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openPipeline is an open-source plug-in for Autodesk Maya that is designed to assist in a Production Pipeline structure and Computer animation. == Development == Created in Maya Embedded Language, openPipeline was initiated at Eyebeam Atelier and further developed at Pratt Institute in the Digital Arts Lab. The initial release date was December 28, 2006. == Contributors == Rob O'Neill (Creator) Paris Mavroidis Meng-Han Ho
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AI warfare refers to the use of artificial intelligence technologies to automate military operation and enhance or bypass human decision-making in armed conflicts. AI is used to rapidly analyze large volumes of military intelligence data, including making recommendations or decisions on who and what to target. Abdul-Rahman al-Rawi, a 20-year-old student, was the first acknowledged civilian killed by AI-assisted airstrike in a U.S. strike in Iraq in 2024. In 2026, the U.S. declared it would become an 'AI-first' warfighting force. Husain et al (2018) coined the term hyperwar to refer to warfare which is algorithmic or controlled by artificial intelligence, with little to no human decision-making. == 2026 Iran war == The 2026 Iran war has been described as the "first AI war", although the Untied States and Israel have previously used AI to identify targets during the Gaza war. The U.S. has used AI tools to attack Iran. These tools have been used for military intelligence, targeting, and damage assessment in the war in Iran. Using the Maven smart system, the U.S. attacked 1,000 targets in the first 24 hours of the war and 5,000 targets over the course of 10 days. While the U.S. had used Maven in 2022 to share targeting information with Ukraine and strike against Iraq, Syria, and against the Houthis in 2024, Iran's attacks are its biggest. Authorities are looking into whether artificial intelligence was involved in the airstrike on an Iranian girls' school that killed 170 civilians, the majority of whom were female students. The United States Central Command emphasized that humans were making final targeting decisions. Per a White House tally released on April 8, the U.S. military hit over 13,000 targets in Iran during the war's first 38 days, including more than 2,000 command-and-control sites, 1,500 air defense targets, and 1,450 industrial infrastructure targets. == Gaza war == As part of the Gaza war, the Israel Defense Forces (IDF) have used artificial intelligence to rapidly and automatically perform much of the process of determining what to bomb. IDF's Unit 8200 developed AI systems, dubbed the Gospel and Lavender, to find targets for the Israeli Air Force to bomb. The Gospel automatically provides targeting recommendations to human analysts, who decide whether to approve strikes. Lavender identified 37,000 Hamas-linked individuals early in the war, and was used alongside the Gospel, which chooses buildings or structures as targets. According to a report by +972 Magazine and Local Call, strikes assisted by Lavender were routinely permitted to kill 5–20 civilians for each suspected Hamas militant, who were often bombed at home with their families. The IDF denies these claims, maintaining that every strike is assessed to minimize collateral damage, and that there is no policy "to kill tens of thousands of people in their homes." Israel deployed AI technologies during the Gaza war for audio analysis, facial recognition, and airstrike targeting. One such system was used to help identify the location of Hamas commander Ibrahim Biari through phone call analysis, leading to strikes that killed him as well as more than 125 civilians. == 2022 Russian Ukraine war == Kyiv launched a project with Palantir called Brave1 Dataroom to build AI systems using the extensive combat data Ukraine has gathered since Russia’s full-scale invasion in 2022. The country has also created tools for in-depth airstrike analysis, introduced AI to process large volumes of intelligence, and incorporated these technologies into the planning of long-range strike operations. == Involved companies == Maven Smart System is developed by Palantir. It integrates Anthropic's Claude as its large language model, and uses Amazon's AWS servers as its cloud infrastructure. Since Anthropic's refusal to support autonomous weapons development and domestic surveillance efforts. In its place, other AI firms, including OpenAI, have been brought in to take over that role. == Involved state actors == In 2024, the United States Department of Defense had 800-plus active AI-related projects and requested $1.8 billion in AI funding, with Project Maven and Project Artemis (AI-resistant drones developed together with Ukraine) being the main ones. The technology has been used in Iran, Iraq, Syria and Yemen to identify targets. China is pursuing intelligentized warfare, integrating AI across all combat domains—land, sea, air, space, and cyber—with military AI spending exceeding $1.6 billion annually. == International regulation == Since 2014, states meeting within the framework of the Convention on Certain Conventional Weapons have discussed lethal autonomous weapon systems. In 2016, the treaty's states parties established an open-ended Group of Governmental Experts on Lethal Autonomous Weapons Systems to continue those discussions. The discussions have addressed international humanitarian law, accountability, possible prohibitions and regulations, and the extent of human control required over AI-enabled weapons.
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Feature engineering is a preprocessing step in supervised machine learning and statistical modeling which transforms raw data into a more effective set of inputs. Each input comprises several attributes, known as features. By providing models with relevant information, feature engineering significantly enhances their predictive accuracy and decision-making capability. Beyond machine learning, the principles of feature engineering are applied in various scientific fields, including physics. For example, physicists construct dimensionless numbers such as the Reynolds number in fluid dynamics, the Nusselt number in heat transfer, and the Archimedes number in sedimentation. They also develop first approximations of solutions, such as analytical solutions for the strength of materials in mechanics. == Clustering == One of the applications of feature engineering has been clustering of feature-objects or sample-objects in a dataset. Especially, feature engineering based on matrix decomposition has been extensively used for data clustering under non-negativity constraints on the feature coefficients. These include Non-Negative Matrix Factorization (NMF), Non-Negative Matrix-Tri Factorization (NMTF), Non-Negative Tensor Decomposition/Factorization (NTF/NTD), etc. The non-negativity constraints on coefficients of the feature vectors mined by the above-stated algorithms yields a part-based representation, and different factor matrices exhibit natural clustering properties. Several extensions of the above-stated feature engineering methods have been reported in literature, including orthogonality-constrained factorization for hard clustering, and manifold learning to overcome inherent issues with these algorithms. Other classes of feature engineering algorithms include leveraging a common hidden structure across multiple inter-related datasets to obtain a consensus (common) clustering scheme. An example is Multi-view Classification based on Consensus Matrix Decomposition (MCMD), which mines a common clustering scheme across multiple datasets. MCMD is designed to output two types of class labels (scale-variant and scale-invariant clustering), and: is computationally robust to missing information, can obtain shape- and scale-based outliers, and can handle high-dimensional data effectively. Coupled matrix and tensor decompositions are popular in multi-view feature engineering. == Predictive modelling == Feature engineering in machine learning and statistical modeling involves selecting, creating, transforming, and extracting data features. Key components include feature creation from existing data, transforming and imputing missing or invalid features, reducing data dimensionality through methods like Principal Components Analysis (PCA), Independent Component Analysis (ICA), and Linear Discriminant Analysis (LDA), and selecting the most relevant features for model training based on importance scores and correlation matrices. Features vary in significance. Even relatively insignificant features may contribute to a model. Feature selection can reduce the number of features to prevent a model from becoming too specific to the training data set (overfitting). Feature explosion occurs when the number of identified features is too large for effective model estimation or optimization. Common causes include: Feature templates - implementing feature templates instead of coding new features Feature combinations - combinations that cannot be represented by a linear system Feature explosion can be limited via techniques such as regularization, kernel methods, and feature selection. == Automation == Automation of feature engineering is a research topic that dates back to the 1990s. Machine learning software that incorporates automated feature engineering has been commercially available since 2016. Related academic literature can be roughly separated into two types: Multi-relational Decision Tree Learning (MRDTL) uses a supervised algorithm that is similar to a decision tree. Deep Feature Synthesis uses simpler methods. === Multi-relational Decision Tree Learning (MRDTL) === Multi-relational Decision Tree Learning (MRDTL) extends traditional decision tree methods to relational databases, handling complex data relationships across tables. It innovatively uses selection graphs as decision nodes, refined systematically until a specific termination criterion is reached. Most MRDTL studies base implementations on relational databases, which results in many redundant operations. These redundancies can be reduced by using techniques such as tuple id propagation. === Open-source implementations === There are a number of open-source libraries and tools that automate feature engineering on relational data and time series: featuretools is a Python library for transforming time series and relational data into feature matrices for machine learning. MCMD: An open-source feature engineering algorithm for joint clustering of multiple datasets. OneBM or One-Button Machine combines feature transformations and feature selection on relational data with feature selection techniques. OneBM helps data scientists reduce data exploration time allowing them to try and error many ideas in short time. On the other hand, it enables non-experts, who are not familiar with data science, to quickly extract value from their data with a little effort, time, and cost. getML community is an open source tool for automated feature engineering on time series and relational data. It is implemented in C/C++ with a Python interface. It has been shown to be at least 60 times faster than tsflex, tsfresh, tsfel, featuretools or kats. tsfresh is a Python library for feature extraction on time series data. It evaluates the quality of the features using hypothesis testing. tsflex is an open source Python library for extracting features from time series data. Despite being 100% written in Python, it has been shown to be faster and more memory efficient than tsfresh, seglearn or tsfel. seglearn is an extension for multivariate, sequential time series data to the scikit-learn Python library. tsfel is a Python package for feature extraction on time series data. kats is a Python toolkit for analyzing time series data. === Deep feature synthesis === The deep feature synthesis (DFS) algorithm beat 615 of 906 human teams in a competition. == Feature stores == The feature store is where the features are stored and organized for the explicit purpose of being used to either train models (by data scientists) or make predictions (by applications that have a trained model). It is a central location where you can either create or update groups of features created from multiple different data sources, or create and update new datasets from those feature groups for training models or for use in applications that do not want to compute the features but just retrieve them when it needs them to make predictions. A feature store includes the ability to store code used to generate features, apply the code to raw data, and serve those features to models upon request. Useful capabilities include feature versioning and policies governing the circumstances under which features can be used. Feature stores can be standalone software tools or built into machine learning platforms. == Alternatives == Feature engineering can be a time-consuming and error-prone process, as it requires domain expertise and often involves trial and error. Deep learning algorithms may be used to process a large raw dataset without having to resort to feature engineering. However, deep learning algorithms still require careful preprocessing and cleaning of the input data. In addition, choosing the right architecture, hyperparameters, and optimization algorithm for a deep neural network can be a challenging and iterative process.
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Evaluation of a binary classifier typically assigns a numerical value, or values, to a classifier that represent its accuracy. An example is error rate, which measures how frequently the classifier makes a mistake. There are many metrics that can be used; different fields have different preferences. For example, in medicine sensitivity and specificity are often used, while in computer science precision and recall are preferred. An important distinction is between metrics that are independent of the prevalence or skew (how often each class occurs in the population), and metrics that depend on the prevalence – both types are useful, but they have very different properties. Often, evaluation is used to compare two methods of classification, so that one can be adopted and the other discarded. Such comparisons are more directly achieved by a form of evaluation that results in a single unitary metric rather than a pair of metrics. == Contingency table == Given a data set, a classification (the output of a classifier on that set) gives two numbers: the number of positives and the number of negatives, which add up to the total size of the set. To evaluate a classifier, one compares its output to another reference classification – ideally a perfect classification, but in practice the output of another gold standard test – and cross tabulates the data into a 2×2 contingency table, comparing the two classifications. One then evaluates the classifier relative to the gold standard by computing summary statistics of these 4 numbers. Generally these statistics will be scale invariant (scaling all the numbers by the same factor does not change the output), to make them independent of population size, which is achieved by using ratios of homogeneous functions, most simply homogeneous linear or homogeneous quadratic functions. Say we test some people for the presence of a disease. Some of these people have the disease, and our test correctly says they are positive. They are called true positives (TP). Some have the disease, but the test incorrectly claims they don't. They are called false negatives (FN). Some don't have the disease, and the test says they don't – true negatives (TN). Finally, there might be healthy people who have a positive test result – false positives (FP). These can be arranged into a 2×2 contingency table (confusion matrix), conventionally with the test result on the vertical axis and the actual condition on the horizontal axis. These numbers can then be totaled, yielding both a grand total and marginal totals. Totaling the entire table, the number of true positives, false negatives, true negatives, and false positives add up to 100% of the set. Totaling the columns (adding vertically) the number of true positives and false positives add up to 100% of the test positives, and likewise for negatives. Totaling the rows (adding horizontally), the number of true positives and false negatives add up to 100% of the condition positives (conversely for negatives). The basic marginal ratio statistics are obtained by dividing the 2×2=4 values in the table by the marginal totals (either rows or columns), yielding 2 auxiliary 2×2 tables, for a total of 8 ratios. These ratios come in 4 complementary pairs, each pair summing to 1, and so each of these derived 2×2 tables can be summarized as a pair of 2 numbers, together with their complements. Further statistics can be obtained by taking ratios of these ratios, ratios of ratios, or more complicated functions. The contingency table and the most common derived ratios are summarized below; see sequel for details. Note that the rows correspond to the condition actually being positive or negative (or classified as such by the gold standard), as indicated by the color-coding, and the associated statistics are prevalence-independent, while the columns correspond to the test being positive or negative, and the associated statistics are prevalence-dependent. There are analogous likelihood ratios for prediction values, but these are less commonly used, and not depicted above. == Pairs of metrics == Often accuracy is evaluated with a pair of metrics composed in a standard pattern. === Sensitivity and specificity === The fundamental prevalence-independent statistics are sensitivity and specificity. Sensitivity or True Positive Rate (TPR), also known as recall, is the proportion of people that tested positive and are positive (True Positive, TP) of all the people that actually are positive (Condition Positive, CP = TP + FN). It can be seen as the probability that the test is positive given that the patient is sick. With higher sensitivity, fewer actual cases of disease go undetected (or, in the case of the factory quality control, fewer faulty products go to the market). Specificity (SPC) or True Negative Rate (TNR) is the proportion of people that tested negative and are negative (True Negative, TN) of all the people that actually are negative (Condition Negative, CN = TN + FP). As with sensitivity, it can be looked at as the probability that the test result is negative given that the patient is not sick. With higher specificity, fewer healthy people are labeled as sick (or, in the factory case, fewer good products are discarded). The relationship between sensitivity and specificity, as well as the performance of the classifier, can be visualized and studied using the Receiver Operating Characteristic (ROC) curve. In theory, sensitivity and specificity are independent in the sense that it is possible to achieve 100% in both (such as in the red/blue ball example given above). In more practical, less contrived instances, however, there is usually a trade-off, such that they are inversely proportional to one another to some extent. This is because we rarely measure the actual thing we would like to classify; rather, we generally measure an indicator of the thing we would like to classify, referred to as a surrogate marker. The reason why 100% is achievable in the ball example is because redness and blueness is determined by directly detecting redness and blueness. However, indicators are sometimes compromised, such as when non-indicators mimic indicators or when indicators are time-dependent, only becoming evident after a certain lag time. The following example of a pregnancy test will make use of such an indicator. Modern pregnancy tests do not use the pregnancy itself to determine pregnancy status; rather, human chorionic gonadotropin is used, or hCG, present in the urine of gravid females, as a surrogate marker to indicate that a woman is pregnant. Because hCG can also be produced by a tumor, the specificity of modern pregnancy tests cannot be 100% (because false positives are possible). Also, because hCG is present in the urine in such small concentrations after fertilization and early embryogenesis, the sensitivity of modern pregnancy tests cannot be 100% (because false negatives are possible). === Positive and negative predictive values === In addition to sensitivity and specificity, the performance of a binary classification test can be measured with positive predictive value (PPV), also known as precision, and negative predictive value (NPV). The positive prediction value answers the question "If the test result is positive, how well does that predict an actual presence of disease?". It is calculated as TP/(TP + FP); that is, it is the proportion of true positives out of all positive results. The negative prediction value is the same, but for negatives, naturally. ==== Impact of prevalence on predictive values ==== Prevalence has a significant impact on prediction values. As an example, suppose there is a test for a disease with 99% sensitivity and 99% specificity. If 2000 people are tested and the prevalence (in the sample) is 50%, 1000 of them are sick and 1000 of them are healthy. Thus about 990 true positives and 990 true negatives are likely, with 10 false positives and 10 false negatives. The positive and negative prediction values would be 99%, so there can be high confidence in the result. However, if the prevalence is only 5%, so of the 2000 people only 100 are really sick, then the prediction values change significantly. The likely result is 99 true positives, 1 false negative, 1881 true negatives and 19 false positives. Of the 19+99 people tested positive, only 99 really have the disease – that means, intuitively, that given that a patient's test result is positive, there is only 84% chance that they really have the disease. On the other hand, given that the patient's test result is negative, there is only 1 chance in 1882, or 0.05% probability, that the patient has the disease despite the test result. === Precision and recall === Precision and recall can be interpreted as (estimated) conditional probabilities: Precision is given by P ( C = P | C ^ = P ) {\displaystyle P(C=P|{\hat {C}}=P)} while recall is given by P ( C ^ = P | C = P ) {\displaystyle P({\hat {C}}=P|C=P)} , where C ^ {\
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The PCVC (Persian Consonant Vowel Combination) Speech Dataset is a Modern Persian speech corpus for speech recognition and also speaker recognition. The dataset contains sound samples of Modern Persian combination of vowel and consonant phonemes from different speakers. Every sound sample contains just one consonant and one vowel So it is somehow labeled in phoneme level. This dataset consists of 23 Persian consonants and 6 vowels. The sound samples are all possible combinations of vowels and consonants (138 samples for each speaker). The sample rate of all speech samples is 48000 which means there are 48000 sound samples in every 1 second. Every sound sample starts with consonant then continues with vowel. In each sample, in average, 0.5 second of each sample is speech and the rest is silence. Each sound sample ends with silence. All of sound samples are denoised with "Adaptive noise reduction" algorithm. Compared to Farsdat speech dataset and Persian speech corpus it is more easy to use because it is prepared in .mat data files. Also it is more based on phoneme based separation and all samples are denoised. == Contents == The corpus is downloadable from its Kaggle web page, and contains the following: .mat data files of sound samples in a 23630000 matrix, in which 23 is number of consonants, 6 is the number of vowels and 30000 is the length of sound sample.
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Purged cross-validation is a variant of k-fold cross-validation designed to prevent look-ahead bias in time series and other structured data, developed in 2017 by Marcos López de Prado at Guggenheim Partners and Cornell University. It is primarily used in financial machine learning to ensure the independence of training and testing samples when labels depend on future events. It provides an alternative to conventional cross-validation and walk-forward backtesting methods, which often yield overly optimistic performance estimates due to information leakage and overfitting. == Motivation == Standard cross-validation assumes that observations are independently and identically distributed (IID), which often does not hold in time series or financial datasets. If the label of a test sample overlaps in time with the features or labels in the training set, the result may be data leakage and overfitting. Purged cross-validation addresses this issue by removing overlapping observations and, optionally, adding a temporal buffer ("embargo") around the test set to further reduce the risk of leakage. The figure below illustrates standard 5 Fold Cross-Validation == Purging == Purging removes from the training set any observation whose timestamp falls within the time range of formation of a label in the test set. This can be the case for train set observations before and after the test set. Their removal ensures that the algorithm cannot learn during train time information that will be used to assess the performance of the algorithm. See the figure below for an illustration of purging. == Embargoing == Embargoing addresses a more subtle form of leakage: even if an observation does not directly overlap the test set, it may still be affected by test events due to market reaction lag or downstream dependencies. To guard against this, a percentage-based embargo is imposed after each test fold. For example, with a 5% embargo and 1000 observations, the 50 observations following each test fold are excluded from training. Unlike purging, embargoing can only occur after the test set. The figure below illustrates the application of embargo: == Applications == Purged and embargoed cross-validation has been useful in: Backtesting of trading strategies Validation of classifiers on labeled event-driven returns Any machine learning task with overlapping label horizons == Example == To illustrate the effect of purging and embargoing, consider the figures below. Both diagrams show the structure of 5-fold cross-validation over a 20-day period. In each row, blue squares indicate training samples and red squares denote test samples. Each label is defined based on the value of the next two observations, hence creating an overlap. If this overlap is left untreated, test set information leaks into the train set. The second figure applies the Purged CV procedure. Notice how purging removes overlapping observations from the training set and the embargo widens the gap between test and training data. This approach ensures that the evaluation more closely resembles a true out-of-sample test and reduces the risk of backtest overfitting. == Combinatorial Purged Cross-Validation == Walk-forward backtesting analysis, another common cross-validation technique in finance, preserves temporal order but evaluates the model on a single sequence of test sets. This leads to high variance in performance estimation, as results are contingent on a specific historical path. Combinatorial Purged Cross-Validation (CPCV) addresses this limitation by systematically constructing multiple train-test splits, purging overlapping samples, and enforcing an embargo period to prevent information leakage. The result is a distribution of out-of-sample performance estimates, enabling robust statistical inference and more realistic assessment of a model's predictive power. === Methodology === CPCV divides a time-series dataset into N sequential, non-overlapping groups. These groups preserve the temporal order of observations. Then, all combinations of k groups (where k < N) are selected as test sets, with the remaining N − k groups used for training. For each combination, the model is trained and evaluated under strict controls to prevent leakage. To eliminate potential contamination between training and test sets, CPCV introduces two additional mechanisms: Purging: Any training observations whose label horizon overlaps with the test period are excluded. This ensures that future information does not influence model training. Embargoing: After the end of each test period, a fixed number of observations (typically a small percentage) are removed from the training set. This prevents leakage due to delayed market reactions or auto-correlated features. Each data point appears in multiple test sets across different combinations. Because test groups are drawn combinatorially, this process produces multiple backtest "paths," each of which simulates a plausible market scenario. From these paths, practitioners can compute a distribution of performance statistics such as the Sharpe ratio, drawdown, or classification accuracy. === Formal definition === Let N be the number of sequential groups into which the dataset is divided, and let k be the number of groups selected as the test set for each split. Then: The number of unique train-test combinations is given by the binomial coefficient: ( N k ) {\displaystyle {\binom {N}{k}}} Each observation is used in k {\displaystyle k} test sets and contributes to φ [ N , k ] {\displaystyle \varphi [N,k]} unique backtest paths: φ [ N , k ] = k N ( N k ) {\displaystyle \varphi [N,k]={\frac {k}{N}}{\binom {N}{k}}} This yields a distribution of performance metrics rather than a single point estimate, making it possible to apply Monte Carlo-based or probabilistic techniques to assess model robustness. === Illustrative example === Consider the case where N = 6 and k = 2. The number of possible test set combinations is ( 6 2 ) = 15 {\displaystyle {\binom {6}{2}}=15} . Each of the six groups appears in five test splits. Consequently, five distinct backtest paths can be constructed, each incorporating one appearance from every group. ==== Test group assignment matrix ==== This table shows the 15 test combinations. An "x" indicates that the corresponding group is included in the test set for that split. ==== Backtest path assignment ==== Each group contributes to five different backtest paths. The number in each cell indicates the path to which the group's result is assigned for that split. === Advantages === Combinatorial Purged Cross-Validation offers several key benefits over conventional methods: It produces a distribution of performance metrics, enabling more rigorous statistical inference. The method systematically eliminates lookahead bias through purging and embargoing. By simulating multiple historical scenarios, it reduces the dependence on any single market regime or realization. It supports high-confidence comparisons between competing models or strategies. CPCV is commonly used in quantitative strategy research, especially for evaluating predictive models such as classifiers, regressors, and portfolio optimizers. It has been applied to estimate realistic Sharpe ratios, assess the risk of overfitting, and support the use of statistical tools such as the Deflated Sharpe Ratio (DSR). === Limitations === The main limitation of CPCV stems from its high computational cost. However, this cost can be managed by sampling a finite number of splits from the space of all possible combinations.
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Multimodal representation learning is a subfield of representation learning focused on integrating and interpreting information from different modalities, such as text, images, audio, or video, by projecting them into a shared latent space. This allows for semantically similar content across modalities to be mapped to nearby points within that space, facilitating a unified understanding of diverse data types. By automatically learning meaningful features from each modality and capturing their inter-modal relationships, multimodal representation learning enables a unified representation that enhances performance in cross-media analysis tasks such as video classification, event detection, and sentiment analysis. It also supports cross-modal retrieval and translation, including image captioning, video description, and text-to-image synthesis. == Motivation == The primary motivations for multimodal representation learning arise from the inherent nature of real-world data and the limitations of unimodal approaches. Since multimodal data offers complementary and supplementary information about an object or event from different perspectives, it is more informative than relying on a single modality. A key motivation is to narrow the heterogeneity gap that exists between different modalities by projecting their features into a shared semantic subspace. This allows semantically similar content across modalities to be represented by similar vectors, facilitating the understanding of relationships and correlations between them. Multimodal representation learning aims to leverage the unique information provided by each modality to achieve a more comprehensive and accurate understanding of concepts. These unified representations are crucial for improving performance in various cross-media analysis tasks such as video classification, event detection, and sentiment analysis. They also enable cross-modal retrieval, allowing users to search and retrieve content across different modalities. Additionally, it facilitates cross-modal translation, where information can be converted from one modality to another, as seen in applications like image captioning and text-to-image synthesis. The abundance of ubiquitous multimodal data in real-world applications, including understudied areas like healthcare, finance, and human-computer interaction (HCI), further motivates the development of effective multimodal representation learning techniques. == Approaches and methods == === Canonical-correlation analysis based methods === Canonical-correlation analysis (CCA) was first introduced in 1936 by Harold Hotelling and is a fundamental approach for multimodal learning. CCA aims to find linear relationships between two sets of variables. Given two data matrices X ∈ R n × p {\displaystyle X\in \mathbb {R} ^{n\times p}} and Y ∈ R n × q {\displaystyle Y\in \mathbb {R} ^{n\times q}} representing different modalities, CCA finds projection vectors w x ∈ R p {\displaystyle w_{x}\in \mathbb {R} ^{p}} and w y ∈ R q {\displaystyle w_{y}\in \mathbb {R} ^{q}} that maximizes the correlation between the projected variables: ρ = max w x , w y w x ⊤ Σ x y w y w x ⊤ Σ x x w x w y ⊤ Σ y y w y {\displaystyle \rho =\max _{w_{x},w_{y}}{\frac {w_{x}^{\top }\Sigma _{xy}w_{y}}{{\sqrt {w_{x}^{\top }\Sigma _{xx}w_{x}}}{\sqrt {w_{y}^{\top }\Sigma _{yy}w_{y}}}}}} such that Σ x x {\displaystyle \Sigma _{xx}} and Σ y y {\displaystyle \Sigma _{yy}} are the within-modality covariance matrices, and Σ x y {\displaystyle \Sigma _{xy}} is the between-modality covariance matrix. However, standard CCA is limited by its linearity, which led to the development of nonlinear extensions, such as kernel CCA and deep CCA. ==== Kernel CCA ==== Kernel canonical correlation analysis (KCCA) extends traditional CCA to capture nonlinear relationships between modalities by implicitly mapping the data into high dimensional feature spaces using kernel functions. Given kernel functions K x {\displaystyle K_{x}} and K y {\displaystyle K_{y}} with corresponding Gram matrices K x ∈ R n × n {\displaystyle K_{x}\in \mathbb {R} ^{n\times n}} and K y ∈ R n × n {\displaystyle K_{y}\in \mathbb {R} ^{n\times n}} , KCCA seeks coefficients α {\displaystyle \alpha } and β {\displaystyle \beta } that maximize: ρ = max α , β α ⊤ K x K y β α ⊤ K x 2 α β ⊤ K y 2 β {\displaystyle \rho =\max _{\alpha ,\beta }{\frac {\alpha ^{\top }K_{x}Ky\beta }{{\sqrt {\alpha ^{\top }K_{x}^{2}\alpha }}{\sqrt {\beta ^{\top }K_{y}^{2}\beta }}}}} To prevent overfitting, regularization terms are typically added, resulting in: ρ = max α , β α T K x K y β α T ( K x 2 + λ x K x ) α β T ( K y 2 + λ y K y ) β {\displaystyle \rho =\max _{\alpha ,\beta }{\frac {\alpha ^{T}K_{x}K_{y}\beta }{{\sqrt {\alpha ^{T}\left(K_{x}^{2}+\lambda _{x}K_{x}\right)\alpha }}{\sqrt {\;\beta ^{T}\left(K_{y}^{2}+\lambda _{y}K_{y}\right)\beta }}}}} where λ x {\displaystyle \lambda _{x}} and λ y {\displaystyle \lambda _{y}} are regularization parameters. KCCA has proven effective for tasks such as cross-modal retrieval and semantic analysis, though it faces computational challenges with large datasets due to its O ( n 2 ) {\displaystyle O(n^{2})} memory requirement for sorting kernel matrices. KCCA was proposed independently by several researchers. ==== Deep CCA ==== Deep canonical correlation analysis (DCCA), introduced in 2013, employs neural networks to learn nonlinear transformations for maximizing the correlation between modalities. DCCA uses separate neural networks f x {\displaystyle f_{x}} and f y {\displaystyle f_{y}} for each modality to transform the original data before applying CCA: max W x , W y , θ x , θ y corr ( f x ( X ; θ x ) , f y ( Y ; θ y ) ) {\displaystyle \max _{W_{x},W_{y},\theta _{x},\theta _{y}}\operatorname {corr} \left(f_{x}(X;\theta _{x}),f_{y}(Y;\theta _{y})\right)} where θ x {\displaystyle \theta _{x}} and θ y {\displaystyle \theta _{y}} represent the parameters of the neural networks, and W x {\displaystyle W_{x}} and W y {\displaystyle W_{y}} are the CCA projection matrices. The correlation objective is computed as: corr ( H x , H y ) = tr ( T − 1 / 2 H x T H y S − 1 / 2 ) {\displaystyle \operatorname {corr} (H_{x},H_{y})=\operatorname {tr} \left(T^{-1/2}H_{x}^{T}H_{y}S^{-1/2}\right)} where H x = f x ( X ) {\displaystyle H_{x}=f_{x}(X)} and H y = f y ( Y ) {\displaystyle H_{y}=f_{y}(Y)} are the network outputs, T = H x T H x + r x I {\displaystyle T=H_{x}^{T}H_{x}+r_{x}I} , S = H y T H y + r y I {\displaystyle S=H_{y}^{T}H_{y}+r_{y}I} and r x , r y {\displaystyle r_{x},r_{y}} are the regularization parameters. DCCA overcomes the limitations of linear CCA and kernel CCA by learning complex nonlinear relationships while maintaining computational efficiency for large datasets through mini-batch optimization. === Graph-based methods === Graph-based approaches for multimodal representation learning leverage graph structure to model relationships between entities across different modalities. These methods typically represent each modality as a graph and then learn embedding that preserve cross-modal similarities, enabling more effective joint representation of heterogeneous data. One such method is cross-modal graph neural networks (CMGNNs) that extend traditional graph neural networks (GNNs) to handle data from multiple modalities by constructing graphs that capture both intra-modal and inter-modal relationships. These networks model interactions across modalities by representing them as nodes and their relationships as edges. Other graph-based methods include Probabilistic Graphical Models (PGMs) such as deep belief networks (DBN) and deep Boltzmann machines (DBM). These models can learn a joint representation across modalities, for instance, a multimodal DBN achieves this by adding a shared restricted Boltzmann Machine (RBM) hidden layer on top of modality-specific DBNs. Additionally, the structure of data in some domains like Human-Computer Interaction (HCI), such as the view hierarchy of app screens, can potentially be modeled using graph-like structures. The field of graph representation learning is also relevant, with ongoing progress in developing evaluation benchmarks. === Diffusion maps === Another set of methods relevant to multimodal representation learning are based on diffusion maps and their extensions to handle multiple modalities. ==== Multi-view diffusion maps ==== Multi-view diffusion maps address the challenge of achieving multi-view dimensionality reduction by effectively utilizing the availability of multiple views to extract a coherent low-dimensional representation of the data. The core idea is to exploit both the intrinsic relations within each view and the mutual relations between the different views, defining a cross-view model where a random walk process implicitly hops between objects in different views. A multi-view kernel matrix is constructed by combining these relations, defining a cross-view diffusion process and associ
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Cross-validation, sometimes called rotation estimation or out-of-sample testing, is any of various similar model validation techniques for assessing how the results of a statistical analysis will generalize to an independent data set. Cross-validation includes resampling and sample splitting methods that use different portions of the data to test and train a model on different iterations. It is often used in settings where the goal is prediction, and one wants to estimate how accurately a predictive model will perform in practice. It can also be used to assess the quality of a fitted model and the stability of its parameters. In a prediction problem, a model is usually given a dataset of known data on which training is run (training dataset), and a dataset of unknown data (or first seen data) against which the model is tested (called the validation dataset or testing set). The goal of cross-validation is to test the model's ability to predict new data that was not used in estimating it, in order to flag problems like overfitting or selection bias and to give an insight on how the model will generalize to an independent dataset (i.e., an unknown dataset, for instance from a real problem). One round of cross-validation involves partitioning a sample of data into complementary subsets, performing the analysis on one subset (called the training set), and validating the analysis on the other subset (called the validation set or testing set). To reduce variability, in most methods multiple rounds of cross-validation are performed using different partitions, and the validation results are combined (e.g. averaged) over the rounds to give an estimate of the model's predictive performance. In summary, cross-validation combines (averages) measures of fitness in prediction to derive a more accurate estimate of model prediction performance. == Motivation == Assume a model with one or more unknown parameters, and a data set to which the model can be fit (the training data set). The fitting process optimizes the model parameters to make the model fit the training data as well as possible. If an independent sample of validation data is taken from the same population as the training data, it will generally turn out that the model does not fit the validation data as well as it fits the training data. The size of this difference is likely to be large especially when the size of the training data set is small, or when the number of parameters in the model is large. Cross-validation is a way to estimate the size of this effect. === Example: linear regression === In linear regression, there exist real response values y 1 , … , y n {\textstyle y_{1},\ldots ,y_{n}} , and n p-dimensional vector covariates x1, ..., xn. The components of the vector xi are denoted xi1, ..., xip. If least squares is used to fit a function in the form of a hyperplane ŷ = a + βTx to the data (xi, yi) 1 ≤ i ≤ n, then the fit can be assessed using the mean squared error (MSE). The MSE for given estimated parameter values a and β on the training set (xi, yi) 1 ≤ i ≤ n is defined as: MSE = 1 n ∑ i = 1 n ( y i − y ^ i ) 2 = 1 n ∑ i = 1 n ( y i − a − β T x i ) 2 = 1 n ∑ i = 1 n ( y i − a − β 1 x i 1 − ⋯ − β p x i p ) 2 {\displaystyle {\begin{aligned}{\text{MSE}}&={\frac {1}{n}}\sum _{i=1}^{n}(y_{i}-{\hat {y}}_{i})^{2}={\frac {1}{n}}\sum _{i=1}^{n}(y_{i}-a-{\boldsymbol {\beta }}^{T}\mathbf {x} _{i})^{2}\\&={\frac {1}{n}}\sum _{i=1}^{n}(y_{i}-a-\beta _{1}x_{i1}-\dots -\beta _{p}x_{ip})^{2}\end{aligned}}} If the model is correctly specified, it can be shown under mild assumptions that the expected value of the MSE for the training set is (n − p − 1)/(n + p + 1) < 1 times the expected value of the MSE for the validation set (the expected value is taken over the distribution of training sets). Thus, a fitted model and computed MSE on the training set will result in an optimistically biased assessment of how well the model will fit an independent data set. This biased estimate is called the in-sample estimate of the fit, whereas the cross-validation estimate is an out-of-sample estimate. Since in linear regression it is possible to directly compute the factor (n − p − 1)/(n + p + 1) by which the training MSE underestimates the validation MSE under the assumption that the model specification is valid, cross-validation can be used for checking whether the model has been overfitted, in which case the MSE in the validation set will substantially exceed its anticipated value. (Cross-validation in the context of linear regression is also useful in that it can be used to select an optimally regularized cost function.) === General case === In most other regression procedures (e.g. logistic regression), there is no simple formula to compute the expected out-of-sample fit. Cross-validation is, thus, a generally applicable way to predict the performance of a model on unavailable data using numerical computation in place of theoretical analysis. == Types == Two types of cross-validation can be distinguished: exhaustive and non-exhaustive cross-validation. === Exhaustive cross-validation === Exhaustive cross-validation methods are cross-validation methods which learn and test on all possible ways to divide the original sample into a training and a validation set. ==== Leave-p-out cross-validation ==== Leave-p-out cross-validation (LpO CV) involves using p observations as the validation set and the remaining observations as the training set. This is repeated on all ways to cut the original sample on a validation set of p observations and a training set. LpO cross-validation require training and validating the model C p n {\displaystyle C_{p}^{n}} times, where n is the number of observations in the original sample, and where C p n {\displaystyle C_{p}^{n}} is the binomial coefficient. For p > 1 and for even moderately large n, LpO CV can become computationally infeasible. For example, with n = 100 and p = 30, C 30 100 ≈ 3 × 10 25 . {\displaystyle C_{30}^{100}\approx 3\times 10^{25}.} A variant of LpO cross-validation with p=2 known as leave-pair-out cross-validation has been recommended as a nearly unbiased method for estimating the area under ROC curve of binary classifiers. ==== Leave-one-out cross-validation ==== Leave-one-out cross-validation (LOOCV) is a particular case of leave-p-out cross-validation with p = 1. The process looks similar to jackknife; however, with cross-validation one computes a statistic on the left-out sample(s), while with jackknifing one computes a statistic from the kept samples only. LOO cross-validation requires less computation time than LpO cross-validation because there are only C 1 n = n {\displaystyle C_{1}^{n}=n} passes rather than C p n {\displaystyle C_{p}^{n}} . However, n {\displaystyle n} passes may still require quite a large computation time, in which case other approaches such as k-fold cross validation may be more appropriate. Pseudo-code algorithm: Input: x, {vector of length N with x-values of incoming points} y, {vector of length N with y-values of the expected result} interpolate( x_in, y_in, x_out ), { returns the estimation for point x_out after the model is trained with x_in-y_in pairs} Output: err, {estimate for the prediction error} Steps: err ← 0 for i ← 1, ..., N do // define the cross-validation subsets x_in ← (x[1], ..., x[i − 1], x[i + 1], ..., x[N]) y_in ← (y[1], ..., y[i − 1], y[i + 1], ..., y[N]) x_out ← x[i] y_out ← interpolate(x_in, y_in, x_out) err ← err + (y[i] − y_out)^2 end for err ← err/N === Non-exhaustive cross-validation === Non-exhaustive cross validation methods do not compute all ways of splitting the original sample. These methods are approximations of leave-p-out cross-validation. ==== k-fold cross-validation ==== In k-fold cross-validation, the original sample is randomly partitioned into k equal sized subsamples, often referred to as "folds". Of the k subsamples, a single subsample is retained as the validation data for testing the model, and the remaining k − 1 subsamples are used as training data. The cross-validation process is then repeated k times, with each of the k subsamples used exactly once as the validation data. The k results can then be averaged to produce a single estimation. The advantage of this method over repeated random sub-sampling (see below) is that all observations are used for both training and validation, and each observation is used for validation exactly once. 10-fold cross-validation is commonly used, but in general k remains an unfixed parameter. For example, setting k = 2 results in 2-fold cross-validation. In 2-fold cross-validation, the dataset is randomly shuffled into two sets d0 and d1, so that both sets are equal size (this is usually implemented by shuffling the data array and then splitting it in two). We then train on d0 and validate on d1, followed by training on d1 and validating on d0. When k = n (the number of observations), k-fold cross-validation is equivalent to leave-one-out cr
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The exploration–exploitation dilemma, also known as the explore–exploit tradeoff, is a fundamental concept in decision-making that arises in many domains. It is depicted as the balancing act between two opposing strategies. Exploitation involves choosing the best option based on current knowledge of the system (which may be incomplete or misleading), while exploration involves trying out new options that may lead to better outcomes in the future at the expense of an exploitation opportunity. Finding the optimal balance between these two strategies is a crucial challenge in many decision-making problems whose goal is to maximize long-term benefits. == Application in machine learning == In the context of machine learning, the exploration–exploitation tradeoff is fundamental in reinforcement learning (RL), a type of machine learning that involves training agents to make decisions based on feedback from the environment. Crucially, this feedback may be incomplete or delayed. The agent must decide whether to exploit the current best-known policy or explore new policies to improve its performance. === Multi-armed bandit methods === The multi-armed bandit (MAB) problem was a classic example of the tradeoff, and many methods were developed for it, such as epsilon-greedy, Thompson sampling, and the upper confidence bound (UCB). See the page on MAB for details. In more complex RL situations than the MAB problem, the agent can treat each choice as a MAB, where the payoff is the expected future reward. For example, if the agent performs an epsilon-greedy method, then the agent will often "pull the best lever" by picking the action that had the best predicted expected reward (exploit). However, it would pick a random action with probability epsilon (explore). Monte Carlo tree search, for example, uses a variant of the UCB method. === Exploration problems === There are some problems that make exploration difficult. Sparse reward. If rewards occur only once a long while, then the agent might not persist in exploring. Furthermore, if the space of actions is large, then the sparse reward would mean the agent would not be guided by the reward to find a good direction for deeper exploration. A standard example is Montezuma's Revenge. Deceptive reward. If some early actions give immediate small reward, but other actions give later large reward, then the agent might be lured away from exploring the other actions. Noisy TV problem. If certain observations are irreducibly noisy (such as a television showing random images), then the agent might be trapped exploring those observations (watching the television). === Exploration reward === This section based on. The exploration reward (also called exploration bonus) methods convert the exploration-exploitation dilemma into a balance of exploitations. That is, instead of trying to get the agent to balance exploration and exploitation, exploration is simply treated as another form of exploitation, and the agent simply attempts to maximize the sum of rewards from exploration and exploitation. The exploration reward can be treated as a form of intrinsic reward. We write these as r t i , r t e {\displaystyle r_{t}^{i},r_{t}^{e}} , meaning the intrinsic and extrinsic rewards at time step t {\displaystyle t} . However, exploration reward is different from exploitation in two regards: The reward of exploitation is not freely chosen, but given by the environment, but the reward of exploration may be picked freely. Indeed, there are many different ways to design r t i {\displaystyle r_{t}^{i}} described below. The reward of exploitation is usually stationary (i.e. the same action in the same state gives the same reward), but the reward of exploration is non-stationary (i.e. the same action in the same state should give less and less reward). Count-based exploration uses N n ( s ) {\displaystyle N_{n}(s)} , the number of visits to a state s {\displaystyle s} during the time-steps 1 : n {\displaystyle 1:n} , to calculate the exploration reward. This is only possible in small and discrete state space. Density-based exploration extends count-based exploration by using a density model ρ n ( s ) {\displaystyle \rho _{n}(s)} . The idea is that, if a state has been visited, then nearby states are also partly-visited. In maximum entropy exploration, the entropy of the agent's policy π {\displaystyle \pi } is included as a term in the intrinsic reward. That is, r t i = − ∑ a π ( a | s t ) ln π ( a | s t ) + ⋯ {\displaystyle r_{t}^{i}=-\sum _{a}\pi (a|s_{t})\ln \pi (a|s_{t})+\cdots } . === Prediction-based === This section based on. The forward dynamics model is a function for predicting the next state based on the current state and the current action: f : ( s t , a t ) ↦ s t + 1 {\displaystyle f:(s_{t},a_{t})\mapsto s_{t+1}} . The forward dynamics model is trained as the agent plays. The model becomes better at predicting state transition for state-action pairs that had been done many times. A forward dynamics model can define an exploration reward by r t i = ‖ f ( s t , a t ) − s t + 1 ‖ 2 2 {\displaystyle r_{t}^{i}=\|f(s_{t},a_{t})-s_{t+1}\|_{2}^{2}} . That is, the reward is the squared-error of the prediction compared to reality. This rewards the agent to perform state-action pairs that had not been done many times. This is however susceptible to the noisy TV problem. Dynamics model can be run in latent space. That is, r t i = ‖ f ( s t , a t ) − ϕ ( s t + 1 ) ‖ 2 2 {\displaystyle r_{t}^{i}=\|f(s_{t},a_{t})-\phi (s_{t+1})\|_{2}^{2}} for some featurizer ϕ {\displaystyle \phi } . The featurizer can be the identity function (i.e. ϕ ( x ) = x {\displaystyle \phi (x)=x} ), randomly generated, the encoder-half of a variational autoencoder, etc. A good featurizer improves forward dynamics exploration. The Intrinsic Curiosity Module (ICM) method trains simultaneously a forward dynamics model and a featurizer. The featurizer is trained by an inverse dynamics model, which is a function for predicting the current action based on the features of the current and the next state: g : ( ϕ ( s t ) , ϕ ( s t + 1 ) ) ↦ a t {\displaystyle g:(\phi (s_{t}),\phi (s_{t+1}))\mapsto a_{t}} . By optimizing the inverse dynamics, both the inverse dynamics model and the featurizer are improved. Then, the improved featurizer improves the forward dynamics model, which improves the exploration of the agent. Random Network Distillation (RND) method attempts to solve this problem by teacher–student distillation. Instead of a forward dynamics model, it has two models f , f ′ {\displaystyle f,f'} . The f ′ {\displaystyle f'} teacher model is fixed, and the f {\displaystyle f} student model is trained to minimize ‖ f ( s ) − f ′ ( s ) ‖ 2 2 {\displaystyle \|f(s)-f'(s)\|_{2}^{2}} on states s {\displaystyle s} . As a state is visited more and more, the student network becomes better at predicting the teacher. Meanwhile, the prediction error is also an exploration reward for the agent, and so the agent learns to perform actions that result in higher prediction error. Thus, we have a student network attempting to minimize the prediction error, while the agent attempting to maximize it, resulting in exploration. The states are normalized by subtracting a running average and dividing a running variance, which is necessary since the teacher model is frozen. The rewards are normalized by dividing with a running variance. Exploration by disagreement trains an ensemble of forward dynamics models, each on a random subset of all ( s t , a t , s t + 1 ) {\displaystyle (s_{t},a_{t},s_{t+1})} tuples. The exploration reward is the variance of the models' predictions. === Noise === For neural network–based agents, the NoisyNet method changes some of its neural network modules by noisy versions. That is, some network parameters are random variables from a probability distribution. The parameters of the distribution are themselves learnable. For example, in a linear layer y = W x + b {\displaystyle y=Wx+b} , both W , b {\displaystyle W,b} are sampled from Gaussian distributions N ( μ W , Σ W ) , N ( μ b , Σ b ) {\displaystyle {\mathcal {N}}(\mu _{W},\Sigma _{W}),{\mathcal {N}}(\mu _{b},\Sigma _{b})} at every step, and the parameters μ W , Σ W , μ b , Σ b {\displaystyle \mu _{W},\Sigma _{W},\mu _{b},\Sigma _{b}} are learned via the reparameterization trick.
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AI literacy or artificial intelligence literacy is "a set of competencies that enables individuals to critically evaluate AI technologies; communicate and collaborate effectively with AI; and use AI as a tool online, at home, and in the workplace." AI is employed in a variety of applications, including self-driving automobiles, virtual assistants and text generation by generative AI models. Users of these tools should be able to make informed decisions. AI literacy may have an impact on students' future employment prospects. With the rise of generative AI platforms, AI literacy has become a topic of conversation in the field of education. Some think AI literacy is essential for school and college students, while others restrict or prohibit the use of AI in assignments, viewing it as a form of academic dishonesty. However, many researchers and educational institutions promote a more nuanced approach, encouraging critical engagement with AI while developing policies that balance academic integrity with opportunities for learning. == Definitions == Other definitions of AI literacy include the ability to understand, use, monitor, and critically reflect on AI applications. That use of the term usually refers to teaching skills and knowledge to the general public, particularly those who are not adept in AI and the ability to understand, use, evaluate, and ethically navigate AI. As research into AI literacy is still emerging and focused on developing context-specific skills, there is not yet a single, broadly agreed-upon definition. AI literacy is linked to other forms of literacy. AI literacy requires digital literacy, whereas scientific and computational literacy may inform it. Data literacy also significantly overlaps with it. == Categories == AI literacy encompasses multiple categories, including a theoretical understanding of how artificial intelligence works, the usage of artificial intelligence technologies, and the critical appraisal of artificial intelligence, and its ethics. === Know and understand AI === Knowledge and understanding of AI refers to a basic understanding of what artificial intelligence is and how it works. This includes familiarity with machine learning algorithms and the limitations and biases present in AI systems. Users who know and understand AI should be familiar with various technologies that use artificial intelligence, including cognitive systems, robotics and machine learning. This includes recognizing that large language models (LLMs) are machine learning models trained on extensive datasets which generate new text rather than retrieving pre-written responses. === Use and apply AI === Using and applying AI refers to the ability to use AI tools to solve problems and perform tasks such as programming and analyzing big data. Some consider prompt engineering, the practice of designing effective prompts to guide generative AI platforms more effectively, as another competency within AI literacy. === Evaluate and create AI === Evaluation and creation refers to the ability to critically evaluate the quality and reliability of AI systems. It also refers to designing and building fair and ethical AI systems. To evaluate correctly, users should also learn in which areas AI is strong, and in which areas it is weak. === AI ethics === AI ethics refers to understanding the moral implications of AI, and the making informed decisions regarding the use of AI tools. This area includes considerations such as: Accountability: Hold AI actors accountable for the operation of AI systems and adherence to ethical ideals. Accuracy: Identify and report sources of error and uncertainty in algorithms and data. Auditability: Enable other parties to audit and assess algorithm behavior via transparent information sharing. Explainability: Make sure that algorithmic judgments and the underlying data can be presented in simple language. Fairness: Prevent biases and consider varied viewpoints. To do so, increase the diversity of researchers in the field. Human Centricity and Well-being: Prioritize human well-being in AI development and deployment. Human rights Alignment: Ensure that technology do not infringe internationally recognized human rights. Inclusivity: Make AI accessible to everyone. Progress: Choose high value initiatives. Responsibility, accountability, and transparency: Foster trust via responsibility, accountability, and fairness. Robustness and Security: Make AI systems safe, secure, and resistant to manipulation or data breach. Sustainability: Choose implementations that generate long-term, useful benefits. Environmental Implications: How this tool impacts the environment, any restrictions or laws, if this impact is worth the effects or not. === Enabling AI === Support AI by developing associated knowledge and skills such as programming and statistics. == Promoting AI literacy == Several governments have recognized the need to promote AI literacy, including among adults. Such programs have been published in the United States, China, Germany and Finland. Programs intended for the general public usually consist of short and easy to understand online study units. Programs intended for children are usually project-based. Programs for students at colleges and universities often address the specific professional needs of the student, depending on their field of study. Beyond the education system, AI literacy can also be developed in the community, for example in museums. === Schools === Schools use diverse pedagogies to promote AI literacy. These include: Performing a Turing test with an intelligent agent Creating chatbots Building apps using Blockly-based programming Project-based learning Building robots Data visualization Training AI models Artificial intelligence curricula can improve students' understanding of topics such as machine learning, neural networks, and deep learning. === Higher education === Before the second decade of the 21st century, artificial intelligence was studied mainly in STEM courses. Later, projects emerged to increase artificial intelligence education, specifically to promote AI literacy. Most courses start with one or more study units that deal with basic questions such as what artificial intelligence is, where it comes from, what it can do and what it can't do. Most courses also refer to machine learning and deep learning. Some of the courses deal with moral issues in artificial intelligence. In Ireland, the Higher Education Authority published Generative AI in Higher Education Teaching & Learning: Policy Framework in December 2025, which encouraged higher education institutions to embed AI literacy across programmes as a core graduate attribute. ==== Disciplinary policy ==== As a response to the increase of generative AI use in education, several disciplines formed committees or task forces to examine context-specific approaches toward AI literacy. In spring 2025, the Modern Language Association and Conference on College Composition and Communication Joint Task Force finished development of three working papers, a guide on AI literacy for students, and a collection of resources addressing AI use in writing. The task force emphasized the need for "a culture of critical AI literacy" and included guidelines not only for students but also educators and institutions, highlighting the need for modeling ethical AI use in planning processes. Similarly, a committee formed by the American Historical Association Council published "Guiding Principles for Artificial Intelligence in History Education" which encouraged "clear and transparent engagement with generative AI." The guidelines demonstrate the value of criticality when working with generative AI in thinking and research.
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In statistical learning theory, the principle of empirical risk minimization defines a family of learning algorithms based on evaluating performance over a known and fixed dataset. The core idea is based on an application of the law of large numbers; more specifically, we cannot know exactly how well a predictive algorithm will work in practice (i.e. the "true risk") because we do not know the true distribution of the data, but we can instead estimate and optimize the performance of the algorithm on a known set of training data. The performance over the known set of training data is referred to as the "empirical risk". == Background == The following situation is a general setting of many supervised learning problems. There are two spaces of objects X {\displaystyle X} and Y {\displaystyle Y} and we would like to learn a function h : X → Y {\displaystyle \ h:X\to Y} (often called hypothesis) which outputs an object y ∈ Y {\displaystyle y\in Y} , given x ∈ X {\displaystyle x\in X} . To do so, there is a training set of n {\displaystyle n} examples ( x 1 , y 1 ) , … , ( x n , y n ) {\displaystyle \ (x_{1},y_{1}),\ldots ,(x_{n},y_{n})} where x i ∈ X {\displaystyle x_{i}\in X} is an input and y i ∈ Y {\displaystyle y_{i}\in Y} is the corresponding response that is desired from h ( x i ) {\displaystyle h(x_{i})} . To put it more formally, assuming that there is a joint probability distribution P ( x , y ) {\displaystyle P(x,y)} over X {\displaystyle X} and Y {\displaystyle Y} , and that the training set consists of n {\displaystyle n} instances ( x 1 , y 1 ) , … , ( x n , y n ) {\displaystyle \ (x_{1},y_{1}),\ldots ,(x_{n},y_{n})} drawn i.i.d. from P ( x , y ) {\displaystyle P(x,y)} . The assumption of a joint probability distribution allows for the modelling of uncertainty in predictions (e.g. from noise in data) because y {\displaystyle y} is not a deterministic function of x {\displaystyle x} , but rather a random variable with conditional distribution P ( y | x ) {\displaystyle P(y|x)} for a fixed x {\displaystyle x} . It is also assumed that there is a non-negative real-valued loss function L ( y ^ , y ) {\displaystyle L({\hat {y}},y)} which measures how different the prediction y ^ {\displaystyle {\hat {y}}} of a hypothesis is from the true outcome y {\displaystyle y} . For classification tasks, these loss functions can be scoring rules. The risk associated with hypothesis h ( x ) {\displaystyle h(x)} is then defined as the expectation of the loss function: R ( h ) = E [ L ( h ( x ) , y ) ] = ∫ L ( h ( x ) , y ) d P ( x , y ) . {\displaystyle R(h)=\mathbf {E} [L(h(x),y)]=\int L(h(x),y)\,dP(x,y).} A loss function commonly used in theory is the 0-1 loss function: L ( y ^ , y ) = { 1 if y ^ ≠ y 0 if y ^ = y {\displaystyle L({\hat {y}},y)={\begin{cases}1&{\mbox{ if }}\quad {\hat {y}}\neq y\\0&{\mbox{ if }}\quad {\hat {y}}=y\end{cases}}} . The ultimate goal of a learning algorithm is to find a hypothesis h ∗ {\displaystyle h^{}} among a fixed class of functions H {\displaystyle {\mathcal {H}}} for which the risk R ( h ) {\displaystyle R(h)} is minimal: h ∗ = a r g m i n h ∈ H R ( h ) . {\displaystyle h^{}={\underset {h\in {\mathcal {H}}}{\operatorname {arg\,min} }}\,{R(h)}.} For classification problems, the Bayes classifier is defined to be the classifier minimizing the risk defined with the 0–1 loss function. == Formal definition == In general, the risk R ( h ) {\displaystyle R(h)} cannot be computed because the distribution P ( x , y ) {\displaystyle P(x,y)} is unknown to the learning algorithm. However, given a sample of iid training data points, we can compute an estimate, called the empirical risk, by computing the average of the loss function over the training set; more formally, computing the expectation with respect to the empirical measure: R emp ( h ) = 1 n ∑ i = 1 n L ( h ( x i ) , y i ) . {\displaystyle \!R_{\text{emp}}(h)={\frac {1}{n}}\sum _{i=1}^{n}L(h(x_{i}),y_{i}).} The empirical risk minimization principle states that the learning algorithm should choose a hypothesis h ^ {\displaystyle {\hat {h}}} which minimizes the empirical risk over the hypothesis class H {\displaystyle {\mathcal {H}}} : h ^ = a r g m i n h ∈ H R emp ( h ) . {\displaystyle {\hat {h}}={\underset {h\in {\mathcal {H}}}{\operatorname {arg\,min} }}\,R_{\text{emp}}(h).} Thus, the learning algorithm defined by the empirical risk minimization principle consists in solving the above optimization problem. == Properties == Guarantees for the performance of empirical risk minimization depend strongly on the function class selected as well as the distributional assumptions made. In general, distribution-free methods are too coarse, and do not lead to practical bounds. However, they are still useful in deriving asymptotic properties of learning algorithms, such as consistency. In particular, distribution-free bounds on the performance of empirical risk minimization given a fixed function class can be derived using bounds on the VC complexity of the function class. For simplicity, considering the case of binary classification tasks, it is possible to bound the probability of the selected classifier, ϕ n {\displaystyle \phi _{n}} being much worse than the best possible classifier ϕ ∗ {\displaystyle \phi ^{}} . Consider the risk L {\displaystyle L} defined over the hypothesis class C {\displaystyle {\mathcal {C}}} with growth function S ( C , n ) {\displaystyle {\mathcal {S}}({\mathcal {C}},n)} given a dataset of size n {\displaystyle n} . Then, for every ϵ > 0 {\displaystyle \epsilon >0} : P ( L ( ϕ n ) − L ( ϕ ∗ ) > ϵ ) ≤ 8 S ( C , n ) exp { − n ϵ 2 / 32 } {\displaystyle \mathbb {P} \left(L(\phi _{n})-L(\phi ^{})>\epsilon \right)\leq {\mathcal {8}}S({\mathcal {C}},n)\exp\{-n\epsilon ^{2}/32\}} Similar results hold for regression tasks. These results are often based on uniform laws of large numbers, which control the deviation of the empirical risk from the true risk, uniformly over the hypothesis class. === Impossibility results === It is also possible to show lower bounds on algorithm performance if no distributional assumptions are made. This is sometimes referred to as the No free lunch theorem. Even though a specific learning algorithm may provide the asymptotically optimal performance for any distribution, the finite sample performance is always poor for at least one data distribution. This means that no classifier can improve on the error for a given sample size for all distributions. Specifically, let ϵ > 0 {\displaystyle \epsilon >0} and consider a sample size n {\displaystyle n} and classification rule ϕ n {\displaystyle \phi _{n}} , there exists a distribution of ( X , Y ) {\displaystyle (X,Y)} with risk L ∗ = 0 {\displaystyle L^{}=0} (meaning that perfect prediction is possible) such that: E L n ≥ 1 / 2 − ϵ . {\displaystyle \mathbb {E} L_{n}\geq 1/2-\epsilon .} It is further possible to show that the convergence rate of a learning algorithm is poor for some distributions. Specifically, given a sequence of decreasing positive numbers a i {\displaystyle a_{i}} converging to zero, it is possible to find a distribution such that: E L n ≥ a i {\displaystyle \mathbb {E} L_{n}\geq a_{i}} for all n {\displaystyle n} . This result shows that universally good classification rules do not exist, in the sense that the rule must be low quality for at least one distribution. === Computational complexity === Empirical risk minimization for a classification problem with a 0-1 loss function is known to be an NP-hard problem even for a relatively simple class of functions such as linear classifiers. Nevertheless, it can be solved efficiently when the minimal empirical risk is zero, i.e., data is linearly separable. In practice, machine learning algorithms cope with this issue either by employing a convex approximation to the 0–1 loss function (like hinge loss for SVM), which is easier to optimize, or by imposing assumptions on the distribution P ( x , y ) {\displaystyle P(x,y)} (and thus stop being agnostic learning algorithms to which the above result applies). In the case of convexification, Zhang's lemma majors the excess risk of the original problem using the excess risk of the convexified problem. Minimizing the latter using convex optimization also allow to control the former. == Tilted empirical risk minimization == Tilted empirical risk minimization is a machine learning technique used to modify standard loss functions like squared error, by introducing a tilt parameter. This parameter dynamically adjusts the weight of data points during training, allowing the algorithm to focus on specific regions or characteristics of the data distribution. Tilted empirical risk minimization is particularly useful in scenarios with imbalanced data or when there is a need to emphasize errors in certain parts of the prediction space.
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Dynamic epistemic logic (DEL) is a logical framework dealing with knowledge and information change. Typically, DEL focuses on situations involving multiple agents and studies how their knowledge changes when events occur. These events can change factual properties of the actual world (they are called ontic events): for example a red card is painted in blue. They can also bring about changes of knowledge without changing factual properties of the world (they are called epistemic events): for example, a card is revealed publicly (or privately) to be red. Originally, DEL focused on epistemic events. Only some of the basic ideas are present in this entry of the original DEL framework; more details about DEL in general can be found in the references. Due to the nature of its object of study and its abstract approach, DEL is related and has applications to numerous research areas, such as computer science (artificial intelligence), philosophy (formal epistemology), economics (game theory) and cognitive science. In computer science, DEL is for example very much related to multi-agent systems, which are systems where multiple intelligent agents interact and exchange information. As a combination of dynamic logic and epistemic logic, dynamic epistemic logic is a young field of research. It really started in 1989 with Plaza's logic of public announcement. Independently, Gerbrandy and Groeneveld proposed a system dealing moreover with private announcement and that was inspired by the work of Veltman. Another system was proposed by van Ditmarsch whose main inspiration was the Cluedo game. But the most influential and original system was the system proposed by Baltag, Moss and Solecki. This system can deal with all the types of situations studied in the works above and its underlying methodology is conceptually grounded. This entry will present some of its basic ideas. Formally, DEL extends ordinary epistemic logic by the inclusion of event models to describe actions, and a product update operator that defines how epistemic models are updated as the consequence of executing actions described through event models. Epistemic logic will first be recalled. Then, actions and events will enter into the picture and we will introduce the DEL framework. == Epistemic logic == Epistemic logic is a modal logic dealing with the notions of knowledge and belief. As a logic, it is concerned with understanding the process of reasoning about knowledge and belief: which principles relating the notions of knowledge and belief are intuitively plausible? Like epistemology, it stems from the Greek word ϵ π ι σ τ η μ η {\displaystyle \epsilon \pi \iota \sigma \tau \eta \mu \eta } or ‘episteme’ meaning knowledge. Epistemology is nevertheless more concerned with analyzing the very nature and scope of knowledge, addressing questions such as “What is the definition of knowledge?” or “How is knowledge acquired?”. In fact, epistemic logic grew out of epistemology in the Middle Ages thanks to the efforts of Burley and Ockham. The formal work, based on modal logic, that inaugurated contemporary research into epistemic logic dates back only to 1962 and is due to Hintikka. It then sparked in the 1960s discussions about the principles of knowledge and belief and many axioms for these notions were proposed and discussed. For example, the interaction axioms K p → B p {\displaystyle Kp\rightarrow Bp} and B p → K B p {\displaystyle Bp\rightarrow KBp} are often considered to be intuitive principles: if an agent Knows p {\displaystyle p} then (s)he also Believes p {\displaystyle p} , or if an agent Believes p {\displaystyle p} , then (s)he Knows that (s)he Believes p {\displaystyle p} . More recently, these kinds of philosophical theories were taken up by researchers in economics, artificial intelligence and theoretical computer science where reasoning about knowledge is a central topic. Due to the new setting in which epistemic logic was used, new perspectives and new features such as computability issues were then added to the research agenda of epistemic logic. === Syntax === In the sequel, A G T S = { 1 , … , n } {\displaystyle AGTS=\{1,\ldots ,n\}} is a finite set whose elements are called agents and P R O P {\displaystyle PROP} is a set of propositional letters. The epistemic language is an extension of the basic multi-modal language of modal logic with a common knowledge operator C A {\displaystyle C_{A}} and a distributed knowledge operator D A {\displaystyle D_{A}} . Formally, the epistemic language L EL C {\displaystyle {\mathcal {L}}_{\textsf {EL}}^{C}} is defined inductively by the following grammar in BNF: L EL C : ϕ ::= p ∣ ¬ ϕ ∣ ( ϕ ∧ ϕ ) ∣ K j ϕ ∣ C A ϕ ∣ D A ϕ {\displaystyle {\mathcal {L}}_{\textsf {EL}}^{C}:\phi ~~::=~~p~\mid ~\neg \phi ~\mid ~(\phi \land \phi )~\mid ~K_{j}\phi ~\mid ~C_{A}\phi ~\mid ~D_{A}\phi } where p ∈ P R O P {\displaystyle p\in PROP} , j ∈ A G T S {\displaystyle j\in {AGTS}} and A ⊆ A G T S {\displaystyle A\subseteq {AGTS}} . The basic epistemic language L E L {\displaystyle {\mathcal {L}}_{EL}} is the language L E L C {\displaystyle {\mathcal {L}}_{EL}^{C}} without the common knowledge and distributed knowledge operators. The formula ⊥ {\displaystyle \bot } is an abbreviation for ¬ p ∧ p {\displaystyle \neg p\land p} (for a given p ∈ P R O P {\displaystyle p\in PROP} ), ⟨ K j ⟩ ϕ {\displaystyle \langle K_{j}\rangle \phi } is an abbreviation for ¬ K j ¬ ϕ {\displaystyle \neg K_{j}\neg \phi } , E A ϕ {\displaystyle E_{A}\phi } is an abbreviation for ⋀ j ∈ A K j ϕ {\displaystyle \bigwedge \limits _{j\in A}K_{j}\phi } and C ϕ {\displaystyle C\phi } an abbreviation for C A G T S ϕ {\displaystyle C_{AGTS}\phi } . Group notions: general, common and distributed knowledge. In a multi-agent setting there are three important epistemic concepts: general knowledge, distributed knowledge and common knowledge. The notion of common knowledge was first studied by Lewis in the context of conventions. It was then applied to distributed systems and to game theory, where it allows to express that the rationality of the players, the rules of the game and the set of players are commonly known. General knowledge. General knowledge of ϕ {\displaystyle \phi } means that everybody in the group of agents A G T S {\displaystyle {AGTS}} knows that ϕ {\displaystyle \phi } . Formally, this corresponds to the following formula: E ϕ := ⋀ j ∈ A G T S K j ϕ . {\displaystyle E\phi :={\underset {j\in {AGTS}}{\bigwedge }}K_{j}\phi .} Common knowledge. Common knowledge of ϕ {\displaystyle \phi } means that everybody knows ϕ {\displaystyle \phi } but also that everybody knows that everybody knows ϕ {\displaystyle \phi } , that everybody knows that everybody knows that everybody knows ϕ {\displaystyle \phi } , and so on ad infinitum. Formally, this corresponds to the following formula C ϕ := E ϕ ∧ E E ϕ ∧ E E E ϕ ∧ … {\displaystyle C\phi :=E\phi \land EE\phi \land EEE\phi \land \ldots } As we do not allow infinite conjunction the notion of common knowledge will have to be introduced as a primitive in our language. Before defining the language with this new operator, we are going to give an example introduced by Lewis that illustrates the difference between the notions of general knowledge and common knowledge. Lewis wanted to know what kind of knowledge is needed so that the statement p {\displaystyle p} : “every driver must drive on the right” be a convention among a group of agents. In other words, he wanted to know what kind of knowledge is needed so that everybody feels safe to drive on the right. Suppose there are only two agents i {\displaystyle i} and j {\displaystyle j} . Then everybody knowing p {\displaystyle p} (formally E p {\displaystyle Ep} ) is not enough. Indeed, it might still be possible that the agent i {\displaystyle i} considers possible that the agent j {\displaystyle j} does not know p {\displaystyle p} (formally ¬ K i K j p {\displaystyle \neg K_{i}K_{j}p} ). In that case the agent i {\displaystyle i} will not feel safe to drive on the right because he might consider that the agent j {\displaystyle j} , not knowing p {\displaystyle p} , could drive on the left. To avoid this problem, we could then assume that everybody knows that everybody knows that p {\displaystyle p} (formally E E p {\displaystyle EEp} ). This is again not enough to ensure that everybody feels safe to drive on the right. Indeed, it might still be possible that agent i {\displaystyle i} considers possible that agent j {\displaystyle j} considers possible that agent i {\displaystyle i} does not know p {\displaystyle p} (formally ¬ K i K j K i p {\displaystyle \neg K_{i}K_{j}K_{i}p} ). In that case and from i {\displaystyle i} ’s point of view, j {\displaystyle j} considers possible that i {\displaystyle i} , not knowing p {\displaystyle p} , will drive on the left. So from i {\displaystyle i} ’s point of view, j {\displaystyle j} might drive on the left as well (by the same argument as abov
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In machine learning, a confusion matrix, also known as error matrix, is a specific table layout that allows visualization of the performance of an algorithm, typically a supervised learning one. In unsupervised learning it is usually called a matching matrix. The term is used specifically in the problem of statistical classification. Each row of the matrix represents the instances in an actual class while each column represents the instances in a predicted class, or vice versa – both variants are found in the literature. The diagonal of the matrix therefore represents all instances that are correctly predicted. The name stems from the fact that it makes it easy to identify whether the system is confusing two classes (i.e., commonly mislabeling one class as another). The confusion matrix has its origins in human perceptual studies of auditory stimuli. It was adapted for machine learning studies and used by Frank Rosenblatt, among other early researchers, to compare human and machine classifications of visual (and later auditory) stimuli. It is a special kind of contingency table, with two dimensions ("actual" and "predicted"), and identical sets of "classes" in both dimensions (each combination of dimension and class is a variable in the contingency table). == Example == Given a sample of 12 individuals, 8 that have been diagnosed with cancer and 4 that are cancer-free, where individuals with cancer belong to class 1 (positive) and non-cancer individuals belong to class 0 (negative), we can display that data as follows: Assume that we have a classifier that distinguishes between individuals with and without cancer in some way, we can take the 12 individuals and run them through the classifier. The classifier then makes 9 accurate predictions and misses 3: 2 individuals with cancer wrongly predicted as being cancer-free (sample 1 and 2), and 1 person without cancer that is wrongly predicted to have cancer (sample 9). Notice, that if we compare the actual classification set to the predicted classification set, there are 4 different outcomes that could result in any particular column: The actual classification is positive and the predicted classification is positive (1,1). This is called a true positive result because the positive sample was correctly identified by the classifier. The actual classification is positive and the predicted classification is negative (1,0). This is called a false negative result because the positive sample is incorrectly identified by the classifier as being negative. The actual classification is negative and the predicted classification is positive (0,1). This is called a false positive result because the negative sample is incorrectly identified by the classifier as being positive. The actual classification is negative and the predicted classification is negative (0,0). This is called a true negative result because the negative sample gets correctly identified by the classifier. We can then perform the comparison between actual and predicted classifications and add this information to the table, making correct results appear in green so they are more easily identifiable. The template for any binary confusion matrix uses the four kinds of results discussed above (true positives, false negatives, false positives, and true negatives) along with the positive and negative classifications. The four outcomes can be formulated in a 2×2 confusion matrix, as follows: The color convention of the three data tables above were picked to match this confusion matrix, in order to easily differentiate the data. Now, we can simply total up each type of result, substitute into the template, and create a confusion matrix that will concisely summarize the results of testing the classifier: In this confusion matrix, of the 8 samples with cancer, the system judged that 2 were cancer-free, and of the 4 samples without cancer, it predicted that 1 did have cancer. All correct predictions are located in the diagonal of the table (highlighted in green), so it is easy to visually inspect the table for prediction errors, as values outside the diagonal will represent them. By summing up the 2 rows of the confusion matrix, one can also deduce the total number of positive (P) and negative (N) samples in the original dataset, i.e. P = T P + F N {\displaystyle P=TP+FN} and N = F P + T N {\displaystyle N=FP+TN} . == Table of confusion == In predictive analytics, a table of confusion (sometimes also called a confusion matrix) is a table with two rows and two columns that reports the number of true positives, false negatives, false positives, and true negatives. This allows more detailed analysis than simply observing the proportion of correct classifications (accuracy). Accuracy will yield misleading results if the data set is unbalanced; that is, when the numbers of observations in different classes vary greatly. For example, if there were 95 cancer samples and only 5 non-cancer samples in the data, a particular classifier might classify all the observations as having cancer. The overall accuracy would be 95%, but in more detail the classifier would have a 100% recognition rate (sensitivity) for the cancer class but a 0% recognition rate for the non-cancer class. F1 score is even more unreliable in such cases, and here would yield over 97.4%, whereas informedness removes such bias and yields 0 as the probability of an informed decision for any form of guessing (here always guessing cancer). According to Davide Chicco and Giuseppe Jurman, the most informative metric to evaluate a confusion matrix is the Matthews correlation coefficient (MCC). Other metrics can be included in a confusion matrix, each of them having their significance and use. Some researchers have argued that the confusion matrix, and the metrics derived from it, do not truly reflect a model's knowledge. In particular, the confusion matrix cannot show whether correct predictions were reached through sound reasoning or merely by chance (a problem known in philosophy as epistemic luck). It also does not capture situations where the facts used to make a prediction later change or turn out to be wrong (defeasibility). This means that while the confusion matrix is a useful tool for measuring classification performance, it may give an incomplete picture of a model’s true reliability. == Confusion matrices with more than two categories == Confusion matrix is not limited to binary classification and can be used in multi-class classifiers as well. The confusion matrices discussed above have only two conditions: positive and negative. For example, the table below summarizes communication of a whistled language between two speakers, with zero values omitted for clarity. == Confusion matrices in multi-label and soft-label classification == Confusion matrices are not limited to single-label classification (where only one class is present) or hard-label settings (where classes are either fully present, 1, or absent, 0). They can also be extended to Multi-label classification (where multiple classes can be predicted at once) and soft-label classification (where classes can be partially present). One such extension is the Transport-based Confusion Matrix (TCM), which builds on the theory of optimal transport and the principle of maximum entropy. TCM applies to single-label, multi-label, and soft-label settings. It retains the familiar structure of the standard confusion matrix: a square matrix sized by the number of classes, with diagonal entries indicating correct predictions and off-diagonal entries indicating confusion. In the single-label case, TCM is identical to the standard confusion matrix. TCM follows the same reasoning as the standard confusion matrix: if class A is overestimated (its predicted value is greater than its label value) and class B is underestimated (its predicted value is less than its label value), A is considered confused with B, and the entry (B, A) is increased. If a class is both predicted and present, it is correctly identified, and the diagonal entry (A, A) increases. Optimal transport and maximum entropy are used to determine the extent to which these entries are updated. TCM enables clearer comparison between predictions and labels in complex classification tasks, while maintaining a consistent matrix format across settings.
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Brain technology, or self-learning know-how systems, defines a technology that employs latest findings in neuroscience. [see also neuro implants] The term was first introduced by the Artificial Intelligence Laboratory in Zurich, Switzerland, in the context of the Roboy project. Brain Technology can be employed in robots, know-how management systems and any other application with self-learning capabilities. In particular, Brain Technology applications allow the visualization of the underlying learning architecture often coined as "know-how maps". == Research and applications == The first demonstrations of BC in humans and animals took place in the 1960s when Grey Walter demonstrated use of non-invasively recorded encephalogram (EEG) signals from a human subject to control a slide projector (Graimann et al., 2010). Soon after Jacques J. Vidal coined the term brain–computer interface (BCI) in 1971, the Defense Advanced Research Projects Agency (DARPA) first starting funding brain–computer interface research and has since funded several brain–computer interface projects. That market is expected to reach a value of $1.72 billion by 2022. Brain–computer interfaces record brain activity, transmit the information out of the body, signal-process the data via algorithms, and convert them into command control signals. In 2012, a landmark study in Nature, led by pioneer Leigh Hochberg, MD, PhD, demonstrated that two people with tetraplegia were able to control robotic arms through thought when connected to the BrainGate neural interface system. The two participants were able to reach for and grasp objects in three-dimensional space, and one participant used the system to serve herself coffee for the first time since becoming paralyzed nearly 15 years prior. And in October 2020, two patients were able to wirelessly control an operating system to text, email, shop and bank using direct thought through the Stentrode brain computer interface (Journal of NeuroInterventional Surgery) in a study led by Thomas Oxley. This was the first time a brain–computer interface was implanted via the patient's blood vessels, eliminating the need for open brain surgery. Currently a number of groups are exploring a range of experimental devices using brain–computer interfaces, which have the potential to fundamentally change the way of life for patients with paralysis and a wide range of neurological disorders. These include: as Elon Musk, Facebook, and the University of California in San Francisco. The systems. This technology is also being explored as a neuromodulation device and may ultimately help diagnose and treat a range of brain pathologies, such as epilepsy and Parkinson's disease.
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Multimodal representation learning is a subfield of representation learning focused on integrating and interpreting information from different modalities, such as text, images, audio, or video, by projecting them into a shared latent space. This allows for semantically similar content across modalities to be mapped to nearby points within that space, facilitating a unified understanding of diverse data types. By automatically learning meaningful features from each modality and capturing their inter-modal relationships, multimodal representation learning enables a unified representation that enhances performance in cross-media analysis tasks such as video classification, event detection, and sentiment analysis. It also supports cross-modal retrieval and translation, including image captioning, video description, and text-to-image synthesis. == Motivation == The primary motivations for multimodal representation learning arise from the inherent nature of real-world data and the limitations of unimodal approaches. Since multimodal data offers complementary and supplementary information about an object or event from different perspectives, it is more informative than relying on a single modality. A key motivation is to narrow the heterogeneity gap that exists between different modalities by projecting their features into a shared semantic subspace. This allows semantically similar content across modalities to be represented by similar vectors, facilitating the understanding of relationships and correlations between them. Multimodal representation learning aims to leverage the unique information provided by each modality to achieve a more comprehensive and accurate understanding of concepts. These unified representations are crucial for improving performance in various cross-media analysis tasks such as video classification, event detection, and sentiment analysis. They also enable cross-modal retrieval, allowing users to search and retrieve content across different modalities. Additionally, it facilitates cross-modal translation, where information can be converted from one modality to another, as seen in applications like image captioning and text-to-image synthesis. The abundance of ubiquitous multimodal data in real-world applications, including understudied areas like healthcare, finance, and human-computer interaction (HCI), further motivates the development of effective multimodal representation learning techniques. == Approaches and methods == === Canonical-correlation analysis based methods === Canonical-correlation analysis (CCA) was first introduced in 1936 by Harold Hotelling and is a fundamental approach for multimodal learning. CCA aims to find linear relationships between two sets of variables. Given two data matrices X ∈ R n × p {\displaystyle X\in \mathbb {R} ^{n\times p}} and Y ∈ R n × q {\displaystyle Y\in \mathbb {R} ^{n\times q}} representing different modalities, CCA finds projection vectors w x ∈ R p {\displaystyle w_{x}\in \mathbb {R} ^{p}} and w y ∈ R q {\displaystyle w_{y}\in \mathbb {R} ^{q}} that maximizes the correlation between the projected variables: ρ = max w x , w y w x ⊤ Σ x y w y w x ⊤ Σ x x w x w y ⊤ Σ y y w y {\displaystyle \rho =\max _{w_{x},w_{y}}{\frac {w_{x}^{\top }\Sigma _{xy}w_{y}}{{\sqrt {w_{x}^{\top }\Sigma _{xx}w_{x}}}{\sqrt {w_{y}^{\top }\Sigma _{yy}w_{y}}}}}} such that Σ x x {\displaystyle \Sigma _{xx}} and Σ y y {\displaystyle \Sigma _{yy}} are the within-modality covariance matrices, and Σ x y {\displaystyle \Sigma _{xy}} is the between-modality covariance matrix. However, standard CCA is limited by its linearity, which led to the development of nonlinear extensions, such as kernel CCA and deep CCA. ==== Kernel CCA ==== Kernel canonical correlation analysis (KCCA) extends traditional CCA to capture nonlinear relationships between modalities by implicitly mapping the data into high dimensional feature spaces using kernel functions. Given kernel functions K x {\displaystyle K_{x}} and K y {\displaystyle K_{y}} with corresponding Gram matrices K x ∈ R n × n {\displaystyle K_{x}\in \mathbb {R} ^{n\times n}} and K y ∈ R n × n {\displaystyle K_{y}\in \mathbb {R} ^{n\times n}} , KCCA seeks coefficients α {\displaystyle \alpha } and β {\displaystyle \beta } that maximize: ρ = max α , β α ⊤ K x K y β α ⊤ K x 2 α β ⊤ K y 2 β {\displaystyle \rho =\max _{\alpha ,\beta }{\frac {\alpha ^{\top }K_{x}Ky\beta }{{\sqrt {\alpha ^{\top }K_{x}^{2}\alpha }}{\sqrt {\beta ^{\top }K_{y}^{2}\beta }}}}} To prevent overfitting, regularization terms are typically added, resulting in: ρ = max α , β α T K x K y β α T ( K x 2 + λ x K x ) α β T ( K y 2 + λ y K y ) β {\displaystyle \rho =\max _{\alpha ,\beta }{\frac {\alpha ^{T}K_{x}K_{y}\beta }{{\sqrt {\alpha ^{T}\left(K_{x}^{2}+\lambda _{x}K_{x}\right)\alpha }}{\sqrt {\;\beta ^{T}\left(K_{y}^{2}+\lambda _{y}K_{y}\right)\beta }}}}} where λ x {\displaystyle \lambda _{x}} and λ y {\displaystyle \lambda _{y}} are regularization parameters. KCCA has proven effective for tasks such as cross-modal retrieval and semantic analysis, though it faces computational challenges with large datasets due to its O ( n 2 ) {\displaystyle O(n^{2})} memory requirement for sorting kernel matrices. KCCA was proposed independently by several researchers. ==== Deep CCA ==== Deep canonical correlation analysis (DCCA), introduced in 2013, employs neural networks to learn nonlinear transformations for maximizing the correlation between modalities. DCCA uses separate neural networks f x {\displaystyle f_{x}} and f y {\displaystyle f_{y}} for each modality to transform the original data before applying CCA: max W x , W y , θ x , θ y corr ( f x ( X ; θ x ) , f y ( Y ; θ y ) ) {\displaystyle \max _{W_{x},W_{y},\theta _{x},\theta _{y}}\operatorname {corr} \left(f_{x}(X;\theta _{x}),f_{y}(Y;\theta _{y})\right)} where θ x {\displaystyle \theta _{x}} and θ y {\displaystyle \theta _{y}} represent the parameters of the neural networks, and W x {\displaystyle W_{x}} and W y {\displaystyle W_{y}} are the CCA projection matrices. The correlation objective is computed as: corr ( H x , H y ) = tr ( T − 1 / 2 H x T H y S − 1 / 2 ) {\displaystyle \operatorname {corr} (H_{x},H_{y})=\operatorname {tr} \left(T^{-1/2}H_{x}^{T}H_{y}S^{-1/2}\right)} where H x = f x ( X ) {\displaystyle H_{x}=f_{x}(X)} and H y = f y ( Y ) {\displaystyle H_{y}=f_{y}(Y)} are the network outputs, T = H x T H x + r x I {\displaystyle T=H_{x}^{T}H_{x}+r_{x}I} , S = H y T H y + r y I {\displaystyle S=H_{y}^{T}H_{y}+r_{y}I} and r x , r y {\displaystyle r_{x},r_{y}} are the regularization parameters. DCCA overcomes the limitations of linear CCA and kernel CCA by learning complex nonlinear relationships while maintaining computational efficiency for large datasets through mini-batch optimization. === Graph-based methods === Graph-based approaches for multimodal representation learning leverage graph structure to model relationships between entities across different modalities. These methods typically represent each modality as a graph and then learn embedding that preserve cross-modal similarities, enabling more effective joint representation of heterogeneous data. One such method is cross-modal graph neural networks (CMGNNs) that extend traditional graph neural networks (GNNs) to handle data from multiple modalities by constructing graphs that capture both intra-modal and inter-modal relationships. These networks model interactions across modalities by representing them as nodes and their relationships as edges. Other graph-based methods include Probabilistic Graphical Models (PGMs) such as deep belief networks (DBN) and deep Boltzmann machines (DBM). These models can learn a joint representation across modalities, for instance, a multimodal DBN achieves this by adding a shared restricted Boltzmann Machine (RBM) hidden layer on top of modality-specific DBNs. Additionally, the structure of data in some domains like Human-Computer Interaction (HCI), such as the view hierarchy of app screens, can potentially be modeled using graph-like structures. The field of graph representation learning is also relevant, with ongoing progress in developing evaluation benchmarks. === Diffusion maps === Another set of methods relevant to multimodal representation learning are based on diffusion maps and their extensions to handle multiple modalities. ==== Multi-view diffusion maps ==== Multi-view diffusion maps address the challenge of achieving multi-view dimensionality reduction by effectively utilizing the availability of multiple views to extract a coherent low-dimensional representation of the data. The core idea is to exploit both the intrinsic relations within each view and the mutual relations between the different views, defining a cross-view model where a random walk process implicitly hops between objects in different views. A multi-view kernel matrix is constructed by combining these relations, defining a cross-view diffusion process and associ
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