Xian Li

Kewei Cheng, Jingfeng Yang, Haoming Jiang et al.

Reasoning encompasses two typical types: deductive reasoning and inductive reasoning. Despite extensive research into the reasoning capabilities of Large Language Models (LLMs), most studies have failed to rigorously differentiate between inductive and deductive reasoning, leading to a blending of the two. This raises an essential question: In LLM reasoning, which poses a greater challenge - deductive or inductive reasoning? While the deductive reasoning capabilities of LLMs, (i.e. their capacity to follow instructions in reasoning tasks), have received considerable attention, their abilities in true inductive reasoning remain largely unexplored. To investigate into the true inductive reasoning capabilities of LLMs, we propose a novel framework, SolverLearner. This framework enables LLMs to learn the underlying function (i.e., $y = f_w(x)$), that maps input data points $(x)$ to their corresponding output values $(y)$, using only in-context examples. By focusing on inductive reasoning and separating it from LLM-based deductive reasoning, we can isolate and investigate inductive reasoning of LLMs in its pure form via SolverLearner. Our observations reveal that LLMs demonstrate remarkable inductive reasoning capabilities through SolverLearner, achieving near-perfect performance with ACC of 1 in most cases. Surprisingly, despite their strong inductive reasoning abilities, LLMs tend to relatively lack deductive reasoning capabilities, particularly in tasks involving ``counterfactual'' reasoning.

Tao Zou, Xian Li, Xuan Liang et al.

This article introduces subbagging (subsample aggregating) estimation approaches for big data analysis with memory constraints of computers. Specifically, for the whole dataset with size $N$, $m_N$ subsamples are randomly drawn, and each subsample with a subsample size $k_N\ll N$ to meet the memory constraint is sampled uniformly without replacement. Aggregating the estimators of $m_N$ subsamples can lead to subbagging estimation. To analyze the theoretical properties of the subbagging estimator, we adapt the incomplete $U$-statistics theory with an infinite order kernel to allow overlapping drawn subsamples in the sampling procedure. Utilizing this novel theoretical framework, we demonstrate that via a proper hyperparameter selection of $k_N$ and $m_N$, the subbagging estimator can achieve $\sqrt{N}$-consistency and asymptotic normality under the condition $(k_Nm_N)/N\to α\in (0,\infty]$. Compared to the full sample estimator, we theoretically show that the $\sqrt{N}$-consistent subbagging estimator has an inflation rate of $1/α$ in its asymptotic variance. Simulation experiments are presented to demonstrate the finite sample performances. An American airline dataset is analyzed to illustrate that the subbagging estimate is numerically close to the full sample estimate, and can be computationally fast under the memory constraint.