A new theoretical framework defines Bayes-sufficient representations in supervised learning, establishing what information is genuinely required for optimal predictions based on loss functions. The work formalizes the concept of Bayes quotients and minimal representations, connecting representation learning to property elicitation theory with experimental validation across synthetic and real datasets.
This research addresses a fundamental question in machine learning: what exactly constitutes 'relevant' information for prediction tasks. Rather than treating relevance as a vague concept, the authors introduce mathematical rigor by defining Bayes-sufficient representations as those enabling a prediction head to implement Bayes-optimal actions for a given loss function. This approach reveals that the required information is inherently loss-dependent, meaning different objective functions demand different representations of the same input data.
The framework connects representation learning to established theory in property elicitation, showing that various loss functions implicitly specify information requirements. Zero-one loss requires the Bayes class, squared loss requires conditional means, and log loss requires the full predictive distribution. This unification provides theoretical grounding for why practitioners choose specific loss functions—each encodes assumptions about what information matters.
The practical implications span multiple domains. In neural network design, understanding Bayes-minimal representations helps practitioners distinguish between information that contributes to optimal decisions versus extraneous features that inflate model complexity. The experiments—including learned neural bottleneck models and real-world iNaturalist taxonomic refinement—demonstrate measurable differences between sufficient, minimal, and over-parameterized representations.
The work has significance for model compression, transfer learning, and interpretability. By formally characterizing minimal sufficient representations, researchers can build more efficient models and better understand which features actually drive predictions. This theoretical clarity helps align model architecture with task requirements, potentially improving generalization and reducing computational overhead in production systems.
- →Bayes-sufficient representations are defined by loss functions, making information relevance mathematically precise rather than intuitive
- →Different loss functions require fundamentally different information structures, from class labels to full distributions
- →Bayes quotients identify which inputs require identical optimal actions, establishing a foundation for minimal representations
- →The framework unifies representation learning with property elicitation theory, connecting supervised learning to established mathematical principles
- →Experimental validation shows meaningful gaps between sufficient, minimal, and over-parameterized representations in practice