Conformal Prediction (CP) is a popular framework for constructing prediction bands with valid coverage in finite samples, while being free of any distributional assumption. A well-known limitation of conformal prediction is the lack of adaptivity, although several works introduced practically efficient alternate procedures. In this work, we build upon recent ideas that rely on recasting the CP problem as a statistical learning problem, directly targeting coverage and adaptivity. This statistical learning problem is based on reproducible kernel Hilbert spaces (RKHS) and kernel sum-of-squares (SoS) methods. First, we extend previous results with a general representer theorem and exhibit the dual formulation of the learning problem. Crucially, such dual formulation can be solved efficiently by accelerated gradient methods with several hundreds or thousands of samples, unlike previous strategies based on off-the-shelf semidefinite programming algorithms. Second, we introduce a new hyperparameter tuning strategy tailored specifically to target adaptivity through bounds on test-conditional coverage. This strategy, based on the Hilbert-Schmidt Independence Criterion (HSIC), is introduced here to tune kernel lengthscales in our framework, but has broader applicability since it could be used in any CP algorithm where the score function is learned. Finally, extensive experiments are conducted to show how our method compares to related work. All figures can be reproduced with the accompanying code at \href{https://www.gitlab.com/drti/ksos-bands}{gitlab.com/drti/ksos-bands}.
An open question in \emph{Imprecise Probabilistic Machine Learning} is how to empirically derive a credal region (i.e., a closed and convex family of probabilities on the output space) from the available data, without any prior knowledge or assumption. In classification problems, credal regions are a tool that is able to provide provable guarantees under realistic assumptions by characterizing the uncertainty about the distribution of the labels. Building on previous work, we show that credal regions can be directly constructed using conformal methods. This allows us to provide a novel extension of classical conformal prediction to problems with ambiguous ground truth, that is, when the exact labels for given inputs are not exactly known. The resulting construction enjoys desirable practical and theoretical properties: (i) conformal coverage guarantees, (ii) smaller prediction sets (compared to classical conformal prediction regions) and (iii) disentanglement of uncertainty sources (epistemic, aleatoric). We empirically verify our findings on both synthetic and real datasets.
The zero-shot capabilities of foundation models (FMs) for time series forecasting offer promising potentials in conformal prediction, as most of the available data can be allocated to calibration. This study compares the performance of Time Series Foundation Models (TSFMs) with traditional methods, including statistical models and gradient boosting, within a conformal prediction setting. Our findings highlight two key advantages of TSFMs. First, when the volume of data is limited, TSFMs provide more reliable conformalized prediction intervals than classic models, thanks to their superior predictive accuracy. Second, the calibration process is more stable because more data are used for calibration. Morever, the fewer data available, the more pronounced these benefits become, as classic models require a substantial amount of data for effective training. These results underscore the potential of foundation models in improving conformal prediction reliability in time series applications, particularly in data-constrained cases. All the code to reproduce the experiments is available.
6D pose confidence region estimation has emerged as a critical direction, aiming to perform uncertainty quantification for assessing the reliability of estimated poses. However, current sampling-based approach suffers from critical limitations that severely impede their practical deployment: 1) the sampling speed significantly decreases as the number of samples increases. 2) the derived confidence regions are often excessively large. To address these challenges, we propose a deterministic and efficient method for estimating pose confidence regions. Our approach uses inductive conformal prediction to calibrate the deterministically regressed Gaussian keypoint distributions into 2D keypoint confidence regions. We then leverage the implicit function theorem to propagate these keypoint confidence regions directly into 6D pose confidence regions. This method avoids the inefficiency and inflated region sizes associated with sampling and ensembling. It provides compact confidence regions that cover the ground-truth poses with a user-defined confidence level. Experimental results on the LineMOD Occlusion and SPEED datasets show that our method achieves higher pose estimation accuracy with reduced computational time. For the same coverage rate, our method yields significantly smaller confidence region volumes, reducing them by up to 99.9\% for rotations and 99.8\% for translations. The code will be available soon.
Given any model, conformal prediction (CP) returns prediction sets guaranteed to include the true label with high adjustable probability. Robust CP (RCP) extends this to inputs with worst-case noise. A well-established approach is to use randomized smoothing for RCP since it is applicable to any black-box model and provides smaller sets compared to deterministic methods. However, current smoothing-based RCP requires many model forward passes per each input which is computationally expensive. We show that conformal prediction attains some robustness even with a forward pass on a single randomly perturbed input. Using any binary certificate we propose a single sample robust CP (RCP1). Our approach returns robust sets with smaller average set size compared to SOTA methods which use many (e.g. around 100) passes per input. Our key insight is to certify the conformal prediction procedure itself rather than individual scores. Our approach is agnostic to the setup (classification and regression). We further extend our approach to smoothing-based robust conformal risk control.
We often attribute human characteristics to large language models (LLMs) and claim that they "know" certain things. LLMs have an internal probabilistic knowledge that represents information retained during training. How can we assess the veracity of this knowledge? We examine two common methods for probing the veracity of LLMs and discover several assumptions that are flawed. To address these flawed assumptions, we introduce sAwMIL (short for Sparse Aware Multiple-Instance Learning), a probing method that utilizes the internal activations of LLMs to separate statements into true, false, and neither. sAwMIL is based on multiple-instance learning and conformal prediction. We evaluate sAwMIL on 5 validity criteria across 16 open-source LLMs, including both default and chat-based variants, as well as on 3 new datasets. Among the insights we provide are: (1) the veracity signal is often concentrated in the third quarter of an LLM's depth; (2) truth and falsehood signals are not always symmetric; (3) linear probes perform better on chat models than on default models; (4) nonlinear probes may be required to capture veracity signals for some LLMs with reinforcement learning from human feedback or knowledge distillation; and (5) LLMs capture a third type of signal that is distinct from true and false and is neither true nor false. These findings provide a reliable method for verifying what LLMs "know" and how certain they are of their probabilistic internal knowledge.
Online conformal prediction has demonstrated its capability to construct a prediction set for each incoming data point that covers the true label with a predetermined probability. To cope with potential distribution shift, multi-model online conformal prediction has been introduced to select and leverage different models from a preselected candidate set. Along with the improved flexibility, the choice of the preselected set also brings challenges. A candidate set that includes a large number of models may increase the computational complexity. In addition, the inclusion of irrelevant models with poor performance may negatively impact the performance and lead to unnecessarily large prediction sets. To address these challenges, we propose a novel multi-model online conformal prediction algorithm that identifies a subset of effective models at each time step by collecting feedback from a bipartite graph, which is refined upon receiving new data. A model is then selected from this subset to construct the prediction set, resulting in reduced computational complexity and smaller prediction sets. Additionally, we demonstrate that using prediction set size as feedback, alongside model loss, can significantly improve efficiency by constructing smaller prediction sets while still satisfying the required coverage guarantee. The proposed algorithms are proven to ensure valid coverage and achieve sublinear regret. Experiments on real and synthetic datasets validate that the proposed methods construct smaller prediction sets and outperform existing multi-model online conformal prediction approaches.
Reliable uncertainty quantification is crucial for the trustworthiness of machine learning applications. Inductive Conformal Prediction (ICP) offers a distribution-free framework for generating prediction sets or intervals with user-specified confidence. However, standard ICP guarantees are marginal and typically require a fresh calibration set for each new prediction to maintain their validity. This paper addresses this practical limitation by demonstrating how e-conformal prediction, in conjunction with Hoeffding's inequality, can enable the repeated use of a single calibration set with a high probability of preserving the desired coverage. Through a case study on the CIFAR-10 dataset, we train a deep neural network and utilise a calibration set to estimate a Hoeffding correction. This correction allows us to apply a modified Markov's inequality, leading to the construction of prediction sets with quantifiable confidence. Our results illustrate the feasibility of maintaining provable performance in conformal prediction while enhancing its practicality by reducing the need for repeated calibration. The code for this work is publicly available.
We consider the problem of safe control in discrete autonomous agents that use learned components for imperfect perception (or more generally, state estimation) from high-dimensional observations. We propose a shield construction that provides run-time safety guarantees under perception errors by restricting the actions available to an agent, modeled as a Markov decision process, as a function of the state estimates. Our construction uses conformal prediction for the perception component, which guarantees that for each observation, the predicted set of estimates includes the actual state with a user-specified probability. The shield allows an action only if it is allowed for all the estimates in the predicted set, resulting in a local safety guarantee. We also articulate and prove a global safety property of existing shield constructions for perfect-perception agents bounding the probability of reaching unsafe states if the agent always chooses actions prescribed by the shield. We illustrate our approach with a case-study of an experimental autonomous system that guides airplanes on taxiways using high-dimensional perception DNNs.
Existing research on Retrieval-Augmented Generation (RAG) primarily focuses on improving overall question-answering accuracy, often overlooking the quality of sub-claims within generated responses. Recent methods that attempt to improve RAG trustworthiness, such as through auto-evaluation metrics, lack probabilistic guarantees or require ground truth answers. To address these limitations, we propose Conformal-RAG, a novel framework inspired by recent applications of conformal prediction (CP) on large language models (LLMs). Conformal-RAG leverages CP and internal information from the RAG mechanism to offer statistical guarantees on response quality. It ensures group-conditional coverage spanning multiple sub-domains without requiring manual labelling of conformal sets, making it suitable for complex RAG applications. Compared to existing RAG auto-evaluation methods, Conformal-RAG offers statistical guarantees on the quality of refined sub-claims, ensuring response reliability without the need for ground truth answers. Additionally, our experiments demonstrate that by leveraging information from the RAG system, Conformal-RAG retains up to 60\% more high-quality sub-claims from the response compared to direct applications of CP to LLMs, while maintaining the same reliability guarantee.
This paper introduces MARCO (Multi-Agent Reinforcement learning with Conformal Optimization), a novel hardware-aware framework for efficient neural architecture search (NAS) targeting resource-constrained edge devices. By significantly reducing search time and maintaining accuracy under strict hardware constraints, MARCO bridges the gap between automated DNN design and CAD for edge AI deployment. MARCO's core technical contribution lies in its unique combination of multi-agent reinforcement learning (MARL) with Conformal Prediction (CP) to accelerate the hardware/software co-design process for deploying deep neural networks. Unlike conventional once-for-all (OFA) supernet approaches that require extensive pretraining, MARCO decomposes the NAS task into a hardware configuration agent (HCA) and a Quantization Agent (QA). The HCA optimizes high-level design parameters, while the QA determines per-layer bit-widths under strict memory and latency budgets using a shared reward signal within a centralized-critic, decentralized-execution (CTDE) paradigm. A key innovation is the integration of a calibrated CP surrogate model that provides statistical guarantees (with a user-defined miscoverage rate) to prune unpromising candidate architectures before incurring the high costs of partial training or hardware simulation. This early filtering drastically reduces the search space while ensuring that high-quality designs are retained with a high probability. Extensive experiments on MNIST, CIFAR-10, and CIFAR-100 demonstrate that MARCO achieves a 3-4x reduction in total search time compared to an OFA baseline while maintaining near-baseline accuracy (within 0.3%). Furthermore, MARCO also reduces inference latency. Validation on a MAX78000 evaluation board confirms that simulator trends hold in practice, with simulator estimates deviating from measured values by less than 5%.
We develop a framework to quantify the time-to-unsafe-sampling - the number of large language model (LLM) generations required to trigger an unsafe (e.g., toxic) response. Estimating this quantity is challenging, since unsafe responses are exceedingly rare in well-aligned LLMs, potentially occurring only once in thousands of generations. As a result, directly estimating time-to-unsafe-sampling would require collecting training data with a prohibitively large number of generations per prompt. However, with realistic sampling budgets, we often cannot generate enough responses to observe an unsafe outcome for every prompt, leaving the time-to-unsafe-sampling unobserved in many cases, making the estimation and evaluation tasks particularly challenging. To address this, we frame this estimation problem as one of survival analysis and develop a provably calibrated lower predictive bound (LPB) on the time-to-unsafe-sampling of a given prompt, leveraging recent advances in conformal prediction. Our key innovation is designing an adaptive, per-prompt sampling strategy, formulated as a convex optimization problem. The objective function guiding this optimized sampling allocation is designed to reduce the variance of the estimators used to construct the LPB, leading to improved statistical efficiency over naive methods that use a fixed sampling budget per prompt. Experiments on both synthetic and real data support our theoretical results and demonstrate the practical utility of our method for safety risk assessment in generative AI models.
This paper studies a Conformal Prediction (CP) methodology for building prediction intervals in a regression setting, given only deterministic lower and upper bounds on the target variable. It proposes a new CP mechanism (CPUL) that goes beyond post-processing by adopting a model selection approach over multiple nested interval construction methods. Paradoxically, many well-established CP methods, including CPUL, may fail to provide adequate coverage in regions where the bounds are tight. To remedy this limitation, the paper proposes an optimal thresholding mechanism, OMLT, that adjusts CPUL intervals in tight regions with undercoverage. The combined CPUL-OMLT is validated on large-scale learning tasks where the goal is to bound the optimal value of a parametric optimization problem. The experimental results demonstrate substantial improvements over baseline methods across various datasets.
The increasing use of generative ML foundation models for image restoration tasks such as super-resolution calls for robust and interpretable uncertainty quantification methods. We address this need by presenting a novel approach based on conformal prediction techniques to create a 'confidence mask' capable of reliably and intuitively communicating where the generated image can be trusted. Our method is adaptable to any black-box generative model, including those locked behind an opaque API, requires only easily attainable data for calibration, and is highly customizable via the choice of a local image similarity metric. We prove strong theoretical guarantees for our method that span fidelity error control (according to our local image similarity metric), reconstruction quality, and robustness in the face of data leakage. Finally, we empirically evaluate these results and establish our method's solid performance.
Uncertainty quantification (UQ) for foundation models is essential to identify and mitigate potential hallucinations in automatically generated text. However, heuristic UQ approaches lack formal guarantees for key metrics such as the false discovery rate (FDR) in selective prediction. Previous work adopts the split conformal prediction (SCP) framework to ensure desired coverage of admissible answers by constructing prediction sets, but these sets often contain incorrect candidates, limiting their practical utility. To address this, we propose COIN, an uncertainty-guarding selection framework that calibrates statistically valid thresholds to filter a single generated answer per question under user-specified FDR constraints. COIN estimates the empirical error rate on a calibration set and applies confidence interval methods such as Clopper-Pearson to establish a high-probability upper bound on the true error rate (i.e., FDR). This enables the selection of the largest uncertainty threshold that ensures FDR control on test data while significantly increasing sample retention. We demonstrate COIN's robustness in risk control, strong test-time power in retaining admissible answers, and predictive efficiency under limited calibration data across both general and multimodal text generation tasks. Furthermore, we show that employing alternative upper bound constructions and UQ strategies can further boost COIN's power performance, which underscores its extensibility and adaptability to diverse application scenarios.
Conformal prediction offers a distribution-free framework for constructing prediction sets with coverage guarantees. In practice, multiple valid conformal prediction sets may be available, arising from different models or methodologies. However, selecting the most desirable set, such as the smallest, can invalidate the coverage guarantees. To address this challenge, we propose a stability-based approach that ensures coverage for the selected prediction set. We extend our results to the online conformal setting, propose several refinements in settings where additional structure is available, and demonstrate its effectiveness through experiments.
Deep neural networks (DNNs) rely heavily on high-quality open-source datasets (e.g., ImageNet) for their success, making dataset ownership verification (DOV) crucial for protecting public dataset copyrights. In this paper, we find existing DOV methods (implicitly) assume that the verification process is faithful, where the suspicious model will directly verify ownership by using the verification samples as input and returning their results. However, this assumption may not necessarily hold in practice and their performance may degrade sharply when subjected to intentional or unintentional perturbations. To address this limitation, we propose the first certified dataset watermark (i.e., CertDW) and CertDW-based certified dataset ownership verification method that ensures reliable verification even under malicious attacks, under certain conditions (e.g., constrained pixel-level perturbation). Specifically, inspired by conformal prediction, we introduce two statistical measures, including principal probability (PP) and watermark robustness (WR), to assess model prediction stability on benign and watermarked samples under noise perturbations. We prove there exists a provable lower bound between PP and WR, enabling ownership verification when a suspicious model's WR value significantly exceeds the PP values of multiple benign models trained on watermark-free datasets. If the number of PP values smaller than WR exceeds a threshold, the suspicious model is regarded as having been trained on the protected dataset. Extensive experiments on benchmark datasets verify the effectiveness of our CertDW method and its resistance to potential adaptive attacks. Our codes are at \href{https://github.com/NcepuQiaoTing/CertDW}{GitHub}.
Modern large language models (LLMs) are often deployed as agents, calling external tools adaptively to solve tasks. Rather than directly calling tools, it can be more effective for LLMs to write code to perform the tool calls, enabling them to automatically generate complex control flow such as conditionals and loops. Such code actions are typically provided as Python code, since LLMs are quite proficient at it; however, Python may not be the ideal language due to limited built-in support for performance, security, and reliability. We propose a novel programming language for code actions, called Quasar, which has several benefits: (1) automated parallelization to improve performance, (2) uncertainty quantification to improve reliability and mitigate hallucinations, and (3) security features enabling the user to validate actions. LLMs can write code in a subset of Python, which is automatically transpiled to Quasar. We evaluate our approach on the ViperGPT visual question answering agent, applied to the GQA dataset, demonstrating that LLMs with Quasar actions instead of Python actions retain strong performance, while reducing execution time when possible by 42%, improving security by reducing user approval interactions when possible by 52%, and improving reliability by applying conformal prediction to achieve a desired target coverage level.
We propose Conformal Mixed-Integer Constraint Learning (C-MICL), a novel framework that provides probabilistic feasibility guarantees for data-driven constraints in optimization problems. While standard Mixed-Integer Constraint Learning methods often violate the true constraints due to model error or data limitations, our C-MICL approach leverages conformal prediction to ensure feasible solutions are ground-truth feasible. This guarantee holds with probability at least $1{-}\alpha$, under a conditional independence assumption. The proposed framework supports both regression and classification tasks without requiring access to the true constraint function, while avoiding the scalability issues associated with ensemble-based heuristics. Experiments on real-world applications demonstrate that C-MICL consistently achieves target feasibility rates, maintains competitive objective performance, and significantly reduces computational cost compared to existing methods. Our work bridges mathematical optimization and machine learning, offering a principled approach to incorporate uncertainty-aware constraints into decision-making with rigorous statistical guarantees.
Incidental detection and quantification of coronary calcium in CT scans could lead to the early introduction of lifesaving clinical interventions. However, over-reporting could negatively affect patient wellbeing and unnecessarily burden the medical system. Therefore, careful considerations should be taken when automatically reporting coronary calcium scores. A cluster-based conditional conformal prediction framework is proposed to provide score intervals with calibrated coverage from trained segmentation networks without retraining. The proposed method was tuned and used to calibrate predictive intervals for 3D UNet models (deterministic, MCDropout and deep ensemble) reaching similar coverage with better triage metrics compared to conventional conformal prediction. Meaningful predictive intervals of calcium scores could help triage patients according to the confidence of their risk category prediction.