Token-Level Uncertainty

• Token-level uncertainty is the measure of a model’s confidence at each prediction step, offering granular insight into model reliability.
• It utilizes metrics like predictive entropy, variation ratio, and ensemble methods, balancing aleatoric and epistemic uncertainty effectively.
• Applications include fact-checking, selective abstention, and calibration in language and vision models, improving overall model performance.

Token-level uncertainty is a foundational concept in the quantification and utilization of model confidence within both LLMs and vision models, as well as in downstream applications such as fact-checking, model cascades, calibration, and selective abstention. It refers specifically to quantifying the degree of (un)certainty the model expresses about its decision at the granularity of individual generated or predicted tokens, as opposed to whole sequences, sentences, or utterances.

1. Formal Definitions and Measurement of Token-Level Uncertainty

Token-level uncertainty quantifies a model’s (lack of) confidence at each prediction step (e.g., each token in LM generation, or each patch in a vision transformer), with several families of metrics in use:

• Predictive Entropy: For a model’s output probability vector $p_\theta(\cdot|c)$ over vocabulary $V$ conditioned on context $c$, token entropy is

$$H(t_k\mid c) = -\sum_{v\in V} p_\theta(v\mid c)\log p_\theta(v\mid c)$$

High $H$ indicates more uncertainty (flatter distributions), while $H\approx 0$ signals near-deterministic outputs (Shorinwa et al., 7 Dec 2024).

• Variation Ratio: Defined as $1 - \max_{v\in V} p_\theta(v|c)$, directly measuring the “gap” between confident and uncertain steps (Shorinwa et al., 7 Dec 2024).
• Negative Log Probability/Surprisal: $-\log p_\theta(\hat t_k|c)$ for the generated token $\hat t_k$. Large values reflect surprising, low-confidence predictions (Gupta et al., 15 Apr 2024).
• Bayesian and Ensemble Measures: By running MC Dropout or low-rank weight perturbations, generate an ensemble of predictive distributions

$$p_\text{ens}(v|c) = \tfrac{1}{M}\sum_{m=1}^M p_{\theta^{(m)}}(v|c)$$

Then, * Predictive entropy $H_\text{tot}$ (total uncertainty) * Average entropy (aleatoric uncertainty) * Mutual information (epistemic uncertainty) $I=H_\text{tot}-\tfrac{1}{M}\sum_m H_m$ (Zhang et al., 16 May 2025, Liu et al., 15 Mar 2025, Shorinwa et al., 7 Dec 2024)

• Evidence-based Metrics: Logits-induced token uncertainty (LogTokU) (Ma et al., 1 Feb 2025) interprets evidence directly from logits, modeling total evidence and decomposing uncertainty into aleatoric and epistemic via a Dirichlet parameter.
• Density-based Scores: Mahalanobis distance of token representations to “in-domain” token manifolds in the hidden state space (Vazhentsev et al., 20 Feb 2025).
• Special Token Emission: Models equipped with an [IDK] token explicitly reflect uncertainty by emitting this token if the maximum softmax probability is insufficiently allocated to any “known” target (Cohen et al., 9 Dec 2024).

Table: Principal Token-Level Uncertainty Metrics

Metric	Formula/Computation	Notes
Entropy	$-\sum_{i}p_i\log p_i$	High for flatter/uncertain distributions
Variation Ratio	$1-\max_i p_i$	Zero only if the model is 100% certain
Negative Log-Prob	$-\log p(\text{chosen token})$	Used in masking/curriculum (Liu et al., 15 Mar 2025)
Mutual Information	$H_\text{tot}-\text{E}[H_m]$	Epistemic uncertainty
MD-based Distance	Mahalanobis distance in hidden space	Requires reference Gaussian
Evidence Decomposition	Dirichlet-derived entropy/inverse concentration	LogTokU: aleatoric/epistemic per token
[IDK] Token	Shifted probability mass to [IDK], adaptive loss	Explicit, human-interpretable abstention

2. Interpretations: Aleatoric vs. Epistemic Uncertainty

Fundamental to the debate is distinguishing between:

• Aleatoric uncertainty (inherent ambiguity in the data, e.g., polysemy or surface-form competition).
• Epistemic uncertainty (ignorance in the model parameters or neglected knowledge).

Bayesian approaches and MC Dropout variants compute expected entropy (aleatoric) and the difference between ensemble predictive entropy and average entropy (epistemic), operationalized as the BALD score (Liu et al., 15 Mar 2025, Zhang et al., 16 May 2025, Shorinwa et al., 7 Dec 2024).

Dirichlet-based and evidence-theoretic methods (e.g., LogTokU) explicitly decompose evidence to separate out these effects at the token level, sidestepping softmax normalization pitfalls (Ma et al., 1 Feb 2025, Shen et al., 2020).

3. Computational Methodologies and Algorithms

White-box Methods

Direct access to logits/hidden states underpins most classic methods. Example pseudocode for entropy, negative log-probability, and LogTokU is provided in (Ma et al., 1 Feb 2025, Liu et al., 15 Mar 2025, Zhang et al., 16 May 2025), with computational steps including:

• For entropy, compute next-token softmax, sum $-\sum_{i}p_i\log p_i$.
• For LogTokU, extract top-$K$ logits (clipped at zero), compute Dirichlet parameters, and derive AU/EU.
• MD-based: extract representations, compute Mahalanobis distances layer-wise (Vazhentsev et al., 20 Feb 2025).
• Ensemble-based: sample $M$ perturbed models, aggregate token probabilities.

Black-Box and Logit-Free Methods

Split conformal methods (e.g., Token-Entropy Conformal Prediction, TECP (Xu, 30 Aug 2025)) conduct repeated generation sampling, empirically estimate entropy distributions per position, and calibrate set-valued outputs via quantile-based thresholds to guarantee coverage without access to internal logits.

Cascade routers and post-hoc deferral (LLM Cascades (Gupta et al., 15 Apr 2024)) engineer aggregate features (e.g., sorted quantiles of token probabilities) to guide selective deferral or abstention.

Structural and Graph-Based Extensions

GENUINE (Wang et al., 9 Sep 2025) introduces hierarchical pooling over dependency-parse token graphs. Token-level uncertainties (probabilities, entropies, white-box features) are embedded as node features, and unsupervised and supervised graph pooling enhances uncertainty aggregation, promoting syntactically and semantically pivotal tokens.

4. Applications and Empirical Impact

• Fact-Checking and Hallucination Detection: Uncertainty scores are used to flag atomic claims or token spans for downstream fact verification (Fadeeva et al., 7 Mar 2024). Claim-Conditioned Probability (CCP) conditions on semantic content to isolate uncertainty specific to a given fact, excluding sequencing and synonymy.
• Selective Abstention / [IDK] Emission: Explicit modeling enables high-precision abstention policies, boosting factual accuracy and F1 (e.g., Mistral-7B, LAMA-RE: Precision +23%; Recall –8%) (Cohen et al., 9 Dec 2024).
• Few-shot Image Classification: BATR-FST (Al-Habib et al., 16 Sep 2025) leverages uncertainty gating of patch tokens for improved generalization in vision transformers.
• Entity Linking: Single-shot, token-level feature regression tracks multi-shot uncertainty with ~90% performance but ~10x lower compute (Bono et al., 24 Sep 2025).
• Reasoning and CoT Evaluation: Low-rank perturbation and mutual information guide best-of-N and particle filtering to boost pass@1 in mathematical reasoning (Zhang et al., 16 May 2025).
• Calibration and Selective Classification: Large-scale calibration analysis on 80 LLMs shows improved ECE and AUROC correlating with model size and reasoning ability, with token-probability-based uncertainty a necessary but not sufficient tool (Tao et al., 29 May 2025).
• Contextual QA: Feature-gap analysis links epistemic uncertainty to interpretable semantic axes (context reliance, comprehension, honesty), achieving up to +13 PRR over state-of-the-art unsupervised UQ (Bakman et al., 3 Oct 2025).

5. Technical Challenges and Limitations

• Type Sensitivity and Calibration: Probability/entropy-based measures conflate knowledge gaps with data ambiguity. In probabilistic scenarios, token probabilities and entropies diverge sharply from theoretical targets despite perfect response validity (Toney-Wails et al., 1 Nov 2025).
• Black-box Constraints: Sampling-based entropy and conformal prediction enable UQ where logits are inaccessible, but incur higher runtime and variance (Xu, 30 Aug 2025).
• Length and Aggregation Biases: Sequence-level aggregation of token-level uncertainties introduces bias (favoring shorter or longer outputs) if naive sums or averages are used (Gupta et al., 15 Apr 2024).
• Mechanistic Interpretability: Layer-wise inference dynamics may not differentiate uncertain and certain predictions in non-trivial ways; increasing competence only mildly associates with delayed commitment (Kim et al., 9 Jul 2025, Brothers et al., 8 Dec 2024).
• Generalization and Domain Shift: Density-based supervised methods (e.g., SATRMD+MSP) fare best with hybrid strategies for out-of-domain robustness; care is needed in unseen contexts (Vazhentsev et al., 20 Feb 2025).

6. Extensions and Open Research Directions

• Hybrid Validation: Incorporating structural priors (e.g., via dependency graphs (Wang et al., 9 Sep 2025)) and latent feature gaps (Bakman et al., 3 Oct 2025) offers improved discrimination and interpretability.
• Fine-Grained Curriculum: Masked MLE and distillation training objectives, guided by token-level losses, accelerate epistemic uncertainty reduction and mitigate overfitting (Liu et al., 15 Mar 2025).
• Evidence- and Feature-Based UQ: Exploring attention-based or energy-based surrogates for per-token evidence may realize improved UQ in both generative and discriminative models (Ma et al., 1 Feb 2025, Bakman et al., 3 Oct 2025).
• Automated Abstention Policies: Calibrated abstention strategies with [IDK] emission balance precision and recall under adaptive thresholds, suggesting direct integration into LLM pretraining (Cohen et al., 9 Dec 2024).
• Black-box Surrogates and Light-Weight Probes: Development of quantile-based routers (Gupta et al., 15 Apr 2024), recurrent probing, and conformal entropy pipelines (Xu, 30 Aug 2025) target single-pass, explainable UQ deployable in restricted API settings.

7. Comparative Performance and Practical Considerations

Empirical studies consistently show:

• Token-level uncertainty metrics (entropy, MD, AU/EU decompositions, CCP) outperform sequence-level aggregates and log-probabilities in flagging errors and hallucinations, typically yielding +0.05–0.15 ROC-AUC gains over baselines (Fadeeva et al., 7 Mar 2024, Vazhentsev et al., 20 Feb 2025, Tao et al., 29 May 2025).
• Incorporation of semantic, graph-based, or feature-gap structure achieves up to 29% AUROC improvement and 15–25% lower calibration error relative to flat entropy-based methods (Wang et al., 9 Sep 2025, Bakman et al., 3 Oct 2025).
• Single-shot approximations (feature regression, layer-averaged scores) recover 80–90% of performance at ~10x lower computational cost than multi-shot ensemble/sampling (Bono et al., 24 Sep 2025).
• Masked MLE + self-distillation regularized training improves in-domain and out-of-domain performance, with a natural curriculum effect as the mask distribution evolves (Liu et al., 15 Mar 2025).
• In multiclass probability scenarios, token-level entropy may be systematically misaligned with target randomness, requiring dual validity-calibration metrics (Toney-Wails et al., 1 Nov 2025).

Collectively, token-level uncertainty comprises a rich axis of control, calibration, and interpretability across language and vision models, yet is challenged by the need to distinguish sources of uncertainty, aggregate granular signals upward, and efficiently place them in the hands of downstream users and automated safety systems.