3 added 232 characters in body edited Jun 15 '14 at 19:38 Nikos M. 583311 Artificial Neural Network design is as much art as it is science. Art in the sense that many problems have varying approaches and designs which may not be uniquely characterized. After this simple prologue, this is a generalisation of the ANN XOR problem which multi-level ANNs have been shown to solve eficiently. Answers: It can also be seen as transformation of the original XOR problem (simply rotate the data by $$\pi/4$$) and explosion by a factor. Usually ANNs employ 3 layers (1-input 1 -intermediate and 1-output), of course more layers can be added. This simply illustrates a trade-off between computational power versus computational complexity. By the universal approximation theorem arbitrary (compact) mappings can be approximated by a (sufficiently complex) MLP ANN . A further approach is to use a hidden layer with $$2n$$ or $$2^n$$ neurons (by symmetry of the problem) and experiment with that. UPDATE: As per the OP's further comments regarding transformations between variables $$\in \{0,1\}$$ to variables $$\in \{-1,1\}$$, a link for an MLP ANN for the XOR problem using -1,1 values Artificial Neural Network design is as much art as it is science. Art in the sense that many problems have varying approaches and designs which may not be uniquely characterized. After this simple prologue, this is a generalisation of the ANN XOR problem which multi-level ANNs have been shown to solve eficiently. Answers: It can also be seen as transformation of the original XOR problem (simply rotate the data by $$\pi/4$$) and explosion by a factor. Usually ANNs employ 3 layers (1-input 1 -intermediate and 1-output), of course more layers can be added. This simply illustrates a trade-off between computational power versus computational complexity. By the universal approximation theorem arbitrary (compact) mappings can be approximated by a (sufficiently complex) MLP ANN . A further approach is to use a hidden layer with $$2n$$ or $$2^n$$ neurons (by symmetry of the problem) and experiment with that. Artificial Neural Network design is as much art as it is science. Art in the sense that many problems have varying approaches and designs which may not be uniquely characterized. After this simple prologue, this is a generalisation of the ANN XOR problem which multi-level ANNs have been shown to solve eficiently. It can also be seen as transformation of the original XOR problem (simply rotate the data by $$\pi/4$$) and explosion by a factor. Usually ANNs employ 3 layers (1-input 1 -intermediate and 1-output), of course more layers can be added. This simply illustrates a trade-off between computational power versus computational complexity. By the universal approximation theorem arbitrary (compact) mappings can be approximated by a (sufficiently complex) MLP ANN . A further approach is to use a hidden layer with $$2n$$ or $$2^n$$ neurons (by symmetry of the problem) and experiment with that. UPDATE: As per the OP's further comments regarding transformations between variables $$\in \{0,1\}$$ to variables $$\in \{-1,1\}$$, a link for an MLP ANN for the XOR problem using -1,1 values 2 i remove some mistype figure edit approved Jun 15 '14 at 19:27 Artificial Neural Network design is as much art as it is science. Art in the sense that many problems have varying approaches and designs which may not be uniquely characterized. After this simple prologue, this is a generalisation of the ANN XOR problem which multi-level ANNs have been shown to solve eficiently. Answers: It can also be seen as transformation of the original XOR problem (simply rotate the data by $$\pi/4$$) and explosion by a factor. Usually ANNs employ 3 layers (1-input 1 -intermediate and 1-output), of course more layers can be added. This simply illustrates a trade-off between computational power versus computational complexity. By the universal approximation theorem arbitrary (compact) mappings can be approximated by a (sufficiently complex) MLP ANN . A further approach is to use a hidden layer with $$2n$$ or $$2^n$$ neurons (by symmetry of the problem) and experiment with that. Artificial Neural Network design is as much art as it is science. Art in the sense that many problems have varying approaches and designs which may not be uniquely characterized. After this simple prologue, this is a generalisation of the ANN XOR problem which multi-level ANNs have been shown to solve eficiently. It can also be seen as transformation of the original XOR problem (simply rotate the data by $$\pi/4$$) and explosion by a factor. Usually ANNs employ 3 layers (1-input 1 -intermediate and 1-output), of course more layers can be added. This simply illustrates a trade-off between computational power versus computational complexity. By the universal approximation theorem arbitrary (compact) mappings can be approximated by a (sufficiently complex) MLP ANN . A further approach is to use a hidden layer with $$2n$$ or $$2^n$$ neurons (by symmetry of the problem) and experiment with that. Artificial Neural Network design is as much art as it is science. Art in the sense that many problems have varying approaches and designs which may not be uniquely characterized. After this simple prologue, this is a generalisation of the ANN XOR problem which multi-level ANNs have been shown to solve eficiently. Answers: It can also be seen as transformation of the original XOR problem (simply rotate the data by $$\pi/4$$) and explosion by a factor. Usually ANNs employ 3 layers (1-input 1 -intermediate and 1-output), of course more layers can be added. This simply illustrates a trade-off between computational power versus computational complexity. By the universal approximation theorem arbitrary (compact) mappings can be approximated by a (sufficiently complex) MLP ANN . A further approach is to use a hidden layer with $$2n$$ or $$2^n$$ neurons (by symmetry of the problem) and experiment with that. 1 answered Jun 15 '14 at 18:13 Nikos M. 583311 Artificial Neural Network design is as much art as it is science. Art in the sense that many problems have varying approaches and designs which may not be uniquely characterized. After this simple prologue, this is a generalisation of the ANN XOR problem which multi-level ANNs have been shown to solve eficiently. It can also be seen as transformation of the original XOR problem (simply rotate the data by $$\pi/4$$) and explosion by a factor. Usually ANNs employ 3 layers (1-input 1 -intermediate and 1-output), of course more layers can be added. This simply illustrates a trade-off between computational power versus computational complexity. By the universal approximation theorem arbitrary (compact) mappings can be approximated by a (sufficiently complex) MLP ANN . A further approach is to use a hidden layer with $$2n$$ or $$2^n$$ neurons (by symmetry of the problem) and experiment with that.