Our achieved test accuracy is comparable to the SOT A VFL methodology.

Bayesian neural networks (BNNs) offer the potential for reliable uncertainty quantification and interpretability, which are critical for trustworthy AI in high-stakes domains. In this work, we advance message passing (MP) for BNNs and present a novel framework that models the predictive posterior as a factor graph. To the best of our knowledge, our framework is the first MP method that handles convolutional neural networks and avoids double-counting training data, a limitation of previous MP methods that causes overconfidence. We evaluate our approach on CIFAR-10 with a convolutional neural network of roughly 890k parameters and find that it can compete with the SOTA baselines AdamW and IVON, even having an edge in terms of calibration. On synthetic data, we validate the uncertainty estimates and observe a strong correlation (0.9) between posterior credible intervals and its probability of covering the true data-generating function outside the training range. While our method scales to an MLP with 5.6 million parameters, further improvements are necessary to match the scale and performance of state-of-the-art variational inference methods. Deep learning models have achieved impressive results across various domains, including natural language processing (Vaswani et al., 2023), computer vision (Ravi et al., 2024), and autonomous systems (Bojarski et al., 2016). Yet, they often produce overconfident but incorrect predictions, particularly in ambiguous or out-of-distribution scenarios. Without the ability to effectively quantify uncertainty, this can foster both overreliance and underreliance on models, as users stop trusting their outputs entirely (Zhang et al., 2024), and in high-stakes domains like healthcare or autonomous driving, its application can be dangerous (Henne et al., 2020). To ensure safer deployment in these settings, models must not only predict outcomes but also express how uncertain they are about those predictions to allow for informed decision-making. Bayesian neural networks (BNNs) offer a principled way to quantify uncertainty by capturing a posterior distribution over the model's weights, rather than relying on point estimates as in traditional neural networks. This allows BNNs to express epistemic uncertainty, the model's lack of knowledge about the underlying data distribution.

This paper introduces a novel approach to embed flow-based models with hierarchical structures. The proposed framework is named Variational Flow Graphical (VFG) Model. VFGs learn the representation of high dimensional data via a message-passing scheme by integrating flow-based functions through variational inference. By leveraging the expressive power of neural networks, VFGs produce a representation of the data using a lower dimension, thus overcoming the drawbacks of many flow-based models, usually requiring a high dimensional latent space involving many trivial variables. Aggregation nodes are introduced in the VFG models to integrate forward-backward hierarchical information via a message passing scheme. Maximizing the evidence lower bound (ELBO) of data likelihood aligns the forward and backward messages in each aggregation node achieving a consistency node state. Algorithms have been developed to learn model parameters through gradient updating regarding the ELBO objective. The consistency of aggregation nodes enable VFGs to be applicable in tractable inference on graphical structures. Besides representation learning and numerical inference, VFGs provide a new approach for distribution modeling on datasets with graphical latent structures. Additionally, theoretical study shows that VFGs are universal approximators by leveraging the implicitly invertible flow-based structures. With flexible graphical structures and superior excessive power, VFGs could potentially be used to improve probabilistic inference. In the experiments, VFGs achieves improved evidence lower bound (ELBO) and likelihood values on multiple datasets.

Continual learning is the ability to acquire new knowledge without forgetting the previously learned one, assuming no further access to past training data. Neural network approximators trained with gradient descent are known to fail in this setting as they must learn from a stream of data-points sampled from a stationary distribution to converge. In this work, we replace the standard neuron by a meta-learned neuron model whom inference and update rules are optimized to minimize catastrophic interference. Our approach can memorize dataset-length sequences of training samples, and its learning capabilities generalize to any domain. Unlike previous continual learning methods, our method does not make any assumption about how tasks are constructed, delivered and how they relate to each other: it simply absorbs and retains training samples one by one, whether the stream of input data is time-correlated or not.

Probability models have been proposed in the literature to account for "intelligent" behavior in many contexts. In this paper, probability propagation is applied to model agent's motion in potentially complex scenarios that include goals and obstacles. The backward flow provides precious background information to the agent's behavior, viz., inferences coming from the future determine the agent's actions. Probability tensors are layered in time in both directions in a manner similar to convolutional neural networks. The discussion is carried out with reference to a set of simulated grids where, despite the apparent task complexity, a solution, if feasible, is always found. The original model proposed by Attias has been extended to include non-absorbing obstacles, multiple goals and multiple agents. The emerging behaviors are very realistic and demonstrate great potentials of the application of this framework to real environments.

Optimal control of stochastic nonlinear dynamical systems is a major challenge in the domain of robot learning. Given the intractability of the global control problem, state-of-the-art algorithms focus on approximate sequential optimization techniques, that heavily rely on heuristics for regularization in order to achieve stable convergence. By building upon the duality between inference and control, we develop the view of Optimal Control as Input Estimation, devising a probabilistic stochastic optimal control formulation that iteratively infers the optimal input distributions by minimizing an upper bound of the control cost. Inference is performed through Expectation Maximization and message passing on a probabilistic graphical model of the dynamical system, and time-varying linear Gaussian feedback controllers are extracted from the joint state-action distribution. This perspective incorporates uncertainty quantification, effective initialization through priors, and the principled regularization inherent to the Bayesian treatment. Moreover, it can be shown that for deterministic linearized systems, our framework derives the maximum entropy linear quadratic optimal control law. We provide a complete and detailed derivation of our probabilistic approach and highlight its advantages in comparison to other deterministic and probabilistic solvers.

Bayesian networks in their Factor Graph Reduced Normal Form (FGrn) are a powerful paradigm for implementing inference graphs. Unfortunately, the computational and memory costs of these networks may be considerable, even for relatively small networks, and this is one of the main reasons why these structures have often been underused in practice. In this work, through a detailed algorithmic and structural analysis, various solutions for cost reduction are proposed. An online version of the classic batch learning algorithm is also analyzed, showing very similar results (in an unsupervised context); which is essential even if multilevel structures are to be built. The solutions proposed, together with the possible online learning algorithm, are included in a C++ library that is quite efficient, especially if compared to the direct use of the well-known sum-product and Maximum Likelihood (ML) algorithms. The results are discussed with particular reference to a Latent Variable Model (LVM) structure.