Tasks are central in machine learning, as they are the most natural objects to assess the capabilities of current models. The trend is to build general models able to address any task. Even though transfer learning and multitask learning try to leverage the underlying task space, no well-founded tools are available to study its structure. This study proposes a theoretically grounded setup to define the notion of task and to compute the inclusion between two tasks from a statistical deficiency point of view. We propose a tractable proxy as information sufficiency to estimate the degree of inclusion between tasks, show its soundness on synthetic data, and use it to reconstruct empirically the classic NLP pipeline.

Assessing the quality of summarizers poses significant challenges—gold summaries are hard to obtain and their suitability depends on the use context of the summarization system. Who is the user of the system, and what do they intend to do with the summary? In response, we propose a novel task-oriented evaluation approach that assesses summarizers based on their capacity to produce summaries while preserving task outcomes. We theoretically establish both a lower and upper bound on the expected error rate of these tasks, which depends on the mutual information between source texts and generated summaries. We introduce COSMIC, a practical implementation of this metric, and demonstrate its strong correlation with human judgment-based metrics, as well as its effectiveness in predicting downstream task performance. Comparative analyses against established metrics like BERTScore and ROUGE highlight the competitive performance of COSMIC.