Current methods for initializing state space models (SSMs) parameters mainly rely on the \textit{HiPPO framework}, which is based on an online approximation of orthogonal polynomials. Recently, diagonal alternatives have shown to reach a similar level of performance while being significantly more efficient due to the simplification in the kernel computation. However, the \textit{HiPPO framework} does not explicitly study the role of its diagonal variants. In this paper, we take a further step to investigate the role of diagonal SSM initialization schemes from the frequency perspective. Our work seeks to systematically understand how to parameterize these models and uncover the learning biases inherent in such diagonal state-space models. Based on our observations, we propose a diagonal initialization on the discrete Fourier domain \textit{S4D-DFouT}. The insights in the role of pole placing in the initialization enable us to further scale them and achieve state-of-the-art results on the Long Range Arena benchmark, allowing us to train from scratch on very large datasets as PathX-256.

In this paper, we find that the training of Normalizing Flows (NFs) are easily affected by the outliers and a small number (or high dimensionality) of training samples. To solve this problem, we propose a Kullback–Leibler (KL) divergence regularization on the Jacobian matrix of NFs. We prove that such regularization is equivalent to adding a set of samples whose covariance matrix is the identity matrix to the training set. Thus, it reduces the negative influence of the outliers and the small sample number on the estimation of the covariance matrix, simultaneously. Therefore, our regularization makes the training of NFs robust. Ultimately, we evaluate the performance of NFs on out-of-distribution (OoD) detection tasks. The excellent results obtained demonstrate the effectiveness of the proposed regularization term. For example, with the help of the proposed regularization, the OoD detection score increases at most 30% compared with the one without the regularization.

This paper studies the use of Curriculum Learning on Reinforcement Learning (RL) to improve the performance of the dispatching policies learned on the Job-shop Scheduling Problem (JSP). Current works in the literature present a large optimality gap when learning end-to-end solutions on this problem. In this regard, we identify the difficulty for RL to learn directly on large instances as part of the issue and use Curriculum Learning (CL) to mitigate this effect. Particularly, CL sequences the learning process in a curriculum of increasing complexity tasks, which allows learning on large instances that otherwise would be impossible to learn from scratch. In this paper, we present a size-agnostic model that enables us to demonstrate that current curriculum strategies have a major impact on the quality of the solution inferred. In addition, we introduce a novel Reinforced Adaptive Staircase Curriculum Learning (RASCL) strategy, which adjusts the difficulty level during the learning process by revisiting the worst-performing instances. Conducted experiments on Taillard’s and Demirkol’s datasets show that the presented approach significantly improves the current stateof-the-art models on the JSP. It reduces the average optimality gap from 19.35% to 10.46% on Taillard’s instances and from 38.43% to 18.85% on Demirkol’s instances.

Network Function Virtualization (NFV) introduces a new network architecture framework that evolves network functions, traditionally deployed over dedicated equipment, to software implementations that run on general-purpose hardware. One of the main challenges for deploying NFV is the optimal resource placement of demanded network services in the NFV infrastructure. The virtual network function placement and network embedding can be formulated as a mathematical optimization problem concerned with a set of feasibility constraints that express the restrictions of the network infrastructure and the services contracted. This problem has been reported to be NP-hard, as a result most of the optimization work carried out in the area has focused on designing heuristic and metaheuristic algorithms. Nevertheless, in highly constrained problems, as in this case, inferring a competitive heuristic can be a daunting task that requires expertise. Consequently, an interesting solution is the use of Reinforcement Learning to model an optimization policy. The work presented here extends the Neural Combinatorial Optimization theory by considering constraints in the definition of the problem. The resulting agent is able to learn placement decisions by exploring the NFV infrastructure with the aim of minimizing the overall power consumption. The experiments conducted demonstrate that when the proposed strategy is also combined with heuristics, highly competitive results are achieved using relatively simple algorithms.

This paper presents a modeling of a virtual firewall, based on Stochastic Petri Nets (SPN) to analyze the performance in terms of throughput and delay. The firewall is part of a virtualized multitenant environment. To ensure that every tenant is protected against intrusion attempts, per tenant firewalls are a must. With this protection, each virtual environment located on a multitenant cloud is isolated and data is protected in case of an attack originating from within the cloud. Petri nets introduce some interactions that we have in the real system; we refer to sequential and parallel processing, concurrency, limited resources and mutual exclusion in shared resource access. The modeling is assessed by simulation and results are compared in different scenarios. The modeling also allows us to evaluate necessary resources that must be allocated to archive the desired throughput. Once the impact of key parameters on the global system performance is analyzed, results under several scenarios indicate that our proposal would succeed in an efficient resource allocation scheme in terms of throughput and delay.