Feed forward (control)

Applications In physiology, feed-forward control is exemplified by the normal anticipatory regulation of heartbeat in advance of actual physical exertion by the central autonomic network.  Feed-forward control can be likened to learned anticipatory responses to known cues (predictive coding).  Feedback regulation of the heartbeat provides further adaptiveness to the running eventualities of physical exertion.  Feedforward systems are also found in biological control of other variables by many regions of animals brains. [citation needed] Even in the case of biological feedforward systems, such as in the human brain, knowledge or a mental model of the plant (body) can be considered to be mathematical as the model is characterized by limits, rhythms, mechanics and patterns.  A pure feed-forward system is different from a homeostatic control system, which has the function of keeping the body's internal environment 'steady' or in a 'prolonged steady state of readiness. ' A homeostatic control system relies mainly on feedback (especially negative), in addition to the feedforward elements of the system.  Feed-forward loops (FFLs), a three-node graph of the form A affects B and C and B affects C, are frequently observed in transcription networks in several organisms including E.  coli and S.  cerevisiae, suggesting that they perform functions that are important for the functioning of these organisms.  In E.  coli and S.  cerevisiae transcription networks have been extensively studied, FFLs occur approximately three times more frequently than expected based on random (Erd��s-R��nyi) networks.  Edges in transcription networks are directed and signed, as they represent activation (+) or repression (-).  The sign of a path in a transcription network can be obtained by multiplying the signs of the edges in the path, so a path with an odd number of negative signs is negative.  There are eight possible three-node FFLs as each of the three arrows can be either repression or activation, which can be classified into coherent or incoherent FFLs.  Coherent FFLs have the same sign for both the paths from A to C, and incoherent FFLs have different signs for the two paths.  The temporal dynamics of FFLs show that coherent FFLs can be sign-sensitive delays that filter input into the circuit.  We consider the differential equations for a Type-I coherent FFL, where all the arrows are positive: �� B �� t = �� B ( A ) ��� �� B B {\displaystyle {\frac {\delta B}{\delta t}}=\beta _{B}(A)-\gamma _{B}B} �� C �� t = �� C ( A , B ) ��� �� C C {\displaystyle {\frac {\delta C}{\delta t}}=\beta _{C}(A,B)-\gamma _{C}C} Where �� y {\displaystyle \beta _{y}} and �� z {\displaystyle \beta _{z}} are increasing functions in A {\displaystyle A} and B {\displaystyle B} representing production, and �� Y {\displaystyle \gamma _{Y}} and �� z {\displaystyle \gamma _{z}} are rate constants representing degradation or dilution of B {\displaystyle B} and C {\displaystyle C} respectively.


Feed forward (control)

Applications �� C ( A , B ) {\displaystyle \beta _{C}(A,B)} can represent an AND gate where �� C ( A , B ) = 0 {\displaystyle \beta _{C}(A,B)=0} if either A = 0 {\displaystyle A=0} or B = 0 {\displaystyle B=0} , for instance if �� C ( A , B ) = �� C �� A ( A > k A C ) �� A ( B > k A B C ) {\displaystyle \beta _{C}(A,B)=\beta _{C}\theta _{A}(A>k_{AC})\theta _{A}(B>k_{ABC})} where �� A {\displaystyle \theta _{A}} and �� B {\displaystyle \theta _{B}} are step functions.  In this case the FFL creates a time-delay between a sustained on-signal, i. e.  increase in A {\displaystyle A} and the output increase in C {\displaystyle C} .  This is because production of A {\displaystyle A} must first induce production of B {\displaystyle B} , which is then needed to induce production of C {\displaystyle C} .  However, there is no time-delay in for an off-signal because a reduction of A {\displaystyle A} immediately results in a decrease in the production term �� C ( A , B ) {\displaystyle \beta _{C}(A,B)} .  This system therefore filters out fluctuations in the on-signal and detects persistent signals.  This is particularly relevant in settings with stochastically fluctuating signals.  In bacteria these circuits create time delays ranging from a few minutes to a few hours.  Similarly, an inclusive-OR gate in which C {\displaystyle C} is activated by either A {\displaystyle A} or B {\displaystyle B} is a sign-sensitive delay with no delay after the ON step but with a delay after the OFF step.  This is because an ON pulse immediately activates B and C, but an OFF step does not immediately result in deactivation of C because B can still be active.  This can protect the system from fluctuations that result in the transient loss of the ON signal and can also provide a form of memory.  Kalir, Mangan, and Alon, 2005 show that the regulatory system for flagella in E.  coli is regulated with a Type 1 coherent feedforward loop.  For instance, the regulation of the shift from one carbon source to another in diauxic growth in E.  coli can be controlled via a type-1 coherent FFL.  In diauxic growth cells growth using two carbon sources by first rapidly consuming the preferred carbon source, and then slowing growth in a lag phase before consuming the second less preferred carbon source.  In E.  coli, glucose is preferred over both arabinose and lactose.  The absence of glucose is represented via a small molecule cAMP.  Diauxic growth in glucose and lactose is regulated by a simple regulatory system involving cAMP and the lac operon.  However, growth in arabinose is regulated by a feedforward loop with an AND gate which confers an approximately 20 minute time delay between the ON-step in which cAMP concentration increases when glucose is consumed and when arabinose transporters are expressed.  There is no time delay with the OFF signal which occurs when glucose is present.


Feed forward (control)

Applications This prevents the cell from shifting to growth on arabinose based on short term fluctuations in glucose availability.  Additionally, feedforward loops can facilitate cellular memory.  Doncic and Skotheim (2003) show this in the regulation in the mating of yeast, where extracellular mating pheromone which indices mating behavior including preventing cells from entering the cell cycle.  The mating pheromone activates the MAPK pathway which then activates the cell-cycle inhibitor Far1 and activates the Ste12 transcription factor that increases the synthesis of inactive Far1.  In this system the concentration of active Far1 depends on the time integral of a function of the external mating pheromone concentration.  This dependence on past levels of mating pheromone is a form of cellular memory.  This system simultaneously allows for the stability and reversibility.  Incoherent feedforward loops, in which the two paths from the input to the output node have different signs result in short pulses in response to an ON signal.  In this system input A simultaneous directly increases and indirectly decreases synthesis of output node C.  If the indirect path to C (via B) is slower than the direct path a pulse of output is produced in the time period before levels of B are high enough to inhibit synthesis of C.  Response to epidermal growth factor (EGF) in dividing mammalian cells is an example of a Type-1 incoherent FFL.  The frequent observation of feed-forward loops in several biological contexts across scales suggests that they have structural properties that are highly adaptive in several contexts.  Several theoretical and experimental studies including those discussed here show that FFLs create a mechanism for biological systems to process and store information, which is important for predictive behavior and survival in complex dynamically changing environments.  In computing, feed-forward normally refers to a perceptron network in which the outputs from all neurons go to following but not preceding layers, so there are no feedback loops.  The connections are set up during a training phase, which in effect is when the system is a feedback system.  In the early 1970s, intercity coaxial transmission systems, including L-carrier, used feed-forward amplifiers to diminish linear distortion.  This more complex method allowed wider bandwidth than earlier feedback systems.  Optical fiber, however, made such systems obsolete before many were built.  Feedforward control is a discipline within the field of automatic controls used in automation.  The method is rather a new technique that changes the phase of an open-loop transfer function of a non-minimum phase system into minimum phase.


Graph neural network

Graph neural network A graph neural network (GNN) is a class of artificial neural networks for processing data that can be represented as graphs. In the more general subject of "geometric deep learning", certain existing neural network architectures can be interpreted as GNNs operating on suitably defined graphs. A convolutional neural network layer, in the context of computer vision, can be seen as a GNN applied to graphs whose nodes are pixels and only adjacent pixels are connected by edges in the graph. A transformer layer, in natural language processing, can be seen as a GNN applied to complete graphs whose nodes are words or tokens in a passage of natural language text. The key design element of GNNs is the use of pairwise message passing, such that graph nodes iteratively update their representations by exchanging information with their neighbors. Since their inception, several different GNN architectures have been proposed, which implement different flavors of message passing, started by recursive or convolutional constructive approaches. As of 2022[update], whether it is possible to define GNN architectures "going beyond" message passing, or if every GNN can be built on message passing over suitably defined graphs, is an open research question. Relevant application domains for GNNs include Natural Language Processing, social networks, citation networks, molecular biology, chemistry, physics and NP-hard combinatorial optimization problems. Several open source libraries implementing graph neural networks are available, such as PyTorch Geometric (PyTorch), TensorFlow GNN (TensorFlow), jraph (Google JAX), and GraphNeuralNetworks.jl (Julia, Flux).


Neural network Gaussian process

Neural network Gaussian process A Neural Network Gaussian Process (NNGP) is a Gaussian process obtained as the limit (in the sense of convergence in distribution) of a sequence of neural networks, and provide a closed form way to evaluate many kinds of neural networks. Mathematically, an NNGP is just a gaussian process. It is distinguished only by how it is obtained (it is an intensional definition): a NNGP is a GP obtained as the limit of a sequence of neural networks, with limit taken in the sense of convergence in distribution. A wide variety of neural network architectures converges in distribution to a gaussian process at the infinitely wide limit. This is proven for: single hidden layer Bayesian neural networks; deep fully connected networks as the number of units per layer is taken to infinity; convolutional neural networks as the number of channels is taken to infinity; transformer networks as the number of attention heads is taken to infinity; recurrent networks as the number of units is taken to infinity. In fact, this NNGP correspondence holds for almost any architecture: Generally, if an architecture can be expressed solely via matrix multiplication and coordinatewise nonlinearities (i.e. a tensor program), then it has an infinite-width GP. This in particular includes all feedforward or recurrent neural networks composed of multilayer perceptron, recurrent neural networks (e.g. LSTMs, GRUs), (nD or graph) convolution, pooling, skip connection, attention, batch normalization, and/or layer normalization.


Radial basis function

RBFs_for_PDEs Radial basis functions are used to approximate functions and so can be used to discretize and numerically solve Partial Differential Equations (PDEs). This was first done in 1990 by E. J. Kansa who developed the first RBF based numerical method. It is called the Kansa method and was used to solve the elliptic Poisson equation and the linear advection-diffusion equation. The function values at points x {\displaystyle \mathbf {x} } in the domain are approximated by the linear combination of RBFs: The derivatives are approximated as such: where N {\displaystyle N} are the number of points in the discretized domain, d {\displaystyle d} the dimension of the domain and �� {\displaystyle \lambda } the scalar coefficients that are unchanged by the differential operator. Different numerical methods based on Radial Basis Functions were developed thereafter. Some methods are the RBF-FD method, the RBF-QR method and the RBF-PUM method.


Residual neural network

Residual neural network A Residual Neural Network (a.k.a. Residual Network, ResNet) is a deep learning model in which the weight layers learn residual functions with reference to the layer inputs. A Residual Network is a network with skip connections that perform identity mappings, merged with the layer outputs by addition. It behaves like a Highway Network whose gates are opened through strongly positive bias weights. This enables deep learning models with tens or hundreds of layers to train easily and approach better accuracy when going deeper. The identity skip connections, often referred to as "residual connections", are also used in the 1997 LSTM networks, Transformer models (e.g., BERT, GPT models such as ChatGPT), the AlphaGo Zero system, the AlphaStar system, and the AlphaFold system. Residual Networks were developed by Kaiming He, Xiangyu Zhang, Shaoqing Ren, and Jian Sun, which won the ImageNet 2015 competition.


Residual neural network

Variants_of_Residual_Blocks A Basic Block is the simplest building block studied in the original ResNet. This block consists of two sequential 3x3 convolutional layers and a residual connection. The input and output dimensions of both layers are equal. A Bottleneck Block consists of three sequential convolutional layers and a residual connection. The first layer in this block is a 1x1 convolution for dimension reduction, e.g., to 1/4 of the input dimension; the second layer performs a 3x3 convolution; the last layer is another 1x1 convolution for dimension restoration. The models of ResNet-50, ResNet-101, and ResNet-152 in are all based on Bottleneck Blocks. The Pre-activation Residual Block applies the activation functions (e.g., non-linearity and normalization) before applying the residual function F {\textstyle F} . Formally, the computation of a Pre-activation Residual Block can be written as: where �� {\textstyle \phi } can be any non-linearity activation (e.g., ReLU) or normalization (e.g., LayerNorm) operation. This design reduces the number of non-identity mappings between Residual Blocks. This design was used to train models with 200 to over 1000 layers. Since GPT-2, the Transformer Blocks have been dominantly implemented as Pre-activation Blocks. This is often referred to as "pre-normalization" in the literature of Transformer models. A Transformer Block is a stack of two Residual Blocks. Each Residual Block has a Residual Connection. The first Residual Block is a Multi-Head Attention Block, which performs (self-)attention computation followed by a linear projection. The second Residual Block is a feed-forward Multi-Layer Perceptron (MLP) Block. This block is analogous to an "inverse" bottleneck block: it has a linear projection layer (which is equivalent to a 1x1 convolution in the context of Convolutional Neural Networks) that increases the dimension, and another linear projection that reduces the dimension. A Transformer Block has a depth of 4 layers (linear projections). The GPT-3 model has 96 Transformer Blocks (in the literature of Transformers, a Transformer Block is often referred to as a "Transformer Layer"). This model has a depth of about 400 projection layers, including 96x4 layers in Transformer Blocks and a few extra layers for input embedding and output prediction. Very deep Transformer models cannot be successfully trained without Residual Connections.


Residual neural network

Related_Work In the book written by Frank Rosenblatt, published in 1961, a three-layer Multilayer Perceptron (MLP) model with skip connections was presented (Chapter 15, p313 in ).  The model was referred to as a "cross-coupled system", and the skip connections were forms of cross-coupled connections.  In two books published in 1994 and 1996, "skip-layer" connections were presented in feed-forward MLP models: "The general definition [of MLP] allows more than one hidden layer, and it also allows 'skip-layer' connections from input to output" (p261 in, p144 in ), ". . .  which allows the non-linear units to perturb a linear functional form" (p262 in ).  This description suggests that the non-linear MLP performs like a residual function (perturbation) added to a linear function.  Sepp Hochreiter analyzed the vanishing gradient problem in 1991 and attributed to it the reason why deep learning did not work well.  To overcome this problem, Long Short-Term Memory (LSTM) recurrent neural networks had skip connections or residual connections with a weight of 1.0 in every LSTM cell (called the constant error carrousel) to compute y t + 1 = F ( x t ) + x t {\textstyle y_{t+1}=F(x_{t})+x_{t}} .  During backpropagation through time, this becomes the above-mentioned residual formula y = F ( x ) + x {\textstyle y=F(x)+x} for feedforward neural networks.  This enables training very deep recurrent neural networks with a very long time span t.  A later LSTM version published in 2000 modulates the identity LSTM connections by so-called forget gates such that their weights are not fixed to 1.0 but can be learned.  In experiments, the forget gates were initialized with positive bias weights, thus being opened, addressing the vanishing gradient problem.  The Highway Network of May 2015 applies these principles to feedforward neural networks.  It was reported to be "the first very deep feedforward network with hundreds of layers".  It is like an LSTM with forget gates unfolded in time, while the later Residual Nets have no equivalent of forget gates and are like the unfolded original LSTM.  If the skip connections in Highway Networks are "without gates", or if their gates are kept open (activation 1.0) through strong positive bias weights, they become the identity skip connections in Residual Networks.  The original Highway Network paper not only introduced the basic principle for very deep feedforward networks, but also included experimental results with 20, 50, and 100 layers networks, and mentioned ongoing experiments with up to 900 layers.  Networks with 50 or 100 layers had lower training error than their plain network counterparts, but no lower training error than their 20 layers counterpart (on the MNIST dataset, Figure 1 in ).  No improvement on test accuracy was reported with networks deeper than 19 layers (on the CIFAR-10 dataset; Table 1 in ).  The ResNet paper, however, provided strong experimental evidence of the benefits of going deeper than 20 layers.


Residual neural network

Related_Work It argued that the identity mapping without modulation is crucial and mentioned that modulation in the skip connection can still lead to vanishing signals in forward and backward propagation (Section 3 in ).  This is also why the forget gates of the 2000 LSTM were initially opened through positive bias weights: as long as the gates are open, it behaves like the 1997 LSTM.  Similarly, a Highway Net whose gates are opened through strongly positive bias weights behaves like a ResNet.  The skip connections used in modern neural networks (e. g. , Transformers) are dominantly identity mappings.  DenseNets in 2016 were designed as deep neural networks that attempt to connect each layer to every other layer.  DenseNets approached this goal by using identity mappings as skip connections.  Unlike ResNets, DenseNets merge the layer output with skip connections by concatenation, not addition.  Neural networks with Stochastic Depth were made possible given the Residual Network architectures.  This training procedure randomly drops a subset of layers and lets the signal propagate through the identity skip connection.  Also known as "DropPath", this is an effective regularization method for training large and deep models, such as the Vision Transformer (ViT).


Softmax function

Computational_complexity_and_remedies In neural network applications, the number K of possible outcomes is often large, e.g. in case of neural language models that predict the most likely outcome out of a vocabulary which might contain millions of possible words. This can make the calculations for the softmax layer (i.e. the matrix multiplications to determine the z i {\displaystyle z_{i}} , followed by the application of the softmax function itself) computationally expensive. What's more, the gradient descent backpropagation method for training such a neural network involves calculating the softmax for every training example, and the number of training examples can also become large. The computational effort for the softmax became a major limiting factor in the development of larger neural language models, motivating various remedies to reduce training times. Approaches that reorganize the softmax layer for more efficient calculation include the hierarchical softmax and the differentiated softmax. The hierarchical softmax (introduced by Morin and Bengio in 2005) uses a binary tree structure where the outcomes (vocabulary words) are the leaves and the intermediate nodes are suitably selected "classes" of outcomes, forming latent variables. The desired probability (softmax value) of a leaf (outcome) can then be calculated as the product of the probabilities of all nodes on the path from the root to that leaf. Ideally, when the tree is balanced, this would reduce the computational complexity from O ( K ) {\displaystyle O(K)} to O ( log 2 ��� K ) {\displaystyle O(\log _{2}K)} . In practice, results depend on choosing a good strategy for clustering the outcomes into classes. A Huffman tree was used for this in Google's word2vec models (introduced in 2013) to achieve scalability. A second kind of remedies is based on approximating the softmax (during training) with modified loss functions that avoid the calculation of the full normalization factor. These include methods that restrict the normalization sum to a sample of outcomes (e.g. Importance Sampling, Target Sampling).


Physics-informed neural networks

Modeling_and_computation A general nonlinear partial differential equations can be: u t + N [ u ; �� ] = 0 , x ��� �� , t ��� [ 0 , T ] {\displaystyle u_{t}+N[u;\lambda ]=0,\quad x\in \Omega ,\quad t\in [0,T]} where u ( t , x ) {\displaystyle u(t,x)} denotes the solution, N [ ��� ; �� ] {\displaystyle N[\cdot ;\lambda ]} is a nonlinear operator parametrized by �� {\displaystyle \lambda } , and �� {\displaystyle \Omega } is a subset of R D {\displaystyle \mathbb {R} ^{D}} .  This general form of governing equations summarizes a wide range of problems in mathematical physics, such as conservative laws, diffusion process, advection-diffusion systems, and kinetic equations.  Given noisy measurements of a generic dynamic system described by the equation above, PINNs can be designed to solve two classes of problems: data-driven solution data-driven discoveryof partial differential equations.  The data-driven solution of PDE computes the hidden state u ( t , x ) {\displaystyle u(t,x)} of the system given boundary data and/or measurements z {\displaystyle z} , and fixed model parameters �� {\displaystyle \lambda } .  We solve: u t + N [ u ] = 0 , x ��� �� , t ��� [ 0 , T ] {\displaystyle u_{t}+N[u]=0,\quad x\in \Omega ,\quad t\in [0,T]} .  By defining the residual f ( t , x ) {\displaystyle f(t,x)} as f := u t + N [ u ] = 0 {\displaystyle f:=u_{t}+N[u]=0} , and approximating u ( t , x ) {\displaystyle u(t,x)} by a deep neural network.  This network can be differentiated using automatic differentiation.  The parameters of u ( t , x ) {\displaystyle u(t,x)} and f ( t , x ) {\displaystyle f(t,x)} can be then learned by minimizing the following loss function L t o t {\displaystyle L_{tot}} : L t o t = L u + L f {\displaystyle L_{tot}=L_{u}+L_{f}} .  Where L u = ��� u ��� z ��� �� {\displaystyle L_{u}=\Vert u-z\Vert _{\Gamma }} is the error between the PINN u ( t , x ) {\displaystyle u(t,x)} and the set of boundary conditions and measured data on the set of points �� {\displaystyle \Gamma } where the boundary conditions and data are defined, and L f = ��� f ��� �� {\displaystyle L_{f}=\Vert f\Vert _{\Gamma }} is the mean-squared error of the residual function.  This second term encourages the PINN to learn the structural information expressed by the partial differential equation during the training process.  This approach has been used to yield computationally efficient physics-informed surrogate models with applications in the forecasting of physical processes, modeling predictive control, multi-physics and multi-scale modeling, and simulation.  It has been shown to converge to the solution of the PDE.


Physics-informed neural networks

Modeling_and_computation Given noisy and incomplete measurements z {\displaystyle z} of the state of the system, the data-driven discovery of PDE results in computing the unknown state u ( t , x ) {\displaystyle u(t,x)} and learning model parameters �� {\displaystyle \lambda } that best describe the observed data and it reads as follows: u t + N [ u ; �� ] = 0 , x ��� �� , t ��� [ 0 , T ] {\displaystyle u_{t}+N[u;\lambda ]=0,\quad x\in \Omega ,\quad t\in [0,T]} .  By defining f ( t , x ) {\displaystyle f(t,x)} as f := u t + N [ u ; �� ] = 0 {\displaystyle f:=u_{t}+N[u;\lambda ]=0} , and approximating u ( t , x ) {\displaystyle u(t,x)} by a deep neural network, f ( t , x ) {\displaystyle f(t,x)} results in a PINN.  This network can be derived using automatic differentiation.  The parameters of u ( t , x ) {\displaystyle u(t,x)} and f ( t , x ) {\displaystyle f(t,x)} , together with the parameter �� {\displaystyle \lambda } of the differential operator can be then learned by minimizing the following loss function L t o t {\displaystyle L_{tot}} : L t o t = L u + L f {\displaystyle L_{tot}=L_{u}+L_{f}} .  Where L u = ��� u ��� z ��� �� {\displaystyle L_{u}=\Vert u-z\Vert _{\Gamma }} , with u {\displaystyle u} and z {\displaystyle z} state solutions and measurements at sparse location �� {\displaystyle \Gamma } , respectively and L f = ��� f ��� �� {\displaystyle L_{f}=\Vert f\Vert _{\Gamma }} residual function.  This second term requires the structured information represented by the partial differential equations to be satisfied in the training process.  This strategy allows for discovering dynamic models described by nonlinear PDEs assembling computationally efficient and fully differentiable surrogate models that may find application in predictive forecasting, control, and data assimilation.


Feedforward neural network

Timeline In 1958, a layered network of perceptrons, consisting of an input layer, a hidden layer with randomized weights that did not learn, and an output layer with learning connections, was introduced already by Frank Rosenblatt in his book Perceptron. This extreme learning machine was not yet a deep learning network.In 1965, the first deep-learning feedforward network, not yet using stochastic gradient descent, was published by Alexey Grigorevich Ivakhnenko and Valentin Lapa, at the time called the Group Method of Data Handling.In 1967, a deep-learning network, using stochastic gradient descent for the first time, was able to classify non-linearily separable pattern classes, as reported Shun'ichi Amari. Amari's student Saito conducted the computer experiments, using a five-layered feedforward network with two learning layers.In 1970, modern backpropagation method, an efficient application of a chain-rule-based supervised learning, was for the first time published by the Finnish researcher Seppo Linnainmaa. The term (i.e. "back-propagating errors") itself has been used by Rosenblatt himself, but he did not know how to implement it, although a continuous precursor of backpropagation was already used in the context of control theory in 1960 by Henry J. Kelley. It is known also as a reverse mode of automatic differentiation.In 1982, backpropagation was applied in the way that has become standard, for the first time by Paul Werbos.In 1985, an experimental analysis of the technique was conducted by David E. Rumelhart et al.. Many improvements to the approach have been made in subsequent decades.In 1987, using a stochastic gradient descent within a (wide 12-layer nonlinear) feed-forward network, Matthew Brand has trained it to reproduce logic functions of nontrivial circuit depth, using small batches of random input/output samples. He, however, concluded that on hardware (sub-megaflop computers) available at the time it was impractical, and proposed using fixed random early layers as an input hash for a single modifiable layer.In 1990s, an (much simpler) alternative to using neural networks, although still related support vector machine approach was developed by Vladimir Vapnik and his colleagues. In addition to performing linear classification, they were able to efficiently perform a non-linear classification using what is called the kernel trick, using high-dimensional feature spaces.In 2003, interest in backpropagation networks returned due to the successes of deep learning being applied to language modelling by Yoshua Bengio with co-authors.In 2017, modern transformer architectures has been introduced.In 2021, a very simple NN architecture combining two deep MLPs with skip connections and layer normalizations was designed and called MLP-Mixer; its realizations featuring 19 to 431 millions of parameters were shown to be comparable to vision transformers of similar size on ImageNet and similar image classification tasks.


Multilayer perceptron

Timeline In 1958, a layered network of perceptrons, consisting of an input layer, a hidden layer with randomized weights that did not learn, and an output layer with learning connections, was introduced already by Frank Rosenblatt in his book Perceptron. This extreme learning machine was not yet a deep learning network.In 1965, the first deep-learning feedforward network, not yet using stochastic gradient descent, was published by Alexey Grigorevich Ivakhnenko and Valentin Lapa, at the time called the Group Method of Data Handling.In 1967, a deep-learning network, which used stochastic gradient descent for the first time, able to classify non-linearily separable pattern classes, was published by Shun'ichi Amari. Amari's student Saito conducted the computer experiments, using a five-layered feedforward network with two learning layers.In 1970, modern backpropagation method, an efficient application of a chain-rule-based supervised learning, was for the first time published by the Finnish researcher Seppo Linnainmaa. The term (i.e. "back-propagating errors") itself has been used by Rosenblatt himself, but he did not know how to implement it, although a continuous precursor of backpropagation was already used in the context of control theory in 1960 by Henry J. Kelley. It is known also as a reverse mode of automatic differentiation.In 1982, backpropagation was applied in the way that has become standard, for the first time by Paul Werbos.In 1985, an experimental analysis of the technique was conducted by David E. Rumelhart et al.. Many improvements to the approach have been made in subsequent decades,.In 1990s, an (much simpler) alternative to using neural networks, although still related support vector machine approach was developed by Vladimir Vapnik and his colleagues. In addition to performing linear classification, they were able to efficiently perform a non-linear classification using what is called the kernel trick, using high-dimensional feature spaces.In 2003, interest in backpropagation networks returned due to the successes of deep learning being applied to language modelling by Yoshua Bengio with co-authors.In 2017, modern transformer architectures has been introduced.In 2021, a very simple NN architecture combining two deep MLPs with skip connections and layer normalizations was designed and called MLP-Mixer; its realizations featuring 19 to 431 millions of parameters were shown to be comparable to vision transformers of similar size on ImageNet and similar image classification tasks.


Restricted Boltzmann machine

Restricted Boltzmann machine A restricted Boltzmann machine (RBM) (also called a restricted Sherrington���Kirkpatrick model with external field or restricted stochastic Ising���Lenz���Little model) is a generative stochastic artificial neural network that can learn a probability distribution over its set of inputs. RBMs were initially proposed under the name Harmonium by Paul Smolensky in 1986, and rose to prominence after Geoffrey Hinton and collaborators used fast learning algorithms for them in the mid-2000. RBMs have found applications in dimensionality reduction, classification, collaborative filtering, feature learning, topic modelling and even many body quantum mechanics. They can be trained in either supervised or unsupervised ways, depending on the task. As their name implies, RBMs are a variant of Boltzmann machines, with the restriction that their neurons must form a bipartite graph: a pair of nodes from each of the two groups of units (commonly referred to as the "visible" and "hidden" units respectively) may have a symmetric connection between them; and there are no connections between nodes within a group. By contrast, "unrestricted" Boltzmann machines may have connections between hidden units. This restriction allows for more efficient training algorithms than are available for the general class of Boltzmann machines, in particular the gradient-based contrastive divergence algorithm. Restricted Boltzmann machines can also be used in deep learning networks. In particular, deep belief networks can be formed by "stacking" RBMs and optionally fine-tuning the resulting deep network with gradient descent and backpropagation.


Restricted Boltzmann machine

Stacked_Restricted_Boltzmann_Machine The difference between the Stacked Restricted Boltzmann Machines and RBM is that RBM has lateral connections within a layer that are prohibited to make analysis tractable. On the other hand, the Stacked Boltzmann consists of a combination of an unsupervised three-layer network with symmetric weights and a supervised fine-tuned top layer for recognizing three classes. The usage of Stacked Boltzmann is to understand Natural languages, retrieve documents, image generation, and classification. These functions are trained with unsupervised pre-training and/or supervised fine-tuning. Unlike the undirected symmetric top layer, with a two-way unsymmetric layer for connection for RBM. The restricted Boltzmann's connection is three-layers with asymmetric weights, and two networks are combined into one. Stacked Boltzmann does share similarities with RBM, the neuron for Stacked Boltzmann is a stochastic binary Hopfield neuron, which is the same as the Restricted Boltzmann Machine. The energy from both Restricted Boltzmann and RBM is given by Gibb's probability measure: E = ��� 1 2 ��� i , j w i j s i s j + ��� i �� i s i {\displaystyle E=-{\frac {1}{2}}\sum _{i,j}{w_{ij}{s_{i}}{s_{j}}}+\sum _{i}{\theta _{i}}{s_{i}}} . The training process of Restricted Boltzmann is similar to RBM. Restricted Boltzmann train one layer at a time and approximate equilibrium state with a 3-segment pass, not performing back propagation. Restricted Boltzmann uses both supervised and unsupervised on different RBM for pre-training for classification and recognition. The training uses contrastive divergence with Gibbs sampling: ��wij = e*(pij - p'ij) The restricted Boltzmann's strength is it performs a non-linear transformation so it's easy to expand, and can give a hierarchical layer of features. The Weakness is that it has complicated calculations of integer and real-valued neurons. It does not follow the gradient of any function, so the approximation of Contrastive divergence to maximum likelihood is improvised.


Markov chain

History Andrey Markov studied Markov processes in the early 20th century, publishing his first paper on the topic in 1906. Markov Processes in continuous time were discovered long before his work in the early 20th century in the form of the Poisson process. Markov was interested in studying an extension of independent random sequences, motivated by a disagreement with Pavel Nekrasov who claimed independence was necessary for the weak law of large numbers to hold. In his first paper on Markov chains, published in 1906, Markov showed that under certain conditions the average outcomes of the Markov chain would converge to a fixed vector of values, so proving a weak law of large numbers without the independence assumption, which had been commonly regarded as a requirement for such mathematical laws to hold. Markov later used Markov chains to study the distribution of vowels in Eugene Onegin, written by Alexander Pushkin, and proved a central limit theorem for such chains. In 1912 Henri Poincar�� studied Markov chains on finite groups with an aim to study card shuffling. Other early uses of Markov chains include a diffusion model, introduced by Paul and Tatyana Ehrenfest in 1907, and a branching process, introduced by Francis Galton and Henry William Watson in 1873, preceding the work of Markov. After the work of Galton and Watson, it was later revealed that their branching process had been independently discovered and studied around three decades earlier by Ir��n��e-Jules Bienaym��. Starting in 1928, Maurice Fr��chet became interested in Markov chains, eventually resulting in him publishing in 1938 a detailed study on Markov chains. Andrey Kolmogorov developed in a 1931 paper a large part of the early theory of continuous-time Markov processes. Kolmogorov was partly inspired by Louis Bachelier's 1900 work on fluctuations in the stock market as well as Norbert Wiener's work on Einstein's model of Brownian movement. He introduced and studied a particular set of Markov processes known as diffusion processes, where he derived a set of differential equations describing the processes. Independent of Kolmogorov's work, Sydney Chapman derived in a 1928 paper an equation, now called the Chapman���Kolmogorov equation, in a less mathematically rigorous way than Kolmogorov, while studying Brownian movement. The differential equations are now called the Kolmogorov equations or the Kolmogorov���Chapman equations. Other mathematicians who contributed significantly to the foundations of Markov processes include William Feller, starting in 1930s, and then later Eugene Dynkin, starting in the 1950s.


Yoshua Bengio

Career_and_research After his PhD, Bengio was a postdoctoral fellow at MIT (supervised by Michael I.  Jordan) and AT&T Bell Labs.  Bengio has been a faculty member at the Universit�� de Montr��al since 1993, heads the MILA (Montreal Institute for Learning Algorithms) and is co-director of the Learning in Machines & Brains program at the Canadian Institute for Advanced Research.  Along with Geoffrey Hinton and Yann LeCun, Bengio is considered by Cade Metz as one of the three people most responsible for the advancement of deep learning during the 1990s and 2000s.  Among the computer scientists with an h-index of at least 100, Bengio was as of 2018 the one with the most recent citations per day, according to MILA.  As of December 2022, he had the 2nd highest Discipline H-index (D-index) in computer science.  Thanks to a 2019 article on a novel RNN architecture, Bengio has an Erd��s number of 3.  In October 2016, Bengio co-founded Element AI, a Montreal-based artificial intelligence incubator that turns AI research into real-world business applications.  The company sold its operations to ServiceNow in November 2020, with Bengio remaining at ServiceNow as an advisor.  Bengio currently serves as scientific and technical advisor for Recursion Pharmaceuticals and scientific advisor for Valence Discovery.  Following concerns raised by AI experts about the existential risks AI poses on humanity, in May 2023, Bengio stated in an interview to BBC that he felt "lost" over his life's work.  He raised his concern about "bad actors" getting hold of AI, especially as it becomes more sophisticated and powerful.  He called for better regulation, product registration, ethical training, and more involvement from governments in tracking and auditing AI products.  Speaking with the Financial Times also in May 2023, Bengio said that he supported the monitoring of access to AI systems such as ChatGPT so that potentially illegal or dangerous uses could be tracked.  In 2017, Bengio was named an Officer of the Order of Canada.  The same year, he was nominated Fellow of the Royal Society of Canada and received the Marie-Victorin Quebec Prize.  Together with Geoffrey Hinton and Yann LeCun, Bengio won the 2018 Turing Award.  In 2020 he was elected a Fellow of the Royal Society.  In 2022 he received the Princess of Asturias Award in the category "Scientific Research" with his peers Yann LeCun, Geoffrey Hinton and Demis Hassabis.  In 2023 Bengio was appointed Knight of the Legion of Honour, France's highest order of merit.  In August 2023 he was appointed to a United Nations scientific advisory council on technological advances.  Ian Goodfellow, Yoshua Bengio and Aaron Courville: Deep Learning (Adaptive Computation and Machine Learning), MIT Press, Cambridge (USA), 2016.  ISBN 978-0262035613.  Dzmitry Bahdanau; Kyunghyun Cho; Yoshua Bengio (2014).  "Neural Machine Translation by Jointly Learning to Align and Translate".  arXiv:1409.0473 [cs. CL].  L��on Bottou, Patrick Haffner, Paul G.  Howard, Patrice Simard, Yoshua Bengio, Yann LeCun: High Quality Document Image Compression with DjVu, In: Journal of Electronic Imaging, Band 7, 1998, S.


Yoshua Bengio

Career_and_research 410���425 doi:10.1117/1.482609 Bengio, Yoshua; Schuurmans, Dale; Lafferty, John; Williams, Chris K.  I.  and Culotta, Aron (eds. ), Advances in Neural Information Processing Systems 22 (NIPS'22), December 7th���10th, 2009, Vancouver, BC, Neural Information Processing Systems (NIPS) Foundation, 2009 Y.  Bengio, Dong-Hyun Lee, Jorg Bornschein, Thomas Mesnard, Zhouhan Lin: Towards Biologically Plausible Deep Learning, arXiv. org, 2016 Bengio contributed one chapter to Architects of Intelligence: The Truth About AI from the People Building it, Packt Publishing, 2018, ISBN 978-1-78-913151-2, by the American futurist Martin Ford.


Ian Goodfellow

Career After graduation, Goodfellow joined Google as part of the Google Brain research team. In March 2016 he left Google to join the newly founded OpenAI research laboratory. Barely 11 months later, in March 2017, Goodfellow returned to Google Research but left again in 2019. In 2019 Goodfellow joined Apple as director of machine learning in the Special Projects Group. He resigned from Apple in April 2022 to protest Apple's plan to require in-person work for its employees. Goodfellow then joined DeepMind as a research scientist.


Demis Hassabis

Career_and_research After graduating from Cambridge, Hassabis worked at Lionhead Studios.  Games designer Peter Molyneux, with whom Hassabis had worked at Bullfrog Productions, had recently founded the company.  At Lionhead, Hassabis worked as lead AI programmer on the 2001 "god" game Black & White.  Hassabis left Lionhead in 1998 to found Elixir Studios, a London-based independent games developer, signing publishing deals with Eidos Interactive, Vivendi Universal and Microsoft.  In addition to managing the company, Hassabis served as executive designer of the BAFTA-nominated games Republic: The Revolution and Evil Genius.  The release of Elixir's first game, Republic: The Revolution, a highly ambitious and unusual political simulation game, was delayed due to its huge scope, which involved an AI simulation of the workings of an entire fictional country.  The final game was reduced from its original vision and greeted with lukewarm reviews, receiving a Metacritic score of 62/100.  Evil Genius, a tongue-in-cheek Bond villain simulator, fared much better with a score of 75/100.  In April 2005 the intellectual property and technology rights were sold to various publishers and the studio was closed.  Following Elixir Studios, Hassabis returned to academia to obtain his PhD in cognitive neuroscience from University College London (UCL) in 2009 supervised by Eleanor Maguire.  He sought to find inspiration in the human brain for new AI algorithms.  He continued his neuroscience and artificial intelligence research as a visiting scientist jointly at Massachusetts Institute of Technology (MIT), in the lab of Tomaso Poggio, and Harvard University, before earning a Henry Wellcome postdoctoral research fellowship to the Gatsby Computational Neuroscience Unit at UCL in 2009 working with Peter Dayan.  Working in the field of imagination, memory and amnesia, he co-authored several influential papers published in Nature, Science, Neuron and PNAS.  His very first academic work, published in PNAS, was a landmark paper that showed systematically for the first time that patients with damage to their hippocampus, known to cause amnesia, were also unable to imagine themselves in new experiences.  The finding established a link between the constructive process of imagination and the reconstructive process of episodic memory recall.  Based on this work and a follow-up functional magnetic resonance imaging (fMRI) study, Hassabis developed a new theoretical account of the episodic memory system identifying scene construction, the generation and online maintenance of a complex and coherent scene, as a key process underlying both memory recall and imagination.  This work received widespread coverage in the mainstream media and was listed in the top 10 scientific breakthroughs of the year by the journal Science.  He later generalised these ideas to advance the notion of a 'simulation engine of the mind' whose role it was to imagine events and scenarios to aid with better planning.  Hassabis is the CEO and co-founder of DeepMind, a machine learning AI startup, founded in London in 2010 with Shane Legg and Mustafa Suleyman.  Hassabis met Legg when both were postdocs at the Gatsby Computational Neuroscience Unit, and he and Suleyman had been friends through family.


Demis Hassabis

Career_and_research Hassabis also recruited his university friend and Elixir partner David Silver.  DeepMind's mission is to "solve intelligence" and then use intelligence "to solve everything else".  More concretely, DeepMind aims to combine insights from systems neuroscience with new developments in machine learning and computing hardware to unlock increasingly powerful general-purpose learning algorithms that will work towards the creation of an artificial general intelligence (AGI).  The company has focused on training learning algorithms to master games, and in December 2013 it announced that it had made a pioneering breakthrough by training an algorithm called a Deep Q-Network (DQN) to play Atari games at a superhuman level by only using the raw pixels on the screen as inputs.  DeepMind's early investors included several high-profile tech entrepreneurs.  In 2014, Google purchased DeepMind for ��400 million.  Although most of the company has remained an independent entity based in London, DeepMind Health has since been directly incorporated into Google Health.  Since the Google acquisition, the company has notched up a number of significant achievements, perhaps the most notable being the creation of AlphaGo, a program that defeated world champion Lee Sedol at the complex game of Go.  Go had been considered a holy grail of AI, for its high number of possible board positions and resistance to existing programming techniques.  However, AlphaGo beat European champion Fan Hui 5���0 in October 2015 before winning 4���1 against former world champion Lee Sedol in March 2016.  Additional DeepMind accomplishments include creating a Neural Turing Machine, reducing the energy used by the cooling systems in Google's data centers by 40%, advancing research on AI safety, and the creation of a partnership with the National Health Service (NHS) of the United Kingdom and Moorfields Eye Hospital to improve medical service and identify the onset of degenerative eye conditions.  More recently, DeepMind turned its artificial intelligence to protein folding, a 50-year grand challenge in science, to predict the 3D structure of a protein from its 1D amino acid sequence.  This is an important problem in biology, as proteins are essential to life, almost every biological function depends on them, and the function of a protein is thought to be related to its structure.  In December 2018, DeepMind's tool AlphaFold won the 13th Critical Assessment of Techniques for Protein Structure Prediction (CASP) by successfully predicting the most accurate structure for 25 out of 43 proteins.  "This is a lighthouse project, our first major investment in terms of people and resources into a fundamental, very important, real-world scientific problem", Hassabis said to The Guardian.  In November 2020, DeepMind again announced world-beating results in the CASP14 edition of the competition, with a median global distance test (GDT) score of 87.0 across protein targets in the challenging free-modeling category, much higher than the same 2018 results with a median GDT < 60, and an overall error of less than the width of an atom, making it competitive with experimental methods.


Demis Hassabis

Career_and_research DeepMind has also been responsible for technical advancements in machine learning, having produced a number of award-winning papers.  In particular, the company has made significant advances in deep learning and reinforcement learning, and pioneered the field of deep reinforcement learning which combines these two methods.  Hassabis has predicted that Artificial Intelligence will be "one of the most beneficial technologies of mankind ever" but that significant ethical issues remain.  In 2023, Hassabis signed the statement that "Mitigating the risk of extinction from AI should be a global priority alongside other societal-scale risks such as pandemics and nuclear war".  He considers however that a pause on AI progress would be very hard to enforce worldwide, and that the potential benefits (e. g.  for health and against climate change) make it worth continuing.  He said that there is an urgent need for research on evaluation tests that measure how capable and controllable new AI models are.


Andrej Karpathy

Andrej Karpathy Andrej Karpathy (born 23 October 1986) is a Slovak-Canadian computer scientist who served as the director of artificial intelligence and Autopilot Vision at Tesla. He currently works for OpenAI, where he specializes in deep learning and computer vision.


Andrej Karpathy

Biography Karpathy was born in Bratislava, Czechoslovakia (now Slovakia) and moved with his family to Toronto when he was 15. He completed his Computer Science and Physics bachelor's degrees at University of Toronto in 2009 and his master's degree at University of British Columbia in 2011, where he worked on physically-simulated figures (for example, a simulated runner or a simulated person in a crowd). Karpathy received a PhD from Stanford University in 2016 under the supervision of Fei-Fei Li, focusing on the intersection of natural language processing and computer vision, and deep learning models suited for this task. He authored and was the primary instructor of the first deep learning course at Stanford, CS 231n: Convolutional Neural Networks for Visual Recognition. It became one of the largest classes at Stanford, growing from 150 students in 2015 to 750 in 2017. Karpathy is a founding member of the artificial intelligence research group OpenAI, where he was a research scientist from 2015 to 2017. In June 2017 he became Tesla's director of artificial intelligence. He was named one of MIT Technology Review's Innovators Under 35 for 2020. After taking a several months-long sabbatical from Tesla, he announced he was leaving the company in July 2022. As of February 2023, he makes YouTube videos on how to create artificial neural networks. In February 2023, Karpathy announced he was returning to OpenAI.


Philosophy of artificial intelligence

Can_a_machine_display_general_intelligence.3F Is it possible to create a machine that can solve all the problems humans solve using their intelligence?  This question defines the scope of what machines could do in the future and guides the direction of AI research.  It only concerns the behavior of machines and ignores the issues of interest to psychologists, cognitive scientists and philosophers, evoking the question: does it matter whether a machine is really thinking, as a person thinks, rather than just producing outcomes that appear to result from thinking?  The basic position of most AI researchers is summed up in this statement, which appeared in the proposal for the Dartmouth workshop of 1956: "Every aspect of learning or any other feature of intelligence can be so precisely described that a machine can be made to simulate it. "Arguments against the basic premise must show that building a working AI system is impossible because there is some practical limit to the abilities of computers or that there is some special quality of the human mind that is necessary for intelligent behavior and yet cannot be duplicated by a machine (or by the methods of current AI research).  Arguments in favor of the basic premise must show that such a system is possible.  It is also possible to sidestep the connection between the two parts of the above proposal.  For instance, machine learning, beginning with Turing's infamous child machine proposal, essentially achieves the desired feature of intelligence without a precise design-time description as to how it would exactly work.  The account on robot tacit knowledge eliminates the need for a precise description altogether.  The first step to answering the question is to clearly define "intelligence".  Alan Turing reduced the problem of defining intelligence to a simple question about conversation.  He suggests that: if a machine can answer any question posed to it, using the same words that an ordinary person would, then we may call that machine intelligent.  A modern version of his experimental design would use an online chat room, where one of the participants is a real person and one of the participants is a computer program.  The program passes the test if no one can tell which of the two participants is human.  Turing notes that no one (except philosophers) ever asks the question "can people think? " He writes "instead of arguing continually over this point, it is usual to have a polite convention that everyone thinks".  Turing's test extends this polite convention to machines: If a machine acts as intelligently as a human being, then it is as intelligent as a human being. One criticism of the Turing test is that it only measures the "humanness" of the machine's behavior, rather than the "intelligence" of the behavior.  Since human behavior and intelligent behavior are not exactly the same thing, the test fails to measure intelligence.  Stuart J.


Philosophy of artificial intelligence

Can_a_machine_display_general_intelligence.3F Russell and Peter Norvig write that "aeronautical engineering texts do not define the goal of their field as 'making machines that fly so exactly like pigeons that they can fool other pigeons'".  Twenty-first century AI research defines intelligence in terms of goal-directed behavior.  It views intelligence as a set of problems that the machine is expected to solve -- the more problems it can solve, and the better its solutions are, the more intelligent the program is.  AI founder John McCarthy defined intelligence as "the computational part of the ability to achieve goals in the world. " Stuart Russell and Peter Norvig formalized this definition using abstract intelligent agents.  An "agent" is something which perceives and acts in an environment.  A "performance measure" defines what counts as success for the agent.  "If an agent acts so as to maximize the expected value of a performance measure based on past experience and knowledge then it is intelligent. "Definitions like this one try to capture the essence of intelligence.  They have the advantage that, unlike the Turing test, they do not also test for unintelligent human traits such as making typing mistakes.  They have the disadvantage that they can fail to differentiate between "things that think" and "things that do not".  By this definition, even a thermostat has a rudimentary intelligence.  Hubert Dreyfus describes this argument as claiming that "if the nervous system obeys the laws of physics and chemistry, which we have every reason to suppose it does, then . . .  we . . .  ought to be able to reproduce the behavior of the nervous system with some physical device".  This argument, first introduced as early as 1943 and vividly described by Hans Moravec in 1988, is now associated with futurist Ray Kurzweil, who estimates that computer power will be sufficient for a complete brain simulation by the year 2029.  A non-real-time simulation of a thalamocortical model that has the size of the human brain (1011 neurons) was performed in 2005, and it took 50 days to simulate 1 second of brain dynamics on a cluster of 27 processors.  Even AI's harshest critics (such as Hubert Dreyfus and John Searle) agree that a brain simulation is possible in theory.  However, Searle points out that, in principle, anything can be simulated by a computer; thus, bringing the definition to its breaking point leads to the conclusion that any process at all can technically be considered "computation".  "What we wanted to know is what distinguishes the mind from thermostats and livers," he writes.  Thus, merely simulating the functioning of a living brain would in itself be an admission of ignorance regarding intelligence and the nature of the mind, like trying to build a jet airliner by copying a living bird precisely, feather by feather, with no theoretical understanding of aeronautical engineering.  In 1963, Allen Newell and Herbert A.  Simon proposed that "symbol manipulation" was the essence of both human and machine intelligence.


Philosophy of artificial intelligence

Can_a_machine_display_general_intelligence.3F They wrote: "A physical symbol system has the necessary and sufficient means of general intelligent action. "This claim is very strong: it implies both that human thinking is a kind of symbol manipulation (because a symbol system is necessary for intelligence) and that machines can be intelligent (because a symbol system is sufficient for intelligence).  Another version of this position was described by philosopher Hubert Dreyfus, who called it "the psychological assumption": "The mind can be viewed as a device operating on bits of information according to formal rules. "The "symbols" that Newell, Simon and Dreyfus discussed were word-like and high level���symbols that directly correspond with objects in the world, such as <dog> and <tail>.  Most AI programs written between 1956 and 1990 used this kind of symbol.  Modern AI, based on statistics and mathematical optimization, does not use the high-level "symbol processing" that Newell and Simon discussed.  These arguments show that human thinking does not consist (solely) of high level symbol manipulation.  They do not show that artificial intelligence is impossible, only that more than symbol processing is required.  In 1931, Kurt G��del proved with an incompleteness theorem that it is always possible to construct a "G��del statement" that a given consistent formal system of logic (such as a high-level symbol manipulation program) could not prove.  Despite being a true statement, the constructed G��del statement is unprovable in the given system.  (The truth of the constructed G��del statement is contingent on the consistency of the given system; applying the same process to a subtly inconsistent system will appear to succeed, but will actually yield a false "G��del statement" instead. )[citation needed] More speculatively, G��del conjectured that the human mind can correctly eventually determine the truth or falsity of any well-grounded mathematical statement (including any possible G��del statement), and that therefore the human mind's power is not reducible to a mechanism.  Philosopher John Lucas (since 1961) and Roger Penrose (since 1989) have championed this philosophical anti-mechanist argument.  G��delian anti-mechanist arguments tend to rely on the innocuous-seeming claim that a system of human mathematicians (or some idealization of human mathematicians) is both consistent (completely free of error) and believes fully in its own consistency (and can make all logical inferences that follow from its own consistency, including belief in its G��del statement)[citation needed].  This is provably impossible for a Turing machine to do (see Halting problem); therefore, the G��delian concludes that human reasoning is too powerful to be captured by a Turing machine, and by extension, any digital mechanical device.  However, the modern consensus in the scientific and mathematical community is that actual human reasoning is inconsistent; that any consistent "idealized version" H of human reasoning would logically be forced to adopt a healthy but counter-intuitive open-minded skepticism about the consistency of H (otherwise H is provably inconsistent); and that G��del's theorems do not lead to any valid argument that humans have mathematical reasoning capabilities beyond what a machine could ever duplicate.


Philosophy of artificial intelligence

Can_a_machine_display_general_intelligence.3F This consensus that G��delian anti-mechanist arguments are doomed to failure is laid out strongly in Artificial Intelligence: "any attempt to utilize (G��del's incompleteness results) to attack the computationalist thesis is bound to be illegitimate, since these results are quite consistent with the computationalist thesis. " Stuart Russell and Peter Norvig agree that G��del's argument does not consider the nature of real-world human reasoning.  It applies to what can theoretically be proved, given an infinite amount of memory and time.  In practice, real machines (including humans) have finite resources and will have difficulty proving many theorems.  It is not necessary to be able to prove everything in order to be an intelligent person.  Less formally, Douglas Hofstadter, in his Pulitzer prize winning book G��del, Escher, Bach: An Eternal Golden Braid, states that these "G��del-statements" always refer to the system itself, drawing an analogy to the way the Epimenides paradox uses statements that refer to themselves, such as "this statement is false" or "I am lying".  But, of course, the Epimenides paradox applies to anything that makes statements, whether they are machines or humans, even Lucas himself.  Consider: Lucas can't assert the truth of this statement. This statement is true but cannot be asserted by Lucas.  This shows that Lucas himself is subject to the same limits that he describes for machines, as are all people, and so Lucas's argument is pointless.  After concluding that human reasoning is non-computable, Penrose went on to controversially speculate that some kind of hypothetical non-computable processes involving the collapse of quantum mechanical states give humans a special advantage over existing computers.  Existing quantum computers are only capable of reducing the complexity of Turing computable tasks and are still restricted to tasks within the scope of Turing machines. [citation needed][clarification needed].  By Penrose and Lucas's arguments, the fact that quantum computers are only able to complete Turing computable tasks implies that they cannot be sufficient for emulating the human mind. [citation needed] Therefore, Penrose seeks for some other process involving new physics, for instance quantum gravity which might manifest new physics at the scale of the Planck mass via spontaneous quantum collapse of the wave function.  These states, he suggested, occur both within neurons and also spanning more than one neuron.  However, other scientists point out that there is no plausible organic mechanism in the brain for harnessing any sort of quantum computation, and furthermore that the timescale of quantum decoherence seems too fast to influence neuron firing.  Hubert Dreyfus argued that human intelligence and expertise depended primarily on fast intuitive judgements rather than step-by-step symbolic manipulation, and argued that these skills would never be captured in formal rules.  Dreyfus's argument had been anticipated by Turing in his 1950 paper Computing machinery and intelligence, where he had classified this as the "argument from the informality of behavior. " Turing argued in response that, just because we do not know the rules that govern a complex behavior, this does not mean that no such rules exist.


Philosophy of artificial intelligence

Can_a_machine_display_general_intelligence.3F He wrote: "we cannot so easily convince ourselves of the absence of complete laws of behaviour . . .  The only way we know of for finding such laws is scientific observation, and we certainly know of no circumstances under which we could say, 'We have searched enough.  There are no such laws. '" Russell and Norvig point out that, in the years since Dreyfus published his critique, progress has been made towards discovering the "rules" that govern unconscious reasoning.  The situated movement in robotics research attempts to capture our unconscious skills at perception and attention.  Computational intelligence paradigms, such as neural nets, evolutionary algorithms and so on are mostly directed at simulated unconscious reasoning and learning.  Statistical approaches to AI can make predictions which approach the accuracy of human intuitive guesses.  Research into commonsense knowledge has focused on reproducing the "background" or context of knowledge.  In fact, AI research in general has moved away from high level symbol manipulation, towards new models that are intended to capture more of our intuitive reasoning.  Cognitive science and psychology eventually came to agree with Dreyfus' description of human expertise.  Daniel Kahnemann and others developed a similar theory where they identified two "systems" that humans use to solve problems, which he called "System 1" (fast intuitive judgements) and "System 2" (slow deliberate step by step thinking).  Although Dreyfus' views have been vindicated in many ways, the work in cognitive science and in AI was in response to specific problems in those fields and was not directly influenced by Dreyfus.  Historian and AI researcher Daniel Crevier wrote that "time has proven the accuracy and perceptiveness of some of Dreyfus's comments.  Had he formulated them less aggressively, constructive actions they suggested might have been taken much earlier.


Clearview AI

Use Following a data leak of Clearview's customer list, Buzzfeed confirmed that 2,200 organizations in 27 countries had accounts with activity.  The listing below was current as of February 27, 2020, prior to Clearview's May 2022 settlement with the ACLU, to only sell its services to law enforcement and government agencies.  Some may only have had trial access, and many organizations denied any connection to Clearview.  Illinois Secretary of State (almost 9,000 searches, has been using since approx Nov 2019) Macon County, Illinois Sheriff's Office (2,000 searches) Naperville, Illinois Police Department (1,700 searches) New York Police Department (over 11,000 searches by over 30 accounts) Raleigh Police Department, North Carolina (a paid client, then its use was banned, then continued to use trial access after the ban) Senoia Police Department, Senoia, Georgia (a paid customer) Chicago Police Department (a paid customer, over 1,500 searches on 30 accounts, paid $49,875 for a two-year license) New York State Police (a paid customer, $15,000 for licenses) Indiana State Police (a paid customer, over 5,700 searches) San Mateo County Sheriffs Office, California (over 2,000 searches) San Diego Police Department (trialed by at least 2 detectives, then use prohibited on February 19, 2020 and reviewing ethical concerns) San Diego County District Attorney's office (unauthorized trials by 8 investigators) Philadelphia Police Department (over 2,000 searches) Miami Police Department (over 3,000 searches) Plano Police Department, Plano, Texas (trialed; a yearly subscription quoted at $10,000) Irving Police Department, Irving, Texas (trialed) Fort Worth Police Department, Fort Worth, Texas (trialed, 250 searches) Texas Department of Public Safety (signed a $24k contract in December 2019) South Plainfield, New Jersey (signed a $2k contract in December 2019) North Dakota Attorney General (signed a $5k contract in January 2020) "White House Tech Office" (6 searches) FBI (5,700 searches) BATF (2,100 searches) US Secret Service (5,600 searches) DEA (2,000 searches) Department of Homeland Security's fusion centers; 10 centers have used it, one, the Louisiana State Analytic and Fusion Exchange, is a paying customer U. S.  Air Force (signed a $50k contract in December 2019) U. S.  Customs and Border Protection (not a paid customer, 280 accounts, 7,500 searches) U. S.


Clearview AI

Use Immigration and Customs Enforcement divisions (60 accounts) including their Child Exploitation Investigations Unit of HSI (a paid customer as part of a pilot program), the Border Enforcement Security Task Force at JFK Airport, the Enforcement and Removal Operations, an HSI office in El Paso, Texas, and an office in Cherry Hill, New Jersey Republican Representative John Ratcliffe, twice nominated as Director of National Intelligence (never logged in or used the account) Virginia Beach Police Republican Representative Mark Walker (a staffer ran over 10 searches) Republican Representative Mike Rogers (never logged in or used the account) Republican Representative Lee Zeldin (never logged in or used the account)Columbia University Southern Methodist University University of Alabama Central Montco Technical High School, Montgomery County, Pennsylvania Somerset Berkley Regional High School, Somerset, Massachusetts Gavin de Becker and Associates (a paid customer with over 3,600 searches) SilverSEAL Global Security Home Depot AT&T (have performed over 200 searches) Verizon T-Mobile Kohls (over 2,000 searches) Rite Aid Best Buy Albertsons Walmart Macys (a paid customer with over 6,000 searches; terminated contract in January 2020) Wells Fargo Bank of America (over 1,900 searches) Coinbase Equinox Fitness National Basketball Association Pechanga Resort & Casino Las Vegas Sands Eventbrite Madison Square Garden Mubadala Investment Company, a sovereign wealth fund of United Arab Emirates (ran over 100 searches) AI Center of Advanced Studies (aka Thakaa), Riyadh, Saudi Arabia SHW Partners, LLC (Jason Miller), listed as "friend" Samarian Group (PE firm), listed as "friend" Droese Raney Architecture, listed as "friend" American Enterprise Institute (logins from AEI posted a banner stating "Richard says hi", presumably referring to Richard Schwartz) The Manhattan Institute (at least a dozen searches, though denied by the think tank) Greylock Partners (a potential investor in 2018) Data Collective Venture Capital (over 270 searches, as recently as Feb 2020) Passport Capital (over 350 searches) Sequoia Capital (over 210 searches in 10 months) Founders Fund (2 accounts and 70 searches) Thiel Capital (one account, never used) ICONIQ Capital (over 70 searches, as recently as Feb 2020) SoftBank RIT Capital Partners The Zellman Group (over 1,700 searches) Bruning Law Group Frontwave Credit Union Navy Federal Credit Union Chicago Cubs baseball team (15 searches)Vadodara City Police, part of the Gujarat Police in Vadodara, India Australian Federal Police Australian Centre to Counter Child Exploitation (7 trial accounts, Nov 2019 ��� Jan 2020) Metropolitan Police Service, London, UK 30 law enforcement agencies in Canada Royal Canadian Mounted Police (paying customer, used for four months in the National Child Exploitation Crime Centre and by others as a trial) Ontario Provincial Police Edmonton Police Service, Edmonton, Alberta (used by three officers without department approval) Halifax Regional Police, Halifax, Nova Scotia (by at least one officer as a trial) Halton Regional Police, Halton, Ontario (trialed) Hamilton Police Service, Hamilton, Ontario (trialed) London Police Service, London, Ontario (trial by seven officers) Niagara Regional Police Service, Niagara Falls, Ontario (trialed) Ottawa Police Service, Ottawa, Ontario (trialed) Toronto Police Service (tested from October 2019 to February 2020) York Regional Police (approximately 500 searches, used a trial without department approval) Peel Regional Police, Mississauga, Ontario Sweden law enforcement Ministry of Defence of Ukraine New Zealand Police (trialed Jan 2020)Australian Centre to Counter Child Exploitation (7 trial accounts, Nov 2019 ��� Jan 2020)Royal Canadian Mounted Police (paying customer, used for four months in the National Child Exploitation Crime Centre and by others as a trial) Ontario Provincial Police Edmonton Police Service, Edmonton, Alberta (used by three officers without department approval) Halifax Regional Police, Halifax, Nova Scotia (by at least one officer as a trial) Halton Regional Police, Halton, Ontario (trialed) Hamilton Police Service, Hamilton, Ontario (trialed) London Police Service, London, Ontario (trial by seven officers) Niagara Regional Police Service, Niagara Falls, Ontario (trialed) Ottawa Police Service, Ottawa, Ontario (trialed) Toronto Police Service (tested from October 2019 to February 2020) York Regional Police (approximately 500 searches, used a trial without department approval) Peel Regional Police, Mississauga, OntarioThe New Zealand Police used it in a trial after being approached by Clearview's Marko Jukic in January 2020.


Clearview AI

Use Jukic said it would have helped identify the Christchurch mosque shooter had the technology been available.  During the police's trial they searched for people "of M��ori or Polynesian ethnicity", as well as "Irish roof contractors" to determine its bias and accuracy.  This raised strong objections once exposed, as neither the users' supervisors or the Privacy Commissioner were aware or approved of its use.  After it was revealed by RNZ, Justice Minister Andrew Little stated "I don't know how it came to be that a person thought that this was a good idea", going on to say "It clearly wasn't endorsed, from the senior police hierarchy, and it clearly didn't get the endorsement from the [Police] Minister nor indeed from the wider cabinet . . .  that is a matter of concern. " Clearview's technology was used for identifying an individual at a May 30, 2020 George Floyd police violence protest in Miami, Florida.  Miami's WTVJ confirmed this, as the arrest report only said she was "identified through investigative means".  The defendant's attorney did not even know it was with Clearview.  Ton-That confirmed its use, noting that it was not being used for surveillance, but only to investigate a crime.  In another Florida case, Clearview's technology was used by defense attorneys to successfully locate a witness, resulting in the dismissal of vehicular homicide charges against the defendant.  According to Ton-That, Clearview also aided in locating a crucial witness for a case against a defendant in Florida.  The person's defense lawyer remarked that the AI was able to get matches in just 3���5 seconds.


Chatbot

Chatbot A chatbot (originally chatterbot) is a software application or web interface that aims to mimic human conversation through text or voice interactions. Modern chatbots are typically online and use artificial intelligence (AI) systems that are capable of maintaining a conversation with a user in natural language and simulating the way a human would behave as a conversational partner. Such technologies often utilize aspects of deep learning and natural language processing, but more simplistic chatbots have been around for decades prior. Recently, this field has gained widespread attention due to the popularity of OpenAI's ChatGPT (using GPT-3 or GPT-4), released in 2022, followed by alternatives such as Microsoft's Bing Chat (which uses OpenAI's GPT-4) and Google's Bard. Such examples reflect the recent practice of such products being built based upon broad foundational large language models that get fine-tuned so as to target specific tasks or applications (i.e. simulating human conversation, in the case of chatbots). Chatbots can also be designed or customized to further target even more specific situations and/or particular subject-matter domains. A major area where chatbots have long been used is in customer service and support, such as with various sorts of virtual assistants. Companies spanning various industries have begun using the latest generative artificial intelligence technologies to power more advanced developments in such areas.


Chatbot

Development Among the most notable early chatbots are ELIZA (1966) and PARRY (1972). More recent notable programs include A.L.I.C.E., Jabberwacky and D.U.D.E (Agence Nationale de la Recherche and CNRS 2006). While ELIZA and PARRY were used exclusively to simulate typed conversation, many chatbots now include other functional features, such as games and web searching abilities. In 1984, a book called The Policeman's Beard is Half Constructed was published, allegedly written by the chatbot Racter (though the program as released would not have been capable of doing so). From 1978 to some time after 1983, the CYRUS project led by Janet Kolodner constructed a chatbot simulating Cyrus Vance (57th United States Secretary of State). It used case-based reasoning, and updated its database daily by parsing wire news from United Press International. The program was unable to process the news items subsequent to the surprise resignation of Cyrus Vance in April 1980, and the team constructed another chatbot simulating his successor, Edmund Muskie. One pertinent field of AI research is natural-language processing. Usually, weak AI fields employ specialized software or programming languages created specifically for the narrow function required. For example, A.L.I.C.E. uses a markup language called AIML, which is specific to its function as a conversational agent, and has since been adopted by various other developers of, so-called, Alicebots. Nevertheless, A.L.I.C.E. is still purely based on pattern matching techniques without any reasoning capabilities, the same technique ELIZA was using back in 1966. This is not strong AI, which would require sapience and logical reasoning abilities. Jabberwacky learns new responses and context based on real-time user interactions, rather than being driven from a static database. Some more recent chatbots also combine real-time learning with evolutionary algorithms that optimize their ability to communicate based on each conversation held. Still, there is currently no general purpose conversational artificial intelligence, and some software developers focus on the practical aspect, information retrieval. Chatbot competitions focus on the Turing test or more specific goals. Two such annual contests are the Loebner Prize and The Chatterbox Challenge (the latter has been offline since 2015, however, materials can still be found from web archives). Chatbots may use neural networks as a language model. For example, generative pre-trained transformers (GPT), which use the transformer architecture, have become common to build sophisticated chatbots. The "pre-training" in its name refers to the initial training process on a large text corpus, which provides a solid foundation for the model to perform well on downstream tasks with limited amounts of task-specific data. An example of a GPT chatbot is ChatGPT. Despite criticism of its accuracy, ChatGPT has gained attention for its detailed responses and historical knowledge. Another example is BioGPT, developed by Microsoft, which focuses on answering biomedical questions. DBpedia created a chatbot during the GSoC of 2017. It can communicate through Facebook Messenger.


Chatbot

See_also Linguistics portalApplications of artificial intelligence Autonomous agent ChatGPT (from OpenAI) Conversational user interface Dead Internet theory Eugene Goostman Friendly artificial intelligence Hybrid intelligent system Intelligent agent Internet bot List of chatbots Multi-agent system Natural language processing Social bot Software agent Software bot Stochastic parrot Twitterbot


List of speech recognition software

Interactive_voice_response The following are interactive voice response (IVR) systems: CSLU Toolkit Genesys HTK ��� copyrighted by Microsoft, but allows altering software for licensee's internal use LumenVox ASR Tellme Networks; acquired by Microsoft


Data compression

Lossless Lossless data compression algorithms usually exploit statistical redundancy to represent data without losing any information, so that the process is reversible.  Lossless compression is possible because most real-world data exhibits statistical redundancy.  For example, an image may have areas of color that do not change over several pixels; instead of coding "red pixel, red pixel, . . . " the data may be encoded as "279 red pixels".  This is a basic example of run-length encoding; there are many schemes to reduce file size by eliminating redundancy.  The Lempel���Ziv (LZ) compression methods are among the most popular algorithms for lossless storage.  DEFLATE is a variation on LZ optimized for decompression speed and compression ratio, but compression can be slow.  In the mid-1980s, following work by Terry Welch, the Lempel���Ziv���Welch (LZW) algorithm rapidly became the method of choice for most general-purpose compression systems.  LZW is used in GIF images, programs such as PKZIP, and hardware devices such as modems.  LZ methods use a table-based compression model where table entries are substituted for repeated strings of data.  For most LZ methods, this table is generated dynamically from earlier data in the input.  The table itself is often Huffman encoded.  Grammar-based codes like this can compress highly repetitive input extremely effectively, for instance, a biological data collection of the same or closely related species, a huge versioned document collection, internet archival, etc.  The basic task of grammar-based codes is constructing a context-free grammar deriving a single string.  Other practical grammar compression algorithms include Sequitur and Re-Pair.  The strongest modern lossless compressors use probabilistic models, such as prediction by partial matching.  The Burrows���Wheeler transform can also be viewed as an indirect form of statistical modelling.  In a further refinement of the direct use of probabilistic modelling, statistical estimates can be coupled to an algorithm called arithmetic coding.  Arithmetic coding is a more modern coding technique that uses the mathematical calculations of a finite-state machine to produce a string of encoded bits from a series of input data symbols.  It can achieve superior compression compared to other techniques such as the better-known Huffman algorithm.  It uses an internal memory state to avoid the need to perform a one-to-one mapping of individual input symbols to distinct representations that use an integer number of bits, and it clears out the internal memory only after encoding the entire string of data symbols.  Arithmetic coding applies especially well to adaptive data compression tasks where the statistics vary and are context-dependent, as it can be easily coupled with an adaptive model of the probability distribution of the input data.  An early example of the use of arithmetic coding was in an optional (but not widely used) feature of the JPEG image coding standard.  It has since been applied in various other designs including H.263, H.264/MPEG-4 AVC and HEVC for video coding.


Data compression

Lossless Archive software typically has the ability to adjust the "dictionary size", where a larger size demands more random-access memory during compression and decompression, but compresses stronger, especially on repeating patterns in files' content.


Laplace filter

Discrete_heat_equation Suppose �� {\textstyle \phi } describes a temperature distribution across a graph, where �� i {\textstyle \phi _{i}} is the temperature at vertex i {\textstyle i} .  According to Newton's law of cooling, the heat transferred from node i {\textstyle i} to node j {\textstyle j} is proportional to �� i ��� �� j {\textstyle \phi _{i}-\phi _{j}} if nodes i {\textstyle i} and j {\textstyle j} are connected (if they are not connected, no heat is transferred).  Then, for thermal conductivity k {\textstyle k} , In matrix-vector notation, which gives Notice that this equation takes the same form as the heat equation, where the matrix ���L is replacing the Laplacian operator ��� 2 {\textstyle \nabla ^{2}} ; hence, the "graph Laplacian".  To find a solution to this differential equation, apply standard techniques for solving a first-order matrix differential equation.  That is, write �� {\textstyle \phi } as a linear combination of eigenvectors v i {\textstyle \mathbf {v} _{i}} of L (so that L v i = �� i v i {\textstyle L\mathbf {v} _{i}=\lambda _{i}\mathbf {v} _{i}} ) with time-dependent coefficients, �� ( t ) = ��� i c i ( t ) v i .  {\textstyle \phi (t)=\sum _{i}c_{i}(t)\mathbf {v} _{i}. } Plugging into the original expression (because L is a symmetric matrix, its unit-norm eigenvectors v i {\textstyle \mathbf {v} _{i}} are orthogonal): whose solution is As shown before, the eigenvalues �� i {\textstyle \lambda _{i}} of L are non-negative, showing that the solution to the diffusion equation approaches an equilibrium, because it only exponentially decays or remains constant.  This also shows that given �� i {\textstyle \lambda _{i}} and the initial condition c i ( 0 ) {\textstyle c_{i}(0)} , the solution at any time t can be found.  To find c i ( 0 ) {\textstyle c_{i}(0)} for each i {\textstyle i} in terms of the overall initial condition �� ( 0 ) {\textstyle \phi (0)} , simply project �� ( 0 ) {\textstyle \phi (0)} onto the unit-norm eigenvectors v i {\textstyle \mathbf {v} _{i}} ; This approach has been applied to quantitative heat transfer modelling on unstructured grids.  In the case of undirected graphs, this works because L {\textstyle L} is symmetric, and by the spectral theorem, its eigenvectors are all orthogonal.  So the projection onto the eigenvectors of L {\textstyle L} is simply an orthogonal coordinate transformation of the initial condition to a set of coordinates which decay exponentially and independently of each other.  To understand lim t ��� ��� �� ( t ) {\textstyle \lim _{t\to \infty }\phi (t)} , the only terms c i ( t ) = c i ( 0 ) e ��� k �� i t {\textstyle c_{i}(t)=c_{i}(0)e^{-k\lambda _{i}t}} that remain are those where �� i = 0 {\textstyle \lambda _{i}=0} , since In other words, the equilibrium state of the system is determined completely by the kernel of L {\textstyle L} .


Laplace filter

Discrete_heat_equation Since by definition, ��� j L i j = 0 {\textstyle \sum _{j}L_{ij}=0} , the vector v 1 {\textstyle \mathbf {v} ^{1}} of all ones is in the kernel.  If there are k {\textstyle k} disjoint connected components in the graph, then this vector of all ones can be split into the sum of k {\textstyle k} independent �� = 0 {\textstyle \lambda =0} eigenvectors of ones and zeros, where each connected component corresponds to an eigenvector with ones at the elements in the connected component and zeros elsewhere.  The consequence of this is that for a given initial condition c ( 0 ) {\textstyle c(0)} for a graph with N {\textstyle N} vertices where For each element �� j {\textstyle \phi _{j}} of �� {\textstyle \phi } , i. e.  for each vertex j {\textstyle j} in the graph, it can be rewritten as In other words, at steady state, the value of �� {\textstyle \phi } converges to the same value at each of the vertices of the graph, which is the average of the initial values at all of the vertices.  Since this is the solution to the heat diffusion equation, this makes perfect sense intuitively.  We expect that neighboring elements in the graph will exchange energy until that energy is spread out evenly throughout all of the elements that are connected to each other.  This section shows an example of a function �� {\textstyle \phi } diffusing over time through a graph.  The graph in this example is constructed on a 2D discrete grid, with points on the grid connected to their eight neighbors.  Three initial points are specified to have a positive value, while the rest of the values in the grid are zero.  Over time, the exponential decay acts to distribute the values at these points evenly throughout the entire grid.  The complete Matlab source code that was used to generate this animation is provided below.  It shows the process of specifying initial conditions, projecting these initial conditions onto the eigenvalues of the Laplacian Matrix, and simulating the exponential decay of these projected initial conditions.


Human Cognitive Abilities

Influence According to Schneider & McGrew, Human Cognitive Abilities was the first ever book to present "an empirically based taxonomy of human cognitive abilities...in a single, coherent, organized, systematic framework". They also described Carroll's book as "a much-needed Rosetta stone" for future human intelligence researchers. Arthur Jensen referred to the book as Carroll's "crowning achievement" and "a truly monumental work. It was a fulfillment of something that most of us would agree needed to be done, but it seemed too vast an undertaking to imagine how it could ever be done effectively and adequately." In 1998, Carroll himself described the book's publication as "the most bracing event of my life" over the previous few years.


Image compression

Lossy_and_lossless_image_compression Image compression may be lossy or lossless.  Lossless compression is preferred for archival purposes and often for medical imaging, technical drawings, clip art, or comics.  Lossy compression methods, especially when used at low bit rates, introduce compression artifacts.  Lossy methods are especially suitable for natural images such as photographs in applications where minor (sometimes imperceptible) loss of fidelity is acceptable to achieve a substantial reduction in bit rate.  Lossy compression that produces negligible differences may be called visually lossless.  Methods for lossy compression: Transform coding ��� This is the most commonly used method.  Discrete Cosine Transform (DCT) ��� The most widely used form of lossy compression.  It is a type of Fourier-related transform, and was originally developed by Nasir Ahmed, T.  Natarajan and K.  R.  Rao in 1974.  The DCT is sometimes referred to as "DCT-II" in the context of a family of discrete cosine transforms (see discrete cosine transform).  It is generally the most efficient form of image compression.  DCT is used in JPEG, the most popular lossy format, and the more recent HEIF.  The more recently developed wavelet transform is also used extensively, followed by quantization and entropy coding.  Color quantization - Reducing the color space to a few "representative" colors in the image.  The selected colors are specified in the color palette in the header of the compressed image.  Each pixel just references the index of a color in the color palette.  This method can be combined with dithering to avoid posterization.  Whole-image palette, typically 256 colors, used in GIF and PNG file formats.  block palette, typically 2 or 4 colors for each block of 4x4 pixels, used in BTC, CCC, S2TC, and S3TC.  Chroma subsampling.  This takes advantage of the fact that the human eye perceives spatial changes of brightness more sharply than those of color, by averaging or dropping some of the chrominance information in the image.  Fractal compression.  More recently, methods based on Machine Learning were applied, using Multilayer perceptrons, Convolutional neural networks and Generative adversarial networks.  Implementations are available in OpenCV, TensorFlow, MATLAB's Image Processing Toolbox (IPT), and the High-Fidelity Generative Image Compression (HiFiC) open source project. Discrete Cosine Transform (DCT) ��� The most widely used form of lossy compression.  It is a type of Fourier-related transform, and was originally developed by Nasir Ahmed, T.  Natarajan and K.  R.  Rao in 1974.  The DCT is sometimes referred to as "DCT-II" in the context of a family of discrete cosine transforms (see discrete cosine transform).  It is generally the most efficient form of image compression.  DCT is used in JPEG, the most popular lossy format, and the more recent HEIF.  The more recently developed wavelet transform is also used extensively, followed by quantization and entropy coding. DCT is used in JPEG, the most popular lossy format, and the more recent HEIF. Whole-image palette, typically 256 colors, used in GIF and PNG file formats.  block palette, typically 2 or 4 colors for each block of 4x4 pixels, used in BTC, CCC, S2TC, and S3TC.


OpenAI Five

OpenAI Five OpenAI Five is a computer program by OpenAI that plays the five-on-five video game Dota 2. Its first public appearance occurred in 2017, where it was demonstrated in a live one-on-one game against the professional player, Dendi, who lost to it. The following year, the system had advanced to the point of performing as a full team of five, and began playing against and showing the capability to defeat professional teams. By choosing a game as complex as Dota 2 to study machine learning, OpenAI thought they could more accurately capture the unpredictability and continuity seen in the real world, thus constructing more general problem-solving systems. The algorithms and code used by OpenAI Five were eventually borrowed by another neural network in development by the company, one which controlled a physical robotic hand. OpenAI Five has been compared to other similar cases of artificial intelligence (AI) playing against and defeating humans, such as AlphaStar in the video game StarCraft II, AlphaGo in the board game Go, Deep Blue in chess, and Watson on the television game show Jeopardy!.


OpenAI Five

History Development on the algorithms used for the bots began in November 2016. OpenAI decided to use Dota 2, a competitive five-on-five video game, as a base due to it being popular on the live streaming platform Twitch, having native support for Linux, and had an application programming interface (API) available. Before becoming a team of five, the first public demonstration occurred at The International 2017 in August, the annual premiere championship tournament for the game, where Dendi, a professional Ukrainian player of the game, lost against an OpenAI bot in a live one-on-one matchup. After the match, CTO Greg Brockman explained that the bot had learned by playing against itself for two weeks of real time, and that the learning software was a step in the direction of creating software that can handle complex tasks "like being a surgeon". OpenAI used a methodology called reinforcement learning, as the bots learn over time by playing against itself hundreds of times a day for months, in which they are rewarded for actions such as killing an enemy and destroying towers. By June 2018, the ability of the bots expanded to play together as a full team of five and were able to defeat teams of amateur and semi-professional players. At The International 2018, OpenAI Five played in two games against professional teams, one against the Brazilian-based paiN Gaming and the other against an all-star team of former Chinese players. Although the bots lost both matches, OpenAI still considered it a successful venture, stating that playing against some of the best players in Dota 2 allowed them to analyze and adjust their algorithms for future games. The bots' final public demonstration occurred in April 2019, where they won a best-of-three series against The International 2018 champions OG at a live event in San Francisco. A four-day online event to play against the bots, open to the public, occurred the same month. There, the bots played in 42,729 public games, winning 99.4% of those games.


OpenAI Five

Architecture Each OpenAI Five bot is a neural network containing a single layer with a 4096-unit LSTM that observes the current game state extracted from the Dota developer's API. The neural network conducts actions via numerous possible action heads (no human data involved), and every head has meaning. For instance, the number of ticks to delay an action, what action to select ��� the X or Y coordinate of this action in a grid around the unit. In addition, action heads are computed independently. The AI system observes the world as a list of 20,000 numbers and takes an action by conducting a list of eight enumeration values. Also, it selects different actions and targets to understand how to encode every action and observe the world. OpenAI Five has been developed as a general-purpose reinforcement learning training system on the "Rapid" infrastructure. Rapid consists of two layers: it spins up thousands of machines and helps them ���talk��� to each other and a second layer runs software. By 2018, OpenAI Five had played around 180 years worth of games in reinforcement learning running on 256 GPUs and 128,000 CPU cores, using Proximal Policy Optimization, a policy gradient method.