While the recent Chain-of-Thought (CoT) technique enhances the reasoning
ability of large language models (LLMs) with the theory of mind, it might still
struggle in handling logical reasoning that relies much on symbolic expressions
and rigid deducing rules. To strengthen the logical reasoning capability of
LLMs, we propose a novel Symbolic Chain-of-Thought, namely SymbCoT, a fully
LLM-based framework that integrates symbolic expressions and logic rules with
CoT prompting. Technically, building upon an LLM, SymbCoT 1) first translates
the natural language context into the symbolic format, and then 2) derives a
step-by-step plan to solve the problem with symbolic logical rules, 3) followed
by a verifier to check the translation and reasoning chain. Via thorough
evaluations on 5 standard datasets with both First-Order Logic and Constraint
Optimization symbolic expressions, SymbCoT shows striking improvements over the
CoT method consistently, meanwhile refreshing the current state-of-the-art
performances. We further demonstrate that our system advances in more faithful,
flexible, and explainable logical reasoning. To our knowledge, this is the
first to combine symbolic expressions and rules into CoT for logical reasoning
with LLMs. Code is open at this https URL

提出了一种基于大型语言模型的新型符号化思维链 (SymbCoT) 框架，通过将符号表达和逻辑规则与语言模型集成，以增强其逻辑推理能力，并在 5 个标准数据集上通过深入评估展示了显著的性能提升。

通过符号化推理保持逻辑的准确性

Faithful Logical Reasoning via Symbolic Chain-of-Thought

Recent advances in TCP congestion control (CC) have achieved tremendous
success with deep reinforcement learning (RL) approaches, which use feedforward
neural networks (NN) to learn complex environment conditions and make better
decisions. However, such "black-box" policies lack interpretability and
reliability, and often, they need to operate outside the traditional TCP
datapath due to the use of complex NNs. This paper proposes a novel two-stage
solution to achieve the best of both worlds: first to train a deep RL agent,
then distill its (over-)parameterized NN policy into white-box, light-weight
rules in the form of symbolic expressions that are much easier to understand
and to implement in constrained environments. At the core of our proposal is a
novel symbolic branching algorithm that enables the rule to be aware of the
context in terms of various network conditions, eventually converting the NN
policy into a symbolic tree. The distilled symbolic rules preserve and often
improve performance over state-of-the-art NN policies while being faster and
simpler than a standard neural network. We validate the performance of our
distilled symbolic rules on both simulation and emulation environments. Our
code is available at this https URL.

本文提出一种基于深度强化学习的深度神经网络模型，在模型训练完成后对模型参数进行压缩，转换成可解释且能够适用于不同网络环境的符号表达式，并提供了一种新的符号分支算法，验证了该方法在模拟和仿真环境中能够保留和提高性能。

基于符号化精简的 TCP 学习型拥塞控制技术

Symbolic Distillation for Learned TCP Congestion Control

In this paper we explore how machine learning techniques can be applied to
the discovery of efficient mathematical identities. We introduce an attribute
grammar framework for representing symbolic expressions. Given a set of grammar
rules we build trees that combine different rules, looking for branches which
yield compositions that are analytically equivalent to a target expression, but
of lower computational complexity. However, as the size of the trees grows
exponentially with the complexity of the target expression, brute force search
is impractical for all but the simplest of expressions. Consequently, we
introduce two novel learning approaches that are able to learn from simpler
expressions to guide the tree search. The first of these is a simple n-gram
model, the other being a recursive neural-network. We show how these approaches
enable us to derive complex identities, beyond reach of brute-force search, or
human derivation.

本文研究机器学习技术如何应用于高效数学等式的发现，并介绍了一种用于表示符号表达式的属性文法框架，同时引入两种新型学习方法，通过从简单表达式学习来指导树搜索，能够生成超出暴力搜索或人工推导范围的复杂等式。