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GCUL: Ambiguity Identification in Text Emotion Classification via Cluster-Guided Learning

Zhongqi Fan, Tianyou Zhang, Fei Chen

arXiv:2609.29327v1stat.MLcs.LG

TL;DR

Selective classification permits abstention on uncertain inputs, but common approaches may overlook collective geometric structure among difficult samples. GCUL identifies and relabels uncertain regions through clustering and derives a geometric feasibility criterion for rejection. Experiments report improved selective accuracy on datasets with concentrated confusion structure and a data-adaptive alternative to prescribed rejection rates.

  • Problem

    Existing selective-classification approaches rely mainly on instance-level statistics or constraints and may overlook collective geometric structure among difficult representations.

    Source: §1 · pp. 1–2

  • Method

    GCUL identifies ambiguous samples as a potential confusion attractor, adds an uncertainty class through a three-phase clustering and relabeling procedure, and derives a selectivity score with a geometric sufficient condition.

    Source: §1 · p. 2

  • Results

    Benchmark experiments indicate GCUL substantially improves selective accuracy on datasets with concentrated confusion structure, with competitive performance across representation dimensions without manually specified rejection rates.

    Source: §1 · p. 2

  • Takeaways & Limitations

    The geometric feasibility criterion offers a pre-deployment way to assess whether a representation space is favorable to selective prediction.

    Source: §1 · p. 2, §5 · p. 8

    Current empirical evaluation is restricted to text-based emotion classification, and the theoretical guarantees assume a dominant confusion attractor that may not hold for multiple disconnected clusters or severe non-Gaussianity.

    Source: §5 · p. 8

Abstract

from arXiv · show

Selective classification enables a model to abstain from predictions on uncertain instances, but existing approaches typically reject them through confidence scores, predefined coverage constraints or instance-level distance measures. These approaches may overlook the collective geometric structure of difficult samples in learned representation spaces. We propose Guided Clustering-based Uncertain Learning (GCUL), a geometric-guided selective classification framework that identifies misclassified and ambiguous instances as a potential confusion attractor in the representation space. GCUL uses a three-phase procedure to initialize, cluster, and explicitly relabel this uncertain region, allowing the rejection boundary to emerge from the underlying representation geometry rather than from a prescribed rejection rate. We further derive a selectivity score and a geometric sufficient condition that characterizes when rejection can provide positive operational utility, enabling pre-deployment feasibility assessment. GCUL improves DistilBERT accuracy from 89.37 percent to 94.98 percent with less than 9 percent rejection. Beyond accuracy, our selectivity score correctly pre-detects the only dataset (GoEmotion) where all baselines fail, and controlled simulations yield 6.1 percent Type-I and 0 percent Type-II errors, validating the sufficient condition's conservatism. These results suggest that collective representation geometry provides a useful alternative perspective for selective prediction.

1 Introduction

Selective classification addresses the risk of costly errors by allowing abstention, but common approaches rely on instance-level confidence or constraints and may miss collective structure in hard examples. GCUL uses representation geometry to identify uncertain samples and introduces a feasibility criterion for when rejection can be useful.

1 Introduction

  • Existing selective methods often use confidence thresholds or predefined constraints, while representation-geometry methods evaluate instances individually and do not explicitly exploit collective structures among hard samples.GCUL is evaluated for short-text multiclass emotion classification on three benchmark datasets.Source: §1 · pp. 1–2
  • BERT feature visualizations show that misclassified and ambiguous samples form localized compact clusters, and misclassified samples can form a compact, linearly separable confusion cluster.The paper interprets this structure as systematic errors concentrated near semantic ambiguity boundaries rather than pure stochastic noise.Source: §1 · p. 2
  • GCUL models ambiguous samples with an uncertainty class through three phases: initial classification, clustering and relabeling of confusing samples, then retraining a classifier with an uncertain class.The clustering stage uses LDA and K-Means with 12 initial centers; clusters with lowest purity are relabeled as uncertain.Source: §1 · p. 2
  • GCUL's theoretical analysis formulates error reduction against rejection cost and derives sufficient geometric conditions and a critical rejection-cost threshold for assessing feasibility before an extensive search.The conditions involve error capture, clean-sample contamination, centroid separation and directional dispersion.Source: §1 · p. 2
  • Benchmark experiments indicate GCUL substantially improves selective accuracy on datasets with concentrated confusion structure, while its value is a data-adaptive rejection formulation rather than universal superiority.Comparisons across representation dimensions also indicate competitive performance without manually specified rejection rates; synthetic experiments support the theoretical feasibility framework's accuracy and stability.Source: §1 · p. 2

2 The GCUL framework

GCUL treats hard-to-classify representations as clusters and introduces an uncertain class to separate confusing samples from more clearly distinguishable classes. Its operational-risk analysis seeks conditions under which this form of rejection yields positive utility.

2 The GCUL framework

  • GCUL shifts from instance-level thresholding toward cluster-guided uncertainty learning because hard-to-classify samples are described as inhabiting compact manifolds.The framework aims to separate the gathering place of confusion samples and label its output uncertain.Source: §2 · p. 2, §2.1 · p. 3

2.1 The three-phase GCUL pipeline

  • The three-phase pipeline trains an initial classifier, clusters and relabels confusing samples as uncertain, then retrains a classifier with an added uncertain class.The framework uses unsupervised clustering because uncertain samples do not initially have special labels.Source: §2.1 · p. 3

2.2 Operational risk formulation and utility gain

  • The operational-risk formulation seeks a formal boundary for when cluster-guided rejection yields positive utility, rather than assuming gains from empirical trials will generalize across datasets.The feasibility domain is intended to distinguish geometric separability from hyperparameter and data-partitioning artifacts and provide an a priori sufficient condition for practitioners.Source: §2.2 · p. 3

3 Theoretical feasibility analysis

The analysis formalizes GCUL as a three-phase procedure and derives when its cluster-guided rejection can yield positive operational utility. The criterion links error capture and clean-sample contamination to geometric bounds under stated assumptions.

3.1 Mathematical framework and foundational assumptions

  • GCUL initializes a base classifier, clusters projected embeddings with clean-class and confusion-attractor centroids, relabels low-purity clusters as uncertain, then retrains a reject-capable classifier.At inference, the uncertainty label triggers deferred rejection for human review.Source: §3.1 · p. 3

Foundational assumptions for feasibility analysis

  • The feasibility analysis assumes a single dominant error attractor, consistent error-pool estimates, stable initialization, and asymptotically Gaussian, sub-Gaussian directional projections.The cost assumptions bound base error between 0 and 1 and normalized rejection cost between 0 and 1.Source: Foundational assumptions for… · pp. 3–4

3.2 Selectivity score and monotonicity

  • The selectivity score exceeds the relative rejection cost when rejection yields positive utility, and increases with error capture while decreasing with clean-sample contamination.The score measures the confusion attractor’s net selectivity, normalized by feature-distribution geometry.Source: §3.2 · p. 4

3.3 Effectiveness threshold and feasibility region

  • GCUL is guaranteed operationally effective when the geometric signal-to-noise ratios satisfy the sufficient condition derived under Assumptions 1–5.The condition uses bounds on error capture and clean contamination based on centroid separation relative to directional variance.Source: §3.3 · pp. 4–5
  • Centroid separation relative to directional variance exponentially depresses boundary loss and clean contamination, supporting closed-form capture and contamination bounds.The resulting signal-to-noise condition supplies a geometric sufficient test for whether the selectivity score can exceed rejection cost.Source: §3.3 · pp. 4–5

3.4 Rigorous capture rate bounds via sub-Gaussian concentration

  • A class-wise error-loss cover separates boundary-truncation losses from directional-tail outliers; Boole’s inequality yields a conservative global capture-rate lower bound.As dispersion vanishes relative to centroid separation, the structural-existence confidence approaches 1 and the bound recovers projection concentration; the bound also avoids measure collapse when dispersion diverges.Source: §3.4 · p. 5

4 Empirical evaluation

GCUL improves accepted-sample accuracy on Kaggle and derives rejection boundaries from representation geometry rather than prescribed rejection rates. Across datasets and controlled synthetic perturbations, its utility depends on the data’s confusion structure, while its feasibility criterion provides a conservative screening signal.

4.1 Benchmark performance on real-world datasets

  • 94.98% selective accuracy on accepted samples versus DistilBERT’s 89.37% accuracy, with 8.49% rejected, for GCUL-LDA on Kaggle.GCUL-PCA reaches 95.85% accuracy, while GCUL-LDA reduces the uncertainty rate from 10.24% to 8.49%.Source: §4.1 · p. 5, Table 1 · p. 5

4.2 Comparison with selective classification baselines

  • GCUL achieves competitive selective performance without a prescribed rejection fraction, while traditional baselines are highly sensitive to explicit operating parameters.MSP varies with rejection cost, SelectiveNet with target coverage, and Mahalanobis rejection with retained percentage.Source: §4.2 · p. 6, Figure 2 · p. 6
  • GCUL’s selective accuracy and rejection rate stabilize across a broad range of representation dimensions, but vary more in extremely low-dimensional settings.The low-dimensional variation occurs where critical geometric structure is lost.Source: §4.2 · p. 6, Figure 3 · p. 6
  • The predicted critical rejection cost tracks the empirical feasibility trend across PCA dimensions while remaining a conservative lower bound.The criterion can be evaluated a priori to assess whether a representation space is suitable for GCUL rejection.Source: §4.2 · pp. 6–7, Figure 4 · p. 7
  • On GoEmotions, no evaluated method provides meaningful utility improvement, and GCUL’s feasibility analysis predicts no feasible operating regime (λ∗ PRE = 0).The MSP baseline rejects nearly all samples for λ < 0.6 and almost none for λ > 0.6.Source: §4.2 · p. 7

4.3 Synthetic phase-transition verification

  • Across the synthetic noise sweep, λ∗ PRE closely tracks λ∗ EMP, including their near-identical monotonic decrease during Noise ∈[3.0, 7.0].The paper reports this alignment as evidence that the sufficient condition gives a tight bound for selective utility.Source: §4.3 · pp. 7–8, Figure 5 · p. 7
  • When noise exceeds 8.5, λ∗ PRE approaches 0.0, while the empirical threshold retains a minor floor without effective utility gain over baseline.The paper attributes the theoretical threshold’s decay to noise polluting cluster geometry.Source: Figure 5 · p. 7, §4.3 · p. 8
  • Across 410 synthetic runs, there are 25 Type-1 violations and no Type-2 violations, consistent with a sufficient rather than necessary feasibility condition.A satisfied condition coincides with no empirical failure in this controlled experiment, while an unsatisfied condition does not necessarily imply ineffectiveness.Source: §4.3 · p. 8, Table 2 · p. 8

5 Conclusion and discussion

GCUL identifies confusion regions from representation geometry and is presented as a wrapper that can reuse standard classifiers and their representations. Its empirical scope and theoretical assumptions constrain generalization, while the appendix derives a closed-form selectivity score.

5 Conclusion and discussion

  • GCUL is a geometry-driven selective-classification framework whose performance is reported for datasets with coherent confusion structures, not as a universal baseline.The paper frames its theoretical feasibility criterion as a way to screen applicability before a full operating-point search.Source: §5 · p. 8
  • GCUL wraps standard classifiers without changing backbone designs, allowing Phase 1 models and representations to be reused.The paper also reports consistent qualitative behavior across classification backbones.Source: §5 · p. 8
  • The current empirical evaluation is limited to text-based emotion classification, and the theoretical guarantees rely on a dominant confusion attractor that may not fit disconnected or severely non-Gaussian uncertain samples.The paper also notes that overly aggressive dimensionality reduction risks losing spatial information, while excessively high dimensions yield conservative clustering.Source: §5 · p. 8

A.1 Derivation of the effectiveness criterion (Eq. 4)

  • The appendix derivation simplifies the selectivity score to a closed-form expression in Eq. 4.The derivation substitutes ρ = εr1 + (1 − ε)r2 before obtaining that expression.Source: §A.1 · p. 10

A.2 Proof of Theorem 3.1 (strict monotonicity)

The proof establishes that the selectivity score rises with error capture and falls with contamination, then reduces cluster membership to a one-dimensional projection boundary. It also frames boundary loss and clean-sample contamination as projection-tail probabilities.

A.2 Proof of Theorem 3.1 (strict monotonicity)

  • The selectivity score is strictly increasing in capture rate r1 and strictly decreasing in contamination rate r2.Both derivative signs are established under 0 < r2 < r1 < 1 and 0 < ε < 1.Source: §A.2 · p. 10

B.1 Proof of 1D Voronoi projection reduction

  • K-Means membership in Cmix reduces to a one-dimensional projection test, with the decision boundary at zc = Dc/2.A sample remains in Cmix when zc < Dc/2, where zc measures displacement from µmix toward µc.Source: §B.1 · p. 10

B.2 Proof of Lemma 3.2 (boundary loss and contamination probabilities)

  • The boundary-loss and contamination analysis uses projection tails for error samples and clean samples, respectively.The proof considers error samples beyond Dc/2 and clean samples penetrating into Cmix.Source: §B.2 · p. 10

B.3 Proof of Theorem 3.3 (global rate bounds)

The proof bounds the global capture and contamination rates by summing class-wise losses and false captures. These bounds are combined with the selectivity score’s monotonicity to establish the global rate result.

B.3 Proof of Theorem 3.3 (global rate bounds)

  • The lower bound for capture rate r1 starts from total base errors and subtracts the expected uncaptured errors across classes.For each class, expected losses are class error counts multiplied by the class loss probability.Source: §B.3 · p. 11
  • The upper bound for contamination rate r2 sums class-wise clean-sample captures into Cmix and divides by the total correctly classified samples.The proof bounds each class’s clean-sample count by its class prior before summing.Source: §B.3 · p. 11
  • The global rate bounds combine class-wise error losses with clean-sample false captures, then use selectivity-score monotonicity to complete the proof.Lost errors are summed across classes to bound capture rate r1; clean samples falsely captured into Cmix are summed to bound contamination rate r2.Source: §B.3 · p. 11

C.1 Proof of lemma for directional chernoff outlier bound (Eq. 13)

The proof bounds directional outliers with a Chernoff argument under a directional sub-Gaussian assumption, then uses the bound in a lower bound for error capture. As the outlier fraction vanishes, the selectivity lower bound converges to the projection-measure concentration bound.

C.1 Proof of lemma for directional chernoff outlier bound (Eq. 13)

  • A Chernoff argument bounds directional outliers under a directional sub-Gaussian assumption, with the optimizing parameter set by Dc and σ²mix,c.The proof minimizes a quadratic exponent over λ > 0.Source: §C.1 · p. 11

C.2 Proof of Theorem 3.5 (rigorous lower bound for r1)

  • The lower bound for capture rate r1 uses a union bound over boundary losses and directional outliers escaping the control region.This combines the empirical capture-rate expression with the class-wise loss and outlier bounds.Source: §C.2 · p. 11

C.3 Proof of corollary 3.6 (asymptotic convergence)

  • As the directional outlier fraction tends to zero, the Chernoff penalty vanishes and the lower bound on selectivity converges to the projection-measure concentration bound.The passage also states that Sexist tends to 1.Source: §C.3 · p. 11

D Detailed dataset statistics and empirical profiling

The three benchmark profiles span substantial differences in class balance and text length. The accompanying analysis states that GCUL’s cluster-guided rejection does not rely on balanced class priors and that sequence length is not a confounding artifact in cluster formation.

D Detailed dataset statistics and empirical profiling

  • Dair-AI/Emotion has a long-tailed class distribution from 6,761 joy samples to 719 surprise samples, with sequence lengths centered near a median of 86 characters.Figure 6 profiles both class counts and sequence lengths.Source: Figure 6 · p. 12
  • GoEmotions is highly imbalanced, with 55,298 neutral instances, while its texts peak sharply around a median length of 69 characters.The dataset profile describes a fine-grained emotion taxonomy and concise texts.Source: Figure 7 · p. 12
  • The Kaggle emotion dataset has roughly 10,000 samples per class except for an empty category with 6,358 samples, and its text lengths have a mean of 103 characters with long-tail outliers.Its class distribution is described as otherwise uniform, while sequence lengths show higher variance.Source: Figure 8 · p. 12
  • Across benchmarks, class balance ranges from roughly 10,000 samples per Kaggle class to 55,298 neutral versus 7,359 confusion instances in GoEmotions.The authors state this range indicates that GCUL’s cluster-guided rejection does not rely on balanced class priors.Source: D Detailed dataset statistics and… · p. 12
  • The three datasets have median sequence lengths from 69 to 92 characters, with outlier tails reaching 800 characters in Kaggle anger.The per-class boxplots are described as showing uniform text-length distributions across semantic emotions, ruling out sequence length as a confounding artifact in cluster formation.Source: D Detailed dataset statistics and… · p. 12

E.1.1 Baseline models implementation

The section lists implementation settings for the baseline models and identifies tables covering GCUL, comparison methods, synthetic-data generation, pipeline parameters, noise injection, and evaluation metrics.

E.1.1 Baseline models implementation

  • Baseline models use validation-loss early stopping, with TF-IDF settings specified for traditional classifiers, including 1–2-gram features and a 10,000-word vocabulary cap.Linear models use C = 1.0; the Random Forest has 100 estimators.Source: §E.1.1 · pp. 12–13
  • TextCNN uses 25,000 vocabulary entries, 100-token sequences, 300-dimensional embeddings, and filter sizes 2, 3, and 4.It uses 100 feature maps per filter size, dropout 0.6, and Adam with learning rate 5 × 10−4.Source: §E.1.1 · p. 13
  • BiLSTM-Attention uses fine-tunable 300-dimensional GloVe embeddings with 84.3% vocabulary coverage and a two-layer BiLSTM.The model uses hidden dimension 128, self-attention dimension 64, dropout 0.5, and Adam with learning rate 1×10−3.Source: §E.1.1 · p. 13
  • DistilBERT is fine-tuned for three epochs with maximum sequence length 128, batch size 32, and AdamW learning rate 3 × 10−5.The specified model is distilbert-base-uncased with 66M parameters, warmup ratio 0.05, and weight decay 0.01.Source: §E.1.1 · p. 13

E.1.2 GCUL framework hyperparameters

  • Table 3 is identified as the GCUL framework hyperparameter configuration.Source: Table 3 · p. 13

E.2 Comparison with selective classification baselines

  • Table 4 is identified as the experimental parameter configuration for selective-classification baselines and GCUL.Source: Table 4 · p. 13

E.3 Experimental setup

F.1.1 Kaggle dataset

The section identifies result tables for selective-classification methods on Kaggle, GoEmotions, and Dair-AI, plus a GCUL noise-sweep table for synthetic data.

F.1.1 Kaggle dataset

F.1.2 GoEmotions dataset

F.1.3 Dair-AI emotion dataset

  • Four tables are identified as reporting MSP, SelectiveNet, Mahalanobis, and GCUL results on the Dair-AI emotion dataset.Source: Table 17 · p. 15, Table 18 · p. 15, Table 19 · p. 15
  • A separate table is identified as reporting GCUL performance across varying noise levels on synthetic data, using seed 16.Source: Table 21

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