Efficient Deterministic Replay Using Complete Race Detection

Data races can significantly affect the executions of multi-threaded programs. Hence, one has to recur the results of data races to deterministically replay a multi-threaded program. However, data races are concealed in enormous number of memory operations in a program. Due to the difficulty of accurately identifying data races, previous multi-threaded deterministic record/replay schemes for commodity multi-processor system give up to record data races directly. Consequently, they either record all shared memory operations, which brings remarkable slowdown to the production run, or record the synchronization only, which introduces significant efforts to replay. Inspired by the advances in data race detection, we propose an efficient software-only deterministic replay scheme for commodity multi-processor systems, which is named RacX. The key insight of RacX is as follows: although it is NP-hard to accurately identify the existence of data races between a pair of memory operations, we can find out all potential data races in a multi-threaded program, in which the false positives can be reduced to a small amount with our automatic false positive reduction techniques. As a result, RacX can efficiently monitor all potential data races to deterministically replay a multi-threaded program. To evaluate RacX, we have carried out experiments over a number of well-known multi-threaded programs from SPLASH-2 benchmark suite and large-scale commercial programs. RacX can precisely recur production runs of these programs with value determinism. Averagely, RacX causes only about 1.21%, 1.89%, 2.20%, and 8.41% slowdown to the original run during recording (for 2-, 4-, 8- and 16-thread programs, respectively). The soundness, efficiency, scalability, and portability of RacX well demonstrate its superiority.Comment: 18 pages, 7 figure

Finding the maximum eigenvalue of a class of tensors with applications in copositivity test and hypergraphs

Finding the maximum eigenvalue of a symmetric tensor is an important topic in tensor computation and numerical multilinear algebra. This paper is devoted to a semi-definite program algorithm for computing the maximum $H$-eigenvalue of a class of tensors with sign structure called $W$-tensors. The class of $W$-tensors extends the well-studied nonnegative tensors and essentially nonnegative tensors, and covers some important tensors arising naturally from spectral hypergraph theory. Our algorithm is based on a new structured sums-of-squares (SOS) decomposition result for a nonnegative homogeneous polynomial induced by a $W$-tensor. This SOS decomposition enables us to show that computing the maximum $H$-eigenvalue of an even order symmetric $W$-tensor is equivalent to solving a semi-definite program, and hence can be accomplished in polynomial time. Numerical examples are given to illustrate that the proposed algorithm can be used to find maximum $H$-eigenvalue of an even order symmetric $W$-tensor with dimension up to $10,000$. We present two applications for our proposed algorithm: we first provide a polynomial time algorithm for computing the maximum $H$-eigenvalues of large size Laplacian tensors of hyper-stars and hyper-trees; second, we show that the proposed SOS algorithm can be used to test the copositivity of a multivariate form associated with symmetric extended $Z$-tensors, whose order may be even or odd. Numerical experiments illustrate that our structured semi-definite program algorithm is effective and promising

Trigonometric protocols for shortcuts to adiabatic transport of cold atoms in anharmonic traps

Shortcuts to adiabaticity have been proposed to speed up the "slow" adiabatic transport of an atom or a wave packet of atoms. However, the freedom of the inverse engineering approach with appropriate boundary conditions provides thousands of trap trajectories for different purposes, for example, time and energy minimizations. In this paper, we propose trigonometric protocols for fast and robust atomic transport, taking into account cubic or quartic anharmonicities. The numerical results have illustrated that such trigonometric protocols, particular cosine ansatz, is more robust and the corresponding final energy excitation is smaller, as compared to sine trajectories implemented in previous experiments.Comment: 5 pages, 5 figure

A Hopf lemma and regularity for fractional p−p-Laplacians

In this paper, we study qualitative properties of the fractional $p$-Laplacian. Specifically, we establish a Hopf type lemma for positive weak super-solutions of the fractional $p-$Laplacian equation with Dirichlet condition. Moreover, an optimal condition is obtained to ensure $(-\triangle)_p^s u\in C^1(\mathbb{R}^n)$ for smooth functions $u$.Comment: 20 page

Understanding the Importance of Single Directions via Representative Substitution

Understanding the internal representations of deep neural networks (DNNs) is crucal to explain their behavior. The interpretation of individual units, which are neurons in MLPs or convolution kernels in convolutional networks, has been paid much attention given their fundamental role. However, recent research (Morcos et al. 2018) presented a counterintuitive phenomenon, which suggests that an individual unit with high class selectivity, called interpretable units, has poor contributions to generalization of DNNs. In this work, we provide a new perspective to understand this counterintuitive phenomenon, which makes sense when we introduce Representative Substitution (RS). Instead of individually selective units with classes, the RS refers to the independence of a unit's representations in the same layer without any annotation. Our experiments demonstrate that interpretable units have high RS which are not critical to network's generalization. The RS provides new insights into the interpretation of DNNs and suggests that we need to focus on the independence and relationship of the representations.Comment: 4 pages, 6 figure

On Modular Training of Neural Acoustics-to-Word Model for LVCSR

End-to-end (E2E) automatic speech recognition (ASR) systems directly map acoustics to words using a unified model. Previous works mostly focus on E2E training a single model which integrates acoustic and language model into a whole. Although E2E training benefits from sequence modeling and simplified decoding pipelines, large amount of transcribed acoustic data is usually required, and traditional acoustic and language modelling techniques cannot be utilized. In this paper, a novel modular training framework of E2E ASR is proposed to separately train neural acoustic and language models during training stage, while still performing end-to-end inference in decoding stage. Here, an acoustics-to-phoneme model (A2P) and a phoneme-to-word model (P2W) are trained using acoustic data and text data respectively. A phone synchronous decoding (PSD) module is inserted between A2P and P2W to reduce sequence lengths without precision loss. Finally, modules are integrated into an acousticsto-word model (A2W) and jointly optimized using acoustic data to retain the advantage of sequence modeling. Experiments on a 300- hour Switchboard task show significant improvement over the direct A2W model. The efficiency in both training and decoding also benefits from the proposed method.Comment: accepted by ICASSP201

Dimer XXZ Spin Ladders: Phase diagram and a Non-Trivial Antiferromagnetic Phase

We study the dimer $XXZ$ spin model on two-leg ladders with isotropic Heisenberg interactions on the rung and anisotropic $XXZ$ interactions along the rail in an external field. Combining both analytical and numerical methods, we set up the ground state phase diagram and investigate the quantum phase transitions and the properties of rich phases, including the full polarized, singlet dimer, Luttinger liquid, triplon solid, and a non-trivial antiferromagnetic phases with gap. The analytical analyses based on solvable effective Hamiltonians are presented for clear view of the phases and transitions. Quantum Monte Carlo and exact diagonalization methods are employed on finite system to verify the exact nature of the phases and transitions. Of all the phases, we pay a special attention to the gapped antiferromagnetic phase, which is disclosed to be a non-trivial one that exhibits the time-reversal symmetry. We also discuss how our findings could be detected in experiment in the light of ultracold atoms technology advances.Comment: 13 pages, 7 figure

A density compensation-based path computing model for measuring semantic similarity

The shortest path between two concepts in a taxonomic ontology is commonly used to represent the semantic distance between concepts in the edge-based semantic similarity measures. In the past, the edge counting is considered to be the default method for the path computation, which is simple, intuitive and has low computational complexity. However, a large lexical taxonomy of such as WordNet has the irregular densities of links between concepts due to its broad domain but. The edge counting-based path computation is powerless for this non-uniformity problem. In this paper, we advocate that the path computation is able to be separated from the edge-based similarity measures and form various general computing models. Therefore, in order to solve the problem of non-uniformity of concept density in a large taxonomic ontology, we propose a new path computing model based on the compensation of local area density of concepts, which is equal to the number of direct hyponyms of the subsumers of concepts in their shortest path. This path model considers the local area density of concepts as an extension of the edge-based path and converts the local area density divided by their depth into the compensation for edge-based path with an adjustable parameter, which idea has been proven to be consistent with the information theory. This model is a general path computing model and can be applied in various edge-based similarity algorithms. The experiment results show that the proposed path model improves the average correlation between edge-based measures with human judgments on Miller and Charles benchmark from less than 0.8 to more than 0.85, and has a big advantage in efficiency than information content (IC) computation in a dynamic ontology, thereby successfully solving the non-uniformity problem of taxonomic ontology.Comment: 17 pages,11 figure

Making Availability as a Service in the Clouds

Cloud computing has achieved great success in modern IT industry as an excellent computing paradigm due to its flexible management and elastic resource sharing. To date, cloud computing takes an irrepalceable position in our socioeconomic system and influences almost every aspect of our daily life. However, it is still in its infancy, many problems still exist.Besides the hotly-debated security problem, availability is also an urgent issue.With the limited power of availability mechanisms provided in present cloud platform, we can hardly get detailed availability information of current applications such as the root causes of availability problem,mean time to failure, etc. Thus a new mechanism based on deep avaliability analysis is neccessary and benificial.Following the prevalent terminology 'XaaS',this paper proposes a new win-win concept for cloud users and providers in term of 'Availability as a Service' (abbreviated as 'AaaS').The aim of 'AaaS' is to provide comprehensive and aimspecific runtime avaliabilty analysis services for cloud users by integrating plent of data-driven and modeldriven approaches. To illustrate this concept, we realize a prototype named 'EagleEye' with all features of 'AaaS'. By subscribing corresponding services in 'EagleEye', cloud users could get specific availability information of their applications deployed in cloud platform. We envision this new kind of service will be merged into the cloud management mechanism in the near future.Comment:

The A-Cycle Problem for Transverse Ising Ring

Traditionally, the transverse Ising model is mapped to the fermionic c-cycle problem, which neglects the boundary effect due to thermodynamic limit. If persisting on a perfect periodic boundary condition, we can get a so-called a-cycle problem that has not been treated seriously so far (Lieb et al., 1961 \textit{Ann. of Phys.} \textbf{16} 407). In this work, we show a little surprising but exact result in this respect. We find the odevity of the number of lattice sites, $N$, in the a-cycle problem plays an unexpected role even in the thermodynamic limit, $N\rightarrow\infty$, due to the boundary constraint. We pay a special attention to the system with $N(\in Odd)\rightarrow\infty$, which is in contrast to the one with $N(\in Even)\rightarrow\infty$, because the former suffers a ring frustration. As a new effect, we find the ring frustration induces a low-energy gapless spectrum above the ground state. By proving a theorem for a new type of Toeplitz determinant, we demonstrate that the ground state in the gapless region exhibits a peculiar longitudinal spin-spin correlation. The entangled nature of the ground state is also disclosed by the evaluation of its entanglement entropy. At low temperatures, new behavior of specific heat is predicted. We also propose an experimental protocol for observing the new phenomenon due to the ring frustration.Comment: 24 pages, 9 figure