AI Assistant Volume

AI Assistant Volume — independent reviews, comparisons, pricing and step-by-step guides on Aizhi.

• 

  Compute (machine learning)

  In machine learning and deep learning, compute is the amount of computing power or computational resources required to train machine learning models and large language models. More broadly, compute is the computational power or resources necessary for a computer or computer program to function. == Definition == Compute is commonly defined as the amount of computing power or computational resources required to train machine learning and large language models. The term "compute" has also been more broadly applied to cloud computing, referencing processing power, memory, networking, storage, and other resources required for the computation of any program. Compute is measured in petaflop/s-days and is used to document AI training. A petaflop/s-day (pfs-day) consists of performing 1015 neural net operations per second for one day, or a total of about 1020 operations. The compute-time product serves as a mental convenience, similar to kilowatt-hour for energy. An amount of compute is meant to give an idea of the number of actual operations performed. == History == In a 2018 analysis titled "AI and compute", artificial intelligence company OpenAI introduced the concept of compute. OpenAI identified two eras of training AI systems in terms of compute-usage. From 1959 to 2012, compute roughly followed Moore’s law. Between 2012 and 2018, the amount of compute used in the largest AI training runs increased exponentially, growing by more than 300,000 times — roughly doubling every 3.4 months. By comparison, Moore’s Law doubled every two years over the same period. One of the largest models, released in 2020, used 600,000 times more computing power than the 2012 model. After 2020, compute growth began to slow down, with the compute needed for the largest AI models continuing to slow down in 2023. The notion of compute has become increasingly used from the mid-2020s onwards. == Compute growth and AI progress == Larger AI models trained on more data and using more computational resources, tend to perform better. This happens even if the algorithms themselves remain unchanged. As early as 2018, OpenAI noted the exponential increase in compute to be have a key role in AI progress. OpenAI considers three factors drive the advance of AI: algorithmic innovation, data, and the amount of compute available for training. AI models with more compute not only improve in the tasks they were trained on but can develop emergent abilities. Incremental improvements can lead to more abrupt leaps in capabilities. AI provider SpaceXAI said in 2026 that their AI progress is driven by compute and used it a key metric in the AI training of its supercomputer Colossus, the which contains 1 million GPUs. Anthropic has a contract of $1.25 billion per month with SpaceXAI to buy all the compute capacity at Colossus 1 data center. === Criticism and policy === Increasing, promoting or constraining progress in artificial intelligence has often be done via controlling the amount of compute. Policymarkers have enacted policies and provided support to make compute resources more accessible to domestic AI researchers. In a January 2022 report, the Center for Security and Emerging Technology (CSET) suggested to institutions that increasingly powerful and generalizable AI (AGI) will likely require other strategies than maximizing compute. Some AI researchers are also concerned that government might exclusively focus on scaling compute instead of other strategies. The CSET has reported on the various bottlenecks which could explain why deep learning needs for compute have slow down: training is expensive and training extremely large models generates traffic jams across many processors that are difficult to manage. there is a limited supply of AI chips (see AI chip memory shortage). CSET advances that the main resource is human capital, specifically talented researchers — according to a 2023 published survey of more than 400 AI researchers, academic and private sector workers. The survey found that AI researchers are not primarily or exclusively constrained by compute access. However, both academic and industry AI researchers equally report concerns that insufficient compute could prevent them from contributing meaningfully to AI research in the future. High compute users are more concerned about compute access. When asked about which resource provided by the government would be the most useful to them, some AI researchers select compute, other prefer grant funding. For this goal, CSET advised policymakers to ensure that even researchers with smaller budgets could effectively contribute to AI research. Other proposed strategies include using contemporary AI algorithms, managing modern AI infrastructure or focusing on interdisciplinary work between the AI field and other fields of computer science. A 2024 study on compute access found that academic-only AI research teams often have less compute intensive research topics, especially foundation models, compared to industry AI labs. As a consequence, academia is likely to play a smaller role in advancing such techniques. The researchers suggest nationally-sponsored computing infrastructure as well as open science initiatives to boost academic compute access. === Data === A 2022 study found that current large language models are significantly under-trained, a consequence of focusing on scaling language models whilst keeping the amount of training data constant. By training over 400 language models of various parameter and token size, they found that "for compute-optimal training", the model size and the number of training tokens should ideally be scaled equally: for every doubling of model size the number of training tokens should also be doubled.

  Read more →
• 

  Reparameterization trick

  The reparameterization trick (aka "reparameterization gradient estimator") is a technique used in statistical machine learning, particularly in variational inference, variational autoencoders, and stochastic optimization. It allows for the efficient computation of gradients through random variables, enabling the optimization of parametric probability models using stochastic gradient descent, and the variance reduction of estimators. It was developed in the 1980s in operations research, under the name of "pathwise gradients", or "stochastic gradients". Its use in variational inference was proposed in 2013. == Mathematics == Let z {\displaystyle z} be a random variable with distribution q ϕ ( z ) {\displaystyle q_{\phi }(z)} , where ϕ {\displaystyle \phi } is a vector containing the parameters of the distribution. === REINFORCE estimator === Consider an objective function of the form: L ( ϕ ) = E z ∼ q ϕ ( z ) [ f ( z ) ] {\displaystyle L(\phi )=\mathbb {E} _{z\sim q_{\phi }(z)}[f(z)]} Without the reparameterization trick, estimating the gradient ∇ ϕ L ( ϕ ) {\displaystyle \nabla _{\phi }L(\phi )} can be challenging, because the parameter appears in the random variable itself. In more detail, we have to statistically estimate: ∇ ϕ L ( ϕ ) = ∇ ϕ ∫ d z q ϕ ( z ) f ( z ) {\displaystyle \nabla _{\phi }L(\phi )=\nabla _{\phi }\int dz\;q_{\phi }(z)f(z)} The REINFORCE estimator, widely used in reinforcement learning and especially policy gradient, uses the following equality: ∇ ϕ L ( ϕ ) = ∫ d z q ϕ ( z ) ∇ ϕ ( ln ⁡ q ϕ ( z ) ) f ( z ) = E z ∼ q ϕ ( z ) [ ∇ ϕ ( ln ⁡ q ϕ ( z ) ) f ( z ) ] {\displaystyle \nabla _{\phi }L(\phi )=\int dz\;q_{\phi }(z)\nabla _{\phi }(\ln q_{\phi }(z))f(z)=\mathbb {E} _{z\sim q_{\phi }(z)}[\nabla _{\phi }(\ln q_{\phi }(z))f(z)]} This allows the gradient to be estimated: ∇ ϕ L ( ϕ ) ≈ 1 N ∑ i = 1 N ∇ ϕ ( ln ⁡ q ϕ ( z i ) ) f ( z i ) {\displaystyle \nabla _{\phi }L(\phi )\approx {\frac {1}{N}}\sum _{i=1}^{N}\nabla _{\phi }(\ln q_{\phi }(z_{i}))f(z_{i})} The REINFORCE estimator has high variance, and many methods were developed to reduce its variance. === Reparameterization estimator === The reparameterization trick expresses z {\displaystyle z} as: z = g ϕ ( ϵ ) , ϵ ∼ p ( ϵ ) {\displaystyle z=g_{\phi }(\epsilon ),\quad \epsilon \sim p(\epsilon )} Here, g ϕ {\displaystyle g_{\phi }} is a deterministic function parameterized by ϕ {\displaystyle \phi } , and ϵ {\displaystyle \epsilon } is a noise variable drawn from a fixed distribution p ( ϵ ) {\displaystyle p(\epsilon )} . This gives: L ( ϕ ) = E ϵ ∼ p ( ϵ ) [ f ( g ϕ ( ϵ ) ) ] {\displaystyle L(\phi )=\mathbb {E} _{\epsilon \sim p(\epsilon )}[f(g_{\phi }(\epsilon ))]} Now, the gradient can be estimated as: ∇ ϕ L ( ϕ ) = E ϵ ∼ p ( ϵ ) [ ∇ ϕ f ( g ϕ ( ϵ ) ) ] ≈ 1 N ∑ i = 1 N ∇ ϕ f ( g ϕ ( ϵ i ) ) {\displaystyle \nabla _{\phi }L(\phi )=\mathbb {E} _{\epsilon \sim p(\epsilon )}[\nabla _{\phi }f(g_{\phi }(\epsilon ))]\approx {\frac {1}{N}}\sum _{i=1}^{N}\nabla _{\phi }f(g_{\phi }(\epsilon _{i}))} == Examples == For some common distributions, the reparameterization trick takes specific forms: Normal distribution: For z ∼ N ( μ , σ 2 ) {\displaystyle z\sim {\mathcal {N}}(\mu ,\sigma ^{2})} , we can use: z = μ + σ ϵ , ϵ ∼ N ( 0 , 1 ) {\displaystyle z=\mu +\sigma \epsilon ,\quad \epsilon \sim {\mathcal {N}}(0,1)} Exponential distribution: For z ∼ Exp ( λ ) {\displaystyle z\sim {\text{Exp}}(\lambda )} , we can use: z = − 1 λ log ⁡ ( ϵ ) , ϵ ∼ Uniform ( 0 , 1 ) {\displaystyle z=-{\frac {1}{\lambda }}\log(\epsilon ),\quad \epsilon \sim {\text{Uniform}}(0,1)} Discrete distribution can be reparameterized by the Gumbel distribution (Gumbel-softmax trick or "concrete distribution") and diffusion models. In general, any distribution that is differentiable with respect to its parameters can be reparameterized by inverting the multivariable CDF function, then apply the implicit method. See for an exposition and application to the Gamma, Beta, Dirichlet, and von Mises distributions. == Applications == === Variational autoencoder === In Variational Autoencoders (VAEs), the VAE objective function, known as the Evidence Lower Bound (ELBO), is given by: ELBO ( ϕ , θ ) = E z ∼ q ϕ ( z | x ) [ log ⁡ p θ ( x | z ) ] − D KL ( q ϕ ( z | x ) | | p ( z ) ) {\displaystyle {\text{ELBO}}(\phi ,\theta )=\mathbb {E} _{z\sim q_{\phi }(z|x)}[\log p_{\theta }(x|z)]-D_{\text{KL}}(q_{\phi }(z|x)||p(z))} where q ϕ ( z | x ) {\displaystyle q_{\phi }(z|x)} is the encoder (recognition model), p θ ( x | z ) {\displaystyle p_{\theta }(x|z)} is the decoder (generative model), and p ( z ) {\displaystyle p(z)} is the prior distribution over latent variables. The gradient of ELBO with respect to θ {\displaystyle \theta } is simply E z ∼ q ϕ ( z | x ) [ ∇ θ log ⁡ p θ ( x | z ) ] ≈ 1 L ∑ l = 1 L ∇ θ log ⁡ p θ ( x | z l ) {\displaystyle \mathbb {E} _{z\sim q_{\phi }(z|x)}[\nabla _{\theta }\log p_{\theta }(x|z)]\approx {\frac {1}{L}}\sum _{l=1}^{L}\nabla _{\theta }\log p_{\theta }(x|z_{l})} but the gradient with respect to ϕ {\displaystyle \phi } requires the trick. Express the sampling operation z ∼ q ϕ ( z | x ) {\displaystyle z\sim q_{\phi }(z|x)} as: z = μ ϕ ( x ) + σ ϕ ( x ) ⊙ ϵ , ϵ ∼ N ( 0 , I ) {\displaystyle z=\mu _{\phi }(x)+\sigma _{\phi }(x)\odot \epsilon ,\quad \epsilon \sim {\mathcal {N}}(0,I)} where μ ϕ ( x ) {\displaystyle \mu _{\phi }(x)} and σ ϕ ( x ) {\displaystyle \sigma _{\phi }(x)} are the outputs of the encoder network, and ⊙ {\displaystyle \odot } denotes element-wise multiplication. Then we have ∇ ϕ ELBO ( ϕ , θ ) = E ϵ ∼ N ( 0 , I ) [ ∇ ϕ log ⁡ p θ ( x | z ) + ∇ ϕ log ⁡ q ϕ ( z | x ) − ∇ ϕ log ⁡ p ( z ) ] {\displaystyle \nabla _{\phi }{\text{ELBO}}(\phi ,\theta )=\mathbb {E} _{\epsilon \sim {\mathcal {N}}(0,I)}[\nabla _{\phi }\log p_{\theta }(x|z)+\nabla _{\phi }\log q_{\phi }(z|x)-\nabla _{\phi }\log p(z)]} where z = μ ϕ ( x ) + σ ϕ ( x ) ⊙ ϵ {\displaystyle z=\mu _{\phi }(x)+\sigma _{\phi }(x)\odot \epsilon } . This allows us to estimate the gradient using Monte Carlo sampling: ∇ ϕ ELBO ( ϕ , θ ) ≈ 1 L ∑ l = 1 L [ ∇ ϕ log ⁡ p θ ( x | z l ) + ∇ ϕ log ⁡ q ϕ ( z l | x ) − ∇ ϕ log ⁡ p ( z l ) ] {\displaystyle \nabla _{\phi }{\text{ELBO}}(\phi ,\theta )\approx {\frac {1}{L}}\sum _{l=1}^{L}[\nabla _{\phi }\log p_{\theta }(x|z_{l})+\nabla _{\phi }\log q_{\phi }(z_{l}|x)-\nabla _{\phi }\log p(z_{l})]} where z l = μ ϕ ( x ) + σ ϕ ( x ) ⊙ ϵ l {\displaystyle z_{l}=\mu _{\phi }(x)+\sigma _{\phi }(x)\odot \epsilon _{l}} and ϵ l ∼ N ( 0 , I ) {\displaystyle \epsilon _{l}\sim {\mathcal {N}}(0,I)} for l = 1 , … , L {\displaystyle l=1,\ldots ,L} . This formulation enables backpropagation through the sampling process, allowing for end-to-end training of the VAE model using stochastic gradient descent or its variants. === Variational inference === More generally, the trick allows using stochastic gradient descent for variational inference. Let the variational objective (ELBO) be of the form: ELBO ( ϕ ) = E z ∼ q ϕ ( z ) [ log ⁡ p ( x , z ) − log ⁡ q ϕ ( z ) ] {\displaystyle {\text{ELBO}}(\phi )=\mathbb {E} _{z\sim q_{\phi }(z)}[\log p(x,z)-\log q_{\phi }(z)]} Using the reparameterization trick, we can estimate the gradient of this objective with respect to ϕ {\displaystyle \phi } : ∇ ϕ ELBO ( ϕ ) ≈ 1 L ∑ l = 1 L ∇ ϕ [ log ⁡ p ( x , g ϕ ( ϵ l ) ) − log ⁡ q ϕ ( g ϕ ( ϵ l ) ) ] , ϵ l ∼ p ( ϵ ) {\displaystyle \nabla _{\phi }{\text{ELBO}}(\phi )\approx {\frac {1}{L}}\sum _{l=1}^{L}\nabla _{\phi }[\log p(x,g_{\phi }(\epsilon _{l}))-\log q_{\phi }(g_{\phi }(\epsilon _{l}))],\quad \epsilon _{l}\sim p(\epsilon )} === Dropout === The reparameterization trick has been applied to reduce the variance in dropout, a regularization technique in neural networks. The original dropout can be reparameterized with Bernoulli distributions: y = ( W ⊙ ϵ ) x , ϵ i j ∼ Bernoulli ( α i j ) {\displaystyle y=(W\odot \epsilon )x,\quad \epsilon _{ij}\sim {\text{Bernoulli}}(\alpha _{ij})} where W {\displaystyle W} is the weight matrix, x {\displaystyle x} is the input, and α i j {\displaystyle \alpha _{ij}} are the (fixed) dropout rates. More generally, other distributions can be used than the Bernoulli distribution, such as the gaussian noise: y i = μ i + σ i ⊙ ϵ i , ϵ i ∼ N ( 0 , I ) {\displaystyle y_{i}=\mu _{i}+\sigma _{i}\odot \epsilon _{i},\quad \epsilon _{i}\sim {\mathcal {N}}(0,I)} where μ i = m i ⊤ x {\displaystyle \mu _{i}=\mathbf {m} _{i}^{\top }x} and σ i 2 = v i ⊤ x 2 {\displaystyle \sigma _{i}^{2}=\mathbf {v} _{i}^{\top }x^{2}} , with m i {\displaystyle \mathbf {m} _{i}} and v i {\displaystyle \mathbf {v} _{i}} being the mean and variance of the i {\displaystyle i} -th output neuron. The reparameterization trick can be applied to all such cases, resulting in the variational dropout method.

  Read more →
• 

  Learning rate

  In machine learning and statistics, the learning rate is a tuning parameter in an optimization algorithm that determines the step size at each iteration while moving toward a minimum of a loss function. Since it influences to what extent newly acquired information overrides old information, it metaphorically represents the speed at which a machine learning model "learns". In the adaptive control literature, the learning rate is commonly referred to as gain. In setting a learning rate, there is a trade-off between the rate of convergence and overshooting. While the descent direction is usually determined from the gradient of the loss function, the learning rate determines how big a step is taken in that direction. Too high a learning rate will make the learning jump over minima, but too low a learning rate will either take too long to converge or get stuck in an undesirable local minimum. In order to achieve faster convergence, prevent oscillations and getting stuck in undesirable local minima the learning rate is often varied during training either in accordance to a learning rate schedule or by using an adaptive learning rate. The learning rate and its adjustments may also differ per parameter, in which case it is a diagonal matrix that can be interpreted as an approximation to the inverse of the Hessian matrix in Newton's method. The learning rate is related to the step length determined by inexact line search in quasi-Newton methods and related optimization algorithms. == Learning rate schedule == Initial rate can be left as system default or can be selected using a range of techniques. A learning rate schedule changes the learning rate during learning and is most often changed between epochs/iterations. This is mainly done with two parameters: decay and momentum. There are many different learning rate schedules but the most common are time-based, step-based and exponential. Decay serves to settle the learning in a nice place and avoid oscillations, a situation that may arise when too high a constant learning rate makes the learning jump back and forth over a minimum, and is controlled by a hyperparameter. Momentum is analogous to a ball rolling down a hill; we want the ball to settle at the lowest point of the hill (corresponding to the lowest error). Momentum both speeds up the learning (increasing the learning rate) when the error cost gradient is heading in the same direction for a long time and also avoids local minima by 'rolling over' small bumps. Momentum is controlled by a hyperparameter analogous to a ball's mass which must be chosen manually—too high and the ball will roll over minima which we wish to find, too low and it will not fulfil its purpose. The formula for factoring in the momentum is more complex than for decay but is most often built in with deep learning libraries such as Keras. Time-based learning schedules alter the learning rate depending on the learning rate of the previous time iteration. Factoring in the decay the mathematical formula for the learning rate is: η n + 1 = η 0 1 + d n {\displaystyle \eta _{n+1}={\frac {\eta _{0}}{1+dn}}} where η {\displaystyle \eta } is the learning rate, η 0 {\displaystyle \eta _{0}} is the original learning rate, d {\displaystyle d} is a decay parameter and n {\displaystyle n} is the iteration step. Step-based learning schedules changes the learning rate according to some predefined steps. The decay application formula is here defined as: η n = η 0 d ⌊ 1 + n r ⌋ {\displaystyle \eta _{n}=\eta _{0}d^{\left\lfloor {\frac {1+n}{r}}\right\rfloor }} where η n {\displaystyle \eta _{n}} is the learning rate at iteration n {\displaystyle n} , η 0 {\displaystyle \eta _{0}} is the initial learning rate, d {\displaystyle d} is how much the learning rate should change at each drop (0.5 corresponds to a halving) and r {\displaystyle r} corresponds to the drop rate, or how often the rate should be dropped (10 corresponds to a drop every 10 iterations). The floor function ( ⌊ … ⌋ {\displaystyle \lfloor \dots \rfloor } ) here drops the value of its input to 0 for all values smaller than 1. Exponential learning schedules are similar to step-based, but instead of steps, a decreasing exponential function is used. The mathematical formula for factoring in the decay is: η n = η 0 e − d n {\displaystyle \eta _{n}=\eta _{0}e^{-dn}} where d {\displaystyle d} is a decay parameter. == Adaptive learning rate == The issue with learning rate schedules is that they all depend on hyperparameters that must be manually chosen for each given learning session and may vary greatly depending on the problem at hand or the model used. To combat this, there are many different types of adaptive gradient descent algorithms such as Adagrad, Adadelta, RMSprop, and Adam which are generally built into deep learning libraries such as Keras.

  Read more →
• 

  Hyperparameter optimization

  In machine learning, hyperparameter optimization or tuning is the problem of choosing a set of optimal hyperparameters for a learning algorithm. A hyperparameter is a parameter whose value is used to control the learning process, which must be configured before the process starts. Hyperparameter optimization determines the set of hyperparameters that yields an optimal model which minimizes a predefined loss function on a given data set. The objective function takes a set of hyperparameters and returns the associated loss. Cross-validation is often used to estimate this generalization performance, and therefore choose the set of values for hyperparameters that maximize it. == Approaches == === Grid search === The traditional method for hyperparameter optimization has been grid search, or a parameter sweep, which is simply an exhaustive searching through a manually specified subset of the hyperparameter space of a learning algorithm. A grid search algorithm must be guided by some performance metric, typically measured by cross-validation on the training set or evaluation on a hold-out validation set. Since the parameter space of a machine learner may include real-valued or unbounded value spaces for certain parameters, manually set bounds and discretization may be necessary before applying grid search. For example, a typical soft-margin SVM classifier equipped with an RBF kernel has at least two hyperparameters that need to be tuned for good performance on unseen data: a regularization constant C and a kernel hyperparameter γ. Both parameters are continuous, so to perform grid search, one selects a finite set of "reasonable" values for each, say C ∈ { 10 , 100 , 1000 } {\displaystyle C\in \{10,100,1000\}} γ ∈ { 0.1 , 0.2 , 0.5 , 1.0 } {\displaystyle \gamma \in \{0.1,0.2,0.5,1.0\}} Grid search then trains an SVM with each pair (C, γ) in the Cartesian product of these two sets and evaluates their performance on a held-out validation set (or by internal cross-validation on the training set, in which case multiple SVMs are trained per pair). Finally, the grid search algorithm outputs the settings that achieved the highest score in the validation procedure. Grid search suffers from the curse of dimensionality, but is often embarrassingly parallel because the hyperparameter settings it evaluates are typically independent of each other. === Random search === Random Search replaces the exhaustive enumeration of all combinations by selecting them randomly. This can be simply applied to the discrete setting described above, but also generalizes to continuous and mixed spaces. A benefit over grid search is that random search can explore many more values than grid search could for continuous hyperparameters. It can outperform Grid search, especially when only a small number of hyperparameters affects the final performance of the machine learning algorithm. In this case, the optimization problem is said to have a low intrinsic dimensionality. Random Search is also embarrassingly parallel, and additionally allows the inclusion of prior knowledge by specifying the distribution from which to sample. Despite its simplicity, random search remains one of the important base-lines against which to compare the performance of new hyperparameter optimization methods. === Bayesian optimization === Bayesian optimization is a global optimization method for noisy black-box functions. Applied to hyperparameter optimization, Bayesian optimization builds a probabilistic model of the function mapping from hyperparameter values to the objective evaluated on a validation set. By iteratively evaluating a promising hyperparameter configuration based on the current model, and then updating it, Bayesian optimization aims to gather observations revealing as much information as possible about this function and, in particular, the location of the optimum. It tries to balance exploration (hyperparameters for which the outcome is most uncertain) and exploitation (hyperparameters expected close to the optimum). In practice, Bayesian optimization has been shown to obtain better results in fewer evaluations compared to grid search and random search, due to the ability to reason about the quality of experiments before they are run. === Gradient-based optimization === For specific learning algorithms, it is possible to compute the gradient with respect to hyperparameters and then optimize the hyperparameters using gradient descent. The first usage of these techniques was focused on neural networks. Since then, these methods have been extended to other models such as support vector machines or logistic regression. A different approach in order to obtain a gradient with respect to hyperparameters consists in differentiating the steps of an iterative optimization algorithm using automatic differentiation. A more recent work along this direction uses the implicit function theorem to calculate hypergradients and proposes a stable approximation of the inverse Hessian. The method scales to millions of hyperparameters and requires constant memory. In a different approach, a hypernetwork is trained to approximate the best response function. One of the advantages of this method is that it can handle discrete hyperparameters as well. Self-tuning networks offer a memory efficient version of this approach by choosing a compact representation for the hypernetwork. More recently, Δ-STN has improved this method further by a slight reparameterization of the hypernetwork which speeds up training. Δ-STN also yields a better approximation of the best-response Jacobian by linearizing the network in the weights, hence removing unnecessary nonlinear effects of large changes in the weights. Apart from hypernetwork approaches, gradient-based methods can be used to optimize discrete hyperparameters also by adopting a continuous relaxation of the parameters. Such methods have been extensively used for the optimization of architecture hyperparameters in neural architecture search. === Evolutionary optimization === Evolutionary optimization is a methodology for the global optimization of noisy black-box functions. In hyperparameter optimization, evolutionary optimization uses evolutionary algorithms to search the space of hyperparameters for a given algorithm. Evolutionary hyperparameter optimization follows a process inspired by the biological concept of evolution: Create an initial population of random solutions (i.e., randomly generate tuples of hyperparameters, typically 100+) Evaluate the hyperparameter tuples and acquire their fitness function (e.g., 10-fold cross-validation accuracy of the machine learning algorithm with those hyperparameters) Rank the hyperparameter tuples by their relative fitness Replace the worst-performing hyperparameter tuples with new ones generated via crossover and mutation Repeat steps 2-4 until satisfactory algorithm performance is reached or is no longer improving. Evolutionary optimization has been used in hyperparameter optimization for statistical machine learning algorithms, automated machine learning, typical neural network and deep neural network architecture search, as well as training of the weights in deep neural networks. === Population-based === Population Based Training (PBT) learns both hyperparameter values and network weights. Multiple learning processes operate independently, using different hyperparameters. As with evolutionary methods, poorly performing models are iteratively replaced with models that adopt modified hyperparameter values and weights based on the better performers. This replacement model warm starting is the primary differentiator between PBT and other evolutionary methods. PBT thus allows the hyperparameters to evolve and eliminates the need for manual hypertuning. The process makes no assumptions regarding model architecture, loss functions or training procedures. PBT and its variants are adaptive methods: they update hyperparameters during the training of the models. On the contrary, non-adaptive methods have the sub-optimal strategy to assign a constant set of hyperparameters for the whole training. === Early stopping-based === A class of early stopping-based hyperparameter optimization algorithms is purpose-built for large search spaces of continuous and discrete hyperparameters, particularly when the computational cost to evaluate the performance of a set of hyperparameters is high. Irace implements the iterated racing algorithm, that focuses the search around the most promising configurations, using statistical tests to discard the ones that perform poorly. Another early stopping hyperparameter optimization algorithm is successive halving (SHA), which begins as a random search but periodically prunes low-performing models, thereby focusing computational resources on more promising models. Asynchronous successive halving (ASHA) further improves upon SHA's resource utilization profile by removing the need to synchronously evaluate a

  Read more →
• 

  BeHafizh

  BeHafizh is a mobile application to assist in the effort to memorize Qur'anic verses. The software runs on the Android operating system. This application was made by a team from Gadjah Mada University (UGM) consisting of Farid Amin Ridwanto, Rian Adam Rajagede and Alfian Try Putranto in order to participate in the National Student Musabaqoh Tilawatil Quran (MTQ) held at University of Indonesia (UI) on 1- August 8, 2015. This application then won a gold medal in the branch of Computer Application Design in the competition. == Features == === Audio Player === Audio player, paragraph can be played repeatedly, with pause, and can be done on a certain range of Quranic verses. === Memorization Test === Memorization testing continues users to improve their memorization. Memorization Recorders improves user's ability to recite Quran. === Colour indicators === === Achievements === === Reminders ===

  Read more →
• 

  Meta-Labeling

  Meta-labeling, also known as corrective AI, is a machine learning (ML) technique utilized in quantitative finance to enhance the performance of investment and trading strategies, developed in 2017 by Marcos López de Prado at Guggenheim Partners and Cornell University. The core idea is to separate the decision of trade direction (side) from the decision of trade sizing, addressing the inefficiencies of simultaneously learning both side and size predictions. The side decision involves forecasting market movements (long, short, neutral), while the size decision focuses on risk management and profitability. It serves as a secondary decision-making layer that evaluates the signals generated by a primary predictive model. By assessing the confidence and likely profitability of those signals, meta-labeling allows investors and algorithms to dynamically size positions and suppress false positives. == Motivation == Meta-labeling is designed to improve precision without sacrificing recall. As noted by López de Prado, attempting to model both the direction and the magnitude of a trade using a single algorithm can result in poor generalization. By separating these tasks, meta-labeling enables greater flexibility and robustness: Enhances control over capital allocation. Reduces overfitting by limiting model complexity. Allows the use of interpretability tools and tailored thresholds to manage risk. Enables dynamic trade suppression in unfavorable regimes. == Applications == Meta-labeling has been applied in a variety of financial ML contexts, including: Algorithmic trading: Filtering and sizing trades to reduce false positives. Portfolio optimization: Scaling exposure across multiple signals with differing confidence levels. Risk management: Dynamically disabling strategies in adverse market conditions. Model validation: Interpreting when and why a model may be underperforming due to regime shifts. == General architecture == Meta-labeling decouples two core components of systematic trading strategies: directional prediction and position sizing. The process involves training a primary model to generate trade signals (e.g., buy, sell, or hold) and then training a secondary model to determine whether each signal is likely to lead to a profitable trade. The second model outputs a probability that is interpreted as the confidence in the forecast, which can be used to adjust the position size or to filter out unreliable trades. Meta-labeling is typically implemented as a three-stage process: Primary model (M1): Predicts the direction or label of a financial outcome using features such as market prices, returns, or volatility indicators. A typical output is directional, e.g., Y ∈ {−1,0,1}, representing short, neutral, or long positions. Secondary model (M2): A binary classifier trained to predict whether the primary model's prediction will be profitable. The target variable is a binary meta-label F ∈ { 0 , 1 } {\displaystyle F\in \{0,1\}} . Inputs can include features used in the primary model, performance diagnostics, or market regime data. Position sizing algorithm (M3): Translates the output probability of the secondary model into a position size. Higher confidence scores result in larger allocations, while lower confidence leads to reduced or zero exposure. === Stage 1: Forecasting side === Primary model architecture Figure 1 Figure 1 presents the architecture of a primary model. It focuses on forecasting the side of the trade. Following the example, this model (M1) takes in input data – such as open-high-low-close data and determines the side of the position to take: a negative number is a short position, and positive number is a long position, the range is set between −1 and 1 (the closer it is to −1 or 1, the stronger the models conviction is). When training the model, the labels are −1 and 1, based on the direction of forward returns for some predefined investment horizon. The researcher may decide to apply a recall check (τ: "Tau") by setting a minimum threshold that the initial output needs to be to qualify of a short or long position (if the threshold is not met, no side forecast is predicted, leading to closing of any open positions), this leads to the primary model output which is one of three possible side forecasts: −1, 0, or 1. The primary model also generates evaluation data which can be used by the secondary model, to improve performance of size forecasts. Some examples of evaluation data include rolling accuracy, F1, recall, precision, and AUC scores. === Stage 2: Filtering out false positives === General meta-labeling architecture Figure 2 Next comes the phase of filtering out false positives, by applying a secondary machine learning model (M2), which is a binary classifier trained to determine if the trade will be profitable or not. The model takes as input four general groupings of data: General input data which is predictive of a false positive. For example the last 30 days rolling volatility of the underlying asset. Evaluation data. Market state and regime data, one may find that macro economic data or clustering the market into regimes may help as specific trading strategies are known to perform better in particular regimes. Example: momentum based strategies perform best in periods with low volatility and strong directional moves. Primary models initial input which is a value between −1 and 1. This highlights the strength of the primary models conviction. The output of the model is a value between −1 and 1 (if using a Tanh function) which will indicate the strength of the conviction that a short or long position is profitable, or it could simply be between 0 and 1 (using a sigmoid function) if one only wanted to know if it made money or not. This output allows filtering out trades that are likely to lead to losses. One could stop at this point or use the outputs of the secondary model as inputs to a position sizing algorithm (M3) which could further enhance strategy performance metrics by translating the output probability of the secondary model into a position size. Higher confidence scores result in larger allocations, while lower confidence leads to reduced or zero exposure. === Stage 3: Optimizing position sizes === ==== Position sizing methods (M3) ==== Various algorithms have been proposed for transforming predicted probabilities into trade sizes: All-or-nothing: Allocate 100% of capital if the probability exceeds a predefined threshold (e.g., 0.5); otherwise, do not trade. Model confidence: Use the probability score directly as the fraction of capital allocated. Linear scaling: Rescale the model's probabilities using min-max normalization based on the training data. Normal CDF (NCDF): Use a normal cumulative distribution function applied to a z-statistic derived from the predicted probability. Empirical CDF (ECDF): Rank probabilities based on their percentile in the training data to ensure relative allocation. Sigmoid Optimal Position Sizing (SOPS): Applies a smooth non-linear sigmoid transformation optimized to maximize risk-adjusted returns (Sharpe ratio). ==== Model calibration ==== Each machine learning algorithm used in meta-labeling tends to produce outputs with different characteristic distributions; for example, some are approximately normally distributed, whereas others exhibit a pronounced U-shape, concentrating probabilities near the extremes. Due to these varying distributions, simply summing the outputs of different models can inadvertently lead to uneven weighting of signals, biasing trade decisions. To address this, model calibration techniques are essential to adjust the predicted probabilities towards frequentist probabilities, ensuring that model outputs reflect true likelihoods more accurately. Two common calibration techniques are: Platt scaling (Sigmoid scaling): Suitable for correcting S-shaped calibration plots typically produced by models such as support vector machines (SVMs). Isotonic regression: Fits a non-decreasing step function to probabilities and is effective particularly with larger datasets, though it can sometimes lead to overfitting. Transforming predictions to frequentist probabilities is crucial as it provides probabilistic outputs that are directly interpretable as the actual likelihood of an event occurring. Such calibration significantly enhances the effectiveness of fixed position sizing methods, reducing maximum drawdowns and increasing risk-adjusted returns. However, calibration has less impact on position sizing methods that directly estimate parameters from the training data, such as ECDF and SOPS, suggesting that calibration is a critical step mainly for fixed methods that rely heavily on raw model outputs. =

  Read more →
• 

  Matchbox Educable Noughts and Crosses Engine

  The Matchbox Educable Noughts and Crosses Engine (sometimes called the Machine Educable Noughts and Crosses Engine or MENACE) was a mechanical computer made from 304 matchboxes designed and built by artificial intelligence researcher Donald Michie and his colleague Roger Chambers, in 1961. It was designed to play human opponents in games of noughts and crosses (tic-tac-toe) by returning a move for any given state of play and to refine its strategy through reinforcement learning. This was one of the first types of artificial intelligence. Michie and Chambers did not have immediate access to a computer; they worked around this by building the engine out of matchboxes. The matchboxes they used each represented a single possible layout of a noughts and crosses grid. When the computer first played, it would randomly choose moves based on the current layout. As it played more games, through a reinforcement loop, it disqualified strategies that led to losing games, and supplemented strategies that led to winning games. Michie held a tournament against MENACE in 1961, wherein he experimented with different openings. Following MENACE's maiden tournament against Michie, it demonstrated successful artificial intelligence in its strategy. Michie's essays on MENACE's weight initialisation and the BOXES algorithm used by MENACE became popular in the field of computer science research. Michie was honoured for his contribution to machine learning research, and was twice commissioned to program a MENACE simulation on an actual computer. == Origin == Donald Michie (1923–2007) had been on the team decrypting the German Tunny Code during World War II. Fifteen years later, he wanted to further display his mathematical and computational prowess with an early convolutional neural network. Since computer equipment was not obtainable for such uses, and Michie did not have a computer readily available, he decided to display and demonstrate artificial intelligence in a more esoteric format and constructed a functional mechanical computer out of matchboxes and beads. MENACE was constructed as the result of a bet with a computer science colleague who postulated that such a machine was impossible. Michie undertook the task of collecting and defining each matchbox as a "fun project", later turned into a demonstration tool. Michie completed his essay on MENACE in 1963, "Experiments on the mechanization of game-learning", as well as his essay on the BOXES Algorithm, written with R. A. Chambers and had built up an AI research unit in Hope Park Square, Edinburgh, Scotland. MENACE learned by playing successive matches of noughts and crosses. Each time, it would eliminate a losing strategy by the human player confiscating the beads that corresponded to each move. It reinforced winning strategies by making the moves more likely, by supplying extra beads. This was one of the earliest versions of the Reinforcement Loop, the schematic algorithm of looping the algorithm, dropping unsuccessful strategies until only the winning ones remain. This model starts as completely random, and gradually learns. == Composition == MENACE was made from 304 matchboxes glued together in an arrangement similar to a chest of drawers. Each box had a code number, which was keyed into a chart. This chart had drawings of tic-tac-toe game grids with various configurations of X, O, and empty squares, corresponding to all possible permutations a game could go through as it progressed. After removing duplicate arrangements (ones that were simply rotations or mirror images of other configurations), MENACE used 304 permutations in its chart and thus that many matchboxes. Each individual matchbox tray contained a collection of coloured beads. Each colour represented a move on a square on the game grid, and so matchboxes with arrangements where positions on the grid were already taken would not have beads for that position. Additionally, at the front of the tray were two extra pieces of card in a "V" shape, the point of the "V" pointing at the front of the matchbox. Michie and his artificial intelligence team called MENACE's algorithm "Boxes", after the apparatus used for the machine. The first stage "Boxes" operated in five phases, each setting a definition and a precedent for the rules of the algorithm in relation to the game. == Operation == MENACE played first, as O, since all matchboxes represented permutations only relevant to the "X" player. To retrieve MENACE's choice of move, the opponent or operator located the matchbox that matched the current game state, or a rotation or mirror image of it. For example, at the start of a game, this would be the matchbox for an empty grid. The tray would be removed and lightly shaken so as to move the beads around. Then, the bead that had rolled into the point of the "V" shape at the front of the tray was the move MENACE had chosen to make. Its colour was then used as the position to play on, and, after accounting for any rotations or flips needed based on the chosen matchbox configuration's relation to the current grid, the O would be placed on that square. Then the player performed their move, the new state was located, a new move selected, and so on, until the game was finished. When the game had finished, the human player observed the game's outcome. As a game was played, each matchbox that was used for MENACE's turn had its tray returned to it ajar, and the bead used kept aside, so that MENACE's choice of moves and the game states they belonged to were recorded. Michie described his reinforcement system with "reward" and "punishment". Once the game was finished, if MENACE had won, it would then receive a "reward" for its victory. The removed beads showed the sequence of the winning moves. These were returned to their respective trays, easily identifiable since they were slightly open, as well as three bonus beads of the same colour. In this way, in future games MENACE would become more likely to repeat those winning moves, reinforcing winning strategies. If it lost, the removed beads were not returned, "punishing" MENACE, and meaning that in future it would be less likely, and eventually incapable if that colour of bead became absent, to repeat the moves that cause a loss. If the game was a draw, one additional bead was added to each box. == Results in practice == === Optimal strategy === Noughts and crosses has a well-known optimal strategy. A player must place their symbol in a way that blocks the other player from achieving any rows while simultaneously making a row themself. However, if both players use this strategy, the game always ends in a draw. If the human player is familiar with the optimal strategy, and MENACE can quickly learn it, then the games will eventually only end in draws. The likelihood of the computer winning increases quickly when the computer plays against a random-playing opponent. When playing against a player using optimal strategy, the odds of a draw grow to 100%. In Donald Michie's official tournament against MENACE in 1961 he used optimal strategy, and he and the computer began to draw consistently after twenty games. Michie's tournament had the following milestones: Michie began by consistently opening with "Variant 0", the middle square. At 15 games, MENACE abandoned all non-corner openings. At just over 20, Michie switched to consistently using "Variant 1", the bottom-right square. At 60, he returned to Variant 0. As he neared 80 games, he moved to "Variant 2", the top-middle. At 110, he switched to "Variant 3", the top right. At 135, he switched to "Variant 4", middle-right. At 190, he returned to Variant 1, and at 210, he returned to Variant 0. The trend in changes of beads in the "2" boxes runs: === Correlation === Depending on the strategy employed by the human player, MENACE produces a different trend on scatter graphs of wins. Using a random turn from the human player results in an almost-perfect positive trend. Playing the optimal strategy returns a slightly slower increase. The reinforcement does not create a perfect standard of wins; the algorithm will draw random uncertain conclusions each time. After the j-th round, the correlation of near-perfect play runs: 1 − D D − D ( j + 2 ) ∑ i = 0 j D ( j i + 1 ) V i {\displaystyle {1-D \over D-D^{(j+2)}}\sum _{i=0}^{j}D^{(ji+1)}V_{i}} Where Vi is the outcome (+1 is win, 0 is draw and -1 is loss) and D is the decay factor (average of past values of wins and losses). Below, Mn is the multiplier for the n-th round of the game. == Legacy == Donald Michie's MENACE proved that a computer could learn from failure and success to become good at a task. It used what would become core principles within the field of machine learning before they had been properly theorised. For example, the combination of how MENACE starts with equal numbers of types of beads in each matchbox, and how these are then selected at random, creates a learning behaviour similar to weight initialisation

  Read more →
• 

  Maximum inner-product search

  Maximum inner-product search (MIPS) is a search problem, with a corresponding class of search algorithms which attempt to maximise the inner product between a query and the data items to be retrieved. MIPS algorithms are used in a wide variety of big data applications, including recommendation algorithms and machine learning. Formally, for a database of vectors x i {\displaystyle x_{i}} defined over a set of labels S {\displaystyle S} in an inner product space with an inner product ⟨ ⋅ , ⋅ ⟩ {\displaystyle \langle \cdot ,\cdot \rangle } defined on it, MIPS search can be defined as the problem of determining a r g m a x i ∈ S ⟨ x i , q ⟩ {\displaystyle {\underset {i\in S}{\operatorname {arg\,max} }}\ \langle x_{i},q\rangle } for a given query q {\displaystyle q} . Although there is an obvious linear-time implementation, it is generally too slow to be used on practical problems. However, efficient algorithms exist to speed up MIPS search. Under the assumption of all vectors in the set having constant norm, MIPS can be viewed as equivalent to a nearest neighbor search (NNS) problem in which maximizing the inner product is equivalent to minimizing the corresponding distance metric in the NNS problem. Like other forms of NNS, MIPS algorithms may be approximate or exact. MIPS search is used as part of DeepMind's RETRO algorithm.

  Read more →
• 

  MyPertamina

  MyPertamina is a digital financial service platform from Pertamina that integrated with the apps LinkAja. This application is used for non-cash fuel oil payments at Pertamina's public fueling stations. == History == Originally, MyPertamina were merchandise outlets of Pertamina products. It was launched on December 21, 2016, with 3 outlets in Jakarta. MyPertamina sells clothes, hats, and other products with Pertamina products brands. One month later (January 2017), Pertamina and Bank Mandiri entered into a partnership to launch the Mandiri Credit Card Pertamina Mastercard product, so that consumers can make payments when users fill up fuel at Pertamina gas stations. In August 2017, MyPertamina app and electronic card were launched through MyPertamina Loyalty program at Gaikindo Indonesia International Auto Show 2017. The card can be used on EDC machines for non-cash payments. Initial balances are in its own app, that can be top up by ATMs and online banking.

  Read more →
• 

  Multi-armed bandit

  In probability theory and machine learning, the multi-armed bandit problem (sometimes called the K- or N-armed bandit problem) is named from imagining a gambler at a row of slot machines (sometimes known as "one-armed bandits"), who has to decide which machines to play, how many times to play each machine and in which order to play them, and whether to continue with the current machine or try a different machine. More generally, it is a problem in which a decision maker iteratively selects one of multiple fixed choices (i.e., arms or actions) when the properties of each choice are only partially known at the time of allocation, and may become better understood as time passes. A fundamental aspect of bandit problems is that choosing an arm does not affect the properties of the arm or other arms. Instances of the multi-armed bandit problem include the task of iteratively allocating a fixed, limited set of resources between competing (alternative) choices in a way that minimizes the regret. A notable alternative setup for the multi-armed bandit problem includes the "best arm identification (BAI)" problem where the goal is instead to identify the best choice by the end of a finite number of rounds. The multi-armed bandit problem is a classic reinforcement learning problem that exemplifies the exploration–exploitation tradeoff dilemma. In contrast to general reinforcement learning, the selected actions in bandit problems do not affect the reward distribution of the arms. The multi-armed bandit problem also falls into the broad category of stochastic scheduling. In the problem, each machine provides a random reward from a probability distribution specific to that machine, that is not known a priori. The objective of the gambler is to maximize the sum of rewards earned through a sequence of lever pulls. The crucial tradeoff the gambler faces at each trial is between "exploitation" of the machine that has the highest expected payoff and "exploration" to get more information about the expected payoffs of the other machines. The trade-off between exploration and exploitation is also faced in machine learning. In practice, multi-armed bandits have been used to model problems such as managing research projects in a large organization, like a science foundation or a pharmaceutical company. In early versions of the problem, the gambler begins with no initial knowledge about the machines. Herbert Robbins in 1952, realizing the importance of the problem, constructed convergent population selection strategies in "some aspects of the sequential design of experiments". A theorem, the Gittins index, first published by John C. Gittins, gives an optimal policy for maximizing the expected discounted reward. == Empirical motivation == The multi-armed bandit problem models an agent that simultaneously attempts to acquire new knowledge (called "exploration") and optimize their decisions based on existing knowledge (called "exploitation"). The agent attempts to balance these competing tasks in order to maximize their total value over the period of time considered. There are many practical applications of the bandit model, for example: clinical trials investigating the effects of different experimental treatments while minimizing patient losses, adaptive routing efforts for minimizing delays in a network, financial portfolio design In these practical examples, the problem requires balancing reward maximization based on the knowledge already acquired with attempting new actions to further increase knowledge. This is known as the exploitation vs. exploration tradeoff in machine learning. The model has also been used to control dynamic allocation of resources to different projects, answering the question of which project to work on, given uncertainty about the difficulty and payoff of each possibility. Originally considered by Allied scientists in World War II, it proved so intractable that, according to Peter Whittle, the problem was proposed to be dropped over Germany so that German scientists could also waste their time on it. The version of the problem now commonly analyzed was formulated by Herbert Robbins in 1952. == The multi-armed bandit model == The multi-armed bandit (short: bandit or MAB) can be seen as a set of real distributions B = { R 1 , … , R K } {\displaystyle B=\{R_{1},\dots ,R_{K}\}} , each distribution being associated with the rewards delivered by one of the K ∈ N + {\displaystyle K\in \mathbb {N} ^{+}} levers. Let μ 1 , … , μ K {\displaystyle \mu _{1},\dots ,\mu _{K}} be the mean values associated with these reward distributions. The gambler iteratively plays one lever per round and observes the associated reward. The objective is to maximize the sum of the collected rewards. The horizon H {\displaystyle H} is the number of rounds that remain to be played. The bandit problem is formally equivalent to a one-state Markov decision process. The regret ρ {\displaystyle \rho } after T {\displaystyle T} rounds is defined as the expected difference between the reward sum associated with an optimal strategy and the sum of the collected rewards: ρ = T μ ∗ − ∑ t = 1 T r ^ t {\displaystyle \rho =T\mu ^{}-\sum _{t=1}^{T}{\widehat {r}}_{t}} , where μ ∗ {\displaystyle \mu ^{}} is the maximal reward mean, μ ∗ = max k { μ k } {\displaystyle \mu ^{}=\max _{k}\{\mu _{k}\}} , and r ^ t {\displaystyle {\widehat {r}}_{t}} is the reward in round t {\displaystyle t} . A zero-regret strategy is a strategy whose average regret per round ρ / T {\displaystyle \rho /T} tends to zero with probability 1 when the number of played rounds tends to infinity. Intuitively, zero-regret strategies are guaranteed to converge to a (not necessarily unique) optimal strategy if enough rounds are played. == Variations == A common formulation is the Binary multi-armed bandit or Bernoulli multi-armed bandit, which issues a reward of one with probability p {\displaystyle p} , and otherwise a reward of zero. Another formulation of the multi-armed bandit has each arm representing an independent Markov machine. Each time a particular arm is played, the state of that machine advances to a new one, chosen according to the Markov state evolution probabilities. There is a reward depending on the current state of the machine. In a generalization called the "restless bandit problem", the states of non-played arms can also evolve over time. There has also been discussion of systems where the number of choices (about which arm to play) increases over time. Computer science researchers have studied multi-armed bandits under worst-case assumptions, obtaining algorithms to minimize regret in both finite and infinite (asymptotic) time horizons for both stochastic and non-stochastic arm payoffs. === Best arm identification === An important variation of the classical regret minimization problem in multi-armed bandits is best arm identification (BAI), also known as pure exploration. This problem is crucial in various applications, including clinical trials, adaptive routing, recommendation systems, and A/B testing. In BAI, the objective is to identify the arm having the highest expected reward. An algorithm in this setting is characterized by a sampling rule, a decision rule, and a stopping rule, described as follows: Sampling rule: ( a t ) t ≥ 1 {\displaystyle (a_{t})_{t\geq 1}} is a sequence of actions at each time step Stopping rule: τ {\displaystyle \tau } is a (random) stopping time which suggests when to stop collecting samples Decision rule: a ^ τ {\displaystyle {\hat {a}}_{\tau }} is a guess on the best arm based on the data collected up to time τ {\displaystyle \tau } There are two predominant settings in BAI: Fixed budget setting: Given a time horizon T ≥ 1 {\displaystyle T\geq 1} , the objective is to identify the arm with the highest expected reward a ⋆ ∈ arg ⁡ max k μ k {\displaystyle a^{\star }\in \arg \max _{k}\mu _{k}} minimizing probability of error δ {\displaystyle \delta } . Fixed confidence setting: Given a confidence level δ ∈ ( 0 , 1 ) {\displaystyle \delta \in (0,1)} , the objective is to identify the arm with the highest expected reward a ⋆ ∈ arg ⁡ max k μ k {\displaystyle a^{\star }\in \arg \max _{k}\mu _{k}} with the least possible amount of trials and with probability of error P ( a ^ τ ≠ a ⋆ ) ≤ δ {\displaystyle \mathbb {P} ({\hat {a}}_{\tau }\neq a^{\star })\leq \delta } . For example using a decision rule, we could use m 1 {\displaystyle m_{1}} where m {\displaystyle m} is the machine no.1 (you can use a different variable respectively) and 1 {\displaystyle 1} is the amount for each time an attempt is made at pulling the lever, where ∫ ∑ m 1 , m 2 , ( . . . ) = M {\displaystyle \int \sum m_{1},m_{2},(...)=M} , identify M {\displaystyle M} as the sum of each attempts m 1 + m 2 {\displaystyle m_{1}+m_{2}} , (...) as needed, and from there you can get a ratio, sum or mean as quantitative probability and sample your formulation for each slots. You can also do ∫ ∑ k ∝ i N − (

  Read more →
• 

  Learning curve (machine learning)

  In machine learning (ML), a learning curve (or training curve) is a graphical representation that shows how a model's performance on a training set (and usually a validation set) changes with the number of training iterations (epochs) or the amount of training data. Typically, the number of training epochs or training set size is plotted on the x-axis, and the value of the loss function (and possibly some other metric such as the cross-validation score) on the y-axis. Synonyms include error curve, experience curve, improvement curve and generalization curve. More abstractly, learning curves plot the difference between learning effort and predictive performance, where "learning effort" usually means the number of training samples, and "predictive performance" means accuracy on testing samples. Learning curves have many useful purposes in ML, including: choosing model parameters during design, adjusting optimization to improve convergence, and diagnosing problems such as overfitting (or underfitting). Learning curves can also be tools for determining how much a model benefits from adding more training data, and whether the model suffers more from a variance error or a bias error. If both the validation score and the training score converge to a certain value, then the model will no longer significantly benefit from more training data. == Formal definition == When creating a function to approximate the distribution of some data, it is necessary to define a loss function L ( f θ ( X ) , Y ) {\displaystyle L(f_{\theta }(X),Y)} to measure how good the model output is (e.g., accuracy for classification tasks or mean squared error for regression). We then define an optimization process which finds model parameters θ {\displaystyle \theta } such that L ( f θ ( X ) , Y ) {\displaystyle L(f_{\theta }(X),Y)} is minimized, referred to as θ ∗ {\displaystyle \theta ^{}} . === Training curve for amount of data === If the training data is { x 1 , x 2 , … , x n } , { y 1 , y 2 , … y n } {\displaystyle \{x_{1},x_{2},\dots ,x_{n}\},\{y_{1},y_{2},\dots y_{n}\}} and the validation data is { x 1 ′ , x 2 ′ , … x m ′ } , { y 1 ′ , y 2 ′ , … y m ′ } {\displaystyle \{x_{1}',x_{2}',\dots x_{m}'\},\{y_{1}',y_{2}',\dots y_{m}'\}} , a learning curve is the plot of the two curves i ↦ L ( f θ ∗ ( X i , Y i ) ( X i ) , Y i ) {\displaystyle i\mapsto L(f_{\theta ^{}(X_{i},Y_{i})}(X_{i}),Y_{i})} i ↦ L ( f θ ∗ ( X i , Y i ) ( X i ′ ) , Y i ′ ) {\displaystyle i\mapsto L(f_{\theta ^{}(X_{i},Y_{i})}(X_{i}'),Y_{i}')} where X i = { x 1 , x 2 , … x i } {\displaystyle X_{i}=\{x_{1},x_{2},\dots x_{i}\}} === Training curve for number of iterations === Many optimization algorithms are iterative, repeating the same step (such as backpropagation) until the process converges to an optimal value. Gradient descent is one such algorithm. If θ i ∗ {\displaystyle \theta _{i}^{}} is the approximation of the optimal θ {\displaystyle \theta } after i {\displaystyle i} steps, a learning curve is the plot of i ↦ L ( f θ i ∗ ( X , Y ) ( X ) , Y ) {\displaystyle i\mapsto L(f_{\theta _{i}^{}(X,Y)}(X),Y)} i ↦ L ( f θ i ∗ ( X , Y ) ( X ′ ) , Y ′ ) {\displaystyle i\mapsto L(f_{\theta _{i}^{}(X,Y)}(X'),Y')}

  Read more →
• 

  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

  Read more →
• 

  Avizo (software)

  Avizo (pronounce: 'a-VEE-zo') is a general-purpose commercial software application for scientific and industrial data visualization and analysis. Avizo is developed by Thermo Fisher Scientific and was originally designed and developed by the Visualization and Data Analysis Group at Zuse Institute Berlin (ZIB) under the name Amira. Avizo was commercially released in November 2007. For the history of its development, see the Wikipedia article about Amira. == Overview == Avizo is a software application which enables users to perform interactive visualization and computation on 3D data sets. The Avizo interface is modelled on the visual programming. Users manipulate data and module components, organized in an interactive graph representation (called Pool), or in a Tree view. Data and modules can be interactively connected together, and controlled with several parameters, creating a visual processing network whose output is displayed in a 3D viewer. With this interface, complex data can be interactively explored and analyzed by applying a controlled sequence of computation and display processes resulting in a meaningful visual representation and associated derived data. == Application areas == Avizo has been designed to support different types of applications and workflows from 2D and 3D image data processing to simulations. It is a versatile and customizable visualization tool used in many fields: Scientific visualization Materials Research Tomography, Microscopy, etc. Nondestructive testing, Industrial Inspection, and Visual Inspection Computer-aided Engineering and simulation data post-processing Porous medium analysis Civil Engineering Seismic Exploration, Reservoir Engineering, Microseismic Monitoring, Borehole Imaging Geology, Digital Rock Physics (DRP), Earth Sciences Archaeology Food technology and agricultural science Physics, Chemistry Climatology, Oceanography, Environmental Studies Astrophysics == Features == Data import: 2D and 3D image stack and volume data: from microscopes (electron, optical), X-ray tomography (CT, micro-/nano-CT, synchrotron), neutron tomography and other acquisition devices (MRI, radiography, GPR) Geometric models (such as point sets, line sets, surfaces, grids) Numerical simulation data (such as Computational fluid dynamics or Finite element analysis data) Molecular data Time series and animations Seismic data Well logs 4D Multivariate Climate Models 2D/3D data visualization: Volume rendering Digital Volume Correlation Visualization of sections, through various slicing and clipping methods Isosurface rendering Polygonal meshes Scalar fields, Vector fields, Tensor representations, Flow visualization (Illuminated Streamlines, Stream Ribbons) Image processing: 2D/3D Alignment of image slices, Image registration Image filtering Mathematical Morphology (erode, dilate, open, close, tophat) Watershed Transform, Distance Transform Image segmentation 3D models reconstruction: Polygonal surface generation from segmented objects Generation of tetrahedral grids Surface reconstruction from point clouds Skeletonization (reconstruction of dendritic, porous or fracture network) Surface model simplification Quantification and analysis: Measurements and statistics Analysis spreadsheet and charting Material properties computation, based on 3D images: Absolute permeability Thermal conductivity Molecular diffusivity Electrical resistivity/formation factor 3D image-based meshing for CFD and FEA: From 3D imaging modalities (CT, micro-CT, MRI, etc.) Surface and volume meshes generation Export to FEA and CFD solvers for simulation Post-processing for simulation analysis Presentation, automation: MovieMaker, Multiscreen, Video wall, collaboration, and VR support TCL Scripting, C++ extension API Avizo is based on Open Inventor 3D graphics toolkits (FEI Visualization Sciences Group).

  Read more →
• 

  Neuro-symbolic AI

  Neuro-symbolic AI is a subfield of artificial intelligence that integrates neural methods (e.g., neural networks and deep learning) with symbolic methods (e.g., formal logic, knowledge representation, and automated reasoning). The goal is to combine the strengths of both approaches, resulting in AI systems that can be trained from raw data and demonstrate robustness against outliers or errors in the base data, while preserving explainability, explicit use of expert knowledge, and explicit cognitive reasoning. As argued by Leslie Valiant and others, the effective construction of rich computational cognitive models demands the combination of symbolic reasoning and efficient machine learning. Gary Marcus argued, "We cannot construct rich cognitive models in an adequate, automated way without the triumvirate of hybrid architecture, rich prior knowledge, and sophisticated techniques for reasoning." Further, "To build a robust, knowledge-driven approach to AI we must have the machinery of symbol manipulation in our toolkit. Too much of useful knowledge is abstract to make do without tools that represent and manipulate abstraction, and to date, the only known machinery that can manipulate such abstract knowledge reliably is the apparatus of symbol manipulation." Angelo Dalli, Henry Kautz, Francesca Rossi, and Bart Selman also argued for such a synthesis. Their arguments attempt to address the two kinds of thinking, as discussed in Daniel Kahneman's book Thinking, Fast and Slow. It describes cognition as encompassing two components: System 1 is fast, reflexive, intuitive, and unconscious. System 2 is slower, step-by-step, and explicit. System 1 is used for pattern recognition. System 2 handles planning, deduction, and deliberative thinking. In this view, deep learning best handles the first kind of cognition, while symbolic reasoning best handles the second kind. Both are necessary for the development of a robust and reliable AI system capable of learning, reasoning, and interacting with humans to accept advice and answer questions. Since the 1990s, dual-process models with explicit references to the two contrasting systems have been the focus of research in both the fields of AI and cognitive science by numerous researchers. In 2025, the adoption of neurosymbolic AI, an approach that integrates neural networks with symbolic reasoning, increased in response to the need to address hallucination issues in large language models. For example, Amazon implemented Neurosymbolic AI in its Vulcan warehouse robots and Rufus shopping assistant to enhance accuracy and decision-making. == Approaches == Approaches for integration are diverse. Henry Kautz's taxonomy of neuro-symbolic architectures follows, along with some examples: Symbolic Neural symbolic is the current approach of many neural models in natural language processing, where words or subword tokens are the ultimate input and output of large language models. Examples include BERT, RoBERTa, and GPT-3. Symbolic[Neural] is exemplified by AlphaGo, where symbolic techniques are used to invoke neural techniques. In this case, the symbolic approach is Monte Carlo tree search and the neural techniques learn how to evaluate game positions. Neural | Symbolic uses a neural architecture to interpret perceptual data as symbols and relationships that are reasoned about symbolically. Neural-Concept Learner is an example. Neural: Symbolic → Neural relies on symbolic reasoning to generate or label training data that is subsequently learned by a deep learning model, e.g., to train a neural model for symbolic computation by using a Macsyma-like symbolic mathematics system to create or label examples. NeuralSymbolic uses a neural net that is generated from symbolic rules. An example is the Neural Theorem Prover, which constructs a neural network from an AND-OR proof tree generated from knowledge base rules and terms. Logic Tensor Networks also fall into this category. Neural[Symbolic] according to Kautz, this approach embeds true symbolic reasoning inside a neural network. These are tightly-coupled neural-symbolic systems, in which the logical inference rules are internal to the neural network. This way, the neural network internally computes the inference from the premises and learns to reason based on logical inference systems. Early work on connectionist modal and temporal logics by Garcez, Lamb, and Gabbay is aligned with this approach. These categories are not exhaustive, as they do not consider multi-agent systems. In 2005, Bader and Hitzler presented a more fine-grained categorization that took into account, e.g., whether the use of symbols included logic and, if so, whether the logic was propositional or first-order logic. The 2005 categorization and Kautz's taxonomy above are compared and contrasted in a 2021 article. Sepp Hochreiter argued that Graph Neural Networks "...are the predominant models of neural-symbolic computing" since "[t]hey describe the properties of molecules, simulate social networks, or predict future states in physical and engineering applications with particle-particle interactions." == Artificial general intelligence == Gary Marcus argues that "...hybrid architectures that combine learning and symbol manipulation are necessary for robust intelligence, but not sufficient", and that there are ...four cognitive prerequisites for building robust artificial intelligence: hybrid architectures that combine large-scale learning with the representational and computational powers of symbol manipulation, large-scale knowledge bases—likely leveraging innate frameworks—that incorporate symbolic knowledge along with other forms of knowledge, reasoning mechanisms capable of leveraging those knowledge bases in tractable ways, and rich cognitive models that work together with those mechanisms and knowledge bases. This echoes earlier calls for hybrid models as early as the 1990s. == History == Garcez and Lamb described research in this area as ongoing, at least since the 1990s. During that period, the terms symbolic and sub-symbolic AI were popular. A series of workshops on neuro-symbolic AI has been held annually since 2005 Neuro-Symbolic Artificial Intelligence. In the early 1990s, an initial set of workshops on this topic were organized. == Research == Key research questions remain, such as: What is the best way to integrate neural and symbolic architectures? How should symbolic structures be represented within neural networks and extracted from them? How should common-sense knowledge be learned and reasoned about? How can abstract knowledge that is hard to encode logically be handled? == Implementations == Implementations of neuro-symbolic approaches include: AllegroGraph: an integrated Knowledge Graph based platform for neuro-symbolic application development. Scallop: a language based on Datalog that supports differentiable logical and relational reasoning. Scallop can be integrated in Python and with a PyTorch learning module. Logic Tensor Networks: encode logical formulas as neural networks and simultaneously learn term encodings, term weights, and formula weights. DeepProbLog: combines neural networks with the probabilistic reasoning of ProbLog. Abductive Learning: integrates machine learning and logical reasoning in a balanced-loop via abductive reasoning, enabling them to work together in a mutually beneficial way. SymbolicAI: a compositional differentiable programming library.

  Read more →
• 

  Smart speaker industry in South Korea

  Smart speakers, or AI speakers, have been developed by multiple domestic electronics and telecommunications firms in South Korea. Since their introduction to the local market in 2016, they have been used by millions of people in the country. == Brands == === Google === In September 2018, Google Home (including the Google Home Mini) launched in South Korea. Running Google Assistant, it featured simultaneous recognition of two languages among a total of seven, including Korean. At launch, it could play music from Bugs!, in addition to YouTube. === Kakao === In November 2017, Kakao launched the Kakao Mini, featuring integrated KakaoTalk functionality. === KT === KT launched the GiGA Genie smart speaker in January 2017, using a Harman Kardon speaker. In November 2017, KT announced GiGA Genie LTE, a portable AI speaker with LTE support. They also released a mini speaker called GiGA Genie Buddy. In 2018, KT created a special version of GiGa Genie with a screen for use in hotels. On 29 April 2019, KT announced the GiGA Genie Table TV, a consumer-oriented smart speaker with a display. It featured paid TV access through Wi-Fi. Based on usage data from the hotel model, KT decided not to add a touchscreen. The Table TV also featured a limited-access "personalized-text-to-speech technology" which could use parents' voice recording inputs to read children books. In February 2022, KT began rolling out Amazon Alexa integration into its speakers for English support. === Naver === In August 2017, Naver announced the Wave smart speaker, operating on Clova. In October 2017, Naver launched the Friends smart speaker, which were designed based on Line characters. ==== LG Uplus ==== In December 2017, LG Uplus launched the Friends+ speaker with Naver, operating on U+ Home AI. === Samsung === In August 2018, Samsung announced the Samsung Galaxy Home in partnership with Spotify. The original size was delayed, while the Galaxy Home Mini appeared briefly as a bonus for Samsung Galaxy S20 preorders in South Korea in February 2020. === SK Telecom === SK Telecom launched the Nugu smart speaker in September 2016, using an Astell & Kern audio system. In August 2017, SKT released a portable speaker named Nugu mini. In July 2018, SKT launched the Nugu Candle, featuring expanded mood lighting. The first-generation Nugu was subsequently discontinued. On 18 April 2019, SKT released the NUGU Nemo AI, which featured a display and JBL stereo speaker. In August 2019, SKT collaborated with SM Entertainment, incorporating functions related to the agency's artists into Nugu. In January 2022, SKT showcased the NUGU Candle SE, introducing Alexa support. == Usage == In 2018, approximately 3 million people in South Korea used smart speakers. According to data from KT in 2018, the most common commands to its speakers were for controlling televisions. Based on a broader survey in 2017, music was selected as the most frequent use case. By 2018, smart speaker companies were partnering with reading and other education services, adding potential use-cases for children. By 2022, smart speakers were being utilized by the South Korean government. SKT, in partnership with 70 regional governments, distributed smart speakers to 12,000 senior citizens living alone. The government paid for monthly subscriptions to help seniors stay mentally engaged. Naver made an agreement with the Seoul Metropolitan Government to provide Clova CareCall, an automated health checkup program to hundreds of senior citizens living alone. KT's AI care service included an emergency dispatch call function and medication notifications. == Criticism == === Communication === In a survey of 300 users in 2017, approximately half reported having some type of communication issue with their smart speakers. === Privacy === South Korean smart speakers sparked privacy concerns when they were found to be collecting and documenting user audio data in 2019. The speaker companies responded that only a minority of data was collected and that it was anonymized. They stated that such recordings were collected for performance improvements.

  Read more →