  In this paper, we propose a novel method, aggregation cross-entropy (ACE),
for sequence recognition from a brand new perspective. The ACE loss function
exhibits competitive performance to CTC and the attention mechanism, with much
quicker implementation (as it involves only four fundamental formulas), faster
inference\back-propagation (approximately O(1) in parallel), less storage
requirement (no parameter and negligible runtime memory), and convenient
employment (by replacing CTC with ACE). Furthermore, the proposed ACE loss
function exhibits two noteworthy properties: (1) it can be directly applied for
2D prediction by flattening the 2D prediction into 1D prediction as the input
and (2) it requires only characters and their numbers in the sequence
annotation for supervision, which allows it to advance beyond sequence
recognition, e.g., counting problem. The code is publicly available at
https://github.com/summerlvsong/Aggregation-Cross-Entropy.
