# Questions tagged [perceptron]

For questions about the perceptron learning algorithm in Machine Learning.

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### Implement perceptron given decision boundary function

Suppose we have a linear classifier for the classes ω1 and ω2 with characteristics vectors Xa=[a a]^T and Xb=[-a -a]^T correspondingly. Also suppose that the decision boundary that is defined by ...
1 vote
170 views

### Why does sklearn perceptron converge for linearly inseparable data points?

I learned that the perceptron algorithm only converges if the dataset is linearly separable. I am implementing this algorithm using scikit learn. The blue and orange points are from the training set, ...
72 views

### How does a sigmoid neuron act like a perceptron in this scenario?

I have been reading Michael Nielsen’s book online on his website at http://neuralnetworksanddeeplearning.com/chap1.html. I am struggling to understand the second exercise: When c approaches infinity, ...
1 vote
76 views

### What is the most accurate way of building a Perceptron using only NumPy?

For context, I am trying to write a bunch of neural network programs using no other packages besides NumPy for educational purposes. I am trying to make them as simple as possible, i.e. removing the ... 219 views

### Is there any variant of perceptron convergence algorithm that ensures uniqueness?

The perceptron convergence algorithm given below ensures the convergence of weights of the perceptron provided enough data points and iterations. Although it ensures convergence by finally getting a ...
35 views

### Was the original perceptron machine really just comparing images to the "average image for each class"?

I've been looking into the history of artificial neural networks, and only recently learned that the original Mark 1 Perceptron was only a single layer network. It would iteratively modify the ...
1 vote
264 views

### Why are today's neural networks not modeled with probability theory?

In the paper The Perceptron: A probabilistic model for information storage and organization in the brain, Rosenblatt used the probability theory to model his perceptron. My professor told me that ...
446 views

### Did the unsolved XOR problem in "Perceptrons: An Introduction to Computational Geometry" 1969 book really cause the winter of the AI in 1974?

Winter of AI definition: periods of reduced funding and interest in artificial intelligence research, due to unmet expectations after a period of hype. There have been at least two major AI winters ...
44 views

### Why isn't my perceptron having the expected costs?

I want to implement a single perceptron for linear regression using the following formulas: The input data for the first case is one column (x(392, 1); y(392, 1)) ...
50 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 ...
296 views

### What's the difference between a "perceptron" and a GLM?

In a comment to this question user nbro comments: As a side note, "perceptrons" and "neural networks" may not be the same thing. People usually use the term perceptron to refer to ...
1 vote
73 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 ...
2k views

### What are (all) the differences between a neuron and a perceptron?

I know two differences between a neuron and a perceptron Neuron employs non-linear activation function and perceptron employs only a threshold activation function. The output of a neuron is not ...
1 vote
33 views

### Could someone help tell what the labels are pointed out by red rectangles?

The following figure comes from the paper The perceptron: A probabilistic model for information storage and organization in the brain I can tell the labels pointed out by blue rectangles are: "...
1 vote
58 views

### What are the labels in figure1 in the Paper "The perceptron: A probabilistic model for information storage and organization in the brain"?

This figure comes from The perceptron: A probabilistic model for information storage and organization in the brain I guess the first circle (neuron) labels RETINA, the second labels perceptron area, ...
1 vote
127 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 $${\frac {1}{s}}\sum _{j=1}^{s}|d_{j}-y_{j}(t)|} \tag{1$$ to denote ...
1 vote
334 views

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

I am currently studying the textbook Neural Networks and Deep Learning by Charu C. Aggarwal. Chapter 1.2.1.3 Choice of Activation and Loss Functions says the following: The classical activation ...
417 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 ...
380 views

### Is my flowchart a good representation of the perceptron learning algorithm?

I made a flowchart for a simplified perceptron leaning algorithm. Here is the process of the learning algorithm. Initialize the weights first. Get a training example randomly and make a prediction. ...
1 vote
101 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 . ...
400 views

### Where does the so-called 'loss' / 'loss function' fit into the idea of a perceptron / artificial neuron (as presented in the figure)?

I am currently studying the textbook Neural Networks and Deep Learning by Charu C. Aggarwal. Chapter 1.2.1.3 Choice of Activation and Loss Functions presents the following figure: $\overline{X}$ is ...
860 views

### How do sigmoid functions make it so that the prediction $\hat{y}$ indicates the probability that the observed value, $y$, is $1$?

I am currently studying the textbook Neural Networks and Deep Learning by Charu C. Aggarwal. Chapter 1.2.1.3 Choice of Activation and Loss Functions says the following: The choice of activation ...
1 vote
48 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 ...
56 views

### In practice, are perceptrons typically implemented as objects?

I'm fairly new to ANNs. I know the general structure, the math, and the algorithms behind them. I figured the logical next step on my journey to fully understanding them would to be implement one ...
67 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) ...
321 views

### Why did the developement of neural networks stop between 50s and 80s?

In a video lecture on the development of neural networks and the history of deep learning (you can start from minute 13), the lecturer (Yann LeCunn) said that the development of neural networks ...
1 vote
53 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 ...
123 views

### 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 ...
1 vote
3k views

### What is the equation to update the weights in the perceptron algorithm?

I'm trying to understand the solution to question 4 of this midterm paper. The question and solution is as follows: I thought that the process for updating weights was: ...
9k views

### Is there a proof to explain why XOR cannot be linearly separable?

Can someone explain to me with a proof or example why you can't linearly separate XOR (and therefore need a neural network, the context I'm looking at it in)? I understand why it's not linearly ...
812 views

### 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 ...
123 views

### Why doesn't the set $\{ -2, +2 \}$ in $E(X) = (y − \text{sign}\{\overline{W} \cdot \overline{X} \}) \in \{ −2, +2 \}$ include $0$?

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 ...
1k views

### Why is the perceptron criterion function differentiable?

I'm reading chapter one of the book called Neural Networks and Deep Learning from Aggarwal. In section 1.2.1.1 of the book, I'm learning about the perceptron. One thing that book says is, if we use ...
1 vote
3k views

### Why can't MLPs perform non-linear regression and classification?

In this page it's told: In Single Perceptron / Multi-layer Perceptron(MLP), we only have linear separability because they are composed of input and output layers(some hidden layers in MLP) What ...
784 views

### What is the simplest classification problem which cannot be solved by a perceptron?

What is the simplest classification problem which cannot be solved by a perceptron (that is a single-layered feed-forward neural network, with no hidden layers and step activation function), but it ...
147 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 ...
340 views

### Which part of "Perceptrons: An Introduction to Computational Geometry" tells that a perceptron cannot solve the XOR problem?

In the book "Perceptrons: An Introduction to Computational Geometry" by Minsky and Papert (1969), which part of this book tells that a single-layer perceptron could not solve the XOR problem? I have ...
67 views

### How do I determine the most appropriate classifier for a certain problem?

Consider a Bayesian classifier used in spam e-mail filtering. It converts an e-mail to a vector, most of the time using the bag-of-words method. Although it learns first before getting employed, it ... 354 views

### What are the reasons a perceptron is not able to learn?

I'm just starting to learn about neural networking and I decided to study a simple 3-input perceptron to get started with. I am also only using binary inputs to gain a full understanding of how the ...
1 vote
122 views

### Can a neuron have both a bias and a threshold?

I have not seen a neuron that uses both a bias and a threshold. Why is this?
707 views

### How do two perceptrons produce different linear decision boundaries when learning?

I've learned that you can use two perceptrons to ultimately create a classifier for non-linearly separable data. I'm trying to understand how / if these two perceptrons converge to two different ...
301 views

### A neural network for digits recognition doesn't work (MNIST, Numpy) [closed]

I'm a beginner in machine learning and I was trying to make a test neural network for digits recognition from scratch using Numpy. I used MNIST dataset for training and testing. Input layer have 28*28 ...
40 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 ...
234 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 ...
1k views

### Why can't the XOR linear inseparability problem be solved with one perceptron like this?

Consider a perceptron where $w_0=1$ and $w_1=1$: Now, suppose that we use the following activation function \begin{align} f(x)= \begin{cases} 1, \text{ if }x =1\\ 0, \text{ otherwise} \end{cases} \...
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### Which Rosenblatt's paper describes Rosenblatt's perceptron training algorithm?

I struggle to find Rosenblatt's perceptron training algorithm in any of his publications from 1957 - 1961, namely: Principles of Neurodynamics: Perceptrons and the Theory of Brain Mechanisms The ...
1k views

### Is the bias supposed to be updated in the perceptron learning algorithm?

I am using the following perceptron formula $\text{step}\left(\sum(w_ix_i)-\theta \right)$. Is $\theta$ supposed to be updated in a perceptron, like the weights $w_i$? If so, what is the formula for ...
2k views

### Perceptron learning algorithm: different accuracies for different training methods

So, my question is a bit theoretical. I have been trying to implement a perceptron based classifier with outputs 1 and 0 depending on the category. I have used 2 methods: The ...  