This paper proposes the use of spectral element methods citep{canuto_spectral_1988} for fast and accurate training of Neural Ordinary Differential Equations (ODE-Nets; citealp{Chen2018NeuralOD}) for system identification. This is achieved by expressi
ng their dynamics as a truncated series of Legendre polynomials. The series coefficients, as well as the network weights, are computed by minimizing the weighted sum of the loss function and the violation of the ODE-Net dynamics. The problem is solved by coordinate descent that alternately minimizes, with respect to the coefficients and the weights, two unconstrained sub-problems using standard backpropagation and gradient methods. The resulting optimization scheme is fully time-parallel and results in a low memory footprint. Experimental comparison to standard methods, such as backpropagation through explicit solvers and the adjoint technique citep{Chen2018NeuralOD}, on training surrogate models of small and medium-scale dynamical systems shows that it is at least one order of magnitude faster at reaching a comparable value of the loss function. The corresponding testing MSE is one order of magnitude smaller as well, suggesting generalization capabilities increase.
This paper introduces Non-Autonomous Input-Output Stable Network(NAIS-Net), a very deep architecture where each stacked processing block is derived from a time-invariant non-autonomous dynamical system. Non-autonomy is implemented by skip connections
from the block input to each of the unrolled processing stages and allows stability to be enforced so that blocks can be unrolled adaptively to a pattern-dependent processing depth. NAIS-Net induces non-trivial, Lipschitz input-output maps, even for an infinite unroll length. We prove that the network is globally asymptotically stable so that for every initial condition there is exactly one input-dependent equilibrium assuming $tanh$ units, and incrementally stable for ReL units. An efficient implementation that enforces the stability under derived conditions for both fully-connected and convolutional layers is also presented. Experimental results show how NAIS-Net exhibits stability in practice, yielding a significant reduction in generalization gap compared to ResNets.
We present a fast algorithm for training MaxPooling Convolutional Networks to segment images. This type of network yields record-breaking performance in a variety of tasks, but is normally trained on a computationally expensive patch-by-patch basis.
Our new method processes each training image in a single pass, which is vastly more efficient. We validate the approach in different scenarios and report a 1500-fold speed-up. In an application to automated steel defect detection and segmentation, we obtain excellent performance with short training times.
We introduce an efficient computational framework for hashing data belonging to multiple modalities into a single representation space where they become mutually comparable. The proposed approach is based on a novel coupled siamese neural network arc
hitecture and allows unified treatment of intra- and inter-modality similarity learning. Unlike existing cross-modality similarity learning approaches, our hashing functions are not limited to binarized linear projections and can assume arbitrarily complex forms. We show experimentally that our method significantly outperforms state-of-the-art hashing approaches on multimedia retrieval tasks.
