  Language generation based on maximum likelihood estimation (MLE) has become
the fundamental approach for text generation. Maximum likelihood estimation is
typically performed by minimizing the log-likelihood loss, also known as the
logarithmic score in statistical decision theory. The logarithmic score is
strictly proper in the sense that it encourages honest forecasts, where the
expected score is maximized only when the model reports true probabilities.
Although many strictly proper scoring rules exist, the logarithmic score is the
only local scoring rule among them that depends exclusively on the probability
of the observed sample, making it capable of handling the exponentially large
sample space of natural text. In this work, we propose a straightforward
strategy for adapting scoring rules to language generation, allowing for
language modeling with any non-local scoring rules. Leveraging this strategy,
we train language generation models using two classic strictly proper scoring
rules, the Brier score and the Spherical score, as alternatives to the
logarithmic score. Experimental results indicate that simply substituting the
loss function, without adjusting other hyperparameters, can yield substantial
improvements in model's generation capabilities. Moreover, these improvements
can scale up to large language models (LLMs) such as LLaMA-7B and LLaMA-13B.
Source code: \url{https://github.com/shaochenze/ScoringRulesLM}.
