Jürgen Schmidhuber (born 17 January 1963) is a German computer scientist noted for his work in the field of artificial intelligence, specifically artificial neural networks. He has been described by media outlets as a leading pioneer of modern artificial intelligence. He is a scientific director of the Dalle Molle Institute for Artificial Intelligence Research in Switzerland. He is also director of the Artificial Intelligence Initiative and professor of the Computer Science program in the Computer, Electrical, and Mathematical Sciences and Engineering (CEMSE) division at the King Abdullah University of Science and Technology (KAUST) in Saudi Arabia. He is best known for his work on long short-term memory (LSTM), a type of neural network architecture which was the dominant technique for various natural language processing tasks in research and commercial applications in the 2010s. He also introduced principles of dynamic neural networks, meta-learning, generative adversarial networks and linear transformers, all of which are widespread in modern AI. == Career == Schmidhuber completed his undergraduate (1987) and PhD (1991) studies at the Technical University of Munich in Munich, Germany. His PhD advisors were Wilfried Brauer and Klaus Schulten. He taught there from 2004 until 2009. From 2009 to 2021, he was a professor of artificial intelligence at the Università della Svizzera Italiana in Lugano, Switzerland. He has served as the director of Dalle Molle Institute for Artificial Intelligence Research (IDSIA), a Swiss AI lab, since 1995. Since 2021, he has also been the director of the AI Initiative at the King Abdullah University of Science and Technology (KAUST). In 2014, Schmidhuber formed a company, NNAISENSE, to work on commercial applications of artificial intelligence in fields such as finance, heavy industry and self-driving cars. Sepp Hochreiter, Jaan Tallinn, and Marcus Hutter are advisers to the company. Sales were under US$11 million in 2016; however, Schmidhuber states that the current emphasis is on research and not revenue. NNAISENSE raised its first round of capital funding in January 2017. Schmidhuber's overall goal is to create an all-purpose AI by training a single AI in sequence on a variety of narrow tasks, but as of 2026 he has said that the focus of NNAISENSE has shifted from artificial general intelligence to asset management. == Research == In the 1980s, backpropagation did not work well for deep learning with long credit assignment paths in artificial neural networks. To overcome this problem, Schmidhuber (1991) proposed a hierarchy of recurrent neural networks (RNNs) pre-trained one level at a time by self-supervised learning. It uses predictive coding to learn internal representations at multiple self-organizing time scales, facilitating downstream deep learning. The RNN hierarchy can be collapsed into a single RNN, by distilling a higher level chunker network into a lower level automatizer network. In 1993, a chunker solved a deep learning task whose depth exceeded 1000. In 1991, Schmidhuber published adversarial neural networks that contest with each other in the form of a zero-sum game, where one network's gain is the other network's loss. The first network is a generative model that models a probability distribution over output patterns. The second network learns by gradient descent to predict the reactions of the environment to these patterns. This was called "artificial curiosity". In 2014, this principle was used in the creation of the generative adversarial network, which Schmidhuber describes as a special case of artificial curiosity where the environmental reaction is 1 or 0 depending on whether the first network's output is in a given set. Schmidhuber supervised the 1991 diploma thesis of his student Sepp Hochreiter which he considered "one of the most important documents in the history of machine learning". It studied the neural history compressor and analyzed and overcame the vanishing gradient problem. This led to the creation of long short-term memory (LSTM), a type of recurrent neural network. The name LSTM was introduced in a tech report in 1995, leading to the most cited LSTM publication, published in 1997 and co-authored by Hochreiter and Schmidhuber. The standard LSTM architecture was introduced in 2000 by Felix Gers, Schmidhuber, and Fred Cummins. Today's "vanilla LSTM" using backpropagation through time was published with his student Alex Graves in 2005, and its connectionist temporal classification (CTC) training algorithm in 2006. CTC was applied to end-to-end speech recognition with LSTM. In 2014, the state of the art was training “very deep neural network” with 20 to 30 layers. Stacking too many layers led to a steep reduction in training accuracy, known as the "degradation" problem. In May 2015, Rupesh Kumar Srivastava, Klaus Greff, and Schmidhuber used LSTM principles to create the highway network, a feedforward neural network with hundreds of layers, much deeper than previous networks. In Dec 2015, the residual neural network (ResNet) was published, which is a variant of the highway network. In 1992, Schmidhuber published fast weights programmer, an alternative to recurrent neural networks. It has a slow feedforward neural network that learns by gradient descent to control the fast weights of another neural network through outer products of self-generated activation patterns, and the fast weights network itself operates over inputs. This was later shown to be equivalent to the unnormalized linear transformer. In 2011, Schmidhuber's team at IDSIA with his postdoc Dan Ciresan also achieved dramatic speedups of convolutional neural networks (CNNs) using graphics processing units (GPUs), based on CNN designs introduced much earlier by Kunihiko Fukushima. An earlier CNN on GPU by Chellapilla et al. (2006) was 4 times faster than an equivalent implementation on CPU. The deep CNN of Dan Ciresan et al. (2011) at IDSIA was 60 times faster and achieved the first superhuman performance in a computer vision contest in August 2011. Between 15 May 2011 and 10 September 2012, these CNNs won four more image competitions and improved the state of the art on multiple image benchmarks. The approach has become central to the field of computer vision. == Credit disputes == Schmidhuber has controversially argued that he and other researchers have been denied adequate recognition for their contribution to the field of deep learning, in favour of Geoffrey Hinton, Yoshua Bengio and Yann LeCun, who shared the 2018 Turing Award for their work in deep learning. He wrote a "scathing" 2015 article arguing that Hinton, Bengio and LeCun "heavily cite each other" but "fail to credit the pioneers of the field". In a statement to the New York Times, Yann LeCun wrote that "Jürgen is manically obsessed with recognition and keeps claiming credit he doesn't deserve for many, many things... It causes him to systematically stand up at the end of every talk and claim credit for what was just presented, generally not in a justified manner." Schmidhuber replied that LeCun did this "without any justification, without providing a single example", and published details of numerous priority disputes with Hinton, Bengio and LeCun. The term "schmidhubered" has been jokingly used in the AI community to describe Schmidhuber's habit of publicly challenging the originality of other researchers' work, a practice seen by some in the AI community as a "rite of passage" for young researchers. Some suggest that Schmidhuber's significant accomplishments have been underappreciated due to his confrontational personality. == Recognition == Schmidhuber received the Helmholtz Award of the International Neural Network Society in 2013, and the Neural Networks Pioneer Award of the IEEE Computational Intelligence Society in 2016 for "pioneering contributions to deep learning and neural networks." He is a member of the European Academy of Sciences and Arts. He has been referred to as the "father of modern AI", the "father of generative AI", and the "father of deep learning". Schmidhuber himself, however, has called Alexey Grigorevich Ivakhnenko the "father of deep learning", and gives credit to many even earlier AI pioneers. The New York Times ran a profile under the headline "When A.I. Matures, It May Call Jürgen Schmidhuber 'Dad'", highlighting his early work on deep learning and his long‑term vision for self‑improving AI. == Views == Schmidhuber is a proponent of open source AI, and believes that they will become competitive against commercial closed-source AI. Since the 1970s, Schmidhuber wanted to create "intelligent machines that could learn and improve on their own and become smarter than him within his lifetime." He differentiates between two types of AIs: tool AI, such as those for improving healthcare, and autonomous AIs that set their own goals, perform their own research, and explore the universe. He has worked on both types for de
Common data model
A common data model (CDM) can refer to any standardised data model which allows for data and information exchange between different applications and data sources. Common data models aim to standardise logical infrastructure so that related applications can "operate on and share the same data", and can be seen as a way to "organize data from many sources that are in different formats into a standard structure". A common data model has been described as one of the components of a "strong information system". A standardised common data model has also been described as a typical component of a well designed agile application besides a common communication protocol. Providing a single common data model within an organisation is one of the typical tasks of a data warehouse. == Examples of common data models == === Border crossings === X-trans.eu was a cross-border pilot project between the Free State of Bavaria (Germany) and Upper Austria with the aim of developing a faster procedure for the application and approval of cross-border large-capacity transports. The portal was based on a common data model that contained all the information required for approval. === Climate data === The Climate Data Store Common Data Model is a common data model set up by the Copernicus Climate Change Service for harmonising essential climate variables from different sources and data providers. === General information technology === Within service-oriented architecture, S-RAMP is a specification released by HP, IBM, Software AG, TIBCO, and Red Hat which defines a common data model for SOA repositories as well as an interaction protocol to facilitate the use of common tooling and sharing of data. Content Management Interoperability Services (CMIS) is an open standard for inter-operation of different content management systems over the internet, and provides a common data model for typed files and folders used with version control. The NetCDF software libraries for array-oriented scientific data implements a common data model called the NetCDF Java common data model, which consists of three layers built on top of each other to add successively richer semantics. === Health === Within genomic and medical data, the Observational Medical Outcomes Partnership (OMOP) research program established under the U.S. National Institutes of Health has created a common data model for claims and electronic health records which can accommodate data from different sources around the world. PCORnet, which was developed by the Patient-Centered Outcomes Research Institute, is another common data model for health data including electronic health records and patient claims. The Sentinel Common Data Model was initially started as Mini-Sentinel in 2008. It is used by the Sentinel Initiative of the USA's Food and Drug Administration. The Generalized Data Model was first published in 2019. It was designed to be a stand-alone data model as well as to allow for further transformation into other data models (e.g., OMOP, PCORNet, Sentinel). It has a hierarchical structure to flexibly capture relationships among data elements. The JANUS clinical trial data repository also provides a common data model which is based on the SDTM standard to represent clinical data submitted to regulatory agencies, such as tabulation datasets, patient profiles, listings, etc. === Logistics === SX000i is a specification developed jointly by the Aerospace and Defence Industries Association of Europe (ASD) and the American Aerospace Industries Association (AIA) to provide information, guidance and instructions to ensure compatibility and the commonality. The associated SX002D specification contains a common data model. === Microsoft Common Data Model === The Microsoft Common Data Model is a collection of many standardised extensible data schemas with entities, attributes, semantic metadata, and relationships, which represent commonly used concepts and activities in various businesses areas. It is maintained by Microsoft and its partners, and is published on GitHub. Microsoft's Common Data Model is used amongst others in Microsoft Dataverse and with various Microsoft Power Platform and Microsoft Dynamics 365 services. === Rail transport === RailTopoModel is a common data model for the railway sector. === Other === There are many more examples of various common data models for different uses published by different sources.
International Conference on Acoustics, Speech, and Signal Processing
ICASSP, the International Conference on Acoustics, Speech, and Signal Processing, is an annual flagship conference organized by IEEE Signal Processing Society. Ei Compendex has indexed all papers included in its proceedings. The first ICASSP was held in 1976 in Philadelphia, Pennsylvania, based on the success of a conference in Massachusetts four years earlier that had focused specifically on speech signals. As ranked by Google Scholar's h-index metric in 2016, ICASSP has the highest h-index of any conference in the Signal Processing field. The Brazilian ministry of education gave the conference an 'A1' rating based on its h-index. == Conference list ==
Pruning (artificial neural network)
In deep learning, pruning is the practice of removing parameters from an existing artificial neural network. The goal of this process is to reduce the size (parameter count) of the neural network (and therefore the computational resources required to run it) whilst maintaining accuracy. This can be compared to the biological process of synaptic pruning which takes place in mammalian brains during development. == Node (neuron) pruning == A basic algorithm for pruning is as follows: Evaluate the importance of each neuron. Rank the neurons according to their importance (assuming there is a clearly defined measure for "importance"). Remove the least important neuron. Check a termination condition (to be determined by the user) to see whether to continue pruning. == Edge (weight) pruning == Most work on neural network pruning does not remove full neurons or layers (structured pruning). Instead, it focuses on removing the most insignificant weights (unstructured pruning), namely, setting their values to zero. This can either be done globally by comparing weights from all layers in the network or locally by comparing weights in each layer separately. Different metrics can be used to measure the importance of each weight. Weight magnitude as well as combinations of weight and gradient information are commonly used metrics. Early work suggested also to change the values of non-pruned weights. == When to prune the neural network? == Pruning can be applied at three different stages: before training, during training, or after training. When pruning is performed during or after training, additional fine-tuning epochs are typically required. Each approach involves different trade-offs between accuracy and computational cost.
Multiclass classification
In machine learning and statistical classification, multiclass classification or multinomial classification is the problem of classifying instances into one of three or more classes (classifying instances into one of two classes is called binary classification). For example, deciding on whether an image is showing a banana, peach, orange, or an apple is a multiclass classification problem, with four possible classes (banana, peach, orange, apple), while deciding on whether an image contains an apple or not is a binary classification problem (with the two possible classes being: apple, no apple). While many classification algorithms (e.g., decision trees, k-NN, neural networks and multinomial logistic regression) naturally permit the use of more than two classes, some are by nature binary algorithms (e.g., classical binary support vector machine) and require decomposition strategies such as one-vs-all, one-vs-one, or ECOC to solve multiclass problems. Multiclass classification should not be confused with multi-label classification, where multiple labels are to be predicted for each instance (e.g., predicting that an image contains both an apple and an orange, in the previous example). == Better-than-random multiclass models == From the confusion matrix of a multiclass model, we can determine whether a model does better than chance. Let K ≥ 3 {\displaystyle K\geq 3} be the number of classes, O {\displaystyle {\mathcal {O}}} a set of observations, y ^ : O → { 1 , . . . , K } {\displaystyle {\hat {y}}:{\mathcal {O}}\to \{1,...,K\}} a model of the target variable y : O → { 1 , . . . , K } {\displaystyle y:{\mathcal {O}}\to \{1,...,K\}} and n i , j {\displaystyle n_{i,j}} be the number of observations in the set { y = i } ∩ { y ^ = j } {\displaystyle \{y=i\}\cap \{{\hat {y}}=j\}} . We note n i . = ∑ j n i , j {\displaystyle n_{i.}=\sum _{j}n_{i,j}} , n . j = ∑ i n i , j {\displaystyle n_{.j}=\sum _{i}n_{i,j}} , n = ∑ j n . j = ∑ i n i . {\displaystyle n=\sum _{j}n_{.j}=\sum _{i}n_{i.}} , λ i = n i . n {\displaystyle \lambda _{i}={\frac {n_{i.}}{n}}} and μ j = n . j n {\displaystyle \mu _{j}={\frac {n_{.j}}{n}}} . It is assumed that the confusion matrix ( n i , j ) i , j {\displaystyle (n_{i,j})_{i,j}} contains at least one non-zero entry in each row, that is λ i > 0 {\displaystyle \lambda _{i}>0} for any i {\displaystyle i} . Finally we call "normalized confusion matrix" the matrix of conditional probabilities ( P ( y ^ = j ∣ y = i ) ) i , j = ( n i , j n i . ) i , j {\displaystyle (\mathbb {P} ({\hat {y}}=j\mid y=i))_{i,j}=\left({\frac {n_{i,j}}{n_{i.}}}\right)_{i,j}} . === Intuitive explanation === The lift is a way of measuring the deviation from independence of two events A {\displaystyle A} and B {\displaystyle B} : L i f t ( A , B ) = P ( A ∩ B ) P ( A ) P ( B ) = P ( A ∣ B ) P ( A ) = P ( B ∣ A ) P ( B ) {\displaystyle \mathrm {Lift} (A,B)={\frac {\mathbb {P} (A\cap B)}{\mathbb {P} (A)\mathbb {P} (B)}}={\frac {\mathbb {P} (A\mid B)}{\mathbb {P} (A)}}={\frac {\mathbb {P} (B\mid A)}{\mathbb {P} (B)}}} We have L i f t ( A , B ) > 1 {\displaystyle \mathrm {Lift} (A,B)>1} if and only if events A {\displaystyle A} and B {\displaystyle B} occur simultaneously with a greater probability than if they were independent. In other words, if one of the two events occurs, the probability of observing the other event increases. A first condition to satisfy is to have L i f t ( y = i , y ^ = i ) ≥ 1 {\displaystyle \mathrm {Lift} (y=i,{\hat {y}}=i)\geq 1} for any i {\displaystyle i} . And the quality of a model (better or worse than chance) does not change if we over- or undersample the dataset, that is if we multiply each row R i {\displaystyle R_{i}} of the confusion matrix by a constant c i {\displaystyle c_{i}} . Thus the second condition is that the necessary and sufficient conditions for doing better than chance need only depend on the normalized confusion matrix. The condition on lifts can be reformulated with One versus Rest binary models : for any i {\displaystyle i} , we define the binary target variable y i {\displaystyle y_{i}} which is the indicator of event { y = i } {\displaystyle \{y=i\}} , and the binary model y ^ i {\displaystyle {\hat {y}}_{i}} of y i {\displaystyle y_{i}} which is the indicator of event { y ^ = i } {\displaystyle \{{\hat {y}}=i\}} . Each of the y ^ i {\displaystyle {\hat {y}}_{i}} models is a "One versus Rest" model. L i f t ( y = i , y ^ = i ) {\displaystyle \mathrm {Lift} (y=i,{\hat {y}}=i)} only depends on the events { y = i } {\displaystyle \{y=i\}} and { y ^ = i } {\displaystyle \{{\hat {y}}=i\}} , so merging or not merging the other classes doesn't change its value. We therefore have L i f t ( y = i , y ^ = i ) = L i f t ( y i = 1 , y ^ i = 1 ) {\displaystyle \mathrm {Lift} (y=i,{\hat {y}}=i)=\mathrm {Lift} (y_{i}=1,{\hat {y}}_{i}=1)} and the first condition is that all binary One versus Rest models are better than chance. ==== Example ==== If K = 2 {\displaystyle K=2} and 2 is the class of interest , the normalized confusion matrix is ( s p e c i f i c i t y 1 − s p e c i f i c i t y 1 − s e n s i t i v i t y s e n s i t i v i t y ) {\displaystyle {\begin{pmatrix}\mathrm {specificity} &1-\mathrm {specificity} \\1-\mathrm {sensitivity} &\mathrm {sensitivity} \end{pmatrix}}} and we have L i f t ( y = 1 , y ^ = 1 ) − 1 = P ( y = y ^ = 1 ) λ 1 μ 1 − 1 = n 1 , 1 n n 1. n .1 − 1 {\displaystyle \mathrm {Lift} (y=1,{\hat {y}}=1)-1={\frac {\mathbb {P} (y={\hat {y}}=1)}{\lambda _{1}\mu _{1}}}-1={\frac {n_{1,1}n}{n_{1.}n_{.1}}}-1} = n 1 , 1 ( n 1 , 1 + n 1 , 2 + n 2 , 1 + n 2 , 2 ) − ( n 1 , 1 + n 1 , 2 ) ( n 1 , 1 + n 2 , 1 ) n 1. n .1 = n 1 , 1 n 2 , 2 − n 1 , 2 n 2 , 1 n 1. n .1 {\displaystyle ={\frac {n_{1,1}(n_{1,1}+n_{1,2}+n_{2,1}+n_{2,2})-(n_{1,1}+n_{1,2})(n_{1,1}+n_{2,1})}{n_{1.}n_{.1}}}={\frac {n_{1,1}n_{2,2}-n_{1,2}n_{2,1}}{n_{1.}n_{.1}}}} . Thus L i f t ( y = 1 , y ^ = 1 ) ≥ 1 ⟺ n 1 , 1 n 2 , 2 − n 1 , 2 n 2 , 1 ≥ 0 {\displaystyle \mathrm {Lift} (y=1,{\hat {y}}=1)\geq 1\iff n_{1,1}n_{2,2}-n_{1,2}n_{2,1}\geq 0} . Similarly, by swapping the roles of 1 and 2, we find that L i f t ( y = 2 , y ^ = 2 ) ≥ 1 ⟺ n 1 , 1 n 2 , 2 − n 1 , 2 n 2 , 1 ≥ 0 {\displaystyle \mathrm {Lift} (y=2,{\hat {y}}=2)\geq 1\iff n_{1,1}n_{2,2}-n_{1,2}n_{2,1}\geq 0} . Dividing by n 1. n 2. {\displaystyle n_{1.}n_{2.}} we find that the necessary and sufficient condition on the normalized confusion matrix is s e n s i t i v i t y s p e c i f i c i t y − ( 1 − s e n s i t i v i t y ) ( 1 − s p e c i f i c i t y ) ≥ 0 ⟺ s e n s i t i v i t y + s p e c i f i c i t y − 1 ≥ 0 ⟺ J ≥ 0 {\displaystyle \mathrm {sensitivity} \ \mathrm {specificity} -(1-\mathrm {sensitivity} )(1-\mathrm {specificity} )\geq 0\iff \mathrm {sensitivity} +\mathrm {specificity} -1\geq 0\iff J\geq 0} . This brings us back to the classical binary condition: Youden's J must be positive (or zero for random models). === Random models === A random model is a model that is independent of the target variable. This property is easily reformulated with the confusion matrix. This proposition shows that the model y ^ {\displaystyle {\hat {y}}} of y {\displaystyle y} is uninformative if and only if there are two families of numbers ( α i ) i {\displaystyle (\alpha _{i})_{i}} and ( β j ) j {\displaystyle (\beta _{j})_{j}} such that P ( { y = i } ∩ { y ^ = j } ) = α i β j {\displaystyle \mathbb {P} (\{y=i\}\cap \{{\hat {y}}=j\})=\alpha _{i}\beta _{j}} for any i {\displaystyle i} and j {\displaystyle j} . === Multiclass likelihood ratios and diagnostic odds ratios === We define generalized likelihood ratios calculated from the normalized confusion matrix: for any i {\displaystyle i} and j ≠ i {\displaystyle j\not =i} , let L R i , j = P ( y ^ = j ∣ y = j ) P ( y ^ = j ∣ y = i ) {\displaystyle \mathrm {LR} _{i,j}={\frac {\mathbb {P} ({\hat {y}}=j\mid y=j)}{\mathbb {P} ({\hat {y}}=j\mid y=i)}}} . When K = 2 {\displaystyle K=2} , if 2 is the class of interest,, we find the classical likelihood ratios L R 1 , 2 = L R + {\displaystyle \mathrm {LR} _{1,2}=\mathrm {LR} _{+}} and L R 2 , 1 = 1 L R − {\displaystyle \mathrm {LR} _{2,1}={\frac {1}{\mathrm {LR} _{-}}}} . Multiclass diagnostic odds ratios can also be defined using the formula D O R i , j = D O R j , i = L R i , j L R j , i = n i , i n j , j n i , j n j , i = P ( y ^ = j ∣ y = j ) / P ( y ^ = i ∣ y = j ) P ( y ^ = j ∣ y = i ) / P ( y ^ = i ∣ y = i ) {\displaystyle \mathrm {DOR} _{i,j}=\mathrm {DOR} _{j,i}=\mathrm {LR} _{i,j}\mathrm {LR} _{j,i}={\frac {n_{i,i}n_{j,j}}{n_{i,j}n_{j,i}}}={\frac {\mathbb {P} ({\hat {y}}=j\mid y=j)/\mathbb {P} ({\hat {y}}=i\mid y=j)}{\mathbb {P} ({\hat {y}}=j\mid y=i)/\mathbb {P} ({\hat {y}}=i\mid y=i)}}} We saw above that a better-than-chance model (or a random model) must verify L i f t ( y = i , y ^ = i ) ≥ 1 {\displaystyle \mathrm {Lift} (y=i,{\hat {y}}=i)\geq 1} for any i {\displaystyle i} and λ i {\displaystyle \lambda _{i}} . According to the previous corollary, likelihood ratios are thus greater
Companion robot
A companion robot is a robot created to create real or apparent companionship for human beings. Target markets for companion robots include the elderly and single children. Companions robots are expected to communicate with non-experts in a natural and intuitive way. They offer a variety of functions, such as monitoring the home remotely, communicating with people, or waking people up in the morning. Their aim is to perform a wide array of tasks including educational functions, home security, diary duties, entertainment and message delivery services, etc. The idea of companionship with robots has already existed on science fictions of 1970s, like R2-D2. Starting from the late 20th century, companion robots became a reality, mostly as robotic pets. Besides entertainment purposes, interactive robots were also introduced as a personal service robot for elderly care around 2000. == Characteristics == Companion robots try to interact with users. They gather information about users based on their interactions and yield feedback. This procedure varies slightly based on their specific roles. For example, social-companion robots make simple conversations, while pet-companion robots mimic being real pets. == Types == Companion robots can perform a variety of tasks and they are produced in a specialized manner according to their purpose or target audience in order to increase convenience and end user satisfaction. === Social companion robots === Social companion robots are designed to provide companionship and be a solution for unwanted solitude. They often mimic adult human, child or pet behaviours appealing to the user base. Robots which are specifically devised for simple conversations, conveying emotions and respond to user feelings fall under this category. === Assistive companion robots === Assistive companion robots are aimed at people who require constant care because of age, disability or rehabilitation purposes. Such robots can help disadvantaged users with their daily tasks, act as reminders (e.g., for regular medication) and facilitate mobility in everyday actions. Assistive companion robots reduce the intensity of labour that should be performed by caretakers, nurses and legal guardians. === Educational companion robots === Educational companion robots perform tutorship for students, regardless of their ages, and can teach desired subjects with activities tailored for the user such as interactive assignments and games. Rather than replacing teachers and instructors, educational companion robots are aides to them. === Therapeutic companion robots === Designed for individuals coping with stress (PTSD in severe cases), anxiety and loneliness; therapeutic companion robots support users' emotional and mental wellbeing. Such robots can be utilized in hospitals and care facilities as well as dwellings where the distressed user may need the most help. Therapeutic companion robots bear a vast resemblance to assistive companion robots to the extent of being a branch of them; the nuance between these two types of companion robots is that the former is for long-term/lifetime usage while the latter is mostly for the duration of the therapy received by the user. === Pet companion robots === Pet companion robots are for individuals who seek an alternative to live pets as live animals demand a considerable amount of care and may not be eligible for people with allergies. These robots aim to be perfect imitations of a pet while diminishing the chore aspect of having one. === Entertainment companion robots === Entertainment companion robots are designed solely for entertainment and can provide numerous ways of entertainment, ranging from dancing to playing games with the user. People who would appreciate an individual to have fun with are the main audience of such products. === Personal assistant robots === Personal assistant robots help people with daily tasks, management, scheduling, reminding etc. Their area of activity can be offices as well as homes and public spaces. === Sex robots === Sex robots are anthropomorphic robotic sex dolls that have human-like movement or behavior, and some degree of artificial intelligence. As of 2026, although elaborately instrumented sex dolls have been created by a number of inventors, no fully animated sex robots yet exist. Simple devices have been created which can speak, make facial expressions, or respond to touch. There is controversy as to whether developing them would be morally justifiable. In 2015, robot ethicist Kathleen Richardson called for a ban on the creation of anthropomorphic sex robots with concerns about normalizing relationships with machines and reinforcing female dehumanization. Questions about their ethics, effects, and possible legal regulations have been discussed since then. == Examples == There are several companion robot prototypes, and these include Paro, CompanionAble, and EmotiRob, among others. === Paro === Paro is a pet-type robot system developed by Japan's National Institute of Advanced Industrial Science and Technology (AIST). The robot, which looked like a small harp seal, was designed as a therapeutic tool for use in hospitals and nursing homes. The robot is programmed to cry for attention and respond to its name. Experiments showed that Paro facilitated elderly residents to communicate with each other, which led to psychological improvements. === CompanionAble === This robot is classified as an FP 7 EU project. It is built to "cooperate with Ambient Assistive Living environment". The autonomous device, which is also built to support the elderly, helps its owner interact with smart home environment as well as caregivers. The robot functions as a mobile friend, by which natural interaction is possible via speech and the touchscreen to detect and track people at home. === EmotiRob === EmotiRob is developed in a robotics project which is the continuity of the MAPH (Active Media For the Handicap) project in emotion synthesis. The aim of the project was to maintain emotional interaction with children. EmotiRob designed in a way that a child can hold it in a his/her arms and with which he/she could interact by talking to it, and then the robot would express itself through body postures or facial expressions. It has cognitive capabilities, which are further extended so that the robot can have a natural linguistic interaction with its owner through the DRAGON speech-recognition software developed by a company called NUANCE. Such interaction is expected to facilitate a child's cognitive development and develop new learning patterns. === LOVOT === Lovot is a Japanese company robot whose only purpose is "to make you happy". It features over 50 sensors that mimic the behavior of a human baby or small pet, a 360° camera with a microphone, the ability to distinguish humans from objects, neoteny eyes, and an internal warmth of 30° celsius. An interactive Lovot Café was opened in Japan October 3, 2020. === NICOBO === Nicobo was developed by Panasonic and was influenced by the loneliness of lockdowns created as a measure of the COVID-19 pandemic. It was designed to appear vulnerable, which creates empathy in its owners. Nicobo's name derives from the Japanese word for "smile". It wags its tail, engages in baby talk, and stays as a housemate. === Hyodol === Hyodol is an advanced care robot designed to support the elderly by reminding them to take their medications and monitoring their movements to keep their guardians informed. Additionally, this innovative robot can detect and respond to the emotional states of its elderly users, adding a layer of personalized care. Hyodol is designed with the appearance and speech style of a 7-year-old Korean grandchild, featuring a soft fabric exterior and user interaction methods such as striking the head or patting the back. It is equipped with various sensors and wireless communication technologies to collect and process data, supporting mobile apps and PC web monitoring systems for remote monitoring from anywhere. In South Korea, approximately 10,000 Hyodol robots are deployed to the homes of elderly individuals living alone, providing essential support and companionship. Local governments, including provincial and county offices, have embraced Hyodol as a solution to address social challenges stemming from the country's rapidly aging society.Furthermore, the robot is widely utilized in the treatment of dementia patients at a university hospital in Gangwon province. Hyodol was honored with the Mobile World Congress (MWC) Global Mobile Awards (GLOMO) in the "Best Mobile Innovation for Connected Health and Wellbeing" category on February 29, 2024. === Moxie === Moxie was a companion robot for autistic children developed by a company called Embodied. Although it had limited motion, it presented itself as a lifelike avatar. It was designed to help the children learn emotional cognition, using remotely hosted large language models to direct its respons
Shattered set
A class of sets is said to shatter another set if it is possible to "pick out" any element of that set using intersection. The concept of shattered sets plays an important role in Vapnik–Chervonenkis theory, also known as VC-theory. Shattering and VC-theory are used in the study of empirical processes as well as in statistical computational learning theory. == Definition == Suppose A is a set and C is a class of sets. The class C shatters the set A if for each subset a of A, there is some element c of C such that a = c ∩ A . {\displaystyle a=c\cap A.} Equivalently, C shatters A when their intersection is equal to A's power set: P(A) = { c ∩ A | c ∈ C }. We employ the letter C to refer to a "class" or "collection" of sets, as in a Vapnik–Chervonenkis class (VC-class). The set A is often assumed to be finite because, in empirical processes, we are interested in the shattering of finite sets of data points. == Example == We will show that the class of all discs in the plane (two-dimensional space) does not shatter every set of four points on the unit circle, yet the class of all convex sets in the plane does shatter every finite set of points on the unit circle. Let A be a set of four points on the unit circle and let C be the class of all discs. To test where C shatters A, we attempt to draw a disc around every subset of points in A. First, we draw a disc around the subsets of each isolated point. Next, we try to draw a disc around every subset of point pairs. This turns out to be doable for adjacent points, but impossible for points on opposite sides of the circle. Any attempt to include those points on the opposite side will necessarily include other points not in that pair. Hence, any pair of opposite points cannot be isolated out of A using intersections with class C and so C does not shatter A. As visualized below: Because there is some subset which can not be isolated by any disc in C, we conclude then that A is not shattered by C. And, with a bit of thought, we can prove that no set of four points is shattered by this C. However, if we redefine C to be the class of all elliptical discs, we find that we can still isolate all the subsets from above, as well as the points that were formerly problematic. Thus, this specific set of 4 points is shattered by the class of elliptical discs. Visualized below: With a bit of thought, we could generalize that any set of finite points on a unit circle could be shattered by the class of all convex sets (visualize connecting the dots). == Shatter coefficient == To quantify the richness of a collection C of sets, we use the concept of shattering coefficients (also known as the growth function). For a collection C of sets s ⊂ Ω {\displaystyle s\subset \Omega } , Ω {\displaystyle \Omega } being any space, often a sample space, we define the nth shattering coefficient of C as S C ( n ) = max ∀ x 1 , x 2 , … , x n ∈ Ω card { { x 1 , x 2 , … , x n } ∩ s , s ∈ C } {\displaystyle S_{C}(n)=\max _{\forall x_{1},x_{2},\dots ,x_{n}\in \Omega }\operatorname {card} \{\,\{\,x_{1},x_{2},\dots ,x_{n}\}\cap s,s\in C\}} where card {\displaystyle \operatorname {card} } denotes the cardinality of the set and x 1 , x 2 , … , x n ∈ Ω {\displaystyle x_{1},x_{2},\dots ,x_{n}\in \Omega } is any set of n points,. S C ( n ) {\displaystyle S_{C}(n)} is the largest number of subsets of any set A of n points that can be formed by intersecting A with the sets in collection C. For example, if set A contains 3 points, its power set, P ( A ) {\displaystyle P(A)} , contains 2 3 = 8 {\displaystyle 2^{3}=8} elements. If C shatters A, its shattering coefficient(3) would be 8 and S C ( 2 ) {\displaystyle S_{C}(2)} would be 2 2 = 4 {\displaystyle 2^{2}=4} . However, if one of those sets in P ( A ) {\displaystyle P(A)} cannot be obtained through intersections in c, then S C ( 3 ) {\displaystyle S_{C}(3)} would only be 7. If none of those sets can be obtained, S C ( 3 ) {\displaystyle S_{C}(3)} would be 0. Additionally, if S C ( 2 ) = 3 {\displaystyle S_{C}(2)=3} , for example, then there is an element in the set of all 2-point sets from A that cannot be obtained from intersections with C. It follows from this that S C ( 3 ) {\displaystyle S_{C}(3)} would also be less than 8 (i.e. C would not shatter A) because we have already located a "missing" set in the smaller power set of 2-point sets. This example illustrates some properties of S C ( n ) {\displaystyle S_{C}(n)} : S C ( n ) ≤ 2 n {\displaystyle S_{C}(n)\leq 2^{n}} for all n because { s ∩ A | s ∈ C } ⊆ P ( A ) {\displaystyle \{s\cap A|s\in C\}\subseteq P(A)} for any A ⊆ Ω {\displaystyle A\subseteq \Omega } . If S C ( n ) = 2 n {\displaystyle S_{C}(n)=2^{n}} , that means there is a set of cardinality n, which can be shattered by C. If S C ( N ) < 2 N {\displaystyle S_{C}(N)<2^{N}} for some N > 1 {\displaystyle N>1} then S C ( n ) < 2 n {\displaystyle S_{C}(n)<2^{n}} for all n ≥ N {\displaystyle n\geq N} . The third property means that if C cannot shatter any set of cardinality N then it can not shatter sets of larger cardinalities. == Vapnik–Chervonenkis class == If A cannot be shattered by C, there will be a smallest value of n that makes the shatter coefficient(n) less than 2 n {\displaystyle 2^{n}} because as n gets larger, there are more sets that could be missed. Alternatively, there is also a largest value of n for which the S C ( n ) {\displaystyle S_{C}(n)} is still 2 n {\displaystyle 2^{n}} , because as n gets smaller, there are fewer sets that could be omitted. The extreme of this is S C ( 0 ) {\displaystyle S_{C}(0)} (the shattering coefficient of the empty set), which must always be 2 0 = 1 {\displaystyle 2^{0}=1} . These statements lends themselves to defining the VC dimension of a class C as: V C ( C ) = min n { n : S C ( n ) < 2 n } {\displaystyle VC(C)={\underset {n}{\min }}\{n:S_{C}(n)<2^{n}\}\,} or, alternatively, as V C 0 ( C ) = max n { n : S C ( n ) = 2 n } . {\displaystyle VC_{0}(C)={\underset {n}{\max }}\{n:S_{C}(n)=2^{n}\}.\,} Note that V C ( C ) = V C 0 ( C ) + 1. {\displaystyle VC(C)=VC_{0}(C)+1.} . The VC dimension is usually defined as V C 0 {\displaystyle VC_{0}} , the largest cardinality of points chosen that will still shatter A (i.e. n such that S C ( n ) = 2 n {\displaystyle S_{C}(n)=2^{n}} ). Altneratively, if for any n there is a set of cardinality n which can be shattered by C, then S C ( n ) = 2 n {\displaystyle S_{C}(n)=2^{n}} for all n and the VC dimension of this class C is infinite. A class with finite VC dimension is called a Vapnik–Chervonenkis class or VC class. A class C is uniformly Glivenko–Cantelli if and only if it is a VC class.