Abstract
Large Language Models (LLMs) exhibit impressive capabilities yet suffer from sensitivity to slight input context variations, hampering reliability. Conventional metrics like accuracy and perplexity fail to assess local prediction robustness, as normalized output probabilities can obscure the underlying resilience of an LLM's internal state to perturbations. We introduce the Token Constraint Bound ($\delta_{\mathrm{TCB}}$), a novel metric that quantifies the maximum internal state perturbation an LLM can withstand before its dominant next-token prediction significantly changes. Intrinsically linked to output embedding space geometry, $\delta_{\mathrm{TCB}}$ provides insights into the stability of the model's internal predictive commitment. Our experiments show $\delta_{\mathrm{TCB}}$ correlates with effective prompt engineering and uncovers critical prediction instabilities missed by perplexity during in-context learning and text generation. $\delta_{\mathrm{TCB}}$ offers a principled, complementary approach to analyze and potentially improve the contextual stability of LLM predictions.
Abstract (translated)
大型语言模型（LLM）展示了令人印象深刻的性能，但它们对输入上下文的细微变化敏感，这影响了其可靠性。传统的准确性、困惑度等评估指标无法衡量局部预测的稳健性，因为归一化的输出概率掩盖了LLM内部状态对扰动的实际抵抗力。我们引入了一种新的度量标准——Token Constraint Bound（$\delta_{\mathrm{TCB}}$），用于量化在大型语言模型的主导下一个标记预测发生显著变化之前，其内部状态能承受的最大扰动程度。该指标与输出嵌入空间几何结构内在关联，能够揭示模型内部预测承诺的稳定性。实验表明，$\delta_{\mathrm{TCB}}$ 与有效的提示工程相关，并且在上下文学习和文本生成过程中发现了困惑度所未能捕捉到的关键预测不稳定性。因此，$\delta_{\mathrm{TCB}}$ 提供了一种原则性的、互补的方法来分析并潜在地改进大型语言模型的上下文稳定性。
URL
https://arxiv.org/abs/2602.10816
