Conformal Cascade (CC), a multi-tier inference framework that uses conformal prediction set size as the deferral rule: accept when the calibrated set collapses to a single answer, defer otherwise, delivers a distribution-free, finite-sample accuracy guarantee.
Abstract
Large language model (LLM) cascades reduce inference cost by routing easy queries to a small model and deferring hard queries to a larger one. Production cascades govern this deferral through a confidence threshold, but LLM confidence scores are miscalibrated, the threshold must be tuned per model pair and per domain, and no setting yields a formal bound on cascade accuracy. We introduce \textbf{Conformal Cascade} (CC), a multi-tier inference framework that uses conformal prediction set size as the deferral rule: accept when the calibrated set collapses to a single answer, defer otherwise. The procedure delivers a distribution-free, finite-sample accuracy guarantee. By a per-tier union bound, the prediction set at the accepting tier covers the correct answer with probability at least $1 - K\alpha$ for any user-specified $\alpha$; under a selection-preservation condition (consistent with, but not strictly implied by, our marginal coverage results), the bound tightens to $1 - \alpha$. We further characterise expected cascade cost as an explicit function of $\alpha$ and the calibration-set acceptance rate. Across 18 multiple-choice benchmarks spanning science, medicine, commonsense, and standardized exams, evaluated on two-tier cascades drawn from four open-weight model families, CC strictly improves over the strongest calibration-tuned heuristic cascade on the majority of family--benchmark pairs, with the largest gains on reasoning-heavy benchmarks where majority vote is unreliable; on easier benchmarks the cascade commits the vast majority of queries to the small model at no accuracy cost. Extension to open-ended generation requires an answer-clustering step that we leave for future work. The method requires no model training and only black-box API access.
It is found that configuration shift consistently erodes CP validity, often driving empirical coverage below the target, and coverage lower bounds are derived that attribute this loss to a discrepancy between calibration and test score distributions.
Yuqicheng Zhu, Jia-Lin Yu, Lin Li et al.· 0 citations
Best-of-$N$ reranking draws independent candidates from a reference policy and selects the response maximal under a fixed, sample-independent strict total order on outcomes. The selected law may differ substantially from the reference in Kullback–Leibler divergence. Prior work introduced a bounded statistic depending only on the accepted response's reference mass and conjectured that its expectation upper-bounds this divergence. This letter proves the conjecture for every finite ordered distribution. The proof applies to the full positive cumulative-distribution-function power family, not only integer sample counts. It combines a strictly monotone binary gauge, a top-atom chain-rule recursion, and induction, and yields an exact nonnegative slack decomposition and a quantitative tightness bound. A beta-quantile representation identifies the universal divergence cap. We also treat reference-preserving reward ties, provide deterministic high-precision illustrations, derive clipped fixed-sample confidence bounds, and specify stable evaluation and exact probability-logging requirements.
Yutong Zhang, Yaoran Yang· IEEE Signal Processing Lette...· 0 citations
Uncertainty quantification is essential when deploying machine learning models in safety-critical applications. Online conformal prediction (OCP) provides theoretically principled uncertainty quantification for arbitrary black-box classifiers and non-i.i.d. data streams by constructing prediction sets that are guaranteed to contain the true label at a user-specified frequency. OCP usually updates prediction sets using feedback from previously deployed predictions. We instead study an OCP setting beyond feedback: on each round, the learner can either output a prediction set or query the correct label, but not both. Thus, no deployed prediction is ever evaluated directly. We reduce this problem to a partial monitoring game in which prediction actions return no observation and a separate query action reveals the label. The reward function is constructed in a way that encourages the learner to output small prediction sets while ensuring that the correct label is covered with a sufficiently high probability. To solve this game, we develop OCP with queries (OCPQ) by adapting the label efficient forecaster of Cesa-Bianchi, Lugosi, and Stoltz (2004) to our setting. For any black box classifier and any (non-i.i.d.) oblivious data stream of length $T$, OCPQ has $O(T^{2/3})$ expected regret and expected coverage at least $\beta-O(T^{-1/3})$ for a user-defined $\beta$, while querying only an expected $T^{-1/3}$ fraction of rounds. This provides coverage comparable to bandit-based OCP methods while requiring no feedback from deployed prediction sets. Experiments on real-world datasets further demonstrate the effectiveness of our approach.
J. Skalse, Edoardo Pona, Osvaldo Simeone et al.· 0 citations
Large language models serve heterogeneous populations structured by domain, topic difficulty, and linguistic style. Conformal risk control (CRC) gives rigorous marginal risk guarantees for selective prediction with abstention, but marginal guarantees do not imply per-group ones: a model can meet the population budget while systematically over-exposing subgroups to errors. Under mild shift in group composition, standard CRC violates the budget in up to 47% of trials. We propose HG-CRC (Hierarchical Group-Conditional CRC), a post-hoc calibration framework enforcing simultaneous risk guarantees across all nodes of a user-defined group hierarchy. It applies a Bonferroni correction over nodes and a leaf-first policy that uses the most specific applicable threshold, falling back to coarser nodes when a finer one is uncertified or rejects the example. It needs only a held-out calibration set, with no retraining. We evaluate on three models (Qwen3-4B, Llama-3.1-8B-Instruct, Gemma-3-4B) and two benchmarks (ARC Challenge, MMLU-Pro) across eight configurations probing IID generalization, heterogeneity, mixture/domain/prompt/difficulty shift, label noise, and quantization. Main result: HG-CRC reaches an empirical 0% violation rate and WGER=0 on ARC Challenge for high-accuracy models (Qwen3-4B, Llama-3.1-8B). At 500 bootstrap trials these zeros are empirical upper bounds (true rate up to 0.6%), not certified. Results are benchmark-specific: on MMLU-Pro these models abstain entirely or (Llama) retain WGER=0.014. Gemma-3-4B, poorly calibrated here, degrades gracefully by abstaining. Participation cost vs. global CRC is 22 to 37 points. Ablations show hierarchical depth clears the budget: removing difficulty level returns violations to about 11%. Bonferroni is needed for the theoretical guarantee, though its empirical effect matters only with many nodes.
Murilo Salem, Luísa Böhm, Daniel Pontes et al.· arXiv.org· 0 citations
Large language model (LLM) cascades answer easy requests with a small model and escalate selected requests to a larger model. Most routers prioritize examples on which the small model appears uncertain or likely to be wrong. This proxy ignores a decisive fact: escalation is useful only when the large model corrects the small model, and it is harmful when the large model replaces a correct answer with an incorrect one. We introduce Signed Rescue Routing (SRR), a budgeted routing method that predicts these two events separately and ranks requests by their difference. We show that this signed conditional gain is the Bayes-optimal routing score under a fixed escalation budget. SRR requires only the small model's output statistics at deployment and adds a lightweight two-head router. We evaluate SRR with Qwen3-4B and Qwen3-8B on TBD examples from MMLU, HellaSwag, and ARC-Challenge. Across the accuracy-compute curve, SRR reaches an area of TBD, compared with TBD for a learned small-model error predictor and TBD for entropy routing. These results show that predicting incremental value, rather than model uncertainty, is a simple and effective objective for efficient LLM cascades.
Zheyuan Wang, Siyu Li, Peiqiao Song et al.· 0 citations
Adaptive conformal inference (ACI) of Gibbs and Cand{\`e}s and its variants are the standard approach to online conformal prediction under distribution shift, but they suffer from three fundamental limitations. First, their guarantees control only the \emph{signed} long-run coverage error: persistent miscoverage in one direction can be masked by compensating errors later, so a method can satisfy the theoretical guarantee while being badly wrong for extended periods. Second, existing guarantees say nothing about prediction-set size, so validity can be achieved trivially at the cost of unduly wide prediction sets. Third, the efficiency guarantees that do exist compare against a \emph{fixed} predictor chosen in hindsight, a benchmark that becomes increasingly less meaningful once the data-generating distribution shifts, since the very notion of an optimal threshold then changes over time. We consider a unified online learning framework that simultaneously controls absolute, non-cancelling coverage violation and prediction-set efficiency against a dynamically evolving benchmark for three important models. In the fully adversarial setting, exploiting the fact that the standard ACI update is exactly projected online gradient descent on the pinball loss, we derive simultaneous coverage and efficiency guarantees for arbitrary monotone Lipschitz efficiency objectives, with no distributional or {\it convexity} assumptions. In the stochastic setting with full-score feedback, we propose a sliding-window quantile tracker and establish a matching minimax lower bound showing our algorithm is rate-optimal. In the covariate-dependent stochastic setting, we develop a partitioned ACI algorithm that tracks a function-valued oracle threshold, and derive simultaneous coverage and efficiency guarantees.
Rahul Vaze· arXiv.org· 0 citations
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