The Knapsack Problem is a classic problem in combinatorial optimisation. Solving these problems may be computationally expensive. Recent years have seen a growing interest in the use of deep learning methods to approximate the solutions to such problems. A core problem is how to enforce or encourage constraint satisfaction in predicted solutions. A promising approach for predicting solutions to constrained optimisation problems is the Lagrangian Dual Framework which builds on the method of Lagrangian Relaxation. In this paper we develop neural network models to approximate Knapsack Problem solutions using the Lagrangian Dual Framework while improving constraint satisfaction. We explore the problems of output interpretation and model selection within this context. Experimental results show strong constraint satisfaction with a minor reduction of optimality as compared to a baseline neural network which does not explicitly model the constraints.
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The problem of relay selection is pivotal in the realm of cooperative communication. However, this issue has not been thoroughly examined, particularly when the background noise is assumed to possess an impulsive characteristic with consistent memory as observed in smart grid communications and some other wireless communication scenarios. In this paper, we investigate the impact of this specific type of noise on the performance of cooperative Wireless Sensor Networks (WSNs) with the Decode and Forward (DF) relaying scheme, considering Symbol-Error-Rate (SER) and battery power consumption fairness across all nodes as the performance metrics. We introduce two innovative relay selection methods that depend on noise state detection and the residual battery power of each relay. The first method encompasses the adaptation of the Max-Min criterion to this specific context, whereas the second employs Reinforcement Learning (RL) to surmount this challenge. Our empirical outcomes demonstrate that the impacts of bursty impulsive noise on the SER performance can be effectively mitigated and that a balance in battery power consumption among all nodes can be established using the proposed methods.
We use Markov categories to develop generalizations of the theory of Markov chains and hidden Markov models in an abstract setting. This comprises characterizations of hidden Markov models in terms of local and global conditional independences as well as existing algorithms for Bayesian filtering and smoothing applicable in all Markov categories with conditionals. We show that these algorithms specialize to existing ones such as the Kalman filter, forward-backward algorithm, and the Rauch-Tung-Striebel smoother when instantiated in appropriate Markov categories. Under slightly stronger assumptions, we also prove that the sequence of outputs of the Bayes filter is itself a Markov chain with a concrete formula for its transition maps. There are two main features of this categorical framework. The first is its generality, as it can be used in any Markov category with conditionals. In particular, it provides a systematic unified account of hidden Markov models and algorithms for filtering and smoothing in discrete probability, Gaussian probability, measure-theoretic probability, possibilistic nondeterminism and others at the same time. The second feature is the intuitive visual representation of information flow in these algorithms in terms of string diagrams.
The attribution of question answering is to provide citations for supporting generated statements, and has attracted wide research attention. The current methods for automatically evaluating the attribution, which are often based on Large Language Models (LLMs), are still inadequate, particularly in recognizing subtle differences between attributions, and complex relationships between citations and statements. To compare these attribution evaluation methods and develop new ones, we introduce a set of fine-grained categories (i.e., supportive, insufficient, contradictory and irrelevant) for measuring the attribution, and develop a Complex Attributed Question Answering (CAQA) benchmark by leveraging knowledge graphs (KGs) for automatically generating attributions of different categories to question-answer pairs. Our analysis reveals that existing evaluators perform poorly under fine-grained attribution settings and exhibit weaknesses in complex citation-statement reasoning. Our CAQA benchmark, validated with human annotations, emerges as a promising tool for selecting and developing LLM attribution evaluators.
Recent semantic communication methods explore effective ways to expand the communication paradigm and improve the system performance of the communication systems. Nonetheless, the common problem of these methods is that the essence of semantics is not explicitly pointed out and directly utilized. A new epistemology suggests that synonymy, which is revealed as the fundamental feature of semantics, guides the establishment of the semantic information theory from a novel viewpoint. Building on this theoretical basis, this paper proposes a semantic arithmetic coding (SAC) method for semantic lossless compression using intuitive semantic synonymy. By constructing reasonable synonymous mappings and performing arithmetic coding procedures over synonymous sets, SAC can achieve higher compression efficiency for meaning-contained source sequences at the semantic level and thereby approximate the semantic entropy limits. Experimental results on edge texture map compression show an evident improvement in coding efficiency using SAC without semantic losses, compared to traditional arithmetic coding, which demonstrates its effectiveness.
We present an experimental validation of a recently proposed optimization technique for reservoir computing, using an optoelectronic setup. Reservoir computing is a robust framework for signal processing applications, and the development of efficient optimization approaches remains a key challenge. The technique we address leverages solely a delayed version of the input signal to identify the optimal operational region of the reservoir, simplifying the traditionally time-consuming task of hyperparameter tuning. We verify the effectiveness of this approach on different benchmark tasks and reservoir operating conditions.
Most formal methods see the correctness of a software system as a binary decision. However, proving the correctness of complex systems completely is difficult because they are composed of multiple components, usage scenarios, and environments. We present QuAC, a modular approach for quantifying the correctness of service-oriented software systems by combining software architecture modeling with deductive verification. Our approach is based on a model of the service-oriented architecture and the probabilistic usage scenarios of the system. The correctness of a single service is approximated by a coverage region, which is a formula describing which inputs for that service are proven to not lead to an erroneous execution. The coverage regions can be determined by a combination of various analyses, e.g., formal verification, expert estimations, or testing. The coverage regions and the software model are then combined into a probabilistic program. From this, we can compute the probability that under a given usage profile no service is called outside its coverage region. If the coverage region is large enough, then instead of attempting to get 100% coverage, which may be prohibitively expensive, run-time verification or testing approaches may be used to deal with inputs outside the coverage region. We also present an implementation of QuAC for Java using the modeling tool Palladio and the deductive verification tool KeY. We demonstrate its usability by applying it to a software simulation of an energy system.
We study the complexity-theoretic boundaries of tractability for three classical problems in the context of Hierarchical Task Network Planning: the validation of a provided plan, whether an executable plan exists, and whether a given state can be reached by some plan. We show that all three problems can be solved in polynomial time on primitive task networks of constant partial order width (and a generalization thereof), whereas for the latter two problems this holds only under a provably necessary restriction to the state space. Next, we obtain an algorithmic meta-theorem along with corresponding lower bounds to identify tight conditions under which general polynomial-time solvability results can be lifted from primitive to general task networks. Finally, we enrich our investigation by analyzing the parameterized complexity of the three considered problems, and show that (1) fixed-parameter tractability for all three problems can be achieved by replacing the partial order width with the vertex cover number of the network as the parameter, and (2) other classical graph-theoretic parameters of the network (including treewidth, treedepth, and the aforementioned partial order width) do not yield fixed-parameter tractability for any of the three problems.
We consider the ubiquitous linear inverse problems with additive Gaussian noise and propose an unsupervised sampling approach called diffusion model based posterior sampling (DMPS) to reconstruct the unknown signal from noisy linear measurements. Specifically, using one diffusion model (DM) as an implicit prior, the fundamental difficulty in performing posterior sampling is that the noise-perturbed likelihood score, i.e., gradient of an annealed likelihood function, is intractable. To circumvent this problem, we introduce a simple yet effective closed-form approximation using an uninformative prior assumption. Extensive experiments are conducted on a variety of noisy linear inverse problems such as noisy super-resolution, denoising, deblurring, and colorization. In all tasks, the proposed DMPS demonstrates highly competitive or even better performances on various tasks while being 3 times faster than the state-of-the-art competitor diffusion posterior sampling (DPS).
Although continuous advances in theoretical modelling of Molecular Communications (MC) are observed, there is still an insuperable gap between theory and experimental testbeds, especially at the microscale. In this paper, the development of the first testbed incorporating engineered yeast cells is reported. Different from the existing literature, eukaryotic yeast cells are considered for both the sender and the receiver, with {\alpha}-factor molecules facilitating the information transfer. The use of such cells is motivated mainly by the well understood biological mechanism of yeast mating, together with their genetic amenability. In addition, recent advances in yeast biosensing establish yeast as a suitable detector and a neat interface to in-body sensor networks. The system under consideration is presented first, and the mathematical models of the underlying biological processes leading to an end-to-end (E2E) system are given. The experimental setup is then described and used to obtain experimental results which validate the developed mathematical models. Beyond that, the ability of the system to effectively generate output pulses in response to repeated stimuli is demonstrated, reporting one event per two hours. However, fast RNA fluctuations indicate cell responses in less than three minutes, demonstrating the potential for much higher rates in the future.
Graph Neural Networks (GNNs) have recently become increasingly popular due to their ability to learn complex systems of relations or interactions arising in a broad spectrum of problems ranging from biology and particle physics to social networks and recommendation systems. Despite the plethora of different models for deep learning on graphs, few approaches have been proposed thus far for dealing with graphs that present some sort of dynamic nature (e.g. evolving features or connectivity over time). In this paper, we present Temporal Graph Networks (TGNs), a generic, efficient framework for deep learning on dynamic graphs represented as sequences of timed events. Thanks to a novel combination of memory modules and graph-based operators, TGNs are able to significantly outperform previous approaches being at the same time more computationally efficient. We furthermore show that several previous models for learning on dynamic graphs can be cast as specific instances of our framework. We perform a detailed ablation study of different components of our framework and devise the best configuration that achieves state-of-the-art performance on several transductive and inductive prediction tasks for dynamic graphs.
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