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Interplay between Excitability and Noise in Analog Spiking Neurons
Léopold Van Brandt, Alon Ascoli, Michele Bonnin, Grégoire Brandsteert, Denis Flandre, Jean-Charles Delvenne
TL;DR
The paper examines how intrinsic transistor noise affects spike timing and addresses the limits of simplified noise models. It uses industrial transient-noise simulation of a CMOS analog neuron, finding accumulating jitter during constant-current oscillation but low jitter for most spikes in the excitability regime.
Problem
Prior analyses relied on simplified neuron models and fixed-intensity noise, while state-dependent noise in nonlinear electronic devices remained unaddressed by data-driven industrial-model analysis.
Source: §I · p. 1Method
The study reproduces biological spike-timing experiments with a CMOS neuron using transient-noise simulations compatible with industrial transistor models.
Source: §I · p. 1, §III · p. 2Results
In the excitability regime, jitter remains low for most spikes and substantially below that of corresponding spikes during constant oscillation, while the oscillatory regime’s reliability-dissipation tradeoff is supported by a thermodynamic uncertainty relation.
Source: §IV · p. 4, B. Thermodynamic Uncertainty Relation · p. 5, C. Discussion · p. 6Takeaways & Limitations
The authors suggest that time-varying input may help minimize jitter, while treating detailed analysis of the neuron dynamics as future work.
Source: C. Discussion · p. 6A detailed study of the neuronal dynamics is left for future work.
Source: C. Discussion · p. 6
Abstract
from arXiv · showhide
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.
I. INTRODUCTION
The paper studies how intrinsic transistor noise affects spike timing in an ultra-low-power CMOS analog neuron. It uses industrial transient-noise SPICE simulation to address limitations of simplified noise models.
I. INTRODUCTION
- The studied ultra-low-power CMOS neuron is representative of more complex neurons, including AdEx cells used in neuromorphic processors.Spike-based neuromorphic computing encodes data in event timing rather than signal amplitude.Source: §I · p. 1
- Industrial transient-noise SPICE simulations assess how intrinsic circuit noise affects spike times under different inputs.The study retains the 65 nm design and deterministic parameters of.Source: §I · p. 1
- Earlier analyses used simplified neuron models and fixed-intensity Gaussian noise, overlooking state-dependent noise in nonlinear devices such as MOS transistors.The authors identify data-driven analysis using industrial component models and circuit simulators as missing from the literature,.Source: §I · p. 1
II. SPIKE TIMING IN BIOLOGICAL NEURONS: NEUROSCIENCE EXPERIMENTS
The biological experiments compare spike timing under constant and time-varying stimulation. The constant stimulus produces accumulating timing uncertainty, whereas the time-varying stimulus is associated with nearly aligned spikes across trials.
II. SPIKE TIMING IN BIOLOGICAL NEURONS: NEUROSCIENCE EXPERIMENTS
- The experiments compare a constant current pulse with a time-varying current formed from a constant component and filtered white Gaussian noise.In the time-varying condition, the same frozen noise realization is injected across trials.Source: §II · p. 2
- Under constant supra-threshold stimulation, spike-time uncertainty accumulates over successive cycles as phase noise.The passage models oscillator phase error as diffusion driven by random noise –.Source: §II · p. 2
- With time-varying stimulation, spikes are nearly aligned across trials, consistent with input-triggered transitions into and out of a limit cycle.The proposed excitable mechanism resets timing uncertainty; a few outliers remain.Source: §II · p. 2
III. SPIKE TIMING IN ANALOG SPIKING NEURONS: NUMERICAL INVESTIGATION
The study reproduces biological spike-timing experiments in a CMOS analog neuron using transient noise simulations compatible with industrial transistor models. The estimated thermal-noise fluctuations are small relative to the membrane-voltage swing.
III. SPIKE TIMING IN ANALOG SPIKING NEURONS: NUMERICAL INVESTIGATION
- The neuron simulations extend the deterministic model with physically generated intrinsic transistor noise using industrial transient-noise SPICE tools.The framework uses foundry transistor models rather than simplified analytical noise models.Source: §III · p. 2
- NOISETRAN adds a physical noise source to each MOS transistor, generates noise realizations at each time step, and solves the circuit equations in time.The foundry model sets each source’s state-dependent intensity.Source: §III · pp. 2–3
- About 0.7 mV is the estimated thermal-noise standard deviation, with typical fluctuations just below 1% as membrane voltage ranges from 0 to almost 200 mV.The estimate uses the effective membrane capacitance and an equilibrium integrated-noise approximation at 300 K.Source: §III · p. 3
A. Neuron in the Oscillatory Regime
This section characterizes the CMOS neuron’s excitability and its response to constant supra-threshold stimulation. Under a sustained 20 pA current, the neuron oscillates and spike-time jitter grows across successive spikes.
A. Neuron in the Oscillatory Regime
- The neuron’s input-output map records which pulse-amplitude and duration combinations produce a spike.The response is reduced to the discrete outcome “spike or not?” under cold initial conditions.Source: A. Neuron in the Oscillatory Regime · p. 3
- About 32 µs is the mean spike period under a constant 20 pA supra-threshold current.The sustained input produces an action-potential train across repeated trials.Source: A. Neuron in the Oscillatory Regime · p. 3
- In the Figure 3 oscillatory configuration, spike-time uncertainty (jitter) increases with spike number, measured at successive rising-edge crossings of vGK at VDD/2 = 100 mV; n reaches 30 during the 1 ms simulation.Source: A. Neuron in the Oscillatory Regime · p. 3
B. Neuron Excited by a Time-Varying Input
A frozen, low-pass-filtered time-varying input with a 5 pA DC component produces excitability rather than self-running oscillation. Spikes are generally closely aligned across trials, although particular spikes remain more variable.
B. Neuron Excited by a Time-Varying Input
- A frozen filtered-noise input uses a 5 pA DC component below the 7 pA threshold and has σ_iex = 20 pA with filter time constant τ = 5 µs.The same realization is injected in every trial, making the time-varying input identical across trials.Source: B. Neuron Excited by a Time-Varying… · p. 4
- With the time-varying input, spikes occur only when fluctuations induce an above-threshold response, and timing does not accumulate jitter as it does in oscillation.The neuron is in the excitability regime, and almost all spike times align closely across 25 trials.Source: B. Neuron Excited by a Time-Varying… · p. 4
- The 4th and 15th spikes are most timing-variable for this input, with the 2nd and 16th also showing smaller variability.The authors regard the 4th and 15th spikes as outliers because the underlying transition mechanisms are beyond the paper's scope.Source: B. Neuron Excited by a Time-Varying… · p. 4
IV. RESULTS AND DISCUSSION
The results compare trial-to-trial spike-time variability across oscillatory and excitability regimes. Jitter accumulates only in the oscillatory case, which the authors identify as a physical reliability limitation highlighted by a thermodynamic uncertainty relation.
IV. RESULTS AND DISCUSSION
- The authors frame significant oscillatory spike-time variation as a physical limitation highlighted by a thermodynamic uncertainty relation.The relation is presented as a quantitative confirmation of conclusions about spike-timing reliability.Source: §IV · p. 4
- Jitter accumulates over time only for oscillatory input; Figure 5 estimates variance from 1,000 trials.The comparison covers the oscillatory and excitability behaviours.Source: Figure 5 · p. 4
- For excitability, the 4th- and 15th-spike variances are 20 and 8 (µs)², respectively, and exceed Figure 5's plot scale.The caption identifies these spikes as unusually variable.Source: Figure 5 · p. 4
A. Jitter Analysis
The analysis estimates accumulated spike-time jitter relative to the first spike over 1,000 trials. In oscillation, jitter accumulates, with results consistent with white thermal noise dominating until deviations emerge at larger n.
A. Jitter Analysis
- The analysis estimates Var{Tn − T1} for n ≥ 2 across 1,000 successive trials to avoid dependence on initial conditions and circuit power-up phase.The quantity is referred to as n-period or accumulated spike-time jitter.Source: A. Jitter Analysis · p. 4
- Jitter accumulates over time in the oscillatory regime.The cited analysis relates the variance of accumulated spike-time differences to the variance of the inter-spike interval.Source: A. Jitter Analysis · p. 4
- Near agreement with relation (2) through about n ≈ 25 supports white, time-decorrelated MOS thermal noise as the dominant source of oscillatory spike-time jitter.The authors associate slight later deviations with time-correlated 1/f noise and question whether the relation is universal given transistor-to-transistor low-frequency-noise variability.Source: A. Jitter Analysis · p. 4
B. Thermodynamic Uncertainty Relation
The thermodynamic uncertainty relation bounds the precision of an overdamped, stationary cyclic process in terms of dissipation. Applied to the neuron’s spike frequency, it links low dissipation to substantial timing uncertainty and sets a physical reliability–dissipation tradeoff.
B. Thermodynamic Uncertainty Relation
- For overdamped Markov systems with constant parameters at stationarity, the thermodynamic uncertainty relation links an odd trajectory observable’s precision to dissipation.The neuron’s net spike count per time, f = N/t, is treated as an empirical frequency; the relation implies that low dissipation entails large spike-time uncertainty in this constant-force cyclic regime.Source: B. Thermodynamic Uncertainty Relation · p. 5
- At constant 20 pA excitation, the neuron dissipates approximately 1 fJ per spike.Per-cycle dissipation is computed by integrating supplied power over a full spike cycle; the expected energy dissipated over time is then used in the relation.Source: B. Thermodynamic Uncertainty Relation · p. 5
- The right-hand side of the neuron’s jitter estimate is a factor 25 above the fundamental lower bound, subject to stated approximations.The comparison uses t = (n − 1) · 32 µs; variance of (T_n − T_1) is used as a proxy for frequency variance, not as a mathematical equivalent.Source: B. Thermodynamic Uncertainty Relation · pp. 5–6
- Regardless of the simulated circuit parameters, lowering the minimum achievable jitter necessarily requires higher dissipation.The expected dissipated energy is averaged over trajectories, and the uncertainty relation supplies a fundamental reliability–dissipation limit.Source: B. Thermodynamic Uncertainty Relation · pp. 5–6
C. Discussion
In the excitability regime, most spikes have substantially lower jitter than corresponding spikes during constant oscillation. The authors attribute this provisionally to input-triggered state transitions and suggest jitter-minimizing input control, while noting that the uncertainty relation does not apply to this non-stationary regime.
C. Discussion
- Most spikes in the excitability regime have substantially lower jitter than corresponding spikes during constant oscillation.The authors provisionally attribute this difference to discrete, time-varying-input-triggered state transitions that reset rather than accumulate phase error.Source: C. Discussion · p. 6
- A possibly random time-varying input could be optimized to minimize jitter and energy consumption.The paper presents this as a preliminary suggestion for an optimal control problem.Source: C. Discussion · p. 6
- The thermodynamic uncertainty relation does not apply to the non-stationary excitability regime, where oscillatory-regime physical limits are alleviated.Source: C. Discussion · p. 6
V. CONCLUSIONS AND PERSPECTIVES
The conclusions connect transistor-noise-driven spike-time variability to the neuron’s operating regime: constant excitation accumulates jitter, while time-varying input reduces it through controlled spike transitions. The authors identify a reliability–dissipation tradeoff in oscillatory operation and propose modeling the dynamics in future work.
V. CONCLUSIONS AND PERSPECTIVES
- Time-varying input substantially reduces jitter by making each spike result from a controlled transition.The conclusion contrasts this with the self-running oscillatory response to constant supra-threshold current.Source: §V · p. 6
- Under constant supra-threshold current, transistor noise causes spike-time variability that accumulates linearly during oscillatory firing.The passage identifies this variability as jitter.Source: §V · p. 6
- A thermodynamic uncertainty relation supports a reliability–dissipation tradeoff in the constant-current oscillatory regime.Source: §V · p. 6
- Industrial circuit simulations reproduced neuroscience experiments using the excitability of a CMOS leaky integrate-and-fire neuron.Source: §V · p. 6
- Future work will model neuronal dynamics to validate assumptions about the distinct spiking mechanisms and predict spike-time statistics.Source: §V · p. 6