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Related Concept Videos

Transformers in Distribution System01:27

Transformers in Distribution System

98
Transformers in distribution systems can be broadly categorized into distribution substation transformers and other distribution transformers. They are crucial for stepping down high transmission voltages to levels suitable for distribution and end-user applications.
Distribution substation transformers come in various ratings and typically use mineral oil for insulation and cooling. To prevent moisture and air from entering the oil, some transformers use an inert gas like nitrogen to fill the...
98
Transformers with Off-Nominal Turns Ratios01:25

Transformers with Off-Nominal Turns Ratios

139
In scenarios involving parallel transformers with disparate ratings, developing per-unit models requires accommodating off-nominal turns ratios. This situation arises when the selected base voltages are not proportional to the transformer’s voltage ratings. Consider a transformer where the rated voltages are related by the term a. If the chosen voltage bases satisfy a relationship involving term b, term c is defined as the ratio of these bases. This ratio is then substituted into the...
139
Three-Winding Transformers01:19

Three-Winding Transformers

200
Three identical single-phase transformers can be configured to form a three-phase transformer connection, which involves high-voltage and low-voltage windings. The high-voltage windings are denoted by capital letters A-B-C, while the low-voltage windings are labeled with lowercase letters a-b-c, representing their respective phases. This notation helps distinguish between the high and low voltage sides of the transformer.
In the per-unit equivalent circuit of a grounded Y-Y three-phase...
200
Types Of Transformers01:16

Types Of Transformers

948
Transformers can provide desired voltages to a circuit by modifying the number of turns in the secondary windings.
If the ratio of the number of turns in the secondary winding to that of the primary winding is greater than one, then the transformer is said to be a step-up transformer. In a step-up transformer, the voltage at the secondary winding is greater than the voltage applied at the primary winding.
However, if this ratio is less than one, the transformer is said to be a step-down...
948
Energy Losses in Transformers01:21

Energy Losses in Transformers

834
In an ideal transformer, it is assumed that there are no energy losses, and, hence, all the power at the primary winding is transferred to the secondary winding. However, in reality,  the transformers always have some energy losses, and, hence, the output power obtained at the secondary winding is less than the input power at the primary winding due to energy losses.
There are four main reasons for energy losses in transformers.
The first cause can be  the high resistance of the...
834
Equivalent Circuits for Practical Transformers01:28

Equivalent Circuits for Practical Transformers

397
The practical equivalent circuits of single-phase two-winding transformers exhibit significant deviations from their idealized versions due to the inherent properties of winding resistance and finite core permeability. These properties result in real and reactive power losses, affecting the transformer's performance. Understanding these deviations is crucial for designing more efficient transformers.
In a practical transformer, each winding exhibits resistance and leakage reactance. The...
397

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Generalization Analysis of Transformers in Distribution Regression.

Peilin Liu1, Ding-Xuan Zhou2

  • 1School of Mathematics and Statistics, University of Sydney, Sydney, NSW 2006, Australia peilin.liu@sydney.edu.au.

Neural Computation
|November 18, 2024
PubMed
Summary
This summary is machine-generated.

This study introduces a mathematical framework for transformer learning, explaining how their attention mechanisms compress data. This provides theoretical support for efficient techniques in large language models (LLMs).

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Area of Science:

  • Deep Learning
  • Artificial Intelligence
  • Machine Learning Theory

Background:

  • Transformer models are key in deep learning, with techniques like parameter-efficient fine-tuning enhancing performance.
  • Existing successful strategies for transformers lack rigorous mathematical theoretical support.

Purpose of the Study:

  • To develop a theoretical framework for understanding transformer mechanisms and related techniques.
  • To mathematically formulate the attention mechanism and analyze transformer capabilities.

Main Methods:

  • Proposed a transformer learning framework based on distribution regression.
  • Introduced a mathematical formulation of the attention mechanism as an "attention operator".
  • Connected a two-stage sampling process with natural language processing.

Main Results:

  • Demonstrated that the attention operator enables transformers to compress distributions into information-preserving function representations.
  • Showed transformers possess superior capability in learning complex functionals compared to CNNs and FCNs.
  • Derived a generalization bound within the distribution regression framework.

Conclusions:

  • The theoretical results offer insights into the mechanisms of transformers and their application in large language models (LLMs).
  • Provided theoretical explanations for techniques such as prompt tuning, parameter-efficient fine-tuning, and efficient scaling within the novel analysis framework.