Recurrent neural network

Summary

A recurrent neural network (RNN) is one of the two broad types of artificial neural network, characterized by direction of the flow of information between its layers. In contrast to uni-directional feedforward neural network, it is a bi-directional artificial neural network, meaning that it allows the output from some nodes to affect subsequent input to the same nodes. Their ability to use internal state (memory) to process arbitrary sequences of inputs makes them applicable to tasks such as unsegmented, connected handwriting recognition or speech recognition. The term "recurrent neural network" is used to refer to the class of networks with an infinite impulse response, whereas "convolutional neural network" refers to the class of finite impulse response. Both classes of networks exhibit temporal dynamic behavior. 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 recur

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https://en.wikipedia.org/wiki/Recurrent_neural_network

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Learning music composition with recurrent neural networks

Florian François Colombo

Throughout this thesis, we are interested in modeling music composition. To do so, we study the association of music theory concepts with the learning capabilities of recurrent neural networks. Especially, we explore numerical formalizations of music so that our models operate on data containing useful information to decide how to combine particular rhythms and notes in specified musical contexts. The first part introduces the Deep Artificial Composer, a generative model of monophonic melodies. We present a network architecture that considers the temporal and instantaneous relationships between the pitch and duration of notes. By combining Irish with klezmer melodies to train the Deep Artificial Composer, we study how it reacts to heterogeneous data. Furthermore, we show how to generate melodies containing Irish or Klezmer folk musicâs characteristics from our probabilistic model of notes. The second part presents BachProp, a model for the composition of polyphonic music. We discover how scores of different styles can be generated from models using neural networks. In particular, we train BachProp with Bachâs chorales and the English folk music corpus Nottingham. Also, we verify that generated compositions share specific properties with the original corpus it processes. Especially, our musical novelty statistics show that BachProp generates musical sequences as innovative as those present in the original corpora. Finally, a large audience appreciated the Ada string quartet performances of BachPropâs compositions. Whereas BachProp operates on any music in the usual MIDI format, the BeethovANN algorithm, introduced in the last part, needs the information contained in scores in the MusicXML format. These digital scores allow us to formalize relevant musical characteristics in order to generate music with BeethovANN. Thus, to create new voices that can be played in accompaniment to Beethoven string quartets, we take into account not only the note sequences, but also the harmonic progression, interactions between voices, and the rhythm of each instrument. Eventually, professional musicians misclassified BeethovANN musical phrases for Beethovenâs original compositions.

EPFL2021

Algorithmic composition of melodies with deep recurrent neural networks

Florian François Colombo

A big challenge in algorithmic composition is to devise a model that is both easily trainable and able to reproduce the long-range temporal dependencies typical of music. Here we investigate how artificial neural networks can be trained on a large corpus of melodies and turned into automated mu- sic composers able to generate new melodies coherent with the style they have been trained on. We employ gated-recurrent unit (GRU) networks that have been shown to be particularly efficient in learning complex sequential activations with arbitrary long time lags. Our model processes rhythm and melody in parallel while modeling the relation between these two properties. Using such an approach, we were able to generate interesting complete melodies or suggest possible continuations of a melody fragment that is coherent with the characteristics of the fragment itself.

2016

Our brain continuously self-organizes to construct and maintain an internal representation of the world based on the information arriving through sensory stimuli. Remarkably, cortical areas related to different sensory modalities appear to share the same functional unit, the neuron, and develop through the same learning mechanism, synaptic plasticity. It motivates the conjecture of a unifying theory to explain cortical representational learning across sensory modalities. In this thesis we present theories and computational models of learning and optimization in neural networks, postulating functional properties of synaptic plasticity that support the apparent universal learning capacity of cortical networks. In the past decades, a variety of theories and models have been proposed to describe receptive field formation in sensory areas. They include normative models such as sparse coding, and bottom-up models such as spike-timing dependent plasticity. We bring together candidate explanations by demonstrating that in fact a single principle is sufficient to explain receptive field development. First, we show that many representative models of sensory development are in fact implementing variations of a common principle: nonlinear Hebbian learning. Second, we reveal that nonlinear Hebbian learning is sufficient for receptive field formation through sensory inputs. A surprising result is that our findings are independent of specific details, and allow for robust predictions of the learned receptive fields. Thus nonlinear Hebbian learning and natural statistics can account for many aspects of receptive field formation across models and sensory modalities. The Hebbian learning theory substantiates that synaptic plasticity can be interpreted as an optimization procedure, implementing stochastic gradient descent. In stochastic gradient descent inputs arrive sequentially, as in sensory streams. However, individual data samples have very little information about the correct learning signal, and it becomes a fundamental problem to know how many samples are required for reliable synaptic changes. Through estimation theory, we develop a novel adaptive learning rate model, that adapts the magnitude of synaptic changes based on the statistics of the learning signal, enabling an optimal use of data samples. Our model has a simple implementation and demonstrates improved learning speed, making this a promising candidate for large artificial neural network applications. The model also makes predictions on how cortical plasticity may modulate synaptic plasticity for optimal learning. The optimal sampling size for reliable learning allows us to estimate optimal learning times for a given model. We apply this theory to derive analytical bounds on times for the optimization of synaptic connections. First, we show this optimization problem to have exponentially many saddle-nodes, which lead to small gradients and slow learning. Second, we show that the number of input synapses to a neuron modulates the magnitude of the initial gradient, determining the duration of learning. Our final result reveals that the learning duration increases supra-linearly with the number of synapses, suggesting an effective limit on synaptic connections and receptive field sizes in developing neural networks.

EPFL2016

Learning music composition with recurrent neural networks

Florian François Colombo

EPFL2021

EPFL2016