Domain adaptation is a field associated with machine learning and transfer learning. It addresses the challenge of training a model on one data distribution (the source domain) and applying it to a related but different data distribution (the target domain). A common example is spam filtering, where a model trained on emails from one user (source domain) is adapted to handle emails for another user with significantly different patterns (target domain). Domain adaptation techniques can also leverage unrelated data sources to improve learning. When multiple source distributions are involved, the problem extends to multi-source domain adaptation. Domain adaptation is a specific type of transfer learning. According to the taxonomy laid out by Pan and Yang (2010), it falls into the category of transductive transfer learning. In this setting, the source and target tasks are the same (e.g., both are object recognition), but the domains differ (different marginal distributions). This distinguishes it from inductive transfer learning (where labeled data is available for the target task) and unsupervised transfer learning (where labels are unavailable in both domains). == Classification of domain adaptation problems == Domain adaptation setups are classified in two different ways: according to the distribution shift between the domains, and according to the available data from the target domain. === Distribution shifts === Common distribution shifts are classified as follows: Covariate Shift occurs when the input distributions of the source and destination change, but the relationship between inputs and labels remains unchanged. The above-mentioned spam filtering example typically falls in this category. Namely, the distributions (patterns) of emails may differ between the domains, but emails labeled as spam in the one domain should similarly be labeled in another. Prior Shift (Label Shift) occurs when the label distribution differs between the source and target datasets, while the conditional distribution of features given labels remains the same. An example is a classifier of hair color in images from Italy (source domain) and Norway (target domain). The proportions of hair colors (labels) differ, but images within classes like blond and black-haired populations remain consistent across domains. A classifier for the Norway population can exploit this prior knowledge of class proportions to improve its estimates. Concept Shift (Conditional Shift) refers to changes in the relationship between features and labels, even if the input distribution remains the same. For instance, in medical diagnosis, the same symptoms (inputs) may indicate entirely different diseases (labels) in different populations (domains). === Data available during training === Domain adaptation problems typically assume that some data from the target domain is available during training. Problems can be classified according to the type of this available data: Unsupervised: Unlabeled data from the target domain is available, but no labeled data. In the above-mentioned example of spam filtering, this corresponds to the case where emails from the target domain (user) are available, but they are not labeled as spam. Domain adaptation methods can benefit from such unlabeled data, by comparing its distribution (patterns) with the labeled source domain data. Semi-supervised: Most data that is available from the target domain is unlabelled, but some labeled data is also available. In the above-mentioned case of spam filter design, this corresponds to the case that the target user has labeled some emails as being spam or not. Supervised: All data that is available from the target domain is labeled. In this case, domain adaptation reduces to refinement of the source domain predictor. In the above-mentioned example classification of hair-color from images, this could correspond to the refinement of a network already trained on a large dataset of labeled images from Italy, using newly available labeled images from Norway. == Formalization == Let X {\displaystyle X} be the input space (or description space) and let Y {\displaystyle Y} be the output space (or label space). The objective of a machine learning algorithm is to learn a mathematical model (a hypothesis) h : X → Y {\displaystyle h:X\to Y} able to attach a label from Y {\displaystyle Y} to an example from X {\displaystyle X} . This model is learned from a learning sample S = { ( x i , y i ) ∈ ( X × Y ) } i = 1 m {\displaystyle S=\{(x_{i},y_{i})\in (X\times Y)\}_{i=1}^{m}} . Usually in supervised learning (without domain adaptation), we suppose that the examples ( x i , y i ) ∈ S {\displaystyle (x_{i},y_{i})\in S} are drawn i.i.d. from a distribution D S {\displaystyle D_{S}} of support X × Y {\displaystyle X\times Y} (unknown and fixed). The objective is then to learn h {\displaystyle h} (from S {\displaystyle S} ) such that it commits the least error possible for labelling new examples coming from the distribution D S {\displaystyle D_{S}} . The main difference between supervised learning and domain adaptation is that in the latter situation we study two different (but related) distributions D S {\displaystyle D_{S}} and D T {\displaystyle D_{T}} on X × Y {\displaystyle X\times Y} . The domain adaptation task then consists of the transfer of knowledge from the source domain D S {\displaystyle D_{S}} to the target one D T {\displaystyle D_{T}} . The goal is then to learn h {\displaystyle h} (from labeled or unlabelled samples coming from the two domains) such that it commits as little error as possible on the target domain D T {\displaystyle D_{T}} . The major issue is the following: if a model is learned from a source domain, what is its capacity to correctly label data coming from the target domain? == Four algorithmic principles == === Reweighting algorithms === The objective is to reweight the source labeled sample such that it "looks like" the target sample (in terms of the error measure considered). === Iterative algorithms === A method for adapting consists in iteratively "auto-labeling" the target examples. The principle is simple: a model h {\displaystyle h} is learned from the labeled examples; h {\displaystyle h} automatically labels some target examples; a new model is learned from the new labeled examples. Note that there exist other iterative approaches, but they usually need target labeled examples. === Search of a common representation space === The goal is to find or construct a common representation space for the two domains. The objective is to obtain a space in which the domains are close to each other while keeping good performances on the source labeling task. This can be achieved through the use of Adversarial machine learning techniques where feature representations from samples in different domains are encouraged to be indistinguishable. === Hierarchical Bayesian Model === The goal is to construct a Bayesian hierarchical model p ( n ) {\displaystyle p(n)} , which is essentially a factorization model for counts n {\displaystyle n} , to derive domain-dependent latent representations allowing both domain-specific and globally shared latent factors. == Software packages == Several compilations of domain adaptation and transfer learning algorithms have been implemented over the past decades: SKADA (Python) ADAPT (Python) TLlib (Python) Domain-Adaptation-Toolbox (MATLAB)
Weight initialization
In deep learning, weight initialization or parameter initialization describes the initial step in creating a neural network. A neural network contains trainable parameters that are modified during training: weight initialization is the pre-training step of assigning initial values to these parameters. The choice of weight initialization method affects the speed of convergence, the scale of neural activation within the network, the scale of gradient signals during backpropagation, and the quality of the final model. Proper initialization is necessary for avoiding issues such as vanishing and exploding gradients and activation function saturation. Note that even though this article is titled "weight initialization", both weights and biases are used in a neural network as trainable parameters, so this article describes how both of these are initialized. Similarly, trainable parameters in convolutional neural networks (CNNs) are called kernels and biases, and this article also describes these. == Constant initialization == We discuss the main methods of initialization in the context of a multilayer perceptron (MLP). Specific strategies for initializing other network architectures are discussed in later sections. For an MLP, there are only two kinds of trainable parameters, called weights and biases. Each layer l {\displaystyle l} contains a weight matrix W ( l ) ∈ R n l − 1 × n l {\displaystyle W^{(l)}\in \mathbb {R} ^{n_{l-1}\times n_{l}}} and a bias vector b ( l ) ∈ R n l {\displaystyle b^{(l)}\in \mathbb {R} ^{n_{l}}} , where n l {\displaystyle n_{l}} is the number of neurons in that layer. A weight initialization method is an algorithm for setting the initial values for W ( l ) , b ( l ) {\displaystyle W^{(l)},b^{(l)}} for each layer l {\displaystyle l} . The simplest form is zero initialization: W ( l ) = 0 , b ( l ) = 0 {\displaystyle W^{(l)}=0,b^{(l)}=0} Zero initialization is usually used for initializing biases, but it is not used for initializing weights, as it leads to symmetry in the network, causing all neurons to learn the same features. In this page, we assume b = 0 {\displaystyle b=0} unless otherwise stated. Recurrent neural networks typically use activation functions with bounded range, such as sigmoid and tanh, since unbounded activation may cause exploding values. (Le, Jaitly, Hinton, 2015) suggested initializing weights in the recurrent parts of the network to identity and zero bias, similar to the idea of residual connections and LSTM with no forget gate. In most cases, the biases are initialized to zero, though some situations can use a nonzero initialization. For example, in multiplicative units, such as the forget gate of LSTM, the bias can be initialized to 1 to allow good gradient signal through the gate. For neurons with ReLU activation, one can initialize the bias to a small positive value like 0.1, so that the gradient is likely nonzero at initialization, avoiding the dying ReLU problem. == Random initialization == Random initialization means sampling the weights from a normal distribution or a uniform distribution, usually independently. === LeCun initialization === LeCun initialization, popularized in (LeCun et al., 1998), is designed to preserve the variance of neural activations during the forward pass. It samples each entry in W ( l ) {\displaystyle W^{(l)}} independently from a distribution with mean 0 and variance 1 / n l − 1 {\displaystyle 1/n_{l-1}} . For example, if the distribution is a continuous uniform distribution, then the distribution is U ( ± 3 / n l − 1 ) {\displaystyle {\mathcal {U}}(\pm {\sqrt {3/n_{l-1}}})} . === Glorot initialization === Glorot initialization (or Xavier initialization) was proposed by Xavier Glorot and Yoshua Bengio. It was designed as a compromise between two goals: to preserve activation variance during the forward pass and to preserve gradient variance during the backward pass. For uniform initialization, it samples each entry in W ( l ) {\displaystyle W^{(l)}} independently and identically from U ( ± 6 / ( n l + 1 + n l − 1 ) ) {\displaystyle {\mathcal {U}}(\pm {\sqrt {6/(n_{l+1}+n_{l-1})}})} . In the context, n l − 1 {\displaystyle n_{l-1}} is also called the "fan-in", and n l + 1 {\displaystyle n_{l+1}} the "fan-out". When the fan-in and fan-out are equal, then Glorot initialization is the same as LeCun initialization. === He initialization === As Glorot initialization performs poorly for ReLU activation, He initialization (or Kaiming initialization) was proposed by Kaiming He et al. for networks with ReLU activation. It samples each entry in W ( l ) {\displaystyle W^{(l)}} from N ( 0 , 2 / n l − 1 ) {\displaystyle {\mathcal {N}}(0,2/n_{l-1})} . === Orthogonal initialization === (Saxe et al. 2013) proposed orthogonal initialization: initializing weight matrices as uniformly random (according to the Haar measure) semi-orthogonal matrices, multiplied by a factor that depends on the activation function of the layer. It was designed so that if one initializes a deep linear network this way, then its training time until convergence is independent of depth. Sampling a uniformly random semi-orthogonal matrix can be done by initializing X {\displaystyle X} by IID sampling its entries from a standard normal distribution, then calculate ( X X ⊤ ) − 1 / 2 X {\displaystyle \left(XX^{\top }\right)^{-1/2}X} or its transpose, depending on whether X {\displaystyle X} is tall or wide. For CNN kernels with odd widths and heights, orthogonal initialization is done this way: initialize the central point by a semi-orthogonal matrix, and fill the other entries with zero. As an illustration, a kernel K {\displaystyle K} of shape 3 × 3 × c × c ′ {\displaystyle 3\times 3\times c\times c'} is initialized by filling K [ 2 , 2 , : , : ] {\displaystyle K[2,2,:,:]} with the entries of a random semi-orthogonal matrix of shape c × c ′ {\displaystyle c\times c'} , and the other entries with zero. (Balduzzi et al., 2017) used it with stride 1 and zero-padding. This is sometimes called the Orthogonal Delta initialization. Related to this approach, unitary initialization proposes to parameterize the weight matrices to be unitary matrices, with the result that at initialization they are random unitary matrices (and throughout training, they remain unitary). This is found to improve long-sequence modelling in LSTM. Orthogonal initialization has been generalized to layer-sequential unit-variance (LSUV) initialization. It is a data-dependent initialization method, and can be used in convolutional neural networks. It first initializes weights of each convolution or fully connected layer with orthonormal matrices. Then, proceeding from the first to the last layer, it runs a forward pass on a random minibatch, and divides the layer's weights by the standard deviation of its output, so that its output has variance approximately 1. === Fixup initialization === In 2015, the introduction of residual connections allowed very deep neural networks to be trained, much deeper than the ~20 layers of the previous state of the art (such as the VGG-19). Residual connections gave rise to their own weight initialization problems and strategies. These are sometimes called "normalization-free" methods, since using residual connection could stabilize the training of a deep neural network so much that normalizations become unnecessary. Fixup initialization is designed specifically for networks with residual connections and without batch normalization, as follows: Initialize the classification layer and the last layer of each residual branch to 0. Initialize every other layer using a standard method (such as He initialization), and scale only the weight layers inside residual branches by L − 1 2 m − 2 {\displaystyle L^{-{\frac {1}{2m-2}}}} . Add a scalar multiplier (initialized at 1) in every branch and a scalar bias (initialized at 0) before each convolution, linear, and element-wise activation layer. Similarly, T-Fixup initialization is designed for Transformers without layer normalization. === Others === Instead of initializing all weights with random values on the order of O ( 1 / n ) {\displaystyle O(1/{\sqrt {n}})} , sparse initialization initialized only a small subset of the weights with larger random values, and the other weights zero, so that the total variance is still on the order of O ( 1 ) {\displaystyle O(1)} . Random walk initialization was designed for MLP so that during backpropagation, the L2 norm of gradient at each layer performs an unbiased random walk as one moves from the last layer to the first. Looks linear initialization was designed to allow the neural network to behave like a deep linear network at initialization, since W R e L U ( x ) − W R e L U ( − x ) = W x {\displaystyle W\;\mathrm {ReLU} (x)-W\;\mathrm {ReLU} (-x)=Wx} . It initializes a matrix W {\displaystyle W} of shape R n 2 × m {\displaystyle \mathbb {R} ^{{\frac {n}{2}}\times m}} by any method, such as orthogonal initialization, t
Time-lock puzzle
A time-lock puzzle, or time-released cryptography, encrypts a message that cannot be decrypted until a specified amount of time has passed. The concept was first described by Timothy C. May, and a solution first introduced by Ron Rivest, Adi Shamir, and David A. Wagner in 1996. Time-lock puzzle are useful in cases where confidentiality of information is determined by time, such as a diarist who does not want their views released until 50 years after their death, an auction where bids are sealed until the bidding period is closed, electronic voting, and contract signing. They can additionally be used in creating further cryptographic primitives, such as verifiable delay functions and zero knowledge proofs. Time-released cryptography can be achieved through several different mechanisms. Use mathematical problems requiring sequential calculations to solve, and cannot be solved with parallelization. Thus, adding more computers to a problem will not help solve the problem faster. Use of a trusted agent, or multiple agents who each hold a part of the message and cryptographic keys, who release the message after a specified time period has passed. Distribute public encryption keys to users, and place private cryptographic keys with a trusted agent in an offline location, to be released at a later date.
Interplanetary Internet
The interplanetary Internet is a conceived computer network in space, consisting of a set of network nodes that can communicate with each other. These nodes are the planet's orbiters and landers, and the Earth ground stations. For example, the orbiters collect the scientific data from the Curiosity rover on Mars through near-Mars communication links, transmit the data to Earth through direct links from the Mars orbiters to the Earth ground stations via the NASA Deep Space Network, and finally the data routed through Earth's internal internet. Interplanetary communication is greatly delayed by interplanetary distances, as data transmission can only go as fast as the speed of light, so a new set of protocols and technologies that are tolerant to large delays and errors are required. The interplanetary Internet has been envisioned as a store and forward network of internets that is often disconnected, has a wireless backbone fraught with error-prone links and delays ranging from tens of minutes to even hours, even when there is a connection. As of 2024 agencies and companies working towards bringing the network to fruition include NASA, ESA, SpaceX and Blue Origin. == Challenges and reasons == In the core implementation of Interplanetary Internet, satellites orbiting a planet communicate to other planet's satellites. Simultaneously, these planets revolve around the Sun with long distances, and thus many challenges face the communications. The reasons and the resultant challenges are: The motion and long distances between planets: The interplanetary communication is greatly delayed due to the interplanetary distances and the motion of the planets. The delay is variable and long, ranging from a couple of minutes (Earth-to-Mars), to a couple of hours (Pluto-to-Earth), depending on their relative positions. The interplanetary communication also suspends due to the solar conjunction, when the sun's radiation hinders the direct communication between the planets. As such, the communication characterizes lossy links and intermittent link connectivity. Low embeddable payload: Satellites can only carry a small payload, which poses challenges to the power, mass, size, and cost for communication hardware design. An asymmetric bandwidth would be the result of this limitation. This asymmetry reaches ratios up to 1000:1 as downlink:uplink bandwidth portion. Absence of fixed infrastructure: The graph of participating nodes in a specific planet-to-planet communication keeps changing over time, due to the constant motion. The routes of the planet-to-planet communication are planned and scheduled rather than being opportunistic. The Interplanetary Internet design must address these challenges to operate successfully and achieve good communication with other planets. It also must use the few available resources efficiently in the system. == Development == Space communication technology has steadily evolved from expensive, one-of-a-kind point-to-point architectures, to the re-use of technology on successive missions, to the development of standard protocols agreed upon by space agencies of many countries. This last phase has gone on since 1982 through the efforts of the Consultative Committee for Space Data Systems (CCSDS), a body composed of the major space agencies of the world. It has 11 member agencies, 32 observer agencies, and over 119 industrial associates. The evolution of space data system standards has gone on in parallel with the evolution of the Internet, with conceptual cross-pollination where fruitful, but largely as a separate evolution. Since the late 1990s, familiar Internet protocols and CCSDS space link protocols have integrated and converged in several ways; for example, the successful FTP file transfer to Earth-orbiting STRV 1B on January 2, 1996, which ran FTP over the CCSDS IPv4-like Space Communications Protocol Specifications (SCPS) protocols. Internet Protocol use without CCSDS has taken place on spacecraft, e.g., demonstrations on the UoSAT-12 satellite, and operationally on the Disaster Monitoring Constellation. Having reached the era where networking and IP on board spacecraft have been shown to be feasible and reliable, a forward-looking study of the bigger picture was the next phase. The Interplanetary Internet study at NASA's Jet Propulsion Laboratory (JPL) was started by a team of scientists at JPL led by internet pioneer Vinton Cerf and the late Adrian Hooke. Cerf was appointed as a distinguished visiting scientist at JPL in 1998, while Hooke was one of the founders and directors of CCSDS. While IP-like SCPS protocols are feasible for short hops, such as ground station to orbiter, rover to lander, lander to orbiter, probe to flyby, and so on, delay-tolerant networking is needed to get information from one region of the Solar System to another. It becomes apparent that the concept of a region is a natural architectural factoring of the Interplanetary Internet. A region is an area where the characteristics of communication are the same. Region characteristics include communications, security, the maintenance of resources, perhaps ownership, and other factors. The Interplanetary Internet is a "network of regional internets". What is needed then, is a standard way to achieve end-to-end communication through multiple regions in a disconnected, variable-delay environment using a generalized suite of protocols. Examples of regions might include the terrestrial Internet as a region, a region on the surface of the Moon or Mars, or a ground-to-orbit region. The recognition of this requirement led to the concept of a "bundle" as a high-level way to address the generalized Store-and-Forward problem. Bundles are an area of new protocol development in the upper layers of the OSI model, above the Transport Layer with the goal of addressing the issue of bundling store-and-forward information so that it can reliably traverse radically dissimilar environments constituting a "network of regional internets". Delay-tolerant networking (DTN) was designed to enable standardized communications over long distances and through time delays. At its core is the Bundle Protocol (BP), which is similar to the Internet Protocol, or IP, that serves as the heart of the Internet here on Earth. The big difference between the regular Internet Protocol (IP) and the Bundle Protocol is that IP assumes a seamless end-to-end data path, while BP is built to account for errors and disconnections — glitches that commonly plague deep-space communications. Bundle Service Layering, implemented as the Bundling protocol suite for delay-tolerant networking, will provide general-purpose delay-tolerant protocol services in support of a range of applications: custody transfer, segmentation and reassembly, end-to-end reliability, end-to-end security, and end-to-end routing among them. The Bundle Protocol was first tested in space on the UK-DMC satellite in 2008. An example of one of these end-to-end applications flown on a space mission is the CCSDS File Delivery Protocol (CFDP), used on the Deep Impact comet mission. CFDP is an international standard for automatic, reliable file transfer in both directions. CFDP should not be confused with Coherent File Distribution Protocol, which has the same acronym and is an IETF-documented experimental protocol for rapidly deploying files to multiple targets in a highly networked environment. In addition to reliably copying a file from one entity (such as a spacecraft or ground station) to another entity, CFDP has the capability to reliably transmit arbitrarily small messages defined by the user, in the metadata accompanying the file, and to reliably transmit commands relating to file system management that are to be executed automatically on the remote end-point entity (such as a spacecraft) upon successful reception of a file. == Protocol == The Consultative Committee for Space Data Systems (CCSDS) packet telemetry standard defines the protocol used for the transmission of spacecraft instrument data over the deep-space channel. Under this standard, an image or other data sent from a spacecraft instrument is transmitted using one or more packets. === CCSDS packet definition === A packet is a block of data with length that can vary between successive packets, ranging from 7 to 65,542 bytes, including the packet header. Packetized data is transmitted via frames, which are fixed-length data blocks. The size of a frame, including frame header and control information, can range up to 2048 bytes. Packet sizes are fixed during the development phase. Because packet lengths are variable but frame lengths are fixed, packet boundaries usually do not coincide with frame boundaries. === Telecom processing notes === Data in a frame is typically protected from channel errors by error-correcting codes. Even when the channel errors exceed the correction capability of the error-correcting code, the presence of errors is nearly always detected by the e
PitchYaGame
PitchYaGame or #PitchYaGame (sometimes abbreviated to PYG) is a volunteer movement hosted on the social media platform Twitter to showcase, and present awards for, independent video games from around the world. == Description == PitchYaGame is hosted on the social media platform Twitter to showcase independent video games from around the world. Video pitches are presented by developers in June and November each year, and use the hashtag #PitchYaGame to identify and reference news about the showcase and the individual pitches, and the presentation of awards. The showcase was founded in May 2020 by Liam Twose, with the mission of recognising independent video games, and "focused on empowering indie game developers to strengthen their position in the industry." Twose has made clear that PitchYaGame is a showcase and not a hardcore competition, with "[j]ust enough of a push to make sure people put their best pitch forward." The team now comprises Twose (@LiamTwose at Twitter), operations manager "Indie Game Lover" (@IndieGameLover), and host Sarah Clancy (@ImSarahNow). The pitches were originally made monthly, with entries split into a number of categories, but this proved unmanageable. PitchYaGame collaborator, Sarah Clancy reported that judging the many entries on a monthly basis was "difficult and unwieldy." Therefore, pitches were later switched to six monthly, "feature creep" was reduced, and awards streamlined into gold, silver, bronze, runners-up, and most viral. == Sponsorship == In June 2021, PitchYaGame prizes were sponsored by Xsolla, and in November 2021 by Aurora Punks and Cold Pixel. No cash prizes were available in 2022, as the organisers moved PitchYaGame into a less-competitive, "more showcase centric format". == Reception == In October 2020, Elijah Beahm at The Escapist wrote that "One of the greatest challenges for any game is landing a solid pitch. You have to sell people, maybe even a publisher, to take your idea seriously. Most of the time, it's an obfuscated process that leaves the average developer scratching their heads, but Liam Twose and his team behind #PitchYaGame, 'PYG' for short, are looking to change all that with some clever social engineering." In March 2021, Cameron Koch at GameSpot wrote that "Using the #PitchYaGame, thousands of indie developers tweeted out pitches for their games on November 2 as part of a social media contest, and the results are astounding." He went on to say that "There is no arguing with the results. According to Twose, around 1100-1300 games were shared with the hashtag, and some real gems look to have shined through." In November 2021, Stafano "Stef" Castelli at IGN Italia wrote that "I myself enjoyed 'browsing through' the competitors, discovering a handful of intriguing video games in development." (translated from Italian). In November 2022, Eric Bartelson at Premortem Games wrote that "It's a great way to get games noticed by fellow developers, but also publishers, investors and press." In June 2023, Mark Plunkett in Kotaku wrote about the impossibility of keeping up with all the video game releases, and described PitchYaGame, which has attracted over 10,000 pitches since 2020, as an "astoundingly simple idea" that has "become an increasingly useful spot to catch up on some excellent-looking games that we may have otherwise completely slept on."
Gooch shading
Gooch shading is a non-photorealistic rendering technique for shading objects. It is also known as "cool to warm" shading, and is widely used in technical illustration. == History == Gooch shading was developed by Amy Gooch et al. at the University of Utah School of Computing and first presented at the 1998 SIGGRAPH conference. It has since been implemented in shader libraries, software, and games released by Autodesk, Nvidia, and Valve. == Process == Gooch shading defines an additional two colors in conjunction with the original model color: a warm color (such as yellow) and a cool color (such as blue). The warm color indicates surfaces that are facing toward the light source while the cool color indicates surfaces facing away. This allows shading to occur only in mid-tones so that edge lines and highlights remain visually prominent. The Gooch shader is typically implemented in two passes: all objects in the scene are first drawn with the "cool to warm" shading, and in the second pass the object's edges are rendered in black.
Batch cryptography
Batch cryptography is a field of cryptology focused on the design of cryptographic protocols that perform operations—such as encryption, decryption, key exchange, and authentication—on multiple inputs simultaneously, rather than processing each input individually. Batching cryptographic operations can significantly reduce the marginal cost of handling individual inputs—a principle that was first introduced by Amos Fiat in 1989.