In Connectionist Temporal Classification (CTC), the simple greedy inference algorithm can yield suboptimal results because multiple alignments map to the same output sequence. For example, given an input $$X$$, let the three most probable alignments be "a_b", "b_b", and "b_bb", with probabilities 0.4, 0.3, and 0.3 respectively. The greedy algorithm chooses the single most probable alignment, "a_b", leading to the output "ab". However, both "b_b" and "b_bb" map to the output "bb". Marginalizing these alignments gives "bb" a total probability of 0.6, making it the most probable overall output sequence.

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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

An on-going but a helpful book resource about NLP
https://web.stanford.edu/~jurafsky/slp3/

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