# Questions tagged [xor-problem]

For questions related to the XOR problem, i.e. the problem of computing/approximating the XOR logical function, i.e. a function $f: \{0, 1\}^2 \rightarrow \{0, 1\}$ that returns 1 only when the two bits are different and 0 otherwise, i.e. $f(a, b) = 1 \iff a \neq b$ and $a, b \in \{0, 1\}$.

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### Bug in backpropagation algorithm

I've been debugging my backpropagation algorithm for nearly a week and I can't seem to find where I went wrong, yet my network doesn't seem to learn correctly. It learns XOR just fine when I use the ...
112 views

### Why does this neural network require 2 hidden layers to completely fit my data?

I have been working toward implementing my own Neural Network library in C++ for fun. I have managed to implement an XOR solving network based on widely available information. Now, I wanted to try a ...
443 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 ...
426 views

### Why does my neural network to solve the XOR problem always output 0.5?

I'm trying to create a neural network to simulate an XOR gate. Here's my dataset: ...
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 ...
177 views

### Can XGBoost solve XOR problem?

I've read that decision trees are able to solve XOR operation so I conclude that XGBoost algorithm can solve it as well. But my tests on the datasets (datasets that should be highly "xor-ish"...
783 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 ...
339 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 ...
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} \...