Perturbation Robustness Profiles Reveal Heterogeneous Capability Degradation and an Evaluation-Modality Blind Spot in Instruction-Tuned Language Models

We study whether instruction-tuned language-model behaviors have the same robustness profile under controlled weight perturbation. We inject per-tensor Gaussian noise into Llama-3. 1-8B-Instruct and evaluate four capability families. Capabilities degrade heterogeneously (IFEval retains 82. 2% at σ=0. 2, GSM8K retains 45. 1%; p=0. 033). Safety refusal behavior shows qualitatively higher seed-level variance (CV=67. 6% vs <13% for capabilities). A component-level sweep initially appeared to show capability-type dissociation; a modality control shows the stronger result is evaluation-modality dissociation: MMLU log-likelihood scoring retains 47. 4% at σ=2. 0 on layer₂9ₐttention while greedy-generation collapses to 4. 4% with 93. 1% extraction failure. Log-likelihood evaluation cannot certify deployment-relevant generation capability after weight modification. Preprint v2. 1 — companion code at https: //github. com/mohitdak24/perturbation-robustness-profiles