Superintelligence ban refers to proposed legal, ethical, or policy measures intended to restrict or prohibit the development of artificial superintelligence, AI systems that would surpass human cognitive abilities in nearly all domains. The idea arises from concerns that such systems could become uncontrollable, potentially posing existential threats to humanity or causing severe social and economic disruption. == Background == The concept of limiting or banning superintelligence research has roots in early 21st-century debates on artificial general intelligence (AGI) safety. Thinkers such as Nick Bostrom and Eliezer Yudkowsky warned that self-improving AI could rapidly exceed human oversight. As advanced models like large-scale language models and autonomous agents began demonstrating complex reasoning abilities, policymakers and ethicists increasingly discussed the need for legal constraints on the creation of systems capable of recursive self-improvement. In October 2025, the Future of Life Institute published a statement calling for "a prohibition on the development of superintelligence, not lifted before there is broad scientific consensus that it will be done safely and controllably, and strong public buy-in." This statement was signed by various public personalities, such as Richard Branson and Steve Wozniak, and AI experts, such as Yoshua Bengio and Geoffrey Hinton. == Rationale == Supporters of a superintelligence ban argue that once AI systems surpass human intelligence, traditional containment, alignment, and control methods may fail. They contend that even limited experimentation with such systems could lead to irreversible outcomes, including loss of human decision-making power or unintended global harm. Some propose international treaties modeled after the nuclear non-proliferation framework to prevent a competitive AI arms race. Opponents argue that a ban would be difficult to define and enforce, given the lack of a precise threshold distinguishing advanced AGI from superintelligence. They also warn that excessive restriction could slow scientific progress, hinder beneficial automation, and encourage unregulated underground research. == Global discussion == Although no government has enacted an explicit superintelligence ban, the idea has been debated within the European Union, United Nations, and several independent AI safety organizations. The Future of Life Institute, Center for AI Safety, and other organizations have called for international cooperation to manage risks associated with the pursuit of superintelligent systems. In 2024 and 2025, proposals for a temporary moratorium on frontier AI research were circulated among major technology firms and research institutes, reflecting growing public concern over the trajectory of AI capabilities.
Deep tomographic reconstruction
Deep Tomographic Reconstruction is a set of methods for using deep learning methods to perform tomographic reconstruction of medical and industrial images. It uses artificial intelligence and machine learning, especially deep artificial neural networks or deep learning, to overcome challenges such as measurement noise, data sparsity, image artifacts, and computational inefficiency. This approach has been applied across various imaging modalities, including CT, MRI, PET, SPECT, ultrasound, and optical imaging == Historical background == Traditional tomographic reconstruction relies on analytic methods such as filtered back-projection, or iterative methods which incrementally compute inverse transformations from measurement data (e.g., Radon or Fourier transform data). However, these approaches are not sufficient for certain imaging techniques such as low-dose CT and fast MRI, or scenarios involving metal artifacts and patient motion. == Use in imaging modalities == === Computed tomography (CT) === In CT, deep learning models can be particularly effective in reducing radiation exposure while maintaining image quality. Deep neural networks can also be able to reconstruct images of fair quality from sparsely sampled data without sacrificing diagnostic performance. Deep learning-based generative AI models can reduce CT metal artifacts. === Magnetic resonance imaging (MRI) === In magnetic resonance imaging (MRI), deep learning can lead to reduced MRI motion artifacts, and increased acquisition speed, referred to as fast MRI. Despite suffering from disadvantages such as lower signal-to-noise ratio (SNR), deep learning can enhance image quality in low field MRI, making these systems clinically viable. === Positron emission tomography (PET) and single-photon emission CT (SPECT) === For PET imaging, deep learning models can provide substantial improvements in low-dose imaging and motion artifact correction. Also, deep learning can help SPECT for generation of attenuation background. A notable technique for PET denoising involves integrating MR data through multimodal networks, which use anatomical information from MRI to enhance PET image quality. === Ultrasound imaging === Deep learning can enhance ultrasound imaging by reducing speckle noise and motion blur. For ultrasound beamforming, deep neural networks can allow superior image quality with limited data at high speed. === Optical imaging and microscopy === Diffuse optical tomography, optical coherence tomography and microscopy can be improved by deep neural networks beyond traditional methods. Furthermore, deep learning can also enhance Photoacoustic imaging (see Deep learning in photoacoustic imaging), addressing challenges like high noise, low contrast, and limited resolution. Deep learning has also been applied to label-free live-cell imaging, where convolutional neural networks predict fluorescence labels from transmitted light images, a technique known as in silico labeling. This method can enable high-throughput, non-invasive cell analysis and phenotyping without the need for traditional fluorescent dyes.
Neural computation
Neural computation is the information processing performed by networks of neurons. Neural computation is affiliated with the philosophical tradition of computationalism, which advances the thesis that neural computation explains cognition. Warren McCulloch and Walter Pitts were the first to propose an account of neural activity as being computational in their seminal 1943 paper "A Logical Calculus of the Ideas Immanent in Nervous Activity." There are three general branches of computationalism, including classicism, connectionism, and computational neuroscience. All three branches agree that cognition is computation, however, they disagree on what sorts of computations constitute cognition. The classicism tradition believes that computation in the brain is digital, analogous to digital computing. Both connectionism and computational neuroscience do not require that the computations that realize cognition are necessarily digital computations. However, the two branches greatly disagree upon which sorts of experimental data should be used to construct explanatory models of cognitive phenomena. Connectionists rely upon behavioral evidence to construct models to explain cognitive phenomena, whereas computational neuroscience leverages neuroanatomical and neurophysiological information to construct mathematical models that explain cognition. When comparing the three main traditions of the computational theory of mind, as well as the different possible forms of computation in the brain, it is helpful to define what we mean by computation in a general sense. Computation is the processing of information, otherwise known as variables or entities, according to a set of rules. A rule in this sense is simply an instruction for executing a manipulation on the current state of the variable, in order to produce a specified output. In other words, a rule dictates which output to produce given a certain input to the computing system. A computing system is a mechanism whose components must be functionally organized to process the information in accordance with the established set of rules. The types of information processed by a computing system determine which type of computations it performs. Traditionally in cognitive science, there have been two proposed types of computation related to neural activity, digital and analog, with the vast majority of theoretical work incorporating a digital understanding of cognition. Computing systems that perform digital computation are functionally organized to execute operations on strings of digits with respect to the type and location of the digit on the string. It has been argued that neural spike train signaling implements some form of digital computation, since neural spikes may be considered as discrete units or digits, like 0 or 1—the neuron either fires an action potential or it does not. Accordingly, neural spike trains could be seen as strings of digits. Alternatively, analog computing systems perform manipulations on non-discrete, irreducibly continuous variables, that is, entities that vary continuously as a function of time. These sorts of operations are characterized by systems of differential equations. Neural computation can be studied by, for example, building models of neural computation. Work on artificial neural networks has been somewhat inspired by knowledge of neural computation.
Model compression
Model compression is a machine learning technique for reducing the size of trained models. Large models can achieve high accuracy, but often at the cost of significant resource requirements. Compression techniques aim to compress models without significant performance reduction. Smaller models require less storage space, and consume less memory and compute during inference. Compressed models enable deployment on resource-constrained devices such as smartphones, embedded systems, edge computing devices, and consumer electronics computers. Efficient inference is also valuable for large corporations that serve large model inference over an API, allowing them to reduce computational costs and improve response times for users. Model compression is not to be confused with knowledge distillation, in which a smaller "student" model is trained to imitate the input-output behavior of a larger "teacher" model (as opposed to using the "teacher"'s trained parameters or the "teacher"'s training targets). == Techniques == Several techniques are employed for model compression. === Pruning === Pruning sparsifies a large model by setting some parameters to exactly zero. This effectively reduces the number of parameters. This allows the use of sparse matrix operations, which are faster than dense matrix operations. Pruning criteria can be based on magnitudes of parameters, the statistical pattern of neural activations, Hessian values, etc. === Quantization === Quantization reduces the numerical precision of weights and activations. For example, instead of storing weights as 32-bit floating-point numbers, they can be represented using 8-bit integers. Low-precision parameters take up less space, and takes less compute to perform arithmetic with. It is also possible to quantize some parameters more aggressively than others, so for example, a less important parameter can have 8-bit precision while another, more important parameter, can have 16-bit precision. Inference with such models requires mixed-precision arithmetic. Quantized models can also be used during training (rather than after training). PyTorch implements automatic mixed-precision (AMP), which performs autocasting, gradient scaling, and loss scaling. === Low-rank factorization === Weight matrices can be approximated by low-rank matrices. Let W {\displaystyle W} be a weight matrix of shape m × n {\displaystyle m\times n} . A low-rank approximation is W ≈ U V T {\displaystyle W\approx UV^{T}} , where U {\displaystyle U} and V {\displaystyle V} are matrices of shapes m × k , n × k {\displaystyle m\times k,n\times k} . When k {\displaystyle k} is small, this both reduces the number of parameters needed to represent W {\displaystyle W} approximately, and accelerates matrix multiplication by W {\displaystyle W} . Low-rank approximations can be found by singular value decomposition (SVD). The choice of rank for each weight matrix is a hyperparameter, and jointly optimized as a mixed discrete-continuous optimization problem. The rank of weight matrices may also be pruned after training, taking into account the effect of activation functions like ReLU on the implicit rank of the weight matrices. == Training == Model compression may be decoupled from training, that is, a model is first trained without regard for how it might be compressed, then it is compressed. However, it may also be combined with training. The "train big, then compress" method trains a large model for a small number of training steps (less than it would be if it were trained to convergence), then heavily compress the model. It is found that at the same compute budget, this method results in a better model than lightly compressed, small models. In Deep Compression, the compression has three steps. First loop (pruning): prune all weights lower than a threshold, then finetune the network, then prune again, etc. Second loop (quantization): cluster weights, then enforce weight sharing among all weights in each cluster, then finetune the network, then cluster again, etc. Third step: Use Huffman coding to losslessly compress the model. The SqueezeNet paper reported that Deep Compression achieved a compression ratio of 35 on AlexNet, and a ratio of ~10 on SqueezeNets.
Deep Learning Super Sampling
Deep Learning Super Sampling (DLSS) is a suite of real-time deep learning image enhancement and upscaling technologies developed by Nvidia that are available in a number of video games. The goal of these technologies is to allow the majority of the graphics pipeline to run at a lower resolution for increased performance, and then infer a higher resolution image from this that approximates the same level of detail as if the image had been rendered at this higher resolution. This allows for higher graphical settings or frame rates for a given output resolution, depending on user preference. All generations of DLSS are available on all RTX-branded cards from Nvidia in supported titles. However, the Frame Generation feature is only supported on RTX 40 series GPUs or newer and Multi Frame Generation is only available on 50 series GPUs. == History == Nvidia advertised DLSS as a key feature of GeForce RTX 20 series GPUs when they launched in September 2018. At that time, the results were limited to a few video games, namely Battlefield V, or Metro Exodus, because the algorithm had to be trained specifically on each game on which it was applied and the results were usually not as good as simple resolution upscaling. In 2019, Control shipped with ray tracing and an image processing algorithm that approximated DLSS, which did not use the Tensor Cores. In April 2020, Nvidia advertised and shipped an improved version of DLSS named DLSS 2 with driver version 445.75. DLSS 2.0 was available for a few existing games including Control and Wolfenstein: Youngblood, and would later be added to many newly released games and game engines such as Unreal Engine and Unity. This time Nvidia said that it used the Tensor Cores again, and that the AI did not need to be trained specifically on each game. Despite sharing the DLSS branding, the two iterations of DLSS differ significantly and are not backwards-compatible. In January 2025, Nvidia stated that there are over 540 games and apps supporting DLSS, and that over 80% of Nvidia RTX users activate DLSS. In March 2025, there were more than 100 games that support DLSS 4, according to Nvidia. By May 2025, over 125 games supported DLSS 4. The first video game console to use DLSS, the Nintendo Switch 2, was released on June 5, 2025. Nvidia announced DLSS 4.5 at CES 2026. In January 2026, Nvidia stated that over 250 games and applications support Multi Frame Generation. On March 16, 2026, at GTC 2026, Nvidia CEO Jensen Huang presented DLSS 5, a real-time AI model based on neural rendering that realistically enhances lighting and material surfaces at up to 4K resolution while retaining the developer's intended art style. It is planned to release in fall of 2026. In a blog post on its website, Nvidia has announced that DLSS 5 will be available in such games as Assassin's Creed Shadows, Delta Force, Hogwarts Legacy, Naraka: Bladepoint, Phantom Blade Zero, Resident Evil Requiem, Starfield, The Elder Scrolls IV: Oblivion Remastered, and more. On May 31, 2026, Nvidia announced an updated version of Ray Reconstruction for DLSS 4.5 in a blog post, scheduled for release on all RTX GPUs in August of the same year. They said it is designed to better embed spatial awareness into scenes and analyze engine data on movements and lighting conditions, resulting in a sharper, more stable, and less noisy image. === Release timeline === == Technology == === DLSS 1 === The first iteration of DLSS is a predominantly spatial image upscaler with two stages, both relying on convolutional auto-encoder neural networks. The first step is an image enhancement network which uses the current frame and motion vectors to perform edge enhancement, and spatial anti-aliasing. The second stage is an image upscaling step which uses the single raw, low-resolution frame to upscale the image to the desired output resolution. Using just a single frame for upscaling means the neural network itself must generate a large amount of new information to produce the high-resolution output, which can result in slight hallucinations such as leaves that differ in style to the source content. The neural networks are trained on a per-game basis by generating a "perfect frame" using traditional supersampling to 64 samples per pixel, as well as the motion vectors for each frame. The data collected must be as comprehensive as possible, including as many levels, times of day, graphical settings, resolutions, etc. as possible. This data is also augmented using common augmentations such as rotations, colour changes, and random noise to help generalize the test data. Training is performed on Nvidia's Saturn V supercomputer. This first iteration received a mixed response, with many criticizing the often soft appearance and artifacts along with glitches in certain situations; likely a side effect of the limited data from only using a single frame input to the neural networks which could not be trained to perform optimally in all scenarios and edge-cases. Nvidia also demonstrated the ability for the auto-encoder networks to learn the ability to recreate depth-of-field and motion blur, although this functionality has never been included in a publicly released product. === DLSS 2 === DLSS 2 is a temporal anti-aliasing upsampling (TAAU) implementation, using data from previous frames extensively through sub-pixel jittering to resolve fine detail and reduce aliasing. The data DLSS 2 collects includes: the raw low-resolution input, motion vectors, depth buffers, and exposure / brightness information. It can also be used as a simpler TAA implementation where the image is rendered at 100% resolution, rather than being upsampled by DLSS, Nvidia brands this as DLAA (Deep Learning Anti-Aliasing). TAA(U) is used in many modern video games and game engines; however, all previous implementations have used some form of manually written heuristics to prevent temporal artifacts such as ghosting and flickering. One example of this is neighborhood clamping which forcefully prevents samples collected in previous frames from deviating too much compared to nearby pixels in newer frames. This helps to identify and fix many temporal artifacts, but deliberately removing fine details in this way is analogous to applying a blur filter, and thus the final image can appear blurry when using this method. DLSS 2 uses a convolutional auto-encoder neural network trained to identify and fix temporal artifacts, instead of manually programmed heuristics as mentioned above. Because of this, DLSS 2 can generally resolve detail better than other TAA and TAAU implementations, while also removing most temporal artifacts. This is why DLSS 2 can sometimes produce a sharper image than rendering at higher, or even native resolutions using traditional TAA. However, no temporal solution is perfect, and artifacts (ghosting in particular) are still visible in some scenarios when using DLSS 2. Because temporal artifacts occur in most art styles and environments in broadly the same way, the neural network that powers DLSS 2 does not need to be retrained when being used in different games. Despite this, Nvidia does frequently ship new minor revisions of DLSS 2 with new titles, so this could suggest some minor training optimizations may be performed as games are released, although Nvidia does not provide changelogs for these minor revisions to confirm this. The main advancements compared to DLSS 1 include: Significantly improved detail retention, a generalized neural network that does not need to be re-trained per-game, and ~2x less overhead (~1–2 ms vs ~2–4 ms). It should also be noted that forms of TAAU such as DLSS 2 are not upscalers in the same sense as techniques such as ESRGAN or DLSS 1, which attempt to create new information from a low-resolution source; instead, TAAU works to recover data from previous frames, rather than creating new data. In practice, this means low resolution textures in games will still appear low-resolution when using current TAAU techniques. This is why Nvidia recommends game developers use higher resolution textures than they would normally for a given rendering resolution by applying a mip-map bias when DLSS 2 is enabled. === DLSS 3 === Augments DLSS 2 with improved image quality and the introduction of a new motion interpolation feature, called Frame Generation. The DLSS Frame Generation algorithm takes two rendered frames from the rendering pipeline and generates a new frame that smoothly transitions between them. For every frame rendered, one additional frame is generated. DLSS 3.0 makes use of a new generation Optical Flow Accelerator (OFA) included in the Ada Lovelace architecture of GeForce RTX 40 series GPUs and with that is exclusive to them. The new OFA is said to be faster and more accurate than the one already available in previous Turing and Ampere RTX GPUs. === DLSS 3.5 === DLSS 3.5 adds Ray Reconstruction, replacing multiple denoising algorithms with a single AI model trained o
Connectionist expert system
Connectionist expert systems are artificial neural network (ANN) based expert systems where the ANN generates inferencing rules e.g., fuzzy-multi layer perceptron where linguistic and natural form of inputs are used. Apart from that, rough set theory may be used for encoding knowledge in the weights better and also genetic algorithms may be used to optimize the search solutions better. Symbolic reasoning methods may also be incorporated (see hybrid intelligent system). (Also see expert system, neural network, clinical decision support system.)
Cross-validation (statistics)
Cross-validation, sometimes called rotation estimation or out-of-sample testing, is any of various similar model validation techniques for assessing how the results of a statistical analysis will generalize to an independent data set. Cross-validation includes resampling and sample splitting methods that use different portions of the data to test and train a model on different iterations. It is often used in settings where the goal is prediction, and one wants to estimate how accurately a predictive model will perform in practice. It can also be used to assess the quality of a fitted model and the stability of its parameters. In a prediction problem, a model is usually given a dataset of known data on which training is run (training dataset), and a dataset of unknown data (or first seen data) against which the model is tested (called the validation dataset or testing set). The goal of cross-validation is to test the model's ability to predict new data that was not used in estimating it, in order to flag problems like overfitting or selection bias and to give an insight on how the model will generalize to an independent dataset (i.e., an unknown dataset, for instance from a real problem). One round of cross-validation involves partitioning a sample of data into complementary subsets, performing the analysis on one subset (called the training set), and validating the analysis on the other subset (called the validation set or testing set). To reduce variability, in most methods multiple rounds of cross-validation are performed using different partitions, and the validation results are combined (e.g. averaged) over the rounds to give an estimate of the model's predictive performance. In summary, cross-validation combines (averages) measures of fitness in prediction to derive a more accurate estimate of model prediction performance. == Motivation == Assume a model with one or more unknown parameters, and a data set to which the model can be fit (the training data set). The fitting process optimizes the model parameters to make the model fit the training data as well as possible. If an independent sample of validation data is taken from the same population as the training data, it will generally turn out that the model does not fit the validation data as well as it fits the training data. The size of this difference is likely to be large especially when the size of the training data set is small, or when the number of parameters in the model is large. Cross-validation is a way to estimate the size of this effect. === Example: linear regression === In linear regression, there exist real response values y 1 , … , y n {\textstyle y_{1},\ldots ,y_{n}} , and n p-dimensional vector covariates x1, ..., xn. The components of the vector xi are denoted xi1, ..., xip. If least squares is used to fit a function in the form of a hyperplane ŷ = a + βTx to the data (xi, yi) 1 ≤ i ≤ n, then the fit can be assessed using the mean squared error (MSE). The MSE for given estimated parameter values a and β on the training set (xi, yi) 1 ≤ i ≤ n is defined as: MSE = 1 n ∑ i = 1 n ( y i − y ^ i ) 2 = 1 n ∑ i = 1 n ( y i − a − β T x i ) 2 = 1 n ∑ i = 1 n ( y i − a − β 1 x i 1 − ⋯ − β p x i p ) 2 {\displaystyle {\begin{aligned}{\text{MSE}}&={\frac {1}{n}}\sum _{i=1}^{n}(y_{i}-{\hat {y}}_{i})^{2}={\frac {1}{n}}\sum _{i=1}^{n}(y_{i}-a-{\boldsymbol {\beta }}^{T}\mathbf {x} _{i})^{2}\\&={\frac {1}{n}}\sum _{i=1}^{n}(y_{i}-a-\beta _{1}x_{i1}-\dots -\beta _{p}x_{ip})^{2}\end{aligned}}} If the model is correctly specified, it can be shown under mild assumptions that the expected value of the MSE for the training set is (n − p − 1)/(n + p + 1) < 1 times the expected value of the MSE for the validation set (the expected value is taken over the distribution of training sets). Thus, a fitted model and computed MSE on the training set will result in an optimistically biased assessment of how well the model will fit an independent data set. This biased estimate is called the in-sample estimate of the fit, whereas the cross-validation estimate is an out-of-sample estimate. Since in linear regression it is possible to directly compute the factor (n − p − 1)/(n + p + 1) by which the training MSE underestimates the validation MSE under the assumption that the model specification is valid, cross-validation can be used for checking whether the model has been overfitted, in which case the MSE in the validation set will substantially exceed its anticipated value. (Cross-validation in the context of linear regression is also useful in that it can be used to select an optimally regularized cost function.) === General case === In most other regression procedures (e.g. logistic regression), there is no simple formula to compute the expected out-of-sample fit. Cross-validation is, thus, a generally applicable way to predict the performance of a model on unavailable data using numerical computation in place of theoretical analysis. == Types == Two types of cross-validation can be distinguished: exhaustive and non-exhaustive cross-validation. === Exhaustive cross-validation === Exhaustive cross-validation methods are cross-validation methods which learn and test on all possible ways to divide the original sample into a training and a validation set. ==== Leave-p-out cross-validation ==== Leave-p-out cross-validation (LpO CV) involves using p observations as the validation set and the remaining observations as the training set. This is repeated on all ways to cut the original sample on a validation set of p observations and a training set. LpO cross-validation require training and validating the model C p n {\displaystyle C_{p}^{n}} times, where n is the number of observations in the original sample, and where C p n {\displaystyle C_{p}^{n}} is the binomial coefficient. For p > 1 and for even moderately large n, LpO CV can become computationally infeasible. For example, with n = 100 and p = 30, C 30 100 ≈ 3 × 10 25 . {\displaystyle C_{30}^{100}\approx 3\times 10^{25}.} A variant of LpO cross-validation with p=2 known as leave-pair-out cross-validation has been recommended as a nearly unbiased method for estimating the area under ROC curve of binary classifiers. ==== Leave-one-out cross-validation ==== Leave-one-out cross-validation (LOOCV) is a particular case of leave-p-out cross-validation with p = 1. The process looks similar to jackknife; however, with cross-validation one computes a statistic on the left-out sample(s), while with jackknifing one computes a statistic from the kept samples only. LOO cross-validation requires less computation time than LpO cross-validation because there are only C 1 n = n {\displaystyle C_{1}^{n}=n} passes rather than C p n {\displaystyle C_{p}^{n}} . However, n {\displaystyle n} passes may still require quite a large computation time, in which case other approaches such as k-fold cross validation may be more appropriate. Pseudo-code algorithm: Input: x, {vector of length N with x-values of incoming points} y, {vector of length N with y-values of the expected result} interpolate( x_in, y_in, x_out ), { returns the estimation for point x_out after the model is trained with x_in-y_in pairs} Output: err, {estimate for the prediction error} Steps: err ← 0 for i ← 1, ..., N do // define the cross-validation subsets x_in ← (x[1], ..., x[i − 1], x[i + 1], ..., x[N]) y_in ← (y[1], ..., y[i − 1], y[i + 1], ..., y[N]) x_out ← x[i] y_out ← interpolate(x_in, y_in, x_out) err ← err + (y[i] − y_out)^2 end for err ← err/N === Non-exhaustive cross-validation === Non-exhaustive cross validation methods do not compute all ways of splitting the original sample. These methods are approximations of leave-p-out cross-validation. ==== k-fold cross-validation ==== In k-fold cross-validation, the original sample is randomly partitioned into k equal sized subsamples, often referred to as "folds". Of the k subsamples, a single subsample is retained as the validation data for testing the model, and the remaining k − 1 subsamples are used as training data. The cross-validation process is then repeated k times, with each of the k subsamples used exactly once as the validation data. The k results can then be averaged to produce a single estimation. The advantage of this method over repeated random sub-sampling (see below) is that all observations are used for both training and validation, and each observation is used for validation exactly once. 10-fold cross-validation is commonly used, but in general k remains an unfixed parameter. For example, setting k = 2 results in 2-fold cross-validation. In 2-fold cross-validation, the dataset is randomly shuffled into two sets d0 and d1, so that both sets are equal size (this is usually implemented by shuffling the data array and then splitting it in two). We then train on d0 and validate on d1, followed by training on d1 and validating on d0. When k = n (the number of observations), k-fold cross-validation is equivalent to leave-one-out cr