Time series analysis is relevant in various disciplines such as physics, biology, chemistry, and finance. In this paper, we present a novel neural network architecture that integrates elements from ResNet structures, while introducing the innovative incorporation of the Taylor series framework. This approach demonstrates notable enhancements in test accuracy across many of the baseline datasets investigated. Furthermore, we extend our method to incorporate a recursive step, which leads to even further improvements in test accuracy. Our findings underscore the potential of our proposed model to significantly advance time series analysis methodologies, offering promising avenues for future research and application.
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Importance sampling is one of the most widely used variance reduction strategies in Monte Carlo rendering. In this paper, we propose a novel importance sampling technique that uses a neural network to learn how to sample from a desired density represented by a set of samples. Our approach considers an existing Monte Carlo rendering algorithm as a black box. During a scene-dependent training phase, we learn to generate samples with a desired density in the primary sample space of the rendering algorithm using maximum likelihood estimation. We leverage a recent neural network architecture that was designed to represent real-valued non-volume preserving ('Real NVP') transformations in high dimensional spaces. We use Real NVP to non-linearly warp primary sample space and obtain desired densities. In addition, Real NVP efficiently computes the determinant of the Jacobian of the warp, which is required to implement the change of integration variables implied by the warp. A main advantage of our approach is that it is agnostic of underlying light transport effects, and can be combined with many existing rendering techniques by treating them as a black box. We show that our approach leads to effective variance reduction in several practical scenarios.
Anderson Acceleration (AA) is a popular algorithm designed to enhance the convergence of fixed-point iterations. In this paper, we introduce a variant of AA based on a Truncated Gram-Schmidt process (AATGS) which has a few advantages over the classical AA. In particular, an attractive feature of AATGS is that its iterates obey a three-term recurrence in the situation when it is applied to solving symmetric linear problems and this can lead to a considerable reduction of memory and computational costs. We analyze the convergence of AATGS in both full-depth and limited-depth scenarios and establish its equivalence to the classical AA in the linear case. We also report on the effectiveness of AATGS through a set of numerical experiments, ranging from solving nonlinear partial differential equations to tackling nonlinear optimization problems. In particular, the performance of the method is compared with that of the classical AA algorithms.
In this paper, we consider the physical layer security of an RIS-assisted multiple-antenna communication system with randomly located eavesdroppers. The exact distributions of the received signal-to-noise-ratios (SNRs) at the legitimate user and the eavesdroppers located according to a Poisson point process (PPP) are derived, and a closed-form expression for the secrecy outage probability (SOP) is obtained. It is revealed that the secrecy performance is mainly affected by the number of RIS reflecting elements, and the impact of the transmit antennas and transmit power at the base station is marginal. In addition, when the locations of the randomly located eavesdroppers are unknown, deploying the RIS closer to the legitimate user rather than to the base station is shown to be more efficient. We also perform an analytical study demonstrating that the secrecy diversity order depends on the path loss exponent of the RIS-to-ground links. Finally, numerical simulations are conducted to verify the accuracy of these theoretical observations.
Dynamic Reward Adjustment in Multi-Reward Reinforcement Learning for Counselor Reflection Generation
In this paper, we study the problem of multi-reward reinforcement learning to jointly optimize for multiple text qualities for natural language generation. We focus on the task of counselor reflection generation, where we optimize the generators to simultaneously improve the fluency, coherence, and reflection quality of generated counselor responses. We introduce two novel bandit methods, DynaOpt and C-DynaOpt, which rely on the broad strategy of combining rewards into a single value and optimizing them simultaneously. Specifically, we employ non-contextual and contextual multi-arm bandits to dynamically adjust multiple reward weights during training. Through automatic and manual evaluations, we show that our proposed techniques, DynaOpt and C-DynaOpt, outperform existing naive and bandit baselines, showcasing their potential for enhancing language models.
In this paper, we propose a multi-task representation learning framework to jointly estimate the identity, gender and age of individuals from their hand images for the purpose of criminal investigations since the hand images are often the only available information in cases of serious crime such as sexual abuse. We investigate different up-to-date deep learning architectures and compare their performance for joint estimation of identity, gender and age from hand images of perpetrators of serious crime. To simplify the age prediction, we create age groups for the age estimation. We make extensive evaluations and comparisons of both convolution-based and transformer-based deep learning architectures on a publicly available 11k hands dataset. Our experimental analysis shows that it is possible to efficiently estimate not only identity but also other attributes such as gender and age of suspects jointly from hand images for criminal investigations, which is crucial in assisting international police forces in the court to identify and convict abusers.
In this paper, we present a new antithetic multilevel Monte Carlo (MLMC) method for the estimation of expectations with respect to laws of diffusion processes that can be elliptic or hypo-elliptic. In particular, we consider the case where one has to resort to time discretization of the diffusion and numerical simulation of such schemes. Motivated by recent developments, we introduce a new MLMC estimator of expectations, which does not require simulation of intractable L\'evy areas but has a weak error of order 2 and achieves the optimal computational complexity. We then show how this approach can be used in the context of the filtering problem associated to partially observed diffusions with discrete time observations. We illustrate with numerical simulations that our new approaches provide efficiency gains for several problems relative to some existing methods.
In this paper, we introduce a novel approach to centroidal state estimation, which plays a crucial role in predictive model-based control strategies for dynamic legged locomotion. Our approach uses the Koopman operator theory to transform the robot's complex nonlinear dynamics into a linear system, by employing dynamic mode decomposition and deep learning for model construction. We evaluate both models on their linearization accuracy and capability to capture both fast and slow dynamic system responses. We then select the most suitable model for estimation purposes, and integrate it within a moving horizon estimator. This estimator is formulated as a convex quadratic program, to facilitate robust, real-time centroidal state estimation. Through extensive simulation experiments on a quadruped robot executing various dynamic gaits, our data-driven framework outperforms conventional filtering techniques based on nonlinear dynamics. Our estimator addresses challenges posed by force/torque measurement noise in highly dynamic motions and accurately recovers the centroidal states, demonstrating the adaptability and effectiveness of the Koopman-based linear representation for complex locomotive behaviors. Importantly, our model based on dynamic mode decomposition, trained with two locomotion patterns (trot and jump), successfully estimates the centroidal states for a different motion (bound) without retraining.
In this paper we define a class of polynomial functors suited for constructing coalgebras representing processes in which uncertainty plays an important role. In these polynomial functors we include upper and lower probability measures, finitely additive probability measures, plausibilty measures (and their duals, belief functions), and possibility measures. We give axioms and inference rules for the associated system of coalgebraic modal logic, and construct the canonical coalgebras to prove a completeness result.
Link prediction is a very fundamental task on graphs. Inspired by traditional path-based methods, in this paper we propose a general and flexible representation learning framework based on paths for link prediction. Specifically, we define the representation of a pair of nodes as the generalized sum of all path representations, with each path representation as the generalized product of the edge representations in the path. Motivated by the Bellman-Ford algorithm for solving the shortest path problem, we show that the proposed path formulation can be efficiently solved by the generalized Bellman-Ford algorithm. To further improve the capacity of the path formulation, we propose the Neural Bellman-Ford Network (NBFNet), a general graph neural network framework that solves the path formulation with learned operators in the generalized Bellman-Ford algorithm. The NBFNet parameterizes the generalized Bellman-Ford algorithm with 3 neural components, namely INDICATOR, MESSAGE and AGGREGATE functions, which corresponds to the boundary condition, multiplication operator, and summation operator respectively. The NBFNet is very general, covers many traditional path-based methods, and can be applied to both homogeneous graphs and multi-relational graphs (e.g., knowledge graphs) in both transductive and inductive settings. Experiments on both homogeneous graphs and knowledge graphs show that the proposed NBFNet outperforms existing methods by a large margin in both transductive and inductive settings, achieving new state-of-the-art results.
In this paper, we propose a novel Feature Decomposition and Reconstruction Learning (FDRL) method for effective facial expression recognition. We view the expression information as the combination of the shared information (expression similarities) across different expressions and the unique information (expression-specific variations) for each expression. More specifically, FDRL mainly consists of two crucial networks: a Feature Decomposition Network (FDN) and a Feature Reconstruction Network (FRN). In particular, FDN first decomposes the basic features extracted from a backbone network into a set of facial action-aware latent features to model expression similarities. Then, FRN captures the intra-feature and inter-feature relationships for latent features to characterize expression-specific variations, and reconstructs the expression feature. To this end, two modules including an intra-feature relation modeling module and an inter-feature relation modeling module are developed in FRN. Experimental results on both the in-the-lab databases (including CK+, MMI, and Oulu-CASIA) and the in-the-wild databases (including RAF-DB and SFEW) show that the proposed FDRL method consistently achieves higher recognition accuracy than several state-of-the-art methods. This clearly highlights the benefit of feature decomposition and reconstruction for classifying expressions.
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