , 1000 } {\displaystyle C\in \{10,100,1000\}} γ ∈ { 0.1 , 0.2 , 0.5 , 1.0 } {\displaystyle \gamma \in \{0.1,0.2,0.5,1.0\}} Grid search then trains an SVM with each pair (C, γ) in the Cartesian product of these two sets and evaluates their performance on a held-out validation set (or by internal cross-validation on the training set, in which case multiple SVMs are trained per pair). Finally, the grid search algorithm outputs the settings that achieved the highest score in the validation procedure. Grid search suffers from the curse of dimensionality, but is often embarrassingly parallel because the hyperparameter settings it evaluates are typically independent of each other. === Random search === Random Search replaces the exhaustive enumeration of all combinations by selecting them randomly. This can be simply applied to the discrete setting described above, but also generalizes to continuous and mixed spaces. A benefit over grid search is that random search can explore many more values than grid search could for continuous hyperparameters. It can outperform Grid search, especially when only a small number of hyperparameters affects the final performance of the machine learning algorithm. In this case, the optimization problem is said to have a low intrinsic dimensionality. Random Search is also embarrassingly parallel, and additionally allows the inclusion of prior knowledge by specifying the distribution from which to sample. Despite its simplicity, random search remains one of the important base-lines against which to compare the performance of new hyperparameter optimization methods. === Bayesian optimization === Bayesian optimization is a global optimization method for noisy black-box functions. Applied to hyperparameter optimization, Bayesian optimization builds a probabilistic model of the function mapping from hyperparameter values to the objective evaluated on a validation set. By iteratively evaluating a promising hyperparameter configuration based on the current model, and then updating it, Bayesian optimization aims to gather observations revealing as much information as possible about this function and, in particular, the location of the optimum. It tries to balance exploration (hyperparameters for which the outcome is most uncertain) and exploitation (hyperparameters expected close to the optimum). In practice, Bayesian optimization has been shown to obtain better results in fewer evaluations compared to grid search and random search, due to the ability to reason about the quality of experiments before they are run. === Gradient-based optimization === For specific learning algorithms, it is possible to compute the gradient with respect to hyperparameters and then optimize the hyperparameters using gradient descent. The first usage of these techniques was focused on neural networks. Since then, these methods have been extended to other models such as support vector machines or logistic regression. A different approach in order to obtain a gradient with respect to hyperparameters consists in differentiating the steps of an iterative optimization algorithm using automatic differentiation. A more recent work along this direction uses the implicit function theorem to calculate hypergradients and proposes a stable approximation of the inverse Hessian. The method scales to millions of hyperparameters and requires constant memory. In a different approach, a hypernetwork is trained to approximate the best response function. One of the advantages of this method is that it can handle discrete hyperparameters as well. Self-tuning networks offer a memory efficient version of this approach by choosing a compact representation for the hypernetwork. More recently, Δ-STN has improved this method further by a slight reparameterization of the hypernetwork which speeds up training. Δ-STN also yields a better approximation of the best-response Jacobian by linearizing the network in the weights, hence removing unnecessary nonlinear effects of large changes in the weights. Apart from hypernetwork approaches, gradient-based methods can be used to optimize discrete hyperparameters also by adopting a continuous relaxation of the parameters. Such methods have been extensively used for the optimization of architecture hyperparameters in neural architecture search. === Evolutionary optimization === Evolutionary optimization is a methodology for the global optimization of noisy black-box functions. In hyperparameter optimization, evolutionary optimization uses evolutionary algorithms to search the space of hyperparameters for a given algorithm. Evolutionary hyperparameter optimization follows a process inspired by the biological concept of evolution: Create an initial population of random solutions (i.e., randomly generate tuples of hyperparameters, typically 100+) Evaluate the hyperparameter tuples and acquire their fitness function (e.g., 10-fold cross-validation accuracy of the machine learning algorithm with those hyperparameters) Rank the hyperparameter tuples by their relative fitness Replace the worst-performing hyperparameter tuples with new ones generated via crossover and mutation Repeat steps 2-4 until satisfactory algorithm performance is reached or is no longer improving. Evolutionary optimization has been used in hyperparameter optimization for statistical machine learning algorithms, automated machine learning, typical neural network and deep neural network architecture search, as well as training of the weights in deep neural networks. === Population-based === Population Based Training (PBT) learns both hyperparameter values and network weights. Multiple learning processes operate independently, using different hyperparameters. As with evolutionary methods, poorly performing models are iteratively replaced with models that adopt modified hyperparameter values and weights based on the better performers. This replacement model warm starting is the primary differentiator between PBT and other evolutionary methods. PBT thus allows the hyperparameters to evolve and eliminates the need for manual hypertuning. The process makes no assumptions regarding model architecture, loss functions or training procedures. PBT and its variants are adaptive methods: they update hyperparameters during the training of the models. On the contrary, non-adaptive methods have the sub-optimal strategy to assign a constant set of hyperparameters for the whole training. === Early stopping-based === A class of early stopping-based hyperparameter optimization algorithms is purpose-built for large search spaces of continuous and discrete hyperparameters, particularly when the computational cost to evaluate the performance of a set of hyperparameters is high. Irace implements the iterated racing algorithm, that focuses the search around the most promising configurations, using statistical tests to discard the ones that perform poorly. Another early stopping hyperparameter optimization algorithm is successive halving (SHA), which begins as a random search but periodically prunes low-performing models, thereby focusing computational resources on more promising models. Asynchronous successive halving (ASHA) further improves upon SHA's resource utilization profile by removing the need to synchronously evaluate a
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DABUS

DABUS (Device for the Autonomous Bootstrapping of Unified Sentience) is an artificial intelligence (AI) system created by Stephen Thaler. It reportedly conceived of two novel products — a food container constructed using fractal geometry, which enables rapid reheating, and a flashing beacon for attracting attention in an emergency. The filing of patent applications designating DABUS as inventor has led to decisions by patent offices and courts on whether a patent can be granted for an invention reportedly made by an AI system. == History in different jurisdictions == === Australia === On 17 September 2019, Thaler filed an application to patent a "Food container and devices and methods for attracting enhanced attention," naming DABUS as the inventor. On 21 September 2020, IP Australia found that section 15(1) of the Patents Act 1990 (Cth) is inconsistent with an artificial intelligence machine being treated as an inventor, and Thaler's application had lapsed. Thaler sought judicial review, and on 30 July 2021, the Federal Court set aside IP Australia's decision and ordered IP Australia to reconsider the application. On 13 April 2022, the Full Court of the Federal Court set aside that decision, holding that only a natural person can be an inventor for the purposes of the Patents Act 1990 (Cth) and the Patents Regulations 1991 (Cth), and that such an inventor must be identified for any person to be entitled to a grant of a patent. On 11 November 2022, Thaler was refused special leave to appeal to the High Court. === European Patent Office === On 17 October 2018 and 7 November 2018, Thaler filed two European patent applications with the European Patent Office. The first claimed invention was a "Food Container" and the second was "Devices and Methods for Attracting Enhanced Attention." On 27 January 2020, the EPO rejected the applications on the grounds that the application listed an AI system named DABUS, and not a human, as the inventor, based on Article 81 and Rule 19(1) of the European Patent Convention (EPC). On 21 December 2021, the Board of Appeal of the EPO dismissed Thaler's appeal from the EPO's primary decision. The Board of Appeal confirmed that "under the EPC the designated inventor has to be a person with legal capacity. This is not merely an assumption on which the EPC was drafted. It is the ordinary meaning of the term inventor." === United Kingdom === Similar applications were filed by Thaler to the United Kingdom Intellectual Property Office on 17 October and 7 November 2018. The Office asked Thaler to file statements of inventorship and of right of grant to a patent (Patent Form 7) in respect of each invention within 16 months of the filing date. Thaler filed those forms naming DABUS as the inventor and explaining in some detail why he believed that machines should be regarded as inventors in the circumstances. His application was rejected on the grounds that: (1) naming a machine as inventor did not meet the requirements of the Patents Act 1977; and (2) the IPO was not satisfied as to the manner in which Thaler had acquired rights that would otherwise vest in the inventor. Thaler was not satisfied with the decision and asked for a hearing before an official known as the "hearing officer". By a decision dated 4 December 2019 the hearing officer rejected Thaler's appeal. Thaler appealed against the hearing officer's decision to the Patents Court (a specialist court within the Chancery Division of the High Court of England and Wales that determines patent disputes). On 21 September 2020, Mr Justice Marcus Smith upheld the decision of the hearing officer. On 21 September 2021, Thaler's further appeal to the Court of Appeal was dismissed by Arnold LJ and Laing LJ (Birss LJ dissenting). On 20 December 2023, the UK Supreme Court dismissed a further appeal by Thaler. In its judgment, the court held that an "inventor" under the Patents Act 1977 must be a natural person. === United States === The patent applications on the inventions were refused by the USPTO, which held that only natural persons can be named as inventors in a patent application. Thaler first fought this result by filing a complaint under the Administrative Procedure Act alleging that the decision was "arbitrary, capricious, an abuse of discretion and not in accordance with the law; unsupported by substantial evidence, and in excess of Defendants’ statutory authority." A month later on August 19, 2019, Thaler filed a petition with the USPTO as allowed in 37 C.F.R. § 1.181 stating that DABUS should be the inventor. The judge and Thaler agreed in this case that Thaler himself is unable to receive the patent on behalf of DABUS. In their August 5, 2022, Thaler decision, the US Court of Appeals for the Federal Circuit affirmed that only a natural person could be an inventor, which means that the AI that invents any other type of invention is not addressed by the "who" mentioned in the legislation. === New Zealand === On January 31, 2022, the Intellectual Property Office of New Zealand (IPONZ) decided that a patent application (776029) filed by Stephen Thaler was void, on the basis that no inventor was identified on the patent application. IPONZ determined that DABUS could not be "an actual devisor of the invention" as required by the Patents Act 2013, and that this must be a natural person as held by the previous patent offices above. The High Court of New Zealand confirmed the decision in 2023. === South Africa === On 24 June 2021, the South African Companies and Intellectual Property Commission (CIPC) accepted Dr Thaler's Patent Cooperation Treaty, for a patent in respect of inventions generated by DABUS. In July 2021, the CIPC released a notice of issuance for the patent. It is the first patent granted for an AI invention. === Switzerland === On June 26, 2025, the Swiss Federal Administrative Court ruled that artificial intelligence systems such as DABUS cannot be listed as inventors in patent applications. The court upheld the existing practice of the Swiss Federal Institute of Intellectual Property (IPI), which requires that only natural persons can be recognized as inventors under Swiss patent law. The case concerned a patent application, which sought to designate DABUS as the sole inventor of a food container designed with a fractal geometry to enhance heat distribution. The IPI had rejected the application, arguing that both the absence of a human inventor and the attribution of inventorship to an AI system were inadmissible. While the court dismissed Thaler's main request, it accepted a subsidiary request: if a human applicant recognizes and files a patent based on an AI-generated invention, that person may be considered the inventor. As a result, the application may proceed with Thaler listed as the inventor. The decision (B-2532/2024) can still be appealed to the Swiss Federal Supreme Court.
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Structural risk minimization

Structural risk minimization (SRM) is an inductive principle of use in machine learning. Commonly in machine learning, a generalized model must be selected from a finite data set, with the consequent problem of overfitting – the model becoming too strongly tailored to the particularities of the training set and generalizing poorly to new data. The SRM principle addresses this problem by balancing the model's complexity against its success at fitting the training data. This principle was first set out in a 1974 book by Vladimir Vapnik and Alexey Chervonenkis and uses the VC dimension. In practical terms, Structural Risk Minimization is implemented by minimizing E t r a i n + β H ( W ) {\displaystyle E_{train}+\beta H(W)} , where E t r a i n {\displaystyle E_{train}} is the train error, the function H ( W ) {\displaystyle H(W)} is called a regularization function, and β {\displaystyle \beta } is a constant. H ( W ) {\displaystyle H(W)} is chosen such that it takes large values on parameters W {\displaystyle W} that belong to high-capacity subsets of the parameter space. Minimizing H ( W ) {\displaystyle H(W)} in effect limits the capacity of the accessible subsets of the parameter space, thereby controlling the trade-off between minimizing the training error and minimizing the expected gap between the training error and test error. The SRM problem can be formulated in terms of data. Given n data points consisting of data x and labels y, the objective J ( θ ) {\displaystyle J(\theta )} is often expressed in the following manner: J ( θ ) = 1 2 n ∑ i = 1 n ( h θ ( x i ) − y i ) 2 + λ 2 ∑ j = 1 d θ j 2 {\displaystyle J(\theta )={\frac {1}{2n}}\sum _{i=1}^{n}(h_{\theta }(x^{i})-y^{i})^{2}+{\frac {\lambda }{2}}\sum _{j=1}^{d}\theta _{j}^{2}} The first term is the mean squared error (MSE) term between the value of the learned model, h θ {\displaystyle h_{\theta }} , and the given labels y {\displaystyle y} . This term is the training error, E t r a i n {\displaystyle E_{train}} , that was discussed earlier. The second term, places a prior over the weights, to favor sparsity and penalize larger weights. The trade-off coefficient, λ {\displaystyle \lambda } , is a hyperparameter that places more or less importance on the regularization term. Larger λ {\displaystyle \lambda } encourages sparser weights at the expense of a more optimal MSE, and smaller λ {\displaystyle \lambda } relaxes regularization allowing the model to fit to data. Note that as λ → ∞ {\displaystyle \lambda \to \infty } the weights become zero, and as λ → 0 {\displaystyle \lambda \to 0} , the model typically suffers from overfitting.
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Signal-to-noise ratio (imaging)

Signal-to-noise ratio (SNR) is used in imaging to characterize image quality. The sensitivity of a (digital or film) imaging system is typically described in the terms of the signal level that yields a threshold level of SNR. Industry standards define sensitivity in terms of the ISO film speed equivalent, using SNR thresholds (at average scene luminance) of 40:1 for "excellent" image quality and 10:1 for "acceptable" image quality. SNR is sometimes quantified in decibels (dB) of signal power relative to noise power, though in the imaging field the concept of "power" is sometimes taken to be the power of a voltage signal proportional to optical power; so a 20 dB SNR may mean either 10:1 or 100:1 optical power, depending on which definition is in use. == Definition of SNR == Traditionally, SNR is defined to be the ratio of the average signal value μ s i g {\displaystyle \mu _{\mathrm {sig} }} to the standard deviation of the signal σ s i g {\displaystyle \sigma _{\mathrm {sig} }} : S N R = μ s i g σ s i g {\displaystyle \mathrm {SNR} ={\frac {\mu _{\mathrm {sig} }}{\sigma _{\mathrm {sig} }}}} when the signal is an optical intensity, or as the square of this value if the signal and noise are viewed as amplitudes (field quantities).
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Journal of Machine Learning Research

The Journal of Machine Learning Research is a peer-reviewed open access scientific journal covering machine learning. It was established in 2000 and the first editor-in-chief was Leslie Kaelbling. The current editors-in-chief are Francis Bach (Inria) and David Blei (Columbia University). == History == The journal was established as an open-access alternative to the journal Machine Learning. In 2001, forty editorial board members of Machine Learning resigned, saying that in the era of the Internet, it was detrimental for researchers to continue publishing their papers in expensive journals with pay-access archives. The open access model employed by the Journal of Machine Learning Research allows authors to publish articles for free and retain copyright, while archives are freely available online. Print editions of the journal were published by MIT Press until 2004 and by Microtome Publishing thereafter. From its inception, the journal received no revenue from the print edition and paid no subvention to MIT Press or Microtome Publishing. In response to the prohibitive costs of arranging workshop and conference proceedings publication with traditional academic publishing companies, the journal launched a proceedings publication arm in 2007 and now publishes proceedings for several leading machine learning conferences, including the International Conference on Machine Learning, COLT, AISTATS, and workshops held at the Conference on Neural Information Processing Systems.
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Quantum machine learning

Quantum machine learning (QML) is the study of quantum algorithms for machine learning. It often refers to quantum algorithms for machine learning tasks which analyze classical data, sometimes called quantum-enhanced machine learning. QML algorithms use qubits and quantum operations to try to improve the space and time complexity of classical machine learning algorithms. Hybrid QML methods involve both classical and quantum processing, where computationally difficult subroutines are outsourced to a quantum device. These routines can be more complex in nature and executed faster on a quantum computer. Furthermore, quantum algorithms can be used to analyze quantum states instead of classical data. The term "quantum machine learning" is sometimes used to refer classical machine learning methods applied to data generated from quantum experiments (i.e. machine learning of quantum systems), such as learning the phase transitions of a quantum system or creating new quantum experiments. QML also extends to a branch of research that explores methodological and structural similarities between certain physical systems and learning systems, in particular neural networks. For example, some mathematical and numerical techniques from quantum physics are applicable to classical deep learning and vice versa. Furthermore, researchers investigate more abstract notions of learning theory with respect to quantum information, sometimes referred to as "quantum learning theory". == Machine learning with quantum computers == Quantum-enhanced machine learning refers to quantum algorithms that solve tasks in machine learning, thereby improving and often expediting classical machine learning techniques. Such algorithms typically require one to encode the given classical data set into a quantum computer to make it accessible for quantum information processing. Subsequently, quantum information processing routines are applied and the result of the quantum computation is read out by measuring the quantum system. For example, the outcome of the measurement of a qubit reveals the result of a binary classification task. While many proposals of QML algorithms are still purely theoretical and require a full-scale universal quantum computer to be tested, others have been implemented on small-scale or special purpose quantum devices. === Quantum associative memories and quantum pattern recognition === Early work on quantum associative memories has been done by Dan Ventura and Tony Martinez and by Carlo A. Trugenberger in the late 1990s and early 2000s. Associative (or content-addressable) memories are able to recognize stored content on the basis of a similarity measure, while random access memories are accessed by the address of stored information and not its content. As such they must be able to retrieve both incomplete and corrupted patterns, the essential machine learning task of pattern recognition. Typical classical associative memories store p patterns in the O ( n 2 ) {\displaystyle O(n^{2})} interactions (synapses) of a real, symmetric energy matrix over a network of n artificial neurons. The encoding is such that the desired patterns are local minima of the energy functional and retrieval is done by minimizing the total energy, starting from an initial configuration. Unfortunately, classical associative memories are severely limited by the phenomenon of cross-talk. When too many patterns are stored, spurious memories appear which quickly proliferate, so that the energy landscape becomes disordered and no retrieval is anymore possible. The number of storable patterns is typically limited by a linear function of the number of neurons, p ≤ O ( n ) {\displaystyle p\leq O(n)} . Quantum associative memories (in their simplest realization) store patterns in a unitary matrix U acting on the Hilbert space of n qubits. Retrieval is realized by the unitary evolution of a fixed initial state to a quantum superposition of the desired patterns with probability distribution peaked on the most similar pattern to an input. By its very quantum nature, the retrieval process is thus probabilistic. Because quantum associative memories are free from cross-talk, however, spurious memories are never generated. Correspondingly, they have a superior capacity than classical ones. The number of parameters in the unitary matrix U is O ( p n ) {\displaystyle O(pn)} . One can thus have efficient, spurious-memory-free quantum associative memories for any polynomial number of patterns. If the matrix U is encoded as a unique operator (as opposed as to a sequence of gates as in the circuit model), e.g. by an optical interferometer, the retrieval becomes efficient even for an exponential number of patterns. === Linear algebra simulation with quantum amplitudes === A number of quantum algorithms for machine learning are based on the idea of amplitude encoding, that is, to associate the amplitudes of a quantum state with the inputs and outputs of computations. Since a state of n {\displaystyle n} qubits is described by 2 n {\displaystyle 2^{n}} complex amplitudes, this information encoding can allow for an exponentially compact representation. Intuitively, this corresponds to associating a discrete probability distribution over binary random variables with a classical vector. The goal of algorithms based on amplitude encoding is to formulate quantum algorithms whose resources grow polynomially in the number of qubits n {\displaystyle n} , which amounts to a logarithmic time complexity in the number of amplitudes and thereby the dimension of the input. Many QML algorithms in this category are based on variations of the quantum algorithm for linear systems of equations (colloquially called HHL, after the paper's authors) which, under specific conditions, performs a matrix inversion using an amount of physical resources growing only logarithmically in the dimensions of the matrix. One of these conditions is that a Hamiltonian which entry-wise corresponds to the matrix can be simulated efficiently, which is known to be possible if the matrix is sparse or low rank. For reference, any known classical algorithm for matrix inversion requires a number of operations that grows more than quadratically in the dimension of the matrix (e.g. O ( n 2.373 ) {\displaystyle O{\mathord {\left(n^{2.373}\right)}}} ), but they are not restricted to sparse matrices. Quantum matrix inversion can be applied to machine learning methods in which the training reduces to solving a linear system of equations, for example in least-squares linear regression, the least-squares version of support vector machines, and Gaussian processes. A crucial bottleneck of methods that simulate linear algebra computations with the amplitudes of quantum states is state preparation, which often requires one to initialise a quantum system in a state whose amplitudes reflect the features of the entire dataset. Although efficient methods for state preparation are known for specific cases, this step easily hides the complexity of the task. === Variational quantum algorithms (VQAs) === In a variational quantum algorithm, a classical computer optimizes the parameters used to prepare a quantum state, while a quantum computer is used to do the actual state preparation and measurement. VQAs are considered promising candidates for noisy intermediate-scale quantum computers. Variational quantum circuits (or parameterized quantum circuits) are a popular class of VQAs where the parameters are those used in a fixed quantum circuit. Researchers have studied VQCs to solve optimization problems and find the ground state energy of complex quantum systems, which were difficult to solve using a classical computer. === Quantum binary classifier === Pattern reorganization is one of the important tasks of machine learning, binary classification is one of the tools or algorithms to find patterns. Binary classification is used in supervised learning and in unsupervised learning. In QML, classical bits are converted to qubits and they are mapped to Hilbert space; complex value data are used in a quantum binary classifier to use the advantage of Hilbert space. By exploiting the quantum mechanic properties such as superposition, entanglement, interference the quantum binary classifier produces the accurate result in short period of time. === Quantum machine learning algorithms based on Grover search === Another approach to improving classical machine learning with quantum information processing uses amplitude amplification methods based on Grover's search algorithm, which has been shown to solve unstructured search problems with a quadratic speedup compared to classical algorithms. These quantum routines can be employed for learning algorithms that translate into an unstructured search task, as can be done, for instance, in the case of the k-medians and the k-nearest neighbors algorithms. Other applications include quadratic speedups in the training of perceptrons. An e
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