We study the robustness of Transformer language models under semantic out-of-distribution (OOD) shifts, where training and test data lie in disjoint latent spaces. Using Wasserstein-1 distance and Gevrey-class smoothness, we derive sub-exponential upper bounds on prediction error. Our theoretical framework explains how smoothness governs generalization under distributional drift. We validate these findings through controlled experiments on arithmetic and Chain-of-Thought tasks with latent permutations and scalings. Results show empirical degradation aligns with our bounds, highlighting the geometric and functional principles underlying OOD generalization in Transformers.

Large vision-language models have become widely adopted to advance in various domains. However, developing a trustworthy system with minimal interpretable characteristics of large-scale models presents a significant challenge. One of the most prevalent terms associated with the fallacy functions caused by these systems is hallucination, where the language model generates a response that does not correspond to the visual content. To mitigate this problem, several approaches have been developed, and one prominent direction is to ameliorate the decoding process. In this paper, we propose a new Bijective Maximum Likelihood Learning (BIMA) approach to hallucination mitigation using normalizing flow theories. The proposed BIMA method can efficiently mitigate the hallucination problem in prevailing vision-language models, resulting in significant improvements. Notably, BIMA achieves the average F1 score of 85.06% on POPE benchmark and remarkably reduce CHAIRS and CHAIRI by 7.6% and 2.6%, respectively. To the best of our knowledge, this is one of the first studies that contemplates the bijection means to reduce hallucination induced by large vision-language models.

Training neural networks on randomly generated artificial datasets yields Bayesian models that capture the prior defined by the dataset-generating distribution. Prior-data Fitted Networks (PFNs) are a class of methods designed to leverage this insight. In an era of rapidly increasing computational resources for pre-training and a near stagnation in the generation of new real-world data in many applications, PFNs are poised to play a more important role across a wide range of applications. They enable the efficient allocation of pre-training compute to low-data scenarios. Originally applied to small Bayesian modeling tasks, the field of PFNs has significantly expanded to address more complex domains and larger datasets. This position paper argues that PFNs and other amortized inference approaches represent the future of Bayesian inference, leveraging amortized learning to tackle data-scarce problems. We thus believe they are a fruitful area of research. In this position paper, we explore their potential and directions to address their current limitations.

Summary: Within the manuscript, the authors extend the continuous time Bayesian Networks by incorporating a mixture prior over the conditional intensity matrices, thereby allowing for a larger class compared to a gamma prior usually employed over these. My main concerns are with clarity / quality as the manuscript is quite densely written with quite some material has either been omitted or shifted to the appendix. For a non-expert in continuous time bayesian networks, it is quite hard to read. Additionally, there are quite a few minor mistakes (see below) that make understanding of the manuscript harder. As it stands, Originality: The authors combine variational inference method from Linzner et al [11], with the new prior over the dependency structure (mixture).

Dropout regularization methods prune a neural network's pre-determined backbone structure to avoid overfitting. However, a deep model still tends to be poorly calibrated with high confidence on incorrect predictions. We propose a unified Bayesian model selection method to jointly infer the most plausible network depth warranted by data, and perform dropout regularization simultaneously. In particular, to infer network depth we define a beta process over the number of hidden layers which allows it to go to infinity. Layer-wise activation probabilities induced by the beta process modulate neuron activation via binary vectors of a conjugate Bernoulli process. Experiments across domains show that by adapting network depth and dropout regularization to data, our method achieves superior performance comparing to state-of-the-art methods with well-calibrated uncertainty estimates. In continual learning, our method enables neural networks to dynamically evolve their depths to accommodate incrementally available data beyond their initial structures, and alleviate catastrophic forgetting.

When data are noisy, a statistical learner's goal is to resolve epistemic uncertainty about the data it will encounter at test-time, i.e., to identify the distribution of test (target) data. Many real-world learning settings introduce sources of epistemic uncertainty that can not be resolved on the basis of training (source) data alone: The source data may arise from multiple tasks (multitask learning), the target data may differ systematically from the source data tasks (distribution shift), and/or the learner may not arrive at an accurate characterization of the source data (imperfect learning). We introduce a principled definition of epistemic error, and provide a generic, decompositional epistemic error bound. Our error bound is the first to (i) consider epistemic error specifically, (ii) accommodate all the sources of epistemic uncertainty above, and (iii) separately attribute the error to each of multiple aspects of the learning procedure and environment. As corollaries of the generic result, we provide (i) epistemic error bounds specialized to the settings of Bayesian transfer learning and distribution shift within $ε$-neighborhoods, and (ii) a set of corresponding generalization bounds. Finally, we provide a novel definition of negative transfer, and validate its insights in a synthetic experimental setting.

In recent years various supervised learning methods that disentangle aleatoric and epistemic uncertainty based on second-order distributions have been proposed. We argue that these methods fail to capture critical components of epistemic uncertainty, particularly due to the often-neglected component of model bias. To show this, we make use of a more fine-grained taxonomy of epistemic uncertainty sources in machine learning models, and analyse how the classical bias-variance decomposition of the expected prediction error can be decomposed into different parts reflecting these uncertainties. By using a simulation-based evaluation protocol which encompasses epistemic uncertainty due to both procedural- and data-driven uncertainty components, we illustrate that current methods rarely capture the full spectrum of epistemic uncertainty. Through theoretical insights and synthetic experiments, we show that high model bias can lead to misleadingly low estimates of epistemic uncertainty, and common second-order uncertainty quantification methods systematically blur bias-induced errors into aleatoric estimates, thereby underrepresenting epistemic uncertainty. Our findings underscore that meaningful aleatoric estimates are feasible only if all relevant sources of epistemic uncertainty are properly represented.

We introduce a novel unsupervised learning method for time series data with latent dynamical structure: the recognition-parametrized Gaussian state space model (RP-GSSM). The RP-GSSM is a probabilistic model that learns Markovian Gaussian latents explaining statistical dependence between observations at different time steps, combining the intuition of contrastive methods with the flexible tools of probabilistic generative models. Unlike contrastive approaches, the RP-GSSM is a valid probabilistic model learned via maximum likelihood. Unlike generative approaches, the RP-GSSM has no need for an explicit network mapping from latents to observations, allowing it to focus model capacity on inference of latents. The model is both tractable and expressive: it admits exact inference thanks to its jointly Gaussian latent prior, while maintaining expressivity with an arbitrarily nonlinear neural network link between observations and latents. These qualities allow the RP-GSSM to learn task-relevant latents without ad-hoc regularization, auxiliary losses, or optimizer scheduling. We show how this approach outperforms alternatives on problems that include learning nonlinear stochastic dynamics from video, with or without background distractors. Our results position the RP-GSSM as a useful foundation model for a variety of downstream applications.

Multilook coherent imaging is a widely used technique in applications such as digital holography, ultrasound imaging, and synthetic aperture radar. A central challenge in these systems is the presence of multiplicative noise, commonly known as speckle, which degrades image quality. Despite the widespread use of coherent imaging systems, their theoretical foundations remain relatively underexplored. In this paper, we study both the theoretical and algorithmic aspects of likelihood-based approaches for multilook coherent imaging, providing a rigorous framework for analysis and method development. Our theoretical contributions include establishing the first theoretical upper bound on the Mean Squared Error (MSE) of the maximum likelihood estimator under the deep image prior hypothesis. Our results capture the dependence of MSE on the number of parameters in the deep image prior, the number of looks, the signal dimension, and the number of measurements per look. On the algorithmic side, we employ projected gradient descent (PGD) as an efficient method for computing the maximum likelihood solution. Furthermore, we introduce two key ideas to enhance the practical performance of PGD. First, we incorporate the Newton-Schulz algorithm to compute matrix inverses within the PGD iterations, significantly reducing computational complexity. Second, we develop a bagging strategy to mitigate projection errors introduced during PGD updates. We demonstrate that combining these techniques with PGD yields state-of-the-art performance. Our code is available at https://github.com/Computational-Imaging-RU/Bagged-DIP-Speckle.

Arena-based evaluation is a fundamental yet significant evaluation paradigm for modern AI models, especially large language models (LLMs). Existing framework based on ELO rating system suffers from the inevitable instability problem due to ranking inconsistency and the lack of attention to the varying abilities of annotators. In this paper, we introduce a novel stable arena framework to address these issues by enhancing the ELO Rating System. Specifically, we replace the iterative update method with a Maximum Likelihood Estimation (MLE) approach, m-ELO, and provide theoretical proof of the consistency and stability of the MLE approach for model ranking. Additionally, we proposed the am-ELO, which modify the Elo Rating's probability function to incorporate annotator abilities, enabling the simultaneous estimation of model scores and annotator reliability. Experiments demonstrate that this method ensures stability, proving that this framework offers a more robust, accurate, and stable evaluation method for LLMs.