57 research outputs found
Generalization and Estimation Error Bounds for Model-based Neural Networks
Model-based neural networks provide unparalleled performance for various
tasks, such as sparse coding and compressed sensing problems. Due to the strong
connection with the sensing model, these networks are interpretable and inherit
prior structure of the problem. In practice, model-based neural networks
exhibit higher generalization capability compared to ReLU neural networks.
However, this phenomenon was not addressed theoretically. Here, we leverage
complexity measures including the global and local Rademacher complexities, in
order to provide upper bounds on the generalization and estimation errors of
model-based networks. We show that the generalization abilities of model-based
networks for sparse recovery outperform those of regular ReLU networks, and
derive practical design rules that allow to construct model-based networks with
guaranteed high generalization. We demonstrate through a series of experiments
that our theoretical insights shed light on a few behaviours experienced in
practice, including the fact that ISTA and ADMM networks exhibit higher
generalization abilities (especially for small number of training samples),
compared to ReLU networks
Identification of Non-Linear RF Systems Using Backpropagation
In this work, we use deep unfolding to view cascaded non-linear RF systems as
model-based neural networks. This view enables the direct use of a wide range
of neural network tools and optimizers to efficiently identify such cascaded
models. We demonstrate the effectiveness of this approach through the example
of digital self-interference cancellation in full-duplex communications where
an IQ imbalance model and a non-linear PA model are cascaded in series. For a
self-interference cancellation performance of approximately 44.5 dB, the number
of model parameters can be reduced by 74% and the number of operations per
sample can be reduced by 79% compared to an expanded linear-in-parameters
polynomial model.Comment: To be presented at the 2020 IEEE International Conference on
Communications (Workshop on Full-Duplex Communications for Future Wireless
Networks
Introducing Nonuniform Sparse Proximal Averaging Network for Seismic Reflectivity Inversion
We consider the problem of seismic reflectivity inversion, which pertains to the high-resolution recovery of interface locations and reflection coefficients from seismic measurements, which are vital for estimating the subsurface structure. We develop two model-based neural networks within the framework of deep-unfolding . First, we propose a nonuniform minimax concave penalty regularized formulation for reflectivity inversion and unfold the resulting iterative algorithm into a network. Second, we propose a nonuniform sparse model that relies on a combination of regularizers (composite regularization) and develop the nonuniform sparse proximal averaging network (NuSPAN). We demonstrate the efficacy of the proposed approaches over the benchmark techniques through numerical experiments on synthetic 1-D seismic traces and 2-D wedge models. We also report validations on the 2-D Marmousi2 simulated model and 3-D real field measurements from the Penobscot 3D survey off the coast of Nova Scotia, Canada. The accuracy of the proposed approaches is higher than the state-of-the-art techniques in terms of amplitude and support recovery. Further, for Marmousi2, the proposed deep-unfolding networks result in 600× faster inference than the fast iterative shrinkage-thresholding algorithm (FISTA). In terms of combined training and inference times, the learned iterative shrinkage-thresholding algorithm (LISTA) is the fastest. The inference speed-up is significant given that the volume of data is typically large in seismic signal processing
Non-Linear Self-Interference Cancellation via Tensor Completion
Non-linear self-interference (SI) cancellation constitutes a fundamental
problem in full-duplex communications, which is typically tackled using either
polynomial models or neural networks. In this work, we explore the
applicability of a recently proposed method based on low-rank tensor
completion, called canonical system identification (CSID), to non-linear SI
cancellation. Our results show that CSID is very effective in modeling and
cancelling the non-linear SI signal and can have lower computational complexity
than existing methods, albeit at the cost of increased memory requirements.Comment: To be presented at the 2020 Asilomar Conference for Signals, Systems,
and Computer
Comparing Semi-Parametric Model Learning Algorithms for Dynamic Model Estimation in Robotics
Physical modeling of robotic system behavior is the foundation for
controlling many robotic mechanisms to a satisfactory degree. Mechanisms are
also typically designed in a way that good model accuracy can be achieved with
relatively simple models and model identification strategies. If the modeling
accuracy using physically based models is not enough or too complex, model-free
methods based on machine learning techniques can help. Of particular interest
to us was therefore the question to what degree semi-parametric modeling
techniques, meaning combinations of physical models with machine learning,
increase the modeling accuracy of inverse dynamics models which are typically
used in robot control. To this end, we evaluated semi-parametric Gaussian
process regression and a novel model-based neural network architecture, and
compared their modeling accuracy to a series of naive semi-parametric,
parametric-only and non-parametric-only regression methods. The comparison has
been carried out on three test scenarios, one involving a real test-bed and two
involving simulated scenarios, with the most complex scenario targeting the
modeling a simulated robot's inverse dynamics model. We found that in all but
one case, semi-parametric Gaussian process regression yields the most accurate
models, also with little tuning required for the training procedure
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