This paper studies the problem of forecasting general stochastic processes using a path-dependent extension of the Neural Jump ODE (NJ-ODE) framework. While NJ-ODE was the first framework to establish convergence guarantees for the prediction of irregularly observed time series, these results were limited to data stemming from It\^o-diffusions with complete observations, in particular Markov processes where all coordinates are observed simultaneously. In this work, we generalise these results to generic, possibly non-Markovian or discontinuous, stochastic processes with incomplete observations, by utilising the reconstruction properties of the signature transform. These theoretical results are supported by empirical studies, where it is shown that the path-dependent NJ-ODE outperforms the original NJ-ODE framework in the case of non-Markovian data. Moreover, we show that PD-NJ-ODE can be applied successfully to classical stochastic filtering problems and to limit order book (LOB) data.
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This paper presents an innovative methodology for improving the robustness and computational efficiency of Spiking Neural Networks (SNNs), a critical component in neuromorphic computing. The proposed approach integrates astrocytes, a type of glial cell prevalent in the human brain, into SNNs, creating astrocyte-augmented networks. To achieve this, we designed and implemented an astrocyte model in two distinct platforms: CPU/GPU and FPGA. Our FPGA implementation notably utilizes Dynamic Function Exchange (DFX) technology, enabling real-time hardware reconfiguration and adaptive model creation based on current operating conditions. The novel approach of leveraging astrocytes significantly improves the fault tolerance of SNNs, thereby enhancing their robustness. Notably, our astrocyte-augmented SNN displays near-zero latency and theoretically infinite throughput, implying exceptional computational efficiency. Through comprehensive comparative analysis with prior works, it's established that our model surpasses others in terms of neuron and synapse count while maintaining an efficient power consumption profile. These results underscore the potential of our methodology in shaping the future of neuromorphic computing, by providing robust and energy-efficient systems.
The application of Physics-Informed Neural Networks (PINNs) is investigated for the first time in solving the one-dimensional Countercurrent spontaneous imbibition (COUCSI) problem at both early and late time (i.e., before and after the imbibition front meets the no-flow boundary). We introduce utilization of Change-of-Variables as a technique for improving performance of PINNs. We formulated the COUCSI problem in three equivalent forms by changing the independent variables. The first describes saturation as function of normalized position X and time T; the second as function of X and Y=T^0.5; and the third as a sole function of Z=X/T^0.5 (valid only at early time). The PINN model was generated using a feed-forward neural network and trained based on minimizing a weighted loss function, including the physics-informed loss term and terms corresponding to the initial and boundary conditions. All three formulations could closely approximate the correct solutions, with water saturation mean absolute errors around 0.019 and 0.009 for XT and XY formulations and 0.012 for the Z formulation at early time. The Z formulation perfectly captured the self-similarity of the system at early time. This was less captured by XT and XY formulations. The total variation of saturation was preserved in the Z formulation, and it was better preserved with XY- than XT formulation. Redefining the problem based on the physics-inspired variables reduced the non-linearity of the problem and allowed higher solution accuracies, a higher degree of loss-landscape convexity, a lower number of required collocation points, smaller network sizes, and more computationally efficient solutions.
We present a physics-informed machine-learning (PIML) approach for the approximation of slow invariant manifolds (SIMs) of singularly perturbed systems, providing functionals in an explicit form that facilitate the construction and numerical integration of reduced order models (ROMs). The proposed scheme solves a partial differential equation corresponding to the invariance equation (IE) within the Geometric Singular Perturbation Theory (GSPT) framework. For the solution of the IE, we used two neural network structures, namely feedforward neural networks (FNNs), and random projection neural networks (RPNNs), with symbolic differentiation for the computation of the gradients required for the learning process. The efficiency of our PIML method is assessed via three benchmark problems, namely the Michaelis-Menten, the target mediated drug disposition reaction mechanism, and the 3D Sel'kov model. We show that the proposed PIML scheme provides approximations, of equivalent or even higher accuracy, than those provided by other traditional GSPT-based methods, and importantly, for any practical purposes, it is not affected by the magnitude of the perturbation parameter. This is of particular importance, as there are many systems for which the gap between the fast and slow timescales is not that big, but still ROMs can be constructed. A comparison of the computational costs between symbolic, automatic and numerical approximation of the required derivatives in the learning process is also provided.
Distribution-dependent stochastic dynamical systems arise widely in engineering and science. We consider a class of such systems which model the limit behaviors of interacting particles moving in a vector field with random fluctuations. We aim to examine the most likely transition path between equilibrium stable states of the vector field. In the small noise regime, the action functional does not involve the solution of the skeleton equation which describes the unperturbed deterministic flow of the vector field shifted by the interaction at zero distance. As a result, we are led to study the most likely transition path for a stochastic differential equation without distribution dependency. This enables the computation of the most likely transition path for these distribution-dependent stochastic dynamical systems by the adaptive minimum action method and we illustrate our approach in two examples.
We propose Gibbs-Duhem-informed neural networks for the prediction of binary activity coefficients at varying compositions. That is, we include the Gibbs-Duhem equation explicitly in the loss function for training neural networks, which is straightforward in standard machine learning (ML) frameworks enabling automatic differentiation. In contrast to recent hybrid ML approaches, our approach does not rely on embedding a specific thermodynamic model inside the neural network and corresponding prediction limitations. Rather, Gibbs-Duhem consistency serves as regularization, with the flexibility of ML models being preserved. Our results show increased thermodynamic consistency and generalization capabilities for activity coefficient predictions by Gibbs-Duhem-informed graph neural networks and matrix completion methods. We also find that the model architecture, particularly the activation function, can have a strong influence on the prediction quality. The approach can be easily extended to account for other thermodynamic consistency conditions.
Markov processes are widely used mathematical models for describing dynamic systems in various fields. However, accurately simulating large-scale systems at long time scales is computationally expensive due to the short time steps required for accurate integration. In this paper, we introduce an inference process that maps complex systems into a simplified representational space and models large jumps in time. To achieve this, we propose Time-lagged Information Bottleneck (T-IB), a principled objective rooted in information theory, which aims to capture relevant temporal features while discarding high-frequency information to simplify the simulation task and minimize the inference error. Our experiments demonstrate that T-IB learns information-optimal representations for accurately modeling the statistical properties and dynamics of the original process at a selected time lag, outperforming existing time-lagged dimensionality reduction methods.
Processing sensitive data and deploying well-designed Intellectual Property (IP) cores on remote Field Programmable Gate Array (FPGA) are prone to private data leakage and IP theft. One effective solution is constructing Trusted Execution Environment (TEE) on FPGA-SoCs (FPGA System on Chips). Researchers have integrated this type TEE with Trusted Platform Module (TPM)-based trusted boot, denoted as FPGA-SoC tbTEE. But there is no effort on secure and trusted runtime customization of FPGA-SoC TEE. This paper extends FPGA-SoC tbTEE to build Runtime Customizable TEE (RCTEE) on FPGA-SoC by additive three major components (our work): 1) CrloadIP, which can load an IP core at runtime such that RCTEE can be adjusted dynamically and securely; 2) CexecIP, which can not only execute an IP core without modifying the operating system of FPGA-SoC TEE, but also prevent insider attacks from executing IPs deployed in RCTEE; 3) CremoAT, which can provide the newly measured RCTEE state and establish a secure and trusted communication path between remote verifiers and RCTEE. We conduct a security analysis of RCTEE and its performance evaluation on Xilinx Zynq UltraScale+ XCZU15EG 2FFVB1156 MPSoC.
Graph Neural Networks (GNNs) have shown promising results on a broad spectrum of applications. Most empirical studies of GNNs directly take the observed graph as input, assuming the observed structure perfectly depicts the accurate and complete relations between nodes. However, graphs in the real world are inevitably noisy or incomplete, which could even exacerbate the quality of graph representations. In this work, we propose a novel Variational Information Bottleneck guided Graph Structure Learning framework, namely VIB-GSL, in the perspective of information theory. VIB-GSL advances the Information Bottleneck (IB) principle for graph structure learning, providing a more elegant and universal framework for mining underlying task-relevant relations. VIB-GSL learns an informative and compressive graph structure to distill the actionable information for specific downstream tasks. VIB-GSL deduces a variational approximation for irregular graph data to form a tractable IB objective function, which facilitates training stability. Extensive experimental results demonstrate that the superior effectiveness and robustness of VIB-GSL.
An effective and efficient architecture performance evaluation scheme is essential for the success of Neural Architecture Search (NAS). To save computational cost, most of existing NAS algorithms often train and evaluate intermediate neural architectures on a small proxy dataset with limited training epochs. But it is difficult to expect an accurate performance estimation of an architecture in such a coarse evaluation way. This paper advocates a new neural architecture evaluation scheme, which aims to determine which architecture would perform better instead of accurately predict the absolute architecture performance. Therefore, we propose a \textbf{relativistic} architecture performance predictor in NAS (ReNAS). We encode neural architectures into feature tensors, and further refining the representations with the predictor. The proposed relativistic performance predictor can be deployed in discrete searching methods to search for the desired architectures without additional evaluation. Experimental results on NAS-Bench-101 dataset suggests that, sampling 424 ($0.1\%$ of the entire search space) neural architectures and their corresponding validation performance is already enough for learning an accurate architecture performance predictor. The accuracies of our searched neural architectures on NAS-Bench-101 and NAS-Bench-201 datasets are higher than that of the state-of-the-art methods and show the priority of the proposed method.
Reasoning with knowledge expressed in natural language and Knowledge Bases (KBs) is a major challenge for Artificial Intelligence, with applications in machine reading, dialogue, and question answering. General neural architectures that jointly learn representations and transformations of text are very data-inefficient, and it is hard to analyse their reasoning process. These issues are addressed by end-to-end differentiable reasoning systems such as Neural Theorem Provers (NTPs), although they can only be used with small-scale symbolic KBs. In this paper we first propose Greedy NTPs (GNTPs), an extension to NTPs addressing their complexity and scalability limitations, thus making them applicable to real-world datasets. This result is achieved by dynamically constructing the computation graph of NTPs and including only the most promising proof paths during inference, thus obtaining orders of magnitude more efficient models. Then, we propose a novel approach for jointly reasoning over KBs and textual mentions, by embedding logic facts and natural language sentences in a shared embedding space. We show that GNTPs perform on par with NTPs at a fraction of their cost while achieving competitive link prediction results on large datasets, providing explanations for predictions, and inducing interpretable models. Source code, datasets, and supplementary material are available online at //github.com/uclnlp/gntp.
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