DEVAL: A Framework for Evaluating and Improving the Derivation Capability of Large Language Models

TL;DR

The paper defines Derivation Capability (DC) as the ability of a model to apply abstract transformation rules (Derivation Relations, DR) under input changes, and formalizes this through a homomorphism-based framework. It introduces DEVAL, a three-part pipeline (Rule Formalization, Dataset Construction, Model Evaluation) to generate DR-consistent datasets and measure DC via the Derivation Capability Score (DCS) with an empirical approximation $\gamma$. Across seven tasks and six models, DC is generally weak, with DRs split into ID, GE, and TS types; a targeted prompt engineering approach, Derivation Prompting (DP), improves DC by $15.2\%$ on average and outperforms baseline prompting methods. The authors further validate DEVAL against robustness benchmarks, explore autonomous DR generation, and compare prompting to fine-tuning, finding that symbolic, DR-focused prompting better promotes abstract reasoning than standard SFT for many tasks. Together, these results provide a framework and practical path to enhance and evaluate abstract reasoning in large language models, with implications for reliability in domain problem solving.

Abstract

Assessing the reasoning ability of Large Language Models (LLMs) over data remains an open and pressing research question. Compared with LLMs, human reasoning can derive corresponding modifications to the output based on certain kinds of changes to the input. This reasoning pattern, which relies on abstract rules that govern relationships between changes of data, has not been comprehensively described or evaluated in LLMs. In this paper, we formally define this reasoning pattern as the Derivation Relation (DR) and introduce the concept of Derivation Capability (DC), i.e. applying DR by making the corresponding modification to the output whenever the input takes certain changes. To assess DC, a systematically constructed evaluation framework named DEVAL is proposed and used to evaluate five popular LLMs and one Large Reasoning Model in seven mainstream tasks. The evaluation results show that mainstream LLMs, such as GPT-4o and Claude3.5, exhibit moderate DR recognition capabilities but reveal significant drop-offs on applying DR effectively in problem-solving scenarios. To improve this, we propose a novel prompt engineering approach called Derivation Prompting (DP). It achieves an average improvement of 15.2% in DC for all tested LLMs, outperforming commonly used prompt engineering techniques.

Figures (10)

• Figure 1: Motivation example of the Derivation Capability.
• Figure 2: Counterexamples in GPT-4o. We run the test 100 times and take the most frequent answer as the final answer.
• Figure 3: The overall structure of the DEVAL framework.
• Figure 5: DC performance in different LLMs and DR types.
• Figure 6: Error pattern evaluation in different DR types.