Generating Chain-of-Thoughts with a Direct Pairwise-Comparison Approach to Searching for the Most Promising Intermediate Thought

To improve the ability of the large language model (LLMs) to handle complex reasoning problems, chain-of-thoughts (CoT) methods were proposed to guide LLMs to reason step-by-step, facilitating problem solving from simple to complex tasks. State-of-the-art approaches for generating such a chain involve interactive collaboration, where the learner generates candidate intermediate thoughts, evaluated by the LLM, guiding the generation of subsequent thoughts. However, a widespread yet understudied problem is that the evaluation from the LLM is typically noisy and unreliable, potentially misleading the generation process in selecting promising intermediate thoughts. In this paper, motivated by Vapnik's principle, we propose a novel comparison-based CoT generation algorithm that directly identifies the most promising thoughts with the noisy feedback from the LLM. In each round, we randomly pair intermediate thoughts and directly prompt the LLM to select the more promising one from each pair, allowing us to identify the most promising thoughts through an iterative process. To further model the noise in the comparison, we resort to the techniques of ensemble and dueling bandits and propose two variants of the proposed algorithm. Experiments on three real-world mathematical and reasoning tasks demonstrate the effectiveness of our proposed algorithm and verify the rationale of the direct pairwise comparison.

Adapting to Continuous Covariate Shift via Online Density Ratio Estimation

Dealing with distribution shifts is one of the central challenges for modern machine learning. One fundamental situation is the \emph{covariate shift}, where the input distributions of data change from training to testing stages while the input-conditional output distribution remains unchanged. In this paper, we initiate the study of a more challenging scenario -- \emph{continuous} covariate shift -- in which the test data appear sequentially, and their distributions can shift continuously. Our goal is to adaptively train the predictor such that its prediction risk accumulated over time can be minimized. Starting with the importance-weighted learning, we show the method works effectively if the time-varying density ratios of test and train inputs can be accurately estimated. However, existing density ratio estimation methods would fail due to data scarcity at each time step. To this end, we propose an online method that can appropriately reuse historical information. Our density ratio estimation method is proven to perform well by enjoying a dynamic regret bound, which finally leads to an excess risk guarantee for the predictor. Empirical results also validate the effectiveness.

Early Abnormal Detection of Sewage Pipe Network: Bagging of Various Abnormal Detection Algorithms

Abnormalities of the sewage pipe network will affect the normal operation of the whole city. Therefore, it is important to detect the abnormalities early. This paper propose an early abnormal-detection method. The abnormalities are detected by using the conventional algorithms, such as isolation forest algorithm, two innovations are given: (1) The current and historical data measured by the sensors placed in the sewage pipe network (such as ultrasonic Doppler flowmeter) are taken as the overall dataset, and then the general dataset is detected by using the conventional anomaly detection method to diagnose the anomaly of the data. The anomaly refers to the sample different from the others samples in the whole dataset. Because the definition of anomaly is not through the algorithm, but the whole dataset, the construction of the whole dataset is the key to propose the early abnormal-detection algorithms. (2) A bagging strategy for a variety of conventional anomaly detection algorithms is proposed to achieve the early detection of anomalies with the high precision and recall. The results show that this method can achieve the early anomaly detection with the highest precision of 98.21%, the recall rate 63.58% and F1-score of 0.774.