Wei_Dai comments on The Brain as a Universal Learning Machine - LessWrong

82 Post author: jacob_cannell 24 June 2015 09:45PM

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Comment author: Wei_Dai 05 July 2015 11:02:51AM 5 points [-]

Your comments made me curious enough to download PyBrain and play around with the sample code, to see if I could modify it to learn the parity function without intermediate parity bits in the output. In the end, I was able to, by trial and error, come up with hyperparameters that allowed the RNN to learn the parity function reliably in a few minutes on my laptop (many other choices of hyperparameters caused the SGD to sometimes get stuck before it converged to a correct solution). I've posted the modified sample code here. (Notice that the network now has 2 input nodes, one for the input string and one to indicate end of string, 2 hidden layers with 3 and 2 nodes, and an output node.)

The machine learning system will have to figure the algorithm on its own, and current approaches can't do it in a general way, even for relatively simple algorithms.

I guess you're basically correct on this, since even with the tweaked hyperparameters, on the parity problem RNN+SGD isn't really doing any better than a brute force search through the space of simple circuits or algorithms. But humans arguably aren't very good at learning algorithms from input/output examples either. The fact that RNNs can learn the parity function, even if barely, makes it less clear that humans have any advantage at this kind of learning.

Comment author: V_V 07 July 2015 04:59:07PM 2 points [-]

Nice work!

Anyway, in a paper published on arXiv yesterday, the Google DeepMind people report being able to train a feed-forward neural network to solve the parity problem, using a sophisticated gating mechanism and weight sharing between the layers. They also obtain state of the art or near state of the art results on other problems.

This result makes me update in the increasing direction my belief about the generality of neural networks.

Comment author: jacob_cannell 07 July 2015 06:40:29PM 1 point [-]

Ah you beat me to it, I just read that paper as well.

Here is the abstract for those that haven't read it yet:

This paper introduces Grid Long Short-Term Memory, a network of LSTM cells arranged in a multidimensional grid that can be applied to vectors, sequences or higher dimensional data such as images. The network differs from existing deep LSTM architectures in that the cells are connected between network layers as well as along the spatiotemporal dimensions of the data. It therefore provides a unified way of using LSTM for both deep and sequential computation. We apply the model to algorithmic tasks such as integer addition and determining the parity of random binary vectors. It is able to solve these problems for 15-digit integers and 250-bit vectors respectively. We then give results for three empirical tasks. We find that 2D Grid LSTM achieves 1.47 bits per character on the Wikipedia character prediction benchmark, which is state-of-the-art among neural approaches. We also observe that a two-dimensional translation model based on Grid LSTM outperforms a phrase-based reference system on a Chinese-to-English translation task, and that 3D Grid LSTM yields a near state-of-the-art error rate of 0.32% on MNIST.

Also, relevant to this discussion:

It is core to the problem that the k-bit string is given to the neural network as a whole through a single projection; considering one bit at a time and remembering the previous partial result in a recurrent or multi-step architecture reduces the problem of learning k-bit parity to the simple one of learning just 2-bit parity.

The version of the problem that humans can learn well is this easier reduction. Humans can not easily learn the hard version of the parity problem, which would correspond to a rapid test where the human is presented with a flash card with a very large number on it (60+ digits to rival the best machine result) and then must respond immediately. The fast response requirement is important to prevent using much easier multi-step serial algorithms.

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