Can Language Models Falsify? Evaluating Algorithmic Reasoning with Counterexample Generation

Enthusiasm about the potential of language models (LMs) to accelerate scientific discovery is continuously growing. Falsifying hypotheses is key to scientific progress as it allows for iterative refinement of claims. This process requires significant effort, logical reasoning, and ingenuity from researchers. However, current benchmarks for LMs predominantly evaluate their ability to generate solutions rather than critically question them.

A promising approach lies in developing benchmarks that evaluate the ability of LMs to generate counterexamples for subtly flawed solutions. This approach focuses on the inverse ability – uncovering flaws in existing solutions. A particularly suitable area for investigating this ability is algorithmic problem-solving, as counterexamples can be automatically verified through code execution.

One example of such a benchmark is REFUTE, a dynamically updated collection of problems and flawed solution attempts from programming competitions. In these cases, human experts have successfully identified counterexamples. The analysis of REFUTE shows that even the most powerful AI models, such as OpenAI o3-mini (high) with code execution feedback, can only generate counterexamples for less than 9% of the flawed solutions in REFUTE. This is remarkable, as evaluations show that the same model can solve up to 48% of these problems from scratch.

The Importance of Falsification for Scientific Progress

The ability to refute hypotheses and find counterexamples is central to scientific progress. It allows for refining theories, verifying assumptions, and improving the understanding of complex systems. In the context of LMs, this means that the models should not only be able to generate solutions but also critically question the validity of these solutions.

The Challenges of Evaluating the Falsification Ability of LMs

Developing benchmarks for evaluating the falsification ability of LMs presents a challenge. It is necessary to develop tasks that contain subtle errors in solutions that can be detected by LMs and refuted through counterexamples. Moreover, the benchmarks need to be dynamically updated to keep pace with the advancements in LM development.

Future Research and Implications

Research in the area of LMs' falsification ability is still in its early stages. Future work should focus on the development of more robust and comprehensive benchmarks. Furthermore, it is important to understand the underlying mechanisms that enable LMs to generate counterexamples and to specifically improve these capabilities. The ability of LMs to falsify flawed solutions is not only crucial for accelerating research but also for the models' ability to self-improve through reliable, reflective thinking. Such self-critical behavior is essential for the responsible use of AI in science and society.