Time scale-plasticity learning rule for dendritic neuron model toachieve online time-invariant sequence processing
Farbod Nosrat Nezami1 , Viktoria Zemliak1 , Pascal Nieters1 , Gordon Pipa1 ,1. Institute of Cognitive Science, University of Osnabrück, Osnabrück, Germany.

Summary. Time scale variability is a common phenomenon of naturally occurring time series.
Sometimes events occur within the same sequence but with stochastically different timing between
events, ex. the speed at which different syllables of a word are uttered. The exact timing of theoccurrences of the event, and thus of the entire sequence, can also expand or shrink, a phenomenon
known as time warping. The following abstract offers a model inspired by the dendritic trees of real
neurons, which utilizes local homeostatic regulation of the length of the plateau potentials in dendritic
compartments to adapt to changes in the time scales of the input sequence.

Neuromorphic computing is a rapidly developing field that seeks to design processors inspired by thehuman brain while improving energy efficiency and optimization, aiming to surpass theoretical limits on
computational power with current architectures that arise from their processing power being constrainedby physical properties such as size and heat dissipation behavior [2]. Pure analog or mixed analog anddigital circuits have become the preferred choice for neuromorphic hardware design due to their superiorenergy consumption profile and ability to simulate complex dynamical systems, such as spiking neurons[7]. This presents a problem, however, since most real-world time series and sequences - the computationof which is an essential requirement of fields ranging from active sensing to spoken language [3] - occur ontime scales far slower than the timescales of the dynamics of the analog electrical components proposed inmany neuromorphic hardware designs [3]. Events within these time series can also occur on varying timescales, a phenomenon known as time warping (ex. the varying speed at which each syllable of a word like”com-pu-ter” is uttered). These varying time scales necessitate the development of a method to handle
such sequences within neuromorphic systems. In this study, we propose a novel model of the neuron
utilizing dendritic computation with local timescale plasticity as a potential solution to this problem oftime variances in naturally occurring time series and sequences.
The biological brain and its neurons can handle processing time-varied sequences, but the precise
mechanism of this process remains a mystery. However, it has been shown that by generating isolated
plateau potentials, dendritic compartments can enable the neuron to possess a short-term memory allowing it to process the input sequence within the sum of its total plateau lengths [4]. There is also evidence
from biology that neurons can modulate the length of the plateau potentials generated at each dendritic
compartment based on the number of NMDA channels available and the concentration of glutamate at
the excitation site [6]. Dendrites have demonstrated considerable computational power, even on the levelof a single neuron, and recent research has shown that dendrites with plateau potentials can provide
partial time-invariant sequence detection [4]. Nevertheless, most current models of neurons in artificial
or spiking neural networks disregard the function of dendrites due to their complexity [5, 1], a trend ourmodel rethinks in the search for a timescale variability adaptation mechanism.
We propose a self-regulating model of dendritic neurons to detect time-varied sequences, for instancedetecting the word ”com-pu-ter” despite the varied speed of utterance of its syllables. In our proposedmodel, the length of the plateau potentials in each dendritic compartment represents the local memory
trace of that compartment. In other words, at each compartment, the plateau potentials enable thecompartment to remember the symbols already detected in the previous compartments. In this model, if
there is no feedback to a compartment, meaning there is no activity in the direct adjacent compartment
earlier in the chain, the compartment assumes that no sequence could be detected due to its short plateau
length. Therefore, the length of the plateau in the compartment will increase. This increase will allow
for a more extended local memory and a longer look-ahead time. However, if there is an increase in
the received feedback, the compartment assumes a higher rate of false positive activity and shortens its
plateau length. The neuron will therefore self-regulate its dendritic compartments’ timescales through thishomeostatic and local time-plasticity mechanism in order to match the timescales of the input sequence,at which point it reaches an equilibrium state (see figure 1 for a visual overview).

Plateau length
is correctAA

com putercom

ter pucom

Forward propagating
Plateau potentials

ter Feedback

Should elongate
Plateu lengths

Comp. A

Plateau length
is too shortA

Plateau length
is too longCo Inpu
mpt
art sequmeents nceFeedbackBshould shorten
plateu length

Equilibrium

BComp. B

Cshould elongate
plateu length
Depolarization byadjacant activity

Should shorten
Plateu lengths

CTime (ms)membranePotential

BComp. C (Soma)

Plataeu potentail

C

Plateau length
Depolarization

Time (ms)

Simplified
neuron model

Figure 1: The proposed model of the local homeostatic timescale plasticity based on example input
sequence {”com”, ”pu”, ”ter”} showing the self-regulatory mechanism of the neuron and its dendritic
compartments
Handling varying timescales in input sequence data is a key problem that computation systems must beable to address. The biological brain may handle this via dendritic plasticity. Our proposed neuromorphic
model incorporates this plasticity with the goal of giving it the same robustness to timescale varianceseen in the biological brain. Neurons using our described local timescale-plasticity mechanism would
eventually learn the timescale statistics of input sequences, allowing our model to offer a simple selfregulating mechanism for handling timescales in sequence processing problems. And, since our model
only utilizes the idea of self-regulation through local feedback, it can be easily implemented in various
continuous-time systems, from software implementation to the electrical design of neuromorphic hardware,
making it a possible solution to the timescale invariance problem in neuromorphic hardware at large.

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[2]

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[3]

Herbert Jaeger and Francky Catthoor. Timescales: the choreography of classical and unconventionalcomputing. Number: arXiv:2301.00893 arXiv:2301.00893 [cs]. Jan. 2023. doi: 10 . 48550 / arXiv .
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[4]

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[6]

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[7]

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