• 대한수학회논문집
• /
• 제4권1호
• /
• pp.5-15
• /
• 1989

• East Asian mathematical journal
• /
• 제10권1호
• /
• pp.211-218
• /
• 1994

• KSII Transactions on Internet and Information Systems (TIIS)
• /
• 제15권3호
• /
• 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.

• 한국정보통신학회논문지
• /
• 제25권4호
• /
• pp.501-507
• /
• 2021

신경망은 미분가능한 활성화 함수를 사용하는 경우에는 입력변수에 대하여 미분가능하다. 본 연구에서는 신경망의 근사 능력을 향상시키기 위하여 신경망의 그래디언트와 헤시안이 블랙-숄즈 미분방정식을 만족하도록 한다. 본 논문은 확률 미분방정식과 블랙-숄즈 편미분 방정식이 옵션 가격과 기초자산의 미분관계를 표현하는 옵션 가격결정에 제안한 방법을 사용한다. 이는 옵션 가격의 일차와 이차미분은 금융공학에서 중요한 역할을 하므로 미분 값을 쉽게 얻을 수 있는 제안한 방법을 적용할 수 있기 때문이다. 제안한 신경망은 (1) 확률 미분방정식이 생성하는 옵션가격의 샘플 경로와 (2) 각 시간과 기초자산 가격에서 블랙-숄즈 방정식을 만족하도록 학습한다. 실험을 통하여 제안한 방법이 옵션가격과 일차와 이차 미분 값을 정확히 예측함을 보인다.

• 대한수학회보
• /
• 제42권3호
• /
• pp.535-541
• /
• 2005

In this paper, we define the ap-Denjoy integral and investigate some properties of the ap-Denjoy integral.

• 대한수학회보
• /
• 제44권3호
• /
• 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.

• 충청수학회지
• /
• 제17권1호
• /
• pp.103-110
• /
• 2004

In this paper, we define the ap-Denjoy integral and investigate some properties of the ap-Denjoy integral.

• 대한수학회논문집
• /
• 제29권2호
• /
• pp.345-349
• /
• 2014

We show that $C^1$-generically, a differentiable map is positively measure expansive if and only if it is expanding.

• 대한수학회보
• /
• 제32권1호
• /
• 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 $$ (0.1) \dot{p} = -\frac{\partial q}{\partial H}(p, q), \dot{q} = \frac{\partial p}{\partial H}(p, q) $$.

• 대한수학회논문집
• /
• 제26권1호
• /
• pp.125-133
• /
• 2011

A new kind of structure is introduced in an even dimensional differentiable Riemannian manifold and some basic properties of this structure is discussed. Also the existence of such structure is shown with an example.