In this work, we introduce DMDIntel which uses *dynamic mode decomposition* (DMD) to make the predictions made by LLMs in a classification task interpretable. It develops an input attribution pipeline, that first decomposes the hidden states of an LLM into prominent patterns, also known as *modes*, and then associates ranks to the input tokens based on the projection values on those modes. Rigorous experiments across three datasets and three model families consistently show that the ranked attribution of input tokens obtained using DMDIntel by far outperforms state-of-the-art techniques such as principal component analysis, integrated gradients and SHAP.