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Related Concept Videos

Linearization and Approximation01:26

Linearization and Approximation

Linearization is a mathematical technique used to approximate complex, nonlinear functions with simpler linear models in the vicinity of a chosen reference point. The method is based on the idea that, although a function may be difficult to evaluate exactly, its behavior near a specific input value can often be closely approximated by the tangent line at that point. This approach is particularly useful when small deviations from a known value are involved.Consider the square root function, for...
Linear Approximations01:23

Linear Approximations

For a differentiable function of two variables, linear approximation estimates values near a known point by replacing the curved surface with its tangent plane. Consider the function\begin{equation*}f(x,y)=x^2+3y^2\end{equation*}near the point (2, 1). The exact value at this point is f(2, 1) = 22 + 3(1)2 = 4 + 3 = 7.The linear approximation of f(x, y)) near (a, b) is\begin{equation*}L(x,y)=f(a,b)+f_x(a,b)(x-a)+f_y(a,b)(y-b)\end{equation*}First, compute the partial derivatives: fx(x, y) = 2x and...
Multi-input and Multi-variable systems01:22

Multi-input and Multi-variable systems

Cruise control systems in cars are designed as multi-input systems to maintain a driver's desired speed while compensating for external disturbances such as changes in terrain. The block diagram for a cruise control system typically includes two main inputs: the desired speed set by the driver and any external disturbances, such as the incline of the road. By adjusting the engine throttle, the system maintains the vehicle's speed as close to the desired value as possible.
In the absence of...
Propagation of Uncertainty from Random Error00:59

Propagation of Uncertainty from Random Error

An experiment often consists of more than a single step. In this case, measurements at each step give rise to uncertainty. Because the measurements occur in successive steps, the uncertainty in one step necessarily contributes to that in the subsequent step. As we perform statistical analysis on these types of experiments, we must learn to account for the propagation of uncertainty from one step to the next. The propagation of uncertainty depends on the type of arithmetic operation performed on...
Mechanistic Models: Compartment Models in Algorithms for Numerical Problem Solving01:29

Mechanistic Models: Compartment Models in Algorithms for Numerical Problem Solving

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...
Propagation of Uncertainty from Systematic Error01:10

Propagation of Uncertainty from Systematic Error

The atomic mass of an element varies due to the relative ratio of its isotopes. A sample's relative proportion of oxygen isotopes influences its average atomic mass. For instance, if we were to measure the atomic mass of oxygen from a sample, the mass would be a weighted average of the isotopic masses of oxygen in that sample. Since a single sample is not likely to perfectly reflect the true atomic mass of oxygen for all the molecules of oxygen on Earth, the mass we obtain from this particular...

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Related Experiment Videos

Beyond feedforward models trained by backpropagation: a practical training tool for a more efficient universal

Roman Ilin1, Robert Kozma, Paul J Werbos

  • 1Department of Computer Science, University of Memphis, Memphis, TN 38117, USA. rilin@memphis.edu

IEEE Transactions on Neural Networks
|June 11, 2008
PubMed
Summary

This study enhances cellular simultaneous recurrent neural networks (SRN) using the extended Kalman filter (EKF) for faster training. The improved SRN model demonstrates superior performance in complex tasks like maze navigation and problem-solving.

Related Experiment Videos

Area of Science:

  • Computational neuroscience
  • Artificial intelligence
  • Machine learning

Background:

  • Cellular simultaneous recurrent neural networks (SRN) offer greater functional approximation power than multilayer perceptrons (MLP).
  • Training speed is a critical factor for the practical application of complex recurrent neural networks.
  • Existing SRN models face computational constraints for certain complex problems.

Purpose of the Study:

  • To improve the training speed and performance of cellular SRN.
  • To implement and evaluate a generic cellular SRN (CSRN) model.
  • To demonstrate the effectiveness of the extended Kalman filter (EKF) in training SRNs.

Main Methods:

  • Implementation of a generic cellular SRN (CSRN).
  • Application of the extended Kalman filter (EKF) for network training.
  • Testing the CSRN model on 2-D maze navigation and a subset of the connectedness problem.

Main Results:

  • Achieved several orders of magnitude improvement in convergence speed for maze navigation compared to previous methods.
  • Demonstrated superior generalization capabilities on the connectedness problem.
  • Validated the efficiency and effectiveness of EKF-trained CSRNs.

Conclusions:

  • The EKF significantly accelerates the training of cellular SRNs, making them more computationally feasible.
  • Enhanced SRN models show promise for solving complex computational problems with improved accuracy and speed.
  • This advancement has significant implications for the application of recurrent neural networks in various fields.