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We give a characterization of those sets of graphs that are both definable in Counting Monadic Second Order Logic (CMS) and context-free, i.e., least solutions of Hyperedge-Replacement (HR)-grammars introduced by Courcelle and Engelfriet. We give the following equivalent characterizations: (a) a set of graphs is recognizable (in the algebra that consists of all graphs and HR-operations) and has bounded tree-width; further, we refine this condition and show equivalence with recognizability in a finite-sort subalgebra of the graph algebra; (b) the set is parsable, i.e., there is an MS-definable transduction from graphs to a set of derivation trees labelled by HR-operations, such that the set of graphs is the image of this set of trees under the evaluation of the HR-operations; (c) the set of graphs is the image of unranked recognizable set of trees under an MS-definable transduction whose inverse is also MS-definable. The main goal of this paper is to present the above characterization, of which several directions are already known, in an accessible and unified way. We rely on a novel connection between two seminal results, a logical characterization of context-free graph languages in terms of tree to graph MS-definable transductions, by Courcelle and Engelfriet~, and a proof that an optimal-width tree decomposition of a graph can be built by an MS-definable transduction, by Bojanczyk and Pilipczuk.

The formulation of Mean Field Games (MFG) typically requires continuous differentiability of the Hamiltonian in order to determine the advective term in the Kolmogorov--Fokker--Planck equation for the density of players. However, in many cases of practical interest, the underlying optimal control problem may exhibit bang-bang controls, which typically lead to nondifferentiable Hamiltonians. We develop the analysis and numerical analysis of stationary MFG for the general case of convex, Lipschitz, but possibly nondifferentiable Hamiltonians. In particular, we propose a generalization of the MFG system as a Partial Differential Inclusion (PDI) based on interpreting the derivative of the Hamiltonian in terms of subdifferentials of convex functions. We establish existence of a weak solution to the MFG PDI system, and we further prove uniqueness under a similar monotonicity condition to the one considered by Lasry and Lions. We then propose a monotone finite element discretization of the problem, and we prove strong $H^1$-norm convergence of the approximations to the value function and strong $L^q$-norm convergence of the approximations of the density function. We illustrate the performance of the numerical method in numerical experiments featuring nonsmooth solutions.

The success of large language models (LLMs), like GPT-4 and ChatGPT, has led to the development of numerous cost-effective and accessible alternatives that are created by finetuning open-access LLMs with task-specific data (e.g., ChatDoctor) or instruction data (e.g., Alpaca). Among the various fine-tuning methods, adapter-based parameter-efficient fine-tuning (PEFT) is undoubtedly one of the most attractive topics, as it only requires fine-tuning a few external parameters instead of the entire LLMs while achieving comparable or even better performance. To enable further research on PEFT methods of LLMs, this paper presents LLM-Adapters, an easy-to-use framework that integrates various adapters into LLMs and can execute these adapter-based PEFT methods of LLMs for different tasks. The framework includes state-of-the-art open-access LLMs such as LLaMA, BLOOM, and GPT-J, as well as widely used adapters such as Series adapters, Parallel adapter, Prompt-based learning and Reparametrization-based methods. Moreover, we conduct extensive empirical studies on the impact of adapter types, placement locations, and hyper-parameters to the best design for each adapter-based methods. We evaluate the effectiveness of the adapters on fourteen datasets from two different reasoning tasks, Arithmetic Reasoning and Commonsense Reasoning. The results demonstrate that using adapter-based PEFT in smaller-scale LLMs (7B) with few extra trainable parameters yields comparable, and in some cases superior, performance to powerful LLMs (175B) in zero-shot inference on both reasoning tasks.

The estimation of origin-destination (OD) matrices is a crucial aspect of Intelligent Transport Systems (ITS). It involves adjusting an initial OD matrix by regressing the current observations like traffic counts of road sections (e.g., using least squares). However, the OD estimation problem lacks sufficient constraints and is mathematically underdetermined. To alleviate this problem, some researchers incorporate a prior OD matrix as a target in the regression to provide more structural constraints. However, this approach is highly dependent on the existing prior matrix, which may be outdated. Others add structural constraints through sensor data, such as vehicle trajectory and speed, which can reflect more current structural constraints in real-time. Our proposed method integrates deep learning and numerical optimization algorithms to infer matrix structure and guide numerical optimization. This approach combines the advantages of both deep learning and numerical optimization algorithms. The neural network(NN) learns to infer structural constraints from probe traffic flows, eliminating dependence on prior information and providing real-time performance. Additionally, due to the generalization capability of NN, this method is economical in engineering. We conducted tests to demonstrate the good generalization performance of our method on a large-scale synthetic dataset. Subsequently, we verified the stability of our method on real traffic data. Our experiments provided confirmation of the benefits of combining NN and numerical optimization.

Blockchain provides decentralization and trustlessness features for the Industrial Internet of Things (IIoT), which expands the application scenarios of IIoT. To address the problem that the blockchain cannot actively obtain off-chain data, the blockchain oracle is proposed as a bridge between the blockchain and external data. However, the existing oracle schemes are difficult to solve the problem of low quality of service caused by frequent data changes and heterogeneous devices in IIoT, and the current oracle node selection schemes are difficult to balance security and quality of service. To tackle these problems, this paper proposes a secure and reliable oracle scheme that can obtain high-quality off-chain data. Specifically, we first design an oracle node selection algorithm based on Verifiable Random Function (VRF) and reputation mechanism to securely select high-quality nodes. Second, we propose a data filtering algorithm based on a sliding window to further improve the consistency of the collected data. We verify the security of the proposed scheme through security analysis. The experimental results show that the proposed scheme can effectively improve the service quality of the oracle.

Large Language Models (LLMs) have the ability to solve a variety of tasks, such as text summarization and mathematical questions, just out of the box, but they are often trained with a single task in mind. Due to high computational costs, the current trend is to use prompt instruction tuning to better adjust monolithic, pretrained LLMs for new -- but often individual -- downstream tasks. Thus, how one would expand prompt tuning to handle -- concomitantly -- heterogeneous tasks and data distributions is a widely open question. To address this gap, we suggest the use of \emph{Mixture of Prompts}, or MoPs, associated with smart gating functionality: the latter -- whose design is one of the contributions of this paper -- can identify relevant skills embedded in different groups of prompts and dynamically assign combined experts (i.e., collection of prompts), based on the target task. Additionally, MoPs are empirically agnostic to any model compression technique applied -- for efficiency reasons -- as well as instruction data source and task composition. In practice, MoPs can simultaneously mitigate prompt training "interference" in multi-task, multi-source scenarios (e.g., task and data heterogeneity across sources), as well as possible implications from model approximations. As a highlight, MoPs manage to decrease final perplexity from $\sim20\%$ up to $\sim70\%$, as compared to baselines, in the federated scenario, and from $\sim 3\%$ up to $\sim30\%$ in the centralized scenario.

Recently, Mutual Information (MI) has attracted attention in bounding the generalization error of Deep Neural Networks (DNNs). However, it is intractable to accurately estimate the MI in DNNs, thus most previous works have to relax the MI bound, which in turn weakens the information theoretic explanation for generalization. To address the limitation, this paper introduces a probabilistic representation of DNNs for accurately estimating the MI. Leveraging the proposed MI estimator, we validate the information theoretic explanation for generalization, and derive a tighter generalization bound than the state-of-the-art relaxations.

Deep neural networks (DNNs) are successful in many computer vision tasks. However, the most accurate DNNs require millions of parameters and operations, making them energy, computation and memory intensive. This impedes the deployment of large DNNs in low-power devices with limited compute resources. Recent research improves DNN models by reducing the memory requirement, energy consumption, and number of operations without significantly decreasing the accuracy. This paper surveys the progress of low-power deep learning and computer vision, specifically in regards to inference, and discusses the methods for compacting and accelerating DNN models. The techniques can be divided into four major categories: (1) parameter quantization and pruning, (2) compressed convolutional filters and matrix factorization, (3) network architecture search, and (4) knowledge distillation. We analyze the accuracy, advantages, disadvantages, and potential solutions to the problems with the techniques in each category. We also discuss new evaluation metrics as a guideline for future research.

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.

Visual Question Answering (VQA) models have struggled with counting objects in natural images so far. We identify a fundamental problem due to soft attention in these models as a cause. To circumvent this problem, we propose a neural network component that allows robust counting from object proposals. Experiments on a toy task show the effectiveness of this component and we obtain state-of-the-art accuracy on the number category of the VQA v2 dataset without negatively affecting other categories, even outperforming ensemble models with our single model. On a difficult balanced pair metric, the component gives a substantial improvement in counting over a strong baseline by 6.6%.