In Connectionist Temporal Classification (CTC), we assume that the output vectors in a single sequence are all independent. Mathematically, let the input sequence be $X=\{x_1, x_2,..,x_n\}$ where $x_i$ are vectors, and let the output alignment be $A=\{a_1, a_2, …, a_n\}$ where $a_i$ are vectors, then $P_{CTC}(A|X)=\prod_{i=1}^{n}p(a_i|X)$.