Diffusion models have emerged as powerful generative frameworks, creating data samples by progressively denoising an initial random state. Traditionally, this initial state is sampled from a simple, fixed distribution like isotropic Gaussian, inherently lacking structure and a direct mechanism for external control. While recent efforts have explored ways to introduce controllability into the diffusion process, particularly at the initialization stage, they often rely on deterministic or heuristic approaches. These methods can be suboptimal, lack expressiveness, and are difficult to scale or integrate into more sophisticated optimization frameworks. In this paper, we introduce NoiseAR, a novel method for AutoRegressive Initial Noise Prior for Diffusion Models. Instead of a static, unstructured source, NoiseAR learns to generate a dynamic and controllable prior distribution for the initial noise. We formulate the generation of the initial noise prior's parameters as an autoregressive probabilistic modeling task over spatial patches or tokens. This approach enables NoiseAR to capture complex spatial dependencies and introduce learned structure into the initial state. Crucially, NoiseAR is designed to be conditional, allowing text prompts to directly influence the learned prior, thereby achieving fine-grained control over the diffusion initialization. Our experiments demonstrate that NoiseAR can generate initial noise priors that lead to improved sample quality and enhanced consistency with conditional inputs, offering a powerful, learned alternative to traditional random initialization. A key advantage of NoiseAR is its probabilistic formulation, which naturally supports seamless integration into probabilistic frameworks like Markov Decision Processes and Reinforcement Learning. Our code will be available at https://github.com/HKUST-SAIL/NoiseAR/

Theory-of-Mind (ToM) enables humans to infer mental states-such as beliefs, desires, and intentions-forming the foundation of social cognition. However, existing computational ToM methods rely on structured workflows with ToM-specific priors or deep model fine-tuning, which struggle with scalability in multimodal environments and fail to generalize as task complexity increases. To address these limitations, we propose a scalable Bayesian ToM planner that decomposes ToM reasoning into stepwise Bayesian updates. Our framework introduces weak-to-strong control, allowing smaller language models (LMs) to specialize in ToM-specific likelihood estimation and transfer their reasoning behaviors to larger LMs (7B to 405B) for integration with social and world knowledge. This synergistic approach aligns large-model inference of human mental states with Bayesian principles. Extensive experiments show that our method achieves a 4.6% accuracy improvement over state-of-the-art techniques on multimodal ToM benchmarks, including challenging unseen scenarios, thereby establishing a new standard for modeling human mental states in complex environments.

The Fourier representation for the uniform distribution over the Boolean cube has found numerous applications in algorithms and complexity analysis. Notably, in learning theory, learnability of Disjunctive Normal Form (DNF) under uniform as well as product distributions has been established through such representations. This paper makes five main contributions. First, it introduces a generalized Fourier expansion that can be used with any distribution $D$ through the representation of the distribution as a Bayesian network (BN). Second, it shows that the main algorithmic tools for learning with the Fourier representation, that use membership queries to approximate functions by recovering their heavy Fourier coefficients, can be used with slight modifications with the generalized expansion. These results hold for any distribution. Third, it analyzes the $L_1$ spectral norm of conjunctions under the new expansion, showing that it is bounded for a class of distributions which can be represented by difference bounded tree BN, where a parent node in the BN representation can change the conditional expectation of a child node by at most $α<0.5$. Lower bounds are presented to show that such constraints are necessary. The fourth contribution uses these results to show the learnability of DNF with membership queries under difference bounded tree BN. The final contribution is to develop an algorithm for learning difference-bounded tree BN distributions, thus extending the DNF learnability result to cases where the distribution is not known in advance.

Model reprogramming adapts pretrained models to downstream tasks by modifying only the input and output spaces. Visual reprogramming (VR) is one instance for vision tasks that adds a trainable noise pattern (i.e., a visual prompt) to input images to facilitate downstream classification. The existing VR approaches for CLIP train a single visual prompt using all descriptions of different downstream classes. However, the limited learning capacity may result in (1) a failure to capture diverse aspects of the descriptions (e.g., shape, color, and texture), and (2) a possible bias toward less informative attributes that do not help distinguish between classes. In this paper, we introduce a decoupling-and-reweighting framework. Our decoupled visual prompts (DVP) are optimized using descriptions grouped by explicit causes (DVP-cse) or unsupervised clusters (DVP-cls). Then, we integrate the outputs of these visual prompts with a probabilistic reweighting matrix (PRM) that measures their contributions to each downstream class. Theoretically, DVP lowers the empirical risk bound. Experimentally, DVP outperforms baselines on average across 11 downstream datasets. Notably, the DVP-PRM integration enables insights into how individual visual prompts influence classification decisions, providing a probabilistic framework for understanding reprogramming. Our code is available at https://github.com/tmlr-group/DecoupledVP.

Uncertainty quantification is critical in safety-sensitive applications but is often omitted from off-the-shelf neural networks due to adverse effects on predictive performance. Retrofitting uncertainty estimates post-hoc typically requires access to model parameters or gradients, limiting feasibility in practice. We propose a theoretically grounded framework for post-hoc uncertainty estimation in regression tasks by fitting an auxiliary model to both original inputs and frozen model outputs. Drawing from principles of maximum likelihood estimation and sequential parameter fitting, we formalize an exact post-hoc optimization objective that recovers the canonical MLE of Gaussian parameters, without requiring sampling or approximation at inference. While prior work has used model outputs to estimate uncertainty, we explicitly characterize the conditions under which this is valid and demonstrate the extent to which structured outputs can support quasi-epistemic inference. We find that using diverse auxiliary data, such as augmented subsets of the original training data, significantly enhances OOD detection and metric performance. Our hypothesis that frozen model outputs contain generalizable latent information about model error and predictive uncertainty is tested and confirmed. Finally, we ensure that our method maintains proper estimation of input-dependent uncertainty without relying exclusively on base model forecasts. These findings are demonstrated in toy problems and adapted to both UCI and depth regression benchmarks. Code: https://github.com/biggzlar/IO-CUE.

This paper critically re-evaluates LLMs' role in causal discovery and argues against their direct involvement in determining causal relationships. We demonstrate that LLMs' autoregressive, correlation-driven modeling inherently lacks the theoretical grounding for causal reasoning and introduces unreliability when used as priors in causal discovery algorithms. Through empirical studies, we expose the limitations of existing LLM-based methods and reveal that deliberate prompt engineering (e.g., injecting ground-truth knowledge) could overstate their performance, helping to explain the consistently favorable results reported in much of the current literature. Based on these findings, we strictly confined LLMs' role to a non-decisional auxiliary capacity: LLMs should not participate in determining the existence or directionality of causal relationships, but can assist the search process for causal graphs (e.g., LLM-based heuristic search). Experiments across various settings confirm that, by strictly isolating LLMs from causal decision-making, LLM-guided heuristic search can accelerate the convergence and outperform both traditional and LLM-based methods in causal structure learning. We conclude with a call for the community to shift focus from naively applying LLMs to developing specialized models and training method that respect the core principles of causal discovery.

Real-world databases are predominantly relational, comprising multiple interlinked tables that contain complex structural and statistical dependencies. Learning generative models on relational data has shown great promise in generating synthetic data and imputing missing values. However, existing methods often struggle to capture this complexity, typically reducing relational data to conditionally generated flat tables and imposing limiting structural assumptions. To address these limitations, we introduce RelDiff, a novel diffusion generative model that synthesizes complete relational databases by explicitly modeling their foreign key graph structure. RelDiff combines a joint graph-conditioned diffusion process across all tables for attribute synthesis, and a $2K+$SBM graph generator based on the Stochastic Block Model for structure generation. The decomposition of graph structure and relational attributes ensures both high fidelity and referential integrity, both of which are crucial aspects of synthetic relational database generation. Experiments on 11 benchmark datasets demonstrate that RelDiff consistently outperforms prior methods in producing realistic and coherent synthetic relational databases. Code is available at https://github.com/ValterH/RelDiff.

Machine learning models, particularly deep neural networks, are vulnerable to privacy attacks such as membership inference attacks (MIAs), which determine whether a specific data point was included in a model's training set [9, 10, 2]. These attacks exploit the tendency of models to exhibit distinct behaviors (e.g. higher confidence or lower loss) on training data compared to unseen data, potentially compromising the confidentiality of sensitive datasets, such as those containing medical or financial records. State-of-the-art MIAs typically rely on extensive knowledge of the target model. For example, shadow model-based approaches [9] train multiple models to mimic the target's behavior, while others, e.g. the likelihood ratio attack (LiRA) by Carlini et al. [2], leverage model outputs or gradients. These methods often induce significant computational costs or require access to model internals, limiting their applicability in scenarios where only model outputs are available. We propose a new MIA method that leverages Bayesian inference for post-hoc analysis of trained model and datasets. Once a ML model, e.g. a neural network, has been trained on member datasets, we pass the test data through the trained ML model, and extract resulting metrics such as accuracy, entropy, perturbation magnitude, and dataset statistics, and uses these metrics to compute posterior probabilities of membership. This approach doesn't require access to a'training' set, although known knowledge about member and non-member datasets can improve its performance. This post-hoc method is computationally efficient, interpretable, requires minimum model query and fine-tuning, making it well-suited for real-world deployment scenarios where privacy assessments are conducted after model training.

Neural network (NN)-based end-to-end (E2E) communication systems, in which each system component may consist of a portion of a neural network, have been investigated as potential tools for developing artificial intelligence (Al)-native E2E systems. In this paper, we propose an NN-based bitwise receiver that improves computational efficiency while maintaining performance comparable to baseline demappers. Building on this foundation, we introduce a novel symbol-wise autoencoder (AE)-based E2E system that jointly optimizes the transmitter and receiver at the physical layer. We evaluate the proposed NN-based receiver using bit-error rate (BER) analysis to confirm that the numerical BER achieved by NN-based receivers or transceivers is accurate. Results demonstrate that the AE-based system outperforms baseline architectures, particularly for higher-order modulation schemes. We further show that the training signal-to-noise ratio (SNR) significantly affects the performance of the systems when inference is conducted at different SNR levels.

Many large enterprises that operate highly governed and complex ICT environments have no efficient and effective way to support their Data and AI teams in rapidly spinning up and tearing down self-service data and compute infrastructure, to experiment with new data analytic tools, and deploy data products into operational use. This paper proposes a key piece of the solution to the overall problem, in the form of an on-demand self-service data-platform infrastructure to empower de-centralised data teams to build data products on top of centralised templates, policies and governance. The core innovation is an efficient method to leverage immutable container operating systems and infrastructure-as-code methodologies for creating, from scratch, vendor-neutral and short-lived Kubernetes clusters on-premises and in any cloud environment. Our proposed approach can serve as a repeatable, portable and cost-efficient alternative or complement to commercial Platform-as-a-Service (PaaS) offerings, and this is particularly important in supporting interoperability in complex data mesh environments with a mix of modern and legacy compute infrastructure.