Abstract: Large language models (LLMs) have revolutionized machine learning due to their ability to capture complex interactions between input features. Popular post-hoc explanation methods like SHAP provide *marginal* feature attributions, while their extensions to interaction importances only scale to small input lengths ($\approx 20$). We propose *Spectral Explainer* (SPEX, a model-agnostic interaction attribution algorithm that efficiently scales to large input lengths ($\approx 1000)$. SPEX exploits underlying natural sparsity among interactions—common in real-world data—and applies a sparse Fourier transform using a channel decoding algorithm to efficiently identify important interactions.We perform experiments across three difficult long-context datasets that require LLMs to utilize interactions between inputs to complete the task. For large inputs, SPEX outperforms marginal attribution methods by up to 20\% in terms of faithfully reconstructing LLM outputs. Further, SPEX successfully identifies key features and interactions that strongly influence model output. For one of our datasets, *HotpotQA*, SPEX provides interactions that align with human annotations. Finally, we use our model-agnostic approach to generate explanations to demonstrate abstract reasoning in closed-source LLMs (*GPT-4o mini*) and compositional reasoning in vision-language models.