Understanding what information neural networks capture is an essential problem in deep learning, and studying whether different models capture similar features is an initial step to achieve this goal. Previous works sought to define metrics over the
feature matrices to measure the difference between two models. However, different metrics sometimes lead to contradictory conclusions, and there has been no consensus on which metric is suitable to use in practice. In this work, we propose a novel metric that goes beyond previous approaches. Recall that one of the most practical scenarios of using the learned representations is to apply them to downstream tasks. We argue that we should design the metric based on a similar principle. For that, we introduce the transferred discrepancy (TD), a new metric that defines the difference between two representations based on their downstream-task performance. Through an asymptotic analysis, we show how TD correlates with downstream tasks and the necessity to define metrics in such a task-dependent fashion. In particular, we also show that under specific conditions, the TD metric is closely related to previous metrics. Our experiments show that TD can provide fine-grained information for varied downstream tasks, and for the models trained from different initializations, the learned features are not the same in terms of downstream-task predictions. We find that TD may also be used to evaluate the effectiveness of different training strategies. For example, we demonstrate that the models trained with proper data augmentations that improve the generalization capture more similar features in terms of TD, while those with data augmentations that hurt the generalization will not. This suggests a training strategy that leads to more robust representation also trains models that generalize better.
Randomized smoothing has achieved state-of-the-art certified robustness against $l_2$-norm adversarial attacks. However, it is not wholly resolved on how to find the optimal base classifier for randomized smoothing. In this work, we employ a Smoothed
WEighted ENsembling (SWEEN) scheme to improve the performance of randomized smoothed classifiers. We show the ensembling generality that SWEEN can help achieve optimal certified robustness. Furthermore, theoretical analysis proves that the optimal SWEEN model can be obtained from training under mild assumptions. We also develop an adaptive prediction algorithm to reduce the prediction and certification cost of SWEEN models. Extensive experiments show that SWEEN models outperform the upper envelope of their corresponding candidate models by a large margin. Moreover, SWEEN models constructed using a few small models can achieve comparable performance to a single large model with a notable reduction in training time.
The factors that affect the thermal conductivity of semiconductors is a topic of great scientific interest, especially in relation to thermoelectrics. Key developments have been the concept of the phonon-glass-electron-crystal (PGEC) and the related
idea of rattling to achieve this. We use first principles phonon and thermal conductivity calculations in order to explore the concept of rattling for stoichiometric ordered half-Heusler compounds. These compounds can be regarded as filled zinc blende materials, and the filling atom could be viewed as a rattler if it is weakly bound. We use two simple metrics, one related to the frequency and the other to bond frustration and anharmonicity. We find that both measures correlate with thermal conductivity. This suggests that both may be useful in screening materials for low thermal conductivity.
Percolation, describing critical behaviors of phase transition in a geometrical context, prompts wide investigations in natural and social networks as a fundamental model. The introduction of quantum-intrinsic interference and tunneling brings percol
ation into quantum regime with more fascinating phenomena and unique features, which, however, hasnt been experimentally explored yet. Here we present an experimental demonstration of quantum transport in hexagonal percolation lattices by successfully mapping such large-scale porous structures into a photonic chip using femtosecond laser direct writing techniques. A quantum percolation threshold of 80% is observed in the prototyped laser-written lattices with up to 1,600 waveguides, which is significantly larger than the classical counterpart of 63%. We also investigate the spatial confinement by localization parameters and exhibit the transition from ballistic to diffusive propagation with the decrease of the occupation probability. Direct observation of quantum percolation may deepen the understanding of the relation among materials, quantum transport, geometric quenching, disorder and localization, and inspire applications for quantum technologies.
We calculate the lattice thermal conductivities of the pyrite-type ZnSe2 at pressures of 0 and 10 GPa using the linearized phonon Boltzmann transport equation. We obtain a very low value [0.69 W/(mK) at room temperature at 0 GPa], comparable to the b
est thermoelectric materials. The vibrational spectrum is characterized by the isolated high-frequency optical phonon modes due to the stretching of Se-Se dimers and low-frequency optical phonon modes due to the rotation of Zn atoms around these dimers. The low-frequency optical phonon modes are characterized by a strong anharmonicity and will substantially increase the three-phonon scattering space which suppress the thermal conductivity. Interestingly, two transverse acoustic phonon modes with similar frequencies and wave vectors have very different degrees of anharmonicity depending on their polarization. We relate this to the low thermal conductivity and show that the anharmonicities of the transverse acoustic phonon modes are connected to the corresponding change in the pyrite parameter, which can be interpreted as a descriptor for the local volume change. To determine the thermoelectric performance of ZnSe2, we also investigate its electrical transport properties. The results show that both p-type or n-type ZnSe2 can show promising electrical transport properties. We trace this back to the complex energy isosurfaces of both valence and conduction bands. The low thermal conductivities and promising electrical transport properties lead to a large thermoelectric figure of merit of ZnSe2 for both p-type and n-type doping.
The high-throughput (HT) computational method is a useful tool to screen high performance functional materials. In this work, using the deformation potential method under the single band model, we evaluate the carrier relaxation time and establish an
electrical descriptor (c{hi}) characterized by the carrier effective masses based on the simple rigid band approximation. The descriptor (c{hi}) can be used to reasonably represent the maximum power factor without solving the electron Boltzmann transport equation. Additionally, the Gruneisen parameter ({gamma}), a descriptor of the lattice anharmonicity and lattice thermal conductivity, is efficiently evaluated using the elastic properties, omitting the costly phonon calculations. Applying two descriptors (c{hi} and {gamma}) to binary chalcogenides, we HT compute 243 semiconductors and screen 50 promising thermoelectric materials. For these theoretically determined compounds, we successfully predict some previously experimentally and theoretically investigated promising thermoelectric materials. Additionally, 9 p-type and 14 n-type previously unreported binary chalcogenides are also predicted as promising thermoelectric materials. Our work provides not only new thermoelectric candidates with perfect crystalline structure for the future investigations, but also reliable descriptors to HT screen high performance thermoelectric materials.
Hitting the exit node from the entrance node faster on a graph is one of the properties that quantum walk algorithms can take advantage of to outperform classical random walk algorithms. Especially, continuous-time quantum walks on central-random glu
ed binary trees have been investigated in theories extensively for their exponentially faster hitting speed over classical random walks. Here, using heralded single photons to represent quantum walkers and waveguide arrays written by femtosecond laser to simulate the theoretical graph, we are able to demonstrate the hitting efficiency of quantum walks with tree depth as high as 16 layers for the first time. Furthermore, we expand the graphs branching rate from 2 to 5, revealing that quantum walks exhibit more superiority over classical random walks as branching rate increases. Our results may shed light on the physical implementation of quantum walk algorithms as well as quantum computation and quantum simulation.
Energy transport is of central importance in understanding a wide variety of transitions of physical states in nature. Recently, the coherence and noise have been identified for their existence and key roles in energy transport processes, for instanc
e, in a photosynthesis complex, DNA, and odor sensing etc, of which one may have to reveal the inner mechanics in the quantum regime. Here we present an analog of Newtons cradle by manipulating a boundary-controlled chain on a photonic chip. Long-range interactions can be mediated by a long chain composed of 21 strongly coupled sites, where single-photon excitations are transferred between two remote sites via simultaneous control of inter-site weak and strong couplings. We observe a high retrieval efficiency in both uniform and defect-doped chain structures. Our results may offer a flexible approach to Hamiltonian engineering beyond geometric limitation, enabling the design and construction of quantum simulators on demand.
In this paper, we show that the GVC (generalized vanishing conjecture) holds for the differential operator $Lambda=(partial_x-Phi(partial_y))partial_y$ and all polynomials $P(x,y)$, where $Phi(t)$ is any polynomial over the base field. The GVC arose from the study of the Jacobian conjecture.
