Knights of Sidonia (Japanese: シドニアの騎士, Hepburn: Shidonia no Kishi) is a Japanese manga series written and illustrated by Tsutomu Nihei. It was serialized by Kodansha's seinen manga magazine Monthly Afternoon between April 2009 and September 2015, with its chapters collected in 15 tankōbon volumes. It tells the story of Nagate Tanikaze, an "under-dweller" destined to become a Garde pilot, whose mission is to defend the generation ship Sidonia from a hostile alien species called Gauna. The manga was licensed for English release in North America by Vertical. An anime television series adaptation was produced by Polygon Pictures. The first season aired from April to June 2014; the second between April and June 2015. An anime film sequel titled Knights of Sidonia: Love Woven in the Stars premiered in June 2021. In 2015, Knights of Sidonia received the 39th Kodansha Manga Award in the general category, as well as the 47th Seiun Award in the Best Comic category in 2016. == Plot == === Setting === The story is set in the year 3394, a thousand years after mankind flees from Earth after it was destroyed by a race of shapeshifting aliens called the Gauna (奇居子（ガウナ）), aboard hundreds of colossal spacecraft created from the remains of the planet. One such ship is the Sidonia, which has developed its own human culture closely based on that of Japan where human cloning, asexual reproduction, and human genetic engineering, such as granting humans photosynthesis, are commonplace. It is also revealed that the top echelons of this society have secretly been granted immortality. With a population of over 500,000 people, Sidonia is possibly the last human settlement remaining, as the fates of the other ships are unknown. Little is known about the true nature of the Gauna or their motivation for attacking humanity. At any given time, a Gauna consists of a nearly impenetrable core protected by a dense layer of malleable flesh known as "placenta" (胞衣, ena). Once the ena is shed away and the core is destroyed, the Gauna's body disintegrates. While Sidonia itself is heavily armed with an arsenal of high-output beam cannons and mass cannons including slow but powerful planet-destroying warheads, it is primarily defended by large mechanized weapons called Gardes (衛人, Morito) whose weaponry and mobility is powered by "Higgs particles" (ヘイグス粒子, Heigusu Ryūshi), armed with a high-output beam cannon for long range assaults and a special spear known as "Kabizashi" for close combat. The tip of the kabizashi is made of a rare and little-understood material which has the unique property of being able to destroy a Gauna's core. Later the Gardes are also equipped with firearms whose ammunition have the same material of the Kabizashi after a means to artificially mass-produce it is discovered. Most people in the surviving human population are screened and drafted as Garde pilots at a young age, if they are shown to be capable of piloting them. === Story === The story follows the adventures of Garde pilot Nagate Tanikaze, who lived in the underground layer of Sidonia since birth and was raised by his grandfather. Never having met anyone else, he trains himself in an old Guardian pilot simulator every day, eventually mastering it. After his grandfather's death, he emerges to the surface and is selected as a Garde pilot, just as Sidonia is once again threatened by the Gauna. == Media == === Manga === Written and illustrated by Tsutomu Nihei, Knights of Sidonia was serialized in Kodansha's seinen manga magazine Monthly Afternoon from April 25, 2009, to September 25, 2015. It was compiled in 15 tankōbon volumes. The manga has been licensed in North America by Vertical, who released all 15 volumes in English between February 5, 2013, and April 26, 2016. === Anime === An anime television series adaptation, produced by Polygon Pictures, aired its first season from April 10 to June 26, 2014, on MBS and later on TBS, CBC and BS-TBS. The series was directed by Kōbun Shizuno, assisted by Hiroyuki Seshita, with scripts by Sadayuki Murai and character designs by Yuki Moriyama. The opening theme song is "Sidonia" (シドニア, Shidonia), performed by Angela, while the ending theme song is "Show" (掌 -show-, Shō), performed by Eri Kitamura. A second season aired from April 11 to June 26, 2015. For the second season, the opening theme song is "Kishi Kōshinkyoku" (騎士行進曲, Knight March), performed by Angela, while the ending theme song is "Requiem" (鎮魂歌 -レクイエム-, Rekuiemu), performed by CustomiZ. The series was localized and streamed by Netflix in all of its territories since July 4, 2014, becoming the service's first original anime, as well as the first anime series on Netflix available in Dolby Vision/HDR. The first season has been licensed for home video release by Sentai Filmworks. The second season was released on Netflix on July 3, 2015, and has been licensed by Sentai Filmworks for home video distribution. In July 2021, Funimation announced they acquired the streaming rights from Netflix to both seasons. === Films === A compilation film of the first season with additional scenes and re-edited sound effects was released on March 6, 2015. A new anime film, titled Knights of Sidonia: Love Woven in the Stars, was announced on July 3, 2020. Hiroyuki Seshita served as chief director, while Tadahiro Yoshihira served as director for the new film, with Polygon Pictures returning for production. Sadayuki Murai and Tetsuya Yamada returned to write scripts, while Shūji Katayama composed the music. The rest of the staff and cast returned to reprise their roles. The first four minutes of the film were shown on YouTube on April 28, 2021. The film was set to premiere on May 14, 2021, but was delayed to June 4, 2021, due to the COVID-19 pandemic. Funimation screened the film in international theaters starting on September 13, 2021. == Reception == === Manga === Knights of Sidonia won the 39th Kodansha Manga Award in the general category in 2015. The manga won the 47th Seiun Award in the Best Comic category in 2016. It also won the Best Seinen category at the 26th Salón del Manga de Barcelona in 2020. It was one of the Jury Recommended works in the Manga Division at the 17th Japan Media Arts Festival in 2013. The Young Adult Library Services Association listed Knights of Sidonia in its 2014 list of Top 10 Graphic Novels for Teens. Carlo Santos from Anime News Network gave the first manga volume a B, stating, "It is got a young man piloting a giant robot against alien enemies, but Knight of Sidonia is no Neon Genesis Evangelion. Yet it is not as bleak or incomprehensible as Tsutomu Nihei works like Blame! or Biomega, either—rather, it is the best of both worlds, bringing Nihei's hard sci-fi mentality into a more conventional space-adventure environment". === Anime === The anime series received positive reviews, even from famous members of the Japanese anime/game industry, like Hideo Kojima, creator of the Metal Gear series, who claims that "It's a kind of anime that we haven't seen for a while that has that sci-fi spirit. Using digital technology cultivated through games, it creates animation that encapsulates Japan's cultural assets like manga, cel animation, kanji, giant robots, etc. What's born is a unique made-in-Japan work that could never be cooked up in Hollywood. Japanese culture has lost its 'cool', and Knights of Sidonia will be the white knight that saves it". Other industry pros left acknowledgements as well, including Akiko Higashimura, Digitarou and Yoshinao Dao.
Bigram
A bigram or digram is a sequence of two adjacent elements from a string of tokens, which are typically letters, syllables, or words. A bigram is an n-gram for n=2. The frequency distribution of every bigram in a string is commonly used for simple statistical analysis of text in many applications, including in computational linguistics, cryptography, and speech recognition. Gappy bigrams or skipping bigrams are word pairs which allow gaps (perhaps avoiding connecting words, or allowing some simulation of dependencies, as in a dependency grammar). == Applications == Bigrams, along with other n-grams, are used in most successful language models for speech recognition. Bigram frequency attacks can be used in cryptography to solve cryptograms. See frequency analysis. Bigram frequency is one approach to statistical language identification. Some activities in logology or recreational linguistics involve bigrams. These include attempts to find English words beginning with every possible bigram, or words containing a string of repeated bigrams, such as logogogue. == Bigram frequency in the English language == The frequency of the most common letter bigrams in a large English corpus is: th 3.56% of 1.17% io 0.83% he 3.07% ed 1.17% le 0.83% in 2.43% is 1.13% ve 0.83% er 2.05% it 1.12% co 0.79% an 1.99% al 1.09% me 0.79% re 1.85% ar 1.07% de 0.76% on 1.76% st 1.05% hi 0.76% at 1.49% to 1.05% ri 0.73% en 1.45% nt 1.04% ro 0.73% nd 1.35% ng 0.95% ic 0.70% ti 1.34% se 0.93% ne 0.69% es 1.34% ha 0.93% ea 0.69% or 1.28% as 0.87% ra 0.69% te 1.20% ou 0.87% ce 0.65%
Wetware (brain)
Wetware is a term drawn from the computer-related idea of hardware or software, but applied to biological life forms. == Usage == The prefix "wet" is a reference to the water found in living creatures. Wetware is used to describe the elements equivalent to hardware and software found in a person, especially the central nervous system (CNS) and the human mind. The term wetware finds use in works of fiction, in scholarly publications and in popularizations. The "hardware" component of wetware concerns the bioelectric and biochemical properties of the CNS, specifically the brain. If the sequence of impulses traveling across the various neurons are thought of symbolically as software, then the physical neurons would be the hardware. The amalgamated interaction of this software and hardware is manifested through continuously changing physical connections, and chemical and electrical influences that spread across the body. The process by which the mind and brain interact to produce the collection of experiences that we define as self-awareness is in question. == History == Although the exact definition has shifted over time, the term Wetware and its fundamental reference to "the physical mind" has been around at least since the mid-1950s. Mostly used in relatively obscure articles and papers, it was not until the heyday of cyberpunk, however, that the term found broad adoption. Among the first uses of the term in popular culture was the Bruce Sterling novel Schismatrix (1985) and the Michael Swanwick novel Vacuum Flowers (1987). Rudy Rucker references the term in a number of books, including one entitled Wetware (1988): ... all sparks and tastes and tangles, all its stimulus/response patterns – the whole bio-cybernetic software of mind. Rucker did not use the word to simply mean a brain, nor in the human-resources sense of employees. He used wetware to stand for the data found in any biological system, analogous perhaps to the firmware that is found in a ROM chip. In Rucker's sense, a seed, a plant graft, an embryo, or a biological virus are all wetware. DNA, the immune system, and the evolved neural architecture of the brain are further examples of wetware in this sense. Rucker describes his conception in a 1992 compendium The Mondo 2000 User's Guide to the New Edge, which he quotes in a 2007 blog entry. Early cyber-guru Arthur Kroker used the term in his blog. With the term getting traction in trendsetting publications, it became a buzzword in the early 1990s. In 1991, Dutch media theorist Geert Lovink organized the Wetware Convention in Amsterdam, which was supposed to be an antidote to the "out-of-body" experiments conducted in high-tech laboratories, such as experiments in virtual reality. Timothy Leary, in an appendix to Info-Psychology originally written in 1975–76 and published in 1989, used the term wetware, writing that "psychedelic neuro-transmitters were the hot new technology for booting-up the 'wetware' of the brain". Another common reference is: "Wetware has 7 plus or minus 2 temporary registers." The numerical allusion is to a classic 1957 article by George A. Miller, The magical number 7 plus or minus two: some limits in our capacity for processing information, which later gave way to Miller's law.
Learning rate
In machine learning and statistics, the learning rate is a tuning parameter in an optimization algorithm that determines the step size at each iteration while moving toward a minimum of a loss function. Since it influences to what extent newly acquired information overrides old information, it metaphorically represents the speed at which a machine learning model "learns". In the adaptive control literature, the learning rate is commonly referred to as gain. In setting a learning rate, there is a trade-off between the rate of convergence and overshooting. While the descent direction is usually determined from the gradient of the loss function, the learning rate determines how big a step is taken in that direction. Too high a learning rate will make the learning jump over minima, but too low a learning rate will either take too long to converge or get stuck in an undesirable local minimum. In order to achieve faster convergence, prevent oscillations and getting stuck in undesirable local minima the learning rate is often varied during training either in accordance to a learning rate schedule or by using an adaptive learning rate. The learning rate and its adjustments may also differ per parameter, in which case it is a diagonal matrix that can be interpreted as an approximation to the inverse of the Hessian matrix in Newton's method. The learning rate is related to the step length determined by inexact line search in quasi-Newton methods and related optimization algorithms. == Learning rate schedule == Initial rate can be left as system default or can be selected using a range of techniques. A learning rate schedule changes the learning rate during learning and is most often changed between epochs/iterations. This is mainly done with two parameters: decay and momentum. There are many different learning rate schedules but the most common are time-based, step-based and exponential. Decay serves to settle the learning in a nice place and avoid oscillations, a situation that may arise when too high a constant learning rate makes the learning jump back and forth over a minimum, and is controlled by a hyperparameter. Momentum is analogous to a ball rolling down a hill; we want the ball to settle at the lowest point of the hill (corresponding to the lowest error). Momentum both speeds up the learning (increasing the learning rate) when the error cost gradient is heading in the same direction for a long time and also avoids local minima by 'rolling over' small bumps. Momentum is controlled by a hyperparameter analogous to a ball's mass which must be chosen manually—too high and the ball will roll over minima which we wish to find, too low and it will not fulfil its purpose. The formula for factoring in the momentum is more complex than for decay but is most often built in with deep learning libraries such as Keras. Time-based learning schedules alter the learning rate depending on the learning rate of the previous time iteration. Factoring in the decay the mathematical formula for the learning rate is: η n + 1 = η 0 1 + d n {\displaystyle \eta _{n+1}={\frac {\eta _{0}}{1+dn}}} where η {\displaystyle \eta } is the learning rate, η 0 {\displaystyle \eta _{0}} is the original learning rate, d {\displaystyle d} is a decay parameter and n {\displaystyle n} is the iteration step. Step-based learning schedules changes the learning rate according to some predefined steps. The decay application formula is here defined as: η n = η 0 d ⌊ 1 + n r ⌋ {\displaystyle \eta _{n}=\eta _{0}d^{\left\lfloor {\frac {1+n}{r}}\right\rfloor }} where η n {\displaystyle \eta _{n}} is the learning rate at iteration n {\displaystyle n} , η 0 {\displaystyle \eta _{0}} is the initial learning rate, d {\displaystyle d} is how much the learning rate should change at each drop (0.5 corresponds to a halving) and r {\displaystyle r} corresponds to the drop rate, or how often the rate should be dropped (10 corresponds to a drop every 10 iterations). The floor function ( ⌊ … ⌋ {\displaystyle \lfloor \dots \rfloor } ) here drops the value of its input to 0 for all values smaller than 1. Exponential learning schedules are similar to step-based, but instead of steps, a decreasing exponential function is used. The mathematical formula for factoring in the decay is: η n = η 0 e − d n {\displaystyle \eta _{n}=\eta _{0}e^{-dn}} where d {\displaystyle d} is a decay parameter. == Adaptive learning rate == The issue with learning rate schedules is that they all depend on hyperparameters that must be manually chosen for each given learning session and may vary greatly depending on the problem at hand or the model used. To combat this, there are many different types of adaptive gradient descent algorithms such as Adagrad, Adadelta, RMSprop, and Adam which are generally built into deep learning libraries such as Keras.
Concept drift
In predictive analytics, data science, machine learning and related fields, concept drift or drift is an evolution of data that invalidates the data model. It happens when the statistical properties of the target variable, which the model is trying to predict, change over time in unforeseen ways. This causes problems because the predictions become less accurate as time passes. Drift detection and drift adaptation are of paramount importance in the fields that involve dynamically changing data and data models. == Predictive model decay == In machine learning and predictive analytics this drift phenomenon is called concept drift. In machine learning, a common element of a data model are the statistical properties, such as probability distribution of the actual data. If they deviate from the statistical properties of the training data set, then the learned predictions may become invalid, if the drift is not addressed. == Data configuration decay == Another important area is software engineering, where three types of data drift affecting data fidelity may be recognized. Changes in the software environment ("infrastructure drift") may invalidate software infrastructure configuration. "Structural drift" happens when the data schema changes, which may invalidate databases. "Semantic drift" is changes in the meaning of data while the structure does not change. In many cases this may happen in complicated applications when many independent developers introduce changes without proper awareness of the effects of their changes in other areas of the software system. For many application systems, the nature of data on which they operate are subject to changes for various reasons, e.g., due to changes in business model, system updates, or switching the platform on which the system operates. In the case of cloud computing, infrastructure drift that may affect the applications running on cloud may be caused by the updates of cloud software. There are several types of detrimental effects of data drift on data fidelity. Data corrosion is passing the drifted data into the system undetected. Data loss happens when valid data are ignored due to non-conformance with the applied schema. Squandering is the phenomenon when new data fields are introduced upstream in the data processing pipeline, but somewhere downstream these data fields are absent. == Inconsistent data == "Data drift" may refer to the phenomenon when database records fail to match the real-world data due to the changes in the latter over time. This is a common problem with databases involving people, such as customers, employees, citizens, residents, etc. Human data drift may be caused by unrecorded changes in personal data, such as place of residence or name, as well as due to errors during data input. "Data drift" may also refer to inconsistency of data elements between several replicas of a database. The reasons can be difficult to identify. A simple drift detection is to run checksum regularly. However the remedy may be not so easy. == Examples == The behavior of the customers in an online shop may change over time. For example, if weekly merchandise sales are to be predicted, and a predictive model has been developed that works satisfactorily. The model may use inputs such as the amount of money spent on advertising, promotions being run, and other metrics that may affect sales. The model is likely to become less and less accurate over time – this is concept drift. In the merchandise sales application, one reason for concept drift may be seasonality, which means that shopping behavior changes seasonally. Perhaps there will be higher sales in the winter holiday season than during the summer, for example. Concept drift generally occurs when the covariates that comprise the data set begin to explain the variation of your target set less accurately — there may be some confounding variables that have emerged, and that one simply cannot account for, which renders the model accuracy to progressively decrease with time. Generally, it is advised to perform health checks as part of the post-production analysis and to re-train the model with new assumptions upon signs of concept drift. == Possible remedies == To prevent deterioration in prediction accuracy because of concept drift, reactive and tracking solutions can be adopted. Reactive solutions retrain the model in reaction to a triggering mechanism, such as a change-detection test or control charts from statistical process control, to explicitly detect concept drift as a change in the statistics of the data-generating process. When concept drift is detected, the current model is no longer up-to-date and must be replaced by a new one to restore prediction accuracy. A shortcoming of reactive approaches is that performance may decay until the change is detected. Tracking solutions seek to track the changes in the concept by continually updating the model. Methods for achieving this include online machine learning, frequent retraining on the most recently observed samples, and maintaining an ensemble of classifiers where one new classifier is trained on the most recent batch of examples and replaces the oldest classifier in the ensemble. Contextual information, when available, can be used to better explain the causes of the concept drift: for instance, in the sales prediction application, concept drift might be compensated by adding information about the season to the model. By providing information about the time of the year, the rate of deterioration of your model is likely to decrease, but concept drift is unlikely to be eliminated altogether. This is because actual shopping behavior does not follow any static, finite model. New factors may arise at any time that influence shopping behavior, the influence of the known factors or their interactions may change. Concept drift cannot be avoided for complex phenomena that are not governed by fixed laws of nature. All processes that arise from human activity, such as socioeconomic processes, and biological processes are likely to experience concept drift. Therefore, periodic retraining, also known as refreshing, of any model is necessary. === Remedy methods === DDM (Drift Detection Method): detects drift by monitoring the model's error rate over time. When the error rate passes a set threshold, it enters a warning phase, and if it passes another threshold, it enters a drift phase. EDDM (Early Drift Detection Method): improves DDM's detection rate by tracking the average distance between two errors instead of only the error rate. ADWIN (Adaptive Windowing): dynamically stores a window of recent data and warns the user if it detects a significant change between the statistics of the window's earlier data compared to more recent data. KSWIN (Kolmogorov–Smirnov Windowing): detects drift based on the Kolmogorov-Smirnov statistical test. DDM and EDDM: Concept Drift Detection online supervised methods that rely on sequential error monitoring to estimate the evolving error rate. ADWIN and KSWIN: Windowing maintain a "window", a subset of the most recent data, of the data stream, which it checks for statistical differences across the window. == Applications in security == Concept drift is a recurring issue in security analytics, especially in malware and intrusion detection. In these systems, models are often trained on past logs, binaries or network traces, but the behaviour of attackers changes over time as new malware families, obfuscation techniques and campaigns appear. When the data no longer resemble the training set, the decision boundaries learned by classifiers or anomaly detectors can become misaligned with the current threat landscape and detection performance can drop unless the models are updated or replaced. Several studies on Windows malware model detection as an evolving data stream and track how performance changes as time passes. They show that classifiers trained on a fixed time window can perform well on nearby data but deteriorate quickly when evaluated on samples collected months or years later, even when large amounts of training data are available. In order to keep up with this, security systems often use sliding or adaptive windows, which restrict training to the most recent portion of the data so that older, less relevant examples are gradually discarded. They also employ drift detectors such as ADWIN and KSWIN that monitor error rates or changes in the distribution of recent observations and signal when the statistics of the incoming stream differ significantly from the past, prompting retraining or model replacement. Related problems appear in spam filtering, fraud detection and intrusion detection, where adversaries change content, patterns of activity or network behavior to evade models trained on historical data. In these settings drift can be gradual, as new types of spam or fraud emerge, or abrupt, after a sudden shift in attack techniques. Common strategies to remain eff
Tribute (website)
Tribute is an American video-sharing website headquartered in Brooklyn. Created in 2014 by Andrew Horn and Rory Petty, the platform lets customers create video montages (called "tributes") for occasions including weddings, birthdays, anniversaries, get well soon, and memorials. Tribute.co allows users to record video messages, request submissions from friends and family, insert photos, add music, and send the resulting video tribute montage to a recipient. == Overview == Tribute's collaborative technology starts with inviting people to contribute via email, SMS or social media. Participants receive a prompt to record a short video via their phone, computer or tablet. The site's video editing software allows users to drag and drop the clips in their desired order without prior video editing experience. == History == When Andrew Horn turned twenty-seven, his girlfriend, Miki Agrawal surprised him with a video montage containing clips of his family and closest friends explaining why they loved him. This resulted in Andrew's idea to create Tribute–a "living eulogy" video-compilation service that he co-founded with software engineer Rory Petty. Founded in 2014, Tribute's activity accelerated in 2020 due to the COVID-19 pandemic, and it had sent over 5 million videos as of December 2021. While social distance restrictions were in effect, the site provided a way for people to connect while in-person celebrations were put on hold. For each video sold, Tribute makes one available to hospitals for free and has partnered with Cleveland Clinic Cancer Center in Ohio, Lurie Children's Hospital in Illinois and CarePoint Health in New Jersey.
Exploration–exploitation dilemma
The exploration–exploitation dilemma, also known as the explore–exploit tradeoff, is a fundamental concept in decision-making that arises in many domains. It is depicted as the balancing act between two opposing strategies. Exploitation involves choosing the best option based on current knowledge of the system (which may be incomplete or misleading), while exploration involves trying out new options that may lead to better outcomes in the future at the expense of an exploitation opportunity. Finding the optimal balance between these two strategies is a crucial challenge in many decision-making problems whose goal is to maximize long-term benefits. == Application in machine learning == In the context of machine learning, the exploration–exploitation tradeoff is fundamental in reinforcement learning (RL), a type of machine learning that involves training agents to make decisions based on feedback from the environment. Crucially, this feedback may be incomplete or delayed. The agent must decide whether to exploit the current best-known policy or explore new policies to improve its performance. === Multi-armed bandit methods === The multi-armed bandit (MAB) problem was a classic example of the tradeoff, and many methods were developed for it, such as epsilon-greedy, Thompson sampling, and the upper confidence bound (UCB). See the page on MAB for details. In more complex RL situations than the MAB problem, the agent can treat each choice as a MAB, where the payoff is the expected future reward. For example, if the agent performs an epsilon-greedy method, then the agent will often "pull the best lever" by picking the action that had the best predicted expected reward (exploit). However, it would pick a random action with probability epsilon (explore). Monte Carlo tree search, for example, uses a variant of the UCB method. === Exploration problems === There are some problems that make exploration difficult. Sparse reward. If rewards occur only once a long while, then the agent might not persist in exploring. Furthermore, if the space of actions is large, then the sparse reward would mean the agent would not be guided by the reward to find a good direction for deeper exploration. A standard example is Montezuma's Revenge. Deceptive reward. If some early actions give immediate small reward, but other actions give later large reward, then the agent might be lured away from exploring the other actions. Noisy TV problem. If certain observations are irreducibly noisy (such as a television showing random images), then the agent might be trapped exploring those observations (watching the television). === Exploration reward === This section based on. The exploration reward (also called exploration bonus) methods convert the exploration-exploitation dilemma into a balance of exploitations. That is, instead of trying to get the agent to balance exploration and exploitation, exploration is simply treated as another form of exploitation, and the agent simply attempts to maximize the sum of rewards from exploration and exploitation. The exploration reward can be treated as a form of intrinsic reward. We write these as r t i , r t e {\displaystyle r_{t}^{i},r_{t}^{e}} , meaning the intrinsic and extrinsic rewards at time step t {\displaystyle t} . However, exploration reward is different from exploitation in two regards: The reward of exploitation is not freely chosen, but given by the environment, but the reward of exploration may be picked freely. Indeed, there are many different ways to design r t i {\displaystyle r_{t}^{i}} described below. The reward of exploitation is usually stationary (i.e. the same action in the same state gives the same reward), but the reward of exploration is non-stationary (i.e. the same action in the same state should give less and less reward). Count-based exploration uses N n ( s ) {\displaystyle N_{n}(s)} , the number of visits to a state s {\displaystyle s} during the time-steps 1 : n {\displaystyle 1:n} , to calculate the exploration reward. This is only possible in small and discrete state space. Density-based exploration extends count-based exploration by using a density model ρ n ( s ) {\displaystyle \rho _{n}(s)} . The idea is that, if a state has been visited, then nearby states are also partly-visited. In maximum entropy exploration, the entropy of the agent's policy π {\displaystyle \pi } is included as a term in the intrinsic reward. That is, r t i = − ∑ a π ( a | s t ) ln π ( a | s t ) + ⋯ {\displaystyle r_{t}^{i}=-\sum _{a}\pi (a|s_{t})\ln \pi (a|s_{t})+\cdots } . === Prediction-based === This section based on. The forward dynamics model is a function for predicting the next state based on the current state and the current action: f : ( s t , a t ) ↦ s t + 1 {\displaystyle f:(s_{t},a_{t})\mapsto s_{t+1}} . The forward dynamics model is trained as the agent plays. The model becomes better at predicting state transition for state-action pairs that had been done many times. A forward dynamics model can define an exploration reward by r t i = ‖ f ( s t , a t ) − s t + 1 ‖ 2 2 {\displaystyle r_{t}^{i}=\|f(s_{t},a_{t})-s_{t+1}\|_{2}^{2}} . That is, the reward is the squared-error of the prediction compared to reality. This rewards the agent to perform state-action pairs that had not been done many times. This is however susceptible to the noisy TV problem. Dynamics model can be run in latent space. That is, r t i = ‖ f ( s t , a t ) − ϕ ( s t + 1 ) ‖ 2 2 {\displaystyle r_{t}^{i}=\|f(s_{t},a_{t})-\phi (s_{t+1})\|_{2}^{2}} for some featurizer ϕ {\displaystyle \phi } . The featurizer can be the identity function (i.e. ϕ ( x ) = x {\displaystyle \phi (x)=x} ), randomly generated, the encoder-half of a variational autoencoder, etc. A good featurizer improves forward dynamics exploration. The Intrinsic Curiosity Module (ICM) method trains simultaneously a forward dynamics model and a featurizer. The featurizer is trained by an inverse dynamics model, which is a function for predicting the current action based on the features of the current and the next state: g : ( ϕ ( s t ) , ϕ ( s t + 1 ) ) ↦ a t {\displaystyle g:(\phi (s_{t}),\phi (s_{t+1}))\mapsto a_{t}} . By optimizing the inverse dynamics, both the inverse dynamics model and the featurizer are improved. Then, the improved featurizer improves the forward dynamics model, which improves the exploration of the agent. Random Network Distillation (RND) method attempts to solve this problem by teacher–student distillation. Instead of a forward dynamics model, it has two models f , f ′ {\displaystyle f,f'} . The f ′ {\displaystyle f'} teacher model is fixed, and the f {\displaystyle f} student model is trained to minimize ‖ f ( s ) − f ′ ( s ) ‖ 2 2 {\displaystyle \|f(s)-f'(s)\|_{2}^{2}} on states s {\displaystyle s} . As a state is visited more and more, the student network becomes better at predicting the teacher. Meanwhile, the prediction error is also an exploration reward for the agent, and so the agent learns to perform actions that result in higher prediction error. Thus, we have a student network attempting to minimize the prediction error, while the agent attempting to maximize it, resulting in exploration. The states are normalized by subtracting a running average and dividing a running variance, which is necessary since the teacher model is frozen. The rewards are normalized by dividing with a running variance. Exploration by disagreement trains an ensemble of forward dynamics models, each on a random subset of all ( s t , a t , s t + 1 ) {\displaystyle (s_{t},a_{t},s_{t+1})} tuples. The exploration reward is the variance of the models' predictions. === Noise === For neural network–based agents, the NoisyNet method changes some of its neural network modules by noisy versions. That is, some network parameters are random variables from a probability distribution. The parameters of the distribution are themselves learnable. For example, in a linear layer y = W x + b {\displaystyle y=Wx+b} , both W , b {\displaystyle W,b} are sampled from Gaussian distributions N ( μ W , Σ W ) , N ( μ b , Σ b ) {\displaystyle {\mathcal {N}}(\mu _{W},\Sigma _{W}),{\mathcal {N}}(\mu _{b},\Sigma _{b})} at every step, and the parameters μ W , Σ W , μ b , Σ b {\displaystyle \mu _{W},\Sigma _{W},\mu _{b},\Sigma _{b}} are learned via the reparameterization trick.