## 2 Related Work
### Research Difficulties
[PERSON] designed an n-best re-scoring non-autoregressive decoding method, where the n-best results from CTC decoding are fed into an attention mechanism for weighted rescoring [40]. This approach ensures accurate decoding results while accelerating the process. However, this method may encounter issues with redundant results in the n-best list, leading to wasted computational resources and affecting the overall efficiency of recognition. Some researchers have aimed to balance both speed and accuracy. [PERSON] et al. proposed an end-to-end approach that combines deep learning with Markov models and incorporates a CTC/attention network [41]. This method was applied to Uzbek speech recognition, where it improved recognition accuracy while reducing training time. However, in the decoding phase, they used a greedy algorithm, which, while effective at selecting the highest probability letter at each step, makes decisions based on local information alone, ignoring global constraints. As a result, this approach often struggles to find the global optimal solution. [PERSON] et al. designed a new network called ESAformer, which integrates a recurrent gated convolutional self-attention mechanism within the Transformer encoder layers [42]. This structure captures multi-order feature interactions while extracting global features, leading to improved recognition accuracy as validated on the Aishell-1, HKUST, and WSJ datasets. [PERSON] et al. introduced innovations to the Conformer model structure, proposing a new model named Zipformer. This model employs a U-net-like structure in the encoding part, designs additional modules to improve the efficiency of calculating attention weights, utilizes a new normalization method called BiasNorm, and introduces new activation functions, SwooshR and SwooshL [43].The model achieved excellent recognition results on the LibriSpeech, Aishell-1, and WenetSpeech datasets, demonstrating the feasibility of their approach. [PERSON] et al. approached the problem from a different angle, classifying models based on their autoregressive nature. They then deeply integrated autoregressive and non-autoregressive models, combining the high recognition accuracy of one with the efficiency of the other [44]. This approach was validated on the Aishell-1 and Librispeech-960 h English databases, yielding promising experimental results. [PERSON] [45] designed a new model structure that integrates an acoustic encoder (wav2 vec2.0) with a pre-trained language encoder (BERT) into an end-to-end ASR model. This model was tested on the CALLHOME corpus and demonstrated superior recognition performance compared to other end-to-end models. [PERSON] et al. proposed an innovative approach that optimizes the decoding process using a continuous wavelet vocoder. By introducing a more efficient speech representation model, this method reduces computational complexity and offers a new perspective on balancing decoding speed and accuracy [6]. While this approach is primarily applied to speech synthesis, its principles provide valuable insights for optimizing the decoding process in continuous speech recognition, particularly in improving decoding efficiency. The method demonstrates considerable potential in real-time applications, especially in scenarios with high demands for both decoding speed and recognition accuracy. However, whether it can fully address the current challenges in decoding efficiency requires further research and validation. Despite significant advancements in the accuracy and efficiency of speech recognition models, challenges remain in the decoding stage, with relatively few innovative studies addressing this issue. Traditional decoding methods, such as beam search, are computationally intensive, thereby affecting decoding speed. Although some recent algorithms have made progress in improving either speed or accuracy, achieving a balance between the two remains a formidable challenge.