arXiv subjects
Publications and source records attributed to Xinyu Wu.
In this note we present a simplified analysis of the quantum and classical complexity of the $k$-XOR Forrelation problem (introduced in the paper of Girish, Raz and Zhan) by a stochastic interpretation of the Forrelation distribution.
We consider a very wide class of models for sparse random Boolean 2CSPs; equivalently, degree-2 optimization problems over~$\{\pm 1\}^n$. For each model $\mathcal{M}$, we identify the "high-probability value"~$s^*_{\mathcal{M}}$ of the natural SDP relaxation (equivalently, the quantum value). That is, for all $\varepsilon > 0$ we show that the SDP optimum of a random $n$-variable instance is (when normalized by~$n$) in the range $(s^*_{\mathcal{M}}-\varepsilon, s^*_{\mathcal{M}}+\varepsilon)$ with high probability. Our class of models includes non-regular CSPs, and ones where the SDP relaxation value is strictly smaller than the spectral relaxation value.
Large-scale distributed training is increasingly becoming communication bound. Many gradient compression algorithms have been proposed to reduce the communication overhead and improve scalability. However, it has been observed that in some cases gradient compression may even harm the performance of distributed training. In this paper, we propose MergeComp, a compression scheduler to optimize the scalability of communication-efficient distributed training. It automatically schedules the compression operations to optimize the performance of compression algorithms without the knowledge of model architectures or system parameters. We have applied MergeComp to nine popular compression algorithms. Our evaluations show that MergeComp can improve the performance of compression algorithms by up to 3.83x without losing accuracy. It can even achieve a scaling factor of distributed training up to 99% over high-speed networks.
In this paper, based on Dynamical Systems (DS), we present an obstacle avoidance method that take into account workspace constraint for serial manipulators. Two modulation matrices that consider the effect of an obstacle and the workspace of a manipulator are determined when the obstacle does not intersect the workspace boundary and when the obstacle intersects the workspace boundary respectively. Using the modulation matrices, an original DS is deformed. The proposed approach can ensure that the trajectory of the manipulator computed according to the deformed DS neither penetrate the obstacle nor go out of the workspace. We validate the effectiveness of the approach in the simulations and experiments on the left arm of the UBTECH humanoid robot.
Mainly because of the heavy computational costs, the real-time whole-body obstacle avoidance for the redundant manipulators has not been well implemented. This paper presents an approach that can ensure that the whole-body of a redundant manipulator can avoid moving obstacles in real-time during the execution of a task. The manipulator is divided into end-effector and non-end-effector portion. Based on dynamical systems (DS), the real-time end-effector obstacle avoidance is obtained. Besides, the end-effector can reach the given target. By using null-space velocity control, the real-time non-endeffector obstacle avoidance is achieved. Finally, a controller is designed to ensure the whole-body obstacle avoidance. We validate the effectiveness of the method in the simulations and experiments on the 7-DOF arm of the UBTECH humanoid robot.
One of the fundamental challenges to scale self-driving is being able to create accurate high definition maps (HD maps) with low cost. Current attempts to automate this process typically focus on simple scenarios, estimate independent maps per frame or do not have the level of precision required by modern self driving vehicles. In contrast, in this paper we focus on drawing the lane boundaries of complex highways with many lanes that contain topology changes due to forks and merges. Towards this goal, we formulate the problem as inference in a directed acyclic graphical model (DAG), where the nodes of the graph encode geometric and topological properties of the local regions of the lane boundaries. Since we do not know a priori the topology of the lanes, we also infer the DAG topology (i.e., nodes and edges) for each region. We demonstrate the effectiveness of our approach on two major North American Highways in two different states and show high precision and recall as well as 89% correct topology.
Let $p(Y_1, \dots, Y_d, Z_1, \dots, Z_e)$ be a self-adjoint noncommutative polynomial, with coefficients from $\mathbb{C}^{r \times r}$, in the indeterminates $Y_1, \dots, Y_d$ (considered to be self-adjoint), the indeterminates $Z_1, \dots, Z_e$, and their adjoints $Z_1^*, \dots, Z_e^*$. Suppose $Y_1, \dots, Y_d$ are replaced by independent random $n \times n$ matching matrices, and $Z_1, \dots, Z_e$ are replaced by independent random $n \times n$ permutation matrices. Assuming for simplicity that $p$'s coefficients are $0$-$1$ matrices, the result can be thought of as a kind of random $rn$-vertex graph $G$. As $n \to \infty$, there will be a natural limiting infinite graph $X$ that covers any finite outcome for $G$. A recent landmark result of Bordenave and Collins shows that for any $\varepsilon > 0$, with high probability the spectrum of a random $G$ will be $\varepsilon$-close in Hausdorff distance to the spectrum of $X$ (once the suitably defined "trivial" eigenvalues are excluded). We say that $G$ is "$\varepsilon$-near fully $X$-Ramanujan". Our work has two contributions: First we study and clarify the class of infinite graphs $X$ that can arise in this way. Second, we derandomize the Bordenave-Collins result: for any $X$, we provide explicit, arbitrarily large graphs $G$ that are covered by $X$ and that have (nontrivial) spectrum at Hausdorff distance at most $\varepsilon$ from that of $X$. This significantly generalizes the recent work of Mohanty et al., which provided explicit near-Ramanujan graphs for every degree $d$ (meaning $d$-regular graphs with all nontrivial eigenvalues bounded in magnitude by $2\sqrt{d-1} + \varepsilon$). As an application of our main technical theorem, we are also able to determine the "eigenvalue relaxation value" for a wide class of average-case degree-$2$ constraint satisfaction problems.
The phase transitions from one plateau to the next plateau or to an insulator in quantum Hall and quantum anomalous Hall (QAH) systems have revealed universal scaling behaviors. A magnetic-field-driven quantum phase transition from a QAH insulator to an axion insulator was recently demonstrated in magnetic topological insulator sandwich samples. Here, we show that the temperature dependence of the derivative of the longitudinal resistance on magnetic field at the transition point follows a characteristic power-law that indicates a universal scaling behavior for the QAH to axion insulator phase transition. Similar to the quantum Hall plateau to plateau transition, the QAH to axion insulator transition can also be understood by the Chalker-Coddington network model. We extract a critical exponent k~ 0.38 in agreement with recent high-precision numerical results on the correlation length exponent of the Chalker-Coddington model at v ~ 2.6, rather than the generally-accepted value of 2.33.
In this paper we propose a novel end-to-end learnable network that performs joint perception, prediction and motion planning for self-driving vehicles and produces interpretable intermediate representations. Unlike existing neural motion planners, our motion planning costs are consistent with our perception and prediction estimates. This is achieved by a novel differentiable semantic occupancy representation that is explicitly used as cost by the motion planning process. Our network is learned end-to-end from human demonstrations. The experiments in a large-scale manual-driving dataset and closed-loop simulation show that the proposed model significantly outperforms state-of-the-art planners in imitating the human behaviors while producing much safer trajectories.
After presentations of Raz and Tal's oracle separation of BQP and PH result, several people (e.g. Ryan O'Donnell, James Lee, Avishay Tal) suggested that the proof may be simplified by stochastic calculus. In this short note, we describe such a simplification.
This paper concerns the dynamics of a layer of incompressible viscous fluid lying above a vertically oscillating rigid plane and with an upper boundary given by a free surface. We consider the problem with gravity and surface tension for horizontally periodic flows. This problem gives rise to flat but vertically oscillating equilibrium solutions, and the main thrust of this paper is to study the asymptotic stability of these equilibria in certain parameter regimes. We prove that both with and without surface tension there exists a parameter regime in which sufficiently small perturbations of the equilibrium at time $t = 0$ give rise to global-in-time solutions that decay to equilibrium at an identified quantitative rate.
Let $κ\in \mathbb{N}_+^\ell$ satisfy $κ_1 + \dots + κ_\ell = n$ and let $\mathcal{U}_κ$ denote the "multislice" of all strings $u$ in $[\ell]^n$ having exactly $κ_i$ coordinates equal to $i$, for all $i \in [\ell]$. Consider the Markov chain on $\mathcal{U}_κ$, where a step is a random transposition of two coordinates of $u$. We show that the log-Sobolev constant $ρ_κ$ for the chain satisfies $$(ρ_κ)^{-1} \leq n \sum_{i=1}^{\ell} \tfrac{1}{2} \log_2(4n/κ_i),$$ which is sharp up to constants whenever $\ell$ is constant. From this, we derive some consequences for small-set expansion and isoperimetry in the multislice, including a KKL Theorem, a Kruskal--Katona Theorem for the multislice, a Friedgut Junta Theorem, and a Nisan--Szegedy Theorem.
Emerging non-volatile memory (NVM), or memristive, devices promise energy-efficient realization of deep learning, when efficiently integrated with mixed-signal integrated circuits on a CMOS substrate. Even though several algorithmic challenges need to be addressed to turn the vision of memristive Neuromorphic Systems-on-a-Chip (NeuSoCs) into reality, issues at the device and circuit interface need immediate attention from the community. In this work, we perform energy-estimation of a NeuSoC system and predict the desirable circuit and device parameters for energy-efficiency optimization. Also, CMOS synapse circuits based on the concept of CMOS memristor emulator are presented as a system prototyping methodology, while practical memristor devices are being developed and integrated with general-purpose CMOS. The proposed mixed-signal memristive synapse can be designed and fabricated using standard CMOS technologies and open doors to interesting applications in cognitive computing circuits.
Brain-inspired learning mechanisms, e.g. spike timing dependent plasticity (STDP), enable agile and fast on-the-fly adaptation capability in a spiking neural network. When incorporating emerging nanoscale resistive non-volatile memory (NVM) devices, with ultra-low power consumption and high-density integration capability, a spiking neural network hardware would result in several orders of magnitude reduction in energy consumption at a very small form factor and potentially herald autonomous learning machines. However, actual memory devices have shown to be intrinsically binary with stochastic switching, and thus impede the realization of ideal STDP with continuous analog values. In this work, a dendritic-inspired processing architecture is proposed in addition to novel CMOS neuron circuits. The utilization of spike attenuations and delays transforms the traditionally undesired stochastic behavior of binary NVMs into a useful leverage that enables biologically-plausible STDP learning. As a result, this work paves a pathway to adopt practical binary emerging NVM devices in brain-inspired neuromorphic computing.
The advent of social networks poses severe threats on user privacy as adversaries can de-anonymize users' identities by mapping them to correlated cross-domain networks. Without ground-truth mapping, prior literature proposes various cost functions in hope of measuring the quality of mappings. However, there is generally a lacking of rationale behind the cost functions, whose minimizer also remains algorithmically unknown. We jointly tackle above concerns under a more practical social network model parameterized by overlapping communities, which, neglected by prior art, can serve as side information for de-anonymization. Regarding the unavailability of ground-truth mapping to adversaries, by virtue of the Minimum Mean Square Error (MMSE), our first contribution is a well-justified cost function minimizing the expected number of mismatched users over all possible true mappings. While proving the NP-hardness of minimizing MMSE, we validly transform it into the weighted-edge matching problem (WEMP), which, as disclosed theoretically, resolves the tension between optimality and complexity: (i) WEMP asymptotically returns a negligible mapping error in large network size under mild conditions facilitated by higher overlapping strength; (ii) WEMP can be algorithmically characterized via the convex-concave based de-anonymization algorithm (CBDA), perfectly finding the optimum of WEMP. Extensive experiments further confirm the effectiveness of CBDA under overlapping communities, in terms of averagely 90% re-identified users in the rare true cross-domain co-author networks when communities overlap densely, and roughly 70% enhanced re-identification ratio compared to non-overlapping cases.
Large-scale integration of emerging nanoscale non-volatile memory devices, e.g. resistive random-access memory (RRAM), can enable a new generation of neuromorphic computers that can solve a wide range of machine learning problems. Such hybrid CMOS-RRAM neuromorphic architectures will result in several orders of magnitude reduction in energy consumption at a very small form factor, and herald autonomous learning machines capable of self-adapting to their environment. However, the progress in this area has been impeded from the realization that the actual memory devices fall well short of their expected behavior. In this work, we discuss the challenges associated with these memory devices and their use in neuromorphic computing circuits, and propose pathways to overcome these limitations by introducing 'dendritic learning'.
Nanoscale resistive memories are expected to fuel dense integration of electronic synapses for large-scale neuromorphic system. To realize such a brain-inspired computing chip, a compact CMOS spiking neuron that performs in-situ learning and computing while driving a large number of resistive synapses is desired. This work presents a novel leaky integrate-and-fire neuron design which implements the dual-mode operation of current integration and synaptic drive, with a single opamp and enables in-situ learning with crossbar resistive synapses. The proposed design was implemented in a 0.18 $μ$m CMOS technology. Measurements show neuron's ability to drive a thousand resistive synapses, and demonstrate an in-situ associative learning. The neuron circuit occupies a small area of 0.01 mm$^2$ and has an energy-efficiency of 9.3 pJ$/$spike$/$synapse.
Neuromorphic systems that densely integrate CMOS spiking neurons and nano-scale memristor synapses open a new avenue of brain-inspired computing. Existing silicon neurons have molded neural biophysical dynamics but are incompatible with memristor synapses, or used extra training circuitry thus eliminating much of the density advantages gained by using memristors, or were energy inefficient. Here we describe a novel CMOS spiking leaky integrate-and-fire neuron circuit. Building on a reconfigurable architecture with a single opamp, the described neuron accommodates a large number of memristor synapses, and enables online spike timing dependent plasticity (STDP) learning with optimized power consumption. Simulation results of an 180nm CMOS design showed 97% power efficiency metric when realizing STDP learning in 10,000 memristor synapses with a nominal 1MΩ memristance, and only 13μA current consumption when integrating input spikes. Therefore, the described CMOS neuron contributes a generalized building block for large-scale brain-inspired neuromorphic systems.