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 $a, b \in \{0, 1\}$.

Filter by
Sorted by
Tagged with
0 votes
0 answers
24 views

Neural Network learning XOR. I collected Data on my networks convergence. Is this expected behavior?

I build a neural network from scratch to get a better understanding of the fundamentals of machine learning. The network contains a bias for each neuron and calculates the final error via the mean ...
user avatar
  • 101
2 votes
1 answer
48 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 ...
user avatar
0 votes
0 answers
30 views

What is the meaning of "The linear model can now describe the function as increasing in $h_1$ and decreasing in $h_2$"?

In the famous Deep Learning book by Goodfellow et al., it is mentioned on page 169 in the caption of Figure 6.1 that The linear model can now describe the function as increasing in $h_1$ and ...
user avatar
2 votes
0 answers
72 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 ...
user avatar
0 votes
1 answer
158 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: ...
user avatar
4 votes
2 answers
3k 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 ...
user avatar
3 votes
0 answers
101 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"...
user avatar
  • 1,039
3 votes
1 answer
534 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 ...
user avatar
  • 31
4 votes
1 answer
158 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 ...
user avatar
2 votes
0 answers
191 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 ...
user avatar
5 votes
5 answers
855 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} \...
user avatar
  • 153
3 votes
3 answers
3k views

What is the best XOR neural network configuration out there in terms of low error?

I'm trying to understand what would be the best neural network for implementing an XOR gate. I'm considering a neural network to be good if it can produce all the expected outcomes with the lowest ...
user avatar
  • 133
10 votes
3 answers
4k views

Did Minsky and Papert know that multi-layer perceptrons could solve XOR?

In their famous book entitled Perceptrons: An Introduction to Computational Geometry, Minsky and Papert show that a perceptron can't solve the XOR problem. This contributed to the first AI winter, ...
user avatar
  • 1,999