Neural network Gaussian process

A Neural Network Gaussian Process (NNGP) is a Gaussian process (GP) obtained as the limit of a certain type of sequence of neural networks. Specifically, a wide variety of network architectures converges to a GP in the infinitely wide limit, in the sense of distribution. The concept constitutes an intensional definition, i.e., a NNGP is just a GP, but distinguished by how it is obtained. == Motivation == Bayesian networks are a modeling tool for assigning probabilities to events, and thereby characterizing the uncertainty in a model's predictions. Deep learning and artificial neural networks are approaches used in machine learning to build computational models which learn from training examples. Bayesian neural networks merge these fields. They are a type of neural network whose parameters and predictions are both probabilistic. While standard neural networks often assign high confidence even to incorrect predictions, Bayesian neural networks can more accurately evaluate how likely their predictions are to be correct. Computation in artificial neural networks is usually organized into sequential layers of artificial neurons. The number of neurons in a layer is called the layer width. When we consider a sequence of Bayesian neural networks with increasingly wide layers (see figure), they converge in distribution to a NNGP. This large width limit is of practical interest, since the networks often improve as layers get wider. And the process may give a closed form way to evaluate networks. NNGPs also appears in several other contexts: It describes the distribution over predictions made by wide non-Bayesian artificial neural networks after random initialization of their parameters, but before training; it appears as a term in neural tangent kernel prediction equations; it is used in deep information propagation to characterize whether hyperparameters and architectures will be trainable. It is related to other large width limits of neural networks. === Scope === The first correspondence result had been established in the 1995 PhD thesis of Radford M. Neal, then supervised by Geoffrey Hinton at University of Toronto. Neal cites David J. C. MacKay as inspiration, who worked in Bayesian learning. Today the correspondence 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. === Illustration === Every setting of a neural network's parameters θ {\displaystyle \theta } corresponds to a specific function computed by the neural network. A prior distribution p ( θ ) {\displaystyle p(\theta )} over neural network parameters therefore corresponds to a prior distribution over functions computed by the network. As neural networks are made infinitely wide, this distribution over functions converges to a Gaussian process for many architectures. The notation used in this section is the same as the notation used below to derive the correspondence between NNGPs and fully connected networks, and more details can be found there. The figure to the right plots the one-dimensional outputs z L ( ⋅ ; θ ) {\displaystyle z^{L}(\cdot ;\theta )} of a neural network for two inputs x {\displaystyle x} and x ∗ {\displaystyle x^{}} against each other. The black dots show the function computed by the neural network on these inputs for random draws of the parameters from p ( θ ) {\displaystyle p(\theta )} . The red lines are iso-probability contours for the joint distribution over network outputs z L ( x ; θ ) {\displaystyle z^{L}(x;\theta )} and z L ( x ∗ ; θ ) {\displaystyle z^{L}(x^{};\theta )} induced by p ( θ ) {\displaystyle p(\theta )} . This is the distribution in function space corresponding to the distribution p ( θ ) {\displaystyle p(\theta )} in parameter space, and the black dots are samples from this distribution. For infinitely wide neural networks, since the distribution over functions computed by the neural network is a Gaussian process, the joint distribution over network outputs is a multivariate Gaussian for any finite set of network inputs. == Discussion == === Infinitely wide fully connected network === This section expands on the correspondence between infinitely wide neural networks and Gaussian processes for the specific case of a fully connected architecture. It provides a proof sketch outlining why the correspondence holds, and introduces the specific functional form of the NNGP for fully connected networks. The proof sketch closely follows the approach by Novak and coauthors. ==== Network architecture specification ==== Consider a fully connected artificial neural network with inputs x {\displaystyle x} , parameters θ {\displaystyle \theta } consisting of weights W l {\displaystyle W^{l}} and biases b l {\displaystyle b^{l}} for each layer l {\displaystyle l} in the network, pre-activations (pre-nonlinearity) z l {\displaystyle z^{l}} , activations (post-nonlinearity) y l {\displaystyle y^{l}} , pointwise nonlinearity ϕ ( ⋅ ) {\displaystyle \phi (\cdot )} , and layer widths n l {\displaystyle n^{l}} . For simplicity, the width n L + 1 {\displaystyle n^{L+1}} of the readout vector z L {\displaystyle z^{L}} is taken to be 1. The parameters of this network have a prior distribution p ( θ ) {\displaystyle p(\theta )} , which consists of an isotropic Gaussian for each weight and bias, with the variance of the weights scaled inversely with layer width. This network is illustrated in the figure to the right, and described by the following set of equations: x ≡ input y l ( x ) = { x l = 0 ϕ ( z l − 1 ( x ) ) l > 0 z i l ( x ) = ∑ j W i j l y j l ( x ) + b i l W i j l ∼ N ( 0 , σ w 2 n l ) b i l ∼ N ( 0 , σ b 2 ) ϕ ( ⋅ ) ≡ nonlinearity y l ( x ) , z l − 1 ( x ) ∈ R n l × 1 n L + 1 = 1 θ = { W 0 , b 0 , … , W L , b L } {\displaystyle {\begin{aligned}x&\equiv {\text{input}}\\y^{l}(x)&=\left\{{\begin{array}{lcl}x&&l=0\\\phi \left(z^{l-1}(x)\right)&&l>0\end{array}}\right.\\z_{i}^{l}(x)&=\sum _{j}W_{ij}^{l}y_{j}^{l}(x)+b_{i}^{l}\\W_{ij}^{l}&\sim {\mathcal {N}}\left(0,{\frac {\sigma _{w}^{2}}{n^{l}}}\right)\\b_{i}^{l}&\sim {\mathcal {N}}\left(0,\sigma _{b}^{2}\right)\\\phi (\cdot )&\equiv {\text{nonlinearity}}\\y^{l}(x),z^{l-1}(x)&\in \mathbb {R} ^{n^{l}\times 1}\\n^{L+1}&=1\\\theta &=\left\{W^{0},b^{0},\dots ,W^{L},b^{L}\right\}\end{aligned}}} ==== ==== z l | y l {\displaystyle z^{l}|y^{l}} is a Gaussian process We first observe that the pre-activations z l {\displaystyle z^{l}} are described by a Gaussian process conditioned on the preceding activations y l {\displaystyle y^{l}} . This result holds even at finite width. Each pre-activation z i l {\displaystyle z_{i}^{l}} is a weighted sum of Gaussian random variables, corresponding to the weights W i j l {\displaystyle W_{ij}^{l}} and biases b i l {\displaystyle b_{i}^{l}} , where the coefficients for each of those Gaussian variables are the preceding activations y j l {\displaystyle y_{j}^{l}} . Because they are a weighted sum of zero-mean Gaussians, the z i l {\displaystyle z_{i}^{l}} are themselves zero-mean Gaussians (conditioned on the coefficients y j l {\displaystyle y_{j}^{l}} ). Since the z l {\displaystyle z^{l}} are jointly Gaussian for any set of y l {\displaystyle y^{l}} , they are described by a Gaussian process conditioned on the preceding activations y l {\displaystyle y^{l}} . The covariance or kernel of this Gaussian process depends on the weight and bias variances σ w 2 {\displaystyle \sigma _{w}^{2}} and σ b 2 {\displaystyle \sigma _{b}^{2}} , as well as the second moment matrix K l {\displaystyle K^{l}} of the preceding activations y l {\displaystyle y^{l}} , z i l ∣ y l ∼ G P ( 0 , σ w 2 K l + σ b 2 ) K l ( x , x ′ ) = 1 n l ∑ i y i l ( x ) y i l ( x ′ ) {\displaystyle {\begin{aligned}z_{i}^{l}\mid y^{l}&\sim {\mathcal {GP}}\left(0,\sigma _{w}^{2}K^{l}+\sigma _{b}^{2}\right)\\K^{l}(x,x')&={\frac {1}{n^{l}}}\sum _{i}y_{i}^{l}(x)y_{i}^{l}(x')\end{aligned}}} The effect of the weight scale σ w 2 {\displaystyle \sigma _{w}^{2}} is to rescale the contribution to the covariance matrix from K l {\displaystyle K^{l}} , while the bias is shared for all inputs, and so σ b 2 {\displaystyle \sigma _{b}^{2}} makes the z i l {\displaystyle z_{i}^{l}} for different datapoints more similar and

Superellipsoid

In mathematics, a superellipsoid (or super-ellipsoid) is a solid whose horizontal sections are superellipses (Lamé curves) with the same squareness parameter ϵ 2 {\displaystyle \epsilon _{2}} , and whose vertical sections through the center are superellipses with the squareness parameter ϵ 1 {\displaystyle \epsilon _{1}} . It is a generalization of an ellipsoid, which is a special case when ϵ 1 = ϵ 2 = 1 {\displaystyle \epsilon _{1}=\epsilon _{2}=1} . Superellipsoids as computer graphics primitives were popularized by Alan H. Barr (who used the name "superquadrics" to refer to both superellipsoids and supertoroids). In modern computer vision and robotics literatures, superquadrics and superellipsoids are used interchangeably, since superellipsoids are the most representative and widely utilized shape among all the superquadrics. Superellipsoids have a rich shape vocabulary, including cuboids, cylinders, ellipsoids, octahedra and their intermediates. It becomes an important geometric primitive widely used in computer vision, robotics, and physical simulation. The main advantage of describing objects and environment with superellipsoids is its conciseness and expressiveness in shape. Furthermore, a closed-form expression of the Minkowski sum between two superellipsoids is available. This makes it a desirable geometric primitive for robot grasping, collision detection, and motion planning. == Special cases == A handful of notable mathematical figures can arise as special cases of superellipsoids given the correct set of values, which are depicted in the above graphic: Cylinder Sphere Steinmetz solid Bicone Regular octahedron Cube, as a limiting case where the exponents tend to infinity Piet Hein's supereggs are also special cases of superellipsoids. == Formulas == === Basic (normalized) superellipsoid === The basic superellipsoid is defined by the implicit function f ( x , y , z ) = ( x 2 ϵ 2 + y 2 ϵ 2 ) ϵ 2 / ϵ 1 + z 2 ϵ 1 {\displaystyle f(x,y,z)=\left(x^{\frac {2}{\epsilon _{2}}}+y^{\frac {2}{\epsilon _{2}}}\right)^{\epsilon _{2}/\epsilon _{1}}+z^{\frac {2}{\epsilon _{1}}}} The parameters ϵ 1 {\displaystyle \epsilon _{1}} and ϵ 2 {\displaystyle \epsilon _{2}} are positive real numbers that control the squareness of the shape. The surface of the superellipsoid is defined by the equation: f ( x , y , z ) = 1 {\displaystyle f(x,y,z)=1} For any given point ( x , y , z ) ∈ R 3 {\displaystyle (x,y,z)\in \mathbb {R} ^{3}} , the point lies inside the superellipsoid if f ( x , y , z ) < 1 {\displaystyle f(x,y,z)<1} , and outside if f ( x , y , z ) > 1 {\displaystyle f(x,y,z)>1} . Any "parallel of latitude" of the superellipsoid (a horizontal section at any constant z between -1 and +1) is a Lamé curve with exponent 2 / ϵ 2 {\displaystyle 2/\epsilon _{2}} , scaled by a = ( 1 − z 2 ϵ 1 ) ϵ 1 2 {\displaystyle a=(1-z^{\frac {2}{\epsilon _{1}}})^{\frac {\epsilon _{1}}{2}}} , which is ( x a ) 2 ϵ 2 + ( y a ) 2 ϵ 2 = 1. {\displaystyle \left({\frac {x}{a}}\right)^{\frac {2}{\epsilon _{2}}}+\left({\frac {y}{a}}\right)^{\frac {2}{\epsilon _{2}}}=1.} Any "meridian of longitude" (a section by any vertical plane through the origin) is a Lamé curve with exponent 2 / ϵ 1 {\displaystyle 2/\epsilon _{1}} , stretched horizontally by a factor w that depends on the sectioning plane. Namely, if x = u cos ⁡ θ {\displaystyle x=u\cos \theta } and y = u sin ⁡ θ {\displaystyle y=u\sin \theta } , for a given θ {\displaystyle \theta } , then the section is ( u w ) 2 ϵ 1 + z 2 ϵ 1 = 1 , {\displaystyle \left({\frac {u}{w}}\right)^{\frac {2}{\epsilon _{1}}}+z^{\frac {2}{\epsilon _{1}}}=1,} where w = ( cos 2 ϵ 2 ⁡ θ + sin 2 ϵ 2 ⁡ θ ) − ϵ 2 2 . {\displaystyle w=(\cos ^{\frac {2}{\epsilon _{2}}}\theta +\sin ^{\frac {2}{\epsilon _{2}}}\theta )^{-{\frac {\epsilon _{2}}{2}}}.} In particular, if ϵ 2 {\displaystyle \epsilon _{2}} is 1, the horizontal cross-sections are circles, and the horizontal stretching w {\displaystyle w} of the vertical sections is 1 for all planes. In that case, the superellipsoid is a solid of revolution, obtained by rotating the Lamé curve with exponent 2 / ϵ 1 {\displaystyle 2/\epsilon _{1}} around the vertical axis. === Superellipsoid === The basic shape above extends from −1 to +1 along each coordinate axis. The general superellipsoid is obtained by scaling the basic shape along each axis by factors a x {\displaystyle a_{x}} , a y {\displaystyle a_{y}} , a z {\displaystyle a_{z}} , the semi-diameters of the resulting solid. The implicit function is F ( x , y , z ) = ( ( x a x ) 2 ϵ 2 + ( y a y ) 2 ϵ 2 ) ϵ 2 ϵ 1 + ( z a z ) 2 ϵ 1 {\displaystyle F(x,y,z)=\left(\left({\frac {x}{a_{x}}}\right)^{\frac {2}{\epsilon _{2}}}+\left({\frac {y}{a_{y}}}\right)^{\frac {2}{\epsilon _{2}}}\right)^{\frac {\epsilon _{2}}{\epsilon _{1}}}+\left({\frac {z}{a_{z}}}\right)^{\frac {2}{\epsilon _{1}}}} . Similarly, the surface of the superellipsoid is defined by the equation F ( x , y , z ) = 1 {\displaystyle F(x,y,z)=1} For any given point ( x , y , z ) ∈ R 3 {\displaystyle (x,y,z)\in \mathbb {R} ^{3}} , the point lies inside the superellipsoid if f ( x , y , z ) < 1 {\displaystyle f(x,y,z)<1} , and outside if f ( x , y , z ) > 1 {\displaystyle f(x,y,z)>1} . Therefore, the implicit function is also called the inside-outside function of the superellipsoid. The superellipsoid has a parametric representation in terms of surface parameters η ∈ [ − π / 2 , π / 2 ) {\displaystyle \eta \in [-\pi /2,\pi /2)} , ω ∈ [ − π , π ) {\displaystyle \omega \in [-\pi ,\pi )} . x ( η , ω ) = a x cos ϵ 1 ⁡ η cos ϵ 2 ⁡ ω {\displaystyle x(\eta ,\omega )=a_{x}\cos ^{\epsilon _{1}}\eta \cos ^{\epsilon _{2}}\omega } y ( η , ω ) = a y cos ϵ 1 ⁡ η sin ϵ 2 ⁡ ω {\displaystyle y(\eta ,\omega )=a_{y}\cos ^{\epsilon _{1}}\eta \sin ^{\epsilon _{2}}\omega } z ( η , ω ) = a z sin ϵ 1 ⁡ η {\displaystyle z(\eta ,\omega )=a_{z}\sin ^{\epsilon _{1}}\eta } === General posed superellipsoid === In computer vision and robotic applications, a superellipsoid with a general pose in the 3D Euclidean space is usually of more interest. For a given Euclidean transformation of the superellipsoid frame g = [ R ∈ S O ( 3 ) , t ∈ R 3 ] ∈ S E ( 3 ) {\displaystyle g=[\mathbf {R} \in SO(3),\mathbf {t} \in \mathbb {R} ^{3}]\in SE(3)} relative to the world frame, the implicit function of a general posed superellipsoid surface defined the world frame is F ( g − 1 ∘ ( x , y , z ) ) = 1 {\displaystyle F\left(g^{-1}\circ (x,y,z)\right)=1} where ∘ {\displaystyle \circ } is the transformation operation that maps the point ( x , y , z ) ∈ R 3 {\displaystyle (x,y,z)\in \mathbb {R} ^{3}} in the world frame into the canonical superellipsoid frame. === Volume of superellipsoid === The volume encompassed by the superelllipsoid surface can be expressed in terms of the beta functions β ( ⋅ , ⋅ ) {\displaystyle \beta (\cdot ,\cdot )} , V ( ϵ 1 , ϵ 2 , a x , a y , a z ) = 2 a x a y a z ϵ 1 ϵ 2 β ( ϵ 1 2 , ϵ 1 + 1 ) β ( ϵ 2 2 , ϵ 2 + 2 2 ) {\displaystyle V(\epsilon _{1},\epsilon _{2},a_{x},a_{y},a_{z})=2a_{x}a_{y}a_{z}\epsilon _{1}\epsilon _{2}\beta ({\frac {\epsilon _{1}}{2}},\epsilon _{1}+1)\beta ({\frac {\epsilon _{2}}{2}},{\frac {\epsilon _{2}+2}{2}})} or equivalently with the Gamma function Γ ( ⋅ ) {\displaystyle \Gamma (\cdot )} , since β ( m , n ) = Γ ( m ) Γ ( n ) Γ ( m + n ) {\displaystyle \beta (m,n)={\frac {\Gamma (m)\Gamma (n)}{\Gamma (m+n)}}} == Recovery from data == Recoverying the superellipsoid (or superquadrics) representation from raw data (e.g., point cloud, mesh, images, and voxels) is an important task in computer vision, robotics, and physical simulation. Traditional computational methods model the problem as a least-square problem. The goal is to find out the optimal set of superellipsoid parameters θ ≐ [ ϵ 1 , ϵ 2 , a x , a y , a z , g ] {\displaystyle \theta \doteq [\epsilon _{1},\epsilon _{2},a_{x},a_{y},a_{z},g]} that minimize an objective function. Other than the shape parameters, g ∈ {\displaystyle g\in } SE(3) is the pose of the superellipsoid frame with respect to the world coordinate. There are two commonly used objective functions. The first one is constructed directly based on the implicit function G 1 ( θ ) = a x a y a z ∑ i = 1 N ( F ϵ 1 ( g − 1 ∘ ( x i , y i , z i ) ) − 1 ) 2 {\displaystyle G_{1}(\theta )=a_{x}a_{y}a_{z}\sum _{i=1}^{N}\left(F^{\epsilon _{1}}\left(g^{-1}\circ (x_{i},y_{i},z_{i})\right)-1\right)^{2}} The minimization of the objective function provides a recovered superellipsoid as close as possible to all the input points { ( x i , y i , z i ) ∈ R 3 , i = 1 , 2 , . . . , N } {\displaystyle \{(x_{i},y_{i},z_{i})\in \mathbb {R} ^{3},i=1,2,...,N\}} . At the mean time, the scalar value a x , a y , a z {\displaystyle a_{x},a_{y},a_{z}} is positively proportional to the volume of the superellipsoid, and thus have the effect of minimizing the volume as well. The other objective function tries to minimized the radial distance between the points and the superellipsoid. That is G 2 ( θ ) = ∑ i = 1 N ( | r

Evolutionary acquisition of neural topologies

Evolutionary acquisition of neural topologies (EANT/EANT2) is an evolutionary reinforcement learning method that evolves both the topology and weights of artificial neural networks. It is closely related to the works of Angeline et al. and Stanley and Miikkulainen. Like the work of Angeline et al., the method uses a type of parametric mutation that comes from evolution strategies and evolutionary programming (now using the most advanced form of the evolution strategies CMA-ES in EANT2), in which adaptive step sizes are used for optimizing the weights of the neural networks. Similar to the work of Stanley (NEAT), the method starts with minimal structures which gain complexity along the evolution path. == Contribution of EANT to neuroevolution == Despite sharing these two properties, the method has the following important features which distinguish it from previous works in neuroevolution. It introduces a genetic encoding called common genetic encoding (CGE) that handles both direct and indirect encoding of neural networks within the same theoretical framework. The encoding has important properties that makes it suitable for evolving neural networks: It is complete in that it is able to represent all types of valid phenotype networks. It is closed, i.e. every valid genotype represents a valid phenotype. (Similarly, the encoding is closed under genetic operators such as structural mutation and crossover.) These properties have been formally proven. For evolving the structure and weights of neural networks, an evolutionary process is used, where the exploration of structures is executed at a larger timescale (structural exploration), and the exploitation of existing structures is done at a smaller timescale (structural exploitation). In the structural exploration phase, new neural structures are developed by gradually adding new structures to an initially minimal network that is used as a starting point. In the structural exploitation phase, the weights of the currently available structures are optimized using an evolution strategy. == Performance == EANT has been tested on some benchmark problems such as the double-pole balancing problem, and the RoboCup keepaway benchmark. In all the tests, EANT was found to perform very well. Moreover, a newer version of EANT, called EANT2, was tested on a visual servoing task and found to outperform NEAT and the traditional iterative Gauss–Newton method. Further experiments include results on a classification problem.

AI takeover

An AI takeover is a theorized future event, often depicted in fiction, in which autonomous artificial intelligence systems acquire the capability to supersede human decisions. This could occur through economic manipulation, infrastructure control, or direct intervention, leading to de facto governance. Scenarios range from gradual economic dominance, as automation supplants the human workforce, up to a sudden or aggressive global takeover by a robot uprising or other forms of rogue AI. Stories of AI takeovers have been popular throughout science fiction. Commentators argue that recent advancements in the field have heightened concern about such scenarios. In public debate, prominent figures such as Stephen Hawking have advocated research into precautionary measures to ensure future superintelligent machines remain under human control. == Types == === Automation of the economy === The traditional consensus among economists has been that technological progress does not cause long-term unemployment. However, recent innovation in the fields of robotics and artificial intelligence has raised worries that human labor will become obsolete, leaving workers in some sectors without employment. Many small and medium-sized firms may also be forced to close if they cannot afford or license the latest robotic and AI technology, and may need to focus on areas or services that cannot easily be replaced for continued viability in the face of such technology. ==== Technologies that may displace workers ==== While these technologies have replaced some traditional workers, they also create new opportunities. Industries that are most susceptible to AI-driven automation include transportation, retail, and the military. AI military technologies, for example, can reduce risk by enabling remote operation. A study in 2024 highlights AI's ability to perform routine and repetitive tasks poses significant risks of job displacement, especially in sectors like manufacturing and administrative support. Author Dave Bond argues that as AI technologies continue to develop and expand, the relationship between humans and robots will change; they will become closely integrated in several aspects of life. AI will likely displace some workers while creating opportunities for new jobs in other sectors, especially in fields where tasks are repeatable. Researchers from Stanford's Digital Economy Lab reported in 2025 that since the widespread adoption of generative AI in late 2022, early-career workers (ages 22–25) in the most AI-exposed occupations have experienced a 13 percent relative decline in employment—even after controlling for firm-level shocks—while overall employment has continued to grow robustly. The study further finds that job losses are concentrated in roles where AI automates routine tasks, whereas occupations that leverage AI to augment human work have seen stable or increasing employment. ==== Computer-integrated manufacturing ==== Computer-integrated manufacturing uses computers to control the production process. This allows individual processes to exchange information with each other and initiate actions. Although manufacturing can be faster and less error-prone through the integration of computers, the main advantage is the ability to create automated manufacturing processes. Computer-integrated manufacturing is used in automotive, aviation, space, and shipbuilding industries. ==== White-collar machines ==== The 21st century has seen a variety of skilled tasks partially taken over by machines, including translation, legal research, and journalism. Care work, entertainment, and other tasks requiring empathy, previously thought safe from automation, are increasingly performed by robots and AI systems. ==== Autonomous cars ==== An autonomous car is a vehicle that is capable of sensing its environment and navigating without human input. Many such vehicles are operational and others are being developed, with legislation rapidly expanding to allow their use. Obstacles to widespread adoption of autonomous vehicles have included concerns about the resulting loss of driving-related jobs in the road transport industry, and safety concerns. On March 18, 2018, a pedestrian was struck and killed in Tempe, Arizona by an Uber self-driving car. ==== AI-generated content ==== In the 2020s, automated content became more relevant due to technological advancements in AI models, such as ChatGPT, DALL-E, and Stable Diffusion. In most cases, AI-generated content such as imagery, literature, and music are produced through text prompts. These AI models are sometimes integrated into creative programs. AI-generated art may sample and conglomerate existing creative works, producing results that appear similar to human-made content. Low-quality AI-generated visual artwork can be informally referred to as AI slop. Some artists use a tool called Nightshade that alters images to make them detrimental to the training of text-to-image models if scraped without permission, while still looking normal to humans. AI-generated images are a potential tool for scammers and those looking to gain followers on social media, either to impersonate a famous individual or group or to monetize their audience. The New York Times has sued OpenAI, alleging copyright infringement related to the training and outputs of its AI models. === Eradication === Scientists such as Stephen Hawking are confident that superhuman artificial intelligence is physically possible, stating "there is no physical law precluding particles from being organised in ways that perform even more advanced computations than the arrangements of particles in human brains". According to Nick Bostrom, a superintelligent machine would not necessarily be motivated by the same emotional desire to collect power that often drives human beings but might rather treat power as a means toward attaining its ultimate goals; taking over the world would both increase its access to resources and help to prevent other agents from stopping the machine's plans. As a simplified example, a paperclip maximizer designed solely to create as many paperclips as possible would want to take over the world so that it can use all of the world's resources to create as many paperclips as possible, and, additionally, prevent humans from shutting it down or using those resources on things other than paperclips. There are debates on how realistic AI takeover scenarios are. According to a 2026 research paper, many of the arguments about existential risks are based on speculative assumptions about how intelligent AI systems could become, how they would behave and what goals they might develop over time. A 2023 Reuters/Ipsos survey showed that 61% of American adults feared AI could pose a threat to civilization. Philosopher Niels Wilde refutes the common thread that artificial intelligence inherently presents a looming threat to humanity, stating that these fears stem from perceived intelligence and lack of transparency in AI systems that more closely reflects the human aspects of it rather than those of a machine. AI alignment research studies how to design AI systems so that they follow intended objectives. == Debate == Physicist Stephen Hawking, Microsoft founder Bill Gates, and SpaceX founder Elon Musk have expressed concerns about the possibility that AI could develop to the point that humans could not control it, with Hawking theorizing that this could "spell the end of the human race". Stephen Hawking said in 2014 that "Success in creating AI would be the biggest event in human history. Unfortunately, it might also be the last, unless we learn how to avoid the risks." Hawking believed that in the coming decades, AI could offer "incalculable benefits and risks" such as "technology outsmarting financial markets, out-inventing human researchers, out-manipulating human leaders, and developing weapons we cannot even understand." In January 2015, Nick Bostrom joined Stephen Hawking, Max Tegmark, Elon Musk, Lord Martin Rees, Jaan Tallinn, and numerous AI researchers in signing the Future of Life Institute's open letter speaking to the potential risks and benefits associated with artificial intelligence. The signatories "believe that research on how to make AI systems robust and beneficial is both important and timely, and that there are concrete research directions that can be pursued today." Some focus has been placed on the development of trustworthy AI. Three statements have been posed as to why AI is not inherently trustworthy: 1. An entity X is trustworthy only if X has the right motivations, goodwill and/or adheres to moral obligations towards the trustor; 2. AI systems lack motivations, goodwill, and moral obligations; 3. Therefore, AI systems cannot be trustworthy. There are additional considerations within this framework of trustworthy AI that go further into the fields of explainable artificial intelligence and respect for human privacy. Zanotti and colleagues

The Last Question

"The Last Question" is a science fiction short story by American writer Isaac Asimov. It first appeared in the November 1956 issue of Science Fiction Quarterly; and in the anthologies in the collections Nine Tomorrows (1959), The Best of Isaac Asimov (1973), Robot Dreams (1986), The Best Science Fiction of Isaac Asimov (1986), the retrospective Opus 100 (1969), and Isaac Asimov: The Complete Stories, Vol. 1 (1990). While he also considered it one of his best works, "The Last Question" was Asimov's favorite short story of his own authorship, and is one of a loosely connected series of stories concerning a fictional computer called Multivac. Through successive generations, humanity questions Multivac on the subject of entropy. The story blends science fiction, theology, and philosophy. It has been recognized as a counterpoint to Fredric Brown's short short story "Answer", published two years earlier. == History == In conceiving Multivac, Asimov was extrapolating the trend towards centralization that characterized computation technology planning in the 1950s to an ultimate centrally managed global computer. After seeing a planetarium adaptation of his work, Asimov "privately" concluded that the story was his best science fiction yet written. He placed it just higher than "The Ugly Little Boy" (September 1958) and "The Bicentennial Man" (1976). The story asks the question of humanity's fate, and human existence as a whole, highlighting Asimov's focus on important aspects of our future like population growth and environmental issues. "The Last Question" ranks with "Nightfall" (1941) as one of Asimov's best-known and most acclaimed short stories. He wrote in 1973 that he appreciated how easy the story was to write after he had the idea. He was so often approached by fans who remembered the story but not the title, that in one instance he gave the answer, correctly, before the fan had even described the story. == Plot summary == By the year 2061, Multivac, a self-adjusting and self-correcting computer, has allowed mankind to reach beyond the planetary confines of Earth and harness solar energy. Two technicians, Adell and Lupov, celebrate Multivac's role in this development. Over drinks, they discuss that the sun will expire due to the second law of thermodynamics, which states that entropy inevitably increases. When Adell asks Multivac whether this can be reversed, the computer responds that it has insufficient data to answer. In several episodes over ten trillion years, increasingly advanced humans pose the same question to the computers of their time. Each time the computer gives the same response. At the heat death of the universe, the last disembodied consciousness of Man asks the question a final time of a computer that resides in hyperspace before merging with it. After collecting the last data from the dead universe, the computer continues to process it alone and finds an answer to the last question. Having no one to tell it to, it proceeds to demonstrate by saying "LET THERE BE LIGHT!" == Themes == === Philosophy === Although science and religion are frequently presented as having an oppositional relationship, "The Last Question" explores some biblical contexts ("Let there be light"). In Asimov's story, aspects like the great meaning of existence are culminated through both technology and human knowledge. The evolution from Multivac to AC also emulates a sort of cycle of existence. === Dystopian happy ending === Multivac's purpose was conceptualized with a desire for knowledge, promoting the idea that more knowledge will lead to a better and more fruitful future for humanity. However, the computer's answers regarding the future suggest an inevitable exhaustion of the Sun, and this thirst for knowledge becomes an obsession with the future. The story's end displays a dichotomy between annihilation and peace. == Dramatic adaptations == === Planetarium shows === "The Last Question" was first adapted for the Abrams Planetarium at Michigan State University (in 1966), featuring the voice of Leonard Nimoy, as Asimov wrote in his autobiography In Joy Still Felt (1980). It was adapted for the Strasenburgh Planetarium in Rochester, New York (in 1969), under the direction of Ian C. McLennan. It was adapted for the Edmonton Space Sciences Centre in Edmonton, Alberta (early 1970s), under the direction of John Hault. It was adapted for the Gates Planetarium at the Denver Museum of Natural History in 1973 under the direction of Mark B. Peterson It subsequently played at the: Fels Planetarium of the Franklin Institute in Philadelphia in 1973 Planetarium of the Reading School District in Reading, Pennsylvania in 1974 Buhl Planetarium, Pittsburgh in 1974 The Space Transit Planetarium of the Museum of Science in Miami during 1977 Vanderbilt Planetarium in Centerport New York, in 1978, read by singer-songwriter and Long Island resident Harry Chapin. Hansen Planetarium in Salt Lake City, Utah (in 1980 and 1989) A reading of the story was played on BBC Radio 7 in 2008 and 2009. Gates Planetarium in Denver, Colorado (in early 2020) In 1989 Asimov updated the star show adaptation to add in quasars and black holes. The story was adapted as a comic book by Don Thompson and drawn by John Estes in the third issue of ORBiT.

Elastic cloud storage

An elastic cloud is a cloud computing offering that provides variable service levels based on changing needs. Elasticity is an attribute that can be applied to most cloud services. It states that the capacity and performance of any given cloud service can expand or contract according to a customer's requirements and that this can potentially be changed automatically as a consequence of some software-driven event or, at worst, can be reconfigured quickly by the customer's infrastructure management team. Elasticity has been described as one of the five main principles of cloud computing by Rosenburg and Mateos in The Cloud at Your Service - Manning 2011. == History == Cloud computing was first described by Gillet and Kapor in 1996; however, the first practical implementation was a consequence of a strategy to leverage Amazon's excess data center capacity. Amazon and other pioneers of the commercial use of this technology were primarily interested in providing a “public” cloud service, whereby they could offer customers the benefits of using the cloud, particularly the utility-based pricing model benefit. Other suppliers followed suit with a range of cloud-based models all offering elasticity as a core component, but these suppliers were only offering this service as an element of their public cloud service. Due to perceived weaknesses in security, or at least a lack of proven compliance, many organizations, particularly in the financial and public sectors, have been slow adopters of cloud technologies. These wary organizations can achieve some of the benefits of cloud computing by adopting private cloud technologies. An alternative form of the elastic cloud has been offered by vendors such as EMC and IBM, whereby the service is based around an enterprise's own infrastructure but still retains elements of elasticity and the potential to bill by consumption. == Description == Elasticity in cloud computing is the ability for the organization to adjust its storage requirements in terms of capacity and processing with respect to operational requirements. This has the following benefits: Operational Benefits - Services can be acquired quickly, meaning that the evolving requirements of the business can be addressed almost immediately, giving an organization a potential agility advantage. A properly implemented elastic system will provision/de-provision according to application demands, so if a particular business has activity spikes then the provision can be enabled to match the demand and the capacity can be re-allocated. Research and Development (R&D) Projects - R&D activities are no longer hindered by a requirement to secure a capex budget prior to a project starting. Capability can simply be provisioned from the cloud and released at the end of the exercise. Testing and Deployment - With most large-scale projects a size test needs to be performed prior to final rollout. By taking advantage of the elasticity of the cloud and creating a full-scale avatar of the proposed production system, realistic data and traffic volumes can be provisioned and released as needed. Expensive Resources Allocated - This will normally apply only in the context where a customer is applying at least some of their own servers as part of a cloud infrastructure, specifically where a business (for performance reasons) has decided to invest in solid-state storage as opposed to spinning platters. There are instances when, due to activity spikes, a less critical process may need to be moved from the high-performance resources to more traditional storage. Server Specification - When a customer has elected to own/lease hardware, they can select and specify servers that are specifically tuned to meet the likely needs of their operation (i.e., directly controlling the cost/benefit equation). Utility Based Payments - There is, of course, a key cost driver in this process, and the notion that you should pay for what you consume is acceptable for many organizations. When hardware capacity is sourced internally, organizations need to over-provision. This applies just as much to traditional outsourcing as it does to capex-related expenditure on in-house servers. Cloud Platform – At the heart of any cloud storage system is the ability to manage hyperscale object storage and a Hadoop Distributed Files System (HDFS). Elastic storage capability is particularly well suited to hyperscale and Hadoop environments, where its capability to rapidly respond to changing circumstances and priorities is essential

AI@50

AI@50, formally known as the "Dartmouth Artificial Intelligence Conference: The Next Fifty Years" (July 13–15, 2006), was a conference organized by James H. Moor, commemorating the 50th anniversary of the Dartmouth workshop which effectively inaugurated the history of artificial intelligence. Five of the original ten attendees were present: Marvin Minsky, Ray Solomonoff, Oliver Selfridge, Trenchard More, and John McCarthy. While sponsored by Dartmouth College, General Electric, and the Frederick Whittemore Foundation, a $200,000 grant from the Defense Advanced Research Projects Agency (DARPA) called for a report of the proceedings that would: Analyze progress on AI's original challenges during the first 50 years, and assess whether the challenges were "easier" or "harder" than originally thought and why Document what the AI@50 participants believe are the major research and development challenges facing this field over the next 50 years, and identify what breakthroughs will be needed to meet those challenges Relate those challenges and breakthroughs against developments and trends in other areas such as control theory, signal processing, information theory, statistics, and optimization theory. A summary report by the conference director, James H. Moor, was published in AI Magazine. == Conference Program and links to published papers == James H. Moor, conference Director, Introduction Carol Folt and Barry Scherr, Welcome Carey Heckman, Tonypandy and the Origins of Science === AI: Past, Present, Future === John McCarthy, What Was Expected, What We Did, and AI Today Marvin Minsky, The Emotion Machine === The Future Model of Thinking === Ron Brachman and Hector Levesque, A Large Part of Human Thought David Mumford, What is the Right Model for 'Thought'? Stuart Russell, The Approach of Modern AI === The Future of Network Models === Geoffrey Hinton & Simon Osindero, From Pandemonium to Graphical Models and Back Again Rick Granger, From Brain Circuits to Mind Manufacture === The Future of Learning & Search === Oliver Selfridge, Learning and Education for Software: New Approaches in Machine Learning Ray Solomonoff, Machine Learning — Past and Future Leslie Pack Kaelbling, Learning to be Intelligent Peter Norvig, Web Search as a Product of and Catalyst for AI === The Future of AI === Rod Brooks, Intelligence and Bodies Nils Nilsson, Routes to the Summit Eric Horvitz, In Pursuit of Artificial Intelligence: Reflections on Challenges and Trajectories === The Future of Vision === Eric Grimson, Intelligent Medical Image Analysis: Computer Assisted Surgery and Disease Monitoring Takeo Kanade, Artificial Intelligence Vision: Progress and Non-Progress Terry Sejnowski, A Critique of Pure Vision === The Future of Reasoning === Alan Bundy, Constructing, Selecting and Repairing Representations of Knowledge Edwina Rissland, The Exquisite Centrality of Examples Bart Selman, The Challenge and Promise of Automated Reasoning === The Future of Language and Cognition === Trenchard More The Birth of Array Theory and Nial Eugene Charniak, Why Natural Language Processing is Now Statistical Natural Language Processing Pat Langley, Intelligent Behavior in Humans and Machines === The Future of the Future === Ray Kurzweil, Why We Can Be Confident of Turing Test Capability Within a Quarter Century George Cybenko, The Future Trajectory of AI Charles J. Holland, DARPA's Perspective === AI and Games === Jonathan Schaeffer, Games as a Test-bed for Artificial Intelligence Research Danny Kopec, Chess and AI Shay Bushinsky, Principle Positions in Deep Junior's Development === Future Interactions with Intelligent Machines === Daniela Rus, Making Bodies Smart Sherry Turkle, From Building Intelligences to Nurturing Sensibilities === Selected Submitted Papers: Future Strategies for AI === J. Storrs Hall, Self-improving AI: An Analysis Selmer Bringsjord, The Logicist Manifesto Vincent C. Müller, Is There a Future for AI Without Representation? Kristinn R. Thórisson, Integrated A.I. Systems === Selected Submitted Papers: Future Possibilities for AI === Eric Steinhart, Survival as a Digital Ghost Colin T. A. Schmidt, Did You Leave That 'Contraption' Alone With Your Little Sister? Michael Anderson & Susan Leigh Anderson, The Status of Machine Ethics Marcello Guarini, Computation, Coherence, and Ethical Reasoning