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What must occur for a neuron to fire?
What must occur for a neuron to fire?
In a perceptron, what is the result when the sum of weighted inputs exceeds the threshold?
In a perceptron, what is the result when the sum of weighted inputs exceeds the threshold?
What term is NOT commonly associated with artificial neural networks?
What term is NOT commonly associated with artificial neural networks?
What role do weighted inputs play in the functioning of a neuron?
What role do weighted inputs play in the functioning of a neuron?
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Which year marks the first learning rule for neural networks?
Which year marks the first learning rule for neural networks?
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What is a key advantage of the brain over computers when processing information?
What is a key advantage of the brain over computers when processing information?
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What function does the sigmoid activation serve in an artificial neuron?
What function does the sigmoid activation serve in an artificial neuron?
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What is required for supervised learning in the context of neural networks?
What is required for supervised learning in the context of neural networks?
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How many neurons does the brain typically contain?
How many neurons does the brain typically contain?
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Which of the following statements about the brain's architecture is true?
Which of the following statements about the brain's architecture is true?
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What significant limitation of the perceptron was noted by Minsky and Papert?
What significant limitation of the perceptron was noted by Minsky and Papert?
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What are dendrites primarily responsible for in the structure of a neuron?
What are dendrites primarily responsible for in the structure of a neuron?
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In which decade did artificial neural networks experience a significant resurgence?
In which decade did artificial neural networks experience a significant resurgence?
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What is one primary function of training a Perceptron?
What is one primary function of training a Perceptron?
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What is meant by linear separability in neural networks?
What is meant by linear separability in neural networks?
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What are the typical components in the training process of a Perceptron?
What are the typical components in the training process of a Perceptron?
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What is the role of a decision boundary in feature space?
What is the role of a decision boundary in feature space?
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Which of the following correctly describes the output of the Perceptron for input patterns in the AND gate?
Which of the following correctly describes the output of the Perceptron for input patterns in the AND gate?
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What happens to the weights in a Perceptron during training?
What happens to the weights in a Perceptron during training?
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Which statement regarding Perceptrons is incorrect?
Which statement regarding Perceptrons is incorrect?
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Which factor does NOT affect the learning process of a Perceptron?
Which factor does NOT affect the learning process of a Perceptron?
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What is the role of the input layer in a neural network?
What is the role of the input layer in a neural network?
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How many hidden layers are sufficient to solve any problem in a neural network?
How many hidden layers are sufficient to solve any problem in a neural network?
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What characteristic is a requirement of activation functions in a neural network?
What characteristic is a requirement of activation functions in a neural network?
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What is the primary function of the output layer in a neural network?
What is the primary function of the output layer in a neural network?
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What is the purpose of using neural networks for engine management?
What is the purpose of using neural networks for engine management?
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In order for a single layer network to function properly, what must be true about the input space?
In order for a single layer network to function properly, what must be true about the input space?
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Which of the following is true regarding extra layers in a neural network?
Which of the following is true regarding extra layers in a neural network?
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What does ALVINN specifically utilize for input in its function?
What does ALVINN specifically utilize for input in its function?
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What does a two-layer perceptron model represent?
What does a two-layer perceptron model represent?
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What type of problems can a three-layer neural network handle?
What type of problems can a three-layer neural network handle?
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What characteristic do neural networks exhibit when they can generalize from training data?
What characteristic do neural networks exhibit when they can generalize from training data?
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What challenge do signature recognition systems overcome?
What challenge do signature recognition systems overcome?
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What does the term 'convex hull' refer to in the context of neural networks?
What does the term 'convex hull' refer to in the context of neural networks?
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Which aspect do neural networks consider in signature recognition to enhance accuracy?
Which aspect do neural networks consider in signature recognition to enhance accuracy?
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What is the primary task of neural networks used in sonar target recognition?
What is the primary task of neural networks used in sonar target recognition?
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What does the concept of 'inputs' signify in the context of neural networks?
What does the concept of 'inputs' signify in the context of neural networks?
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What is the primary function of technical trading?
What is the primary function of technical trading?
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How do neural networks improve mortgage assessments?
How do neural networks improve mortgage assessments?
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What is a challenge associated with neural networks as mentioned in the content?
What is a challenge associated with neural networks as mentioned in the content?
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Which parameter is suggested to have a small value for effective training in neural networks?
Which parameter is suggested to have a small value for effective training in neural networks?
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What is a common method employed to avoid overfitting in neural networks?
What is a common method employed to avoid overfitting in neural networks?
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What should prompt the stopping of training in neural networks?
What should prompt the stopping of training in neural networks?
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What is generally true about the training time of neural networks?
What is generally true about the training time of neural networks?
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What might be a consequence of using too many neurons in a neural network?
What might be a consequence of using too many neurons in a neural network?
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Study Notes
Lecture 2: Data Mining and Analysis
- Course: CBD-3335
- Institution: Lambton College
- School: Computer Studies
Artificial Neural Networks
- The brain
- Brain vs. Computers
- The Perceptron
- Multilayer networks
- Some Applications
Other terms/names
- connectionist
- parallel distributed processing
- neural computation
- adaptive networks
History
- 1943-McCulloch & Pitts: Recognized as the first neural network designers.
- 1949: First learning rule developed
- 1969-Minsky & Papert: Identified limitations of perceptrons and led to the decline of ANNs.
- 1980s: Re-emergence of ANNs, particularly multi-layer networks
Brain and Machine
- The Brain
- Pattern Recognition
- Association
- Complexity
- Noise Tolerance
- The Machine
- Calculation
- Precision
- Logic
The contrast in architecture
- Von Neumann Architecture: Uses a single processing unit; tens of millions of operations per second; absolute arithmetic precision.
- The brain uses many slow, unreliable processors acting in parallel.
Features of the Brain
- Ten billion (1010) neurons
- On average, several thousand connections per neuron
- Hundreds of operations per second
- Neurons die off frequently (never replaced)
- Compensates for problems through massive parallelism
The biological inspiration
- Extensive study of the brain by scientists
- Vast complexity makes full understanding difficult
- Even individual neuron behavior is complex
The biological inspiration
- Single "percepts" distributed across many neurons
- Localized parts of the brain handle specific functions (e.g., vision, motion)
The Structure of Neurons
- A neuron has a cell body (soma), a branching input structure (dendrite), and a branching output structure (axon).
- Axons connect to dendrites via synapses
- Electro-chemical signals propagate from the dendritic input, through the cell body and down the axon to other neurons.
- A neuron fires when its input signal exceeds a threshold value within a short time interval.
- Synapses have varying strengths (strong vs. weak connections. Stronger connections allow larger signals while weaker connections allow weak signals)
Inspiration: Neuron Cells
- Neurons accept information from multiple inputs
- Transmit information to other neurons
- Multiply inputs by weights along edges
- Apply a function to the inputs at each node
- If the output of the function exceeds a threshold, the neuron “fires”
The Artificial Neuron (Perceptron)
- Input values (a1, a2, ..., an)
- Weights (wj0, wj1, wj2, ..., wjn)
- Input signal sum with a bias unit +1 : ∑ wij * ai + wj0 = Σ wij, ai + c
- Activation function (f(Sj))
- Output value (xj)
- Activation level: the input signal sum subtracted from the threshold
A Simple Model of a Neuron (Perceptron)
- Each neuron has a threshold value
- Each neuron has weighted inputs from other neurons
- The weighted sum of input signals is calculated
- The neuron fires if the activation level exceeds the threshold
An Artificial Neuron
- Each hidden/output neuron receives weighted inputs from the preceding layer.
- A unit calculates a weighted sum of its inputs and subtracts its threshold. This defines its activation level.
- The activation level is transformed by a sigmoid function to produce the output
Supervised Learning
- Training and test data sets
- Training set; Input Data and Target Outputs
Perceptron Training
- Use of linear threshold
- W: weight value
- t: threshold value
Simple Network
- AND with a biased input
Learning Algorithm
- Epoch: The entire training set is presented to the neural network. For AND, four input sets are used.
- Error: The difference between the network's output and the target value. If the network outputs 1 when the target is 0, the error is -1.
- Ij: Input presented to a neuron
- Wj: Weight from input neuron to output neuron
- LR: learning rate (typically 0.1)
Training Perceptrons
- Weights are initialized with random values.
Learning in Neural Networks
- Weights are learned from input/output pairs.
- Start with random weights on the connections.
- Load training example input
- Observe the computed input
- Modify weights to reduce the difference between outputs and the target outputs
- Iterate over all training examples
- Terminate when weights stop changing, or the error is small
- Learn to generalize
Decision Boundaries
- In simple cases, divide feature space using a hyperplane.
- Called decision boundary
- Discriminant function returns different values on opposite sides of the hyperplane
- Linearly separable problems can be classified.
Linear Separability
- Data that can be separated by a straight line (a hyperplane in higher dimensions).
Rugby players & Ballet Dancers
- Example of linearly non-separable data.
Hyperplane Partitions
- Single perceptron can perform and learn a linear separation.
- Perceptrons have a step function activation function.
Hyperplane Partitions
- An extra layer models a convex hull, which is an area with no dents.
- Perceptrons can’t learn convex hulls
- Two layers using Sigmoid functions add convex hulls together.
- Sufficient for classifying nearly any reasonable problem.
Types of Layers
- Input layer
- Introduces input values to the network.
- No activation function or processing
- Hidden layer(s)
- Perform classification of features
- Two hidden layers are sufficient, with more layers potentially beneficial.
- Output layer
- Functionally similar to hidden layers
- Outputs are passed to the external environment
Multilayer Perceptron (MLP)
- Output layer
- Adjustable weights
- Input layer
- Input signals (external stimuli)
Different Non-Linearly Separable Problems
- Single Layer: Can classify input space into half-planes
- Two layers: Can classify input space into convex open or closed regions
- Three Layers (Arbitrary): Can classify input space into arbitrary regions, subject to some limits based on node count
Activation Functions
- Transforms a neuron’s input into an output
- Features of activation functions:
- A squashing effect is required
- Prevents accelerating to excessive activation levels through the network
- Activation equations should be simple and easy to calculate
Standard Activation Functions
- The hard-limiting threshold function.
- Corresponds to a biological paradigm, where neurons either fire or not.
- Sigmoid function
- The logistic function; S-shaped curve output
- Hyperbolic tangent (symmetrcial); S-shaped curve output
- The shape of the curve is more important than specific equations
Training Algorithms
- Adjust neural network weights to map inputs to outputs
- Use a set of sample patterns where the desired outputs are known
- Learn to generalize, recognizing features common to good and bad exemplars
Training Algorithms
- Cascade neurons together
- Output from one layer (output) is input to the next layer
- Each layer has its own sets of weights.
Training Algorithms
- Predictions are fed forward through the network to classify.
- Network outputs classifications
Regularization
- L1, L2 regularization (weight decay)
- Dropout
- Randomly turn off some neurons, independently
- Allows for individual neuron performance assessment
Back-Propagation
- Training procedure allowing multiple layered feedforward Neural Networks to be trained
- Can theoretically perform any input-output mapping
- Can perform linearly inseparable problem mappings
Back-Propagation
- Training Procedure for feedforward Neural Networks.
Gradient Descent
- Method used to update network weights to achieve better results.
Gradient Descent in Multi-layer Nets
- How to update layers in multi-layered networks.
- Backpropagation of error from higher to lower layers (important)
Mini-batch Gradient Descent
- Rather than using all training examples for each update, a smaller batch is used instead.
- Cycles through all training examples many times
- Results in faster training
Backpropagation: Error
- Output units: use identity output or least squares loss
- Hidden units: involves derivation
Applications
- Neural Networks are useful for learning complex mappings between inputs and outputs from sample data
- Difficult to firmly predict neural network behaviors
- Unsuitable for safety critical applications
- Involves limited understanding of the process from trainer
Neural Networks for OCR
- Feedforward networks are used for optical character recognition
- Trained using back-propagation
OCR for 8x10 characters
- Neural networks can be used to generalize
- Partitioning of input space is involved
- A single layer network input space must be linearly separable
Engine Management
- Car engine behavior is influenced by many parameters (temperature, fuel/air mixture, lubricant viscosity)
- Neural networks can dynamically tune engine outputs based on current operating parameters
ALVINN
- Self-driving car
- 30x32 pixel input images
- 30 steering outputs and 4 hidden units
Signature Recognition
- Signatures are structurally different (and are difficult to identify these structural/quantifiable differences).
- Machine learning models can accurately identify signatures with speed in addition to gross shape
Sonar Target Recognition
- Distinguish mines from rocks using sonar signals, which have many parameters
- The training data involves sets of sonar signals from mines and rocks
Stock Market Prediction
- Using techniques like "technical trading," which are based solely on past observed data from the market.
- Neural Networks have tried to predict future market trends based on past data and observable patterns.
Mortgage Assessment
- Risk assessments for individuals based on opinions from expert underwriters
Neural Network Problems
- Many parameters to set and tune
- Risk of overfitting
- Long training times
- Additional problems likely to emerge
Parameter Setting
- Number of layers
- Number of neurons (too many neurons require excessive training time)
- Learning rate (~0.1, which is empirically determined)
- Momentum term
Over-fitting
- Training a model to perfectly match a set of training data may result in poorly performing models on future sets of data.
- Use cross-validation techniques (using 30% of training data) to evaluate training and tuning accuracy.
- Monitor the error rate and stop training when it begins to rise (or performance drops off).
Training Time
- How many training epochs to run?
- Error may improve or reach a minimum, then plateau
- Rate of error improvement may reduce below a threshold
- Error rate might reach an acceptable level
- A fixed number of epochs (determined by experiment)
References
- Specific URL references provided in the slide deck. (These would otherwise be hidden)
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Description
Explore the fundamentals of Artificial Neural Networks in this quiz. Covering key concepts such as the perceptron, multilayer networks, and historical advancements in the field, you'll gain insights into how these networks mimic brain functions. Test your understanding of both theoretical and practical aspects of neural computation.
