Models are susceptible to adversarially out-of-distribution (OOD) data despite large training-compute investments into their robustification. Zaremba et al. (2025) make progress on this problem at test time, showing LLM reasoning improves satisfaction of model specifications designed to thwart attacks, resulting in a correlation between reasoning effort and robustness to jailbreaks. However, this benefit of test compute fades when attackers are given access to gradients or multimodal inputs. We address this gap, clarifying that inference-compute offers benefits even in such cases. Our approach argues that compositional generalization, through which OOD data is understandable via its in-distribution (ID) components, enables adherence to defensive specifications on adversarially OOD inputs. Namely, we posit the Robustness from Inference Compute Hypothesis (RICH): inference-compute defenses profit as the model's training data better reflects the attacked data's components. We empirically support this hypothesis across vision language model and attack types, finding robustness gains from test-time compute if specification following on OOD data is unlocked by compositional generalization. For example, InternVL 3.5 gpt-oss 20B gains little robustness when its test compute is scaled, but such scaling adds significant robustness if we first robustify its vision encoder. This correlation of inference-compute's robustness benefit with base model robustness is the rich-get-richer dynamic of the RICH: attacked data components are more ID for robustified models, aiding compositional generalization to OOD data. Thus, we advise layering train-time and test-time defenses to obtain their synergistic benefit.

As large language models (LLMs) are increasingly deployed in diverse applications, including chatbot assistants and code generation, aligning their behavior with safety and ethical standards has become paramount. However, jailbreak attacks, which exploit vulnerabilities to elicit unintended or harmful outputs, threaten LLMs' safety significantly. In this paper, we introduce Layer-AdvPatcher, a novel methodology designed to defend against jailbreak attacks by utilizing an unlearning strategy to patch specific layers within LLMs through self-augmented datasets. Our insight is that certain layer(s), tend to produce affirmative tokens when faced with harmful prompts. By identifying these layers and adversarially exposing them to generate more harmful data, one can understand their inherent and diverse vulnerabilities to attacks. With these exposures, we then "unlearn" these issues, reducing the impact of affirmative tokens and hence minimizing jailbreak risks while keeping the model's responses to safe queries intact. We conduct extensive experiments on two models, four benchmark datasets, and multiple state-of-the-art jailbreak attacks to demonstrate the efficacy of our approach. Results indicate that our framework reduces the harmfulness and attack success rate of jailbreak attacks without compromising utility for benign queries compared to recent defense methods. Our code is publicly available at: https://github.com/oyy2000/LayerAdvPatcher