MathBridge: A Large Corpus Dataset for Translating Spoken Mathematical Expressions into $LaTeX$ Formulas for Improved Readability

Understanding sentences that contain mathematical expressions in text form poses significant challenges. To address this, the importance of converting these expressions into a compiled formula is highlighted. For instance, the expression ``x equals minus b plus or minus the square root of b squared minus four a c, all over two a'' from automatic speech recognition (ASR) is more readily comprehensible when displayed as a compiled formula $x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$. To develop a text-to-formula conversion system, we can break down the process into text-to-LaTeX and LaTeX-to-formula conversions, with the latter managed by various existing LaTeX engines. However, the former approach has been notably hindered by the severe scarcity of text-to-LaTeX paired data, which presents a significant challenge in this field. In this context, we introduce MathBridge, the first extensive dataset for translating mathematical spoken expressions into LaTeX, to establish a robust baseline for future research on text-to-LaTeX translation. MathBridge comprises approximately 23 million LaTeX formulas paired with the corresponding spoken English expressions. Through comprehensive evaluations, including fine-tuning and testing with data, we discovered that MathBridge significantly enhances the capabilities of pretrained language models for text-to-LaTeX translation. Specifically, for the T5-large model, the sacreBLEU score increased from 4.77 to 46.8, demonstrating substantial enhancement. Our findings indicate the need for a new metric, specifically for text-to-LaTeX conversion evaluations.

Mathematical Vocoder Algorithm : Modified Spectral Inversion for Efficient Neural Speech Synthesis

In this work, we propose a new mathematical vocoder algorithm(modified spectral inversion) that generates a waveform from acoustic features without phase estimation. The main benefit of using our proposed method is that it excludes the training stage of the neural vocoder from the end-to-end speech synthesis model. Our implementation can synthesize high fidelity speech at approximately 20 Mhz on CPU and 59.6MHz on GPU. This is 909 and 2,702 times faster compared to real-time. Since the proposed methodology is not a data-driven method, it is applicable to unseen voices and multiple languages without any additional work. The proposed method is expected to adapt for researching on neural network models capable of synthesizing speech at the studio recording level.