In image processing, the free boundary condition is the convention used when applying a convolution kernel to a digital image in which pixel locations that lie outside the image boundaries are interpreted as having a value of zero.[1] The question of what value to assign out-of-bounds pixels may arise, for instance, when applying a 3×3 kernel to the corner pixel in an image.
Cloud-based integration
Cloud-based integration is a form of systems integration business delivered as a cloud computing service that addresses data, process, service-oriented architecture (SOA) and application integration. == Description == Integration platform as a service (iPaaS) is a suite of cloud services enabling customers to develop, execute and govern integration flows between disparate applications. Under the cloud-based iPaaS integration model, customers drive the development and deployment of integrations without installing or managing any hardware or middleware. The iPaaS model allows businesses to achieve integration without big investment into skills or licensed middleware software. iPaaS used to be regarded primarily as an integration tool for cloud-based software applications, used mainly by small to mid-sized business. Over time, a hybrid type of iPaaS—hybrid-IT iPaaS—that connects cloud to on-premises, is becoming increasingly popular. Additionally, large enterprises are exploring new ways of integrating iPaaS into their existing IT infrastructures. Cloud integration was created to break down the data silos, improve connectivity and optimize the business process. Cloud integration has increased in popularity as the usage of Software as a Service solutions has grown. Prior to the emergence of cloud computing in the early 2000s, integration could be categorized as either internal or business to business (B2B). Internal integration requirements were serviced through an on-premises middleware platform and typically utilized a service bus to manage exchange of data between systems. B2B integration was serviced through EDI gateways or value-added network (VAN). The advent of SaaS applications created a new kind of demand which was met through cloud-based integration. Since their emergence, many such services have also developed the capability to integrate legacy or on-premises applications, as well as function as EDI gateways. The following essential features were proposed by one marketing company: Deployed on a multi-tenant, elastic cloud infrastructure Subscription model pricing (operating expense, not capital expenditure) No software development (required connectors should already be available) Users do not perform deployment or manage the platform itself Presence of integration management and monitoring features The emergence of this sector led to new cloud-based business process management tools that do not need to build integration layers - since those are now a separate service. Drivers of growth include the need to integrate mobile app capabilities with proliferating API publishing resources and the growth in demand for the Internet of things functionalities as more 'things' connect to the Internet.
Luciano Floridi
Luciano Floridi (Italian: [luˈtʃaːno ˈflɔːridi]; born 16 November 1964) is an Italian and British philosopher. He is John K. Castle Professor in the Practice of Cognitive Science and Founding Director of the Digital Ethics Center at Yale University. He is also a Professor of Sociology of Culture and Communication at the University of Bologna, Department of Legal Studies, where he is the director of the Centre for Digital Ethics. Furthermore, he is adjunct professor ("distinguished scholar in residence") at the Department of Economics, American University, Washington D.C. He is married to the neuroscientist Anna Christina Nobre. Floridi is best known for his work on two areas of philosophical research: the philosophy of information, and information ethics (also known as digital ethics or computer ethics), for which he received many awards, including the Knight of the Grand Cross of the Order of Merit, Italy's most prestigious honor. According to Scopus, Floridi was the most cited living philosopher in the world in 2020. Between 2008 and 2013, he held the research chair in philosophy of information and the UNESCO Chair in Information and Computer Ethics at the University of Hertfordshire. He was the founder and director of the IEG, an interdepartmental research group on the philosophy of information at the University of Oxford, and of the GPI the research Group in Philosophy of Information at the University of Hertfordshire. He was the founder and director of the SWIF, the Italian e-journal of philosophy (1995–2008). He is a former Governing Body Fellow of St Cross College, Oxford. == Early life and education == Floridi was born in Rome in 1964, and studied at Rome University La Sapienza (laurea, first class with distinction, 1988), where he was originally educated as a historian of philosophy. He soon became interested in analytic philosophy and wrote his tesi di laurea (roughly equivalent to an M.A. thesis) in philosophy of logic, on Michael Dummett's anti-realism. He obtained his Master of Philosophy (1989) and PhD degree (1990) from the University of Warwick, working in epistemology and philosophy of logic with Susan Haack (who was his PhD supervisor) and Michael Dummett. Floridi's early student years are partly recounted in the non-fiction book The Lost Painting: The Quest for a Caravaggio Masterpiece, where he is "Luciano". During his graduate and postdoctoral years, he covered the standard topics in analytic philosophy in search of a new methodology. He sought to approach contemporary problems from a heuristically powerful and intellectually enriching perspective when dealing with lively philosophical issues. During his graduate studies, he began to distance himself from classical analytic philosophy. In his view, the analytic movement had lost its way. For this reason, he worked on pragmatism (especially Peirce) and foundationalist issues in epistemology and philosophy of logic, as well as the history of skepticism. == Academic career and previous positions == Floridi started his academic career as a lecturer in philosophy at the University of Warwick in 1990–1991. He joined the Faculty of Philosophy of the University of Oxford in 1990 and the OUCL (Oxford's Department of Computer Science) in 1999. He was junior research fellow (JRF) in philosophy at Wolfson College, Oxford University (1990–1994), a Frances Yates Fellow in the History of Ideas at the Warburg Institute, University of London (1994–1995) and Research Fellow in philosophy at Wolfson College, Oxford University (1994–2001). During these years in Oxford, he held lectureships in different Colleges. Between 1994 and 1996, he also held a post-doctoral research scholarship at the Department of Philosophy, University of Turin. Between 2001 and 2006, he was Markle Foundation Senior Research Fellow in Information Policy at the Programme in Comparative Media Law and Policy, Oxford University. Between 2002 and 2008, he was associate professor of logic at the Università degli Studi di Bari. In 2006, he became Fellow by Special Election of St Cross College, Oxford University, where he played for the squash team. In 2008, he was appointed full professor of philosophy at the University of Hertfordshire, to hold the newly established research chair in philosophy of information and, in 2009, the UNESCO Chair in Information and Computer Ethics, a position which he held until 2013, when he moved back to Oxford. In 2017, Floridi became a fellow of the Alan Turing Institute and the chair of its Data Ethics Group, holding these positions until 2021 and 2020, respectively. Since 2010 he has been editor-in-chief of Philosophy & Technology (Springer). In January 2023, Floridi announced he would move to Yale at the beginning of the academic year 2023–2024, to take over the position of founding director of the Yale Digital Ethics Center. == Philosophical views == One of Floridi's key contributions is his formulation of the 'Philosophy of Information' (PoI). The PoI provides a framework for understanding the nature of information and its role in the world. According to Floridi, information is a vital resource that shapes our knowledge and understanding of the world. It is not simply a neutral representation of reality but a part of the world, with its own properties, effects, and moral implications. Floridi's PoI has several key components including an 'ontology of information', which defines the nature of information, an 'ethics of information', which provides a framework for evaluating the moral implications of information and information technologies, an 'epistemology of information', that analyses the role of information in the development of knowledge and science, and a 'logic of information', the concentrates on the more formal aspects. The PoI also includes a theory of the 'information environment', the infosphere, which encompasses the physical, social, and cultural contexts in which information is produced, used, and communicated. == Recognitions and awards == 2022 - Knight of the Grand Cross - First Class of the Order of Merit (Cavaliere di Gran Croce Ordine al Merito della Repubblica Italiana, the highest honor in the Italian Republic), awarded through a special decree by the president of the Italian Republic Sergio Mattarella for his work on the philosophy and ethics of information. 2022 - Fellow of the Accademia delle Scienze dell'Istituto di Bologna 2021 - Honorary Doctorate (Laurea honoris causa) in Informatics, University of Skövde, Sweden, for "his groundbreaking work on the philosophy of information". 2020 - Premio Udine Filosofia, Mimesis Festival, for The Logic of Information (OUP, 2019) 2020 - Premio Socrate, Cesare Landa Foundation, for philosophical communication 2019 - CogX Award, for "outstanding achievement in ethics of AI" 2019 - Gilbert Ryle Lectures, Trent University 2019 - Premio Aretè "Maestro della Responsabilità", Nuvolaverde, Confindustria, Gruppo 24 Ore Salone della CSR e dell'innovazione sociale, for ethics of communication 2018 - Thinker Award, IBM, for AI Ethics 2018 - Premio Conoscenza, Conferenza dei Rettori delle Università Italiane (CRUI, equivalent of Universities UK), for achievements in research and communication about digital ethics 2017 - Fellow of the Academy of Social Sciences 2016 - J. Ong Award, Media Ecology Association, for The Fourth Revolution (OUP, 2016) 2016 - Copernicus Scientist Award, Institute for Advanced Studies of the University of Ferrara, in recognition of research in the ethics and philosophy of information 2015 - Fernand Braudel Senior Fellow, European University Institute 2014-15 - Cátedras de Excelencia, University Carlos III of Madrid, for research in philosophy and ethics of information 2013 - Member of the Académie Internationale de Philosophie des Sciences 2013 - Fellow of the British Computer Society 2013 - Weizenbaum Award, International Society for Ethics and Information Technology, for "very significant contribution to the field of information and computer ethics, through his research, service, and vision" 2012 - Covey Award, International Association for Computing and Philosophy, for "outstanding research in computing and philosophy" 2011-12 - Fellow, Center for Information Policy Research, University of Wisconsin–Milwaukee 2011 - Honorary Doctorate (Laurea honoris causa) in philosophy, University of Suceava, Romania, for "his leading research in the philosophy and ethics of information" 2011 - Fellow, World Technology Network, NY, in the category "ethics and technology" 2010 - Vice Chancellor Research Award, University of Hertfordshire 2009 - Fellow of the Society for the Study of Artificial Intelligence and the Simulation of Behaviour (AIBS) 2009-10 - Gauss Professor of the Akademie der Wissenschaften, Göttingen, in recognition of research in the philosophy of information (first philosopher to receive the award, generally given to mathematicians or physicists) 2009 - Barwise Prize, American Philosophical Asso
Transparency in Frontier Artificial Intelligence Act
The Transparency in Frontier Artificial Intelligence Act, also referred to as SB-53, is a 2025 California law which mandates increased transparency for companies building artificial intelligence. SB-53 is primarily focused on assessing and reducing potential catastrophic risks from AI, and is the first bill addressing such risks to be passed into law in America. The bill requires companies to create publicly accessible documents assessing potential "catastrophic risk[s]" from their AI models, as well as publishing documentation on how the model incorporates national and international safety standards. SB-53 also sets up whistleblower protections and procedures for alerting the government to a "critical safety incident". == History == SB-53 was preceded in 2024 by the unsuccessful Safe and Secure Innovation for Frontier Artificial Intelligence Models Act ("SB-1047"), a proposed bill authored by Senator Scott Wiener which was vetoed by Governor Gavin Newsom. Afterwords, Newsom created a "Joint California AI Policy Working Group" to provide recommendations for AI regulation, which guided the drafting of SB-53. Senator Scott Wiener introduced the bill on January 7, 2025, and after a series of amendments, SB-53 passed the Senate 29-8 on September 13. Governor Gavin Newsom approved the bill on September 25, passing it into law. == Provisions == SB-53 applies primarily to companies making at least $500 million in yearly gross revenue. It defines a “frontier model” as any AI trained with over 1026 FLOPS (including fine-tuning), including unreleased internal models. Both the financial and computational thresholds must be met before most of the law is applied, although the threshold can be lowered or otherwise updated by the California Department of Technology in an annual review starting in 2027. Most of the bill's provisions are focused on "catastrophic risks" from AI, which are defined as incidents in which a model contributes to more than 50 deaths or serious injuries, or causes more than one billion dollars ($1,000,000,000) in economic damage from AI-assisted acts (such as cyberattacks or the creation of biological weapons). The bill requires companies to provide publicly accessible safety frameworks for frontier AI models, describing how the company tests for catastrophic risk from its AI, and how it implements protections against such risks. This includes addressing the possibility that the AI may attempt to circumvent internal guardrails or oversight mechanisms. (Certain safety incidents, such as dangerously deceptive model behavior, physical injury, or death, must be reported to California Office of Emergency Services (OES) within 15 days, unless the incident poses imminent physical risk, in which case it must be reported immediately.) The company must follow its published framework, and if any changes are made, the framework should be updated within 30 days, and justification for said changes must also be made public. Additionally, all frontier companies are required to publish basic information about newly released frontier models (such as terms of service, supported languages, and intended use), although only large companies (making over $500 million annually) need to publish full safety frameworks. SB-53 also establishes various whistleblower protections for covered employees. Large companies must have anonymous whistleblowing channels in place which protect employees from retaliation from reporting risks to state or federal authorities if they have reasonable cause to believe that their employer is substantially risking public health and safety.
Mathematical model
A mathematical model is an abstract description of a concrete system using mathematical concepts and language. The process of developing a mathematical model is termed mathematical modeling. Mathematical models are used in many fields, including applied mathematics, natural sciences, social sciences and engineering. In particular, the field of operations research studies the use of mathematical modelling and related tools to solve problems in business or military operations. A model may help to characterize a system by studying the effects of different components, which may be used to make predictions about behavior or solve specific problems. == Elements of a mathematical model == Mathematical models can take many forms, including dynamical systems, statistical models, differential equations, or game theoretic models. These and other types of models can overlap, with a given model involving a variety of abstract structures. In many cases, the quality of a scientific field depends on how well the mathematical models developed on the theoretical side agree with results of repeatable experiments. Lack of agreement between theoretical mathematical models and experimental measurements often leads to important advances as better theories are developed. In the physical sciences, a traditional mathematical model contains most of the following elements: Governing equations Supplementary sub-models Defining equations Constitutive equations Assumptions and constraints Initial and boundary conditions Classical constraints and kinematic equations == Classifications == Mathematical models are of different types: === Linear vs. nonlinear === If all the operators in a mathematical model exhibit linearity, the resulting mathematical model is defined as linear. All other models are considered nonlinear. The definition of linearity and nonlinearity is dependent on context, and linear models may have nonlinear expressions in them. For example, in a statistical linear model, it is assumed that a relationship is linear in the parameters, but it may be nonlinear in the predictor variables. Similarly, a differential equation is said to be linear if it can be written with linear differential operators, but it can still have nonlinear expressions in it. In a mathematical programming model, if the objective functions and constraints are represented entirely by linear equations, then the model is regarded as a linear model. If one or more of the objective functions or constraints are represented with a nonlinear equation, then the model is known as a nonlinear model. Linear structure implies that a problem can be decomposed into simpler parts that can be treated independently or analyzed at a different scale, and therefore that the results will remain valid if the initial is recomposed or rescaled. Nonlinearity, even in fairly simple systems, is often associated with phenomena such as chaos and irreversibility. Although there are exceptions, nonlinear systems and models tend to be more difficult to study than linear ones. A common approach to nonlinear problems is linearization, but this can be problematic if one is trying to study aspects such as irreversibility, which are strongly tied to nonlinearity. === Static vs. dynamic === A dynamic model accounts for time-dependent changes in the state of the system, while a static (or steady-state) model calculates the system in equilibrium, and thus is time-invariant. Dynamic models are typically represented by differential equations or difference equations. === Explicit vs. implicit === If all of the input parameters of the overall model are known, and the output parameters can be calculated by a finite series of computations, the model is said to be explicit. But sometimes it is the output parameters which are known, and the corresponding inputs must be solved for by an iterative procedure, such as Newton's method or Broyden's method. In such a case the model is said to be implicit. For example, a jet engine's physical properties such as turbine and nozzle throat areas can be explicitly calculated given a design thermodynamic cycle (air and fuel flow rates, pressures, and temperatures) at a specific flight condition and power setting, but the engine's operating cycles at other flight conditions and power settings cannot be explicitly calculated from the constant physical properties. === Discrete vs. continuous === A discrete model treats objects as discrete, such as the particles in a molecular model or the states in a statistical model; while a continuous model represents the objects in a continuous manner, such as the velocity field of fluid in pipe flows, temperatures and stresses in a solid, and electric field that applies continuously over the entire model due to a point charge. === Deterministic vs. probabilistic (stochastic) === A deterministic model is one in which every set of variable states is uniquely determined by parameters in the model and by sets of previous states of these variables; therefore, a deterministic model always performs the same way for a given set of initial conditions. Conversely, in a stochastic model—usually called a "statistical model"—randomness is present, and variable states are not described by unique values, but rather by probability distributions. === Deductive, inductive, or floating === A deductive model is a logical structure based on a theory. An inductive model arises from empirical findings and generalization from them. If a model rests on neither theory nor observation, it may be described as a 'floating' model. Application of mathematics in social sciences outside of economics has been criticized for unfounded models. Application of catastrophe theory in science has been characterized as a floating model. === Strategic vs. non-strategic === Models used in game theory are distinct in the sense that they model agents with incompatible incentives, such as competing species or bidders in an auction. Strategic models assume that players are autonomous decision makers who rationally choose actions that maximize their objective function. A key challenge of using strategic models is defining and computing solution concepts such as the Nash equilibrium. An interesting property of strategic models is that they separate reasoning about rules of the game from reasoning about behavior of the players. == Construction == In business and engineering, mathematical models may be used to maximize a certain output. The system under consideration will require certain inputs. The system relating inputs to outputs depends on other variables too: decision variables, state variables, exogenous variables, and random variables. Decision variables are sometimes known as independent variables. Exogenous variables are sometimes known as parameters or constants. The variables are not independent of each other as the state variables are dependent on the decision, input, random, and exogenous variables. Furthermore, the output variables are dependent on the state of the system (represented by the state variables). Objectives and constraints of the system and its users can be represented as functions of the output variables or state variables. The objective functions will depend on the perspective of the model's user. Depending on the context, an objective function is also known as an index of performance, as it is some measure of interest to the user. Although there is no limit to the number of objective functions and constraints a model can have, using or optimizing the model becomes more involved (computationally) as the number increases. For example, economists often apply linear algebra when using input–output models. Complicated mathematical models that have many variables may be consolidated by use of vectors where one symbol represents several variables. === A priori information === Mathematical modeling problems are often classified into black box or white box models, according to how much a priori information on the system is available. A black-box model is a system of which there is no a priori information available. A white-box model (also called glass box or clear box) is a system where all necessary information is available. Practically all systems are somewhere between the black-box and white-box models, so this concept is useful only as an intuitive guide for deciding which approach to take. Usually, it is preferable to use as much a priori information as possible to make the model more accurate. Therefore, the white-box models are usually considered easier, because if you have used the information correctly, then the model will behave correctly. Often the a priori information comes in forms of knowing the type of functions relating different variables. For example, if we make a model of how a medicine works in a human system, we know that usually the amount of medicine in the blood is an exponentially decaying function, but we are still left with several unknown parameters; how
PagedAttention
PagedAttention is an attention algorithm for efficient serving of large language models (LLMs). It was introduced in 2023 by Woosuk Kwon and colleagues in the paper Efficient Memory Management for Large Language Model Serving with PagedAttention, alongside the vLLM serving engine. The method stores the key–value cache used during autoregressive decoding in fixed-size blocks that can be mapped to non-contiguous physical memory, borrowing ideas from virtual memory, paging, and operating system design. == Background == In transformer inference, the key–value cache grows with sequence length and the number of concurrent requests. Kwon et al. argued that earlier serving systems typically reserved contiguous cache regions in advance, which caused reserved space, internal fragmentation, and external fragmentation. In their experiments, the paper reported that the effective memory utilization of previous systems could fall as low as 20.4%. == Description == PagedAttention partitions the cache of each sequence into fixed-size KV blocks. A request's cache is represented as a sequence of logical blocks, while a block table maps those logical blocks to physical GPU-memory blocks. As a result, neighboring logical blocks do not need to be contiguous in physical memory, and new blocks can be allocated on demand as generation proceeds. The design also makes it easier to share cache state across related decoding paths. In vLLM, physical blocks can be reference-counted and shared among requests or branches, with block-granularity copy-on-write used when a shared block must be modified. The original paper applied this design to parallel sampling, beam search, and prompts with shared prefixes. == Mathematical formulation == For a query token i {\displaystyle i} in causal self-attention, the standard attention output can be written as a i j = exp ( q i ⊤ k j / d ) ∑ t = 1 i exp ( q i ⊤ k t / d ) , o i = ∑ j = 1 i a i j v j {\displaystyle a_{ij}={\frac {\exp(\mathbf {q} _{i}^{\top }\mathbf {k} _{j}/{\sqrt {d}})}{\sum _{t=1}^{i}\exp(\mathbf {q} _{i}^{\top }\mathbf {k} _{t}/{\sqrt {d}})}},\;\mathbf {o} _{i}=\sum _{j=1}^{i}a_{ij}\mathbf {v} _{j}} where q i {\displaystyle \mathbf {q} _{i}} , k j {\displaystyle \mathbf {k} _{j}} , and v j {\displaystyle \mathbf {v} _{j}} are the query, key, and value vectors, and d {\displaystyle d} is the attention dimension. If the cache is partitioned into blocks of size B {\displaystyle B} , the key and value blocks may be written as K j = ( k ( j − 1 ) B + 1 , … , k j B ) , V j = ( v ( j − 1 ) B + 1 , … , v j B ) {\displaystyle \mathbf {K} _{j}=(\mathbf {k} _{(j-1)B+1},\ldots ,\mathbf {k} _{jB}),\;\mathbf {V} _{j}=(\mathbf {v} _{(j-1)B+1},\ldots ,\mathbf {v} _{jB})} PagedAttention then performs the computation blockwise: A i j = exp ( q i ⊤ K j / d ) ∑ t = 1 ⌈ i / B ⌉ exp ( q i ⊤ K t / d ) , o i = ∑ j = 1 ⌈ i / B ⌉ V j A i j ⊤ {\displaystyle \mathbf {A} _{ij}={\frac {\exp(\mathbf {q} _{i}^{\top }\mathbf {K} _{j}/{\sqrt {d}})}{\sum _{t=1}^{\lceil i/B\rceil }\exp(\mathbf {q} _{i}^{\top }\mathbf {K} _{t}/{\sqrt {d}})}},\;\mathbf {o} _{i}=\sum _{j=1}^{\lceil i/B\rceil }\mathbf {V} _{j}\mathbf {A} _{ij}^{\top }} where A i j {\displaystyle \mathbf {A} _{ij}} is the vector of attention scores for the j {\displaystyle j} -th KV block. In the formulation given by Kwon et al., this preserves the causal attention calculation while allowing the key and value blocks to reside in non-contiguous physical memory. == Performance and use == The vLLM paper reported that, on its evaluated workloads, the use of PagedAttention and the associated memory-management design improved serving throughput by 2–4× over the compared baselines, including FasterTransformer and Orca, while preserving model outputs. In experiments on OPT-13B with the Alpaca trace, the paper also reported memory savings of 6.1–9.8% for parallel sampling and 37.6–55.2% for beam search through KV-block sharing. A 2024 survey of LLM serving systems described PagedAttention as having become an industry norm in LLM serving frameworks, citing support in TGI, vLLM, and TensorRT-LLM. == Limitations and alternatives == Subsequent work has described trade-offs in the approach. The 2025 vAttention paper argued that PagedAttention requires attention kernels to be rewritten to support paging and increases software complexity, portability issues, redundancy, and execution overhead, proposing instead a memory manager that keeps the cache contiguous in virtual memory while relying on demand paging for physical allocation. === vAttention === Unlike PagedAttention, vAttention does not introduce a different attention rule; it retains the standard attention computation Attention ( q i , K , V ) = softmax ( q i K ⊤ s c a l e ) V . {\displaystyle \operatorname {Attention} (q_{i},K,V)=\operatorname {softmax} \left({\frac {q_{i}K^{\top }}{\mathrm {scale} }}\right)V.} In the notation of Prabhu et al., the key and value tensors for a request seen so far are K , V ∈ R L ′ × ( H × D ) {\displaystyle K,V\in \mathbb {R} ^{L'\times (H\times D)}} , where L ′ {\displaystyle L'} is the context length seen so far, H {\displaystyle H} is the number of KV heads on a worker, and D {\displaystyle D} is the dimension of each KV head. In systems prior to PagedAttention, the K cache (or V cache) at each layer of a worker is typically allocated as a 4D tensor of shape [ B , L , H , D ] , {\displaystyle [B,L,H,D],} where B {\displaystyle B} is batch size and L {\displaystyle L} is the maximum context length supported by the model. vAttention preserves this contiguous virtual-memory view while deferring physical-memory allocation to runtime. A serving framework maintains separate K and V tensors for each layer, so vAttention reserves 2 N {\displaystyle 2N} virtual-memory buffers on a worker, where N {\displaystyle N} is the number of layers managed by that worker. The maximum size of one virtual-memory buffer is B S = B × S , {\displaystyle BS=B\times S,} where S {\displaystyle S} is the maximum size of a single request's per-layer K cache (or V cache) on a worker. The paper defines S = L × H × D × P , {\displaystyle S=L\times H\times D\times P,} where P {\displaystyle P} is the number of bytes needed to store one element. In this formulation, vAttention keeps the KV cache contiguous in virtual memory and relies on demand paging for physical allocation, rather than modifying the attention kernel to operate over non-contiguous KV-cache blocks.
Predictive Model Markup Language
The Predictive Model Markup Language (PMML) is an XML-based predictive model interchange format conceived by Robert Lee Grossman, then the director of the National Center for Data Mining at the University of Illinois at Chicago. PMML provides a way for analytic applications to describe and exchange predictive models produced by data mining and machine learning algorithms. It supports common models such as logistic regression and other feedforward neural networks. Version 0.9 was published in 1998. Subsequent versions have been developed by the Data Mining Group. Since PMML is an XML-based standard, the specification comes in the form of an XML schema. PMML itself is a mature standard with over 30 organizations having announced products supporting PMML. == PMML components == A PMML file can be described by the following components: Header: contains general information about the PMML document, such as copyright information for the model, its description, and information about the application used to generate the model such as name and version. It also contains an attribute for a timestamp which can be used to specify the date of model creation. Data Dictionary: contains definitions for all the possible fields used by the model. It is here that a field is defined as continuous, categorical, or ordinal (attribute optype). Depending on this definition, the appropriate value ranges are then defined as well as the data type (such as, string or double). Data Transformations: transformations allow for the mapping of user data into a more desirable form to be used by the mining model. PMML defines several kinds of simple data transformations. Normalization: map values to numbers, the input can be continuous or discrete. Discretization: map continuous values to discrete values. Value mapping: map discrete values to discrete values. Functions (custom and built-in): derive a value by applying a function to one or more parameters. Aggregation: used to summarize or collect groups of values. Model: contains the definition of the data mining model. E.g., A multi-layered feedforward neural network is represented in PMML by a "NeuralNetwork" element which contains attributes such as: Model Name (attribute modelName) Function Name (attribute functionName) Algorithm Name (attribute algorithmName) Activation Function (attribute activationFunction) Number of Layers (attribute numberOfLayers) This information is then followed by three kinds of neural layers which specify the architecture of the neural network model being represented in the PMML document. These attributes are NeuralInputs, NeuralLayer, and NeuralOutputs. Besides neural networks, PMML allows for the representation of many other types of models including support vector machines, association rules, Naive Bayes classifier, clustering models, text models, decision trees, and different regression models. Mining Schema: a list of all fields used in the model. This can be a subset of the fields as defined in the data dictionary. It contains specific information about each field, such as: Name (attribute name): must refer to a field in the data dictionary Usage type (attribute usageType): defines the way a field is to be used in the model. Typical values are: active, predicted, and supplementary. Predicted fields are those whose values are predicted by the model. Outlier Treatment (attribute outliers): defines the outlier treatment to be use. In PMML, outliers can be treated as missing values, as extreme values (based on the definition of high and low values for a particular field), or as is. Missing Value Replacement Policy (attribute missingValueReplacement): if this attribute is specified then a missing value is automatically replaced by the given values. Missing Value Treatment (attribute missingValueTreatment): indicates how the missing value replacement was derived (e.g. as value, mean or median). Targets: allows for post-processing of the predicted value in the format of scaling if the output of the model is continuous. Targets can also be used for classification tasks. In this case, the attribute priorProbability specifies a default probability for the corresponding target category. It is used if the prediction logic itself did not produce a result. This can happen, e.g., if an input value is missing and there is no other method for treating missing values. Output: this element can be used to name all the desired output fields expected from the model. These are features of the predicted field and so are typically the predicted value itself, the probability, cluster affinity (for clustering models), standard error, etc. The latest release of PMML, PMML 4.1, extended Output to allow for generic post-processing of model outputs. In PMML 4.1, all the built-in and custom functions that were originally available only for pre-processing became available for post-processing too. == PMML 4.0, 4.1, 4.2 and 4.3 == PMML 4.0 was released on June 16, 2009. Examples of new features included: Improved Pre-Processing Capabilities: Additions to built-in functions include a range of Boolean operations and an If-Then-Else function. Time Series Models: New exponential Smoothing models; also place holders for ARIMA, Seasonal Trend Decomposition, and Spectral density estimation, which are to be supported in the near future. Model Explanation: Saving of evaluation and model performance measures to the PMML file itself. Multiple Models: Capabilities for model composition, ensembles, and segmentation (e.g., combining of regression and decision trees). Extensions of Existing Elements: Addition of multi-class classification for Support Vector Machines, improved representation for Association Rules, and the addition of Cox Regression Models. PMML 4.1 was released on December 31, 2011. New features included: New model elements for representing Scorecards, k-Nearest Neighbors (KNN) and Baseline Models. Simplification of multiple models. In PMML 4.1, the same element is used to represent model segmentation, ensemble, and chaining. Overall definition of field scope and field names. A new attribute that identifies for each model element if the model is ready or not for production deployment. Enhanced post-processing capabilities (via the Output element). PMML 4.2 was released on February 28, 2014. New features include: Transformations: New elements for implementing text mining New built-in functions for implementing regular expressions: matches, concat, and replace Simplified outputs for post-processing Enhancements to Scorecard and Naive Bayes model elements PMML 4.3 was released on August 23, 2016. New features include: New Model Types: Gaussian Process Bayesian Network New built-in functions Usage clarifications Documentation improvements Version 4.4 was released in November 2019. == Release history == == Data Mining Group == The Data Mining Group is a consortium managed by the Center for Computational Science Research, Inc., a nonprofit founded in 2008. The Data Mining Group also developed a standard called Portable Format for Analytics, or PFA, which is complementary to PMML.