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Related Concept Videos

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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.
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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.
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A toggle clamp is a mechanical device commonly used for holding and clamping objects in various applications, such as woodworking, metalworking, and assembly operations. Consider a toggle clamp subjected to a force of 200 N at the handle. The vertical clamping force can be calculated, provided the dimensions of the toggle clamp are known.
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Statically indeterminate problems are those where statics alone can not determine the internal forces or reactions. Consider a structure comprising two cylindrical rods made of steel and brass. These rods are joined at point B and restrained by rigid supports at points A and C. Now, the reactions at points A and C and the deflection at point B are to be determined. This rod structure is classified as statically indeterminate as the structure has more supports than are necessary for maintaining...
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Deep Neural Networks for Image-Based Dietary Assessment
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Optimal training of integer-valued neural networks with mixed integer programming.

Tómas Thorbjarnarson1, Neil Yorke-Smith1

  • 1Algorithmics Group, Faculty of Electrical Engineering, Mathematics and Computer Science, Delft University of Technology, Delft, The Netherlands.

Plos One
|February 1, 2023
PubMed
Summary
This summary is machine-generated.

Training neural networks (NNs) with Mixed Integer Programming (MIP) solvers is enhanced by new methods. These approaches improve efficiency, handle more data, and optimize network architecture, outperforming prior state-of-the-art for data-limited scenarios.

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Area of Science:

  • Artificial Intelligence
  • Machine Learning
  • Optimization

Background:

  • Current neural network (NN) training relies heavily on gradient-based methods, demanding substantial data, GPU computation, and hyper-parameter tuning.
  • Training NNs using Mixed Integer Programming (MIP) solvers is an emerging area, offering potential advantages like reduced GPU and hyper-parameter tuning needs.
  • Existing MIP-based NN training methods are limited by their capacity to handle only small datasets.

Purpose of the Study:

  • To explore and advance the under-researched approach of training neural networks (NNs) using Mixed Integer Programming (MIP) solvers.
  • To develop novel MIP formulations that enhance training efficiency and enable the training of integer-valued neural networks (INNs).
  • To address the data limitations of current MIP-based NN training methods and optimize NN architecture during the training process.

Main Methods:

  • Formulation of new Mixed Integer Programming (MIP) models for training neural networks (NNs), specifically targeting binarized NNs and integer-valued neural networks (INNs).
  • Introduction of a novel method to optimize the number of neurons within the NN during the training phase, reducing reliance on pre-defined architectures.
  • Development of a batch training approach to significantly increase the volume of training data that MIP solvers can effectively process.

Main Results:

  • The proposed MIP models demonstrate improved training efficiency compared to previous methods.
  • The new methods successfully train integer-valued neural networks (INNs) and optimize network architecture dynamically.
  • Experimental results on two real-world, data-limited datasets show superior performance in accuracy, training time, and data utilization compared to the state-of-the-art in MIP-based NN training.

Conclusions:

  • This research presents a significant advancement in training neural networks (NNs) using Mixed Integer Programming (MIP), particularly for data-limited scenarios.
  • The methodology is proficient in training NNs with minimal data and low memory requirements, making it suitable for resource-constrained deployments.
  • The developed techniques offer a promising direction for leveraging MIP solvers in NN training, overcoming previous scalability and efficiency challenges.