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Really? Better inform all the researchers working on this that they're wasting their time then: https://arxiv.org/abs/2001.05016 https://arxiv.org/abs/2001.0501
by yldedly 5y ago
Really? Better inform all the researchers working on this that they're wasting their time then: https://arxiv.org/abs/2001.05016 https://arxiv.org/abs/2001.05016
More fundamentally, any finite neural net is either constant or linear outside the training sample,depending on the activation function. Unless you design special neurons like in the paper above, which solves this specific problem for arithmetic, but not the general problem of extrapolation.
- FeepingCreature 5y agoIsn't that per-layer?
- yldedly 5y agoNo, no matter how many piecewise linear functions you compose, the result is still piecewise linear.
- FeepingCreature 5y agoWell sure, but neurons are still universal approximators. Any CPU is a sum of piecewise linear functions. I don't see where this meaningfully limits the capabilities of an AI, since once we're multilayer there's no 1:1 relation between training samples and piece placement in the output.
- yldedly 5y agohttps://medium.com/analytics-vidhya/you-dont-understand-neural-networks-until-you-understand-the-universal-approximation-theorem-85b3e7677126 https://medium.com/analytics-vidhya/you-dont-understand-neur...
- FeepingCreature 5y agoI just don't see how that's relevant. Nobody uses one-hidden-layer networks anymore. Whatever GPT is doing, it has nothing to do with approximating a collection of samples by assembling piecewise functions, except in the way that Microsoft Word is based on the Transistor.
- yldedly 5y agoSounds like no amount of math will convince you otherwise.
- FeepingCreature 5y agoShould math about a vaguely related topic convince me about this? Multilevel ANNs act differently than one-level ANNs. Transformers simply don't have anything to do with the model of approximating functions by assembling piecewise functions. This is akin to arguing that computers can't copy files because the disjunctive normal form sometimes needs exponential terms on bit inputs, so obviously it cannot scale to large data sets - yes, that is true about the DNF, but copying files on a computer simply does not use boolean operations in a way that would run into that limitation. The way that Transformers learn has more to do with their multilayering than with the transformation across any one layer. Universal approximation only describes the things the network learns across any pair of layers, but the input and output features that it learns about in the middle are only tangentially related to the training samples. You cannot predict the capabilities of a deep neural network by considering the limitations of a one-layer learner.
- mjburgess 5y ago> any finite neural net is either constant or linear outside the training sample Hence why the structure of our bodies has to include the capacity for imagination. Our brain structure does not record everything that has happened. It permits is to imagine an infinite number of things which might happen. We do not come to understand the world by having a brain-structure isomorphic to world structure -- this is none-sense for, at least, the above reason. But also, there really isnt anything like "world structure" to be isomorphic to. Ie., brains arent HDDs. They are, at least, simulators. I dont think we'll find anything in the brain like "leaves are green" because that is just a generated public representation of a latent-simulating-thought. There isnt much to be learned about the world from these, they only make sense to us. That all the text of human history has associations between words is the statistical coincidence that modern NLP uses for its smoke-and-mirrors. As a theory of language it's madness.