probabilistic neural modelling

This work addresses the problem of verifying the safety of neural networks under randomly perturbed inputs by proposing an efficient probabilistic verification framework. The approach integrates regression tree-guided state space partitioning, boundary-aware sampling, and probabilistic convex hull construction, complemented by an iterative refinement mechanism with probabilistic prioritization to compute a guaranteed probability interval that the network’s output satisfies given safety constraints. Experimental evaluations on standard benchmarks—including the ACAS Xu airborne collision avoidance system and rocket landing controllers—demonstrate that the proposed method significantly outperforms existing techniques in both verification accuracy and computational efficiency.

This work addresses the challenge that existing machine learning models struggle to effectively quantify uncertainty and incorporate physical constraints in chemical process modeling. We propose a novel probabilistic neural network framework that, for the first time, rigorously embeds linear equality constraints—such as mass conservation—directly into probabilistic modeling, guaranteeing predictions satisfy physical laws within a prescribed tolerance. The method simultaneously achieves well-calibrated uncertainty estimates and efficient training: in small-data regimes, it significantly improves prediction accuracy, constraint satisfaction, and uncertainty reliability; under large-scale data settings, it maintains performance advantages while substantially accelerating convergence.

This work addresses the challenge of analyzing the propagation of input probability density distributions through neural networks when inputs are uncountable or countably infinite, a setting where exhaustive testing is infeasible. It introduces, for the first time, a systematic application of probabilistic abstract interpretation to neural network analysis. The authors propose a grid-based abstract domain and corresponding abstract transformers, combined with the Moore–Penrose pseudoinverse to construct a computable model of density flow. This approach effectively captures the evolution of input distributions throughout the network. Empirical evaluations on multiple real-world case studies demonstrate the framework’s ability to accurately model input density transformations, highlighting its practical applicability and effectiveness in realistic scenarios.

This study addresses the high computational complexity of probabilistic inference and challenges in uncertainty modeling by proposing probabilistic circuits as a novel reasoning framework. By introducing structural constraints, the approach enables exact inference in polynomial time and innovatively integrates deep learning with symbolic paradigms to construct hybrid models supporting Bayesian learning. This research establishes a foundational theoretical system for probabilistic circuits, achieving efficient, exact computation and scalable deployment across diverse inference tasks. Ultimately, this work effectively bridges the gap between neural and symbolic AI, systematically advancing the development of probabilistic circuits at both theoretical and applied levels.

This work addresses the issue of overconfidence in statistical inference arising from machine learning approximations in scientific simulations, which can compromise result reliability. To mitigate this, the authors propose two complementary approaches: first, a “balanced” regularization strategy that explicitly suppresses model overconfidence; and second, a simulation-aware Bayesian neural network prior that naturally alleviates overconfidence without additional regularization, even in small-sample regimes. By integrating neural ratio estimation with uncertainty quantification techniques, the proposed methods significantly improve inference calibration, yielding posterior estimates that are either closer to the ground truth or conservatively biased. This enhanced calibration strengthens the credibility of simulation-based inference in scientific applications.

This work addresses the challenge of performing efficient probabilistic inference in quantized (low-precision) discrete parameter spaces to learn continuous distributions—a setting where conventional Bayesian inference struggles due to incompatibility with discrete hardware. We propose the first approximate Bayesian inference framework tailored for quantized parameter spaces: model parameters are encoded as bitstrings; structured priors are modeled via coupled probabilistic circuits; and a variational inference algorithm is explicitly designed for the discrete domain. Our approach unifies low-precision computation with principled probabilistic modeling, substantially improving inference efficiency and scalability while preserving model interpretability. Extensive evaluation on multiple quantized neural networks demonstrates that our method achieves significant speedups over baseline approaches—without sacrificing predictive accuracy—thereby establishing a novel paradigm for interpretable Bayesian learning on edge devices.

This work proposes a novel distribution-to-distribution (D2D) prediction paradigm for probabilistic forecasting in dynamical systems, circumventing the limitations of conventional trajectory-based ensemble simulations that struggle to directly model the evolution of predictive distributions. The approach introduces an end-to-end neural architecture that represents input distributions via kernel mean embeddings, parameterizes output distributions using mixture density networks, and recursively propagates uncertainty through interchangeable neural modules—enabling direct learning of distributional dynamics without explicit ensemble simulation. Experiments on the Lorenz63 system demonstrate that the method accurately captures the evolution of probability distributions under nonlinear dynamics, yielding high-skill probabilistic forecasts that match or even surpass the performance of a reduced perfect-model benchmark.

This work addresses the interpretability of predictive models—such as binary neural networks and Boolean networks—under multivariate Bernoulli inputs. Method: We propose an L² oblique projection analysis framework grounded in Hoeffding decomposition. Theoretically, we establish, for the first time, the explicit structure of Hoeffding decomposition under Bernoulli distributions: all higher-order interaction terms are orthogonal to the one-dimensional main subspace, enabling exact reverse engineering and closed-form solutions. This structure permits explicit derivation of global sensitivity metrics, including Sobol’ indices and Shapley effects. Computationally, the framework integrates Hoeffding decomposition, L² oblique projection, and variance attribution theory. Results: Numerical experiments demonstrate its effectiveness and scalability in high-dimensional, sparse binary input settings. To our knowledge, this is the first unified framework for model interpretation under discrete, finite-support inputs that simultaneously ensures theoretical rigor and computational feasibility.

Bayesian neural networks (BNNs) suffer from high inference overhead on resource-constrained devices due to repeated weight sampling, hindering practical deployment. Method: This paper proposes a single-forward uncertainty estimation method based on Gaussian propagation, replacing the conventional stochastic variational inference (SVI) paradigm requiring multiple weight samples. We design a Gaussian propagation operator library supporting both MLPs and CNNs, and integrate it with the TVM compiler and automated tuning strategies for end-to-end efficient deployment. Contribution/Results: Evaluated on Dirty-MNIST, our approach matches standard BNNs in classification accuracy and out-of-distribution (OOD) detection performance, while accelerating batched inference by up to 4200× and substantially reducing computational cost. This enables feasible deployment of BNNs in safety-critical embedded systems.

This study addresses the challenge classical frequentist statisticians face in understanding neural networks by proposing a reconstruction of neural networks through the lens of linear regression. By simplifying network architecture and integrating statistical interpretability techniques, the approach reformulates deep learning models into a modeling paradigm familiar to statisticians. The method preserves the expressive power of neural networks while offering intuitive parameter interpretations and customizable pathways, thereby significantly lowering the cognitive barrier for statisticians entering the field of deep learning. The resulting framework balances theoretical rigor with practical usability, fostering meaningful integration and methodological exchange between traditional statistics and modern deep learning.