## 2 Related Work
### Research Difficulties
[PERSON] [35], analyzing the deep learning optimization problem from a probabilistic perspective, pointed out that the size of mini-batches can influence the range of parameter exploration, thereby affecting the model's ability to avoid local minima. Although these new perspectives and methods offer some advancements, their optimization effects in practical applications are still less than ideal, especially when dealing with high-dimensional data and complex models, where the issue of local optima persists. This suggests that, while technological advancements have simplified and enhanced the architecture of speech recognition models, particularly through the use of end-to-end approaches that streamline the training and computation processes, these models' inherent reliance on neural networks gives rise to certain challenges. Specifically, during training, issues such as overfitting and convergence to local optima can arise, leading to poor generalization to unseen data and limited robustness in real-world applications. These limitations, in turn, hinder the broader adoption and effectiveness of speech recognition technology. In recent years, many scholars have focused more on improving model architectures or innovating within specific application domains. As a result, the decoding process often relies on existing algorithms with little modification, leading to relatively few studies on decoding algorithm innovations. However, decoding remains a crucial part of speech recognition, as it is primarily responsible for converting the output of the acoustic model into text. Some researchers have recently dedicated efforts to designing new algorithms to enhance decoding speed or accuracy, thereby improving the search efficiency of decoders. Regarding speed improvements, the Viterbi algorithm is a dynamic programming algorithm that can perform space-synchronous operations and search space pruning [36]. It is widely used in speech recognition to find the optimal state sequence in Markov models. However, in the context of high-dimensional data and complex models--especially in modern speech recognition scenarios that demand intricate models and deep learning techniques--the Viterbi algorithm can lead to high computational complexity, making it difficult to adapt to current application environments and methodologies. On the other hand, the asynchronous A* search algorithm is a novel heuristic approach that speeds up the process of finding the shortest path by parallel processing and avoiding the need to wait for all branches to fully expand [37]. This method can accelerate decoding to some extent, but it may encounter issues of uneven load distribution in practical applications, where some processing nodes become overloaded while others remain idle, ultimately affecting recognition accuracy. In terms of accuracy improvements, [PERSON] et al. explored the impact of different beam widths on decoding performance, discovering that a larger beam width leads to more accurate recognition at the cost of increased computational demands [38]. They also introduced a language model during the decoding phase, which further improved recognition accuracy. However, the computational cost of beam search grows exponentially with increasing beam width, significantly slowing down the decoding process. Additionally, incorporating a language model requires extra training and tuning, adding to the system's complexity and making it challenging to implement in practical production environments. [PERSON] directly utilized the CTC (connectionist temporal classification) decoding function from the Keras backend, applying the best path method for decoding to enhance model recognition accuracy [39]. While CTC decoding performs well in handling variable-length inputs and outputs, it assumes that each label in the output sequence is independent, ignoring contextual information. This limitation can reduce its effectiveness in recognizing long sentences or conversations with complex contextual relationships.