European Option Pricing Formula Under Stochastic Interest Rate

Abstract: This paper reviews the option pricing model and its application, on the basis of former studies, we assume that the interest rate satisfy a given Vasicek stochastic di erential equation, using option pricing by martingale method to study the stochastic interest rate model of European option pricing and obtain its pricing formula. Finally, we compare the di erences between the standard European option pricing formula and European option pricing formula under stochastic interest rate.Key words: Option Pricing; Stochastic Interest Rates; Vasicek model; Brownian motion

Algorithm Hardware Codesign for High Performance Neuromorphic Computing

Driven by the massive application of Internet of Things (IoT), embedded system and Cyber Physical System (CPS) etc., there is an increasing demand to apply machine intelligence on these power limited scenarios. Though deep learning has achieved impressive performance on various realistic and practical tasks such as anomaly detection, pattern recognition, machine vision etc., the ever-increasing computational complexity and model size of Deep Neural Networks (DNN) make it challenging to deploy them onto aforementioned scenarios where computation, memory and energy resource are all limited. Early studies show that biological systems\u27 energy efficiency can be orders of magnitude higher than that of digital systems. Hence taking inspiration from biological systems, neuromorphic computing and Spiking Neural Network (SNN) have drawn attention as alternative solutions for energy-efficient machine intelligence. Though believed promising, neuromorphic computing are hardly used for real world applications. A major problem is that the performance of SNN is limited compared with DNNs due to the lack of efficient training algorithm. In SNN, neuron\u27s output is spike, which is represented by Dirac Delta function mathematically. Becauase of the non-differentiable nature of spike, gradient descent cannot be directly used to train SNN. Hence algorithm level innovation is desirable. Next, as an emerging computing paradigm, hardware and architecture level innovation is also required to support new algorithms and to explore the potential of neuromorphic computing. In this work, we present a comprehensive algorithm-hardware codesign for neuromorphic computing. On the algorithm side, we address the training difficulty. We first derive a flexible SNN model that retains critical neural dynamics, and then develop algorithm to train SNN to learn temporal patterns. Next, we apply proposed algorithm to multivariate time series classification tasks to demonstrate its advantages. On hardware level, we develop a systematic solution on FPGA that is optimized for proposed SNN model to enable high performance inference. In addition, we also explore emerging devices, a memristor-based neuromorphic design is proposed. We carry out a neuron and synapse circuit which can replicate the important neural dynamics such as filter effect and adaptive threshold

Exploiting Neuron and Synapse Filter Dynamics in Spatial Temporal Learning of Deep Spiking Neural Network

The recent discovered spatial-temporal information processing capability of bio-inspired Spiking neural networks (SNN) has enabled some interesting models and applications. However designing large-scale and high-performance model is yet a challenge due to the lack of robust training algorithms. A bio-plausible SNN model with spatial-temporal property is a complex dynamic system. Each synapse and neuron behave as filters capable of preserving temporal information. As such neuron dynamics and filter effects are ignored in existing training algorithms, the SNN downgrades into a memoryless system and loses the ability of temporal signal processing. Furthermore, spike timing plays an important role in information representation, but conventional rate-based spike coding models only consider spike trains statistically, and discard information carried by its temporal structures. To address the above issues, and exploit the temporal dynamics of SNNs, we formulate SNN as a network of infinite impulse response (IIR) filters with neuron nonlinearity. We proposed a training algorithm that is capable to learn spatial-temporal patterns by searching for the optimal synapse filter kernels and weights. The proposed model and training algorithm are applied to construct associative memories and classifiers for synthetic and public datasets including MNIST, NMNIST, DVS 128 etc.; and their accuracy outperforms state-of-art approaches

Neuromorphic Online Learning for Spatiotemporal Patterns with a Forward-only Timeline

Spiking neural networks (SNNs) are bio-plausible computing models with high energy efficiency. The temporal dynamics of neurons and synapses enable them to detect temporal patterns and generate sequences. While Backpropagation Through Time (BPTT) is traditionally used to train SNNs, it is not suitable for online learning of embedded applications due to its high computation and memory cost as well as extended latency. Previous works have proposed online learning algorithms, but they often utilize highly simplified spiking neuron models without synaptic dynamics and reset feedback, resulting in subpar performance. In this work, we present Spatiotemporal Online Learning for Synaptic Adaptation (SOLSA), specifically designed for online learning of SNNs composed of Leaky Integrate and Fire (LIF) neurons with exponentially decayed synapses and soft reset. The algorithm not only learns the synaptic weight but also adapts the temporal filters associated to the synapses. Compared to the BPTT algorithm, SOLSA has much lower memory requirement and achieves a more balanced temporal workload distribution. Moreover, SOLSA incorporates enhancement techniques such as scheduled weight update, early stop training and adaptive synapse filter, which speed up the convergence and enhance the learning performance. When compared to other non-BPTT based SNN learning, SOLSA demonstrates an average learning accuracy improvement of 14.2%. Furthermore, compared to BPTT, SOLSA achieves a 5% higher average learning accuracy with a 72% reduction in memory cost.Comment: 9 pages,8 figure

Securing the Spike: On the Transferabilty and Security of Spiking Neural Networks to Adversarial Examples

Spiking neural networks (SNNs) have attracted much attention for their high energy efficiency and for recent advances in their classification performance. However, unlike traditional deep learning approaches, the analysis and study of the robustness of SNNs to adversarial examples remains relatively underdeveloped. In this work we advance the field of adversarial machine learning through experimentation and analyses of three important SNN security attributes. First, we show that successful white-box adversarial attacks on SNNs are highly dependent on the underlying surrogate gradient technique. Second, we analyze the transferability of adversarial examples generated by SNNs and other state-of-the-art architectures like Vision Transformers and Big Transfer CNNs. We demonstrate that SNNs are not often deceived by adversarial examples generated by Vision Transformers and certain types of CNNs. Lastly, we develop a novel white-box attack that generates adversarial examples capable of fooling both SNN models and non-SNN models simultaneously. Our experiments and analyses are broad and rigorous covering two datasets (CIFAR-10 and CIFAR-100), five different white-box attacks and twelve different classifier models

Neurogenesis Dynamics-inspired Spiking Neural Network Training Acceleration

Biologically inspired Spiking Neural Networks (SNNs) have attracted significant attention for their ability to provide extremely energy-efficient machine intelligence through event-driven operation and sparse activities. As artificial intelligence (AI) becomes ever more democratized, there is an increasing need to execute SNN models on edge devices. Existing works adopt weight pruning to reduce SNN model size and accelerate inference. However, these methods mainly focus on how to obtain a sparse model for efficient inference, rather than training efficiency. To overcome these drawbacks, in this paper, we propose a Neurogenesis Dynamics-inspired Spiking Neural Network training acceleration framework, NDSNN. Our framework is computational efficient and trains a model from scratch with dynamic sparsity without sacrificing model fidelity. Specifically, we design a new drop-and-grow strategy with decreasing number of non-zero weights, to maintain extreme high sparsity and high accuracy. We evaluate NDSNN using VGG-16 and ResNet-19 on CIFAR-10, CIFAR-100 and TinyImageNet. Experimental results show that NDSNN achieves up to 20.52\% improvement in accuracy on Tiny-ImageNet using ResNet-19 (with a sparsity of 99\%) as compared to other SOTA methods (e.g., Lottery Ticket Hypothesis (LTH), SET-SNN, RigL-SNN). In addition, the training cost of NDSNN is only 40.89\% of the LTH training cost on ResNet-19 and 31.35\% of the LTH training cost on VGG-16 on CIFAR-10