The document describes the backpropagation algorithm for training multilayer neural networks. It discusses how backpropagation uses gradient descent to minimize error between network outputs and targets by calculating error gradients with respect to weights. The algorithm iterates over examples, calculates error, computes gradients to update weights. Momentum can be added to help escape local minima. Backpropagation can learn representations in hidden layers and is prone to overfitting without validation data to select the best model.
Advanced topics in artificial neural networksswapnac12
The document discusses various advanced topics in artificial neural networks including alternative error functions, error minimization procedures, recurrent networks, and dynamically modifying network structure. It describes adding penalty terms to the error function to reduce weights and overfitting, using line search and conjugate gradient methods for error minimization, how recurrent networks can capture dependencies over time, and algorithms for growing or pruning network complexity like cascade correlation.
Search techniques in ai, Uninformed : namely Breadth First Search and Depth First Search, Informed Search strategies : A*, Best first Search and Constraint Satisfaction Problem: criptarithmatic
This document provides an overview of artificial neural networks and the backpropagation algorithm. It discusses how neural networks are inspired by biological neural systems and how they represent problems as interconnected nodes. The backpropagation algorithm is introduced as a way to train multilayer neural networks by calculating error gradients to update weights. An example application of neural network for face recognition is also mentioned. Key aspects of neural network representations, perceptrons, the perceptron training rule, and gradient descent/delta rule for training are summarized.
This document discusses inductive bias in machine learning. It defines inductive bias as the assumptions that allow an inductive learning system to generalize beyond its training data. Without some biases, a learning system cannot rationally classify new examples. The document compares different learning algorithms based on the strength of their inductive biases, from weak biases like rote learning to stronger biases like preferring more specific hypotheses. It argues that all inductive learning systems require some inductive biases to generalize at all.
This document provides an overview of Bayesian learning methods. It discusses key concepts like Bayes' theorem, maximum a posteriori hypotheses, maximum likelihood hypotheses, and how Bayesian learning relates to concept learning problems. Bayesian learning allows prior knowledge to be combined with observed data, hypotheses can make probabilistic predictions, and new examples are classified by weighting multiple hypotheses by their probabilities. While computationally intensive, Bayesian methods provide an optimal standard for decision making.
1) The document discusses concept learning, which involves inferring a Boolean function from training examples. It focuses on a concept learning task where hypotheses are represented as vectors of constraints on attribute values.
2) It describes the FIND-S algorithm, which finds the most specific hypothesis consistent with positive examples by generalizing constraints. However, FIND-S has limitations like ignoring negative examples.
3) The Candidate-Elimination algorithm represents the version space of all hypotheses consistent with examples to address FIND-S limitations. It outputs the version space rather than a single hypothesis.
This document discusses evaluating hypotheses and estimating hypothesis accuracy. It provides the following key points:
- The accuracy of a hypothesis estimated from a training set may be different from its true accuracy due to bias and variance. Testing the hypothesis on an independent test set provides an unbiased estimate.
- Given a hypothesis h that makes r errors on a test set of n examples, the sample error r/n provides an unbiased estimate of the true error. The variance of this estimate depends on r and n based on the binomial distribution.
- For large n, the binomial distribution can be approximated by the normal distribution. Confidence intervals for the true error can then be determined based on the sample error and standard deviation
Instance-based learning algorithms like k-nearest neighbors (KNN) and locally weighted regression are conceptually straightforward approaches to function approximation problems. These algorithms store all training data and classify new query instances based on similarity to near neighbors in the training set. There are three main approaches: lazy learning with KNN, radial basis functions using weighted methods, and case-based reasoning. Locally weighted regression generalizes KNN by constructing an explicit local approximation to the target function for each query. Radial basis functions are another related approach using Gaussian kernel functions centered on training points.
Advanced topics in artificial neural networksswapnac12
The document discusses various advanced topics in artificial neural networks including alternative error functions, error minimization procedures, recurrent networks, and dynamically modifying network structure. It describes adding penalty terms to the error function to reduce weights and overfitting, using line search and conjugate gradient methods for error minimization, how recurrent networks can capture dependencies over time, and algorithms for growing or pruning network complexity like cascade correlation.
Search techniques in ai, Uninformed : namely Breadth First Search and Depth First Search, Informed Search strategies : A*, Best first Search and Constraint Satisfaction Problem: criptarithmatic
This document provides an overview of artificial neural networks and the backpropagation algorithm. It discusses how neural networks are inspired by biological neural systems and how they represent problems as interconnected nodes. The backpropagation algorithm is introduced as a way to train multilayer neural networks by calculating error gradients to update weights. An example application of neural network for face recognition is also mentioned. Key aspects of neural network representations, perceptrons, the perceptron training rule, and gradient descent/delta rule for training are summarized.
This document discusses inductive bias in machine learning. It defines inductive bias as the assumptions that allow an inductive learning system to generalize beyond its training data. Without some biases, a learning system cannot rationally classify new examples. The document compares different learning algorithms based on the strength of their inductive biases, from weak biases like rote learning to stronger biases like preferring more specific hypotheses. It argues that all inductive learning systems require some inductive biases to generalize at all.
This document provides an overview of Bayesian learning methods. It discusses key concepts like Bayes' theorem, maximum a posteriori hypotheses, maximum likelihood hypotheses, and how Bayesian learning relates to concept learning problems. Bayesian learning allows prior knowledge to be combined with observed data, hypotheses can make probabilistic predictions, and new examples are classified by weighting multiple hypotheses by their probabilities. While computationally intensive, Bayesian methods provide an optimal standard for decision making.
1) The document discusses concept learning, which involves inferring a Boolean function from training examples. It focuses on a concept learning task where hypotheses are represented as vectors of constraints on attribute values.
2) It describes the FIND-S algorithm, which finds the most specific hypothesis consistent with positive examples by generalizing constraints. However, FIND-S has limitations like ignoring negative examples.
3) The Candidate-Elimination algorithm represents the version space of all hypotheses consistent with examples to address FIND-S limitations. It outputs the version space rather than a single hypothesis.
This document discusses evaluating hypotheses and estimating hypothesis accuracy. It provides the following key points:
- The accuracy of a hypothesis estimated from a training set may be different from its true accuracy due to bias and variance. Testing the hypothesis on an independent test set provides an unbiased estimate.
- Given a hypothesis h that makes r errors on a test set of n examples, the sample error r/n provides an unbiased estimate of the true error. The variance of this estimate depends on r and n based on the binomial distribution.
- For large n, the binomial distribution can be approximated by the normal distribution. Confidence intervals for the true error can then be determined based on the sample error and standard deviation
Instance-based learning algorithms like k-nearest neighbors (KNN) and locally weighted regression are conceptually straightforward approaches to function approximation problems. These algorithms store all training data and classify new query instances based on similarity to near neighbors in the training set. There are three main approaches: lazy learning with KNN, radial basis functions using weighted methods, and case-based reasoning. Locally weighted regression generalizes KNN by constructing an explicit local approximation to the target function for each query. Radial basis functions are another related approach using Gaussian kernel functions centered on training points.
Performance analysis and randamized agorithamlilyMalar1
The document discusses performance analysis of algorithms in terms of space and time complexity. It provides examples to show how to calculate the space and time complexity of algorithms. Specifically, it analyzes the space and time complexity of a sum algorithm. For space complexity, it identifies the fixed and variable components, showing the space complexity is O(n). For time complexity, it analyzes the number of steps and their frequency to determine the time complexity is O(2n+3). The document also discusses other algorithm analysis topics like asymptotic notations, amortized analysis, and randomized algorithms.
The document discusses multilayer neural networks and the backpropagation algorithm. It begins by introducing sigmoid units as differentiable threshold functions that allow gradient descent to be used. It then describes the backpropagation algorithm, which employs gradient descent to minimize error by adjusting weights. Key aspects covered include defining error terms for multiple outputs, deriving the weight update rules, and generalizing to arbitrary acyclic networks. Issues like local minima and representational power are also addressed.
The document discusses space complexity, which refers to the amount of memory required by an algorithm. It explains how to calculate the space complexity of an algorithm by considering the fixed parts, like code and constants, and variable parts, like arrays and recursion stacks. It provides an example of calculating the space complexity of an addition algorithm as O(c+3) words and a recursive sum algorithm as O(c+4n+4) words.
Threads provide concurrency within a process by allowing parallel execution. A thread is a flow of execution that has its own program counter, registers, and stack. Threads share code and data segments with other threads in the same process. There are two types: user threads managed by a library and kernel threads managed by the operating system kernel. Kernel threads allow true parallelism but have more overhead than user threads. Multithreading models include many-to-one, one-to-one, and many-to-many depending on how user threads map to kernel threads. Threads improve performance over single-threaded processes and allow for scalability across multiple CPUs.
The document provides an overview of machine learning concepts including:
- Defining machine learning as computer algorithms that improve with experience and data
- Describing examples like speech recognition, medical diagnosis, and game playing
- Outlining the components of designing a machine learning system like choosing the target function, representation, and learning algorithm
- Explaining concepts like version spaces, decision trees, and neural networks that are used in machine learning applications
Loop optimization is a technique to improve the performance of programs by optimizing the inner loops which take a large amount of time. Some common loop optimization methods include code motion, induction variable and strength reduction, loop invariant code motion, loop unrolling, and loop fusion. Code motion moves loop-invariant code outside the loop to avoid unnecessary computations. Induction variable and strength reduction techniques optimize computations involving induction variables. Loop invariant code motion avoids repeating computations inside loops. Loop unrolling replicates loop bodies to reduce loop control overhead. Loop fusion combines multiple nested loops to reduce the total number of iterations.
This document discusses feature selection concepts and methods. It defines features as attributes that determine which class an instance belongs to. Feature selection aims to select a relevant subset of features by removing irrelevant, redundant and unnecessary data. This improves learning accuracy, model performance and interpretability. The document categorizes feature selection algorithms as filter, wrapper or embedded methods based on how they evaluate feature subsets. It also discusses concepts like feature relevance, search strategies, successor generation and evaluation measures used in feature selection algorithms.
The document discusses the theoretical framework of computational learning theory and PAC (Probably Approximately Correct) learning. It defines what makes a learning problem PAC learnable and examines how the number of training examples needed for learning is affected by factors like the hypothesis space size, error tolerance, and confidence level. Key questions addressed include determining learnability of problem classes and bounding the sample complexity of learning algorithms.
The document discusses decision tree learning and the ID3 algorithm. It begins by introducing decision trees and how they are used to classify instances by sorting them from the root node to a leaf node. It then discusses how ID3 builds decision trees in a top-down greedy manner by selecting the attribute that best splits the data at each node based on information gain. The document also covers issues like overfitting, handling continuous attributes, and pruning decision trees.
Bayesian Learning by Dr.C.R.Dhivyaa Kongu Engineering CollegeDhivyaa C.R
This document provides an overview of Bayesian learning methods. It discusses key concepts like Bayes' theorem, maximum a posteriori hypotheses, and maximum likelihood hypotheses. Bayes' theorem allows calculating the posterior probability of a hypothesis given observed data and prior probabilities. The maximum a posteriori hypothesis is the one with the highest posterior probability. Maximum likelihood hypotheses maximize the likelihood of the data. Bayesian learning faces challenges from requiring many initial probabilities and high computational costs but provides a useful perspective on machine learning algorithms.
The document discusses analytical learning methods like explanation-based learning. It explains that analytical learning uses prior knowledge and deductive reasoning to augment training examples, allowing it to generalize better than methods relying solely on data. Explanation-based learning analyzes examples according to prior knowledge to infer relevant features. The document provides examples of using explanation-based learning to learn chess concepts and safe stacking of objects. It also describes the PROLOG-EBG algorithm for explanation-based learning.
1) The document discusses various search algorithms including uninformed searches like breadth-first search as well as informed searches using heuristics.
2) It describes greedy best-first search which uses a heuristic function to select the node closest to the goal at each step, and A* search which uses both path cost and heuristic cost to guide the search.
3) Genetic algorithms are introduced as a search technique that generates successors by combining two parent states through crossover and mutation rather than expanding single nodes.
Learning can occur through various methods like memorization, being taught directly, learning from examples, induction, and deduction. Rote learning involves simply memorizing information without understanding. Learning from advice involves translating advice from experts into operational rules. Learning from examples involves classifying things without explicit rules by being corrected when wrong. Various learning mechanisms exist, with rote learning being the simplest form of storing information, while learning from examples and analogies requires more complex inference.
Concept learning and candidate elimination algorithmswapnac12
This document discusses concept learning, which involves inferring a Boolean-valued function from training examples of its input and output. It describes a concept learning task where each hypothesis is a vector of six constraints specifying values for six attributes. The most general and most specific hypotheses are provided. It also discusses the FIND-S algorithm for finding a maximally specific hypothesis consistent with positive examples, and its limitations in dealing with noise or multiple consistent hypotheses. Finally, it introduces the candidate-elimination algorithm and version spaces as an improvement over FIND-S that can represent all consistent hypotheses.
This document discusses Bayesian learning and the Bayes theorem. Some key points:
- Bayesian learning uses probabilities to calculate the likelihood of hypotheses given observed data and prior probabilities. The naive Bayes classifier is an example.
- The Bayes theorem provides a way to calculate the posterior probability of a hypothesis given observed training data by considering the prior probability and likelihood of the data under the hypothesis.
- Bayesian methods can incorporate prior knowledge and probabilistic predictions, and classify new instances by combining predictions from multiple hypotheses weighted by their probabilities.
Introdution and designing a learning systemswapnac12
The document discusses machine learning and provides definitions and examples. It covers the following key points:
- Machine learning is a subfield of artificial intelligence concerned with developing algorithms that allow computers to learn from data without being explicitly programmed.
- Well-posed learning problems have a defined task, performance measure, and training experience. Examples given include learning to play checkers and recognize handwritten words.
- Designing a machine learning system involves choosing a training experience, target function, representation of the target function, and learning algorithm to approximate the function. A checkers-playing example is used to illustrate these design decisions.
A thread is an independent path of execution within a Java program. The Thread class in Java is used to create threads and control their behavior and execution. There are two main ways to create threads - by extending the Thread class or implementing the Runnable interface. The run() method contains the code for the thread's task and threads can be started using the start() method. Threads have different states like New, Runnable, Running, Waiting etc during their lifecycle.
Greedy algorithms work by making locally optimal choices at each step to arrive at a global optimal solution. They require that the problem exhibits the greedy choice property and optimal substructure. Examples that can be solved with greedy algorithms include fractional knapsack problem, minimum spanning tree, and activity selection. The fractional knapsack problem is solved greedily by sorting items by value/weight ratio and filling the knapsack completely. The 0/1 knapsack problem differs in that items are indivisible.
This document discusses neural networks and multilayer feedforward neural network architectures. It describes how multilayer networks can solve nonlinear classification problems using hidden layers. The backpropagation algorithm is introduced as a way to train these networks by propagating error backwards from the output to adjust weights. The architecture of a neural network is explained, including input, hidden, and output nodes. Backpropagation is then described in more detail through its training process of forward passing input, calculating error at the output, and propagating this error backwards to update weights. Examples of backpropagation and its applications are also provided.
Web Spam Classification Using Supervised Artificial Neural Network Algorithmsaciijournal
Due to the rapid growth in technology employed by the spammers, there is a need of classifiers that are
more efficient, generic and highly adaptive. Neural Network based technologies have high ability of
adaption as well as generalization. As per our knowledge, very little work has been done in this field using
neural network. We present this paper to fill this gap. This paper evaluates performance of three supervised
learning algorithms of artificial neural network by creating classifiers for the complex problem of latest
web spam pattern classification. These algorithms are Conjugate Gradient algorithm, Resilient Backpropagation learning, and Levenberg-Marquardt algorithm.
Performance analysis and randamized agorithamlilyMalar1
The document discusses performance analysis of algorithms in terms of space and time complexity. It provides examples to show how to calculate the space and time complexity of algorithms. Specifically, it analyzes the space and time complexity of a sum algorithm. For space complexity, it identifies the fixed and variable components, showing the space complexity is O(n). For time complexity, it analyzes the number of steps and their frequency to determine the time complexity is O(2n+3). The document also discusses other algorithm analysis topics like asymptotic notations, amortized analysis, and randomized algorithms.
The document discusses multilayer neural networks and the backpropagation algorithm. It begins by introducing sigmoid units as differentiable threshold functions that allow gradient descent to be used. It then describes the backpropagation algorithm, which employs gradient descent to minimize error by adjusting weights. Key aspects covered include defining error terms for multiple outputs, deriving the weight update rules, and generalizing to arbitrary acyclic networks. Issues like local minima and representational power are also addressed.
The document discusses space complexity, which refers to the amount of memory required by an algorithm. It explains how to calculate the space complexity of an algorithm by considering the fixed parts, like code and constants, and variable parts, like arrays and recursion stacks. It provides an example of calculating the space complexity of an addition algorithm as O(c+3) words and a recursive sum algorithm as O(c+4n+4) words.
Threads provide concurrency within a process by allowing parallel execution. A thread is a flow of execution that has its own program counter, registers, and stack. Threads share code and data segments with other threads in the same process. There are two types: user threads managed by a library and kernel threads managed by the operating system kernel. Kernel threads allow true parallelism but have more overhead than user threads. Multithreading models include many-to-one, one-to-one, and many-to-many depending on how user threads map to kernel threads. Threads improve performance over single-threaded processes and allow for scalability across multiple CPUs.
The document provides an overview of machine learning concepts including:
- Defining machine learning as computer algorithms that improve with experience and data
- Describing examples like speech recognition, medical diagnosis, and game playing
- Outlining the components of designing a machine learning system like choosing the target function, representation, and learning algorithm
- Explaining concepts like version spaces, decision trees, and neural networks that are used in machine learning applications
Loop optimization is a technique to improve the performance of programs by optimizing the inner loops which take a large amount of time. Some common loop optimization methods include code motion, induction variable and strength reduction, loop invariant code motion, loop unrolling, and loop fusion. Code motion moves loop-invariant code outside the loop to avoid unnecessary computations. Induction variable and strength reduction techniques optimize computations involving induction variables. Loop invariant code motion avoids repeating computations inside loops. Loop unrolling replicates loop bodies to reduce loop control overhead. Loop fusion combines multiple nested loops to reduce the total number of iterations.
This document discusses feature selection concepts and methods. It defines features as attributes that determine which class an instance belongs to. Feature selection aims to select a relevant subset of features by removing irrelevant, redundant and unnecessary data. This improves learning accuracy, model performance and interpretability. The document categorizes feature selection algorithms as filter, wrapper or embedded methods based on how they evaluate feature subsets. It also discusses concepts like feature relevance, search strategies, successor generation and evaluation measures used in feature selection algorithms.
The document discusses the theoretical framework of computational learning theory and PAC (Probably Approximately Correct) learning. It defines what makes a learning problem PAC learnable and examines how the number of training examples needed for learning is affected by factors like the hypothesis space size, error tolerance, and confidence level. Key questions addressed include determining learnability of problem classes and bounding the sample complexity of learning algorithms.
The document discusses decision tree learning and the ID3 algorithm. It begins by introducing decision trees and how they are used to classify instances by sorting them from the root node to a leaf node. It then discusses how ID3 builds decision trees in a top-down greedy manner by selecting the attribute that best splits the data at each node based on information gain. The document also covers issues like overfitting, handling continuous attributes, and pruning decision trees.
Bayesian Learning by Dr.C.R.Dhivyaa Kongu Engineering CollegeDhivyaa C.R
This document provides an overview of Bayesian learning methods. It discusses key concepts like Bayes' theorem, maximum a posteriori hypotheses, and maximum likelihood hypotheses. Bayes' theorem allows calculating the posterior probability of a hypothesis given observed data and prior probabilities. The maximum a posteriori hypothesis is the one with the highest posterior probability. Maximum likelihood hypotheses maximize the likelihood of the data. Bayesian learning faces challenges from requiring many initial probabilities and high computational costs but provides a useful perspective on machine learning algorithms.
The document discusses analytical learning methods like explanation-based learning. It explains that analytical learning uses prior knowledge and deductive reasoning to augment training examples, allowing it to generalize better than methods relying solely on data. Explanation-based learning analyzes examples according to prior knowledge to infer relevant features. The document provides examples of using explanation-based learning to learn chess concepts and safe stacking of objects. It also describes the PROLOG-EBG algorithm for explanation-based learning.
1) The document discusses various search algorithms including uninformed searches like breadth-first search as well as informed searches using heuristics.
2) It describes greedy best-first search which uses a heuristic function to select the node closest to the goal at each step, and A* search which uses both path cost and heuristic cost to guide the search.
3) Genetic algorithms are introduced as a search technique that generates successors by combining two parent states through crossover and mutation rather than expanding single nodes.
Learning can occur through various methods like memorization, being taught directly, learning from examples, induction, and deduction. Rote learning involves simply memorizing information without understanding. Learning from advice involves translating advice from experts into operational rules. Learning from examples involves classifying things without explicit rules by being corrected when wrong. Various learning mechanisms exist, with rote learning being the simplest form of storing information, while learning from examples and analogies requires more complex inference.
Concept learning and candidate elimination algorithmswapnac12
This document discusses concept learning, which involves inferring a Boolean-valued function from training examples of its input and output. It describes a concept learning task where each hypothesis is a vector of six constraints specifying values for six attributes. The most general and most specific hypotheses are provided. It also discusses the FIND-S algorithm for finding a maximally specific hypothesis consistent with positive examples, and its limitations in dealing with noise or multiple consistent hypotheses. Finally, it introduces the candidate-elimination algorithm and version spaces as an improvement over FIND-S that can represent all consistent hypotheses.
This document discusses Bayesian learning and the Bayes theorem. Some key points:
- Bayesian learning uses probabilities to calculate the likelihood of hypotheses given observed data and prior probabilities. The naive Bayes classifier is an example.
- The Bayes theorem provides a way to calculate the posterior probability of a hypothesis given observed training data by considering the prior probability and likelihood of the data under the hypothesis.
- Bayesian methods can incorporate prior knowledge and probabilistic predictions, and classify new instances by combining predictions from multiple hypotheses weighted by their probabilities.
Introdution and designing a learning systemswapnac12
The document discusses machine learning and provides definitions and examples. It covers the following key points:
- Machine learning is a subfield of artificial intelligence concerned with developing algorithms that allow computers to learn from data without being explicitly programmed.
- Well-posed learning problems have a defined task, performance measure, and training experience. Examples given include learning to play checkers and recognize handwritten words.
- Designing a machine learning system involves choosing a training experience, target function, representation of the target function, and learning algorithm to approximate the function. A checkers-playing example is used to illustrate these design decisions.
A thread is an independent path of execution within a Java program. The Thread class in Java is used to create threads and control their behavior and execution. There are two main ways to create threads - by extending the Thread class or implementing the Runnable interface. The run() method contains the code for the thread's task and threads can be started using the start() method. Threads have different states like New, Runnable, Running, Waiting etc during their lifecycle.
Greedy algorithms work by making locally optimal choices at each step to arrive at a global optimal solution. They require that the problem exhibits the greedy choice property and optimal substructure. Examples that can be solved with greedy algorithms include fractional knapsack problem, minimum spanning tree, and activity selection. The fractional knapsack problem is solved greedily by sorting items by value/weight ratio and filling the knapsack completely. The 0/1 knapsack problem differs in that items are indivisible.
This document discusses neural networks and multilayer feedforward neural network architectures. It describes how multilayer networks can solve nonlinear classification problems using hidden layers. The backpropagation algorithm is introduced as a way to train these networks by propagating error backwards from the output to adjust weights. The architecture of a neural network is explained, including input, hidden, and output nodes. Backpropagation is then described in more detail through its training process of forward passing input, calculating error at the output, and propagating this error backwards to update weights. Examples of backpropagation and its applications are also provided.
Web Spam Classification Using Supervised Artificial Neural Network Algorithmsaciijournal
Due to the rapid growth in technology employed by the spammers, there is a need of classifiers that are
more efficient, generic and highly adaptive. Neural Network based technologies have high ability of
adaption as well as generalization. As per our knowledge, very little work has been done in this field using
neural network. We present this paper to fill this gap. This paper evaluates performance of three supervised
learning algorithms of artificial neural network by creating classifiers for the complex problem of latest
web spam pattern classification. These algorithms are Conjugate Gradient algorithm, Resilient Backpropagation learning, and Levenberg-Marquardt algorithm.
Web spam classification using supervised artificial neural network algorithmsaciijournal
Due to the rapid growth in technology employed by the spammers, there is a need of classifiers that are more efficient, generic and highly adaptive. Neural Network based technologies have high ability of adaption as well as generalization. As per our knowledge, very little work has been done in this field using neural network. We present this paper to fill this gap. This paper evaluates performance of three supervised learning algorithms of artificial neural network by creating classifiers for the complex problem of latest web spam pattern classification. These algorithms are Conjugate Gradient algorithm, Resilient Backpropagation learning, and Levenberg-Marquardt algorithm.
1) Researchers developed a hardware implementation of the Restricted Boltzmann Machine (RBM) algorithm on an FPGA to speed up training. The RBM is commonly used for feature learning in neural networks.
2) The hardware implementation pipelines and parallelizes the matrix multiplication and weight update stages of the RBM algorithm to increase throughput and decrease latency.
3) Experimental results found the hardware implementation provided over 35 times speed up compared to a software-only approach, allowing the RBM to be scaled to larger network sizes.
Back propagation networks are neural networks that use a learning algorithm called backpropagation. The key characteristics are:
1. Neurons in one layer connect to all neurons in the next layer.
2. Each neuron has its own input weights.
3. Training involves passing input values through the network layers to calculate the output, then using backpropagation to adjust the weights to reduce error.
4. The network must have at least an input and output layer, with optional hidden layers.
The document discusses artificial neural networks and backpropagation. It provides an overview of backpropagation algorithms, including how they were developed over time, the basic methodology of propagating errors backwards, and typical network architectures. It also gives examples of applying backpropagation to problems like robotics, space robots, handwritten digit recognition, and face recognition.
The document provides an overview of backpropagation, a common algorithm used to train multi-layer neural networks. It discusses:
- How backpropagation works by calculating error terms for output nodes and propagating these errors back through the network to adjust weights.
- The stages of feedforward activation and backpropagation of errors to update weights.
- Options like initial random weights, number of training cycles and hidden nodes.
- An example of using backpropagation to train a network to learn the XOR function over multiple training passes of forward passing and backward error propagation and weight updating.
1) Artificial neural networks are made up of nodes that pass signals through connection links. Each node applies an activation function to determine its output signal.
2) Neural networks can be classified based on number of layers (single, bi-layer, multi-layer) or direction of information flow (feed forward, recurrent).
3) Backpropagation is commonly used for training, which involves passing inputs forward and propagating errors backward to adjust weights. Other algorithms like conjugate gradient and radial basis function training also exist.
The document discusses key concepts in neural networks including units, layers, batch normalization, cost/loss functions, regularization techniques, activation functions, backpropagation, learning rates, and optimization methods. It provides definitions and explanations of these concepts at a high level. For example, it defines units as the activation function that transforms inputs via a nonlinear function, and hidden layers as layers other than the input and output layers that receive weighted input and pass transformed values to the next layer. It also summarizes common cost functions, regularization approaches like dropout, and optimization methods like gradient descent and stochastic gradient descent.
The document discusses artificial neural networks and the backpropagation algorithm. It provides an overview of ANN structure and learning process. Specifically, it discusses using ANN to control an autonomous vehicle, the backpropagation algorithm which aims to minimize error, and an example of an ANN learning a simple identity function.
ARTIFICIAL NEURAL NETWORK APPROACH TO MODELING OF POLYPROPYLENE REACTORijac123
This paper shows modeling of highly nonlinear polymerization process using the artificial neural network approach for the model predictive purposes. Polymerization occurs in a fluidized bed polypropylene reactor using Ziegler - Natta catalyst and the main objective was modeling of the reactor production rate.
The data set used for an identification of the model is a real process data received from an existing polypropylene plant and the identified model is a nonlinear autoregressive neural network with the exogenous input. Performance of a trained network has been verified using the real process data and the
ability of the production rate prediction is shown in the conclusion.
This document discusses various types of neural networks including feedback neural networks, self-organizing feature maps, and Hopfield networks. It provides details on Hopfield networks such as their architecture, training and testing algorithms. It also discusses issues like false minima problem in neural networks and techniques to address it like simulated annealing and stochastic update. Furthermore, it covers associative memory models like bidirectional associative memory and self-organizing maps.
This document provides instructions for three exercises using artificial neural networks (ANNs) in Matlab: function fitting, pattern recognition, and clustering. It begins with background on ANNs including their structure, learning rules, training process, and common architectures. The exercises then guide using ANNs in Matlab for regression to predict house prices from data, classification of tumors as benign or malignant, and clustering of data. Instructions include loading data, creating and training networks, and evaluating results using both the GUI and command line. Improving results through retraining or adding neurons is also discussed.
Introduction Of Artificial neural networkNagarajan
The document summarizes different types of artificial neural networks including their structure, learning paradigms, and learning rules. It discusses artificial neural networks (ANN), their advantages, and major learning paradigms - supervised, unsupervised, and reinforcement learning. It also explains different mathematical synaptic modification rules like backpropagation of error, correlative Hebbian, and temporally-asymmetric Hebbian learning rules. Specific learning rules discussed include the delta rule, the pattern associator, and the Hebb rule.
This document provides legal notices and disclaimers for an informational presentation by Intel. It states that the presentation is for informational purposes only and that Intel makes no warranties. It also notes that Intel technologies' features and benefits depend on system configuration. Finally, it specifies that the sample source code in the presentation is released under the Intel Sample Source Code License Agreement and that Intel and its logo are trademarks.
Design of airfoil using backpropagation training with mixed approachEditor Jacotech
Levenberg-Marquardt back-propagation training method has some limitations associated with over fitting and local optimum problems. Here, we proposed a new algorithm to increase the convergence speed of Backpropagation learning to design the airfoil. The aerodynamic force coefficients corresponding to series of airfoil are stored in a database along with the airfoil coordinates. A feedforward neural network is created with aerodynamic coefficient as input to produce the airfoil coordinates as output. In the proposed algorithm, for output layer, we used the cost function having linear & nonlinear error terms then for the hidden layer, we used steepest descent cost function. Results indicate that this mixed approach greatly enhances the training of artificial neural network and may accurately predict airfoil profile.
Design of airfoil using backpropagation training with mixed approachEditor Jacotech
The document describes a new algorithm for designing airfoils using neural networks. The algorithm uses a mixed training approach: it trains the output layer of the neural network using a cost function with linear and nonlinear error terms for faster convergence, while training the hidden layer using steepest descent. Results show the mixed approach converges much faster than traditional backpropagation or Levenberg-Marquardt algorithms alone. The algorithm more accurately predicts airfoil profiles with fewer training iterations.
Modeling of neural image compression using gradient decent technologytheijes
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Formal Languages and Automata Theory unit 5Srimatre K
This document summarizes key concepts from Unit 5, including types of Turing machines, undecidability, recursively enumerable languages, Post's correspondence problem, and counter machines. It defines undecidable problems as those with no algorithm to solve them. Examples of undecidable problems include the halting problem and determining if a Turing machine accepts a language that is not recursively enumerable. Post's correspondence problem and its modified version are presented with examples. Recursively enumerable languages are defined and properties like concatenation, Kleene closure, union, and intersection are described. Counter machines are defined as having states, input alphabet, start/final states, and transitions that allow incrementing, decrementing, and checking if a
Formal Languages and Automata Theory unit 4Srimatre K
The document discusses various topics related to context-free grammars including:
1. Normal forms like Chomsky normal form and Greibach normal form that put constraints on the structure of productions in a context-free grammar.
2. The pumping lemma for context-free languages and how it can be used to prove that a language is not context-free.
3. Closure properties of context-free languages like their closure under union, concatenation and Kleene star but not under intersection and complement.
4. Decision properties of context-free languages and how questions of emptiness, membership and finiteness can be solved.
5. An introduction to Turing machines as accepting devices for recursively enumerable
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1. A syllabus covering regular expressions, applications of regular expressions, algebraic laws, conversion of automata to expressions, and the pumping lemma.
2. Details of regular expressions including operators, precedence, applications, and algebraic laws.
3. How to convert between finite automata and regular expressions using Arden's theorem and state elimination methods.
4. Properties of regular languages including closure properties and how regular languages satisfy the pumping lemma.
Formal Languages and Automata Theory Unit 1Srimatre K
The document describes the minimization of a deterministic finite automaton (DFA) using the equivalence theorem. It involves partitioning the states into sets where states in the same set are indistinguishable based on their transitions. The initial partition P0 separates final and non-final states. Subsequent partitions P1, P2, etc. further split sets if states within are distinguishable. The process stops when the partition no longer changes, resulting in the minimized DFA with states merged within each final set. An example application of the steps to a 6-state DFA is also provided.
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2. Multilayer Networks
Multilayer networks using gradient descent algorithm.
In Perceptron its discontinuous threshold makes it
undifferentiable and hence unsuitable for gradient descent.
3. Differentiable Threshold Unit:
Sigmoid unit is a smoothed, differentiable threshold
function.
Like the perceptron, the sigmoid unit first computes a
linear combination of its inputs, then applies a threshold
to the result. In the case of the sigmoid unit, however, the
threshold output is a continuous function of its input.
4. More precisely, the sigmoid unit computes its output o as
Where
is often called the sigmoid function or, alternatively,
the logistic function. Its output ranges between 0 and 1,
increasing monotonically with its input.
It maps a very large input domain to a small range of
outputs, it is often referred to as the squashing function of
the unit. The sigmoid function has the useful property that
its derivative is easily expressed in terms of its output.
The function tanh is also sometimes used in place
of the sigmoid function
6. The BACKPROPAGATION ALGORITHM:
The BACKPROPAGATION Algorithm learns the weights
for a multilayer network, given a network with a fixed set
of units and interconnections.
It employs gradient descent to attempt to minimize the
squared error between the network output values and the
target values for these outputs.
we are considering networks with multiple output units
rather than single units as before, we begin by redefining
E to sum the errors over all of the network output units.
7. where outputs is the set of output units in the network,
and tkd and okd are the target and output values
associated with the kth output unit and training
example d.
One major difference in the case of multilayer
networks is that the error surface can have multiple
local minima, in contrast to the single-minimum
parabolic error surface.
This is the incremental, or stochastic gradient
descent version of BACKPROPAGATION.
8.
9.
10. The algorithm applies to layered feedforward networks containing
2 layers of sigmoid units, with units at each layer connected to all
units from the preceding layer.
BACK-PROPAGATION.
Notations:
11. Constructing a network with the desired number of hidden and
output units and initializing all network weights to small
random values.
Given this fixed network structure, the main loop of the
algorithm then repeatedly iterates over the training examples.
calculates the error of the network output for this example,
computes the gradient with respect to the error on this example,
then updates all weights in the network.
This gradient descent step is iterated until the network performs
acceptably well.
12. The gradient descent weight-update rule is similar to the
delta training rule.
Like the delta rule, it updates each weight in proportion to
the learning rate , the input value xji to which the weight is
applied, and the error in the output of the unit. The only
difference is that the error (t - o) in the delta rule is
replaced by a more complex error term.
The weight-update loop in BACKPROPAGATION
Algorithm be iterated thousands of times in a typical
application.
13. Derivation of the BACKPROPAGATION Rule
Recall that stochastic gradient descent involves iterating
through the training examples one at a time, for each
training example d descending the gradient of the error Ed
with respect to this single example. In other words, for
each training example d every weight wji is updated by
adding to it
where Ed is the error on training example d, summed over
all output units in the network.
Here outputs is the set of output units in the network, tk is
the target value of unit k for training example d, and ok is
the output of unit k given training example d.
14. The derivation of the stochastic gradient descent rule is
conceptually straightforward, but requires keeping track of
a number of subscripts and variables.
We will follow the notation adding a subscript j to denote
to the jth unit of the network as follows:
We can use the chain rule to write
15.
16. We consider two cases in turn: the case where unit j is an
output unit for the network, and the case where j is an
internal unit.
Case 1: Training Rule for Output Unit Weights. Just as
wji can influence the rest of the network only through net,,
net, can influence the network only through oj. Therefore,
we can invoke the chain rule again to write
17.
18. We have the stochastic gradient descent rule for output
units
19. Case 2: Training Rule for Hidden Unit Weights.
In the case where j is an internal, or hidden unit in the
network, the derivation of the training rule for wji
must take into account the indirect ways in which wji can
influence the network outputs and hence Ed.
Notice that netj can influence the network output
only through the units in Downstream(j).
20.
21. A variety of termination conditions can be used to halt
the procedure:
One may choose to halt after a fixed number of iterations
through the loop, or once the error on the training
examples falls below some threshold, or once the error on
a separate validation set of examples meets some criterion.
The choice of termination criterion is an important one,
because too few iterations can fail to reduce error
sufficiently, and too many can lead to overfitting
the training data.
22. ADDING MOMENTUM
In the algorithm by making the weight update on the nth
iteration depend partially on the update that occurred
during the (n - 1)th iteration, as follows:
is the weight update performed during the
nth iteration through the main loop of the algorithm,
and 0 < < 1 is a constant called the momentum.
The 1st term in the right equation is weight-update rule
and 2nd term momentum term.
23. The effect of is to add momentum that tends to keep the
ball rolling in the same direction from one iteration to the
next.
This can sometimes have the effect of keeping the ball
rolling through small local minima in the error surface, or
along flat regions in the surface where the ball would stop
if there were no momentum.
It also has the effect of gradually increasing the step size
of the search in regions where the gradient is unchanging,
thereby speeding convergence.
24. LEARNING IN ARBITRARY ACYCLIC
NETWORKS
The definition of BACKPROPAGATION applies only to
two-layer networks.
In general, the value for a unit r in layer m is
computed from the values at the next deeper layer m+1
according to
We really saying here is that this step may be repeated for
any number of hidden layers in the network.
25. It is equally straightforward to generalize the algorithm to
any directed acyclic graph, regardless of whether the
network units are arranged in uniform layers as we have
assumed up to now. In the case that they are not, the rule
for calculating for any internal unit is
Where Downstream(r) is the set of units immediately
downstream from unit r in the network: that is, all units
whose inputs include the output of unit r.
27. REMARKS ON THE BACKPROPAGATION
ALGORITHM
Convergence and Local Minima:
BACKPROPAGATION over multilayer networks is only
guaranteed to converge toward some local minimum in E
and not necessarily to the global minimum error.
When gradient descent falls into a local minimum with
respect to one of these weights, it will not necessarily be
in a local minimum with respect to the other weights.
A second perspective on local minima can be gained by
considering the manner in which network weights evolve
as the number of training iterations increases.
28. Common heuristics to attempt to alleviate the
problem of local minima include:
Add a momentum term to the weight-update rule.
Momentum can sometimes carry the gradient descent
procedure through narrow local minima.
Use stochastic gradient descent rather than true gradient
descent.
Train multiple networks using the same data, but
initializing each network with different random weights.
If the different training efforts lead to different local
minima, then the network with the best performance over
a separate validation data set can be selected.
29. Representational Power of FeedForward
Networks
3 general rules of FeedForward network.
Boolean functions. Every Boolean function can be
represented exactly by some network with two layers of
units, although the number of hidden units required grows
exponentially in the worst case with the number of
network inputs.
Continuous functions. Every bounded continuous
function can be approximated with arbitrarily small error
(under a finite norm) by a network with two layers of units
30. Arbitrary functions. Any function can be approximated to
arbitrary accuracy by a network with three layers of units
(Cybenko 1988). Again, the output layer uses linear units,
the two hidden layers use sigmoid units, and the number
of units required at each layer is not known in general.
The proof of this involves showing that any function can
be approximated by a linear combination of many
localized functions that have value 0 everywhere except
for some small region, and then showing that two layers of
sigmoid units are sufficient to produce good local
approximations.
31. Hypothesis Space Search and Inductive
Bias
hypothesis space is the n-dimensional Euclidean space of
the n network weights. This hypothesis space is
continuous, in contrast to the hypothesis spaces of
decision tree learning and other methods based on discrete
representations.
Inductive Bias is depends on the interplay between the
gradient descent search and the way in which the weight
space spans the space of represent able functions.
However, one can roughly characterize it as smooth
interpolation between data points.
32. Hidden Layer Representations
One intriguing property of BACKPROPAGATION its
ability to discover useful intermediate representations
at the hidden unit layers inside the network.
33. Generalization, Overfitting, and Stopping
Criterion
BACKPROPAGATION is susceptible to overfitting the
training examples at the cost of decreasing generalization
accuracy over other unseen examples.
BACKPROPAGATION will often be able to create
overly complex decision surfaces that fit noise in the
training data or unrepresentative characteristics of the
particular training sample.
Several techniques are available to address the overfitting
problem for BACKPROPAGATION learning. One
approach, known as weight decay, is to decrease each
weight by some small factor during each iteration.
34. One of the most successful methods for overcoming the
overfitting problem is to simply provide a set of validation
data to the algorithm in addition to the training data.
The algorithm monitors the error with respect to this
validation set, while using the training set to drive the
gradient descent search.
The problem of overfitting is most severe for small
training sets.
35. In these cases, a k-fold cross-validation approach is
sometimes used, in which cross validation is performed k
different times, each time using a different partitioning of
the data into training and validation sets, and the results
are then averaged.
In one version of this approach, them available examples
are partitioned into k disjoint subsets, each of size m/k.
The cross validation procedure is then run k times, each
time using a different one of these subsets as the
validation set and combining the other subsets for the
training set.