From Confidence to Collapse in LLM Factual Robustness (2025)

Abstract: Ensuring the robustness of factual knowledge in LLMs is critical for reliable applications in tasks such as question answering and reasoning. However, existing evaluation methods predominantly focus on performance-based metrics, often investigating from the perspective of prompt perturbations, which captures only the externally triggered side of knowledge robustness. To bridge this gap, we introduce a principled approach to measure factual robustness from the perspective of the generation process by analyzing token distribution entropy in combination with temperature scaling sensitivity. These two factors build the Factual Robustness Score (FRS), a novel metric which quantifies the stability of a fact against perturbations in decoding conditions, given its initial uncertainty. To validate our approach, we conduct extensive experiments on 5 LLMs across 3 closed-book QA datasets (SQuAD, TriviaQA, and HotpotQA). We show that factual robustness varies significantly – smaller models report an FRS of 0.76, larger ones 0.93 – with accuracy degrading by ~60% under increased uncertainty. These insights demonstrate how entropy and temperature scaling impact factual accuracy, and lay a foundation for developing more robust knowledge retention and retrieval in future models. We release our code at https://github.com/afastowski/frs.

## introduction large language models (llms) have revolutionized natural language understanding and generation, demonstrating remarkable capabilities across tasks such as question answering, knowledgeintensive text generation, and reasoning @xcite @xcite . however, despite their strong performance, factual stability remains an open challenge. while a model may provide a correct answer under one set of decoding conditions, it may fail to do so when faced with minor perturbations, such as variations in sampling temperature. this raises a fundamental question: how robustly is factual knowledge embedded in llms? traditional evaluations of factual knowledge in llms rely on accuracy-based metrics, which measure correctness under fixed conditions @xcite @xcite . however, these methods do not account for uncertainty in fact retrieval -whether a model is inherently confident in its answer or if its correctness is fragile under perturbations. additionally, prior techniques often focus on single-temperature evaluations, failing to systematically analyze how factual outputs degrade as uncertainty is introduced @xcite . to bridge this gap, we introduce a novel perspective: factual robustness, which examines not just whether an answer is correct but how resistant it is to internal uncertainty and temperature-induced variability. to quantify this, we propose the factual robustness score (frs), a new metric designed to measure the stability of factual knowledge within an llm. unlike previous work that assesses model performance at isolated temperature values, frs integrates both entropy and temperature, providing a comprehensive robustness assessment. entropy quantifies the model's intrinsic confidence in an answer, while the so-called "breaking" temperature is the first temperature greater than zero, at which the generation produces an incorrect answer. in other words, it captures how much uncertainty the generation process can withstand, before shifting from the correctly produced answer to an incorrect one. by combining these two dimensions, frs moves beyond simple accuracy and provides a deeper insight into how reliably knowledge is stored and retrieved within llms. through extensive experiments across multiple llm architectures and datasets, we show that higher-entropy facts degrade more under temperature perturbations, while lower-entropy facts remain more stable. model size alone does not dictate robustness, as architectural and training differences also play a role. additionally, factual stability varies by knowledge type, with numerical facts proving more resilient than others. our contributions are multifold: ## preliminaries entropy is a measure of disorder and randomness in a system. in text generation, it measures the spread of the probability distribution over possible tokens, with higher entropy indicating more randomness, and lower entropy reflecting more confident, deterministic predictions (see equation ( 1 )). following the intuition of entropy, we consider it as the first factor in our robustness assessments. temperature is a parameter that controls the sharpness of the probability distribution during text generation. it operates by scaling the logits before applying the softmax, as defined in equation (2): ## conclusion this study provides a comprehensive analysis of factual robustness in llms and introduces the factual robustness score (frs) as a novel metric for evaluating factual stability under varying conditions. unlike traditional accuracy-based assessments, frs captures both internal generation uncertainty (entropy) and sensitivity to temperature, offering a more nuanced measure of robustness. our findings show that increasing temperature reduces factual accuracy, with models that are more confident in their initial answers maintaining correctness longer. however, since entropy alone does not fully predict breaking temperature t b , frs integrates both factors for a more complete evaluation. while larger models generally exhibit greater robustness, architectural and training differences mean that some smaller models outperform their larger counterparts. additionally, factual robustness varies by knowledge type, with numerical facts proving more stable than others. in a practical sense, frs holds potential for enhancing a model's factual accuracy through continued pretraining: by evaluating a model's frs, one can identify areas of weakness (specific facts where the model underperforms) and use these as targeted data for further training. beyond introducing frs, this study highlights limitations in current evaluation methodologies and demonstrates that factual robustness is influenced by both model properties and the nature of the knowledge itself. future work could explore (1) finding the optimal breaking temperature for each model based on the initial entropy, (2) higher-temperature effects, and (3) strategies for enhancing factual retention to improve the reliability of llms in real-world applications.