arXiv subjects

Léopold Van Brandt

Publications and source records attributed to Léopold Van Brandt.

9 recordsLinked to original sources

arXiv2026

Interplay between Excitability and Noise in Analog Spiking Neurons

A spiking neuron is a dynamical system exhibiting a limit cycle (a spike) when subject to sufficiently excitatory input. Famous neuroscience experiments by Bryant and Segundo as well as Mainen and Sejnowski revealed that the spike times of some biological neurons are more reliable when subject to time-varying stimuli compared to constant ones. Provided with an industrial physics-based transient noise SPICE simulation framework compatible with foundry transistor compact models, we have demonstrated similar behaviours for a CMOS analog spiking neuron designed for neuromorphic computing hardware platforms. Under constant excitation current, the neuron operates in oscillatory regime and the empirical periods (interspike intervals) suffer from accumulated phase noise (jitter) during successive cycles, mainly due to the thermal noise of transistors. A time-varying input is reported to be capable of triggering output spikes according to a controlled statetransition mechanism, thereby significantly reducing the spike time jitter in the excitability regime. The physical limitation of the oscillatory or rate-coding regime in terms of reliabilitydissipation tradeoff is further evidenced by a stochastic thermodynamic uncertainty relation, a theorem that applies to general overdamped dissipative stochastic dynamical systems.

q-bio.NC↗

arXiv2025

On the Excitability of Ultra-Low-Power CMOS Analog Spiking Neurons

The excitability property of spiking neurons describes their capability to output an action potential as a real-time response to an input synaptic excitation current and is central to the event-based neuromorphic computing paradigm. The spiking mechanism is analysed in a representative ultra-low-power analog neuron from the circuit literature. Relying on conventional SPICE simulations compatible with industrial transistor compact models, we establish a excitation criterion, quantified either in terms of critical supplied charge or membrane potential threshold. Only the latter is found intrinsic to the neuron, i.e. independent of the input stimulus. Rigorous analysis of the nonlinear neuron dynamics provides insight but still needs to be explored further, as well as the effect of the intrinsic noise.

cond-mat.stat-mech↗

arXiv2025

Noise-dissipation relation for nonlinear electronic circuits

An extension of fluctuation-dissipation theorem is used to derive a "speed limit" theorem for nonlinear electronic devices. This speed limit provides a lower bound on the dissipation that is incurred when transferring a given amount of electric charge in a certain amount of time with a certain noise level (average variance of the current). This bound, which implies a high energy dissipation for fast, low-noise operations (such as switching a bit in a digital memory), brings together recent results of stochastic thermodynamics into a form that is usable for practical nonlinear electronic circuits, as we illustrate on a switching circuit made of an nMOS pass gate in a state-of-the-art industrial technology.

cond-mat.stat-mech↗

arXiv2024

Predicting State Transitions in Autonomous Nonlinear Bistable Systems with Hidden Stochasticity

Bistable autonomous systems can be found inmany areas of science. When the intrinsic noise intensity is large, these systems exhibits stochastic transitions from onemetastable steady state to another. In electronic bistable memories, these transitions are failures, usually simulated in a Monte-Carlo fashion at a high CPU-time price. Existing closed-form formulas, relying on near-stable-steady-state approximations of the nonlinear system dynamics to estimate the mean transition time, have turned out inaccurate. Our contribution is twofold. From a unidimensional stochastic model of overdamped autonomous systems, we propose an extended Eyring-Kramers analytical formula accounting for both nonlinear drift and state-dependent white noise variance, rigorously derived from Itô stochastic calculus. We also adapt it to practical system engineering situations where the intrinsic noise sources are hidden and can only be inferred from the fluctuations of observables measured in steady states. First numerical trials on an industrial electronic case study suggest that our approximate prediction formula achieve remarkable accuracy, outperforming previous non-Monte-Carlo approaches.

cond-mat.stat-mech↗

arXiv2024

Moments of Entropy Production in Dissipative Devices

We characterize the possible moments of entropy production for general overdamped Markovian systems. We find a general formulation of the problem, and derive a new necessary condition between the second and third moment. We determine all possible first, second and third moments of entropy production for a white noise process. As a consequence, we obtain a lower bound for the skewness of the current fluctuations in dissipative devices such as transistors, thereby demonstrating that the Gaussianity assumption widely used in electronic engineering is thermodynamically inconsistent.

cond-mat.stat-mech↗

arXiv2024

Variability-Aware Noise-Induced Dynamic Instability of Ultra-Low-Voltage SRAM Bitcells

Stability of ultra-low-voltage SRAM bitcells in retention mode is threatened by two types of uncertainty: process variability and intrinsic noise. While variability dominates the failure probability, noise-induced bit flips in weakened bitcells lead to dynamic instability. We study both effects jointly in a unified SPICE simulation framework. Starting from a synthetic representation of process variations introduced in a previous work, we identify the cases of poor noise immunity that require thorough noise analyses. Relying on a rigorous and systematic methodology, we simulate them in the time domain so as to emulate a true data retention operation. Short times to failure, unacceptable for a practical ultra-low-power memory system application, are recorded. The transient bit-flip mechanism is analysed and a dynamic failure criterion involving the unstable point is established. We conclude that, beyond static variability, the dynamic noise inflates defectiveness among SRAM bitcells. We also discuss the limits of existing analytical formulas from the literature, which rely on a linear near-equilibrium approximation of the SRAM dynamics to, inaccurately, predict the mean time to failure.

cs.AR↗

arXiv2024

Stochastic Nonlinear Dynamical Modelling of SRAM Bitcells in Retention Mode

SRAM bitcells in retention mode behave as autonomous stochastic nonlinear dynamical systems. From observation of variability-aware transient noise simulations, we provide an unidimensional model, fully characterizable by conventional deterministic SPICE simulations, insightfully explaining the mechanism of intrinsic noise-induced bit flips. The proposed model is exploited to, first, explain the reported inaccuracy of existing closed-form near-equilibrium formulas aimed at predicting the mean time to failure and, secondly, to propose a closer estimate attractive in terms of CPU time.

cs.AR↗

arXiv2023

The non-Landauer Bound for the Dissipation of Bit Writing Operation

We propose a novel bound on the mimimum dissipation required in any circumstances to transfer a certain amount of charge through any resistive device. We illustrate it on the task of writing a logical 1 (encoded as a prescribed voltage) into a capacitance, through various linear or nonlinear devices. We show that, even though the celebrated Landauer bound (which only applies to bit erasure) does not apply here, one can still formulate a "non- Landauer" lower bound on dissipation, that crucially depends on the time budget to perform the operation, as well as the average conductance of the driving device. We compare our bound with empirical results reported in the literature and realistic simulations of CMOS pass and transmission gates in decananometer technology. Our non-Landauer bound turns out to be a quantitative benchmark to assess the (non-)optimality of a writing operation.

cond-mat.stat-mech↗

arXiv2023

Bounding Variance and Skewness of Fluctuations in Nonlinear Mesoscopic Systems with Stochastic Thermodynamics

Fluctuations arising in nonlinear dissipative systems (diode, transistors, chemical reaction, etc.) subject to an external drive (voltage, chemical potential, etc.) are well known to elude any simple characterization such as the fluctuation-dissipation theorem (also called Johnson-Nyquist law, or Einstein's law in specific contexts). Using results from stochastic thermodynamics, we show that the variance of these fluctuations exceeds the variance predicted by a suitably extended version of Johnson-Nyquist's formula, by an amount that is controlled by the skewness (third moment) of the fluctuations. As a consequence, symmetric fluctuations necessarily obey the extended Johnson-Nyquist formula. This shows the physical inconsistency of Gaussian approximation for the noise arising in some nonlinear models, such as MOS transistors or chemical reactions. More generally, this suggests the need for a stochastic nonlinear systems theory that is compatible with the teachings of thermodynamics.

cond-mat.stat-mech↗