• Title/Summary/Keyword: differentiable

Search Result 196, Processing Time 0.021 seconds

Robustness of Differentiable Neural Computer Using Limited Retention Vector-based Memory Deallocation in Language Model

  • Lee, Donghyun;Park, Hosung;Seo, Soonshin;Son, Hyunsoo;Kim, Gyujin;Kim, Ji-Hwan
    • KSII Transactions on Internet and Information Systems (TIIS)
    • /
    • v.15 no.3
    • /
    • pp.837-852
    • /
    • 2021

  • Recurrent neural network (RNN) architectures have been used for language modeling (LM) tasks that require learning long-range word or character sequences. However, the RNN architecture is still suffered from unstable gradients on long-range sequences. To address the issue of long-range sequences, an attention mechanism has been used, showing state-of-the-art (SOTA) performance in all LM tasks. A differentiable neural computer (DNC) is a deep learning architecture using an attention mechanism. The DNC architecture is a neural network augmented with a content-addressable external memory. However, in the write operation, some information unrelated to the input word remains in memory. Moreover, DNCs have been found to perform poorly with low numbers of weight parameters. Therefore, we propose a robust memory deallocation method using a limited retention vector. The limited retention vector determines whether the network increases or decreases its usage of information in external memory according to a threshold. We experimentally evaluate the robustness of a DNC implementing the proposed approach according to the size of the controller and external memory on the enwik8 LM task. When we decreased the number of weight parameters by 32.47%, the proposed DNC showed a low bits-per-character (BPC) degradation of 4.30%, demonstrating the effectiveness of our approach in language modeling tasks.

  • https://doi.org/10.3837/tiis.2021.03.002 인용 PDF KSCI HTML

Option Pricing using Differentiable Neural Networks (미분가능 신경망을 이용한 옵션 가격결정)

  • Chi, Sang-Mun
    • Journal of the Korea Institute of Information and Communication Engineering
    • /
    • v.25 no.4
    • /
    • pp.501-507
    • /
    • 2021

  • Neural networks with differentiable activation functions are differentiable with respect to input variables. We improve the approximation capability of neural networks by using the gradient and Hessian of neural networks to satisfy the differential equations of the problems of interest. We apply differential neural networks to the pricing of financial options, where stochastic differential equations and the Black-Scholes partial differential equation represent the differential relation of price of option and underlying assets, and the first and second derivatives of option price play an important role in financial engineering. The proposed neural network learns - (a) the sample paths of option prices generated by stochastic differential equations and (b) the Black-Scholes equation at each time and asset price. Experimental results show that the proposed method gives accurate option values and the first and second derivatives.

  • https://doi.org/10.6109/jkiice.2021.25.4.501 인용 PDF KSCI

APPROXIMATING THE STIELTJES INTEGRAL OF BOUNDED FUNCTIONS AND APPLICATIONS FOR THREE POINT QUADRATURE RULES

  • Dragomir, Sever Silvestru
    • Bulletin of the Korean Mathematical Society
    • /
    • v.44 no.3
    • /
    • pp.523-536
    • /
    • 2007

  • Sharp error estimates in approximating the Stieltjes integral with bounded integrands and bounded integrators respectively, are given. Applications for three point quadrature rules of n-time differentiable functions are also provided.

  • https://doi.org/10.4134/BKMS.2007.44.3.523 인용 PDF KSCI

HOMOCLINIC ORBITS FOR HAMILTONIAN SYSTEMS

  • Kim, June-Gi
    • Bulletin of the Korean Mathematical Society
    • /
    • v.32 no.1
    • /
    • pp.1-11
    • /
    • 1995

  • Let $p, q \in R^2 and H : R^{2n} \to R^n$ be differentiable. An autonomous Hamiltonian system has the form $$ (0.1) \dot{p} = -\frac{\partial q}{\partial H}(p, q), \dot{q} = \frac{\partial p}{\partial H}(p, q) $$.

  • PDF