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This paper develops a Bayesian mechanics for adaptive systems. Firstly, we model the interface between a system and its environment with a Markov blanket. This affords conditions under which states internal to the blanket encode information about external states. Second, we introduce dynamics and represent adaptive systems as Markov blankets at steady state. This allows us to identify a wide class of systems whose internal states appear to infer external states, consistent with variational inference in Bayesian statistics and theoretical neuroscience. Finally, we partition the blanket into sensory and active states. It follows that active states can be seen as performing active inference and well-known forms of stochastic control (such as PID control), which are prominent formulations of adaptive behaviour in theoretical biology and engineering.

In this paper, we consider how certain longstanding philosophical questions about mental representation may be answered on the assumption that cognitive and perceptual systems implement hierarchical generative models, such as those discussed within the prediction error minimization (PEM) framework. We build on existing treatments of representation via structural resemblance, such as those in Gładziejewski (Synthese 193(2):559–582, 2016) and Gładziejewski and Miłkowski (Biol Philos, 2017), to argue for a representationalist interpretation of the PEM framework. We further motivate the proposed approach to content by arguing that it is consistent with approaches implicit in theories of unsupervised learning in neural networks. In the course of this discussion, we argue that the structural representation proposal, properly understood, has more in common with functional-role than with causal/informational or teleosemantic theories. In the remainder of the paper, we describe the PEM framework for approximate Bayesian inference in some detail, and discuss how structural representations might arise within the proposed Bayesian hierarchies. After explicating the notion of variational inference, we define a subjectively accessible measure of misrepresentation for hierarchical Bayesian networks by appeal to the Kullbach–Leibler divergence between posterior generative and approximate recognition densities, and discuss a related measure of objective misrepresentation in terms of correspondence with the facts.

Theory of mind (ToM) is considered crucial for understanding social-cognitive abilities and impairments. However, verbal theories of the mechanisms underlying ToM are often criticized as under-specified and mutually incompatible. This leads to measures of ToM being unreliable, to the extent that even canonical experimental tasks do not require representation of others’ mental states. There have been attempts at making computational models of ToM, but these are not easily available for broad research application. In order to help meet these challenges, we here introduce the Python package tomsup: Theory of mind simulations using Python. The package provides a computational eco-system for investigating and comparing computational models of hypothesized ToM mechanisms and for using them as experimental stimuli. The package notably includes an easy-to-use implementation of the variational recursive Bayesian k -ToM model developed by (Devaine, Hollard, & Daunizeau, 2014b ) and of simpler non-recursive decision models, for comparison. We provide a series of tutorials on how to: (i) simulate agents relying on the k -ToM model and on a range of simpler types of mechanisms; (ii) employ those agents to generate online experimental stimuli; (iii) analyze the data generated in such experimental setup, and (iv) specify new custom ToM and heuristic cognitive models.

Active inference is a normative framework for explaining behaviour under the free energy principle—a theory of self-organisation originating in neuroscience. It specifies neuronal dynamics for state-estimation in terms of a descent on (variational) free energy—a measure of the fit between an internal (generative) model and sensory observations. The free energy gradient is a prediction error—plausibly encoded in the average membrane potentials of neuronal populations. Conversely, the expected probability of a state can be expressed in terms of neuronal firing rates. We show that this is consistent with current models of neuronal dynamics and establish face validity by synthesising plausible electrophysiological responses. We then show that these neuronal dynamics approximate natural gradient descent, a well-known optimisation algorithm from information geometry that follows the steepest descent of the objective in information space. We compare the information length of belief updating in both schemes, a measure of the distance travelled in information space that has a direct interpretation in terms of metabolic cost. We show that neural dynamics under active inference are metabolically efficient and suggest that neural representations in biological agents may evolve by approximating steepest descent in information space towards the point of optimal inference.

Sparse reconstruction-based imaging techniques can be utilized to solve forward-looking imaging problems with limited azimuth resolution. However, these methods perform well only under the traditional model for the platform with low speed, and the performance deteriorates for the maneuvering trajectory. In this paper, a structured Bayesian super-resolution forward-looking imaging algorithm for maneuvering platforms under an enhanced sparsity model is proposed. An enhanced sparsity model for maneuvering platforms is established to address the reconstruction problem, and a hierarchical Student-t (ST) prior is designed to model the distribution characteristics of the sparse imaging scene. To further leverage prior information about structural characteristics of the scatterings, coupled patterns among neighboring pixels are incorporated to construct a structured sparse prior. Finally, forward-looking imaging parameters are estimated using the expectation/maximization-based variational Bayesian inference. Numerical simulations validate the effectiveness of the proposed algorithm and the superiority over conventional methods based on pixel sparse assumptions in forward-looking scenes for maneuvering platforms.

To tackle the challenge of enhancing moving target detection performance in environments characterized by small sample sizes and non-uniformity, methods rooted in sparse signal reconstruction have been incorporated into Space-Time Adaptive Processing (STAP) algorithms. Given the prominent sparse nature of clutter spectra in the angle-Doppler domain, adopting sparse recovery algorithms has proven to be a feasible approach for accurately estimating high-resolution spatio-temporal two-dimensional clutter spectra. Sparse Bayesian Learning (SBL) is a pivotal tool in sparse signal reconstruction and has been previously utilized, yet it has demonstrated limited success in enhancing sparsity, resulting in insufficient robustness in local fitting. To significantly improve sparsity, this paper introduces a hierarchical Bayesian prior framework and derives iterative parameter update formulas through variational inference techniques. However, this algorithm encounters significant computational hurdles during the parameter update process. To overcome this obstacle, the paper proposes an enhanced Variational Bayesian Inference (VBI) method that leverages prior information on the rank of the temporal clutter covariance matrix to refine the parameter update formulas, thereby significantly reducing computational complexity. Furthermore, this method fully exploits the joint sparsity of the Multiple Measurement Vector (MMV) model to achieve greater sparsity without compromising accuracy, and employs a first-order Taylor expansion to eliminate grid mismatch in the dictionary. The research presented in this paper enhances the moving target detection capabilities of STAP algorithms in complex environments and provides new perspectives and methodologies for the application of sparse signal reconstruction in related fields.

The current self-calibration approaches based on sparse Bayesian learning (SBL) demonstrate robust performance under uniform white noise conditions. However, their efficacy degrades significantly in non-uniform noise environments due to acute sensitivity to noise power estimation inaccuracies. To address this limitation, this paper proposes an orientation estimation method based on variational Bayesian inference to combat non-uniform noise and gain/phase error. The gain and phase errors of the array are modeled separately for calibration purposes, with the objective of improving the accuracy of the fit during the iterative process. Subsequently, the noise of each element of the array is characterized via independent Gaussian distributions, and the correlation between the array gain deviation and the noise power is incorporated to enhance the robustness of this method when operating in non-uniform noise environments. Furthermore, the Cramér–Rao Lower Bound (CRLB) under non-uniform noise and gain-phase deviation is presented. Numerical simulations and experimental results are provided to validate the superiority of this proposed method.

Understanding the way in which the degradation of a system's component is coupled to the system's dynamics is highly relevant for the monitoring and control of modern engineering systems. This paper focuses on the identification of coupling functions that describe the relationship between the system's dynamics and the degradation rate in solid-oxide fuel cell (SOFC) stacks. Based on the degradation dynamics estimated from data acquired online, we can design timely mitigation actions as well as optimal maintenance interventions. We introduce a computationally tractable identification approach that takes into account prior knowledge of the form of the coupling function that is found experimentally for a certain degradation mechanism. The nonlinear coupling function is estimated using variational Bayesian inference. The approach is tested on a 1600 h recording from a SOFC system. It is shown that the use of the prior form of the coupling function results in a superior prediction of the degradation, when compared with that obtained using purely data-driven black-box models. The reliable convergence of the variational Bayesian method and the simplicity of its implementation make it a promising tool for the in-field performance monitoring of SOFC systems. This article is part of the theme issue ‘Coupling functions: dynamical interaction mechanisms in the physical, biological and social sciences’.

In high-speed cigarette manufacturing industries, occasional minor cosmetic cigarette defects and a scarcity of samples significantly hinder the rapid and accurate detection of defects. To tackle this challenge, we propose an enhanced single-shot multibox detector (SSD) model that uses variational Bayesian inference for improved detection of tiny defects given sporadic occurrences and limited samples. The enhanced SSD model incorporates a bounded intersection over union (BIoU) loss function to reduce sensitivity to minor deviations and uses exponential linear unit (ELU) and leaky rectified linear unit (ReLU) activation functions to mitigate vanishing gradients and neuron death in deep neural networks. Empirical results show that the enhanced SSD300 and SSD512 models increase the model's detection accuracy mean average precision (mAP) by up to 1.2% for small defects. Ablation studies further reveal that the model's mAP increases by 1.5%, which reduces the computational requirements by 5.92 GFLOPs. The model also shows improved inference in scenarios with limited samples, thus highlighting its effectiveness and applicability in high-speed, precision-oriented cigarette manufacturing industries.

In practical array signal processing applications, direction-of-arrival (DOA) estimation often suffers from degraded accuracy under low signal-to-noise ratio (SNR) and limited snapshot conditions. To address these challenges, we propose an off-grid DOA estimation method based on Fast Variational Bayesian Inference (OGFVBI). Within the variational Bayesian framework, we design a fixed-point criterion rooted in root-finding theory to accelerate the convergence of hyperparameter learning. We further introduce a grid fission and adaptive refinement strategy to dynamically adjust the sparse representation, effectively alleviating grid mismatch issues in traditional off-grid approaches. To address frequency dispersion in wideband signals, we develop an improved subspace focusing technique that transforms multi-frequency data into an equivalent narrowband model, enhancing compatibility with subspace DOA estimators. We demonstrate through simulations that OGFVBI achieves high estimation accuracy and resolution while significantly reducing computational time. Specifically, our method achieves more than 37.6% reduction in RMSE and at least 28.5% runtime improvement compared to other methods under low SNR and limited snapshot scenarios, indicating strong potential for real-time and resource-constrained applications.