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Multi-stage optimization which invokes a stochastic algorithm restarting with the returned solution of previous stage, has been widely employed in stochastic optimization. Momentum acceleration technique is famously known for building gradient-based algorithms with fast convergence in large-scale optimization. In order to take the advantage of this acceleration in multi-stage stochastic optimization, we develop a multi-stage stochastic gradient descent with momentum acceleration method, named MAGNET, for first-order stochastic convex optimization. The main ingredient is the employment of a negative momentum, which extends the Nesterov’s momentum to the multi-stage optimization. It can be incorporated in a stochastic gradient-based algorithm in multi-stage mechanism and provide acceleration. The proposed algorithm obtains an accelerated rate of convergence, and is adaptive and free from hyper-parameter tuning. The experimental results demonstrate that our algorithm is competitive with some state-of-the-art methods for solving several typical optimization problems in machine learning.

The interaction between terahertz (THz) resonance modes and element deformation in rectangular split-ring resonator (RSRR)-based meta-atoms (MAs) is investigated experimentally. Two types of RSRR-based MAs are presented: lateral-varied SRR (LV-SRR) and arm-twisted SRR (AT-SRR). When the distances from the gaps to the opposite sides of above meta-atoms increase from 10 to 40 μm, the inductive-capacitive (LC) resonance modes and dipole oscillation modes exhibit redshift behavior. The quality factor (Q factor) of LC resonance decreases while that of dipole oscillation modes increases. The THz mode interaction is subject to the distance between the gap and opposite side. An extension of lateral side contributes much more to the enhancement of Q factor of dipole oscillation mode than the twisted arms. The relationship between the near-field coupling effect and THz modes is revealed by the analysis of surface currents as well as the electric energy density distribution, as is in agreement with the experimental results.

We experimentally investigate the terahertz (THz) electromagnetically-induced transparency (EIT)-like phenomenon in a metamolecule (MM) of three-body system. This system involves a couple of geometrically identical split-ring resonators (SRRs) in orthogonal layout conductively coupled by a cut-wire resonator. Such a three-body system exhibits two frequency response properties upon to the polarization of incident THz beam: One is the dark-bright-bright layout to the horizontally polarized THz beam, where there is no EIT-like effect; the other is bright-dark-dark layout to the vertically polarized THz beam, where an EIT-like effect is observable. The transparency window can be tuned from 0.71 THz to 0.74 THz by the displacement of cut-wire inside the trimer MM. A maximum of 7.5 ps group delay of THz wave is found at the transparent window of 0.74 THz. When the cut-wire moved to the mid-point of lateral-side of SRR, the EIT-like phenomenon disappears, this leads to a localized THz slow-light effect. The distribution of surface currents and electric energy reveals that the excited inductive-capacitive (LC) oscillation of bright-SRR dominates the high frequency side-mode, which is isolated to the displacement of cut-wire resonator. However, the low frequency side-mode originates from the constructive hybridization of LC resonance in dark-SRR coupled with a localized S-shaped dipole oscillator, which is tunable by the displacement of cut-wire. As a consequence, the group delay as well as the spectral configuration of transparency window can be manipulated by tuning one side-mode while fixing the other. Such an experimental finding reveal the EIT-like effect in a conductively coupled three-body system and manifests a novel approach to achieve tunable THz slow-light device.

The evolution of terahertz resonance modes in an individual split-ring resonator (SRR) is investigated experimentally by locally structural deformation. The length reduction of opposite-side results in a frequency blueshift of resonance modes. Simultaneously, the Q factor of inductive–capacitive oscillation mode is enhanced while the dipole oscillation is suppressed. The numerical simulation indicates that the lateral-side and arms will take the place of opposite-side contributing to the dipole oscillation in deformed SRR. A further apex-angle increasing leads to a huge coupling loss so that the dipole oscillation is suppressed in right triangle SRR and obtuse triangle SRR.

In blind image deconvolution, priors are often leveraged to constrain the solution space, so as to alleviate the under-determinacy. Priors which are trained separately from the task of deconvolution tend to be unstable. We propose the Golf Optimizer, a novel but simple form of network that learns deep priors from data with better propagation behavior. Like playing golf, our method first estimates an aggressive propagation towards optimum using one network, and recurrently applies a residual CNN to learn the gradient of prior for delicate correction on restoration. Experiments show that our network achieves competitive performance on GoPro dataset, and our model is extremely lightweight compared with the state-of-the-art works.

Stochastic optimization on large-scale machine learning problems has been developed dramatically since stochastic gradient methods with variance reduction technique were introduced. Several stochastic second-order methods, which approximate curvature information by the Hessian in stochastic setting, have been proposed for improvements. In this paper, we introduce a Stochastic Sub-Sampled Newton method with Variance Reduction (S2NMVR), which incorporates the sub-sampled Newton method and stochastic variance-reduced gradient. For many machine learning problems, the linear time Hessian-vector production provides evidence to the computational efficiency of S2NMVR. We then develop two variations of S2NMVR that preserve the estimation of Hessian inverse and decrease the computational cost of Hessian-vector product for nonlinear problems.

We demonstrate a localized slow light phenomenon in a symmetry broken metamolecule (MM) of conductively coupled dark resonators at a terahertz band. Under a dark-mode excitation condition, the single mode resonance becomes dual modes by breaking the uniaxial symmetry of MM. Thus, a transparency window exists in between dual modes. An interaction of V-shaped plasmonic antenna-type (VA) resonances results in a plasmon-induced transparency (PIT) when the asymmetric deviation is below 13 μm. A maximum 25.9 ps group-delay of incident THz pulse is observed at the transparency window. When the asymmetric deviation is beyond 13 μm, one excitation pathway switches from VA resonance to the inductor-capacitor (LC) resonance, which dominates the high-frequency side-mode. Then, the PIT effect transfers to the PIT-like behavior and the slow light phenomenon vanishes. The aforementioned discovery allows for a speed modulation of slow light via symmetry breaking in MM.