Earlier studies have revealed that Maxwell's demon must obey the second law of thermodynamics. However, it is still an open question whether there is a fundamental net gain and indispensability of using information. Here, gain refers to free energy or mechanical work. In this paper, we report a novel generalization of the second law of thermodynamics that answers this question in affirmative. The entropy production can be split into two contributions: the entropy productions of the individual subsystems and the decrease in the correlations internally between subsystems. Our novel generalization of the second law implies that information is indispensable and that a positive net gain can be realized if an agent exploits the latter contribution of this split. Particularly, it is shown that the total entropy production has a lower bound corresponding to the positive quantity that emerges when the internal correlations of the target system diminish without the correlation between an agent and the target of its control. In other words, the target information is indispensable for exploiting the internal correlations to extract free energy or work. As the internal correlations can grow linearly with the number of the subsystems constituting the target system, the control with such correlations, i.e., feedback control, can provide substantial gain that exceeds the operational cost paid for performing the feedback control, which is negligible in the thermodynamic limit. Thus, the generalized second law presented in this paper can be interpreted as a physical principle that explains the mechanism through which information becomes not only substantially beneficial and but also inevitable at the macroscopic scale.
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In this paper, we study a distributed privacy-preserving learning problem in social networks with general topology. The agents can communicate with each other over the network, which may result in privacy disclosure, since the trustworthiness of the agents cannot be guaranteed. Given a set of options which yield unknown stochastic rewards, each agent is required to learn the best one, aiming at maximizing the resulting expected average cumulative reward. To serve the above goal, we propose a four-staged distributed algorithm which efficiently exploits the collaboration among the agents while preserving the local privacy for each of them. In particular, our algorithm proceeds iteratively, and in every round, each agent i) randomly perturbs its adoption for the privacy-preserving purpose, ii) disseminates the perturbed adoption over the social network in a nearly uniform manner through random walking, iii) selects an option by referring to the perturbed suggestions received from its peers, and iv) decides whether or not to adopt the selected option as preference according to its latest reward feedback. Through solid theoretical analysis, we quantify the trade-off among the number of agents (or communication overhead), privacy preserving and learning utility. We also perform extensive simulations to verify the efficacy of our proposed social learning algorithm.
We address the problem of learning the dynamics of an unknown non-parametric system linking a target and a feature time series. The feature time series is measured on a sparse and irregular grid, while we have access to only a few points of the target time series. Once learned, we can use these dynamics to predict values of the target from the previous values of the feature time series. We frame this task as learning the solution map of a controlled differential equation (CDE). By leveraging the rich theory of signatures, we are able to cast this non-linear problem as a high-dimensional linear regression. We provide an oracle bound on the prediction error which exhibits explicit dependencies on the individual-specific sampling schemes. Our theoretical results are illustrated by simulations which show that our method outperforms existing algorithms for recovering the full time series while being computationally cheap. We conclude by demonstrating its potential on real-world epidemiological data.
We propose a novel machine learning method based on differentiable vortex particles to infer and predict fluid dynamics from a single video. The key design of our system is a particle-based latent space to encapsulate the hidden, Lagrangian vortical evolution underpinning the observable, Eulerian flow phenomena. We devise a novel differentiable vortex particle system in conjunction with their learnable, vortex-to-velocity dynamics mapping to effectively capture and represent the complex flow features in a reduced space. We further design an end-to-end training pipeline to directly learn and synthesize simulators from data, that can reliably deliver future video rollouts based on limited observation. The value of our method is twofold: first, our learned simulator enables the inference of hidden physics quantities (e.g. velocity field) purely from visual observation, to be used for motion analysis; secondly, it also supports future prediction, constructing the input video's sequel along with its future dynamics evolution. We demonstrate our method's efficacy by comparing quantitatively and qualitatively with a range of existing methods on both synthetic and real-world videos, displaying improved data correspondence, visual plausibility, and physical integrity.
Most of the literature on learning in games has focused on the restrictive setting where the underlying repeated game does not change over time. Much less is known about the convergence of no-regret learning algorithms in dynamic multiagent settings. In this paper, we characterize the convergence of \emph{optimistic gradient descent (OGD)} in time-varying games by drawing a strong connection with \emph{dynamic regret}. Our framework yields sharp convergence bounds for the equilibrium gap of OGD in zero-sum games parameterized on the \emph{minimal} first-order variation of the Nash equilibria and the second-order variation of the payoff matrices, subsuming known results for static games. Furthermore, we establish improved \emph{second-order} variation bounds under strong convexity-concavity, as long as each game is repeated multiple times. Our results also apply to time-varying \emph{general-sum} multi-player games via a bilinear formulation of correlated equilibria, which has novel implications for meta-learning and for obtaining refined variation-dependent regret bounds, addressing questions left open in prior papers. Finally, we leverage our framework to also provide new insights on dynamic regret guarantees in static games.
We develop a model of coordination and allocation of decentralized multi-sided markets, in which our theoretical analysis is promisingly optimizing the decentralized transaction packaging process at high-throughput blockchains or Web 3.0 platforms. In contrast to the stylized centralized platform, the decentralized platform is powered by blockchain technology, which allows for secure and transparent Peer-to-Peer transactions among users. Traditional single-chain-based blockchains suffer from the well-known blockchain trilemma. Beyond the single-chain-based scheme, decentralized high-throughput blockchains adopt parallel protocols to reconcile the blockchain trilemma, implementing any tasking and desired allocation. However, unneglectable network latency may induce partial observability, resulting in incoordination and misallocation issues for the decentralized transaction packaging process at the current high-throughput blockchain protocols. To address this problem, we consider a strategic coordination mechanism for the decentralized transaction packaging process by using a game-theoretic approach. Under a tractable two-period model, we find a Bayesian Nash equilibrium of the miner's strategic transaction packaging under partial observability. Along with novel algorithms for computing equilibrium payoffs, we show that the decentralized platform can achieve an efficient and stable market outcome. The model also highlights that the proposed mechanism can endogenously offer a base fee per gas without any restructuration of the initial blockchain transaction fee mechanism. The theoretical results that underlie the algorithms also imply bounds on the computational complexity of equilibrium payoffs.
This paper studies how to use relation algebras, which are useful for high-level specification and verification, for proving the correctness of lower-level array-based implementations of algorithms. We give a simple relation-algebraic semantics of read and write operations on associative arrays. The array operations seamlessly integrate with assignments in computation models supporting while-programs. As a result, relation algebras can be used for verifying programs with associative arrays. We verify the correctness of an array-based implementation of disjoint-set forests using the union-by-rank strategy and find operations with path compression, path splitting and path halving. All results are formally proved in Isabelle/HOL. This paper is an extended version of [1].
The conjoining of dynamical systems and deep learning has become a topic of great interest. In particular, neural differential equations (NDEs) demonstrate that neural networks and differential equation are two sides of the same coin. Traditional parameterised differential equations are a special case. Many popular neural network architectures, such as residual networks and recurrent networks, are discretisations. NDEs are suitable for tackling generative problems, dynamical systems, and time series (particularly in physics, finance, ...) and are thus of interest to both modern machine learning and traditional mathematical modelling. NDEs offer high-capacity function approximation, strong priors on model space, the ability to handle irregular data, memory efficiency, and a wealth of available theory on both sides. This doctoral thesis provides an in-depth survey of the field. Topics include: neural ordinary differential equations (e.g. for hybrid neural/mechanistic modelling of physical systems); neural controlled differential equations (e.g. for learning functions of irregular time series); and neural stochastic differential equations (e.g. to produce generative models capable of representing complex stochastic dynamics, or sampling from complex high-dimensional distributions). Further topics include: numerical methods for NDEs (e.g. reversible differential equations solvers, backpropagation through differential equations, Brownian reconstruction); symbolic regression for dynamical systems (e.g. via regularised evolution); and deep implicit models (e.g. deep equilibrium models, differentiable optimisation). We anticipate this thesis will be of interest to anyone interested in the marriage of deep learning with dynamical systems, and hope it will provide a useful reference for the current state of the art.
This paper focuses on the expected difference in borrower's repayment when there is a change in the lender's credit decisions. Classical estimators overlook the confounding effects and hence the estimation error can be magnificent. As such, we propose another approach to construct the estimators such that the error can be greatly reduced. The proposed estimators are shown to be unbiased, consistent, and robust through a combination of theoretical analysis and numerical testing. Moreover, we compare the power of estimating the causal quantities between the classical estimators and the proposed estimators. The comparison is tested across a wide range of models, including linear regression models, tree-based models, and neural network-based models, under different simulated datasets that exhibit different levels of causality, different degrees of nonlinearity, and different distributional properties. Most importantly, we apply our approaches to a large observational dataset provided by a global technology firm that operates in both the e-commerce and the lending business. We find that the relative reduction of estimation error is strikingly substantial if the causal effects are accounted for correctly.
This paper addresses the difficulty of forecasting multiple financial time series (TS) conjointly using deep neural networks (DNN). We investigate whether DNN-based models could forecast these TS more efficiently by learning their representation directly. To this end, we make use of the dynamic factor graph (DFG) from that we enhance by proposing a novel variable-length attention-based mechanism to render it memory-augmented. Using this mechanism, we propose an unsupervised DNN architecture for multivariate TS forecasting that allows to learn and take advantage of the relationships between these TS. We test our model on two datasets covering 19 years of investment funds activities. Our experimental results show that our proposed approach outperforms significantly typical DNN-based and statistical models at forecasting their 21-day price trajectory.
Over the past few years, we have seen fundamental breakthroughs in core problems in machine learning, largely driven by advances in deep neural networks. At the same time, the amount of data collected in a wide array of scientific domains is dramatically increasing in both size and complexity. Taken together, this suggests many exciting opportunities for deep learning applications in scientific settings. But a significant challenge to this is simply knowing where to start. The sheer breadth and diversity of different deep learning techniques makes it difficult to determine what scientific problems might be most amenable to these methods, or which specific combination of methods might offer the most promising first approach. In this survey, we focus on addressing this central issue, providing an overview of many widely used deep learning models, spanning visual, sequential and graph structured data, associated tasks and different training methods, along with techniques to use deep learning with less data and better interpret these complex models --- two central considerations for many scientific use cases. We also include overviews of the full design process, implementation tips, and links to a plethora of tutorials, research summaries and open-sourced deep learning pipelines and pretrained models, developed by the community. We hope that this survey will help accelerate the use of deep learning across different scientific domains.
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