Timotéo Carletti

Raina Zakir, Timoteo Carletti, Marco Dorigo et al.

Minimalistic robot swarms offer a scalable, robust, and cost-effective approach to performing complex tasks with the potential to transform applications in healthcare, disaster response, and environmental monitoring. However, coordinating such decentralised systems remains a fundamental challenge, particularly when robots are constrained in communication, computation, and memory. In our study, individual robots frequently make errors when sensing the environment, yet the swarm can rapidly and reliably reach consensus on the best among $n$ discrete options. We compare two canonical mechanisms of opinion dynamics -- direct-switch and cross-inhibition -- which are simple yet effective rules for collective information processing observed in biological systems across scales, from neural populations to insect colonies. We generalise the existing mean-field models by considering asocial biases influencing the opinion dynamics. While swarms using direct-switch reliably select the best option in absence of asocial dynamics, their performance deteriorates once such biases are introduced, often resulting in decision deadlocks. In contrast, bio-inspired cross-inhibition enables faster, more cohesive, accurate, robust, and scalable decisions across a wide range of biased conditions. Our findings provide theoretical and practical insights into the coordination of minimal swarms and offer insights that extend to a broad class of decentralised decision-making systems in biology and engineering.

Lorenzo Chicchi, Duccio Fanelli, Lorenzo Giambagli et al.

A novel strategy to automated classification is introduced which exploits a fully trained dynamical system to steer items belonging to different categories toward distinct asymptotic attractors. These latter are incorporated into the model by taking advantage of the spectral decomposition of the operator that rules the linear evolution across the processing network. Non-linear terms act for a transient and allow to disentangle the data supplied as initial condition to the discrete dynamical system, shaping the boundaries of different attractors. The network can be equipped with several memory kernels which can be sequentially activated for serial datasets handling. Our novel approach to classification, that we here term Recurrent Spectral Network (RSN), is successfully challenged against a simple test-bed model, created for illustrative purposes, as well as a standard dataset for image processing training.

Lorenzo Chicchi, Lorenzo Giambagli, Lorenzo Buffoni et al.

Deep neural networks can be trained in reciprocal space, by acting on the eigenvalues and eigenvectors of suitable transfer operators in direct space. Adjusting the eigenvalues, while freezing the eigenvectors, yields a substantial compression of the parameter space. This latter scales by definition with the number of computing neurons. The classification scores, as measured by the displayed accuracy, are however inferior to those attained when the learning is carried in direct space, for an identical architecture and by employing the full set of trainable parameters (with a quadratic dependence on the size of neighbor layers). In this Letter, we propose a variant of the spectral learning method as appeared in Giambagli et al {Nat. Comm.} 2021, which leverages on two sets of eigenvalues, for each mapping between adjacent layers. The eigenvalues act as veritable knobs which can be freely tuned so as to (i) enhance, or alternatively silence, the contribution of the input nodes, (ii) modulate the excitability of the receiving nodes with a mechanism which we interpret as the artificial analogue of the homeostatic plasticity. The number of trainable parameters is still a linear function of the network size, but the performances of the trained device gets much closer to those obtained via conventional algorithms, these latter requiring however a considerably heavier computational cost. The residual gap between conventional and spectral trainings can be eventually filled by employing a suitable decomposition for the non trivial block of the eigenvectors matrix. Each spectral parameter reflects back on the whole set of inter-nodes weights, an attribute which we shall effectively exploit to yield sparse networks with stunning classification abilities, as compared to their homologues trained with conventional means.

Johan Barthélemy, Morgane Dumont, Timoteo Carletti

Classification, the process of assigning a label (or class) to an observation given its features, is a common task in many applications. Nonetheless in most real-life applications, the labels can not be fully explained by the observed features. Indeed there can be many factors hidden to the modellers. The unexplained variation is then treated as some random noise which is handled differently depending on the method retained by the practitioner. This work focuses on two simple and widely used supervised classification algorithms: discrete choice models and artificial neural networks in the context of binary classification. Through various numerical experiments involving continuous or discrete explanatory features, we present a comparison of the retained methods' performance in presence of missing variables. The impact of the distribution of the two classes in the training data is also investigated. The outcomes of those experiments highlight the fact that artificial neural networks outperforms the discrete choice models, except when the distribution of the classes in the training data is highly unbalanced. Finally, this work provides some guidelines for choosing the right classifier with respect to the training data.