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And why its architecture is awesome, at a top level. This post has also been published to my personal blog A coding dance Here’s a post concerning the new (future) react-native architecture React Native is often presented as a game changer that allows to run JavaScript code inside a mobile environment. Its main strength is that it doesn’t rely on like other competitors ( , , …), but on the actual real materials provided by the different platforms. It has built-in access to all the native views and components, and to about 70 specific device APIs by default ( ). webviews Phonegap Ionic Cordova you can extend it When writing React Native apps, we build native UIs. And that’s the key point, we create instances just like we would have with platform specific languages: UIView RCTView implements UIView My first assumption on this framework was something like: They probably create an from the JS code and transform it to make it run on multiple devices. AST That would make sense and that’s actually what G does while building apps (with ). But that’s not the React Native way. oogle/Flutter Dartlang The main problem with this approach is that targeting platforms for compilation based on JavaScript code would imply the creation of new compilers. I don’t know any existing tool accepting JavaScript as entry code that is able to produce code for every targeted platform ( ). eventuall see Jasonette NB: some have tried but only for mobile development with opinionated approaches But what currently exist are compilers that target their own specific platform. For example, we have compilers that accept Java / Kotlin code and target Android platform, or Obj-C / Swift targeting iOS platform. It exists many compilers for different languages and targets. They do their job well because to create optimised artefacts for them. they have been designed React Native is built in such a way that it uses existing compilers: It’s built with a really opened architecture that allows the code to be run, not only on mobile devices, but also on other platforms: Desktop applications Virtual Reality Many more It can also be used with other frameworks: , a React Native port of . Weex Vuejs a custom . Angular renderer that allows to run ng apps in devices, with React Native So how did the team build such a framework, that is platform and framework agnostic, by using the existing tools & compilers? Multiple realms interacting, nothing else Let’s take a step back and look at the big picture of React Native. React Native deals with two realms, the JavaScript one and the Native one. Both of them are able to share information. They communicate using a “bridge”, which is definitely the very heart of the React Native architecture, the part that offers so much flexibility. The bridge is the concept that provides a way for bidirectional and asynchronous communications between these two universes. What’s important here is that they are completely written in different technologies, but they are able to communicate. JS threads communicates with the native ones through the bridge Remember your backend side Let’s remember when we were coding distributed backend applications with multi-service communications. How do we manage communication between two services that are completely different at a language/platform level ? We used interoperable languages, such as JSON or XML, and we relied on asynchronous protocols such as (or any other). AMQP Bidirectional communications between heterogeneous services If we want these two services to communicate, we rely on a message queue. The first service pushes some commands inside the queue and the other one has to execute these commands . when possible React Native behaves the same way. The JavaScript realm sends asynchronous JSON messages describing the action the Native part is supposed to accomplish. For example, the JavaScript side will send information concerning When the Native side is ready, it will effectively create the views: the views that must be created by the Native side. JavaScript sends commands asynchronously to the Native side for view management, with JSON In React Native, the bridge endorses the message broker role, handling asynchronous commands between the two different worlds. It offers multiple possibilities: since it’s asynchronous, it’s non blocking, and therefore allows for smooth view management on the screen (~6O fps is the React Native golden goal) since it’s decoupled and based on interoperable languages, it’s wide open to other frameworks and rendering systems provided that they respect the React Native bridge command interface The more the bridge’s language is ubiquitous and universal, the more the possibilities are… and it indeed! is The bridge implementation The bridge is built in C/C++ and thus, can be run on multiple platforms, OS etc... It embeds the in, which exposes APIs to access the actual JavacriptCore VM capabilities. Many people use these APIs on the Obj-C and Swift world. But there is a C API, and the Obj-C one is actually just a wrapper. Apple JavaScriptCore framework With this in mind, JavaScript code can be run inside a C/C++ program. It can inject variables, functions and declare globals to enhance the JavaScript existing code. React Native relies on this kind of magic to make JavaScript communicate with the native world and thus trigger actions in the C/C++ world. Injecting stuff inside the JavaScript code also means that functions can be executed by the C/C++ code. This diagram quickly sums up how the JavaScript world is able to deal with the C/C++ one: The JS code is managed by the JSCore framework The native side The communication on the native side is “the easiest” part. Let’s begin with the iOS platform. Since Obj-C is an extension of the C language, it can communicate with it natively. This way, exchanges between the bridge and the Swift / Obj-C world are easy and natural. High level diagram of JS interacting with iOS world On Android, we need to rely on the to dialog with the bridge. Java Native Interface High level diagram of JS interacting with Android world Here’s an old but really awesome and deep post explaining how the bridge is implemented . on iOS by Tadeu Zagallo Let me know if you have further questions regarding React Native internals. I’ll try to provide all that I know on the topic. Thanks to my mates @ and for the reviews ! Zenika @M6Web

Understanding the React Native bridge concept

Comprender el concepto de puente de React Native

This paper is available on arxiv under CC BY-NC-ND 4.0 DEED license.
Authors:
(1) U Jin Choi, Department of mathematical science, Korea Advanced Institute of Science and Technology & ujchoi@kaist.ac.kr;
(2) Kyung Soo Rim, Department of mathematics, Sogang University & ksrim@sogang.ac.kr. Table of Links Introduction
Organization and notation
Problem Setting and Preliminaries
Generalized Wiener algebra and Fréchet derivative
Characterization of coefficients
Coefficients from an ergodic process
Conclusion & References To state the main theorem of this section we need the following lemma. This completes the proof. This paper is available on arxiv under CC BY-NC-ND 4.0 DEED license. Authors: (1) U Jin Choi, Department of mathematical science, Korea Advanced Institute of Science and Technology & ujchoi@kaist.ac.kr; (2) Kyung Soo Rim, Department of mathematics, Sogang University & ksrim@sogang.ac.kr. This paper is available on arxiv under CC BY-NC-ND 4.0 DEED license. Authors: Authors: (1) U Jin Choi, Department of mathematical science, Korea Advanced Institute of Science and Technology & ujchoi@kaist.ac.kr; (2) Kyung Soo Rim, Department of mathematics, Sogang University & ksrim@sogang.ac.kr. Table of Links Introduction Organization and notation Problem Setting and Preliminaries Generalized Wiener algebra and Fréchet derivative Characterization of coefficients Coefficients from an ergodic process Conclusion & References Introduction Introduction Organization and notation Organization and notation Problem Setting and Preliminaries Problem Setting and Preliminaries Generalized Wiener algebra and Fréchet derivative Generalized Wiener algebra and Fréchet derivative Characterization of coefficients Characterization of coefficients Coefficients from an ergodic process Coefficients from an ergodic process Conclusion & References Conclusion & References To state the main theorem of this section we need the following lemma. This completes the proof.

Variational Non-Bayesian Inference: Generalized Wiener Algebra and Fréchet Derivative

This paper is available on arxiv under CC BY-NC-ND 4.0 DEED license.
Authors:
(1) U Jin Choi, Department of mathematical science, Korea Advanced Institute of Science and Technology & ujchoi@kaist.ac.kr;
(2) Kyung Soo Rim, Department of mathematics, Sogang University & ksrim@sogang.ac.kr. Table of Links Introduction
Organization and notation
Problem Setting and Preliminaries
Generalized Wiener algebra and Fréchet derivative
Characterization of coefficients
Coefficients from an ergodic process
Conclusion & References Conclusion In this mathematical study, we delve into the realm of statistical inference and introduce a novel approach to variational non-Bayesian inference. Most significantly, we propose a new method for uniquely determining the hidden PDF solely from a random sample while leveraging theory. Beyond merely approximating the shape of the unrevealed PDF, we yield results that provide practical assistance in inferring important moments, such as the mean and variance, from the estimated PDF. These days, methods utilizing artificial intelligence are widely employed, but they generally exhibit a drawback of depending on initial conditions, i.e., a prior distribution, and iterative computations, i.e., a backpropagation. The limitations of such approaches lie in their reliance on these conditions to achieve global optimization. We emphasize the significant contribution of the proposed method to predictive and classification models, even without any information on populations, highlighting its potential applications in various domains such as finance, economics, weather forecasting, and machine learning, all of which present unique challenges. The most well-known method for approximating hidden PDFs is the variational approach in a Bayesian context. In contrast, our study extends this problem by seeking to precisely determine unknown PDFs through a system of equations. Our approach includes proving the Fréchet differentiability of entropy to establish the uniqueness of the energy function space in the Wiener algebra. We then derive the unique determination of the energy function through the minimization of KL-divergence. Leveraging the Ergodic theorem, we elucidate that solutions to equations comprising polynomial function series are the coefficients of the energy function and numerically substantiate the convergence of partial sums of the energy function obtained from a finite number of equations. In summary, our mathematical exploration has unveiled the potential of variational Non-Bayesian inference in Wiener space. We anticipate that these mathematical ideas can offer an innovative framework for probability density estimation and predictive modeling. Ultimately, our research emphasizes its potential contribution to reshaping mathematical horizons and expanding the boundaries of knowledge in the field of statistical methodology. REFERENCES [1] K. Bharath A. Saha and S. Kurtek, A geometric variational approach to bayesian inference, Journal of the American Statistical Association 115 (2020), no. 530, 822–835. [2] P. Alquier and J. Ridgway, Concentration of tempered posteriors and of their variational approximations, The Annals of Statistics 48 (2020), no. 3, 1475–1497. [3] A. R. Barron and C. Sheu, Approximation of density functions by sequences of exponential families, The Annals of Statistics 19 (1991), no. 3, 1347–1369. [4] C. M. Bishop and M. E. Tipping, Probabilistic principal component analysis, J. R. Statist. Soc. B 61 (1999), no. 3, 611–622. [5] F. W. Olver, D. Lozier, R. F. Boisvert and C. W. Clark, NIST Handbook of Mathematical Functions, Cambridge University Press, 2010. [6] C Brouder and F Patras, One-particle irreducibility with initial correlations, (2011). [7] I. Csiszar, I-divergence geometry of probability distributions and minimization problems, Ann. Probab. 3 (1975), no. 1, 146–158. [8] G. Cybenko, Approximation by superpositions of a sigmoidal function, Mathematics of Control, Signals and Systems 2 (1989), 303–314. [9] L. Grafakos, Classical and Modern Fourier Analysis, Prentice Hall, 2003. [10] D. E. Rumelhart, G. E. Hinton and R. Williams, Learning representations by back-propagating errors, Nature 323 (1986), 533–536. [11] G. E. Hinton, A Practical Guide to Training Restricted Boltzmann Machines, University of Toronto, 2010. [12] K. Hornik, Approximation capabilities of multilayer feedforward networks, Neural Networks 4 (1991), no. 2, 251–257. [13] Y. Katznelson, An introduction to harmonic analysis (third ed.), New York: Cambridge Mathematical Library, 2004. [14] D. M. Blei, A. Kucukelbir and J. D. McAuliffe, Variational inference: A review for statisticians, Jour. of the American Statistical Association 112 (2017), no. 518, 859–877. [15] S. Kullback and R. A. Leibler, On information and sufficiency, Ann. Math. Statistics 22 (1951), no. 1, 79–86. [16] H. M. Möller and R. Tenberg, Multivariate polynomial system solving using intersections of eigenspaces, Journal of Symbolic Computation 32 (2001), no. 5, 513–531. [17] B. Mourrain, V. Y. Pan and O. Ruatta, Accelerated solution of multivariate polynomial systems of equations, SIAM Journal on Computing 32 (2003), no. 2, 435–454. [18] W. Rudin, Functional Analysis, McGraw-Hill, 1991. [19] D. W. Stroock, Probability theory, an analytic view, Cambridge University Press, 1993. [20] B. Sturmfels, Solving systems of polynomial equations (cbms regional conference series in mathematics), Amer. Math. Soc., 2002. [21] N. Wiener, Tauberian theorems, Annals of Mathematics 33 (1932), no. 1, 1–100. [22] F. Zhang and C. Gao, Convergence rates of variational posterior distributions, The Annals of Statistics 48 (2020), no. 4, 2180–2207. This paper is available on arxiv under CC BY-NC-ND 4.0 DEED license. Authors: (1) U Jin Choi, Department of mathematical science, Korea Advanced Institute of Science and Technology & ujchoi@kaist.ac.kr; (2) Kyung Soo Rim, Department of mathematics, Sogang University & ksrim@sogang.ac.kr. This paper is available on arxiv under CC BY-NC-ND 4.0 DEED license. Authors: Authors: (1) U Jin Choi, Department of mathematical science, Korea Advanced Institute of Science and Technology & ujchoi@kaist.ac.kr; (2) Kyung Soo Rim, Department of mathematics, Sogang University & ksrim@sogang.ac.kr. Table of Links Introduction Organization and notation Problem Setting and Preliminaries Generalized Wiener algebra and Fréchet derivative Characterization of coefficients Coefficients from an ergodic process Conclusion & References Introduction Introduction Organization and notation Organization and notation Problem Setting and Preliminaries Problem Setting and Preliminaries Generalized Wiener algebra and Fréchet derivative Generalized Wiener algebra and Fréchet derivative Characterization of coefficients Characterization of coefficients Coefficients from an ergodic process Coefficients from an ergodic process Conclusion & References Conclusion & References Conclusion In this mathematical study, we delve into the realm of statistical inference and introduce a novel approach to variational non-Bayesian inference. Most significantly, we propose a new method for uniquely determining the hidden PDF solely from a random sample while leveraging theory. Beyond merely approximating the shape of the unrevealed PDF, we yield results that provide practical assistance in inferring important moments, such as the mean and variance, from the estimated PDF. These days, methods utilizing artificial intelligence are widely employed, but they generally exhibit a drawback of depending on initial conditions, i.e., a prior distribution, and iterative computations, i.e., a backpropagation. The limitations of such approaches lie in their reliance on these conditions to achieve global optimization. We emphasize the significant contribution of the proposed method to predictive and classification models, even without any information on populations, highlighting its potential applications in various domains such as finance, economics, weather forecasting, and machine learning, all of which present unique challenges. The most well-known method for approximating hidden PDFs is the variational approach in a Bayesian context. In contrast, our study extends this problem by seeking to precisely determine unknown PDFs through a system of equations. Our approach includes proving the Fréchet differentiability of entropy to establish the uniqueness of the energy function space in the Wiener algebra. We then derive the unique determination of the energy function through the minimization of KL-divergence. Leveraging the Ergodic theorem, we elucidate that solutions to equations comprising polynomial function series are the coefficients of the energy function and numerically substantiate the convergence of partial sums of the energy function obtained from a finite number of equations. In summary, our mathematical exploration has unveiled the potential of variational Non-Bayesian inference in Wiener space. We anticipate that these mathematical ideas can offer an innovative framework for probability density estimation and predictive modeling. Ultimately, our research emphasizes its potential contribution to reshaping mathematical horizons and expanding the boundaries of knowledge in the field of statistical methodology. REFERENCES [1] K. Bharath A. Saha and S. Kurtek, A geometric variational approach to bayesian inference, Journal of the American Statistical Association 115 (2020), no. 530, 822–835. [2] P. Alquier and J. Ridgway, Concentration of tempered posteriors and of their variational approximations, The Annals of Statistics 48 (2020), no. 3, 1475–1497. [3] A. R. Barron and C. Sheu, Approximation of density functions by sequences of exponential families, The Annals of Statistics 19 (1991), no. 3, 1347–1369. [4] C. M. Bishop and M. E. Tipping, Probabilistic principal component analysis, J. R. Statist. Soc. B 61 (1999), no. 3, 611–622. [5] F. W. Olver, D. Lozier, R. F. Boisvert and C. W. Clark, NIST Handbook of Mathematical Functions, Cambridge University Press, 2010. [6] C Brouder and F Patras, One-particle irreducibility with initial correlations, (2011). [7] I. Csiszar, I-divergence geometry of probability distributions and minimization problems, Ann. Probab. 3 (1975), no. 1, 146–158. [8] G. Cybenko, Approximation by superpositions of a sigmoidal function, Mathematics of Control, Signals and Systems 2 (1989), 303–314. [9] L. Grafakos, Classical and Modern Fourier Analysis, Prentice Hall, 2003. [10] D. E. Rumelhart, G. E. Hinton and R. Williams, Learning representations by back-propagating errors, Nature 323 (1986), 533–536. [11] G. E. Hinton, A Practical Guide to Training Restricted Boltzmann Machines, University of Toronto, 2010. [12] K. Hornik, Approximation capabilities of multilayer feedforward networks, Neural Networks 4 (1991), no. 2, 251–257. [13] Y. Katznelson, An introduction to harmonic analysis (third ed.), New York: Cambridge Mathematical Library, 2004. [14] D. M. Blei, A. Kucukelbir and J. D. McAuliffe, Variational inference: A review for statisticians, Jour. of the American Statistical Association 112 (2017), no. 518, 859–877. [15] S. Kullback and R. A. Leibler, On information and sufficiency, Ann. Math. Statistics 22 (1951), no. 1, 79–86. [16] H. M. Möller and R. Tenberg, Multivariate polynomial system solving using intersections of eigenspaces, Journal of Symbolic Computation 32 (2001), no. 5, 513–531. [17] B. Mourrain, V. Y. Pan and O. Ruatta, Accelerated solution of multivariate polynomial systems of equations, SIAM Journal on Computing 32 (2003), no. 2, 435–454. [18] W. Rudin, Functional Analysis, McGraw-Hill, 1991. [19] D. W. Stroock, Probability theory, an analytic view, Cambridge University Press, 1993. [20] B. Sturmfels, Solving systems of polynomial equations (cbms regional conference series in mathematics), Amer. Math. Soc., 2002. [21] N. Wiener, Tauberian theorems, Annals of Mathematics 33 (1932), no. 1, 1–100. [22] F. Zhang and C. Gao, Convergence rates of variational posterior distributions, The Annals of Statistics 48 (2020), no. 4, 2180–2207.

Variational Non-Bayesian Inference of the Probability Density Function: Conclusion & References

This paper is available on arxiv under CC BY-NC-ND 4.0 DEED license.
Authors:
(1) U Jin Choi, Department of mathematical science, Korea Advanced Institute of Science and Technology & ujchoi@kaist.ac.kr;
(2) Kyung Soo Rim, Department of mathematics, Sogang University & ksrim@sogang.ac.kr. Table of Links Introduction
Organization and notation
Problem Setting and Preliminaries
Generalized Wiener algebra and Fréchet derivative
Characterization of coefficients
Coefficients from an ergodic process
Conclusion & References PROOF. By Taylor’s series expansion of the exponential function, the triangle inequality, and the uniform convergence, we have This paper is available on arxiv under CC BY-NC-ND 4.0 DEED license. Authors: (1) U Jin Choi, Department of mathematical science, Korea Advanced Institute of Science and Technology & ujchoi@kaist.ac.kr; (2) Kyung Soo Rim, Department of mathematics, Sogang University & ksrim@sogang.ac.kr. This paper is available on arxiv under CC BY-NC-ND 4.0 DEED license. Authors: Authors: (1) U Jin Choi, Department of mathematical science, Korea Advanced Institute of Science and Technology & ujchoi@kaist.ac.kr; (2) Kyung Soo Rim, Department of mathematics, Sogang University & ksrim@sogang.ac.kr. Table of Links Introduction Organization and notation Problem Setting and Preliminaries Generalized Wiener algebra and Fréchet derivative Characterization of coefficients Coefficients from an ergodic process Conclusion & References Introduction Introduction Organization and notation Organization and notation Problem Setting and Preliminaries Problem Setting and Preliminaries Generalized Wiener algebra and Fréchet derivative Generalized Wiener algebra and Fréchet derivative Characterization of coefficients Characterization of coefficients Coefficients from an ergodic process Coefficients from an ergodic process Conclusion & References Conclusion & References PROOF. By Taylor’s series expansion of the exponential function, the triangle inequality, and the uniform convergence, we have

Variational Non-Bayesian Inference of the Probability Density: Characterization of Coefficients

This paper is available on arxiv under CC BY-NC-ND 4.0 DEED license.
Authors:
(1) U Jin Choi, Department of mathematical science, Korea Advanced Institute of Science and Technology & ujchoi@kaist.ac.kr;
(2) Kyung Soo Rim, Department of mathematics, Sogang University & ksrim@sogang.ac.kr. Table of Links Introduction
Organization and notation
Problem Setting and Preliminaries
Generalized Wiener algebra and Fréchet derivative
Characterization of coefficients
Coefficients from an ergodic process
Conclusion & References The left-hand sides of the equations (6.4) and (6.5) depend only on X, while the right-hand sides are comprised of sums of homogeneous polynomials in the components of y. Therefore, the equations reveal themselves as algebraic systems of polynomial series in the components of y. We summarize it as follows, in which the result does not assume a statistical model for the unrevealed PDF. In the following subsection, we will use a random sample drawn from the bivariate normal distribution as a hidden PDF to verify the numerical approximations. Two systems of (6.6) and (6.7) are composed of linear combinations of homogeneous polynomials. There have been many research results to approximate their solutions, and there are various algorithms available ([16, 17, 20]). In this experiment, we use the solve () function in MATLAB to find the solution. Finally, we demonstrate the feasibility of the methods presented with the following numerical results. This paper is available on arxiv under CC BY-NC-ND 4.0 DEED license. Authors: (1) U Jin Choi, Department of mathematical science, Korea Advanced Institute of Science and Technology & ujchoi@kaist.ac.kr; (2) Kyung Soo Rim, Department of mathematics, Sogang University & ksrim@sogang.ac.kr. This paper is available on arxiv under CC BY-NC-ND 4.0 DEED license. Authors: Authors: (1) U Jin Choi, Department of mathematical science, Korea Advanced Institute of Science and Technology & ujchoi@kaist.ac.kr; (2) Kyung Soo Rim, Department of mathematics, Sogang University & ksrim@sogang.ac.kr. Table of Links Introduction Organization and notation Problem Setting and Preliminaries Generalized Wiener algebra and Fréchet derivative Characterization of coefficients Coefficients from an ergodic process Conclusion & References Introduction Introduction Organization and notation Organization and notation Problem Setting and Preliminaries Problem Setting and Preliminaries Generalized Wiener algebra and Fréchet derivative Generalized Wiener algebra and Fréchet derivative Characterization of coefficients Characterization of coefficients Coefficients from an ergodic process Coefficients from an ergodic process Conclusion & References Conclusion & References The left-hand sides of the equations (6.4) and (6.5) depend only on X , while the right-hand sides are comprised of sums of homogeneous polynomials in the components of y . Therefore, the equations reveal themselves as algebraic systems of polynomial series in the components of y . We summarize it as follows, in which the result does not assume a statistical model for the unrevealed PDF. X y y In the following subsection, we will use a random sample drawn from the bivariate normal distribution as a hidden PDF to verify the numerical approximations. Two systems of (6.6) and (6.7) are composed of linear combinations of homogeneous polynomials. There have been many research results to approximate their solutions, and there are various algorithms available ([16, 17, 20]). In this experiment, we use the solve () function in MATLAB to find the solution. Finally, we demonstrate the feasibility of the methods presented with the following numerical results. solve ()

Variational Non-Bayesian Inference: Coefficients From an Ergodic Process

This paper is available on arxiv under CC BY-NC-ND 4.0 DEED license.
Authors:
(1) U Jin Choi, Department of mathematical science, Korea Advanced Institute of Science and Technology & ujchoi@kaist.ac.kr;
(2) Kyung Soo Rim, Department of mathematics, Sogang University & ksrim@sogang.ac.kr. Table of Links Introduction
Organization and notation
Problem Setting and Preliminaries
Generalized Wiener algebra and Fréchet derivative
Characterization of coefficients
Coefficients from an ergodic process
Conclusion & References 3. Problem Setting and Preliminaries. This section will set the mathematical model that is being addressed and provide basic background information relevant to understanding it. This paper is available on arxiv under CC BY-NC-ND 4.0 DEED license. Authors: (1) U Jin Choi, Department of mathematical science, Korea Advanced Institute of Science and Technology & ujchoi@kaist.ac.kr; (2) Kyung Soo Rim, Department of mathematics, Sogang University & ksrim@sogang.ac.kr. This paper is available on arxiv under CC BY-NC-ND 4.0 DEED license. Authors: Authors: (1) U Jin Choi, Department of mathematical science, Korea Advanced Institute of Science and Technology & ujchoi@kaist.ac.kr; (2) Kyung Soo Rim, Department of mathematics, Sogang University & ksrim@sogang.ac.kr. Table of Links Introduction Organization and notation Problem Setting and Preliminaries Generalized Wiener algebra and Fréchet derivative Characterization of coefficients Coefficients from an ergodic process Conclusion & References Introduction Introduction Organization and notation Organization and notation Problem Setting and Preliminaries Problem Setting and Preliminaries Generalized Wiener algebra and Fréchet derivative Generalized Wiener algebra and Fréchet derivative Characterization of coefficients Characterization of coefficients Coefficients from an ergodic process Coefficients from an ergodic process Conclusion & References Conclusion & References 3. Problem Setting and Preliminaries. This section will set the mathematical model that is being addressed and provide basic background information relevant to understanding it.

Variational Non-Bayesian Inference: Problem Setting and Preliminaries

This paper is available on arxiv under CC BY-NC-ND 4.0 DEED license.
Authors:
(1) U Jin Choi, Department of mathematical science, Korea Advanced Institute of Science and Technology & ujchoi@kaist.ac.kr;
(2) Kyung Soo Rim, Department of mathematics, Sogang University & ksrim@sogang.ac.kr. Table of Links Introduction
Organization and notation
Problem Setting and Preliminaries
Generalized Wiener algebra and Fréchet derivative
Characterization of coefficients
Coefficients from an ergodic process
Conclusion & References This paper presents a research study focused on uncovering the hidden population distribution from the viewpoint of a variational non-Bayesian approach. It asserts that if the hidden probability density function (PDF) has continuous partial derivatives of at least half the dimension’s order, it can be perfectly reconstructed from a stationary ergodic process: First, we establish that if the PDF belongs to the Wiener algebra, its canonical ensemble form is uniquely determined through the Fréchet differentiation of the KullbackLeibler divergence, aiming to minimize their cross-entropy. Second, we utilize the result that the differentiability of the PDF implies its membership in the Wiener algebra. Third, as the energy function of the canonical ensemble is defined as a series, the problem transforms into finding solutions to the equations of analytic series for the coefficients in the energy function. Naturally, through the use of truncated polynomial series and by demonstrating the convergence of partial sums of the energy function, we ensure the efficiency of approximation with a finite number of data points. Finally, through numerical experiments, we approximate the PDF from a random sample obtained from a bivariate normal distribution and also provide approximations for the mean and covariance from the PDF. This study substantiates the excellence of its results and their practical applicability. 1. Introduction. Statistical inference enables us to draw meaningful conclusions about a population’s distribution by studying a representative sample. Numerous facets of scientific research implicitly or explicitly require the estimation of population’s distribution from a sample. By analyzing a subset of individuals or observations, we can gather information that applies to the larger group, even when studying the entire population is impractical or impossible. Drawing from the works of two authors ([8, 12]), machine learning methods have gained popularity for predicting hidden information from data. Today, most emerging artificial neural networks incorporate statistical methods. Nevertheless, these computations do not achieve global optimization of learning results because of the inherent challenges related to setting initial conditions and handling the small magnitudes of high-dimensional differential values. To address this issue, many scholars have applied statistical inferences. Among these methods, variational Bayesian method is a commonly used technique for estimating posterior information. It’s worth noting that there are numerous excellent studies on the method. One can refer to the citations [1, 2, 14, 22] as examples of the most recent works. Our study aims to identify the hidden probability density function (PDF) without the need for a prior distribution in a non-Bayesian context. This is achieved solely from a stationary ergodic process using entropy minimization. Additionally, we aim to estimate moments of the PDF, such as the mean and variance. We provide a proof of the norm convergence of sequences of approximated PDFs from a finite sample size, which is useful in practical applications. In most probability models arising from natural phenomena, assuming the boundedness of a random variable within a specific window becomes reasonable when considering a sufficiently wide range of variability. Moreover, we assume ergodicity in the context of a stationary process, as is common in many scientific communities. The basic framework of the idea to find the hidden PDF is as follows: First, we express the PDF in the form of a canonical ensemble, resembling a mechanical heat system. Second, by embedding the problem in an infinite-dimensional function space, we establish the existence of the Fréchet derivative of an entropy induced from the energy function of the PDF (for more information on the Fréchet derivative, refer to [18]). Third, we uniquely determine the energy function by minimizing the Kullback-Leibler divergence (KL-divergence) ([7, 15]). The concept of KL-divergence, valuable in information theory, finds widespread use, even in artificial intelligence (for example, see [10], [4], [11]). Finally, we derive a system of polynomial series that corresponds to the sample means of complex exponentials and present their numerical solutions from random samples in a bivariate normal distribution. Using the approximated PDFs that we obtained, we compare approximations of the mean and variance from the bivariate normal distribution. This paper is available on arxiv under CC BY-NC-ND 4.0 DEED license. Authors: (1) U Jin Choi, Department of mathematical science, Korea Advanced Institute of Science and Technology & ujchoi@kaist.ac.kr; (2) Kyung Soo Rim, Department of mathematics, Sogang University & ksrim@sogang.ac.kr. This paper is available on arxiv under CC BY-NC-ND 4.0 DEED license. Authors: Authors: (1) U Jin Choi, Department of mathematical science, Korea Advanced Institute of Science and Technology & ujchoi@kaist.ac.kr; (2) Kyung Soo Rim, Department of mathematics, Sogang University & ksrim@sogang.ac.kr. Table of Links Introduction Organization and notation Problem Setting and Preliminaries Generalized Wiener algebra and Fréchet derivative Characterization of coefficients Coefficients from an ergodic process Conclusion & References Introduction Introduction Organization and notation Organization and notation Problem Setting and Preliminaries Problem Setting and Preliminaries Generalized Wiener algebra and Fréchet derivative Generalized Wiener algebra and Fréchet derivative Characterization of coefficients Characterization of coefficients Coefficients from an ergodic process Coefficients from an ergodic process Conclusion & References Conclusion & References This paper presents a research study focused on uncovering the hidden population distribution from the viewpoint of a variational non-Bayesian approach. It asserts that if the hidden probability density function (PDF) has continuous partial derivatives of at least half the dimension’s order, it can be perfectly reconstructed from a stationary ergodic process: First, we establish that if the PDF belongs to the Wiener algebra, its canonical ensemble form is uniquely determined through the Fréchet differentiation of the KullbackLeibler divergence, aiming to minimize their cross-entropy. Second, we utilize the result that the differentiability of the PDF implies its membership in the Wiener algebra. Third, as the energy function of the canonical ensemble is defined as a series, the problem transforms into finding solutions to the equations of analytic series for the coefficients in the energy function. Naturally, through the use of truncated polynomial series and by demonstrating the convergence of partial sums of the energy function, we ensure the efficiency of approximation with a finite number of data points. Finally, through numerical experiments, we approximate the PDF from a random sample obtained from a bivariate normal distribution and also provide approximations for the mean and covariance from the PDF. This study substantiates the excellence of its results and their practical applicability. 1. Introduction. Statistical inference enables us to draw meaningful conclusions about a population’s distribution by studying a representative sample. Numerous facets of scientific research implicitly or explicitly require the estimation of population’s distribution from a sample. By analyzing a subset of individuals or observations, we can gather information that applies to the larger group, even when studying the entire population is impractical or impossible. Drawing from the works of two authors ([8, 12]), machine learning methods have gained popularity for predicting hidden information from data. Today, most emerging artificial neural networks incorporate statistical methods. Nevertheless, these computations do not achieve global optimization of learning results because of the inherent challenges related to setting initial conditions and handling the small magnitudes of high-dimensional differential values. To address this issue, many scholars have applied statistical inferences. Among these methods, variational Bayesian method is a commonly used technique for estimating posterior information. It’s worth noting that there are numerous excellent studies on the method. One can refer to the citations [1, 2, 14, 22] as examples of the most recent works. Our study aims to identify the hidden probability density function (PDF) without the need for a prior distribution in a non-Bayesian context. This is achieved solely from a stationary ergodic process using entropy minimization. Additionally, we aim to estimate moments of the PDF, such as the mean and variance. We provide a proof of the norm convergence of sequences of approximated PDFs from a finite sample size, which is useful in practical applications. In most probability models arising from natural phenomena, assuming the boundedness of a random variable within a specific window becomes reasonable when considering a sufficiently wide range of variability. Moreover, we assume ergodicity in the context of a stationary process, as is common in many scientific communities. The basic framework of the idea to find the hidden PDF is as follows: First, we express the PDF in the form of a canonical ensemble, resembling a mechanical heat system. Second, by embedding the problem in an infinite-dimensional function space, we establish the existence of the Fréchet derivative of an entropy induced from the energy function of the PDF (for more information on the Fréchet derivative, refer to [18]). Third, we uniquely determine the energy function by minimizing the Kullback-Leibler divergence (KL-divergence) ([7, 15]). The concept of KL-divergence, valuable in information theory, finds widespread use, even in artificial intelligence (for example, see [10], [4], [11]). Finally, we derive a system of polynomial series that corresponds to the sample means of complex exponentials and present their numerical solutions from random samples in a bivariate normal distribution. Using the approximated PDFs that we obtained, we compare approximations of the mean and variance from the bivariate normal distribution.

Variational Non-Bayesian Inference of the Probability Density Function: Introduction

This paper is available on arxiv under CC BY-NC-ND 4.0 DEED license.
Authors:
(1) U Jin Choi, Department of mathematical science, Korea Advanced Institute of Science and Technology & ujchoi@kaist.ac.kr;
(2) Kyung Soo Rim, Department of mathematics, Sogang University & ksrim@sogang.ac.kr. Table of Links Introduction
Organization and notation
Problem Setting and Preliminaries
Generalized Wiener algebra and Fréchet derivative
Characterization of coefficients
Coefficients from an ergodic process
Conclusion & References 2. Organization and notation. This article is organized as follows: In the next section, we formulate the problem by defining the energy and partition function for the hidden PDF in a generalized Wiener algebra. We observe that the nonlinearity of energy functions poses challenges in maximizing likelihood functions. To overcome this issue, we adopt the KLdivergence between two distribution functions. In Section 4, we embed energy functions into a generalized Wiener algebra, thereby transforming the nonlinearity of the energy function into a system of equations in the function space and simultaneously converting the min-max problem into a problem of solving equations. We showthe Fréchet differentiability of the KL-divergence with respect to coefficients in the generalized Wiener algebra. From this property, we then uniquely obtain the existence such that its energy function yields a KL-divergence of 0. We establish a characterization of the coefficients of the energy function by expressing them in relation to the Fourier coefficients found within the (classical) Wiener algebra, as demonstrated in Section 5. This serves as an example of the generalized Wiener algebra. In the concluding Section 6, when dealing with a random sample that consists of realizations of a stationary ergodic process, we formulate a system of polynomial series with the coefficients of the energy function as variables, which consists of infinitely many equations in infinitely many variables. From the convergence property of the partial sums of an energy function in Section 4, the truncated system, consisting of a finite number of equations with partial sums, offers an avenue for coefficient approximations. The estimated coefficients effectively serve as estimators for the coefficients. More precisely, the hidden PDF can be approximated using these estimators. Furthermore, we provide a numerical example that emphasizes the approximation of the PDF, as well as the calculation of the mean and variance from the PDF using a random sample. This sample is generated from a bivariate normal distribution. In this paper, we consistently employ the following general notations (Table 1). Some notations will be elaborated upon in more detail when they are introduced. This paper is available on arxiv under CC BY-NC-ND 4.0 DEED license. Authors: (1) U Jin Choi, Department of mathematical science, Korea Advanced Institute of Science and Technology & ujchoi@kaist.ac.kr; (2) Kyung Soo Rim, Department of mathematics, Sogang University & ksrim@sogang.ac.kr. This paper is available on arxiv under CC BY-NC-ND 4.0 DEED license. Authors: Authors: (1) U Jin Choi, Department of mathematical science, Korea Advanced Institute of Science and Technology & ujchoi@kaist.ac.kr; (2) Kyung Soo Rim, Department of mathematics, Sogang University & ksrim@sogang.ac.kr. Table of Links Introduction Organization and notation Problem Setting and Preliminaries Generalized Wiener algebra and Fréchet derivative Characterization of coefficients Coefficients from an ergodic process Conclusion & References Introduction Introduction Organization and notation Organization and notation Problem Setting and Preliminaries Problem Setting and Preliminaries Generalized Wiener algebra and Fréchet derivative Generalized Wiener algebra and Fréchet derivative Characterization of coefficients Characterization of coefficients Coefficients from an ergodic process Coefficients from an ergodic process Conclusion & References Conclusion & References 2. Organization and notation. This article is organized as follows: In the next section, we formulate the problem by defining the energy and partition function for the hidden PDF in a generalized Wiener algebra. We observe that the nonlinearity of energy functions poses challenges in maximizing likelihood functions. To overcome this issue, we adopt the KLdivergence between two distribution functions. In Section 4, we embed energy functions into a generalized Wiener algebra, thereby transforming the nonlinearity of the energy function into a system of equations in the function space and simultaneously converting the min-max problem into a problem of solving equations. We showthe Fréchet differentiability of the KL-divergence with respect to coefficients in the generalized Wiener algebra. From this property, we then uniquely obtain the existence such that its energy function yields a KL-divergence of 0. We establish a characterization of the coefficients of the energy function by expressing them in relation to the Fourier coefficients found within the (classical) Wiener algebra, as demonstrated in Section 5. This serves as an example of the generalized Wiener algebra. In the concluding Section 6, when dealing with a random sample that consists of realizations of a stationary ergodic process, we formulate a system of polynomial series with the coefficients of the energy function as variables, which consists of infinitely many equations in infinitely many variables. From the convergence property of the partial sums of an energy function in Section 4, the truncated system, consisting of a finite number of equations with partial sums, offers an avenue for coefficient approximations. The estimated coefficients effectively serve as estimators for the coefficients. More precisely, the hidden PDF can be approximated using these estimators. Furthermore, we provide a numerical example that emphasizes the approximation of the PDF, as well as the calculation of the mean and variance from the PDF using a random sample. This sample is generated from a bivariate normal distribution. In this paper, we consistently employ the following general notations (Table 1). Some notations will be elaborated upon in more detail when they are introduced.

Variational Non-Bayesian Inference of the Probability Density Function: Organization and Notation

This paper is available on arxiv under CC 4.0 license. Authors: (1) Thomas Pethick, EPFL (LIONS) thomas.pethick@epfl.ch; (2) Wanyun Xie, EPFL (LIONS) wanyun.xie@epfl.ch; (3) Volkan Cevher, EPFL (LIONS) volkan.cevher@epfl.ch. Table of Links Abstract & Introduction Related work Setup Inexact Krasnosel’ski˘ı-Mann iterations Approximating the resolvent Last iterate under cohypomonotonicity Analysis of Lookahea Experiments Conclusion & limitations Acknowledgements & References 8 Experiments This section demonstrates that linear interpolation can lead to an improvement over common baselines. Figures 2 and 3 demonstrate RAPP, LA-GDA and LA-CEG+ on a host of nonmonotone problems (Hsieh et al. (2021, Ex. 5.2), Pethick et al. (2022, Ex. 3(iii)), Pethick et al. (2022, Ex. 5)). See Appendix H.2 for definitions and further details. Synthetic examples Image generation We replicate the experimental setup of Chavdarova et al. (2020); Miyato et al. (2018), which uses hinge version of the non-saturated loss and a ResNet with spectral normalization for the discriminator (see Appendix H.2 for details). To evaluate the performance we rely on the commonly used Inception score (ISC) (Salimans et al., 2016) and Fréchet inception distance (FID) (Heusel et al., 2017) and report the best iterate. We demonstrate the methods on the CIFAR10 dataset (Krizhevsky et al., 2009). The aim is not to beat the state-of-the-art, but rather to complement the already exhaustive numerical evidence provided in Chavdarova et al. (2020). For a fair computational comparison we count the number of gradient computations instead of iterations k as in Chavdarova et al. (2020). Maybe surprisingly, we find that the extrapolation methods such as EG and RAPP still outperform the baseline, despite having fewer effective iterations. RAPP improves over EG, which suggest that it can be worthwhile to spend more computation on refining the updates at the cost of making fewer updates. The first experiment we conduct matches the setting of Chavdarova et al. (2020) by relying on the Adam optimizer and using and update ratio of 5 : 1 between the discriminator and generator. We find in Table 2 that LA-ExtraAdam+ has the highest ISC (8.08) while LA-ExtraAdam has the lowest FID (15.88). In contrast, we confirm that Adam is unstable while Lookahead prevents divergence as apparent from Figure 4, which is in agreement with Chavdarova et al. (2020). In addition, the outer loop of Lookahead achieves better empirical performance, which corroborate the theoretical result (cf. Remark 7.4). Notice that ExtraAdam+ has slow convergence (without Lookahead), which is possibly due to the 1/2-smaller stepsize. We additionally simplify the setup by using GDA-based optimizers with an update ratio of 1 : 1, which avoids the complexity of diagonal adaptation, gradient history and multiple steps of the discriminator as in the Adam-based experiments. The results are found in Table 3. The learning rates are tuned for GDA and we use those parameters fixed across all other methods. Despite being tuned on GDA, we find that extragradient methods, Lookahead-based methods and RAPP all still outperform GDA in terms of FID. The biggest improvement comes from the linear interpolation based methods Lookahead and RAPP (see Figure 8 for further discussion on EG+). Interesting, the Lookahead-based methods are roughly comparable with their Adam variants (Table 2) while GDA even performs better than Adam.

Stable Nonconvex-Nonconcave Training via Linear Interpolation: Experiments

Aspects of Thermal QCD Phenomenology at Intermediate Gauge/'t Hooft Coupling: Bibliography

This paper is available on arxiv under CC 4.0 license. . Authors: Gemini Team, Google Table of Links Abstract and Introduction Model Architecture Training Infrastructure Training Dataset Evaluation Responsible Deployment Discussion and Conclusion, References Contributions and Acknowledgments Appendix 8. Contributions and Acknowledgments Leads Rohan Anil, Co-Lead, Text Sebastian Borgeaud, Co-Lead, Text Yonghui Wu, Co-Lead, Text Jean-Baptiste Alayrac, Co-Lead, MM Vision Jiahui Yu, Co-Lead, MM Vision Radu Soricut*, Co-Lead, MM Vision* Johan Schalkwyk, Lead, MM Audio Andrew M. Dai, Co-Lead, Data Anja Hauth*, Co-Lead, Data* Katie Millican, Co-Lead, Data David Silver, Co-Lead, Fine-Tuning Slav Petrov, Co-Lead, Fine-Tuning Melvin Johnson, Lead, Instruction Tuning Ioannis Antonoglou*, Co-Lead, RL Techniques* Julian Schrittwieser, Co-Lead, RL Techniques Amelia Glaese, Lead, Human Data Jilin Chen, Lead, Safety Emily Pitler, Co-Lead, Tool Use Timothy Lillicrap, Co-Lead, Tool Use Angeliki Lazaridou, Co-Lead, Eval Orhan Firat, Co-Lead, Eval James Molloy, Co-Lead, Infra Michael Isard, Co-Lead, Infra Paul R. Barham, Co-Lead, Infra Tom Hennigan, Co-Lead, Infra Benjamin Lee, Co-Lead, Codebase & Parallelism Fabio Viola, Co-Lead, Codebase & Parallelism Malcolm Reynolds, Co-Lead, Codebase & Parallelism Yuanzhong Xu, Co-Lead, Codebase & Parallelism Ryan Doherty, Lead, Ecosystem Eli Collins, Lead, Product Clemens Meyer, Co-Lead, Operations Eliza Rutherford, Co-Lead, Operations Erica Moreira, Co-Lead, Operations Kareem Ayoub, Co-Lead, Operations Megha Goel, Co-Lead, Operations Core Contributors George Tucker Enrique Piqueras Maxim Krikun Iain Barr Nikolay Savinov Ivo Danihelka Becca Roelofs Core Contributors Anaïs White Anders Andreassen Tamara von Glehn Lakshman Yagati Mehran Kazemi Lucas Gonzalez Misha Khalman Jakub Sygnowski Alexandre Frechette Charlotte Smith Laura Culp Lev Proleev Yi Luan Xi Chen James Lottes Nathan Schucher Federico Lebron Alban Rrustemi Natalie Clay Phil Crone Tomas Kocisky Jeffrey Zhao Bartek Perz Dian Yu Heidi Howard Adam Bloniarz Jack W. Rae Han Lu Laurent Sifre Marcello Maggioni Fred Alcober Dan Garrette Megan Barnes Shantanu Thakoor Jacob Austin Gabriel Barth-Maron William Wong Rishabh Joshi Rahma Chaabouni Deeni Fatiha Arun Ahuja Ruibo Liu Yunxuan Li Sarah Cogan Jeremy Chen Core Contributors Chao Jia Chenjie Gu Qiao Zhang Jordan Grimstad Ale Jakse Hartman Martin Chadwick Gaurav Singh Tomar Xavier Garcia Evan Senter Emanuel Taropa Thanumalayan Sankaranarayana Pillai Jacob Devlin Michael Laskin Diego de Las Casas Dasha Valter Connie Tao Lorenzo Blanco Adrià Puigdomènech Badia David Reitter Mianna Chen Jenny Brennan Clara Rivera Sergey Brin Shariq Iqbal Gabriela Surita Jane Labanowski Abhi Rao Stephanie Winkler Emilio Parisotto Yiming Gu Kate Olszewska Yujing Zhang Ravi Addanki Antoine Miech Annie Louis Laurent El Shafey Denis Teplyashin Geoff Brown Elliot Catt Nithya Attaluri Jan Balaguer Jackie Xiang Pidong Wang Zoe Ashwood Anton Briukhov Albert Webson Sanjay Ganapathy Smit Sanghavi Core Contributors Ajay Kannan Ming-Wei Chang Axel Stjerngren Josip Djolonga Yuting Sun Ankur Bapna Matthew Aitchison Pedram Pejman Henryk Michalewski Tianhe Yu Cindy Wang Juliette Love Junwhan Ahn Dawn Bloxwich Kehang Han Peter Humphreys Thibault Sellam James Bradbury Varun Godbole Sina Samangooei Bogdan Damoc Alex Kaskasoli Sébastien M. R. Arnold Vijay Vasudevan Shubham Agrawal Jason Riesa Dmitry Lepikhin Richard Tanburn Srivatsan Srinivasan Hyeontaek Lim Sarah Hodkinson Pranav Shyam Johan Ferret Steven Hand Ankush Garg Tom Le Paine Jian Li Yujia Li Minh Giang Alexander Neitz Zaheer Abbas Sarah York Machel Reid Elizabeth Cole Aakanksha Chowdhery Dipanjan Das Dominika Rogozińska Vitaly Nikolaev Core Contributors Pablo Sprechmann Zachary Nado Lukas Zilka Flavien Prost Luheng He Marianne Monteiro Gaurav Mishra Chris Welty Josh Newlan Dawei Jia Miltiadis Allamanis Clara Huiyi Hu Raoul de Liedekerke Justin Gilmer Carl Saroufim Shruti Rijhwani Shaobo Hou Disha Shrivastava Anirudh Baddepudi Alex Goldin Adnan Ozturel Albin Cassirer Yunhan Xu Daniel Sohn Devendra Sachan Reinald Kim Amplayo Craig Swanson Dessie Petrova Shashi Narayan Arthur Guez Siddhartha Brahma Jessica Landon Miteyan Patel Ruizhe Zhao Kevin Villela Luyu Wang Wenhao Jia Matthew Rahtz Mai Giménez Legg Yeung Hanzhao Lin James Keeling Petko Georgiev Diana Mincu Boxi Wu Salem Haykal Rachel Saputro Kiran Vodrahalli Core Contributors James Qin Zeynep Cankara Abhanshu Sharma Nick Fernando Will Hawkins Behnam Neyshabur Solomon Kim Adrian Hutter Priyanka Agrawal Alex Castro-Ros George van den Driessche Tao Wang Fan Yang Shuo-yiin Chang Paul Komarek Ross McIlroy Mario Lučić Guodong Zhang Wael Farhan Michael Sharman Paul Natsev Paul Michel Yong Cheng Yamini Bansal Siyuan Qiao Kris Cao Siamak Shakeri Christina Butterfield Justin Chung Paul Kishan Rubenstein Shivani Agrawal Arthur Mensch Kedar Soparkar Karel Lenc Timothy Chung Aedan Pope Loren Maggiore Jackie Kay Priya Jhakra Shibo Wang Joshua Maynez Mary Phuong Taylor Tobin Andrea Tacchetti Maja Trebacz Kevin Robinson Yash Katariya Sebastian Riedel Core Contributors Paige Bailey Kefan Xiao Nimesh Ghelani Lora Aroyo Ambrose Slone Neil Houlsby Xuehan Xiong Zhen Yang Elena Gribovskaya Jonas Adler Mateo Wirth Lisa Lee Music Li Thais Kagohara Jay Pavagadhi Sophie Bridgers Anna Bortsova Sanjay Ghemawat Zafarali Ahmed Tianqi Liu Richard Powell Vijay Bolina Mariko Iinuma Polina Zablotskaia James Besley Da-Woon Chung Timothy Dozat Ramona Comanescu Xiance Si Jeremy Greer Guolong Su Martin Polacek Raphaël Lopez Kaufman Simon Tokumine Hexiang Hu Elena Buchatskaya Yingjie Miao Mohamed Elhawaty Aditya Siddhant Nenad Tomasev Jinwei Xing Christina Greer Helen Miller Shereen Ashraf Aurko Roy Zizhao Zhang Ada Ma Angelos Filos Core Contributors Milos Besta Rory Blevins Ted Klimenko Chih-Kuan Yeh Soravit Changpinyo Jiaqi Mu Oscar Chang Mantas Pajarskas Carrie Muir Vered Cohen Charline Le Lan Krishna Haridasan Amit Marathe Steven Hansen Sholto Douglas Rajkumar Samuel Mingqiu Wang Sophia Austin Chang Lan Jiepu Jiang Justin Chiu Jaime Alonso Lorenzo Lars Lowe Sjösund Sébastien Cevey Zach Gleicher Thi Avrahami Anudhyan Boral Hansa Srinivasan Vittorio Selo Rhys May Konstantinos Aisopos Léonard Hussenot Livio Baldini Soares Kate Baumli Michael B. 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Choquette-Choo Yunjie Li TJ Lu Abe Ittycheriah Prakash Shroff Pei Sun Mani Varadarajan Sanaz Bahargam Rob Willoughby David Gaddy Ishita Dasgupta Guillaume Desjardins Marco Cornero Brona Robenek Bhavishya Mittal Ben Albrecht Ashish Shenoy Fedor Moiseev Henrik Jacobsson Alireza Ghaffarkhah Morgane Rivière Alanna Walton Clément Crepy Alicia Parrish Contributors Yuan Liu Zongwei Zhou Clement Farabet Carey Radebaugh Praveen Srinivasan Claudia van der Salm Andreas Fidjeland Salvatore Scellato Eri Latorre-Chimoto Hanna Klimczak-Plucińska David Bridson Dario de Cesare Tom Hudson Piermaria Mendolicchio Lexi Walker Alex Morris Ivo Penchev Matthew Mauger Alexey Guseynov Alison Reid Seth Odoom Lucia Loher Victor Cotruta Madhavi Yenugula Dominik Grewe Anastasia Petrushkina Tom Duerig Antonio Sanchez Steve Yadlowsky Amy Shen Amir Globerson Adam Kurzrok Lynette Webb Sahil Dua Dong Li Preethi Lahoti Surya Bhupatiraju Dan Hurt Haroon Qureshi Ananth Agarwal Tomer Shani Matan Eyal Anuj Khare Shreyas Rammohan Belle Lei Wang Chetan Tekur Mihir Sanjay Kale Jinliang Wei Contributors Ruoxin Sang Brennan Saeta Tyler Liechty Yi Sun Yao Zhao Stephan Lee Pandu Nayak Doug Fritz Manish Reddy Vuyyuru John Aslanides Nidhi Vyas Martin Wicke Xiao Ma Taylan Bilal Evgenii Eltyshev Daniel Balle Nina Martin Hardie Cate James Manyika Keyvan Amiri Yelin Kim Xi Xiong Kai Kang Florian Luisier Nilesh Tripuraneni David Madras Mandy Guo Austin Waters Oliver Wang Joshua Ainslie Jason Baldridge Han Zhang Garima Pruthi Jakob Bauer Feng Yang Riham Mansour Jason Gelman Yang Xu George Polovets Ji Liu Honglong Cai Warren Chen XiangHai Sheng Emily Xue Sherjil Ozair Adams Yu Christof Angermueller Contributors Xiaowei Li Weiren Wang Julia Wiesinger Emmanouil Koukoumidis Yuan Tian Anand Iyer Madhu Gurumurthy Mark Goldenson Parashar Shah MK Blake Hongkun Yu Anthony Urbanowicz Jennimaria Palomaki Chrisantha Fernando Kevin Brooks Ken Durden Harsh Mehta Nikola Momchev Elahe Rahimtoroghi Maria Georgaki Amit Raul Sebastian Ruder Morgan Redshaw Jinhyuk Lee Komal Jalan Dinghua Li Ginger Perng Blake Hechtman Parker Schuh Milad Nasr Mia Chen Kieran Milan Vladimir Mikulik Trevor Strohman Juliana Franco Tim Green Program Leads Demis Hassabis Koray Kavukcuoglu Overall Technical Leads (equal contribution) Jeffrey Dean Oriol Vinyals The roles are defined as below: • : Individual(s) responsible for the sub-team throughout the project. Lead Individual that had significant impact throughout the project. • Core Contributor: : Individual that had contributions to the project and was partially involved with the effort. • Contributor Responsible for the organizational aspects of the Gemini effort • Program Lead: Responsible for the technical direction of the overall Gemini effort • Overall Technical Lead: Within each role, contributions are equal, and are listed in a randomized order. Ordering within each role does not indicate ordering of the contributions. Gemini is a cross-Google effort, with members from Google DeepMind (GDM), Google Research (GR), Knowledge and Information (K&I), Core ML, Cloud, Labs, and more. We thank our reviewers and colleagues for their valuable discussions and feedback on the report— Alexandra Belias, Arielle Bier, Eleanor Tomlinson, Emily Hossellman, Gaby Pearl, Helen King, Hollie Dobson, Jaclyn Konzelmann, Jennifer Beroshi, Joel Moss, Jon Small, Jonathan Fildes, Oli Gaymond, Rebecca Bland, Reena Jana, and Tom Lue. Our work is made possible by the dedication and efforts of numerous teams at Google. We would like to acknowledge the support from Abhi Mohan, Adekunle Bello, Aishwarya Nagarajan, Alaa Saade, Alejandro Lince, Alexander Chen, Alexander Kolbasov, Alexander Schiffhauer, Amar Subramanya, Ameya Shringi, Amin Vahdat, Anda Rabatić, Anthonie Gross, Antoine Yang, Anthony Green, Anton Ruddock, Art Khurshudov, Artemis Chen, Arthur Argenson, Avinatan Hassidim, Beiye Liu, Benjamin Schroeder, Bin Ni, Brett Daw, Bryan Chiang, Burak Gokturk, Carl Crous, Carrie Grimes Bostock, Charbel Kaed, Charlotte Banks, Che Diaz, Chris Larkin, Christy Lian, Claire Cui, Clare Bycroft, Corentin Tallec, Daniel Herndon, Dave Burke, David Battle, David Engel, Dipannita Shaw, Donghyun Koo, Doug Ritchie, Dragos Stefanescu, Elissa Wolf, Emre Sargin, Eran Ofek, Eric Herren, Estella King, Fatema Alkhanaizi, Felix Gimeno, Fernando Pereira, Florent Altché, Gabriel Carvajal, Gaurav Gandhi, George Powell, Goran Pavičić, Harry Richardson, Hassan Wassel, Hongji Li, Idan Szpektor, Igor Ivanisevic, Ivan Jambrešić, Ivan Jurin, Jade Fowler, James Assiene, Jay Yagnik, Jeanbastien Grill, Jeff Seibert, Jenna LaPlante, Jessica Austin, Jianxing Lu, Jim O’Keeffe, Jin Huang, Joe Heyward, Johannes Welbl, John Jumper, Jonathan Caton, Josh Woodward, Joshua Foster, Kathryn Tunyasuvunakool, Katrina Wong, Kavya Kopparapu, Kelvin Nguyen, Kira Yin, Konstantin Sharlaimov, Kun Li, Lee Hong, Lilly Taylor, Longfei Shen, Luc Mercier, Maciej Mikuła, Mania Abdi, Manuel Sanchez, Maria Ines Aranguren, Mario Carlos Cortes III, Matthew Tait, Matthias Lochbrunner, Mehdi Ghissassi, Micah Mosley, Michael Bendersky, Michael Figurnov, Michael Harris, Michael Mathieu, Michael O’Neill, Michael Vorburger, Mihir Paradkar, Nandita Dukkipati, Nathan Carter, Nathan Watson, Neil Rabinowitz, Nikhil Dandekar, Nishant Ranka, Obaid Sarvana, Olcan Sercinoglu, Olivier Lacombe, Ottavia Bertolli, Paul Caron, Pranesh Srinivasan, Praveen Kumar, Rahul Sukthankar, Raia Hadsell, Rajagopal Ananthanarayanan, Roberto Lupi, Rosie Zou, Sachin Menezes, Sadegh Jazayeri, Sam Cheung, Sameer Bidichandani, Sania Alex, Sanjiv Kumar, Sara Wiltberger, Sarah Fitzgerald, Saz Basu, Sebastian Nowozin, Shannon Hepburn, Shayne Cardwell, Sissie Hsiao, Srinivasan Venkatachary, Sugato Basu, Sundar Pichai, Sundeep Tirumalareddy, Susannah Young, Swetha Vijayaraghavan, Tania Bedrax-Weiss, Taylor Applebaum, Teiva Harsanyi, Terry Chen, Tim Blyth, Ting Liu, Tom Cobley, Tomas Izo, Trystan Upstill, Varun Singhai, Vedrana Klarić Trupčević, Victor Cai, Vladimir Pudovkin, Vu Dang, Wenbo Zhao, Wesley Crow, Wesley Szeng, Xiaodan Song, Yazhou Zu, Ye Tian, Yicong Wang, Yixing Wang, Yossi Matias, Yunlong Jiao, Zachary Jessup, Zhenchuan Pang, Žiga Avsec, Zimeng Yang, and Zoubin Ghahramani. We’d also like to recognize the AlphaCode team, the Borg Scheduling team, the Facilities team, the Gemini Demo Team, the Global Server Ops (GSO) team, the JAX team, the the Legal team, ML SRE team, the ML Supercomputer (MLSC) team, the PartIR team, the Platforms Infrastructure Engineering (PIE) team, and the XLA Compiler team. We thank everyone at Google not explicitly mentioned above, who have shared excitement, given feedback on early Gemini models or created interesting demo uses of Gemini, and worked with or supported the core Gemini team on many aspects of this project.

Gemini -  A Family of Highly Capable Multimodal Models: Contributions and Acknowledgments

Gemini - A Family of Highly Capable Multimodal Models: Discussion and Conclusion, References

Plan of War when the Destruction of the Enemy is the Object

On the Economy of Machinery and Manufactures by Charles Babbage is part of the HackerNoon Books Series. You can jump to any chapter in this book . On the Division of Labour here Chapter 20. On the Division of Labour We have already mentioned what may, perhaps, appear paradoxical to some of our readers that the division of labour can be applied with equal success to mental as to mechanical operations, and that it ensures in both the same economy of time. A short account of its practical application, in the most extensive series of calculations ever executed, will offer an interesting illustration of this fact, whilst at the same time it will afford an occasion for shewing that the arrangements which ought to regulate the interior economy of a manufactory, are founded on principles of deeper root than may have been supposed, and are capable of being usefully employed in preparing the road to some of the sublimest investigations of the human mind. In the midst of that excitement which accompanied the Revolution of France and the succeeding wars, the ambition of the nation, unexhausted by its fatal passion for military renown, was at the same time directed to some of the nobler and more permanent triumphs which mark the era of a people's greatness and which receive the applause of posterity long after their conquests have been wrested from them, or even when their existence as a nation may be told only by the page of history. Amongst their enterprises of science, the French Government was desirous of producing a series of mathematical tables, to facilitate the application of the decimal system which they had so recently adopted. They directed, therefore, their mathematicians to construct such tables, on the most extensive scale. Their most distinguished philosophers, responding fully to the call of their country, invented new methods for this laborious task; and a work, completely answering the large demands of the Government, was produced in a remarkably short period of time. M. Prony, to whom the superintendence of this great undertaking was confided, in speaking of its commencement, observes: Je m'y livrai avec toute l'ardeur dont j'etois capable, et je m'occupai d'abord du plan general de l'execution. Toutes les conditions que j'avois a remplir necessitoient l'emploi d'un grand nombre de calculateurs; et il me vint bientot a la pensee d'appliquer a la connection de ces Tables la division du travail, dont les Arts de Commerce tirent un parti si avantageux pour reunir a la pernection de main-d'oeuvre l'economie de la depense et du temps. The circumstance which gave rise to this singular application of the principle of the division on labour is so interesting, that no apology is necessary for introducing it from a small pamphlet printed at Paris a few years since, when a proposition was made by the English to the French Government, that the two countries should print these tables at their joint expense. The origin of the idea is related in the following extract: C'est a un chapitre d'un ouvrage Anglais,(1*) justement celebre, (I.) qu'est probablement due l'existence de l'ouvrage dont le gouvernement Britannique veut faire jouir le monde savant: Voici l'anecdote: M. de Prony s'etait engage. avec les comites de gouvernement. a composer pour la division centesimale du cercle, des tables logarithmiques et trigonometriques, qui, non seulement ne laissassent rien a desirer quant a l'exactitude, mais qui formassent le monument de calcul 1e plus vaste et le plus imposant qui eut jamais ete execute, ou meme concu. Les logarithmes des nombres de 1 a 200.000 formaient a ce travail un supplement necessaire et exige. Il fut aise a M. de Prony de s'assurer que meme en s'associant trois ou quatre habiles co-operateurs. La plus grande duree presumable de sa vie ne lui sufirai pas pour remplir ses engagements. Il etait occupe de cette facheuse pensee lorsque. Se trouvant devant la boutique d'un marchand de livres. Il appercut la belle edition Anglaise de Smith, donnee a Londres en 1776: il ouvrit le livre au hazard. et tomba sur le premier chapitre, qui traite de la division du travail, et ou la fabrication des epingles est citee pour exemple. A peine avait-il parcouru les premieres pages, que, par une espece d'inspiration. il concut l'expedient de mettre ses logarithmes en manufacture comme les epingles. Il faisait en ce moment, a l'ecole polytechnique, des lecons sur une partie d'analyse liee a ce genre de travail, la methode des differences, et ses applications a l'interpolation. Il alla passer quelques jours a la campagne. et revint a Paris avec le plan de fabrication. qui a ete suivi dans l'execution. Il rassembla deux ateliers. qui faisai ent separement les memes calculs, et se servaient de verification reciproque.(2*) The ancient methods of computing tables were altogether inapplicable to such a proceeding. M. Prony, therefore, wishing to avail himself of all the talent of his country in devising new methods, formed the first section of those who were to take part in this enterprise out of five or six of the most eminent mathematicians in France. First section. The duty of this first section was to investigate, amongst the various analytical expressions which could be found for the same function, that which was most readily adapted to simple numerical calculation by many individuals employed at the same time. This section had little or nothing to do with the actual numerical work. When its labours were concluded, the formulae on the use of which it had decided, were delivered to the second section. Second section. This section consisted of seven or eight persons of considerable acquaintance with mathematics: and their duty was to convert into numbers the formulae put into their hands by the first section an operation of great labour; and then to deliver out these formulae to the members of the third section, and receive from them the finished calculations. The members of this second section had certain means of verifying the calculations without the necessity of repeating, or even of examining, the whole of the work done by the third section. Third section. The members of this section, whose number varied from sixty to eighty, received certain numbers from the second section, and, using nothing more than simple addition and subtraction, they returned to that section the tables in a finished state. It is remarkable that nine-tenths of this class had no knowledge of arithmetic beyond the two first rules which they were thus called upon to exercise, and that these persons were usually found more correct in their calculations, than those who possessed a more extensive knowledge of the subject. When it is stated that the tables thus computed occupy seventeen large folio volumes, some idea may perhaps be formed of the labour. From that part executed by the third class, which may almost be termed mechanical, requiring the least knowledge and by far the greatest exertions, the first class were entirely exempt. Such labour can always be purchased at an easy rate. The duties of the second class, although requiring considerable skill in arithmetical operations, were yet in some measure relieved by the higher interest naturally felt in those more difficult operations. The exertions of the first class are not likely to require, upon another occasion, so much skill and labour as they did upon the first attempt to introduce such a method; but when the completion of a calculating engine shall have produced a substitute for the whole of the third section of computers, the attention of analysts will naturally be directed to simplifying its application, by a new discussion of the methods of converting analytical formulae into numbers. The proceeding of M. Prony, in this celebrated system of calculation, much resembles that of a skilful person about to construct a cotton or silk mill, or any similar establishment. Having, by his own genius, or through the aid of his friends, found that some improved machinery may be successfully applied to his pursuit, he makes drawings of his plans of the machinery, and may himself be considered as constituting the first section. He next requires the assistance of operative engineers capable of executing the machinery he has designed, some of whom should understand the nature of the processes to be carried on; and these constitute his second section. When a sufficient number of machines have been made, a multitude of other persons, possessed of a lower degree of skill, must be employed in using them; these form the third section: but their work, and the just performance of the machines, must be still superintended by the second class. As the possibility of performing arithmetical calculations by machinery may appear to non-mathematical readers to be rather too large a postulate, and as it is connected with the subject of the division of labour, I shall here endeavour, in a few lines, to give some slight perception of the manner in which this can be done—and thus to remove a small portion of the veil which covers that apparent mystery. That nearly all tables of numbers which follow any law, however complicated, may be formed, to a greater or less extent, solely by the proper arrangement of the successive addition and subtraction of numbers befitting each table, is a general principle which can be demonstrated to those only who are well acquainted with mathematics; but the mind, even of the reader who is but very slightly acquainted with that science, will readily conceive that it is not impossible, by attending to the following example. The subjoined table is the beginning of one in very extensive use, which has been printed and reprinted very frequently in many countries, and is called a table of square numbers. Terms of Table A Table B first Difference C second Difference 1 1
                            3
    2 4 2
                            5
    3 9 2
                            7
    4 16 2
                            9
    5 25 2
                           11
    6 36 2
                           13
    7 49 Any number in the table, column A, may be obtained, by multiplying the number which expresses the distance of that term from the commencement of the table by itself; thus, 25 is the fifth term from the beginning of the table, and 5 multiplied by itself, or by 5, is equal to 25. Let us now subtract each term of this table from the next succeeding term, and place the results in another column (B), which may be called first difference column. If we again subtract each term of this first difference from the succeeding term, we find the result is always the number 2, (column C); and that the same number will always recur in that column, which may be called the second difference, will appear to any person who takes the trouble to carry on the table a few terms further. Now when once this is admitted, it is quite clear that, provided the first term (1) of the table, the first term (3) of the first differences, and the first term (2) of the second or constant difference, are originally given, we can continue the table of square numbers to any extent, merely by addition: for the series of first differences may be formed by repeatedly adding the constant difference (2) to (3) the first number in column B, and we then have the series of numbers, 3, 5, 6, etc.: and again, by successively adding each of these to the first number (1) of the table, we produce the square numbers. Having thus, I hope, thrown some light upon the theoretical part of the question, I shall endeavour to shew that the mechanical execution of such an engine, as would produce this series of numbers, is not so far removed from that of ordinary machinery as might be conceived.(3*) Let the reader imagine three clocks, placed on a table side by side, each having only one hand, and each having a thousand divisions instead of twelve hours marked on the face; and every time a string is pulled, let them strike on a bell the numbers of the divisions to which their hands point. Let him further suppose that two of the clocks, for the sake of distinction called B and C, have some mechanism by which the clock C advances the hand of the clock B one division, for each stroke it makes upon its own bell: and let the clock B by a similar contrivance advance the hand of the clock A one division, for each stroke it makes on its own bell. With such an arrangement, having set the hand of the clock A to the division I, that of B to III, and that of C to II, let the reader imagine the repeating parts of the clocks to be set in motion continually in the following order: viz.—pull the string of clock A; pull the string of clock B; pull the string of clock C. The table on the following page will then express the series of movements and their results. If now only those divisions struck or pointed at by the clock A be attended to and written down, it will be found that they produce the series of the squares of the natural numbers. Such a series could, of course, be carried by this mechanism only so far as the numbers which can be expressed by three figures; but this may be sufficient to give some idea of the construction—and was, in fact, the point to which the first model of the calculating engine, now in progress, extended. We have seen, then, that the effect of the division of labour, both in mechanical and in mental operations, is, that it enables us to purchase and apply to each process precisely that quantity of skill and knowledge which is required for it: we avoid employing any part of the time of a man who can get eight or ten shillings a day by his skill in tempering needles, in turning a wheel, which can be done for sixpence a day; and we equally avoid the loss arising from the employment of an accomplished mathematician in performing the lowest processes of arithmetic. The division of labour cannot be successfully practised unless there exists a great demand for its produce; and it requires a large capital to be employed in those arts in which it is used. In watchmaking it has been carried, perhaps, to the greatest extent. It was stated in evidence before a committee of the House of Commons, that there are a hundred and two distinct branches of this art, to each of which a boy may be put apprentice: and that he only learns his master's department, and is unable, after his apprenticeship has expired, without subsequent instruction, to work at any other branch. The watch-finisher, whose business is to put together the scattered parts, is the only one, out of the hundred and two persons, who can work in any other department than his own. In one of the most difficult arts, that of mining, great improvements have resulted from the judicious distribution of the duties; and under the arrangments which have gradually been introduced, the whole system of the mine and its government is now placed under the control of the following officers. A manager, who has the general knowledge of all that is to be done, and who may be assisted by one or more skilful persons. Underground captains direct the proper mining operations, and govern the working miners. The purser and book-keeper manage the accounts. The engineer erects the engines, and superintends the men who work them. A chief pitman has charge of the pumps and the apparatus of the shafts. A surface-captain, with assistants, receives the ores raised, and directs the dressing department, the object of which is to render them marketable. The head carpenter superintends many constructions. The foreman of the smiths regulates the ironwork and tools. A materials man selects, purchases, receives and delivers all articles required. The roper has charge of ropes and cordage of all sorts. Notes: An Enquiry into the Nature and Causes of the Wealth of Nations, by Adam Smith. Note sur la publication, proposee par le gouvernement Anglais des grandes tables logarithmiques et trigonometriques de M de Prony De l'imprimerie de F. Didot, December 1, 1829, p. 7 Since the publication of the second edition of this work, one portion of the engine which I have been constructing for some years past has been put together. It calculates, in three columns, a table with its first and second differences. Each column can be expressed as far as five figures, so that these fifteen figures constitute about one ninth part of the larger engine. The ease and precision with which it works leave no room to doubt its success in the more extended form. Besides tables of squares, cubes, and portions of logarithmic tables, it possesses the power of calculating certain series whose differences are not constant; and it has already tabulated parts of series formed from the following equations: The third differential of ux = units figur of delta ux The third differential of ux = nearest whole no. to (1/10,000 delta ux) The subjoined is one amongst the series which it has calculated: 0 3, 486 42,972 0 4,991 50,532 1 6,907 58,812 14 9,295 67,826 70 12,236 77,602 230 15,741 88,202
495 19,861 99,627
916 24,597 111,928
1,504 30,010 125,116
2,340 36,131 139,272 The general term of this is, ux = (x(x-1)(x-2))/(1 X 2 X 3) + the whole number in x/10 + 10 Sigma^3 (units figure of (x(x-1)/2) About HackerNoon Book Series: We bring you the most important technical, scientific, and insightful public domain books. This book is part of the public domain. Charles Babbage (2003). On the Economy of Machinery and Manufactures. Urbana, Illinois: Project Gutenberg. Retrieved https://www.gutenberg.org/cache/epub/4238/pg4238.html This eBook is for the use of anyone anywhere at no cost and with almost no restrictions whatsoever. You may copy it, give it away or re-use it under the terms of the Project Gutenberg License included with this eBook or online at , located at . www.gutenberg.org https://www.gutenberg.org/policy/license.html

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