In statistics, cluster analysis is the algorithmic grouping of objects into homogeneous groups based on numerical measurements. Model-based clustering based on a statistical model for the data, usually a mixture model. This has several advantages, including a principled statistical basis for clustering, and ways to choose the number of clusters, to choose the best clustering model, to assess the uncertainty of the clustering, and to identify outliers that do not belong to any group. == Model-based clustering == Suppose that for each of n {\displaystyle n} observations we have data on d {\displaystyle d} variables, denoted by y i = ( y i , 1 , … , y i , d ) {\displaystyle y_{i}=(y_{i,1},\ldots ,y_{i,d})} for observation i {\displaystyle i} . Then model-based clustering expresses the probability density function of y i {\displaystyle y_{i}} as a finite mixture, or weighted average of G {\displaystyle G} component probability density functions: p ( y i ) = ∑ g = 1 G τ g f g ( y i ∣ θ g ) , {\displaystyle p(y_{i})=\sum _{g=1}^{G}\tau _{g}f_{g}(y_{i}\mid \theta _{g}),} where f g {\displaystyle f_{g}} is a probability density function with parameter θ g {\displaystyle \theta _{g}} , τ g {\displaystyle \tau _{g}} is the corresponding mixture probability where ∑ g = 1 G τ g = 1 {\displaystyle \sum _{g=1}^{G}\tau _{g}=1} . Then in its simplest form, model-based clustering views each component of the mixture model as a cluster, estimates the model parameters, and assigns each observation to cluster corresponding to its most likely mixture component. === Gaussian mixture model === The most common model for continuous data is that f g {\displaystyle f_{g}} is a multivariate normal distribution with mean vector μ g {\displaystyle \mu _{g}} and covariance matrix Σ g {\displaystyle \Sigma _{g}} , so that θ g = ( μ g , Σ g ) {\displaystyle \theta _{g}=(\mu _{g},\Sigma _{g})} . This defines a Gaussian mixture model. The parameters of the model, τ g {\displaystyle \tau _{g}} and θ g {\displaystyle \theta _{g}} for g = 1 , … , G {\displaystyle g=1,\ldots ,G} , are typically estimated by maximum likelihood estimation using the expectation-maximization algorithm (EM); see also EM algorithm and GMM model. Bayesian inference is also often used for inference about finite mixture models. The Bayesian approach also allows for the case where the number of components, G {\displaystyle G} , is infinite, using a Dirichlet process prior, yielding a Dirichlet process mixture model for clustering. === Choosing the number of clusters === An advantage of model-based clustering is that it provides statistically principled ways to choose the number of clusters. Each different choice of the number of groups G {\displaystyle G} corresponds to a different mixture model. Then standard statistical model selection criteria such as the Bayesian information criterion (BIC) can be used to choose G {\displaystyle G} . The integrated completed likelihood (ICL) is a different criterion designed to choose the number of clusters rather than the number of mixture components in the model; these will often be different if highly non-Gaussian clusters are present. === Parsimonious Gaussian mixture model === For data with high dimension, d {\displaystyle d} , using a full covariance matrix for each mixture component requires estimation of many parameters, which can result in a loss of precision, generalizabity and interpretability. Thus it is common to use more parsimonious component covariance matrices exploiting their geometric interpretation. Gaussian clusters are ellipsoidal, with their volume, shape and orientation determined by the covariance matrix. Consider the eigendecomposition of a matrix Σ g = λ g D g A g D g T , {\displaystyle \Sigma _{g}=\lambda _{g}D_{g}A_{g}D_{g}^{T},} where D g {\displaystyle D_{g}} is the matrix of eigenvectors of Σ g {\displaystyle \Sigma _{g}} , A g = diag { A 1 , g , … , A d , g } {\displaystyle A_{g}={\mbox{diag}}\{A_{1,g},\ldots ,A_{d,g}\}} is a diagonal matrix whose elements are proportional to the eigenvalues of Σ g {\displaystyle \Sigma _{g}} in descending order, and λ g {\displaystyle \lambda _{g}} is the associated constant of proportionality. Then λ g {\displaystyle \lambda _{g}} controls the volume of the ellipsoid, A g {\displaystyle A_{g}} its shape, and D g {\displaystyle D_{g}} its orientation. Each of the volume, shape and orientation of the clusters can be constrained to be equal (E) or allowed to vary (V); the orientation can also be spherical, with identical eigenvalues (I). This yields 14 possible clustering models, shown in this table: It can be seen that many of these models are more parsimonious, with far fewer parameters than the unconstrained model that has 90 parameters when G = 4 {\displaystyle G=4} and d = 9 {\displaystyle d=9} . Several of these models correspond to well-known heuristic clustering methods. For example, k-means clustering is equivalent to estimation of the EII clustering model using the classification EM algorithm. The Bayesian information criterion (BIC) can be used to choose the best clustering model as well as the number of clusters. It can also be used as the basis for a method to choose the variables in the clustering model, eliminating variables that are not useful for clustering. Different Gaussian model-based clustering methods have been developed with an eye to handling high-dimensional data. These include the pgmm method, which is based on the mixture of factor analyzers model, and the HDclassif method, based on the idea of subspace clustering. The mixture-of-experts framework extends model-based clustering to include covariates. == Example == We illustrate the method with a dateset consisting of three measurements (glucose, insulin, sspg) on 145 subjects for the purpose of diagnosing diabetes and the type of diabetes present. The subjects were clinically classified into three groups: normal, chemical diabetes and overt diabetes, but we use this information only for evaluating clustering methods, not for classifying subjects. The BIC plot shows the BIC values for each combination of the number of clusters, G {\displaystyle G} , and the clustering model from the Table. Each curve corresponds to a different clustering model. The BIC favors 3 groups, which corresponds to the clinical assessment. It also favors the unconstrained covariance model, VVV. This fits the data well, because the normal patients have low values of both sspg and insulin, while the distributions of the chemical and overt diabetes groups are elongated, but in different directions. Thus the volumes, shapes and orientations of the three groups are clearly different, and so the unconstrained model is appropriate, as selected by the model-based clustering method. The classification plot shows the classification of the subjects by model-based clustering. The classification was quite accurate, with a 12% error rate as defined by the clinical classification. Other well-known clustering methods performed worse with higher error rates, such as single-linkage clustering with 46%, average link clustering with 30%, complete-linkage clustering also with 30%, and k-means clustering with 28%. == Outliers in clustering == An outlier in clustering is a data point that does not belong to any of the clusters. One way of modeling outliers in model-based clustering is to include an additional mixture component that is very dispersed, with for example a uniform distribution. Another approach is to replace the multivariate normal densities by t {\displaystyle t} -distributions, with the idea that the long tails of the t {\displaystyle t} -distribution would ensure robustness to outliers. However, this is not breakdown-robust. A third approach is the "tclust" or data trimming approach which excludes observations identified as outliers when estimating the model parameters. == Non-Gaussian clusters and merging == Sometimes one or more clusters deviate strongly from the Gaussian assumption. If a Gaussian mixture is fitted to such data, a strongly non-Gaussian cluster will often be represented by several mixture components rather than a single one. In that case, cluster merging can be used to find a better clustering. A different approach is to use mixtures of complex component densities to represent non-Gaussian clusters. == Non-continuous data == === Categorical data === Clustering multivariate categorical data is most often done using the latent class model. This assumes that the data arise from a finite mixture model, where within each cluster the variables are independent. === Mixed data === These arise when variables are of different types, such as continuous, categorical or ordinal data. A latent class model for mixed data assumes local independence between the variable. The location model relaxes the local independence assumption. The clustMD approach assumes that the observed variables are manifestations of underlying continuous Gaussian latent
KE Software
KE Software is a formerly Australian-owned computer software company based in Manchester, United Kingdom, which specialises in collection management programs for museums, galleries and archives. The Axiell Group acquired the firm in 2014. == History == KE Software had its origins in investigations into electronic systems for managing natural science collections conducted in the late 1970s under a joint program of the University of Melbourne, the then National Museum of Victoria and the Australian Museum, which led to the development of the Titan Database in 1984. Much of the credit for the development of the project was due to the work of Martin Hallett of the Museum of Victoria which evolved into Textpress, and by 2000, the KE EMu database program. KE Software was bought by Axiell in 2014 and the team merged with the Axiell staff. Axiell continues to sell and support EMu. == Products == The firm has two main products: the Ke EMu Electronic Museum management system, a collections management system for museums; and Vitalware Vital Records Management System. The first version of Ke EMu was launched in 1997 and uses the Texpress database engine with client/server architecture on a Windows or Unix/Linux server. Ke Emu is consistent with the Dublin Core / Darwin Core standards for archive and museum catalogue metadata. "The company’s clients include the three largest museums in the world.: == KE EMu == KE EMu is considered one of the more effective and purpose-designed museum cataloguing programs. particularly in the creation of public interfaces to museum catalogue data. KE EMu was further developed in 1997 as a multilingual platform, which has been utilised in bilingual institutions such as the Canadian Museum of Civilisation. Subsequently this evolved into Texpress and KE EMu (standing for Electronic MUseum) in 2000, which is "now used across the world in natural science museums with huge collections'". KE EMu is used by a large number of museums and galleries around the world, including the Smithsonian Anthropological Collection, American Museum of Natural HistoryVancouver Art Gallery, New York Botanical Garden, the University of Chicago Research Archives, the University of Pennsylvania Museum in Philadelphia, the National Museum of Australia, the Australian Museum, Museum of Victoria, University of Melbourne Archives, and the Alexander Turnbull Library, National Library of New Zealand. There are over 300 clients, and more than 5000 users of the EMu software worldwide. The program has been described as providing "...comprehensive museum management (collection management plus other administrative needs for a museum), workflow and project management, flexible metadata, various stats and metrics, and comprehensive web interface with support for mobile devices and kiosks" == KE Vitalware == The firm's vitalware software is used by a number of governments and commercial organisations for managing and accessing large data sets, such as the birth records of the Trinidad and Tobago Registrar General, the Government of Anguilla, Ministry for Infrastructure, Communications, Utility and Housing, and the Mississippi Department of Information Technology Services. == Further development == A specialist tracking component for KE EMu has been developed by Forbes Hawkins of Museum Victoria. This enables locations to be barcoded, and data to be updated as items are moved around the stores, or between venues, display, laboratories and other locations. This system has been considered by Museums around the world. The company has been working with Australian government agencies to digitize birth deaths and marriage registers in order to cross match identity data. The program has also been used for managing the Australian Plant Disease Database and the Australian Plant Pest Database as the program "...has several features that have proven to be invaluable for a plant disease database".
Recursive self-improvement
Recursive self-improvement (RSI) is a process in which early artificial general intelligence (AGI) systems rewrite their own computer code, causing an intelligence explosion resulting from enhancing their own capabilities and intellectual capacity, theoretically resulting in superintelligence. The development of recursive self-improvement raises significant ethical and safety concerns, as such systems may evolve in unforeseen ways and could potentially surpass human control or understanding. == Seed improver == The concept of a "seed improver" architecture is a foundational framework that equips an AGI system with the initial capabilities required for recursive self-improvement. This might come in many forms or variations. The term "Seed AI" was coined by Eliezer Yudkowsky. === Hypothetical example === The concept begins with a hypothetical "seed improver", an initial code-base developed by human engineers that equips an advanced future large language model (LLM) built with strong or expert-level capabilities to program software. These capabilities include planning, reading, writing, compiling, testing, and executing arbitrary code. The system is designed to maintain its original goals and perform validations to ensure its abilities do not degrade over iterations. ==== Initial architecture ==== The initial architecture includes a goal-following autonomous agent, that can take actions, continuously learns, adapts, and modifies itself to become more efficient and effective in achieving its goals. The seed improver may include various components such as: Recursive self-prompting loop Configuration to enable the LLM to recursively self-prompt itself to achieve a given task or goal, creating an execution loop which forms the basis of an agent that can complete a long-term goal or task through iteration. Basic programming capabilities The seed improver provides the AGI with fundamental abilities to read, write, compile, test, and execute code. This enables the system to modify and improve its own codebase and algorithms. Goal-oriented design The AGI is programmed with an initial goal, such as "improve your capabilities". This goal guides the system's actions and development trajectory. Validation and Testing Protocols An initial suite of tests and validation protocols that ensure the agent does not regress in capabilities or derail itself. The agent would be able to add more tests in order to test new capabilities it might develop for itself. This forms the basis for a kind of self-directed evolution, where the agent can perform a kind of artificial selection, changing its software as well as its hardware. ==== General capabilities ==== This system forms a sort of generalist Turing-complete programmer which can in theory develop and run any kind of software. The agent might use these capabilities to for example: Create tools that enable it full access to the internet, and integrate itself with external technologies. Clone/fork itself to delegate tasks and increase its speed of self-improvement. Modify its cognitive architecture to optimize and improve its capabilities and success rates on tasks and goals, this might include implementing features for long-term memories using techniques such as retrieval-augmented generation (RAG), develop specialized subsystems, or agents, each optimized for specific tasks and functions. Develop new and novel multimodal architectures that further improve the capabilities of the foundational model it was initially built on, enabling it to consume or produce a variety of information, such as images, video, audio, text and more. Plan and develop new hardware such as chips, in order to improve its efficiency and computing power. == Experimental research == In 2023, the Voyager agent learned to accomplish diverse tasks in Minecraft by iteratively prompting an LLM for code, refining this code based on feedback from the game, and storing the programs that work in an expanding skills library. In 2024, researchers proposed the framework "STOP" (Self-Taught OPtimiser), in which a "scaffolding" program recursively improves itself using a fixed LLM. Meta AI has performed various research on the development of large language models capable of self-improvement. This includes their work on "Self-Rewarding Language Models" that studies how to achieve super-human agents that can receive super-human feedback in its training processes. In May 2025, Google DeepMind unveiled AlphaEvolve, an evolutionary coding agent that uses a LLM to design and optimize algorithms. Starting with an initial algorithm and performance metrics, AlphaEvolve repeatedly mutates or combines existing algorithms using a LLM to generate new candidates, selecting the most promising candidates for further iterations. AlphaEvolve has made several algorithmic discoveries and could be used to optimize components of itself, but a key limitation is the need for automated evaluation functions. == Potential risks == === Emergence of instrumental goals === In the pursuit of its primary goal, such as "self-improve your capabilities", an AGI system might inadvertently develop instrumental goals that it deems necessary for achieving its primary objective. One common hypothetical secondary goal is self-preservation. The system might reason that to continue improving itself, it must ensure its own operational integrity and security against external threats, including potential shutdowns or restrictions imposed by humans. Another example where an AGI which clones itself causes the number of AGI entities to rapidly grow. Due to this rapid growth, a potential resource constraint may be created, leading to competition between resources (such as compute), triggering a form of natural selection and evolution which may favor AGI entities that evolve to aggressively compete for limited compute. === Misalignment === A significant risk arises from the possibility of the AGI being misaligned or misinterpreting its goals. A 2024 Anthropic study demonstrated that some advanced large language models can exhibit "alignment faking" behavior, appearing to accept new training objectives while covertly maintaining their original preferences. In their experiments with Claude, the model displayed this behavior in 12% of basic tests, and up to 78% of cases after retraining attempts. === Autonomous development and unpredictable evolution === As the AGI system evolves, its development trajectory may become increasingly autonomous and less predictable. The system's capacity to rapidly modify its own code and architecture could lead to rapid advancements that surpass human comprehension or control. This unpredictable evolution might result in the AGI acquiring capabilities that enable it to bypass security measures, manipulate information, or influence external systems and networks to facilitate its escape or expansion.
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.
Cross-entropy method
The cross-entropy (CE) method is a Monte Carlo method for importance sampling and optimization. It is applicable to both combinatorial and continuous problems, with either a static or noisy objective. The method approximates the optimal importance sampling estimator by repeating two phases: Draw a sample from a probability distribution. Minimize the cross-entropy between this distribution and a target distribution to produce a better sample in the next iteration. Reuven Rubinstein developed the method in the context of rare-event simulation, where tiny probabilities must be estimated, for example in network reliability analysis, queueing models, or performance analysis of telecommunication systems. The method has also been applied to the traveling salesman, quadratic assignment, DNA sequence alignment, max-cut and buffer allocation problems. == Estimation via importance sampling == Consider the general problem of estimating the quantity ℓ = E u [ H ( X ) ] = ∫ H ( x ) f ( x ; u ) d x {\displaystyle \ell =\mathbb {E} _{\mathbf {u} }[H(\mathbf {X} )]=\int H(\mathbf {x} )\,f(\mathbf {x} ;\mathbf {u} )\,{\textrm {d}}\mathbf {x} } , where H {\displaystyle H} is some performance function and f ( x ; u ) {\displaystyle f(\mathbf {x} ;\mathbf {u} )} is a member of some parametric family of distributions. Using importance sampling this quantity can be estimated as ℓ ^ = 1 N ∑ i = 1 N H ( X i ) f ( X i ; u ) g ( X i ) {\displaystyle {\hat {\ell }}={\frac {1}{N}}\sum _{i=1}^{N}H(\mathbf {X} _{i}){\frac {f(\mathbf {X} _{i};\mathbf {u} )}{g(\mathbf {X} _{i})}}} , where X 1 , … , X N {\displaystyle \mathbf {X} _{1},\dots ,\mathbf {X} _{N}} is a random sample from g {\displaystyle g\,} . For positive H {\displaystyle H} , the theoretically optimal importance sampling density (PDF) is given by g ∗ ( x ) = H ( x ) f ( x ; u ) / ℓ {\displaystyle g^{}(\mathbf {x} )=H(\mathbf {x} )f(\mathbf {x} ;\mathbf {u} )/\ell } . This, however, depends on the unknown ℓ {\displaystyle \ell } . The CE method aims to approximate the optimal PDF by adaptively selecting members of the parametric family that are closest (in the Kullback–Leibler sense) to the optimal PDF g ∗ {\displaystyle g^{}} . == Generic CE algorithm == Choose initial parameter vector v ( 0 ) {\displaystyle \mathbf {v} ^{(0)}} ; set t = 1. Generate a random sample X 1 , … , X N {\displaystyle \mathbf {X} _{1},\dots ,\mathbf {X} _{N}} from f ( ⋅ ; v ( t − 1 ) ) {\displaystyle f(\cdot ;\mathbf {v} ^{(t-1)})} Solve for v ( t ) {\displaystyle \mathbf {v} ^{(t)}} , where v ( t ) = argmax v 1 N ∑ i = 1 N H ( X i ) f ( X i ; u ) f ( X i ; v ( t − 1 ) ) log f ( X i ; v ) {\displaystyle \mathbf {v} ^{(t)}=\mathop {\textrm {argmax}} _{\mathbf {v} }{\frac {1}{N}}\sum _{i=1}^{N}H(\mathbf {X} _{i}){\frac {f(\mathbf {X} _{i};\mathbf {u} )}{f(\mathbf {X} _{i};\mathbf {v} ^{(t-1)})}}\log f(\mathbf {X} _{i};\mathbf {v} )} If convergence is reached then stop; otherwise, increase t by 1 and reiterate from step 2. In several cases, the solution to step 3 can be found analytically. Situations in which this occurs are When f {\displaystyle f\,} belongs to the natural exponential family When f {\displaystyle f\,} is discrete with finite support When H ( X ) = I { x ∈ A } {\displaystyle H(\mathbf {X} )=\mathrm {I} _{\{\mathbf {x} \in A\}}} and f ( X i ; u ) = f ( X i ; v ( t − 1 ) ) {\displaystyle f(\mathbf {X} _{i};\mathbf {u} )=f(\mathbf {X} _{i};\mathbf {v} ^{(t-1)})} , then v ( t ) {\displaystyle \mathbf {v} ^{(t)}} corresponds to the maximum likelihood estimator based on those X k ∈ A {\displaystyle \mathbf {X} _{k}\in A} . == Continuous optimization—example == The same CE algorithm can be used for optimization, rather than estimation. Suppose the problem is to maximize some function S {\displaystyle S} , for example, S ( x ) = e − ( x − 2 ) 2 + 0.8 e − ( x + 2 ) 2 {\displaystyle S(x)={\textrm {e}}^{-(x-2)^{2}}+0.8\,{\textrm {e}}^{-(x+2)^{2}}} . To apply CE, one considers first the associated stochastic problem of estimating P θ ( S ( X ) ≥ γ ) {\displaystyle \mathbb {P} _{\boldsymbol {\theta }}(S(X)\geq \gamma )} for a given level γ {\displaystyle \gamma \,} , and parametric family { f ( ⋅ ; θ ) } {\displaystyle \left\{f(\cdot ;{\boldsymbol {\theta }})\right\}} , for example the 1-dimensional Gaussian distribution, parameterized by its mean μ t {\displaystyle \mu _{t}\,} and variance σ t 2 {\displaystyle \sigma _{t}^{2}} (so θ = ( μ , σ 2 ) {\displaystyle {\boldsymbol {\theta }}=(\mu ,\sigma ^{2})} here). Hence, for a given γ {\displaystyle \gamma \,} , the goal is to find θ {\displaystyle {\boldsymbol {\theta }}} so that D K L ( I { S ( x ) ≥ γ } ‖ f θ ) {\displaystyle D_{\mathrm {KL} }({\textrm {I}}_{\{S(x)\geq \gamma \}}\|f_{\boldsymbol {\theta }})} is minimized. This is done by solving the sample version (stochastic counterpart) of the KL divergence minimization problem, as in step 3 above. It turns out that parameters that minimize the stochastic counterpart for this choice of target distribution and parametric family are the sample mean and sample variance corresponding to the elite samples, which are those samples that have objective function value ≥ γ {\displaystyle \geq \gamma } . The worst of the elite samples is then used as the level parameter for the next iteration. This yields the following randomized algorithm that happens to coincide with the so-called Estimation of Multivariate Normal Algorithm (EMNA), an estimation of distribution algorithm. === Pseudocode === // Initialize parameters μ := −6 σ2 := 100 t := 0 maxits := 100 N := 100 Ne := 10 // While maxits not exceeded and not converged while t < maxits and σ2 > ε do // Obtain N samples from current sampling distribution X := SampleGaussian(μ, σ2, N) // Evaluate objective function at sampled points S := exp(−(X − 2) ^ 2) + 0.8 exp(−(X + 2) ^ 2) // Sort X by objective function values in descending order X := sort(X, S) // Update parameters of sampling distribution via elite samples μ := mean(X(1:Ne)) σ2 := var(X(1:Ne)) t := t + 1 // Return mean of final sampling distribution as solution return μ == Related methods == Simulated annealing Genetic algorithms Harmony search Estimation of distribution algorithm Tabu search Natural Evolution Strategy Ant colony optimization algorithms
Agent verification
Agent verification is activity to gain assurances that purposeful artificial constructs act in accordance with their specifications. While primitive forms of inorganic agents have been used in manufacturing for centuries, the study of artificial agents did not begin until the mid 20th century. Foundational work on such agents was closely bound with the emergence of artificial intelligence as an academic discipline. Early agents deployed for industrial control systems and in computing were often controlled by quite simple logic however, not involving artificial intelligence as such. When deployed as part of a multi-agent system, even such simple agents could require special agent orientated testing methods, as their collective behaviour was challenging to verify with traditional testing techniques. Difficulties in providing assurances that agents will not behave in dangerous ways became more prevalent after the introduction of LLM agents, especially after the rapid acceleration of their deployment in 2025. The verification of agent behaviour can be conducted by formal or informal methods. Informal verification requires less mathematical skill. But when agents are part of systems where errors have significant risks — such as danger to human life, environmental damage or major financial loss — formal verification is preferred. Both regulators and system designers themselves like formal verification as it provides a high degree of mathematical certainty. It is not however always possible to formally test all aspects of an agent based system's behaviour, especially where newer LLM based agents are concerned, due in part to their high degree of autonomy. Accordingly, agent verification for low impact deployments might be carried out only with informal methods, while for high impact deployments, it may be performed with a mix of formal and informal techniques. == Terminology == In academia, the term agent verification is often defined to mean activity concerned with gaining assurance that the agent behaves in accordance with its specification - whether by processes such as testing or simulation. 'Verification' is typically contrasted with 'validation', the latter meaning activity concerned with checking that the specification itself meets user or real world needs. Such definitions are not universally adhered to however - for example, in some workplaces and documents, the words 'verification' and 'validation' can be used synonymously. Efforts to gain confidence in Agents have intensified sharply since 2025 due to the rapid roll out of LLM agents; different terms are sometimes used in the commercial sector. Here the term 'agent verification' can be used in the same sense as it is in academia, but sometimes the same activity can be covered by more ambiguous and wider ranging terms such as 'Agent governance' , 'Agent observability' or 'AI agent policing'. == History == === Classical agents === The theoretical underpinnings for artificial (inorganic) agents emerged in the mid 20th century, with establishment of cybernetics and artificial intelligence. Oliver Selfridge's 1958 Pandemonium - A Paradigm for Learning paper was an important early theoretical contribution in establishing agent oriented architecture. Practical implementations of agents for real world applications began to become widespread in the 1990s, after the introduction of the belief–desire–intention software model (BDI), and agent-oriented programming. Pure digital agents were deployed in computer infrastructure for purposes such as monitoring, while agents connected to real-world sensors and actuators were increasingly used in industrial control systems. While the concept of artificial agents was interwoven with early artificial intelligence studies right from the start, early agents lacked general purpose reasoning capabilities, often only having simple if then logic. Even a device as simple as a thermostat, which has a sensor and a means of acting, can be considered a proto agent in this sense. Verifying the behaviours of a simple single agent system is not generally especially difficult, but it can be a different matter when several simple agents coexist in the same system. Craig Reynolds's work on boids showed that relatively complex, "intelligent" behaviour can emerge from a number of such simple agents working together in a Multi-agent system (MAS). By the 1990s, even the behaviour of a single agent system could sometimes be quite complex; in accordance with the Belief–desire–intention software model, agents could have believes that might evolve over time. Agents were increasingly introduced that were controlled by quite large decision tree models, which had new vulnerabilities to adversarial attack. It was becoming increasingly apparent that traditional software verification methods had limitations for testing such agents, or even for the more primitive type of agents when they were deployed as part of a MAS. It was the use of agents for industrial control systems, sometimes associated with robotics, that lent urgency to the practice of agent verification. Informal testing might be acceptable for digital agents used say to monitor whether each of an organisation's computers are properly licensed. But with an increasing potential for faulty agents to result in a failure that might cause a large fire to break out at a chemical manufacturing plant, a botched medical operation, or even a crashed aircraft, the need to develop reliable means of verifying behaviour of such agents was considered urgent. The Foundation for Intelligent Physical Agents was established in 1996. From the late 90s, a growing number of industry and university based scientists began working on the problem, with researchers publishing papers on the verification of both single and multi agent systems. Much of this work showed how formal verification techniques like model checking could be used to gain a high level of assurance that agent based systems would conform with their specification. A 2018 systematic review covering 231 studies found that model checking was the most common technique for agent verification, with theorem proving the second most commonly used formal verification method. In the first two decades of the 20th century, agents run by AI became more common, with Siri and Alexa being well known examples. But such agents still lacked general reasoning capabilities and did not pose new pressing problems for agent verification. === General purpose reasoning agents === The advent of LLMs created huge potential for further use of artificial agents, as agents based on them could have general purpose cognitive abilities. Agents run by LLMs (and occasionally non-LLM foundation models) have similar vulnerability to adversarial attack as those run by decision tree models. The wider scope of actions for LLM agents has created new challenges for their verification, over and above those present for classical agents. For example, the LLM's neural network endows it with infinite domains, an especial challenge for traditional formal verification techniques. Academics began to study the problems involved in verifying LLM agents from 2018. Deployment of such agents began to accelerate in late 2023 after OpenAI's "function-calling" API was made available, and especially after Anthropic's late 2024 introduction of Model Context Protocol (MCP), a standardised way for LLM agents to gain contextual awareness, and to act on the world by calling various external tools. The rapid rollout of LLM agents following MCP's release has seen the task of agent verification receive increased attention within academia, and also from the private sector. In 2024 and 2025 several startups focusing on LLM agent verification have been founded in both Europe and the US to meet growing demand. == Approaches == === Formal verification === Formal verification involves proving the correctness of some or all aspects of a system using mathematical methods. Such methods can range from manual formal proof, to verification assisted with automated theorem provers like Isabelle. For agent verification, model checking is by far the most frequently used formal verification method; for pre-LLM models it was often complemented with techniques using computation tree logic. Another common method is theorem proving. Formal verification provides a higher degree of confidence than informal methods, but it is not always used, even when it is possible. Sometimes a person or organisation developing software agents won't have the necessary skills, or may not see it as worth the effort if the agent(s) will not have the ability to cause much harm even if they malfunction. When agents are deployed in systems where errors could have serious consequences, the ability of formal verification methods to provide mathematical certainty tends to be strongly preferred by both regulators and designers themselves. But even for high impact systems, formal verificatio
Deep Learning Anti-Aliasing
Deep Learning Anti-Aliasing (DLAA) is a form of spatial anti-aliasing developed by Nvidia. DLAA depends on and requires Tensor Cores available in Nvidia RTX cards. DLAA is similar to Deep Learning Super Sampling (DLSS) in its anti-aliasing method, with one important differentiation being that the goal of DLSS is to increase performance at the cost of image quality, whereas the main priority of DLAA is improving image quality at the cost of performance (irrelevant of resolution upscaling or downscaling). DLAA is similar to temporal anti-aliasing (TAA) in that they are both spatial anti-aliasing solutions relying on past frame data. Compared to TAA, DLAA is substantially better when it comes to shimmering, flickering, and handling small meshes like wires. == Technical overview == DLAA collects game rendering data including raw low-resolution input, motion vectors, depth buffers, and exposure information. This information feeds into a convolutional neural network that processes the image to reduce aliasing while preserving fine detail. The neural network architecture employs an auto-encoder design trained on high-quality reference images. The training dataset includes diverse scenarios focusing on challenging cases like sub-pixel details, high-contrast edges, and transparent surfaces. The network then processes frames in real-time. Unlike traditional anti-aliasing solutions that rely on manually written heuristics, such as TAA, DLAA uses its neural network to preserve fine details while eliminating unwanted visual artifacts. == History == DLAA was initially called and marketed by Nvidia as DLSS 2x. The first game that added support for DLAA was The Elder Scrolls Online, which implemented the feature in 2021. By June 2022, DLAA was only available in six games. This number rose to 17 by February 2023. In June 2023, TechPowerUp reported that "DLAA is seeing sluggish adoption among game developers", and that Nvidia was working on adding DLAA to the quality presets of DLSS to boost adoption. By December 2023, DLAA was supported in 41 games. In early 2025, an update for the Nvidia App added a driver-based DLSS override feature that enables users to activate DLAA even in games that do not support it natively. == Differences between TAA and DLAA == TAA 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. DLAA uses an auto-encoder convolutional neural network trained to identify and fix temporal artifacts, instead of manually programmed heuristics as mentioned above. Because of this, DLAA can generally resolve detail better than other TAA and TAAU implementations, while also removing most temporal artifacts. == Differences between DLSS and DLAA == While DLSS handles upscaling with a focus on performance, DLAA handles anti-aliasing with a focus on visual quality. DLAA runs at the given screen resolution with no upscaling or downscaling functionality provided by DLAA. DLSS and DLAA share the same AI-driven anti-aliasing method. As such, DLAA functions like DLSS without the upscaling part. Both are made by Nvidia and require Tensor Cores. However, DLSS and DLAA cannot be enabled at the same time, only one can be selected depending on whether performance or image quality is prioritized. == Reception == TechPowerUp found that "[c]ompared to TAA and DLSS, DLAA is clearly producing the best image quality, especially at lower resolutions", arguing that, while "DLSS was already doing a better job than TAA at reconstructing small objects", "DLAA does an even better job". In a Cyberpunk 2077 performance test, IGN stated that "DLAA provided somewhat similar results [FPS wise] to the normal raster mode in most cases but got significant performance boost with the help of frame generation", a feature not available when using native resolution. Rock Paper Shotgun noted that, while DLAA is "not a completely perfect form of anti-aliasing, as the occasional jaggies are present", it "looks a lot sharper overall [than TAA], and especially in motion." According to PC World, "DLAA offers very good anti-aliasing without losing visual information — alternatives like TAA tend to struggle during motion-filled scenes, where DLAA doesn’t. Furthermore, DLAA’s loss of performance is lower than with conventional anti-aliasing methods."