Deep learning has achieved remarkable success across various domains, largely thanks to the efficiency of backpropagation (BP). However, BP's reliance on differentiability poses challenges in neurosymbolic learning, where discrete computation is combined with neural models. We show that applying BP to Godel logic, which represents conjunction and disjunction as min and max, is equivalent to a local search algorithm for SAT solving, enabling the optimisation of discrete Boolean formulas without sacrificing differentiability. However, deterministic local search algorithms get stuck in local optima. Therefore, we propose the Godel Trick, which adds noise to the model's logits to escape local optima. We evaluate the Godel Trick on SATLIB, and demonstrate its ability to solve a broad range of SAT problems. Additionally, we apply it to neurosymbolic models and achieve state-of-the-art performance on Visual Sudoku, all while avoiding expensive probabilistic reasoning. These results highlight the Godel Trick's potential as a robust, scalable approach for integrating symbolic reasoning with neural architectures.

Generalized Bayesian Inference (GBI) provides a flexible framework for updating prior distributions using various loss functions instead of the traditional likelihoods, thereby enhancing the model robustness to model misspecification. However, GBI often suffers the problem associated with intractable likelihoods. Kernelized Stein Discrepancy (KSD), as utilized in a recent study, addresses this challenge by relying only on the gradient of the log-likelihood. Despite this innovation, KSD-Bayes suffers from critical pathologies, including insensitivity to well-separated modes in multimodal posteriors. To address this limitation, we propose a weighted KSD method that retains computational efficiency while effectively capturing multimodal structures. Our method improves the GBI framework for handling intractable multimodal posteriors while maintaining key theoretical properties such as posterior consistency and asymptotic normality. Experimental results demonstrate that our method substantially improves mode sensitivity compared to standard KSD-Bayes, while retaining robust performance in unimodal settings and in the presence of outliers.

Understanding consumer choice is fundamental to marketing and management research, as firms increasingly seek to personalize offerings and optimize customer engagement. Traditional choice modeling frameworks, such as multinomial logit (MNL) and mixed logit models, impose rigid parametric assumptions that limit their ability to capture the complexity of consumer decision-making. This study introduces the Mixture of Experts (MoE) framework as a machine learning-driven alternative that dynamically segments consumers based on latent behavioral patterns. By leveraging probabilistic gating functions and specialized expert networks, MoE provides a flexible, nonparametric approach to modeling heterogeneous preferences. Empirical validation using large-scale retail data demonstrates that MoE significantly enhances predictive accuracy over traditional econometric models, capturing nonlinear consumer responses to price variations, brand preferences, and product attributes. The findings underscore MoEs potential to improve demand forecasting, optimize targeted marketing strategies, and refine segmentation practices. By offering a more granular and adaptive framework, this study bridges the gap between data-driven machine learning approaches and marketing theory, advocating for the integration of AI techniques in managerial decision-making and strategic consumer insights.

Uncertainty in LiDAR sensor-based object detection arises from environmental variability and sensor performance limitations. Representing these uncertainties is essential for ensuring the Safety of the Intended Functionality (SOTIF), which focuses on preventing hazards in automated driving scenarios. This paper presents a systematic approach to identifying, classifying, and representing uncertainties in LiDAR-based object detection within a SOTIF-related scenario. Dempster-Shafer Theory (DST) is employed to construct a Frame of Discernment (FoD) to represent detection outcomes. Conditional Basic Probability Assignments (BPAs) are applied based on dependencies among identified uncertainty sources. Yager's Rule of Combination is used to resolve conflicting evidence from multiple sources, providing a structured framework to evaluate uncertainties' effects on detection accuracy. The study applies variance-based sensitivity analysis (VBSA) to quantify and prioritize uncertainties, detailing their specific impact on detection performance.

Designing proper experiments and selecting optimal intervention targets is a longstanding problem in scientific or causal discovery. Identifying the underlying causal structure from observational data alone is inherently difficult. Obtaining interventional data, on the other hand, is crucial to causal discovery, yet it is usually expensive and time-consuming to gather sufficient interventional data to facilitate causal discovery. Previous approaches commonly utilize uncertainty or gradient signals to determine the intervention targets. However, numerical-based approaches may yield suboptimal results due to the inaccurate estimation of the guiding signals at the beginning when with limited interventional data. In this work, we investigate a different approach, whether we can leverage Large Language Models (LLMs) to assist with the intervention targeting in causal discovery by making use of the rich world knowledge about the experimental design in LLMs. Specifically, we present Large Language Model Guided Intervention Targeting (LeGIT) -- a robust framework that effectively incorporates LLMs to augment existing numerical approaches for the intervention targeting in causal discovery. Across 4 realistic benchmark scales, LeGIT demonstrates significant improvements and robustness over existing methods and even surpasses humans, which demonstrates the usefulness of LLMs in assisting with experimental design for scientific discovery.

Ephemerality meets LiDAR-based Lifelong Mapping Hyeonjae Gil 1, Dongjae Lee 1, Giseop Kim 2, and A young Kim 1 Abstract -- Lifelong mapping is crucial for the long-term deployment of robots in dynamic environments. In this paper, we present ELite, an ephemerality-aided LiDAR-based lifelong mapping framework which can seamlessly align multiple session data, remove dynamic objects, and update maps in an end-to-end fashion. Map elements are typically classified as static or dynamic, but cases like parked cars indicate the need for more detailed categories than binary. Central to our approach is the probabilistic modeling of the world into two-stage ephemerality, which represent the transiency of points in the map within two different time scales. By leveraging the spatiotemporal context encoded in ephemeralities, ELite can accurately infer transient map elements, maintain a reliable up-to-date static map, and improve robustness in aligning the new data in a more fine-grained manner . Extensive real-world experiments on long-term datasets demonstrate the robustness and effectiveness of our system. I. INTRODUCTION Over the past decade, Light Detection and Ranging (LiDAR)-based mapping has significantly advanced [1-4], increasing the demand for long-term deployment of such systems in various fields, including urban areas or construction sites [5]. These environments are inherently dynamic; objects frequently move, and layouts change.

Simulation-based inference (SBI) methods typically require fully observed data to infer parameters of models with intractable likelihood functions. However, datasets often contain missing values due to incomplete observations, data corruptions (common in astrophysics), or instrument limitations (e.g., in high-energy physics applications). In such scenarios, missing data must be imputed before applying any SBI method. We formalize the problem of missing data in SBI and demonstrate that naive imputation methods can introduce bias in the estimation of SBI posterior. We also introduce a novel amortized method that addresses this issue by jointly learning the imputation model and the inference network within a neural posterior estimation (NPE) framework. Extensive empirical results on SBI benchmarks show that our approach provides robust inference outcomes compared to standard baselines for varying levels of missing data. Moreover, we demonstrate the merits of our imputation model on two real-world bioactivity datasets (Adrenergic and Kinase assays). Code is available at https://github.com/Aalto-QuML/RISE.

Autoregressive models have emerged as a powerful framework for modeling exchangeable sequences - i.i.d. observations when conditioned on some latent factor - enabling direct modeling of uncertainty from missing data (rather than a latent). Motivated by the critical role posterior inference plays as a subroutine in decision-making (e.g., active learning, bandits), we study the inferential and architectural inductive biases that are most effective for exchangeable sequence modeling. For the inference stage, we highlight a fundamental limitation of the prevalent single-step generation approach: inability to distinguish between epistemic and aleatoric uncertainty. Instead, a long line of works in Bayesian statistics advocates for multi-step autoregressive generation; we demonstrate this "correct approach" enables superior uncertainty quantification that translates into better performance on downstream decision-making tasks. This naturally leads to the next question: which architectures are best suited for multi-step inference? We identify a subtle yet important gap between recently proposed Transformer architectures for exchangeable sequences (Muller et al., 2022; Nguyen & Grover, 2022; Ye & Namkoong, 2024), and prove that they in fact cannot guarantee exchangeability despite introducing significant computational overhead. We illustrate our findings using controlled synthetic settings, demonstrating how custom architectures can significantly underperform standard causal masks, underscoring the need for new architectural innovations.

We study the problem of posterior sampling in discrete-state spaces using discrete diffusion models. While posterior sampling methods for continuous diffusion models have achieved remarkable progress, analogous methods for discrete diffusion models remain challenging. In this work, we introduce a principled plug-and-play discrete diffusion posterior sampling algorithm based on split Gibbs sampling, which we call SG-DPS. Our algorithm enables reward-guided generation and solving inverse problems in discrete-state spaces. We demonstrate that SG-DPS converges to the true posterior distribution on synthetic benchmarks, and enjoys state-of-the-art posterior sampling performance on a range of benchmarks for discrete data, achieving up to 2x improved performance compared to existing baselines.

How can we learn generative models to sample data with arbitrary logical compositions of statistically independent attributes? The prevailing solution is to sample from distributions expressed as a composition of attributes' conditional marginal distributions under the assumption that they are statistically independent. This paper shows that standard conditional diffusion models violate this assumption, even when all attribute compositions are observed during training. And, this violation is significantly more severe when only a subset of the compositions is observed. We propose CoInD to address this problem. It explicitly enforces statistical independence between the conditional marginal distributions by minimizing Fisher's divergence between the joint and marginal distributions. The theoretical advantages of CoInD are reflected in both qualitative and quantitative experiments, demonstrating a significantly more faithful and controlled generation of samples for arbitrary logical compositions of attributes. The benefit is more pronounced for scenarios that current solutions relying on the assumption of conditionally independent marginals struggle with, namely, logical compositions involving the NOT operation and when only a subset of compositions are observed during training.