Supercomputers have revolutionized how industries and scientific fields process large amounts of data. These machines group hundreds or thousands of computing nodes working together to execute time-consuming programs that require a large amount of computational resources. Over the years, supercomputers have expanded to include new and different technologies characterizing them as heterogeneous. However, executing a program in a heterogeneous environment requires attention to a specific aspect of performance degradation: load imbalance. In this research, we address the challenges associated with load imbalance when scheduling many homogeneous tasks in a heterogeneous environment. To address this issue, we introduce the concept of adaptive asynchronous work-stealing. This approach collects information about the nodes and utilizes it to improve work-stealing aspects, such as victim selection and task offloading. Additionally, the proposed approach eliminates the need for extra threads to communicate information, thereby reducing overhead when implementing a fully asynchronous approach. Our experimental results demonstrate a performance improvement of approximately 10.1\% compared to other conventional and state-of-the-art implementations.
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We study the performance of stochastic first-order methods for finding saddle points of convex-concave functions. A notorious challenge faced by such methods is that the gradients can grow arbitrarily large during optimization, which may result in instability and divergence. In this paper, we propose a simple and effective regularization technique that stabilizes the iterates and yields meaningful performance guarantees even if the domain and the gradient noise scales linearly with the size of the iterates (and is thus potentially unbounded). Besides providing a set of general results, we also apply our algorithm to a specific problem in reinforcement learning, where it leads to performance guarantees for finding near-optimal policies in an average-reward MDP without prior knowledge of the bias span.
In this paper we propose a reinforcement learning based weakly supervised system for localisation. We train a controller function to localise regions of interest within an image by introducing a novel reward definition that utilises non-binarised classification probability, generated by a pre-trained binary classifier which classifies object presence in images or image crops. The object-presence classifier may then inform the controller of its localisation quality by quantifying the likelihood of the image containing an object. Such an approach allows us to minimize any potential labelling or human bias propagated via human labelling for fully supervised localisation. We evaluate our proposed approach for a task of cancerous lesion localisation on a large dataset of real clinical bi-parametric MR images of the prostate. Comparisons to the commonly used multiple-instance learning weakly supervised localisation and to a fully supervised baseline show that our proposed method outperforms the multi-instance learning and performs comparably to fully-supervised learning, using only image-level classification labels for training.
The scale function holds significant importance within the fluctuation theory of Levy processes, particularly in addressing exit problems. However, its definition is established through the Laplace transform, thereby lacking explicit representations in general. This paper introduces a novel series representation for this scale function, employing Laguerre polynomials to construct a uniformly convergent approximate sequence. Additionally, we derive statistical inference based on specific discrete observations, presenting estimators of scale functions that are asymptotically normal.
Graph states are used to represent mathematical graphs as quantum states on quantum computers. They can be formulated through stabilizer codes or directly quantum gates and quantum states. In this paper we show that a quantum graph neural network model can be understood and realized based on graph states. We show that they can be used either as a parameterized quantum circuits to represent neural networks or as an underlying structure to construct graph neural networks on quantum computers.
We present a unification and generalization of sequentially and hierarchically semi-separable (SSS and HSS) matrices called tree semi-separable (TSS) matrices. Our main result is to show that any dense matrix can be expressed in a TSS format. Here, the dimensions of the generators are specified by the ranks of the Hankel blocks of the matrix. TSS matrices satisfy a graph-induced rank structure (GIRS) property. It is shown that TSS matrices generalize the algebraic properties of SSS and HSS matrices under addition, products, and inversion. Subsequently, TSS matrices admit linear time matrix-vector multiply, matrix-matrix multiply, matrix-matrix addition, inversion, and solvers.
We propose a novel methodology to solve a key eigenvalue optimization problem which arises in the contractivity analysis of neural ODEs. When looking at contractivity properties of a one layer weight-tied neural ODE $\dot{u}(t)=\sigma(Au(t)+b)$ (with $u,b \in {\mathbb R}^n$, $A$ is a given $n \times n$ matrix, $\sigma : {\mathbb R} \to {\mathbb R}^+$ denotes an activation function and for a vector $z \in {\mathbb R}^n$, $\sigma(z) \in {\mathbb R}^n$ has to be interpreted entry-wise), we are led to study the logarithmic norm of a set of products of type $D A$, where $D$ is a diagonal matrix such that ${\mathrm{diag}}(D) \in \sigma'({\mathbb R}^n)$. Specifically, given a real number $c$ (usually $c=0$), the problem consists in finding the largest positive interval $\chi\subseteq \mathbb [0,\infty)$ such that the logarithmic norm $\mu(DA) \le c$ for all diagonal matrices $D$ with $D_{ii}\in \chi$. We propose a two-level nested methodology: an inner level where, for a given $\chi$, we compute an optimizer $D^\star(\chi)$ by a gradient system approach, and an outer level where we tune $\chi$ so that the value $c$ is reached by $\mu(D^\star(\chi)A)$. We extend the proposed two-level approach to the general multilayer, and possibly time-dependent, case $\dot{u}(t) = \sigma( A_k(t) \ldots \sigma ( A_{1}(t) u(t) + b_{1}(t) ) \ldots + b_{k}(t) )$ and we propose several numerical examples to illustrate its behaviour, including its stabilizing performance on a one-layer neural ODE applied to the classification of the MNIST handwritten digits dataset.
Covariate adjustment is a ubiquitous method used to estimate the average treatment effect (ATE) from observational data. Assuming a known graphical structure of the data generating model, recent results give graphical criteria for optimal adjustment, which enables efficient estimation of the ATE. However, graphical approaches are challenging for high-dimensional and complex data, and it is not straightforward to specify a meaningful graphical model of non-Euclidean data such as texts. We propose an general framework that accommodates adjustment for any subset of information expressed by the covariates. We generalize prior works and leverage these results to identify the optimal covariate information for efficient adjustment. This information is minimally sufficient for prediction of the outcome conditionally on treatment. Based on our theoretical results, we propose the Debiased Outcome-adapted Propensity Estimator (DOPE) for efficient estimation of the ATE, and we provide asymptotic results for the DOPE under general conditions. Compared to the augmented inverse propensity weighted (AIPW) estimator, the DOPE can retain its efficiency even when the covariates are highly predictive of treatment. We illustrate this with a single-index model, and with an implementation of the DOPE based on neural networks, we demonstrate its performance on simulated and real data. Our results show that the DOPE provides an efficient and robust methodology for ATE estimation in various observational settings.
The word order of a sentence is shaped by multiple principles. The principle of syntactic dependency distance minimization is in conflict with the principle of surprisal minimization (or predictability maximization) in single head syntactic dependency structures: while the former predicts that the head should be placed at the center of the linear arrangement, the latter predicts that the head should be placed at one of the ends (either first or last). A critical question is when surprisal minimization (or predictability maximization) should surpass syntactic dependency distance minimization. In the context of single head structures, it has been predicted that this is more likely to happen when two conditions are met, i.e. (a) fewer words are involved and (b) words are shorter. Here we test the prediction on the noun phrase when its composed of a demonstrative, a numeral, an adjective and a noun. We find that, across preferred orders in languages, the noun tends to be placed at one of the ends, confirming the theoretical prediction. We also show evidence of anti locality effects: syntactic dependency distances in preferred orders are longer than expected by chance.
Incomplete knowledge of the environment leads an agent to make decisions under uncertainty. One of the major dilemmas in Reinforcement Learning (RL) where an autonomous agent has to balance two contrasting needs in making its decisions is: exploiting the current knowledge of the environment to maximize the cumulative reward as well as exploring actions that allow improving the knowledge of the environment, hopefully leading to higher reward values (exploration-exploitation trade-off). Concurrently, another relevant issue regards the full observability of the states, which may not be assumed in all applications. For instance, when 2D images are considered as input in an RL approach used for finding the best actions within a 3D simulation environment. In this work, we address these issues by deploying and testing several techniques to balance exploration and exploitation trade-off on partially observable systems for predicting steering wheels in autonomous driving scenarios. More precisely, the final aim is to investigate the effects of using both adaptive and deterministic exploration strategies coupled with a Deep Recurrent Q-Network. Additionally, we adapted and evaluated the impact of a modified quadratic loss function to improve the learning phase of the underlying Convolutional Recurrent Neural Network. We show that adaptive methods better approximate the trade-off between exploration and exploitation and, in general, Softmax and Max-Boltzmann strategies outperform epsilon-greedy techniques.
In large-scale systems there are fundamental challenges when centralised techniques are used for task allocation. The number of interactions is limited by resource constraints such as on computation, storage, and network communication. We can increase scalability by implementing the system as a distributed task-allocation system, sharing tasks across many agents. However, this also increases the resource cost of communications and synchronisation, and is difficult to scale. In this paper we present four algorithms to solve these problems. The combination of these algorithms enable each agent to improve their task allocation strategy through reinforcement learning, while changing how much they explore the system in response to how optimal they believe their current strategy is, given their past experience. We focus on distributed agent systems where the agents' behaviours are constrained by resource usage limits, limiting agents to local rather than system-wide knowledge. We evaluate these algorithms in a simulated environment where agents are given a task composed of multiple subtasks that must be allocated to other agents with differing capabilities, to then carry out those tasks. We also simulate real-life system effects such as networking instability. Our solution is shown to solve the task allocation problem to 6.7% of the theoretical optimal within the system configurations considered. It provides 5x better performance recovery over no-knowledge retention approaches when system connectivity is impacted, and is tested against systems up to 100 agents with less than a 9% impact on the algorithms' performance.
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