A drawback of the simple greedy inference algorithm in Connectionist Temporal Classification (CTC) is that it maximizes the probability of a single alignment rather than the final output sequence. To find the optimal output sequence, the inference algorithm should choose the output $$Y$$ that has the maximum conditional probability by marginalizing over all alignments $$A$$ that produce $$Y$$. Mathematically, the probability of an output sequence is $$P_{CTC}(Y|X)=\sum_{\text{all A that produce Y}}p(A|X)$$, and the optimal sequence is $$\hat{Y}=\text{argmax}_{\text{all possible Y}} P_{CTC}(Y|X)$$.

Maximum Conditional Probability Inference in Connectionist Temporal Classification

In Connectionist Temporal Classification (CTC), the simple greedy inference algorithm finds the most probable alignment by selecting the most likely label at each time step. Mathematically, let $$\mathcal{C}$$ be the set of all possible labels. The predicted label $$\hat{a}_i$$ at time step $$i$$ is $$\hat{a}_i=\text{argmax}_{c\in\mathcal{C}} p_i(c|X)$$, where $$p_i(c|X)$$ is the probability of label $$c$$ at time step $$i$$ given the input sequence $$X$$.

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

Strong Conditional Independence Assumption in Connectionist Temporal Classification

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https://web.stanford.edu/~jurafsky/slp3/

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