For example, the déjà vu method shows that for certain representation learning models and training images, it is sometimes possible to correctly predict the foreground label given only the representation of the background - better than through dataset-level correlations.

In contrast, we show that the computation of one PI-explanation for an NBC can be achieved in log-linear time, and that the same result also applies to the more general class of linear classifiers. Furthermore, we show that the enumeration ofPI-explanations can beobtained with polynomial delay. Experimental results demonstrate the performance gains ofthe newalgorithms when compared with earlierwork.

Iterative self-improvement fine-tunes an autoregressive large language model (LLM) on reward-verified outputs generated by the LLM itself. In contrast to the empirical success of self-improvement, the theoretical foundation of this generative, iterative procedure in a practical, finite-sample setting remains limited. We make progress toward this goal by modeling each round of self-improvement as maximum-likelihood fine-tuning on a reward-filtered distribution and deriving finite-sample guarantees for the expected reward. Our analysis reveals an explicit feedback loop where better models accept more data per iteration, supporting sustained self-improvement while explaining eventual saturation of such improvement. Adopting a task-centric view by considering reasoning tasks with multiple difficulty levels, we further prove quantifiable conditions on model initialization, task difficulty, and sample budget where easy-to-hard curricula provably achieve better guarantees than training on fixed mixtures of tasks. Our analyses are validated via Monte-Carlo simulations and controlled experiments on graph-based reasoning tasks.

Conditional Value-at-Risk (CVaR) is a central tail-risk measure in stochastic structural mechanics, yet its accurate evaluation under high-dimensional, spatially correlated material uncertainty remains computationally prohibitive for classical Monte Carlo methods. Leveraging bounded-expectation reformulations of CVaR compatible with quantum amplitude estimation, we develop a quantum-enhanced inference framework that casts CVaR evaluation as a statistically consistent, confidence-constrained maximum-likelihood amplitude estimation problem. The proposed method extends iterative quantum amplitude estimation (IQAE) by embedding explicit maximum-likelihood inference within a rigorously controlled interval-tracking architecture. To ensure global correctness under finite-shot noise and the non-injective oscillatory response induced by Grover amplification, we introduce a stabilized inference scheme incorporating multi-hypothesis feasibility tracking, periodic low-depth disambiguation, and a bounded restart mechanism governed by an explicit failure-probability budget. This formulation preserves the quadratic oracle-complexity advantage of amplitude estimation while providing finite-sample confidence guarantees and reduced estimator variance. The framework is demonstrated on benchmark problems with spatially correlated lognormal Young's modulus fields generated using a Nystrom low-rank Gaussian kernel model. Numerical results show that the proposed estimator achieves substantially lower oracle complexity than classical Monte Carlo CVaR estimation at comparable confidence levels, while maintaining rigorous statistical reliability. This work establishes a practically robust and theoretically grounded quantum-enhanced methodology for tail-risk quantification in stochastic continuum mechanics.