Continuous signal sparse encoding using analog neuromorphic variability

TL;DR

The paper tackles robust, real-time encoding of continuous temporal signals on neuromorphic hardware by exploiting intrinsic analog variability. It introduces a shallow network of exponential LIF neurons that produce sparse first-spike encodings, using a median-spike-time reference $\bar{t}$ to form $\vec{y}^*$, which is then decoded linearly to stimulus parameters; ADM converts inputs to spikes and an evolutionary protocol tunes time constants $\tau_{ ext{mem}},\tau_{ ext{syn}+},\tau_{ ext{syn}-}$ and integer weights. Validated on DYNAP-SE hardware and in simulations across four signal types, the approach achieves high linear-decodeability (e.g., $\text{Pearson } r \approx 0.94$, $\text{Kendall } \tau \approx 0.88$) with robust performance under jitter, spike deletions, and reduced heterogeneity, and exhibits stereotyped, signal-type-specific spike sequences with shift-invariant classification. The method aligns with biological variability, offers a low-complexity, hardware-friendly alternative to reservoir computing, and enables fast, low-power, always-on processing of temporal data on mixed-signal neuromorphic substrates.

Abstract

Achieving fast and reliable temporal signal encoding is crucial for low-power, always-on systems. While current spike-based encoding algorithms rely on complex networks or precise timing references, simple and robust encoding models can be obtained by leveraging the intrinsic properties of analog hardware substrates. We propose an encoding framework inspired by biological principles that leverages intrinsic neuronal variability to robustly encode continuous stimuli into spatio-temporal patterns, using at most one spike per neuron. The encoder has low model complexity, relying on a shallow network of heterogeneous neurons. It relies on an internal time reference, allowing for continuous processing. Moreover, stimulus parameters can be linearly decoded from the spiking patterns, granting fast information retrieval. Our approach, validated on both analog neuromorphic hardware and simulation, demonstrates high robustness to noise, spike jitter, and reduced heterogeneity. Consistently with biological observations, we observed the spontaneous emergence of patterns with stereotyped spiking order. The proposed encoding scheme facilitates fast, robust and continuous information processing, making it well-suited for low-power, low-latency processing of temporal data on analog neuromorphic substrates.

Figures (6)

• Figure 1: Continuous stimulus encoding with at most one spike per neuron. Stimuli $\{x\}$ were sampled from the stimulus parameter space and injected into a shallow network of N neurons. Each neuron was allowed to spike at most one spike upon receiving the stimulus. Each stimulus ($\vec{x}_A(t),\vec{x}_B(t),\vec{x}_C(t)$) was encoded into an N-dimensional vector ($\vec{y}_A^*,\vec{y}_B^*,\vec{y}_C^*$) with spike times of each neuron relative to the population median (dotted lines). The N-dimensional vector was then linearly regressed to the stimulus parameters.
• Figure 2: On-chip neural encoding performances across four synthetic signals.A) Online signal processing evolution. A continuous ADM-encoded signal is fed into the hardware in an always-on manner (top row: six Double-Gaussian signals provided as input). The middle row shows the spiking output recorded from the DYNAP-SE chip for each neuron, sorted by first spiking time and stored in memory for a fixed time window (represented by the black horizontal line). Simultaneously, a counter tracks the rolling number of spikes occurring within the same time window, with the cumulative sum illustrated in the bottom row. When the spike count starts to decrease, spike times from the previous window (colored area) are used to compute the median value $bar{t}$ and the spiking signal representation $y^*$. B) Kendall-tau correlation between $\vec{p}$ and $\vec{\hat{p}}$ computed in a transformed space via PCA, as a function of the number of principal components sorted by explained variance (experiment run on populations of 128 neurons with a Double Gauss signal). While the inclusion of low-explained-variance components improves the training set score, it negatively affects generalization to the validation set, resulting in a drop in Kendall-tau correlation. The optimal number of $k$ components is selected as the value that maximizes the performance on the validation set. The averaged cumulative explained variance is shown for the first $k$ principal components ($0.98$) and for the remaining components ($0.02$), highlighting the contribution of high-explained-variance components to decoding performance. C) Example snippets for each synthetic signal type: Gabor, Sinusoidal, SingleGauss, and DoubleGauss. D) Pearson r and Kendall-tau correlation between $\vec{p}$ and $\vec{\hat{p}}$ for networks with 16 and 128 neurons. The decoding is performed using the first $k$ PC of the population response. E) Mean stereotyped spiking sequences for networks of 16 and 128 neurons for each input signal type, sorted in ascending order of spike time relative to the median response. Inset: standard deviation between mean sequences with the same network size as a function of the distance from the median.
• Figure 3: Impact of neuronal variability and noise on on-chip encoding performance. On-chip results assessing the algorithm robustness to variability reduction, temporal jitter and spike deletion on DoubleGauss signal decoding. First row) graphical representation of the robustness experiment. Second row) results from on-chip measurement for networks with 16 and 128 analog neurons (black and orange lines, respectively). For all tests, the score was computed as the percentage of the Kendall-tau correlation in the unperturbed case. A) Kendall-tau correlation as a function of weight variability ($\text{w}^H(\%)$). B) Kendall-tau correlation heatmap illustrating the influence of a temporal jitter applied to the output spike trains during the training and testing phases. C) Kendall-tau correlation score heatmap illustrating the influence of spike deletion in the output spike trains applied during the training and testing phases.
• Figure 4: Enconding algorithm characterization on simulated networks. Single-spike encoding algorithm leveraging the variability of a simulated shallow network of exp-LIF neurons tested on the same input signal types used for on-chip testing. A) Kendall-tau and Pearson r correlation between original and decoded stimulus parameters for networks with an increasing number of neurons. Stimulus decoding with the first $k$ principal components (PC) consistently showed improved correlation as the network size increased.B) The parameter ratio between the excitatory synapses time constant ($\tau_{syn_{+}}$) and the membrane time constant ($\tau_{mem}$) averaged over multiple runs across multiple network sizes for the four signal types. The mean ratio consistently remains above 1 for all signal types. C) The parameter ratio between the excitatory synapses time constant ($\tau_{syn_{+}}$) and the inhibitory synapses time constant ($\tau_{syn_{-}}$) averaged over multiple runs across multiple network sizes for the four signal types. The mean ratio consistently remains above 1 for all signal types. D) Contour map showing the regions where the Kendall-tau correlation heatmap for each signal type remained above 0.85, as a function of weight variability ($\text{w}^{H}(\%)$) and time constant variability ($\tau^{H}(\%)$). Larger contour areas indicate smaller sensitivity to variability, with weight variability generally having a stronger impact than time constant variability.
• Figure 5: Stimulus-specific spiking patterns in one simulated network.A) We injected stimuli from all 4 signal types into one simulated trained network and obtained the mean spiking order for each stimulus type. Each row represents the mean spiking activity for stimulus type $i$, sorted according to the mean spiking order of stimulus type $j$. B) Classification of stimulus type from the encoding of one network using time and order information. For both information types we observed an increase in classification accuracy when increasing the network size. Order information produced a classification accuracy higher than the one obtained with time information. C) Linear decoding of stimulus parameters for all stimulus types in one network. Pearson $r$ was higher for the stimulus type the network has been trained on (in-type) compared to the mean of the other stimulus types (out-type). On average, Pearson $r$ increased with the network size till a plateau was reached.