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The Handwritten Mathematical Expression Recognition (HMER) task is a criticalbranch in the field of OCR. Recent studies have demonstrated that incorporatingbidirectional context information significantly improves the performance ofHMER models. However, existing methods fail to effectively utilizebidirectional context information during the inference stage. Furthermore,current bidirectional training methods are primarily designed for stringdecoders and cannot adequately generalize to tree decoders, which offersuperior generalization capabilities and structural analysis capacity. In orderto overcome these limitations, we propose the Mirror-Flipped Symbol Layout Tree(MF-SLT) and Bidirectional Asynchronous Training (BAT) structure. Our methodextends the bidirectional training strategy to the tree decoder, allowing formore effective training by leveraging bidirectional information. Additionally,we analyze the impact of the visual and linguistic perception of the HMER modelseparately and introduce the Shared Language Modeling (SLM) mechanism. Throughthe SLM, we enhance the model's robustness and generalization when dealing withvisual ambiguity, particularly in scenarios with abundant training data. Ourapproach has been validated through extensive experiments, demonstrating itsability to achieve new state-of-the-art results on the CROHME 2014, 2016, and2019 datasets, as well as the HME100K dataset. The code used in our experimentswill be publicly available.

Bidirectional Trained Tree-Structured Decoder for Handwritten Mathematical Expression Recognition