Ivan Yu. Tyukin

In this article we introduce the process by which we developed, trained and tested an AI classifier with the aim that it can identify forms of terra sigillata vessels from photographs of sherds of this material. We highlight the problems we faced with this identification process before focusing on how these have been addressed. AI systems are not perfect and can sometimes make mistakes. This can pose even greater problems when such systems are used blindly in fields like archaeology where the level of uncertainty is particularly high. Despite augmenting our training dataset with simulated images to counteract our low numbers of images of real sherds, the classifier still did not exhibit a very high performance. Many of its mistakes were no doubt due to it being forced to generate an output despite being uncertain of its decision. In this article we introduce a new approach to handling such uncertainty that uses weakly supervised error correctors that help catch errors without requiring potentially large amounts of additional training data, are easy to construct, and are computationally fast at runtime. In contrast to direct approaches to correcting AI errors whereby an AI correcting algorithm seeks to replace the original AI decision with an alternative, our correctors aim to detect instances of potentially risky decisions, where the probability of making an erroneous decision is high. In such instances our correctors instruct the AI system to avoid making such high-risk decisions altogether. We show how the proposed AI correctors can be deployed to improve the performance of the baseline AI without expensive model retraining. The development of a system for the complexity of archaeological data is an excellent illustration of the general efficiency and practical utility of such an approach.

This article discusses the process for creating a dataset to train and test the core and the corrector AI classifiers of the Arch-I-Scan Project. This dataset includes the photographs of real sherds that were compiled by the project from the collections of our project partners as well as synthetic sherds that were generated to supplement the low numbers of real sherd training data and to account for the imbalances among the numbers of real sherds per class (i.e., per vessel form). This article presents the simulation process used to create the synthetic sherds, as well as the process we used to decrease the differences between images of real and simulated sherds so that they were useable together for training the machine. Finally, the compilation and size of the resulting overall dataset are outlined.

Data-driven artificial intelligence (AI) systems, particularly neural networks, have demonstrated significant success across various applications. The increasing availability of digital imaging, sensor technology, and computational modelling has positioned data-driven AI as a transformative methodological tool for archaeology. Automated systems based on deep learning can support the recognition and classification of artefacts from photographic or 3D data at an unprecedented scale. However, commonly-used networks may fail to deliver high-quality decisions for datasets such as the Arch-I-Scan Project’s chosen dataset, comprising 2D photographs of fragmentary ceramic remains. This is due to such datasets’ low-sample properties and the various limitations of each artefact (e.g. archaeological artefacts are usually incomplete, the extant fragments have hugely varying geometries, and, at least for ceramic vessels, appropriate type labelling is often scarce) resulting in high uncertainty of identification of the specific type of the original artefact. The deployment of data-driven AI in archaeology and dealing with such complex, high-dimensional data is, therefore, accompanied by theoretical, computational, and epistemological challenges. This article outlines recent work on synthetic data generation, error correction, and the mathematics of AI stability and dimensionality, and outlines the main advantages and limitations of using AI for the classification of archaeological artefacts through photographic images of them. Our experience in carrying out this project highlights the importance of advancing mathematical theory and methods to improve AI models' stability, accuracy, and verifiability in high-dimensional data tasks.

This article presents a pilot study of machine learning-based analysis of ceramics dating to the 5th and 4th centuries BCE from the site of the city of Olynthos in northern Greece. This work is inspired by the work of the Arch-I-Scan team (Núñez Jareño et al. 2021). The aim has been to explore: first, whether machine learning can be used to classify sherds consistently by fabric, using magnified photographs of broken surfaces and an automated preprocessing pipeline; and second, whether an algorithm can create and consistently implement its own classificatory system. The ultimate goal was to evaluate the feasibility of developing an algorithm that could reliably be used by inexperienced team members to sort fragmentary ceramic assemblages into different fabrics with the aid of equipment that is readily available, thus freeing up experienced specialists to focus on other aspects of field study.

Local driving is usually expected to spread activity through a diffusive system. We show that this intuition can fail when motion is constrained. We study a one-dimensional lattice gas on a ring in which particles move only through paired hops that preserve the overall center of mass, while a local source continuously injects adjacent particles and on-site pairs are removed. Contrary to the expectation that steady injection delocalizes activity around the ring, the system self-organizes into a sharply localized active core around the driven bond, where the density away from this core decays rapidly to near zero. We prove an exact steady-state balance that fixes the total number of on-site pairs, independent of system size and hopping rate. Simulations show that once the active core is well separated from the boundaries, its width and peak amplitude collapse under two dimensionless control parameters and become independent of system size. For multiple identical drives, the single-core width predicts when neighboring active patches begin to overlap and the inactive region disappears. The results identify a simple mechanism by which local pumping and constrained motion generate self-localized steady states.

In many scientific domains, high-dimensional data are ubiquitous. Despite residing in a high-dimensional space, such data often lie near a much lower-dimensional manifold. The intrinsic dimension of a dataset refers to the minimum number of variables required to accurately represent the underlying structure of the data and several estimators have been proposed so far. However, the intrinsic dimension of time series data and dynamical systems still remains unexplored. Therefore, the paper has three main objectives. First, we extend the existing intrinsic dimension estimator to multivariate time series and compute the intrinsic dimension of the time series datasets and the neural reservoir in the associated echo state network. Echo state networks are a class of the reservoir computing paradigm based on dynamical systems that is widely used in machine learning and provides a simplified framework for brain dynamics. Second, we assess the intrinsic dimension of the neural reservoir relative to the input dimension. This sheds light on how recurrent neurons may augment the information inherent in the input signals. Lastly, a further evaluation of the classification performance using echo state networks also reveals possible correspondence between intrinsic dimension and learning capability of dynamical systems.

We introduce a physics-informed method for finding numerical solutions of large systems of equations governing aggregation kinetics. The method enables accurate reconstruction of density distributions for both large and small clusters, with notable improvements for small cluster sizes, as compared to previous numerical approaches. The efficiency and accuracy are improved by restricting the physics-informed loss to a small interval, enabling long time horizons with minimal extra computational cost. The superiority of the method has been demonstrated for basic aggregation kernels – constant, additive, multiplicative and generalised Brownian kernel, showing that one simple neural architecture can be used for four distinct kernels. In addition to numerical examples, we provide rigorous mathematical justification for the approach and derive relevant analytical error bounds. Combined high efficiency and low error margins of the method indicate strong potential for long-term prediction and integration into broader computational systems.

This article advances the theoretical foundations of stochastic configuration networks (SCNs) by rigorously analyzing their convergence properties, approximation guarantees, and the limitations of nonadaptive randomized methods. We introduce a principled objective function that aligns incremental training with orthogonal projection, ensuring maximal residual reduction at each iteration without recomputing output weights. Under this formulation, we derive a novel necessary and sufficient condition for strong convergence in Hilbert spaces and establish sufficient conditions for uniform geometric convergence, offering the first theoretical justification of the SCN residual constraint. To assess the feasibility of unguided random initialization, we present a probabilistic analysis showing that even small support shifts markedly reduce the likelihood of sampling effective nodes in high-dimensional settings, thereby highlighting the necessity of adaptive refinement in the sampling distribution. Motivated by these insights, we propose greedy SCNs (GSCNs) and two optimized variants—Newton–Raphson GSCN (NR-GSCN) and particle swarm optimization GSCN (PSO-GSCN)—that incorporate Newton–Raphson refinement and particle swarm-based exploration to improve node selection. Empirical results on synthetic and real-world datasets demonstrate that the proposed methods achieve faster convergence, better approximation accuracy, and more compact architectures compared to existing SCN training schemes. Collectively, this work establishes a rigorous theoretical and algorithmic framework for SCNs, laying out a principled foundation for subsequent developments in the field of randomized neural network (NN) training.

In this work, we analyse the fundamental question: how many senses are optimal for memory and learning. To answer this question, we introduce and analyse a novel kinetic model of memory engrams. The model, built on basic general principles and phenomenology, captures the engrams’ emergence and evolution driven by their interaction with external environment, learning, and forgetting. We derive the corresponding kinetic equation governing the dynamics and evolution of engrams over time. We then solve this equation analytically and numerically through Monte Carlo simulations. We observe the formation of a steady state with a steady number of different engrams covering a fraction of the conceptual space. We analyze the impact of the dimension of the conceptual space on the steady state and discover the existence of a critical dimension, at which the number of different engrams is maximal; we provide a theoretical explanation of this observation. If each feature is associated with a different sense, the critical dimension corresponds to an optimal number of senses for a system aiming at keeping the maximal number of different concepts in its memory. We also reveal an apparent tension between the system’s receptivity to new stimuli and concept sharpness—the higher the receptivity, the less sharp the learned concept becomes.