Reservoir learning device, signal generation device, method for generating trained model, and signal generation method

Abstract

According to the present invention, there is achieved a learning device suitable for the learning of a time series over a long period or a complex time series. A reservoir learning device (1) comprises: a reservoir (20) that includes a plurality of neuron elements (21); an oscillation unit (50) that inputs a plurality of oscillation waveform signals into the reservoir; an output layer (30) that generates an output signal on the basis of the output from the reservoir; a learning unit (40) that adjusts a parameter; and a feedback unit (60) that inputs the output signal into the reservoir as feedback.

Description

Reservoir learning device, signal generation device, trained model generation method, and signal generation method

[0001] The present invention relates to a reservoir calculation system.

[0002] In recent years, reservoir computing systems, which use reservoir networks with random recurrent connections, have attracted attention and are used for time-series learning with low computational cost.

[0003] In a reservoir computing system, input signals to the input layer excite units in the reservoir, and output signals are generated by linearly combining these units. It is common to adjust only the weights in the linear combination to reduce the error between the output signal and the teacher signal, without changing the recurrent weights in the reservoir. Therefore, reservoir computing systems have the advantage of significantly lower computational cost compared to recurrent neural networks, which adjust the weights of the entire network.

[0004] Non-Patent Document 1 discloses a technique that enables timing learning by inputting the outputs of multiple oscillators into a reservoir. This reservoir system is reported to be robust against noise or node loss.

[0005] International Publication WO2020 / 013069

[0006] P. Vincent-Lamarre, G. Lajoie, and J.-P. Thivierge, “Driving reservoir models with oscillations: a solution to the extreme structural sensitivity of chaotic networks”, Journal of Computational Neuroscience, vol.41, pp.305-322, 2016

[0007] A reservoir is a neural network that can memorize the time series information of an input signal as its internal state. It was thought that inputting an external signal unrelated to the input signal to be learned into the reservoir could inhibit learning.

[0008] In the configuration described in Non-Patent Document 1, the output of an oscillator unrelated to the input signal to be learned is input to a reservoir. Although the configuration described in Non-Patent Document 1 is capable of timing learning to a certain extent, it is not suitable for learning long-term time series and complex time series, such as chaotic time series.

[0009] An object of one aspect of the present invention is to realize a learning device suitable for learning a time series that spans a long period of time or a complex time series.

[0010] A reservoir learning device according to one embodiment of the present invention comprises a reservoir including a plurality of interconnected neuron elements, an input layer that inputs an input signal to the reservoir, a vibration unit that inputs a plurality of vibration waveform signals to the reservoir, an output layer that generates an output signal based on the output from the reservoir, a learning unit that adjusts parameters used in the output layer, and a feedback unit that inputs the output signal as feedback to the reservoir.

[0011] A signal generating device according to one embodiment of the present invention comprises a reservoir including a plurality of interconnected neuron elements, an input layer that inputs an input signal to the reservoir, an oscillation unit that inputs a plurality of oscillation waveform signals to the reservoir, an output layer that generates an output signal based on the output from the reservoir and learned parameters, and a feedback unit that inputs the output signal to the reservoir as feedback.

[0012] A method for generating a trained model according to one aspect of the present invention includes an input step of inputting an input signal to a reservoir including a plurality of interconnected neuron elements, a vibration input step of inputting a plurality of vibration waveform signals to the reservoir, an output step of generating an output signal based on the output from the reservoir, a learning step of adjusting parameters used in the output step, and a feedback step of inputting the output signal as feedback to the reservoir.

[0013] A signal generation method according to one aspect of the present invention includes an input step of inputting an input signal to a reservoir including a plurality of interconnected neuron elements, a vibration input step of inputting a plurality of vibration waveform signals to the reservoir, an output step of generating an output signal based on the output from the reservoir and learned parameters, and a feedback step of inputting the output signal to the reservoir as feedback.

[0014] According to one aspect of the present invention, it is possible to realize a learning device that is suitable for learning a time series that spans a long period of time or a complex time series.

[0015] FIG. 1 is a model diagram showing the configuration of a reservoir learning device according to one embodiment of the present invention; FIG. 2 is a diagram showing the processing flow of the reservoir learning device in the learning phase; FIG. 3 is a model diagram showing the configuration of a reservoir learning device according to one embodiment of the present invention; FIG. 4 is a diagram showing the output signal of a trained reservoir learning device, the state of the reservoir, and the state of the oscillator; FIG. 5 is a diagram comparing intervals and performance for various reservoir learning devices; FIG. 6 is a diagram showing timing capacity for various reservoir learning devices; FIG. 7 is a diagram showing the relationship between the number of oscillators Nos and timing capacity for a reservoir learning device; FIG. 8 is a diagram showing the output signal of a comparative example reservoir learning device without an oscillator unit that has trained a chaotic time series; FIG. 9 is a diagram showing the output signal of a reservoir learning device according to one embodiment that has trained a chaotic time series; FIG. 10 is a diagram depicting the output signal of a reservoir learning device according to one embodiment that has trained a chaotic time series in three-dimensional space; FIG. 11 is a diagram showing a Lorenz map of the output signal of a reservoir learning device according to one embodiment that has trained a chaotic time series; FIG. 11 is a diagram showing the output signal of a reservoir learning device according to one embodiment that has trained a chaotic time series. FIG. 10 is a diagram showing a Lorenz map of the output signal from the reservoir learning device of one embodiment that has learned a chaotic time series.

[0016] [Embodiment 1] Fig. 1 is a model diagram showing the configuration of a reservoir learning device 1 according to this embodiment. The reservoir learning device 1 includes an input layer 10, a reservoir 20, an output layer 30, a learning unit 40, a vibration unit 50, and a feedback unit 60. The reservoir learning device 1 is a reservoir calculation system that uses the reservoir 20. The reservoir learning device 1 learns the relationship between an input signal s(t) as an input and a target signal d(t) as an output.

[0017] The input layer 10 acquires an input signal s(t) that serves as a trigger from the outside and outputs it to the reservoir 20 .

[0018] The reservoir 20 includes a plurality of interconnected neuron elements 21. The connections between the plurality of neuron elements 21 are random.

[0019] The output layer 30 generates an output signal y(t) based on the output from the reservoir 20 and readout weights (parameters). The output layer 30 outputs the output signal y(t) to an external device, the learning unit 40, and the feedback unit 60.

[0020] The learning unit 40 acquires the output signal y(t) and the target signal d(t). Based on the output signal y(t) and the target signal d(t), the learning unit 40 adjusts the readout weights, which are parameters used in the process of generating the output signal y(t) from the output of the reservoir 20 in the output layer 30.

[0021] The vibration unit 50 includes a plurality of vibrators 51. The plurality of vibrators 51 generate a plurality of vibration waveform signals o(t) having waveforms that are different from one another. The plurality of vibrators 51 output the plurality of vibration waveform signals o(t) to the reservoir 20. Here, the plurality of vibrators 51 generate a plurality of vibration waveform signals o(t) having frequencies that are different from one another. For example, the plurality of vibration waveform signals o(t) are sine waves having frequencies that are different from one another. The vibration unit 50 may randomly determine the frequency of the vibration waveform signal o(t) generated by each vibrator 51. The vibration unit 50 may output a plurality of vibration waveform signals o(t) (e.g., sine waves) having frequencies that are random and different from one another to the reservoir 20.

[0022] The feedback unit 60 receives the output signal y(t) and outputs the output signal y(t) to the reservoir 20 as feedback.

[0023] (State of the reservoir 20) The state of the reservoir 20 when the reservoir 20 is composed of N neuron elements 21 will be specifically described. The state of the N neuron elements 21 at time t is represented by a vector x(t). x(t)=(x １ , x ２ , ..., x Ｎ ) Ｔ x Ｎ is a scalar representing the state value of the Nth neuron element 21. T represents the transpose matrix. Each neuron element 21 has one state value. The reservoir 20 updates the states x(t+Δt) of multiple neuron elements 21 after a time step Δt according to the following equation: Here, τ represents the time constant of the neuron element 21. W is the reservoir internal weight matrix. Wos is the oscillator input weight matrix. Win is the input signal input weight matrix. Wfb is the feedback weight matrix. o(t) is a vector representing the vibration waveform signal at time t. s(t) is a scalar representing the input signal at time t. y(t) is a vector representing the output signal at time t. r(t) is a vector representing the activation state of each neuron element 21 at time t. The initial state value of each neuron element 21 is randomly determined from the range [-1, 1]. Here, the time step Δt is defined as 1 ms.

[0024] The activation function of the neuron element 21 is a hyperbolic tangent. Each component of r(t) is the value of the activation function at each component of x(t). r(t) is the output from each neuron element 21 to each neuron element 21 inside the reservoir, including itself.

[0025] The reservoir internal weight matrix W is a weight matrix with N rows and N columns, and each component has a non-zero value with a connection probability p. That is, whether or not each neuron element 21 connects to another neuron element 21 is determined with a connection probability p. Different neuron elements 21 have different connection strengths (weights). Here, the average of the components of the reservoir internal weight matrix W is 0, and each component has a standard deviation g / (pN). １／２ where g is the gain (scaling coefficient) of the reservoir internal weight. A weighted linear sum of the outputs r(t) of multiple neuron elements 21 using the reservoir internal weight matrix W is input to each neuron element 21.

[0026] The vibration unit 50 includes Nos vibrators 51. The vector representing the Nos vibration waveform signals is o(t)=(sin(2πf １ t+φ １ ), sin(2πf ２ t+φ ２ ),...,sin(2πf Ｎｏｓ t+φ Ｎｏｓ )) Ｔ where f ｉis a frequency randomly drawn from a uniform distribution in the interval [fmin, fmax], and φ ｉ is a random initial phase. ｉ and φ ｉ is a fixed value and is not changed during learning or prediction after learning.

[0027] The oscillator input weight matrix Wos is a weight matrix with N rows and Nos columns. The average of the elements of the oscillator input weight matrix Wos is 0, and each element has a standard deviation g ｏｓ / (Nos) １／２ It is drawn from a normal distribution of g ｏｓ is the gain of the oscillator input weight. A weighted linear sum of multiple vibration waveform signals o(t) using the oscillator input weight matrix Wos is input to each neuron element 21. That is, the vibration waveform signal of each oscillator 51 is input to all neuron elements 21.

[0028] The input signal s(t) is a scalar. Here, the input signal s(t) is a single pulse. This input signal s(t) resets the state of the reservoir 20 and acts to suppress the initial value dependency of the reservoir 20. The input signal s(t) is 1 from time -50 ms to 0 ms, and 0 at other times.

[0029] The input signal input weight matrix Win is a weight matrix with 1 row and N columns, that is, a weight vector with N elements. The average of the elements of the input signal input weight matrix Win is 0, and each element has a standard deviation g ｉｎ It is drawn from a normal distribution of g ｉｎ is the gain of the input signal input weight. The input signal s(t) is input to each neuron element 21 with the weight of the input signal input weight matrix Win.

[0030] The output layer 30 generates an output signal y(t)=(y １ , y ２ , ..., y Ｎｒｏ ) Ｔ where y(t) is given by: Here, Wro(t) is a readout weight matrix with Nro rows and N columns. Nro is the number of variables in the target signal d(t) to be learned. Nro varies depending on the task being learned. For example, when learning time-series changes in the X, Y, and Z coordinates, such as the Lorenz system, Nro = 3. The reservoir 20 outputs the activation states r(t) of multiple neuron elements 21 to the output layer 30. The output layer 30 outputs the weighted linear sum of the activation states r(t) using the readout weight matrix Wro(t) as the output signal y(t).

[0031] The feedback weight matrix Wfb is a weight matrix with N rows and Nro columns. The average of the elements of the feedback weight matrix Wfb is 0, and each element has a standard deviation g ｆｂ / (Nro) １／２ It is drawn from a normal distribution of g ｆｂ is the gain of the feedback weight.

[0032] The learning unit 40 adjusts the readout weight matrix Wro(t) by online learning, specifically by the recursive least squares method. The initial value of Wro(t) is a zero matrix. The learning unit 40 adjusts the readout weight matrix Wro(t) so as to minimize the error e(t) between the output signal y(t) and the target signal d(t). At time t, Wro(t) is updated using the following equation: Here, P(t) is a matrix with N rows and N columns, and is updated by the following formula: The initial value of P(t) is (1 / α)I, where I is the identity matrix and α is a constant.

[0033] (Learning Phase) Figure 2 is a diagram showing the processing flow of the reservoir learning device 1 in the learning phase. The reservoir learning device 1 performs learning using training data. The training data includes multiple data sets of input signals s(t) and corresponding target signals d(t). At time t, the reservoir learning device 1 performs the following processing.

[0034] The input layer 10 inputs an input signal s(t) to the reservoir 20 (S1).

[0035] The vibration unit 50 inputs a plurality of vibration waveform signals o(t) to the reservoir 20 (S2).

[0036] The output layer 30 generates an output signal y(t) based on the output from the reservoir 20 and the readout weights (S3).

[0037] The feedback unit 60 feeds back the output signal y(t) to the reservoir 20 (S4).

[0038] The reservoir 20 updates the states x(t) of the multiple neuron elements 21 based on the input (S5).

[0039] The learning section 40 adjusts the readout weight based on the output signal y(t) and the target signal d(t) (S6).

[0040] The reservoir learning device 1 advances time t by Δt and repeats steps S1 to S6. The reservoir learning device 1 performs the above process on multiple data sets of training data to obtain trained readout weights. In this way, the reservoir learning device 1 generates a trained model including an input layer 10, a reservoir 20, an output layer 30, a vibration unit 50, and a feedback unit 60. The trained model includes trained readout weights.

[0041] (Prediction Phase) The trained reservoir learning device 1 (signal generating device) predicts and generates an output signal y(t) based on an input signal s(t) input from the outside. In the prediction phase, there is no learning step S6. The trained reservoir learning device 1 performs the following processes.

[0042] The input layer 10 inputs an input signal s(t) to the reservoir 20 (S1).

[0043] The vibration unit 50 inputs a plurality of vibration waveform signals o(t) to the reservoir 20 (S2). The initial phases of the plurality of vibration waveform signals o(t) are the same as those during learning.

[0044] The output layer 30 generates an output signal y(t) based on the output from the reservoir 20 and the learned readout weights (S3).

[0045] The feedback unit 60 feeds back the output signal y(t) to the reservoir 20 (S4).

[0046] The reservoir 20 updates the states x(t) of the multiple neuron elements 21 based on the input (S5).

[0047] Note that the signal generating device that predicts and generates the output signal y(t) from the input signal s(t) only needs to have learned readout weights and does not need to have the learning unit 40. When learning and prediction are performed by an edge device, the signal generating device has the learning unit 40.

[0048] [Embodiment 2] Another embodiment of the present invention will be described below. For ease of explanation, components having the same functions as those described in the above embodiment will be denoted by the same reference numerals, and their description will not be repeated. In this embodiment, the method of generating a vibration waveform signal differs from that of the above embodiment.

[0049] 3 is a model diagram showing the configuration of a reservoir learning device 1a according to this embodiment. The reservoir learning device 1a includes an input layer 10, a reservoir 20, an output layer 30, a learning unit 40, a vibration unit 50a, and a feedback unit 60.

[0050] The input layer 10 acquires an input signal s(t) that serves as a trigger from the outside and outputs it to the reservoir 20 and the vibration unit 50a.

[0051] The vibration unit 50a includes a plurality of oscillators 51a. Each of the plurality of oscillators 51a is an independent recurrent neural network. The plurality of oscillators 51a generates a plurality of vibration waveform signals o(t) having waveforms that are different from one another and repeatedly increase and decrease. The plurality of oscillators 51a outputs the plurality of vibration waveform signals o(t) to the reservoir 20. Here, the plurality of oscillators 51a generate a plurality of vibration waveform signals o(t) having frequencies that are different from one another. In the plurality of recurrent neural networks, internal parameters may be determined randomly. The plurality of oscillators 51a output a plurality of vibration waveform signals o(t) having frequencies that are different from one another and that are random to the reservoir 20.

[0052] For example, the vibrating unit 50a includes Nos oscillators 51a. Each oscillator 51a is a random neural network including Nnr units (neuron elements). The states of the Nnr units of the i-th oscillator 51a at time t are expressed as a vector x ｉ (t) x ｉ (t) = (x ｉ１ , x ｉ２ , ..., x ｉＮｎｒ ) Ｔ x ｉＮｎｒ is a scalar representing the state value of the Nnrth unit. Each unit has one state value. The oscillator 51a calculates the state x of multiple units. ｉ (t) is updated according to the following formula: Here, τnr represents the time constant of the unit. ｎｒ is the oscillator internal weight matrix. ｎｒ is the oscillator input signal weight matrix. ｉ (t) is a vector representing the activation state of each unit at time t. The initial state value of each unit is randomly determined within the range of [-1, 1]. W ｎｒ and Win ｎｒ differs for each vibrator 51a.

[0053] Oscillator internal weight matrix W ｎｒ is a weight matrix with Nnr rows and Nnr columns, and each element has a non-zero value with a joint probability p. Here, the weight matrix W ｎｒ The mean of the components is 0, and each component has a standard deviation g ｎｒ / (pNnr) １／２ are drawn from a normal distribution where g ｎｒ is the gain of the internal weight of the oscillator.

[0054] Oscillator input signal weight matrix Win ｎｒ is a weight matrix with 1 row and Nnr columns, that is, a weight vector with Nnr elements. ｎｒ The mean of the components is 0, and each component has a standard deviation g ｉｎ It is drawn from a normal distribution of g ｉｎ is the gain of the oscillator input signal weight. The input signal s(t) is the oscillator input signal weight matrix Winｎｒ are input to each unit with weights of

[0055] Each oscillator 51a outputs the state value of one unit randomly selected from each recurrent neural network as a vibration waveform signal o ｉ (t) to the reservoir 20. When the vibration waveform signal of a certain oscillator 51a does not change over time and becomes a fixed value, or when it becomes almost the same as the vibration waveform signal of another oscillator 51a, the oscillator internal weight matrix W ｎｒ It should be noted that the size Nnr of the vibrator 51a may be smaller than the size N of the reservoir 20 as long as the waveforms of the plurality of vibration waveform signals o(t) are different from one another.

[0056] The operations of the reservoir 20, the output layer 30, the learning unit 40, and the feedback unit 60 are the same as those in the first embodiment. ｎｒ and the oscillator input signal weight matrix Win ｎｒ is fixed and does not change with learning.

[0057] The reservoir learning device 1a does not need to generate a sine wave signal; instead, it can generate a vibration waveform signal using a recurrent neural network. Therefore, the arithmetic processing required by the reservoir learning device 1 can be performed using product-sum operations (weighted linear sums). For example, the state of each neuron element 21 and unit may be represented by a pulse signal with a length corresponding to the state value. Using this pulse signal, a product-sum operation can be performed in an analog circuit using known technology (see Patent Document 1). Therefore, the reservoir learning device 1a does not need a separate circuit for generating a sine wave signal; instead, the circuit that performs the calculations for the reservoir 20 can be used to generate the vibration waveform signal. Therefore, the reservoir learning device 1a is advantageous when implemented using analog circuits in edge devices, etc.

[0058] (Modification) Each transducer 51a may output a weighted linear sum of state values ​​of a plurality of units as an output (vibration waveform signal) of the transducer 51a, like the output of the reservoir 20.

[0059] Alternatively, the vibration unit 50a may output state values ​​of multiple units in one vibrator 51a as multiple vibration waveform signals. Also, the vibration unit 50a may output weighted linear sums of state values ​​of multiple units in one vibrator 51a using different weighting matrices as multiple vibration waveform signals. In these cases, the vibration unit 50a may be configured to have a single vibrator 51a.

[0060] [Learning Example] The results of learning a time series prediction task using the reservoir learning devices 1 and 1a of the first and second embodiments will be described. The time step Δt is set to 1 ms. However, adjustment of the learning unit 40 is performed once every two steps. The start time of the simulation is set to -250 ms, and learning by the learning unit 40 continues until the end of the task (the end of each signal in the training data). The training data contains 10 sets of data (training is performed 10 times). Unless otherwise specified, the parameters are set to the following values. Number of oscillators Nos = 10. Gain of reservoir internal weight g = 1.5. Gain of oscillator input weight g ｏｓ = 0.5. Gain of input signal input weight g ｉｎ = 5. Gain of feedback weight g ｆｂ = 3. Joint probability p = 0.1. Time constant τ = 10 ms. Constant α = 1 for the initial value of the recursive least squares method.

[0061] (Learning Timing Time Series) In the timing time series prediction task, a one-dimensional time series was used as the target signal (Nro = 1). The target signal had a single Gaussian pulse with a peak magnitude of 1 and a standard deviation of 30 ms at a specific time a predetermined interval after the end of the input signal pulse (time 0 ms). Outside of the Gaussian pulse, the target signal had a constant value of 0.2. The task duration was the interval + 150 ms. In the timing time series prediction task, the reservoir size N = 400, and the frequencies of the multiple oscillators were set to a minimum of 0.1 Hz and a maximum of 1 Hz. Performance was evaluated by varying the interval from 1 s to 120 s.

[0062] FIG. 4 shows the output signal of the trained reservoir learning device 1, the state of the reservoir 20, and the state of the oscillator 51. The horizontal axis represents time. The output in the upper part of FIG. 4 represents the output signal of the trained reservoir learning device 1 to which an input signal has been input. The reservoir activity in the middle part of FIG. 4 represents the state values ​​of 10 neuron elements 21 randomly selected from the reservoir 20. The sine waves in the lower part of FIG. 4 represent the vibration waveform signals of 10 oscillators 51. In FIG. 4, the results of 10 trials in which the initial value of the reservoir 20 was changed are superimposed. The activity of the reservoir 20, which was random depending on the initial value before 0 ms, is stabilized to the same trajectory each time by the input signal. In this example (interval = 5 s), the reservoir learning device 1 is able to output an output signal with a peak 5 s after the input signal pulse.

[0063] It is generally known that reservoir activity becomes chaotic when the gain g of the reservoir's internal weight is greater than 1.0. Feedback to the reservoir is thought to contribute to short-term time series learning, but it also destabilizes reservoir activity. Therefore, feedback to the reservoir is detrimental to long-term time series learning. On the other hand, oscillatory waveform signals unrelated to the input signal may also inhibit learning.

[0064] However, in reality, in the reservoir learning device 1, even though the gain g of the reservoir internal weights is as large as 1.5, the activity of the reservoir 20 is stabilized and not chaotic due to the input of the vibration waveform signal to the reservoir 20, as shown in Figure 4. Furthermore, by providing feedback to the reservoir 20, an extremely high time-series learning ability can be obtained, as shown below. Note that the gain g of the reservoir internal weights may be greater than 1.0. Also, the gain g of the reservoir internal weights may be less than 1.0.

[0065] Figure 5 is a graph comparing intervals and performance for various reservoir learning devices. The horizontal axis is interval, and the vertical axis is performance R. ２ Performance R ２ is the square of the correlation coefficient between y(t) and d(t) for the task period from 1 ms. ２The closer to 1, the better the performance. R ２ The average values ​​are shown in FIG.

[0066] In Figure 5, the results obtained by the reservoir learning device 1 of embodiment 1 are shown as ODRCw / FB (oscillator-driven reservoir computing with feedback). As comparative examples, results obtained by Innate, reBASICS, and ODRCw / oFB are also shown. Innate is reservoir computing that adjusts the recurrent weights in the reservoir. The number of neuron elements in the reservoir is set to 400. Innate requires a high computational load to adjust the recurrent weights in the reservoir. reBASICS is reservoir computing with M reservoir modules, each with Nm neuron elements. In this example, Nm = 100 and M = 400. Therefore, the total number of neuron elements is 40,000, so reBASICS requires a high computational load. ODRCw / oFB (without ODRC feedback) is the reservoir learning device 1 without the feedback unit 60.

[0067] In the reservoir learning device 1, even if the interval is 120 seconds, ２ The time constant τ of the neuron element 21 was 10 ms, but the reservoir learning device 1 can appropriately learn target signals over a very long period of time. Furthermore, the reservoir learning device 1 can appropriately learn target signals over a very long period of time compared to other systems such as Innate, reBASICS, and ODRCw / oFB.

[0068] FIG. 6 shows the timing capacity for various reservoir learning devices. Here, the R ２The area under the curve is defined as the timing capacity. The timing capacity of the reservoir learning device 1 is significantly larger than that of Innate and ODRCw / oFB. Furthermore, the timing capacity of the reservoir learning device 1 is larger than that of reBASICS, which has 100 times the total number of neuron elements and a high computational load. In other words, the reservoir learning device 1 can efficiently learn and more appropriately predict long-term time series.

[0069] FIG. 7 shows the relationship between the number of oscillators Nos and timing capacity for the reservoir learning device 1. The horizontal axis represents the number of oscillators Nos. The vertical axis represents timing capacity. Compared to Nos = 1, a significantly larger timing capacity can be obtained when Nos ≥ 2. The timing capacity peaks at Nos = 5 and remains almost constant above that number. The reservoir learning device 1 may be configured with at least two oscillators 51, and preferably, five or more oscillators 51. The same can be said for the reservoir learning device 1a. Combining multiple vibration waveform signals with different waveforms (different frequencies) input to the reservoir 20 generates longer-period swells, which is thought to contribute to long-term learning.

[0070] (Learning of Chaotic Time Series) In the chaotic time series prediction task, the target signal is a Lorenz system, which is a three-dimensional time series (Nro = 3). The target signal (x, y, z) changes according to the following equation: Here, p = 10, r = 28, b = 8 / 3, and x(0) = 0.1, y(0) = 0, and z(0) = 0. The magnitude was normalized and the time scale was adjusted to obtain a target signal d(t) for 20 s. Therefore, the task duration was 20 s. For the chaotic time series prediction task, the reservoir size N = 3000, and the frequencies of the multiple oscillators were set in the range of 10 Hz minimum to 25 Hz maximum.

[0071] FIG. 8 is a diagram showing the output signal of a comparative reservoir learning device that has learned a chaotic time series and does not have an oscillator. The horizontal axis is time. The vertical axis is the output signal (x, y, z). The learning period (task period) is from 0 s to 20 s, and the period after 20 s is an unlearned period (post-task period). The comparative reservoir learning device has a feedback unit but does not have an oscillator. In the comparative reservoir learning device, the output signal deviates from the target signal even during the learning period before 20 s, and the motion of the Lorenz system cannot be predicted.

[0072] Although not shown, we also performed training on a reservoir learning device (ODRCw / oFB) without a feedback section. The output signal of the ODRCw / oFB closely matched the target signal during the training period before 20 s. However, during the untrained period after 20 s, the ODRCw / oFB generated a random output signal that did not resemble the Lorenz system.

[0073] FIG. 9 is a diagram showing the output signal from the reservoir learning device 1 of embodiment 1 that has learned a chaotic time series. The horizontal axis represents time, and the vertical axis represents the output signal (x, y, z). In the reservoir learning device 1 of embodiment 1, the output signal accurately matches the target signal during the learning period up to 20 s. Furthermore, during the unlearned period after 20 s, although there is a discrepancy between the output signal and the target signal, an output signal similar to the change pattern of the Lorenz system was obtained.

[0074] 10 is a three-dimensional diagram of the output signals from the reservoir learning device 1 of embodiment 1, which has learned a chaotic time series. In the figure, the output signals from the learning period before 20 s are shown in black, and the output signals from the unlearned period after 20 s are shown in gray. It can be seen that the reservoir learning device 1 produces a typical Lorenz system output.

[0075] 11 is a diagram showing Lorenz maps of output signals from the reservoir learning device 1 of embodiment 1 that has learned a chaotic time series. The vertical axis represents the relative maximum value of z, and the horizontal axis represents the relative maximum value of z prior to that point. The tent-shaped distribution characteristic of the Lorenz system is well reproduced not only for the output signals from the learning period before 20 s, but also for the output signals from the unlearned period after 20 s.

[0076] FIG. 12 shows the output signal of the reservoir learning device 1a of the second embodiment, which has learned a chaotic time series. The horizontal axis represents time, and the vertical axis represents the output signal (x, y, z). In the reservoir learning device 1a of the second embodiment, the output signal also accurately matches the target signal during the learning period up to 20 s. Furthermore, during the unlearned period after 20 s, although there is a discrepancy between the output signal and the target signal, an output signal similar to the change pattern of the Lorenz system was obtained.

[0077] 13 shows Lorenz maps of the output signals from the reservoir learning device 1a of the second embodiment, which has learned a chaotic time series. The vertical axis represents the relative maximum value of z, and the horizontal axis represents the relative maximum value of z before that point. The tent-shaped distribution characteristic of the Lorenz system is well reproduced not only for the output signals from the learning period before 20 s, but also for the output signals from the unlearned period after 20 s.

[0078] As described above, the reservoir learning devices 1 and 1a of the first and second embodiments are capable of learning complex chaotic time series and making highly accurate predictions. Furthermore, they are capable of generalizing and learning chaotic time series, and generating output signals that predict the continuation of the chaotic time series even during unlearned periods. The reservoir learning devices 1 and 1a feed back output signals to the reservoir 20 and input multiple vibration waveform signals to the reservoir 20. This allows for excellent learning capabilities that can handle complex time series such as chaotic time series while suppressing instability of the reservoir 20.

[0079] The time series learning capabilities of the reservoir learning devices 1 and 1a have been described above using timing time series prediction tasks and chaos time series prediction tasks as examples. However, the reservoir learning devices 1 and 1a can also be used to learn any combination of input signal and target signal, and to generate an output signal that predicts the target signal. The input signal is not limited to a pulse signal, and may be any signal to be learned.

[0080] [Summary] The reservoir learning device according to aspect 1 of the present invention comprises a reservoir including a plurality of interconnected neuron elements, an input layer that inputs an input signal to the reservoir, a vibration unit that inputs a plurality of vibration waveform signals to the reservoir, an output layer that generates an output signal based on the output from the reservoir, a learning unit that adjusts parameters used in the output layer, and a feedback unit that inputs the output signal as feedback to the reservoir.

[0081] A reservoir learning device according to a second aspect of the present invention may be configured in the above-mentioned first aspect such that the vibration unit inputs the plurality of vibration waveform signals having different frequencies to the reservoir.

[0082] A reservoir learning device according to a third aspect of the present invention may be configured in the first aspect as described above, wherein the vibration unit inputs the plurality of vibration waveform signals having random frequencies that are different from one another to the reservoir.

[0083] A reservoir learning device according to Aspect 4 of the present invention may be configured in any one of Aspects 1 to 3 above, wherein the vibration unit has a recurrent neural network that generates the vibration waveform signal.

[0084] A reservoir learning device according to Aspect 5 of the present invention may be configured in the above-mentioned Aspect 4, wherein the size of the recurrent neural network is smaller than the size of the reservoir, and the internal weights of the recurrent neural network are fixed.

[0085] A reservoir learning device according to a sixth aspect of the present invention is the reservoir learning device of the fourth or fifth aspect, wherein the input layer inputs the input signal to the recurrent neural network.

[0086] A signal generating device according to a seventh aspect of the present invention comprises a reservoir including a plurality of interconnected neuron elements, an input layer that inputs an input signal to the reservoir, a vibration unit that inputs a plurality of vibration waveform signals to the reservoir, an output layer that generates an output signal based on the output from the reservoir and learned parameters, and a feedback unit that inputs the output signal to the reservoir as feedback.

[0087] A method for generating a trained model according to aspect 8 of the present invention includes an input step of inputting an input signal to a reservoir including a plurality of interconnected neuron elements, a vibration input step of inputting a plurality of vibration waveform signals to the reservoir, an output step of generating an output signal based on the output from the reservoir, a learning step of adjusting parameters used in the output step, and a feedback step of inputting the output signal as feedback to the reservoir.

[0088] A signal generation method according to aspect 9 of the present invention is a method including an input step of inputting an input signal to a reservoir including a plurality of interconnected neuron elements, a vibration input step of inputting a plurality of vibration waveform signals to the reservoir, an output step of generating an output signal based on the output from the reservoir and learned parameters, and a feedback step of inputting the output signal to the reservoir as feedback.

[0089] [Example of software implementation] The functions of the reservoir learning device 1, 1a (hereinafter referred to as the "device") can be realized by a program that causes a computer to function as the device, and a program that causes a computer to function as each control block of the device.

[0090] In this case, the device includes a computer having at least one control device (e.g., a processor) and at least one storage device (e.g., a memory) as hardware for executing the program. The functions described in each of the above embodiments are realized by executing the program using the control device and storage device.

[0091] The program may be non-transitory and may be recorded on one or more computer-readable recording media. The recording media may or may not be included in the device. In the latter case, the program may be supplied to the device via any wired or wireless transmission medium.

[0092] Furthermore, some or all of the functions of the control blocks can be realized by logic circuits. For example, an integrated circuit in which a logic circuit that functions as each of the control blocks is formed is also included in the scope of the present invention. In addition, the functions of the control blocks can also be realized by, for example, a quantum computer.

[0093] The present invention is not limited to the above-described embodiments, and various modifications are possible within the scope of the claims. Embodiments obtained by appropriately combining the technical means disclosed in different embodiments are also included in the technical scope of the present invention.

[0094] 1, 1a Reservoir learning device 10 Input layer 20 Reservoir 21 Neuron element 30 Output layer 40 Learning unit 50, 50a Oscillator unit 51, 51a Oscillator 60 Feedback unit

Claims

1. A reservoir learning device comprising: a reservoir including a plurality of interconnected neuron elements; an input layer that inputs an input signal to the reservoir; an oscillation unit that inputs a plurality of oscillation waveform signals to the reservoir; an output layer that generates an output signal based on the output from the reservoir; a learning unit that adjusts parameters used in the output layer; and a feedback unit that inputs the output signal to the reservoir as feedback.

2. The reservoir learning device according to claim 1, wherein the vibration unit inputs the plurality of vibration waveform signals having mutually different frequencies to the reservoir.

3. The reservoir learning device according to claim 1, wherein the vibration unit inputs the plurality of vibration waveform signals having random frequencies that are different from one another to the reservoir.

4. The reservoir learning device of claim 1, wherein the vibration unit includes a recurrent neural network that generates the vibration waveform signal.

5. The reservoir learning device of claim 4, wherein the size of the recurrent neural network is smaller than the size of the reservoir, and the internal weights of the recurrent neural network are fixed.

6. The reservoir learning device according to claim 4 or 5, wherein the input layer inputs the input signal to the recurrent neural network.

7. A signal generating device comprising: a reservoir including a plurality of interconnected neuron elements; an input layer that inputs an input signal to the reservoir; an oscillation unit that inputs a plurality of oscillation waveform signals to the reservoir; an output layer that generates an output signal based on the output from the reservoir and learned parameters; and a feedback unit that inputs the output signal to the reservoir as feedback.

8. A method for generating a trained model, comprising: an input step of inputting an input signal to a reservoir including a plurality of interconnected neuron elements; a vibration input step of inputting a plurality of vibration waveform signals to the reservoir; an output step of generating an output signal based on the output from the reservoir; a learning step of adjusting parameters used in the output step; and a feedback step of inputting the output signal as feedback to the reservoir.

9. A signal generation method comprising: an input step of inputting an input signal to a reservoir including a plurality of interconnected neuron elements; a vibration input step of inputting a plurality of vibration waveform signals to the reservoir; an output step of generating an output signal based on the output from the reservoir and learned parameters; and a feedback step of inputting the output signal to the reservoir as feedback.

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