Attention (as Discrete-Time Markov) Chains

We introduce a new interpretation of the attention matrix as a discrete-time Markov chain. Our interpretation sheds light on common operations involving attention scores such as selection, summation, and averaging in a unified framework. It further extends them by considering indirect attention, propagated through the Markov chain, as opposed to previous studies that only model immediate effects. Our key observation is that tokens linked to semantically similar regions form metastable states, i.e., regions where attention tends to concentrate, while noisy attention scores dissipate. Metastable states and their prevalence can be easily computed through simple matrix multiplication and eigenanalysis, respectively. Using these lightweight tools, we demonstrate state-of-the-art zero-shot segmentation. Lastly, we define TokenRank