Generalized Correctness Models: Learning Calibrated and Model-Agnostic Correctness Predictors from Historical Patterns (2509.24988v1)

Abstract: Generating accurate and calibrated confidence estimates is critical for deploying LLMs in high-stakes or user-facing applications, and remains an open challenge. Prior research has often framed confidence as a problem of eliciting a model's "self-knowledge", i.e., the ability of an LLM to judge whether its own answers are correct; this approach implicitly assumes that there is some privileged information about the answer's correctness that is accessible to the model itself. However, our experiments reveal that an LLM attempting to predict the correctness of its own outputs generally performs no better than an unrelated LLM. Moreover, we hypothesize that a key factor in building a "Correctness Model" (CM) is exposure to a target model's historical predictions. We propose multiple methods to inject this historical correctness information, creating a Generalized Correctness Model (GCM). We first show that GCMs can be trained on the correctness data from many LLMs and learn patterns for correctness prediction applicable across datasets and models. We then use CMs as a lens for studying the source of correctness prediction ability and its generalization, systematically controlling their training data and finding that answer phrasing is a strong predictor for correctness. We further explore alternative methods of injecting history without training an LLM, finding that including history as in-context examples can help improve correctness prediction, and post-hoc calibration can provide complementary reductions in calibration error. We evaluate GCMs based on Qwen3-8B across 5 model families and the MMLU and TriviaQA datasets, as well as on a downstream selective prediction task, finding that reliable LLM confidence estimation is a generalizable and model-agnostic skill learned by systematically encoding correctness history rather than a model-specific skill reliant on self-introspection.

• The paper demonstrates that LLMs lack superior self-knowledge for predicting correctness, prompting a shift to history-based models.
• The paper introduces GCMs that leverage historical patterns, answer phrasing, and world knowledge to improve accuracy and reduce calibration error.
• The paper validates GCMs through cross-model and cross-dataset comparisons, enabling robust selective prediction for safety-critical applications.

Generalized Correctness Models: Model-Agnostic, Calibrated Correctness Prediction from Historical Patterns

Introduction and Motivation

The paper "Generalized Correctness Models: Learning Calibrated and Model-Agnostic Correctness Predictors from Historical Patterns" (2509.24988) addresses the challenge of producing reliable, calibrated confidence estimates for LLM outputs—a critical requirement for deploying LLMs in high-stakes or user-facing applications. The prevailing paradigm in LLM confidence estimation has been to elicit "self-knowledge" from the model, i.e., to have the LLM predict the correctness of its own outputs. This approach assumes that the model possesses privileged internal information about its own correctness. However, the authors empirically demonstrate that this assumption does not hold: LLMs do not exhibit superior ability to predict the correctness of their own outputs compared to other models, even when trained or prompted specifically for this task.

This insight motivates a shift from self-referential correctness modeling to a more general, history-driven approach. The authors propose Generalized Correctness Models (GCMs), which are trained on historical correctness data from multiple LLMs and are designed to predict the correctness of outputs in a model-agnostic and highly calibrated manner. The GCM framework leverages patterns in historical predictions, answer phrasing, and world knowledge, rather than relying on model-specific introspection.

Empirical Analysis: Self-Knowledge vs. Generalized Correctness

The first core finding is that LLMs lack privileged self-knowledge for correctness estimation. Experiments show that a model's ability to predict its own correctness is statistically indistinguishable from its ability to predict the correctness of other models, and vice versa. For example, Qwen2.5-7B outperforms Llama3.1-8B in predicting both its own and Llama's correctness, but this is attributable to Qwen's higher parametric knowledge, not to any self-referential advantage.

Figure 1: Self- vs. cross-model correctness prediction and the impact of historical information on calibration. GCMs trained on multiple models' histories achieve high accuracy and low calibration error, outperforming both self-prediction and larger models' logits.

Figure 2: Correctness prediction in answerful (with responses) and answerless (without responses) settings. Performance is driven by dataset signals and world knowledge, not privileged self-knowledge.

This result holds across both answerful and answerless settings, and is robust to training-free and in-context learning (ICL) approaches. The implication is that correctness prediction is not a model-specific skill, but rather a generalizable capability that can be learned from historical data.

Generalized Correctness Models: Architecture and Training

The GCM is instantiated as a finetuned LLM (e.g., Qwen3-8B) trained on the concatenation of correctness datasets from multiple LLMs. The input to the GCM includes the query, the full response, and the extracted answer, optionally with the model identity. The output is a calibrated probability $P(\text{is\_correct}(\hat{r})|q, r, \hat{r})$.

Key implementation details:

• Finetuning: LoRA with rank 32, batch size 16, 1 epoch, cross-entropy loss.
• Datasets: MMLU and TriviaQA, with correctness labels generated by a judge model.
• Evaluation: Accuracy, Expected Calibration Error (ECE), Root Mean Squared Calibration Error (RMSCE), and AUROC.

The GCM is compared to Specific Correctness Models (SCMs) trained on individual models, as well as to baseline confidence elicitation methods (logit-based, verbalized, ICL, post-hoc calibration).

Generalization and Transfer

GCMs exhibit strong generalization across model families, model sizes, and even to held-out models not seen during training. Notably, a Qwen3-8B GCM trained on eight models outperforms SCMs trained on individual models by 2.22% accuracy and 0.041 AUROC on average, and surpasses the self-emitted confidences of Llama3-70B by 2.4% accuracy and 0.265 AUROC on MMLU.

GCMs also transfer across datasets, outperforming SCMs trained on the target dataset in AUROC and matching their ECE and accuracy after post-hoc calibration with as little as 5% of the target dataset. However, cross-dataset generalization is less robust than cross-model generalization, indicating that dataset-specific features still play a role in correctness prediction.

Conditioning Factors and Ablations

Ablation studies reveal the relative importance of different conditioning variables:

• Answer phrasing: The way an answer is elaborated in the response is a strong predictor of correctness, beyond the answer choice itself.
• World knowledge: The model's parametric knowledge about the answer, independent of the generating model, is a key enabler for generalization.
• Model identity: Including the target model's name provides a minor benefit, but most of the GCM's predictive power is model-agnostic.

Figure 3: Conditioning factors ablation. Each component (query, answer, response) contributes to correctness prediction, with answer phrasing and world knowledge being especially important.

Alternative History Injection: In-Context Learning and Post-Hoc Calibration

The authors explore training-free methods for injecting historical information:

• In-Context Learning (ICL): Supplying semantically similar historical examples in the prompt improves accuracy and calibration for larger models, but is less effective for smaller models and incurs significant inference cost.
• Post-hoc Calibration: Spline calibration and other post-processing methods can align GCM outputs to new datasets with minimal data, reducing ECE and matching SCM performance.

These methods provide practical alternatives when finetuning is infeasible, but GCMs remain more efficient and robust for large-scale deployment.

Downstream Applications: Selective Prediction

GCMs enable improved selective prediction, where the system abstains from answering when confidence is low. Risk-coverage curves show that GCMs achieve lower risk at the same coverage compared to SCMs and self-emitted confidences from large models, making them preferable for robust deployment in safety-critical settings.

(Figure 4)

Figure 4: Risk-coverage curves for selective prediction. GCMs achieve lower risk at equivalent coverage, indicating more reliable abstention and improved safety.

Implementation Considerations and Practical Guidance

• Resource Requirements: GCMs can be trained efficiently on moderate hardware (e.g., a single A100 for Qwen3-8B), with training times on the order of hours for datasets of ~10k examples.
• Inference Efficiency: GCMs require only a single forward pass per example, in contrast to ICL methods that multiply prompt length and latency.
• Scalability: The approach is agnostic to the number of target models and can be extended to new models or datasets with minimal retraining or calibration.
• Limitations: Cross-dataset generalization is less robust; calibration may degrade on out-of-distribution data without post-hoc adjustment. The method assumes access to correctness-labeled historical data, which may be expensive to generate for proprietary or closed models.

Theoretical and Practical Implications

The findings challenge the notion that LLMs possess privileged self-knowledge for correctness estimation, reframing confidence prediction as a generalizable, history-driven task. This has implications for the design of AI systems in high-stakes domains: rather than relying on introspective confidence from the deployed model, practitioners should leverage GCMs trained on diverse historical data for robust, calibrated correctness estimation.

The GCM framework also provides a foundation for future research in model-agnostic evaluation, scalable oversight, and risk-aware deployment. It suggests that correctness prediction is a transferable skill, and that calibration can be systematically improved by encoding historical patterns rather than relying on model-specific introspection.

Conclusion

Generalized Correctness Models represent a paradigm shift in LLM confidence estimation, demonstrating that calibrated, model-agnostic correctness prediction is achievable by leveraging historical patterns across models and datasets. GCMs outperform both self-prediction and larger models' confidences, generalize across architectures, and enable robust selective prediction. The approach is practical, scalable, and well-suited for deployment in safety-critical applications, provided that historical correctness data is available and post-hoc calibration is applied for out-of-distribution settings. This work lays the groundwork for more reliable, trustworthy AI systems by decoupling correctness estimation from model-specific introspection and emphasizing the value of systematic historical encoding.