Toward Practical Quantum Embedding Simulation of Realistic Chemical Systems on Near-term Quantum Computers

Quantum computing has recently exhibited great potentials in predicting chemical properties for various applications in drug discovery, material design, and catalyst optimization. Progress has been made in simulating small molecules, such as LiH and hydrogen chains of up to 12 qubits, by using quantum algorithms such as variational quantum eigensolver (VQE). Yet, originating from limitations of the size and the fidelity of near-term quantum hardware, how to accurately simulate large realistic molecules remains a challenge. Here, integrating an adaptive energy sorting strategy and a classical computational method, the density matrix embedding theory, which effectively finds a shallower quantum circuit and reduces the problem size, respectively, we show a means to circumvent the limitations and demonstrate the potential toward solving real chemical problems. We numerically test the method for the hydrogenation reaction of C6H8 and the equilibrium geometry of the C18 molecule, with basis sets up to cc-pVDZ (at most 144 qubits). The simulation results show accuracies comparable to those of advanced quantum chemistry methods such as coupled-cluster or even full configuration interaction, while the number of qubits required is reduced by an order of magnitude (from 144 qubits to 16 qubits for the C18 molecule) compared to conventional VQE. Our work implies the possibility of solving industrial chemical problems on near-term quantum devices.

Harnessing Perceptual Adversarial Patches for Crowd Counting

Crowd counting, which is significantly important for estimating the number of people in safety-critical scenes, has been shown to be vulnerable to adversarial examples in the physical world (e.g., adversarial patches). Though harmful, adversarial examples are also valuable for assessing and better understanding model robustness. However, existing adversarial example generation methods in crowd counting scenarios lack strong transferability among different black-box models. Motivated by the fact that transferability is positively correlated to the model-invariant characteristics, this paper proposes the Perceptual Adversarial Patch (PAP) generation framework to learn the shared perceptual features between models by exploiting both the model scale perception and position perception. Specifically, PAP exploits differentiable interpolation and density attention to help learn the invariance between models during training, leading to better transferability. In addition, we surprisingly found that our adversarial patches could also be utilized to benefit the performance of vanilla models for alleviating several challenges including cross datasets and complex backgrounds. Extensive experiments under both digital and physical world scenarios demonstrate the effectiveness of our PAP.

Efficient Differentiable Simulation of Articulated Bodies

We present a method for efficient differentiable simulation of articulated bodies. This enables integration of articulated body dynamics into deep learning frameworks, and gradient-based optimization of neural networks that operate on articulated bodies. We derive the gradients of the forward dynamics using spatial algebra and the adjoint method. Our approach is an order of magnitude faster than autodiff tools. By only saving the initial states throughout the simulation process, our method reduces memory requirements by two orders of magnitude. We demonstrate the utility of efficient differentiable dynamics for articulated bodies in a variety of applications. We show that reinforcement learning with articulated systems can be accelerated using gradients provided by our method. In applications to control and inverse problems, gradient-based optimization enabled by our work accelerates convergence by more than an order of magnitude.

Language Models are Few-shot Multilingual Learners

General-purpose language models have demonstrated impressive capabilities, performing on par with state-of-the-art approaches on a range of downstream natural language processing (NLP) tasks and benchmarks when inferring instructions from very few examples. Here, we evaluate the multilingual skills of the GPT and T5 models in conducting multi-class classification on non-English languages without any parameter updates. We show that, given a few English examples as context, pre-trained language models can predict not only English test samples but also non-English ones. Finally, we find the in-context few-shot cross-lingual prediction results of language models are significantly better than random prediction, and they are competitive compared to the existing state-of-the-art cross-lingual models.

Unit Selection with Causal Diagram

The unit selection problem aims to identify a set of individuals who are most likely to exhibit a desired mode of behavior, for example, selecting individuals who would respond one way if encouraged and a different way if not encouraged. Using a combination of experimental and observational data, Li and Pearl derived tight bounds on the benefit function - the payoff/cost associated with selecting an individual with given characteristics. This paper shows that these bounds can be narrowed significantly (enough to change decisions) when structural information is available in the form of a causal model. We address the problem of estimating the benefit function using observational and experimental data when specific graphical criteria are assumed to hold.

Fast Magnetic Reconnection induced by Resistivity Gradients in 2D Magnetohydrodynamics

Using 2-dimensional (2D) magnetohydrodynamics (MHD) simulations, we show that Petschek-type magnetic reconnection can be induced using a simple resistivity gradient in the reconnection outflow direction, revealing the key ingredient of steady fast reconnection in the collisional limit. We find that the diffusion region self-adjusts its half-length to fit the given gradient scale of resistivity. The induced reconnection x-line and flow stagnation point always reside within the resistivity transition region closer to the higher resistivity end. The opening of one exhaust by this resistivity gradient will lead to the opening of the other exhaust located on the other side of the x-line, within the region of uniform resistivity. Potential applications of this setup to reconnection-based thrusters and solar spicules are discussed. In a separate set of numerical experiments, we explore the maximum plausible reconnection rate using a large and spatially localized resistivity right at the x-line. Interestingly, the resulting current density at the x-line drops significantly so that the normalized reconnection rate remains bounded by the value $simeq 0.2$, consistent with the theoretical prediction.

Cross-Register Projection for Headline Part of Speech Tagging

Part of speech (POS) tagging is a familiar NLP task. State of the art taggers routinely achieve token-level accuracies of over 97% on news body text, evidence that the problem is well understood. However, the register of English news headlines, headlinese, is very different from the register of long-form text, causing POS tagging models to underperform on headlines. In this work, we automatically annotate news headlines with POS tags by projecting predicted tags from corresponding sentences in news bodies. We train a multi-domain POS tagger on both long-form and headline text and show that joint training on both registers improves over training on just one or naively concatenating training sets. We evaluate on a newly-annotated corpus of over 5,248 English news headlines from the Google sentence compression corpus, and show that our model yields a 23% relative error reduction per token and 19% per headline. In addition, we demonstrate that better headline POS tags can improve the performance of a syntax-based open information extraction system. We make POSH, the POS-tagged Headline corpus, available to encourage research in improved NLP models for news headlines.

Adversarial Mixing Policy for Relaxing Locally Linear Constraints in Mixup

Mixup is a recent regularizer for current deep classification networks. Through training a neural network on convex combinations of pairs of examples and their labels, it imposes locally linear constraints on the models input space. However, such strict linear constraints often lead to under-fitting which degrades the effects of regularization. Noticeably, this issue is getting more serious when the resource is extremely limited. To address these issues, we propose the Adversarial Mixing Policy (AMP), organized in a min-max-rand formulation, to relax the Locally Linear Constraints in Mixup. Specifically, AMP adds a small adversarial perturbation to the mixing coefficients rather than the examples. Thus, slight non-linearity is injected in-between the synthetic examples and synthetic labels. By training on these data, the deep networks are further regularized, and thus achieve a lower predictive error rate. Experiments on five text classification benchmarks and five backbone models have empirically shown that our methods reduce the error rate over Mixup variants in a significant margin (up to 31.3%), especially in low-resource conditions (up to 17.5%).

Influence of the growth gradient on surface wrinkling and pattern transition in growing tubular tissues

Growth-induced pattern formations in curved film-substrate structures have attracted extensive attentions recently. In most existing literature, the growth tensor is assumed to be homogeneous or piecewise homogeneous. In this paper, we aim at clarifying the influence of a growth gradient on pattern formation and pattern evolution in bilayered tubular tissues under plane-strain deformation. In the framework of finite elasticity, a bifurcation condition is derived for a general material model and a generic growth function. Then we suppose that both layers are composed of neo-Hookean materials. In particular, the growth function is assumed to decay linearly from the inner surface or from the outer surface. It is found that a gradient in the growth has a weak effect on the critical state, compared to the homogeneous growth type where both layers share the same growth factor. Furthermore, a finite element model is built to validate the theoretical model and to investigate the post-buckling behaviors. It is found that the associated pattern transition is not controlled by the growth gradient but by the ratio of the shear modulus between two layers. Different morphologies can occur when the modulus ratio is varied. The current analysis could provide useful insight into the influence of a growth gradient on surface instabilities and suggests that a homogeneous growth field may provide a good approximation on interpreting complicated morphological formations in multiple systems.

Soliton resolution for the Wadati-Konno-Ichikawa equation with weighted Sobolev initial data

In this work, we employ the $bar{partial}$-steepest descent method to investigate the Cauchy problem of the Wadati-Konno-Ichikawa (WKI) equation with initial conditions in weighted Sobolev space $mathcal{H}(mathbb{R})$. The long time asymptotic behavior of the solution $q(x,t)$ is derived in a fixed space-time cone $S(y_{1},y_{2},v_{1},v_{2})={(y,t)inmathbb{R}^{2}: y=y_{0}+vt, ~y_{0}in[y_{1},y_{2}], ~vin[v_{1},v_{2}]}$. Based on the resulting asymptotic behavior, we prove the soliton resolution conjecture of the WKI equation which includes the soliton term confirmed by $N(mathcal{I})$-soliton on discrete spectrum and the $t^{-frac{1}{2}}$ order term on continuous spectrum with residual error up to $O(t^{-frac{3}{4}})$.