Abstraction-of-Thought Makes Language Models Better Reasoners (2024)

Abstract: Abstract reasoning, the ability to reason from the abstract essence of a problem, serves as a key to generalization in human reasoning. However, eliciting language models to perform reasoning with abstraction remains unexplored. This paper seeks to bridge this gap by introducing a novel structured reasoning format called Abstraction-of-Thought (AoT). The uniqueness of AoT lies in its explicit requirement for varying levels of abstraction within the reasoning process. This approach could elicit language models to first contemplate on the abstract level before incorporating concrete details, which is overlooked by the prevailing step-by-step Chain-of-Thought (CoT) method. To align models with the AoT format, we present AoT Collection, a generic finetuning dataset consisting of 348k high-quality samples with AoT reasoning processes, collected via an automated and scalable pipeline. We finetune a wide range of language models with AoT Collection and conduct extensive evaluations on 23 unseen tasks from the challenging benchmark Big-Bench Hard. Experimental results indicate that models aligned to AoT reasoning format substantially outperform those aligned to CoT in many reasoning tasks.

## introduction the complex reasoning ability is one of the longterm pursuits of artificial intelligence. in recent years, language models (lms) have seen rapid development and achieved impressive performance on a variety of reasoning benchmarks @xcite . among the advancements in reasoning methods, the chain-of-thought (cot) technique has emerged as a prominent reasoning tool @xcite . this technique, when employed in large language models (llms), serves as figure 1 : reasoning with abstraction attempts to answer questions from the perspective of abstract essences, which may be overlooked by step-by-step chain-of-thought (cot) reasoning. the reasoning process with abstraction contains multiple levels of abstract information. the lower levels (blue nodes) are responsible for performing concrete reasoning and are typically rich in detail. conversely, the higher levels (red nodes) are abstractions of lower levels, organizing the entire reasoning process. a guide that enables the model to initially generate intermediate reasoning processes before ultimately producing the final answer. the generated reasoning processes significantly help large language models improve their reasoning performance in zero-shot and few-shot scenarios. this discovery has sparked a great deal of research interest and further improvement @xcite @xcite @xcite . meanwhile, for medium-scale language models, training models on data containing cot has been proven to be an effective method to enhance the reasoning performance of language models @xcite @xcite @xcite . the prevailing cot paradigm typically follows a sequential, step-by-step reasoning process, which may leave the exploration of abstraction in reasoning largely untapped. abstraction is the key to human cognition and reasoning @xcite . when dealing with complex tasks, reasoning with abstraction first tackles the essence and the most crucial parts, then utilizes the abstract skeletal solution as a guide to solve the rest of the problem @xcite . abstraction allows reasoning to perform at a higher and more essential level, resulting in a more generalizable and efficient solution. as shown in figure 1 , when dealing with a specific problem of solving a quadratic equation, reasoning with abstraction suggests first deriving the general quadratic formula and then substituting the specific coefficients to get the answer. this approach offers a more fundamental solution, applicable to problems with similar reasoning patterns. the existing cot, in the absence of explicit constraints, does not guarantee that abstraction will necessarily be incorporated into the problem-solving process. in this paper, we explore how to elicit language models to reason with abstraction. we propose a novel format of reasoning processes named abstraction-of-thought (aot), which is a constrained variant of the cot. reasoning with abstraction typically starts with a rough skeletal solution from an abstraction perspective (e.g., the red nodes in figure 1(b) ), and then gradually concretizes the solution until the problem is solved. we suggest that employing an abstract skeletal solution to organize the entire reasoning process could be the key to eliciting abstract reasoning. thus, in contrast to the unconstrained cot, the aot format explicitly demands the inclusion of varying levels of abstraction throughout the reasoning process. the higher level is an abstraction of the lower level, containing fewer concrete details but stating the objective and functionality of the reasoning step. for example, functions and classes in programs are abstractions of the following specific code fragments, while main claims in argumentative discourses @xcite are abstractions of subsequent supportive evidence. specifically, we focus on the two-level aot in this paper, which contains an additional level of abstraction over the cot, to serve as an preliminary exploration of whether abstraction helps language models reasoning. to align language models to the aot format, we present the aot collection, a supervised finetuning dataset that augments 348k aot reasoning processes from the flan collection @xcite . aot collection covers 216 generic tasks that are not specifically designed for a certain domain or dataset. we design an automatic and scalable pipeline to collect high-quality aot reasoning processes with the involvement of llms. in addition to the aot reasoning processes represented in natural language, the aot collection also includes aot with programming language. such a hybrid training strategy could not only unleash the potential of the code use, but also allow the flexibility of preferring different reasoning processes for different reasoning problems @xcite . we use aot collection to finetune a wide range of language models. we conduct exhaustive experiments on 23 unseen tasks from big-bench hard @xcite , a subset of the most challenging reasoning tasks of @xcite that necessitates various reasoning abilities. experimental results show that aot makes language models better reasoners. remarkably, models with aot-finetuning achieve substantial improvements in both zero-shot and few-shot performance across various reasoning tasks, compared to those with cot-finetuning. our findings highlight the potential of aot in eliciting and training more effective models capable of reasoning with abstraction. ## abstraction-of-thought (aot) the abstraction-of-thought (aot) reasoning format draws inspiration from the human application of abstract thinking to solve complex reasoning and planning problems @xcite . in trying to solve a complex problem, a good strategy adopted by human reasoners is to proceed topdown. they start from a rough abstract solution and then gradually refine it until a concrete solution is found. for instance, when faced with a complex programming task, seasoned programmers often commence by sketching out a rough algorithmic framework and identifying abstract function features. subsequently, they progressively delve into the specifics of the code implementation. similarly, in argumentative discourse @xcite , the arguer often first presents the main claims, followed by detailed explanations and supportive evidence for these claims. therefore, complex problem solutions frequently contain information at diverse abstraction levels, which serves to organize the entire reasoning process hierarchically. these high levels (e.g., functions in a coding solution or main claims in an argument) encapsulate the functionality and objectives of lower levels, thereby structuring the internal reasoning process. we suggest that the explicit inclusion of such multiple levels of abstraction in the reasoning process could be the key to eliciting abstract reasoning in lms and propose the aot format (figure 2 ). specifically, an n-step aot reasoning process can be expressed as as a preliminary exploration into whether abstract content aids in the reasoning of llms, this paper focuses on the two-level aot. compared to the unconstrained cot, the two-level aot already ## conclusion this paper explores how to elicit language models to perform reasoning with abstraction, from the perspective of the reasoning format. we propose a 2000 novel structured reasoning format, aot, which explicitly requires multiple levels of abstraction to be included in the reasoning process. we construct the aot collection, containing 348k high-quality aot reasoning processes, for fine-tuning models to align them to the aot format. experimental results show that aot-finetuned language models can achieve advanced reasoning performance compared to baseline approaches.