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.

This study investigates the application of Genetic Fuzzy Systems (GFS) to model the self-noise generated by airfoils, a key issue in aeroacoustics with significant implications for aerospace, automotive, and drone applications. Using the publicly available "Airfoil Self Noise" dataset, various fuzzy regression strategies are explored and compared. The paper evaluates a brute-force Takagi-Sugeno-Kang (TSK) fuzzy system with high rule density, a cascading Genetic Fuzzy Tree (GFT) architecture, and a novel clustered approach based on Fuzzy C-Means (FCM) to reduce the model's complexity. This highlights the viability of clustering-assisted fuzzy inference as an effective regression tool for complex aero-acoustic phenomena.

Determining conditional independence (CI) relationships between random variables is a fundamental yet challenging task in machine learning and statistics, especially in high-dimensional settings. Existing generative model-based CI testing methods, such as those utilizing generative adversarial networks (GANs), often struggle with undesirable modeling of conditional distributions and training instability, resulting in subpar performance. To address these issues, we propose a novel CI testing method via score-based generative modeling, which achieves precise Type I error control and strong testing power. Concretely, we first employ a sliced conditional score matching scheme to accurately estimate conditional score and use Langevin dynamics conditional sampling to generate null hypothesis samples, ensuring precise Type I error control. Then, we incorporate a goodness-of-fit stage into the method to verify generated samples and enhance interpretability in practice. We theoretically establish the error bound of conditional distributions modeled by score-based generative models and prove the validity of our CI tests. Extensive experiments on both synthetic and real-world datasets show that our method significantly outperforms existing state-of-the-art methods, providing a promising way to revitalize generative model-based CI testing.

Multi-Modal Learning (MML) integrates information from diverse modalities to improve predictive accuracy. However, existing methods mainly aggregate gradients with fixed weights and treat all dimensions equally, overlooking the intrinsic gradient uncertainty of each modality. This may lead to (i) excessive updates in sensitive dimensions, degrading performance, and (ii) insufficient updates in less sensitive dimensions, hindering learning. To address this issue, we propose BOGC-MML, a Bayesian-Oriented Gradient Calibration method for MML to explicitly model the gradient uncertainty and guide the model optimization towards the optimal direction. Specifically, we first model each modality's gradient as a random variable and derive its probability distribution, capturing the full uncertainty in the gradient space. Then, we propose an effective method that converts the precision (inverse variance) of each gradient distribution into a scalar evidence. This evidence quantifies the confidence of each modality in every gradient dimension. Using these evidences, we explicitly quantify per-dimension uncertainties and fuse them via a reduced Dempster-Shafer rule. The resulting uncertainty-weighted aggregation produces a calibrated update direction that balances sensitivity and conservatism across dimensions. Extensive experiments on multiple benchmark datasets demonstrate the effectiveness and advantages of the proposed method.

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.

Unexpected stimuli induce "error" or "surprise" signals in the brain. The theory of predictive coding promises to explain these observations in terms of Bayesian inference by suggesting that the cortex implements variational inference in a probabilistic graphical model. However, when applied to machine learning tasks, this family of algorithms has yet to perform on par with other variational approaches in high-dimensional, structured inference problems. To address this, we introduce a novel predictive coding algorithm for structured generative models, that we call divide-and-conquer predictive coding (DCPC); it differs from other formulations of predictive coding, as it respects the correlation structure of the generative model and provably performs maximum-likelihood updates of model parameters, all without sacrificing biological plausibility. Empirically, DCPC achieves better numerical performance than competing algorithms and provides accurate inference in a number of problems not previously addressed with predictive coding.