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Related Concept Videos

Transfer Function to State Space01:23

Transfer Function to State Space

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State-space representation is a powerful tool for simulating physical systems on digital computers, necessitating the conversion of the transfer function into state-space form. Consider an nth-order linear differential equation with constant coefficients, like those encountered in an RLC circuit. The state variables are selected as the output and its n−1 derivatives. Differentiating these variables and substituting them back into the original equation produces the state equations.
In an RLC...
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State Space to Transfer Function01:21

State Space to Transfer Function

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The conversion of state-space representation to a transfer function is a fundamental process in system analysis. It provides a method for transitioning from a time-domain description to a frequency-domain representation, which is crucial for simplifying the analysis and design of control systems.
The transformation process begins with the state-space representation, characterized by the state equation and the output equation. These equations are typically represented as:
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Higher Mental Functions of Brain: Learning and Memory01:26

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Memory is one of the most vital higher mental functions of the brain. Memory is closely related to learning because it enables us to retain information and experiences from our past to use them in our present life. It also helps us to remember facts, events, and skills, such as riding a bike or swimming. There are two types of memory — declarative memory, which involves memorizing facts or events, and procedural memory, which enables us to remember how to do something like writing or...
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Machines01:19

Machines

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Machines are complex structures consisting of movable, pin-connected multi-force members that work together to transmit forces. One example of a machine is the cutting plier, which is used to cut wires by applying forces to its handles. When equal and opposite forces are exerted on the handles of the cutting plier, they cause the cutting edges to come together and apply equal and opposite reaction forces on the wire, which are greater than the applied forces.
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Space Trusses01:25

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A space truss is a three-dimensional counterpart of a planar truss. These structures consist of members connected at their ends, often utilizing ball-and-socket joints to create a stable and versatile framework. The space truss is widely used in various construction projects due to its adaptability and capacity to withstand complex loads.
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The frequency-domain technique, commonly used in analyzing and designing feedback control systems, is effective for linear, time-invariant systems. However, it falls short when dealing with nonlinear, time-varying, and multiple-input multiple-output systems. The time-domain or state-space approach addresses these limitations by utilizing state variables to construct simultaneous, first-order differential equations, known as state equations, for an nth-order system.
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Exploring the Function Space of Deep-Learning Machines.

Bo Li1, David Saad2

  • 1Department of Physics, The Hong Kong University of Science and Technology, Hong Kong.

Physical Review Letters
|June 30, 2018
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Summary
This summary is machine-generated.

Deep learning function spaces are explored using entropy and physics-inspired methods. This reveals layerwise convergence and the importance of network depth for improved accuracy.

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Area of Science:

  • Artificial Intelligence
  • Machine Learning
  • Deep Learning Theory

Background:

  • Deep learning models possess complex function spaces.
  • Understanding function space geometry is crucial for model interpretability and optimization.
  • Current methods often lack theoretical grounding in physics principles.

Purpose of the Study:

  • To investigate the function space of deep learning machines.
  • To analyze the role of network architecture and depth in function space exploration.
  • To understand the impact of error on function space convergence.

Main Methods:

  • Studied the growth in entropy of functions with respect to a reference function.
  • Employed physics-inspired methods to analyze function spaces.
  • Investigated both sparsely and densely connected deep learning architectures.
  • Examined layerwise convergence and entropy reduction as functions approach a reference.

Main Results:

  • Observed layerwise convergence of candidate functions towards a reference function.
  • Demonstrated a reduction in entropy correlating with improved accuracy.
  • Gained insights into the significance of a large number of layers in deep networks.
  • Identified phase transitions in function space behavior as error increases.

Conclusions:

  • The study provides a physics-inspired framework for understanding deep learning function spaces.
  • Layerwise convergence and entropy reduction are key indicators of learning progress.
  • Network depth plays a critical role in navigating the function space effectively.
  • The findings offer theoretical insights into deep learning optimization and generalization.