  Recent studies have found that model performance has a smooth power-law
relationship, or scaling laws, with training data and model size, for a wide
range of problems. These scaling laws allow one to choose nearly optimal data
and model sizes. We study whether this scaling property is also applicable to
second-pass rescoring, which is an important component of speech recognition
systems. We focus on RescoreBERT as the rescoring model, which uses a
pre-trained Transformer-based architecture fined tuned with an ASR
discriminative loss. Using such a rescoring model, we show that the word error
rate (WER) follows a scaling law for over two orders of magnitude as training
data and model size increase. In addition, it is found that a pre-trained model
would require less data than a randomly initialized model of the same size,
representing effective data transferred from pre-training step. This effective
data transferred is found to also follow a scaling law with the data and model
size.
