相关实验视频
Updated: Mar 11, 2026

13:19
Deep Neural Networks for Image-Based Dietary Assessment
Published on: March 13, 2021
10.1K
在神经PDE解答器和操作者学习中基于残余的适应性的一个变化框架.
Juan Diego Toscano1, Daniel T Chen1, Vivek Ooomen2
1Division of Applied Mathematics, Brown University, Providence, RI USA.
概括
我们在科学机器学习中引入了基于残余的适应性策略的变化框架. 这种方法使启发式方法正式化,使系统设计成为可能,并减少对增强学习动态的分类错误.
科学领域:
- 科学机器学习科学机器学习
- 数字分析 数字分析
- 优化理论 优化理论
背景情况:
- 基于残留的自适应策略在科学机器学习中至关重要,但往往缺乏理论基础.
- 目前的方法在很大程度上是启发式的,限制了系统的设计和优化.
- 需要一个正式的框架来将适应性策略与底层的错误指标和学习目标联系起来.
研究的目的:
- 引入一个可变的框架,将基于残余的适应性策略正式化.
- 为了证明残余环的凸变是如何适应特定目标函数和采样分布的适应权重.
- 为设计适应性方案建立一个原则基础,减少分类错误,改善学习动态.
主要方法:
- 开发了一个变化框架,使用剩余的凸变换.
- 将不同的转换 (例如指数,线性权重) 与不同的目标函数 (例如统一,二次误差最小化) 联系起来.
- 将框架扩展到操作员学习问题,分析其对优化器和架构的影响.
主要成果:
- 该框架提供了适应权重的原则性方法,将离散选择与错误指标联系起来.
- 通过降低估计器方差,证明了对离散化误差的减少.
- 通过改进的梯度信号与噪声比,展示了增强的学习动态.
- 在各种优化器和架构中实现了操作员学习的实质性性能提升.
结论:
- 变化框架为科学机器学习中的基于残余的适应性提供了一个理论视角.
- 建立了原则性离散和培训策略的基础.
- 突出了系统设计的潜力,并改进了适应性方法的性能.
相关概念视频
Linear Approximation in Frequency Domain
412
Linear systems are characterized by two main properties: superposition and homogeneity. Superposition allows the response to multiple inputs to be the sum of the responses to each individual input. Homogeneity ensures that scaling an input by a scalar results in the response being scaled by the same scalar.
In contrast, nonlinear systems do not inherently possess these properties. However, for small deviations around an operating point, a nonlinear system can often be approximated as linear....
In contrast, nonlinear systems do not inherently possess these properties. However, for small deviations around an operating point, a nonlinear system can often be approximated as linear....
412
State Function, Exact and Inexact Differentials
44
A state function is a thermodynamic property that depends solely on the current state of a system, irrespective of its history or how it arrived at that state. These functions are represented by capital letters, such as U, H, and S, which stand for internal energy, enthalpy, and entropy, respectively.For instance, the value of internal energy depends on the system's state variables and remains unaffected by the process path. This means that whether the system underwent a linear process or a...
44
Modeling with Differential Equations
138
Population dynamics can be described mathematically by considering the population size P(t) as a function of time. The rate of change of the population is then represented by the derivative of P(t). A simple assumption is that the rate of growth is proportional to the size of the population itself. This leads to an exponential growth model, where the population increases rapidly without bound. While this is a useful first approximation, it does not reflect realistic long-term...
138
Separable Differential Equations
186
A separable differential equation is a type of first-order differential equation where the derivative dy/dx can be expressed as a product of two functions: one that depends only on x and another that depends only on y. This allows for the rearrangement of the equation so that all terms involving y are on one side, and all terms involving x are on the other. This process, known as the separation of variables, simplifies the process of solving the equation by enabling the integration of both...
186
Mechanistic Models: Compartment Models in Algorithms for Numerical Problem Solving
376
Mechanistic models play a crucial role in algorithms for numerical problem-solving, particularly in nonlinear mixed effects modeling (NMEM). These models aim to minimize specific objective functions by evaluating various parameter estimates, leading to the development of systematic algorithms. In some cases, linearization techniques approximate the model using linear equations.
In individual population analyses, different algorithms are employed, such as Cauchy's method, which uses a...
In individual population analyses, different algorithms are employed, such as Cauchy's method, which uses a...
376
Second Derivatives and Laplace Operator
2.7K
The first order operators using the del operator include the gradient, divergence and curl. Certain combinations of first order operators on a scalar or vector function yield second order expressions. Second-order expressions play a very important role in mathematics and physics. Some second order expressions include the divergence and curl of a gradient function, the divergence and curl of a curl function, and the gradient of a divergence function.
Consider a scalar function. The curl of its...
Consider a scalar function. The curl of its...
2.7K