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The Skolem problem is a long-standing open problem in linear dynamical systems: can a linear recurrence sequence (LRS) ever reach 0 from a given initial configuration? Similarly, the positivity problem asks whether the LRS stays positive from an initial configuration. Deciding Skolem (or positivity) has been open for half a century: the best known decidability results are for LRS with special properties (e.g., low order recurrences). But these problems are easier for "uninitialized" variants, where the initial configuration is not fixed but can vary arbitrarily: checking if there is an initial configuration from which the LRS stays positive can be decided in polynomial time (Tiwari in 2004, Braverman in 2006). In this paper, we consider problems that lie between the initialized and uninitialized variant. More precisely, we ask if 0 (resp. negative numbers) can be avoided from every initial configuration in a neighborhood of a given initial configuration. This can be considered as a robust variant of the Skolem (resp. positivity) problem. We show that these problems lie at the frontier of decidability: if the neighbourhood is given as part of the input, then robust Skolem and robust positivity are Diophantine hard, i.e., solving either would entail major breakthrough in Diophantine approximations, as happens for (non-robust) positivity. However, if one asks whether such a neighbourhood exists, then the problems turn out to be decidable with PSPACE complexity. Our techniques also allow us to tackle robustness for ultimate positivity, which asks whether there is a bound on the number of steps after which the LRS remains positive. There are two variants depending on whether we ask for a "uniform" bound on this number of steps. For the non-uniform variant, when the neighbourhood is open, the problem turns out to be tractable, even when the neighbourhood is given as input.

Environmental perception is a key element of autonomous driving because the information received from the perception module influences core driving decisions. An outstanding challenge in real-time perception for autonomous driving lies in finding the best trade-off between detection quality and latency. Major constraints on both computation and power have to be taken into account for real-time perception in autonomous vehicles. Larger object detection models tend to produce the best results, but are also slower at runtime. Since the most accurate detectors cannot run in real-time locally, we investigate the possibility of offloading computation to edge and cloud platforms, which are less resource-constrained. We create a synthetic dataset to train object detection models and evaluate different offloading strategies. Using real hardware and network simulations, we compare different trade-offs between prediction quality and end-to-end delay. Since sending raw frames over the network implies additional transmission delays, we also explore the use of JPEG and H.265 compression at varying qualities and measure their impact on prediction metrics. We show that models with adequate compression can be run in real-time on the cloud while outperforming local detection performance.

The primary method for identifying mental disorders automatically has traditionally involved using binary classifiers. These classifiers are trained using behavioral data obtained from an interview setup. In this training process, data from individuals with the specific disorder under consideration are categorized as the positive class, while data from all other participants constitute the negative class. In practice, it is widely recognized that certain mental disorders share similar symptoms, causing the collected behavioral data to encompass a variety of attributes associated with multiple disorders. Consequently, attributes linked to the targeted mental disorder might also be present within the negative class. This data impurity may lead to sub-optimal training of the classifier for a mental disorder of interest. In this study, we investigate this hypothesis in the context of major depressive disorder (MDD) and post-traumatic stress disorder detection (PTSD). The results show that upon removal of such data impurity, MDD and PTSD detection performances are significantly improved.

The curse-of-dimensionality (CoD) taxes computational resources heavily with exponentially increasing computational cost as the dimension increases. This poses great challenges in solving high-dimensional PDEs as Richard Bellman first pointed out over 60 years ago. While there has been some recent success in solving numerically partial differential equations (PDEs) in high dimensions, such computations are prohibitively expensive, and true scaling of general nonlinear PDEs to high dimensions has never been achieved. In this paper, we develop a new method of scaling up physics-informed neural networks (PINNs) to solve arbitrary high-dimensional PDEs. The new method, called Stochastic Dimension Gradient Descent (SDGD), decomposes a gradient of PDEs into pieces corresponding to different dimensions and samples randomly a subset of these dimensional pieces in each iteration of training PINNs. We theoretically prove the convergence guarantee and other desired properties of the proposed method. We experimentally demonstrate that the proposed method allows us to solve many notoriously hard high-dimensional PDEs, including the Hamilton-Jacobi-Bellman (HJB) and the Schr\"{o}dinger equations in thousands of dimensions very fast on a single GPU using the PINNs mesh-free approach. For instance, we solve nontrivial nonlinear PDEs (one HJB equation and one Black-Scholes equation) in 100,000 dimensions in 6 hours on a single GPU using SDGD with PINNs. Since SDGD is a general training methodology of PINNs, SDGD can be applied to any current and future variants of PINNs to scale them up for arbitrary high-dimensional PDEs.

Neural Machine Translation (NMT) is widely applied in software engineering tasks. The effectiveness of NMT for code retrieval relies on the ability to learn from the sequence of tokens in the source language to the sequence of tokens in the target language. While NMT performs well in pseudocode-to-code translation, it might have challenges in learning to translate from natural language query to source code in newly curated real-world code documentation/ implementation datasets. In this work, we analyze the performance of NMT in natural language-to-code translation in the newly curated CAT benchmark that includes the optimized versions of three Java datasets TLCodeSum, CodeSearchNet, Funcom, and a Python dataset PCSD. Our evaluation shows that NMT has low accuracy, measured by CrystalBLEU and Meteor metrics in this task. To alleviate the duty of NMT in learning complex representation of source code, we propose ASTTrans Representation, a tailored representation of an Abstract Syntax Tree (AST) using a subset of non-terminal nodes. We show that the classical approach NMT performs significantly better in learning ASTTrans Representation over code tokens with up to 36% improvement on Meteor score. Moreover, we leverage ASTTrans Representation to conduct combined code search processes from the state-of-the-art code search processes using GraphCodeBERT and UniXcoder. Our NMT models of learning ASTTrans Representation can boost the Mean Reciprocal Rank of these state-of-the-art code search processes by up to 3.08% and improve 23.08% of queries' results over the CAT benchmark.

Machine learning (ML) components are increasingly incorporated into software products, yet developers face challenges in transitioning from ML prototypes to products. Academic researchers struggle to propose solutions to these challenges and evaluate interventions because they often do not have access to close-sourced ML products from industry. In this study, we define and identify open-source ML products, curating a dataset of 262 repositories from GitHub, to facilitate further research and education. As a start, we explore six broad research questions related to different development activities and report 21 findings from a sample of 30 ML products from the dataset. Our findings reveal a variety of development practices and architectural decisions surrounding different types and uses of ML models that offer ample opportunities for future research innovations. We also find very little evidence of industry best practices such as model testing and pipeline automation within the open-source ML products, which leaves room for further investigation to understand its potential impact on the development and eventual end-user experience for the products.

Online Food Recommendation Service (OFRS) has remarkable spatiotemporal characteristics and the advantage of being able to conveniently satisfy users' needs in a timely manner. There have been a variety of studies that have begun to explore its spatiotemporal properties, but a comprehensive and in-depth analysis of the OFRS spatiotemporal features is yet to be conducted. Therefore, this paper studies the OFRS based on three questions: how spatiotemporal features play a role; why self-attention cannot be used to model the spatiotemporal sequences of OFRS; and how to combine spatiotemporal features to improve the efficiency of OFRS. Firstly, through experimental analysis, we systemically extracted the spatiotemporal features of OFRS, identified the most valuable features and designed an effective combination method. Secondly, we conducted a detailed analysis of the spatiotemporal sequences, which revealed the shortcomings of self-attention in OFRS, and proposed a more optimized spatiotemporal sequence method for replacing self-attention. In addition, we also designed a Dynamic Context Adaptation Model to further improve the efficiency and performance of OFRS. Through the offline experiments on two large datasets and online experiments for a week, the feasibility and superiority of our model were proven.

A sparse polynomial (also called a lacunary polynomial) is a polynomial that has relatively few terms compared to its degree. The sparse-representation of a polynomial represents the polynomial as a list of its non-zero terms (coefficient-degree pairs). In particular, the degree of a sparse polynomial can be exponential in the sparse-representation size. We prove that for monic polynomials $f, g \in \mathbb{C}[x]$ such that $g$ divides $f$, the $\ell_2$-norm of the quotient polynomial $f/g$ is bounded by $\lVert f \rVert_1 \cdot \tilde{O}(\lVert{g}\rVert_0^3\text{deg}^2{ f})^{\lVert{g}\rVert_0 - 1}$. This improves upon the exponential (in $\text{deg}{ f}$) bounds for general polynomials and implies that the trivial long division algorithm runs in time quasi-linear in the input size and number of terms of the quotient polynomial $f/g$, thus solving a long-standing problem on exact divisibility of sparse polynomials. We also study the problem of bounding the number of terms of $f/g$ in some special cases. When $f, g \in \mathbb{Z}[x]$ and $g$ is a cyclotomic-free (i.e., it has no cyclotomic factors) trinomial, we prove that $\lVert{f/g}\rVert_0 \leq O(\lVert{f}\rVert_0 \text{size}({f})^2 \cdot \log^6{\text{deg}{ g}})$. When $g$ is a binomial with $g(\pm 1) \neq 0$, we prove that the sparsity is at most $O(\lVert{f}\rVert_0 ( \log{\lVert{f}\rVert_0} + \log{\lVert{f}\rVert_{\infty}}))$. Both upper bounds are polynomial in the input-size. We leverage these results and give a polynomial time algorithm for deciding whether a cyclotomic-free trinomial divides a sparse polynomial over the integers. As our last result, we present a polynomial time algorithm for testing divisibility by pentanomials over small finite fields when $\text{deg}{ f} = \tilde{O}(\text{deg}{ g})$.

Artificial Intelligence (AI) and its applications have sparked extraordinary interest in recent years. This achievement can be ascribed in part to advances in AI subfields including Machine Learning (ML), Computer Vision (CV), and Natural Language Processing (NLP). Deep learning, a sub-field of machine learning that employs artificial neural network concepts, has enabled the most rapid growth in these domains. The integration of vision and language has sparked a lot of attention as a result of this. The tasks have been created in such a way that they properly exemplify the concepts of deep learning. In this review paper, we provide a thorough and an extensive review of the state of the arts approaches, key models design principles and discuss existing datasets, methods, their problem formulation and evaluation measures for VQA and Visual reasoning tasks to understand vision and language representation learning. We also present some potential future paths in this field of research, with the hope that our study may generate new ideas and novel approaches to handle existing difficulties and develop new applications.

Within the rapidly developing Internet of Things (IoT), numerous and diverse physical devices, Edge devices, Cloud infrastructure, and their quality of service requirements (QoS), need to be represented within a unified specification in order to enable rapid IoT application development, monitoring, and dynamic reconfiguration. But heterogeneities among different configuration knowledge representation models pose limitations for acquisition, discovery and curation of configuration knowledge for coordinated IoT applications. This paper proposes a unified data model to represent IoT resource configuration knowledge artifacts. It also proposes IoT-CANE (Context-Aware recommendatioN systEm) to facilitate incremental knowledge acquisition and declarative context driven knowledge recommendation.