Conformal Prediction

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Latest papers 334

55 papers in the last four weeks, up 57% on the four weeks before. 0.3% of all new papers.

May 18, 2026

Dual-Channel Tensor Neural Networks: Finite-Sample Theory and Conformal Structure Selection

Tensor-valued data arise naturally in neuroimaging, genomics, climate science, and spatiotemporal networks, where multilinear dependencies across modes carry information that is destroyed under vectorization. Existing approaches either impose a single low-rank structure, which can miss localized signal, or treat the tensor as a long vector, which discards its multiway geometry. We propose a Dual-Channel Tensor Neural Network (DC-TNN) that decomposes each tensor input into a low-rank core and a sparse refinement, and processes the two components through coupled neural channels. The framework is structure-agnostic and accommodates CP, Tucker, and tensor-train cores within a single architecture. For estimation, we establish non-asymptotic risk bounds for the DC-TNN estimator that decompose into network approximation, core estimation, and refinement-selection terms, and show that the effective dimension is determined jointly by the core rank and refinement sparsity rather than by the ambient tensor size. For inference, we develop a structure-aware conformal ROC procedure that calibrates within the core-refinement latent space and produces ROC and AUC confidence bands with finite-sample, distribution-free coverage. Building on this, we propose a conformal structure selector that, to our knowledge, is the first distribution-free procedure for choosing among candidate tensor decompositions with finite-sample validity. Simulations and an analysis of a protein dataset demonstrate competitive predictive accuracy, reliable uncertainty quantification, and consistent recovery of the tensor structure.

Elynn Chen, Jiayu Li, Zheshi Zheng +1

New York University · University of Michigan · Duke University

Tensor Networks Uncertainty Quantification Tensor Decomposition Conformal Prediction Neural Network Approximation Theory

May 18, 2026

Conformal Prediction via Transported Beta Laws

Split conformal prediction provides finite-sample marginal coverage under exchangeability, but this guarantee averages over the random calibration sample. We study instead the law of the calibration-conditional coverage induced by a realized conformal threshold. In the continuous i.i.d. setting this law is exactly

Beta(k,n+1-k)

, so the usual marginal guarantee corresponds to its mean. We take this beta law as a finite-sample reference object and quantify departures from it using Wasserstein distances on

[0,1]

. The framework yields direct bounds on marginal coverage gaps and on bad-calibration probabilities, and separates different sources of non-i.i.d. behavior according to how they deform the beta reference: test-side shift acts through a transport map on the coverage scale, while calibration dependence changes the order-statistic law itself. We instantiate the framework in scale-shift, clustered, and stationary mixing settings, where the induced deformations can be characterized explicitly or through Berry-Esseen approximations. Simulations on dependent processes confirm that the first-order approximation tracks the empirical Wasserstein distance even at moderate sample sizes.

Thiago R. Ramos, Helton Graziadei, Luben M. C. Cabezas

Federal University of S˜ao Carlos · Federal University of S˜ao Carlos, University of S˜ao Paulo, Inria and Universit´e Grenoble Alpes

Distribution Shift Robustness Conformal Prediction

May 18, 2026

Decoupled Conformal Optimisation: Efficient Prediction Sets via Independent Tuning and Calibration

Bayesian conformal optimisation methods often use the same held-out data both to search for efficient prediction sets and to certify coverage or risk. This coupling is natural for high-probability risk-control guarantees, but it is not necessary when the target is standard finite-sample marginal conformal coverage. We propose Decoupled Conformal Optimisation (DCO), a train-tune-calibrate design principle that uses an independent tuning split for efficiency-oriented structural selection and a fresh calibration split for the final conformal quantile. Conditional on the tuned structure, standard split-conformal exchangeability yields finite-sample marginal coverage for any candidate class, without a confidence parameter or multiple-testing correction. DCO therefore targets a different finite-sample guarantee from PAC-style methods: marginal conformal coverage rather than high-probability risk control. Under consistency assumptions on the coupled risk bound, the two approaches nevertheless converge to the same population threshold. Across classification and regression benchmarks, including ImageNet-A, CIFAR-100, Diabetes, California Housing, and Concrete, DCO tracks the nominal coverage level closely while often reducing average prediction-set size or interval width relative to PAC-style calibration. On ImageNet-A, for example, the average set size decreases from

26.52

to

25.26

and the 95th-percentile set size from

58.95

to

53.73

; on Diabetes, the average interval width decreases from

2.098

to

1.914

.

Fanyi Wu, Lihua Niu, Samuel Kaski +1

Department of Computer Science, University of Manchester, Manchester, UK · UKRI AI Centre for Doctoral Training in Decision Making for Complex Systems · Department of Computer Science, Aalto University, Espoo, Finland +1

Conformal Prediction Regression Prediction Intervals

May 18, 2026

Concise and Logically Consistent Conformal Sets for Neuro-Symbolic Concept-Based Models

Neuro-Symbolic Concept-based Models (NeSy-CBMs) are a family of architectures that integrate neural networks with symbolic reasoning for enhanced reliability in high-stakes applications. They work by first extracting high-level concepts from the input and then inferring a task label from these compatibly with given logical constraints. Yet, their label and concept predictions can be overconfident, making it difficult for stakeholders to gauge when the model's decisions can be trusted. We address this issue by integrating ideas from Conformal Prediction (CP), a framework providing rigorous, distribution-free coverage guarantees. We formalize three desiderata -- consistency, coverage, and conciseness -- that any conformal method for NeSy-CBMs should satisfy, and show that existing approaches fall short of at least one. We then introduce COCOCO, a post-hoc framework that conformalizes concepts and labels jointly and reconciles them via a single deduction-abduction revision step. COCOCO satisfies all three desiderata, retains distribution-free coverage, is robust to imperfect knowledge and supports user-specified size budgets. Our experiments on 8 data sets highlight how COCOCO compares favorably against competitors and natural baselines in terms of performance and set size.

Samuele Bortolotti, Emanuele Marconato, Andrea Pugnana +2

Department of Information Engineering and Computer Science, University of Trento, Italy · CIMeC, University of Trento, Rovereto, Italy

Concept Bottleneck Models Conformal Prediction Neuro-Symbolic Reasoning

May 18, 2026

Online Conformal Prediction for Non-Exchangeable Panel Data

We study online conformal prediction in a partially observed panel: a new cross-section of peer outcomes is observed before each target outcome, target feedback may be intermittent or absent, and neither units nor rounds need be exchangeable. We propose Weighted Temporal Quantile Adjustment (W-TQA), which combines similarity weights learned from unit histories with an adaptive target-specific miscoverage level. We prove that neither target-peer mismatch nor coverage on unrevealed rounds is identifiable, so assumptions on cross-unit similarity and on the feedback mechanism cannot be avoided. We bound the past-conditional miscoverage in terms of this mismatch, quantify the cost of learning the weights under a profile-similarity assumption, and show that the implemented procedure, which falls back on the largest peer score, attains long-run average coverage under missing-completely-at-random feedback and a feasibility condition on the calibration panel. On synthetic panels and four real panels, including a genuinely asynchronous U.S.-to-Tokyo equity panel, W-TQA attains the highest coverage on the worst-covered target units on every panel; similarity weighting contributes most when target feedback is scarce, and temporal adaptation more as feedback accumulates.

Daohong Tu, Kay Giesecke

Department of Management Science and Engineering Stanford University

Weighted Conformal Prediction Conformal Prediction Regression Prediction Intervals

May 15, 2026

Skew-adaptive conformal prediction

We develop a skew-adaptive extension of split conformal prediction for regression. The method starts from an asymmetric interval family centered at a point prediction and uses the gauge approach to deduce the conformity score induced by this family. The inverse hyperbolic sine transform of signed scaled residuals provides the training target for an additional predictive model, whose role is to learn how predictive uncertainty should tilt across the feature space. The resulting procedure preserves the finite-sample marginal validity of split conformal prediction under exchangeability, while producing intervals that adapt to both local scale and local skewness. We also develop a calibration-sample-based estimator for comparing the expected relative future width of the skew-adaptive and classical scaled-score intervals. Experiments on a variety of datasets indicate gains in prediction interval efficiency over the scaled-score construction and conformalized quantile regression, and show that the proposed estimator closely matches the corresponding average width ratio observed on the test sample.

Paulo C. Marques F., Helton Graziadei

Insper Institute of Education and Research S˜ao Paulo, SP, 04546-042, Brazil · Department of Statistics Federal University of S˜ao Carlos S˜ao Carlos, SP, 13565-905, Brazil

Conformal Prediction Regression Prediction Intervals

May 14, 2026

Efficient Online Conformal Selection with Limited Feedback

We address the problem of conformal selection, where an agent must select a minimal subset of options to ensure that at least one

success'' is identified with a pre-specified target probability $φ$. While traditional online conformal prediction focuses on maintaining validity for the observed sequence, minimizing the resource cost (efficiency) of such selections, especially under limited feedback, remains a significant challenge. In this work, we consider settings with the most limited

bandit'' feedback, and demonstrate that the simple Adaptive Conformal Inference (ACI) update rule, when applied to the appropriate control parameter or dual variable, is both adversarially valid, ensuring the success target is met on average for any input sequence (and hence under distribution shifts), and stochastically efficient, achieving sublinear efficiency regret for

i.i.d.

inputs against an appropriate stochastic benchmark. We show such guarantees under canonical models capturing bandit and semi-bandit feedback to the agent via a unifying algorithmic technique, and analytic framework involving Lyapunov functions. Our approach handles more complex settings than prior work, while requiring significantly less feedback, and our results provide a new theoretical bridge between efficient online learning with limited feedback and distribution-free uncertainty quantification.

Sreenivas Gollapudi, Kostas Kollias, Kamesh Munagala +1

Google Research, Mountain View, CA, USA. · Department of Computer Science, Duke University, Durham, NC, USA.

Conformal Prediction Adaptive Conformal Inference

May 14, 2026

On the Burden of Achieving Fairness in Conformal Prediction

Conformal prediction is often calibrated with a single pooled threshold, but this can hide cross-group heterogeneity in score distributions and distort group-wise coverage. We study this phenomenon through the population score distributions underlying split conformal calibration. First, we derive a conservation law and lower bound showing that pooled calibration incurs irreducible group-wise coverage distortion at a scale set by cross-group quantile heterogeneity. Second, we demonstrate that the two leading fairness definitions for conformal prediction, Equalized Coverage and Equalized Set Size, are fundamentally in tension. Third, we quantify the cost of moving between policies which treat groups separately or pool them. Experiments on synthetic and real data confirm the same bidirectional trade-off after finite-sample calibration. Our results show that, for the policy families studied here, calibration choice does not remove cross-group heterogeneity; it determines whether the resulting distortion appears in the coverage or size dimension, providing a principled lens for analyzing fairness-oriented calibration choices in practice.

Ziang Gao, Pengqi Liu, Archer Yi Yang +3

McGill University Montreal, Canada · TD Insurance Montreal, Canada · Layer 6 AI Toronto, Canada

Conformal Prediction Group Fairness

May 13, 2026

Pause and Reflect: Conformal Aggregation for Chain-of-Thought Reasoning

Chain-of-thought (CoT) reasoning with self-consistency improves performance by aggregating multiple sampled reasoning paths. In this setting, correctness is no longer tied to a single reasoning trace but to the aggregation rule over a pool of candidate paths, making aggregation uncertainty the central challenge. This issue is critical where confidently incorrect answers are far more costly than abstentions. We introduce a conformal procedure for CoT reasoning that directly addresses aggregation uncertainty. Our approach replaces majority voting with weighted score aggregation over reasoning paths and calibrates an abstention rule using conformal risk control. This approach leads to finite-sample guarantees on the confident-error rate--the probability that the system answers and is wrong. We further identify score separability as the key condition under which abstention provably improves selective accuracy, and derive closed-form expressions that predict accuracy gains from calibration data alone. The method is fully inference-time, and requires no retraining. Across four benchmarks, four open-source models, and three score classes, realized confident-error rates are consistent with the prescribed targets up to calibration-split and test-set variability. Our method achieves

90.1\%

selective accuracy on GSM8K by abstaining on less than

5\%

of problems, compared with

82\%

accuracy under majority-voting baseline.

Yu Gu, Zijun Yu, Vahid Partovi Nia +1

Department of Mathematics and Statistics McGill University Montréal, QC, Canada · Department of Mathematics and Industrial Engineering Polytechnique de Montréal Montréal, QC, Canada

Selective Prediction Self-Consistency Decoding CoT Reasoning Conformal Prediction Conformal Risk Control LLM Reasoning

May 13, 2026

Conformal Anomaly Detection in Python: Moving Beyond Heuristic Thresholds with 'nonconform'

Most anomaly detection systems output scores rather than calibrated decisions, leaving practitioners to choose thresholds heuristically and without clear statistical interpretation. Conformal anomaly detection addresses this limitation by converting anomaly scores into calibrated p-values that are valid under the statistical assumption of data exchangeability, with a growing literature extending this idea beyond that setting. We present 'nonconform', a Python package for applying conformal anomaly detection within existing machine-learning workflows, and use it as the basis for an implementation-grounded introduction to the field. The package integrates with 'scikit-learn', 'pyod', and custom anomaly detectors, and provides a unified interface for calibration, p-value generation, and false discovery rate control. It supports several conformalization strategies, ranging from simple split-conformal calibration to more data-efficient and shift-aware extensions. Through a progression from foundational concepts to advanced conformalization strategies, complemented by code examples, the paper connects the statistical ideas behind conformal anomaly detection to their practical use in 'nonconform'. Empirical results demonstrate that the implemented methods enable statistically principled anomaly detection. Together, the package and exposition aim to make core conformal anomaly detection workflows more accessible and reproducible in experimental and production-oriented settings.

Oliver Hennhöfer, Maximilian Kirsch, Christine Preisach

Intelligent Systems Research Group, Karlsruhe University of Applied Sciences

FDR Control Conformal Prediction Anomaly Detection

May 13, 2026

Vision-Based Runtime Monitoring under Varying Specifications using Semantic Latent Representations

We study certified runtime monitoring of past-time signal temporal logic (ptSTL) from visual observations under partial observability. The monitor must infer safety-relevant quantities from images and provide finite-sample guarantees, while being reusable: once trained and calibrated, it should certify any formula in a target fragment without per-formula retraining. For fragments induced by a finite dictionary of temporal atoms, we prove that the semantic basis, the vector of atom robustness scores, is the minimum prediction target within the class of monotone, 1-Lipschitz reusable interfaces: any formula is evaluated by a deterministic decoder derived from the parse tree, and a single conformal calibration pass certifies the entire fragment with no union bound. We also introduce a rolling prediction monitor that predicts only current predicate values and reconstructs temporal history online; this is easier to learn but grows conservative at long horizons. On a pedestrian-crossroad benchmark, rolling achieves tighter certified bounds at short horizons while the semantic-basis monitor is up to 4-times tighter at long horizons. We validate the presented monitors on real-world Waymo driving data, where both monitors satisfy the conformal coverage guarantee empirically.

Bardh Hoxha, Oliver Schön, Hideki Okamoto +2

Toyota NA R&D · ETH Zürich

Signal Temporal Logic Conformal Prediction

May 13, 2026

Local Conformal Calibration of Dynamics Uncertainty from Semantic Images

We introduce Observation-aware Conformal Uncertainty Local-Calibration (OCULAR), a conformal prediction-based algorithm that uses perception information to provide uncertainty quantification guarantees for unseen test-time environments. While previous conformal approaches lack the ability to discriminate between state-action space regions leading to higher or lower model mismatch, and require environment-specific data, our method uses data collected from visually similar environments to provably calibrate a linear Gaussian dynamics model of arbitrary fidelity. The prediction regions generated from OCULAR are guaranteed to contain the future system states with, at least, a user-set likelihood, despite both aleatoric and epistemic uncertainty -- i.e., uncertainty arising from both stochastic disturbances and lack of data. Our guarantees are non-asymptotic and distribution-free, not requiring strong assumptions about the unknown real system dynamics. Our calibration procedure enables distinguishing between observation-velocity-action inputs leading to higher and lower next-state-uncertainty, which is helpful for probabilistically-safe planning. We numerically validate our algorithm on a double-integrator system subject to random perturbations and significant model mismatch, using both a simplified sensor and a more realistic simulated camera. Our approach calibrates approximate uncertainty estimates both when in-distribution and out-of-distribution, producing volume-efficient prediction regions without requiring environment-specific data.

Luís Marques, Dmitry Berenson

Robotics Department, University of Michigan, Ann Arbor, MI 48109, USA

Uncertainty Quantification Conformal Prediction Model Calibration

May 13, 2026

Adaptive Conformal Prediction for Reliable and Explainable Medical Image Classification

Deep learning models for medical imaging often exhibit overconfidence, creating safety risks in ambiguous diagnostic scenarios. While Conformal Prediction (CP) provides distribution-free statistical guarantees, standard methods such as Regularized Adaptive Prediction Sets (RAPS) optimize for average efficiency and can mask severe failures on difficult inputs. We propose an Adaptive Lambda Criterion for RAPS that minimizes the worst-case coverage violation across prediction set size strata. On OrganAMNIST (58,850 abdominal CT images, 11 classes), standard size-optimized RAPS converges to near-deterministic behavior with stratified undercoverage on uncertain samples, while our method achieves 95.72 percent global coverage with average set size 1.09 and at least 90 percent coverage across all strata. Cross-domain validation on PathMNIST (107,180 pathology images, 9 classes) confirms generalizability. Quantitative Grad-CAM analysis (rho = -0.30, p < 1e-22) shows that multi-label predictions correspond to focused attention on anatomically ambiguous regions. These results demonstrate that the proposed method improves reliability while maintaining efficiency, making it suitable for safety-critical medical AI applications.

One Octadion, Novanto Yudistira, Lailil Muflikhah

Faculty of Computer Science, Universitas Brawijaya, Malang, Indonesia

Conformal Prediction Medical Image Classification Explainable Medical Image Analysis

May 12, 2026

Online Conformal Prediction: Enforcing monotonicity via Online Optimization

Conformal prediction provides a principled framework for uncertainty quantification with finite-sample coverage guarantees. While recent work has extended conformal prediction to online and sequential settings, existing methods typically focus on a single coverage level and do not ensure consistency across multiple confidence levels. In many real-world applications, such as weather forecasting, macroeconomic prediction, and risk management, different users operate under heterogeneous risk tolerances and require calibrated uncertainty estimates across a range of coverage levels. In such settings, it is desirable to produce prediction sets corresponding to different coverage levels that are nested and valid simultaneously. In this paper, we propose two novel online conformal prediction methods that output nested prediction sets across a range of coverage levels, enabling simultaneous uncertainty quantification across the entire risk spectrum. Beyond interpretability, jointly estimating multiple coverage levels is known to improve statistical efficiency in classical quantile regression by enforcing non-crossing constraints and sharing information across quantiles. Our approaches leverage an online optimization perspective with small regret that translates to quantile estimation error control while enforcing nestedness of prediction sets. Empirical results on synthetic and real-world datasets, including applications in forecasting tasks with heterogeneous risk requirements, demonstrate that our method achieves stable coverage across all levels, strictly nested prediction sets, and improved efficiency compared to existing online conformal baselines.

Eduardo Ochoa Rivera, Ambuj Tewari

University of Michigan · Ann Arbor, USA

Conformal Prediction Uncertainty Calibration

May 12, 2026

Multi-Variable Conformal Prediction: Optimizing Prediction Sets without Data Splitting

Conformal prediction constructs prediction sets with finite-sample coverage guarantees, but its calibration stage is structurally constrained to a scalar score function and a single threshold variable - forcing shapes of prediction sets to be fixed before calibration, typically through data splitting. We introduce multi-variable conformal prediction (MCP), a framework that extends conformal prediction to vector-valued score functions with multiple simultaneous calibration variables. Building on scenario theory as a principled framework for certifying data-driven decisions, MCP unifies prediction set design and calibration into a single optimization problem, eliminating data splitting without sacrificing coverage guarantees. We propose two computationally efficient variants: RemMCP, grounded in constrained optimization with constraint removal, which admits a clean generalization of split conformal prediction; and RelMCP, based on iterative optimization with constraint relaxation, which supports non-convex score functions at the cost of possibly greater conservatism. Through numerical experiments on ellipsoidal and multi-modal prediction sets, we demonstrate that RemMCP and RelMCP consistently meet the target coverage with prediction set sizes smaller than or comparable to those of baselines with data split, while considerably reducing variance across calibration runs - a direct consequence of using all available data for shape optimization and calibration simultaneously.

Laura Lützow, Simone Garatti, Marco C. Campi +2

TU Munich & MCML, Germany · Politecnico di Milano, Italy · University of Brescia, Italy +1

Conformal Prediction

May 12, 2026

Fair Conformal Classification via Learning Representation-Based Groups

Conformal prediction methods provide statistically rigorous marginal coverage guarantees for machine learning models, but such guarantees fail to account for algorithmic biases, thereby undermining fairness and trust. This paper introduces a fair conformal inference framework for classification tasks. The proposed method constructs prediction sets that guarantee conditional coverage on adaptively identified subgroups, which can be implicitly defined through nonlinear feature combinations. By balancing effectiveness and efficiency in producing compact, informative prediction sets and ensuring adaptive equalized coverage across unfairly treated subgroups, our approach paves a practical pathway toward trustworthy machine learning. Extensive experiments on both synthetic and real-world datasets demonstrate the effectiveness of the framework.

Senrong Xu, Yanke Zhou, Yuhao Tan +5

State Key Lab of Novel Software Technology, Nanjing University, China · ETH Zürich · Birkbeck, University of London

Group-Conditional Conformal Prediction Conformal Prediction Group Fairness

May 12, 2026

PASC: Pipeline-Aware Conformal Prediction with Joint Coverage Guarantees for Multi-Stage NLP and LLM Pipelines

Modern NLP and LLM systems are pipelines: named entity recognition (NER) -> entity disambiguation (NED) -> entity typing, retrieval-augmented generation (retriever -> reader), and agentic chains of planner -> tool -> critic. Errors compound across stages, but existing uncertainty quantification methods either calibrate each stage independently (no joint coverage) or apply a Bonferroni union bound (joint coverage, but conservative). We present PASC (Pipeline-Aware Split Conformal), which reduces multi-stage joint coverage to a single scalar conformal prediction problem on the joint maximum nonconformity score. PASC provides a finite-sample distribution-free guarantee that all K stages are simultaneously covered with probability at least 1 - alpha, and is nearly tight up to a 1/(n+1) factor. On a three-stage NER -> NED -> entity-typing pipeline over CoNLL-2003, PASC achieves 96.4% end-to-end coverage versus 93.4% for Bonferroni and 86.5% for independent CP, at identical average prediction set size (1.083). Under distribution shift to WNUT-17 Twitter and WikiNEuRal Wikipedia data, PASC empirically maintains the target coverage in the tested shift settings while independent CP collapses to 59%. PASC requires a single quantile computation, runs 1.7x faster than Bonferroni, and scales to K = 6 stages where independent CP drops to 0.53 end-to-end coverage. The same joint-maximum-score reduction applies directly to compound LLM systems and agent pipelines.

Varun Kotte

Independent Researcher.

Conformal Prediction

May 12, 2026

Partial Model Sharing Improves Byzantine Resilience in Federated Conformal Prediction

We propose a Byzantine-resilient federated conformal prediction (FCP) method that leverages partial model sharing, where only a subset of model parameters is exchanged each round. Unlike existing robust FCP approaches that primarily harden the calibration stage, our method protects both the federated training and conformal calibration phases. During training, partial sharing inherently restricts the attack surface and attenuates poisoned updates while reducing communication. During calibration, clients compress their non-conformity scores into histogram-based characterization vectors, enabling the server to detect Byzantine clients via distance-based maliciousness scores and to estimate the conformal quantile using only benign contributors. Experiments across diverse Byzantine attack scenarios show that the proposed method achieves closer-to-nominal coverage with substantially tighter prediction intervals than standard FCP, establishing a robust and communication-efficient approach to federated uncertainty quantification.

Ehsan Lari, Reza Arablouei, Stefan Werner

Department of Electronic Systems, Norwegian University of Science and Technology, Trondheim, Norway · 2CSIRO’s Data61, Pullenvale QLD 4069, Australia · Department of Information and Communications Engineering, Aalto University, Finland

Byzantine-Robust Federated Learning Conformal Prediction Regression Prediction Intervals

May 11, 2026

Federated Language Models Under Bandwidth Budgets: Distillation Rates and Conformal Coverage

Hospitals, companies, and research consortia want language models that learn from, and answer questions over, data that must stay where it is held, over links with limited bandwidth, such as the satellite links of remote clinics and ships. Averaging the sites' model parameters makes each message grow with the model and requires one shared architecture; methods that exchange predictions avoid both limits, but, to our knowledge, none bounds what compressing those predictions costs. We introduce two methods that compress every message at a small and predictable cost. Federated Probe-Logit Distillation (FPLD) trains a shared language model: each site sends compressed logits on shared unlabeled probes, and a hub distills one model from their average. Federated Conformal Retrieval-Augmented Generation (FC-RAG) answers questions: each site scores candidate answers using its own documents and sends compressed scores, and the hub returns a conformal prediction set that contains the correct answer at a guaranteed rate. Both use one codec, which centers each message and rounds it after adding a random offset known to the receiver. For logits within a fixed clipping range, we bound the expected log-loss added by compression independently of vocabulary size; the bound depends only on the bits, the range, and the number of sites, falls as more sites take part, and lets the bit budget be set before deployment. We also prove that recalibrating after compression keeps the coverage guarantee, and that FPLD's training error bounds how far coverage can slip when a threshold is reused after a model update. In experiments with GPT-2 and Qwen2.5, 8 bits per number cause no detectable loss in the trained model or in coverage. FPLD also trains a shared model across different architectures, where parameter averaging does not apply; with one shared architecture, parameter averaging remains more accurate.

Prasanjit Dubey, Xiaoming Huo

H. Milton Stewart School of Industrial and Systems Engineering, Georgia Institute of Technology, Atlanta, GA 30332, U.S.A.

Retrieval-Augmented Generation Communication-Efficient Distributed Training Conformal Prediction Federated Learning

May 9, 2026

RareCP: Regime-Aware Retrieval for Efficient Conformal Prediction

Recent advances in uncertainty quantification for time series forecasting show that conformal prediction can provide reliable prediction intervals, yet standard conformal methods are often inefficient under temporal dependence, drift, and heterogeneous error behavior. Existing methods typically either update miscoverage rates over time or learn unconstrained calibration weights, without explicitly separating two central sources of nonstationarity: smoothly drifting error distributions and co-existing distinct error regimes. We introduce RareCP, a regime-aware retrieval method for adaptive conformal time series prediction. RareCP learns local calibration representations through a mixture of cosine-attention experts that each capture distinct error regimes, while a compact hypernetwork adapts the kernel parameters to track temporal drift. Given a new forecasting context, RareCP retrieves the top-k most relevant calibration examples, assigns similarity weights, and forms a weighted conformal quantile over their signed residuals, yielding asymmetric prediction intervals. The adaptive kernel is trained using a smooth interval score objective, with a parameter-space anchor to a lightweight teacher kernel to preserve stable local representations. On the GIFT-Eval benchmark, RareCP improves interval efficiency over recent conformal baselines and foundation model uncertainty estimates while maintaining empirical coverage. Ablations confirm that regime-specific experts, drift-adaptive kernels, sparse retrieval, and teacher anchoring each contribute to the final performance.

Manuel Heurich, Maximilian Granz, Tim Landgraf

Institute for Computer Science Freie Universität Berlin Arnimallee 7 14195 Berlin

Weighted Conformal Prediction Time Series Forecasting Conformal Prediction Adaptive Conformal Inference Regression Prediction Intervals

May 8, 2026

CONTRA: Conformal Prediction Region via Normalizing Flow Transformation

Density estimation and reliable prediction regions for outputs are crucial in supervised and unsupervised learning. While conformal prediction effectively generates coverage-guaranteed regions, it struggles with multi-dimensional outputs due to reliance on one-dimensional nonconformity scores. To address this, we introduce CONTRA: CONformal prediction region via normalizing flow TRAnsformation. CONTRA utilizes the latent spaces of normalizing flows to define nonconformity scores based on distances from the center. This allows for the mapping of high-density regions in latent space to sharp prediction regions in the output space, surpassing traditional hyperrectangular or elliptical conformal regions. Further, for scenarios where other predictive models are favored over flow-based models, we extend CONTRA to enhance any such model with a reliable prediction region by training a simple normalizing flow on the residuals. We demonstrate that both CONTRA and its extension maintain guaranteed coverage probability and outperform existing methods in generating accurate prediction regions across various datasets. We conclude that CONTRA is an effective tool for (conditional) density estimation, addressing the under-explored challenge of delivering multi-dimensional prediction regions.

Zhenhan Fang, Aixin Tan, Jian Huang

Department of Statistics and Actuarial Science The University of Iowa Iowa City, IA 52242, USA · Department of Applied Mathematics The Hong Kong Polytechnic University Hongkong, China

Conformal Prediction Conditional Distribution Estimation

May 8, 2026

Learning Polyhedral Conformal Sets for Robust Optimization

Robust optimization (RO) provides a principled framework for decision-making under uncertainty, but its performance critically depends on the choice of the uncertainty set. While large sets ensure reliability, they often lead to overly conservative decisions, whereas small sets risk excluding the true outcome. Recent data-driven approaches, particularly conformal prediction, offer finite-sample validity guarantees but remain largely task-agnostic, ignoring the downstream decision structure. In this paper, we propose a decision-aware conformal framework that learns uncertainty sets tailored to robust optimization objectives. Our approach parameterizes a flexible family of polyhedral sets via data-driven hyperplanes and learns their geometry by directly minimizing the induced robust loss, while preserving statistical validity through conformal calibration. To correct for data-dependent selection, we incorporate a re-calibration step on an independent dataset to restore coverage. The resulting sets capture directional and anisotropic uncertainty aligned with the decision objective while remaining computationally tractable. We provide finite-sample coverage guarantees and bounds on the sub-optimality gap to an oracle decision. This work bridges the gap between statistical validity and decision optimality, providing a principled framework for data-driven robust optimization.

Shuyi Chen, Wenbin Zhou, Shixiang Zhu

Carnegie Mellon University

Conformal Prediction Robust Optimization Decision-Making under Uncertainty

May 8, 2026

Conformal Path Reasoning: Trustworthy Knowledge Graph Question Answering via Path-Level Calibration

Knowledge Graph Question Answering (KGQA) offers grounded, interpretable reasoning, but existing methods often fail to provide reliable coverage guarantees over retrieved answers. While Conformal Prediction (CP) offers a principled framework for producing prediction sets with statistical guarantees, prior conformal KGQA methods suffer from two critical pitfalls: violated coverage guarantees due to invalid calibration, and weak score discriminability that yields excessively large prediction sets. We propose Conformal Path Reasoning (CPR), a novel trustworthy KGQA framework built on two key innovations. First, query-level conformal calibration over path-level scores preserves exchangeability to ensure valid coverage guarantees. Second, we introduce the Residual Conformal Value Network (RCVNet), a lightweight module trained via PUCT-guided exploration to learn discriminative path-level nonconformity scores. Extensive experiments show that CPR significantly improves the Empirical Coverage Rate by 45% while reducing prediction set size by 52% on average over conformal baselines across benchmark datasets, highlighting its effectiveness for reliable conformal reasoning over knowledge graphs.

Shuhang Lin, Chuhao Zhou, Xiao Lin +5

Rutgers University · Independent Researcher · University of Illinois Urbana-Champaign +1

Conformal Prediction Knowledge Graph Question Answering Knowledge Graphs

May 8, 2026

GRAPHLCP: Structure-Aware Localized Conformal Prediction on Graphs

Conformal prediction (CP) provides a distribution-free approach to uncertainty quantification with finite-sample guarantees. However, applying CP to graph neural networks (GNNs) remains challenging as the combinatorial nature of graphs often leads to insufficiently certain predictions and indiscriminative embeddings. Existing methods primarily rely on embedding-space proximity for localization, which can be unreliable for graphs and yield inefficient prediction sets. We propose GRAPHLCP, a proximity-based localized CP framework that explicitly incorporates graph topology and inter-node dependencies into localization and weighting. Our approach introduces a feature-aware densification step to mitigate locality bias in sparse graphs, followed by a Personalized PageRank-based kernel computation to model structural proximity. This enables topology-dependent anchor sampling and calibration weighting that captures both local and long-range dependencies. Extensive experiments on several regression and classification datasets demonstrate that GRAPHLCP guarantees marginal coverage with finite samples while efficiently attaining favorable test conditional coverage across various conditioning scenarios.

Peyman Baghershahi, Fangxin Wang, Debmalya Mandal +1

Department of Computer Science, University of Illinois Chicago · Department of Computer Science, University of Warwick

Graph Neural Networks Conformal Prediction

May 8, 2026

Aggregation in conformal e-classification

Aggregating conformal predictors is a standard way of balancing their predictive and computational efficiency while retaining their validity, at least approximately. An important advantage of conformal e-predictors is that they are easier to aggregate without sacrificing their validity. This paper studies experimentally cross-conformal e-prediction, which is an existing method of aggregating conformal e-predictors, and its modifications that are conceptually simpler and more flexible.

Vladimir Vovk

Conformal Prediction

May 8, 2026

Probabilistic Object Detection with Conformal Prediction

Conformal Prediction (CP) is a distribution-free method for constructing prediction sets with marginal finite-sample coverage guarantees, making it a suitable framework for reliable uncertainty quantification in safety-critical object detection. However, object detection introduces structured multi-output predictions, complicating the application of classical CP theory developed for single outputs. In addition, standard, unscaled CP produces fixed-width prediction intervals across inputs, leading to unnecessary width for low-uncertainty predictions. While scaled CP addresses this by adapting the interval width to an input-dependent uncertainty estimate, prior work has neither systematically compared unscaled and scaled CP for multi-class object detection, nor integrated CP with a complementary uncertainty quantification method in this setting. We fill this gap by: (i) applying CP coordinate-wise to bounding box corners with a Bonferroni correction for box-level guarantees; (ii) scaling the resulting intervals using per-prediction aleatoric uncertainty estimates derived from a probabilistic object detector trained with loss attenuation, evaluated in uncalibrated and two calibrated variants; (iii) extending to a two-step pipeline that constructs prediction sets for the class using RAPS and conditions the conformalized bounding boxes on the predicted class set. Across three autonomous driving datasets (KITTI, BDD, CODA), including a cross-domain setting under distribution shift, scaled CP consistently improves interval sharpness over unscaled CP, achieving up to 19% higher IoU and 39% lower interval scores, without sacrificing coverage. Class-wise calibration further improves coverage for both variants with a negligible effect on sharpness. Together, these improvements yield more actionable uncertainty estimates for real-time, real-world object detection.

Christopher Ries, Moussa Kassem Sbeyti, Nicolas Bianco +1

Karlsruhe Institute of Technology (KIT), Karlsruhe, Germany

Autonomous Driving Perception Conformal Prediction Object Detection Uncertainty Calibration

May 8, 2026

Conformal-Style Quantile Analyses for Stochastic Bandits

Stochastic bandit algorithms are usually analyzed under a mean-reward criterion, yet many problems favor arms with strong upper-tail performance, which we study herein. For a fixed miscoverage level

α

, the natural upper-tail target of arm

j

is the upper endpoint

F_j^{-1}(1-α/2)

of a central prediction interval. This target can rank arms differently from their means, creating a central mismatch with the classical bandit objective. To this end, we propose ACP-UCB1, a conformal-style policy that combines an adaptive conformal estimate of the upper endpoint with a UCB-type optimism bonus. The technical challenge is that the conformity scores used by ACP-UCB1 are recomputed from evolving empirical quantile estimates and evaluated at an adaptive level. We control this endpoint through reward-quantile concentration, a perturbation argument for recomputed score quantiles, and deterministic localization of the adaptive level. ACP-UCB1 achieves logarithmic upper-quantile regret with per-arm contribution

O(\nicefrac{\log n}{Δ_j^{\mathrm{ACP}}})

. We also provide metric-specific regret decompositions comparing ACP-UCB1 with UCB1 and use numerical experiments to validate performance and improvement.

Chengyu Du, Mengfan Xu

University of Massachusetts Amherst

Multi-Armed Bandits Conformal Prediction UCB Algorithms

May 8, 2026

TRACE: Transport Alignment Conformal Prediction via Diffusion and Flow Matching Models

Constructing valid and informative conformal prediction regions for multi-dimensional outputs remains a fundamental challenge. While conformal prediction provides finite-sample, distribution-free coverage guarantees, its practical performance critically depends on the choice of nonconformity score. Existing approaches often rely on restrictive geometric assumptions or require explicit likelihood evaluation and invertible transformations, limiting their applicability in complex generative settings. In this work, we introduce TRACE (TRansport Alignment Conformal Estimation), a conformal prediction framework that defines nonconformity through transport alignment in diffusion and flow matching models. Rather than evaluating likelihoods, we measure how well a candidate output aligns with the learned generative dynamics by averaging denoising or velocity-matching errors along stochastic transport trajectories. The resulting transport-based scores are scalar-valued and can be calibrated using split conformal prediction, yielding valid marginal coverage under exchangeability. We further analyze the statistical properties of the proposed scores and their sensitivity to computational budget. Experiments on synthetic and real datasets demonstrate valid coverage and show that the resulting regions adapt naturally to multimodal and non-convex conditional distributions.

Zhenhan Fang, Aixin Tan, Jian Huang

Department of Statistics and Actuarial Science University of Iowa Iowa, IA 52242, USA · Departments of Data Science and AI, and Applied Mathematics The Hong Kong Polytechnic University Hong Kong, China

Conformal Prediction

May 7, 2026

Decentralized Conformal Novelty Detection via Quantized Model Exchange

This work studies decentralized novelty detection with global false discovery rate (FDR) control across heterogeneous composite null distributions, without sharing the raw data due to privacy and bandwidth considerations. We propose a framework based on the exchange of quantized surrogate models, allowing independent agents to share low-precision representations of locally learned non-conformity score functions. We prove that evaluating data against these quantized composite scores preserves conditional exchangeability, providing rigorous finite-sample guarantees for global FDR control. Empirical studies on synthetic datasets confirm our theoretical results, demonstrating that the proposed approach maintains competitive statistical power while drastically reducing the communication cost.

Kyle Loh, Yu Xiang

Department of Mathematics and Statistics · Florida Atlantic University · Boca Raton, Florida

FDR Control Conformal Prediction Decentralized Learning

May 7, 2026

Conformal Agent Error Attribution

When multi-agent systems (MAS) fail, identifying where the decisive error occurred is the first step for automated recovery to an earlier state. Error attribution remains a fundamental challenge due to the long interaction traces that large language model-based MAS generate. This paper presents a framework for error attribution based on conformal prediction (CP) which provides finite-sample, distribution-free coverage guarantees. We introduce new algorithms for filtration-based CP designed for sequential data such as agent trajectories. Unlike existing CP algorithms, our approach predicts sets that are contiguous sequences to enable efficient recovery and debugging. We verify our theoretical guarantees on a variety of agents and datasets, show that errors can be precisely isolated, then use prediction sets to rollback MAS to correct their own errors. Our overall approach is model-agnostic, and offers a principled uncertainty layer for MAS error attribution. We release code at https://github.com/layer6ai-labs/conformal-agent-error-attribution.

Naihe Feng, Yi Sui, Shiyi Hou +2

Dalhousie University · Halifax, NS, Canada · Layer 6 AI +1

Agent Failure Analysis AI Agent Reliability Multi-Agent LLM Systems Conformal Prediction