Despite being the best known objective for learning speech representations, the HuBERT objective has not been further developed and improved. We argue that it is the lack of an underlying principle that stalls the development, and, in this paper, we show that predictive coding under a variational view is the principle behind the HuBERT objective. Due to its generality, our formulation provides opportunities to improve parameterization and optimization, and we show two simple modifications that bring immediate improvements to the HuBERT objective. In addition, the predictive coding formulation has tight connections to various other objectives, such as APC, CPC, wav2vec, and BEST-RQ. Empirically, the improvement in pre-training brings significant improvements to four downstream tasks: phone classification, f0 tracking, speaker recognition, and automatic speech recognition, highlighting the importance of the predictive coding interpretation.

Recent speech language models rely on encoders that are optimized separately from autoregressive models. Since these encoders are unaware of the downstream objectives, the extracted representations may not be optimal for downstream tasks. To address this limitation, we introduce a discrete latent variable model on mel spectrograms that jointly optimizes the encoder and the speech language model. Joint optimization not only brings improvements over codec-based and other mel-spectrogram-based baselines on zero-shot Text-to-Speech (TTS) and Speech-to-Text (STT) tasks, but also effectively alleviates common issues in autoregressive mel spectrogram modeling, such as prolonged silence generation and word omissions. Samples are available at the [demo page](https://anonymous29300909.github.io/anonymous2930-demo/).