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Chi Zhang

Publications and source records attributed to Chi Zhang.

At least 631 records · Page 35Linked to original sources

Symbology for elliptic multiple polylogarithms and the symbol prime

Elliptic multiple polylogarithms occur in Feynman integrals and in particular in scattering amplitudes. They can be characterized by their symbol, a tensor product in the so-called symbol letters. In contrast to the non-elliptic case, the elliptic letters themselves satisfy highly non-trivial identities, which we discuss in this paper. Moreover, we introduce the symbol prime, an analog of the symbol for elliptic symbol letters, which makes these identities manifest. We demonstrate its use in two concrete examples at two-loop order: the unequal-mass sunrise integral in two dimensions and the ten-point double-box integral in four dimensions. Finally, we also report the result of the polylogarithmic nine-point double-box integral, which arises as the soft limit of the ten-point integral.

hep-th↗

Reachability Analysis of Neural Network Control Systems

Neural network controllers (NNCs) have shown great promise in autonomous and cyber-physical systems. Despite the various verification approaches for neural networks, the safety analysis of NNCs remains an open problem. Existing verification approaches for neural network control systems (NNCSs) either can only work on a limited type of activation functions, or result in non-trivial over-approximation errors with time evolving. This paper proposes a verification framework for NNCS based on Lipschitzian optimisation, called DeepNNC. We first prove the Lipschitz continuity of closed-loop NNCSs by unrolling and eliminating the loops. We then reveal the working principles of applying Lipschitzian optimisation on NNCS verification and illustrate it by verifying an adaptive cruise control model. Compared to state-of-the-art verification approaches, DeepNNC shows superior performance in terms of efficiency and accuracy over a wide range of NNCs. We also provide a case study to demonstrate the capability of DeepNNC to handle a real-world, practical, and complex system. Our tool \textbf{DeepNNC} is available at \url{https://github.com/TrustAI/DeepNNC}.

cs.LG↗

Characterizing the Fundamental Bending Vibration of a Linear Polyatomic Molecule for Symmetry Violation Searches

Polyatomic molecules have been identified as sensitive probes of charge-parity violating and parity-violating physics beyond the Standard Model (BSM). For example, many linear triatomic molecules are both laser-coolable and have parity doublets in the ground electronic $\tilde{X} {}^2Σ^+ (010)$ state arising from the bending vibration, both features that can greatly aid BSM searches. Understanding the $\tilde{X} {}^2Σ^+ (010)$ state is a crucial prerequisite to precision measurements with linear polyatomic molecules. Here, we characterize fundamental bending vibration of ${}^{174}$YbOH using high-resolution optical spectroscopy on the nominally forbidden $\tilde{X} {}^2Σ^+ (010) \rightarrow \tilde{A} {}^2Π_{1/2} (000)$ transition at 588 nm. We assign 39 transitions originating from the lowest rotational levels of the $\tilde{X} {}^2Σ^+ (010)$ state, and accurately model the state's structure with an effective Hamiltonian using best-fit parameters. Additionally, we perform Stark and Zeeman spectroscopy on the $\tilde{X} {}^2Σ^+ (010)$ state and fit the molecule-frame dipole moment to $D_\mathrm{mol}=2.16(1)$ D and the effective electron $g$-factor to $g_S=2.07(2)$. Further, we use an empirical model to explain observed anomalous line intensities in terms of interference from spin-orbit and vibronic perturbations in the excited $\tilde{A} {}^2Π_{1/2} (000)$ state. Our work is an essential step toward searches for BSM physics in YbOH and other linear polyatomic molecules.

physics.atom-ph↗

Probing temperature-responsivity of microgels and its interplay with a solid surface by superresolution microscopy and numerical simulations

Superresolution microscopy has become a powerful tool to investigate the internal structure of complex colloidal and polymeric systems, such as microgels, at the nanometer scale. The ability to monitor microgels response to temperature changes in situ opens new and exciting opportunities to design and precisely control their behaviour for various applications. When performing advanced microscopy experiments, interactions between the particle and the environment can be important. Often microgels are deposited on a substrate since they have to remain still for several minutes during the experiment. This study uses dSTORM microscopy and advanced coarse-grained molecular dynamics simulations to investigate, for the first time, how individual microgels anchored on hydrophilic and hydrophobic surfaces undergo their volume phase transition in temperature. We find that, in the presence of a hydrophilic substrate, the structure of the microgel is unperturbed and the resulting density profiles quantitatively agree with simulations performed in bulk conditions. Instead, when a hydrophobic surface is used, the microgel spreads at the interface and an interesting competition between the two hydrophobic strengths -- monomer-monomer vs monomer-surface -- comes into play at high temperatures. The remarkable agreement between experiments and simulations makes the present study a fundamental step to establish this high-resolution monitoring technique as a platform for investigating more complex systems, being these either macromolecules with peculiar internal structure or nanocomplexes where molecules of interest can be encapsulated in the microgel network and controllably released with temperature.

cond-mat.soft↗

Bootstrapping elliptic Feynman integrals using Schubert analysis

The symbol bootstrap has proven to be a powerful tool for calculating polylogarithmic Feynman integrals and scattering amplitudes. In this letter, we initiate the symbol bootstrap for elliptic Feynman integrals. Concretely, we bootstrap the symbol of the twelve-point two-loop double-box integral in four dimensions, which depends on nine dual-conformal cross ratios. We obtain the symbol alphabet, which contains 100 logarithms as well as 9 simple elliptic integrals, via a Schubert-type analysis, which we equally generalize to the elliptic case. In particular, we find a compact, one-line formula for the (2,2)-coproduct of the result.

hep-th↗

Efficient Few-Shot Object Detection via Knowledge Inheritance

Few-shot object detection (FSOD), which aims at learning a generic detector that can adapt to unseen tasks with scarce training samples, has witnessed consistent improvement recently. However, most existing methods ignore the efficiency issues, e.g., high computational complexity and slow adaptation speed. Notably, efficiency has become an increasingly important evaluation metric for few-shot techniques due to an emerging trend toward embedded AI. To this end, we present an efficient pretrain-transfer framework (PTF) baseline with no computational increment, which achieves comparable results with previous state-of-the-art (SOTA) methods. Upon this baseline, we devise an initializer named knowledge inheritance (KI) to reliably initialize the novel weights for the box classifier, which effectively facilitates the knowledge transfer process and boosts the adaptation speed. Within the KI initializer, we propose an adaptive length re-scaling (ALR) strategy to alleviate the vector length inconsistency between the predicted novel weights and the pretrained base weights. Finally, our approach not only achieves the SOTA results across three public benchmarks, i.e., PASCAL VOC, COCO and LVIS, but also exhibits high efficiency with 1.8-100x faster adaptation speed against the other methods on COCO/LVIS benchmark during few-shot transfer. To our best knowledge, this is the first work to consider the efficiency problem in FSOD. We hope to motivate a trend toward powerful yet efficient few-shot technique development. The codes are publicly available at https://github.com/Ze-Yang/Efficient-FSOD.

cs.CV↗

BEAR: Physics-Principled Building Environment for Control and Reinforcement Learning

Recent advancements in reinforcement learning algorithms have opened doors for researchers to operate and optimize building energy management systems autonomously. However, the lack of an easily configurable building dynamical model and energy management task simulation and evaluation platform has arguably slowed the progress in developing advanced and dedicated reinforcement learning (RL) and control algorithms for building operation tasks. Here we propose "BEAR", a physics-principled Building Environment for Control And Reinforcement Learning. The platform allows researchers to benchmark both model-based and model-free controllers using a broad collection of standard building models in Python without co-simulation using external building simulators. In this paper, we discuss the design of this platform and compare it with other existing building simulation frameworks. We demonstrate the compatibility and performance of BEAR with different controllers, including both model predictive control (MPC) and several state-of-the-art RL methods with two case studies.

eess.SY↗

AXI-Pack: Near-Memory Bus Packing for Bandwidth-Efficient Irregular Workloads

Data-intensive applications involving irregular memory streams are inefficiently handled by modern processors and memory systems highly optimized for regular, contiguous data. Recent work tackles these inefficiencies in hardware through core-side stream extensions or memory-side prefetchers and accelerators, but fails to provide end-to-end solutions which also achieve high efficiency in on-chip interconnects. We propose AXI-Pack, an extension to ARM's AXI4 protocol introducing bandwidth-efficient strided and indirect bursts to enable end-to-end irregular streams. AXI-Pack adds irregular stream semantics to memory requests and avoids inefficient narrow-bus transfers by packing multiple narrow data elements onto a wide bus. It retains full compatibility with AXI4 and does not require modifications to non-burst-reshaping interconnect IPs. To demonstrate our approach end-to-end, we extend an open-source RISC-V vector processor to leverage AXI-Pack at its memory interface for strided and indexed accesses. On the memory side, we design a banked memory controller efficiently handling AXI-Pack requests. On a system with a 256-bit-wide interconnect running FP32 workloads, AXI-Pack achieves near-ideal peak on-chip bus utilizations of 87% and 39%, speedups of 5.4x and 2.4x, and energy efficiency improvements of 5.3x and 2.1x over a baseline using an AXI4 bus on strided and indirect benchmarks, respectively.

cs.AR↗

A Markov Process Theory for Network Growth Processes of DAG-based Blockchain Systems

Note that the serial structure of blockchain has many essential pitfalls, thus a data network structure and its DAG-based blockchain are introduced to resolve the blockchain pitfalls. From such a network perspective, analysis of the DAG-based blockchain systems becomes interesting and challenging. So, the simulation models are adopted widely. In this paper, we first describe a simple Markov model for the DAG-based blockchain with IOTA Tangle by means of two layers of tips and internal tips' impatient connection behavior. Then we set up a continuous-time Markov process to analyze the DAG-based blockchain system and show that this Markov process is a level-dependent quasi-birth-and-death (QBD) process. Based on this, we prove that the QBD process must be irreducible and positive recurrent. Furthermore, once the stationary probability vector of the QBD process is given, we provide performance analysis of the DAG-based blockchain system. Next, we propose a new effective method for computing the average confirmation time of any arriving internal tip at this system by means of the first passage times and the PH distributions. Finally, we use numerical examples to check the validity of our theoretical results and indicate how some key system parameters influence the performance measures of this system. Therefore, we hope that the methodology and results developed in this paper can be applicable to deal with more general DAG-based blockchain systems such that a series of promising research can be developed potentially.

cs.PF↗

On the Perils of Cascading Robust Classifiers

Ensembling certifiably robust neural networks is a promising approach for improving the \emph{certified robust accuracy} of neural models. Black-box ensembles that assume only query-access to the constituent models (and their robustness certifiers) during prediction are particularly attractive due to their modular structure. Cascading ensembles are a popular instance of black-box ensembles that appear to improve certified robust accuracies in practice. However, we show that the robustness certifier used by a cascading ensemble is unsound. That is, when a cascading ensemble is certified as locally robust at an input $x$ (with respect to $ε$), there can be inputs $x'$ in the $ε$-ball centered at $x$, such that the cascade's prediction at $x'$ is different from $x$ and thus the ensemble is not locally robust. Our theoretical findings are accompanied by empirical results that further demonstrate this unsoundness. We present \emph{cascade attack} (CasA), an adversarial attack against cascading ensembles, and show that: (1) there exists an adversarial input for up to 88\% of the samples where the ensemble claims to be certifiably robust and accurate; and (2) the accuracy of a cascading ensemble under our attack is as low as 11\% when it claims to be certifiably robust and accurate on 97\% of the test set. Our work reveals a critical pitfall of cascading certifiably robust models by showing that the seemingly beneficial strategy of cascading can actually hurt the robustness of the resulting ensemble. Our code is available at \url{https://github.com/TristaChi/ensembleKW}.

cs.LG↗

Hierarchical Normalization for Robust Monocular Depth Estimation

In this paper, we address monocular depth estimation with deep neural networks. To enable training of deep monocular estimation models with various sources of datasets, state-of-the-art methods adopt image-level normalization strategies to generate affine-invariant depth representations. However, learning with image-level normalization mainly emphasizes the relations of pixel representations with the global statistic in the images, such as the structure of the scene, while the fine-grained depth difference may be overlooked. In this paper, we propose a novel multi-scale depth normalization method that hierarchically normalizes the depth representations based on spatial information and depth distributions. Compared with previous normalization strategies applied only at the holistic image level, the proposed hierarchical normalization can effectively preserve the fine-grained details and improve accuracy. We present two strategies that define the hierarchical normalization contexts in the depth domain and the spatial domain, respectively. Our extensive experiments show that the proposed normalization strategy remarkably outperforms previous normalization methods, and we set new state-of-the-art on five zero-shot transfer benchmark datasets.

cs.CV↗

An hourglass-free formulation for total Lagrangian smoothed particle hydrodynamics

The total Lagrangian smoothed particle hydrodynamics (TL-SPH) for elastic solid dynamics suffers from hourglass modes which can grow and lead to the failure of simulation for problems with large deformation. To address this long-standing issue, we present an hourglass-free formulation based on volumetric-devioatric stress decomposition. Inspired by the fact that the artifact of nonphysical zigzag particle distribution induced by the hourglass modes is mainly characterized by shear deformation and the standard SPH discretization for the viscous term in the Navier-Stokes (NS) equation, the present formulation computes the action of shear stress directly through the Laplacian of displacement other than from the divergence of shear stress. A comprehensive set of challenging benchmark cases are simulated to demonstrate that, while improving accuracy and computational efficiency, the present formulation is able to eliminate the hourglass modes and achieves very good numerical stability with a single general effective parameter. In addition, the deformation of a practically relevant stent structure is simulated to demonstrate the potential of the present method in the field of biomechanics.

physics.flu-dyn↗

Dual Clustering Co-teaching with Consistent Sample Mining for Unsupervised Person Re-Identification

In unsupervised person Re-ID, peer-teaching strategy leveraging two networks to facilitate training has been proven to be an effective method to deal with the pseudo label noise. However, training two networks with a set of noisy pseudo labels reduces the complementarity of the two networks and results in label noise accumulation. To handle this issue, this paper proposes a novel Dual Clustering Co-teaching (DCCT) approach. DCCT mainly exploits the features extracted by two networks to generate two sets of pseudo labels separately by clustering with different parameters. Each network is trained with the pseudo labels generated by its peer network, which can increase the complementarity of the two networks to reduce the impact of noises. Furthermore, we propose dual clustering with dynamic parameters (DCDP) to make the network adaptive and robust to dynamically changing clustering parameters. Moreover, Consistent Sample Mining (CSM) is proposed to find the samples with unchanged pseudo labels during training for potential noisy sample removal. Extensive experiments demonstrate the effectiveness of the proposed method, which outperforms the state-of-the-art unsupervised person Re-ID methods by a considerable margin and surpasses most methods utilizing camera information.

cs.CV↗

Harrison center and products of sums of powers

This paper is mainly concerned with identities like \[ (x_1^d + x_2^d + \cdots + x_r^d) (y_1^d + y_2^d + \cdots y_n^d) = z_1^d + z_2^d + \cdots + z_n^d \] where $d>2,$ $x=(x_1, x_2, \dots, x_r)$ and $y=(y_1, y_2, \dots, y_n)$ are systems of indeterminates and each $z_k$ is a linear form in $y$ with coefficients in the rational function field $\k (x)$ over any field $\k$ of characteristic $0$ or greater than $d.$ These identities are higher degree analogue of the well-known composition formulas of sums of squares of Hurwitz, Radon and Pfister. We show that such composition identities of sums of powers of degree at least $3$ are trivial, i.e., if $d>2,$ then $r=1.$ Our proof is simple and elementary, in which the crux is Harrison's center theory of homogeneous polynomials.

math.RA↗

On the Learning Mechanisms in Physical Reasoning

Is dynamics prediction indispensable for physical reasoning? If so, what kind of roles do the dynamics prediction modules play during the physical reasoning process? Most studies focus on designing dynamics prediction networks and treating physical reasoning as a downstream task without investigating the questions above, taking for granted that the designed dynamics prediction would undoubtedly help the reasoning process. In this work, we take a closer look at this assumption, exploring this fundamental hypothesis by comparing two learning mechanisms: Learning from Dynamics (LfD) and Learning from Intuition (LfI). In the first experiment, we directly examine and compare these two mechanisms. Results show a surprising finding: Simple LfI is better than or on par with state-of-the-art LfD. This observation leads to the second experiment with Ground-truth Dynamics, the ideal case of LfD wherein dynamics are obtained directly from a simulator. Results show that dynamics, if directly given instead of approximated, would achieve much higher performance than LfI alone on physical reasoning; this essentially serves as the performance upper bound. Yet practically, LfD mechanism can only predict Approximate Dynamics using dynamics learning modules that mimic the physical laws, making the following downstream physical reasoning modules degenerate into the LfI paradigm; see the third experiment. We note that this issue is hard to mitigate, as dynamics prediction errors inevitably accumulate in the long horizon. Finally, in the fourth experiment, we note that LfI, the extremely simpler strategy when done right, is more effective in learning to solve physical reasoning problems. Taken together, the results on the challenging benchmark of PHYRE show that LfI is, if not better, as good as LfD for dynamics prediction. However, the potential improvement from LfD, though challenging, remains lucrative.

cs.LG↗

A nice two-loop next-to-next-to-MHV amplitude in ${\cal N}=4$ super-Yang-Mills

We study a scalar component of the 8-point next-to-next-to-maximally-helicity-violating (N${}^2$MHV) amplitude at two-loop level in ${\cal N}=4$ super-Yang-Mills theory; it has a leading singularity proportional to the inverse of the four-mass-box square root and receives contributions from only two types of non-trivial integrals with one-loop infrared (IR) divergences. We compute such two-loop 8-point integrals by taking (double-)collinear limits of certain finite, dual-conformal-invariant integrals, and they nicely give the IR-safe ratio function after subtracting divergences. As the first genuine two-loop N${}^2$MHV amplitude computed explicitly, we find remarkable structures in its symbol and alphabet: similar to the next-to-MHV (NMHV) case, there are still 9 algebraic letters associated with the square root, and the latter also becomes a letter for the first time; unlike the NMHV case, such algebraic letters appear at either one or all of the second, third and last entry, and the part with three odd letters is particularly simple.

hep-th↗

Infrared: A Meta Bug Detector

The recent breakthroughs in deep learning methods have sparked a wave of interest in learning-based bug detectors. Compared to the traditional static analysis tools, these bug detectors are directly learned from data, thus, easier to create. On the other hand, they are difficult to train, requiring a large amount of data which is not readily available. In this paper, we propose a new approach, called meta bug detection, which offers three crucial advantages over existing learning-based bug detectors: bug-type generic (i.e., capable of catching the types of bugs that are totally unobserved during training), self-explainable (i.e., capable of explaining its own prediction without any external interpretability methods) and sample efficient (i.e., requiring substantially less training data than standard bug detectors). Our extensive evaluation shows our meta bug detector (MBD) is effective in catching a variety of bugs including null pointer dereference, array index out-of-bound, file handle leak, and even data races in concurrent programs; in the process MBD also significantly outperforms several noteworthy baselines including Facebook Infer, a prominent static analysis tool, and FICS, the latest anomaly detection method.

cs.SE↗

MRF-PINN: A Multi-Receptive-Field convolutional physics-informed neural network for solving partial differential equations

Compared with conventional numerical approaches to solving partial differential equations (PDEs), physics-informed neural networks (PINN) have manifested the capability to save development effort and computational cost, especially in scenarios of reconstructing the physics field and solving the inverse problem. Considering the advantages of parameter sharing, spatial feature extraction and low inference cost, convolutional neural networks (CNN) are increasingly used in PINN. However, some challenges still remain as follows. To adapt convolutional PINN to solve different PDEs, considerable effort is usually needed for tuning critical hyperparameters. Furthermore, the effects of the finite difference accuracy, and the mesh resolution on the predictivity of convolutional PINN are not settled. To fill the gaps above, we propose three initiatives in this paper: (1) A Multi-Receptive-Field PINN (MRF-PINN) model is established to solve different types of PDEs on various mesh resolutions without manual tuning; (2) The dimensional balance method is used to estimate the loss weights when solving Navier-Stokes equations; (3) The Taylor polynomial is used to pad the virtual nodes near the boundaries for implementing high-order finite difference. The proposed MRF-PINN is tested for solving three typical linear PDEs (elliptic, parabolic, hyperbolic) and a series of nonlinear PDEs (Navier-Stokes PDEs) to demonstrate its generality and superiority. This paper shows that MRF-PINN can adapt to completely different equation types and mesh resolutions without any hyperparameter tuning. The dimensional balance method saves computational time and improves the convergence for solving Navier-Stokes PDEs. Further, the solving error is significantly decreased under high-order finite difference, large channel number, and high mesh resolution, which is expected to be a general convolutional PINN scheme.

cs.LG↗