# Precise Spiking Motifs in Neurobiological and Neuromorphic Data

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## Abstract

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## 1. Introduction: Importance of Precise Spike Timings in the Brain

#### 1.1. Is There a Neural Code?

#### 1.2. Dynamics of Vision and Consequences on the Neural Code

#### 1.3. How Precise Spike Timing May Encode Vectors of Real Values

## 2. Role of Precise Spike Timing in Neural Assemblies

#### 2.1. One First Hypothesis: Synchronous Firing in Cell Assemblies

#### 2.2. A Further Hypothesis: Travelling Waves

#### 2.3. A Rediscovered Hypothesis: Precise Spiking Motifs in Cell Assemblies

## 3. Understanding Precise Spiking Motifs in Neurobiology

#### 3.1. Decoding Neural Activity from Firing Rates

#### 3.2. Decoding Neural Activity Using Spike Distances

#### 3.3. Scaling up to Very Large Scale Data

## 4. What Biological Mechanism Could Allow Learning Spiking Motifs?

#### 4.1. Biological Observations of Delay Adaptation

#### 4.2. The Importance of Myelination

#### 4.3. Interplay of Delay Adaptation and Neural Activity

## 5. Modeling Precise Spiking Motifs in Theoretical and Computational Neuroscience

#### 5.1. Izhikevich’s Polychronization Model

#### 5.2. Learning Synaptic Delays

#### 5.3. Real-World Applications

## 6. Applications of Precise Spiking Motifs in Neuromorphic Engineering

#### 6.1. The Emergence of Novel Computational Architectures

#### 6.2. On the Importance of Spatio-Temporal Information in Silicon Retinas

#### 6.3. Computations with Delays in Neuromorphic Hardware

## 7. Discussion

#### 7.1. Summary

- The efficiency of neural systems, and in particular the visual system, imposes strong constraints on the structure of neural activity which highlights the importance of precise spike times;
- Growing evidence from neurobiology proves that neural systems are more than integrators and may use synchrony detection in different forms: synfire chains, travelling waves on arbitrary spiking motifs, and notably that an encoding based on precise spiking motifs may provide huge computational benefits;
- Many theoretical models already exist, taking into account the specificity of spiking motifs, notably by using heterogeneous delays;
- Using precise spiking motifs could ultimately be a key ingredient in neuromorphic systems to reach similar efficiencies as biological neural systems.

#### 7.2. Limits

#### 7.3. Perspectives

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**Latency of the different processing steps along the human visual pathway.Though the visual system is highly inter-connected, one can follow the sequence of activations whenever an image (here a yellow star) is flashed in front of the eyes. Different areas are schematically represented by ellipses, and arrows denote the fastest feed-forward activation, ordered with respect to their activation latency in $\mathrm{m}\mathrm{s}$. In order, the retina is first activated (20–40 $\mathrm{m}\mathrm{s}$), then the thalamus and the primary visual cortex (V1, 60–90 $\mathrm{m}\mathrm{s}$). This visual information projects to the temporal lobe to reach the infero-temporal area (IT, 150 $\mathrm{m}\mathrm{s}$) for object recognition. It then reaches the prefrontal cortex (PFC, $180\phantom{\rule{3.33333pt}{0ex}}\mathrm{m}\mathrm{s}$), which modulates decision making to evoke the motor cortex (MC, $220\phantom{\rule{3.33333pt}{0ex}}\mathrm{m}\mathrm{s}$) which may mediate an action. This is eventually relayed through the spinal cord to trigger finger muscles, with latencies of about 280–400 $\mathrm{m}\mathrm{s}$.

**Figure 2.**Reproducibility of the spiking response of a neuron. The timing of the spikes produced following the repetition of a step stimulus is less reproducible than that to a noisy stimulus. The stimulus current value over time for a step stimulus (top left) and for a noisy one (top right). Trial repetitions of a leaky integrate-and-fire neuron stimulated by the stimulus on the upper row (middle row). Membrane potential is represented by dark blue color when light yellow colors when depolarized) and quantified by the average firing rate across trials (lower row). While this seems paradoxical at first sight, it highlights the consequence of using the same frozen noise at each repetition and highlights the highly reproducible pattern of spikes when it is driven by a highly dynamic input. See this notebook for a replication of the results from [33] using a simple LIF model.

**Figure 3.**Simulation of a synfire propagation using Brian. The model consists of 10 groups (arranged with the first group represented in the lowest row) of 100 neurons each. Five pulses with decreasing jitter are generated in the first group around times 10, 30, 50, 70 and 90 $\mathrm{m}\mathrm{s}$ (with jitters given by a standard deviation which linearly decreases from 5 to 1 $\mathrm{m}\mathrm{s}$). This generates a pulse after a certain processing delay in the second group with a different jitter. While the first two pulses progressively vanish in the following groups, starting from the third input pulse (with a jitter of $3\phantom{\rule{3.33333pt}{0ex}}\mathrm{m}\mathrm{s}$), it is propagated to the following groups. This allows the propagation of the synchronous activity along the chain of the neural groups.

**Figure 4.**An example of a precise temporal motif observed in two subsequent days. In this study by [109], an analysis of calcium fluorescence (heatmap) of hippocampal CA1 neurons participating to run sequences in consecutive imaging sessions shows repetitions of precise spiking motifs with a time scale of the order of seconds. Cells were selected and ordered with respect to their activity in the first imaging session. The black line on top represents the speed of the mouse. Futher analysis showed that more than the majority of the cells participating in run sequences on the first day were recruited again in run sequences on the next day. Modified from Figure 1-A from [109] under the CC-BY PNAS License.

**Figure 6.**Core mechanism of polychrony detection [111]. (

**Left**) In this example, three presynaptic neurons denoted b, c and, d are fully connected to two post-synaptic neurons a and e, with different delays of respectively 1, 5, and $9\phantom{\rule{3.33333pt}{0ex}}\mathrm{m}\mathrm{s}$ for a and 8, 5, and $1\phantom{\rule{3.33333pt}{0ex}}\mathrm{m}\mathrm{s}$ for e. (

**Middle**) If three synchronous pulses are emitted from presynaptic neurons, this will generate post-synaptic potentials that will reach a and e asynchronously because of the heterogeneous delays, and they may not be sufficient to reach the membrane threshold in either of the post-synaptic neurons; therefore, no spike will be emitted, as this is not sufficient to reach the membrane threshold of the post synaptic neuron, so no output spike is emitted. (

**Right**) If the pulses are emitted from presynaptic neurons such that, taking into account the delays, they reach the post-synaptic neuron a at the same time (here, at $t=10\phantom{\rule{3.33333pt}{0ex}}\mathrm{m}\mathrm{s}$), the post-synaptic potentials evoked by the three pre-synaptic neurons sum up, causing the voltage threshold to be crossed and thus to the emission of an output spike (red color), while none is emitted from post-synaptic neuron e.

**Figure 7.**Detecting event-based motifs using spiking neurons with heterogeneous delays. (

**a**) Given a generic raster plot defined by a set of spikes occurring on specific neuron addresses and at specific times, one may consider that this information consists of the repeated occurrence of groups of precise spiking motifs. (

**b**) The generative model is defined by this set of motifs (here 4 of them) each defined by different weights at heterogeneous delays (red for excitatory, blue for inhibitory). (

**c**) Generalizing the core polychrony detection model (see Figure 6), one can define a layer of neurons that detect the identity and timing of these spiking motifs [196]. (

**d**) Knowing the results of this detection, one may for illustration purposes highlight them by different colors in the raster plots, showing that in this synthetic example, all spikes are now associated with a motif.

**Figure 8.**A miniature, event-based ATIS sensor. Contrary to a classical frame-based camera for which a full dense image representation is given at discrete, regularly spaced timings, the event-based camera provides events at the micro-second resolution. These are sparse, as they represent luminance increments or decrements (ON and OFF events, respectively). Figure courtesy of Sio-Hoi Ieng (Sorbonne Université/UPMC, Institut de la Vision).

**Figure 9.**Detecting visual motion in an event stream with heterogeneous delays. Extending the polychrony detection model to the spatial domain, Grimaldi and Perrinet [196] have applied a supervised learning scheme to the detection of motion. The models’ parameters are represented by different spatio-temporal kernels, and we show three examples as pairs of rows, one targeting ON spikes, the other OFF spikes, the first column representing the corresponding motion detected. When trained on a set of natural images, it shows the emergence of localized, oriented kernels organized in a so-called push–pull organization for which weights to an ON spike are negatively proportional to that to an OFF cell [72]. Global weight is globally decreasing from the lowest delay (

**right**) to less recent information (

**left**).

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## Share and Cite

**MDPI and ACS Style**

Grimaldi, A.; Gruel, A.; Besnainou, C.; Jérémie, J.-N.; Martinet, J.; Perrinet, L.U.
Precise Spiking Motifs in Neurobiological and Neuromorphic Data. *Brain Sci.* **2023**, *13*, 68.
https://doi.org/10.3390/brainsci13010068

**AMA Style**

Grimaldi A, Gruel A, Besnainou C, Jérémie J-N, Martinet J, Perrinet LU.
Precise Spiking Motifs in Neurobiological and Neuromorphic Data. *Brain Sciences*. 2023; 13(1):68.
https://doi.org/10.3390/brainsci13010068

**Chicago/Turabian Style**

Grimaldi, Antoine, Amélie Gruel, Camille Besnainou, Jean-Nicolas Jérémie, Jean Martinet, and Laurent U. Perrinet.
2023. "Precise Spiking Motifs in Neurobiological and Neuromorphic Data" *Brain Sciences* 13, no. 1: 68.
https://doi.org/10.3390/brainsci13010068