[2026-04-16]

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Contact me @ laurent.perrinet@univ-amu.fr

Hello, I’m Laurent Perrinet from the Institut des Neurosciences de la Timone, a joint AMU / CNRS unit, and during this talk at this AIROV workshop on Recent Advances in SNNs.

Today, I will be speaking about working memory, that is storing patterns with duration of the order of seconds, in spiking neural networks. This is a hard problem as spiking neurons have a limited memory of the order of tens of milliseconds. How can one extend this memory to larger durations? Here, I will be presenting a method for building WM in Spiking Neural Networks by using Heterogeneous Delays.

I’d like to thank Antoine for the invitation and you for listening. These slides are available from my web-site, along with a number of references. The outline of the talk is as follows: first, I’ll describe how one may perform computations using Heterogeneous Delays - and present a toy model example; then, I’ll show real scale example quantifying the performance on synthetic data.

Spiking Neural Networks: Leaky Integrate-and-Fire

[Grimaldi *et al*, 2023, [Precise Spiking Motifs](https://laurentperrinet.github.io/publication/grimaldi-22-polychronies/)] — [Grimaldi *et al*, 2023, Precise Spiking Motifs]

Spiking Neural Networks: neurobiology

[[Mainen & Sejnowski, 1995](https://github.com/SpikeAI/2022_polychronies-review/blob/main/src/Figure_2_MainenSejnowski1995.ipynb)] — [Mainen & Sejnowski, 1995]

Spiking Neural Networks: neurobiology

[[Diesmann et al. 1999](https://github.com/SpikeAI/2022_polychronies-review/blob/main/src/Figure_3_Diesmann_et_al_1999.py)] — [Diesmann et al. 1999]

Spiking Neural Networks: neurobiology

[[Haimerl et al, 2019](https://laurentperrinet.github.io/publication/grimaldi-22-polychronies/)] — [Haimerl et al, 2019]

Spiking Neural Networks: Leaky Integrate-and-Fire

Review on [Precise Spiking Motifs](https://laurentperrinet.github.io/publication/grimaldi-22-polychronies/). — Review on Precise Spiking Motifs.

Spiking Neural Networks: Heterogeneous Delays

Heterogeneous Delays Spiking Neural Network: HD-SNN

Spiking Neural Network: Polychronization

[Izhikevich (2006)](https://doi.org/10.1162/089976606775093882) — Izhikevich (2006)

Spiking Neural Network: Polychronization

[LP (2026)](https://arxiv.org/abs/2604.14096) — LP (2026)

Methods : BPTT (snn Torch) - synthetic target

Methods : Weight initialization

$$ I_j(t) = \sum_{i=1}^{N} \bigl ( \sum_{d=1}^{D} \mathbf{W}_{j, i, d} \cdot s_i(t-d) \bigr ) $$ $$ u_j(t) = \beta \cdot u_j(t-1) \cdot (1 - s_j(t-1)) + I_j(t) $$ $$ s_j(t) = \mathbf{H}[u_j(t) \geq \vartheta] $$ $$ \mathbf{W} \mathbf{C} \approx \mathbf{S} $$ $$ w_{j, i, d} = \frac{1}{N \cdot D \cdot p_A \cdot M} \sum_{\mu=1}^{M} \sum_{t=D+1}^{T} s_{j}^{\mu}(t) \cdot s_i^{\mu}(t-d) $$