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In PDE-constrained optimization, one aims to find design parameters that minimize some objective, subject to the satisfaction of a partial differential equation. A major challenges is computing gradients of the objective to the design parameters, as applying the chain rule requires computing the Jacobian of the design parameters to the PDE's state. The adjoint method avoids this Jacobian by computing partial derivatives of a Lagrangian. Evaluating these derivatives requires the solution of a second PDE with the adjoint differential operator to the constraint, resulting in a backwards-in-time simulation. Particle-based Monte Carlo solvers are often used to compute the solution to high-dimensional PDEs. However, such solvers have the drawback of introducing noise to the computed results, thus requiring stochastic optimization methods. To guarantee convergence in this setting, both the constraint and adjoint Monte Carlo simulations should simulate the same particle trajectories. For large simulations, storing full paths from the constraint equation for re-use in the adjoint equation becomes infeasible due to memory limitations. In this paper, we provide a reversible extension to the family of permuted congruential pseudorandom number generators (PCG). We then use such a generator to recompute these time-reversed paths for the heat equation, avoiding these memory issues.

This research proposes an enhanced measurement method for VoIP quality assessment which provides an improvement to accuracy and reliability. To improve the objective measurement tool called the simplified E-model for the selected codec, G.729, it has been enhanced by utilizing a subjective MOS prediction model based on native Thai users, who use the Thai-tonal language. Then, the different results from the simplified E-model and subjective MOS prediction model were used to create the Bias function, before adding to the simplified E-model. Finally, it has been found that the outputs from the enhanced simplified E-model for the G.729 codec shows better accuracy when compared to the original simplified E-model, specially, after the enhanced model has been evaluated with 4 test sets. The major contribution of this enhancement is that errors are reduced by 58.87 % when compared to the generic simplified E-model. That means the enhanced simplified E-model as proposed in this study can provide improvement beyond the original simplified one significantly.

As advancements in artificial intelligence (AI) propel progress in the life sciences, they may also enable the weaponisation and misuse of biological agents. This article differentiates two classes of AI tools that could pose such biosecurity risks: large language models (LLMs) and biological design tools (BDTs). LLMs, such as GPT-4 and its successors, might provide dual-use information and thus remove some barriers encountered by historical biological weapons efforts. As LLMs are turned into multi-modal lab assistants and autonomous science tools, this will increase their ability to support non-experts in performing laboratory work. Thus, LLMs may in particular lower barriers to biological misuse. In contrast, BDTs will expand the capabilities of sophisticated actors. Concretely, BDTs may enable the creation of pandemic pathogens substantially worse than anything seen to date and could enable forms of more predictable and targeted biological weapons. In combination, the convergence of LLMs and BDTs could raise the ceiling of harm from biological agents and could make them broadly accessible. A range of interventions would help to manage risks. Independent pre-release evaluations could help understand the capabilities of models and the effectiveness of safeguards. Options for differentiated access to such tools should be carefully weighed with the benefits of openly releasing systems. Lastly, essential for mitigating risks will be universal and enhanced screening of gene synthesis products.

In this work, we present the physics-informed neural network (PINN) model applied particularly to dynamic problems in solid mechanics. We focus on forward and inverse problems. Particularly, we show how a PINN model can be used efficiently for material identification in a dynamic setting. In this work, we assume linear continuum elasticity. We show results for two-dimensional (2D) plane strain problem and then we proceed to apply the same techniques for a three-dimensional (3D) problem. As for the training data we use the solution based on the finite element method. We rigorously show that PINN models are accurate, robust and computationally efficient, especially as a surrogate model for material identification problems. Also, we employ state-of-the-art techniques from the PINN literature which are an improvement to the vanilla implementation of PINN. Based on our results, we believe that the framework we have developed can be readily adapted to computational platforms for solving multiple dynamic problems in solid mechanics.

Quantum Extreme Learning Machines (QELMs) have emerged as a promising framework for quantum machine learning. Their appeal lies in the rich feature map induced by the dynamics of a quantum substrate - the quantum reservoir - and the efficient post-measurement training via linear regression. Here we study the expressivity of QELMs by decomposing the prediction of QELMs into a Fourier series. We show that the achievable Fourier frequencies are determined by the data encoding scheme, while Fourier coefficients depend on both the reservoir and the measurement. Notably, the expressivity of QELMs is fundamentally limited by the number of Fourier frequencies and the number of observables, while the complexity of the prediction hinges on the reservoir. As a cautionary note on scalability, we identify four sources that can lead to the exponential concentration of the observables as the system size grows (randomness, hardware noise, entanglement, and global measurements) and show how this can turn QELMs into useless input-agnostic oracles. Our analysis elucidates the potential and fundamental limitations of QELMs, and lays the groundwork for systematically exploring quantum reservoir systems for other machine learning tasks.

As in many fields of medical research, survival analysis has witnessed a growing interest in the application of deep learning techniques to model complex, high-dimensional, heterogeneous, incomplete, and censored medical data. Current methods often make assumptions about the relations between data that may not be valid in practice. In response, we introduce SAVAE (Survival Analysis Variational Autoencoder), a novel approach based on Variational Autoencoders. SAVAE contributes significantly to the field by introducing a tailored ELBO formulation for survival analysis, supporting various parametric distributions for covariates and survival time (as long as the log-likelihood is differentiable). It offers a general method that consistently performs well on various metrics, demonstrating robustness and stability through different experiments. Our proposal effectively estimates time-to-event, accounting for censoring, covariate interactions, and time-varying risk associations. We validate our model in diverse datasets, including genomic, clinical, and demographic data, with varying levels of censoring. This approach demonstrates competitive performance compared to state-of-the-art techniques, as assessed by the Concordance Index and the Integrated Brier Score. SAVAE also offers an interpretable model that parametrically models covariates and time. Moreover, its generative architecture facilitates further applications such as clustering, data imputation, and the generation of synthetic patient data through latent space inference from survival data.

In recent years many efforts have been devoted to finding bidiagonal factorizations of nonsingular totally positive matrices, since their accurate computation allows to numerically solve several important algebraic problems with great precision, even for large ill-conditioned matrices. In this framework, the present work provides the factorization of the collocation matrices of Newton bases -- of relevance when considering the Lagrange interpolation problem -- together with an algorithm that allows to numerically compute it to high relative accuracy. This further allows to determine the coefficients of the interpolating polynomial and to compute the singular values and the inverse of the collocation matrix. Conditions that guarantee high relative accuracy for these methods and, in the former case, for the classical recursion formula of divided differences, are determined. Numerical errors due to imprecise computer arithmetic or perturbed input data in the computation of the factorization are analyzed. Finally, numerical experiments illustrate the accuracy and effectiveness of the proposed methods with several algebraic problems, in stark contrast with traditional approaches.

Deep neural network based recommendation systems have achieved great success as information filtering techniques in recent years. However, since model training from scratch requires sufficient data, deep learning-based recommendation methods still face the bottlenecks of insufficient data and computational inefficiency. Meta-learning, as an emerging paradigm that learns to improve the learning efficiency and generalization ability of algorithms, has shown its strength in tackling the data sparsity issue. Recently, a growing number of studies on deep meta-learning based recommenddation systems have emerged for improving the performance under recommendation scenarios where available data is limited, e.g. user cold-start and item cold-start. Therefore, this survey provides a timely and comprehensive overview of current deep meta-learning based recommendation methods. Specifically, we propose a taxonomy to discuss existing methods according to recommendation scenarios, meta-learning techniques, and meta-knowledge representations, which could provide the design space for meta-learning based recommendation methods. For each recommendation scenario, we further discuss technical details about how existing methods apply meta-learning to improve the generalization ability of recommendation models. Finally, we also point out several limitations in current research and highlight some promising directions for future research in this area.

When and why can a neural network be successfully trained? This article provides an overview of optimization algorithms and theory for training neural networks. First, we discuss the issue of gradient explosion/vanishing and the more general issue of undesirable spectrum, and then discuss practical solutions including careful initialization and normalization methods. Second, we review generic optimization methods used in training neural networks, such as SGD, adaptive gradient methods and distributed methods, and theoretical results for these algorithms. Third, we review existing research on the global issues of neural network training, including results on bad local minima, mode connectivity, lottery ticket hypothesis and infinite-width analysis.

Graph representation learning for hypergraphs can be used to extract patterns among higher-order interactions that are critically important in many real world problems. Current approaches designed for hypergraphs, however, are unable to handle different types of hypergraphs and are typically not generic for various learning tasks. Indeed, models that can predict variable-sized heterogeneous hyperedges have not been available. Here we develop a new self-attention based graph neural network called Hyper-SAGNN applicable to homogeneous and heterogeneous hypergraphs with variable hyperedge sizes. We perform extensive evaluations on multiple datasets, including four benchmark network datasets and two single-cell Hi-C datasets in genomics. We demonstrate that Hyper-SAGNN significantly outperforms the state-of-the-art methods on traditional tasks while also achieving great performance on a new task called outsider identification. Hyper-SAGNN will be useful for graph representation learning to uncover complex higher-order interactions in different applications.