CN113900795A - Impulse neural network mapping method - Google Patents
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Abstract
The invention discloses a pulse neural network mapping method, which comprises an improved ant colony algorithm under a multi-to-one topological mapping scene, wherein indexes of neurons are given, node indexes deployed by the neurons are obtained through the mapping algorithm, and R is increased in probability compared with the traditional ant colony algorithmj(t) represents the node r at the t-th cyclejI.e. more towards deploying neurons on nodes with high occupancy, deploying different neurons on the same node directly avoids traffic between them. The invention has the advantages that: the ant colony mapping algorithm is improved, and in addition, the application scene of the proposed algorithm is more the situation that a plurality of neurons can be deployed on a single node.
Description
Technical Field
The invention relates to the technical field of pulse neural network mapping, in particular to a pulse neural network mapping method.
Background
An important problem faced by computers adopting a neuromorphic computing architecture for simulation is how to map a complex neural network into a node network, namely, a mapping problem between a logical network and a physical network. The scale of the logic network, namely the problem network and the task network, especially when the simulation of the biological neural network is needed, is huge, and is reflected in two aspects: firstly, the number of neurons is large, and secondly, the connection between neurons is complex. In addition, the logical network has various structures for different application scenarios, and it is impossible to design the topology of the physical network specifically for a certain logical network. Meanwhile, the capacity of the nodes of the physical network is limited, the number of neurons that can be supported is limited, and the capacity of the routing unit is limited. Thus, how to map the logical network with the physical network becomes a key step in system design.
Disclosure of Invention
In order to solve the various problems, the invention provides an impulse neural network mapping method of an improved ant colony mapping algorithm.
In order to solve the technical problems, the technical scheme provided by the invention is as follows: an impulse neural network mapping method comprises an ant colony algorithm improved under a many-to-one topological mapping scene, wherein the ant colony algorithm improved under the many-to-one topological mapping scene defines the mapping algorithm as follows:
nodeidx＝ω(neuronidx)
that is, the index of a given neuron is subjected to a mapping algorithm to obtain the index of the node deployed by the neuron. The optimization target is the average hop count, and the objective function is as follows:
wherein c (v) is all forwarding times required by a pulse sent by the neuron v, and it should be noted that since the communication mode is selected as multicast, if a plurality of target nodes are in the same forwarding direction, only one forwarding is required, and p (v) refers to a proportion of pulses generated by the neuron v in all neuron pulses, and in a random case, the proportion of all neurons can be considered to be the same.
Initialization, heuristic information is defined as follows:
i.e. neurons viMapping to node rjThe heuristic information of (2) is determined by the importance degree of the neuron and the center degree of the node, wherein the importance degree import (i) of the neuron is the number of the neuron connected with the neuron.
importance(i)＝Fanin(i)+Fanout(i)
The degree of the center of a node is determined by its manhattan distance from the remaining nodes.
The central degree of the node is the sum of the Manhattan distances from the node to other nodes, the value reflects the communication capacity of the node, the smaller the Manhattan distance sum is, the higher the central degree of the node is, the stronger the communication capacity of the node is, therefore, under the condition of no other factors, the more neurons are deployed on the node with the higher central degree, the more neurons are connected with the output of the neurons, the higher the communication pressure of the neurons is, the more the neurons are placed on the node with the higher central degree, therefore, the heuristic information is in direct proportion to the importance degree of the neurons and in inverse proportion to the central degree, and the higher the possibility that the neurons with the higher communication pressure are deployed on the node with the higher communication capacity is made.
Constructing a solution, in the traditional ant colony algorithm, in the t iteration, the kth ant leads the neuron viMapping to node rjThe probability of (c) is:
in the above formula, τi，j(t) is at the t-th cycle, Rj(t) is node r at the t-th cyclejOccupancy rate of, neurons viMapping to node rjThe normalized pheromone concentration, here the decision probability mentioned above is improved,
compared with the traditional ant colony algorithm, the method increases R in probabilityj(t) represents the node r at the t-th cyclejThat is, neurons are more likely to be deployed on nodes with high occupancy, and the deployment of different neurons on the same node directly avoids the communication traffic between them, and when the occupancy is 0, Rj(t) is set the same as deploying one neuron.
Alpha and beta are weights for weighing the alpha and the beta, the greater the value of alpha, the greater the possibility that ants select a path with high pheromone concentration, namely the greater the possibility of selecting a path tried before, so that the randomness of searching is reduced, and the greater the value of beta, the more easily ant colony selects a local shorter path, can accelerate the convergence speed, but is more easily trapped in local optimum.
all is a node set which can be deployed by neurons at present, because the capacity of the node is limited, part of the nodes are full along with the deployment process of the neurons, and only the nodes which are not full can be selected.
The pheromone update rule is as follows:
wherein p is attenuation factor, the pheromone left by ant will be attenuated with time under natural state, q is amplification factor, if the neuron v is connectediMapping to node rjIn the minimum cost mapping mode of all ants in the iteration, the corresponding pheromone is amplified by q times.
Compared with the prior art, the invention has the advantages that: the improved ant colony mapping algorithm is provided, and in addition, it is worth mentioning that the application scenario of the algorithm provided herein is more that a plurality of neurons can be deployed on a single node, and the algorithm is different from the VOPD task that only one node can be deployed, and has a wider application space.
Drawings
Fig. 1 is a schematic diagram of the improved ant colony algorithm mapping cost of the present invention as a function of the number of iterations.
Fig. 2 is a schematic diagram comparing a conventional ant colony algorithm with an improved ant colony algorithm according to the present invention.
FIG. 3 is a diagram of the ant colony algorithm and CNDE mapping cost as a function of iteration number in accordance with the present invention.
Fig. 4 is a diagram of VOPD communication cores of the present invention.
Detailed Description
The present invention will be described in further detail with reference to the accompanying drawings and examples.
With reference to fig. 1 to 4, an impulse neural network mapping method includes an ant colony algorithm improved in a many-to-one topological mapping scenario, where the ant colony algorithm improved in the many-to-one topological mapping scenario defines a mapping algorithm as follows:
nodeidx＝ω(neuronidx)
that is, the index of a given neuron is subjected to a mapping algorithm to obtain the index of the node deployed by the neuron. The optimization target is the average hop count, and the objective function is as follows:
wherein c (v) is all forwarding times required by a pulse sent by the neuron v, and it should be noted that since the communication mode is selected as multicast, if a plurality of target nodes are in the same forwarding direction, only one forwarding is required, and p (v) refers to a proportion of pulses generated by the neuron v in all neuron pulses, and in a random case, the proportion of all neurons can be considered to be the same.
Initialization, heuristic information is defined as follows:
i.e. neurons viMapping to node rjIs determined by the importance degree of the neuron and the center degree of the node, wherein the importance degree of the neuronDegree import (i) is the number of neurons connected to it.
importance(i)＝Fanin(i)+Fanout(i)
The degree of the center of a node is determined by its manhattan distance from the remaining nodes.
The central degree of the node is the sum of the Manhattan distances from the node to other nodes, the value reflects the communication capacity of the node, the smaller the Manhattan distance sum is, the higher the central degree of the node is, the stronger the communication capacity of the node is, therefore, under the condition of no other factors, the more neurons are deployed on the node with the higher central degree, the more neurons are connected with the output of the neurons, the higher the communication pressure of the neurons is, the more the neurons are placed on the node with the higher central degree, therefore, the heuristic information is in direct proportion to the importance degree of the neurons and in inverse proportion to the central degree, and the higher the possibility that the neurons with the higher communication pressure are deployed on the node with the higher communication capacity is made.
Constructing a solution, in the traditional ant colony algorithm, in the t iteration, the kth ant leads the neuron viMapping to node rjThe probability of (c) is:
in the above formula, τi，j(t) is at the t-th cycle, Rj(t) is node r at the t-th cyclejOccupancy rate of, neurons viMapping to node rjThe normalized pheromone concentration, here the decision probability mentioned above is improved,
compared with the traditional ant colony algorithm, the method increases R in probabilityj(t) generationTable node r at t-th cyclejThat is, neurons are more likely to be deployed on nodes with high occupancy, and the deployment of different neurons on the same node directly avoids the communication traffic between them, and when the occupancy is 0, Rj(t) is set the same as deploying one neuron.
Alpha and beta are weights for weighing the alpha and the beta, the greater the value of alpha, the greater the possibility that ants select a path with high pheromone concentration, namely the greater the possibility of selecting a path tried before, so that the randomness of searching is reduced, and the greater the value of beta, the more easily ant colony selects a local shorter path, can accelerate the convergence speed, but is more easily trapped in local optimum.
all is a node set which can be deployed by neurons at present, because the capacity of the node is limited, part of the nodes are full along with the deployment process of the neurons, and only the nodes which are not full can be selected.
The pheromone update rule is as follows:
wherein p is attenuation factor, the pheromone left by ant will be attenuated with time under natural state, q is amplification factor, if the neuron v is connectediMapping to node rjIn the minimum cost mapping mode of all ants in the iteration, the corresponding pheromone is amplified by q times.
Based on the contents of the above formula and the like, the ant colony algorithm-based mapping algorithm can be obtained as follows:
firstly, calculating the importance degree of the neurons and the node center degree according to the connection condition of the neurons and the quantity information of the nodes, and further obtaining the mapping heuristic information.
Second, pheromone information is initialized.
Thirdly, in each iteration, all ants generate a mapping mode according to the probability determined by the current pheromone and the heuristic confidence, then the cost of the mapping modes is calculated, and the minimum cost mapping mode of the iteration is selected.
And then, updating the pheromone according to the minimum cost mapping mode and the inherent attenuation of the iteration.
And terminating the iteration if the maximum iteration number is reached or the cost meets the requirement, and otherwise, repeating the iteration process.
In the biological nervous system, connections between neurons are very complex and disordered, but the connections between neurons have a fundamental characteristic that the probability of connection between neurons decreases exponentially as the distance between them increases, and the probability that a connection exists between neurons at a longer distance is lower.
Therefore, based on this basic fact, a connection matrix CM is randomly generated, and if CM [ i ] [ j ] ═ 1 in the connection matrix, it indicates that one connection from neuron i to neuron j exists in the neural network.
(1) Logical network generation algorithm
Firstly, randomly generating coordinate information of neurons in a three-dimensional space, wherein the probability of connection between two neurons is as follows:
in the formula, D (i, j) represents the euclidean distance between the neuron i and the neuron j, λ is a hyperparameter, and the larger λ is, the larger the average connection number of the neurons is. In algorithm 4.2B (1, p) represents a 0-1 distribution.
(2) Hyper-parameter settings
A plurality of hyper-parameters need to be set in simulation, including:
random connection matrix parameter λ: λ determines the number of connections of the neuron, the smaller λ the smaller the number of connections of the neuron.
Ant colony algorithm related parameters: p is 0.5, q is 2, α is 1, β is 1, and ant _ num is 100.
(3) Contrast group setting
Because the connections of the neural system adopted by the simulation are random, the contrast group adopted by the simulation is random mapping, namely, each neuron is randomly mapped to a certain node, if the node is not fully deployed, the node is deployed on the node, otherwise, the node is reselected until a node which is not fully deployed is found.
The above mapping algorithm is simulated by using different parameters, and the simulation result is shown in the following table:
TABLE 4.1 Ant colony Algorithm simulation results
When the number of simulated neurons is 1000, the average number of connections per neuron is 12.1 when λ is 0.02, and the average number of connections per neuron is 100.6 when λ is 0.1.
From the simulation results, it can be seen that:
(1) the ant colony algorithm can bring significant improvement relative to random mapping, wherein the performance improvement of the simulation number 5 reaches 64.20%.
(2) Comparing simulation 1 and simulation 2, it can be seen that as the number of connections of neurons increases, the performance improvement brought by the ant colony algorithm decreases, because more complex connections are more difficult to mitigate their hop count through reasonable mapping.
(3) Comparing simulation numbers 3 and 5, when the node capacity increases, the average hop count of the system does not significantly decrease in the random mapping, but based on the ant colony algorithm and the improvements proposed herein, the benefit from the node capacity increase can be utilized, and the average hop count significantly decreases.
(4) Comparing simulation numbers 1 and 5 with simulation numbers 2 and 6, under the condition of the same node capacity and the same neuron number, although the traditional ant colony algorithm can obtain certain performance benefit, theoretically, when the node number is increased, the performance of the system cannot be reduced, the traditional ant colony algorithm is partially optimized in iteration, and the performance benefit brought by node increase cannot be fully utilized. In contrast, the improved ant colony algorithm is more able to exploit this benefit, with an average hop count of 8 × 8 nodes being similar to 4 × 4 nodes.
For simulation number 1, fig. 1 shows that in the iteration process, the cost corresponding to the mapping selection of each ant varies with the number of iterations.
Fig. 2 shows a graph of the minimum hop count and the average hop count of the conventional ant colony algorithm and the improved ant colony algorithm as a function of the number of iterations, and it can be seen from the graph that, on the one hand, the final convergence result of the improved ant colony algorithm is significantly better than that of the conventional ant colony algorithm, and on the other hand, the convergence rate is also faster than that of the improved ant colony algorithm.
The CNDE algorithm is reproduced and simulated comparison is carried out. Fig. 3 is a graph showing the variation of the cost with the number of iterations obtained by using the CNDE algorithm with the same parameter settings as those of the above simulation No. 1.
Comparing the CNDE algorithm with the mapping algorithm provided herein, it can be found that the number of CNDE algorithm iterations is much greater than that of the ant colony algorithm, and the final convergence result is also more advantageous for the ant colony algorithm provided herein.
In summary, the ant colony algorithm-based mapping algorithm provided herein can provide significant performance improvement for the optimization index of the average hop count, and meets the expected design requirements.
VOPD is a classic problem map in the topological mapping problem, and the communication map thereof is shown in the following figure, which has 16 cores, and the application scenario of analogy text is 16 neurons. Different from the simulation in the foregoing, the pulse transmission frequency of the neurons is different here, i.e., the information transmission amount of the communication core is different.
The total energy consumption of the system is optimized by using the proposed CNDE algorithm, and the omitted part with smaller occupation ratio mainly analyzes two parts of link energy consumption and router energy consumption.
E＝EL+ER
The link energy consumption is determined by the distance of all connections in the system and the number of bits transmitted correspondingly.
Router energy consumption is determined by the amount of information sent and received by the nodes.
The problem is very similar to the problem in background, and only the transmission frequency of the neurons is different, so that the cost function can be migrated to the problem by modifying the ant colony algorithm-based mapping algorithm provided by the invention.
Compared with the CNDE algorithm, the CNDE algorithm adopts the same problem background and the same iteration jump-out condition, and after multiple times of simulation averaging, the CNDE algorithm is improved by 50.71% relative to random mapping performance and 56.44% relative to random mapping performance, and the performance is obviously improved.
In addition, it is worth mentioning that the application scenario of the algorithm proposed herein is more that a plurality of neurons can be deployed on a single node, and is different from the situation that only one single node of the VOPD task is deployed, and has a wider application space.
The present invention and its embodiments have been described above, and the description is not intended to be limiting, and the drawings are only one embodiment of the present invention, and the actual structure is not limited thereto. In summary, those skilled in the art should appreciate that they can readily use the disclosed conception and specific embodiments as a basis for designing or modifying other structures for carrying out the same purposes of the present invention without departing from the spirit and scope of the invention as defined by the appended claims.
Claims (4)
1. An impulse neural network mapping method comprises an ant colony algorithm improved under a many-to-one topological mapping scene, and is characterized in that: the ant colony algorithm definition mapping algorithm improved under the scene of many-to-one topological mapping is as follows:
nodeidx＝ω(neuronidx)
that is, the index of a given neuron is subjected to a mapping algorithm to obtain the index of the node deployed by the neuron. The optimization target is the average hop count, and the objective function is as follows:
wherein c (v) is all forwarding times required by a pulse sent by the neuron v, and it should be noted that since the communication mode is selected as multicast, if a plurality of target nodes are in the same forwarding direction, only one forwarding is required, and p (v) refers to a proportion of pulses generated by the neuron v in all neuron pulses, and in a random case, the proportion of all neurons can be considered to be the same.
2. The impulse neural network mapping method of claim 1, wherein: initialization, heuristic information is defined as follows:
i.e. neurons viMapping to node rjThe heuristic information of (2) is determined by the importance degree of the neuron and the center degree of the node, wherein the importance degree import (i) of the neuron is the number of the neuron connected with the neuron.
importance(i)＝Fanin(i)+Fanout(i)
The degree of the center of a node is determined by its manhattan distance from the remaining nodes.
The central degree of the node is the sum of the Manhattan distances from the node to other nodes, the value reflects the communication capacity of the node, the smaller the Manhattan distance sum is, the higher the central degree of the node is, the stronger the communication capacity of the node is, therefore, under the condition of no other factors, the more neurons are deployed on the node with the higher central degree, the more neurons are connected with the output of the neurons, the higher the communication pressure of the neurons is, the more the neurons are placed on the node with the higher central degree, therefore, the heuristic information is in direct proportion to the importance degree of the neurons and in inverse proportion to the central degree, and the higher the possibility that the neurons with the higher communication pressure are deployed on the node with the higher communication capacity is made.
3. The impulse neural network mapping method of claim 1, wherein: constructing a solution, in the traditional ant colony algorithm, in the t iteration, the kth ant leads the neuron viMapping to node rjThe probability of (c) is:
in the above formula, τi，j(t) is at the t-th cycle, Rj(t) is node r at the t-th cyclejOccupancy rate of, neurons viMapping to node rjThe normalized pheromone concentration, here the decision probability mentioned above is improved,
compared with the traditional ant colony algorithm, the method increases R in probabilityj(t) represents the node r at the t-th cyclejThat is, neurons are more likely to be deployed on nodes with high occupancy, and the deployment of different neurons on the same node directly avoids the communication traffic between them, and when the occupancy is 0, Rj(t) is set the same as deploying one neuron.
Alpha and beta are weights for weighing the alpha and the beta, the greater the value of alpha, the greater the possibility that ants select a path with high pheromone concentration, namely the greater the possibility of selecting a path tried before, so that the randomness of searching is reduced, and the greater the value of beta, the more easily ant colony selects a local shorter path, can accelerate the convergence speed, but is more easily trapped in local optimum.
all is a node set which can be deployed by neurons at present, because the capacity of the node is limited, part of the nodes are full along with the deployment process of the neurons, and only the nodes which are not full can be selected.
4. The impulse neural network mapping method of claim 1, wherein: the pheromone update rule is as follows:
wherein p is attenuation factor, the pheromone left by ant will be attenuated with time under natural state, q is amplification factor, if the neuron v is connectediMapping to node rjIn the minimum cost mapping mode of all ants in the iteration, the corresponding pheromone is amplified by q times.
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| CN102508935A (en) * | 2011-09-22 | 2012-06-20 | 南京大学 | On-chip network mapping method based on ant-colony chaos genetic algorithm |
| US20160247062A1 (en) * | 2015-02-19 | 2016-08-25 | International Business Machines Corporation | Mapping of algorithms to neurosynaptic hardware |
| CN108418623A (en) * | 2018-03-21 | 2018-08-17 | 大连大学 | A kind of satellite QoS routing algorithms based on improvement ant group algorithm |
| CN111882065A (en) * | 2020-08-03 | 2020-11-03 | 中国人民解放军国防科技大学 | Method, system, and medium for mapping a spiking neural network to a brain-like computing platform |
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