GoR: A Unified and Extensible Generative Framework for Ordinal Regression
Authors: Hongxu Ma
Han Zhou
Kai Tian
Xuefeng Zhang
Chunjie Chen
Han Li
Jihong Guan
Shuigeng Zhou
Venue: ICLR 2026 Poster (2026)
Keywords: Ordinal Regression
Generative Regression
Vocabulary Design
Primary area: generative models

Abstract: Ordinal Regression (OR), which predicts the target values with inherent order, underpins a wide spectrum of applications within diverse domains. 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.

Published as a conference paper at ICLR 2026
GoR: A UNIFIED AND EXTENSIBLE GENERATIVE FRAMEWORK FOR ORDINAL REGRESSION
Hongxu Ma Han Zhou** Kai Tian', Xuefeng Zhang?, Chunjie Chen', Han Li?, Jihong Guan', Shuigeng Zhou
1 Shanghai Key Lab of Intelligent Information Processing, and
College of Computer Science and Artificial Intelligence,
Fudan University, Shanghai, China
KKuaishou Technology. Beijing, China
SScoool of Computer Science and Technology.
Tongji University, Shanghai, China
"Shanghai University of Finance and Economics, Shanghai, China
ABSTRACT
Ordinal Regression (OR), which predicts the target values with inherent order, underpins wide spectrum of applications within diverse domains. The intrinsic ordinal structure and non-stationary inter-class boundaries make OR fundamen- tally 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 am- biguity. Alternative baskd 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), explic- itly capturing ordinal dependencies while enabling adaptive resolution and inter- pretable step-wise refinement. To support this process, we theoretically establish a bias-variance decomposed error bound and propose the Coverage Distinctiveness wwverage-Distiettvvenee
Index (CoDi), a principled metric for vocabulary construction that balances quan- tization 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 negligible adaptation cost. Extensive experiments on 15 diverse ordinal regression benchmarks across five major domains demonstrate GoR's powerful generalization and consistent superiority over SOTA OR methods. The code is available http::/ggitubbcccmom//mmm2222222
INTRODUCTION
Ordinal Regression (OR), also referred to as ordinal classification, addresses the prediction tasks where the target categories (or values) exhibit inherent ordinal relationships. As shown in Fig. (a), this paradigm has broad applications across various domains such as computer vision (e.g., facial age estimation (Niu al., 2016; Li al., 2022), image aesthetic assessment (She al., 2021; He et al., 2022)) and recommendation systems (e.g., watch time prediction (Sun et al., 2024; Zhao al., 2024), lifetime value prediction (Drachen et al., 2018: Ma et al., 2018)). Unlike conventional multi-class classification and continuous regression, the fundamental challenge in OR lies in explicitly modeling two critical properties: (1) the inherent ordinal structure among output labels, and (2) the non-stationary nature of semantic boundaries between adjacent categories.
Previous OR works have predominantly relied on Continuous Space Discretization (CSD) (Wang et al., 2025), illustrated in Fig. 1(b). This strategy quantizes the target output space, potentially continuous
Bott authors contributed equally this research. Work done during the internship at Kuaishou Technology. CCoresponding author: Shuigeng Zhou <sgzhou @ Sudan.edu..cm

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Contimuous Space
Facial Age Estimation
Order: From Young
(1) Instance Ambiguity
bing! (1.))
Fly May
Pr. Sing
Watch Time Prediction
Order From Short Lang
bia bis, Rank--base
Weighted Expectarion
(a)
(b)
(c)
Figure I: Overview of Universal Ordinal Regression. (a) Representative Ordinal Regression tasks with ordered labels. (b) The Continuous Space Discretization (CSD) workflow: discretizing continuous space into bins and using weighted expectation for prediction. (c) Two key research directions explored under the CSD framework.
or fine-graine grained ordinal, into finite set of ordered discrete bins. The model typically outputs a softmax probability distribution over these bins, mapped a prediction via probability bebbbbllty-weiigtedd expectation. Essentially, CSD simplifies learning by transforming the problem into a multi-class classification. Under this framework, subsequent research mainly explores two directions.
As shown in Fig. 1(c), one is to tackle ambiguous inter-class boundaries by enhancing discrimination of coundary-prxximee samples through reference comparisons (Li et al., 2021; Shin et al., 2022). However, its performance critically depends on efficient reference selection, which is often governed by unstable heuristics and limits the gains in wide-range scenarios where combinatorial reference points escalate selection complexity. Another is rank-based that implicitly encodes the ordinality via label transformation, reframing OR into sequential binary subtasks (Niu et al., 2016; Wang et al., 2023). Despite empirical success with theoretical guarantees (Chen et al., 2017), its order dependency resides solely in label definitions, leaving bin-wise predictions independent (See Proposition 1). Besides, the predefined discretization introduces rigidity: it amplifies head-category errors in long- tailed distributions, frequently seen in real-world tasks, and makes performance highly sensitive to bin gramularity wide intervals blur semantics, while narrow ones induce sparsity (Sun et al., 2024).
Inspired by the advances in generative language models (Liu et al.. 2024; Liu et al.; Wang et al., 2026), we propose Generative Ordinal Regression (GoR), novel framework that reformulates ordinal regression as sequential token generation. GoR autoregressively predicts tokens representing ordinal value segments, whose cumulative summation yields the final prediction upon generating the (EOS) token. This design explicitly models sequential ordinal dependencies through conditional generation while enabling adaptive resolution via dynamic (EOS) prediction, circumventing the rigidity of fixed binning. For instance, in facial age estimation, the model may first predict coarse token (50), then finer adjustments (+5, +3), culminating in the estimate (50+5+3=55 years). Each step progressively reduces prediction error by selecting tokens that provide an increasingly precise approximation. This step-wise refinement process mirrors human cognitive progression from coarse to precise estimation and implements successive approximation, offering interpretable intermediate predictions.
However, adapting this paradigm to general ordinal regression poses two key challenges. First, unlike purely compositional tokens in nature language process (NLP) tasks, GoR tokens uniquely encode dual semantics, i.e., sequential ordinality and additive numerical relationships, necessitating specialized mechanisms to disentangle and exploit these intertwined properties. Since numerical values are infinitely decomposable and combinable, vocabulary design demands principled strategies to balance expressiveness and efficiency. Second, domain heterogeneity in ordinal label distributions, spanning diverse value ranges (e.g., [o, 1] for quality scores vs. [0. 100] for age estimation) and label granularity types (discrete continuous), requires robust cross-domain generalization capabilities. Hence, effectively adapting the autoregression mechanism to universal OR tasks requires systematic vocabulary design and label decomposition strategies.
Through birs-neri decomposition, we derive a glosed-form Mean Squared Error (MSE) bound that quantifies token selection trade-off between quantization bias and statistical variance, pro- viding a theoretical foundation for vocabulary design. Building on this, we further propose the Coverage Distinctiveness Index (CoDi) to optimize token selection maximizing coverage (bias
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minimization) while suppressing common segments (variance reduction) yielding compact, recoverable vocabulary that enhances cross-task adaptability. Besides, as model-agnostic frame- work, GoR's core component, i... the encoder-decoder architecture, permits flexible substitution with task-specific implementations and can be seamlessly integrated with existing optimization strategies (Bengio al., 2009; Goodman al., 2020; Shao al., 2024) negligible adaptation cost, thereby ensuring its flexibility and extensibility for broader applications.
Our contributions are fourfold: (i) We expose the theoretical limitations of prevailing rank-based methods under the CSD paradigm and, in turn propose the first generative formulation of ordinal regression as an autoregressive sequence generation task. (ii) We introduce GoR, unified frame- work that models sequential ordinal dependencies via dynamic (EOS) JEOS)-terminn -terminated token generation, offering adaptive resolution and interpretable step-wise refinement. (iii) We establish a theoretical foundation based on MSE decomposition, accompanied by the Deverage-Distinctivin (CoDi) to optimize the token vocabulary by varsivar trade-off. (iv) We perform extensive experiments across 15 ordinal regression benchmarks spanning five domains, demonstrating GoR's strong generalization and consistent superiority over SOTA baselines.
Index
The remainder of this paper is organized follows. Section 2 formalizes the problem, theoretically analyzes uunk-based methods' limitation, and introduces the proposed GoR framework. including its error-bound formulation, vocabulary construction, ordinal target sequencing. and encoder-decodee design. Section 3 reports extensive experiments and analyses across diverse domains. Section concludes the paper. Due to space limit, provide related work review in Appendix. B.
METHOD
2.1
PROBLEM DEFINITION
We consider the ordinal regression problem on a dataset D {2 ((),,,;) where x; denotes an input instance from heterogeneous modalities (e.g., visual data or multimodal embeddings) and y: E R2o represents its associated ordinal label. While conventional methods aim to learn a direct mapping g(2,) ys, GoR reformulates this task sequence generation problem by establishing bijection between the continuous label space and a discrete token sequence space. Specifically, each label Yi is encoded into a variable-length sequence :; = { } of length T, where each token of is drawn from a predefined vocabulary = ( size V. To close the loop between the discrete and continuous spaces, a sequence scoring function r(-) is defined to reconstruct the numerical label via an additive lookup table Ω + R, such that augmented with control tokens {(SOS), (EOS), (PAD)) for parallel sequence processing; however, as these tokens carry null semantic value in the label space (v(w) 0), they are omitted from the formal mathematical derivations for clarity.
r(T,) Σ m(r²). In practice, 12 is
2.2 THEORETICAL ANALYSIS
Our theoretical analysis consists of two parts: characterizing the limitation of rank-based CSD approaches, and establishing GoR's 's theoretical foundation via MSE decomposition, which derives closed-form MSE bound to guide vocabulary design.
Limitation of rank-based methods.
Assumption 1. Define a sequence of binary random variables BTTh = 1(y: Cm). where 1(-) denotes the indicator function and Cm is the right boundary of the m--th interval. Then B, [ BM3 constitutes a set of mon-mutullly exclusive binary decisions that together describe the position of yt. Rank-based methods approximate the true conditional distribution Preee (B;
x; m==1 m B <m xx) ) by assuming conditional independence across all binary decisions:
P
B x.) m== P(B." [x;) Based on this factorization, the final prediction is obtained as
M ΣM= P(B. = 1). (cm- Cm-1)-
0:
Building on this conditional independence assumption, we quantify the resulting approximation error:
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where Published as a conference paper at ICLR 2026
Prodictol S4
sum
Compuser Vision Related Tasks
hiáden repecacation
lngretic soone
logistic score
logistic seare
Aagidie soure
inlel
FFN
Recommnte dation
Model-agnostic Decoder
Reboed
Tosks
Task-speeifie Encoder
Vocabulary
Ordinal Target Sequencing
Figure 2: The framework of our proposed Generative Ordinal Regression (GoR), which adopts a flexible encoder-decoder architecture with the model-agnostic nature of both the encoder and decoder.
Proposition (Independence Limitation in Rank-based CSD methods).
M Σ [D
DKL (Bi PPoii xx))
E
EBS
(m) KtL
m=
where (m) KL measures the divergence between P Th x.) and P(B,") B B,r x.).
The complete derivations are provided in Appendix C. Proposition reveals that naive discretization exhibits systematic modeling errors stemming from its inability to capture inter-interval dependencies. This phenomenon manifests as an approximation error quantified by cumulative KL divergence scaling with the conditional mutual information between adjacent intervals. To overcome this limitation, we recast ordinal regression through an autoregressive framework that explicitly captures sequential dependencies among latent tokens.
MSE bound. We denote v(T))) discrete random variable C which takes values in v(w, )
The model aims approximate C with its prediction C Let B max, BBC² |0 C denote
the maximum per-step bias, and define the variance term Vear max V(C)) S [wmins Wmnx]] is the range of {
(wimo Wari
Theorem (Error Bound of Generative Ordinal Regression). By bias-variance decomposition
(ignoring irreducible noise), the mean squared error of GoR satisfies:
E [ -.) TT +TV BT + TTP (Wmax Wiiin )²
The detailed derivation and illustrations is in Appendix D. This error bound demonstrates that minimizing prediction error requires coordinated control of three critical factors: (i) token-sequence length T. (ii) maximum per-step bias B, and (ii) per-step variance Vear- Guided by these findings, we formulate three axiomatic principles for vocabulary design: (1) Ω must support approximation of all target values {ys ) through finite unique tokens, ensuring bounded approximation bias. (2) Joint optimization of bias and variance via dual mechanisms pechhnnssss-preeentinng sample imbalance bias through coverage constraint while suppressing variance via vocabulary sparsity control. (3) Parametric invariance across datasets, enforcing robustness to distribution shifts through scale-agnostic token contributions. These principles collectively ensure rigorous error control while maintaining practical applicability.
2.3 FRAMEWORK
As illustrated in Fig. 2, GoR reformulates the regression task by employing model-agnostic encoder-decoder architecture to learn the conditional probability distribution P(r x)) over a discrete token sequence. This architecture comprises two key components: (1) task-specific encoder for feature extraction, and (2) an architecture -ggnossii autoregressive decoder for sequential prediction. The encoder adapts to arbitrary input modalities (e.g., text, images, or tabular), while the decoder
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generalizes across sequence modeling paradigms compatible with both RNN-based (Schuster & Paliwal, 1997; Chung et al., 2014) and Transformer- based architectures (Vaswani et al., 2017)'.
2.3.1
PROBABILISTIC FORMULATION
Instead of directly regressing the scalar target yr, GoR models the conditional distribution of its sequence representation T given the latent feature h4 By applying the probability chain rule, the joint probability of generating the complete sequence is factorized autoregressively follows:
T:
Pa( h2) = Po(T, Po( T: hv) = II Po(Ti hs, f,
(3)
where 9 denotes the model parameters.
2.3.2 ARCHITECTURE.
Encoder. The encoder is input modality speciifc. Structured feature vectors employ Feedforward Net- work (FFN), while images use convolutional networks like ResNet (He et al., 2016) or ViT (Dosovit- skiy al., 2020). Formally, the encoder maps æ;; latent representation hę Encoder(x:) E RRLDD where denotes the feature dimension and is the input length expected by the decoder.
Decoder. Conditioned the latent representation h; the decoder recursively generates the token sequence 9; (f) ..... :.T).. At each time step the model predicts the next token f is sampled as:
P arg max Pa(wi,, ax = arg max Softmax (ho f,²1)) wEd
WESt
Here, fo outputs the unnormalized logits, while Po denotes the normalized probability distribution.
Extensibility. Beyond ficxible substitution with task-specific implementations, GoR can integrate existing optimization strategies with negligible adaptation cost, including curriculum learning (Bengio et al., 2009), N-gram (Goodman et al., 2020), and reinforcement learning such as GRPO (Shao et al., 2024). The detailed discussion of these extensions is provided in Sec. 3.2.4.
2.4 TOKENIZATION
2.4.1 VOCABULARY
We initialize the vocabulary W = {
1=1 through a quantile-based selection strategy, which iteratively selects tokens based on fixed percentile of the remaining label values, and subtracts them from the exceeding labels until residuals are negligible (Details in Alg. 2 of Appendix E). This initialization ensures comprehensive coverage of the observed value distribution while introducing computational challenges due to excessive vocabulary size. We therefore develop principled pruning strategy based on our proposed Coverage- Distinccvesin Index (CoDi) for tokens as follows:
count (wj. T4)
CoDi,
log
(5)
T;
+1
Coverage
Distinctiveness
Here count(w), Tú)) is the count of token wj in the sequence 7; while |[ wy E n denotes the number of sequences containing Wj- In CoDi, the Coverage term measures token usage frequency, which affects approximation bias, while the Distinctiveness term evaluates token uniqueness, influencing model variance.
Based on CoDi, we design top-down vocabulary pruning strategy in Alg. 1: starting with the initial vocabulary, we iteratively remove tokens with the lowest CoDi in the initial vocabulary W. After each removal, the retained percentage and threshold preserving representational fidelity, achieving a favorable trade-off between computational efficiency and modeling power. The refined vocabulary !22 then serves the foundation for formalizing Ordinal Target Sequencing.
utilized to control vocabulary size while
Too intuitively illustrate the generative process, Fig. depicts an RNN-based decoder, which can replaced with any other decoder architecture.
Without loss of generality, the token indices in the vocabulary are also sorted descending numerical order.
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Algorithm 1: Vocabulary pruning with CoDi
Input: Label set Y = (we } Sequence set { J Threshold e; Initial vocabulary W = {w; W j=1 Minimum percentage of initial vocabulary retained
Output: Pruned vocabulary 1 with err <
Q < W;
Compute CoDi for all wi E 92;
err <- evaluate(S)):
while err 6 and [ 2 3| do
w arg min En CoDiy;
Ω Q {: Update sequence set (T:) based S2;
Update error metric err +- max 1/ (-r((r) N
11=1
end
10 return !
2.4.2 ORDINAL. TARGET SEQUENCING
Ordinal target sequencing aims to encode each target into token sequence т; by adhering to three core principles. First, for efficiency, the sequence length T; must be minimized to simplify the learning process. Second, for representational accuracy, the reconstruction error must be bounded 6. Finally, the sequence must enforce coarse-to-fine
by relative tolerance c, i.e., |
34
monotonicity through descending order of token values (T 2 T To satisfy these principles. we develop a greedy decomposition algorithm that iteratively selects the largest admissible token
r Ω from the residual value 7/- max E Ω v(w) S/ EE= (-1 p(r))) terminating when the residual falls below This procedure guarantees: (i) minimal T; for given by design, (ii) monotonic token values ensured by the decomposition process, and (iii) O([s2) time complexity pre-sorted vocabulary search. The resultant sequences provide compact yet precise representations while maintaining generation consistency across the dataset..
2.5 TRAINING AND INFERENCE
Training loss. The primary objective is to minimize the negative likelihood:
LNLL log Po( h2)
log Po(t! hy #21)
(6)
To incorporate ordinal relationships into the predictions, we follow (Liu et al., 2018) to employ the Huber loss (Huber, 1992) as the regression loss Creg. The final objective is:
Liinnt = LNLL + freg
where À is a hyperparameter that balances the two losses.
Inference process. The encoder processes the input z, derive hidden representation h; analogous to the training phase. The decoder then initiates the generation of sequence ř autoregressively, beginning with the (SOS) token and proceeding until the (EOS) token is generated. Finally, the predicted value is computed by ýi E/ v(+!).
EXPERIMENTS
We first present GoR's 's overall performance across multiple domains, then introduce in-depth analyses of architectural choices, interval-wise performance, distributional analysis, extensibility, vocabulary ablation, and token semantics elucidate its underlying mechanisms. Evaluation metrics include Mean Absolute Error (MAE), Cumulative Score (CS), XAUC (Zhan et al., 2022), Linear Correlation Coefficient (LCC), and Spearman's 's Rank Correlation Coefficient (SRCC). Due to space limit, detailed metric definitions, implementation settings, and additional results moved to Appendix F.

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ICAASIX
ICAAL7X
Orrepie
TADASE
Df
GGB (ANE
5H40
135
4.0
SRAG K30 6/12
CAAST
Ald
TAOESK
150
5P60
SRO2
AWA
GROC
12M
140h
(M)
(b)
Figure 3: Aesthetics assessment results four benchmarks (Best viewed in color).
Criten-SSC
Kaggle
0.54
3.04
Method
MAE 1
SRCC
SRCC
SWOC
0.53
1,02
Two-stage (Dmachen et.,, 2018)
MTL TTE- (Ma et al.,, 2018)
21.190
21.719
0.2478
0.2386
74.065
74.782
0.433
0.431
ZILN (Wang et 2019)
20,880
0.2434
72.528
0.524
100)
0.51
1.00
MDME (Li et al., 2022)
16.598
0.2269
72.900
0.516
MDAN (Lin al.,, 2024)
20.030
0.2470
73.940
0.437
0:08
OptDist (Weng al., 2024)
15.784
0,2505
70.929
0.525
0.49
HiLTV (Xu et al., 2025)
14.764
0.2645
69.331
0.512
SACC
LCC
MAE
GoR
12.965
0,3036
67.075
0.536
Performanceon the TAD66K dataset with different decoder architectures.
Figure 4:
Table 1: Performance comparison on LTV datasets with the MAE and SRCC metrics.
3.1 OVERALL PERFORMANCE
3.1.1 IMAGE AESTHETICS ASSESSMENT (IAA)
Following (He et al., 2023), we select 14 representative and state-of-the-art (SOTA) baselines for evaluation four datasets: TAD66K (He et al., 2022), AVA (Murray et al., 2012). ICAA17K (He et al., 2023), and SPAQ (Fang et al., 2020), with four metrics: MAE, XAUC, LCC, and SRCC. Recognizing the critical importance of visual features in the IAA task (He al., 2022), we evaluate GoR by employing three distinct encoder backbones: ResNet50 (He et al., 2016), a representative legacy architecture (He al., 2022), and recent SOTA model (Gao al., 2024).
Performance. Fig. demonstrates GoR's superiority over SOTA methods across four metrics, with three critical observations: (1) Compatibility: GoR with standard ResNet50 matches SOTA models with expert-designed architectures; (2) Robustness: Even paired with outdated TANet, GoR sigmificant improvements over the SOTA methods-as compelling
comtllllnnmmllinngggggg result given the critical dependence of IAA tasks on feature quality; (3) Synergy: Combined with a modern AesMamba encoder, GoR achieves new SOTA (detailed metries Appendix F.2.2). These results validate the universal efficacy of our generative ordinal modeling paradigm across different encoder architectures.
3.1.2 LIFE TIME VALUE PREDICTION (LTV)
Following (Weng et al., 2024), we evaluate GoR on the Criteo-SSC and Kaggle datasets with MAE and SRCC metrics. A Feed-Forwar Network (FFN) serves as the encoder of GoR. Details regarding the encoder architecture, the baseline methods, and datasets are in Appendix F.4.
Across both ordinal (SRCC) and numeric (MAE) metrics, GoR consistently surpasses existing methods (see Tab. 1). It improves HiLTY by 3.25% in MAE (reduction) and 2. 1% in SRCC on Kaggle. Notably, for Criteo-SSC, GoR achieves 12.2% reduction in MAE and 14.8% improvement in SRCC compared to the SOTA method HiLTV, substantiating the superiority of GoR.
Performance.
3.1.3 WATCH TIME PREDICTION (WTP)
Following (Lin et al., 2023; Zhao al., 2024), three publicly available datasets (CIKM16. KuaiRec (Gao et al., 2022a) and KuaiRand (Gao et al., 2022b)) and one industrial dataset from real-world short-video app used to evaluate the proposed GoR, with the metrics of MAE and
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Table 2: Performance comparison among different approaches on WTP task for four datasets.
KuuiRand
CIKMI6
Indust. MAB.
Method
MAE
XAUC 1
MAE J
XAUC
MAE L XAUC
XAUC
VR Regression)
7.634
12.349
1,039
WLR (Covington et al., 2016)
6.047
0.545
11.582
0.529
0.998
0.672
36.342
0.588
D2Q (Zhan
2022)
5,426
0.565
10.564
0.537
0.899
0.661
32.349
0.592
CWM (Zhao et al. 2024) 2024)
3,452
0.580
8.696
0.561
0.891
0.662
33.323
0.591
TPM (Lin et al., al,3 2023)
3,456
0.571
9.573
0.542
0.850
0.676
32.437
0.597
CREAD
2024)
3.307
0.678
29.997
SWaT (Yang et al., 2025)
3.438
0.585
9.553
0.544
0.857
0.685
31.245
0.599
Our GoR
3.194
0.616
7,032
0.567
0.808
0.696
28.166
0.611
Table 3: Facial age estimation results on four benchmarks
UTKFace
FG-NET
MORPH
CACD
Method
MAF.
CS(%)
MAF L
CS(S)
MAF.J
CS(S))
MAF
CS(%) ?
OR-CNN (Niu ol., 2016)
4.40
63.67
5.09
$3.80
2.83
61.97
4.01
73.41
DLDL (Gan al., 2017)
4.39
63.65
5.26
83.83
2.81
62.43
3.96
73.37
SORD (Diaz & Marathe, 2019)
4.36
64.25
5.59
82.83
2,81
61.31
3.96
73.48
et
4.42
4.07
Unimodal (Li et al.,, 2022)
4.47
62.67
5.13
83.97
2.78
63.15
4.10
73.55
FaRL (Papllidm et 2024)
3,87
84.52
3.96
Our GoR
3.43
66.58
4.68
85.66
2.69
64.95
3.73
75.29
XAUC. The encoder is consistent with the LTV task implementation in Sec. 3.1.2, and comprehensive details about datasets and compared baselines are in Appendix F.3.1.
Performance. We compare GoR with 6 existing methods and the results are presented in Tab. 2. Compared to the second-best method (marked in underline). GoR achieves relative reductions in MAE of 3.41% (KuaiRec), 19. 14% (KnaiRand), and 4.94% (CIKM16), alongside relative improve- ments in XAUC of 3.7% (KuaiRec), 1.07% (KuaiRand), and 1.61% (CIKM16). The comprehensive improvements in both MAE and XAUC substantiate the superiority of the GoR method. Besides, GoR exhibits a 5,44% relative decrease in MAE and a 1.16% improvement in XAUC on the Indust dataset, demonstrating its potential significantly enhance real-world user experiences.
3.1.4 FACIAL AGE ESTIMATION (FAE)
FAE is a discrete ordinal regression problem (e.g. 0-100 years old) unlike some previous tasks that involve continuous ordinal labels. Consistent with the datasets, baselines, and evaluation protocol used in (Paplhám et al., 2024), we evaluate GoR on four FAE datasets (UTKFace (Zhang et al., 2017), FG-NET (Lanitis al., 2002), MORPH (Ricanek Tesafaye. 2006). and CACD (Chen al., 2014)) with MAF and CS (tolerance I 5) metrics, and use FaRI. (Zheng et al., 2022) as the encoder.
The results in Tab. show that our GoR model achieves SOTA performance, signifi- cantly surpassing all baselines across all datasets in both evaluation metrics. GoR delivers consistent and substantial improvements - MAE reductions between 5.8% (MORPH) and 14.1% % (FG-NET), and CS improvements between 1.5% (CACD) and 2.7% (FG-NET) demonstrating its generality over diverse ordinal regression tasks, from continuous to discrete labels.
Performance.
3.1.5 HISTORICAL IMAGE DATING (HID)
Historical Image Dating (HID) represents typical discrete OR task, analogous to Facial Age Estimation task. Following (Wang et al., 2023), we utilize the HCI dataset (Palermo et al., 2012) with stratified 80-5-15 split vaiitinng/aliddttiootetnnnggg per decade. We employ 10-fold cross cross-valides validation and report the average Mean Absolute Error (MAE) in Tab. 4. To ensure fair comparison, all methods leverage unified ResNet50 (He et al., 2016) backbone. GoR achieves state-of-the-art performance, delivering a 3.77% MAE reduction over Ord2Seq.
3.2 FURTHER ANALYSIS
3.2.1
ARCHITECTURE-AGNOSSS ANALYSIS
We investigate the impact of different decoder architectures on the IAA task using the TAD66K dataset, as illustrated in Fig. 4. By instantiating GoR with various sequence modeling mecha- nisms-including including RNN (Schuster Paliwal, 1997). GRU (Chung et al., 2014), LSTM (Hochreiter & Schmidhuber, 1997), and Transformer (Vaswani et al., 2017) observe consistent trend: all
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Table 4: Performance comparison among different methods on the HCI Dataset.
Tatssess
Medhoda
(Palemme e sl,, 20130
Palermo at.l.
CNNPORR (I al. 2018)
GP DNNOR in 2019)
SORD (Dor Maraite, 7019)
FOE (áa al. 2011)
(Shis ctal. a 3002
NEWR
(Whng et A0yy)
Orü2Scy
Gok
HCI
MAE1
0095
0,76
0.70
0.5
0.33
0.51
Table 5: MAE comparison across varying Ground Truth (GT) time intervals on the KuaiRec dataset.
Table Statistical comparison (Mean and Var) of the predicted distributions.
Time Intervals (Seconds)
Distribution
Mean (11)
Var (a²2
Method
0-2s
2-4s
4-6s
6-8s
8-10s
>10s
GT
7.69
11,46
TPM
7.70
5.92
3.79
1.72
1.37
6.25
TPM
9.11
2.56
CREAD
7.07
4.96
3.14
1.26
6.71
CREAD
8.54
1.81
GoR
5.50
3,95
2.28
1.06
6.26
GoR
7.73
2.88
variants successfully outperform current SOTA methods. While the Transformer-based variant yields the optimal performance, the universal improvement across all architectures strongly validates the robustness and architectural independence of our GoR framework.
3.2.2 PREDICTIONS ANALYSIS
To evaluate fine- the-grained predictive capabilities, dissect model performance across varying watch- time segments on the KuaiRec dataset, where approximately 80% of instances possess a Ground Truth (GT) of under 10 seconds. As detailed in Tab. 5, GoR demonstrates substantial superiority over CREAD and TPM across all high-frequency short-to-medium duration brackets (0-10s). Although TPM exhibits marginal edge in the sparse > >10s regime, GoR consistently minimizes the Mean Absolute Error (MAE) for the vast majority of user interactions.
We further scrutinize the global statistical properties of the predictions in Tab. 6. GoR achieves exceptional calibration, generating predictive distribution whose mean (μx = 7.73) aligns remarkably well with the GT (μ 7.69). This statistical fidelity is largely attributed to GoR's coarse-to coasee-tofinn fine tokenization, which dynamically adapts to varying granularities. Conversely, both CREAD and TPM suffer from pronounced overestimation biases, outputting significantly higher means (8.54 and 9.11, respectively). This systemic overestimation inherently stems from their reliance on rigid discretization boundaries, where broad intervals in tail buckets disproportionately inflate errors for the more prevalent, shorter GTs.
3.2.3 VOCABULARY ANALYSIS
We investigate the impact of vocabulary initialization by comparing our proposed approach against two baseline strategies: manual strategy (defined by intervals of [1, 1, 5, 7] x 10") and binary strategy (using power-of-two intervals 2" starting from 1). As detailed in Tab. 7, our analysis reveals three key findings: (1) The maanille-bssd method consistently outperforms both manual and binary strategies, primarily benefiting from a more balanced token distribution (see Fig. 5(a)). (2) The integration of CoDi universally enhances all initialization strategies. This improvement is attributed to CoDi's ability to yield a more uniform token frequency distribution, thereby mitigating token-level variance and per-step bias B, which perfectly aligns with our theoretical expectations. (3) The sensitivity analysis in Fig. 5(b) demonstrates non monotonic performance trend as / decreases and more tokens are filtered. This phenomenon exemplifies the classical bias-variance trade-off: an initial reduction in vocabulary size effectively suppresses variance, whereas excessive compression drastically increases bias, strictly corroborating Theorem 1.
3.2.4 COMPATIBILITY WITH GENERATIVE OPTIMIZATION STRATEGIES.
As discussed in Sec. 1, GoR can seamlessly accommodate optimization strategies for generative language model with negligible adaptation cost. Here, we assess this compatibility by incorporating several representative strategies prevalent in language models: 1) Teacher Forcing (TF) (Sutskever, 2014) is a training method that feeds the ground-truth token at step t into the decoder at step t. 2) Curriculum Learning (CL) (Bengio et al., 2015) progressively shifts the training strategy from full TF to a strategy that closely mimics autoregressive inference. 3) N-gram Prediction (NP) (Goodman al., 2020) simultaneously predicts N tokens to improve predictive lookahead and compensate for

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Published as a conference paper at ICLR 2026
6.0
3.0
3.375
MAE XAUC
0.015
3.350
Man. 6 Bin.
4.0
2.0
Olian. Fromy, (8)
3.325
0.610
Free PNo
3.300
3.0
XAUC
1.275
0.000
2.0
3,250
1.0
0.5
3.225
3.200
0.590
Quan. Quan.
1.0
0.8
0.5
(a)
(b)
Figure 5: Vocabulary analysis on KuaiRec dataset for WTP task: (a) Token frequency distributions under different vocabulary strategies. (b) The sensitivity analysis of f3.
Table 7: Performance Across Vocabulary Table 8: Compatibility with existing generative opti-
Construction Strategies (w/ vs. w/o CoDi) mization strategies WTP and LTV tasks.
Vocabulary design
Kuniee
XAUC
MAF.
CIKM16
XAUC
Stratogy
KuaiRee
XAUCC
Criteo-SSC
SRCC
Manual (Man.)
3.281
0.604
0.825
0.685
(a)
3.359
0.588
16.198
0.252
Binary (Bin.)
3.268
0.505
0.821
0.687
(b)
3.299
0.592
14.893
0.264
Quantile (Quan.)
0.820
(c)
3.241
0.604
13.996
0.276
Man CCDDi
3.253
0.610
0.819
0.699
(d)
Bin.+CoDi
3.239
0.611
0.815
0.691
(e)
3.194
0.616
12.965
0.304
Quan.+CoDi
0.808
(e) w/ DPO
3.185
0.620
12,438
0.309
strategy that optimizes model outputs via preference alignment. Our GoR requires explicit reward model, instead using beam-search candidates with MAE against labels as implicit preference signals. The results in Tab. 8 indicate that this compatibility significantly enhances model performance. Crucially, these improvements are achieved without introducing additional model parameters, demonstrating a cost-effective and scalable enhancement that facilitates GoR's future exploration in wider applications.
output-to-input gradients. 4) DPO (Rafailov et al., 2023) is reinforcementtleamiing--
4 CONCLUSION
In this paper, propose GoR, the first generative framework tailored for Ordinal Regression (OR). Diverging from traditional rigid binning methods, GoR innovatively formulates OR as an autoregressive sequence generation task. By predicting tokens for ordinal value segments in step-by-step manner, this paradigm explicitly models inherent sequential dependencies and enables adaptive resolution. Our methodology is rigorously supported by comprehensive bias-variance theoretical analysis, which motivates the proposed CoDi metric for optimal vocabulary construction. Empirically, GoR consistently achieves state-of-the the-art (SOTA) performance across 15 diverse benchmarks spanning 5 distinct domains, highlighting its remarkable robustness and generalizability. Ultimately, GoR not only unlocks the potential generative architectures for ordinal data but also establishes a strong. versatile baseline for future generative OR research.
4.1 LIMITATION AND FUTURE
While GoR establishes novel generative paradigm for ordinal regression and achieves state-of-the art performance, several limitations exist, opening promising avenues for future research. First, the autoregressive nature of GoR, while enabling sequential modeling, incurs an inference latency cost that is proportional to the output sequence length. This poses a challenge for tasks requiring rapid prediction of long sequences. Second, GoR, like other language generation models, is susceptible to the risk of error accumulation. Errors in predicting earlier tokens can compound in subsequent steps, potentially leading to larger deviations in the final prediction. Exploring sequence-level optimization calibration strategies, such those based reinforcement learning, could help alleviate this issue.
TT avoid the prolonged training time associated with cerfoorcmmmet--caannnn--eeeee post-training, while effective, all results reported using the efficient setup from line (e).
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ACKNOWLEDGMENTS
This work was partially supported by Kuaishou Technology. The computations in this research were partially performed using the CFFF platform of Fudan University.
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Diederik P Kingma and Jimmy Ba. Adam: A method for stochastic optimization. arXiv preprint 14Xiv:14/2.6940 2.6000 2014.
Xin Lu. Zhe Lin, Hailin Jin, et al. Rapid: Rating pictorial aesthetics using deep learning. In Proceedings of the 22nd ACM international conference on Multimedia, 2014.
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Shu Kong, Xiaohui Shen, Zhe Lin, Radomir Mech, and Charless Fowlkes. Photo aesthetics ranking network with attributes and content adaptation. In Computer Esion-ECCV 2016, 2016.
Jian Ren, Xiaohui Shen, Zhe Lin, Radomir Mech, and David Foran. Personalized image aesthetics. In Proceedings of the IEEE international conference on computer vision, 2017.
Shuang Ma, Jing Liu, and Chang Wen Chen. A-lamp: Adaptive layout-aware multi-patch deep convolutional neural network for photo aesthetic assessment. In Proceedings of the IEEE conference on computer vision and pattern recognition, 2017.
Kekai Sheng, Weiming Dong, Chongyang Ma, Xing Mci, Feiyue Huang, and Bao-Gang Hu. Attention- based multi-patch aggregation for image aesthetic assessment. In Proceedings of the 26th ACM international conference on Multimedia, 2018.
Vlad Hosu, Bastian Goldlucke, and Dietmar Saupe. Effective aesthetics prediction with multi-level spatially pooled features. In Proceedings of the IEEE/CVF conference on computer vision and pattern recognition, 2019.
Hancheng Zhu, Leida Li, Jinjian Wu, Sicheng Zhao, Guiguang Ding, and Guangming Shi. Person- alized image aesthetics assessment via meta-learning with bilevel gradient optimization. IEEE Transactions Cybernetics, 2020.
Hui Zeng, Zisheng Cao, Lei Zhang, and Alan Bovik. A unified probabilistic formulation of image aesthetic assessment. IEEE Transactions on Image Processing, 2019.
Zhengzhong Tu, Hossein Talebi, Han Zhang, Feng Yang, Peyman Milanfar, Alan Bovik, and Yinxiao Li. Maxvit: Muiti-axis vision transformer. In European conference on computer vision, 2022.
Junjie Ke, Qifei Wang, Yilin Wang, Peyman Milanfar, and Feng Yang. Musiq; Multi-scale image quality transformer. In Proceedings of the IEEE/CVF international conference computer vision, 2021.
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APPENDIX
A
THE USE OF LARGE LANGUAGE MODELS (LLMS)
Generative AI tools (e.g., ChatGPT) were used solely to improve the manuscript's clarity and readability during the writing stage. These tools were not employed for generating any novel content, such as text, figures, tables, code, or experimental results. No generative Al was used in the conception, implementation, analysis, or evaluation of the research itself. The authors take full responsibility for the integrity and accuracy of the final manuscript.
B RELATED WORK
B.1 ORDINAL REGRESSION (OR)
OR addresses prediction tasks with ordered targets, widely applied in diverse domains like facial age estimation (Niu et al., 2016; Chen et al., 2017), image aesthetic/quality assessment (He et al., 2022; 2023), watch-time prediction Ma et al. (2024); Sun et al. (2024); Lin et al. (2023), life- time value prediction (Wang et al., 2019; Li et al., 2022; Weng et al., 2024). Prior OR works have predominantly relied on Continuous Space Discretization (CSD) (Wang et al., 2025), transforming OR into classification. Within the CSD paradigm, key directions include methods that enhance boundary discrimination via reference comparisons (Shin et al., 2022; Li et al., 2021; Zheng et al., 2024), but are sensitive to heuristic reference selection. Another prevalent rank-based approach implicitly encodes ordinality via label transformation into sequential binary subtasks (Niu et al., 2016; Lin et al., 2023; Sun al., 2024; Chen et al., 2017: Liu et al., 2018:?). While effective, the fixed discretization leads to prediction rigidity and can amplify errors for head categories, particularly in long-tailed distributions. Recent CLiP-based works align image features with textual ordinal descriptions to enhance the semantic understanding and generalization of ordinal relationships, representing a rapidly growing and promising research direction. The Learnable Prompts strategy (Li al., 2022; Yu et al., 2024) employs trainable context vectors to automatically capture ordinal relationships and extract rank concepts from CLIP's latent space. Conversely, Semantic Alignment approaches (Wang et al., 2023; Du et al., 2024) focus constructing rank-specific textual descriptions. In contrast, GoR adopts a fundamentally different, generative perspective of autoregressive sequence modeling in language models, which inherently captures explicit sequential dependencies and employs a dynamic termination mechanism to generate sequences variable lengths. This grants significantly greater flexibility in output granularity compared to methods constrained by fixed bins, enabling adaptation to varying data distributions and prediction requirements.
B.2 SEQUENCE PREDICTION
Sequence prediction, which necessitates models to comprehend input context and produce output sequences, initially focuses on natural language processing (NLP) tasks such as machine transla- tion (Sutskever, 2014; Cho, 2014) and text summarization (Wang et al., 2019; Xiao et al., 2020; Liu et al., 2025). With the advancement of deep learning (Hui et al., 2026; Gu et al., 2026; Ma et al., 2025; Liu et al., 2025; b024 LIU et al., 2026), the advent of the Transformer architecture (Vaswani et al., 2017: Ma et al., 2025; Zhang et al., 2025; Kang et al., 2025; Liu et al., 2023a;b) significantly improves sequence prediction capabilities, leading numerous derivative models (Liu al., 2019; Yang et al., 2019; Zhou et al., 2025) and expanding its application to fields such as computer vision (CV) (Tian al., 2024; Wang et al.. 2024; Zhou al., 2026) and recommendation systems (Hidasi, 2015; Sun et al., 2019) through the successful reformulation of their tasks as effective end-to-end sequence prediction problems. However, sequence prediction has not yet been applied to OR, and our work pioneers sequence prediction perspective for OR, offering a fundamentally novel modeling paradigm. A related work is Ord2Seq (Wang et al., 2023). It maps generated sequences to fixed bins and, in essence, remains sequential binary subtasks under the rank-based paradigm and does not scale well when the number of categories or the value range is large its reported validation has been limited to at most eight ordinal groups. In contrast, GoR employs a generative autoregressive formulation with a dynamic (EOS), enabling adaptive ordinal segmentation rather than relying on predefined bins.
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B.3 TOKENIZER DESIGN
Tokenizer design is widely employed in generative language models for compact vocabulary represen- tation and broadly falls into two categories: bottom-up merging and top-down pruning. The former, exemplified by BPE (Sennrich et al., 2016) and WordPiece (Wu et al., 2016), iteratively combines subword units based on statistical criteria. Conversely, top-down pruning methods, represented by Unigram (Kudo & Richardson, 2018), reduce large initial sets by evaluating and eliminating subwords according their contributions. Building upon these foundational strategies, recent literature has explored various enhancements and adaptations (Xu et al., 2021; Hofmann et al., 2022; Yehezkel Pinter, 2023; Schmidt et al., 2024), further improving tokenization efficiency. However, these not directly applicable to our GoR, where tokens inherently exhibit dual sequential and numerical additive semantics, necessitating customized methodologies. While related work (Ma et al., 2024) attempts to address similar issues, it remains domain- specific method rather than a general-purposs purpose framework. Furthermore, it relies on a heuristic vocabulary design without rigorous theoretical optimization, which inherently limits its modeling accuracy.
traditional NLP tokenization strategies
C PROOF OF PROPOSITION 1
C.I THEBRETICAL ANALYSIS
This section provides theoretical analysis of these limitations, demonstrating the importance of capturing temporal dependencies to improve prediction accuracy.
Let {1r,, 36) }) be the training [cm-1, Cm) with boundaries cp < ... < CM Define binary variables B = 1 > Cm) for m ,,...,,,,, M, and let B; = [
Discretize the value range of y; into M intervals dm
B. with decision history B =
The label transformation methods with sequential binary subtasks implicitly assume conditional independence across these discretized intervals:
P Puaive (B 24))=
II P(B." x.).
(8)
In contrast, the true conditional distribution factorizes sequentially:
Pinee [B;
x:))
II m=1
P(B
B B xx))
(9)
The KL divergence between these two distributions given by:
Pinee (B,
DKL (Pone Punice)
Σ
Pine (B; xx)) log Paavee B,
xx,)
B.
M m=
P(B."
B ..)
Σ
iree (B; xx)) log
P(B." [
(10)
B,
Σ B.
Pine (B; (:))
log
P(B
B B ..4
P(B.
m=
Rearranging the summation terms, derive the total KL divergence that quantifies the error introduced by ignoring dependencies among discretized intervals:
P(B."
B mx)
DEL (Paue Puniee) =
Pine log
P(B." x1)
(11)
P(B," B Sm xT) P(B." x4)
EBB Pine
log
We decompose this expectation using the Law of Iterated Expectations:
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P(B." Th B x.)
D.t.(Pems Pasiv))
B
E B? 1
log
P(B.'X.) X.)
M
P(B." = =0" [, m, ;x,)
Σ
Σ
P(B," 6tth B. 5T x.) log
(12)
P(B. = x.)
BB
cm
This can be explicitly expressed as the conditional KL divergence for each bucket:
(m)
DKL (P(B."
24, B, (B
P(B T
xx:))
Σ
P(B, dn
34 B 5 log
PBB. 6th
I B B
(13)
P P(B.
bm
(mEE(0.1)
This expectation can be expressed as:
B
D (m) KT.
[B:": ;, B |xx),
(14)
where 7(":; B xn4) denotes the conditional mutual information between the current decision B and all preceding decisions B Beth given the features z₁. The detailed proof is in the following:
P(b b0m, xx.)
[B B
Σ bmm Am
2.) log P(b <m 6t
P(b xx)
P(b" bxm .2;)
Σ
P(b <m
x Σ
P(b b <m xx. log
P(b" xxx)
(15)
b
Σ P(b x.) (DKz (P(B."
P(B." (x))))
b
A B
D(m) KL
The derived KI divergence decomposition illustrates that the error introduced by the naive discretized modeling approach which ignores dependencies across intervals, can be quantified precisely as the cumulative sum of conditional mutual information across all discretized intervals. Specifically, intervals are entirely independent (i.e., mutual information = 0), the resulting KL divergence error is zero; conversely, strong dependencies exist among intervals (I 0), the error increases proportionally to the strength of these dependencies.
C.2 EMPIRICAL VALIDATION
To empirically validate Proposition 1, we conduct additional experiments using an SOTA baseline SWaT (Yang et al., 2025) on the CIKM16 dataset of watch-time prediction task. Specifically, introduce explicit sequential dependencies by modeling previous bin features with an RNN for joint prediction. The results in Tab. demonstrate performance gains, substantiating our theoretical claims.
Table 9: Empirical validation of Proposition the CIKM16 dataset.
Method
MAE J
XAUC
SW&T SWa++RNN
0.857
0.685
0.831
0.689
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D PROOF OF THEOREM
We provide a formal bias-variance decomposition of the expected squared error in GoR. Our goal is upper bound the prediction error of model that generates sequence of value tokens.
Let the true label be defined as:
((T)).
(16)
t=1
and the predicted label be:
(tt))
(17)
where T; represents the overall length of the token sequence for sample i, of and ff denote the ground-truth and predicted tokens at step t, and v/.) maps a token to its corresponding numeric value.
We model v((T)) discrete random variable, denoted as Cj. The probability distribution of C₁ is given by: P(C) = w), w E ( which denotes the probability of C; taking the value w. So, the predicted token output be modeled as it = Σí= Oi
We now analyze the expected squared error:
Bi(,: yx) E
0
C
(18)
Let A = Õj Cj.
Then we can write:
E
Σ 1
Σ
E
A
+
Σ A
(19)
2
Variance
bc
V(A.) + Σ Cov(Ar, Ar),
(20)
Life!!
where 6; := E]A. =E[ Cj. This formulation captures the compounding errors of autoregres- sive models through the covariance term, which reflects correlations between errors at different steps. Next, we analyze the bias and variance terms separately to derive their upper bounds.
Bias Upper Bound. If the model unbiased at each step, b, = 0. Otherwise, we assume:
|el S B, V1,
(21)
where B represents the maximum bias across all time steps in the prediction sequence, mainly governed by the model's predictive accuracy. In practice, B corresponds to the extreme case where the predicted token deviates most from the ground-truth token at the current step. Hence, it can be bounded by the largest token value at the current step B max Cf. Then, ISTTT:
Σ b < B2
(22)
Variance Upper Bound.
Applying the Schwwrz inequality:
Cov(A,, Ar) < VV(A.)V(Ar)) < [T, - 1)
2 max V VA:)).
(23)
We then analyze the item max, V(Ar).
v(A.) = v ( c.) = =V (c:) + +V(C)) - 2Cov (c+, C:)
(24)
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Assume that the predicted variable and the true variable two independent random variables. Since the vocabulary is the same, the range of values for both the predicted and the true items is identical. Assuming token values are bounded in [min Wmax. apply Popoviciu's inequality:
v(C)) 5
(Wmxx
Wmin
(25)
Let:
V var max V(A,) (Wmax Wmin
(26)
Then total variance becomes:
A S Vaar-
(27)
Final Bound. Combining both components, obtain:
E (+: - y.) s TT, +T? (Wmax Wmin) )
(28)
4
This theoretical bound reveals three critical insights for GoR optimization: (1) prediction error grows quadratically with sequence length T;, suggesting shorter sequences are preferable when possible; (2) both bias and variance contribute proportionally to overall error, necessitating balanced optimization; and (3) token value range (Wmax - (mii) directly impacts variance, indicating that carefully designed vocabularies with appropriate value distributions can substantially improve model performance. These findings provide a principled foundation for our vocabulary construction strategy.
E QUANTILE-BASED VOCABULARY INITIALIZATION STRATEGY
This section details the Quantile-based Vocabulary Initialization Strategy adopted in Sec. 2.4.1. As shown in Alg. 2, this iterative strategy constructs the vocabulary by selecting tokens based on a fixed percentile y of the remaining label values, subtracting them from exceeding values, and repeating until residuals are negligible. Alg. 2 serves as the initialization stage: it provides coarse yet comprehensive token set. Building on this, Alg. Sec. 2.4.1 further prunes and refines the vocabulary via the CoDi criterion, yiclding compact and task-adaptive representation.
F ADDITIONAL EXPERIMENTS
F.1 EXPERIMENTAL SETTINGS
F.1.1 METRICS.
set of performance metrics is utilized to evaluate the proposed method across various tasks. Task requirements determine the specific metrics applied for each task:
MAE (Mean Absolute Error): This regression precision is measured as the average absolute error between the value prediction { and the ground truth {y: N and is formulated as
+ Σ
y: -
CS (Cumulative Score): This metric quantifies the proportion of instances in the test set for which the absolute error between the predicted value ii and the ground truth value yi is less than or equal to a specified tolerance L.
XAUC (Zhan et al., 2022): This metric measures the agreement between the predicted ranks and the ground truth order for pairs of samples. Calculated over uniformly sampled pairs, XAUC represents the proportion of pairs where the predicted relative order consistent with the true relative order. Higher XAUC indicates superior performance in capturing ordinal relationships.
LCC (Linear Correlation Coefficient) (Talebi & Milanfar, 2018): This metric quantifies the linear relationship between the predicted values { J.N and the ground truth values [w It is computed as their covariance divided by the product of their standard deviations. The LCC ranges in (-1, 1}, with values closer +1 indicating stronger linear correlation.
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Algorithm 2: Quantile-based Vocabulary Initialization
Input: Dataset labels Y {y: Precision threshold E; Fixed percentile g
Output: Initial vocabulary W
Initialization
Sort Y in descending order to obtain residual set Y = {01....... ...
W f- 2, k err
while err > do
Compute the g-percentile of Y
2 = then
break end
// Terminate if no positive gain available
W W-UU (=x}
// Update residual labels
foreach ù E y do
1t 2 2 then
1/4 91 2k
end
13
end
// Evaluate relative convergence
err f max in 14
- k +1
16 end
17 return W
SRCC (Spearman's Rank Correlation Coefficient) (Talebi & Milanfar, 2018): SRCC assesses the monotonic relationship between the ranks of the predicted values { and the ranks of the ground truth values { As non-parametric measure of rank correlation, it ranges in [-1, 1]. Values closer +1 indicate stronger monotonic correlation. SRCC is less sensitive outliers compared to LCC.
F.1.2 IMPLEMENTATION DETAILS.
Unless otherwise specified in the respective experimental sections, the following training protocol adopted. The proposed GoR architecture employs an encoder-decoder framework. The encoder architecture in GoR is tailored to the specific task, with details regarding data processing and encoder configurations provided in the corresponding experimental sections. The decoder GoR is two- layer Transformer decoder utilizing 4-head attention mechanism. The hyperparameter À in Eq. (7) set to 10. For vocabulary construction, Alg. 2 for initial vocabulary, is set to 0.9, E is set to 0.005. In Alg. 1, 8 applied. The Adam optimizer (Kingma & Ba, 2014) with default parameters (B) = 0.9, Bn = 0.999) and learning rate of 5e-4 are used minimize the objective function. For experiments involving image data (common in computer vision tasks), training is conducted for 100 epochs with a batch size of 128. For the tasks involving structured data (WTP and LTV),, training is performed for 20 epochs using batch size of 1024. Experiments are conducted on a system equipped with an NVIDIA RTX 4090 GPU.
0.7 and is 0.005. To mitigate overfitting, dropout rate of 0. is
F.1.3 REPRODUCIBILITY AND FAIR COMPARISON.
Each experiment is repeated five times, and we report both the mean and standard deviation (See Appendix. F.5). As noted in prior work (Paplhám et al., 2024), state-of-the-art methods in the FAE field often exhibit large performance variance due to inconsistent dataset splits, preprocessing protocols, and evaluation criteria, rendering many results incomparable and irreproducible. Motivated by this, (Paplhám et al., 2024) proposed standardized evaluation protocol. We observe the same issue the IAA domain Consequently, we reproduced all baselines under their original hyperparameter settings in their respective papers and averaged the results. This strategy offers two key benefits: (1)
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Table 10: The results of Image Aesthetics Assessment task on TAD66K and AVA datasets
TAD66K
AVA
Method
MAR. 4
XAUC
LCC
SRCC 1
MAE
XAUC 1
LCC
SRCC1
RAPID (Lu ct 2014)
1.766
0.510
0.332
0.314
0.978
0.513
0.336
0.327
AADB (Kong et al., 2016)
1,463
0.523
0.400
0.379
0.784
0.534
0.431
0.408
PAM (Ren et al., 2017)
1.314
0.534
0.440
0.422
0.614
0.619
0.531
0.521
NIMA (Talebi & Milanfar, 2018)
1.422
0.511
0.405
0.390
0.715
0.532
0.472
0.447
ALamp (Ma al., 2017)
1.349
0.523
0.422
0.411
0.657
0.579
0.498
0.487
MP (Sheng
2018)
1.191
0.589
0.408
0.389
0.602
0.632
0.543
0.531
MLSP (Hosu et al., 2019)
1.132
0.620
0.432
0,409
0.579
0.657
0.563
0.553
BIAA (Zhu ct 2020)
1.329
0.538
0.431
0.348
0.672
0.566
0.496
0.476
UIAA (Zeng et ul., 2019)
1.281
0,548
0.441
0.361
0.608
0.626
0.535
0.525
HGCN (She et al., 2021)
1.141
0.615
0.419
0.406
0.578
0.511
0.486
TANet (Ile al., 2022)
1,081
0.649
0.659
0.568
0.554
MaxViT (Tu al., 2022)
1,054
0.659
0.472
0.441
0.559
0.679
0.594
0.571
Delegate (He et al.. 2023)
1,041
0.661
0.477
0.451
0,541
0,688
0.642
0.634
AesMamba (Gao et al., 2024)
1,035
0.666
0.482
0.468
0.522
0.697
0,663
0.656
GoR with ResNet
1,036
0.667
0.485
0.471
0.526
0.701
0.668
0.657
GoR with TANet
1.013
0.672
0.523
0.499
0.428
0.735
0.689
0.686
GoR with AesMamba
0,996
0.677
0.541
0,513
0.395
0.751
0.726
0,701
ensures fair and consistent comparisons; and (2) establishes GoR as a reliable baseline facilitate standardized evaluations in future research.
F.2 IMAGE AESTHETICS ASSESSMENT (IAA)
F.2.1 DATASETS, BASELINES, AND EXPERIMENTAL SETUP.
GoR is evaluated on four widely used IAA datasets: TAD66K (He et al., 2022), AVA (Murray et al., 2012), ICAA17K (He al., 2023), and SPAQ (Fang al., 2020). Data randomly split into 80% for training, 10% for validation, and 10% for testing. Due to the relatively small range of aesthetics scores (typically 0-10), labels were scaled by 100 for GoR's vocabulary construction and ordinal target sequencing. Predictions were scaled back by 100 for evaluation metric computation to ensure fair comparison.
Baselines were chosen based on two criteria: I) classical architectures with available code, and 2) state-of-the-art (SOTA) performance in specific areas, such as personalized TAA. For a fair comparison, these baselines were trained using their recommended hyperparameter settings and evaluated under identical training and testing configurations. Consistent with the approach in (He et al., 2023), all compared baselines were subjected to identical data preprocessing.
Given the critical role of visual features in image aesthetics assessment, we evaluate GoR by employing three different encoder backbones: ResNet50 (He et al., 2016) widely recognized standard, a representative older architecture (He et al., 2022), and recent SOTA model (Gao et al., 2024). This strategy also helps to ensure that observed performance gains due the GoR framework itself, rather than simply an increase in model parameters.
F.2.2 COMPREHENSIVE BASELINES COMPARISON FOR IMAGE AESTIETICS ASSESSMENT.
Due to space constraints in Sec. 3.1.1 of the main paper, comprehensive baseline comparisons for the Image Aesthetics Assessment task are presented here. Tab. 10 and Tab. 11 detail the performance of all compared methods on the TAD66K/AVA and ICAA17K/SPAQ datasets, respectively.
F.3 WATCH TIME PREDICTION (WTP)
F.3.1
DATASETS AND EXPERIMENTAL SETUP
Three publicly available datasets and one industrial dataset used evaluate the proposed method. The large-scale industrial dataset (Indust. for short) is sourced from a real-world streaming short-video app with over 400 million DAUs and multi-billion impressions each day. We collect interaction logs
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Table 11: The results of Image Aesthetics Assessment task on ICAAI7K and SPAQ datasets.
ICAAI7K
SPAQ
Method
MAE 4
XAUC
LCC
SRCC f
MAF.
XAUC 1
LCC
SRCC1
RAPID (Lu ct al., 2014)
0.7415
0.6416
0.5164
0.5083
1,0890
0.6997
0.6565
0.6128
AADB (Kong et al., 2016)
0.7142
0.6661
0.5311
0.5195
1.083
0.7036
0.6646
0.6162
(Ren et al., 2017)
0.7070
0.6729
0.5385
0.5247
1.0726
0.7104
0.6691
0.6222
ALamp (Ma et al., 2017)
0.6948
0.6847
0.5478
0.5339
1.0511
0.7250
0.6835
0.6349
NIMA (Talchi & Milanfar, 2018)
0.6957
0.6839
0.5458
0.5333
1,0756
0.7084
0.6709
0.6204
MP udl (Sheng al., 2018)
0.6948
0.6848
0.5485
0.5340
1.0525
0.7240
0.6808
0.6341
MLSP (Hosu et al., 2019)
0.6814
0.6983
0.5606
0.5445
1.0428
0.7306
0.6952
0.6402
MT-A (Fang ct 2020)
0.6855
0.6940
0.5558
0,5412
1.0455
0.7289
0.6862
0.6384
BIAA (Zhu et al., 2020)
0.6864
0.6932
0.5552
0.5405
1.0497
0.7259
0.6826
0.6358
UIAA (Zeng et 2019)
0.6889
0.6907
0.5559
0.5386
1.0469
0.7278
0.6862
0,6376
MUSIQ (Ke et al., 2021)
0.6740
0.7059
0.5632
0.5504
1.0427
0.7308
0.6925
0.6401
HGCN (She et al., 2021)
0.6813
0.6983
0.5566
0.5445
1.040
0.7328
0.6934
0.6417
TANet (Hc al., 2022)
0.6789
0.7008
0,5599
0,5465
1.0469
0.7279
0.6844
0.6375
MaxViT (Tu ct al., 2022)
0.6582
0.7227
0.5853
0.5636
1.042
0.7308
0.6925
0.6401
Delegate (He et al., 2023)
0.6345
0.7498
0.6034
0.5847
1.019
0.7473
0,7114
0.6545
AesMamba (Gao et al., 2024)
0.6129
0.7663
0.6137
0.6294
0.9875
0.7522
0.7261
0.6895
GoR with ResNet
0.6115
0.7653
0.6133
0.6305
0.9911
0,7588
0.7322
0.6886
GoR with TANet
0.5994
0.7838
0.6744
0.6675
0,9489
0.7644
0.7406
0.7189
GoR with Mamaa
0.5842
0.7913
0.6823
0.6789
0.8722
0.7648
0.7434
0.7233
from 2025-09-01 to 2025-09-06 and utilize the subsequent day's data for evaluation. The CIKM16*, sourced from the CIKM16 Cup competition, is designed to predict user engagement duration in online search sessions. It contains 310,302 sessions, 122,991 items, and an average session length of 3.981. Both KuaiRand (Gao et al., 2022b) and KuaiRec (Gao al., 2022a) are real-world datasets collected from Kuaishou app video view logs. KuaiRand comprises 26,988 users, 6,598 items, and 1,266,560 impressions, while the larger KuaiRec dataset consists of 7,176 users, 10,728 items, and 12,530,806 impressions.
Unlike traditional user behavior modeling tasks in recommendation systems, WTP does not inherently depend on history action sequences. Consequently, we employ a two-layer Multi-Layer Perceptron (MLP) as the encoder, maintaining the same configuration as the compared baseline methods.
F.3.2 BASELINES
To demonstrate the effectiveness of our proposed approach, we comprehensively evaluate it against several state-of-the-art watch time prediction (WTP) baselines. The comparative methods are detailed as follows:
1. VR (Value Regression): A straightforward regression baseline that directly fits the continuous viewing duration. It is typically optimized by minimizing the Mean Squared Error (MSE) between the predicted and actual watch times.
2. WLR (Covington et al., 2016): This approach casts the continuous prediction task into binary classification framework. Specifically, assigns the observed watch time as the sample weight during the optimization of the logistic loss.
D2Q (Zhan et al., 2022): A duration-aware strategy that first partitions videos into distinct groups according to their total lengths. It then estimates a relative watch time quantile for the specific group. which is subsequently mapped back to an absolute time value to form the final prediction. CWM (Zhao et al., 2024): Operating from a causal inference perspective, this method leverages cost-dependent transformation to infer genuine watch time (CWT). The model parameters are learned by maximizing a counterfactual likelihood function constructed from observational data.
preferences, yielding the counterfactual
TPM (Lin et al., 2023): This technique constructs a hierarchical tree architecture to capture the dependencies among time segments at multiple resolutions. By formulating the task via ordinal regression, the expected watch time is aggregated through a weighted summation of interval lengths and their corresponding path probabilities.
httt:///oommttiiiosscccaccaaoonr 1161
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Published as a conference paper at ICLR 2026
6. CREAD (Sun et al., 2024): Building upon the principles of ordinal regression, this method introduces an adaptive mechanism to dynamically discretize continuous time into varying intervals based on error bounds. It employs sequential binary classifiers to predict the survival probability across these bins, deriving the final continuous output via expected value aggregation.
7. SWaT (Yang et al., 2025): Formulated upon user viewing behavioral assumptions, this statistical paradigm addresses the non-stationary nature watch probabilities through a specialized buck- etization strategy. The final duration prediction is similarly computed via probability-weighted expectations.
F.4 LIFE TIME VALUE PREDICTION (LTV)
F.4.1 DATASETS AND EXPERIMENTAL SETUP
We evaluate GoR on the Criteo-SSC and Kaggle datasets. For both datasets, a random split of 7:1:2 is used for training, validation, and testing. respectively. Criteo-SSC is a large-scale public dataset derived from Criteo Predictive Search (CPS) logs. Each instance represents a user's click behavior, with the task being to predict conversion and associated 30-day revenue. The product price feature was excluded from the inputs. The Kaggle Dataset contains transaction records. Following (Weng al., 2024), the task involves predicting user's total purchase value from a specific company in the year following their initial purchase. Our experiments focus on initial purchases within 2012-03-00 and 2012-07-01 using data from the three companies with the highest transaction volume.
F.4.2 BASELINES
To rigorously evaluate the effectiveness of our proposed approach, we benchmark it against variety of advanced, state-of-the-art customer lifetime value (LTV) prediction models (Drachen et al., 2018; Ma et al., 2018; Wang et al., 2019; Li et al., 2022; Liu et al., 2024; Weng et al., 2024). The specifics of these baselines are detailed as follows:
1. Two-stage (Drachen al., 2018): This method splits the LTV estimation process into two distinct phases. Initially, a binary classification module determines the likelihood user churn, which is followed by continuous regression task to calculate the expected monetary value generated by the retained users.
2. MTL-MSE (Ma et al., 2018): Adopting multi-task learning architecture, this baseline con- currently predicts the purchase conversion rate and the continuous LTV.. The entire network is optimized by minimizing standard Mean Squared Error (MSH) objective function.
3. ZILN (Wang al., 2019): To address the highly skewed and long-tailed nature of LTV data, this approach models the target variable using a zero-inflated log-normal distribution. Deep neural networks are utilized directly output the distribution parameters: the conversion probability p. alongside the mean 1a and standard deviation a.
4. MDME (Li et al., 2022): This strategy partitions the overarching LTV distribution into several distinct buckets. It first formulates a classification problem to assign instances to their respective buckets, and subsequently refines the estimation by predicting the intra-bucket residual bias, yielding a highly granular final LTV prediction.
5. MDAN (Liu al., 2024): This technique categorizes users into pre-established value buckets via a multi-class classifier while concurrently learning bucket-specific embeddings through multi- channel network. The final feature representation is constructed by aggregating these embeddings based on the classifier's ' probability outputs (via a weighted sum). which is then fed into the LTV regression module.
OptDist (Weng et al., 2024): Featuring dynamic routing framework, this method adaptively assigns the most fitting sub-distribution each user. It comprises Distribution Learning Module (DLM) to capture diverse data patterns and a Distribution Selection Module (DSM) that dynamically routes individual customers to their optimal sub-distribution networks.
HiLTV (Xu et al., 2025): multi-level architecture specifically designed for gaming LTV prediction. It effectively captures complex, multi-modal purchasing patterns utilizing a Zero-
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Published as a conference paper at ICLR 2026
Inflated Mixture-ou of of-Losistic loss, and incorporates specialized calibration component to enhance prediction robustness for newly registered users.
For this task, employ the same encoder architecture for GoR in Appendix F.3.I.
F.5 ADDITIONAL. RESULTS WITH MEAN AND STANDARD DEVIATION
To complement the main results, we report here the complete performance with mean and standard deviation across five runs for all datasets and tasks. Significance is assessed using paired t-tests against the strongest bascline, with improvements marked as (p<0.05) and (p<0.01). These results provide a more comprehensive view of GoR's robustness and stability across domains.
Table 12: Image Aesthetics Assessment Results.
Meebed
TADM6K
AWA
MAE 1
XUAC
LCC
SRCC
MAE 1
XAUC
LCC
SROC
Golt
0.99h 0000"*
067/1000
034130012
0S1SEDO1 1*
0.055
0.75
0701110010
Method
ICAA
SPAQ
MAE &
XLACT
LOC
SROCT
MAET
XAUC
LEC
SRCC
0.5842-000
07913300102
08789100132
08722-0
0.723300.013
Table 13: Life Time Value Prediction Results.
Criteo-SSC
Kaggle
Method
MAE 4
SRCC
MAE +
SRCC1
GoR
12.965:10.53"*
0.3033-10.094
67.075.10.11 11
0.5363-10.041
Table 14: Watch Time Prediction Results.
Method
KuniRee
KuaiRand
CIKM16
MAE
XAUC 1
MAE
XAUC ~
MAEL
XAUC
GoR
3.194+
0.616+0.007**
7.032-0.132*
0.567+0.006*
0,808 0.80000001
0.696+00.006
Table 15: Facial Age Estimation Results.
Method
UTKFace
EG-NET
MORPH
CACD
MAB
MAE
CST
MAE
MAE
GoR
4324
66. 145
1.68:001115-
85 461600032
2.6
64.95-002222
3.7310.068
75,29 1054
27


Reviews:
[{"review_id": "WDj5ZK4ptI", "reviewer": "Reviewer_n5TF", "summary": "This paper proposes a new method for ordinal regression that treats it as a sequence generation task, predicting segments step by step until an END token. It avoids issues in traditional methods like boundary ambiguity and rigid binning, and introduces a way to balance bias and variance using a new metric called CoDI. It works well across many datasets and is easy to plug into existing generative models.", "questions": "See Weaknesses.", "limitations": "", "rating": 4, "confidence": 4, "soundness": 2, "presentation": 3, "contribution": 2, "strengths": "- This paper is well-written and easy to follow. \n- The experiments show consistent improvements over SOTA across 17 datasets in 6 domains", "weaknesses": "- Is it possible that vocabulary pruning may lead to loss of information, especially affecting minority classes in imbalanced datasets?\n- Does GoR support control over output sequence length, or does it only rely on detecting <EOS>? If no, how to control the maximum length of the output sequence, and will it take a longer time for inference? If yes, what would be the performance when limiting the maximum length of the output sequence to a certain value, e.g., 1? What are the impacts on inference time and performance if the sequence length is limited? More evaluations should be included to demonstrate. \n- How was the threshold $\\epsilon$ and percentage $\\beta$ determined and are there any effects on the final results?", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "gD3wTJvKbi", "reviewer": "Reviewer_BLVB", "summary": "This paper introduces a novel generative framework termed GoR for ordinal regression that reformulates scalar ordinal prediction as autoregressive token generation. By explicitly modeling ordinal dependencies and dynamically controlling prediction granularity via a learnable ⟨EOS⟩ token, the method overcomes the rigidity and boundary ambiguity in conventional discretization- and ranking-based approaches. The proposed CoDi-guided vocabulary construction is theoretically grounded through a bias–variance decomposed MSE bound, ensuring both representational flexibility and cross-domain adaptability. Extensive experiments across diverse tasks demonstrate consistent and substantial improvements over strong baselines, highlighting GoR as a promising and unified paradigm for future research in ordinal modeling.", "questions": "-It remains unclear whether the improvements can be mainly attributed to the proposed paradigm or simply from the stronger autoregressive decoder; further controlled ablations are needed.\n\n-The effectiveness of the proposed method depends on empirical tuning, which may limit robustness across tasks.\n\n-The sequential generation introduces longer prediction paths and potentially higher latency, which poses concerns for efficiency and industrial deployment.\n\n-Autoregressive decoding may suffer from compounding errors. The paper does not sufficiently address exposure bias, nor analyze the trade-off between robustness gains from beam search and increased inference cost.\n\n-The sequence length varies with label range and distribution, potentially affecting stability and efficiency. More evidence is needed to verify consistent performance across tasks with diverse label scales.", "limitations": "", "rating": 6, "confidence": 2, "soundness": 3, "presentation": 3, "contribution": 3, "strengths": "-The sequential generation with a dynamic ⟨EOS⟩ explicitly models ordinal dependencies and enables coarse-to-fine refinement, which can offer strong interpretability and flexibility.\n\n-The paper delivers rigorous analysis of limitations in rank-based methods and a principled MSE error bound, which provides solid justification for the proposed approach.\n\n-Extensive experiments across diverse domains show clear and consistent improvements over strong baselines, thereby demonstrating strong generalizability.", "weaknesses": "-It remains unclear whether the improvements can be mainly attributed to the proposed paradigm or simply from the stronger autoregressive decoder; further controlled ablations are needed.\n\n-The effectiveness of the proposed method depends on empirical tuning, which may limit robustness across tasks.\n\n-The sequential generation introduces longer prediction paths and potentially higher latency, which poses concerns for efficiency and industrial deployment.\n\n-Autoregressive decoding may suffer from compounding errors. The paper does not sufficiently address exposure bias, nor analyze the trade-off between robustness gains from beam search and increased inference cost.\n\n-The sequence length varies with label range and distribution, potentially affecting stability and efficiency. More evidence is needed to verify consistent performance across tasks with diverse label scales.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "j6jIxbRGz6", "reviewer": "Reviewer_yYd1", "summary": "This paper introduces GoR (Generative Ordinal Regression), a novel generative framework that formulates ordinal regression as an autoregressive token generation task, terminating with a dynamic <EOS> token. Instead of relying on traditional continuous space discretization or rank-based classification approaches, GoR represents the target ordinal value as a sequence of additive segments drawn from a learned vocabulary. To support this framework, the authors derive a bias-variance decomposed MSE error bound and propose Coverage–Distinctiveness index for principled vocabulary construction, addressing the trade-off between quantization bias and statistical variance. The framework is model-agnostic, supporting a wide range of encoders and decoders, and is extensible to standard generative learning techniques. Extensive experiments show that GoR achieves state-of-the-art performance consistently.", "questions": "See Weaknesses Above.", "limitations": "", "rating": 8, "confidence": 4, "soundness": 2, "presentation": 4, "contribution": 3, "strengths": "1. The proposal to model ordinal regression as sequential generative modeling is a novel paradigm shift.\n2. The bias-variance decomposition provides theoretical grounding for vocabulary design.\n3. Good potential for future works as it is compatible with standard training techniques used in generative modeling\n4. Achieves consistent gains on the benchmarks.", "weaknesses": "1. Decoding time grows linearly with the number of tokens, which itself varies with the resolution and magnitude of the target ordinal value. The author should consider to include efficiency evaluation.\n2. No comparisons with other generative-based models like DDPM or Normalizing Flows in continuous ordinal prediction.\n3. Longer sequences amplify token-level noise due to accumulating prediction errors across steps. Prediction accuracy may degrade on long sequences or in fine-resolution tasks, especially under greedy decoding. The authors should consider to analyse the trade-off of the model.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "3Z8bzJtuAF", "reviewer": "Reviewer_EExj", "summary": "GoR reframes OR as a sequential generation task, where the model autoregressively predicts tokens representing ordinal value segments based on Coverage-Distinctiveness Index (CoDi) and Quantile-based Vocabulary. This method is novel and interesting. Although similar methods have been applied in other visual fields such as image generation and depth estimation, the contribution of applying generative models to the general ordinal regression task is commendable. Despite this paper facing a few weaknesses in qualitative analysis and missing some related works, I think the current version of the paper has reached the acceptance bar of ICLR. If the author can address my concerns, I will consider further improving my score.", "questions": "1. This method is based on discrete modeling via vocabulary construction. What if using continuous modeling methods? Existing methods show that continuous modeling may be a better choice than discrete modeling in some fields[1].  Has the author conducted any relevant experiments? \n\n   [1] Autoregressive Image Generation without Vector Quantization, NIPS2024.", "limitations": "", "rating": 8, "confidence": 5, "soundness": 4, "presentation": 3, "contribution": 3, "strengths": "1. The method is novel and interesting.\n\n2. Experimental results show the effectiveness of the proposed method. \n\n3. Model-agnostic framework compatible with various architectures makes the model practical and flexible.", "weaknesses": "1. There is a lack of analysis of the distribution of model improvements. In other words, which part of the corrections leads to the performance improvements? boundary samples, small category samples, or most samples in the whole distribution?\n\n2. Medical disease grading is a common OR task. The medical datasets possess boundary ambiguity and long-tail problems. Testing on medical datasets can enhance the influence and persuasion of the proposed method. \n\n3. Regarding the related work on ordinal regression, the author seems to overlook a recent development—the methods of introducing CLIP and language models, e.g, OrdinalCLIP, L2RCLIP, NumCLIP and so on. \n\n4. Lack of experimental comparison to some popular or latest OR methods like PoE (Li et al, CVPR2021), Ord2seq (Wang et al, ICCV2023), and NumCLIP (Du et al, ECCV2024).", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}]

Author rebuttal:

Decision: Accept (Poster)