91 research outputs found
Simple Cycle Reservoirs are Universal
Reservoir computation models form a subclass of recurrent neural networks
with fixed non-trainable input and dynamic coupling weights. Only the static
readout from the state space (reservoir) is trainable, thus avoiding the known
problems with propagation of gradient information backwards through time.
Reservoir models have been successfully applied in a variety of tasks and were
shown to be universal approximators of time-invariant fading memory dynamic
filters under various settings. Simple cycle reservoirs (SCR) have been
suggested as severely restricted reservoir architecture, with equal weight ring
connectivity of the reservoir units and input-to-reservoir weights of binary
nature with the same absolute value. Such architectures are well suited for
hardware implementations without performance degradation in many practical
tasks. In this contribution, we rigorously study the expressive power of SCR in
the complex domain and show that they are capable of universal approximation of
any unrestricted linear reservoir system (with continuous readout) and hence
any time-invariant fading memory filter over uniformly bounded input streams.Comment: 21 page
A Survey on Neural Network Interpretability
Along with the great success of deep neural networks, there is also growing
concern about their black-box nature. The interpretability issue affects
people's trust on deep learning systems. It is also related to many ethical
problems, e.g., algorithmic discrimination. Moreover, interpretability is a
desired property for deep networks to become powerful tools in other research
fields, e.g., drug discovery and genomics. In this survey, we conduct a
comprehensive review of the neural network interpretability research. We first
clarify the definition of interpretability as it has been used in many
different contexts. Then we elaborate on the importance of interpretability and
propose a novel taxonomy organized along three dimensions: type of engagement
(passive vs. active interpretation approaches), the type of explanation, and
the focus (from local to global interpretability). This taxonomy provides a
meaningful 3D view of distribution of papers from the relevant literature as
two of the dimensions are not simply categorical but allow ordinal
subcategories. Finally, we summarize the existing interpretability evaluation
methods and suggest possible research directions inspired by our new taxonomy.Comment: This work has been accepted by IEEE-TETC
Kernel regression estimates of time delays between gravitationally lensed fluxes
Strongly lensed variable quasars can serve as precise cosmological probes,
provided that time delays between the image fluxes can be accurately measured.
A number of methods have been proposed to address this problem. In this paper,
we explore in detail a new approach based on kernel regression estimates, which
is able to estimate a single time delay given several datasets for the same
quasar. We develop realistic artificial data sets in order to carry out
controlled experiments to test of performance of this new approach. We also
test our method on real data from strongly lensed quasar Q0957+561 and compare
our estimates against existing results.Comment: Updated to match published versio
Dynamics and topographic organization of recursive self-organizing maps
Recently there has been an outburst of interest in extending topographic maps of vectorial data to more general data structures, such as sequences or trees. However, there is no general consensus as to how best to process sequences using topographicmaps, and this topic remains an active focus of neurocomputational research. The representational capabilities and internal representations of the models are not well understood. Here, we rigorously analyze a generalization of the self-organizingmap (SOM) for processing sequential data, recursive SOM (RecSOM) (Voegtlin, 2002), as a nonautonomous dynamical system consisting of a set of fixed input maps. We argue that contractive fixed-input maps are likely to produce Markovian organizations of receptive fields on the RecSOM map. We derive bounds on parameter β (weighting the importance of importing past information when processing sequences) under which contractiveness of the fixed-input maps is guaranteed. Some generalizations of SOM contain a dynamic module responsible for processing temporal contexts as an integral part of the model. We show that Markovian topographic maps of sequential data can be produced using a simple fixed (nonadaptable) dynamic module externally feeding a standard topographic model designed to process static vectorial data of fixed dimensionality (e.g., SOM). However, by allowing trainable feedback connections, one can obtain Markovian maps with superior memory depth and topography preservation. We elaborate on the importance of non-Markovian organizations in topographic maps of sequential data. © 2006 Massachusetts Institute of Technology
Spatial-temporal modelling of fMRI data through spatially regularized mixture of hidden process models.
Previous work investigated a range of spatio-temporal constraints for fMRI data analysis to provide robust detection of neural activation. We present a mixture-based method for the spatio-temporal modelling of fMRI data. This approach assumes that fMRI time series are generated by a probabilistic superposition of a small set of spatio-temporal prototypes (mixture components). Each prototype comprises a temporal model that explains fMRI signals on a single voxel and the model's "region of influence" through a spatial prior over the voxel space. As the key ingredient of our temporal model, the Hidden Process Model (HPM) framework proposed in Hutchinson et al. (2009) is adopted to infer the overlapping cognitive processes triggered by stimuli. Unlike the original HPM framework, we use a parametric model of Haemodynamic Response Function (HRF) so that biological constraints are naturally incorporated in the HRF estimation. The spatial priors are defined in terms of a parameterised distribution. Thus, the total number of parameters in the model does not depend on the number of voxels. The resulting model provides a conceptually principled and computationally efficient approach to identify spatio-temporal patterns of neural activation from fMRI data, in contrast to most conventional approaches in the literature focusing on the detection of spatial patterns. We first verify the proposed model in a controlled experimental setting using synthetic data. The model is further validated on real fMRI data obtained from a rapid event-related visual recognition experiment (Mayhew et al., 2012). Our model enables us to evaluate in a principled manner the variability of neural activations within individual regions of interest (ROIs). The results strongly suggest that, compared with occipitotemporal regions, the frontal ones are less homogeneous, requiring two HPM prototypes per region. Despite the rapid event-related experimental design, the model is capable of disentangling the perceptual judgement and motor response processes that are both activated in the frontal ROIs. Spatio-temporal heterogeneity in the frontal regions seems to be associated with diverse dynamic localizations of the two hidden processes in different subregions of frontal ROIs
A new framework for analysis of coevolutionary systems:Directed graph representation and random walks
Studying coevolutionary systems in the context of simplified models (i.e. games with pairwise interactions between coevolving solutions modelled as self plays) remains an open challenge since the rich underlying structures associated with pairwise comparison-based fitness measures are often not taken fully into account. Although cyclic dynamics have been demonstrated in several contexts (such as intransitivity in coevolutionary problems), there is no complete characterization of cycle structures and their effects on coevolutionary search. We develop a new framework to address this issue. At the core of our approach is the directed graph (digraph) representation of coevolutionary problem that fully captures structures in the relations between candidate solutions. Coevolutionary processes are modelled as a specific type of Markov chains ? random walks on digraphs. Using this framework, we show that coevolutionary problems admit a qualitative characterization: a coevolutionary problem is either solvable (there is a subset of solutions that dominates the remaining candidate solutions) or not. This has an implication on coevolutionary search. We further develop our framework that provide the means to construct quantitative tools for analysis of coevolutionary processes and demonstrate their applications through case studies. We show that coevolution of solvable problems corresponds to an absorbing Markov chain for which we can compute the expected hitting time of the absorbing class. Otherwise, coevolution will cycle indefinitely and the quantity of interest will be the limiting invariant distribution of the Markov chain. We also provide an index for characterizing complexity in coevolutionary problems and show how they can be generated in a controlled mannerauthorsversionPeer reviewe
Richness of Deep Echo State Network Dynamics
Reservoir Computing (RC) is a popular methodology for the efficient design of
Recurrent Neural Networks (RNNs). Recently, the advantages of the RC approach
have been extended to the context of multi-layered RNNs, with the introduction
of the Deep Echo State Network (DeepESN) model. In this paper, we study the
quality of state dynamics in progressively higher layers of DeepESNs, using
tools from the areas of information theory and numerical analysis. Our
experimental results on RC benchmark datasets reveal the fundamental role
played by the strength of inter-reservoir connections to increasingly enrich
the representations developed in higher layers. Our analysis also gives
interesting insights into the possibility of effective exploitation of training
algorithms based on stochastic gradient descent in the RC field.Comment: Preprint of the paper accepted at IWANN 201
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