MZI-based photoelectric fusion neural network system

Abstract

The invention provides a photoelectric fusion neural network system based on MZI, and belongs to the field of artificial intelligence hardware acceleration. Comprising an input layer, a hidden layer and an output layer, the input layer transmits an N-dimensional input vector matrix Ein to the hidden layer, wherein the N-dimensional input vector matrix Ein corresponds to N different light intensity inputs; the hidden layer comprises a linear part and a non-linear part, the linear part adopts an MZI interferometer array to carry out matrix multiplication operation, matrix multiplication of a weight matrix and an input vector matrix is achieved, modulated light subjected to linear operation is obtained, and the non-linear part configures an independent activation unit for each neuron; the nonlinear modulator is used for carrying out nonlinear modulation on the modulated light subjected to linear operation; and the output layer converts the optical signal after nonlinear modulation into an electric signal through a photoelectric conversion module, and is equipped with a memory and a Softmax processing module to complete final result output. According to the invention, high-efficiency neural network calculation is realized through an innovative photoelectric hybrid architecture.

Description

Technical Field

[0001] The present invention belongs to the field of artificial intelligence hardware acceleration and relates to an MZI-based optoelectronic fusion neural network system. Specifically, it is an optoelectronic hybrid computing architecture parameter model based on a Mach-Zehnder interferometer (MZI), which is suitable for optical neural network reasoning tasks that require real-time computing, such as speech recognition. Background Art

[0002] Currently, electronic computing remains the most crucial computing power for executing AI algorithms, especially deep ANN models. While specific hardware architectures vary, they all employ von Neumann computing principles, completing computational tasks through complex logic circuits and processor chips. Deep learning's demand for computing power is insatiable. While silicon-based electronic components can still support current computing demands, traditional deep learning has quietly reached a bottleneck due to limitations in electrical signal interference, energy consumption, and physical limits. Academia and industry are seeking alternative methods to address the shortcomings of traditional electronic computing in deep learning. Because light travels at a speed of 300,000 kilometers per second—300 times the speed of electrons—it carries 2×10^4 times more information than electrical channels, and offers high parallelism and strong interference resistance, offering significant advantages in information transmission and optical computing. Replacing electricity with light has become a potential and promising approach.

[0003] Therefore, existing technologies attempt to construct neural networks optically to achieve deep learning architectures. Optical neural networks (ONNs) have emerged as the times require. They have the characteristics of high bandwidth, high connectivity, and internal parallel processing, and can accelerate some operations of software and electronic hardware, even reaching the "speed of light", making them a promising alternative to artificial neural networks. In optical neural networks, matrix multiplication can be performed at the speed of light, which can effectively solve the efficiency problem of dense matrix multiplication in artificial neural networks and reduce energy and time consumption. Moreover, nonlinearity in artificial neural networks can also be achieved through nonlinear optical elements. Once the training of the optical neural network is completed, the entire structure can perform optical signal calculations at the speed of light without the need for additional energy input.

[0004] However, existing research on optical neural networks has primarily focused on exploring new optical computing hardware or novel network structures, with little attention paid to the modeling and optimization of optoelectronic fusion neural networks. Due to the heterogeneous integration characteristics of optoelectronic fusion computing architectures, design simulations are difficult to perform using existing EDA tools, making it difficult to simulate and evaluate the hardware performance of the designs. Summary of the Invention

[0005] In view of the deficiencies in the prior art, the present invention provides an MZI-based optoelectronic fusion neural network system, which realizes efficient neural network calculation by integrating optical devices and electronic components.

[0006] To achieve the above object, the present invention adopts the following technical solutions:

[0007] An MZI-based optoelectronic fusion neural network system includes: an input layer, a hidden layer, and an output layer; the input layer converts the N-dimensional input vector matrix E in Transmitted to the hidden layer, N-dimensional input vector matrix E in Corresponding to N different light intensity inputs; the hidden layer includes a linear part and a nonlinear part. The linear part uses an MZI interferometer array to perform matrix multiplication operations to realize matrix multiplication of a weight matrix and an input vector matrix to obtain modulated light after linear operation. The nonlinear part configures an independent activation unit for each neuron to perform nonlinear modulation on the modulated light after linear operation; the output layer converts the nonlinearly modulated optical signal into an electrical signal through a photoelectric conversion module, and is equipped with a memory and a Softmax processing module to complete the final result output.

[0008] Optionally, the input layer uses an electrical signal buffer and a photoelectric conversion module as a front-end interface to convert the electrical signal into an optical signal, where the optical signal is input modulated light loaded into a specific wavelength band.

[0009] Optionally, the electrical signal buffer has an 8-bit data width and 32 parallel channels.

[0010] Optionally, the linear part arranges 2×2 calculation basic units composed of the MZI interferometer array according to a triangular decomposition rule for performing matrix multiplication operations.

[0011] Optionally, the MZI interferometer array is composed of 8×8 MZI units, each MZI unit has a size of 100 μm×60 μm, and an effective refractive index of 3.5.

[0012] Optionally, the activation unit of the nonlinear part includes a directional coupler, a photodetector, a current amplifier, a transimpedance amplifier and a nonlinear signal conditioner; for an input signal with an amplitude of z, it first enters a directional coupler with a coupling coefficient of α, and a portion of the input optical power is converted to is directed to a photodetector, which converts the received optical power into a photocurrent Where R is the responsivity of the photodetector; the photocurrent then passes through the current amplifier, and the output current is I pdQ ; The transimpedance amplifier with a gain of G converts the current I pdQ Converted to voltage V G =G·IpdQ ; voltage V G is subsequently adjusted by a non-linear signal conditioner with a transfer function H, the adjusted voltage signal H(V G ) is combined with a static bias voltage V b to generate a modulated signal V m = V b + H(V G ).

[0013] Optionally, the memory is 8-bit data width, with 8 parallel channels; the Softmax processing module adopts 64-way parallel architecture.

[0014] Optionally, the system loads input data in the initialization stage, and by default reads MFCC feature data in Excel format from a specified path, and if loading fails, 195 random data is automatically generated as a substitute.

[0015] Optionally, the system further comprises an interactive interface, which allows the user to set network parameters, including input layer dimension, number of hidden layers, number of neurons in each layer, and output layer dimension.

[0016] The beneficial effects of the present application are:

[0017] The photoelectric fusion neural network system provided by the present application has significant technical advantages and positive effects compared to traditional neural network implementation schemes. By combining optical computing and electrical control, the photoelectric fusion neural network system exhibits excellent performance in terms of computing speed, energy efficiency, and integration.

[0018] (1) In terms of computing performance, the system utilizes optical parallel processing characteristics to achieve ultra-high speed matrix operation capability through wavelength multiplexing technology, with a computing speed of up to 100 billion MAC operations per second, which is several orders of magnitude higher than traditional pure electronic neural networks. The model uses optical MZI units, which not only greatly reduces the operation delay, but also achieves high-density parallel computing through wavelength division multiplexing, effectively overcoming the "memory wall" bottleneck problem of traditional electronic chips.

[0019] (2) In terms of energy efficiency, the low energy consumption characteristic of optical computing significantly reduces the overall power consumption of the system, and the optimization design of laser light source and optical-electric conversion module further improves the energy utilization efficiency. Tests show that the energy consumption per MAC operation of this architecture can be as low as picojoules, which is about 100 times more energy-efficient than traditional GPU solutions, making it suitable for deployment in energy-sensitive edge computing scenarios.

[0020] (3) In terms of system integration, the modular design realizes the high integration of optoelectronic components. Through reasonable layout of the optical waveguide network and the electronic control circuit, the physical area is greatly reduced while maintaining the integrity of the function. The system supports dynamic reconstruction of the weight matrix and can flexibly adapt to different depth neural network models.

[0021] (4) Through the intelligent parameter optimization interface, non-optical professionals can also conveniently complete the design and performance evaluation of complex optoelectronic neural networks, greatly reducing the application threshold of optoelectronic computing technology. The intuitive architecture display and quantitative performance analysis provided by the visualization tool provide a reliable basis for system-level optimization, shortening the design iteration cycle.

[0022] These features make the present application have broad application prospects in the fields of artificial intelligence acceleration and optical communication signal processing. BRIEF DESCRIPTION OF DRAWINGS

[0023] Figure 1 is a neural network schematic diagram of the MZI-based optoelectronic fusion neural network system.

[0024] Figure 2 is a structure diagram of the MZI unit in the linear part.

[0025] Figure 3 is a structure diagram of the activation unit in the nonlinear part.

[0026] Figure 4 is a schematic diagram of triangular decomposition and diamond decomposition.

[0027] Figure 5 is an architecture diagram of the MZI-based optoelectronic fusion neural network system.

[0028] Figure 6 is a visualization result diagram of input data. DETAILED DESCRIPTION

[0029] The technical solutions in the embodiments of the present application will be described clearly and completely below in combination with the drawings in the embodiments of the present application.

[0030] In an embodiment, the present application provides a MZI-based optoelectronic fusion neural network system, which realizes efficient neural network computing through an innovative optoelectronic hybrid architecture. The core of this technical solution is to build a complete hardware implementation framework.

[0031] In terms of system architecture, the application adopts a layered design, including a complete neural network structure of input layer, hidden layer and output layer. The input layer uses a telecommunication signal buffer and an optoelectronic conversion module as a front-end interface to convert the electrical signal into an optical signal. The buffer buffer is located at the front end of the input layer of the optoelectronic neural network and is used for buffering input data. When a large amount of data in the form of a one-dimensional matrix with an ultra-long dimension enters the input layer, the problem of excessive number of input layer neurons leading to large overall floor area, excessive power consumption and difficulty in hardware implementation is solved. The hidden layer is composed of multiple MZI weight matrices and optical nonlinear activation functions, which realize the core computing function of the neural network. The output layer converts the optical signal back to the electrical signal through the optoelectronic conversion module, and is equipped with a memory and a Softmax processing module to complete the final result output. The high-speed data transmission between layers is realized through an optimized optical interconnection network.

[0032] For the implementation of the MZI weight matrix, the application provides two optional decomposition schemes: a triangular decomposition scheme requiring N(N-1) / 2 MZI units, and a rhombus decomposition scheme requiring (N-1)^2 MZI units. Users can choose between precision and hardware complexity according to specific application scenarios. Each MZI unit adopts a compact design of 100μm×60μm, and realizes efficient optical calculation based on an effective refractive index of 3.5. In the design of the optoelectronic interface, the system is configured with multiple groups of parallel optoelectronic conversion modules, each supporting 32 parallel channels, with a bandwidth range of 1-800Gbps, a data precision of 8 bits, and a delay control within 2ns. The input buffer uses a 32-channel parallel architecture with a bandwidth of 1-5GHz; the output memory is configured with an 8-channel parallel interface with a bandwidth of 10-200GB / s, providing efficient data throughput for the system. For the nonlinear processing link, the application adopts a distributed optical nonlinear activation scheme, with each neuron configured with an independent activation unit and a power threshold set to 0.1mW, realizing nonlinear transformation without introducing additional delay. The Softmax processing of the output layer adopts a 64-way parallel architecture, with a processing time of 4ns per batch and a power consumption of 5mW, improving overall efficiency through batch processing.

[0033] In terms of system performance optimization, the extreme value performance parameters (including speed, power consumption, delay and efficiency) of each batch processing are dynamically calculated to realize real-time monitoring of the running state of the whole system. An innovative power consumption and delay decomposition analysis method is adopted to subdivide the total power consumption into nonlinear layer, linear layer, memory, buffer and photoelectric conversion components, and to decompose the total delay into linear layer, nonlinear layer, memory, buffer and photoelectric conversion links, thereby providing accurate guidance basis for system optimization. The data visualization scheme of the application simultaneously displays the network architecture and input data characteristics, and intuitively presents the MZI unit distribution, photoelectric module configuration and data statistical characteristics through a graphical interface. The system supports importing actual application data from an Excel file and also provides a random data generation function to ensure effective testing and verification in various scenarios.

[0034] The neural network structure of the MZI-based optoelectronic fusion neural network system is shown in Figure 1 , the input is input modulated light loaded to a certain waveband (such as 1550 nm) after processing by an optical modulator and a laser, and the N-dimensional input vector matrix E in corresponds to N different light intensity inputs. The input matrix enters the neurons X inN of the first layer input layer in the form of different light intensities. Since the input layer only has the function of transmitting light into the neural network, the input layer is only an optical waveguide.

[0035] Then, the light propagates to the first weight matrix, which is a linear part, and the basic unit structure of the linear part is shown in Figure 2 . The basic principle of the linear part is that any discrete finite-dimensional unitary operator can be constructed and implemented by optical equipment. Based on this, 2x2 optical matrix multiplication can be performed to realize matrix multiplication of the weight matrix and the input vector. Therefore, the linear part based on the MZI unit needs to follow the triangular decomposition rule to perform multi-dimensional matrix multiplication of greater than 2x2 unitary matrices, as shown in Figure 4 . Taking 4x4 matrix multiplication as an example, I1-I4 are the inputs of the optical multiplication matrix, O1-O4 are the outputs of the optical multiplication matrix, and the intermediate structure is the arrangement of the 2x2 calculation basic units according to the triangular decomposition rule.

[0036] Next, the modulated light after linear operation continues to transmit to the neurons θ N of the nonlinear part, which mainly has the function of nonlinear modulation of the modulated light, and the structure of a single neuron is shown in Figure 3 . For an input signal with amplitude z, first enter the directional coupler with coupling coefficient a, and guide a part of the input light power to the photodetector. The photodetector converts the received light power into photocurrent ​where R is the responsivity of the photodetector. The output current is then amplified by a current amplifier to amplify the possibly weak photocurrent, and the output current is I pdQ . A transimpedance amplifier with gain G then converts the amplified current to a voltage V G = G I pdQ . The output voltage of the photoconversion circuit is then converted by a nonlinear signal conditioner with transfer function H. Finally, the conditioned voltage signal H(V G ) is combined with a static bias voltage V b to generate the modulated signal V m = V b + H(V G ). This implements the first complete linear-nonlinear computation, corresponding to the first y1= W1X1+ b1 operation in a neural network.

[0037] The process is then repeated according to the number of layers in the neural network, until the final output layer neuron γ N , where the structure is still as shown in Figure 3 , finally outputs the processing result.

[0038] The detailed implementation of the MZI-based optoelectronic fusion neural network system is described as follows:

[0039] The system initialization stage first loads the input data, which by default reads the MFCC feature data in Excel format from a specified path. If the loading fails, 195-dimensional random data is automatically generated as a substitute. Users set network parameters through an interactive interface, including key parameters such as input layer dimension, number of hidden layers and number of neurons in each layer, output layer dimension, etc. The system supports two MZI weight matrix decomposition methods (triangular decomposition and rhombus decomposition), and users can choose according to their needs. The system automatically calculates the number of MZI interferometer units required for each layer.

[0040] In hardware architecture implementation, the system contains multiple functional modules: the electrical signal processing part is composed of a parallel channel buffer (8-bit data width, 32 parallel channels) and a memory unit (8-bit data width, 8 parallel channels); the photoelectric conversion module realizes the bidirectional conversion of electrical and optical signals; the core computing part uses an MZI interferometer array to realize matrix multiplication operation, each MZI unit has a size of 100 μm x 60 μm, and the effective refractive index is 3.5; the nonlinear activation is realized through an optical threshold device, and the power threshold is 0.1 mW; the output layer is followed by a Softmax processing module, which supports 64-way data parallel processing. The performance calculation module comprehensively considers the characteristics of each component: the transmission delay of optical signals in the MZI is calculated based on the speed of light of 3 x 10^8 m / s and the effective refractive index; the electrical signal processing delay includes buffer delay (4 ns), memory delay (800 ns) and photoelectric conversion delay (2 ns); the power consumption model covers laser power, buffer and memory power consumption (10 mW and 2 mW respectively), photoelectric conversion power consumption (5 mW) and Softmax processing power consumption (5 mW / batch). The system automatically calculates key indicators such as total delay, throughput (MAC / sec), energy efficiency (J / MAC) and chip area. The visualization module generates a double-panel diagram: the left architecture is as shown in Figure 5 , which uses color coding to display each component (orange oval represents neuron layer, pink rectangle is MZI matrix, purple circle is activation function, light blue is buffer / storage module, light green is photoelectric converter, and gold represents Sofimax module); the right panel is as shown in Figure 6 , which displays input data waveforms and statistical characteristics. The performance analysis panel provides extreme batch comparison, power consumption / delay distribution pie chart and detailed performance table including Softmax parameters.

[0041] The following device configuration is required for implementation: a computer equipped with Python3.7 or later environment, basic scientific computing libraries such as numpy, pandas and matplotlib; an optical experiment platform requires a 1550 nm waveband laser source, a silicon-based MZI interferometer array and a high-speed photodetector array; the electronic part uses Xilinx Zynq UltraScale+RFSoC to realize high-speed data conversion and storage control. System parameters can be flexibly adjusted by modifying class attributes, especially suitable for real-time computing scenarios such as speech feature processing. This implementation uses a photoelectric hybrid computing architecture to significantly improve computing speed while maintaining the integrity of the neural network function. The system design takes into account actual engineering constraints, including device size, power budget and signal integrity requirements, providing a feasible solution for the practical application of optical neural networks. The MZI performance parameter data is shown in Table 1.

[0042] Table 1 MZI performance parameter data

[0043] Parameter Value Parameter Value Speed (MAC / sec) <![CDATA[7.68×10 12 ]]> Area (mm 2 ) 18.4 Total power consumption (mW) 26.8 MZI units 118 MZI delay (ns) 0.0 Decomposition Triangular decomposition Activation delay (ns) 0.4 Softmax power consumption (mW) 1620.0 Total optical delay (ns) 0.4 Softmax latency (ns) 1296.0 Buffer delay (ns) 2.0 Softmax processing batch 324 Memory delay (ns) 100.0 Total delay (ns) 106.4 Total electrical delay (ns) 106.0 Efficiency (J / MAC) 3.49 x 10 -15 ]]

[0044] In another embodiment, the present application proposes an optical neural network architecture visualization and performance evaluation system, which is implemented for the aforementioned MZI-based optoelectronic fusion neural network system. The optical neural network architecture visualization and performance evaluation system comprises:

[0045] a data loading module for loading input data from external files and performing flat processing;

[0046] a user input module for receiving user input of network architecture parameters and optical parameters;

[0047] a performance calculation module for calculating optical characteristics, hardware requirements and performance indicators of the network;

[0048] a visualization module for generating network architecture diagrams and performance data visualization charts;

[0049] a parameter storage module for storing hardware parameters such as buffers, memories, and optoelectronic conversion.

[0050] In this embodiment, the data loading module comprises:

[0051] an Excel file reading unit for reading MFCC feature data;

[0052] a data flattening unit for converting two-dimensional input data into a one-dimensional vector;

[0053] an exception handling unit for using random data to replace failed data loading.

[0054] In this embodiment, the user input module comprises:

[0055] an optical parameter input unit for receiving optical parameters;

[0056] a network architecture input unit for receiving the number of neurons in the input layer, hidden layer and output layer;

[0057] an input verification unit to ensure that the input value is a valid positive integer.

[0058] In this embodiment, the performance calculation module comprises:

[0059] an optical characteristic calculation unit for calculating the free spectral range, full width at half maximum and maximum channel number;

[0060] a hardware requirement calculation unit for calculating the number of MZI units, buffer and memory requirements;

[0061] a performance indicator calculation unit for calculating the calculation speed, total power consumption, delay and physical area;

[0062] Softmax computing unit, calculating batch, power consumption and delay of Softmax processing.

[0063] In this embodiment, the visualization module includes:

[0064] Network architecture diagram unit, showing the structure of each layer of the neural network in a graphical manner;

[0065] Parameter table unit, displaying optical parameters and performance indicators in a table form;

[0066] Data visualization unit, drawing input data curves and statistical information;

[0067] Extreme value analysis unit, showing the performance comparison of the best and worst batches.

[0068] In this embodiment, the parameter storage module includes:

[0069] Buffer parameter unit, storing delay, bandwidth, data bit number and parallel channel number;

[0070] Memory parameter unit, storing delay, bandwidth range and data bit number;

[0071] Optoelectronic parameter unit, storing conversion delay and bandwidth range;

[0072] MRR parameter unit, storing size and power consumption characteristics.

[0073] In this embodiment, the network architecture diagram unit uses different geometric shapes and colors to distinguish:

[0074] Rectangles represent hardware modules (buffers, memories);

[0075] Ovals represent neural network layers;

[0076] Circles represent neuron nodes;

[0077] Arrows represent data flow direction.

[0078] In the embodiments disclosed in the present application, the computer storage medium can be a tangible medium which can contain or store programs for use by or in connection with an instruction execution system, apparatus or device. The computer storage medium can include, but is not limited to, electronic, magnetic, optical, electromagnetic, infrared, or semiconductor system, apparatus or device, or any suitable combination of the above. More specific examples of computer storage medium can include one or more wires, portable computer disks, hard drives, random access memory (RAM), read-only memory (ROM), erasable programmable read-only memory (EPROM or flash memory), fiber optics, compact disk read-only memory (CD-ROM), optical storage devices, magnetic storage devices, or any suitable combination of the above.

[0079] Those skilled in the art can realize that the units and algorithm steps of each example described in combination with the embodiments disclosed in the present application can be realized by electronic hardware or a combination of computer software and electronic hardware. Whether the functions are realized in hardware or software manner depends on the specific application and design constraints of the technical solutions. The skilled person can use different methods to realize the described functions for each specific application, but such implementation should not be considered beyond the scope of the present application.

[0080] The above is only the preferred embodiment of the present application, and the protection scope of the present application is not limited to the above-mentioned embodiments. Any technical solution falling within the concept of the present application shall fall within the protection scope of the present application. It should be noted that, for ordinary skilled persons in the art, some improvements and refinements without departing from the principles of the present application shall be considered within the protection scope of the present application.

Claims

1. An MZI-based optoelectronic fusion neural network system, characterized in that: include: Input layer, hidden layer, and output layer; The input layer converts the N-dimensional input vector matrix E in Transmitted to the hidden layer, N-dimensional input vector matrix E in Corresponding to N different light intensity inputs; the hidden layer includes a linear part and a nonlinear part. The linear part uses an MZI interferometer array to perform matrix multiplication operations to realize matrix multiplication of a weight matrix and an input vector matrix to obtain modulated light after linear operation. The nonlinear part configures an independent activation unit for each neuron to perform nonlinear modulation on the modulated light after linear operation; the output layer converts the nonlinearly modulated optical signal into an electrical signal through a photoelectric conversion module, and is equipped with a memory and a Softmax processing module to complete the final result output.

2. The MZI-based optoelectronic fusion neural network system according to claim 1, characterized in that: The input layer uses an electrical signal buffer and a photoelectric conversion module as a front-end interface to convert electrical signals into optical signals, where the optical signals are input modulated light loaded into a specific wavelength band.

3. The MZI-based optoelectronic fusion neural network system according to claim 2, characterized in that: The electrical signal buffer has an 8-bit data width and 32 parallel channels.

4. The MZI-based optoelectronic fusion neural network system according to claim 1, characterized in that: The linear part arranges 2×2 basic calculation units composed of the MZI interferometer array according to the triangular decomposition rule for performing matrix multiplication operations.

5. The MZI-based optoelectronic fusion neural network system according to claim 4, characterized in that: The MZI interferometer array is composed of 8×8 MZI units, each MZI unit has a size of 100 μm×60 μm, and an effective refractive index of 3.

5.

6. The MZI-based optoelectronic fusion neural network system according to claim 1, characterized in that: The activation unit of the nonlinear part includes a directional coupler, a photodetector, a current amplifier, a transimpedance amplifier and a nonlinear signal conditioner; for an input signal with an amplitude of z, it first enters a directional coupler with a coupling coefficient of α, and converts a portion of the input optical power into is directed to a photodetector, which converts the received optical power into a photocurrent Where R is the responsivity of the photodetector; the photocurrent then passes through the current amplifier, and the output current is I pdQ ; The transimpedance amplifier with a gain of G converts the current I pdQ Converted to voltage V G =G·I pdQ Voltage V G Then it is regulated by a nonlinear signal conditioner with a transfer function H, and the regulated voltage signal H (V G ) and the static bias voltage V b Combined to generate the modulation signal V m =V b +H(V G ).

7. The MZI-based optoelectronic fusion neural network system according to claim 1, characterized in that: The memory has an 8-bit data width and 8 parallel channels; the Softmax processing module adopts a 64-way parallel architecture.

8. The MZI-based optoelectronic fusion neural network system according to claim 1, characterized in that: The system loads input data during the initialization phase. By default, it reads MFCC feature data in Excel format from the specified path. If the loading fails, 195 random data are automatically generated as a replacement.

9. The MZI-based optoelectronic fusion neural network system according to claim 1, characterized in that: The system also includes an interactive interface that allows users to set network parameters, including input layer dimensions, number of hidden layers, number of neurons in each layer, and output layer dimensions.

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