Reconstruction of sparse wavelet signals from partial Fourier measurements

In this paper, we show that high-dimensional sparse wavelet signals of finite levels can be constructed from their partial Fourier measurements on a deterministic sampling set with cardinality about a multiple of signal sparsity

Kinematic Basis of Emergent Energetics of Complex Dynamics

Stochastic kinematic description of a complex dynamics is shown to dictate an energetic and thermodynamic structure. An energy function $\varphi(x)$ emerges as the limit of the generalized, nonequilibrium free energy of a Markovian dynamics with vanishing fluctuations. In terms of the $\nabla\varphi$ and its orthogonal field $\gamma(x)\perp\nabla\varphi$, a general vector field $b(x)$ can be decomposed into $-D(x)\nabla\varphi+\gamma$, where $\nabla\cdot\big(\omega(x)\gamma(x)\big)=$ $-\nabla\omega D(x)\nabla\varphi$. The matrix $D(x)$ and scalar $\omega(x)$, two additional characteristics to the $b(x)$ alone, represent the local geometry and density of states intrinsic to the statistical motion in the state space at $x$. $\varphi(x)$ and $\omega(x)$ are interpreted as the emergent energy and degeneracy of the motion, with an energy balance equation $d\varphi(x(t))/dt=\gamma D^{-1}\gamma-bD^{-1}b$, reflecting the geometrical $\|D\nabla\varphi\|^2+\|\gamma\|^2=\|b\|^2$. The partition function employed in statistical mechanics and J. W. Gibbs' method of ensemble change naturally arise; a fluctuation-dissipation theorem is established via the two leading-order asymptotics of entropy production as $\epsilon\to 0$. The present theory provides a mathematical basis for P. W. Anderson's emergent behavior in the hierarchical structure of complexity science.Comment: 7 page

DARTS-ASR: Differentiable Architecture Search for Multilingual Speech Recognition and Adaptation

In previous works, only parameter weights of ASR models are optimized under fixed-topology architecture. However, the design of successful model architecture has always relied on human experience and intuition. Besides, many hyperparameters related to model architecture need to be manually tuned. Therefore in this paper, we propose an ASR approach with efficient gradient-based architecture search, DARTS-ASR. In order to examine the generalizability of DARTS-ASR, we apply our approach not only on many languages to perform monolingual ASR, but also on a multilingual ASR setting. Following previous works, we conducted experiments on a multilingual dataset, IARPA BABEL. The experiment results show that our approach outperformed the baseline fixed-topology architecture by 10.2% and 10.0% relative reduction on character error rates under monolingual and multilingual ASR settings respectively. Furthermore, we perform some analysis on the searched architectures by DARTS-ASR.Comment: Accepted at INTERSPEECH 202