PRISM: A Geometric Risk Bound that Decomposes Drift into Scale, Shape, and Head
Existing methods struggle to diagnose representation drift in post-training variants of large language models—such as quantization or LoRA fine-tuning—as they can only assess performance degradation without identifying root causes or guiding mitigation. This work proposes PRISM, a method that leverages the linear output head and near-isometric backbone structure of LLMs to derive a closed-form upper bound on cross-entropy risk discrepancy. PRISM uniquely decomposes representation drift into three geometrically interpretable and independently measurable axes: scale, shape, and head. Notably, the shape component is differentiable and can be employed as a regularizer to mitigate catastrophic forgetting. Experiments show that PRISM achieves Spearman correlation coefficients of 0.820 and 0.831 in risk ranking for quantized and LoRA-adapted models, respectively, across two model families and five benchmarks; moreover, shape-based regularization outperforms experience replay in alleviating downstream forgetting.