Have Large Language Models Learned to Reason? A Characterization via 3-SAT Phase Transition

Large Language Models (LLMs) have been touted as AI models possessing advanced reasoning abilities. In theory, autoregressive LLMs with Chain-of-Thought (CoT) can perform more serial computations to solve complex reasoning tasks. However, recent studies suggest that, despite this capacity, LLMs do not truly learn to reason but instead fit on statistical features. To study the reasoning capabilities in a principled fashion, we adopt a computational theory perspective and propose an experimental protocol centered on 3-SAT -- the prototypical NP-complete problem lying at the core of logical reasoning and constraint satisfaction tasks. Specifically, we examine the phase transitions in random 3-SAT and characterize the reasoning abilities of state-of-the-art LLMs by varying the inherent hardness of the problem instances. By comparing DeepSeek R1 with other LLMs, our findings reveal two key insights (1) LLM accuracy drops significantly on harder instances, suggesting all current models struggle when statistical shortcuts are unavailable (2) Unlike other LLMs, R1 shows signs of having learned the underlying reasoning. Following a principled experimental protocol, our study moves beyond the benchmark-driven evidence often found in LLM reasoning research. Our findings highlight important gaps and suggest clear directions for future research.

Relational Neurosymbolic Markov Models

Sequential problems are ubiquitous in AI, such as in reinforcement learning or natural language processing. State-of-the-art deep sequential models, like transformers, excel in these settings but fail to guarantee the satisfaction of constraints necessary for trustworthy deployment. In contrast, neurosymbolic AI (NeSy) provides a sound formalism to enforce constraints in deep probabilistic models but scales exponentially on sequential problems. To overcome these limitations, we introduce relational neurosymbolic Markov models (NeSy-MMs), a new class of end-to-end differentiable sequential models that integrate and provably satisfy relational logical constraints. We propose a strategy for inference and learning that scales on sequential settings, and that combines approximate Bayesian inference, automated reasoning, and gradient estimation. Our experiments show that NeSy-MMs can solve problems beyond the current state-of-the-art in neurosymbolic AI and still provide strong guarantees with respect to desired properties. Moreover, we show that our models are more interpretable and that constraints can be adapted at test time to out-of-distribution scenarios.

Can Large Language Models Reason? A Characterization via 3-SAT

Large Language Models (LLMs) are said to possess advanced reasoning abilities. However, some skepticism exists as recent works show how LLMs often bypass true reasoning using shortcuts. Current methods for assessing the reasoning abilities of LLMs typically rely on open-source benchmarks that may be overrepresented in LLM training data, potentially skewing performance. We instead provide a computational theory perspective of reasoning, using 3-SAT -- the prototypical NP-complete problem that lies at the core of logical reasoning and constraint satisfaction tasks. By examining the phase transitions in 3-SAT, we empirically characterize the reasoning abilities of LLMs and show how they vary with the inherent hardness of the problems. Our experimental evidence shows that LLMs cannot perform true reasoning, as is required for solving 3-SAT problems.