Online Conformal Probabilistic Numerics via Adaptive Edge-Cloud Offloading

Consider an edge computing setting in which a user submits queries for the solution of a linear system to an edge processor, which is subject to time-varying computing availability. The edge processor applies a probabilistic linear solver (PLS) so as to be able to respond to the user's query within the allotted time and computing budget. Feedback to the user is in the form of an uncertainty set. Due to model misspecification, the uncertainty set obtained via a direct application of PLS does not come with coverage guarantees with respect to the true solution of the linear system. This work introduces a new method to calibrate the uncertainty sets produced by PLS with the aim of guaranteeing long-term coverage requirements. The proposed method, referred to as online conformal prediction-PLS (OCP-PLS), assumes sporadic feedback from cloud to edge. This enables the online calibration of uncertainty thresholds via online conformal prediction (OCP), an online optimization method previously studied in the context of prediction models. The validity of OCP-PLS is verified via experiments that bring insights into trade-offs between coverage, prediction set size, and cloud usage.

Convergence Analysis of alpha-SVRG under Strong Convexity

Stochastic first-order methods for empirical risk minimization employ gradient approximations based on sampled data in lieu of exact gradients. Such constructions introduce noise into the learning dynamics, which can be corrected through variance-reduction techniques. There is increasing evidence in the literature that in many modern learning applications noise can have a beneficial effect on optimization and generalization. To this end, the recently proposed variance-reduction technique, alpha-SVRG [Yin et al., 2023] allows for fine-grained control of the level of residual noise in the learning dynamics, and has been reported to empirically outperform both SGD and SVRG in modern deep learning scenarios. By focusing on strongly convex environments, we first provide a unified convergence rate expression for alpha-SVRG under fixed learning rate, which reduces to that of either SGD or SVRG by setting alpha=0 or alpha=1, respectively. We show that alpha-SVRG has faster convergence rate compared to SGD and SVRG under suitable choice of alpha. Simulation results on linear regression validate our theory.

FedRand: Enhancing Privacy in Federated Learning with Randomized LoRA Subparameter Updates

Federated Learning (FL) is a widely used framework for training models in a decentralized manner, ensuring that the central server does not have direct access to data from local clients. However, this approach may still fail to fully preserve data privacy, as models from local clients are exposed to the central server during the aggregation process. This issue becomes even more critical when training vision-language models (VLMs) with FL, as VLMs can easily memorize training data instances, making them vulnerable to membership inference attacks (MIAs). To address this challenge, we propose the FedRand framework, which avoids disclosing the full set of client parameters. In this framework, each client randomly selects subparameters of Low-Rank Adaptation (LoRA) from the server and keeps the remaining counterparts of the LoRA weights as private parameters. After training both parameters on the client's private dataset, only the non-private client parameters are sent back to the server for aggregation. This approach mitigates the risk of exposing client-side VLM parameters, thereby enhancing data privacy. We empirically validate that FedRand improves robustness against MIAs compared to relevant baselines while achieving accuracy comparable to methods that communicate full LoRA parameters across several benchmark datasets.

Calibrating Wireless AI via Meta-Learned Context-Dependent Conformal Prediction

Modern software-defined networks, such as Open Radio Access Network (O-RAN) systems, rely on artificial intelligence (AI)-powered applications running on controllers interfaced with the radio access network. To ensure that these AI applications operate reliably at runtime, they must be properly calibrated before deployment. A promising and theoretically grounded approach to calibration is conformal prediction (CP), which enhances any AI model by transforming it into a provably reliable set predictor that provides error bars for estimates and decisions. CP requires calibration data that matches the distribution of the environment encountered during runtime. However, in practical scenarios, network controllers often have access only to data collected under different contexts -- such as varying traffic patterns and network conditions -- leading to a mismatch between the calibration and runtime distributions. This paper introduces a novel methodology to address this calibration-test distribution shift. The approach leverages meta-learning to develop a zero-shot estimator of distribution shifts, relying solely on contextual information. The proposed method, called meta-learned context-dependent weighted conformal prediction (ML-WCP), enables effective calibration of AI applications without requiring data from the current context. Additionally, it can incorporate data from multiple contexts to further enhance calibration reliability.

Distilling Calibration via Conformalized Credal Inference

Deploying artificial intelligence (AI) models on edge devices involves a delicate balance between meeting stringent complexity constraints, such as limited memory and energy resources, and ensuring reliable performance in sensitive decision-making tasks. One way to enhance reliability is through uncertainty quantification via Bayesian inference. This approach, however, typically necessitates maintaining and running multiple models in an ensemble, which may exceed the computational limits of edge devices. This paper introduces a low-complexity methodology to address this challenge by distilling calibration information from a more complex model. In an offline phase, predictive probabilities generated by a high-complexity cloud-based model are leveraged to determine a threshold based on the typical divergence between the cloud and edge models. At run time, this threshold is used to construct credal sets -- ranges of predictive probabilities that are guaranteed, with a user-selected confidence level, to include the predictions of the cloud model. The credal sets are obtained through thresholding of a divergence measure in the simplex of predictive probabilities. Experiments on visual and language tasks demonstrate that the proposed approach, termed Conformalized Distillation for Credal Inference (CD-CI), significantly improves calibration performance compared to low-complexity Bayesian methods, such as Laplace approximation, making it a practical and efficient solution for edge AI deployments.

VLM-HOI: Vision Language Models for Interpretable Human-Object Interaction Analysis

The Large Vision Language Model (VLM) has recently addressed remarkable progress in bridging two fundamental modalities. VLM, trained by a sufficiently large dataset, exhibits a comprehensive understanding of both visual and linguistic to perform diverse tasks. To distill this knowledge accurately, in this paper, we introduce a novel approach that explicitly utilizes VLM as an objective function form for the Human-Object Interaction (HOI) detection task (\textbf{VLM-HOI}). Specifically, we propose a method that quantifies the similarity of the predicted HOI triplet using the Image-Text matching technique. We represent HOI triplets linguistically to fully utilize the language comprehension of VLMs, which are more suitable than CLIP models due to their localization and object-centric nature. This matching score is used as an objective for contrastive optimization. To our knowledge, this is the first utilization of VLM language abilities for HOI detection. Experiments demonstrate the effectiveness of our method, achieving state-of-the-art HOI detection accuracy on benchmarks. We believe integrating VLMs into HOI detection represents important progress towards more advanced and interpretable analysis of human-object interactions.

Robust Bayesian Optimization via Localized Online Conformal Prediction

Bayesian optimization (BO) is a sequential approach for optimizing black-box objective functions using zeroth-order noisy observations. In BO, Gaussian processes (GPs) are employed as probabilistic surrogate models to estimate the objective function based on past observations, guiding the selection of future queries to maximize utility. However, the performance of BO heavily relies on the quality of these probabilistic estimates, which can deteriorate significantly under model misspecification. To address this issue, we introduce localized online conformal prediction-based Bayesian optimization (LOCBO), a BO algorithm that calibrates the GP model through localized online conformal prediction (CP). LOCBO corrects the GP likelihood based on predictive sets produced by LOCBO, and the corrected GP likelihood is then denoised to obtain a calibrated posterior distribution on the objective function. The likelihood calibration step leverages an input-dependent calibration threshold to tailor coverage guarantees to different regions of the input space. Under minimal noise assumptions, we provide theoretical performance guarantees for LOCBO's iterates that hold for the unobserved objective function. These theoretical findings are validated through experiments on synthetic and real-world optimization tasks, demonstrating that LOCBO consistently outperforms state-of-the-art BO algorithms in the presence of model misspecification.

Expanding Search Space with Diverse Prompting Agents: An Efficient Sampling Approach for LLM Mathematical Reasoning

Large Language Models (LLMs) have exhibited remarkable capabilities in many complex tasks including mathematical reasoning. However, traditional approaches heavily rely on ensuring self-consistency within single prompting method, which limits the exploration of diverse problem-solving strategies. This study addresses these limitations by performing an experimental analysis of distinct prompting methods within the domain of mathematical reasoning. Our findings demonstrate that each method explores a distinct search space, and this differentiation becomes more evident with increasing problem complexity. To leverage this phenomenon, we applied efficient sampling process that uniformly combines samples from these diverse methods, which not only expands the maximum search space but achieves higher performance with fewer runs compared to single methods. Especially, within the subset of difficult questions of MATH dataset named MATH-hard, The maximum search space was achieved while utilizing approximately 43% fewer runs than single methods on average. These findings highlight the importance of integrating diverse problem-solving strategies to enhance the reasoning abilities of LLMs.

Conformal Distributed Remote Inference in Sensor Networks Under Reliability and Communication Constraints

This paper presents communication-constrained distributed conformal risk control (CD-CRC) framework, a novel decision-making framework for sensor networks under communication constraints. Targeting multi-label classification problems, such as segmentation, CD-CRC dynamically adjusts local and global thresholds used to identify significant labels with the goal of ensuring a target false negative rate (FNR), while adhering to communication capacity limits. CD-CRC builds on online exponentiated gradient descent to estimate the relative quality of the observations of different sensors, and on online conformal risk control (CRC) as a mechanism to control local and global thresholds. CD-CRC is proved to offer deterministic worst-case performance guarantees in terms of FNR and communication overhead, while the regret performance in terms of false positive rate (FPR) is characterized as a function of the key hyperparameters. Simulation results highlight the effectiveness of CD-CRC, particularly in communication resource-constrained environments, making it a valuable tool for enhancing the performance and reliability of distributed sensor networks.

Quantile Learn-Then-Test: Quantile-Based Risk Control for Hyperparameter Optimization

The increasing adoption of Artificial Intelligence (AI) in engineering problems calls for the development of calibration methods capable of offering robust statistical reliability guarantees. The calibration of black box AI models is carried out via the optimization of hyperparameters dictating architecture, optimization, and/or inference configuration. Prior work has introduced learn-then-test (LTT), a calibration procedure for hyperparameter optimization (HPO) that provides statistical guarantees on average performance measures. Recognizing the importance of controlling risk-aware objectives in engineering contexts, this work introduces a variant of LTT that is designed to provide statistical guarantees on quantiles of a risk measure. We illustrate the practical advantages of this approach by applying the proposed algorithm to a radio access scheduling problem.