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Related Concept Videos

Introduction to Learning01:18

Introduction to Learning

Learning is the process of acquiring knowledge or skills through practice or experience, leading to long-lasting behavioral changes. This acquisition occurs through interaction with the environment and requires practice or experience. For instance, mastering a skill such as surfing requires considerable practice and experience, highlighting the essential role of repeated interactions with the environment in learning.
In contrast to learned behaviors, unlearned behaviors such as crying, sexual...
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.
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Associative Learning01:27

Associative Learning

Associative learning is a fundamental concept in behavioral psychology, wherein a connection is established between two stimuli or events, leading to a learned response. This process is critical in understanding how behaviors are acquired and modified. Conditioning, the mechanism through which associations are formed, can be divided into two main types: classical conditioning and operant conditioning, each elucidating different aspects of associative learning.
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Cognitive Learning01:21

Cognitive Learning

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Application of Linearization and Approximation01:29

Application of Linearization and Approximation

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Related Experiment Video

Updated: Jul 7, 2026

Augmenting Large Language Models via Vector Embeddings to Improve Domain-Specific Responsiveness
03:14

Augmenting Large Language Models via Vector Embeddings to Improve Domain-Specific Responsiveness

Published on: December 6, 2024

LMS learning algorithms: misconceptions and new results on converence.

Z Q Wang1, M T Manry, J L Schiano

  • 1FAS Technologies, Dallas, TX 75238, USA. zwang@fas.com

IEEE Transactions on Neural Networks
|February 6, 2008
PubMed
Summary
This summary is machine-generated.

The Widrow-Hoff delta rule, used in neural network training, does not generally converge. Under repetitive learning, this popular Widrow-Hoff rule converges only to a limit cycle, contrary to common belief.

Related Experiment Videos

Last Updated: Jul 7, 2026

Augmenting Large Language Models via Vector Embeddings to Improve Domain-Specific Responsiveness
03:14

Augmenting Large Language Models via Vector Embeddings to Improve Domain-Specific Responsiveness

Published on: December 6, 2024

Area of Science:

  • Machine Learning
  • Artificial Intelligence
  • Neural Networks

Background:

  • The Widrow-Hoff delta rule is a widely used algorithm for training neural networks, including the ADALINE and nonlinear networks.
  • Despite its popularity, there are misconceptions regarding its convergence properties.

Purpose of the Study:

  • To provide an in-depth analysis of the Widrow-Hoff rule's convergence properties.
  • To clarify misconceptions about the rule's behavior under repetitive learning.

Main Methods:

  • Analysis within the least mean square (LMS) framework.
  • Consideration of repetitive learning scenarios with a fixed training dataset.

Main Results:

  • The nonbatch Widrow-Hoff rule does not converge in general when using a fixed set of training samples.
  • Convergence is limited to a limit cycle, challenging common assumptions.

Conclusions:

  • The Widrow-Hoff rule's convergence is not guaranteed under repetitive learning.
  • Understanding these limitations is crucial for effective neural network training and application.