Digital computers implement computations using circuits, as do many naturally occurring systems (e.g., gene regulatory networks). The topology of any such circuit restricts which variables may be physically coupled during the operation of a circuit. We investigate how such restrictions on the physical coupling affects the thermodynamic costs of running the circuit. To do this we first calculate the minimal additional entropy production that arises when we run a given gate in a circuit. We then build on this calculation, to analyze how the thermodynamic costs of implementing a computation with a full circuit, comprising multiple connected gates, depends on the topology of that circuit. This analysis provides a rich new set of optimization problems that must be addressed by any designer of a circuit, if they wish to minimize thermodynamic costs.
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Next Point-of-Interest (POI) recommendation is a critical task in location-based services that aim to provide personalized suggestions for the user's next destination. Previous works on POI recommendation have laid focused on modeling the user's spatial preference. However, existing works that leverage spatial information are only based on the aggregation of users' previous visited positions, which discourages the model from recommending POIs in novel areas. This trait of position-based methods will harm the model's performance in many situations. Additionally, incorporating sequential information into the user's spatial preference remains a challenge. In this paper, we propose Diff-POI: a Diffusion-based model that samples the user's spatial preference for the next POI recommendation. Inspired by the wide application of diffusion algorithm in sampling from distributions, Diff-POI encodes the user's visiting sequence and spatial character with two tailor-designed graph encoding modules, followed by a diffusion-based sampling strategy to explore the user's spatial visiting trends. We leverage the diffusion process and its reversed form to sample from the posterior distribution and optimized the corresponding score function. We design a joint training and inference framework to optimize and evaluate the proposed Diff-POI. Extensive experiments on four real-world POI recommendation datasets demonstrate the superiority of our Diff-POI over state-of-the-art baseline methods. Further ablation and parameter studies on Diff-POI reveal the functionality and effectiveness of the proposed diffusion-based sampling strategy for addressing the limitations of existing methods.
The modeling and simulation of high-dimensional multiscale systems is a critical challenge across all areas of science and engineering. It is broadly believed that even with today's computer advances resolving all spatiotemporal scales described by the governing equations remains a remote target. This realization has prompted intense efforts to develop model order reduction techniques. In recent years, techniques based on deep recurrent neural networks have produced promising results for the modeling and simulation of complex spatiotemporal systems and offer large flexibility in model development as they can incorporate experimental and computational data. However, neural networks lack interpretability, which limits their utility and generalizability across complex systems. Here we propose a novel framework of Interpretable Learning Effective Dynamics (iLED) that offers comparable accuracy to state-of-the-art recurrent neural network-based approaches while providing the added benefit of interpretability. The iLED framework is motivated by Mori-Zwanzig and Koopman operator theory, which justifies the choice of the specific architecture. We demonstrate the effectiveness of the proposed framework in simulations of three benchmark multiscale systems. Our results show that the iLED framework can generate accurate predictions and obtain interpretable dynamics, making it a promising approach for solving high-dimensional multiscale systems.
Towards generalisable and calibrated synthetic speech detection with self-supervised representations
Generalisation -- the ability of a model to perform well on unseen data -- is crucial for building reliable deep fake detectors. However, recent studies have shown that the current audio deep fake models fall short of this desideratum. In this paper we show that pretrained self-supervised representations followed by a simple logistic regression classifier achieve strong generalisation capabilities, reducing the equal error rate from 30% to 8% on the newly introduced In-the-Wild dataset. Importantly, this approach also produces considerably better calibrated models when compared to previous approaches. This means that we can trust our model's predictions more and use these for downstream tasks, such as uncertainty estimation. In particular, we show that the entropy of the estimated probabilities provides a reliable way of rejecting uncertain samples and further improving the accuracy.
Conditional graph entropy is known to be the minimal rate for a natural functional compression problem with side information at the receiver. In this paper we show that it can be formulated as an alternating minimization problem, which gives rise to a simple iterative algorithm for numerically computing (conditional) graph entropy. This also leads to a new formula which shows that conditional graph entropy is part of a more general framework: the solution of an optimization problem over a convex corner. In the special case of graph entropy (i.e., unconditioned version) this was known due to Csisz\'ar, K\"orner, Lov\'asz, Marton, and Simonyi. In that case the role of the convex corner was played by the so-called vertex packing polytope. In the conditional version it is a more intricate convex body but the function to minimize is the same. Furthermore, we describe a dual problem that leads to an optimality check and an error bound for the iterative algorithm.
The 3D reconstruction of simultaneous localization and mapping (SLAM) is an important topic in the field for transport systems such as drones, service robots and mobile AR/VR devices. Compared to a point cloud representation, the 3D reconstruction based on meshes and voxels is particularly useful for high-level functions, like obstacle avoidance or interaction with the physical environment. This article reviews the implementation of a visual-based 3D scene reconstruction pipeline on resource-constrained hardware platforms. Real-time performances, memory management and low power consumption are critical for embedded systems. A conventional SLAM pipeline from sensors to 3D reconstruction is described, including the potential use of deep learning. The implementation of advanced functions with limited resources is detailed. Recent systems propose the embedded implementation of 3D reconstruction methods with different granularities. The trade-off between required accuracy and resource consumption for real-time localization and reconstruction is one of the open research questions identified and discussed in this paper.
With the increasing availability of large scale datasets, computational power and tools like automatic differentiation and expressive neural network architectures, sequential data are now often treated in a data-driven way, with a dynamical model trained from the observation data. While neural networks are often seen as uninterpretable black-box architectures, they can still benefit from physical priors on the data and from mathematical knowledge. In this paper, we use a neural network architecture which leverages the long-known Koopman operator theory to embed dynamical systems in latent spaces where their dynamics can be described linearly, enabling a number of appealing features. We introduce methods that enable to train such a model for long-term continuous reconstruction, even in difficult contexts where the data comes in irregularly-sampled time series. The potential for self-supervised learning is also demonstrated, as we show the promising use of trained dynamical models as priors for variational data assimilation techniques, with applications to e.g. time series interpolation and forecasting.
In this research work, we propose a high-order time adapted scheme for pricing a coupled system of fixed-free boundary constant elasticity of variance (CEV) model on both equidistant and locally refined space-grid. The performance of our method is substantially enhanced to improve irregularities in the model which are both inherent and induced. Furthermore, the system of coupled PDEs is strongly nonlinear and involves several time-dependent coefficients that include the first-order derivative of the early exercise boundary. These coefficients are approximated from a fourth-order analytical approximation which is derived using a regularized square-root function. The semi-discrete equation for the option value and delta sensitivity is obtained from a non-uniform fourth-order compact finite difference scheme. Fifth-order 5(4) Dormand-Prince time integration method is used to solve the coupled system of discrete equations. Enhancing the performance of our proposed method with local mesh refinement and adaptive strategies enables us to obtain highly accurate solution with very coarse space grids, hence reducing computational runtime substantially. We further verify the performance of our methodology as compared with some of the well-known and better-performing existing methods.
We develop an automated computational modeling framework for rapid gradient-based design of multistable soft mechanical structures composed of non-identical bistable unit cells with appropriate geometric parameterization. This framework includes a custom isogeometric analysis-based continuum mechanics solver that is robust and end-to-end differentiable, which enables geometric and material optimization to achieve a desired multistability pattern. We apply this numerical modeling approach in two dimensions to design a variety of multistable structures, accounting for various geometric and material constraints. Our framework demonstrates consistent agreement with experimental results, and robust performance in designing for multistability, which facilities soft actuator design with high precision and reliability.
We study a subspace constrained version of the randomized Kaczmarz algorithm for solving large linear systems in which the iterates are confined to the space of solutions of a selected subsystem. We show that the subspace constraint leads to an accelerated convergence rate, especially when the system has structure such as having coherent rows or being approximately low-rank. On Gaussian-like random data, it results in a form of dimension reduction that effectively improves the aspect ratio of the system. Furthermore, this method serves as a building block for a second, quantile-based algorithm for the problem of solving linear systems with arbitrary sparse corruptions, which is able to efficiently exploit partial external knowledge about uncorrupted equations and achieve convergence in difficult settings such as in almost-square systems. Numerical experiments on synthetic and real-world data support our theoretical results and demonstrate the validity of the proposed methods for even more general data models than guaranteed by the theory.
Digital memcomputing machines (DMMs) are a new class of computing machines that employ non-quantum dynamical systems with memory to solve combinatorial optimization problems. Here, we show that the time to solution (TTS) of DMMs follows an inverse Gaussian distribution, with the TTS self-averaging with increasing problem size, irrespective of the problem they solve. We provide both an analytical understanding of this phenomenon and numerical evidence by solving instances of the 3-SAT (satisfiability) problem. The self-averaging property of DMMs with problem size implies that they are increasingly insensitive to the detailed features of the instances they solve. This is in sharp contrast to traditional algorithms applied to the same problems, illustrating another advantage of this physics-based approach to computation.
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