Generative Spoken Language Modeling (GSLM) enables text-free speech modeling by training language models (LMs) using discrete speech representations instead of textual transcription. In this paper, we investigate the performance of GSLM on speech synthesis and continuation using discrete speech representations with varying bitrates. We segment speech representations with fixed widths and train K-means models in multiple cluster sizes, resulting in various bitrate settings. We demonstrate that intelligible and natural speech can be synthesized at lower bitrate settings than the baseline. Furthermore, speech continuation quality remains stable at lower bitrates across multiple metrics, suggesting that the conventional GSLM setting may be redundant for effective speech generation. Although LLM-based metrics show higher correlation with human subjective score than conventional metrics, it remains low, highlighting the need for more stable automatic evaluation methods.
Optimal Transport has become recently a powerful method for domain adaptation by aligning source and target distributions. We study a supervised domain adaptation problem where source and target domains are related by a rotation or a translation or a homothety in $\mathbb{R}^2$. We prove that the optimal transport map recovers the underlying map when using a $p-$norm cost with $p \geq 2$. Based on this insight, we develop a method combining $K-$means and optimal transport to estimate the underlying map, enabling adaptation of linear regression models when target data is scarce. Simulations demonstrate improved performance over baseline methods. Rather than relying on highly expressive deep learning architectures, we focus on classical machine learning models to emphasize interpretability and theoretical insight. This perspective allows us to explicitly characterize the role of optimal transport in recovering geometric transformations such as rotations, translations, and homotheties. Our contributions include a theoretical result linking optimal transport and rotations, translations and homothecies in $\mathbb{R}^2$, and a practical method for adaptation in linear regression offering both conceptual clarity and applied value in domain adaptation tasks in this space.