The deployment and application of Large Language Models (LLMs) is hindered by their memory inefficiency, computational demands, and the high costs of API inferences. Traditional distillation methods, which transfer the capabilities of LLMs to smaller models, often fail to determine whether the knowledge has been sufficiently transferred, potentially resulting in high costs or incomplete distillation. In this paper, we propose an Explanation-Guided LLMs Active Distillation (ELAD) framework that employs an active learning strategy to optimize the balance between annotation costs and model performance. To improve efficient sample selection, we introduce an explanation-guided sample selection method that identifies samples challenging its reasoning by exploiting uncertainties in explanation steps. Additionally, we present a customized LLM-annotated explanation revision technique where the teacher model detects and corrects flaws in the student model's reasoning. Our experiments across various reasoning datasets demonstrate that our framework significantly enhances the efficiency of LLM knowledge distillation.

This paper is to consider the problems of estimation and recognition from the perspective of sigma-max inference (probability-possibility inference), with a focus on discovering whether some of the unknown quantities involved could be more faithfully modeled as fuzzy uncertainty. Two related key issues are addressed: 1) the random-fuzzy dual interpretation of unknown quantity being estimated; 2) the principle of selecting sigma-max operator for practical problems, such as estimation and recognition. Our perspective, conceived from definitions of randomness and fuzziness, is that continuous unknown quantity involved in estimation with inaccurate prior should be more appropriately modeled as randomness and handled by sigma inference; whereas discrete unknown quantity involved in recognition with insufficient (and inaccurate) prior could be better modeled as fuzziness and handled by max inference. The philosophy was demonstrated by an updated version of the well-known interacting multiple model (IMM) filter, for which the jump Markovian System is reformulated as a hybrid uncertainty system, with continuous state evolution modeled as usual as model-conditioned stochastic system and discrete mode transitions modeled as fuzzy system by a possibility (instead of probability) transition matrix, and hypotheses mixing is conducted by using the operation of "max" instead of "sigma". For our example of maneuvering target tracking using simulated data from both a short-range fire control radar and a long-range surveillance radar, the updated IMM filter shows significant improvement over the classic IMM filter, due to its peculiarity of hard decision of system model and a faster response to the transition of discrete mode.