Social media began in the form of generalized online communities. These online communities formed on websites like Geocities.com in 1994, Theglobe.com in 1995, and Tripod.com in 1995. Many of these early communities focused on social interaction by bringing people together through the use of chat rooms. The chat rooms encouraged users to share personal information, ideas, or even personal web pages. Later the social networking community Classmates took a different approach by simply having people link to each other by using their personal email addresses. By the late 1990s, social networking websites began to develop more advanced features to help users find and manage friends. These newer generation of social networking websites began to flourish with the emergence of SixDegrees.com in 1997, Makeoutclub in 2000, Hub Culture in 2002, and Friendster in 2002. However, the first profitable mass social networking website was the South Korean service, Cyworld. Cyworld initially launched as a blog-based website in 1999 and social networking features were added to the website in 2001. Other social networking websites emerged like Myspace in 2002, LinkedIn in 2003, and Bebo in 2005. In 2009, the social networking website Facebook (launched in 2004) became the largest social networking website in the world. Both Instagram and Kik were launched in October 2010. Active users of Facebook increased from just a million in 2004 to over 750 million by the year 2011. Making internet-based social networking both a cultural and financial phenomenon. In September 2011, Snapchat was launched and reported over 300 million users in 2021. == Psychology of social networking == A social network is a social structure made up of individuals or organizations who communicate and interact with each other. Social networking sites – such as Facebook, Twitter, Instagram, Pinterest and LinkedIn – are defined as technology-enabled tools that assist users with creating and maintaining their relationships. A study found that middle schoolers reported using social media to see what their friends are doing, to post pictures, and to connect with friends. Human behavior related to social networking is influenced by major individual differences, meaning that people differ quite systematically in the quantity and quality of their social relationships. Two of the main personality traits that are responsible for this variability are the traits of extraversion and introversion. Extraversion refers to the tendency to be socially dominant, exert leadership, and influence on others. In contrast, introversion reflects a tendency towards shyness, social phobia, or even avoid social situations altogether, which could potentially reduce the number of social contacts a person may have. These individual differences may result in different social networking outcomes. Other psychology factors related to social media and Media psychology are depression, anxiety, attachment, self-identity, well-being, and the need to belong. === Neuroscience === The three domains that neural systems rely on to be strengthened to support social media use are social cognition, self-referential cognition, and social rewarding. When someone posts something on social media, they think of how their audience will react, while the audience thinks of the motivations behind posting the information. Both parties are analyzing the other's thoughts and feelings, which coherently rely on multiple network systems of the brain including the dorsomedial prefrontal cortex, bilateral temporoparietal junction, anterior temporal lobes, inferior frontal gyri, and posterior cingulate cortex. All of these systems work to help us process social behaviors and thoughts drawn out on social media. Social media requires a great deal of self-referential thought. People use social media as a platform to express their opinions and show off their past and present selves. In other words, as Bailey Parnell said in her Ted Talk, we're showing off our "highlight reel" (4). When one receives feedback from others, the individual obtains more reflected self-appraisal which leads to comparisons of their social behaviors or "highlights" to other users. Self-referential thought involves activity in the medial prefrontal cortex and the posterior cingulate cortex. The brain uses these systems when thinking of oneself. A 2021 umbrella review found that most associations between adolescent social media use and mental health were characterized as weak or inconsistent, though certain studies identified 'substantial' negative impacts, particularly linked to passive consumption and problematic use. Social media also provides a constant supply of rewards that keeps users coming back for more. Whenever users receive a like or a new follower, it activates the brain's social reward system which includes the ventromedial prefrontal cortex, ventral striatum, and ventral tegmental area. This system has been found to activate in response to positive feedback from peers, suggesting that users experience online acceptance in a similar manner to other material rewards or positive experiences, further acting as a potential reward. While these areas of the brain become strengthened, other parts of the brain start to weaken. Technology is encouraging multi-tasking, especially because of how easy it is to switch from one task to another by opening another tab or using two devices at once. The brain's hippocampus is mainly associated with long-term memory. In a study done by Russell Poldark, a professor at UCLA, they found that "for the task learned without distraction, the hippocampus was involved. However, for the task learned with the distraction of the beeps, the hippocampus was not involved; but the striatum was, which is the brain system that underlies our ability to learn new skills." The study concludes that multitasking can cause reliance on the striatum more than the hippocampus, which can change the way we learn. The striatum is known to be connected to mainly the brain's reward system. The brain will strengthen the neurons to the striatum while it weakens the neurons to the hippocampus to make the brain more efficient. Because our brain starts to rely on the striatum more than the hippocampus, it becomes harder for us to process new information. Nicholas Carr, author of The Shallows: How The Internet Is Changing Our Brains, agrees: "What psychologists and brain scientists tell us about interruptions is that they have a fairly profound effect on the way we think. It becomes much harder to sustain attention, to think about one thing for a long period of time, and to think deeply when new stimuli are pouring at you all day long. I argue that the price we pay for being constantly inundated with information is a loss of our ability to be contemplative and to engage in the kind of deep thinking that requires you to concentrate on one thing." === Well-Being === How does well-being relate to social media? In an article titled Social Impact of Psychological Research on Well-Being Shared in Social Media, Pulido et al. found a 15.7% social impact in their results. These new results were compared to a previous study conducted by Pulido et al., which had a high of 4.98% compared to 27.5% in the new study. These results show the ESISM, which is evidence of social impact present. In a two-year span, the difference between social impact rose 22.52% according to these studies. When taking into consideration that an increasingly large number of teens report either being active on, or having used, some form of social media, ranging from apps such as Facebook to TikTok, researching the effects of social media on the well-being of teens and young adults has become more of a topic of focus in recent years. === Depression === Especially in today's society, social media has gained a new perspective on younger generations. It is what younger generations are born into and are growing up to use, particularly what is running today's society. Social Media has its downfalls regarding depression and mental health. Many users often compare their lives regarding what they see on these platforms. In an article Does Social Media Cause Depression? by the Child Mind Institute, Miller states that "several studies, teenage and young adult users who spend the most time on Instagram, Facebook and other platforms for have shown to have substantially (from 13 to 66 percent) higher rates of reported depression than those who spent the least time", what the study shows how Facebook and Instagram, platforms showcasing daily lives and or lifestyles, or less fulfilling or less satisfied or more flaunting base or superficial. Instead of social community, there has become a perception of individuals striving for a life that is not real, whether that is editing photos or making life seem perfect when it is not. This causes a sense of depression by the weight of a comparing game. In "How Social Media Affects Y
Multi-agent reinforcement learning
Multi-agent reinforcement learning (MARL) is a sub-field of reinforcement learning. It focuses on studying the behavior of multiple learning agents that coexist in a shared environment. Each agent is motivated by its own rewards, and does actions to advance its own interests; in some environments these interests are opposed to the interests of other agents, resulting in complex group dynamics. Multi-agent reinforcement learning is closely related to game theory and especially repeated games, as well as multi-agent systems. Its study combines the pursuit of finding ideal algorithms that maximize rewards with a more sociological set of concepts. While research in single-agent reinforcement learning is concerned with finding the algorithm that gets the biggest number of points for one agent, research in multi-agent reinforcement learning evaluates and quantifies social metrics, such as cooperation, reciprocity, equity, social influence, language and discrimination. == Definition == Similarly to single-agent reinforcement learning, multi-agent reinforcement learning is modeled as some form of a Markov decision process (MDP). Fix a set of agents I = { 1 , . . . , N } {\displaystyle I=\{1,...,N\}} . We then define: A set S {\displaystyle S} of environment states. One set A i {\displaystyle {\mathcal {A}}_{i}} of actions for each of the agents i ∈ I = { 1 , … , N } {\displaystyle i\in I=\{1,\dots ,N\}} . P a → ( s , s ′ ) = Pr ( s t + 1 = s ′ ∣ s t = s , a → t = a → ) {\displaystyle P_{\vec {a}}(s,s')=\Pr(s_{t+1}=s'\mid s_{t}=s,{\vec {a}}_{t}={\vec {a}})} is the probability of transition (at time t {\displaystyle t} ) from state s {\displaystyle s} to state s ′ {\displaystyle s'} under joint action a → {\displaystyle {\vec {a}}} . R → a → ( s , s ′ ) {\displaystyle {\vec {R}}_{\vec {a}}(s,s')} is the immediate joint reward after the transition from s {\displaystyle s} to s ′ {\displaystyle s'} with joint action a → {\displaystyle {\vec {a}}} . In settings with perfect information, such as the games of chess and Go, the MDP would be fully observable. In settings with imperfect information, especially in real-world applications like self-driving cars, each agent would access an observation that only has part of the information about the current state. In the partially observable setting, the core model is the partially observable stochastic game in the general case, and the decentralized POMDP in the cooperative case. == Cooperation vs. competition == When multiple agents are acting in a shared environment their interests might be aligned or misaligned. MARL allows exploring all the different alignments and how they affect the agents' behavior: In pure competition settings, the agents' rewards are exactly opposite to each other, and therefore they are playing against each other. Pure cooperation settings are the other extreme, in which agents get the exact same rewards, and therefore they are playing with each other. Mixed-sum settings cover all the games that combine elements of both cooperation and competition. === Pure competition settings === When two agents are playing a zero-sum game, they are in pure competition with each other. Many traditional games such as chess and Go fall under this category, as do two-player variants of video games like StarCraft. Because each agent can only win at the expense of the other agent, many complexities are stripped away. There is no prospect of communication or social dilemmas, as neither agent is incentivized to take actions that benefit its opponent. The Deep Blue and AlphaGo projects demonstrate how to optimize the performance of agents in pure competition settings. One complexity that is not stripped away in pure competition settings is autocurricula. As the agents' policy is improved using self-play, multiple layers of learning may occur. === Pure cooperation settings === MARL is used to explore how separate agents with identical interests can communicate and work together. Pure cooperation settings are explored in recreational cooperative games such as Overcooked, as well as real-world scenarios in robotics. In pure cooperation settings all the agents get identical rewards, which means that social dilemmas do not occur. In pure cooperation settings, oftentimes there are an arbitrary number of coordination strategies, and agents converge to specific "conventions" when coordinating with each other. The notion of conventions has been studied in language and also alluded to in more general multi-agent collaborative tasks. === Mixed-sum settings === Most real-world scenarios involving multiple agents have elements of both cooperation and competition. For example, when multiple self-driving cars are planning their respective paths, each of them has interests that are diverging but not exclusive: Each car is minimizing the amount of time it's taking to reach its destination, but all cars have the shared interest of avoiding a traffic collision. Zero-sum settings with three or more agents often exhibit similar properties to mixed-sum settings, since each pair of agents might have a non-zero utility sum between them. Mixed-sum settings can be explored using classic matrix games such as prisoner's dilemma, more complex sequential social dilemmas, and recreational games such as Among Us, Diplomacy and StarCraft II. Mixed-sum settings can give rise to communication and social dilemmas. == Social dilemmas == As in game theory, much of the research in MARL revolves around social dilemmas, such as prisoner's dilemma, chicken and stag hunt. While game theory research might focus on Nash equilibria and what an ideal policy for an agent would be, MARL research focuses on how the agents would learn these ideal policies using a trial-and-error process. The reinforcement learning algorithms that are used to train the agents are maximizing the agent's own reward; the conflict between the needs of the agents and the needs of the group is a subject of active research. Various techniques have been explored in order to induce cooperation in agents: Modifying the environment rules, adding intrinsic rewards, and more. === Sequential social dilemmas === Social dilemmas like prisoner's dilemma, chicken and stag hunt are "matrix games". Each agent takes only one action from a choice of two possible actions, and a simple 2x2 matrix is used to describe the reward that each agent will get, given the actions that each agent took. In humans and other living creatures, social dilemmas tend to be more complex. Agents take multiple actions over time, and the distinction between cooperating and defecting is not as clear cut as in matrix games. The concept of a sequential social dilemma (SSD) was introduced in 2017 as an attempt to model that complexity. There is ongoing research into defining different kinds of SSDs and showing cooperative behavior in the agents that act in them. == Autocurricula == An autocurriculum (plural: autocurricula) is a reinforcement learning concept that's salient in multi-agent experiments. As agents improve their performance, they change their environment; this change in the environment affects themselves and the other agents. The feedback loop results in several distinct phases of learning, each depending on the previous one. The stacked layers of learning are called an autocurriculum. Autocurricula are especially apparent in adversarial settings, where each group of agents is racing to counter the current strategy of the opposing group. The Hide and Seek game is an accessible example of an autocurriculum occurring in an adversarial setting. In this experiment, a team of seekers is competing against a team of hiders. Whenever one of the teams learns a new strategy, the opposing team adapts its strategy to give the best possible counter. When the hiders learn to use boxes to build a shelter, the seekers respond by learning to use a ramp to break into that shelter. The hiders respond by locking the ramps, making them unavailable for the seekers to use. The seekers then respond by "box surfing", exploiting a glitch in the game to penetrate the shelter. Each "level" of learning is an emergent phenomenon, with the previous level as its premise. This results in a stack of behaviors, each dependent on its predecessor. Autocurricula in reinforcement learning experiments are compared to the stages of the evolution of life on Earth and the development of human culture. A major stage in evolution happened 2-3 billion years ago, when photosynthesizing life forms started to produce massive amounts of oxygen, changing the balance of gases in the atmosphere. In the next stages of evolution, oxygen-breathing life forms evolved, eventually leading up to land mammals and human beings. These later stages could only happen after the photosynthesis stage made oxygen widely available. Similarly, human culture could not have gone through the Industrial Revolution in the 18th century without the resources and insights gaine
Neural field
In machine learning, a neural field (also known as implicit neural representation, neural implicit, or coordinate-based neural network), is a mathematical field that is fully or partially parametrized by a neural network. Initially developed to tackle visual computing tasks, such as rendering or reconstruction (e.g., neural radiance fields), neural fields emerged as a promising strategy to deal with a wider range of problems, including surrogate modelling of partial differential equations, such as in physics-informed neural networks. Differently from traditional machine learning algorithms, such as feed-forward neural networks, convolutional neural networks, or transformers, neural fields do not work with discrete data (e.g. sequences, images, tokens), but map continuous inputs (e.g., spatial coordinates, time) to continuous outputs (i.e., scalars, vectors, etc.). This makes neural fields not only discretization independent, but also easily differentiable. Moreover, dealing with continuous data allows for a significant reduction in space complexity, which translates to a much more lightweight network. == Formulation and training == According to the universal approximation theorem, provided adequate learning, sufficient number of hidden units, and the presence of a deterministic relationship between the input and the output, a neural network can approximate any function to any degree of accuracy. Hence, in mathematical terms, given a field y = Φ ( x ) {\textstyle {\boldsymbol {y}}=\Phi ({\boldsymbol {x}})} , with x ∈ R n {\displaystyle {\boldsymbol {x}}\in \mathbb {R} ^{n}} and y ∈ R m {\displaystyle {\boldsymbol {y}}\in \mathbb {R} ^{m}} , a neural field Ψ θ {\displaystyle \Psi _{\theta }} , with parameters θ {\displaystyle {\boldsymbol {\theta }}} , is such that: Ψ θ ( x ) = y ^ ≈ y {\displaystyle \Psi _{\theta }({\boldsymbol {x}})={\hat {\boldsymbol {y}}}\approx {\boldsymbol {y}}} === Training === For supervised tasks, given N {\displaystyle N} examples in the training dataset (i.e., ( x i , y i ) ∈ D t r a i n , i = 1 , … , N {\displaystyle ({\boldsymbol {x_{i}}},{\boldsymbol {y_{i}}})\in {\mathcal {D_{train}}},i=1,\dots ,N} ), the neural field parameters can be learned by minimizing a loss function L {\displaystyle {\mathcal {L}}} (e.g., mean squared error). The parameters θ ~ {\displaystyle {\tilde {\theta }}} that satisfy the optimization problem are found as: θ ~ = argmin θ 1 N ∑ ( x i , y i ) ∈ D t r a i n L ( Ψ θ ( x i ) , y i ) {\displaystyle {\tilde {\boldsymbol {\theta }}}={\underset {\boldsymbol {\theta }}{\text{argmin}}}\;{\frac {1}{N}}\sum _{({\boldsymbol {x_{i}}},{\boldsymbol {y_{i}}})\in {\mathcal {D_{train}}}}{\mathcal {L}}(\Psi _{\theta }({\boldsymbol {x}}_{i}),{\boldsymbol {y}}_{i})} Notably, it is not necessary to know the analytical expression of Φ {\displaystyle \Phi } , for the previously reported training procedure only requires input-output pairs. Indeed, a neural field is able to offer a continuous and differentiable surrogate of the true field, even from purely experimental data. Moreover, neural fields can be used in unsupervised settings, with training objectives that depend on the specific task. For example, physics-informed neural networks may be trained on just the residual. === Spectral bias === As for any artificial neural network, neural fields may be characterized by a spectral bias (i.e., the tendency to preferably learn the low frequency content of a field), possibly leading to a poor representation of the ground truth. In order to overcome this limitation, several strategies have been developed. For example, SIREN uses sinusoidal activations, while the Fourier-features approach embeds the input through sines and cosines. == Conditional neural fields == In many real-world cases, however, learning a single field is not enough. For example, when reconstructing 3D vehicle shapes from Lidar data, it is desirable to have a machine learning model that can work with arbitrary shapes (e.g., a car, a bicycle, a truck, etc.). The solution is to include additional parameters, the latent variables (or latent code) z ∈ R d {\displaystyle {\boldsymbol {z}}\in \mathbb {R} ^{d}} , to vary the field and adapt it to diverse tasks. === Latent code production === When dealing with conditional neural fields, the first design choice is represented by the way in which the latent code is produced. Specifically, two main strategies can be identified: Encoder: the latent code is the output of a second neural network, acting as an encoder. During training, the loss function is the objective used to learn the parameters of both the neural field and the encoder. Auto-decoding: each training example has its own latent code, jointly trained with the neural field parameters. When the model has to process new examples (i.e., not originally present in the training dataset), a small optimization problem is solved, keeping the network parameters fixed and only learning the new latent variables. Since the latter strategy requires additional optimization steps at inference time, it sacrifices speed, but keeps the overall model smaller. Moreover, despite being simpler to implement, an encoder may harm the generalization capabilities of the model. For example, when dealing with a physical scalar field f : R 2 → R {\displaystyle f:\mathbb {R} ^{2}\rightarrow \mathbb {R} } (e.g., the pressure of a 2D fluid), an auto-decoder-based conditional neural field can map a single point to the corresponding value of the field, following a learned latent code z {\displaystyle {\boldsymbol {z}}} . However, if the latent variables were produced by an encoder, it would require access to the entire set of points and corresponding values (e.g. as a regular grid or a mesh graph), leading to a less robust model. === Global and local conditioning === In a neural field with global conditioning, the latent code does not depend on the input and, hence, it offers a global representation (e.g., the overall shape of a vehicle). However, depending on the task, it may be more useful to divide the domain of x {\displaystyle {\boldsymbol {x}}} in several subdomains, and learn different latent codes for each of them (e.g., splitting a large and complex scene in sub-scenes for a more efficient rendering). This is called local conditioning. === Conditioning strategies === There are several strategies to include the conditioning information in the neural field. In the general mathematical framework, conditioning the neural field with the latent variables is equivalent to mapping them to a subset θ ∗ {\displaystyle {\boldsymbol {\theta }}^{}} of the neural field parameters: θ ∗ = Γ ( z ) {\displaystyle {\boldsymbol {\theta }}^{}=\Gamma ({\boldsymbol {z}})} In practice, notable strategies are: Concatenation: the neural field receives, as input, the concatenation of the original input x {\displaystyle {\boldsymbol {x}}} with the latent codes z {\displaystyle {\boldsymbol {z}}} . For feed-forward neural networks, this is equivalent to setting θ ∗ {\displaystyle {\boldsymbol {\theta }}^{}} as the bias of the first layer and Γ ( z ) {\displaystyle \Gamma ({\boldsymbol {z}})} as an affine transformation. Hypernetworks: a hypernetwork is a neural network that outputs the parameters of another neural network. Specifically, it consists of approximating Γ ( z ) {\displaystyle \Gamma ({\boldsymbol {z}})} with a neural network Γ ^ γ ( z ) {\displaystyle {\hat {\Gamma }}_{\gamma }({\boldsymbol {z}})} , where γ {\displaystyle {\boldsymbol {\gamma }}} are the trainable parameters of the hypernetwork. This approach is the most general, as it allows to learn the optimal mapping from latent codes to neural field parameters. However, hypernetworks are associated to larger computational and memory complexity, due to the large number of trainable parameters. Hence, leaner approaches have been developed. For example, in the Feature-wise Linear Modulation (FiLM), the hypernetwork only produces scale and bias coefficients for the neural field layers. === Meta-learning === Instead of relying on the latent code to adapt the neural field to a specific task, it is also possible to exploit gradient-based meta-learning. In this case, the neural field is seen as the specialization of an underlying meta-neural-field, whose parameters are modified to fit the specific task, through a few steps of gradient descent. An extension of this meta-learning framework is the CAVIA algorithm, that splits the trainable parameters in context-specific and shared groups, improving parallelization and interpretability, while reducing meta-overfitting. This strategy is similar to the auto-decoding conditional neural field, but the training procedure is substantially different. == Applications == Thanks to the possibility of efficiently modelling diverse mathematical fields with neural networks, neural fields have been applied to a wide range of problems: 3D scene reconstruction: neural fields can be used to model t
CLAWS (linguistics)
The Constituent Likelihood Automatic Word-tagging System (CLAWS) is a program that performs part-of-speech tagging. It was developed in the 1980s at Lancaster University by the University Centre for Computer Corpus Research on Language. It has an overall accuracy rate of 96–97% with the latest version (CLAWS4) tagging around 100 million words of the British National Corpus. == History == A Part-Of-Speech Tagger (POS Tagger) is a piece of software that reads text in some language and assigns parts of speech to each word (and other token), such as noun, verb, adjective, etc., although generally computational applications use more fine-grained POS tags like 'noun-plural'. Developed in the early 1980s, CLAWS was built to fill the ever-growing gap created by always-changing POS necessities. Originally created to add part-of-speech tags to the LOB corpus of British English, the CLAWS tagset has since been adapted to other languages as well, including Urdu and Arabic. Since its inception, CLAWS has been hailed for its functionality and adaptability. Still, it is not without flaws, and though it boasts an error-rate of only 1.5% when judged in major categories, CLAWS still remains with c.3.3% ambiguities unresolved. Ambiguity arises in cases such as with the word flies, and whether it should be classified as a noun or a verb. It's these ambiguities that will require the various upgrades and tagsets that CLAWS will endure. == Rules and processing == CLAWS uses a Hidden Markov model to determine the likelihood of sequences of words in anticipating each part-of-speech label. === Sample output === This excerpt from Bram Stoker's Dracula (1897) has been tagged using both the CLAWS C5 and C7 tagsets. This is what a CLAWS output will generally look like, with the most likely part-of-speech tag following each word. == Tagsets == === CLAWS1 tagset === The first tagset developed in CLAWS, CLAWS1 tagset, has 132 word tags. In terms of form and application, C1 tagset is similar to Brown Corpus tags. See Table of tags in C1 tagset here. === CLAWS2 tagset === From 1983 to 1986, updated versions leading to CLAWS2 were part of a larger attempt to deal with aspects such as recognizing sentence breaks, in order to avoid the need for manual pre-processing of a text before the tags were applied, moving instead to optional manual post-editing to adjust the output of the automatic annotation, if needed. The CLAWS2 tagset has 166 word tags. See Table of tags in C2 tagset here. === CLAWS4 tagset === The CLAWS4 was used for the 100-million-word British National Corpus (BNC). A general-purpose grammatical tagger, it is a successor of the CLAWS1 tagger. In tagging the BNC, the many rounds of work that went into CLAWS4 focused on making the CLAWS program independent from the tagsets. For example, the BNC project used two tagset versions: "a main tagset (C5) with 62 tags with which the whole of the corpus has been tagged, and a larger (C7) tagset with 152 tags, which has been used to make a selected 'core' sample corpus of two million words." The latest version of CLAWS4 is offered by UCREL, a research center of Lancaster University. === CLAWS5 tagset === The CLAWS5 tagset, which was used for BNC, has over 60 tags. See Table of tags in C5 tagset here. === CLAWS6 tagset === The CLAWS6 tagset was used for the BNC sampler corpus and the COLT corpus. It has over 160 tags, including 13 determiner subtypes. See Table of tags in C6 tagset here. === CLAWS7 tagset === The standard CLAWS7 tagset is used currently. It is only different in the punctuation tags when compared to the CLAWS6 tagset. See Table of tags in C7 tagset here. === CLAWS8 tagset === CLAWS8 tagset was extended from C7 tagset with further distinctions in the determiner and pronoun categories, as well as 37 new auxiliary tags for forms of be, do, and have. See Table of tags in C8 tagset here
Latent semantic analysis
Latent semantic analysis (LSA) is a technique in natural language processing, in particular distributional semantics, of analyzing relationships between a set of documents and the terms they contain by producing a set of concepts related to the documents and terms. LSA assumes that words that are close in meaning will occur in similar pieces of text (the distributional hypothesis). A matrix containing word counts per document (rows represent unique words and columns represent each document) is constructed from a large piece of text and a mathematical technique called singular value decomposition (SVD) is used to reduce the number of rows while preserving the similarity structure among columns. Documents are then compared by cosine similarity between any two columns. Values close to 1 represent very similar documents while values close to 0 represent very dissimilar documents. An information retrieval technique using latent semantic structure was patented in 1988 by Scott Deerwester, Susan Dumais, George Furnas, Richard Harshman, Thomas Landauer, Karen Lochbaum and Lynn Streeter. In the context of its application to information retrieval, it is sometimes called latent semantic indexing (LSI). == Overview == === Occurrence matrix === LSA can use a document-term matrix which describes the occurrences of terms in documents; it is a sparse matrix whose rows correspond to terms and whose columns correspond to documents. A typical example of the weighting of the elements of the matrix is tf-idf (term frequency–inverse document frequency): the weight of an element of the matrix is proportional to the number of times the terms appear in each document, where rare terms are upweighted to reflect their relative importance. This matrix is also common to standard semantic models, though it is not necessarily explicitly expressed as a matrix, since the mathematical properties of matrices are not always used. === Rank lowering === After the construction of the occurrence matrix, LSA finds a low-rank approximation to the term-document matrix. There could be various reasons for these approximations: The original term-document matrix is presumed too large for the computing resources; in this case, the approximated low rank matrix is interpreted as an approximation (a "least and necessary evil"). The original term-document matrix is presumed noisy: for example, anecdotal instances of terms are to be eliminated. From this point of view, the approximated matrix is interpreted as a de-noisified matrix (a better matrix than the original). The original term-document matrix is presumed overly sparse relative to the "true" term-document matrix. That is, the original matrix lists only the words actually in each document, whereas we might be interested in all words related to each document—generally a much larger set due to synonymy. The consequence of the rank lowering is that some dimensions are combined and depend on more than one term: {(car), (truck), (flower)} → {(1.3452 car + 0.2828 truck), (flower)} This mitigates the problem of identifying synonymy, as the rank lowering is expected to merge the dimensions associated with terms that have similar meanings. It also partially mitigates the problem with polysemy, since components of polysemous words that point in the "right" direction are added to the components of words that share a similar meaning. Conversely, components that point in other directions tend to either simply cancel out, or, at worst, to be smaller than components in the directions corresponding to the intended sense. === Derivation === Let X {\displaystyle X} be a matrix where element ( i , j ) {\displaystyle (i,j)} describes the occurrence of term i {\displaystyle i} in document j {\displaystyle j} (this can be, for example, the frequency). X {\displaystyle X} will look like this: d j ↓ t i T → [ x 1 , 1 … x 1 , j … x 1 , n ⋮ ⋱ ⋮ ⋱ ⋮ x i , 1 … x i , j … x i , n ⋮ ⋱ ⋮ ⋱ ⋮ x m , 1 … x m , j … x m , n ] {\displaystyle {\begin{matrix}&{\textbf {d}}_{j}\\&\downarrow \\{\textbf {t}}_{i}^{T}\rightarrow &{\begin{bmatrix}x_{1,1}&\dots &x_{1,j}&\dots &x_{1,n}\\\vdots &\ddots &\vdots &\ddots &\vdots \\x_{i,1}&\dots &x_{i,j}&\dots &x_{i,n}\\\vdots &\ddots &\vdots &\ddots &\vdots \\x_{m,1}&\dots &x_{m,j}&\dots &x_{m,n}\\\end{bmatrix}}\end{matrix}}} Now a row in this matrix will be a vector corresponding to a term, giving its relation to each document: t i T = [ x i , 1 … x i , j … x i , n ] {\displaystyle {\textbf {t}}_{i}^{T}={\begin{bmatrix}x_{i,1}&\dots &x_{i,j}&\dots &x_{i,n}\end{bmatrix}}} Likewise, a column in this matrix will be a vector corresponding to a document, giving its relation to each term: d j = [ x 1 , j ⋮ x i , j ⋮ x m , j ] {\displaystyle {\textbf {d}}_{j}={\begin{bmatrix}x_{1,j}\\\vdots \\x_{i,j}\\\vdots \\x_{m,j}\\\end{bmatrix}}} Now the dot product t i T t p {\displaystyle {\textbf {t}}_{i}^{T}{\textbf {t}}_{p}} between two term vectors gives the correlation between the terms over the set of documents. The matrix product X X T {\displaystyle XX^{T}} contains all these dot products. Element ( i , p ) {\displaystyle (i,p)} (which is equal to element ( p , i ) {\displaystyle (p,i)} ) contains the dot product t i T t p {\displaystyle {\textbf {t}}_{i}^{T}{\textbf {t}}_{p}} ( = t p T t i {\displaystyle ={\textbf {t}}_{p}^{T}{\textbf {t}}_{i}} ). Likewise, the matrix X T X {\displaystyle X^{T}X} contains the dot products between all the document vectors, giving their correlation over the terms: d j T d q = d q T d j {\displaystyle {\textbf {d}}_{j}^{T}{\textbf {d}}_{q}={\textbf {d}}_{q}^{T}{\textbf {d}}_{j}} . Now, from the theory of linear algebra, there exists a decomposition of X {\displaystyle X} such that U {\displaystyle U} and V {\displaystyle V} are orthogonal matrices and Σ {\displaystyle \Sigma } is a diagonal matrix. This is called a singular value decomposition (SVD): X = U Σ V T {\displaystyle {\begin{matrix}X=U\Sigma V^{T}\end{matrix}}} The matrix products giving us the term and document correlations then become X X T = ( U Σ V T ) ( U Σ V T ) T = ( U Σ V T ) ( V T T Σ T U T ) = U Σ V T V Σ T U T = U Σ Σ T U T X T X = ( U Σ V T ) T ( U Σ V T ) = ( V T T Σ T U T ) ( U Σ V T ) = V Σ T U T U Σ V T = V Σ T Σ V T {\displaystyle {\begin{matrix}XX^{T}&=&(U\Sigma V^{T})(U\Sigma V^{T})^{T}=(U\Sigma V^{T})(V^{T^{T}}\Sigma ^{T}U^{T})=U\Sigma V^{T}V\Sigma ^{T}U^{T}=U\Sigma \Sigma ^{T}U^{T}\\X^{T}X&=&(U\Sigma V^{T})^{T}(U\Sigma V^{T})=(V^{T^{T}}\Sigma ^{T}U^{T})(U\Sigma V^{T})=V\Sigma ^{T}U^{T}U\Sigma V^{T}=V\Sigma ^{T}\Sigma V^{T}\end{matrix}}} Since Σ Σ T {\displaystyle \Sigma \Sigma ^{T}} and Σ T Σ {\displaystyle \Sigma ^{T}\Sigma } are diagonal we see that U {\displaystyle U} must contain the eigenvectors of X X T {\displaystyle XX^{T}} , while V {\displaystyle V} must be the eigenvectors of X T X {\displaystyle X^{T}X} . Both products have the same non-zero eigenvalues, given by the non-zero entries of Σ Σ T {\displaystyle \Sigma \Sigma ^{T}} , or equally, by the non-zero entries of Σ T Σ {\displaystyle \Sigma ^{T}\Sigma } . Now the decomposition looks like this: X U Σ V T ( d j ) ( d ^ j ) ↓ ↓ ( t i T ) → [ x 1 , 1 … x 1 , j … x 1 , n ⋮ ⋱ ⋮ ⋱ ⋮ x i , 1 … x i , j … x i , n ⋮ ⋱ ⋮ ⋱ ⋮ x m , 1 … x m , j … x m , n ] = ( t ^ i T ) → [ [ u 1 ] … [ u l ] ] ⋅ [ σ 1 … 0 ⋮ ⋱ ⋮ 0 … σ l ] ⋅ [ [ v 1 ] ⋮ [ v l ] ] {\displaystyle {\begin{matrix}&X&&&U&&\Sigma &&V^{T}\\&({\textbf {d}}_{j})&&&&&&&({\hat {\textbf {d}}}_{j})\\&\downarrow &&&&&&&\downarrow \\({\textbf {t}}_{i}^{T})\rightarrow &{\begin{bmatrix}x_{1,1}&\dots &x_{1,j}&\dots &x_{1,n}\\\vdots &\ddots &\vdots &\ddots &\vdots \\x_{i,1}&\dots &x_{i,j}&\dots &x_{i,n}\\\vdots &\ddots &\vdots &\ddots &\vdots \\x_{m,1}&\dots &x_{m,j}&\dots &x_{m,n}\\\end{bmatrix}}&=&({\hat {\textbf {t}}}_{i}^{T})\rightarrow &{\begin{bmatrix}{\begin{bmatrix}\,\\\,\\{\textbf {u}}_{1}\\\,\\\,\end{bmatrix}}\dots {\begin{bmatrix}\,\\\,\\{\textbf {u}}_{l}\\\,\\\,\end{bmatrix}}\end{bmatrix}}&\cdot &{\begin{bmatrix}\sigma _{1}&\dots &0\\\vdots &\ddots &\vdots \\0&\dots &\sigma _{l}\\\end{bmatrix}}&\cdot &{\begin{bmatrix}{\begin{bmatrix}&&{\textbf {v}}_{1}&&\end{bmatrix}}\\\vdots \\{\begin{bmatrix}&&{\textbf {v}}_{l}&&\end{bmatrix}}\end{bmatrix}}\end{matrix}}} The values σ 1 , … , σ l {\displaystyle \sigma _{1},\dots ,\sigma _{l}} are called the singular values, and u 1 , … , u l {\displaystyle u_{1},\dots ,u_{l}} and v 1 , … , v l {\displaystyle v_{1},\dots ,v_{l}} the left and right singular vectors. Notice the only part of U {\displaystyle U} that contributes to t i {\displaystyle {\textbf {t}}_{i}} is the i 'th {\displaystyle i{\textrm {'th}}} row. Let this row vector be called t ^ i T {\displaystyle {\hat {\textrm {t}}}_{i}^{T}} . Likewise, the only part of V T {\displaystyle V^{T}} that contributes to d j {\displaystyle {\textbf {d}}_{j}} is the j 'th {\displaystyle j{\textrm {'th}}} column, d ^ j {\displaystyle {\hat {\textrm {d}}}_{j}} . These are not the eigenvectors, but depend on all the eigenvectors. I
Eigenmoments
EigenMoments is a set of orthogonal, noise robust, invariant to rotation, scaling and translation and distribution sensitive moments. Their application can be found in signal processing and computer vision as descriptors of the signal or image. The descriptors can later be used for classification purposes. It is obtained by performing orthogonalization, via eigen analysis on geometric moments. == Framework summary == EigenMoments are computed by performing eigen analysis on the moment space of an image by maximizing signal-to-noise ratio in the feature space in form of Rayleigh quotient. This approach has several benefits in Image processing applications: Dependency of moments in the moment space on the distribution of the images being transformed, ensures decorrelation of the final feature space after eigen analysis on the moment space. The ability of EigenMoments to take into account distribution of the image makes it more versatile and adaptable for different genres. Generated moment kernels are orthogonal and therefore analysis on the moment space becomes easier. Transformation with orthogonal moment kernels into moment space is analogous to projection of the image onto a number of orthogonal axes. Nosiy components can be removed. This makes EigenMoments robust for classification applications. Optimal information compaction can be obtained and therefore a few number of moments are needed to characterize the images. == Problem formulation == Assume that a signal vector s ∈ R n {\displaystyle s\in {\mathcal {R}}^{n}} is taken from a certain distribution having correlation C ∈ R n × n {\displaystyle C\in {\mathcal {R}}^{n\times n}} , i.e. C = E [ s s T ] {\displaystyle C=E[ss^{T}]} where E[.] denotes expected value. Dimension of signal space, n, is often too large to be useful for practical application such as pattern classification, we need to transform the signal space into a space with lower dimensionality. This is performed by a two-step linear transformation: q = W T X T s , {\displaystyle q=W^{T}X^{T}s,} where q = [ q 1 , . . . , q n ] T ∈ R k {\displaystyle q=[q_{1},...,q_{n}]^{T}\in {\mathcal {R}}^{k}} is the transformed signal, X = [ x 1 , . . . , x n ] T ∈ R n × m {\displaystyle X=[x_{1},...,x_{n}]^{T}\in {\mathcal {R}}^{n\times m}} a fixed transformation matrix which transforms the signal into the moment space, and W = [ w 1 , . . . , w n ] T ∈ R m × k {\displaystyle W=[w_{1},...,w_{n}]^{T}\in {\mathcal {R}}^{m\times k}} the transformation matrix which we are going to determine by maximizing the SNR of the feature space resided by q {\displaystyle q} . For the case of Geometric Moments, X would be the monomials. If m = k = n {\displaystyle m=k=n} , a full rank transformation would result, however usually we have m ≤ n {\displaystyle m\leq n} and k ≤ m {\displaystyle k\leq m} . This is specially the case when n {\displaystyle n} is of high dimensions. Finding W {\displaystyle W} that maximizes the SNR of the feature space: S N R t r a n s f o r m = w T X T C X w w T X T N X w , {\displaystyle SNR_{transform}={\frac {w^{T}X^{T}CXw}{w^{T}X^{T}NXw}},} where N is the correlation matrix of the noise signal. The problem can thus be formulated as w 1 , . . . , w k = a r g m a x w w T X T C X w w T X T N X w {\displaystyle {w_{1},...,w_{k}}=argmax_{w}{\frac {w^{T}X^{T}CXw}{w^{T}X^{T}NXw}}} subject to constraints: w i T X T N X w j = δ i j , {\displaystyle w_{i}^{T}X^{T}NXw_{j}=\delta _{ij},} where δ i j {\displaystyle \delta _{ij}} is the Kronecker delta. It can be observed that this maximization is Rayleigh quotient by letting A = X T C X {\displaystyle A=X^{T}CX} and B = X T N X {\displaystyle B=X^{T}NX} and therefore can be written as: w 1 , . . . , w k = a r g m a x x w T A w w T B w {\displaystyle {w_{1},...,w_{k}}={\underset {x}{\operatorname {arg\,max} }}{\frac {w^{T}Aw}{w^{T}Bw}}} , w i T B w j = δ i j {\displaystyle w_{i}^{T}Bw_{j}=\delta _{ij}} === Rayleigh quotient === Optimization of Rayleigh quotient has the form: max w R ( w ) = max w w T A w w T B w {\displaystyle \max _{w}R(w)=\max _{w}{\frac {w^{T}Aw}{w^{T}Bw}}} and A {\displaystyle A} and B {\displaystyle B} , both are symmetric and B {\displaystyle B} is positive definite and therefore invertible. Scaling w {\displaystyle w} does not change the value of the object function and hence and additional scalar constraint w T B w = 1 {\displaystyle w^{T}Bw=1} can be imposed on w {\displaystyle w} and no solution would be lost when the objective function is optimized. This constraint optimization problem can be solved using Lagrangian multiplier: max w w T A w {\displaystyle \max _{w}{w^{T}Aw}} subject to w T B w = 1 {\displaystyle {w^{T}Bw}=1} max w L ( w ) = max w ( w T A w − λ w T B w ) {\displaystyle \max _{w}{\mathcal {L}}(w)=\max _{w}(w{T}Aw-\lambda w^{T}Bw)} equating first derivative to zero and we will have: A w = λ B w {\displaystyle Aw=\lambda Bw} which is an instance of Generalized Eigenvalue Problem (GEP). The GEP has the form: A w = λ B w {\displaystyle Aw=\lambda Bw} for any pair ( w , λ ) {\displaystyle (w,\lambda )} that is a solution to above equation, w {\displaystyle w} is called a generalized eigenvector and λ {\displaystyle \lambda } is called a generalized eigenvalue. Finding w {\displaystyle w} and λ {\displaystyle \lambda } that satisfies this equations would produce the result which optimizes Rayleigh quotient. One way of maximizing Rayleigh quotient is through solving the Generalized Eigen Problem. Dimension reduction can be performed by simply choosing the first components w i {\displaystyle w_{i}} , i = 1 , . . . , k {\displaystyle i=1,...,k} , with the highest values for R ( w ) {\displaystyle R(w)} out of the m {\displaystyle m} components, and discard the rest. Interpretation of this transformation is rotating and scaling the moment space, transforming it into a feature space with maximized SNR and therefore, the first k {\displaystyle k} components are the components with highest k {\displaystyle k} SNR values. The other method to look at this solution is to use the concept of simultaneous diagonalization instead of Generalized Eigen Problem. === Simultaneous diagonalization === Let A = X T C X {\displaystyle A=X^{T}CX} and B = X T N X {\displaystyle B=X^{T}NX} as mentioned earlier. We can write W {\displaystyle W} as two separate transformation matrices: W = W 1 W 2 . {\displaystyle W=W_{1}W_{2}.} W 1 {\displaystyle W_{1}} can be found by first diagonalize B: P T B P = D B {\displaystyle P^{T}BP=D_{B}} . Where D B {\displaystyle D_{B}} is a diagonal matrix sorted in increasing order. Since B {\displaystyle B} is positive definite, thus D B > 0 {\displaystyle D_{B}>0} . We can discard those eigenvalues that large and retain those close to 0, since this means the energy of the noise is close to 0 in this space, at this stage it is also possible to discard those eigenvectors that have large eigenvalues. Let P ^ {\displaystyle {\hat {P}}} be the first k {\displaystyle k} columns of P {\displaystyle P} , now P T ^ B P ^ = D B ^ {\displaystyle {\hat {P^{T}}}B{\hat {P}}={\hat {D_{B}}}} where D B ^ {\displaystyle {\hat {D_{B}}}} is the k × k {\displaystyle k\times k} principal submatrix of D B {\displaystyle D_{B}} . Let W 1 = P ^ D B ^ − 1 / 2 {\displaystyle W_{1}={\hat {P}}{\hat {D_{B}}}^{-1/2}} and hence: W 1 T B W 1 = ( P ^ D B ^ − 1 / 2 ) T B ( P ^ D B ^ − 1 / 2 ) = I {\displaystyle W_{1}^{T}BW_{1}=({\hat {P}}{\hat {D_{B}}}^{-1/2})^{T}B({\hat {P}}{\hat {D_{B}}}^{-1/2})=I} . W 1 {\displaystyle W_{1}} whiten B {\displaystyle B} and reduces the dimensionality from m {\displaystyle m} to k {\displaystyle k} . The transformed space resided by q ′ = W 1 T X T s {\displaystyle q'=W_{1}^{T}X^{T}s} is called the noise space. Then, we diagonalize W 1 T A W 1 {\displaystyle W_{1}^{T}AW_{1}} : W 2 T W 1 T A W 1 W 2 = D A {\displaystyle W_{2}^{T}W_{1}^{T}AW_{1}W_{2}=D_{A}} , where W 2 T W 2 = I {\displaystyle W_{2}^{T}W_{2}=I} . D A {\displaystyle D_{A}} is the matrix with eigenvalues of W 1 T A W 1 {\displaystyle W_{1}^{T}AW_{1}} on its diagonal. We may retain all the eigenvalues and their corresponding eigenvectors since most of the noise are already discarded in previous step. Finally the transformation is given by: W = W 1 W 2 {\displaystyle W=W_{1}W_{2}} where W {\displaystyle W} diagonalizes both the numerator and denominator of the SNR, W T A W = D A {\displaystyle W^{T}AW=D_{A}} , W T B W = I {\displaystyle W^{T}BW=I} and the transformation of signal s {\displaystyle s} is defined as q = W T X T s = W 2 T W 1 T X T s {\displaystyle q=W^{T}X^{T}s=W_{2}^{T}W_{1}^{T}X^{T}s} . === Information loss === To find the information loss when we discard some of the eigenvalues and eigenvectors we can perform following analysis: η = 1 − t r a c e ( W 1 T A W 1 ) t r a c e ( D B − 1 / 2 P T A P D B − 1 / 2 ) = 1 − t r a c e ( D B ^ − 1 / 2 P ^ T A P ^ D B ^ − 1 / 2 ) t r a c e ( D B − 1 / 2 P T A P D B − 1 / 2 ) {\displaystyle {\begin{array}{lll}\eta &=&
XLNet
The XLNet was an autoregressive Transformer designed as an improvement over BERT, with 340M parameters and trained on 33 billion words. It was released on 19 June 2019, under the Apache 2.0 license. It achieved state-of-the-art results on a variety of natural language processing tasks, including language modeling, question answering, and natural language inference. == Architecture == The main idea of XLNet is to model language autoregressively like the GPT models, but allow for all possible permutations of a sentence. Concretely, consider the following sentence:My dog is cute.In standard autoregressive language modeling, the model would be tasked with predicting the probability of each word, conditioned on the previous words as its context: We factorize the joint probability of a sequence of words x 1 , … , x T {\displaystyle x_{1},\ldots ,x_{T}} using the chain rule: Pr ( x 1 , … , x T ) = Pr ( x 1 ) Pr ( x 2 | x 1 ) Pr ( x 3 | x 1 , x 2 ) … Pr ( x T | x 1 , … , x T − 1 ) . {\displaystyle \Pr(x_{1},\ldots ,x_{T})=\Pr(x_{1})\Pr(x_{2}|x_{1})\Pr(x_{3}|x_{1},x_{2})\ldots \Pr(x_{T}|x_{1},\ldots ,x_{T-1}).} For example, the sentence "My dog is cute" is factorized as: Pr ( My , dog , is , cute ) = Pr ( My ) Pr ( dog | My ) Pr ( is | My , dog ) Pr ( cute | My , dog , is ) . {\displaystyle \Pr({\text{My}},{\text{dog}},{\text{is}},{\text{cute}})=\Pr({\text{My}})\Pr({\text{dog}}|{\text{My}})\Pr({\text{is}}|{\text{My}},{\text{dog}})\Pr({\text{cute}}|{\text{My}},{\text{dog}},{\text{is}}).} Schematically, we can write it as