Set Of Possible Operators Research Articles

On finite algebras with probability limit laws

An algebraic system has a probability limit law if the values of terms with independent identically distributed random variables have probability distributions that tend to a certain limit (the limit law) as the number of variables in a term grows. For algebraic systems on finite sets, it is shown that, under some geometric conditions on the set of term value distributions, the existence of a limit law strongly restricts the set of possible operations in the algebraic system. In particular, a system that has a limit law without zero components necessarily consists of quasigroup operations (with arbitrary arity), while the limit law is necessarily uniform. Sufficient conditions are also proved for a system to have a probability limit law, which partly match the necessary ones.

FlexiBERT: Are Current Transformer Architectures too Homogeneous and Rigid?

The existence of a plethora of language models makes the problem of selecting the best one for a custom task challenging. Most state-of-the-art methods leverage transformer-based models (e.g., BERT) or their variants. However, training such models and exploring their hyperparameter space is computationally expensive. Prior work proposes several neural architecture search (NAS) methods that employ performance predictors (e.g., surrogate models) to address this issue; however, such works limit analysis to homogeneous models that use fixed dimensionality throughout the network. This leads to sub-optimal architectures. To address this limitation, we propose a suite of heterogeneous and flexible models, namely FlexiBERT, that have varied encoder layers with a diverse set of possible operations and different hidden dimensions. For better-posed surrogate modeling in this expanded design space, we propose a new graph-similarity-based embedding scheme. We also propose a novel NAS policy, called BOSHNAS, that leverages this new scheme, Bayesian modeling, and second-order optimization, to quickly train and use a neural surrogate model to converge to the optimal architecture. A comprehensive set of experiments shows that the proposed policy, when applied to the FlexiBERT design space, pushes the performance frontier upwards compared to traditional models. FlexiBERT-Mini, one of our proposed models, has 3% fewer parameters than BERT-Mini and achieves 8.9% higher GLUE score. A FlexiBERT model with equivalent performance as the best homogeneous model has 2.6× smaller size. FlexiBERT-Large, another proposed model, attains state-of-the-art results, outperforming the baseline models by at least 5.7% on the GLUE benchmark.

The long path to narrative generation

Narrative generation, understood as the task of constructing computational models of the way in which humans build stories, has been shown to involve a number of separate processes, related to different purposes to which it can be applied, and focusing on specific features that make stories valuable. This paper reviews a set of story generation systems developed by the authors of this contribution, each focusing on different aspects and functions of stories. These systems provide an initial breakdown of how the term “storytelling” might be either instantiated or broken down into component processes. The systems cover functionalities such as generating valid plot structures, simulating character's behaviors or the evolution of affinities between them, either reporting or fictionalizing events observed in real life, and revising a story draft to maximize the suspense it induces in its readers. These functionalities are not intended to exhaust the set of possible operations involved in storytelling, but they constitute an initial set to understand the complexity of the task. The paper also includes two proposals—one theoretical and one technological—for understanding how a set of such functionalities might be composed into a broader operational process that produces more elaborate stories.

A cost assignment policy for home care patients

The patient assignment problem in Home care (HC) consists of allocating each newly admitted patient to his/her reference operator, chosen among a set of possible operators. The continuity of care, where pursued, imposes that the assignment is not changed for a long period. The main goal of the assignment is to balance the workload among the operators. In the literature, the problem is usually solved with numerical approaches based on mathematical programming that do not consider the stochastic aspects of the problem. We derive a structural policy to assign a newly admitted patient while balancing the workload among the operators, by minimizing the expected value of a cost function that penalizes the overtime of operators. The workloads already loaded to the operators are assumed to be random variables as they are in the practice, while the demand related to the new patient is considered both deterministic and stochastic. Results show that the variability of the new patient’s demand is negligible with respect to the variability of the already assigned workloads and that similar assignments are obtained both in the presence or in the absence of this demand variability. A numerical comparison with the current practice of assigning the new patient to the operator with the highest expected available capacity shows that better balancings and cost savings can be reached by implementing the proposed policy.

Shared quantum remote control: quantum operation sharing

We consider three-party sharing of unitary operations with the help of the shared entanglement and LOCC. We propose three separate schemes corresponding to decreasing resource requirements and increasing restrictions on the set of possible operations. It can be shown that our protocols are optimal.

On the stability of asynchronous iterative processes

We consider an iterative process in which one out of a finite set of possible operators is applied at each iteration. We obtain necessary and sufficient conditions for convergence to a common fixed point of these operators, when the order at which different operators are applied is left completely free, except for the requirement that each operator is applied infinitely many times. The theory developed is similar in spirit to Lyapunov stability theory. We also derive some very different, qualitatively, results for partially asynchronous iterative processes, that is, for the case where certain constraints are imposed on the order at which the different operators are applied.