Samuel J. Bell

As large language models (LLMs) are increasingly deployed to perform tasks with minimal human oversight, it is crucial that these models operate robustly. In particular, a model that can solve a given problem should not fail simply because certain entities—such as names, numbers, or other contextual details—have changed while the underlying problem logic remains the same. Prior work suggests that current LLMs still struggle with this form of robustness: they often succeed on some variations of a problem but fail on others. However, existing evaluations often lack a systematic way to identify which logic-preserving variations are most likely to induce failure. Instead, they typically test a random subset of allowable variations, which can overstate robustness. To address this gap, we introduce logic-preserving difficulty scaling (LPDS), a framework that (i) quantifies the difficulty of a problem variation and (ii) systematically searches the space of allowable variations to find those that maximize difficulty and expose failures. We show that as difficulty increases, performance declines and errors in the models' reasoning chains become more pronounced. We further demonstrate that LPDS efficiently finds difficult problem variations for a model, resulting in performance drops up to $5\times$ larger compared to random sampling. Finally, we show that fine-tuning on more difficult variations leads to more consistent robustness gains than training on easier ones.

For Large Language Models (LLMs) to be reliable, they must learn robust knowledge that can be generally applied in diverse settings---often unlike those seen during training. Yet, extensive research has shown that LLM performance can be brittle, with models exhibiting excessive sensitivity to trivial input variations. In this work, we explore whether this brittleness is a direct result of unstable internal knowledge representations. To explore this question, we build on previous work showing that LLM representations encode statement truthfulness---i.e., true, factual statements can be easily separated from false, inaccurate ones. Specifically, we test the robustness of learned knowledge by evaluating representation separability on samples that have undergone superficial transformations to drive them out-of-distribution (OOD), such as typos or reformulations. By applying semantically-preserving perturbations, we study how separability degrades as statements become more OOD, across four LLM families, five evaluation datasets, and three knowledge probing methods. Our results reveal that internal representations of statement truthfulness collapse as the samples' presentations become less similar to those seen during pre-training. While LLMs can often distinguish between true and false statements when they closely resemble the pre-training data, this ability is highly dependent on the statement's exact surface form. These findings offer a possible explanation for brittle benchmark performance: LLMs may learn shallow, non-robust knowledge representations that allow for only limited generalizability. Our work presents a fundamental challenge for the utility of truthfulness probes, and more broadly, calls for further research on improving the robustness of learned knowledge representations.