![]() The weights will correspond to exponents. So one way to make a multiplicative neuron layer for positive inputs, is to apply a logarithm to the inputs, then run them through a linear layer, then exponentiate the output. The logarithm of a product is the sum of logarithms of the factors. It can be plugged in for a linear layer, although costs more to compute, and has more parameters to train. The last one, NALU from Deepmind, apparently is a great success, and exists in community implementations for several NN frameworks. Also neurons that interpolate (at least approximately) between addition and multiplication: Multiplicative neurons have been explored. The next layers could consist of standard additive neurons, giving linear combinations of the features. Exploring other types of neurons can be useful.Ī concrete application of multiplicative neurons could be to have an initial layer that generates an arbitrary number of compounded features from the inputs, generalizing beyond a fixed set of polynomial terms with non-negative integer exponents below a given value. Then comes the issue of efficient learning, because ability to represent does not mean ability to learn efficiently. The small letters tell that the target function must be bounded, and that you may need a really wide hidden layer to get a big value range, when the output of each unit is bounded to e.g. The "universal approximation" of a standard neural network is not universal. In which case, once someone can show this you will find it would get support across actively-developed libraries pretty quickly since it seems straightforward to implement. There is the possibility that this situation is an oversight, and the idea is generally useful. Keras) have no reason to implement or support it. However, this is not an architecture that has proven itself useful, so authors of higher-level libraries (e.g. Why neural networks models do not allow for multiplication of inputs? If you just want to explore other NN structures to see whether they work, you can still do so, but without a specific target you will be searching for a problem to solve (unless by chance you stumble upon something generally useful that has been overlooked before). ![]() ![]() If you can find a good match from your vector multiplication model to a specific problem domain, then that's an indication that it may be worth implementing in order to test that theory. The design of a 2-dimensional CNN layer has a logical match to how pixels in an image relate to each other locally - defining edges, textures etc, so the architecture in the model nicely matches to some problem domains. ![]() The ones that have become popular have all proven themselves on some task or other, and often have associated papers demonstrating their usefulness.įor example Convolutional Neural Networks have proven themselves good at image-based tasks. No doubt there have been explorations of all sorts of variations to the standard NN model over time. The reason is usually that these additions improve the speed or scope of what can be learned, they generalise better from training data, or they model something from a problem domain really well. So, invention and use of new architectures needs some reason. The universal approximation theorem essentially states that in order to have a network that could learn a specific function, you don't need anything more than one hidden layer using the standard matrix multiplying In TensorFlow, you also get automated gradient calculations, so you should be able to still define a cost function and use existing optimisers, without needing to analyse the new design yourself or re-write back propagation formulae. Using a low-level library, such as Theano or TensorFlow, it is likely that you can construct new schemes for reducing tensors (maybe via some learnable weight vector etc). ![]()
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