20 research outputs found
Function and form in networks of interacting agents
The main problem we address in this paper is whether function determines form
when a society of agents organizes itself for some purpose or whether the
organizing method is more important than the functionality in determining the
structure of the ensemble. As an example, we use a neural network that learns
the same function by two different learning methods. For sufficiently large
networks, very different structures may indeed be obtained for the same
functionality. Clustering, characteristic path length and hierarchy are
structural differences, which in turn have implications on the robustness and
adaptability of the networks. In networks, as opposed to simple graphs, the
connections between the agents are not necessarily symmetric and may have
positive or negative signs. New characteristic coefficients are introduced to
characterize this richer connectivity structure.Comment: 27 pages Latex, 11 figure
Deep Learning on Lie Groups for Skeleton-based Action Recognition
In recent years, skeleton-based action recognition has become a popular 3D
classification problem. State-of-the-art methods typically first represent each
motion sequence as a high-dimensional trajectory on a Lie group with an
additional dynamic time warping, and then shallowly learn favorable Lie group
features. In this paper we incorporate the Lie group structure into a deep
network architecture to learn more appropriate Lie group features for 3D action
recognition. Within the network structure, we design rotation mapping layers to
transform the input Lie group features into desirable ones, which are aligned
better in the temporal domain. To reduce the high feature dimensionality, the
architecture is equipped with rotation pooling layers for the elements on the
Lie group. Furthermore, we propose a logarithm mapping layer to map the
resulting manifold data into a tangent space that facilitates the application
of regular output layers for the final classification. Evaluations of the
proposed network for standard 3D human action recognition datasets clearly
demonstrate its superiority over existing shallow Lie group feature learning
methods as well as most conventional deep learning methods.Comment: Accepted to CVPR 201
Response Characterization for Auditing Cell Dynamics in Long Short-term Memory Networks
In this paper, we introduce a novel method to interpret recurrent neural
networks (RNNs), particularly long short-term memory networks (LSTMs) at the
cellular level. We propose a systematic pipeline for interpreting individual
hidden state dynamics within the network using response characterization
methods. The ranked contribution of individual cells to the network's output is
computed by analyzing a set of interpretable metrics of their decoupled step
and sinusoidal responses. As a result, our method is able to uniquely identify
neurons with insightful dynamics, quantify relationships between dynamical
properties and test accuracy through ablation analysis, and interpret the
impact of network capacity on a network's dynamical distribution. Finally, we
demonstrate generalizability and scalability of our method by evaluating a
series of different benchmark sequential datasets
A memory ann computing structure for nonlinear systems emulation identification
Currently, almost all efforts for using artificial neural networks for control oriented process identification are based on feed-forward networks. Provided the system order or the upper limit of the order is known, a neural network design is feasible for which all the collection of previous values of the inputs and outputs of the system to be identified can be used as input data to train in the network computing structures to learn the input-output map. This work reports on a novel technique that makes use of memory artificial neural network architecture that can learn and transform so as to emulate any non-linear input-output map for multi-input-multi-output systems when no prior knowledge on specific system features exists
Dynamic Function Learning through Control of Ensemble Systems
Learning tasks involving function approximation are preva- lent in numerous domains of science and engineering. The underlying idea is to design a learning algorithm that gener- ates a sequence of functions converging to the desired target function with arbitrary accuracy by using the available data samples. In this paper, we present a novel interpretation of iterative function learning through the lens of ensemble dy- namical systems, with an emphasis on establishing the equiv- alence between convergence of function learning algorithms and asymptotic behavior of ensemble systems. In particular, given a set of observation data in a function learning task, we prove that the procedure of generating an approximation sequence can be represented as a steering problem of a dy- namic ensemble system defined on a function space. This in turn gives rise to an ensemble systems-theoretic approach to the design of “continuous-time” function learning algorithms, which have a great potential to reach better generalizability compared with classical “discrete-time” learning algorithms
Non-parametric estimation of mixed discrete choice models
In this paper, different strands of literature are combined in order to
obtain algorithms for semi-parametric estimation of discrete choice models that
include the modelling of unobserved heterogeneity by using mixing distributions
for the parameters defining the preferences. The models use the theory on
non-parametric maximum likelihood estimation (NP-MLE) that has been developed
for general mixing models. The expectation-maximization (EM) techniques used in
the NP-MLE literature are combined with strategies for choosing appropriate
approximating models using adaptive grid techniques. \\ Jointly this leads to
techniques for specification and estimation that can be used to obtain a
consistent specification of the mixing distribution. Additionally, also
algorithms for the estimation are developed that help to decrease problems due
to the curse of dimensionality. \\ The proposed algorithms are demonstrated in
a small scale simulation study to be useful for the specification and
estimation of mixture models in the discrete choice context providing some
information on the specification of the mixing distribution. The simulations
document that some aspects of the mixing distribution such as the expectation
can be estimated reliably. They also demonstrate, however, that typically
different approximations to the mixing distribution lead to similar values of
the likelihood and hence are hard to discriminate. Therefore it does not appear
to be possible to reliably infer the most appropriate parametric form for the
estimated mixing distribution.Comment: Paper presented at the International Choice Modelling Conference
(ICMC2019) in Kobe, Japa
Nonlinear Systems Identification Using Additive Dynamic Neural Networks--Two On Line Approaches.
This paper proposes a class of additive dynamic connectionist (ADC) models for identification of unknown dynamic systems. These models work in continuous time and are linear in their parameters. Also, for this kind of model two on-line learning or parameter adaptation algorithms are developed: one based on gradient techniques and sensitivity analysis of the model output trajectories versus the model parameters and the other based on variational calculus, that lead to an off-line solution and an invariant imbedding technique that converts the off-line solution to an on-line one. These learning methods are developed using matrix calculus techniques in order to implement them in an automatic manner with the help of a symbolic manipulation package. The good behavior of the class of identification models and the two learning methods is tested on two simulated plants and a data set from a real plant and compared, in this case, with a feedforward static (FFS) identifier.Peer Reviewe