Title: GoR: A Unified and Extensible Generative Framework for Ordinal Regression
Primary area: generative models
Keywords: Ordinal Regression, Generative Regression, Vocabulary Design

Abstract: Ordinal Regression (OR), which predicts the target values with inherent order, underpins a wide spectrum of applications from computer vision to recommendation systems. The intrinsic ordinal structure and non-stationary inter-class boundaries make OR fundamentally more challenging than conventional classification or regression. Existing approaches, predominantly based on Continuous Space Discretization (CSD), struggle to model these ordinal relationships, but are hampered by boundary ambiguity. Alternative rank-based methods, while effective, rely on implicit order dependencies and suffer from the rigidity of fixed binning.

Inspired by the advances of generative language models, we propose **G**enerative **O**rdinal **R**egression (**GoR**), a novel generative paradigm that reframes OR as a sequential generation task. GoR autoregressively predicts ordinal segments until a dynamic ⟨EOS⟩, explicitly capturing ordinal dependencies while enabling adaptive resolution and interpretable step-wise refinement. To support this process, we theoretically establish a bias–variance decomposed error bound and propose the **Co**verage–**Di**stinctiveness Index (**CoDi**), a principled metric for vocabulary construction that balances quantization bias against statistical variance. The GoR framework is model-agnostic, ensuring broad compatibility with arbitrary task-specific architectures. Moreover, it can be seamlessly integrated with established optimization strategies for generative models at a negligible adaptation cost. Extensive experiments on **17** diverse ordinal regression benchmarks across **six** major domains demonstrate GoR's powerful generalization and consistent superiority over state-of-the-art OR methods.