AI News, Graph-based machine learning: Part I

Graph-based machine learning: Part I

Many important problems can be represented and studied using graphs — social networks, interacting bacterias, brain network modules, hierarchical image clustering and many more.

If we accept graphs as a basic means of structuring and analyzing data about the world, we shouldn’t be surprised to see them being widely used in Machine Learning as a powerful tool that can enable intuitive properties and power a lot of useful features.

See more in this recent blog post from Google Research This post explores the tendencies of nodes in a graph to spontaneously form clusters of internally dense linkage (hereby termed “community”);

This has a lot of advantages since it typically only requires a knowledge of first degree neighbors and small incremental merging steps, to bring the global solution towards stepwise equilibriums.

The basic approach does indeed consists of iteratively merging nodes that optimize a local modularity so let’s go ahead and define that as well: This is part of the magic for me as this local optimization function can easily be translated to an interpretable metric within the domain of your graph.

In other words, the weighted links can be a function of the type of nodes computed on-the-fly (useful if you’re dealing with a multidimensional graph with various types of relationships and nodes).

It can be a lot of things: a maximum number of iterations, a minimum modularity gain during the transfer phase, or any other relevant piece of information related to your data that would inform you that it needs to stop.

Recurrent neural network

A recurrent neural network (RNN) is a class of artificial neural network where connections between nodes form a directed graph along a sequence.

The term 'recurrent neural network' is used indiscriminately to refer to two broad classes of networks with a similar general structure, where one is finite impulse and the other is infinite impulse.

A finite impulse recurrent network is a directed acyclic graph that can be unrolled and replaced with a strictly feedforward neural network, while an infinite impulse recurrent network is a directed cyclic graph that can not be unrolled.

Both finite impulse and infinite impulse recurrent networks can have additional stored state, and the storage can be under direct control by the neural network.

Such controlled states are referred to as gated state or gated memory, and are part of long short-term memorys (LSTMs) and gated recurrent units.

In 1993, a neural history compressor system solved a 'Very Deep Learning' task that required more than 1000 subsequent layers in an RNN unfolded in time.[5]

In 2014, the Chinese search giant Baidu used CTC-trained RNNs to break the Switchboard Hub5'00 speech recognition benchmark without using any traditional speech processing methods.[10]

Basic RNNs are a network of neuron-like nodes organized into successive 'layers', each node in a given layer is connected with a directed (one-way) connection to every other node in the next successive layer.[citation needed]

Nodes are either input nodes (receiving data from outside the network), output nodes (yielding results), or hidden nodes (that modify the data en route from input to output).

For supervised learning in discrete time settings, sequences of real-valued input vectors arrive at the input nodes, one vector at a time.

At any given time step, each non-input unit computes its current activation (result) as a nonlinear function of the weighted sum of the activations of all units that connect to it.

For example, if the input sequence is a speech signal corresponding to a spoken digit, the final target output at the end of the sequence may be a label classifying the digit.

Instead a fitness function or reward function is occasionally used to evaluate the RNN's performance, which influences its input stream through output units connected to actuators that affect the environment.

The gradient backpropagation can be easily regulated to avoid gradient vanishing and exploding while keeping long-term memory as well as memory of any range.

An Elman network is a three-layer network (arranged horizontally as x, y, and z in the illustration) with the addition of a set of 'context units' (u in the illustration).

The fixed back-connections save a copy of the previous values of the hidden units in the context units (since they propagate over the connections before the learning rule is applied).

Thus the network can maintain a sort of state, allowing it to perform such tasks as sequence-prediction that are beyond the power of a standard multilayer perceptron.

Given a lot of learnable predictability in the incoming data sequence, the highest level RNN can use supervised learning to easily classify even deep sequences with long intervals between important events.

Once the chunker has learned to predict and compress inputs that are unpredictable by the automatizer, then the automatizer can be forced in the next learning phase to predict or imitate through additional units the hidden units of the more slowly changing chunker.

LSTM works even given long delays between significant events and can handle signals that mix low and high frequency components.

to find an RNN weight matrix that maximizes the probability of the label sequences in a training set, given the corresponding input sequences.

continuous time recurrent neural network (CTRNN) uses a system of ordinary differential equations to model the effects on a neuron of the incoming spike train.

Note that, by the Shannon sampling theorem, discrete time recurrent neural networks can be viewed as continuous-time recurrent neural networks where the differential equations have transformed into equivalent difference equations.

multiple timescales recurrent neural network (MTRNN) is a neural-based computational model that can simulate the functional hierarchy of the brain through self-organization that depends on spatial connection between neurons and on distinct types of neuron activities, each with distinct time properties.[53][54]

With such varied neuronal activities, continuous sequences of any set of behaviors are segmented into reusable primitives, which in turn are flexibly integrated into diverse sequential behaviors.

In neural networks, it can be used to minimize the error term by changing each weight in proportion to the derivative of the error with respect to that weight, provided the non-linear activation functions are differentiable.

In this context, local in space means that a unit's weight vector can be updated using only information stored in the connected units and the unit itself such that update complexity of a single unit is linear in the dimensionality of the weight vector.

Local in time means that the updates take place continually (on-line) and depend only on the most recent time step rather than on multiple time steps within a given time horizon as in BPTT.

For recursively computing the partial derivatives, RTRL has a time-complexity of O(number of hidden x number of weights) per time step for computing the Jacobian matrices, while BPTT only takes O(number of weights) per time step, at the cost of storing all forward activations within the given time horizon.[63]

major problem with gradient descent for standard RNN architectures is that error gradients vanish exponentially quickly with the size of the time lag between important events.[34][67]

This fact improves stability of the algorithm, providing a unifying view on gradient calculation techniques for recurrent networks with local feedback.

A target function can be formed to evaluate the fitness or error of a particular weight vector as follows: First, the weights in the network are set according to the weight vector.

Initially, the genetic algorithm is encoded with the neural network weights in a predefined manner where one gene in the chromosome represents one weight link.The whole network is represented as a single chromosome.

Other global (and/or evolutionary) optimization techniques may be used to seek a good set of weights, such as simulated annealing or particle swarm optimization.

Whereas recursive neural networks operate on any hierarchical structure, combining child representations into parent representations, recurrent neural networks operate on the linear progression of time, combining the previous time step and a hidden representation into the representation for the current time step.

In particular, RNNs can appear as nonlinear versions of finite impulse response and infinite impulse response filters and also as a nonlinear autoregressive exogenous model (NARX).[74]

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