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.

We propose a combinatorial and graph-theoretic theory of dropout by modeling training as a random walk over a high-dimensional graph of binary subnetworks. Each node represents a masked version of the network, and dropout induces stochastic traversal across this space. We define a subnetwork contribution score that quantifies generalization and show that it varies smoothly over the graph. Using tools from spectral graph theory, PAC-Bayes analysis, and combinatorics, we prove that generalizing subnetworks form large, connected, low-resistance clusters, and that their number grows exponentially with network width. This reveals dropout as a mechanism for sampling from a robust, structured ensemble of well-generalizing subnetworks with built-in redundancy. Extensive experiments validate every theoretical claim across diverse architectures. Together, our results offer a unified foundation for understanding dropout and suggest new directions for mask-guided regularization and subnetwork optimization.

Attractor dynamics are a hallmark of many complex systems, including the brain. Understanding how such self-organizing dynamics emerge from first principles is crucial for advancing our understanding of neuronal computations and the design of artificial intelligence systems. Here we formalize how attractor networks emerge from the free energy principle applied to a universal partitioning of random dynamical systems. Our approach obviates the need for explicitly imposed learning and inference rules and identifies emergent, but efficient and biologically plausible inference and learning dynamics for such self-organizing systems. These result in a collective, multi-level Bayesian active inference process. Attractors on the free energy landscape encode prior beliefs; inference integrates sensory data into posterior beliefs; and learning fine-tunes couplings to minimize long-term surprise. Analytically and via simulations, we establish that the proposed networks favor approximately orthogonalized attractor representations, a consequence of simultaneously optimizing predictive accuracy and model complexity. These attractors efficiently span the input subspace, enhancing generalization and the mutual information between hidden causes and observable effects. Furthermore, while random data presentation leads to symmetric and sparse couplings, sequential data fosters asymmetric couplings and non-equilibrium steady-state dynamics, offering a natural extension to conventional Boltzmann Machines. Our findings offer a unifying theory of self-organizing attractor networks, providing novel insights for AI and neuroscience.