Calibration refers to the statistical estimation of unknown model parameters in computer experiments, such that computer experiments can match underlying physical systems. This work develops a new calibration method for imperfect computer models, Sobolev calibration, which can rule out calibration parameters that generate overfitting calibrated functions. We prove that the Sobolev calibration enjoys desired theoretical properties including fast convergence rate, asymptotic normality and semiparametric efficiency. We also demonstrate an interesting property that the Sobolev calibration can bridge the gap between two influential methods: $L_2$ calibration and Kennedy and O'Hagan's calibration. In addition to exploring the deterministic physical experiments, we theoretically justify that our method can transfer to the case when the physical process is indeed a Gaussian process, which follows the original idea of Kennedy and O'Hagan's. Numerical simulations as well as a real-world example illustrate the competitive performance of the proposed method.
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ACM/IEEE第23屆模型驅動工程語言和系統國際會議，是模型驅動軟件和系統工程的首要會議系列，由ACM-SIGSOFT和IEEE-TCSE支持組織。自1998年以來，模型涵蓋了建模的各個方面，從語言和方法到工具和應用程序。模特的參加者來自不同的背景，包括研究人員、學者、工程師和工業專業人士。MODELS 2019是一個論壇，參與者可以圍繞建模和模型驅動的軟件和系統交流前沿研究成果和創新實踐經驗。今年的版本將為建模社區提供進一步推進建模基礎的機會，并在網絡物理系統、嵌入式系統、社會技術系統、云計算、大數據、機器學習、安全、開源等新興領域提出建模的創新應用以及可持續性。
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When optimizing machine learning models, there are various scenarios where gradient computations are challenging or even infeasible. Furthermore, in reinforcement learning (RL), preference-based RL that only compares between options has wide applications, including reinforcement learning with human feedback in large language models. In this paper, we systematically study optimization of a smooth function $f\colon\mathbb{R}^n\to\mathbb{R}$ only assuming an oracle that compares function values at two points and tells which is larger. When $f$ is convex, we give two algorithms using $\tilde{O}(n/\epsilon)$ and $\tilde{O}(n^{2})$ comparison queries to find an $\epsilon$-optimal solution, respectively. When $f$ is nonconvex, our algorithm uses $\tilde{O}(n/\epsilon^2)$ comparison queries to find an $\epsilon$-approximate stationary point. All these results match the best-known zeroth-order algorithms with function evaluation queries in $n$ dependence, thus suggest that \emph{comparisons are all you need for optimizing smooth functions using derivative-free methods}. In addition, we also give an algorithm for escaping saddle points and reaching an $\epsilon$-second order stationary point of a nonconvex $f$, using $\tilde{O}(n^{1.5}/\epsilon^{2.5})$ comparison queries.
We investigate the learning of implicit neural representation (INR) using an overparameterized multilayer perceptron (MLP) via a novel nonparametric teaching perspective. The latter offers an efficient example selection framework for teaching nonparametrically defined (viz. non-closed-form) target functions, such as image functions defined by 2D grids of pixels. To address the costly training of INRs, we propose a paradigm called Implicit Neural Teaching (INT) that treats INR learning as a nonparametric teaching problem, where the given signal being fitted serves as the target function. The teacher then selects signal fragments for iterative training of the MLP to achieve fast convergence. By establishing a connection between MLP evolution through parameter-based gradient descent and that of function evolution through functional gradient descent in nonparametric teaching, we show for the first time that teaching an overparameterized MLP is consistent with teaching a nonparametric learner. This new discovery readily permits a convenient drop-in of nonparametric teaching algorithms to broadly enhance INR training efficiency, demonstrating 30%+ training time savings across various input modalities.
Copyright infringement may occur when a generative model produces samples substantially similar to some copyrighted data that it had access to during the training phase. The notion of access usually refers to including copyrighted samples directly in the training dataset, which one may inspect to identify an infringement. We argue that such visual auditing largely overlooks a concealed copyright infringement, where one constructs a disguise that looks drastically different from the copyrighted sample yet still induces the effect of training Latent Diffusion Models on it. Such disguises only require indirect access to the copyrighted material and cannot be visually distinguished, thus easily circumventing the current auditing tools. In this paper, we provide a better understanding of such disguised copyright infringement by uncovering the disguises generation algorithm, the revelation of the disguises, and importantly, how to detect them to augment the existing toolbox. Additionally, we introduce a broader notion of acknowledgment for comprehending such indirect access.
The purpose of a consensus protocol is to keep a distributed network of nodes "in sync," even in the presence of an unpredictable communication network and adversarial behavior by some of the participating nodes. In the permissionless setting, these nodes may be operated by unknown players, with each player free to use multiple identifiers and to start or stop running the protocol at any time. Establishing that a permissionless consensus protocol is "secure" thus requires both a distributed computing argument (that the protocol guarantees consistency and liveness unless the fraction of adversarial participation is sufficiently large) and an economic argument (that carrying out an attack would be prohibitively expensive for an attacker). There is a mature toolbox for assembling arguments of the former type; the goal of this paper is to lay the foundations for arguments of the latter type. An ideal permissionless consensus protocol would, in addition to satisfying standard consistency and liveness guarantees, render consistency violations prohibitively expensive for the attacker without collateral damage to honest participants. We make this idea precise with our notion of the EAAC (expensive to attack in the absence of collapse) property, and prove the following results: 1. In the synchronous and dynamically available setting, with an adversary that controls at least one-half of the overall resources, no protocol can be EAAC. 2. In the partially synchronous and quasi-permissionless setting, with an adversary that controls at least one-third of the overall resources, no protocol can be EAAC. 3. In the synchronous and quasi-permissionless setting, there is a proof-of-stake protocol that, provided the adversary controls less than two-thirds of the overall stake, satisfies the EAAC property. All three results are optimal with respect to the size of the adversary.
We define a graph-based rate optimization problem and consider its computation, which provides a unified approach to the computation of various theoretical limits, such as the (conditional) graph entropy, rate-distortion functions and capacity-cost functions with two-sided information. Our contributions are twofold. On the theoretical side, we simplify the graph-based problem by constructing explicit graph contractions in some special cases. These efforts reduce the number of decision variables in the optimization problem. Graph characterizations for rate-distortion and capacity-cost functions with two-sided information are simplified by specializing the results. On the computational side, we design an alternating minimization algorithm for the graph-based problem, which deals with the inequality constraint by a flexible multiplier update strategy. Moreover, deflation techniques are introduced, so that the computing time can be largely reduced. Theoretical analysis shows that the algorithm converges to an optimal solution. The accuracy and efficiency of the algorithm are illustrated by numerical experiments.
State estimation of nonlinear dynamical systems has long aimed to balance accuracy, computational efficiency, robustness, and reliability. The rapid evolution of various industries has amplified the demand for estimation frameworks that satisfy all these factors. This study introduces a neuromorphic approach for robust filtering of nonlinear dynamical systems: SNN-EMSIF (spiking neural network-extended modified sliding innovation filter). SNN-EMSIF combines the computational efficiency and scalability of SNNs with the robustness of EMSIF, an estimation framework designed for nonlinear systems with zero-mean Gaussian noise. Notably, the weight matrices are designed according to the system model, eliminating the need for a learning process. The framework's efficacy is evaluated through comprehensive Monte Carlo simulations, comparing SNN-EMSIF with EKF and EMSIF. Additionally, it is compared with SNN-EKF in the presence of modeling uncertainties and neuron loss, using RMSEs as a metric. The results demonstrate the superior accuracy and robustness of SNN-EMSIF. Further analysis of runtimes and spiking patterns reveals an impressive reduction of 85% in emitted spikes compared to possible spikes, highlighting the computational efficiency of SNN-EMSIF. This framework offers a promising solution for robust estimation in nonlinear dynamical systems, opening new avenues for efficient and reliable estimation in various industries that can benefit from neuromorphic computing.
As soon as abstract mathematical computations were adapted to computation on digital computers, the problem of efficient representation, manipulation, and communication of the numerical values in those computations arose. Strongly related to the problem of numerical representation is the problem of quantization: in what manner should a set of continuous real-valued numbers be distributed over a fixed discrete set of numbers to minimize the number of bits required and also to maximize the accuracy of the attendant computations? This perennial problem of quantization is particularly relevant whenever memory and/or computational resources are severely restricted, and it has come to the forefront in recent years due to the remarkable performance of Neural Network models in computer vision, natural language processing, and related areas. Moving from floating-point representations to low-precision fixed integer values represented in four bits or less holds the potential to reduce the memory footprint and latency by a factor of 16x; and, in fact, reductions of 4x to 8x are often realized in practice in these applications. Thus, it is not surprising that quantization has emerged recently as an important and very active sub-area of research in the efficient implementation of computations associated with Neural Networks. In this article, we survey approaches to the problem of quantizing the numerical values in deep Neural Network computations, covering the advantages/disadvantages of current methods. With this survey and its organization, we hope to have presented a useful snapshot of the current research in quantization for Neural Networks and to have given an intelligent organization to ease the evaluation of future research in this area.
Transformers have achieved great success in many artificial intelligence fields, such as natural language processing, computer vision, and audio processing. Therefore, it is natural to attract lots of interest from academic and industry researchers. Up to the present, a great variety of Transformer variants (a.k.a. X-formers) have been proposed, however, a systematic and comprehensive literature review on these Transformer variants is still missing. In this survey, we provide a comprehensive review of various X-formers. We first briefly introduce the vanilla Transformer and then propose a new taxonomy of X-formers. Next, we introduce the various X-formers from three perspectives: architectural modification, pre-training, and applications. Finally, we outline some potential directions for future research.
We consider the problem of explaining the predictions of graph neural networks (GNNs), which otherwise are considered as black boxes. Existing methods invariably focus on explaining the importance of graph nodes or edges but ignore the substructures of graphs, which are more intuitive and human-intelligible. In this work, we propose a novel method, known as SubgraphX, to explain GNNs by identifying important subgraphs. Given a trained GNN model and an input graph, our SubgraphX explains its predictions by efficiently exploring different subgraphs with Monte Carlo tree search. To make the tree search more effective, we propose to use Shapley values as a measure of subgraph importance, which can also capture the interactions among different subgraphs. To expedite computations, we propose efficient approximation schemes to compute Shapley values for graph data. Our work represents the first attempt to explain GNNs via identifying subgraphs explicitly and directly. Experimental results show that our SubgraphX achieves significantly improved explanations, while keeping computations at a reasonable level.
Residual networks (ResNets) have displayed impressive results in pattern recognition and, recently, have garnered considerable theoretical interest due to a perceived link with neural ordinary differential equations (neural ODEs). This link relies on the convergence of network weights to a smooth function as the number of layers increases. We investigate the properties of weights trained by stochastic gradient descent and their scaling with network depth through detailed numerical experiments. We observe the existence of scaling regimes markedly different from those assumed in neural ODE literature. Depending on certain features of the network architecture, such as the smoothness of the activation function, one may obtain an alternative ODE limit, a stochastic differential equation or neither of these. These findings cast doubts on the validity of the neural ODE model as an adequate asymptotic description of deep ResNets and point to an alternative class of differential equations as a better description of the deep network limit.
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