assess extrapolation robustness

This work addresses the prohibitive computational cost of classical probabilistic Richardson extrapolation in high-dimensional settings, where the curse of dimensionality leads to a super-exponential growth in the number of required simulations as tolerance parameters increase. To overcome this limitation, the authors propose a sparse probabilistic Richardson extrapolation framework that reformulates numerical computation as an extrapolation problem with respect to tolerance parameters. By incorporating a sparsity assumption, the method effectively reduces the effective dimensionality of the extrapolation task and integrates multi-fidelity simulations with optimal experimental design. The resulting approach substantially decreases the number of simulations needed in high-dimensional scenarios while preserving accuracy, offering a computationally efficient solution that is both theoretically well-founded and empirically effective, without sacrificing simplicity.

This work addresses the challenge of selecting the regularization parameter (nugget) in ill-posed linear systems arising in machine learning, where existing adaptive methods lack compatibility with automatic differentiation and suffer from computational inefficiency. To overcome these limitations, we introduce autonugget, a lightweight Python package fully compatible with JAX’s automatic differentiation framework. Our approach uniquely integrates Richardson extrapolation with Tikhonov regularized solutions computed across multiple nugget values, thereby preserving end-to-end differentiability while avoiding the information loss inherent in single-solution strategies. Experimental results demonstrate that autonugget significantly enhances solution accuracy and training stability without compromising rapid prototyping capabilities.

Traditional conformal prediction (CP) provides only marginal coverage guarantees under small-sample calibration, exhibiting high variance in coverage distribution and frequent violations below the nominal level—thereby undermining reliability in uncertainty quantification. To address this, we propose a novel conformal prediction framework that, for the first time, delivers probabilistic coverage guarantees for individual predictors—e.g., $ mathbb{P}( ext{Coverage} geq 1-alpha) geq 1-delta $—overcoming the fundamental limitation of marginal guarantees. This guarantee holds rigorously even with limited calibration data and asymptotically recovers classical CP guarantees under large samples. Our method leverages nonparametric concentration inequalities, requires no assumptions on error distributions, and integrates seamlessly with mainstream CP libraries. Experiments demonstrate substantial improvements in coverage stability and safety under low-data regimes, providing verifiable statistical guarantees for uncertainty quantification in resource-constrained settings.

Offline optimization of expensive black-box functions in materials engineering suffers from poor robustness due to the high sensitivity of surrogate models to parameter perturbations. Method: We propose, for the first time, an optimizable surrogate sensitivity metric and design a sensitivity-aware regularization method orthogonal to existing frameworks. This approach integrates gradient-based sensitivity analysis with deep-learning-based surrogate modeling and is compatible with mainstream paradigms such as offline Bayesian optimization. Contribution/Results: Evaluated on multiple materials design benchmarks, our method significantly improves optimization success rate (average gain of +23.6%) and solution quality (objective value improvement up to 17.4%). Empirical results demonstrate that explicit sensitivity control delivers critical performance gains for offline optimization of expensive black-box functions in materials engineering.

This work addresses the challenge that existing machine learning methods struggle to distinguish between epistemic and aleatoric uncertainty under extrapolation scenarios and often lack rigorous coverage guarantees. The authors propose a model-agnostic conformal fuzzy inference framework that, for the first time, integrates conformal prediction with fuzzy reasoning. By incorporating a distance-aware mechanism, the method generates fuzzy predictions—formally represented as probability boxes—with theoretical validity guarantees. This approach enables adaptive uncertainty quantification under distributional shift and demonstrates superior robustness and reliable coverage compared to conventional probabilistic methods on both synthetic and benchmark datasets, with particularly pronounced advantages in data-scarce regimes.

This work investigates how to simultaneously enhance functional correctness and computational efficiency in code generation without additional training, by leveraging model weight combinations. The approach trains multiple checkpoints using rewards derived from unit test coverage, then applies linear interpolation and extrapolation of weights, augmented with an inference-time ensemble strategy. The key contribution lies in the first demonstration that weight extrapolation effectively expands the correctness–efficiency Pareto frontier in reinforcement learning for code generation. Experiments show that, on the LCB/hard benchmark, the extrapolation-based ensemble improves the pass@250 metric by 3.3% over the best single model, with consistent gains across three distinct settings: pure inference, tool-augmented reasoning, and agent-based coding.

This work addresses the issue of unphysical predictions commonly arising in zero-noise extrapolation (ZNE) due to the absence of physical constraints. For the first time, physical boundedness is explicitly incorporated into mainstream ZNE models through novel bounded polynomial, exponential, and hybrid extrapolation methods. These approaches enforce valid ranges for quantum observables via parameterized optimization without altering existing ZNE workflows. Evaluated on a synthetic benchmark comprising 180,000 circuits and 3.6 million experimental runs, the proposed methods substantially reduce unphysical outcomes. Validation on real IBM quantum hardware further demonstrates that the bounded models maintain high accuracy while significantly improving result reliability and usable coverage.

This study addresses the stability of the solution operator with respect to perturbations in the input parameter distribution within the framework of nonparametric Bayesian computer model calibration. By integrating nonparametric Bayesian inference, weak convergence theory of probability measures, and total variation metric analysis, the work establishes—for the first time—a systematic continuity theory for the solution operator in this calibration setting. The primary contributions include proving the uniform continuity of the solution operator under the total variation metric and demonstrating its continuity under the weak topology for a broad class of prior distributions. These results provide a rigorous theoretical foundation for the robustness of nonparametric Bayesian calibration methods in complex scientific applications.