## Tesi etd-07032016-181443 |

Thesis type

Tesi di laurea specialistica

Author

DI NARDO, ENRICO

URN

etd-07032016-181443

Title

Memory retrieval in balanced neural networks with dynamical synapses

Struttura

FISICA

Corso di studi

SCIENZE FISICHE

Supervisors

**relatore**Prof. Rossi, Paolo

**relatore**Dott. Mongillo, Gianluigi

Parole chiave

- attractor
- memory
- neural nteworks
- short-term plasticity
- synaptic dinamics

Data inizio appello

21/07/2016;

Consultabilità

Completa

Riassunto analitico

Neuronal recordings from animals performing memory tasks have revealed

a phenomenon known as selective persistent activity: the presentation of

stimuli to be remembered increase the level of activity of selective (i.e., depending

on the specific stimulus) neuronal populations which then persist

long after stimulus offset. Such persistent activity is considered to be a major

neuronal correlate of short-term memory.

A time-honored theoretical account of persistent activity is the attrac-

tor hypothesis, originated from the first studies of spin-glass inspired neural

network models [1]. According to this hypothesis, the neurons within the

selective populations have strong recurrent excitatory couplings. The resulting

positive feedback, together with the the nonlinearity of the single-cell

response function, allows such populations to have two stable states of activity:

one corresponding to the spontaneous activity, the other (at higher

rate) corresponding to the mnemonic retention of the stimulus.

Since the neuron response function is typically S-shaped, and the recurrent

input is a linear function of the activity, the stable states generically

occur outside the dynamic range of the neuron function, that is near extremely

low or high activity levels. This constitutes a major inconsistency of

the model, as experimental data show that the activity level at which cortical

neurons operate is much lower than saturation.

It is well established that synapses display activity-dependent modulations

of their efficacy, like short-term depression(STD): whenever a neuron

stays active, the intensity of the signals transmitted through its synapses is

gradually reduced[2]. In the thesis we examined the possibility to obtain

bistability far from saturation by making the recurrent excitatory inputs a

non-linear function of the activity through STD.

The study have been carried out within the framework of balanced networks

[3] as it captures essential features of cortical networks activity while remaining

analytically tractable.

The first chapter, after a short summary of the relevant neurophysiological

background, is dedicated to review the standard balanced network model

of binary neurons and its general properties.

In the second chapter, it is illustrated a possible extension of balanced

networks to the attractor framework: reinforcing suitably the excitatory couplings

between the neurons of certain populations, the system can have multiple

stable attractors corresponding to memory states. This allows us to

illustrate the issue of unrealistically high level of activity in memory states.

The remaining chapters contain the original part of the work.

In the third chapter, the phenomenological model which mimics STD is

introduced. As a first step, it is considered a balanced network endowed

with STD in absence of memory-supporting reinforcement of the couplings.

A mean-field description have been derived to characterize the stationary

states of the network; this has been done by neglecting the time delayed

autocorrelations of the neuron’s activities, which have been approximated as

Markov process to obtain a system of equations in closed form. Numerical

simulations of the network show that, despite the approximation, the meanfield

theory gives an excellent quantitative prediction for the system’s order

parameters.

The content of the fourth chapter is the implementation of the STD

synaptic dynamics into the memory model introduced in chapter two and

the extension of the mean-field theory to the scenario with multiple memory

states. The theoretical analysis of the model shows that it’s indeed possible

to produce stable states with biologically plausible levels of activity, far from

saturation, and network simulations confirm the result. Moreover, the network

operates in a regime such that temporal fluctuations and spatial inhomogeneities

of the neuron’s activity are generated by the dynamics (without

the addition of any source of external noise), reproducing the experimentally

observed statistics of neural activity.

a phenomenon known as selective persistent activity: the presentation of

stimuli to be remembered increase the level of activity of selective (i.e., depending

on the specific stimulus) neuronal populations which then persist

long after stimulus offset. Such persistent activity is considered to be a major

neuronal correlate of short-term memory.

A time-honored theoretical account of persistent activity is the attrac-

tor hypothesis, originated from the first studies of spin-glass inspired neural

network models [1]. According to this hypothesis, the neurons within the

selective populations have strong recurrent excitatory couplings. The resulting

positive feedback, together with the the nonlinearity of the single-cell

response function, allows such populations to have two stable states of activity:

one corresponding to the spontaneous activity, the other (at higher

rate) corresponding to the mnemonic retention of the stimulus.

Since the neuron response function is typically S-shaped, and the recurrent

input is a linear function of the activity, the stable states generically

occur outside the dynamic range of the neuron function, that is near extremely

low or high activity levels. This constitutes a major inconsistency of

the model, as experimental data show that the activity level at which cortical

neurons operate is much lower than saturation.

It is well established that synapses display activity-dependent modulations

of their efficacy, like short-term depression(STD): whenever a neuron

stays active, the intensity of the signals transmitted through its synapses is

gradually reduced[2]. In the thesis we examined the possibility to obtain

bistability far from saturation by making the recurrent excitatory inputs a

non-linear function of the activity through STD.

The study have been carried out within the framework of balanced networks

[3] as it captures essential features of cortical networks activity while remaining

analytically tractable.

The first chapter, after a short summary of the relevant neurophysiological

background, is dedicated to review the standard balanced network model

of binary neurons and its general properties.

In the second chapter, it is illustrated a possible extension of balanced

networks to the attractor framework: reinforcing suitably the excitatory couplings

between the neurons of certain populations, the system can have multiple

stable attractors corresponding to memory states. This allows us to

illustrate the issue of unrealistically high level of activity in memory states.

The remaining chapters contain the original part of the work.

In the third chapter, the phenomenological model which mimics STD is

introduced. As a first step, it is considered a balanced network endowed

with STD in absence of memory-supporting reinforcement of the couplings.

A mean-field description have been derived to characterize the stationary

states of the network; this has been done by neglecting the time delayed

autocorrelations of the neuron’s activities, which have been approximated as

Markov process to obtain a system of equations in closed form. Numerical

simulations of the network show that, despite the approximation, the meanfield

theory gives an excellent quantitative prediction for the system’s order

parameters.

The content of the fourth chapter is the implementation of the STD

synaptic dynamics into the memory model introduced in chapter two and

the extension of the mean-field theory to the scenario with multiple memory

states. The theoretical analysis of the model shows that it’s indeed possible

to produce stable states with biologically plausible levels of activity, far from

saturation, and network simulations confirm the result. Moreover, the network

operates in a regime such that temporal fluctuations and spatial inhomogeneities

of the neuron’s activity are generated by the dynamics (without

the addition of any source of external noise), reproducing the experimentally

observed statistics of neural activity.

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