Aligning Language Models with Selective Prediction

Large language models (LLMs) are increasingly deployed in question answering (QA) systems, yet they may generate hallucinated or misaligned responses without reliable confidence estimates. Uncertainty quantification (UQ) offers a natural basis for selective answering, where a system answers only when its prediction is deemed reliable and abstains otherwise. However, existing uncertainty scores for LLMs are often heuristic: a threshold chosen on such scores does not, by itself, provide statistical guarantees on the error rate among accepted answers. We propose CIC, a confidence-interval-based calibration framework that converts arbitrary uncertainty scores into risk-controlled selective answering rules. Given a held-out calibration set, CIC evaluates each generated response using an application-specific alignment criterion and associates it with an uncertainty score and a binary error label. For each candidate uncertainty threshold, CIC estimates the acceptance-conditioned error rate and constructs a high-probability upper confidence bound using either Hoeffding-style or Clopper-Pearson confidence intervals. It then selects the largest threshold whose upper bound is below a user-specified risk level $α$, thereby maximizing the answering rate subject to a finite-sample reliability constraint. Under exchangeability, CIC guarantees with probability at least $1-δ$ that the selected threshold, if non-null, controls the error rate among accepted answers at level $α$. We evaluate CIC on both closed-ended and open-ended QA benchmarks across seven LLMs and multiple uncertainty estimators. Experimental results show that CIC consistently achieves valid risk control while retaining strong answering efficiency, providing a practical and statistically grounded mechanism for deploying LLMs in reliability-sensitive QA workflows.

Large Language Models (LLMs) often produce plausible but poorly-calibrated answers, limiting their reliability on reasoning-intensive tasks. Recent research suggests that Chain-of-Thought (CoT) reasoning paths are inherent in pre-trained LLMs and can be elicited by simply altering the decoding process, where the presence of a CoT path correlates with higher answer confidence. Building on these insights, we present Reinforcement Learning from Self-Feedback (RLSF), a post-training stage that utilises the model's intrinsic confidence as a self-generated reward. By generating multiple CoT decoding beams from a frozen LLM, we compute the confidence of each final answer span and rank the resulting traces accordingly to create synthetic preferences. These preferences are subsequently utilised to fine-tune the policy through standard preference optimisation, requiring no human labels, gold answers, or externally curated rewards. RLSF simultaneously (i) refines the model's probability estimates--restoring well-behaved calibration--and (ii) strengthens step-by-step reasoning, yielding improved performance on arithmetic reasoning and multiple-choice question answering. By converting a model's own uncertainty into structured self-feedback, RLSF affirms reinforcement learning on intrinsic model behaviour as a principled and data-efficient component of the LLM post-training pipeline. Our results demonstrate that leveraging these inherent reasoning capabilities provides a robust path for enhancing model reliability without manual prompt engineering or external supervision.

Preference-based post-training aligns LLMs with human intent, yet safety behavior often remains brittle. A model may refuse a harmful request in a standard prompt but comply when the same intent is wrapped in adversarial wording. We suggest that robust safety requires context-invariant alignment, where behavior depends on the underlying intent rather than surface form. Enforcing invariance is difficult in alignment because not all training signals are equally trustworthy; for some prompt variants we can obtain verifiable feedback (e.g., multiple-choice), while for open-ended variants we typically rely on noisy, gameable reward proxies (e.g., learned judges). As a result, standard symmetric invariance regularizers can reduce cross-context discrepancies by lowering performance on reliable variants instead of improving open-ended robustness. To address this, we introduce Anchor Invariance Regularization (AIR), which treats verifiable prompts as anchors and uses a stop-gradient target to regularize only the open-ended variants toward the anchor performance. AIR is implemented as a plug-in auxiliary loss and combined with group-based preference optimization (e.g., GRPO) via heterogeneous prompt grouping. Across Safety, Moral Reasoning, and Math, AIR improves context invariance, boosting in-distribution group accuracy by 12.71% and out-of-distribution consistency by 33.49%, making safety constraints robust to adversarial framings.