Deep neural network system and method based on infinite impulse response layer

Abstract

The present invention relates to a deep neural network system based on an infinite impulse response layer, and more specifically, as a deep neural network system, the invention is characterized by comprising at least one IIR layer, which is a layer that learns using IIR filter coefficients, which are filter coefficients of an infinite impulse response (IIR) filter among digital filters, as weights. According to the deep neural network system and method based on an infinite impulse response layer proposed in the present invention, by including at least one IIR layer which is a layer for learning IIR filter coefficients, which are filter coefficients of an IIR filter among digital filters, superior performance can be achieved compared to existing convolutional layer-based deep neural networks through an IIR layer that can model more complex functions with fewer parameters than existing convolutional layers interpreted as layers for learning FIR filter coefficients. In addition, according to the deep neural network system and method based on an infinite impulse response layer proposed in the present invention, both the forward function and the backward function of the IIR layer are presented to enable learning and inference of the IIR layer, thereby allowing convolutional layers in various deep neural network systems to be replaced with the proposed IIR layer. Furthermore, since a part or the whole of the deep neural network can be easily replaced with an IIR layer for learning in numerous fields using deep learning, it is easy to apply to various industries. Furthermore, according to the deep neural network system and method based on an infinite impulse response layer proposed in the present invention, the final performance of the deep neural network system can be improved by applying an IIR layer, which can model more complex functions with fewer parameters, to the deep neural network.

Description

Technology Field

[0001] The present invention relates to a deep neural network system and method, and more specifically, to a deep neural network system and method based on an infinite impulse response layer. Background Technology

[0002] The content described in this section merely provides background information regarding an embodiment of the present invention and does not constitute prior art.

[0004] Deep neural networks, a type of machine learning technology, are utilized in various fields. Learning using these deep neural networks is called deep learning, and deep learning is currently the most actively developing technology. Recently, it has become so widely used that it is difficult to find a field where deep learning is not utilized.

[0006] Deep learning is being used in actual applications such as image and video processing, speech processing, and Natural Language Processing (NLP). According to IMARC, the global deep learning market reached $17.2 billion in 2022 and is expected to reach $113 billion by 2028, growing at an annual rate of 38.2% (IMARC, “Deep Learning Market: Global Industry Trends, Share, Size, Growth, Opportunity and Forecast 2023-2028”, February 2023).

[0008] Deep neural networks are composed of multiple neural network layers; for example, a Convolutional Neural Network (CNN), a type of deep neural network, consists of three types of layers: convolutional layers, pooling layers, and fully connected layers. Various layers for constructing deep neural networks have been studied and proposed.

[0010] Meanwhile, prior art related to the present invention has been disclosed, such as Published Patent No. 10-2021-0022455 (Title of invention: Deep neural network learning device and method thereof, Date of publication: March 3, 2021).

[0012] The aforementioned background technology is technical information that the inventor possessed for the derivation of the present invention or acquired during the process of deriving the present invention, and it cannot be considered as publicly known technology disclosed to the general public prior to the filing of the present invention. The problem to be solved

[0013] The present invention is proposed to solve the aforementioned problems of previously proposed methods, and aims to provide a deep neural network system and method based on an infinite impulse response layer that can achieve superior performance compared to existing convolutional layer-based deep neural networks by including at least one IIR layer, which is a layer for learning IIR filter coefficients, which are filter coefficients of an infinite impulse response (IIR) filter among digital filters, thereby enabling the modeling of more complex functions with fewer parameters than existing convolutional layers interpreted as layers for learning filter coefficients of finite impulse response (FIR) filters.

[0015] In addition, the present invention has another objective of providing a deep neural network system and method based on an infinite impulse response layer, which is easy to apply to various industries because it allows the convolutional layer to be replaced with the proposed IIR layer by presenting both the forward and backward functions of the IIR layer to enable learning and inference of the IIR layer, and because part or all of the deep neural network can be easily replaced with the IIR layer for learning in numerous fields using deep learning.

[0017] In addition, another objective of the present invention is to provide a deep neural network system and method based on an infinite impulse response layer, which can improve the final performance of a deep neural network system by applying an IIR layer capable of modeling more complex functions with fewer parameters to the deep neural network.

[0019] However, the technical problem that the present invention aims to solve is not limited to the technical problem described above, and other technical problems may exist. It goes without saying that objectives or effects that can be understood from the means of solving the problem or the embodiments, even if not explicitly mentioned, are also included. means of solving the problem

[0020] A deep neural network system based on an infinite impulse response layer according to the features of the present invention for achieving the above-mentioned purpose is,

[0021] As a deep neural network system,

[0022] The configuration is characterized by including at least one IIR layer, which is a layer that learns using IIR filter coefficients, which are filter coefficients of an Infinite Impulse Response (IIR) filter among digital filters, as weights.

[0024] Preferably, the IIR layer is,

[0025] It is possible to learn the first weight (a) applied to the input and the second weight (b) applied to the output of the previous time component.

[0027] More preferably, the forward function of the IIR layer is,

[0028] A function that calculates the output y given the input x, for n=0, … , T-1 It can be defined as.

[0029] Here, x is the input to the IIR layer, with a size of C×T, x[i,n] (i=0, …, C-1, n=0, …, T-1) is the i-th channel and n-th time component, and a and b are the weights to be learned, with sizes of C×K1 and C×K2, respectively, and y is the output of the IIR layer forward function, with a size of C×T, y[j,n] (j=0, …, C-1, n=0, …, T-1) is the j-th channel and n-th time component.

[0031] Even more preferably, the backward function of the IIR layer is,

[0032] If given , and A function that calculates, which can be defined by the following mathematical formula for n=T-1, … , 0.

[0033] [Mathematical Formula]

[0034]

[0035] Here, L is the loss function.

[0037] A deep neural network method based on an infinite impulse response layer according to the features of the present invention for achieving the above-mentioned purpose is,

[0038] As a deep neural network learning method performed on a computer,

[0039] The configuration is characterized by training a deep neural network that includes at least one IIR layer, which is a layer that learns using IIR filter coefficients, which are filter coefficients of an Infinite Impulse Response (IIR) filter among digital filters, as weights.

[0041] Preferably, the IIR layer is,

[0042] It is possible to learn the first weight (a) applied to the input and the second weight (b) applied to the output of the previous time component.

[0044] More preferably, the forward function of the IIR layer is,

[0045] A function that calculates the output y given the input x, for n=0, … , T-1 It can be defined as.

[0046] Here, x is the input to the IIR layer, with a size of C×T, x[i,n] (i=0, …, C-1, n=0, …, T-1) is the i-th channel and n-th time component, and a and b are the weights to be learned, with sizes of C×K1 and C×K2, respectively, and y is the output of the IIR layer forward function, with a size of C×T, y[j,n] (j=0, …, C-1, n=0, …, T-1) is the j-th channel and n-th time component.

[0048] Even more preferably, the backward function of the IIR layer is,

[0049] If given , and A function that calculates, which can be defined by the following mathematical formula for n=T-1, … , 0.

[0050] [Mathematical Formula]

[0051]

[0052] Here, L is the loss function.

[0054] The present invention is characterized by a computer program stored on a computer-readable recording medium for executing a deep neural network method based on an infinite impulse response layer according to the features of the present invention for achieving the above-mentioned purpose. Effects of the invention

[0055] According to the deep neural network system and method based on an infinite impulse response layer proposed in the present invention, by including at least one IIR layer which is a layer for learning IIR filter coefficients, which are filter coefficients of an IIR filter among digital filters, superior performance can be achieved compared to existing convolutional layer-based deep neural networks through an IIR layer that can model more complex functions with fewer parameters than existing convolutional layers interpreted as layers for learning FIR filter coefficients.

[0057] In addition, according to the deep neural network system and method based on an infinite impulse response layer proposed in the present invention, both the forward function and the backward function of the IIR layer are presented to enable learning and inference of the IIR layer, thereby allowing convolutional layers in various deep neural network systems to be replaced with the proposed IIR layer. Furthermore, since a part or the whole of the deep neural network can be easily replaced with an IIR layer for learning in numerous fields using deep learning, it is easy to apply to various industries.

[0059] Furthermore, according to the deep neural network system and method based on an infinite impulse response layer proposed in the present invention, the final performance of the deep neural network system can be improved by applying an IIR layer, which can model more complex functions with fewer parameters, to the deep neural network.

[0061] Furthermore, the various and beneficial advantages and effects of the present invention are not limited to those described above and may be more easily understood in the process of explaining specific embodiments of the present invention. Brief explanation of the drawing

[0062] Figure 1 is a diagram illustrating the structure of a deep neural network. Figure 2 is a diagram illustrating the FIR filtering process. Figure 3 is a diagram illustrating the IIR filtering process. FIG. 4 is a diagram illustrating the configuration of a deep neural network system based on an infinite impulse response layer according to an embodiment of the present invention. FIG. 5 is a diagram illustrating the inference process of an IIR layer of a deep neural network system based on an infinite impulse response layer according to an embodiment of the present invention. FIG. 6 is a diagram illustrating the backpropagation process of an IIR layer of a deep neural network system based on an infinite impulse response layer according to an embodiment of the present invention. FIG. 7 is a diagram illustrating a method for configuring a deep neural network system based on an infinite impulse response layer according to an embodiment of the present invention. Specific details for implementing the invention

[0063] Embodiments of the present invention are described below with reference to the attached drawings so that those skilled in the art can easily implement the invention. However, the present invention may be embodied in various different forms and is not limited to the embodiments described herein. Furthermore, in order to clearly explain the present invention in the drawings, parts unrelated to the explanation have been omitted, and similar parts throughout the specification are denoted by similar reference numerals.

[0065] Throughout the specification, when a part is described as being "connected" to another part, this includes not only cases where they are "directly connected" but also cases where they are "indirectly connected" with other elements interposed between them. Furthermore, when a part is described as "including" a component, this means that, unless specifically stated otherwise, it does not exclude other components but rather allows for the inclusion of additional components; it should be understood that this does not preclude the existence or addition of one or more other features, numbers, steps, actions, components, parts, or combinations thereof.

[0067] The following examples are detailed descriptions to aid in understanding the present invention and are not intended to limit the scope of the present invention. Accordingly, inventions within the same scope that perform the same function as the present invention will also fall within the scope of the present invention.

[0069] In addition, each component, process, procedure, or method included in each embodiment of the present invention may be shared within a scope that is not technically contradictory to one another.

[0071] In addition, some of the operations or functions described as being performed by a terminal, device, or device in the present invention may instead be performed by a server connected to said terminal, device, or device. Likewise, some of the operations or functions described as being performed by a server may also be performed by a terminal, device, or device connected to said server.

[0073] In particular, the means for executing the system according to each embodiment of the present invention may be an application or a web server, and the terminal, which is the means for reading the recording medium on which the application or web server is recorded, may include not only general PCs such as general desktops or laptops, but also mobile terminals such as smartphones and tablet PCs.

[0075] Hereinafter, embodiments of the present invention will be described in detail with reference to the attached drawings.

[0077] To understand the present invention, knowledge of deep neural network inference, learning, forward and backward functions of artificial neural network layers, filtering, and convolutional layers is required. Therefore, sections 1) to 3) present technical content for understanding prior knowledge, and section 4) presents the problems of the prior art and the IIR layer that can improve them.

[0079] 1) Deep Neural Network

[0080] Artificial intelligence is a technology that artificially implements human abilities such as learning, reasoning, and perception. Deep learning is a field of artificial intelligence and is a method of training deep neural networks. A deep neural network is a model consisting of layers of artificial neural networks that artificially mimic the human neural network, and Figure 1 is a diagram illustrating the structure of a deep neural network. In Figure 1, the circle at the far left (x) represents the input, the circle at the far right (y) represents the model's final output, the circle in between (h) represents the hidden layer output, and the arrow (W) represents the weight or parameter that the deep neural network will learn. Training a deep neural network requires a very large number of (input, output) data pairs. The goal of deep learning is to effectively learn the model weights of the deep neural network using a dataset, and once training is complete, it can produce a corresponding output when an arbitrary input is given. For example, if deep learning is applied to speech enhancement, when noisy speech is given as input to the model, it can output clean speech with the noise removed.

[0082] 1-1) Forward Function

[0083] The deep neural network of Fig. 1 consists of fully connected layers, which are the most basic layers. Each layer consists of inputs / outputs represented by circles and weights represented by arrows. Specifically, the k-th layer of the deep neural network has an input h k-1 , output is h k , the weight is W k is, h i k-1 , h j k , W i,j k It is connected. The input and output of the k-th fully connected layer are mathematically equal to the following Equation 1.

[0085]

[0087] Here, σ(·) is a separately defined non-linear function, commonly using functions such as ReLU or sigmoid. Also, is the forward function of the k-th layer. Now, the input x 1:L When it comes in, in the first layer, according to the formula above, h 1:M 1 can calculate. And in the second layer, h 1:M 2 You can calculate, and if you repeat this up to the last layer, y 1:p It can calculate. The process of producing an output when an input enters a deep neural network is called inference, and for inference, the forward function of the layer used in the deep neural network must be defined.

[0089] 1-2) Backward Function

[0090] The purpose of deep learning training is that when an input x is given to the model, the output When appears, the correct output y and the model's output The goal is to update the model's weights W so that the loss L, which is the difference, is minimized. To achieve this, the model's backward operation must be understood, and the specific learning algorithm is as follows.

[0092] 1. Initialize the weights W of the deep neural network to arbitrary values.

[0093] 2. Select (x,y) from the dataset. When x is given as input to the model, the deep neural network produces a certain output through forward propagation will give.

[0094] 3. Output of the deep neural network Calculate L, which is the difference between and the actual desired output y.

[0095] 4. The derivative of L with respect to W Calculate.

[0096] 5. For a sufficiently small value ε, adjust W as in Equation 2 below. Then, under certain conditions, It is known that L, the difference between and y, decreases statistically.

[0098]

[0100] 6. Repeat steps 2 through 5 a great many times. Then, eventually, for an arbitrary input x within the dataset, the output of the deep neural network The difference L between and the actual desired output y will become very small.

[0102] The key to deep learning training is The question is how to calculate it. If Given, the layer's backward function and If you know and It can be obtained using the following mathematical formula 3.

[0104]

[0106] Using this, first, L is the output of the deep neural network The value differentiated with respect to Calculate, and at the Kth layer and It can calculate, and at the K-1th layer and If you can obtain it and repeat this up to the first layer It can be calculated. As such, to train a deep neural network, one must define not only the forward function of the layer used but also the backward function.

[0108] 2) Finite Impulse Response (FIR) and Infinite Impulse Response (IIR) Filters

[0109] Filters serve the role of allowing only signals with desired characteristics to pass through from an input signal. Among them, digital filters are broadly classified into two types: FIR filters and IIR filters.

[0111] Figure 2 is a diagram illustrating the FIR filtering process. The process of obtaining an output signal y by applying FIR filter coefficients h[k] (k=0, 1, ,… ,N-1) of length N to an input signal x can be expressed mathematically as Equation 4 below.

[0113]

[0115] Figure 3 is a diagram illustrating the IIR filtering process. Unlike FIR filters, IIR filters use not only x[n], x[n-1], … but also y[n-1], y[n-2], … to produce the output y[n]. The IIR filtering process can be expressed mathematically as Equation 5 below.

[0117]

[0119] Here, a[k] (k=0, 1, ,… ,N-1) and b[k] (k=0, 1, ,… ,M-1) are the IIR filter coefficients. IIR filters can model more complex functions using only a smaller number of filter coefficients compared to FIR filters.

[0121] 3) Convolutional layer

[0122] A deep neural network is a structure in which a very large number of artificial neural network layers are stacked deeply. There are various types of artificial neural network layers, including the fully connected layer illustrated in Fig. 1, and among them, one of the commonly used layers is the convolutional layer. Convolutional layers can be 1D, 2D, or 3D, but here we will explain only the 1D convolutional layer. The input to convolution is a multi-channel sequence, and the channel size is C in Let x[i,n] (i=0, …, C in It can be represented as -1, n=0,1,2,…). A convolutional layer consists of input x and weights W[j,i,k] (j=0, …, C out -1, i=0, … , C in Output y[k,n] (j=0, …, C) with -1, k=0, … ,K-1). out It generates -1, n=0,1,2,… and is expressed as the mathematical formula 6 below.

[0124]

[0126] 4) IIR layer

[0127] Looking at Equations 4 and 6 above, the convolutional layer can be interpreted as multi-channel FIR filtering. In other words, the convolutional layer can be viewed as a layer that learns FIR filter coefficients.

[0129] However, as explained in the comparison of FIR filters and IIR filters in section 2) above, IIR filters can model more complex functions than FIR filters using only a smaller number of filter coefficients. Therefore, the present invention proposes a novel IIR layer for learning IIR filter coefficients. The IIR layer can achieve better performance with fewer parameters compared to convolutional layers, which are frequently used in existing deep neural networks.

[0131] FIG. 4 is a diagram illustrating the configuration of a deep neural network system based on an infinite impulse response layer according to an embodiment of the present invention. As shown in FIG. 4, the deep neural network system based on an infinite impulse response layer according to an embodiment of the present invention may include at least one IIR layer (100), which is a layer that learns using IIR filter coefficients, which are filter coefficients of an infinite impulse response filter among digital filters, as weights.

[0133] In addition, a deep neural network learning method including an infinite impulse response layer according to an embodiment of the present invention is a deep neural network learning method performed on a computer, and can be implemented by learning a deep neural network that includes at least one IIR layer (100), which is a layer that learns using IIR filter coefficients, which are filter coefficients of an infinite impulse response filter among digital filters, as weights.

[0135] That is, the present invention relates to a deep neural network system comprising an IIR layer (100) and a method for learning the same. The IIR layer (100) is characterized by learning IIR filter coefficients, unlike a convolutional layer that learns FIR filter coefficients. More specifically, the IIR layer (100) can learn a first weight (a) applied to the input and a second weight (b) applied to the output of the previous time component.

[0137] Below, the forward and backward functions of the IIR layer (100) will be described.

[0139] First, the inputs and outputs of the forward and backward functions are defined in detail.

[0141] x: Input to the IIR layer (100). The size is C×T. x[i,n] (i=0, …, C-1, n=0, …, T-1) is the i-th channel and n-th time component.

[0142] a, b: Weights to be learned. Their sizes are C×K1 and C×K2, respectively.

[0143] y: Output of the IIR layer (100) forward function. The magnitude is C×T. y[j,n] (j=0, …, C-1, n=0, …, T-1) is the j-th channel, n-th time component.

[0144] : It is the derivative of Loss L with respect to the forward function output y, and its magnitude is C×T.

[0145] , : This is the derivative of Loss L with respect to weights a and b, with magnitudes of C×K1 and C×K2, respectively.

[0146] : This is the derivative of Loss L with respect to the forward function input x, and its magnitude is C×T.

[0148] FIG. 5 is a diagram illustrating the inference process of an IIR layer (100) of a deep neural network system based on an infinite impulse response layer according to an embodiment of the present invention. As shown in FIG. 5, the forward function (110) of the IIR layer (100) of the deep neural network system based on an infinite impulse response layer according to an embodiment of the present invention is a function that calculates y when x is given. Through this, the inference of the deep neural network can be performed to produce a desired output when an arbitrary input is received.

[0150] More specifically, the forward function (110) of the IIR layer (100) is as shown in Equation 7 below for n=0, … , T-1.

[0152]

[0154] FIG. 6 is a diagram illustrating the backpropagation process of an IIR layer (100) of a deep neural network system based on an infinite impulse response layer according to an embodiment of the present invention. As shown in FIG. 6, the backward function (120) of the IIR layer (100) of a deep neural network system based on an infinite impulse response layer according to an embodiment of the present invention is, If given (in other words, , )and Calculate. and The parameters a and b of the corresponding IIR layer (100) can be learned using , and You can learn the previous layer using it. In other words, you can proceed with training the deep neural network.

[0156] The backward function (120) of the IIR layer (100) is as shown in Equation 8 below for n=T-1, … , 0.

[0158]

[0160] Conventional convolutional layers can be interpreted as layers that learn FIR filter coefficients. However, FIR filters have lower expressive power compared to IIR filters. That is, IIR filters can model more complex functions with fewer parameters compared to FIR filters. Therefore, the present invention proposes a new IIR layer (100) that learns IIR filter coefficients, and by presenting both the forward function (110) and the backward function (120) of the IIR layer (100), it is possible to learn and infer the IIR layer (100).

[0162] FIG. 7 is a diagram illustrating a method for configuring a deep neural network system based on an infinite impulse response layer according to an embodiment of the present invention. As shown in FIG. 7, the deep neural network system based on an infinite impulse response layer according to an embodiment of the present invention can be implemented by replacing the convolutional layer in various deep neural network systems with an IIR layer (100), and the final performance of the system can be improved.

[0164] The IIR layer (100) proposed in the present invention is easy to apply to industries because it allows a part or the whole of a deep neural network to be easily replaced with the IIR layer (100) for training in numerous fields using deep learning. In addition, it shows excellent business potential because it can improve the performance of deep neural networks that are actually being used in a wide variety of services recently.

[0166] Embodiments of the present invention may also be implemented in the form of a computer program stored on a computer-readable recording medium to execute a deep neural network learning method including an infinite impulse response layer according to one embodiment of the present invention as described above on a computer.

[0168] Here, a computer-readable medium may be any available medium accessible by a computer and includes both volatile and non-volatile media, and both removable and non-removable media. Additionally, a computer-readable medium may include both computer storage media and communication media. A computer storage medium includes both volatile and non-volatile, removable and non-removable media implemented by any method or technique for storing information such as computer-readable instructions, data structures, program modules, or other data. A communication medium typically includes computer-readable instructions, data structures, program modules, or other data of a modulated data signal such as a carrier wave, or other transmission mechanisms, and includes any information transmission medium.

[0170] As described above, according to the deep neural network system and method based on an infinite impulse response layer proposed in the present invention, by including at least one IIR layer (100), which is a layer for learning IIR filter coefficients, which are filter coefficients of an infinite impulse response filter among digital filters, it is possible to achieve superior performance compared to a conventional convolutional layer-based deep neural network through an IIR layer (100) that can model a more complex function with fewer parameters than a conventional convolutional layer interpreted as a layer for learning FIR filter coefficients.

[0172] In addition, according to the deep neural network system and method based on an infinite impulse response layer proposed in the present invention, by presenting both the forward function (110) and the backward function (120) of the IIR layer (100) to enable learning and inference of the IIR layer (100), convolutional layers in various deep neural network systems can be replaced with the proposed IIR layer (100), and since part or all of the deep neural network can be easily replaced with the IIR layer (100) for learning in numerous fields using deep learning, it is easy to apply to various industries.

[0174] In addition, according to the deep neural network system and method based on an infinite impulse response layer proposed in the present invention, the final performance of the deep neural network system can be improved by applying an IIR layer (100) to the deep neural network, which can model more complex functions with fewer parameters.

[0176] The foregoing description of the present invention is for illustrative purposes only, and those skilled in the art will understand that other specific forms can be easily modified without altering the technical spirit or essential features of the present invention. Therefore, the embodiments described above should be understood as illustrative in all respects and not restrictive. For example, each component described as a single unit may be implemented in a distributed manner, and components described as distributed may likewise be implemented in a combined form.

[0178] The scope of the present invention is defined by the claims set forth below rather than by the detailed description above, and all modifications or variations derived from the meaning and scope of the claims and equivalent concepts thereof should be interpreted as being included within the scope of the present invention. Explanation of the symbols

[0179] 100: IIR layer 110: Forward function of the IIR layer 120: Backward function of the IIR layer

Claims

Claim 1 delete Claim 2 delete Claim 3 delete Claim 4 delete Claim 5 A deep neural network learning method performed on a computer, wherein the deep neural network is learned by including at least one IIR layer, which is a layer that learns using IIR filter coefficients, which are filter coefficients of an Infinite Impulse Response (IIR) filter among digital filters, as weights, and wherein the IIR layer learns a first weight (a) applied to the input and a second weight (b) applied to the output of the previous time component, and wherein the forward function of the IIR layer is a function that calculates an output y given an input x, for n=0, … , T-1 A deep neural network learning method comprising an infinite impulse response layer, characterized by being defined as follows: where x is the input to the IIR layer, with a size of C×T, x[i,n] (i=0, …, C-1, n=0, …, T-1) is the i-th channel and n-th time component, and a and b are weights to be learned, with sizes of C×K1 and C×K2, respectively, and y is the output of the IIR layer forward function, with a size of C×T, y[j,n] (j=0, …, C-1, n=0, …, T-1) is the j-th channel and n-th time component. Claim 6 delete Claim 7 delete Claim 8 In paragraph 5, the backward function of the IIR layer is, If given , and A deep neural network learning method including an infinite impulse response layer, characterized by a function that calculates, defined by the following mathematical formula for n=T-1, …, 0.[Mathematical Formula] Here, L is the loss function. Claim 9 A computer program stored on a computer-readable recording medium for executing a deep neural network learning method including an infinite impulse response layer of claim 5 or 8 on a computer.

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