Latent Ordinal Evidence, Misaligned Outputs: Inference-Time Ordinal Lens Alignment for Multimodal LLMs

Multimodal LLMs apply the language model interface to visual inputs, where ordinal regression tasks such as age estimation, image quality assessment, and disease grading require autoregressive decisions over ordered class labels. We ask whether MLLMs reliably convert internal ordinal evidence into ordered digit-token outputs. Across four ordinal benchmarks and four MLLM backbones, ordinal labels are linearly recoverable from hidden states with Spearman correlation up to 0.938, and a task-designed prompt further sharpens this structure. Yet native digit-token outputs weakly expose it: the unembedding matrix filters the ordinal direction, and the digit-token row space retains below 1.15% across all 16 model-dataset combinations, with a 16 to 77 absolute-point accuracy gap between linear-probe and native outputs. We introduce Ordinal Lens Alignment (OLA), a frozen-backbone inference-time method that trains lightweight W_S-anchored lenses on mid-to-deep decoder layers, fuses them into an ordinal distribution, and corrects only digit-token logits at generation. OLA outperforms the SOTA LoRA-tuned OrderChain baseline in most settings while keeping the MLLM frozen, surpasses discriminative ordinal baselines in most cells, and improves over an offline lens in every setting.

Few-Shot Ordinal Learning for Day-Wise Freshness Estimation with Hyperspectral Fish Images

Non-destructive food quality assessment has increasingly benefited from hyperspectral imaging (HSI), which captures spectral signatures linked to biochemical changes during storage. Estimating day-wise freshness, however, remains challenging owing to strong inter-fillet variability and scarce labelled data per product. All existing deep learning approaches for HSI-based freshness prediction operate under full supervision, requiring densely annotated training sets that are costly to obtain at the individual-product level. We introduce, to the best of our knowledge, the first few-shot learning framework for HSI-based food quality estimation. Each fillet defines a distinct episodic task, and a CORAL-style ordinal prediction head captures the ranked nature of freshness progression through cumulative threshold modelling. Biologically grounded monotonicity and embedding smoothness constraints further guide predictions toward plausible trajectories. On a 16-day salmon HSI dataset under a strict unseen-fillet protocol, our method achieves a mean absolute error of 1.58 days and 2-day accuracy of 72.3% with only three labelled days per fillet, substantially outperforming scalar regression and label-distribution baselines under an identical unseen-fillet protocol.

Unimodality-Promoting Regularized Learning for Ordinal Regression

Ordinal regression, also called ordinal classification, is classification of ordinal data, in which the underlying target variable is categorical and considered to have a natural ordinal relation. Previous works have indicated that, in many real-world ordinal data, the conditional probability distribution (CPD) of the target variable given a value of the explanatory variable would be unimodal in a large domain of the explanatory variable and close to be unimodal even in a remaining domain. Therefore, unimodality-promoting regularized learning (UPRL), which promotes a predicted CPD closer to be unimodal with the aim of decreasing a prediction variance without inducing much bias for ordinal data of the unimodality, is promising to improve the prediction performance especially with small-size training data. In this study, we show that previous UPRL methods promote a predicted CPD to not only become closer to be unimodal but also have a larger scale (in other words, be smoother or less-confident). Therefore, we develop a novel method that more strictly reflects the idea of UPRL and evades a scale-related bias, and verify through experimental comparison that the unimodality-promotion indeed contributes to improve the prediction performance. Additionally, while our proposed UPRL method could perform better for smaller-scale data or with larger-size training data compared to a previous UPRL method, our analysis explains this experimental observation in terms of the presence or absence of an unexpected scale-related bias.

D3O: Dynamic Distribution Distillation for Ordinal Regression

Ordinal regression is widely used in scenarios where labels are discrete yet inherently ordered. In practice, however, ordinal labels are often obtained by discretizing underlying continuous semantics through subjective human judgment, resulting in ambiguous boundaries and annotation noise. Such uncertainty challenges existing methods that rely on fixed supervision targets, which may reinforce biased ordering under subjective annotations. To address this limitation, we propose D3O, a dynamic distribution distillation framework that replaces static supervision with training-driven evolution of ordinal label distributions via self-distillation. Specifically, we introduce a contrastive ordinal-aware label enhancement module that leverages vision-language alignment to recover refined label distributions capturing both inter-class ambiguity and instance-level uncertainty. Furthermore, we design a CDF-based cross-layer interaction distillation mechanism to propagate cumulative ordinal structure across network hierarchy, ensuring consistent ordinal geometry in intermediate representations. Extensive experiments on four general ordinal regression tasks demonstrate that our proposed D3O consistently outperforms existing approaches, particularly under severe class imbalance and noisy supervision. These results highlight the effectiveness of dynamic supervision in learning robust ordinal representations beyond fixed targets. The code will be publicly available.

Application of machine learning to monster level prediction in tabletop RPG game design

Designing balanced adversaries is a central but labor-intensive task in tabletop role-playing game (TTRPG) development. In systems such as Pathfinder, each monster is described by many numerical attributes that jointly determine its power, summarized as an ordinal level. We investigate whether machine learning can support designers by predicting this level from a monster's attributes, framing the task as tabular ordinal regression. We introduce what is, to our knowledge, the first dataset built specifically for TTRPG monster-level prediction, derived from publicly available Pathfinder Second Edition data. Using it, we compare classical regression models with rounding schemes, dedicated tabular ordinal regression algorithms, and neural networks with ordinal-aware losses. To mirror real design workflows, we evaluate all models under chronological and expanding-window protocols with several complementary metrics. Results show that tree-based ensembles outperform linear models and neural approaches, achieving near-perfect ordinal ranking and high predictive accuracy. Explainable AI analyses, such as feature importance and error distributions, show that the model is aligned with human intuition and follows patterns grounded in game rules. Together, these results show that machine learning can reliably approximate designer judgments and serve as an effective computer-aided tool for monster balancing and broader TTRPG system design.

Contrastive Order Learning: A General Framework for Ordinal Regression

We propose contrastive order learning (ConOrd), a contrastive learning framework for ordinal regression that integrates the strengths of contrastive learning and order learning. While contrastive learning effectively leverages all samples in a batch, it typically ignores the inherent ordering among rank labels. Conversely, order learning explicitly models label ordinality but often relies on local, margin-based comparisons, limiting its ability to capture global ordinal structure. ConOrd addresses these limitations by introducing a contrastive order loss with soft affinity and disparity weights based on rank differences, enabling fine-grained modeling of ordinal relationships across all sample pairs within a batch. Extensive experiments on a range of ordinal regression tasks, including facial age estimation, blind image quality assessment, and blind video quality assessment, demonstrate that ConOrd consistently achieves state-of-the-art performance and generalizes well across diverse ordinal regression scenarios. The source code is available at https://github.com/cwlee00/ConOrd.

Stochastic Order Learning: An Approach to Rank Estimation Using Noisy Data

Rank estimation under label noise poses a fundamental challenge, as ordinal annotations often exhibit structured uncertainty rather than simple label corruption. In this paper, we reformulate rank estimation with noisy ordinal labels as a stochastic ordering problem, in which each instance is inherently associated with multiple plausible ranks instead of a single deterministic label. Based on this view, we propose stochastic order learning (SOL), a learning framework that captures ordinal label uncertainty and learns an embedding space through two complementary objectives: a discriminative loss that structures instance--centroid interactions and a stochastic order loss that enforces probabilistic ordering relations between instances. Extensive experiments across diverse datasets demonstrate that SOL enables reliable rank estimation under various types and levels of label noise. The source code is available at https://github.com/cwlee00/SOL.

Be Indiscrete: The Benefits of Learning Continuous Spine Degeneration Severity Scores

Lumbar spine degeneration is a major contributor to chronic low back pain and is routinely assessed on MRI using ordinal grading systems, e.g. normal, mild, moderate, severe. Consequently, most approaches to train models to grade these MRIs formulate grading as a multi-class classification problem, treating ordinal grades as categorical, ignoring differences in misclassification severity, and imposing hard decision boundaries on a continuous disease process. This work explores modeling spinal degeneration as a continuous severity ranking problem. We introduce SpineRankNet, a framework that learns scalar severity scores from lumbar spinal MRI, and compare it against multi-class classification and ordinal regression. Using multiple degeneration measures from the Genodisc dataset, we show that a model trained using a ranking loss to produce a continuous score enables fine-grained ordering of MRI scans. Furthermore, the ordinal grading classes can be recovered from the score with comparable accuracy to those from a model trained directly for classification. The score learned by ranking even improves discrimination between more distant classes. Source code is available at https://github.com/spinetools/spineranknet.

Rank-Then-Act: Reward-Free Control from Frame-Order Progress

We introduce Rank-Then-Act (RTA), a framework for learning control policies from expert video demonstrations without environment rewards. RTA trains a Vision-Language Model (VLM) offline as a progress-based ordinal scorer, using a Group Relative Policy Optimization (GRPO) objective over shuffled frame sequences, which forces the model to recover temporal ordering from visual semantics rather than trivial time cues. Importantly, instead of using the scorer directly as a scalar reward model, we propose a correlation-based reward function for reinforcement learning: at each interaction window, we compute the Spearman rank correlation between predicted progress rankings and true temporal indices, yielding a bounded, scale-invariant learning signal. This design decouples reward learning from absolute calibration and enables stable transfer across tasks and environments. We evaluate RTA on discrete control benchmarks (PyBoy: Catrap, Kirby) and continuous control tasks (PointMaze, MetaWorld). RTA consistently matches or outperforms prior video-based reward learning methods and rank-based baselines, while demonstrating strong cross-task reuse of a single pretrained progress scorer. Our results suggest that correlation-structured supervision over video-derived ordinal signals is sufficient for policy learning, offering a scalable alternative to explicit reward design.

LOPA: Enhancing Spoken Language Assessment via Latent Ordinal Prototype Alignment

Fueled by increasing model scale and multimodal inputs, Multimodal Large Language Models (MLLMs) have emerged as a promising paradigm for Spoken Language Assessment (SLA). While effective, this paradigm often overlooks the intrinsic ordinal structure of language acquisition. This paper works around the necessity of large-scale MLLMs by introducing Latent Ordinal Prototype Alignment (LOPA) for SLA, a prototype-based regularizer that enforces an ordinal geometric prior directly on the latent space. Coupled with Semantic-Anchored Layer Routing (SALR), which adaptively harvests multi-depth representations from a frozen Whisper encoder, our framework achieves an RMSE of 0.361. This performance rivals billion-parameter systems without the need for LLM-based fine-tuning. Further analysis reveals that SALR's synergy with LOPA offers interpretable, criterion-aligned preferences, thereby supporting an efficient and ordinal-aware modeling alternative to current scaling-centric models for SLA.

Deep Neural Networks with Ordinal Loss for Medical Applications

In many prediction problems in medical applications, target labels exhibit an inherent ordinal structure, where class ordering reflects clinically meaningful severity levels. The cost associated with misclassification is often non-uniform and asymmetric, as errors between distant ordinal categories may have substantially more severe consequences than errors between adjacent ones, and overestimating disease severity may have different clinical implications than underestimating it. Traditional loss functions such as multi-class cross-entropy treat all misclassifications equally and fail to incorporate this ordering information. Recent advances in ordinal regression aim to address this limitation by integrating rank-based structures into deep learning models. In this work, we introduce the \textbf{Ordinal Cross-Entropy (OCE)} framework, a general and architecture-independent approach for learning from ordinal data. The proposed method extends the standard cross-entropy formulation to account for misclassification severity through an ordinal cost matrix while preserving the probabilistic interpretation and optimization benefits of the conventional loss. We provide a theoretical analysis of the OCE gradient behavior and show that it yields smoother optimization dynamics and improved ordinal consistency. Experiments on benchmark datasets show that our method achieves lower prediction error costs and better calibration compared to existing state-of-the-art ordinal approaches, establishing OCE as a simple yet effective solution for ordinal regression in deep neural networks.

Multimodal Ordinal Modeling of Alzheimer's Disease Severity Using Structural MRI and Clinical Data

Neurodegenerative diseases such as Alzheimer's disease (AD) require accurate and scalable tools for assessing disease severity, yet current clinical staging remains time-intensive and prone to variability. We propose an attention-enhanced multimodal machine learning framework with ordinal regression for automated and interpretable AD severity staging. The framework integrates T1-weighted MRI with demographic and genetic variables and compares unimodal and multimodal architectures using ordinal and non-ordinal prediction heads. Models were trained and validated using cohort-stratified splits derived from the ADNI, AIBL, and NIFD datasets. A strictly held-out test set was constructed using subjects excluded from all training, validation, preprocessing, and hyperparameter tuning procedures, with subject-level splitting employed throughout to prevent data leakage. Among unimodal approaches, the T1-weighted MRI model achieved slightly higher adjacent-stage accuracy (0.963) and agreement with clinical staging (QWK 0.444) than the tabular model (QWK 0.433). Integrating imaging, demographic, and genetic information improved overall performance. The multimodal non-ordinal baseline achieved the lowest prediction error (MAE 0.340), whereas the ordinal multimodal model achieved the highest adjacent-stage accuracy (0.970) and strongest agreement with clinical staging (QWK 0.549). These findings indicate that ordinal formulations better capture the ordered structure of the CDR scale and yield predictions more consistent with clinical staging. Explainability analyses using Grad CAM++ and SHAP demonstrated anatomically and clinically plausible model behavior, supporting transparent decision-making. Overall, attention-based multimodal learning with ordinal regression represents a robust, interpretable, and scalable approach for automated AD severity staging and AI-assisted clinical decision support.