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  Spike-and-slab regression

  Spike-and-slab regression is a type of Bayesian linear regression in which a particular hierarchical prior distribution for the regression coefficients is chosen such that only a subset of the possible regressors is retained. The technique is particularly useful when the number of possible predictors is larger than the number of observations. The idea of the spike-and-slab model was originally proposed by Mitchell & Beauchamp (1988). The approach was further significantly developed by Madigan & Raftery (1994) and George & McCulloch (1997). A recent and important contribution to this literature is Ishwaran & Rao (2005). == Model description == Suppose we have P possible predictors in some model. Vector γ has a length equal to P and consists of zeros and ones. This vector indicates whether a particular variable is included in the regression or not. If no specific prior information on initial inclusion probabilities of particular variables is available, a Bernoulli prior distribution is a common default choice. Conditional on a predictor being in the regression, we identify a prior distribution for the model coefficient, which corresponds to that variable (β). A common choice on that step is to use a normal prior with a mean equal to zero and a large variance calculated based on ( X T X ) − 1 {\displaystyle (X^{T}X)^{-1}} (where X {\displaystyle X} is a design matrix of explanatory variables of the model). A draw of γ from its prior distribution is a list of the variables included in the regression. Conditional on this set of selected variables, we take a draw from the prior distribution of the regression coefficients (if γi = 1 then βi ≠ 0 and if γi = 0 then βi = 0). βγ denotes the subset of β for which γi = 1. In the next step, we calculate a posterior probability for both inclusion and coefficients by applying a standard statistical procedure. All steps of the described algorithm are repeated thousands of times using the Markov chain Monte Carlo (MCMC) technique. As a result, we obtain a posterior distribution of γ (variable inclusion in the model), β (regression coefficient values) and the corresponding prediction of y. The model got its name (spike-and-slab) due to the shape of the two prior distributions. The "spike" is the probability of a particular coefficient in the model to be zero. The "slab" is the prior distribution for the regression coefficient values. An advantage of Bayesian variable selection techniques is that they are able to make use of prior knowledge about the model. In the absence of such knowledge, some reasonable default values can be used; to quote Scott and Varian (2013): "For the analyst who prefers simplicity at the cost of some reasonable assumptions, useful prior information can be reduced to an expected model size, an expected R2, and a sample size ν determining the weight given to the guess at R2." Some researchers suggest the following default values: R2 = 0.5, ν = 0.01, and π = 0.5 (parameter of a prior Bernoulli distribution).

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  Case-based reasoning

  Case-based reasoning (CBR), broadly construed, is the process of solving new problems based on the solutions of similar past problems. In everyday life, an auto mechanic who fixes an engine by recalling another car that exhibited similar symptoms is using case-based reasoning. A lawyer who advocates a particular outcome in a trial based on legal precedents or a judge who creates case law is using case-based reasoning. So, too, an engineer copying working elements of nature (practicing biomimicry) is treating nature as a database of solutions to problems. Case-based reasoning is a prominent type of analogy solution making. It has been argued that case-based reasoning is not only a powerful method for computer reasoning, but also a pervasive behavior in everyday human problem solving; or, more radically, that all reasoning is based on past cases personally experienced. This view is related to prototype theory, which is most deeply explored in cognitive science. == Process == Case-based reasoning has been formalized for purposes of computer reasoning as a four-step process: Retrieve: Given a target problem, retrieve cases relevant to solving it from memory. A case consists of a problem, its solution, and, typically, annotations about how the solution was derived. For example, suppose Fred wants to prepare blueberry pancakes. Being a novice cook, the most relevant experience he can recall is one in which he successfully made plain pancakes. The procedure he followed for making the plain pancakes, together with justifications for decisions made along the way, constitutes Fred's retrieved case. Reuse: Map the solution from the previous case to the target problem. This may involve adapting the solution as needed to fit the new situation. In the pancake example, Fred must adapt his retrieved solution to include the addition of blueberries. Revise: Having mapped the previous solution to the target situation, test the new solution in the real world (or a simulation) and, if necessary, revise. Suppose Fred adapted his pancake solution by adding blueberries to the batter. After mixing, he discovers that the batter has turned blue – an undesired effect. This suggests the following revision: delay the addition of blueberries until after the batter has been ladled into the pan. Retain: After the solution has been successfully adapted to the target problem, store the resulting experience as a new case in memory. Fred, accordingly, records his new-found procedure for making blueberry pancakes, thereby enriching his set of stored experiences, and better preparing him for future pancake-making demands. == Comparison to other methods == At first glance, CBR may seem similar to the rule induction algorithms of machine learning. Like a rule-induction algorithm, CBR starts with a set of cases or training examples; it forms generalizations of these examples, albeit implicit ones, by identifying commonalities between a retrieved case and the target problem. If for instance a procedure for plain pancakes is mapped to blueberry pancakes, a decision is made to use the same basic batter and frying method, thus implicitly generalizing the set of situations under which the batter and frying method can be used. The key difference, however, between the implicit generalization in CBR and the generalization in rule induction lies in when the generalization is made. A rule-induction algorithm draws its generalizations from a set of training examples before the target problem is even known; that is, it performs eager generalization. For instance, if a rule-induction algorithm were given recipes for plain pancakes, Dutch apple pancakes, and banana pancakes as its training examples, it would have to derive, at training time, a set of general rules for making all types of pancakes. It would not be until testing time that it would be given, say, the task of cooking blueberry pancakes. The difficulty for the rule-induction algorithm is in anticipating the different directions in which it should attempt to generalize its training examples. This is in contrast to CBR, which delays (implicit) generalization of its cases until testing time – a strategy of lazy generalization. In the pancake example, CBR has already been given the target problem of cooking blueberry pancakes; thus it can generalize its cases exactly as needed to cover this situation. CBR therefore tends to be a good approach for rich, complex domains in which there are myriad ways to generalize a case. In law, there is often explicit delegation of CBR to courts, recognizing the limits of rule based reasons: limiting delay, limited knowledge of future context, limit of negotiated agreement, etc. While CBR in law and cognitively inspired CBR have long been associated, the former is more clearly an interpolation of rule based reasoning, and judgment, while the latter is more closely tied to recall and process adaptation. The difference is clear in their attitude toward error and appellate review. Another name for case-based reasoning in problem solving is symptomatic strategies. It does require à priori domain knowledge that is gleaned from past experience which established connections between symptoms and causes. This knowledge is referred to as shallow, compiled, evidential, history-based as well as case-based knowledge. This is the strategy most associated with diagnosis by experts. Diagnosis of a problem transpires as a rapid recognition process in which symptoms evoke appropriate situation categories. An expert knows the cause by virtue of having previously encountered similar cases. Case-based reasoning is the most powerful strategy, and that used most commonly. However, the strategy won't work independently with truly novel problems, or where deeper understanding of whatever is taking place is sought. An alternative approach to problem solving is the topographic strategy which falls into the category of deep reasoning. With deep reasoning, in-depth knowledge of a system is used. Topography in this context means a description or an analysis of a structured entity, showing the relations among its elements. Also known as reasoning from first principles, deep reasoning is applied to novel faults when experience-based approaches aren't viable. The topographic strategy is therefore linked to à priori domain knowledge that is developed from a more a fundamental understanding of a system, possibly using first-principles knowledge. Such knowledge is referred to as deep, causal or model-based knowledge. Hoc and Carlier noted that symptomatic approaches may need to be supported by topographic approaches because symptoms can be defined in diverse terms. The converse is also true – shallow reasoning can be used abductively to generate causal hypotheses, and deductively to evaluate those hypotheses, in a topographical search. == Criticism == Critics of CBR argue that it is an approach that accepts anecdotal evidence as its main operating principle. Without statistically relevant data for backing and implicit generalization, there is no guarantee that the generalization is correct. However, all inductive reasoning where data is too scarce for statistical relevance is inherently based on anecdotal evidence. == History == CBR traces its roots to the work of Roger Schank and his students at Yale University in the early 1980s. Schank's model of dynamic memory was the basis for the earliest CBR systems: Janet Kolodner's CYRUS and Michael Lebowitz's IPP. Other schools of CBR and closely allied fields emerged in the 1980s, which directed at topics such as legal reasoning, memory-based reasoning (a way of reasoning from examples on massively parallel machines), and combinations of CBR with other reasoning methods. In the 1990s, interest in CBR grew internationally, as evidenced by the establishment of an International Conference on Case-Based Reasoning in 1995, as well as European, German, British, Italian, and other CBR workshops. CBR technology has resulted in the deployment of a number of successful systems, the earliest being Lockheed's CLAVIER, a system for laying out composite parts to be baked in an industrial convection oven. CBR has been used extensively in applications such as the Compaq SMART system and has found a major application area in the health sciences, as well as in structural safety management. There is recent work that develops CBR within a statistical framework and formalizes case-based inference as a specific type of probabilistic inference. Thus, it becomes possible to produce case-based predictions equipped with a certain level of confidence. One description of the difference between CBR and induction from instances is that statistical inference aims to find what tends to make cases similar while CBR aims to encode what suffices to claim similarly.

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  PagedAttention

  PagedAttention is an attention algorithm for efficient serving of large language models (LLMs). It was introduced in 2023 by Woosuk Kwon and colleagues in the paper Efficient Memory Management for Large Language Model Serving with PagedAttention, alongside the vLLM serving engine. The method stores the key–value cache used during autoregressive decoding in fixed-size blocks that can be mapped to non-contiguous physical memory, borrowing ideas from virtual memory, paging, and operating system design. == Background == In transformer inference, the key–value cache grows with sequence length and the number of concurrent requests. Kwon et al. argued that earlier serving systems typically reserved contiguous cache regions in advance, which caused reserved space, internal fragmentation, and external fragmentation. In their experiments, the paper reported that the effective memory utilization of previous systems could fall as low as 20.4%. == Description == PagedAttention partitions the cache of each sequence into fixed-size KV blocks. A request's cache is represented as a sequence of logical blocks, while a block table maps those logical blocks to physical GPU-memory blocks. As a result, neighboring logical blocks do not need to be contiguous in physical memory, and new blocks can be allocated on demand as generation proceeds. The design also makes it easier to share cache state across related decoding paths. In vLLM, physical blocks can be reference-counted and shared among requests or branches, with block-granularity copy-on-write used when a shared block must be modified. The original paper applied this design to parallel sampling, beam search, and prompts with shared prefixes. == Mathematical formulation == For a query token i {\displaystyle i} in causal self-attention, the standard attention output can be written as a i j = exp ⁡ ( q i ⊤ k j / d ) ∑ t = 1 i exp ⁡ ( q i ⊤ k t / d ) , o i = ∑ j = 1 i a i j v j {\displaystyle a_{ij}={\frac {\exp(\mathbf {q} _{i}^{\top }\mathbf {k} _{j}/{\sqrt {d}})}{\sum _{t=1}^{i}\exp(\mathbf {q} _{i}^{\top }\mathbf {k} _{t}/{\sqrt {d}})}},\;\mathbf {o} _{i}=\sum _{j=1}^{i}a_{ij}\mathbf {v} _{j}} where q i {\displaystyle \mathbf {q} _{i}} , k j {\displaystyle \mathbf {k} _{j}} , and v j {\displaystyle \mathbf {v} _{j}} are the query, key, and value vectors, and d {\displaystyle d} is the attention dimension. If the cache is partitioned into blocks of size B {\displaystyle B} , the key and value blocks may be written as K j = ( k ( j − 1 ) B + 1 , … , k j B ) , V j = ( v ( j − 1 ) B + 1 , … , v j B ) {\displaystyle \mathbf {K} _{j}=(\mathbf {k} _{(j-1)B+1},\ldots ,\mathbf {k} _{jB}),\;\mathbf {V} _{j}=(\mathbf {v} _{(j-1)B+1},\ldots ,\mathbf {v} _{jB})} PagedAttention then performs the computation blockwise: A i j = exp ⁡ ( q i ⊤ K j / d ) ∑ t = 1 ⌈ i / B ⌉ exp ⁡ ( q i ⊤ K t / d ) , o i = ∑ j = 1 ⌈ i / B ⌉ V j A i j ⊤ {\displaystyle \mathbf {A} _{ij}={\frac {\exp(\mathbf {q} _{i}^{\top }\mathbf {K} _{j}/{\sqrt {d}})}{\sum _{t=1}^{\lceil i/B\rceil }\exp(\mathbf {q} _{i}^{\top }\mathbf {K} _{t}/{\sqrt {d}})}},\;\mathbf {o} _{i}=\sum _{j=1}^{\lceil i/B\rceil }\mathbf {V} _{j}\mathbf {A} _{ij}^{\top }} where A i j {\displaystyle \mathbf {A} _{ij}} is the vector of attention scores for the j {\displaystyle j} -th KV block. In the formulation given by Kwon et al., this preserves the causal attention calculation while allowing the key and value blocks to reside in non-contiguous physical memory. == Performance and use == The vLLM paper reported that, on its evaluated workloads, the use of PagedAttention and the associated memory-management design improved serving throughput by 2–4× over the compared baselines, including FasterTransformer and Orca, while preserving model outputs. In experiments on OPT-13B with the Alpaca trace, the paper also reported memory savings of 6.1–9.8% for parallel sampling and 37.6–55.2% for beam search through KV-block sharing. A 2024 survey of LLM serving systems described PagedAttention as having become an industry norm in LLM serving frameworks, citing support in TGI, vLLM, and TensorRT-LLM. == Limitations and alternatives == Subsequent work has described trade-offs in the approach. The 2025 vAttention paper argued that PagedAttention requires attention kernels to be rewritten to support paging and increases software complexity, portability issues, redundancy, and execution overhead, proposing instead a memory manager that keeps the cache contiguous in virtual memory while relying on demand paging for physical allocation. === vAttention === Unlike PagedAttention, vAttention does not introduce a different attention rule; it retains the standard attention computation Attention ⁡ ( q i , K , V ) = softmax ⁡ ( q i K ⊤ s c a l e ) V . {\displaystyle \operatorname {Attention} (q_{i},K,V)=\operatorname {softmax} \left({\frac {q_{i}K^{\top }}{\mathrm {scale} }}\right)V.} In the notation of Prabhu et al., the key and value tensors for a request seen so far are K , V ∈ R L ′ × ( H × D ) {\displaystyle K,V\in \mathbb {R} ^{L'\times (H\times D)}} , where L ′ {\displaystyle L'} is the context length seen so far, H {\displaystyle H} is the number of KV heads on a worker, and D {\displaystyle D} is the dimension of each KV head. In systems prior to PagedAttention, the K cache (or V cache) at each layer of a worker is typically allocated as a 4D tensor of shape [ B , L , H , D ] , {\displaystyle [B,L,H,D],} where B {\displaystyle B} is batch size and L {\displaystyle L} is the maximum context length supported by the model. vAttention preserves this contiguous virtual-memory view while deferring physical-memory allocation to runtime. A serving framework maintains separate K and V tensors for each layer, so vAttention reserves 2 N {\displaystyle 2N} virtual-memory buffers on a worker, where N {\displaystyle N} is the number of layers managed by that worker. The maximum size of one virtual-memory buffer is B S = B × S , {\displaystyle BS=B\times S,} where S {\displaystyle S} is the maximum size of a single request's per-layer K cache (or V cache) on a worker. The paper defines S = L × H × D × P , {\displaystyle S=L\times H\times D\times P,} where P {\displaystyle P} is the number of bytes needed to store one element. In this formulation, vAttention keeps the KV cache contiguous in virtual memory and relies on demand paging for physical allocation, rather than modifying the attention kernel to operate over non-contiguous KV-cache blocks.

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  Stability (learning theory)

  Stability, also known as algorithmic stability, is a notion in computational learning theory of how a machine learning algorithm output is changed with small perturbations to its inputs. A stable learning algorithm is one for which the prediction does not change much when the training data is modified slightly. For instance, consider a machine learning algorithm that is being trained to recognize handwritten letters of the alphabet, using 1000 examples of handwritten letters and their labels ("A" to "Z") as a training set. One way to modify this training set is to leave out an example, so that only 999 examples of handwritten letters and their labels are available. A stable learning algorithm would produce a similar classifier with both the 1000-element and 999-element training sets. Stability can be studied for many types of learning problems, from language learning to inverse problems in physics and engineering, as it is a property of the learning process rather than the type of information being learned. The study of stability gained importance in computational learning theory in the 2000s when it was shown to have a connection with generalization. It was shown that for large classes of learning algorithms, notably empirical risk minimization algorithms, certain types of stability ensure good generalization. == History == A central goal in designing a machine learning system is to guarantee that the learning algorithm will generalize, or perform accurately on new examples after being trained on a finite number of them. In the 1990s, milestones were reached in obtaining generalization bounds for supervised learning algorithms. The technique historically used to prove generalization was to show that an algorithm was consistent, using the uniform convergence properties of empirical quantities to their means. This technique was used to obtain generalization bounds for the large class of empirical risk minimization (ERM) algorithms. An ERM algorithm is one that selects a solution from a hypothesis space H {\displaystyle H} in such a way to minimize the empirical error on a training set S {\displaystyle S} . A general result, proved by Vladimir Vapnik for an ERM binary classification algorithms, is that for any target function and input distribution, any hypothesis space H {\displaystyle H} with VC-dimension d {\displaystyle d} , and n {\displaystyle n} training examples, the algorithm is consistent and will produce a training error that is at most O ( d n ) {\displaystyle O\left({\sqrt {\frac {d}{n}}}\right)} (plus logarithmic factors) from the true error. The result was later extended to almost-ERM algorithms with function classes that do not have unique minimizers. Vapnik's work, using what became known as VC theory, established a relationship between generalization of a learning algorithm and properties of the hypothesis space H {\displaystyle H} of functions being learned. However, these results could not be applied to algorithms with hypothesis spaces of unbounded VC-dimension. Put another way, these results could not be applied when the information being learned had a complexity that was too large to measure. Some of the simplest machine learning algorithms—for instance, for regression—have hypothesis spaces with unbounded VC-dimension. Another example is language learning algorithms that can produce sentences of arbitrary length. Stability analysis was developed in the 2000s for computational learning theory and is an alternative method for obtaining generalization bounds. The stability of an algorithm is a property of the learning process, rather than a direct property of the hypothesis space H {\displaystyle H} , and it can be assessed in algorithms that have hypothesis spaces with unbounded or undefined VC-dimension such as nearest neighbor. A stable learning algorithm is one for which the learned function does not change much when the training set is slightly modified, for instance by leaving out an example. A measure of Leave one out error is used in a Cross Validation Leave One Out (CVloo) algorithm to evaluate a learning algorithm's stability with respect to the loss function. As such, stability analysis is the application of sensitivity analysis to machine learning. == Summary of classic results == Early 1900s - Stability in learning theory was earliest described in terms of continuity of the learning map L {\displaystyle L} , traced to Andrey Nikolayevich Tikhonov. 1979 - Devroye and Wagner observed that the leave-one-out behavior of an algorithm is related to its sensitivity to small changes in the sample. 1999 - Kearns and Ron discovered a connection between finite VC-dimension and stability. 2002 - In a landmark paper, Bousquet and Elisseeff proposed the notion of uniform hypothesis stability of a learning algorithm and showed that it implies low generalization error. Uniform hypothesis stability, however, is a strong condition that does not apply to large classes of algorithms, including ERM algorithms with a hypothesis space of only two functions. 2002 - Kutin and Niyogi extended Bousquet and Elisseeff's results by providing generalization bounds for several weaker forms of stability which they called almost-everywhere stability. Furthermore, they took an initial step in establishing the relationship between stability and consistency in ERM algorithms in the Probably Approximately Correct (PAC) setting. 2004 - Poggio et al. proved a general relationship between stability and ERM consistency. They proposed a statistical form of leave-one-out-stability which they called CVEEEloo stability, and showed that it is a) sufficient for generalization in bounded loss classes, and b) necessary and sufficient for consistency (and thus generalization) of ERM algorithms for certain loss functions such as the square loss, the absolute value and the binary classification loss. 2010 - Shalev Shwartz et al. noticed problems with the original results of Vapnik due to the complex relations between hypothesis space and loss class. They discuss stability notions that capture different loss classes and different types of learning, supervised and unsupervised. 2016 - Moritz Hardt et al. proved stability of gradient descent given certain assumption on the hypothesis and number of times each instance is used to update the model. == Preliminary definitions == We define several terms related to learning algorithms training sets, so that we can then define stability in multiple ways and present theorems from the field. A machine learning algorithm, also known as a learning map L {\displaystyle L} , maps a training data set, which is a set of labeled examples ( x , y ) {\displaystyle (x,y)} , onto a function f {\displaystyle f} from X {\displaystyle X} to Y {\displaystyle Y} , where X {\displaystyle X} and Y {\displaystyle Y} are in the same space of the training examples. The functions f {\displaystyle f} are selected from a hypothesis space of functions called H {\displaystyle H} . The training set from which an algorithm learns is defined as S = { z 1 = ( x 1 , y 1 ) , . . , z m = ( x m , y m ) } {\displaystyle S=\{z_{1}=(x_{1},\ y_{1})\ ,..,\ z_{m}=(x_{m},\ y_{m})\}} and is of size m {\displaystyle m} in Z = X × Y {\displaystyle Z=X\times Y} drawn i.i.d. from an unknown distribution D. Thus, the learning map L {\displaystyle L} is defined as a mapping from Z m {\displaystyle Z_{m}} into H {\displaystyle H} , mapping a training set S {\displaystyle S} onto a function f S {\displaystyle f_{S}} from X {\displaystyle X} to Y {\displaystyle Y} . Here, we consider only deterministic algorithms where L {\displaystyle L} is symmetric with respect to S {\displaystyle S} , i.e. it does not depend on the order of the elements in the training set. Furthermore, we assume that all functions are measurable and all sets are countable. The loss V {\displaystyle V} of a hypothesis f {\displaystyle f} with respect to an example z = ( x , y ) {\displaystyle z=(x,y)} is then defined as V ( f , z ) = V ( f ( x ) , y ) {\displaystyle V(f,z)=V(f(x),y)} . The empirical error of f {\displaystyle f} is I S [ f ] = 1 n ∑ V ( f , z i ) {\displaystyle I_{S}[f]={\frac {1}{n}}\sum V(f,z_{i})} . The true error of f {\displaystyle f} is I [ f ] = E z V ( f , z ) {\displaystyle I[f]=\mathbb {E} _{z}V(f,z)} Given a training set S of size m, we will build, for all i = 1....,m, modified training sets as follows: By removing the i-th element S | i = { z 1 , . . . , z i − 1 , z i + 1 , . . . , z m } {\displaystyle S^{|i}=\{z_{1},...,\ z_{i-1},\ z_{i+1},...,\ z_{m}\}} By replacing the i-th element S i = { z 1 , . . . , z i − 1 , z i ′ , z i + 1 , . . . , z m } {\displaystyle S^{i}=\{z_{1},...,\ z_{i-1},\ z_{i}',\ z_{i+1},...,\ z_{m}\}} == Definitions of stability == === Hypothesis Stability === An algorithm L {\displaystyle L} has hypothesis stability β with respect to the loss function V if the following holds: ∀ i ∈ { 1 , . . . , m } , E S , z [ | V ( f S , z ) − V ( f S |

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  Packed pixel

  In packed pixel or chunky framebuffer organization, the bits defining each pixel are clustered and stored consecutively. For example, if there are 16 bits per pixel, each pixel is represented in two consecutive (contiguous) 8-bit bytes in the framebuffer. If there are 4 bits per pixel, each framebuffer byte defines two pixels, one in each nibble. The latter example is as opposed to storing a single 4-bit pixel in a byte, leaving 4 bits of the byte unused. If a pixel has more than one channel, the channels are interleaved when using packed pixel organization. Packed pixel displays were common on early microcomputer system that shared a single main memory for both the central processing unit (CPU) and display driver. In such systems, memory was normally accessed a byte at a time, so by packing the pixels, the display system could read out several pixels worth of data in a single read operation. Packed pixel is one of two major ways to organize graphics data in memory, the other being planar organization, where each pixel is made of individual bits stored in their own plane. For a 4-bit color value, memory would be organized as four screen-sized planes of one bit each and a single pixel's value built up by selecting the appropriate bit from each plane. Planar organization has the advantage that the data can be accessed in parallel, and is used when memory bandwidth is an issue.

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  Graphics processing unit

  A graphics processing unit (GPU) is a specialized electronic circuit designed for digital image processing and to accelerate computer graphics, being present either as a component on a discrete graphics card or embedded on motherboards, mobile phones, personal computers, workstations, and game consoles. GPUs are increasingly being used for artificial intelligence (AI) processing due to linear algebra acceleration, which is also used extensively in graphics processing. Although there is no single definition of the term, and it may be used to describe any video display system, in modern use a GPU includes the ability to internally perform the calculations needed for various graphics tasks, like rotating and scaling 3D images, and often the additional ability to run custom programs known as shaders. This contrasts with earlier graphics controllers known as video display controllers which had no internal calculation capabilities, or blitters, which performed only basic memory movement operations. The modern GPU emerged during the 1990s, adding the ability to perform operations like drawing lines and text without CPU help, and later adding 3D functionality. Graphics functions are generally independent and this lends these tasks to being implemented on separate calculation engines. Modern GPUs include hundreds, or thousands, of calculation units. This made them useful for non-graphic calculations involving embarrassingly parallel problems due to their parallel structure. The ability of GPUs to rapidly perform vast numbers of calculations has led to their adoption in diverse fields including artificial intelligence (AI) where they excel at handling data-intensive and computationally demanding tasks. Other non-graphical uses include the training of neural networks and cryptocurrency mining. == History == === 1960s === Dedicated 3D graphics hardware dates back to graphic terminals such as the Adage AGT-30 from 1967 with analog matrix processors. In 1969 Evans & Sutherland (E&S) introduced the Line Drawing System-1 (LDS-1), which was the first all-digital system to provide matrix multiplication. Also in 1969, the low-cost graphics terminal IMLAC PDS-1 was introduced. It later saw use as an early 3D gaming machine with the likes of Maze War. === 1970s === In professional hardware, in 1972 PLATO IV system becomes operational at the University of Illinois Urbana-Champaign. Between around 1973 and 1978, several networked multiplayer wireframe 3D games are implemented and popularized by users of the system. Also in 1972, the E&S Continuous Tone 1 (CT1) "Watkins box" system (consisting of an E&S LDS-2 and Shaded Picture System) is delivered to Case Western Reserve University. It offered the first real-time Gouraud shading. In 1975, a joint effort between Evans & Sutherland Computer Corporation and the University of Utah's computer graphics department results in the first ever MOSFET video framebuffer, capable of color and smooth shading. E&S Continuous Tone 3 (CT3) system was delivered in 1977 to Lufthansa for pilot training using computer simulation. It was the first graphics system capable of real-time texture mapping. Ikonas made graphics systems with 8- and 24-bit graphics and 3D acceleration in the late 70s. Arcade system boards have used specialized 2D graphics circuits since the 1970s. In early video game hardware, RAM for frame buffers was expensive, so video chips composited data together as the display was being scanned out on the monitor. A specialized barrel shifter circuit helped the CPU animate the framebuffer graphics for various 1970s arcade video games from Midway and Taito, such as Gun Fight (1975), Sea Wolf (1976), and Space Invaders (1978). The Namco Galaxian arcade system in 1979 used specialized graphics hardware that supported RGB color, multi-colored sprites, and tilemap backgrounds. The Galaxian hardware was widely used during the golden age of arcade video games, by game companies such as Namco, Centuri, Gremlin, Irem, Konami, Midway, Nichibutsu, Sega, and Taito. The Atari 2600 in 1977 used a video shifter called the Television Interface Adaptor. Atari 8-bit computers (1979) had ANTIC, a video processor which interpreted instructions describing a "display list"—the way the scan lines map to specific bitmapped or character modes and where the memory is stored (so there did not need to be a contiguous frame buffer). 6502 machine code subroutines could be triggered on scan lines by setting a bit on a display list instruction. ANTIC also supported smooth vertical and horizontal scrolling independent of the CPU. === 1980s === In the 1980s significant advancements were made in professional 3D graphics hardware. Perhaps most impactful was the 1981 development of the Geometry Engine, a VLSI vector processor ASIC designed by Jim Clark and Marc Hannah at Stanford University. This processor is the forerunner of modern tensor cores and other similar processors marketed for graphics and AI. The Geometry Engine went on to be used in Silicon Graphics workstations for many years. Silicon Graphics's first product, shipped in November 1983, was the IRIS 1000, a terminal with hardware-accelerated 3D graphics based on the Geometry Engine. The Geometry Engine was capable of approximately 6 million operations per second. The 1981 NEC μPD7220 was the first implementation of a personal computer graphics display processor as a single large-scale integration (LSI) integrated circuit chip. This enabled the design of low-cost, high-performance video graphics cards such as those from Number Nine Visual Technology. It became the best-known GPU until the mid-1980s. It was the first fully integrated VLSI (very large-scale integration) metal–oxide–semiconductor (NMOS) graphics display processor for PCs, supported up to 1024×1024 resolution, and laid the foundations for the PC graphics market. It was used in a number of graphics cards and was licensed for clones such as the Intel 82720, the first of Intel's graphics processing units. The Williams Electronics arcade games Robotron: 2084, Joust, Sinistar, and Bubbles, all released in 1982, contain custom blitter chips for operating on 16-color bitmaps. In 1984, Hitachi released the ARTC HD63484, the first major CMOS graphics processor for personal computers. The ARTC could display up to 4K resolution when in monochrome mode. It was used in a number of graphics cards and terminals during the late 1980s. In 1985, the Amiga was released with a custom graphics chip called Agnus including a blitter for bitmap manipulation, line drawing, and area fill. It also included a coprocessor with its own simple instruction set, that was capable of manipulating graphics hardware registers in sync with the video beam (e.g. for per-scanline palette switches, sprite multiplexing, and hardware windowing), or driving the blitter. Also in 1985, IBM released the Professional Graphics Controller, designed by later to be Nvidia co-founder Curtis Priem, which was a rudimentary 3D card with 640 × 480 256-color graphics which used a dedicated CPU to draw graphics independently of the main system. It was used as the basis of cards by a number of makers (including Matrox) and its analog RGB signaling led directly to the VGA video standard. Priem later in the 80s worked on the influential Sun Microsystems GX (also known as cgsix) accelerated 2D graphics card. In 1986, Texas Instruments released the TMS34010, the first fully programmable graphics processor. It could run general-purpose code but also had a graphics-oriented instruction set. During 1990–1992, this chip became the basis of the Texas Instruments Graphics Architecture ("TIGA") Windows accelerator cards. Following in 1987, the IBM 8514 graphics system was released. It was one of the first video cards for IBM PC compatibles that implemented fixed-function 2D primitives in electronic hardware. Sharp's X68000, released in 1987, used a custom graphics chipset with a 65,536 color palette and hardware support for sprites, scrolling, and multiple playfields. It served as a development machine for Capcom's CP System arcade board. Fujitsu's FM Towns computer, released in 1989, had support for a 16,777,216 color palette. For context, IBM also introduced its Video Graphics Array (VGA) display system in 1987, with a maximum resolution of 640 × 480 pixels. Unlike 8514/A, VGA had no hardware acceleration features. In November 1988, NEC Home Electronics announced its creation of the Video Electronics Standards Association (VESA) to develop and promote a Super VGA (SVGA) computer display standard as a successor to VGA. Super VGA enabled graphics display resolutions up to 800 × 600 pixels, a 56% increase. In 1988 SGI sold IRIS workstation graphics with 10-12 Geometry Engines and introduced the IrisVision add-in board for IBM MicroChannel bus (RS/6000) based on the Geometry Engine as well. In 1988 as well, the first dedicated polygonal 3D graphics boards in arcade machines were introduced wit

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  Self-management (computer science)

  Self-management is the process by which computer systems manage their own operation without human intervention. Self-management technologies are expected to pervade the next generation of network management systems. The growing complexity of modern networked computer systems is a limiting factor in their expansion. The increasing heterogeneity of corporate computer systems, the inclusion of mobile computing devices, and the combination of different networking technologies like WLAN, cellular phone networks, and mobile ad hoc networks make the conventional, manual management difficult, time-consuming, and error-prone. More recently, self-management has been suggested as a solution to increasing complexity in cloud computing. An industrial initiative towards realizing self-management is the Autonomic Computing Initiative (ACI) started by IBM in 2001. The ACI defines the following four functional areas: Self-configuration Auto-configuration of components Self-healing Automatic discovery, and correction of faults; automatically applying all necessary actions to bring system back to normal operation Self-optimization Automatic monitoring and control of resources to ensure the optimal functioning with respect to the defined requirements Self-protection Proactive identification and protection from arbitrary attacks

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  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

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  Security type system

  In computer science, a type system can be described as a syntactic framework which contains a set of rules that are used to assign a type property (int, boolean, char etc.) to various components of a computer program, such as variables or functions. A security type system works in a similar way, only with a main focus on the security of the computer program, through information flow control. Thus, the various components of the program are assigned security types, or labels. The aim of a such system is to ultimately be able to verify that a given program conforms to the type system rules and satisfies non-interference. Security type systems is one of many security techniques used in the field of language-based security, and is tightly connected to information flow and information flow policies. In simple terms, a security type system can be used to detect if there exists any kind of violation of confidentiality or integrity in a program, i.e. the programmer wants to detect if the program is in line with the information flow policy or not. == A simple information flow policy == Suppose there are two users, A and B. In a program, the following security classes (SC) are introduced: SC = {∅, {A}, {B}, {A,B}}, where ∅ is the empty set. The information flow policy should define the direction that information is allowed to flow, which is dependent on whether the policy allows read or write operations. This example considers read operations (confidentiality). The following flows are allowed: → = {({A}, {A}), ({B}, {B}), ({A,B}, {A,B}), ({A,B}, {A}), ({A,B}, {B}), ({A}, ∅), ({B}, ∅), ({A,B}, ∅)} This can also be described as a superset (⊇). In words: information is allowed to flow towards stricter levels of confidentiality. The combination operator (⊕) can express how security classes can perform read operations with respect to other security classes. For example: {A} ⊕ {A,B} = {A} — the only security class that can read from both {A} and {A,B} is {A}. {A} ⊕ {B} = ∅ — neither {A} nor {B} are allowed to read from both {A} and {B}. This can also be described as an intersection (∩) between security classes. An information flow policy can be illustrated as a Hasse diagram. The policy should also be a lattice, that is, it has a greatest lower-bound and least upper-bound (there always exists a combination between security classes). In the case of integrity, information will flow in the opposite direction, thus the policy will be inverted. == Information flow policy in security type systems == Once the policy is in place, the software developer can apply the security classes to the program components. Use of a security type system is usually combined with a compiler that can perform the verification of the information flow according to the type system rules. For the sake of simplicity, a very simple computer program, together with the information flow policy as described in the previous section, can be used as a demonstration. The simple program is given in the following pseudocode: if y{A} = 1 then x{A,B} := 0 else x{A,B} := 1 Here, an equality check is made on a variable y that is assigned the security class {A}. A variable x with a lower security class ({A,B}) is influenced by this check. This means that information is leaking from class {A} to class {A,B}, which is a violation of the confidentiality policy. This leak should be detected by the security type system. === Example === Designing a security type system requires a function (also known as a security environment) that creates a mapping from variables to security types, or classes. This function can be called Γ, such that Γ(x) = τ, where x is a variable and τ is the security class, or type. Security classes are assigned (also called "judgement") to program components, using the following notation: Types are assigned to read operations by: Γ ⊢ e : τ. Types are assigned to write operations by: Γ ⊢ S : τ cmd. Constants can be assigned any type. The following bottom-up notation can be used to decompose the program: ⁠assumption1 ... assumptionn/conclusion⁠. Once the program is decomposed into trivial judgements, by which the type can easily be determined, the types for the less trivial parts of the program can be derived. Each "numerator" is considered in isolation, looking at the type of each statement to see if an allowed type can be derived for the "denominator", based on the defined type system "rules". ==== Rules ==== The main part of the security type system is the rules. They say how the program should be decomposed and how type verification should be performed. This toy program consists of a conditional test and two possible variable assignments. Rules for these two events are defined as follows: Applying this to the simple program introduced above yields: The type system detects the policy violation in line 2, where a read operation of security class {A} is performed, followed by two write operations of a less strict security class {A,B}. In more formalized terms, {A} ⋢ {A,B}, {A,B} (from the rule of the conditional test). Thus, the program is classified as "not typeable". === Soundness === The soundness of a security type system can be informally defined as: If program P is well typed, P satisfies non-interference. Volpano, Smith and Irvine were the first to prove soundness of a security type system for a deterministic imperative programming language with a standard (non-instrumented) semantics using the notion of non-interference.

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  Meta-learning (computer science)

  Meta-learning is a subfield of machine learning where automatic learning algorithms are applied to metadata about machine learning experiments. As of 2017, the term had not found a standard interpretation, however the main goal is to use such metadata to understand how automatic learning can become flexible in solving learning problems, hence to improve the performance of existing learning algorithms or to learn (induce) the learning algorithm itself, hence the alternative term learning to learn. Flexibility is important because each learning algorithm is based on a set of assumptions about the data, its inductive bias. This means that it will only learn well if the bias matches the learning problem. A learning algorithm may perform very well in one domain, but not on the next. This poses strong restrictions on the use of machine learning or data mining techniques, since the relationship between the learning problem (often some kind of database) and the effectiveness of different learning algorithms is not yet understood. By using different kinds of metadata, like properties of the learning problem, algorithm properties (like performance measures), or patterns previously derived from the data, it is possible to learn, select, alter or combine different learning algorithms to effectively solve a given learning problem. Critiques of meta-learning approaches bear a strong resemblance to the critique of metaheuristic, a possibly related problem. A good analogy to meta-learning, and the inspiration for Jürgen Schmidhuber's early work (1987) and Yoshua Bengio et al.'s work (1991), considers that genetic evolution learns the learning procedure encoded in genes and executed in each individual's brain. In an open-ended hierarchical meta-learning system using genetic programming, better evolutionary methods can be learned by meta evolution, which itself can be improved by meta meta evolution, etc. == Definition == A proposed definition for a meta-learning system combines three requirements: The system must include a learning subsystem. Experience is gained by exploiting meta knowledge extracted in a previous learning episode on a single dataset, or from different domains. Learning bias must be chosen dynamically. Bias refers to the assumptions that influence the choice of explanatory hypotheses and not the notion of bias represented in the bias-variance dilemma. Meta-learning is concerned with two aspects of learning bias. Declarative bias specifies the representation of the space of hypotheses, and affects the size of the search space (e.g., represent hypotheses using linear functions only). Procedural bias imposes constraints on the ordering of the inductive hypotheses (e.g., preferring smaller hypotheses). == Common approaches == There are three common approaches: using (cyclic) networks with external or internal memory (model-based) learning effective distance metrics (metrics-based) explicitly optimizing model parameters for fast learning (optimization-based). === Model-Based === Model-based meta-learning models updates its parameters rapidly with a few training steps, which can be achieved by its internal architecture or controlled by another meta-learner model. ==== Memory-Augmented Neural Networks ==== A Memory-Augmented Neural Network, or MANN for short, is claimed to be able to encode new information quickly and thus to adapt to new tasks after only a few examples. ==== Meta Networks ==== Meta Networks (MetaNet) learns a meta-level knowledge across tasks and shifts its inductive biases via fast parameterization for rapid generalization. === Metric-Based === The core idea in metric-based meta-learning is similar to nearest neighbors algorithms, which weight is generated by a kernel function. It aims to learn a metric or distance function over objects. The notion of a good metric is problem-dependent. It should represent the relationship between inputs in the task space and facilitate problem solving. ==== Convolutional Siamese Neural Network ==== Siamese neural network is composed of two twin networks whose output is jointly trained. There is a function above to learn the relationship between input data sample pairs. The two networks are the same, sharing the same weight and network parameters. ==== Matching Networks ==== Matching Networks learn a network that maps a small labelled support set and an unlabelled example to its label, obviating the need for fine-tuning to adapt to new class types. ==== Relation Network ==== The Relation Network (RN), is trained end-to-end from scratch. During meta-learning, it learns to learn a deep distance metric to compare a small number of images within episodes, each of which is designed to simulate the few-shot setting. ==== Prototypical Networks ==== Prototypical Networks learn a metric space in which classification can be performed by computing distances to prototype representations of each class. Compared to recent approaches for few-shot learning, they reflect a simpler inductive bias that is beneficial in this limited-data regime, and achieve satisfied results. === Optimization-Based === What optimization-based meta-learning algorithms intend for is to adjust the optimization algorithm so that the model can be good at learning with a few examples. ==== LSTM Meta-Learner ==== LSTM-based meta-learner is to learn the exact optimization algorithm used to train another learner neural network classifier in the few-shot regime. The parametrization allows it to learn appropriate parameter updates specifically for the scenario where a set amount of updates will be made, while also learning a general initialization of the learner (classifier) network that allows for quick convergence of training. ==== Temporal Discreteness ==== Model-Agnostic Meta-Learning (MAML) is a fairly general optimization algorithm, compatible with any model that learns through gradient descent. ==== Reptile ==== Reptile is a remarkably simple meta-learning optimization algorithm, given that both of its components rely on meta-optimization through gradient descent and both are model-agnostic. == Examples == Some approaches which have been viewed as instances of meta-learning: Recurrent neural networks (RNNs) are universal computers. In 1993, Jürgen Schmidhuber showed how "self-referential" RNNs can in principle learn by backpropagation to run their own weight change algorithm, which may be quite different from backpropagation. In 2001, Sepp Hochreiter & A.S. Younger & P.R. Conwell built a successful supervised meta-learner based on Long short-term memory RNNs. It learned through backpropagation a learning algorithm for quadratic functions that is much faster than backpropagation. Researchers at Deepmind (Marcin Andrychowicz et al.) extended this approach to optimization in 2017. In the 1990s, Meta Reinforcement Learning or Meta RL was achieved in Schmidhuber's research group through self-modifying policies written in a universal programming language that contains special instructions for changing the policy itself. There is a single lifelong trial. The goal of the RL agent is to maximize reward. It learns to accelerate reward intake by continually improving its own learning algorithm which is part of the "self-referential" policy. An extreme type of Meta Reinforcement Learning is embodied by the Gödel machine, a theoretical construct which can inspect and modify any part of its own software which also contains a general theorem prover. It can achieve recursive self-improvement in a provably optimal way. Model-Agnostic Meta-Learning (MAML) was introduced in 2017 by Chelsea Finn et al. Given a sequence of tasks, the parameters of a given model are trained such that few iterations of gradient descent with few training data from a new task will lead to good generalization performance on that task. MAML "trains the model to be easy to fine-tune." MAML was successfully applied to few-shot image classification benchmarks and to policy-gradient-based reinforcement learning. Variational Bayes-Adaptive Deep RL (VariBAD) was introduced in 2019. While MAML is optimization-based, VariBAD is a model-based method for meta reinforcement learning, and leverages a variational autoencoder to capture the task information in an internal memory, thus conditioning its decision making on the task. When addressing a set of tasks, most meta learning approaches optimize the average score across all tasks. Hence, certain tasks may be sacrificed in favor of the average score, which is often unacceptable in real-world applications. By contrast, Robust Meta Reinforcement Learning (RoML) focuses on improving low-score tasks, increasing robustness to the selection of task. RoML works as a meta-algorithm, as it can be applied on top of other meta learning algorithms (such as MAML and VariBAD) to increase their robustness. It is applicable to both supervised meta learning and meta reinforcement learning. Discovering meta-knowledge works by inducing knowledge

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  Symbolic artificial intelligence

  In artificial intelligence, symbolic artificial intelligence (also known as classical artificial intelligence or logic-based artificial intelligence) is the term for the collection of all methods in artificial intelligence research that are based on high-level symbolic (human-readable) representations of problems, logic, and search. Symbolic AI used tools such as logic programming, production rules, semantic nets and frames, and it developed applications such as knowledge-based systems (in particular, expert systems), symbolic mathematics, automated theorem provers, ontologies, the semantic web, and automated planning and scheduling systems. The Symbolic AI paradigm led to important ideas in search, symbolic programming languages, agents, multi-agent systems, the semantic web, and the strengths and limitations of formal knowledge and reasoning systems. Symbolic AI was the dominant paradigm of AI research from the mid-1950s until the mid-1990s. Researchers in the 1960s and the 1970s were convinced that symbolic approaches would eventually succeed in creating a machine with artificial general intelligence and considered this the ultimate goal of their field. An early boom, with early successes such as the Logic Theorist and Samuel's Checkers Playing Program, led to unrealistic expectations and promises and was followed by the first AI Winter as funding dried up. A second boom (1969–1986) occurred with the rise of expert systems, their promise of capturing corporate expertise, and an enthusiastic corporate embrace. That boom, and some early successes, e.g., with XCON at DEC, was followed again by later disappointment. Problems with difficulties in knowledge acquisition, maintaining large knowledge bases, and brittleness in handling out-of-domain problems arose. Another, second, AI Winter (1988–2011) followed. Subsequently, AI researchers focused on addressing underlying problems in handling uncertainty and in knowledge acquisition. Uncertainty was addressed with formal methods such as hidden Markov models, Bayesian reasoning, and statistical relational learning. Symbolic machine learning addressed the knowledge acquisition problem with contributions including Version Space, Valiant's PAC learning, Quinlan's ID3 decision-tree learning, case-based learning, and inductive logic programming to learn relations. Neural networks, a subsymbolic approach, had been pursued from early days and reemerged strongly in 2012. Early examples are Rosenblatt's perceptron learning work, the backpropagation work of Rumelhart, Hinton and Williams, and work in convolutional neural networks by LeCun et al. in 1989. However, neural networks were not viewed as successful until about 2012: "Until Big Data became commonplace, the general consensus in the Al community was that the so-called neural-network approach was hopeless. Systems just didn't work that well, compared to other methods. ... A revolution came in 2012, when a number of people, including a team of researchers working with Hinton, worked out a way to use the power of GPUs to enormously increase the power of neural networks." Over the next several years, deep learning had spectacular success in handling vision, speech recognition, speech synthesis, image generation, and machine translation, though symbolic approaches continue to be useful in a few domains such as computer algebra systems and proof assistants. == History == A short history of symbolic AI to the present day follows below. Time periods and titles are drawn from Henry Kautz's 2020 AAAI Robert S. Engelmore Memorial Lecture and the longer Wikipedia article on the History of AI, with dates and titles differing slightly for increased clarity. === The first AI summer: irrational exuberance, 1948–1966 === Success at early attempts in AI occurred in three main areas: artificial neural networks, knowledge representation, and heuristic search, contributing to high expectations. This section summarizes Kautz's reprise of early AI history. ==== Approaches inspired by human or animal cognition or behavior ==== Cybernetic approaches attempted to replicate the feedback loops between animals and their environments. A robotic turtle, with sensors, motors for driving and steering, and seven vacuum tubes for control, based on a preprogrammed neural net, was built as early as 1948. This work can be seen as an early precursor to later work in neural networks, reinforcement learning, and situated robotics. An important early symbolic AI program was the Logic theorist, written by Allen Newell, Herbert Simon and Cliff Shaw in 1955–56, as it was able to prove 38 elementary theorems from Whitehead and Russell's Principia Mathematica. Newell, Simon, and Shaw later generalized this work to create a domain-independent problem solver, GPS (General Problem Solver). GPS solved problems represented with formal operators via state-space search using means-ends analysis. During the 1960s, symbolic approaches achieved great success at simulating intelligent behavior in structured environments such as game-playing, symbolic mathematics, and theorem-proving. AI research was concentrated in four institutions in the 1960s: Carnegie Mellon University, Stanford, MIT and (later) University of Edinburgh. Each one developed its own style of research. Earlier approaches based on cybernetics or artificial neural networks were abandoned or pushed into the background. Herbert Simon and Allen Newell studied human problem-solving skills and attempted to formalize them, and their work laid the foundations of the field of artificial intelligence, as well as cognitive science, operations research and management science. Their research team used the results of psychological experiments to develop programs that simulated the techniques that people used to solve problems. This tradition, centered at Carnegie Mellon University would eventually culminate in the development of the Soar architecture in the middle 1980s. ==== Heuristic search ==== In addition to the highly specialized domain-specific kinds of knowledge that we will see later used in expert systems, early symbolic AI researchers discovered another more general application of knowledge. These were called heuristics, rules of thumb that guide a search in promising directions: "How can non-enumerative search be practical when the underlying problem is exponentially hard? The approach advocated by Simon and Newell is to employ heuristics: fast algorithms that may fail on some inputs or output suboptimal solutions." Another important advance was to find a way to apply these heuristics that guarantees a solution will be found, if there is one, not withstanding the occasional fallibility of heuristics: "The A algorithm provided a general frame for complete and optimal heuristically guided search. A is used as a subroutine within practically every AI algorithm today but is still no magic bullet; its guarantee of completeness is bought at the cost of worst-case exponential time. ==== Early work on knowledge representation and reasoning ==== Early work covered both applications of formal reasoning emphasizing first-order logic, along with attempts to handle common-sense reasoning in a less formal manner. ===== Modeling formal reasoning with logic: the "neats" ===== Unlike Simon and Newell, John McCarthy felt that machines did not need to simulate the exact mechanisms of human thought, but could instead try to find the essence of abstract reasoning and problem-solving with logic, regardless of whether people used the same algorithms. His laboratory at Stanford (SAIL) focused on using formal logic to solve a wide variety of problems, including knowledge representation, planning and learning. Logic was also the focus of the work at the University of Edinburgh and elsewhere in Europe which led to the development of the programming language Prolog and the science of logic programming. ===== Modeling implicit common-sense knowledge with frames and scripts: the "scruffies" ===== Researchers at MIT (such as Marvin Minsky and Seymour Papert) found that solving difficult problems in vision and natural language processing required ad hoc solutions—they argued that no simple and general principle (like logic) would capture all the aspects of intelligent behavior. Roger Schank described their "anti-logic" approaches as "scruffy" (as opposed to the "neat" paradigms at CMU and Stanford). Commonsense knowledge bases (such as Doug Lenat's Cyc) are an example of "scruffy" AI, since they must be built by hand, one complicated concept at a time. === The first AI winter: crushed dreams, 1967–1977 === The first AI winter was a shock: During the first AI summer, many people thought that machine intelligence could be achieved in just a few years. The Defense Advance Research Projects Agency (DARPA) launched programs to support AI research to use AI to solve problems of national security; in particular, to automate the translation of Russian to English for inte

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  Cognitive philology

  Cognitive philology is the science that studies written and oral texts as the product of human mental processes. Studies in cognitive philology compare documentary evidence emerging from textual investigations with results of experimental research, especially in the fields of cognitive and ecological psychology, neurosciences and artificial intelligence. "The point is not the text, but the mind that made it". Cognitive Philology aims to foster communication between literary, textual, philological disciplines on the one hand and researches across the whole range of the cognitive, evolutionary, ecological and human sciences on the other. Cognitive philology: investigates transmission of oral and written text, and categorization processes which lead to classification of knowledge, mostly relying on the information theory; studies how narratives emerge in so called natural conversation and selective process which lead to the rise of literary standards for storytelling, mostly relying on embodied semantics; explores the evolutive and evolutionary role played by rhythm and metre in human ontogenetic and phylogenetic development and the pertinence of the semantic association during processing of cognitive maps; Provides the scientific ground for multimedia critical editions of literary texts. Among the founding thinkers and noteworthy scholars devoted to such investigations are: Alan Richardson: Studies Theory of Mind in early-modern and contemporary literature. Anatole Pierre Fuksas Benoît de Cornulier David Herman: Professor of English at North Carolina State University and an adjunct professor of linguistics at Duke University. He is the author of "Universal Grammar and Narrative Form" and the editor of "Narratologies: New Perspectives on Narrative Analysis". Domenico Fiormonte François Recanati Gilles Fauconnier, a professor in Cognitive science at the University of California, San Diego. He was one of the founders of cognitive linguistics in the 1970s through his work on pragmatic scales and mental spaces. His research explores the areas of conceptual integration and compressions of conceptual mappings in terms of the emergent structure in language. Julián Santano Moreno Luca Nobile Manfred Jahn in Germany Mark Turner Paolo Canettieri

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  DoorDash

  DoorDash, Inc. is an American company operating online food ordering and food delivery. It trades under the symbol DASH. With a 56% market share, DoorDash is the largest food delivery platform in the United States. It also has a 60% market share in the convenience delivery category. As of December 31, 2020, the platform was used by 450,000 merchants, 20 million consumers, and had over one million delivery couriers. Founded by Tony Xu, Andy Fang, Stanley Tang and Evan Moore, DoorDash made its debut on the Fortune 500 list in 2024, ranking No. 443. DoorDash has been sued for or held legally liable for withholding tips, reducing tip transparency, antitrust price manipulation, listing restaurants without permission, misclassifying workers, withholding sick time, and illegally selling personal data. As of April 2026, DoorDash operates in the United States (including Puerto Rico), Canada, Australia, and New Zealand. Through its subsidiaries Deliveroo and Wolt, the company also operates across Europe, as well as in Azerbaijan, Georgia, Israel, Kazakhstan, Kuwait, and the United Arab Emirates. == History == In January 2013, Stanford University students Tony Xu, Stanley Tang, Andy Fang and Evan Moore launched PaloAltoDelivery.com in Palo Alto, California. In the summer of 2013, it received US$120,000 in seed money from Y Combinator in exchange for a 7% stake. It incorporated as DoorDash in June 2013. DoorDash's first partnership with a fast food burger restaurant chain was in April 2016, when it partnered with CKE Restaurants, parent company of Carl's Jr. and Hardee's, for food delivery. In December 2017, DoorDash announced its partnership with Wendy's for delivery from its restaurants. In December 2018, DoorDash overtook Uber Eats to hold the second position in total US food delivery sales, behind GrubHub. By March 2019, it had exceeded GrubHub in total sales, at 27.6% of the on-demand delivery market. By early 2019, DoorDash was the largest food delivery provider in the U.S., as measured by consumer spending. In October 2019, DoorDash opened its first ghost kitchen, DoorDash Kitchen, in Redwood City, California, with four restaurants operating at the location. By June 2020, DoorDash had raised more than $2.5 billion over several financing rounds from investors including Y Combinator, Charles River Ventures, SV Angel, Khosla Ventures, Sequoia Capital, SoftBank Group, GIC, and Kleiner Perkins. DoorDash announced a partnership with KFC in September 2020, followed by Taco Bell in October 2020. In November 2020, DoorDash announced the opening of its first physical restaurant location, partnering up with Bay Area restaurant Burma Bites to offer delivery and pick-up orders. In December 2020, it became a public company via an initial public offering, raising $3.37 billion. In November 2021, DoorDash acquired Finland's Wolt for €7bn. In August 2022, DoorDash announced it would end its partnership with Walmart in September, ending the companies' cooperation agreement from 2018. In November 2022, DoorDash announced plans to lay off 1,250 corporate employees, or about six percent of its workforce, to rein in expenses. In June 2023, DoorDash announced it would give its drivers the option of earning an hourly minimum wage instead of being paid per delivery. However, drivers are only paid hourly when on an active delivery. In September 2023, the company transferred its stock listing from the New York Stock Exchange to the Nasdaq. On December 18, 2023, DoorDash was added to the Nasdaq-100 index. In March 2025, DoorDash announced a partnership with Klarna, a Buy Now, Pay Later (BNPL) service, letting customers schedule small payments over a set period of time. DoorDash received widespread criticism from this decision, including internet mockery, given concerns about the increase of household debt in America. In 2025, DoorDash acquired the UK-based delivery service Deliveroo for $3.88 billion. The combined company operates in 40 countries and serves 50 million users monthly. In September 2025, DoorDash and Ace Hardware (the largest hardware cooperative) announced their partnership to offer delivery for home use products from over 4,000 Ace locations. == Lawsuits against DoorDash == === 2017 class-action lawsuit for misclassifying workers === In 2017, a class-action lawsuit was filed against DoorDash for allegedly misclassifying delivery drivers in California and Massachusetts as independent contractors. In 2022, a tentative settlement was reached in which DoorDash would pay $100 million total, with $61 million going to over 900,000 drivers, paying out just over $130 per driver, and $28 million for the lawyers. Gizmodo criticized the settlement, noting that the $413 million that DoorDash CEO Tony Xu received the previous year was one of the largest CEO compensation packages of all time. === 2019 data breach lawsuit === On May 4, 2019, DoorDash confirmed 4.9 million customers, delivery workers and merchants had sensitive information stolen via a data breach. Those who joined the platform after April 5, 2018, were unaffected by the breach. A class-action lawsuit for the breach was filed against DoorDash in October 2019. === Withholding of tips and subsequent class-action lawsuits === In July 2019, the company's tipping policy was criticized by The New York Times, and later The Verge and Vox and Gothamist. Drivers receive a guaranteed minimum per order that is paid by DoorDash by default. When a customer added a tip, instead of going directly to the driver, it first went to the company to cover the guaranteed minimum. Drivers then only directly received the part of the tip that exceeded the guaranteed minimum per order. In January 2020, it was reported that DoorDash had lied about skimming tips from its drivers, causing them to earn an average of $1.45 an hour after expenses, and that after the company had allegedly overhauled its tipping system, DoorDash was still manipulating per-delivery payouts at the expense of drivers. A DoorDash customer filed a class action lawsuit against the company for its "materially false and misleading" tipping policy. The case was referred to arbitration in August 2020. Under pressure, the company revised its policy. The company settled a lawsuit with District of Columbia Attorney General Karl Racine for $2.5 million, with funds going to deliverers, the government, and to charity. ==== 2021 driver strike for tip transparency ==== In July 2021, DoorDash drivers went on strike to protest lack of tip transparency and to ask for higher pay. At the time of the strike, and, as of June 2022, DoorDash did not allow drivers to see the full tip amounts prior to accepting a delivery in the app. If customers tip over a set amount for the order total, Doordash hides a portion of the tip until the delivery is complete. The strike occurred after DoorDash rewrote its code to cut off access to Para, a third-party app that drivers had been using to see the full tip amounts. ==== 2025 class-action lawsuit settlement ==== In 2025, DoorDash agreed to pay around $17 million for "misleading both consumers and delivery workers" with tips being docked from drivers' pay instead of directly going to drivers. === 2020 antitrust litigation === In April 2020, in the case of Davitashvili v. GrubHub Inc. DoorDash, Grubhub, Postmates, and Uber Eats were accused of monopolistic power by only listing restaurants on its apps if the restaurant owners signed contracts which include clauses that require prices be the same for dine-in customers as for customers receiving delivery. The plaintiffs stated that this arrangement increases the cost for dine-in customers, as they are required to subsidize the cost of delivery; and that the apps charge "exorbitant" fees, which range from 13% to 40% of revenue, while the average restaurant's profit ranges from 3% to 9% of revenue. The lawsuit seeks treble damages, including for overcharges, since April 14, 2016, for dine-in and delivery customers in the United States at restaurants using the defendants’ delivery apps. Although several preliminary documents in the case have now been filed, a trial date has not yet been set. === Litigation for illegal unauthorized restaurant listing === In May 2021, DoorDash was criticized for unauthorized listings of restaurants who had not given permission to appear on the app. The company was sued by Lona's Lil Eats in St. Louis, with the lawsuit claiming that DoorDash had listed them without permission, then prevented any orders to the restaurant from going through and redirecting customers to other restaurants instead, because Lona's was "too far away," when in reality it had not paid DoorDash a fee for listing. This aspect of DoorDash's business practice is illegal in California. === 2021 lawsuit by the city of Chicago === In August 2021, the city of Chicago sued DoorDash and GrubHub. According to Chicago mayor Lori Lightfoot, the companies broke the law by using "unfair and deceptive t

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  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.

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  Artificial intelligence controversies

  The controversies surrounding artificial intelligence encompass a broad range of public, academic, and political debates regarding the societal effects of artificial intelligence (AI). These debates intensified particularly in the late 2010s and 2020s, coinciding with an accelerated period of development known as the AI boom. While advocates emphasize the technology's potential to solve complex problems and enhance human quality of life, detractors highlight a wide array of dangers and challenges. These include concerns over ethics, plagiarism and theft, fraud, safety and alignment, environmental impacts, technological unemployment, and the spread of misinformation. It also covers severe future or theoretical challenges, such as the emergence of artificial superintelligence and existential risks. == 2016 == === Microsoft Tay chatbot (2016) === On March 23, 2016, Microsoft released Tay, a chatbot designed to mimic the language patterns of a 19-year-old American girl and learn from interactions with Twitter users. Soon after its launch, Tay began posting racist, sexist, and otherwise inflammatory tweets after Twitter users deliberately taught it offensive phrases and exploited its "repeat after me" capability. Examples of controversial outputs included Holocaust denial and calls for genocide using racial slurs. Within 16 hours of its release, Microsoft suspended the Twitter account, deleted the offensive tweets, and stated that Tay had suffered from a "coordinated attack by a subset of people" that "exploited a vulnerability." Tay was briefly and accidentally re-released on March 30 during testing, after which it was permanently shut down. Microsoft CEO Satya Nadella later stated that Tay "has had a great influence on how Microsoft is approaching AI" and taught the company the importance of taking accountability. == 2022 == === Voiceverse NFT plagiarism scandal (2022) === On January 14, 2022, voice actor Troy Baker announced a partnership with Voiceverse, a blockchain-based company that marketed proprietary AI voice cloning technology as non-fungible tokens (NFT), triggering immediate backlash over environmental concerns, fears that AI could displace human voice actors, and concerns about fraud. Later that same day, the pseudonymous creator of 15.ai—a free, non-commercial AI voice synthesis research project—revealed through server logs that Voiceverse had used 15.ai to generate voice samples, pitch-shifted them to make them unrecognizable, and falsely marketed them as their own proprietary technology before selling them as NFTs; the developer of 15.ai had previously stated that they had no interest in incorporating NFTs into their work. Voiceverse confessed within an hour and stated that their marketing team had used 15.ai without attribution while rushing to create a demo. News publications and AI watchdog groups universally characterized the incident as theft stemming from generative artificial intelligence. === Théâtre D'opéra Spatial (2022) === On August 29, 2022, Jason Michael Allen won first place in the "emerging artist" (non-professional) division of the "Digital Arts/Digitally-Manipulated Photography" category of the Colorado State Fair's fine arts competition with Théâtre D'opéra Spatial, a digital artwork created using the AI image generator Midjourney, Adobe Photoshop, and AI upscaling tools, becoming one of the first images made using generative AI to win such a prize. Allen disclosed his use of Midjourney when submitting, though the judges did not know it was an AI tool but stated they would have awarded him first place regardless. While there was little contention about the image at the fair, reactions to the win on social media were negative. On September 5, 2023, the United States Copyright Office ruled that the work was not eligible for copyright protection as the human creative input was de minimis and that copyright rules "exclude works produced by non-humans." == 2023 == === Statements on AI risk (2023) === On March 22, 2023, the Future of Life Institute published an open letter calling on "all AI labs to immediately pause for at least 6 months the training of AI systems more powerful than GPT-4", citing risks such as AI-generated propaganda, extreme automation of jobs, human obsolescence, and a society-wide loss of control. The letter, published a week after the release of OpenAI's GPT-4, asserted that current large language models were "becoming human-competitive at general tasks". It received more than 30,000 signatures, including academic AI researchers and industry CEOs such as Yoshua Bengio, Stuart Russell, Elon Musk, Steve Wozniak and Yuval Noah Harari. The letter was criticized for diverting attention from more immediate societal risks such as algorithmic biases, with Timnit Gebru and others arguing that it amplified "some futuristic, dystopian sci-fi scenario" instead of current problems with AI. On May 30, 2023, the Center for AI Safety released a one-sentence statement signed by hundreds of artificial intelligence experts and other notable figures: "Mitigating the risk of extinction from AI should be a global priority alongside other societal-scale risks such as pandemics and nuclear war." Signatories included Turing laureates Geoffrey Hinton and Yoshua Bengio, as well as the scientific and executive leaders of several major AI companies, including Sam Altman, Demis Hassabis, and Bill Gates. The statement prompted responses from political leaders, including UK Prime Minister Rishi Sunak, who retweeted it with a statement that the UK government would look carefully into it, and White House Press Secretary Karine Jean-Pierre, who commented that AI "is one of the most powerful technologies that we see currently in our time." Skeptics, including from Human Rights Watch, argued that scientists should focus on known risks of AI instead of speculative future risks. === Removal of Sam Altman from OpenAI (2023) === On November 17, 2023, OpenAI's board of directors ousted co-founder and chief executive Sam Altman, stating that "the board no longer has confidence in his ability to continue leading OpenAI." The removal was precipitated by employee concerns about his handling of artificial intelligence safety and allegations of abusive behavior. Altman was reinstated on November 22 after pressure from employees and investors, including a letter signed by 745 of OpenAI's 770 employees threatening mass resignations if the board did not resign. The removal and subsequent reinstatement caused widespread reactions, including Microsoft's stock falling nearly three percent following the initial announcement and then rising over two percent to an all-time high after Altman was hired to lead a Microsoft AI research team before his reinstatement. The incident also prompted investigations from the Competition and Markets Authority and the Federal Trade Commission into Microsoft's relationship with OpenAI. == 2024 == === Taylor Swift deepfake pornography controversy (2024) === In late January 2024, sexually explicit AI-generated deepfake images of Taylor Swift were proliferated on X, with one post reported to have been seen over 47 million times before its removal. Disinformation research firm Graphika traced the images back to 4chan, while members of a Telegram group had discussed ways to circumvent censorship safeguards of AI image generators to create pornographic images of celebrities. The images prompted responses from anti-sexual assault advocacy groups, US politicians, and Swifties. Microsoft CEO Satya Nadella called the incident "alarming and terrible." X briefly blocked searches of Swift's name on January 27, 2024, and Microsoft enhanced its text-to-image model safeguards to prevent future abuse. On January 30, US senators Dick Durbin, Lindsey Graham, Amy Klobuchar, and Josh Hawley introduced a bipartisan bill that would allow victims to sue individuals who produced or possessed "digital forgeries" with intent to distribute, or those who received the material knowing it was made without consent. === Google Gemini image generation controversy (2024) === In February 2024, social media users reported that Google's Gemini chatbot was generating images that featured people of color and women in historically inaccurate contexts—such as Vikings, Nazi soldiers, and the Founding Fathers—and refusing prompts to generate images of white people. The images were derided on social media, including by conservatives who cited them as evidence of Google's "wokeness", and criticized by Elon Musk, who denounced Google's products as biased and racist. In response, Google paused Gemini's ability to generate images of people. Google executive Prabhakar Raghavan released a statement explaining that Gemini had "overcompensate[d]" in its efforts to strive for diversity and acknowledging that the images were "embarrassing and wrong". Google CEO Sundar Pichai called the incident offensive and unacceptable in an internal memo, promising struc

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