Bayesian optimization is a methodology to optimize black-box functions.

Our results shed light on the relative advantages of existing algorithms while bringing into question some claims from past work.

Precise and comprehensive situational awareness is a critical capability of modern autonomous systems. Deep neural networks that perceive task-critical details from rich sensory signals have become ubiquitous; however, their black-box behavior and sensitivity to environmental uncertainty and distribution shifts make them challenging to verify formally. Abstraction-based verification techniques for vision-based autonomy produce safety guarantees contingent on rigid assumptions, such as bounded errors or known unique distributions. Such overly restrictive and inflexible assumptions limit the validity of the guarantees, especially in diverse and uncertain test-time environments. We propose a methodology that unifies the verification models of perception with their offline validation. Our methodology leverages interval MDPs and provides a flexible end-to-end guarantee that adapts directly to the out-of-distribution test-time conditions. We evaluate our methodology on a synthetic perception Markov chain with well-defined state estimation distributions and a mountain car benchmark. Our findings reveal that we can guarantee tight yet rigorous bounds on overall system safety.

Similarity choice data occur when humans make choices among alternatives based on their similarity to a target, e.g., in the context of information retrieval and in embedding learning settings. Classical metric-based models of similarity choice assume independence of irrelevant alternatives (IIA), a property that allows for a simpler formulation. While IIA violations have been detected in many discrete choice settings, the similarity choice setting has received scant attention. This is because the target-dependent nature of the choice complicates IIA testing. We propose two statistical methods to test for IIA: a classical goodness-of-fit test and a Bayesian counterpart based on the framework of Posterior Predictive Checks (PPC). This Bayesian approach, our main technical contribution, quantifies the degree of IIA violation beyond its mere significance. We curate two datasets: one with choice sets designed to elicit IIA violations, and another with randomly generated choice sets from the same item universe. Our tests confirmed significant IIA violations on both datasets, and notably, we find a comparable degree of violation between them. Further, we devise a new PPC test for population homogeneity. Results show that the population is indeed homogenous, suggesting that the IIA violations are driven by context effects -- specifically, interactions within the choice sets. These results highlight the need for new similarity choice models that account for such context effects.

Fine-tuning large language models (LLMs) with low-rank adaptaion (LoRA) is a cost-effective way to incorporate information from a specific dataset. However, it is often unclear how well the fine-tuned LLM will generalize, i.e., how well it will perform on unseen datasets. Methods have been proposed to improve generalization by optimizing with in-context prompts, or by using meta-learning to fine-tune LLMs. However, these methods are expensive in memory and computation, requiring either long-context prompts or saving copies of parameters and using second-order gradient updates. To address these challenges, we propose Amortized Bayesian Meta-Learning for LoRA (ABMLL). This method builds on amortized Bayesian meta-learning for smaller models, adapting this approach to LLMs while maintaining its computational efficiency. We reframe task-specific and global parameters in the context of LoRA and use a set of new hyperparameters to balance reconstruction accuracy and the fidelity of task-specific parameters to the global ones. ABMLL provides effective generalization and scales to large models such as Llama3-8B. Furthermore, as a result of using a Bayesian framework, ABMLL provides improved uncertainty quantification. We test ABMLL on Unified-QA and CrossFit datasets and find that it outperforms existing methods on these benchmarks in terms of both accuracy and expected calibration error.

Shapley values are widely recognized as a principled method for attributing importance to input features in machine learning. However, the exact computation of Shapley values scales exponentially with the number of features, severely limiting the practical application of this powerful approach. The challenge is further compounded when the predictive model is probabilistic - as in Gaussian processes (GPs) - where the outputs are random variables rather than point estimates, necessitating additional computational effort in modeling higher-order moments. In this work, we demonstrate that for an important class of GPs known as FANOVA GP, which explicitly models all main effects and interactions, *exact* Shapley attributions for both local and global explanations can be computed in *quadratic time*. For local, instance-wise explanations, we define a stochastic cooperative game over function components and compute the exact stochastic Shapley value in quadratic time only, capturing both the expected contribution and uncertainty. For global explanations, we introduce a deterministic, variance-based value function and compute exact Shapley values that quantify each feature's contribution to the model's overall sensitivity. Our methods leverage a closed-form (stochastic) Möbius representation of the FANOVA decomposition and introduce recursive algorithms, inspired by Newton's identities, to efficiently compute the mean and variance of Shapley values. Our work enhances the utility of explainable AI, as demonstrated by empirical studies, by providing more scalable, axiomatically sound, and uncertainty-aware explanations for predictions generated by structured probabilistic models.

Intelligence is fundamentally non-ergodic: it emerges not from uniform sampling or optimization from scratch, but from the structured reuse of prior inference trajectories. We introduce Memory-Amortized Inference (MAI) as a formal framework in which cognition is modeled as inference over latent cycles in memory, rather than recomputation through gradient descent. MAI systems encode inductive biases via structural reuse, minimizing entropy and enabling context-aware, structure-preserving inference. This approach reframes cognitive systems not as ergodic samplers, but as navigators over constrained latent manifolds, guided by persistent topological memory. Through the lens of delta-homology, we show that MAI provides a principled foundation for Mountcastle's Universal Cortical Algorithm, modeling each cortical column as a local inference operator over cycle-consistent memory states. Furthermore, we establish a time-reversal duality between MAI and reinforcement learning: whereas RL propagates value forward from reward, MAI reconstructs latent causes backward from memory. This inversion paves a path toward energy-efficient inference and addresses the computational bottlenecks facing modern AI. MAI thus offers a unified, biologically grounded theory of intelligence based on structure, reuse, and memory. We also briefly discuss the profound implications of MAI for achieving artificial general intelligence (AGI).

Continuous Descent Operations (CDO) involve smooth, idle-thrust descents that avoid level-offs, reducing fuel burn, emissions, and noise while improving efficiency and passenger comfort. Despite its operational and environmental benefits, limited research has systematically examined the factors influencing CDO performance. Moreover, many existing methods in related areas, such as trajectory optimization, lack the transparency required in aviation, where explainability is critical for safety and stakeholder trust. This study addresses these gaps by proposing a Fuzzy-Enhanced Explainable AI (FEXAI) framework that integrates fuzzy logic with machine learning and SHapley Additive exPlanations (SHAP) analysis. For this purpose, a comprehensive dataset of 29 features, including 11 operational and 18 weather-related features, was collected from 1,094 flights using Automatic Dependent Surveillance-Broadcast (ADS-B) data. Machine learning models and SHAP were then applied to classify flights' CDO adherence levels and rank features by importance. The three most influential features, as identified by SHAP scores, were then used to construct a fuzzy rule-based classifier, enabling the extraction of interpretable fuzzy rules. All models achieved classification accuracies above 90%, with FEXAI providing meaningful, human-readable rules for operational users. Results indicated that the average descent rate within the arrival route, the number of descent segments, and the average change in directional heading during descent were the strongest predictors of CDO performance. The FEXAI method proposed in this study presents a novel pathway for operational decision support and could be integrated into aviation tools to enable real-time advisories that maintain CDO adherence under varying operational conditions.