CN113643749A - Method and system for constructing model of grid cells - Google Patents

Abstract

The invention discloses a method and a system for constructing a model of grid cells, wherein the method comprises the following steps: s1, modeling the grid cell group by adopting a two-dimensional plane continuous attractor model; s2, constructing a neural plate consisting of grid cells in planar distribution; s3, encoding a path integration result in a specific direction by using the fringe discharge generated in the fringe cells; s4, discharging and projecting plasma cells of a plurality of stripe cell groups with the same spacing in different directions onto the same grid cell neural plate; and S5, generating a superposition discharge response by using the grid cells to form grid discharge. Has the advantages that: the invention provides that the striped cell discharge is used as the forward signal input of the grid cells, a plurality of flowing striped waves jointly drive the grid cells to encode the space, and a flowing two-dimensional discharge grid is formed, so that the information transmission and processing mode accords with the physiological basis.

Description

A method and system for model building of grid cells

technical field

The present invention relates to the technical field of neurobiological model construction, in particular, to a method and system for model construction of grid cells.

Background technique

The Moser couple found grid cells in the second layer of the olfactory cortex in the rat hippocampus, but unlike place cells and head-facing cells, grid cells were more dispersed and had weaker firing. As shown in Figure 4, the grid cells in different regions along the dorsal-ventral axis in the entorhinal cortex have different grid period scales. Hexagonal structure, 120 degree angle to each other.

In order to further verify the existence of grid cells, Hafting et al designed experiments to change the size of the test box. The grid cell network changed as the rats explored an unknown environment, but remained stable thereafter. Even with dramatic changes in this environment during animal movement, the grid cell network remains largely unchanged. Each grid cell does not have only one discharge field. When the rat moves to a certain position in space, the grid cell will fire. The firing activity of grid cells also did not depend on external cues. When rats were placed in a dark environment, the activity pattern of grid cells did not change as long as the new environment was not changed. Moreover, the grid field of grid cells can always cover all areas of the space environment. Biologists speculate that grid cells may have a path integration effect on the space.

Previous research models only used head-orientation cells and place cells to construct cognitive maps of spatial relationships at arbitrary scales. This discrete representation of the activities of individual head-orientation cells and place cells is not sufficient to support the navigation behavior from one location to another. . Grid cells provide the main information input for place cells and are path integrators inside the brain. The periodic discharge fields of which can cover the entire spatial environment as animals explore the environment, providing a basis for the formation of cognitive maps. Spatial measure. Therefore, the present invention provides a grid cell model construction method and system.

SUMMARY OF THE INVENTION

In view of the problems in the related art, the present invention proposes a grid cell model construction method and system to overcome the above-mentioned technical problems existing in the related art.

For this reason, the concrete technical scheme that the present invention adopts is as follows:

According to one aspect of the present invention, a method for constructing a grid cell model is provided, the method comprising the following steps:

S1. Use a two-dimensional plane continuous attractor model to model the grid cell population;

S2. Construct a neural plate composed of grid cells distributed in a plane;

S3. Use the streak discharges generated in the streak cells to encode the path integration results in a specific direction;

S4. Project the plasma cell discharges of a plurality of stripe cell families with the same spacing in different directions to the same grid cell neural plate;

S5, using grid cells to generate superimposed discharge responses to form grid discharges.

Further, the attractors in the attractor model in S1 represent grid cells, and the active state of the grid cells is related to the forward input of the upstream stripe cells.

Further, the activation input of each grid cell in S2 is obtained from the streak cells in all directions on the corresponding phase.

Further, the grid discharge fields of the grid cells have three spatial characteristic parameters of grid spacing, grid orientation and grid phase, wherein the grid spacing represents the distance between adjacent discharge fields, so The grid orientation represents the inclination angle of the connection line between the discharge field nodes relative to the external reference point, and the grid phase represents the displacement relative to the external reference point.

Further, the discharge kinetic model of the striped cells is as follows:

Among them, τ represents the time constant of the neuron, and the neuron transfer function f is a simple nonlinear rectification function. When x>0, f(x)=x, when x<0, f(x)=0, The firing state of neuron i at the current position is s _i , W _ij is the connection weight of neuron j to neuron i in the neural strip, ∑ _j W _ij s _j is the inhibitory recursion projected to neuron i input, B _i is the forward excitatory input from the upstream head toward the cell;

The connection weight matrix of the striped cells is:

表示沿θ_j方向的单位向量。in,

represents the unit vector along the θ _j direction.

According to another aspect of the present invention, a grid cell model building system is provided, the system includes a grid cell population modeling module, a neural plate building module, a path integral result encoding module, a discharge projection module and a grid discharge module ;

The grid cell group modeling module is used for modeling the grid cell group using a two-dimensional plane continuous attractor model;

The neural board building module is used to construct a neural board composed of grid cells distributed in a plane;

The path integration result encoding module is used to encode the path integration result of a specific direction by using the streak discharges generated in the streak cells;

The discharge projection module is used for projecting the plasma cell discharges of a plurality of stripe cell families with the same spacing in different directions to the same grid cell neural plate;

The grid discharge module is used for using grid cells to generate superimposed discharge responses to form grid discharges.

Further, the attractors in the attractor model represent grid cells, and the active state of the grid cells is related to the forward input of the upstream stripe cells.

Further, the activation input of each grid cell is obtained from streak cells in all directions on the corresponding phase.

Further, the grid discharge fields of the grid cells have three spatial characteristic parameters of grid spacing, grid orientation and grid phase, wherein the grid spacing represents the distance between adjacent discharge fields, so The grid orientation represents the inclination angle of the connection line between the discharge field nodes relative to the external reference point, and the grid phase represents the displacement relative to the external reference point.

The beneficial effects of the invention are as follows: the invention proposes that the discharge of the stripe cells is used as the forward signal input of the grid cells, and multiple flowing stripe waves jointly drive the grid cells to encode the space to form a flowing two-dimensional discharge grid. The method of information transmission and processing conforms to the physiological basis; in addition, in the present invention, when the rat moves, the discharge modal flow of the stripe cells is driven, so that the grid cells also generate flowing discharge grids, so that the path of the grid cells to the space can be realized. integration of information.

Description of drawings

In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the accompanying drawings required in the embodiments will be briefly introduced below. Obviously, the drawings in the following description are only some of the present invention. In the embodiments, for those of ordinary skill in the art, other drawings can also be obtained according to these drawings without any creative effort.

1 is a schematic flowchart of a method for constructing a grid cell model according to an embodiment of the present invention;

2 is a schematic diagram of grid characteristic parameters in a method for constructing a grid cell model according to an embodiment of the present invention;

3 is a schematic diagram of a grid cell model coding principle in a grid cell model construction method according to an embodiment of the present invention;

4 is a schematic diagram of a streak cell neural plate model in a method for constructing a grid cell model according to an embodiment of the present invention;

5 is a schematic diagram of a Mexican hat weight profile in a method for constructing a grid cell model according to an embodiment of the present invention;

FIG. 6 is a schematic diagram of the offset contour of stripe cell weights in a method for constructing a grid cell model according to an embodiment of the present invention.

Detailed ways

In order to further illustrate the various embodiments, the present invention provides accompanying drawings, which are part of the disclosure of the present invention, and are mainly used to illustrate the embodiments, and can be used in conjunction with the relevant descriptions in the specification to explain the operation principles of the embodiments. For these, those of ordinary skill in the art will understand other possible implementations and the advantages of the present invention. Components in the figures are not drawn to scale, and similar component symbols are generally used to represent similar components.

According to the embodiments of the present invention, a method and system for constructing a grid cell model are provided.

The present invention will now be further described with reference to the accompanying drawings and specific embodiments. As shown in Figures 1-6, according to an embodiment of the present invention, a method for constructing a grid cell model is provided, and the method includes the following steps:

S1. Use a two-dimensional plane continuous attractor model to model the grid cell population;

Wherein, each attractor in the attractor model represents a grid cell, and the activity state of the grid cell is related to the forward input of the upstream stripe cell.

S2. Construct a neural plate composed of grid cells distributed in a plane;

Wherein, each grid cell in S2 has to obtain activation input from the stripe cells in all directions on the corresponding phase, that is, superimpose the stripe discharge information.

S3. Use the streak discharges generated in the streak cells to encode the path integration result (ie relative displacement) in a specific direction;

According to the attractor model theory, the strip-shaped neural plate shown in Figure 4 is constructed in this embodiment, and there are synaptic connections between neurons in the length direction and no connection in the width direction. Each neural plate can fire in response to movement in a specific direction, which is determined by the preferential direction of its upstream head toward the cell. The periodic firing of neurons, driven by the velocity information encoded by the upstream head toward the cell, produces a flowing streak wave on the neural plate, which encodes the position of the rat based on the phase change of the streak wave. The environment for robots to explore is immeasurable, and the size of the neuron panel is limited, which inevitably involves the boundary problem of the attractor network. In order to solve this problem, the neurons on the left and right sides of the longitudinal direction of the strip neural plate are connected to form a ring-shaped continuous attractor model.

Since there is no connection between neurons in the width direction of the strip neural plate, the firing responses are independent of each other, and only the phase in the length direction is considered in the model calculation. In order to form the streak discharge characteristics, the synaptic connection weights between neurons in the length direction are set to be mutually inhibitory, and the velocity regulation signal generated by the head-facing cell is used as the forward input of the streak cell. The following firing rate-based firing kinetic model of streak cells can be constructed, and the firing kinetic model of the streak cells is as follows:

Among them, τ represents the time constant of the neuron, and the neuron transfer function f is a simple nonlinear rectification function. When x>0, f(x)=x, when x<0, f(x)=0, The firing state of neuron i at the current position is s _i , W _ij is the connection weight of neuron j to neuron i in the neural strip, ∑ _j W _ij s _j is the inhibitory recursion projected to neuron i input, B _i is the forward excitatory input from the upstream head toward the cell;

In order to realize the driving of the stripes by the forward excitation input from the head-facing cells, the neurons i and i+1 in the left and right adjacent phases are set to correspond to two types of upstream head-facing cells with opposite preferential directions, and the neurons are set to the peripheral nerves. The element's inhibitory weight matrix is offset in its preferred direction. When there is only inhibitory input between neurons, the neural plate spontaneously forms steady-state streak firing. When there is forward excitatory input, only the half of neurons with the same preferential direction get the excitatory input, and the other half of the neurons with the opposite preferential direction have zero input, so the original steady state is broken, and all neurons are affected by peripheral nerves. The weight matrix of the meta-inhibitory input will be shifted in the direction of velocity, thereby driving the fringe wave and velocity to produce coupled motion.

The connection weight matrix of the striped cells is:

表示沿θ_j方向的单位向量，如图5所示权值矩阵形成一个中间高两边低的墨西哥帽形状分布。设定每个神经元的投射出去的权值矩阵会沿优先方向偏移k个神经元位置，由于神经板上的相邻神经元具有相反的优先方向，如图6所示，神经细胞权值矩阵的中心位置为x-k,x+k。我们设定γ＝1.05×β,β＝3/λ²，λ是神经板上形成条纹的周期。当a＝1时，所有的连接都是抑制性的，局部周围抑制性连接通过相互作用，产生条纹细胞响应。in,

Represents a unit vector along the direction of θ _j , as shown in Figure 5, the weight matrix forms a Mexican hat-shaped distribution with high middle and low sides. Setting the projected weight matrix of each neuron will shift k neuron positions along the preferential direction. Since the adjacent neurons on the neuron board have opposite preferential directions, as shown in Figure 6, the neuron weights The center position of the matrix is xk, x+k. We set γ=1.05×β, β=3/λ ² , where λ is the period of streak formation on the neural plate. When a=1, all junctions are inhibitory, and local peripheral inhibitory junctions interact to generate streak cell responses.

The forward input on neuron i is:

表示沿神经元i所在的优先方向上的单位矢量，

为大鼠当前速度方向上的单位矢量。若系数k或a为0，则生成静态条纹。如果k和a都为非0，则大鼠的速度

与条纹神经板的动力学耦合，驱动形成流动的条纹波。k和a的乘积决定速度输入对条纹流驱动的强度。条纹波只有在输出权值偏移量k比较小的时候才能保持稳定的条纹图案。在k固定的基础上，则由a决定条纹细胞网络对速度响应的增益。如果

远远小于1时，输入的速度驱动不会破坏已形成的条纹形态。in,

represents the unit vector along the preferential direction in which neuron i is located,

is the unit vector in the direction of the current speed of the rat. If the coefficient k or a is 0, static fringes are generated. If both k and a are non-zero, the speed of the rat

Coupling with the dynamics of the striated neural plate drives the formation of flowing striated waves. The product of k and a determines how strongly the velocity input drives the streak flow. The fringe wave can maintain a stable fringe pattern only when the output weight offset k is relatively small. On the basis of fixed k, the gain of the streak cell network to the velocity response is determined by a. if

Much less than 1, the input velocity drive will not disrupt the formed fringe morphology.

S4. Project the plasma cell discharges of a plurality of stripe cell families with the same spacing in different directions to the same grid cell neural plate;

S5, using grid cells to generate superimposed discharge responses to form grid discharges.

As shown in FIG. 2 , the grid discharge field of the grid cell has three spatial characteristic parameters of grid spacing (λ), grid orientation (θ) and grid phase (Δx, Δy). The grid spacing represents the distance between adjacent discharge fields, the grid orientation represents the inclination angle of the connection line between the discharge field nodes relative to the external reference point, and the grid phase represents the displacement relative to the external reference point.

According to another embodiment of the present invention, a grid cell model building system is provided, which includes a grid cell population modeling module, a neural plate building module, a path integral result encoding module, a discharge projection module, and a grid discharge module. module;

The grid cell group modeling module is used for modeling the grid cell group using a two-dimensional plane continuous attractor model;

The neural board building module is used to construct a neural board composed of grid cells distributed in a plane;

The path integration result encoding module is used to encode the path integration result of a specific direction by using the streak discharges generated in the streak cells;

The discharge projection module is used for projecting the plasma cell discharges of a plurality of stripe cell families with the same spacing in different directions to the same grid cell neural plate;

The grid discharge module is used for using grid cells to generate superimposed discharge responses to form grid discharges.

Wherein, each attractor in the attractor model represents a grid cell, and the active state of the grid cell is related to the forward input of the upstream stripe cell; the activation input of each grid cell is derived from the corresponding obtained from streak cells in all directions on the phase; the grid discharge field of the grid cell has three spatial characteristic parameters of grid spacing, grid orientation and grid phase, wherein the grid spacing represents adjacent discharges The distance between the fields, the grid orientation represents the inclination angle of the connection line between the discharge field nodes relative to the external reference point, and the grid phase represents the displacement relative to the external reference point.

To sum up, with the help of the above technical solutions of the present invention, the present invention proposes that the discharge of the streak cells is used as the forward signal input of the grid cells, and multiple flowing streak waves jointly drive the grid cells to encode the space to form a flow. In addition, in the present invention, when the rat moves, the discharge modal flow of the stripe cells is driven, so that the grid cells also generate flowing discharge grids, so the realization of Grid cells integrate spatial path information.

The above descriptions are only preferred embodiments of the present invention, and are not intended to limit the present invention. Any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the present invention shall be included in the scope of the present invention. within the scope of protection.

Claims (9)

1. A method for constructing a model of a lattice cell, the method comprising the steps of:

s1, modeling the grid cell group by adopting a two-dimensional plane continuous attractor model;

s2, constructing a neural plate consisting of grid cells in planar distribution;

s3, encoding a path integration result in a specific direction by using the fringe discharge generated in the fringe cells;

s4, discharging and projecting plasma cells of a plurality of stripe cell groups with the same spacing in different directions onto the same grid cell neural plate;

and S5, generating a superposition discharge response by using the grid cells to form grid discharge.

2. The method of claim 1, wherein the attractors in the attractor model in S1 represent grid cells, and the activity status of the grid cells is associated with the forward input of the upstream striped cells.

3. The method of claim 1, wherein the activation input of each grid cell in S2 is obtained from striped cells in each direction on the corresponding phase.

4. The method of claim 1, wherein the grid discharge fields of the grid cells have three spatial characteristic parameters of grid spacing, grid orientation and grid phase, wherein the grid spacing represents a distance between adjacent discharge fields, the grid orientation represents a tilt angle of a connecting line between the nodes of the discharge fields relative to an external reference point, and the grid phase represents a displacement relative to the external reference point.

5. The method of claim 1, wherein the model of the grid cells is obtained by performing a discharge dynamics modeling of the striped cells as follows:

where τ represents the time constant of the neuron, and the neuron transfer function f is a simple nonlinear rectification function when x is>When 0, f (x) is x, when x is<When 0, f (x) is 0, the discharge state of the neuron i at the current position is s_i，W_ijIs the weight, Σ, of the connection from neuron j to neuron i in the strip neural plate_jW_ijs_jIs an inhibitory recursive input, B, projected onto neuron i_iIs a forward excitatory input from the upstream head towards the cell;

the connection weight matrix of the stripe cells is as follows:

wherein,

denotes the edge theta_jUnit vector of direction.

6. A grid cell model construction system for implementing the steps of the grid cell model construction method according to any one of claims 1 to 5, wherein the system comprises a grid cell group modeling module, a neural plate construction module, a path integration result coding module, a discharge projection module and a grid discharge module;

the grid cell group modeling module is used for modeling the grid cell group by adopting a two-dimensional plane continuous attractor model;

the neural plate construction module is used for constructing a neural plate consisting of grid cells distributed in a plane;

the path integration result coding module is used for coding a path integration result in a specific direction by using fringe discharge generated in fringe cells;

the discharge projection module is used for projecting plasma cells of a plurality of stripe cell families with different directions and the same interval to the same grid cell neural plate in a discharge manner;

the grid discharge module is used for generating superposition discharge response by utilizing grid cells to form grid discharge.

7. The system of claim 6, wherein the attractors in the attractor model represent grid cells, and the activity state of the grid cells is associated with the forward input of the upstream striped cells.

8. The system of claim 6, wherein the activation input for each of the grid cells is derived from striped cells in each direction on the corresponding phase.

9. The system of claim 6, wherein the grid discharge fields of the grid cells have three spatial characteristic parameters of grid spacing, grid orientation and grid phase, wherein the grid spacing represents a distance between adjacent discharge fields, the grid orientation represents a tilt angle of a line between nodes of the discharge fields relative to an external reference point, and the grid phase represents a displacement relative to the external reference point.

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