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Alessio Franci

Publications and source records attributed to Alessio Franci.

At least 19 recordsLinked to original sources

A Fully Tunable Ultra-Low Power Current-Mode Memory Cell in Standard CMOS Technology

This work introduces a fully tunable, ultra-low power unipolar memory cell inspired by the Schmitt-trigger comparator and designed in CMOS using only nine transistors. The proposed circuit operates entirely in the current domain and exploits a novel feedback configuration between two interdependent Heaviside-like thresholding elements to produce tunable bistable switching behavior. Its three key parameters-threshold current, hysteresis width, and output gain-are independently tunable via programmable bias currents, enabling flexibility across diverse analog computing applications. Unlike prior Schmitt-trigger designs, it simultaneously achieves current-mode operation, nanowatt-range power consumption, temperature stability, and full tunability, solely using standard MOSFET elements. Schematic-level simulations in a 180 nm CMOS process confirm robust hysteresis and resilience to device mismatch. Building on this circuit, we develop a complete family of spike-based logic gates using three-level current encoding, where the bistable memory retains the polarity of the last spike on each input indefinitely, enabling asynchronous logic operations without temporal windowing or refresh mechanisms. The same circuit also serves as the primitive for Bistable Memory Recurrent Units in analog neural networks, where the quantized hidden states provide inherent noise immunity. Together, these capabilities position the design as a versatile building block for next-generation neuromorphic processors integrating memory, logic, and recurrent computation.

eess.SP

Neuromodulation supports robust rhythmic pattern transitions in degenerate central pattern generators with fixed connectivity

Many essential biological functions, such as breathing and locomotion, rely on the coordination of robust and adaptable rhythmic patterns, governed by specific network architectures known as connectomes. Rhythmic adaptation is often linked to slow structural modifications of the connectome through synaptic plasticity, but such mechanisms are too slow to support rapid, localized rhythmic transitions. Here, we propose a neuromodulation-based control architecture for dynamically reconfiguring rhythmic activity in networks with fixed connectivity. The key control challenge is to achieve reliable rhythm switching despite neuronal degeneracy, a form of structured variability where widely different parameter combinations produce similar functional output. Using equivariant bifurcation theory, we derive necessary symmetry conditions on the neuromodulatory projection topology for the existence of target gaits. We then show that an adaptive neuromodulation controller, operating in a low-dimensional feedback gain space, robustly enforces gait transitions in conductance-based neuron models despite large parametric variability. The framework is validated in simulation on a quadrupedal gait control problem, demonstrating reliable gallop-to-trot transitions across 200 degenerate networks with up to fivefold conductance variability.

math.DS

State-space fading memory

The fading-memory (FM) property captures the progressive loss of influence of past inputs on a system's current output and has originally been formalized by Boyd and Chua in an operator-theoretic framework. Despite its importance for systems approximation, reservoir computing, and recurrent neural networks, its connection with state-space notions of nonlinear stability, especially incremental ones, remains understudied. This paper introduces a state-space definition of FM. In state-space, FM can be interpreted as an extension of incremental input-to-output stability ($\delta$IOS) that explicitly incorporates a memory kernel upper-bounding the decay of past input differences. It is also closely related to Boyd and Chua's FM definition, with the sole difference of requiring uniform, instead of general, continuity of the memory functional with respect to an input-fading norm. We demonstrate that incremental input-to-state stability ($\delta$ISS) implies FM semi-globally for time-invariant systems under an equibounded input assumption. Notably, Boyd and Chua's approximation theorems apply to $\delta$ISS state-space models. As a closing application, we show that, under mild assumptions, the state-space model of a current-driven memristive device possesses the FM property.

eess.SY

A Neuromodulable Current-Mode Silicon Neuron for Robust and Adaptive Neuromorphic Systems

Neuromorphic engineering makes use of mixed-signal analog and digital circuits to directly emulate the computational principles of biological brains. Such electronic systems offer a high degree of adaptability, robustness, and energy efficiency across a wide range of tasks, from edge computing to robotics. Within this context, we investigate a key feature of biological neurons: their ability to carry out robust and reliable computation by adapting their input responses and spiking patterns to context through neuromodulation. Achieving analogous levels of robustness and adaptation in neuromorphic circuits through modulatory mechanisms is a largely unexplored path. We present a novel current-mode neuron design that supports robust neuromodulation with minimal model complexity, compatible with standard CMOS technologies. We first introduce a mathematical model of the circuit and provide tools to analyze and tune the neuron behavior; we then demonstrate both theoretically and experimentally the biologically plausible neuromodulation adaptation capabilities of the circuit over a wide range of parameters. All theoretical predictions were verified in experiments on a low-power 180 nm CMOS implementation of the proposed neuron circuit. Due to the analog underlying feedback structure, the proposed adaptive neuromodulable neuron exhibits a high degree of robustness, flexibility, and scalability across operating ranges of currents and temperatures, making it a perfect candidate for real-world neuromorphic applications.

eess.SY

Spiking control systems for soft robotics: a rhythmic case study in a soft robotic crawler

Inspired by spiking neural feedback, we propose a spiking controller to engineer the locomotion of a soft robotic crawler. Its bistability, akin to neural fast positive feedback, combined with a sensorimotor slow negative feedback loop, generates rhythmic spiking and self-sustained peristaltic locomotion. We analytically characterize the local equilibrium bifurcations induced by the sensorimotor gain and complement this analysis through numerical continuation of periodic orbits. The resulting bifurcation diagram reveals the emergence of qualitatively distinct solutions, including resting and crawling behaviors. For a representative regime with separated mechanical and electrical timescales, Geometric Singular Perturbation Theory reveals the geometry of the relaxation oscillations leading to endogenous crawling. Within this singularly perturbed regime, we formulate and analytically solve an optimization problem, proving that locomotion speed is maximized at mechanical resonance through a matching of neuromechanical scales. Given the importance and ubiquity of rhythms and waves in soft-bodied locomotion, we envision that spiking control systems could be utilized in a variety of soft-robotic morphologies and modular distributed architectures.

eess.SY

Formalizing Neuromorphic Control Systems: A General Proposal and A Rhythmic Case Study

Neuromorphic control is receiving growing attention due to the multifaceted advantages it brings over more classical control approaches, including: sparse and on-demand sensing, information transmission, and actuation; energy-efficient designs and realizations in neuromorphic hardware; event-based signal processing and control signal computation. However, a general control-theoretical formalization of what "neuromorphic control systems" are and how we can rigorously analyze, design, and control them is still largely missing. In this note, we suggest a possible path toward formalizing neuromorphic control systems. We apply the proposed framework to a rhythmic control case study and rigorously show how it has the potential to make neuromorphic control systems analysis and design amenable to mature control theoretical approaches like describing function analysis and harmonic balance, fast-slow analysis, discrete and hybrid systems, and robust optimization.

eess.SY

Singular networks and ultrasensitive terminal behaviors

Negative conductance elements are key to shape the input-output behavior at the terminals of a network through localized positive feedback amplification. The balance of positive and negative differential conductances creates singularities at which rich, intrinsically nonlinear, and ultrasensitive terminal behaviors emerge. Motivated by neuromorphic engineering applications, in this note we extend a recently introduced nonlinear network graphical modeling framework to include negative conductance elements. We use this extended framework to define the class of singular networks and to characterize their ultra-sensitive input/output behaviors at given terminals. Our results are grounded in the Lyapunov-Schmidt reduction method, which is shown to fully characterize the singularities and bifurcations of the input-output behavior at the network terminals, including when the underlying input-output relation is not explicitly computable through other reduction methods.

math.OC

Bifurcation analysis of an opinion dynamics model coupled with an environmental dynamics

We consider an opinion dynamics model coupled with an environmental dynamics. Based on a forward invariance argument, we can simplify the analysis of the asymptotic behavior to the case when all the opinions in the social network are synchronized. Our goal is to emphasize the role of the trust given to the environmental signal in the asymptotic behavior of the opinion dynamics and implicitly of the coupled system. To do that, we conduct a bifurcation analysis of the system around the origin when the trust parameter is varying. Specific conditions are presented for both pitchfork and Hopf bifurcation. Numerical illustration completes the theoretical findings.

eess.SY

Tunable Thresholds and Frequency Encoding in a Spiking NOD Controller

Spiking Nonlinear Opinion Dynamics (S-NOD) is an excitable decision-making model inspired by the spiking dynamics of neurons. S-NOD enables the design of agile decision-making that can rapidly switch between decision options in response to a changing environment. In S-NOD, decisions are represented by discrete opinion spikes that evolve in continuous time. Here, we extend previous analysis of S-NOD and explore its potential as a nonlinear controller with a tunable balance between robustness and responsiveness to input. We identify and provide necessary conditions for the bifurcation that determines the onset of periodic opinion spiking. We leverage this analysis to characterize the tunability of the input-output threshold for opinion spiking as a function of the model basal sensitivity and the tunable dependence of opinion spiking frequency on input magnitude above the threshold. We conclude with a discussion of S-NOD as a new neuromorphic control block and its extension to distributed spiking controllers.

eess.SY

Directional excitability in Hilbert spaces

We introduce a generalized excitable system in which spikes can happen in a continuum of directions, therefore drastically enriching the expressivity and control capability of the spiking dynamics. In this generalized excitable system, spiking trajectories happen in a Hilbert space with an excitable resting state at the origin and spike responses that can be triggered in any direction as a function of the system's state and inputs. State-dependence of the spiking direction provide the system with a vanishing spiking memory trace, which enables robust tracking and integration of inputs in the spiking direction history. The model exhibits generalized forms of both Hodgkin's Type I and Type II excitability, capturing their usual bifurcation behaviors in an abstract setting. When used as the controller of a two-dimensional navigation task, this model facilitates both the sparseness of the actuation and its sensitivity to environmental inputs. These results highlight the potential of the proposed generalized excitable model for excitable control in high- and infinite-dimensional spaces.

eess.SY

Waves and symbols in neuromorphic hardware: from analog signal processing to digital computing on the same computational substrate

Neural systems use the same underlying computational substrate to carry out analog filtering and signal processing operations, as well as discrete symbol manipulation and digital computation. Inspired by the computational principles of canonical cortical microcircuits, we propose a framework for using recurrent spiking neural networks to seamlessly and robustly switch between analog signal processing and categorical and discrete computation. We provide theoretical analysis and practical neural network design tools to formally determine the conditions for inducing this switch. We demonstrate the robustness of this framework experimentally with hardware soft Winner-Take-All and mixed-feedback recurrent spiking neural networks, implemented by appropriately configuring the analog neuron and synapse circuits of a mixed-signal neuromorphic processor chip.

cs.NE

Fast-and-flexible decision-making with modulatory interactions

Multi-agent systems in biology, society, and engineering are capable of making decisions through the dynamic interaction of their elements. Nonlinearity of the interactions is key for the speed, robustness, and flexibility of multi-agent decision-making. In this work we introduce modulatory, that is, multiplicative, in contrast to additive, interactions in a nonlinear opinion dynamics model of fast-and-flexible decision-making. The original model is nonlinear because network interactions, although additive, are saturated. Modulatory interactions introduce an extra source of nonlinearity that greatly enriches the model decision-making behavior in a mathematically tractable way. Modulatory interactions are widespread in both biological and social decision-making networks; our model provides new tools to understand the role of these interactions in networked decision-making and to engineer them in artificial systems.

math.DS

Spatially-invariant opinion dynamics on the circle

We propose and analyze a nonlinear opinion dynamics model for an agent making decisions about a continuous distribution of options in the presence of input. Inspired by perceptual decision-making, we develop new theory for opinion formation in response to inputs about options distributed on the circle. Options on the circle can represent, e.g., the possible directions of perceived objects and resulting heading directions in planar robotic navigation problems. Interactions among options are encoded through a spatially invariant kernel, which we design to ensure that only a small (finite) subset of options can be favored over the continuum. We leverage the spatial invariance of the model linearization to design flexible, distributed opinion-forming behaviors using spatiotemporal frequency domain and bifurcation analysis. We illustrate our model's versatility with an application to robotic navigation in crowded spaces.

math.AP

Spiking Nonlinear Opinion Dynamics (S-NOD) for Agile Decision-Making

We present, analyze, and illustrate a first-of-its-kind model of two-dimensional excitable (spiking) dynamics for decision-making over two options. The model, Spiking Nonlinear Opinion Dynamics (S-NOD), provides superior agility, characterized by fast, flexible, and adaptive response to rapid and unpredictable changes in context, environment, or information received about available options. S-NOD derives through the introduction of a single extra term to the previously presented Nonlinear Opinion Dynamics (NOD) for fast and flexible multi-agent decision-making behavior. The extra term is inspired by the fast-positive, slow-negative mixed-feedback structure of excitable systems. The agile behaviors brought about by the new excitable nature of decision-making driven by S-NOD are analyzed in a general setting and illustrated in an application to multi-robot navigation around human movers.

eess.SY

Excitable crawling

We propose and analyze the suitability of a spiking controller to engineer the locomotion of a soft robotic crawler. Inspired by the FitzHugh-Nagumo model of neural excitability, we design a bistable controller with an electrical flipflop circuit representation capable of generating spikes on-demand when coupled to the passive crawler mechanics. A proprioceptive sensory signal from the crawler mechanics turns bistability of the controller into a rhythmic spiking. The output voltage, in turn, activates the crawler's actuators to generate movement through peristaltic waves. We show through geometric analysis that this control strategy achieves endogenous crawling. The electro-mechanical sensorimotor interconnection provides embodied negative feedback regulation, facilitating locomotion. Dimensional analysis provides insights on the characteristic scales in the crawler's mechanical and electrical dynamics, and how they determine the crawling gait. Adaptive control of the electrical scales to optimally match the mechanical scales can be envisioned to achieve further efficiency, as in homeostatic regulation of neuronal circuits. Our approach can scale up to multiple sensorimotor loops inspired by biological central pattern generators.

eess.SY

Dimensionality reduction of neuronal degeneracy reveals two interfering physiological mechanisms

Neuronal systems maintain stable functions despite large variability in their physiological components. Ion channel expression, in particular, is highly variable in neurons exhibiting similar electrophysiological phenotypes, which poses questions regarding how specific ion channel subsets reliably shape neuron intrinsic properties. Here, we use detailed conductance-based modeling to explore the origin of stable neuronal function from variable channel composition. Using dimensionality reduction, we uncover two principal dimensions in the channel conductance space that capture most of the variance of the observed variability. Those two dimensions correspond to two physiologically relevant sources of variability that can be explained by feedback mechanisms underlying regulation of neuronal activity, providing quantitative insights into how channel composition links to neuronal electrophysiological activity. These insights allowed us to understand and design a model-independent, reliable neuromodulation rule for variable neuronal populations.

q-bio.NC

Neuromorphic Control of a Pendulum

We illustrate the potential of neuromorphic control on the simple mechanical model of a pendulum, with both event-based actuation and sensing. The controller and the pendulum are regarded as event-based systems that occasionally interact to coordinate their respective rhythms. Control occurs through a proper timing of the interacting events. We illustrate the mixed nature of the control design: the design of a rhythmic automaton, able to generate the right sequence of events, and the design of a feedback regulator, able to tune the timing of events.

eess.SY

Sparse dynamic network reconstruction through L1-regularization of a Lyapunov equation

An important problem in many areas of science is that of recovering interaction networks from simultaneous time-series of many interacting dynamical processes. A common approach is to use the elements of the correlation matrix or its inverse as proxies of the interaction strengths, but the reconstructed networks are necessarily undirected. Transfer entropy methods have been proposed to reconstruct directed networks but the reconstructed network lacks information about interaction strengths. We propose a network reconstruction method that inherits the best of the two approaches by reconstructing a directed weighted network from noisy data under the assumption that the network is sparse and the dynamics are governed by a linear (or weakly-nonlinear) stochastic dynamical system. The two steps of our method are i) constructing an (infinite) family of candidate networks by solving the covariance matrix Lyapunov equation for the state matrix and ii) using L1-regularization to select a sparse solution. We further show how to use prior information on the (non)existence of a few directed edges to drastically improve the quality of the reconstruction.

eess.SY