Questions tagged [perceptron]

For questions about the perceptron learning algorithm in Machine Learning.

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How should we interpret this figure that relates the perceptron criterion and the hinge loss?

I am currently studying the textbook Neural Networks and Deep Learning by Charu C. Aggarwal. Chapter 1.2.1.2 Relationship with Support Vector Machines says the following: The perceptron criterion is ...
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33 views

Batch PTA stopping condition

I am reviewing my Neural Network lectures and I have a doubt: My book's (Haykin) batch PTA describes a cost function which is defined over the set of the misclassified inputs. I have always been ...
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1answer
41 views

Is $(y_i - \hat y_i)x_i$, part of the formula for updating weights for perceptron, the gradient of some kind of loss function?

A post gives a formula for perceptron to update weights I understand almost all the parts of it, except for the part $(y_i - \hat y_i)x_i$ where does it come from? Is it the gradient of some kind of ...
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44 views

Backpropagation not working as expected

I'm new to neural networks and I try to make a model that is guessing if a point is below or above relative to a function output. The idea is inspired from this video https://youtu.be/DGxIcDjPzac . ...
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162 views

If we use a perceptron with a non-monotonic activation function, can it solve the XOR problem?

I found several papers about how to build a perceptron able to solve the XOR problem. The papers describe a solution where the heaviside step function is replaced by a non-monotonic activation ...
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1answer
126 views

Is there a mathematical theory behind why MLP can classify handwritten digits?

I'm trying to really understand how multi-layer perceptrons work. I want to prove mathematically that MLP's can classify handwritten digits. The only thing I really have is that each perceptron can ...
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24 views

Is the main difference between the logistic regression and the perceptron the activation function they use?

I went through a Stats StackExchange's post about the difference between logistic regression and perceptron, which is too long to get the key point. I'd like to consider the question in terms of the ...
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28 views

Is the formula $\frac {1}{s}\sum _{j=1}^{s}|d_{j}-y_{j}(t)|$ the correct form of 0-1 loss function, in the context of Perceptron?

Per page 7 of this MIT lecture notes, the original single-layer Perceptron uses 0-1 loss function. Wikipedia uses $${\displaystyle {\frac {1}{s}}\sum _{j=1}^{s}|d_{j}-y_{j}(t)|} \tag{1}$$ to denote ...
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1answer
53 views

Flowchart for a simplified perceptron leaning algorithm [critique request]

I made a flowchart for a simplified perceptron leaning algorithm. Here is the process of the leaning algorithm. Step_1: Initialize the weights first. Step_2: Get a training example randomly and make ...
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27 views

Is it possible to train a perceptron to tell if a picture is a dog or cat?

I know perceptron is a linear classifier that tells linearly separable binary class data, such as iris setosa vs. iris versicolor via their sepal's length and width. I'd just like to know if I have 2 ...
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32 views

What is the smallest upper bound for a number of functions in a range that are computable by a perceptron?

I'm reading this book chapter, and I'm looking at the questions on the last page. Can someone explain question 2 on the last page to me, or show me an example of a solution so I can understand it? The ...
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27 views

How can I adapt this script (to test the robustness of a perceptron) to test the robustness of a multi-layer perceptron?

The following script is from Trappenberg's Fundamentals of Computational Neuroscience and is used to test a perceptron's robustness against noise. However, how would one alter it to test the output ...
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1answer
25 views

How to show $\rho > 0$ when $\rho$ be minimum attainable from $y_n(W^{*T}X_n)$, where $W^*$ the vector that separates the data?

In the book Learning from Data written (by Abu Mostafa), we have the following exercise: Let $\rho$ be minimum attainable from $y_n(W^{*T}X_n)$ where $W^*$ is the vector that separates the data. Show ...
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19 views

What's the effect of increasing hidden nodes?

Topic Demarcation I find many topics on "how to choose the number of hidden nodes". I'm not interested in the answer to that question. What I learned I learned, that if you increase the ...
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35 views

An explanation involving the sign activation, its affect on the loss function, and the perceptron and perceptron criterion: what is this saying? (#2)

I recently asked a very similar question here, but the answer only seems to address the first part of the quote, rather than the second part that contains the perceptron criterion example. Therefore, ...
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24 views

Incorporating regularization for the kernel perceptron

To my understanding, the following is how the kernel perceptron works.    Kernel perceptron algorithm       The parameters to be calculated are $\alpha = \begin{pmatrix} \alpha_1 &\ldots &\...
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43 views

What are the math theorems regarding the Multilayer Perceptron?

I've come across a theorem "Convergence theorem Simple Perceptron" for the first time, here-> https://zaguan.unizar.es/record/69205/files/TAZ-TFG-2018-148.pdf, page 27, (is in Spanish) ...
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What are the general inequalities needed for the logic gate perceptrons?

I'm trying to understand how the logic gates (e.g. AND, OR, NOT, NAND) can be built into single-layer perceptrons. I understand specific examples of weights and thresholds for the gates, but I'm stuck ...