While self-correction has shown promise in improving LLM outputs in terms of
style and quality (e.g. Chen et al., 2023; Madaan et al., 2023), recent
attempts to self-correct logical or reasoning errors often cause correct
answers to become incorrect, resulting in worse performances overall (Huang et
al., 2023). In this paper, we break down the self-correction process into two
core components: mistake finding and output correction. For mistake finding, we
release BIG-Bench Mistake, a dataset of logical mistakes in Chain-of-Thought
reasoning traces. We provide benchmark numbers for several state-of-the-art
LLMs, and demonstrate that LLMs generally struggle with finding logical
mistakes. For output correction, we propose a backtracking method which
provides large improvements when given information on mistake location. We
construe backtracking as a lightweight alternative to reinforcement learning
methods, and show that it remains effective with a reward model at 60-70%
accuracy.

本文将自我纠错过程分解为失误发现和输出校正两个核心组成部分，并对几种最先进的 LLM 进行了基准测试，结果显示 LLM 在发现逻辑错误方面普遍存在困难。针对输出校正，我们提出了一种回溯法，并证明当提供失误位置信息时，该方法能够明显改善性能。我们将回溯法视为轻量级替代强化学习方法的方式，并展示在准确率达到 60-70% 的奖励模型下依然有效。

LLMs 不能发现推理错误，但可以修正它们！

LLMs cannot find reasoning errors, but can correct them!

We study the problem of high-dimensional regression when there may be
interacting variables. Approaches using sparsity-inducing penalty functions
such as the Lasso can be useful for producing interpretable models. However,
when the number variables runs into the thousands, and so even two-way
interactions number in the millions, these methods may become computationally
infeasible. Typically variable screening based on model fits using only main
effects must be performed first. One problem with screening is that important
variables may be missed if they are only useful for prediction when certain
interaction terms are also present in the model.
To tackle this issue, we introduce a new method we call Backtracking. It can
be incorporated into many existing high-dimensional methods based on penalty
functions, and works by building increasing sets of candidate interactions
iteratively. Models fitted on the main effects and interactions selected early
on in this process guide the selection of future interactions. By also making
use of previous fits for computation, as well as performing calculations is
parallel, the overall run-time of the algorithm can be greatly reduced.
The effectiveness of our method when applied to regression and classification
problems is demonstrated on simulated and real data sets. In the case of using
Backtracking with the Lasso, we also give some theoretical support for our
procedure.

本论文研究了高维回归问题中存在交互变量的情况，引入了一种名为 Backtracking 的新方法，可解决使用稀疏性惩罚函数（如 Lasso）产生可解释模型过程中的计算效率问题，并在回归和分类问题的模拟和真实数据集上进行了实证分析。