arXiv subjects

Tong Yang

Publications and source records attributed to Tong Yang.

At least 163 records · Page 9Linked to original sources

arXiv2023

Sparse Waypoint Validity Checking for Self-Entanglement-Free Tethered Path Planning

A novel mechanism to derive self-entanglement-free (SEF) path for tethered differential-driven robots is proposed in this work. The problem is tailored to the deployment of tethered differential-driven robots in situations where an omni-directional tether re-tractor is not available. This is frequently encountered when it is impractical to concurrently equip an omni-directional tether retracting mechanism with other geometrically intricate devices, such as a manipulator, which is notably relevant in applications like disaster recovery, spatial exploration, etc. Without specific attention to the spatial relation between the shape of the tether and the pose of the mobile unit, the issue of self-entanglement arises when the robot moves, resulting in unsafe robot movements and the risk of damaging the tether. In this paper, the SEF constraint is first formulated as the boundedness of a relative angle function which characterises the angular difference between the tether stretching direction and the robot's heading direction. Then, a constrained searching-based path planning algorithm is proposed which produces a path that is sub-optimal whilst ensuring the avoidance of tether self-entanglement. Finally, the algorithmic efficiency of the proposed path planner is further enhanced by proving the conditioned sparsity of the primitive path validity checking module. The effectiveness of the proposed algorithm is assessed through case studies, comparing its performance against untethered differential-driven planners in challenging planning scenarios. A comparative analysis is further conducted between the normal node expansion module and the improved node expansion module which incorporates sparse waypoint validity checking. Real-world tests are also conducted to validate the algorithm's performance. An open-source implementation has also made available for the benefit of the robotics community.

cs.RO↗

arXiv2023

A new understanding of grazing limit

The grazing limit of the Boltzmann equation to Landau equation is well-known and has been justified by using cutoff near the grazing angle with some suitable scaling. In this paper, we will provide a new understanding by simply applying a natural scaling on the Boltzmann operator without angular cutoff. The proof is based on a new well-posedness theory on the Boltzmann equation without angular cutoff in the regime with optimal ranges of parameters so that the grazing limit can be justified directly for any $γ>-5$ that includes the Coulomb potential corresponding to $γ=-3$. With this new understanding, the scaled Boltzmann operator in fact can be decomposed into two components. The first one converges to the Landau operator when the singular parameter $s$ of interaction angle tends to $1^{-}$ and the second one vanishes in this limit.

math.AP↗

arXiv2023

ChainedFilter: Combining Membership Filters by Chain Rule

Membership (membership query / membership testing) is a fundamental problem across databases, networks and security. However, previous research has primarily focused on either approximate solutions, such as Bloom Filters, or exact methods, like perfect hashing and dictionaries, without attempting to develop a an integral theory. In this paper, we propose a unified and complete theory, namely chain rule, for general membership problems, which encompasses both approximate and exact membership as extreme cases. Building upon the chain rule, we introduce a straightforward yet versatile algorithm framework, namely ChainedFilter, to combine different elementary filters without losing information. Our evaluation results demonstrate that ChainedFilter performs well in many applications: (1) it requires only 26% additional space over the theoretical lower bound for implicit static dictionary, (2) it requires only 0.22 additional bit per item over the theoretical lower bound for lossless data compression, (3) it reduces up to 31% external memory access than raw Cuckoo Hashing, (4) it reduces up to 36% P99 tail point query latency than Bloom Filter under the same space cost in RocksDB database, and (5) it reduces up to 99.1% filter space than original Learned Bloom Filter.

cs.DB↗

arXiv2023

ChameleMon: Shifting Measurement Attention as Network State Changes

Flow-level network measurement is critical to many network applications. Among various measurement tasks, packet loss detection and heavy-hitter detection are two most important measurement tasks, which we call the two key tasks. In practice, the two key tasks are often required at the same time, but existing works seldom handle both tasks. In this paper, we design ChameleMon to support the two key tasks simultaneously. One key design/novelty of ChameleMon is to shift measurement attention as network state changes, through two dimensions of dynamics: 1) dynamically allocating memory between the two key tasks; 2) dynamically monitoring the flows of importance. To realize the key design, we propose a key technique, leveraging Fermat's little theorem to devise a flexible data structure, namely FermatSketch. FermatSketch is dividable, additive, and subtractive, supporting the two key tasks. We have fully implemented a ChameleMon prototype on a testbed with a Fat-tree topology. We conduct extensive experiments and the results show ChameleMon supports the two key tasks with low memory/bandwidth overhead, and more importantly, it can automatically shift measurement attention as network state changes.

cs.NI↗

arXiv2023

Solving Constrained Variational Inequalities via a First-order Interior Point-based Method

We develop an interior-point approach to solve constrained variational inequality (cVI) problems. Inspired by the efficacy of the alternating direction method of multipliers (ADMM) method in the single-objective context, we generalize ADMM to derive a first-order method for cVIs, that we refer to as ADMM-based interior-point method for constrained VIs (ACVI). We provide convergence guarantees for ACVI in two general classes of problems: (i) when the operator is $ξ$-monotone, and (ii) when it is monotone, some constraints are active and the game is not purely rotational. When the operator is, in addition, L-Lipschitz for the latter case, we match known lower bounds on rates for the gap function of $\mathcal{O}(1/\sqrt{K})$ and $\mathcal{O}(1/K)$ for the last and average iterate, respectively. To the best of our knowledge, this is the first presentation of a first-order interior-point method for the general cVI problem that has a global convergence guarantee. Moreover, unlike previous work in this setting, ACVI provides a means to solve cVIs when the constraints are nontrivial. Empirical analyses demonstrate clear advantages of ACVI over common first-order methods. In particular, (i) cyclical behavior is notably reduced as our methods approach the solution from the analytic center, and (ii) unlike projection-based methods that zigzag when near a constraint, ACVI efficiently handles the constraints.

stat.ML↗

arXiv2023

Optimization for Amortized Inverse Problems

Incorporating a deep generative model as the prior distribution in inverse problems has established substantial success in reconstructing images from corrupted observations. Notwithstanding, the existing optimization approaches use gradient descent largely without adapting to the non-convex nature of the problem and can be sensitive to initial values, impeding further performance improvement. In this paper, we propose an efficient amortized optimization scheme for inverse problems with a deep generative prior. Specifically, the optimization task with high degrees of difficulty is decomposed into optimizing a sequence of much easier ones. We provide a theoretical guarantee of the proposed algorithm and empirically validate it on different inverse problems. As a result, our approach outperforms baseline methods qualitatively and quantitatively by a large margin.

cs.LG↗

arXiv2022

An explicit coercivity estimate of the linearized quantum Boltzmann operator without angular cutoff

The quantum Boltzmann-Bose equation describes a large system of Bose-Einstein particles in the weak-coupling regime. If the particle interaction is governed by the inverse power law, the corresponding collision kernel has angular singularity. In this paper, we give a constructive proof of the coercivity estimate for the linearized quantum Boltzmann-Bose operator to capture the effects of the singularity and the fugacity. Precisely, the estimate explicitly reveals the dependence on the fugacity parameter before the Bose-Einstein condensation. With the coercivity estimate, the global in time well-posedness of the inhomogeneous quantum Boltzmann-Bose equation in the perturbative framework and stability of the Bose-Einstein equilibrium can be established.

math.AP↗

arXiv2022

Q-ViT: Fully Differentiable Quantization for Vision Transformer

In this paper, we propose a fully differentiable quantization method for vision transformer (ViT) named as Q-ViT, in which both of the quantization scales and bit-widths are learnable parameters. Specifically, based on our observation that heads in ViT display different quantization robustness, we leverage head-wise bit-width to squeeze the size of Q-ViT while preserving performance. In addition, we propose a novel technique named switchable scale to resolve the convergence problem in the joint training of quantization scales and bit-widths. In this way, Q-ViT pushes the limits of ViT quantization to 3-bit without heavy performance drop. Moreover, we analyze the quantization robustness of every architecture component of ViT and show that the Multi-head Self-Attention (MSA) and the Gaussian Error Linear Units (GELU) are the key aspects for ViT quantization. This study provides some insights for further research about ViT quantization. Extensive experiments on different ViT models, such as DeiT and Swin Transformer show the effectiveness of our quantization method. In particular, our method outperforms the state-of-the-art uniform quantization method by 1.5% on DeiT-Tiny.

cs.CV↗

arXiv2022

Global Well-posedness of a Prandtl Model from MHD in Gevrey Function Spaces

We consider a Prandtl model derived from MHD in the Prandtl-Hartmann regime that has a damping term due to the effect of the Hartmann boundary layer. A global-in-time well-posedness is obtained in the Gevrey function space with the optimal index $2$. The proof is based on a cancellation mechanism through some auxiliary functions from the study of the Prandtl equation and an observation about the structure of the loss of one order tangential derivatives through twice operations of the Prandtl operator

math.AP↗

arXiv2022

Efficient Distance-Optimal Tethered Path Planning in Planar Environments: The Workspace Convexity

The main contribution of this paper is the proof of the convexity of the omni-directional tethered robot workspace (namely, the set of all tether-length-admissible robot configurations), as well as a set of distance-optimal tethered path planning algorithms that leverage the workspace convexity. The workspace is proven to be topologically a simply-connected subset and geometrically a convex subset of the set of all configurations. As a direct result, the tether-length-admissible optimal path between two configurations is proven exactly the untethered collision-free locally shortest path in the homotopy specified by the concatenation of the tether curve of the given configurations, which can be simply constructed by performing an untethered path shortening process in the 2D environment instead of a path searching process in the pre-calculated workspace. The convexity is an intrinsic property to the tethered robot kinematics, thus has universal impacts on all high-level distance-optimal tethered path planning tasks: The most time-consuming workspace pre-calculation (WP) process is replaced with a goal configuration pre-calculation (GCP) process, and the homotopy-aware path searching process is replaced with untethered path shortening processes. Motivated by the workspace convexity, efficient algorithms to solve the following problems are naturally proposed: (a) The optimal tethered reconfiguration (TR) planning problem is solved by a locally untethered path shortening (UPS) process, (b) The classic optimal tethered path (TP) planning problem (from a starting configuration to a goal location whereby the target tether state is not assigned) is solved by a GCP process and $n$ UPS processes, where $n$ is the number of tether-length-admissible configurations that visit the goal location, (c) The optimal tethered motion to visit a sequence of multiple goal locations, referred to as

cs.RO↗

arXiv2022

Efficient Search of the k Shortest Non-Homotopic Paths by Eliminating Non-k-Optimal Topologies

An efficient algorithm to solve the $k$ shortest non-homotopic path planning ($k$-SNPP) problem in a 2D environment is proposed in this paper. Motivated by accelerating the inefficient exploration of the homotopy-augmented space of the 2D environment, our fundamental idea is to identify the non-$k$-optimal path topologies as early as possible and terminate the pathfinding along them. This is a non-trivial practice because it has to be done at an intermediate state of the path planning process when locally shortest paths have not been fully constructed. In other words, the paths to be compared have not rendezvoused at the goal location, which makes the homotopy theory, modelling the spatial relationship among the paths having the same endpoint, not applicable. This paper is the first work that develops a systematic distance-based topology simplification mechanism to solve the $k$-SNPP task, whose core contribution is to assert the distance-based order of non-homotopic locally shortest paths before constructing them. If the order can be predicted, then those path topologies having more than $k$ better topologies are proven free of the desired $k$ paths and thus can be safely discarded during the path planning process. To this end, a hierarchical topological tree is proposed as an implementation of the mechanism, whose nodes are proven to expand in non-homotopic directions and edges (collision-free path segments) are proven locally shortest. With efficient criteria that observe the order relations between partly constructed locally shortest paths being imparted into the tree, the tree nodes that expand in non-$k$-optimal topologies will not be expanded. As a result, the computational time for solving the $k$-SNPP problem is reduced by near two orders of magnitude.

cs.RO↗

arXiv2022

LGD: Label-guided Self-distillation for Object Detection

In this paper, we propose the first self-distillation framework for general object detection, termed LGD (Label-Guided self-Distillation). Previous studies rely on a strong pretrained teacher to provide instructive knowledge that could be unavailable in real-world scenarios. Instead, we generate an instructive knowledge based only on student representations and regular labels. Our framework includes sparse label-appearance encoder, inter-object relation adapter and intra-object knowledge mapper that jointly form an implicit teacher at training phase, dynamically dependent on labels and evolving student representations. They are trained end-to-end with detector and discarded in inference. Experimentally, LGD obtains decent results on various detectors, datasets, and extensive tasks like instance segmentation. For example in MS-COCO dataset, LGD improves RetinaNet with ResNet-50 under 2x single-scale training from 36.2% to 39.0% mAP (+ 2.8%). It boosts much stronger detectors like FCOS with ResNeXt-101 DCN v2 under 2x multi-scale training from 46.1% to 47.9% (+ 1.8%). Compared with a classical teacher-based method FGFI, LGD not only performs better without requiring pretrained teacher but also reduces 51% training cost beyond inherent student learning. Codes are available at https://github.com/megvii-research/LGD.

cs.CV↗

arXiv2022

3D hyperbolic Navier-Stokes equations in a thin strip: global well-posedness and hydrostatic limit in Gevrey space

We consider the hyperbolic version of three-dimensional anisotropic Naver-Stokes equations in a thin strip and its hydrostatic limit that is a hyperbolic Prandtl type equations. We prove the global-in-time existence and uniqueness for the two systems and the hydrostatic limit when the initial data belong to the Gevrey function space with index 2. The proof is based on a direct energy method by observing the damping effect in the systems.

math.AP↗

arXiv2022

Heat transfer problem for the Boltzmann equation in a channel with diffusive boundary condition

In this paper, we study the 1D steady Boltzmann flow in a channel. The walls of the channel are assumed to have vanishing velocity and given temperatures $θ_0$ and $θ_1$. This problem was studied by Esposito et al [13,14] where they showed that the solution tends to a local Maxwellian with parameters satisfying the compressible Navier-Stokes equation with no-slip boundary condition. However, a lot of numerical experiments reveal that the fluid layer does not entirely stick to the boundary. In the regime where the Knudsen number is reasonably small, the slip phenomenon is significant near the boundary. Thus, we revisit this problem by taking into account the slip boundary conditions. Following the lines of [9], we will first give a formal asymptotic analysis to see that the flow governed by the Boltzmann equation is accurately approximated by a superposition of a steady CNS equation with a temperature jump condition and two Knudsen layers located at end points. Then we will establish a uniform $L^\infty$ estimate on the remainder and derive the slip boundary condition for compressible Navier-Stokes equations rigorously.

math.AP↗

arXiv2022

Tensor-networks for High-order Polynomial Approximation: A Many-body Physics Perspective

We analyze the problem of high-order polynomial approximation from a many-body physics perspective, and demonstrate the descriptive power of entanglement entropy in capturing model capacity and task complexity. Instantiated with a high-order nonlinear dynamics modeling problem, tensor-network models are investigated and exhibit promising modeling advantages. This novel perspective establish a connection between quantum information and functional approximation, which worth further exploration in future research.

quant-ph↗

arXiv2022

Cannikin's Law in Tensor Modeling: A Rank Study for Entanglement and Separability in Tensor Complexity and Model Capacity

This study clarifies the proper criteria to assess the modeling capacity of a general tensor model. The work analyze the problem based on the study of tensor ranks, which is not a well-defined quantity for higher order tensors. To process, the author introduces the separability issue to discuss the Cannikin's law of tensor modeling. Interestingly, a connection between entanglement studied in information theory and tensor analysis is established, shedding new light on the theoretical understanding for modeling capacity problems.

quant-ph↗

arXiv2022

Knowledgebra: An Algebraic Learning Framework for Knowledge Graph

Knowledge graph (KG) representation learning aims to encode entities and relations into dense continuous vector spaces such that knowledge contained in a dataset could be consistently represented. Dense embeddings trained from KG datasets benefit a variety of downstream tasks such as KG completion and link prediction. However, existing KG embedding methods fell short to provide a systematic solution for the global consistency of knowledge representation. We developed a mathematical language for KG based on an observation of their inherent algebraic structure, which we termed as Knowledgebra. By analyzing five distinct algebraic properties, we proved that the semigroup is the most reasonable algebraic structure for the relation embedding of a general knowledge graph. We implemented an instantiation model, SemE, using simple matrix semigroups, which exhibits state-of-the-art performance on standard datasets. Moreover, we proposed a regularization-based method to integrate chain-like logic rules derived from human knowledge into embedding training, which further demonstrates the power of the developed language. As far as we know, by applying abstract algebra in statistical learning, this work develops the first formal language for general knowledge graphs, and also sheds light on the problem of neural-symbolic integration from an algebraic perspective.

cs.LG↗

arXiv2022

Linear instability analysis on compressible Navier-Stokes equations with strong boundary layer

It is a classical problem in fluid dynamics about the stability and instability of different hydrodynamic patterns in various physical settings, in particular in the high Reynolds number limit of laminar flow with boundary layer. However, there are very few mathematical results on the compressible fluid despite the extensive studies when the fluid is governed by the incompressible Navier-Stokes equations. This paper aims to introduce a new approach to study the compressible Navier-Stokes equations in the subsonic and high Reynolds number regime where a subtle quasi-compressible and Stokes iteration is developed. As a byproduct, we show the spectral instability of subsonic boundary layer.

math.AP↗