We investigate the tensor network representations of fermionic crystalline symmetry-protected topological (SPT) phases on two-dimensional lattices. As a mapping from virtual indices to physical indices, projected entangled-pair state (PEPS) serves as
a concrete way to construct the wavefunctions of 2D crystalline fermionic SPT (fSPT) phases protected by 17 wallpaper group symmetries, for both spinless and spin-1/2 fermions. Based on PEPS, the full classification of 2D crystalline fSPT phases with wallpaper groups can be obtained. Tensor network states provide a natural framework for studying 2D crystalline fSPT phases.
Online tracking of multiple objects in videos requires strong capacity of modeling and matching object appearances. Previous methods for learning appearance embedding mostly rely on instance-level matching without considering the temporal continuity
provided by videos. We design a new instance-to-track matching objective to learn appearance embedding that compares a candidate detection to the embedding of the tracks persisted in the tracker. It enables us to learn not only from videos labeled with complete tracks, but also unlabeled or partially labeled videos. We implement this learning objective in a unified form following the spirit of constrastive loss. Experiments on multiple object tracking datasets demonstrate that our method can effectively learning discriminative appearance embeddings in a semi-supervised fashion and outperform state of the art methods on representative benchmarks.
In label-noise learning, estimating the transition matrix is a hot topic as the matrix plays an important role in building statistically consistent classifiers. Traditionally, the transition from clean distribution to noisy distribution (i.e., clean
label transition matrix) has been widely exploited to learn a clean label classifier by employing the noisy data. Motivated by that classifiers mostly output Bayes optimal labels for prediction, in this paper, we study to directly model the transition from Bayes optimal distribution to noisy distribution (i.e., Bayes label transition matrix) and learn a Bayes optimal label classifier. Note that given only noisy data, it is ill-posed to estimate either the clean label transition matrix or the Bayes label transition matrix. But favorably, Bayes optimal labels are less uncertain compared with the clean labels, i.e., the class posteriors of Bayes optimal labels are one-hot vectors while those of clean labels are not. This enables two advantages to estimate the Bayes label transition matrix, i.e., (a) we could theoretically recover a set of Bayes optimal labels under mild conditions; (b) the feasible solution space is much smaller. By exploiting the advantages, we estimate the Bayes label transition matrix by employing a deep neural network in a parameterized way, leading to better generalization and superior classification performance.
We tackle the problem of visual search under resource constraints. Existing systems use the same embedding model to compute representations (embeddings) for the query and gallery images. Such systems inherently face a hard accuracy-efficiency trade-o
ff: the embedding model needs to be large enough to ensure high accuracy, yet small enough to enable query-embedding computation on resource-constrained platforms. This trade-off could be mitigated if gallery embeddings are generated from a large model and query embeddings are extracted using a compact model. The key to building such a system is to ensure representation compatibility between the query and gallery models. In this paper, we address two forms of compatibility: One enforced by modifying the parameters of each model that computes the embeddings. The other by modifying the architectures that compute the embeddings, leading to compatibility-aware neural architecture search (CMP-NAS). We test CMP-NAS on challenging retrieval tasks for fashion images (DeepFashion2), and face images (IJB-C). Compared to ordinary (homogeneous) visual search using the largest embedding model (paragon), CMP-NAS achieves 80-fold and 23-fold cost reduction while maintaining accuracy within 0.3% and 1.6% of the paragon on DeepFashion2 and IJB-C respectively.
Dynamical systems with a distributed yet interconnected structure, like multi-rigid-body robots or large-scale multi-agent systems, introduce valuable sparsity into the system dynamics that can be exploited in an optimal control setting for speeding
up computation and improving numerical conditioning. Conventional approaches for solving the Optimal Control Problem (OCP) rarely capitalize on such structural sparsity, and hence suffer from a cubic computational complexity growth as the dimensionality of the system scales. In this paper, we present an OCP formulation that relies on graphical models to capture the sparsely-interconnected nature of the system dynamics. Such a representational choice allows the use of contemporary graphical inference algorithms that enable our solver to achieve a linear time complexity in the state and control dimensions as well as the time horizon. We demonstrate the numerical and computational advantages of our approach on a canonical dynamical system in simulation.
The Ericksen model for nematic liquid crystals couples a director field with a scalar degree of orientation variable, and allows the formation of various defects with finite energy. We propose a simple but novel finite element approximation of the pr
oblem that can be implemented easily within standard finite element packages. Our scheme is projection-free and thus circumvents the use of weakly acute meshes, which are quite restrictive in 3D but are required by recent algorithms for convergence. We prove stability and $Gamma$-convergence properties of the new method in the presence of defects. We also design an effective nested gradient flow algorithm for computing minimizers that controls the violation of the unit-length constraint of the director. We present several simulations in 2D and 3D that document the performance of the proposed scheme and its ability to capture quite intriguing defects.
We consider the combinatorial bandits problem, where at each time step, the online learner selects a size-$k$ subset $s$ from the arms set $mathcal{A}$, where $left|mathcal{A}right| = n$, and observes a stochastic reward of each arm in the selected s
et $s$. The goal of the online learner is to minimize the regret, induced by not selecting $s^*$ which maximizes the expected total reward. Specifically, we focus on a challenging setting where 1) the reward distribution of an arm depends on the set $s$ it is part of, and crucially 2) there is textit{no total order} for the arms in $mathcal{A}$. In this paper, we formally present a reward model that captures set-dependent reward distribution and assumes no total order for arms. Correspondingly, we propose an Upper Confidence Bound (UCB) algorithm that maintains UCB for each individual arm and selects the arms with top-$k$ UCB. We develop a novel regret analysis and show an $Oleft(frac{k^2 n log T}{epsilon}right)$ gap-dependent regret bound as well as an $Oleft(k^2sqrt{n T log T}right)$ gap-independent regret bound. We also provide a lower bound for the proposed reward model, which shows our proposed algorithm is near-optimal for any constant $k$. Empirical results on various reward models demonstrate the broad applicability of our algorithm.
We propose to accelerate existing linear bandit algorithms to achieve per-step time complexity sublinear in the number of arms $K$. The key to sublinear complexity is the realization that the arm selection in many linear bandit algorithms reduces to
the maximum inner product search (MIPS) problem. Correspondingly, we propose an algorithm that approximately solves the MIPS problem for a sequence of adaptive queries yielding near-linear preprocessing time complexity and sublinear query time complexity. Using the proposed MIPS solver as a sub-routine, we present two bandit algorithms (one based on UCB, and the other based on TS) that achieve sublinear time complexity. We explicitly characterize the tradeoff between the per-step time complexity and regret, and show that our proposed algorithms can achieve $O(K^{1-alpha(T)})$ per-step complexity for some $alpha(T) > 0$ and $widetilde O(sqrt{T})$ regret, where $T$ is the time horizon. Further, we present the theoretical limit of the tradeoff, which provides a lower bound for the per-step time complexity. We also discuss other choices of approximate MIPS algorithms and other applications to linear bandit problems.
The construction and classification of crystalline symmetry protected topological (SPT) phases in interacting bosonic and fermionic systems have been intensively studied in the past few years. Crystalline SPT phases are not only of conceptual importa
nce, but also provide great opportunities towards experimental realization since space group symmetries naturally exist for any realistic material. In this paper, we systematically classify the crystalline topological superconductors (TSC) and topological insulators (TI) in 2D interacting fermionic systems by using an explicit real-space construction. In particular, we discover an intriguing fermionic crystalline topological superconductor that can only be realized in interacting fermionic systems (i.e., not in free-fermion or bosonic SPT systems). Moreover, we also verify the recently conjectured crystalline equivalence principle for generic 2D interacting fermionic systems.
Measuring the vector boson scattering (VBS) precisely is an important step towards understanding the electroweak symmetry breaking of the standard model (SM) and detecting new physics beyond the SM. We propose a neural network which compress the feat
ures of the VBS into three dimensional latent space. The consistency of the SM prediction and the experimental data is tested by the binned log-likelihood analysis in the latent space. We will show that the network is capable of distinguish different polarization modes of $WWjj$ production in both dileptonic channel and semi-leptonic channel. The method is also applied to constrain the effective field theory and two Higgs Doublet Model. The results demonstrate that the method is sensitive to generic new physics contributing to the VBS.
