Determining the chronology of ancient handwritten manuscripts is essential for reconstructing the evolution of ideas. For the Dead Sea Scrolls, this is particularly important. However, there is an almost complete lack of date-bearing manuscripts evenly distributed across the timeline and written in similar scripts available for palaeographic comparison. Here, we present Enoch, a state-of-the-art AI-based date-prediction model, trained on the basis of new radiocarbon-dated samples of the scrolls. Enoch uses established handwriting-style descriptors and applies Bayesian ridge regression. The challenge of this study is that the number of radiocarbon-dated manuscripts is small, while current machine learning requires an abundance of training data. We show that by using combined angular and allographic writing style feature vectors and applying Bayesian ridge regression, Enoch could predict the radiocarbon-based dates from style, supported by leave-one-out validation, with varied MAEs of 27.9 to 30.7 years relative to the radiocarbon dating. Enoch was then used to estimate the dates of 135 unseen manuscripts, revealing that 79 per cent of the samples were considered 'realistic' upon palaeographic post-hoc evaluation. We present a new chronology of the scrolls. The radiocarbon ranges and Enoch's style-based predictions are often older than the traditionally assumed palaeographic estimates. In the range of 300-50 BCE, Enoch's date prediction provides an improved granularity. The study is in line with current developments in multimodal machine-learning techniques, and the methods can be used for date prediction in other partially-dated manuscript collections. This research shows how Enoch's quantitative, probability-based approach can be a tool for palaeographers and historians, re-dating ancient Jewish key texts and contributing to current debates on Jewish and Christian origins.

Simulation-based methods for statistical inference have evolved dramatically over the past 50 years, keeping pace with technological advancements. The field is undergoing a new revolution as it embraces the representational capacity of neural networks, optimisation libraries and graphics processing units for learning complex mappings between data and inferential targets. The resulting tools are amortised, in the sense that they allow rapid inference through fast feedforward operations. In this article we review recent progress in the context of point estimation, approximate Bayesian inference, summary-statistic construction, and likelihood approximation. We also cover software, and include a simple illustration to showcase the wide array of tools available for amortised inference and the benefits they offer over Markov chain Monte Carlo methods. The article concludes with an overview of relevant topics and an outlook on future research directions.

A reliable knowledge structure is a prerequisite for building effective adaptive learning systems and intelligent tutoring systems. Pursuing an explainable and trustworthy knowledge structure, we propose a method for constructing causal knowledge networks. This approach leverages Bayesian networks as a foundation and incorporates causal relationship analysis to derive a causal network. Additionally, we introduce a dependable knowledge-learning path recommendation technique built upon this framework, improving teaching and learning quality while maintaining transparency in the decision-making process.

Artificial intelligence (AI) is currently based largely on black-box machine learning models which lack interpretability. The field of eXplainable AI (XAI) strives to address this major concern, being critical in high-stakes areas such as the finance, legal and health sectors. We present an approach to defining AI models and their interpretability based on category theory. For this we employ the notion of a compositional model, which sees a model in terms of formal string diagrams which capture its abstract structure together with its concrete implementation. This comprehensive view incorporates deterministic, probabilistic and quantum models. We compare a wide range of AI models as compositional models, including linear and rule-based models, (recurrent) neural networks, transformers, VAEs, and causal and DisCoCirc models. Next we give a definition of interpretation of a model in terms of its compositional structure, demonstrating how to analyse the interpretability of a model, and using this to clarify common themes in XAI. We find that what makes the standard 'intrinsically interpretable' models so transparent is brought out most clearly diagrammatically. This leads us to the more general notion of compositionally-interpretable (CI) models, which additionally include, for instance, causal, conceptual space, and DisCoCirc models. We next demonstrate the explainability benefits of CI models. Firstly, their compositional structure may allow the computation of other quantities of interest, and may facilitate inference from the model to the modelled phenomenon by matching its structure. Secondly, they allow for diagrammatic explanations for their behaviour, based on influence constraints, diagram surgery and rewrite explanations. Finally, we discuss many future directions for the approach, raising the question of how to learn such meaningfully structured models in practice.

Test-time augmentation (TTA) is a well-known technique employed during the testing phase of computer vision tasks. It involves aggregating multiple augmented versions of input data. Combining predictions using a simple average formulation is a common and straightforward approach after performing TTA. This paper introduces a novel framework for optimizing TTA, called BayTTA (Bayesian-based TTA), which is based on Bayesian Model Averaging (BMA). First, we generate a model list associated with different variations of the input data created through TTA. Then, we use BMA to combine model predictions weighted by their respective posterior probabilities. Such an approach allows one to take into account model uncertainty, and thus to enhance the predictive performance of the related machine learning or deep learning model. We evaluate the performance of BayTTA on various public data, including three medical image datasets comprising skin cancer, breast cancer, and chest X-ray images and two well-known gene editing datasets, CRISPOR and GUIDE-seq. Our experimental results indicate that BayTTA can be effectively integrated into state-of-the-art deep learning models used in medical image analysis as well as into some popular pre-trained CNN models such as VGG-16, MobileNetV2, DenseNet201, ResNet152V2, and InceptionRes-NetV2, leading to the enhancement in their accuracy and robustness performance.

Specifying a prior distribution is an essential part of solving Bayesian inverse problems. The prior encodes a belief on the nature of the solution and this regularizes the problem. In this article we completely characterize a Gaussian prior that encodes the belief that the solution is a structured tensor. We first define the notion of (A,b)-constrained tensors and show that they describe a large variety of different structures such as Hankel, circulant, triangular, symmetric, and so on. Then we completely characterize the Gaussian probability distribution of such tensors by specifying its mean vector and covariance matrix. Furthermore, explicit expressions are proved for the covariance matrix of tensors whose entries are invariant under a permutation. These results unlock a whole new class of priors for Bayesian inverse problems. We illustrate how new kernel functions can be designed and efficiently computed and apply our results on two particular Bayesian inverse problems: completing a Hankel matrix from a few noisy measurements and learning an image classifier of handwritten digits. The effectiveness of the proposed priors is demonstrated for both problems. All applications have been implemented as reactive Pluto notebooks in Julia.

In this paper, we study efficient approximate sampling for probability distributions known up to normalization constants. We specifically focus on a problem class arising in Bayesian inference for large-scale inverse problems in science and engineering applications. The computational challenges we address with the proposed methodology are: (i) the need for repeated evaluations of expensive forward models; (ii) the potential existence of multiple modes; and (iii) the fact that gradient of, or adjoint solver for, the forward model might not be feasible. While existing Bayesian inference methods meet some of these challenges individually, we propose a framework that tackles all three systematically. Our approach builds upon the Fisher-Rao gradient flow in probability space, yielding a dynamical system for probability densities that converges towards the target distribution at a uniform exponential rate. This rapid convergence is advantageous for the computational burden outlined in (i). We apply Gaussian mixture approximations with operator splitting techniques to simulate the flow numerically; the resulting approximation can capture multiple modes thus addressing (ii). Furthermore, we employ the Kalman methodology to facilitate a derivative-free update of these Gaussian components and their respective weights, addressing the issue in (iii). The proposed methodology results in an efficient derivative-free sampler flexible enough to handle multi-modal distributions: Gaussian Mixture Kalman Inversion (GMKI). The effectiveness of GMKI is demonstrated both theoretically and numerically in several experiments with multimodal target distributions, including proof-of-concept and two-dimensional examples, as well as a large-scale application: recovering the Navier-Stokes initial condition from solution data at positive times.

This paper addresses the challenge of representing complex human action (HA) in a nuclear power plant (NPP) digital twin (DT) and minimizing latency in partial computation offloading (PCO) in sixth-generation-enabled computing in the network (COIN) assisted multiaccess edge computing (MEC). Accurate HA representation in the DT-HA model is vital for modeling human interventions that are crucial for the safe and efficient operation of NPPs. In this context, DT-enabled COIN-assisted MEC harnesses DT (known as a cybertwin) capabilities to optimize resource allocation and reduce latency effectively. A two-stage approach is employed to address system complexity. First, a probabilistic graphical model (PGM) is introduced to capture HAs in the DT abstraction. In the PGM, HA and NPP asset-twin abstractions form coupled systems that evolve and interact through observable data and control input. Next, the underlying PCO problem is formulated as a multiuser game, where NPP assets can partially offload tasks to COIN and MEC. We propose a decentralized algorithm to optimize offloading decisions, offloading ratios, and resource allocation. The simulation results demonstrate the effectiveness of the proposed method in capturing complex HAs and optimal resource allocation in DT-enabled NPPs.

Mixture of experts is a prediction aggregation method in machine learning that aggregates the predictions of specialized experts. This method often outperforms Bayesian methods despite the Bayesian having stronger inductive guarantees. We argue that this is due to the greater functional capacity of mixture of experts. We prove that in a limiting case of mixture of experts will have greater capacity than equivalent Bayesian methods, which we vouchsafe through experiments on non-limiting cases. Finally, we conclude that mixture of experts is a type of abductive reasoning in the Peircian sense of hypothesis construction.

Reliable uncertainty estimation plays a crucial role in various safety-critical applications such as medical diagnosis and autonomous driving. In recent years, Bayesian neural networks (BayesNNs) have gained substantial research and industrial interests due to their capability to make accurate predictions with reliable uncertainty estimation. However, the algorithmic complexity and the resulting hardware performance of BayesNNs hinder their adoption in real-life applications. To bridge this gap, this paper proposes an algorithm and hardware co-design framework that can generate field-programmable gate array (FPGA)-based accelerators for efficient BayesNNs. At the algorithm level, we propose novel multi-exit dropout-based BayesNNs with reduced computational and memory overheads while achieving high accuracy and quality of uncertainty estimation. At the hardware level, this paper introduces a transformation framework that can generate FPGA-based accelerators for the proposed efficient multi-exit BayesNNs. Several optimization techniques such as the mix of spatial and temporal mappings are introduced to reduce resource consumption and improve the overall hardware performance. Comprehensive experiments demonstrate that our approach can achieve higher energy efficiency compared to CPU, GPU, and other state-of-the-art hardware implementations. To support the future development of this research, we have open-sourced our code at: https://github.com/os-hxfan/MCME_FPGA_Acc.git