anhinga_anhinga (![[personal profile]](https://www.dreamwidth.org/img/silk/identity/user.png)
anhinga_anhinga) wrote2016-12-27 01:29 am
anhinga_anhinga) wrote2016-12-27 01:29 am
Dataflow matrix machines as generalized recurrent neural networks
A year ago I posted about dataflow programming and linear models of computation:
http://anhinga-anhinga.livejournal.com/82757.html
It turns out that those dataflow matrix machines are a fairly powerful generalization of recurrent neural networks.
The main feature of dataflow matrix machines (DMMs) are vector neurons. While recurrent neural networks process streams of numbers, dataflow matrix machines process streams of representations of arbitrary vectors (linear streams).
Another important feature of DMMs is that neurons of arbitrary input and output arity are allowed, and a rich set of built-in transformations of linear streams is provided.
Recurrent neural networks are Turing-complete, but they are an esoteric programming language, and not a convenient general-purpose programming platform. DMMs provide a formalism friendly to handling sparse vectors, conditionals, and more, and there are indications that DMMs will grow to become a powerful general-purpose programming platform, in addition to being a convenient machine learning platform.
In this context, it is possible to represent large classes of programs by matrices of real numbers, which allows us to modify programs in continuous fashion and to synthesize programs by synthesizing matrices of real numbers.
Further details and preprints
Self-referential mechanism: Consider a linear stream of matrices describing the connectivity pattern and weights of a DMM. Select a dedicated neuron Self emitting such a stream on its output, and use the latest value of that stream as the current network matrix (matrix describing the connectivity pattern and weights of our DMM). A typical Self neuron would work as an accumulator taking additive updates from other neurons in the network. This mechanism enables reflection facilities and powerful dynamic self-modification facilities. In particular, the networks in question have facilities for dynamic expansion.
The recent DMM-related preprints by our group:
https://arxiv.org/abs/1603.09002
https://arxiv.org/abs/1605.05296
https://arxiv.org/abs/1606.09470
https://arxiv.org/abs/1610.00831
Modern recurrent neural networks with good machine learning properties such as LSTM and Gated Recurrent Unit networks are naturally understood in the DMM framework as networks having linear and bilinear neurons in addition to neurons with more traditional sigmoid activation functions.
Our new open source effort
The new open-source implementation of core DMM primitives in Clojure:
https://github.com/jsa-aerial/DMM
This open-source implementation features a new vector space of recurrent maps (space of "mixed rank tensors"), which allows us to represent a large variety of linear streams as streams of recurrent maps. The vector space of recurrent maps also makes it possible to express variadic neurons as neurons having just one argument.
Therefore a type of neuron is simply a function transforming recurrent maps, which is a great simplification compared to the formalism presented in the preprints above. See the design notes within this open-source implementation for further details.
http://anhinga-anhinga.livejournal.com/82757.html
It turns out that those dataflow matrix machines are a fairly powerful generalization of recurrent neural networks.
The main feature of dataflow matrix machines (DMMs) are vector neurons. While recurrent neural networks process streams of numbers, dataflow matrix machines process streams of representations of arbitrary vectors (linear streams).
Another important feature of DMMs is that neurons of arbitrary input and output arity are allowed, and a rich set of built-in transformations of linear streams is provided.
Recurrent neural networks are Turing-complete, but they are an esoteric programming language, and not a convenient general-purpose programming platform. DMMs provide a formalism friendly to handling sparse vectors, conditionals, and more, and there are indications that DMMs will grow to become a powerful general-purpose programming platform, in addition to being a convenient machine learning platform.
In this context, it is possible to represent large classes of programs by matrices of real numbers, which allows us to modify programs in continuous fashion and to synthesize programs by synthesizing matrices of real numbers.
Further details and preprints
Self-referential mechanism: Consider a linear stream of matrices describing the connectivity pattern and weights of a DMM. Select a dedicated neuron Self emitting such a stream on its output, and use the latest value of that stream as the current network matrix (matrix describing the connectivity pattern and weights of our DMM). A typical Self neuron would work as an accumulator taking additive updates from other neurons in the network. This mechanism enables reflection facilities and powerful dynamic self-modification facilities. In particular, the networks in question have facilities for dynamic expansion.
The recent DMM-related preprints by our group:
https://arxiv.org/abs/1603.09002
https://arxiv.org/abs/1605.05296
https://arxiv.org/abs/1606.09470
https://arxiv.org/abs/1610.00831
Modern recurrent neural networks with good machine learning properties such as LSTM and Gated Recurrent Unit networks are naturally understood in the DMM framework as networks having linear and bilinear neurons in addition to neurons with more traditional sigmoid activation functions.
Our new open source effort
The new open-source implementation of core DMM primitives in Clojure:
https://github.com/jsa-aerial/DMM
This open-source implementation features a new vector space of recurrent maps (space of "mixed rank tensors"), which allows us to represent a large variety of linear streams as streams of recurrent maps. The vector space of recurrent maps also makes it possible to express variadic neurons as neurons having just one argument.
Therefore a type of neuron is simply a function transforming recurrent maps, which is a great simplification compared to the formalism presented in the preprints above. See the design notes within this open-source implementation for further details.
no subject
First of all, one should think about recurrent neural networks (RNNs) and about DMMs as "two-stroke engines" (двухтактные двигатели). On the "up movement", the "activation functions" built into the neurons are applied to the inputs of the neurons, and the outputs of the neurons are produced. On the "down movement", the neuron inputs are recomputed from the neuron outputs using the network matrix. This cycle of "up movement"/"down movement" is repeated indefinitely.
The network matrix defines the topology and the weights of the network. The columns of the network matrix are indexed by the neuron outputs, and the rows of the network matrix are indexed by the neuron inputs. If a particular weight is zero, this means that the corresponding output and input are not connected, so the sparsity structure of the matrix defines the topology of the network.
It was traditional to have the same activation function for all neurons in the network, and it was traditional to use some kind of sigmoid for this purpose, but these days it is a common place to mix a few different kinds of activation functions within the same network. Besides sigmoid functions such as logistic ("soft step") and hyperbolic tangent, a particularly popular function in recent years is ReLU (rectifier, y=max(0,x) ). The table in the following Wikipedia article compares some of the activation functions people are trying.
https://en.wikipedia.org/wiki/Activation_function