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  Shopify

  Shopify Inc., stylized as shopify, is a Canadian multinational e-commerce company headquartered in Ottawa, Ontario that operates a platform for retail point-of-sale systems. The company has over 5 million customers and processed US$292.3 billion in transactions in 2024, of which 57% was in the United States. Major customers include Tesla, LVMH, Nestlé, PepsiCo, AB InBev, Kraft Heinz, Lindt, Whole Foods Market, Red Bull, and Hyatt. The company's software has been praised for its ease of use and reasonable fee structure. It has been described as the "go-to e-commerce platform for startups". However, the company has faced criticism for allegedly inflating their sales data and for associating with controversial sellers. == History == === 2006: Founding === Shopify was founded in 2006 by friends Tobias Lütke, Daniel Weinand and Scott Lake after launching Snowdevil, an online store for snowboarding equipment, in 2004. Dissatisfied with the existing e-commerce products on the market, Lütke, a computer programmer by trade, instead built his own. Lütke used the open source web application framework Ruby on Rails to build Snowdevil's online store and launched it after two months of development. The Snowdevil founders launched the platform as Shopify in June 2006. Shopify created an open-source template language called Liquid, which is written in Ruby and has been used since 2006. In June 2009, Shopify launched an application programming interface (API) platform and App Store. The API allows developers to create applications for Shopify online stores and then sell them on the Shopify App Store. === 2010s === In January 2010, Shopify started its Build-A-Business competition, in which participants create a business using its commerce platform. The winners of the competition received cash prizes and mentorship from entrepreneurs, such as Richard Branson, Eric Ries and others. In April of that year, Shopify launched a free mobile app on the Apple App Store. The app allows Shopify store owners to view and manage their stores from iOS mobile devices. In December 2010, Shopify raised $7 million from a series A round from Bessemer Venture Partners, FirstMark Capital, and Felicis Ventures at a $20 million pre-money valuation. At that time, the company had annualized transaction value of $132 million. In October 2011, it raised $15 million in a Series B round. In August 2013, Shopify launched Shopify Payments in partnership with Stripe. Shopify Payments allows merchants to accept payments without requiring a third-party payment gateway. The company also announced the launch of a point of sale system to enable in-person sales in addition to online. The company received $100 million in Series C funding in December 2013. Shopify earned $105 million in revenue in 2014, twice as much as it raised the previous year. In February 2014, Shopify released "Shopify Plus" for large e-commerce businesses seeking access to additional features and support. Shopify went public via an initial public offering on May 21, 2015 raising more than $131 million. In September 2015, Amazon.com closed its Amazon Webstore service for merchants and selected Shopify as the preferred migration provider; In April 2016, Shopify announced Shopify Capital, a cash advance product. Shopify Capital was initially piloted to merchants within the US and allowed merchants to receive an advance on future earnings processed through its payment gateway. Since its launch in 2016, Shopify Capital has provided more than $5.1 billion in funding to Shopify merchants, with a maximum advance of $2 million. On June 7, 2016, Shopify launched its Shopify Plus Partners Program, to help agencies connect with evolving businesses in ecommerce space. On October 3, 2016, Shopify acquired Boltmade. In November 2016, Shopify partnered with Paystack which allowed Nigerian online retailers to accept payments from customers around the world. On November 22, 2016, Shopify launched Frenzy, a mobile app that improves flash sales. In January 2017, Shopify announced integration with Amazon that would allow merchants to sell on Amazon from their Shopify stores. In April 2017, Shopify introduced its Chip & Swipe Reader, a Bluetooth enabled debit and credit card reader for brick and mortar retail purchases. The company has since released additional technology for brick and mortar retailers, including a point-of-sale system with a Dock and Retail Stand similar to that offered by Square, and a tappable chip card reader. Shopify announced a one-click accelerated checkout feature called Shopify Pay in April 2017 as an exclusive feature for merchants using Shopify Payments as their payment processor. Customers can save their shipping and payment information for future purchases from all participating Shopify stores. In November 2017 Shopify announced Arrive, a mobile application to help customers track packages from both Shopify merchants and other e-commerce websites. In September 2018, Shopify announced plans to expand its office space in Toronto's King West neighborhood in 2022 as part of "The Well" complex, jointly owned by Allied Properties REIT and RioCan REIT. In October 2018, Shopify opened its first flagship, a physical space for business owners in Los Angeles. The space offered educational classes, coworking space, a "genius bar" for companies that use Shopify software, and workshops. Online cannabis sales in Ontario, Canada, used Shopify's software when the drug was legalized in October 2018. Shopify's software is also used for in-person cannabis sales in Ontario since becoming legal in 2019. In January 2019, Shopify announced the launch of Shopify Studios, a full-service television and film content and production house. On March 22, 2019, Shopify and email marketing platform Mailchimp ended an integration agreement over disputes involving customer privacy and data collection. In April 2019, Shopify announced an integration with Snapchat to allow Shopify merchants to buy and manage Snapchat Story ads directly on the Shopify platform. The company had previously secured similar integration partnerships with Facebook and Google. On August 14, 2019, Shopify launched Shopify Chat, a new native chat function that allows merchants to have real-time conversations with customers visiting Shopify stores online. === 2020s === In January 2020, the company announced plans to hire in Vancouver, Canada. Additionally, the effects of the COVID-19 pandemic contributed to lifting stock prices. On February 21, 2020, Shopify announced plans to join the Diem Association, known as Libra Association at the time. Also that month, Shopify Pay was rebranded as Shop Pay. In April, Arrive was rebranded as Shop, combining both customer-facing features under a single brand. In May, during the COVID-19 pandemic, Shopify announced it would shift most of its global workforce to permanent remote work. It was reported that Shopify's valuation would likely rise on the back of options it had in the company Affirm that was expecting to go public shortly. In November 2020, Shopify announced a partnership with Alipay to support merchants with cross-border payments. Shopify also provided the opportunity for users to connect Alibaba and AliExpress to Shopify through a Alibaba Dropshipping app that could be purchased through the Shopify App Store. Multiple applications launched between 2021 and 2024 allowed customers to connect their Shopify store to their Alibaba account and then import and publish your products. The integration automatically syncs inventory and orders between both platforms so that Alibaba vendors can ship directly to dropshipping customers.As a result of Affirm's January 13, 2021 IPO, Shopify's 8% stake in Affirm was worth $2 billion. About half of Shopify's C-level executives left the company in early 2021. On June 29, 2021, Shopify removed the 20% revenue share for app developers that make less than US$1 million per year. On January 18, 2022, Shopify announced a partnership with JD.com to let U.S. merchants expand their operations in China, listing their products on JD's cross-border e-commerce platform JD Worldwide. On March 22, 2022, Shopify introduced Linkpop, a product to create a branded, social marketplace through which merchants can advertise and market their products via links to be added on social media channels. The following month, Shopify, Alphabet Inc., Meta Platforms, McKinsey & Company, and Stripe, Inc. announced a $925 million advance market commitment of carbon dioxide removal (CDR) from companies that are developing CDR technology over the next 9 years. In June 2022, Shopify partnered with Twitter. As a part of the deal, Twitter announced that it would launch a sales channel app for all of Shopify's U.S. merchants through its app store. Shopify also partnered with PayPal to offer Shopify Payments to merchants in France. On July 26, 2022, Lütke announced immediate layoffs totalling roughly 10 percent of its workforce. In

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  Expectation propagation

  Expectation propagation (EP) is a technique in Bayesian machine learning. EP finds approximations to a probability distribution. It uses an iterative approach that uses the factorization structure of the target distribution. It differs from other Bayesian approximation approaches such as variational Bayesian methods. More specifically, suppose we wish to approximate an intractable probability distribution p ( x ) {\displaystyle p(\mathbf {x} )} with a tractable distribution q ( x ) {\displaystyle q(\mathbf {x} )} . Expectation propagation achieves this approximation by minimizing the Kullback–Leibler divergence K L ( p | | q ) {\displaystyle \mathrm {KL} (p||q)} . Variational Bayesian methods minimize K L ( q | | p ) {\displaystyle \mathrm {KL} (q||p)} instead. If q ( x ) {\displaystyle q(\mathbf {x} )} is a Gaussian N ( x | μ , Σ ) {\displaystyle {\mathcal {N}}(\mathbf {x} |\mu ,\Sigma )} , then K L ( p | | q ) {\displaystyle \mathrm {KL} (p||q)} is minimized with μ {\displaystyle \mu } and Σ {\displaystyle \Sigma } being equal to the mean of p ( x ) {\displaystyle p(\mathbf {x} )} and the covariance of p ( x ) {\displaystyle p(\mathbf {x} )} , respectively; this is called moment matching. == Applications == Expectation propagation via moment matching plays a vital role in approximation for indicator functions that appear when deriving the message passing equations for TrueSkill.

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  AIXI

  AIXI is a theoretical mathematical formalism for artificial general intelligence. It combines Solomonoff induction with sequential decision theory. AIXI was first proposed by Marcus Hutter in 2000 and several results regarding AIXI are proved in Hutter's 2005 book Universal Artificial Intelligence. AIXI is a reinforcement learning (RL) agent. It maximizes the expected total rewards received from the environment. Intuitively, it simultaneously considers every computable hypothesis (or environment). In each time step, it looks at every possible program and evaluates how many rewards that program generates depending on the next action taken. The promised rewards are then weighted by the subjective belief that this program constitutes the true environment. This belief is computed from the length of the program: longer programs are considered less likely, in line with Occam's razor. AIXI then selects the action that has the highest expected total reward in the weighted sum of all these programs. == Etymology == According to Hutter, the word "AIXI" can have several interpretations. AIXI can stand for AI based on Solomonoff's distribution, denoted by ξ {\displaystyle \xi } (which is the Greek letter xi), or e.g. it can stand for AI "crossed" (X) with induction (I). There are other interpretations. == Definition == AIXI is a reinforcement learning agent that interacts with some stochastic and unknown but computable environment μ {\displaystyle \mu } . The interaction proceeds in time steps, from t = 1 {\displaystyle t=1} to t = m {\displaystyle t=m} , where m ∈ N {\displaystyle m\in \mathbb {N} } is the lifespan of the AIXI agent. At time step t, the agent chooses an action a t ∈ A {\displaystyle a_{t}\in {\mathcal {A}}} (e.g. a limb movement) and executes it in the environment, and the environment responds with a "percept" e t ∈ E = O × R {\displaystyle e_{t}\in {\mathcal {E}}={\mathcal {O}}\times \mathbb {R} } , which consists of an "observation" o t ∈ O {\displaystyle o_{t}\in {\mathcal {O}}} (e.g., a camera image) and a reward r t ∈ R {\displaystyle r_{t}\in \mathbb {R} } , distributed according to the conditional probability μ ( o t r t | a 1 o 1 r 1 . . . a t − 1 o t − 1 r t − 1 a t ) {\displaystyle \mu (o_{t}r_{t}|a_{1}o_{1}r_{1}...a_{t-1}o_{t-1}r_{t-1}a_{t})} , where a 1 o 1 r 1 . . . a t − 1 o t − 1 r t − 1 a t {\displaystyle a_{1}o_{1}r_{1}...a_{t-1}o_{t-1}r_{t-1}a_{t}} is the "history" of actions, observations and rewards. The environment μ {\displaystyle \mu } is thus mathematically represented as a probability distribution over "percepts" (observations and rewards) which depend on the full history, so there is no Markov assumption (as opposed to other RL algorithms). Note again that this probability distribution is unknown to the AIXI agent. Furthermore, note again that μ {\displaystyle \mu } is computable, that is, the observations and rewards received by the agent from the environment μ {\displaystyle \mu } can be computed by some program (which runs on a Turing machine), given the past actions of the AIXI agent. The only goal of the AIXI agent is to maximize ∑ t = 1 m r t {\displaystyle \sum _{t=1}^{m}r_{t}} , that is, the sum of rewards from time step 1 to m. The AIXI agent is associated with a stochastic policy π : ( A × E ) ∗ → A {\displaystyle \pi :({\mathcal {A}}\times {\mathcal {E}})^{}\rightarrow {\mathcal {A}}} , which is the function it uses to choose actions at every time step, where A {\displaystyle {\mathcal {A}}} is the space of all possible actions that AIXI can take and E {\displaystyle {\mathcal {E}}} is the space of all possible "percepts" that can be produced by the environment. The environment (or probability distribution) μ {\displaystyle \mu } can also be thought of as a stochastic policy (which is a function): μ : ( A × E ) ∗ × A → E {\displaystyle \mu :({\mathcal {A}}\times {\mathcal {E}})^{}\times {\mathcal {A}}\rightarrow {\mathcal {E}}} , where the ∗ {\displaystyle } is the Kleene star operation. In general, at time step t {\displaystyle t} (which ranges from 1 to m), AIXI, having previously executed actions a 1 … a t − 1 {\displaystyle a_{1}\dots a_{t-1}} (which is often abbreviated in the literature as a < t {\displaystyle a_{ Read more →

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  Hierarchical control system

  A hierarchical control system (HCS) is a form of control system in which a set of devices and governing software is arranged in a hierarchical tree. When the links in the tree are implemented by a computer network, then that hierarchical control system is also a form of networked control system. == Overview == A human-built system with complex behavior is often organized as a hierarchy. For example, a command hierarchy has among its notable features the organizational chart of superiors, subordinates, and lines of organizational communication. Hierarchical control systems are organized similarly to divide the decision making responsibility. Each element of the hierarchy is a linked node in the tree. Commands, tasks and goals to be achieved flow down the tree from superior nodes to subordinate nodes, whereas sensations and command results flow up the tree from subordinate to superior nodes. Nodes may also exchange messages with their siblings. The two distinguishing features of a hierarchical control system are related to its layers. Each higher layer of the tree operates with a longer interval of planning and execution time than its immediately lower layer. The lower layers have local tasks, goals, and sensations, and their activities are planned and coordinated by higher layers which do not generally override their decisions. The layers form a hybrid intelligent system in which the lowest, reactive layers are sub-symbolic. The higher layers, having relaxed time constraints, are capable of reasoning from an abstract world model and performing planning. A hierarchical task network is a good fit for planning in a hierarchical control system. Besides artificial systems, an animal's control systems are proposed to be organized as a hierarchy. In perceptual control theory, which postulates that an organism's behavior is a means of controlling its perceptions, the organism's control systems are suggested to be organized in a hierarchical pattern as their perceptions are constructed so. == Control system structure == The accompanying diagram is a general hierarchical model which shows functional manufacturing levels using computerised control of an industrial control system. Referring to the diagram; Level 0 contains the field devices such as flow and temperature sensors, and final control elements, such as control valves Level 1 contains the industrialised Input/Output (I/O) modules, and their associated distributed electronic processors. Level 2 contains the supervisory computers, which collate information from processor nodes on the system, and provide the operator control screens. Level 3 is the production control level, which does not directly control the process, but is concerned with monitoring production and monitoring targets Level 4 is the production scheduling level. == Applications == === Manufacturing, robotics and vehicles === Among the robotic paradigms is the hierarchical paradigm in which a robot operates in a top-down fashion, heavy on planning, especially motion planning. Computer-aided production engineering has been a research focus at NIST since the 1980s. Its Automated Manufacturing Research Facility was used to develop a five layer production control model. In the early 1990s DARPA sponsored research to develop distributed (i.e. networked) intelligent control systems for applications such as military command and control systems. NIST built on earlier research to develop its Real-Time Control System (RCS) and Real-time Control System Software which is a generic hierarchical control system that has been used to operate a manufacturing cell, a robot crane, and an automated vehicle. In November 2007, DARPA held the Urban Challenge. The winning entry, Tartan Racing employed a hierarchical control system, with layered mission planning, motion planning, behavior generation, perception, world modelling, and mechatronics. === Artificial intelligence === Subsumption architecture is a methodology for developing artificial intelligence that is heavily associated with behavior based robotics. This architecture is a way of decomposing complicated intelligent behavior into many "simple" behavior modules, which are in turn organized into layers. Each layer implements a particular goal of the software agent (i.e. system as a whole), and higher layers are increasingly more abstract. Each layer's goal subsumes that of the underlying layers, e.g. the decision to move forward by the eat-food layer takes into account the decision of the lowest obstacle-avoidance layer. Behavior need not be planned by a superior layer, rather behaviors may be triggered by sensory inputs and so are only active under circumstances where they might be appropriate. Reinforcement learning has been used to acquire behavior in a hierarchical control system in which each node can learn to improve its behavior with experience. James Albus, while at NIST, developed a theory for intelligent system design named the Reference Model Architecture (RMA), which is a hierarchical control system inspired by RCS. Albus defines each node to contain these components. Behavior generation is responsible for executing tasks received from the superior, parent node. It also plans for, and issues tasks to, the subordinate nodes. Sensory perception is responsible for receiving sensations from the subordinate nodes, then grouping, filtering, and otherwise processing them into higher level abstractions that update the local state and which form sensations that are sent to the superior node. Value judgment is responsible for evaluating the updated situation and evaluating alternative plans. World Model is the local state that provides a model for the controlled system, controlled process, or environment at the abstraction level of the subordinate nodes. At its lowest levels, the RMA can be implemented as a subsumption architecture, in which the world model is mapped directly to the controlled process or real world, avoiding the need for a mathematical abstraction, and in which time-constrained reactive planning can be implemented as a finite-state machine. Higher levels of the RMA however, may have sophisticated mathematical world models and behavior implemented by automated planning and scheduling. Planning is required when certain behaviors cannot be triggered by current sensations, but rather by predicted or anticipated sensations, especially those that come about as result of the node's actions.

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  Cross-validation (statistics)

  Cross-validation, sometimes called rotation estimation or out-of-sample testing, is any of various similar model validation techniques for assessing how the results of a statistical analysis will generalize to an independent data set. Cross-validation includes resampling and sample splitting methods that use different portions of the data to test and train a model on different iterations. It is often used in settings where the goal is prediction, and one wants to estimate how accurately a predictive model will perform in practice. It can also be used to assess the quality of a fitted model and the stability of its parameters. In a prediction problem, a model is usually given a dataset of known data on which training is run (training dataset), and a dataset of unknown data (or first seen data) against which the model is tested (called the validation dataset or testing set). The goal of cross-validation is to test the model's ability to predict new data that was not used in estimating it, in order to flag problems like overfitting or selection bias and to give an insight on how the model will generalize to an independent dataset (i.e., an unknown dataset, for instance from a real problem). One round of cross-validation involves partitioning a sample of data into complementary subsets, performing the analysis on one subset (called the training set), and validating the analysis on the other subset (called the validation set or testing set). To reduce variability, in most methods multiple rounds of cross-validation are performed using different partitions, and the validation results are combined (e.g. averaged) over the rounds to give an estimate of the model's predictive performance. In summary, cross-validation combines (averages) measures of fitness in prediction to derive a more accurate estimate of model prediction performance. == Motivation == Assume a model with one or more unknown parameters, and a data set to which the model can be fit (the training data set). The fitting process optimizes the model parameters to make the model fit the training data as well as possible. If an independent sample of validation data is taken from the same population as the training data, it will generally turn out that the model does not fit the validation data as well as it fits the training data. The size of this difference is likely to be large especially when the size of the training data set is small, or when the number of parameters in the model is large. Cross-validation is a way to estimate the size of this effect. === Example: linear regression === In linear regression, there exist real response values y 1 , … , y n {\textstyle y_{1},\ldots ,y_{n}} , and n p-dimensional vector covariates x1, ..., xn. The components of the vector xi are denoted xi1, ..., xip. If least squares is used to fit a function in the form of a hyperplane ŷ = a + βTx to the data (xi, yi) 1 ≤ i ≤ n, then the fit can be assessed using the mean squared error (MSE). The MSE for given estimated parameter values a and β on the training set (xi, yi) 1 ≤ i ≤ n is defined as: MSE = 1 n ∑ i = 1 n ( y i − y ^ i ) 2 = 1 n ∑ i = 1 n ( y i − a − β T x i ) 2 = 1 n ∑ i = 1 n ( y i − a − β 1 x i 1 − ⋯ − β p x i p ) 2 {\displaystyle {\begin{aligned}{\text{MSE}}&={\frac {1}{n}}\sum _{i=1}^{n}(y_{i}-{\hat {y}}_{i})^{2}={\frac {1}{n}}\sum _{i=1}^{n}(y_{i}-a-{\boldsymbol {\beta }}^{T}\mathbf {x} _{i})^{2}\\&={\frac {1}{n}}\sum _{i=1}^{n}(y_{i}-a-\beta _{1}x_{i1}-\dots -\beta _{p}x_{ip})^{2}\end{aligned}}} If the model is correctly specified, it can be shown under mild assumptions that the expected value of the MSE for the training set is (n − p − 1)/(n + p + 1) < 1 times the expected value of the MSE for the validation set (the expected value is taken over the distribution of training sets). Thus, a fitted model and computed MSE on the training set will result in an optimistically biased assessment of how well the model will fit an independent data set. This biased estimate is called the in-sample estimate of the fit, whereas the cross-validation estimate is an out-of-sample estimate. Since in linear regression it is possible to directly compute the factor (n − p − 1)/(n + p + 1) by which the training MSE underestimates the validation MSE under the assumption that the model specification is valid, cross-validation can be used for checking whether the model has been overfitted, in which case the MSE in the validation set will substantially exceed its anticipated value. (Cross-validation in the context of linear regression is also useful in that it can be used to select an optimally regularized cost function.) === General case === In most other regression procedures (e.g. logistic regression), there is no simple formula to compute the expected out-of-sample fit. Cross-validation is, thus, a generally applicable way to predict the performance of a model on unavailable data using numerical computation in place of theoretical analysis. == Types == Two types of cross-validation can be distinguished: exhaustive and non-exhaustive cross-validation. === Exhaustive cross-validation === Exhaustive cross-validation methods are cross-validation methods which learn and test on all possible ways to divide the original sample into a training and a validation set. ==== Leave-p-out cross-validation ==== Leave-p-out cross-validation (LpO CV) involves using p observations as the validation set and the remaining observations as the training set. This is repeated on all ways to cut the original sample on a validation set of p observations and a training set. LpO cross-validation require training and validating the model C p n {\displaystyle C_{p}^{n}} times, where n is the number of observations in the original sample, and where C p n {\displaystyle C_{p}^{n}} is the binomial coefficient. For p > 1 and for even moderately large n, LpO CV can become computationally infeasible. For example, with n = 100 and p = 30, C 30 100 ≈ 3 × 10 25 . {\displaystyle C_{30}^{100}\approx 3\times 10^{25}.} A variant of LpO cross-validation with p=2 known as leave-pair-out cross-validation has been recommended as a nearly unbiased method for estimating the area under ROC curve of binary classifiers. ==== Leave-one-out cross-validation ==== Leave-one-out cross-validation (LOOCV) is a particular case of leave-p-out cross-validation with p = 1. The process looks similar to jackknife; however, with cross-validation one computes a statistic on the left-out sample(s), while with jackknifing one computes a statistic from the kept samples only. LOO cross-validation requires less computation time than LpO cross-validation because there are only C 1 n = n {\displaystyle C_{1}^{n}=n} passes rather than C p n {\displaystyle C_{p}^{n}} . However, n {\displaystyle n} passes may still require quite a large computation time, in which case other approaches such as k-fold cross validation may be more appropriate. Pseudo-code algorithm: Input: x, {vector of length N with x-values of incoming points} y, {vector of length N with y-values of the expected result} interpolate( x_in, y_in, x_out ), { returns the estimation for point x_out after the model is trained with x_in-y_in pairs} Output: err, {estimate for the prediction error} Steps: err ← 0 for i ← 1, ..., N do // define the cross-validation subsets x_in ← (x[1], ..., x[i − 1], x[i + 1], ..., x[N]) y_in ← (y[1], ..., y[i − 1], y[i + 1], ..., y[N]) x_out ← x[i] y_out ← interpolate(x_in, y_in, x_out) err ← err + (y[i] − y_out)^2 end for err ← err/N === Non-exhaustive cross-validation === Non-exhaustive cross validation methods do not compute all ways of splitting the original sample. These methods are approximations of leave-p-out cross-validation. ==== k-fold cross-validation ==== In k-fold cross-validation, the original sample is randomly partitioned into k equal sized subsamples, often referred to as "folds". Of the k subsamples, a single subsample is retained as the validation data for testing the model, and the remaining k − 1 subsamples are used as training data. The cross-validation process is then repeated k times, with each of the k subsamples used exactly once as the validation data. The k results can then be averaged to produce a single estimation. The advantage of this method over repeated random sub-sampling (see below) is that all observations are used for both training and validation, and each observation is used for validation exactly once. 10-fold cross-validation is commonly used, but in general k remains an unfixed parameter. For example, setting k = 2 results in 2-fold cross-validation. In 2-fold cross-validation, the dataset is randomly shuffled into two sets d0 and d1, so that both sets are equal size (this is usually implemented by shuffling the data array and then splitting it in two). We then train on d0 and validate on d1, followed by training on d1 and validating on d0. When k = n (the number of observations), k-fold cross-validation is equivalent to leave-one-out cr

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  CrewAI

  CrewAI is an open-source software framework and platform for building AI agents and multi-agent systems. Written primarily in Python, it is used to define artificial-intelligence agents, assign tasks to them, and coordinate their work through agent teams and workflows. The framework is associated with CrewAI Inc., a startup developing enterprise tools for automating business workflows with large language model-based agents. == History == CrewAI was first released on the Python Package Index in December 2023. The project was created by João Moura and later developed by CrewAI Inc. and open-source contributors. In October 2024, TechCrunch reported that CrewAI had raised $18 million across seed and Series A funding rounds from investors including Boldstart Ventures, Craft Ventures, Earl Grey Capital, and Insight Partners. The report also stated that Andrew Ng and HubSpot co-founder Dharmesh Shah had invested in the company. SiliconANGLE described the company as the developer of an open-source framework for building artificial-intelligence agents and reported that the funding consisted of a seed round led by Boldstart Ventures and a Series A led by Insight Partners. By late 2024, CrewAI had introduced commercial enterprise products built on top of its open-source components. TechCrunch reported that the company's enterprise offering added access controls, analytics, support, and templates for workflow automation. == Features == CrewAI is designed around groups of agents, sometimes called "crews", that can be assigned roles, goals, and tasks. The framework supports agent collaboration, task delegation, tool use, memory, and knowledge sources for retrieval-augmented generation workflows. The project describes two main building blocks: "Crews", which are used for autonomous agent collaboration, and "Flows", which are used for more controlled event-driven workflows. The framework is independent of LangChain and is released under the MIT License. It can be installed as a Python package and is commonly used with external large language model APIs or local models, depending on the developer's configuration. == Business model == CrewAI combines an open-source framework with commercial enterprise products. Its enterprise products are intended for organizations that need to build, monitor, and manage agent-based automations with additional security, observability, and administrative controls.

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  Machine unlearning

  Machine unlearning is a branch of machine learning focused on removing specific undesired element, such as private data, wrong or manipulated training data, outdated information, copyrighted material, harmful content, dangerous abilities, or misinformation, without needing to rebuild models from the ground up. Large language models, like the ones powering ChatGPT, may be asked not just to remove specific elements but also to unlearn a "concept," "fact," or "knowledge," which aren't easily linked to specific examples. New terms such as "model editing," "concept editing," and "knowledge unlearning" have emerged to describe this process. == History == Early research efforts were largely motivated by Article 17 of the GDPR, the European Union's privacy regulation commonly known as the "right to be forgotten" (RTBF), introduced in 2014. The GDPR did not anticipate that the development of large language models would make data erasure a complex task. This issue has since led to research on "machine unlearning," with a growing focus on removing copyrighted material, harmful content, dangerous capabilities, and misinformation. Just as early experiences in humans shape later ones, some concepts are more fundamental and harder to unlearn. A piece of knowledge may be so deeply embedded in the model's knowledge graph that unlearning it could cause internal contradictions, requiring adjustments to other parts of the graph to resolve them. Researchers have now also started studying unlearning in the context of removing incorrect or adversarially manipulated training data such as systematically biased labels or poisoning attacks. == Motivations == At present, machine unlearning is motivated by a growing range of concerns that extend well beyond the field's original focus on data privacy. A widely used taxonomy in the literature distinguishes two high-level categories of motivation. Access revocation covers cases where a data subject or rights holder requests the removal of data they own or control. This is most commonly associated with RTBF established by the European Union's General Data Protection Regulation (GDPR) and analogous legislation such as the California Consumer Privacy Act (CCPA). These regulations grant individuals the legal right to request erasure of their personal data from any system that has processed it, including models that were trained on it. Access revocation also encompasses the removal of copyrighted or pay-walled content that was incorporated into training corpora without the necessary licenses, a concern that has become prominent with the widespread use of largely web-scraped pre-training datasets. Model correction covers cases where the model exhibits undesirable behavior arising from the training data, regardless of any individual's request. This includes: Removal of toxic, biased, or unsafe outputs introduced by harmful content in the training set Correction of stale or factually incorrect associations, such as outdated knowledge encoded in a deployed model Removal of dangerous capabilities, such as detailed knowledge of the synthesis of chemical or biological agents Correction of the influence of data poisoning or adversarial attacks that have corrupted model behavior This second category has been formalized as corrective machine unlearning, which frames unlearning as a post-training mechanism for repairing the effects of bad or harmful training data. It is closely related to the AI safety literature, where data filtering alone has been found insufficient to prevent hazardous knowledge from being encoded in model weights, motivating unlearning as a complementary risk mitigation strategy. A further distinction has been drawn in the literature between removal {eliminating the influence of specific training data on model parameters) and suppression (preventing the model from generating specific outputs regardless of how that knowledge is encoded). These two goals are not equivalent: removing training data does not guarantee meaningful output suppression, and suppressing outputs does not constitute removal of the underlying training data's influence. == SISA Training == SISA is a training strategy consisting of four mechanisms designed to make machine unlearning more efficient by structuring how models are trained and updated. Its goal is to allow a system to remove the influence of specific data points without retraining an entire model from scratch. By reorganizing training data and workflows, SISA reduces the computational burden of unlearning requests. Sharding divides the training dataset into multiple disjoint subsets, or shards. Each shard is used to train a separate model instance. This ensures that a single data point affects only one shard, so unlearning it requires updating only the corresponding shard rather than the full model. Isolation refers to training each shard independently, with nothing shared across shards during the training process. This separation prevents cross-contamination between shards, ensuring that forgetting data in one shard does not require adjustments to any others. Slicing breaks the data within each shard into sequential slices and stores model states after each slice is trained on. When an unlearning request targets a piece of data, the system can roll back to the checkpoint before the point was seen and retrain only from that slice forward. This reduces retraining time even within a shard. Aggregation occurs at inference, when the model is queried. It combines the outputs of each shard to determine the output of the overall model. This is often through majority voting or averaging. This allows SISA-trained systems to behave like a single model despite being composed of multiple shard-level models. Together, these mechanisms enable machine learning systems to forget specific data points with far lower computational cost than full retraining. The trade-off is that sharding and slicing can lead to reduced model accuracy, worse generalization, and increased storage requirements for the intermediate checkpoints. This can be tolerable based on the needs of the individual or organization to comply with "right to be forgotten" or efficiently recover from backdoor attacks. == Algorithms == Machine unlearning algorithms are broadly categorized into exact and approximate methods, reflecting a fundamental trade-off between formal guarantees and computational tractability. === Exact Unlearning === Exact unlearning methods produce a model that is statistically indistinguishable from one retrained from scratch on the dataset with the forget data removed. The canonical framework for exact unlearning is SISA Training (Sharded, Isolated, Sliced, and Aggregated), introduced by Bourtoule et al. (2021). SISA partitions the training dataset into disjoint shards and trains a separate sub-model on each. At inference time, predictions are aggregated across sub-models. When an unlearning request is received, only the sub-model corresponding to the shard containing the target data requires retraining, reducing computational overhead proportionally to the number of shards. Exact methods provide the strongest guarantees but become prohibitively expensive for large pre-trained neural networks and are generally limited to settings where training can be structured in advance. === Approximate Unlearning === Approximate unlearning methods seek to produce a model whose behavior is sufficiently close to an exactly unlearned model without the cost of full retraining. These methods dominate practical applications. Common approaches include: Gradient Ascent: The model is fine-tuned by maximizing the loss on the forget set, directly degrading its performance on targeted data. This is the most direct approach but risks destabilizing performance on retained data. Random Labelling: The model is fine-tuned on the forget set using randomly shuffled labels, confusing its associations with the targeted data while producing a less aggressive weight shift than pure gradient ascent. Gradient Difference: Combines gradient ascent on the forget set with simultaneous gradient descent on the retain set, using the retain objective as a regularizer to preserve general model utility. KL Divergence Regularization: Minimizes the KL divergence between the outputs of the unlearned model and the original model on the retain set, anchoring behavior on data the model should remember. Weight Pruning and Fine-tuning: Parameters with the smallest L1-norm are pruned — targeting weights most weakly associated with general knowledge and potentially most associated with the forget set — followed by fine-tuning on the retain set to restore utility. Layer Reset and Fine-tuning: The first or last k layers are re-initialized to random weights and the model is subsequently fine-tuned on the retain set. This is a coarse but computationally simple approach. Selective Synaptic Dampening: Uses influence functions to estimate the effect of individual trainin

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  Astrostatistics

  Astrostatistics is a discipline which spans astrophysics, statistical analysis and data mining. It is used to process the vast amount of data produced by automated scanning of the cosmos, to characterize complex datasets, and to link astronomical data to astrophysical theory. Many branches of statistics are involved in astronomical analysis including nonparametrics, multivariate regression and multivariate classification, time series analysis, and especially Bayesian inference. The field is closely related to astroinformatics.

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  Microscope image processing

  Microscope image processing is a broad term that covers the use of digital image processing techniques to process, analyze and present images obtained from a microscope. Such processing is now commonplace in a number of diverse fields such as medicine, biological research, cancer research, drug testing, metallurgy, etc. A number of manufacturers of microscopes now specifically design in features that allow the microscopes to interface to an image processing system. == Image acquisition == Until the early 1990s, most image acquisition in video microscopy applications was typically done with an analog video camera, often simply closed circuit TV cameras. While this required the use of a frame grabber to digitize the images, video cameras provided images at full video frame rate (25-30 frames per second) allowing live video recording and processing. While the advent of solid state detectors yielded several advantages, the real-time video camera was actually superior in many respects. Today, acquisition is usually done using a CCD camera mounted in the optical path of the microscope. The camera may be full colour or monochrome. Very often, very high resolution cameras are employed to gain as much direct information as possible. Cryogenic cooling is also common, to minimise noise. Often digital cameras used for this application provide pixel intensity data to a resolution of 12-16 bits, much higher than is used in consumer imaging products. Ironically, in recent years, much effort has been put into acquiring data at video rates, or higher (25-30 frames per second or higher). What was once easy with off-the-shelf video cameras now requires special, high speed electronics to handle the vast digital data bandwidth. Higher speed acquisition allows dynamic processes to be observed in real time, or stored for later playback and analysis. Combined with the high image resolution, this approach can generate vast quantities of raw data, which can be a challenge to deal with, even with a modern computer system. While current CCD detectors allow very high image resolution, often this involves a trade-off because, for a given chip size, as the pixel count increases, the pixel size decreases. As the pixels get smaller, their well depth decreases, reducing the number of electrons that can be stored. In turn, this results in a poorer signal-to-noise ratio. For best results, one must select an appropriate sensor for a given application. Because microscope images have an intrinsic limiting resolution, it often makes little sense to use a noisy, high resolution detector for image acquisition. A more modest detector, with larger pixels, can often produce much higher quality images because of reduced noise. This is especially important in low-light applications such as fluorescence microscopy. Moreover, one must also consider the temporal resolution requirements of the application. A lower resolution detector will often have a significantly higher acquisition rate, permitting the observation of faster events. Conversely, if the observed object is motionless, one may wish to acquire images at the highest possible spatial resolution without regard to the time required to acquire a single image. == 2D image techniques == Image processing for microscopy application begins with fundamental techniques intended to most accurately reproduce the information contained in the microscopic sample. This might include adjusting the brightness and contrast of the image, averaging images to reduce image noise and correcting for illumination non-uniformities. Such processing involves only basic arithmetic operations between images (i.e. addition, subtraction, multiplication and division). The vast majority of processing done on microscope image is of this nature. Another class of common 2D operations called image convolution are often used to reduce or enhance image details. Such "blurring" and "sharpening" algorithms in most programs work by altering a pixel's value based on a weighted sum of that and the surrounding pixels (a more detailed description of kernel based convolution deserves an entry for itself) or by altering the frequency domain function of the image using Fourier Transform. Most image processing techniques are performed in the Frequency domain. Other basic two dimensional techniques include operations such as image rotation, warping, color balancing etc. At times, advanced techniques are employed with the goal of "undoing" the distortion of the optical path of the microscope, thus eliminating distortions and blurring caused by the instrumentation. This process is called deconvolution, and a variety of algorithms have been developed, some of great mathematical complexity. The end result is an image far sharper and clearer than could be obtained in the optical domain alone. This is typically a 3-dimensional operation, that analyzes a volumetric image (i.e. images taken at a variety of focal planes through the sample) and uses this data to reconstruct a more accurate 3-dimensional image. == 3D image techniques == Another common requirement is to take a series of images at a fixed position, but at different focal depths. Since most microscopic samples are essentially transparent, and the depth of field of the focused sample is exceptionally narrow, it is possible to capture images "through" a three-dimensional object using 2D equipment like confocal microscopes. Software is then able to reconstruct a 3D model of the original sample which may be manipulated appropriately. The processing turns a 2D instrument into a 3D instrument, which would not otherwise exist. In recent times this technique has led to a number of scientific discoveries in cell biology. == Analysis == Analysis of images will vary considerably according to application. Typical analysis includes determining where the edges of an object are, counting similar objects, calculating the area, perimeter length and other useful measurements of each object. A common approach is to create an image mask which only includes pixels that match certain criteria, then perform simpler scanning operations on the resulting mask. It is also possible to label objects and track their motion over a series of frames in a video sequence.

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  Discovery system (artificial intelligence)

  A discovery system is an artificial intelligence system that attempts to discover new scientific concepts or laws. The aim of discovery systems is to automate scientific data analysis and the scientific discovery process. Ideally, an artificial intelligence system should be able to search systematically through the space of all possible hypotheses and yield the hypothesis - or set of equally likely hypotheses - that best describes the complex patterns in data. During the era known as the second AI summer (approximately 1978–1987), various systems akin to the era's dominant expert systems were developed to tackle the problem of extracting scientific hypotheses from data, with or without interacting with a human scientist. These systems included Autoclass, Automated Mathematician, Eurisko, which aimed at general-purpose hypothesis discovery, and more specific systems such as Dalton, which uncovers molecular properties from data. The dream of building systems that discover scientific hypotheses was pushed to the background with the second AI winter and the subsequent resurgence of subsymbolic methods such as neural networks. Subsymbolic methods emphasize prediction over explanation, and yield models which works well but are difficult or impossible to explain which has earned them the name black box AI. A black-box model cannot be considered a scientific hypothesis, and this development has even led some researchers to suggest that the traditional aim of science - to uncover hypotheses and theories about the structure of reality - is obsolete. Other researchers disagree and argue that subsymbolic methods are useful in many cases, just not for generating scientific theories. == Discovery systems from the 1970s and 1980s == Autoclass was a Bayesian Classification System written in 1986 Automated Mathematician was one of the earliest successful discovery systems. It was written in 1977 and worked by generating a modifying small Lisp programs Eurisko was a Sequel to Automated Mathematician written in 1984 Dalton is a still maintained program capable of calculating various molecular properties initially launched in 1983 and available in open source since 2017 Glauber is a scientific discovery method written in the context of computational philosophy of science launched in 1983 == Modern discovery systems (2009–present) == After a couple of decades with little interest in discovery systems, the interest in using AI to uncover natural laws and scientific explanations was renewed by the work of Michael Schmidt, then a PhD student in Computational Biology at Cornell University. Schmidt and his advisor, Hod Lipson, invented Eureqa, which they described as a symbolic regression approach to "distilling free-form natural laws from experimental data". This work effectively demonstrated that symbolic regression was a promising way forward for AI-driven scientific discovery. Since 2009, symbolic regression has matured further, and today, various commercial and open source systems are actively used in scientific research. Notable examples include Eureqa, now a part of DataRobot AI Cloud Platform, AI Feynman, and QLattice.

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  Solomonoff's theory of inductive inference

  Solomonoff's theory of inductive inference proves that, under its common sense assumptions (axioms), the best possible scientific model is the shortest algorithm that generates the empirical data under consideration. In addition to the choice of data, other assumptions are that, to avoid the post-hoc fallacy, the programming language must be chosen prior to the data and that the environment being observed is generated by an unknown algorithm. This is also called a theory of induction. Due to its basis in the dynamical (state-space model) character of Algorithmic Information Theory, it encompasses statistical as well as dynamical information criteria for model selection. It was introduced by Ray Solomonoff, based on probability theory and theoretical computer science. In essence, Solomonoff's induction derives the posterior probability of any computable theory, given a sequence of observed data. This posterior probability is derived from Bayes' rule and some universal prior, that is, a prior that assigns a positive probability to any computable theory. Solomonoff proved that this induction is incomputable (or more precisely, lower semi-computable), but noted that "this incomputability is of a very benign kind", and that it "in no way inhibits its use for practical prediction" (as it can be approximated from below more accurately with more computational resources). It is only "incomputable" in the benign sense that no scientific consensus is able to prove that the best current scientific theory is the best of all possible theories. However, Solomonoff's theory does provide an objective criterion for deciding among the current scientific theories explaining a given set of observations. Solomonoff's induction naturally formalizes Occam's razor by assigning larger prior credences to theories that require a shorter algorithmic description. == Origin == === Philosophical === The theory is based in philosophical foundations, and was founded by Ray Solomonoff around 1960. It is a mathematically formalized combination of Occam's razor and the Principle of Multiple Explanations. All computable theories which perfectly describe previous observations are used to calculate the probability of the next observation, with more weight put on the shorter computable theories. Marcus Hutter's universal artificial intelligence builds upon this to calculate the expected value of an action. === Principle === Solomonoff's induction has been argued to be the computational formalization of pure Bayesianism. To understand, recall that Bayesianism derives the posterior probability P [ T | D ] {\displaystyle \mathbb {P} [T|D]} of a theory T {\displaystyle T} given data D {\displaystyle D} by applying Bayes rule, which yields P [ T | D ] = P [ D | T ] P [ T ] P [ D | T ] P [ T ] + ∑ A ≠ T P [ D | A ] P [ A ] {\displaystyle \mathbb {P} [T|D]={\frac {\mathbb {P} [D|T]\mathbb {P} [T]}{\mathbb {P} [D|T]\mathbb {P} [T]+\sum _{A\neq T}\mathbb {P} [D|A]\mathbb {P} [A]}}} where theories A {\displaystyle A} are alternatives to theory T {\displaystyle T} . For this equation to make sense, the quantities P [ D | T ] {\displaystyle \mathbb {P} [D|T]} and P [ D | A ] {\displaystyle \mathbb {P} [D|A]} must be well-defined for all theories T {\displaystyle T} and A {\displaystyle A} . In other words, any theory must define a probability distribution over observable data D {\displaystyle D} . Solomonoff's induction essentially boils down to demanding that all such probability distributions be computable. Interestingly, the set of computable probability distributions is a subset of the set of all programs, which is countable. Similarly, the sets of observable data considered by Solomonoff were finite. Without loss of generality, we can thus consider that any observable data is a finite bit string. As a result, Solomonoff's induction can be defined by only invoking discrete probability distributions. Solomonoff's induction then allows to make probabilistic predictions of future data F {\displaystyle F} , by simply obeying the laws of probability. Namely, we have P [ F | D ] = E T [ P [ F | T , D ] ] = ∑ T P [ F | T , D ] P [ T | D ] {\displaystyle \mathbb {P} [F|D]=\mathbb {E} _{T}[\mathbb {P} [F|T,D]]=\sum _{T}\mathbb {P} [F|T,D]\mathbb {P} [T|D]} . This quantity can be interpreted as the average predictions P [ F | T , D ] {\displaystyle \mathbb {P} [F|T,D]} of all theories T {\displaystyle T} given past data D {\displaystyle D} , weighted by their posterior credences P [ T | D ] {\displaystyle \mathbb {P} [T|D]} . === Mathematical === The proof of the "razor" is based on the known mathematical properties of a probability distribution over a countable set. These properties are relevant because the infinite set of all programs is a denumerable set. The sum S of the probabilities of all programs must be exactly equal to one (as per the definition of probability) thus the probabilities must roughly decrease as we enumerate the infinite set of all programs, otherwise S will be strictly greater than one. To be more precise, for every ϵ {\displaystyle \epsilon } > 0, there is some length l such that the probability of all programs longer than l is at most ϵ {\displaystyle \epsilon } . This does not, however, preclude very long programs from having very high probability. Fundamental ingredients of the theory are the concepts of algorithmic probability and Kolmogorov complexity. The universal prior probability of any prefix p of a computable sequence x is the sum of the probabilities of all programs (for a universal computer) that compute something starting with p. Given some p and any computable but unknown probability distribution from which x is sampled, the universal prior and Bayes' theorem can be used to predict the yet unseen parts of x in optimal fashion. == Mathematical guarantees == === Solomonoff's completeness === The remarkable property of Solomonoff's induction is its completeness. In essence, the completeness theorem guarantees that the expected cumulative errors made by the predictions based on Solomonoff's induction are upper-bounded by the Kolmogorov complexity of the (stochastic) data generating process. The errors can be measured using the Kullback–Leibler divergence or the square of the difference between the induction's prediction and the probability assigned by the (stochastic) data generating process. === Solomonoff's uncomputability === Unfortunately, Solomonoff also proved that Solomonoff's induction is uncomputable. In fact, he showed that computability and completeness are mutually exclusive: any complete theory must be uncomputable. The proof of this is derived from a game between the induction and the environment. Essentially, any computable induction can be tricked by a computable environment, by choosing the computable environment that negates the computable induction's prediction. This fact can be regarded as an instance of the no free lunch theorem. == Modern applications == === Artificial intelligence === Though Solomonoff's inductive inference is not computable, several AIXI-derived algorithms approximate it in order to make it run on a modern computer. The more computing power they are given, the closer their predictions are to the predictions of inductive inference (their mathematical limit is Solomonoff's inductive inference). Another direction of inductive inference is based on E. Mark Gold's model of learning in the limit from 1967 and has developed since then more and more models of learning. The general scenario is the following: Given a class S of computable functions, is there a learner (that is, recursive functional) which for any input of the form (f(0),f(1),...,f(n)) outputs a hypothesis (an index e with respect to a previously agreed on acceptable numbering of all computable functions; the indexed function may be required consistent with the given values of f). A learner M learns a function f if almost all its hypotheses are the same index e, which generates the function f; M learns S if M learns every f in S. Basic results are that all recursively enumerable classes of functions are learnable while the class REC of all computable functions is not learnable. Many related models have been considered and also the learning of classes of recursively enumerable sets from positive data is a topic studied from Gold's pioneering paper in 1967 onwards. A far reaching extension of the Gold’s approach is developed by Schmidhuber's theory of generalized Kolmogorov complexities, which are kinds of super-recursive algorithms.

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  Developmental robotics

  Developmental robotics (DevRob), sometimes called epigenetic robotics, is a scientific field which aims at studying the developmental mechanisms, architectures and constraints that allow lifelong and open-ended learning of new skills and new knowledge in embodied machines. As in human children, learning is expected to be cumulative and of progressively increasing complexity, and to result from self-exploration of the world in combination with social interaction. The typical methodological approach consists in starting from theories of human and animal development elaborated in fields such as developmental psychology, neuroscience, developmental and evolutionary biology, and linguistics, then to formalize and implement them in robots, sometimes exploring extensions or variants of them. The experimentation of those models in robots allows researchers to confront them with reality, and as a consequence, developmental robotics also provides feedback and novel hypotheses on theories of human and animal development. Developmental robotics is related to but differs from evolutionary robotics (ER). ER uses populations of robots that evolve over time, whereas DevRob is interested in how the organization of a single robot's control system develops through experience, over time. DevRob is also related to work done in the domains of robotics and artificial life. == Background == Can a robot learn like a child? Can it learn a variety of new skills and new knowledge unspecified at design time and in a partially unknown and changing environment? How can it discover its body and its relationships with the physical and social environment? How can its cognitive capacities continuously develop without the intervention of an engineer once it is "out of the factory"? What can it learn through natural social interactions with humans? These are the questions at the center of developmental robotics. Alan Turing, as well as a number of other pioneers of cybernetics, already formulated those questions and the general approach in 1950, but it is only since the end of the 20th century that they began to be investigated systematically. Because the concept of adaptive intelligent machines is central to developmental robotics, it has relationships with fields such as artificial intelligence, machine learning, cognitive robotics or computational neuroscience. Yet, while it may reuse some of the techniques elaborated in these fields, it differs from them from many perspectives. It differs from classical artificial intelligence because it does not assume the capability of advanced symbolic reasoning and focuses on embodied and situated sensorimotor and social skills rather than on abstract symbolic problems. It differs from cognitive robotics because it focuses on the processes that allow the formation of cognitive capabilities rather than these capabilities themselves. It differs from computational neuroscience because it focuses on functional modeling of integrated architectures of development and learning. More generally, developmental robotics is uniquely characterized by the following three features: It targets task-independent architectures and learning mechanisms, i.e. the machine/robot has to be able to learn new tasks that are unknown by the engineer; It emphasizes open-ended development and lifelong learning, i.e. the capacity of an organism to acquire continuously novel skills. This should not be understood as a capacity for learning "anything" or even “everything”, but just that the set of skills that is acquired can be infinitely extended at least in some (not all) directions; The complexity of acquired knowledge and skills shall increase (and the increase be controlled) progressively. Developmental robotics emerged at the crossroads of several research communities including embodied artificial intelligence, enactive and dynamical systems cognitive science, connectionism. Starting from the essential idea that learning and development happen as the self-organized result of the dynamical interactions among brains, bodies and their physical and social environment, and trying to understand how this self-organization can be harnessed to provide task-independent lifelong learning of skills of increasing complexity, developmental robotics strongly interacts with fields such as developmental psychology, developmental and cognitive neuroscience, developmental biology (embryology), evolutionary biology, and cognitive linguistics. As many of the theories coming from these sciences are verbal and/or descriptive, this implies a crucial formalization and computational modeling activity in developmental robotics. These computational models are then not only used as ways to explore how to build more versatile and adaptive machines but also as a way to evaluate their coherence and possibly explore alternative explanations for understanding biological development. == Research directions == === Skill domains === Due to the general approach and methodology, developmental robotics projects typically focus on having robots develop the same types of skills as human infants. A first category that is important being investigated is the acquisition of sensorimotor skills. These include the discovery of one's own body, including its structure and dynamics such as hand-eye coordination, locomotion, and interaction with objects as well as tool use, with a particular focus on the discovery and learning of affordances. A second category of skills targeted by developmental robots are social and linguistic skills: the acquisition of simple social behavioural games such as turn-taking, coordinated interaction, lexicons, syntax and grammar, and the grounding of these linguistic skills into sensorimotor skills (sometimes referred as symbol grounding). In parallel, the acquisition of associated cognitive skills are being investigated such as the emergence of the self/non-self distinction, the development of attentional capabilities, of categorization systems and higher-level representations of affordances or social constructs, of the emergence of values, empathy, or theories of mind. === Mechanisms and constraints === The sensorimotor and social spaces in which humans and robot live are so large and complex that only a small part of potentially learnable skills can actually be explored and learnt within a life-time. Thus, mechanisms and constraints are necessary to guide developmental organisms in their development and control of the growth of complexity. There are several important families of these guiding mechanisms and constraints which are studied in developmental robotics, all inspired by human development: Motivational systems, generating internal reward signals that drive exploration and learning, which can be of two main types: extrinsic motivations push robots/organisms to maintain basic specific internal properties such as food and water level, physical integrity, or light (e.g. in phototropic systems); intrinsic motivations push robot to search for novelty, challenge, compression or learning progress per se, thus generating what is sometimes called curiosity-driven learning and exploration, or alternatively active learning and exploration; Social guidance: as humans learn a lot by interacting with their peers, developmental robotics investigates mechanisms that can allow robots to participate to human-like social interaction. By perceiving and interpreting social cues, this may allow robots both to learn from humans (through diverse means such as imitation, emulation, stimulus enhancement, demonstration, etc. ...) and to trigger natural human pedagogy. Thus, social acceptance of developmental robots is also investigated; Statistical inference biases and cumulative knowledge/skill reuse: biases characterizing both representations/encodings and inference mechanisms can typically allow considerable improvement of the efficiency of learning and are thus studied. Related to this, mechanisms allowing to infer new knowledge and acquire new skills by reusing previously learnt structures is also an essential field of study; The properties of embodiment, including geometry, materials, or innate motor primitives/synergies often encoded as dynamical systems, can considerably simplify the acquisition of sensorimotor or social skills, and is sometimes referred as morphological computation. The interaction of these constraints with other constraints is an important axis of investigation; Maturational constraints: In human infants, both the body and the neural system grow progressively, rather than being full-fledged already at birth. This implies, for example, that new degrees of freedom, as well as increases of the volume and resolution of available sensorimotor signals, may appear as learning and development unfold. Transposing these mechanisms in developmental robots, and understanding how it may hinder or on the contrary ease the acquisition of novel complex skills is a central questi

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  Machine translation software usability

  The sections below give objective criteria for evaluating the usability of machine translation software output. == Stationarity or canonical form == Do repeated translations converge on a single expression in both languages? I.e. does the translation method show stationarity or produce a canonical form? Does the translation become stationary without losing the original meaning? This metric has been criticized as not being well correlated with BLEU (BiLingual Evaluation Understudy) scores. == Adaptive to colloquialism, argot or slang == Is the system adaptive to colloquialism, argot or slang? The French language has many rules for creating words in the speech and writing of popular culture. Two such rules are: (a) The reverse spelling of words such as femme to meuf. (This is called verlan.) (b) The attachment of the suffix -ard to a noun or verb to form a proper noun. For example, the noun faluche means "student hat". The word faluchard formed from faluche colloquially can mean, depending on context, "a group of students", "a gathering of students" and "behavior typical of a student". The Google translator as of 28 December 2006 doesn't derive the constructed words as for example from rule (b), as shown here: Il y a une chorale falucharde mercredi, venez nombreux, les faluchards chantent des paillardes! ==> There is a choral society falucharde Wednesday, come many, the faluchards sing loose-living women! French argot has three levels of usage: familier or friendly, acceptable among friends, family and peers but not at work grossier or swear words, acceptable among friends and peers but not at work or in family verlan or ghetto slang, acceptable among lower classes but not among middle or upper classes The United States National Institute of Standards and Technology conducts annual evaluations [1] Archived 2009-03-22 at the Wayback Machine of machine translation systems based on the BLEU-4 criterion [2]. A combined method called IQmt which incorporates BLEU and additional metrics NIST, GTM, ROUGE and METEOR has been implemented by Gimenez and Amigo [3]. == Well-formed output == Is the output grammatical or well-formed in the target language? Using an interlingua should be helpful in this regard, because with a fixed interlingua one should be able to write a grammatical mapping to the target language from the interlingua. Consider the following Arabic language input and English language translation result from the Google translator as of 27 December 2006 [4]. This Google translator output doesn't parse using a reasonable English grammar: وعن حوادث التدافع عند شعيرة رمي الجمرات -التي كثيرا ما يسقط فيها العديد من الضحايا- أشار الأمير نايف إلى إدخال "تحسينات كثيرة في جسر الجمرات ستمنع بإذن الله حدوث أي تزاحم". ==> And incidents at the push Carbuncles-throwing ritual, which often fall where many of the victims - Prince Nayef pointed to the introduction of "many improvements in bridge Carbuncles God would stop the occurrence of any competing." == Semantics preservation == Do repeated re-translations preserve the semantics of the original sentence? For example, consider the following English input passed multiple times into and out of French using the Google translator as of 27 December 2006: Better a day earlier than a day late. ==> Améliorer un jour plus tôt qu'un jour tard. ==> To improve one day earlier than a day late. ==> Pour améliorer un jour plus tôt qu'un jour tard. ==> To improve one day earlier than a day late. As noted above and in, this kind of round-trip translation is a very unreliable method of evaluation. == Trustworthiness and security == An interesting peculiarity of Google Translate as of 24 January 2008 (corrected as of 25 January 2008) is the following result when translating from English to Spanish, which shows an embedded joke in the English-Spanish dictionary which has some added poignancy given recent events: Heath Ledger is dead ==> Tom Cruise está muerto This raises the issue of trustworthiness when relying on a machine translation system embedded in a Life-critical system in which the translation system has input to a Safety Critical Decision Making process. Conjointly it raises the issue of whether in a given use the software of the machine translation system is safe from hackers. It is not known whether this feature of Google Translate was the result of a joke/hack or perhaps an unintended consequence of the use of a method such as statistical machine translation. Reporters from CNET Networks asked Google for an explanation on January 24, 2008; Google said only that it was an "internal issue with Google Translate". The mistranslation was the subject of much hilarity and speculation on the Internet. If it is an unintended consequence of the use of a method such as statistical machine translation, and not a joke/hack, then this event is a demonstration of a potential source of critical unreliability in the statistical machine translation method. In human translations, in particular on the part of interpreters, selectivity on the part of the translator in performing a translation is often commented on when one of the two parties being served by the interpreter knows both languages. This leads to the issue of whether a particular translation could be considered verifiable. In this case, a converging round-trip translation would be a kind of verification.

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  Histogram of oriented displacements

  Histogram of oriented displacements (HOD) is a 2D trajectory descriptor. The trajectory is described using a histogram of the directions between each two consecutive points. Given a trajectory T = {P1, P2, P3, ..., Pn}, where Pt is the 2D position at time t. For each pair of positions Pt and Pt+1, calculate the direction angle θ(t, t+1). Value of θ is between 0 and 360. A histogram of the quantized values of θ is created. If the histogram is of 8 bins, the first bin represents all θs between 0 and 45. The histogram accumulates the lengths of the consecutive moves. For each θ, a specific histogram bin is determined. The length of the line between Pt and Pt+1 is then added to the specific histogram bin. To show the intuition behind the descriptor, consider the action of waving hands. At the end of the action, the hand falls down. When describing this down movement, the descriptor does not care about the position from which the hand started to fall. This fall will affect the histogram with the appropriate angles and lengths, regardless of the position where the hand started to fall. HOD records for each moving point: how much it moves in each range of directions. HOD has a clear physical interpretation. It proposes that, a simple way to describe the motion of an object, is to indicate how much distance it moves in each direction. If the movement in all directions are saved accurately, the movement can be repeated from the initial position to the final destination regardless of the displacements order. However, the temporal information will be lost, as the order of movements is not stored-this is what we solve by applying the temporal pyramid, as shown in section \ref{sec:temp-pyramid}. If the angles quantization range is small, classifiers that use the descriptor will overfit. Generalization needs some slack in directions-which can be done by increasing the quantization range.

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  Attention (machine learning)

  In machine learning, attention is a method that determines the importance of each component in a sequence relative to the other components in that sequence. In natural language processing, importance is represented by "soft" weights assigned to each word in a sentence. More generally, attention encodes vectors called token embeddings across a fixed-width sequence that can range from tens to millions of tokens in size. Unlike "hard" weights, which are computed during the backwards training pass, "soft" weights exist only in the forward pass and therefore change with every step of the input. Earlier designs implemented the attention mechanism in a serial recurrent neural network (RNN) language translation system, but a more recent design, namely the transformer, removed the slower sequential RNN and relied more heavily on the faster parallel attention scheme. Inspired by ideas about attention in humans, the attention mechanism was developed to address the weaknesses of using information from the hidden layers of recurrent neural networks. Recurrent neural networks favor information contained in words at the end of a sentence and thus deemed more recent, thereby tending to attenuate the significance and associated predictive weight assigned to information earlier in the sentence. Attention allows a token equal access to any part of a sentence directly, rather than only through the previous state. == History == Additional surveys of the attention mechanism in deep learning are provided by Niu et al. and Soydaner. The major breakthrough came with self-attention, where each element in the input sequence attends to all others, enabling the model to capture global dependencies. This idea was central to the Transformer architecture, which replaced recurrence with attention mechanisms. As a result, Transformers became the foundation for models like BERT, T5 and generative pre-trained transformers (GPT). == Overview == The modern era of machine attention was revitalized by grafting an attention mechanism (Fig 1. orange) to an Encoder-Decoder. Figure 2 shows the internal step-by-step operation of the attention block (A) in Fig 1. === Interpreting attention weights === In translating between languages, alignment is the process of matching words from the source sentence to words of the translated sentence. Networks that perform verbatim translation without regard to word order would show the highest scores along the (dominant) diagonal of the matrix. The off-diagonal dominance shows that the attention mechanism is more nuanced. Consider an example of translating I love you to French. On the first pass through the decoder, 94% of the attention weight is on the first English word I, so the network offers the word je. On the second pass of the decoder, 88% of the attention weight is on the third English word you, so it offers t'. On the last pass, 95% of the attention weight is on the second English word love, so it offers aime. In the I love you example, the second word love is aligned with the third word aime. Stacking soft row vectors together for je, t', and aime yields an alignment matrix: Sometimes, alignment can be multiple-to-multiple. For example, the English phrase look it up corresponds to cherchez-le. Thus, "soft" attention weights work better than "hard" attention weights (setting one attention weight to 1, and the others to 0), as we would like the model to make a context vector consisting of a weighted sum of the hidden vectors, rather than "the best one", as there may not be a best hidden vector. == Variants == Many variants of attention implement soft weights, such as fast weight programmers, or fast weight controllers (1992). A "slow" neural network outputs the "fast" weights of another neural network through outer products. The slow network learns by gradient descent. It was later renamed as "linearized self-attention". Bahdanau-style attention, also referred to as additive attention, Luong-style attention, which is known as multiplicative attention, Early attention mechanisms similar to modern self-attention were proposed using recurrent neural networks. However, the highly parallelizable self-attention was introduced in 2017 and successfully used in the Transformer model, positional attention and factorized positional attention. For convolutional neural networks, attention mechanisms can be distinguished by the dimension on which they operate, namely: spatial attention, channel attention, or combinations. These variants recombine the encoder-side inputs to redistribute those effects to each target output. Often, a correlation-style matrix of dot products provides the re-weighting coefficients. In the figures below, W is the matrix of context attention weights, similar to the formula in Overview section above. == Optimizations == === Flash attention === The size of the attention matrix is proportional to the square of the number of input tokens. Therefore, when the input is long, calculating the attention matrix requires a lot of GPU memory. Flash attention is an implementation that reduces the memory needs and increases efficiency without sacrificing accuracy. It achieves this by partitioning the attention computation into smaller blocks that fit into the GPU's faster on-chip memory, reducing the need to store large intermediate matrices and thus lowering memory usage while increasing computational efficiency. === FlexAttention === FlexAttention is an attention kernel developed by Meta that allows users to modify attention scores prior to softmax and dynamically chooses the optimal attention algorithm. == Applications == Attention is widely used in natural language processing, computer vision, and speech recognition. In NLP, it improves context understanding in tasks like question answering and summarization. In vision, visual attention helps models focus on relevant image regions, enhancing object detection and image captioning. === Attention maps as explanations for vision transformers === From the original paper on vision transformers (ViT), visualizing attention scores as a heat map (called saliency maps or attention maps) has become an important and routine way to inspect the decision making process of ViT models. One can compute the attention maps with respect to any attention head at any layer, while the deeper layers tend to show more semantically meaningful visualization. Attention rollout is a recursive algorithm to combine attention scores across all layers, by computing the dot product of successive attention maps. Because vision transformers are typically trained in a self-supervised manner, attention maps are generally not class-sensitive. When a classification head is attached to the ViT backbone, class-discriminative attention maps (CDAM) combines attention maps and gradients with respect to the class [CLS] token. Some class-sensitive interpretability methods originally developed for convolutional neural networks can be also applied to ViT, such as GradCAM, which back-propagates the gradients to the outputs of the final attention layer. Using attention as basis of explanation for the transformers in language and vision is not without debate. While some pioneering papers analyzed and framed attention scores as explanations, higher attention scores do not always correlate with greater impact on model performances. == Mathematical representation == === Standard scaled dot-product attention === For matrices: Q ∈ R m × d k , K ∈ R n × d k {\displaystyle Q\in \mathbb {R} ^{m\times d_{k}},K\in \mathbb {R} ^{n\times d_{k}}} and V ∈ R n × d v {\displaystyle V\in \mathbb {R} ^{n\times d_{v}}} , the scaled dot-product, or QKV attention, is defined as: Attention ( Q , K , V ) = softmax ( Q K T d k ) V ∈ R m × d v {\displaystyle {\text{Attention}}(Q,K,V)={\text{softmax}}\left({\frac {QK^{T}}{\sqrt {d_{k}}}}\right)V\in \mathbb {R} ^{m\times d_{v}}} where T {\displaystyle {}^{T}} denotes transpose and the softmax function is applied independently to every row of its argument. The matrix Q {\displaystyle Q} contains m {\displaystyle m} queries, while matrices K , V {\displaystyle K,V} jointly contain an unordered set of n {\displaystyle n} key-value pairs. Value vectors in matrix V {\displaystyle V} are weighted using the weights resulting from the softmax operation, so that the rows of the m {\displaystyle m} -by- d v {\displaystyle d_{v}} output matrix are confined to the convex hull of the points in R d v {\displaystyle \mathbb {R} ^{d_{v}}} given by the rows of V {\displaystyle V} . To understand the permutation invariance and permutation equivariance properties of QKV attention, let A ∈ R m × m {\displaystyle A\in \mathbb {R} ^{m\times m}} and B ∈ R n × n {\displaystyle B\in \mathbb {R} ^{n\times n}} be permutation matrices; and D ∈ R m × n {\displaystyle D\in \mathbb {R} ^{m\times n}} an arbitrary matrix. The softmax function is permutation equivariant in the sense that: softmax ( A D B ) = A softmax ( D ) B {\displays

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