Although weight quantization helps large language models (LLMs) in resource-constrained environments, its influence on the uncertainty calibration remains unexplored.To bridge this gap, we present a comprehensive investigation of uncertainty calibration for quantized LLMs in this work.Specifically, we propose an analytic method to estimate the upper bound of calibration error (UBCE) for LLMs.Our method separately discusses the calibration error of the model's correct and incorrect predictions, indicating a theoretical improvement of calibration error caused by weight quantization.Our study demonstrates that quantized models consistently exhibit worse calibration performance than full-precision models, supported by consistent analysis across multiple LLMs and datasets.To address the calibration issues of quantized models, we propose a novel post-calibration method to recover the calibration performance of quantized models through soft-prompt tuning.Specifically, we inject soft tokens into quantized models after the embedding layers and optimize these tokens to recover the calibration error caused by weight quantization.Experimental results on multiple datasets demonstrate its effectiveness in improving the uncertainty calibration of quantized LLMs, facilitating more reliable weight quantization in resource-constrained environments.

The unmanned surface vehicle (USV) has been widely used to accomplish tasks that cannot be completed by ships with human drivers on certain sea areas. It is not only necessary but essential to obtain a robust strategy in order to ensure multiple USVs accomplish collaborative tasks successfully and efficiently. To meet the challenge, a deep reinforcement learning method is proposed, which is combined with an improved A star algorithm. A statistically promising collaborative strategy is achieved by the proposed method under the guidance from the unmanned aerial vehicles (UAVs). After the collaborative strategy is generated, the improved A star algorithm is used to navigate the USVs. To verify the proposed algorithm, several tasks are tested on a simulation platform. Experimental results demonstrate that the proposed method outperforms state-of-the-art reinforcement learning methods such as DQN and DeepSarsa. © 2019 The authors and IOS Press. All rights reserved.

In this paper, we present the evolution of adaptive resonance theory (ART) neural network architectures (classifiers) using a multiobjective optimization approach. In particular, we propose the use of a multiobjective evolutionary approach to simultaneously evolve the weights and the topology of three well-known ART architectures; fuzzy ARTMAP (FAM), ellipsoidal ARTMAP (EAM), and Gaussian ARTMAP (GAM). We refer to the resulting architectures as MO-GFAM, MO-GEAM, and MO-GGAM, and collectively as MO-GART. The major advantage of MO-GART is that it produces a number of solutions for the classification problem at hand that have different levels of merit [accuracy on unseen data (generalization) and size (number of categories created)]. MO-GART is shown to be more elegant (does not require user intervention to define the network parameters), more effective (of better accuracy and smaller size), and more efficient (faster to produce the solution networks) than other ART neural network architectures that have appeared in the literature. Furthermore, MO-GART is shown to be competitive with other popular classifiers, such as classification and regression tree (CART) and support vector machines (SVMs).

Pruning is one of the key procedures in training decision tree classifiers. It removes trivial rules from the raw knowledge base built from training examples, in order to avoid over-using noisy, conflicting, or fuzzy inputs, so that the refined model can generalize better with unseen cases. In this paper, we present a number of properties of k-norm pruning, a recently proposed pruning algorithm, which has clear theoretical interpretation. In an earlier paper it was shown that k-norm pruning compares very favorably in terms of accuracy and size with minimal cost-complexity pruning and error based pruning, two of the most cited decision tree pruning methods; it was also shown that k-norm pruning is more efficient, at times orders of magnitude more efficient than minimal cost-complexity pruning and error based pruning. In this paper, we demonstrate the validity of the k-norm properties through a series of theorems, and explain their practical significance.

Probabilistic neural networks (PNN) and general regression neural networks (GRNN) represent knowledge by simple but interpretable models that approximate the optimal classifier or predictor in the sense of expected value of the accuracy. These models require the specification of an important smoothing parameter, which is usually chosen by cross-validation or clustering. In this article, we demonstrate the problems with the cross-validation and clustering approaches to specify the smoothing parameter, discuss the relationship between this parameter and some of the data statistics, and attempt to develop a fast approach to determine the optimal value of this parameter. Finally, through experimentation, we show that our approach, referred to as a gap-based estimation approach, is superior in speed to the compared approaches, including support vector machine, and yields good and stable accuracy.

Probabilistic neural networks (PNN) and general regression neural networks (GRNN) represent the knowledge by a simple but interpretable model that approximates the optimal classifier/predictor in the sense of expected value of accuracy. This model requires an important preset smoothing parameter, which is usually chosen by cross-validation or clustering. In this paper, we demonstrate the difficulties of both these approaches, discuss the relationship between this parameter and some of the data statistics, and attempt to develop a fast approach to determine the optimal value of this parameter. Finally, through experimentation we show that our approach, referred to as a gap-based estimation approach, is superior to the compared approaches.

Fuzzy ARTMAP (FAM) is currently considered as one of the premier neural network architectures in solving classification problems. Safe ARTMAP, a modified version of FAM, was introduced to remedy the category proliferation problem that has been extensively reported in the literature. However, Safe ARTMAP's performance depends on a number of parameters. In this paper, we analyzed each parameter to set up the candidate values for evaluation. We performed an exhaustive experimentation to identify good default values for these parameters for a variety of problems, and compared the best performing Safe ARTMAP network with other best performing ART networks, including those that claim to solve the category proliferation problem.