A significant abundance of primordial black hole (PBH) dark matter can be produced by curvature perturbations with power spectrum $Delta_zeta^2(k_{mathrm{peak}})sim mathcal{O}(10^{-2})$ at small scales, associated with the generation of observable sc
alar induced gravitational waves (SIGWs). However, the primordial non-Gaussianity may play a non-negligible role, which is not usually considered. We propose two inflation models that predict double peaks of order $mathcal{O}(10^{-2})$ in the power spectrum and study the effects of primordial non-Gaussianity on PBHs and SIGWs. This model is driven by a power-law potential, and has a noncanonical kinetic term whose coupling function admits two peaks. By field-redefinition, it can be recast into a canonical inflation model with two quasi-inflection points in the potential. We find that the PBH abundance will be altered saliently if non-Gaussianity parameter satisfies $|f_{mathrm{NL}}(k_{text{peak}},k_{text{peak}},k_{text{peak}})|gtrsim Delta^2_{zeta}(k_{mathrm{peak}})/(23delta^3_c) sim mathcal{O}(10^{-2})$. Whether the PBH abundance is suppressed or enhanced depends on the $f_{mathrm{NL}}$ being positive or negative, respectively. In our model, non-Gaussianity parameter $f_{mathrm{NL}}(k_{mathrm{peak}},k_{mathrm{peak}},k_{mathrm{peak}})sim mathcal{O}(1)$ takes positive sign, thus PBH abundance is suppressed dramatically. On the contrary, SIGWs are insensitive to primordial non-Gaussianity and hardly affected, so they are still within the sensitivities of space-based GWs observatories and Square Kilometer Array.
The newly proposed island formula for entanglement entropy of Hawking radiation is applied to spherically symmetric 4-dimensional eternal Kaluza-Klein (KK) black holes (BHs). The charge $Q$ of a KK BH quantifies its deviation from a Schwarzschild BH.
The impact of $Q$ on the island is studied at both early and late times. The early size of the island, emph{if exists}, is of order Planck length $ell_{mathrm{P}}$, and will be shortened by $Q$ by a factor $1/sqrt2$ at most. The late-time island, whose boundary is on the outside but within a Planckian distance of the horizon, is slightly extended. While the no-island entropy grows linearly, the late-time entanglement entropy is given by island configuration with twice the Bekenstein-Hawking entropy. Thus we reproduce the Page curve for the eternal KK BHs. Compared with Schwarzschild results, the Page time and the scrambling time are marginally delayed. Moreover, the higher-dimensional generalization is presented. Skeptically, in both early and late times, there are Planck length scales involved, in which a semi-classical description of quantum fields breaks down.
In this paper, our aim is to highlight Tactile Perceptual Aliasing as a problem when using deep neural networks and other discriminative models. Perceptual aliasing will arise wherever a physical variable extracted from tactile data is subject to amb
iguity between stimuli that are physically distinct. Here we address this problem using a probabilistic discriminative model implemented as a 5-component mixture density network comprised of a deep neural network that predicts the parameters of a Gaussian mixture model. We show that discriminative regression models such as deep neural networks and Gaussian process regression perform poorly on aliased data, only making accurate predictions when the sources of aliasing are removed. In contrast, the mixture density network identifies aliased data with improved prediction accuracy. The uncertain predictions of the model form patterns that are consistent with the various sources of perceptual ambiguity. In our view, perceptual aliasing will become an unavoidable issue for robot touch as the field progresses to training robots that act in uncertain and unstructured environments, such as with deep reinforcement learning.
Meta learning with multiple objectives can be formulated as a Multi-Objective Bi-Level optimization Problem (MOBLP) where the upper-level subproblem is to solve several possible conflicting targets for the meta learner. However, existing studies eith
er apply an inefficient evolutionary algorithm or linearly combine multiple objectives as a single-objective problem with the need to tune combination weights. In this paper, we propose a unified gradient-based Multi-Objective Meta Learning (MOML) framework and devise the first gradient-based optimization algorithm to solve the MOBLP by alternatively solving the lower-level and upper-level subproblems via the gradient descent method and the gradient-based multi-objective optimization method, respectively. Theoretically, we prove the convergence properties of the proposed gradient-based optimization algorithm. Empirically, we show the effectiveness of the proposed MOML framework in several meta learning problems, including few-shot learning, neural architecture search, domain adaptation, and multi-task learning.
Enormous information about interactions is contained in the non-Gaussianities of the primordial curvature perturbations, which are essential to break the degeneracy of inflationary models. We study the primordial bispectra for G-inflation models pred
icting both sharp and broad peaks in the primordial scalar power spectrum. We calculate the non-Gaussianity parameter $f_{mathrm{NL}}$ in the equilateral limit and squeezed limit numerically, and confirm that the consistency relation holds in these models. Even though $f_{mathrm{NL}}$ becomes large at the scales before the power spectrum reaches the peak and the scales where there are wiggles in the power spectrum, it remains to be small at the peak scales. Therefore, the contributions of non-Gaussianity to the scalar induced secondary gravitational waves and primordial black hole abundance are expected to be negligible.
Deep neural networks have achieved impressive performance in various areas, but they are shown to be vulnerable to adversarial attacks. Previous works on adversarial attacks mainly focused on the single-task setting. However, in real applications, it
is often desirable to attack several models for different tasks simultaneously. To this end, we propose Multi-Task adversarial Attack (MTA), a unified framework that can craft adversarial examples for multiple tasks efficiently by leveraging shared knowledge among tasks, which helps enable large-scale applications of adversarial attacks on real-world systems. More specifically, MTA uses a generator for adversarial perturbations which consists of a shared encoder for all tasks and multiple task-specific decoders. Thanks to the shared encoder, MTA reduces the storage cost and speeds up the inference when attacking multiple tasks simultaneously. Moreover, the proposed framework can be used to generate per-instance and universal perturbations for targeted and non-targeted attacks. Experimental results on the Office-31 and NYUv2 datasets demonstrate that MTA can improve the quality of attacks when compared with its single-task counterpart.
Recent advances in adversarial attacks show the vulnerability of deep neural networks searched by Neural Architecture Search (NAS). Although NAS methods can find network architectures with the state-of-the-art performance, the adversarial robustness
and resource constraint are often ignored in NAS. To solve this problem, we propose an Effective, Efficient, and Robust Neural Architecture Search (E2RNAS) method to search a neural network architecture by taking the performance, robustness, and resource constraint into consideration. The objective function of the proposed E2RNAS method is formulated as a bi-level multi-objective optimization problem with the upper-level problem as a multi-objective optimization problem, which is different from existing NAS methods. To solve the proposed objective function, we integrate the multiple-gradient descent algorithm, a widely studied gradient-based multi-objective optimization algorithm, with the bi-level optimization. Experiments on benchmark datasets show that the proposed E2RNAS method can find adversarially robust architectures with optimized model size and comparable classification accuracy.
In the framework of spatially covariant gravity, it is natural to extend a gravitational theory by putting the lapse function $N$ and the spatial metric $h_{ij}$ on an equal footing. We find two sufficient and necessary conditions for ensuring two ph
ysical degrees of freedom (DoF) for the theory with the lapse function being dynamical by Hamiltonian analysis. A class of quadratic actions with only two DoF is constructed. In the case that the coupling functions depend on $N$ only, we find that the spatial curvature term cannot enter the Lagrangian and thus this theory possesses no wave solution and cannot recover general relativity (GR). In the case that the coupling functions depend on the spatial derivatives of $N$, we perform a spatially conformal transformation on a class of quadratic actions with nondynamical lapse function to obtain a class of quadratic actions with $dot{N}$. We confirm this theory has two DoF by checking the two sufficient and necessary conditions. Besides, we find that a class of quadratic actions with two DoF can be transformed from GR by disformal transformation.
The possibility that in the mass range around $10^{-12} M_odot$ most of dark matter constitutes of primordial black holes (PBHs) is a very interesting topic. To produce PBHs with this mass, the primordial scalar power spectrum needs to be enhanced to
the order of 0.01 at the scale $ksim 10^{12} text{Mpc}^{-1}$. The enhanced power spectrum also produces large secondary gravitational waves at the mHz band. A phenomenological delta function power spectrum is usually used to discuss the production of PBHs and secondary gravitational waves. Based on G and k inflations, we propose a new mechanism to enhance the power spectrum at small scales by introducing a non-canonical kinetic term $[1-2G(phi)]X$ with the function $G(phi)$ having a peak. Away from the peak, $G(phi)$ is negligible and we recover the usual slow-roll inflation which is constrained by the cosmic microwave background anisotrpy observations. Around the peak, the slow-roll inflation transiently turns to ultra slow-roll inflation. The enhancement of the power spectrum can be obtained with generic potentials, and there is no need to fine tune the parameters in $G(phi)$. The energy spectrum $Omega_{GW}(f)$ of secondary gravitational waves have the characteristic power law behaviour $Omega_{GW}(f)sim f^{n}$ and is testable by pulsar timing array and space based gravitational wave detectors.
We derive a lower bound on the field excursion for the tachyon inflation, which is determined by the amplitude of the scalar perturbation and the number of $e$-folds before the end of inflation. Using the relation between the observables like $n_s$ a
nd $r$ with the slow-roll parameters, we reconstruct three classes of tachyon potentials. The model parameters are determined from the observations before the potentials are reconstructed, and the observations prefer the concave potential. We also discuss the constraints from the reheating phase preceding the radiation domination for the three classes of models by assuming the equation of state parameter $w_{re}$ during reheating is a constant. Depending on the model parameters and the value of $w_{re}$, the constraints on $N_{re}$ and $T_{re}$ are different. As $n_s$ increases, the allowed reheating epoch becomes longer for $w_{re}=-1/3$, 0 and $1/6$ while the allowed reheating epoch becomes shorter for $w_{re}=2/3$.
