An Information Theory Inspired Study of Memristor Devices and their Potential Use in Neuromorphic Circuits

这个拟议的项目与EPSRC工程主题一致，最好归类为人工智能技术研究领域。它旨在从通信和信息理论的角度探索忆阻器设备作为神经形态电路中的突触电路元件的潜在用途，其灵感来自Friston的自由能原理以解释大脑的功能[1]。我想探索使用忆阻器（一类电阻可以通过施加电压进行调制的器件）的潜力。它们在1971年被Leon Chua正式定义为一种新的双端电路元件[2]，以完成4个理想无源电路元件的集合，通过仿真和实际演示来实际实现理论所描述的过程。一些形式的忆阻器是模仿具有非线性阈值的二进制激活单元的功能的良好候选者我之前已经探索了忆阻器作为存储设备的潜在用途，使用生成对抗网络（GAN）将它们建模为通信通道，以及使用自动编码器架构来压缩并通过有噪声的忆阻器通道传输数据：一种称为深度联合源通道编码的技术。深度学习的技术可以在整个项目过程中扩展，以便对设备及其非理想性进行建模，例如编程后的不完美值或电阻随时间的漂移。其想法是创建一个使用控制和优化规则进行学习的神经形态架构。这些规则将来自物理系统的动力学，而不是来自编程规则，并将通过电子电路中错误函数的负反馈来实现。这种优化方法不需要显式梯度计算，与参数相对于损失函数的梯度的显式计算相反，因为机器学习和深度学习领域中的绝大多数当前神经网络架构通过反向传播算法执行。当前忆阻神经网络已经尝试将反向传播算法转化为硬件-乘法采用欧姆定律，加法采用基尔霍夫电流定律。然而，它们确实展示了另一个优势：降低功耗和提高速度。许多机器学习算法使用外部存储器在GPU硬件上运行。对于忆阻神经元，（网络权重的）处理和存储是相互分离的。由于架构的根本转变，处理和存储是相关联的：忆阻器具有它们自己的存储，其存储形式是它们在被电压或电流控制后保留的电阻值。这意味着加工和储存都是以所谓的“原位”方式完成的-都在同一个位置。这是从传统的冯·诺依曼（独立存储和处理器）计算机架构向功能更类似于人类大脑中发现的生物尖峰网络的架构的转变。这减少了在处理单元和存储设备之间传输数据所花费的功率和时间。[1]弗里斯顿湾（2010年）。自由能原理：统一的大脑理论？Nature Reviews Neuroscience，Vol. 11，pp. 127-138. [2]L. Chua，“Memristor-The missing circuit element”，IEEE Trans. Circuit Theory，vol.18，no.5，pp. 507-519，1971年。

This proposed project is aligned with the EPSRC Engineering theme and is best categorised under the Artificial Intelligence Technologies Research Area. It aims to explore, from a communications and information-theoretic perspective, the potential use of memristor devices as synaptic circuit elements in neuromorphic circuits, inspired by Friston's Free Energy Principle to explain the function of the brain [1]. I would like to explore the potential to use devices called memristors (a class of devices whose resistance can be modulated using an applied voltage. They were formalised as a new two-terminal circuit element by Leon Chua in 1971 [2], to complete the set of 4 ideal passive circuit elements) to practically implement the processes described by the theory, through simulation and, if possible, through practical demonstration. Some forms of memristor are good candidates for mimicking the function of binary activation units with a nonlinear thresholding (such as neurons in the human brain) for use in novel neural architectures.I have previously explored the potential use of memristors as storage devices, modelling them as communication channels using a Generative Adversarial Network (GAN), and using an Autoencoder architecture to compress and transmit data over the noisy memristor channel: a technique known as Deep Joint Source-Channel Coding. Such techniques from deep learning can be extended throughout the course of the project in order to model the devices and their non-idealities, such as imperfect values after programming or resistance drift over time.The idea is to create a neuromorphic architecture that uses control and optimisation rules to learn. These rules will come from the dynamics of a physical system rather than from programmed rules and will be implemented through negative feedback of an error function in an electronic circuit. This method of optimisation requires no explicit gradient computation, in contrast to the explicit computation of the gradient of the parameters with respect to a loss function, as the overwhelming majority of current neural network architectures in the field of Machine Learning and Deep Learning perform through the algorithm of back propagation.Current memristive neural networks have attempted to translate the algorithm of back propagation into hardware - using Ohm's law for multiplication and Kirchhoff's current law for addition. They do however demonstrate another advantage: a reduction in power consumption and increase in speed. Many machine learning algorithms run on GPU hardware, using an external memory. For memristive neurons, processing and storage (of weights of the network) are separate from one another. Processing and memory are associated due to a fundamental shift in architecture: memristors have their own storage in the form of the resistance value that they retain after they have been controlled by a voltage or a current. This means that processing and storage are both done in a so called "in-situ" fashion - both in the same location. This is a move from the traditional Von-Neumann (separate storage and processor) architecture of computers towards architectures that function more similarly to the biological, spiking networks found in the human brain. This reduces power and time expended in transferring data between a processing unit and a storage device.[1] Friston, K. (2010). The free-energy principle: A unified brain theory? Nature Reviews Neuroscience, Vol. 11, pp. 127-138.[2] L. Chua, "Memristor-The missing circuit element," IEEE Trans. Circuit Theory, vol. 18, no. 5, pp. 507-519, 1971.