644 research outputs found
On probabilistic analog automata
We consider probabilistic automata on a general state space and study their
computational power. The model is based on the concept of language recognition
by probabilistic automata due to Rabin and models of analog computation in a
noisy environment suggested by Maass and Orponen, and Maass and Sontag. Our
main result is a generalization of Rabin's reduction theorem that implies that
under very mild conditions, the computational power of the automaton is limited
to regular languages
A Survey on Continuous Time Computations
We provide an overview of theories of continuous time computation. These
theories allow us to understand both the hardness of questions related to
continuous time dynamical systems and the computational power of continuous
time analog models. We survey the existing models, summarizing results, and
point to relevant references in the literature
Computation with perturbed dynamical systems
This paper analyzes the computational power of dynamical systems robust to infinitesimal perturbations. Previous work on the subject has delved on very specific types of systems. Here we obtain results for broader classes of dynamical systems (including those systems defined by Lipschitz/analytic functions). In particular we show that systems robust to infinitesimal perturbations only recognize recursive languages. We also show the converse direction: every recursive language can be robustly recognized by a computable system. By other words we show that robustness is equivalent to decidability. (C) 2013 Elsevier Inc. All rights reserved.INRIA program "Equipe Associee" ComputR; Fundacao para a Ciencia e a Tecnologia; EU FEDER POCTI/POCI via SQIG - Instituto de Telecomunicacoes through the FCT project [PEst-OE/EEI/LA0008/2011]info:eu-repo/semantics/publishedVersio
Computational Aspects of Feedback in Neural Circuits
It has previously been shown that generic cortical microcircuit models can perform complex real-time computations on
continuous input streams, provided that these computations can be carried out with a rapidly fading memory. We
investigate the computational capability of such circuits in the more realistic case where not only readout neurons, but
in addition a few neurons within the circuit, have been trained for specific tasks. This is essentially equivalent to the
case where the output of trained readout neurons is fed back into the circuit. We show that this new model overcomes
the limitation of a rapidly fading memory. In fact, we prove that in the idealized case without noise it can carry out any
conceivable digital or analog computation on time-varying inputs. But even with noise, the resulting computational
model can perform a large class of biologically relevant real-time computations that require a nonfading memory. We
demonstrate these computational implications of feedback both theoretically, and through computer simulations of
detailed cortical microcircuit models that are subject to noise and have complex inherent dynamics. We show that the
application of simple learning procedures (such as linear regression or perceptron learning) to a few neurons enables
such circuits to represent time over behaviorally relevant long time spans, to integrate evidence from incoming spike
trains over longer periods of time, and to process new information contained in such spike trains in diverse ways
according to the current internal state of the circuit. In particular we show that such generic cortical microcircuits with
feedback provide a new model for working memory that is consistent with a large set of biological constraints.
Although this article examines primarily the computational role of feedback in circuits of neurons, the mathematical
principles on which its analysis is based apply to a variety of dynamical systems. Hence they may also throw new light on the computational role of feedback in other complex biological dynamical systems, such as, for example, genetic regulatory networks
Reservoir Computing: computation with dynamical systems
In het onderzoeksgebied Machine Learning worden systemen onderzocht die kunnen leren op basis van voorbeelden. Binnen dit onderzoeksgebied zijn de recurrente neurale netwerken een belangrijke deelgroep. Deze netwerken zijn abstracte modellen van de werking van delen van de hersenen. Zij zijn in staat om zeer complexe temporele problemen op te lossen maar zijn over het algemeen zeer moeilijk om te trainen. Recentelijk zijn een aantal gelijkaardige methodes voorgesteld die dit trainingsprobleem elimineren. Deze methodes worden aangeduid met de naam Reservoir Computing. Reservoir Computing combineert de indrukwekkende rekenkracht van recurrente neurale netwerken met een eenvoudige trainingsmethode. Bovendien blijkt dat deze trainingsmethoden niet beperkt zijn tot neurale netwerken, maar kunnen toegepast worden op generieke dynamische systemen. Waarom deze systemen goed werken en welke eigenschappen bepalend zijn voor de prestatie is evenwel nog niet duidelijk.
Voor dit proefschrift is onderzoek gedaan naar de dynamische eigenschappen van generieke Reservoir Computing systemen. Zo is experimenteel aangetoond dat de idee van Reservoir Computing ook toepasbaar is op niet-neurale netwerken van dynamische knopen. Verder is een maat voorgesteld die gebruikt kan worden om het dynamisch regime van een reservoir te meten. Tenslotte is een adaptatieregel geïntroduceerd die voor een breed scala reservoirtypes de dynamica van het reservoir kan afregelen tot het gewenste dynamisch regime. De technieken beschreven in dit proefschrift zijn gedemonstreerd op verschillende academische en ingenieurstoepassingen
Deep Learning Techniques for Music Generation -- A Survey
This paper is a survey and an analysis of different ways of using deep
learning (deep artificial neural networks) to generate musical content. We
propose a methodology based on five dimensions for our analysis:
Objective - What musical content is to be generated? Examples are: melody,
polyphony, accompaniment or counterpoint. - For what destination and for what
use? To be performed by a human(s) (in the case of a musical score), or by a
machine (in the case of an audio file).
Representation - What are the concepts to be manipulated? Examples are:
waveform, spectrogram, note, chord, meter and beat. - What format is to be
used? Examples are: MIDI, piano roll or text. - How will the representation be
encoded? Examples are: scalar, one-hot or many-hot.
Architecture - What type(s) of deep neural network is (are) to be used?
Examples are: feedforward network, recurrent network, autoencoder or generative
adversarial networks.
Challenge - What are the limitations and open challenges? Examples are:
variability, interactivity and creativity.
Strategy - How do we model and control the process of generation? Examples
are: single-step feedforward, iterative feedforward, sampling or input
manipulation.
For each dimension, we conduct a comparative analysis of various models and
techniques and we propose some tentative multidimensional typology. This
typology is bottom-up, based on the analysis of many existing deep-learning
based systems for music generation selected from the relevant literature. These
systems are described and are used to exemplify the various choices of
objective, representation, architecture, challenge and strategy. The last
section includes some discussion and some prospects.Comment: 209 pages. This paper is a simplified version of the book: J.-P.
Briot, G. Hadjeres and F.-D. Pachet, Deep Learning Techniques for Music
Generation, Computational Synthesis and Creative Systems, Springer, 201
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