MNESIS — Working Memory in a Recurrent Spiking Neural Network with Heterogeneous Synaptic Delays

MNESIS — Memory Network Every Spike Is Sacred

This repository contains the full implementation, experiments, and paper source for MNESIS, a recurrent spiking neural network (SNN) with heterogeneous synaptic delays that stores and recalls arbitrary spike patterns as sequential chains of overlapping Spiking Motifs.

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Overview

Working memory in biological neural circuits relies on precise spike timing rather than sustained firing rates. MNESIS models this by equipping every synapse with $D = 41$ learnable delays, parameterised as a single weight tensor $\mathbf{W} \in \mathbb{R}^{N \times N \times D}$. Each stored pattern is encoded as a chain of overlapping Spiking Motifs: contiguous context windows of length $D$ that uniquely predict the next time step of activity. A closed-form Hebbian initialisation derived by deconvolving the LIF membrane response achieves perfect recall ($F_1 = 1.0$) before any gradient step, while surrogate-gradient BPTT provides robustness to noise.

Key results:

• Perfect recall of $M = 16$ patterns of $T = 1000,\mathrm{ms}$ with $N = 1024$ neurons
• $F_1 = 1.0$ from analytical initialisation alone — no gradient step required
• Tolerates 25% bit-flip noise in the trigger window (attractor dynamics)
• Memory capacity scales as $N^2 D$, linear in delay depth

Paper: Laurent U. Perrinet (2026). Working Memory in a Recurrent Spiking Neural Network with Heterogeneous Synaptic Delays. AIROV 2026. tex/Perrinet26mnesis.pdf · https://laurentperrinet.github.io/publication/perrinet-26-icann/

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Repository structure

MNESIS/
├── src/                           # Source code and Jupyter notebooks
│   ├── mnesis_boilerplate.py                 # Imports, device setup, Params dataclass, utilities
│   ├── mnesis_chains.py                      # SpikingPattern generators, HD_SNN class, analytical init
│   └── notebooks (numbered pipeline, run sequentially):
│       ├── 10_MNESIS_generative-model.ipynb      # Generative model for synthetic patterns
│       ├── 11_MNESIS_learn-synthetic.ipynb       # Training on synthetic patterns
│       ├── 13_MNESIS_testing-inference.ipynb     # Sequential retrieval of M patterns
│       ├── 14_MNESIS_testing-noise.ipynb         # Robustness to bit-flip noise
│       ├── 15_MNESIS_testing-trigger-duration.ipynb   # Effect of trigger-window length
│       ├── 16_MNESIS_testing-trigger-fraction.ipynb   # Effect of partial neuron coverage
│       ├── 20_MNESIS_scanning-parameters.ipynb # Parameter scans (D, T, p_A, ...)
│       ├── 25_MNESIS_optuna.ipynb               # Hyperparameter optimisation (Optuna)
│       ├── 30_MNESIS_learn-periodic.ipynb       # Learning and retrieval of periodic memories
│       ├── 32_MNESIS_learn-travelling-waves.ipynb # Structured spatiotemporal travelling waves
│       ├── 34_MNESIS_learn-Lorenz-attractor.ipynb # Chaotic trajectory encoding and recall
│       ├── 40_MNESIS_learn-SHD.ipynb            # Spiking Heidelberg Digits experiments
│       ├── 99_MNESIS_run-all.ipynb              # End-to-end notebook orchestrator
│       └── requirements.txt                     # Python dependencies for notebook runs
├── figures/                      # Generated figures (PDF/PNG)
├── tex/                          # Paper source
│   ├── Perrinet26mnesis.tex      # Main LaTeX source
│   ├── Perrinet26mnesis.pdf      # Compiled paper
│   ├── mnesis.bib                # Bibliography
│   ├── llncs.cls                 # Springer LNCS class
│   └── splncs04.bst              # BibTeX style
├── cached_data/                  # Cached weights and scan results (git-ignored)
├── LICENSE
└── README.md

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Quickstart

Install dependencies

pip install -r src/requirements.txt

Core dependencies: torch, snntorch, numpy, scipy, matplotlib, jupyter.

Run the notebooks in order

The notebooks are numbered and designed to be run sequentially. They import shared infrastructure from the Python modules mnesis_boilerplate.py (imports, device detection, Params dataclass, utilities) and mnesis_chains.py (HD_SNN class, pattern generators). Each notebook saves its outputs (model weights, scan results) to cached_data/ so that downstream notebooks can load them without recomputation. Notebook 99 can orchestrate a full multi-notebook run in one place.

cd src
jupyter notebook

#	Notebook / Module	Purpose
—	mnesis_boilerplate.py	Shared imports, device detection (MPS / CUDA / CPU), random-seed utilities, Params dataclass, and helper functions reused by all downstream notebooks.
—	mnesis_chains.py	Defines SpikingPattern, StochasticSpikingPattern, and the HD_SNN class with analytical weight initialisation (Hebbian cross-correlation with LIF deconvolution, targeting $\vartheta_0 = 0.8 < \vartheta = 1$). Corresponds to the Methods section of the paper.
10	10_MNESIS_generative-model.ipynb	Implements the generative model for synthetic sparse patterns: draws Gaussian logit maps $\ell \sim \mathcal{N}(0, E_\mathrm{SM})$, thresholds to keep the top $p_\mathrm{SM}$ fraction, convolves with the biphasic spike shape, and samples Bernoulli spike trains at rate $p_A$. Visualises the resulting patterns.
11	11_MNESIS_learn-synthetic.ipynb	Trains the network on $M = 16$ synthetic sparse patterns. Demonstrates that the analytical init alone reaches $F_1 = 1.0$; gradient training with AdamW and cosine schedule then improves noise robustness.
13	13_MNESIS_testing-inference.ipynb	Concatenates all $M = 16$ patterns in sequence with $N_\mathrm{pretime} = 50$ steps of spontaneous inter-trial activity; evaluates sliding-window $F_1$ to confirm selective, cross-interference-free retrieval.
14	14_MNESIS_testing-noise.ipynb	Bit-flip noise on the trigger window ($p_\mathrm{flip} \in [0, 1]$). Quantifies attractor-like robustness; $F_1 = 0.967$ at $p_\mathrm{flip} = 0.25$.
15	15_MNESIS_testing-trigger-duration.ipynb	Truncated trigger window (0 to $D-1$ steps). Finds the minimum cue length for reliable recall; $F_1 = 0.862$ at 75% of $D$.
16	16_MNESIS_testing-trigger-fraction.ipynb	Partial neuron coverage (0 to $N$ neurons silenced in trigger). Perfect recall maintained with 87.5% of neurons active.
20	20_MNESIS_scanning-parameters.ipynb	Systematic one-at-a-time scans over $D$, $T$, $p_A$, $N$, $E_\mathrm{SM}$, $p_\mathrm{SM}$, etc. with $N_\mathrm{cv} = 10$ seeds. Produces the parameter-scan figures of the paper.
25	25_MNESIS_optuna.ipynb	Automated hyperparameter search with Optuna over learning dynamics, thresholds, and regularisation.
30	30_MNESIS_learn-periodic.ipynb	Builds periodic targets, trains periodic memories, and evaluates retrieval robustness under increasing input noise.
32	32_MNESIS_learn-travelling-waves.ipynb	Introduces MotionClouds-based travelling-wave patterns and benchmarks retrieval with structured spatiotemporal motifs.
34	34_MNESIS_learn-Lorenz-attractor.ipynb	Encodes Lorenz chaotic trajectories into spike codes and evaluates memory recall on non-periodic continuous dynamics.
40	40_MNESIS_learn-SHD.ipynb	Integrates Spiking Heidelberg Digits data loading/preprocessing for dataset-grounded experiments.
99	99_MNESIS_run-all.ipynb	Scripted orchestrator to run the full notebook pipeline with progress timestamps.

Cached data

Results are saved to cached_data/ (excluded from git via .gitignore):

File pattern	Content
*_init.pth	Analytically initialised weights (pseudo-inverse or Hebbian)
*.pth	Trained model weights after gradient steps
*_scan_*.json	Parameter sweep results (loss, precision, recall per condition)
*_periodic-with-noise.npz	Periodic-memory robustness curves across noise levels and time chunks
*_TW_*.json	Travelling-wave parameter scans
*_lorenz_chaotic_*.json	Lorenz-attractor scan and optimisation outputs
*_optuna.sqlite3	Optuna studies for synthetic, travelling-wave, and Lorenz experiments

Delete a cached .pth, .json, .npz, or .sqlite3 file to force recomputation; set RECOMPUTE = True at the top of any notebook to invalidate the full cache for that notebook.

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Model

Membrane dynamics

Each neuron $j$ evolves as:

$$u_j(t) = \beta \cdot u_j(t-1) \cdot (1 - s_j(t-1)) + \sum_{i=1}^{N} \sum_{d=1}^{D} W_{j,i,d} \cdot s_i(t-d)$$

with $\beta = 0.7$ ($\tau \approx 2.8,\mathrm{ms}$), threshold $\vartheta = 1$, and zero-reset after each spike.

Analytical initialisation

The LIF membrane is a causal IIR lowpass $H(z) = 1/(1 - \beta z^{-1})$. The optimal input current that places the membrane at a sub-threshold target $\vartheta_0 = 0.8$ at each target spike time is obtained by deconvolution:

$$I^__j(t) = \vartheta_0 \bigl(s^__j(t) - \beta \cdot s^*_j(t-1)\bigr)$$

The closed-form initialisation follows from the Gram-matrix approximation $\mathbf{C}\mathbf{C}^\top \approx N D p_A \mathbf{I}$:

$$w_{i,j,d} = \frac{\vartheta_0}{N \cdot D \cdot p_A \cdot M} \sum_{\mu,,t} s_i^{_(\mu)}(t-d) \cdot \bigl(s_j^{_(\mu)}(t) - \beta \cdot s_j^{*(\mu)}(t-1)\bigr)$$

The safety margin $\delta = \vartheta - \vartheta_0 = 0.2$ maximises surrogate gradient sensitivity at initialisation ($\sigma'_{15}(-0.2) \approx 0.94$) while preventing spurious spikes from partial contexts.

Training

• Loss: $\mathcal{L} = 1 - F_1$ (harmonic mean of precision and recall, evaluated after the trigger window) — SpikeF1scoreLoss
• Optimiser: SGD by default (sgd), configurable via Params.optimizer (also supports adam, adamw, rmsprop, adadelta)
• Surrogate: fast sigmoid by default, sharpness $\alpha = 12$ — configurable via Params.surrogate_name / Params.alpha_surrogate
• Regularisation: dropout $p = 0.10$, weight decay $\lambda = 0$
• LIF dynamics: $\beta = 0.8$, $\vartheta = 0.8$, zero-reset (subtract)
• Hardware: Apple M3 Ultra (MPS) or NVIDIA GPU (CUDA / Jean Zay GENCI)

An AI assistant was used to improve the readability and structure of this codebase — not to create it.

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Results summary

Experiment	Key result
Training (NB 11)	$F_1 = 1.0$ with Hebbian init alone; gradient training adds noise robustness
Sequential retrieval (NB 13)	All 16 patterns retrieved without cross-interference
Noise robustness (NB 14)	$F_1 = 0.967$ at $p_\mathrm{flip} = 0.25$; chance only near $p_\mathrm{flip} = 0.5$
Trigger duration (NB 15)	$F_1 = 0.862$ at 75% of $D$; reliable above $D/2$
Neuron coverage (NB 16)	$F_1 = 1.0$ with 87.5% of neurons active in trigger
Delay scan (NB 20)	$\mathcal{L} \approx 0.85$ at $D=3$; $\mathcal{L} \to 0$ at $D=127$
Duration scan (NB 20)	$\mathcal{L} \approx 0.004$ at $T=64$; $\mathcal{L} \approx 0.08$ at $T=2048$
Rate scan (NB 20)	Optimal at $p_A \in [10^{-4}, 10^{-3}]$; degrades for $p_A \geq 2\times10^{-3}$
Periodic memory (NB 30)	Stable periodic retrieval with dedicated robustness evaluation under progressive bit-flip noise
Travelling waves (NB 32)	MotionClouds-derived structured motifs can be stored/recalled with the same HD-SNN framework
Lorenz attractor (NB 34)	Extends retrieval tests to non-periodic chaotic trajectories encoded as spike events
SHD integration (NB 40)	Adds real-event dataset loading and preprocessing for external benchmark experiments
Full orchestrator (NB 99)	Provides a single notebook entry point for sequential multi-notebook execution

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Citation

@inproceedings{Perrinet2026MNESIS,
  author    = {Perrinet, Laurent U.},
  title     = {Working Memory in a Recurrent Spiking Neural Network
               with Heterogeneous Synaptic Delays},
  booktitle = {AIROV 2026},
  year      = {2026},
  url       = {https://laurentperrinet.github.io/publication/perrinet-26-icann/}
}

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License

GPL-3.0 — see LICENSE.

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Institut de Neurosciences de la Timone (UMR 7289), Aix Marseille Université / CNRS, Marseille, France. Supported by GENCI-IDRIS (Grant 2025–AD010314955R2).