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GoR: A Unified and Extensible Generative Framework for Ordinal Regression

ICLR 2026 Conference SubmissionAnonymous Authors
OpenReview Score: 6.5Download Report PDF
Ordinal RegressionGenerative RegressionVocabulary 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 Generative Ordinal Regression (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 Coverage–Distinctiveness 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.

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This report is AI-GENERATED using Large Language Models and WisPaper (A scholar search engine). It analyzes academic papers' tasks and contributions against retrieved prior work. While this system identifies POTENTIAL overlaps and novel directions, ITS COVERAGE IS NOT EXHAUSTIVE AND JUDGMENTS ARE APPROXIMATE. These results are intended to assist human reviewers and SHOULD NOT be relied upon as a definitive verdict on novelty.
NOTE that some papers exist in multiple, slightly different versions (e.g., with different titles or URLs). The system may retrieve several versions of the same underlying work. The current automated pipeline does not reliably align or distinguish these cases, so human reviewers will need to disambiguate them manually.
If you have any questions, please contact: mingzhang23@m.fudan.edu.cn

Overview

Overall Novelty Assessment

The paper proposes Generative Ordinal Regression (GoR), which reframes ordinal regression as an autoregressive sequence generation task, predicting ordinal segments until a dynamic end-of-sequence token. This work resides in the 'Generative and Autoregressive Ordinal Models' leaf, which contains only three papers total including the original. The leaf sits within a broader taxonomy of 50 papers across ordinal regression methodologies, indicating this generative paradigm represents a relatively sparse but emerging research direction compared to more established threshold-based or discriminative approaches.

The taxonomy reveals that GoR's immediate neighbors include Ord2Seq, which also treats ordinal labels as sequences, and diffusion-based generative methods for medical imaging. The broader parent branch encompasses discriminative models with ordinal constraints, loss function design, and ranking-based approaches—each containing two to three papers. Adjacent branches cover parametric statistical models (proportional odds, probit) with eight papers and tree-based methods with three papers, suggesting the field remains anchored in classical threshold models while generative formulations represent a newer, less crowded frontier.

Among nine candidates examined through limited semantic search, none clearly refute the three main contributions. The GoR framework itself was compared against three candidates with no overlapping prior work identified. The Coverage–Distinctiveness Index (CoDi) for vocabulary construction examined four candidates without finding refutation. The theoretical MSE error bound analysis reviewed two candidates, again with no clear precedent. This suggests the specific combination of autoregressive generation, adaptive resolution, and principled vocabulary metrics may be novel within the examined scope, though the search scale remains modest.

The analysis reflects a constrained literature search rather than exhaustive coverage, examining fewer than ten semantically similar papers. While the generative autoregressive approach appears distinctive within this limited sample and the sparse taxonomy leaf, the field's broader structure shows active development in adjacent discriminative and loss-based methods. The work's novelty appears strongest in its specific generative formulation and vocabulary construction metric, though comprehensive assessment would require examining additional candidates beyond the top-K semantic matches.

Taxonomy

Core-task Taxonomy Papers
50
3
Claimed Contributions
9
Contribution Candidate Papers Compared
0
Refutable Paper

Research Landscape Overview

Core task: predicting ordinal values with inherent order relationships. The field organizes around several complementary perspectives. Ordinal Regression Methodologies and Theoretical Foundations encompasses core algorithms, loss functions, and generative or autoregressive formulations that respect rank structure, as seen in works like GoR Ordinal Regression[0] and Ord2Seq[23]. Domain-Specific Applications of Ordinal Prediction translate these methods into areas such as medical diagnosis (Forecasting Schizophrenia States[3], Diffusion Diabetic Retinopathy[8]) and infrastructure assessment. Data Representation and Encoding for Ordinal Tasks addresses how to embed or transform ordinal labels—ranging from soft-label schemes (Soft Labels Ordinal[33]) to vision-language approaches (OrdinalCLIP[7])—while Multivariate and Multi-Attribute Ordinal Modeling tackles settings with multiple interacting ordinal outcomes. Finally, Ordinal Prediction with Auxiliary Information explores leveraging side data or uncertainty estimates (Uncertainty Ordinal Classification[9]) to improve predictions. Within the methodological core, a key tension emerges between threshold-based models rooted in classical cumulative-link ideas (Ordinal Regression Survey[2], Ordinal Data Regression[31]) and newer generative or sequence-based paradigms that treat ordinal prediction as a structured generation problem. GoR Ordinal Regression[0] sits squarely in the latter camp, proposing a generative autoregressive framework that contrasts with traditional threshold approaches and aligns closely with Ord2Seq[23], which also frames ordinal labels as sequences. Nearby works like Diffusion Diabetic Retinopathy[8] explore diffusion-based generative strategies for ordinal medical imaging, highlighting a broader shift toward probabilistic generation. Meanwhile, methods emphasizing explainability (Explainable Distance Ordinal[4]) or robust loss design (SLACE Monotone Loss[22]) offer alternative angles on enforcing ordinality. The original paper thus contributes to an active line of research reimagining ordinal regression through generative modeling, offering a fresh perspective on capturing rank dependencies beyond classical cumulative models.

Claimed Contributions

Generative Ordinal Regression (GoR) framework

The authors introduce GoR, a framework that reformulates ordinal regression as an autoregressive sequence generation task. The model predicts ordinal value segments as tokens until generating a dynamic end-of-sequence token, explicitly capturing ordinal dependencies while enabling adaptive resolution and interpretable step-wise refinement.

3 retrieved papers
Coverage–Distinctiveness Index (CoDi) for vocabulary construction

The authors develop CoDi, a metric that guides vocabulary design by balancing coverage (minimizing quantization bias) and distinctiveness (reducing statistical variance). This metric is grounded in a theoretical bias-variance decomposition that establishes a closed-form MSE error bound for the generative ordinal regression task.

4 retrieved papers
Theoretical analysis of rank-based methods and MSE error bound

The authors provide a theoretical characterization of the limitations of rank-based continuous space discretization methods through conditional independence analysis. They also derive an MSE error bound via bias-variance decomposition that quantifies the trade-off between token selection, sequence length, and prediction accuracy.

2 retrieved papers

Core Task Comparisons

Comparisons with papers in the same taxonomy category

Contribution Analysis

Detailed comparisons for each claimed contribution

Contribution

Generative Ordinal Regression (GoR) framework

The authors introduce GoR, a framework that reformulates ordinal regression as an autoregressive sequence generation task. The model predicts ordinal value segments as tokens until generating a dynamic end-of-sequence token, explicitly capturing ordinal dependencies while enabling adaptive resolution and interpretable step-wise refinement.

Contribution

Coverage–Distinctiveness Index (CoDi) for vocabulary construction

The authors develop CoDi, a metric that guides vocabulary design by balancing coverage (minimizing quantization bias) and distinctiveness (reducing statistical variance). This metric is grounded in a theoretical bias-variance decomposition that establishes a closed-form MSE error bound for the generative ordinal regression task.

Contribution

Theoretical analysis of rank-based methods and MSE error bound

The authors provide a theoretical characterization of the limitations of rank-based continuous space discretization methods through conditional independence analysis. They also derive an MSE error bound via bias-variance decomposition that quantifies the trade-off between token selection, sequence length, and prediction accuracy.

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