OpenRaiser/Intern-Atlas huggingface dataset:
Dynamic Social Balance and Convergent Appraisals via Homophily and Influence Mechanisms
Venue: arXiv cs.SI 2019
Year: 2019

Social balance theory describes allowable and forbidden configurations of the topologies of signed directed social appraisal networks. In this paper, we propose two discrete-time dynamical systems that explain how an appraisal network \textcolor{blue}{converges to} social balance from an initially unbalanced configuration. These two models are based on two different socio-psychological mechanisms respectively: the homophily mechanism and the influence mechanism. Our main theoretical contribution is a comprehensive analysis for both models in three steps. First, we establish the well-posedness and bounded evolution of the interpersonal appraisals. Second, we fully characterize the set of equilibrium points; for both models, each equilibrium network is composed by an arbitrary number of complete subgraphs satisfying structural balance. Third, we establish the equivalence among three distinct properties: non-vanishing appraisals, convergence to all-to-all appraisal networks, and finite-time achievement of social balance. In addition to theoretical analysis, Monte Carlo validations illustrates how the non-vanishing appraisal condition holds for generic initial conditions in both models. Moreover, numerical comparison between the two models indicate that the homophily-based model might be a more universal explanation for the formation of social balance. Finally, adopting the homophily-based model, we present numerical results on the mediation and globalization of local conflicts, the competition for allies, and the asymptotic formation of a single versus two factions.
A Generative Model for Volume Rendering
Venue: arXiv cs.GR 2019
Year: 2019

We present a technique to synthesize and analyze volume-rendered images using generative models. We use the Generative Adversarial Network (GAN) framework to compute a model from a large collection of volume renderings, conditioned on (1) viewpoint and (2) transfer functions for opacity and color. Our approach facilitates tasks for volume analysis that are challenging to achieve using existing rendering techniques such as ray casting or texture-based methods. We show how to guide the user in transfer function editing by quantifying expected change in the output image. Additionally, the generative model transforms transfer functions into a view-invariant latent space specifically designed to synthesize volume-rendered images. We use this space directly for rendering, enabling the user to explore the space of volume-rendered images. As our model is independent of the choice of volume rendering process, we show how to analyze volume-rendered images produced by direct and global illumination lighting, for a variety of volume datasets.
Reality-Aware Social Choice
Venue: arXiv cs.CY 2019
Year: 2019

Social Choice theory generalizes voting on one proposal to ranking multiple proposals. Yet, while a vote on a single proposal has the status quo (Reality) as a default, Reality has been forsaken during this generalization. Here, we propose to restore this default social state and to incorporate Reality explicitly into Social Choice. We show that doing so gives rise to a new theory, complete with its domain restrictions, voting rules with their Reality-aware axiomatic properties, and certain game-theoretic aspects. In particular, we show how Reality can be used in a principled way to break Condorcet cycles and develop an efficient Reality-aware Condorcet-consistent agenda. We then discuss several applications of Reality-Aware Social Choice.
Distributed Server Allocation for Content Delivery Networks
Venue: arXiv cs.PF 2019
Year: 2019

We propose a dynamic formulation of file-sharing networks in terms of an average cost Markov decision process with constraints. By analyzing a Whittle-like relaxation thereof, we propose an index policy in the spirit of Whittle and compare it by simulations with other natural heuristics.
Multi-View Data Generation Without View Supervision
Venue: arXiv cs.CV 2019
Year: 2019

The development of high-dimensional generative models has recently gained a great surge of interest with the introduction of variational auto-encoders and generative adversarial neural networks. Different variants have been proposed where the underlying latent space is structured, for example, based on attributes describing the data to generate. We focus on a particular problem where one aims at generating samples corresponding to a number of objects under various views. We assume that the distribution of the data is driven by two independent latent factors: the content, which represents the intrinsic features of an object, and the view, which stands for the settings of a particular observation of that object. Therefore, we propose a generative model and a conditional variant built on such a disentangled latent space. This approach allows us to generate realistic samples corresponding to various objects in a high variety of views. Unlike many multi-view approaches, our model doesn't need any supervision on the views but only on the content. Compared to other conditional generation approaches that are mostly based on binary or categorical attributes, we make no such assumption about the factors of variations. Our model can be used on problems with a huge, potentially infinite, number of categories. We experiment it on four image datasets on which we demonstrate the effectiveness of the model and its ability to generalize.
Typically-Correct Derandomization for Small Time and Space
Venue: arXiv cs.CC 2019
Year: 2019

Suppose a language $L$ can be decided by a bounded-error randomized algorithm that runs in space $S$ and time $n \cdot \text{poly}(S)$. We give a randomized algorithm for $L$ that still runs in space $O(S)$ and time $n \cdot \text{poly}(S)$ that uses only $O(S)$ random bits; our algorithm has a low failure probability on all but a negligible fraction of inputs of each length. An immediate corollary is a deterministic algorithm for $L$ that runs in space $O(S)$ and succeeds on all but a negligible fraction of inputs of each length. We also give several other complexity-theoretic applications of our technique.
Quantum Programming Made Easy
Venue: arXiv cs.LO 2019
Year: 2019

We present IQu, namely a quantum programming language that extends Reynold's Idealized Algol, the paradigmatic core of Algol-like languages. IQu combines imperative programming with high-order features, mediated by a simple type theory. IQu mildly merges its quantum features with the classical programming style that we can experiment through Idealized Algol, the aim being to ease a transition towards the quantum programming world. The proposed extension is done along two main directions. First, IQu makes the access to quantum co-processors by means of quantum stores. Second, IQu includes some support for the direct manipulation of quantum circuits, in accordance with recent trends in the development of quantum programming languages. Finally, we show that IQu is quite effective in expressing well-known quantum algorithms.
People as Sensors: Imputing Maps from Human Actions
Venue: arXiv cs.RO 2019
Year: 2019

Despite growing attention in autonomy, there are still many open problems, including how autonomous vehicles will interact and communicate with other agents, such as human drivers and pedestrians. Unlike most approaches that focus on pedestrian detection and planning for collision avoidance, this paper considers modeling the interaction between human drivers and pedestrians and how it might influence map estimation, as a proxy for detection. We take a mapping inspired approach and incorporate people as sensors into mapping frameworks. By taking advantage of other agents' actions, we demonstrate how we can impute portions of the map that would otherwise be occluded. We evaluate our framework in human driving experiments and on real-world data, using occupancy grids and landmark-based mapping approaches. Our approach significantly improves overall environment awareness and out-performs standard mapping techniques.
An Optimal Distributed $(Δ+1)$-Coloring Algorithm?
Venue: arXiv cs.DC 2019
Year: 2019

Vertex coloring is one of the classic symmetry breaking problems studied in distributed computing. In this paper we present a new algorithm for $(Δ+1)$-list coloring in the randomized ${\sf LOCAL}$ model running in $O(\mathsf{Det}_{\scriptscriptstyle d}(\text{poly} \log n))$ time, where $\mathsf{Det}_{\scriptscriptstyle d}(n')$ is the deterministic complexity of $(\text{deg}+1)$-list coloring on $n'$-vertex graphs. (In this problem, each $v$ has a palette of size $\text{deg}(v)+1$.) This improves upon a previous randomized algorithm of Harris, Schneider, and Su [STOC'16, JACM'18] with complexity $O(\sqrt{\log Δ} + \log\log n + \mathsf{Det}_{\scriptscriptstyle d}(\text{poly} \log n))$, and, for some range of $Δ$, is much faster than the best known deterministic algorithm of Fraigniaud, Heinrich, and Kosowski [FOCS'16] and Barenboim, Elkin, and Goldenberg [PODC'18], with complexity $O(\sqrt{Δ\log Δ}\log^\ast Δ+ \log^* n)$. Our algorithm "appears to be" optimal, in view of the $Ω(\mathsf{Det}(\text{poly} \log n))$ randomized lower bound due to Chang, Kopelowitz, and Pettie [FOCS'16], where $\mathsf{Det}$ is the deterministic complexity of $(Δ+1)$-list coloring. At present, the best upper bounds on $\mathsf{Det}_{\scriptscriptstyle d}(n')$ and $\mathsf{Det}(n')$ are both $2^{O(\sqrt{\log n'})}$ and use a black box application of network decompositions (Panconesi and Srinivasan [Journal of Algorithms'96]). It is quite possible that the true complexities of both problems are the same, asymptotically, which would imply the randomized optimality of our $(Δ+1)$-list coloring algorithm.
A Faster Distributed Single-Source Shortest Paths Algorithm
Venue: arXiv cs.DC 2019
Year: 2019

We devise new algorithms for the single-source shortest paths (SSSP) problem with non-negative edge weights in the CONGEST model of distributed computing. While close-to-optimal solutions, in terms of the number of rounds spent by the algorithm, have recently been developed for computing SSSP approximately, the fastest known exact algorithms are still far away from matching the lower bound of $ \tilde Ω(\sqrt{n} + D) $ rounds by Peleg and Rubinovich [SIAM Journal on Computing 2000], where $ n $ is the number of nodes in the network and $ D $ is its diameter. The state of the art is Elkin's randomized algorithm [STOC 2017] that performs $ \tilde O(n^{2/3} D^{1/3} + n^{5/6}) $ rounds. We significantly improve upon this upper bound with our two new randomized algorithms for polynomially bounded integer edge weights, the first performing $ \tilde O (\sqrt{n D}) $ rounds and the second performing $ \tilde O (\sqrt{n} D^{1/4} + n^{3/5} + D) $ rounds. Our bounds also compare favorably to the independent result by Ghaffari and Li [STOC 2018]. As side results, we obtain a $ (1 + ε) $-approximation $ \tilde O ((\sqrt{n} D^{1/4} + D) / ε) $-round algorithm for directed SSSP and a new work/depth trade-off for exact SSSP on directed graphs in the PRAM model.
Maximum Entropy Distributions: Bit Complexity and Stability
Venue: arXiv cs.DS 2019
Year: 2019

Maximum entropy distributions with discrete support in $m$ dimensions arise in machine learning, statistics, information theory, and theoretical computer science. While structural and computational properties of max-entropy distributions have been extensively studied, basic questions such as: Do max-entropy distributions over a large support (e.g., $2^m$) with a specified marginal vector have succinct descriptions (polynomial-size in the input description)? and: Are entropy maximizing distributions "stable" under the perturbation of the marginal vector? have resisted a rigorous resolution. Here we show that these questions are related and resolve both of them. Our main result shows a ${\rm poly}(m, \log 1/\varepsilon)$ bound on the bit complexity of $\varepsilon$-optimal dual solutions to the maximum entropy convex program -- for very general support sets and with no restriction on the marginal vector. Applications of this result include polynomial time algorithms to compute max-entropy distributions over several new and old polytopes for any marginal vector in a unified manner, a polynomial time algorithm to compute the Brascamp-Lieb constant in the rank-1 case. The proof of this result allows us to show that changing the marginal vector by $δ$ changes the max-entropy distribution in the total variation distance roughly by a factor of ${\rm poly}(m, \log 1/δ)\sqrtδ$ -- even when the size of the support set is exponential. Together, our results put max-entropy distributions on a mathematically sound footing -- these distributions are robust and computationally feasible models for data.
Algorithms to Approximate Column-Sparse Packing Problems
Venue: arXiv cs.DS 2019
Year: 2019

Column-sparse packing problems arise in several contexts in both deterministic and stochastic discrete optimization. We present two unifying ideas, (non-uniform) attenuation and multiple-chance algorithms, to obtain improved approximation algorithms for some well-known families of such problems. As three main examples, we attain the integrality gap, up to lower-order terms, for known LP relaxations for k-column sparse packing integer programs (Bansal et al., Theory of Computing, 2012) and stochastic k-set packing (Bansal et al., Algorithmica, 2012), and go "half the remaining distance" to optimal for a major integrality-gap conjecture of Furedi, Kahn and Seymour on hypergraph matching (Combinatorica, 1993).
Computing exact minimum cuts without knowing the graph
Venue: arXiv cs.DS 2019
Year: 2019

We give query-efficient algorithms for the global min-cut and the s-t cut problem in unweighted, undirected graphs. Our oracle model is inspired by the submodular function minimization problem: on query $S \subset V$, the oracle returns the size of the cut between $S$ and $V \setminus S$. We provide algorithms computing an exact minimum $s$-$t$ cut in $G$ with $\tilde{O}(n^{5/3})$ queries, and computing an exact global minimum cut of $G$ with only $\tilde{O}(n)$ queries (while learning the graph requires $\tildeΘ(n^2)$ queries).
Learning Markov Chain in Unordered Dataset
Venue: arXiv cs.LG 2019
Year: 2019

The assumption that data samples are independently identically distributed is the backbone of many learning algorithms. Nevertheless, datasets often exhibit rich structure in practice, and we argue that there exist some unknown order within the data instances. In this technical report, we introduce OrderNet that can be used to extract the order of data instances in an unsupervised way. By assuming that the instances are sampled from a Markov chain, our goal is to learn the transitional operator of the underlying Markov chain, as well as the order by maximizing the generation probability under all possible data permutations. Specifically, we use neural network as a compact and soft lookup table to approximate the possibly huge, but discrete transition matrix. This strategy allows us to amortize the space complexity with a single model. Furthermore, this simple and compact representation also provides a short description to the dataset and generalizes to unseen instances as well. To ensure that the learned Markov chain is ergodic, we propose a greedy batch-wise permutation scheme that allows fast training. Empirically, we show that OrderNet is able to discover an order among data instances. We also extend the proposed OrderNet to one-shot recognition task and demonstrate favorable results.
Fast Distributed Approximation for TAP and 2-Edge-Connectivity
Venue: arXiv cs.DS 2019
Year: 2019

The tree augmentation problem (TAP) is a fundamental network design problem, in which the input is a graph $G$ and a spanning tree $T$ for it, and the goal is to augment $T$ with a minimum set of edges $Aug$ from $G$, such that $T \cup Aug$ is 2-edge-connected. TAP has been widely studied in the sequential setting. The best known approximation ratio of 2 for the weighted case dates back to the work of Frederickson and JáJá, SICOMP 1981. Recently, a 3/2-approximation was given for unweighted TAP by Kortsarz and Nutov, TALG 2016. Recent breakthroughs give an approximation of 1.458 for unweighted TAP [Grandoni et al., STOC 2018], and approximations better than 2 for bounded weights [Adjiashvili, SODA 2017; Fiorini et al., SODA 2018]. In this paper, we provide the first fast distributed approximations for TAP. We present a distributed $2$-approximation for weighted TAP which completes in $O(h)$ rounds, where $h$ is the height of $T$. When $h$ is large, we show a much faster 4-approximation algorithm for the unweighted case, completing in $O(D+\sqrt{n}\log^*{n})$ rounds, where $n$ is the number of vertices and $D$ is the diameter of $G$. Immediate consequences of our results are an $O(D)$-round 2-approximation algorithm for the minimum size 2-edge-connected spanning subgraph, which significantly improves upon the running time of previous approximation algorithms, and an $O(h_{MST}+\sqrt{n}\log^{*}{n})$-round 3-approximation algorithm for the weighted case, where $h_{MST}$ is the height of the MST of the graph. Additional applications are algorithms for verifying 2-edge-connectivity and for augmenting the connectivity of any connected spanning subgraph to 2. Finally, we complement our study with proving lower bounds for distributed approximations of TAP.
Counting hypergraph colorings in the local lemma regime
Venue: arXiv cs.DS 2019
Year: 2019

We give a fully polynomial-time approximation scheme (FPTAS) to count the number of $q$-colorings for $k$-uniform hypergraphs with maximum degree $Δ$ if $k\ge 28$ and $q >357Δ^{\frac{14}{k-14}}$ . We also obtain a polynomial-time almost uniform sampler if $q>931Δ^{\frac{16}{k-16/3}}$. These are the first approximate counting and sampling algorithms in the regime $q\llΔ$ (for large $Δ$ and $k$) without any additional assumptions. Our method is based on the recent work of Moitra (STOC, 2017). One important contribution of ours is to remove the dependency of $k$ and $Δ$ in Moitra's approach.
A Friendly Smoothed Analysis of the Simplex Method
Venue: arXiv cs.DS 2019
Year: 2019

Explaining the excellent practical performance of the simplex method for linear programming has been a major topic of research for over 50 years. One of the most successful frameworks for understanding the simplex method was given by Spielman and Teng (JACM `04), who developed the notion of smoothed analysis. Starting from an arbitrary linear program with $d$ variables and $n$ constraints, Spielman and Teng analyzed the expected runtime over random perturbations of the LP (smoothed LP), where variance $σ^2$ Gaussian noise is added to the LP data. In particular, they gave a two-stage shadow vertex simplex algorithm which uses an expected $\widetilde{O}(d^{55} n^{86} σ^{-30})$ number of simplex pivots to solve the smoothed LP. Their analysis and runtime was substantially improved by Deshpande and Spielman (FOCS `05) and later Vershynin (SICOMP `09). The fastest current algorithm, due to Vershynin, solves the smoothed LP using an expected $O(d^3 σ^{-4} \log^3 n + d^9\log^7 n)$ number of pivots, improving the dependence on $n$ from polynomial to poly-logarithmic. While the original proof of Spielman and Teng has now been substantially simplified, the resulting analyses are still quite long and complex and the parameter dependencies far from optimal. In this work, we make substantial progress on this front, providing an improved and simpler analysis of shadow simplex methods, where our algorithm requires an expected \[ O(d^2 \sqrt{\log n} σ^{-2} + d^3 \log^{3/2} n) \] number of simplex pivots. We obtain our results via an improved \emph{shadow bound}, key to earlier analyses as well, combined with improvements on algorithmic techniques of Vershynin. As an added bonus, our analysis is completely modular, allowing us to obtain non-trivial bounds for perturbations beyond Gaussians, such as Laplace perturbations.
Training Simplification and Model Simplification for Deep Learning: A Minimal Effort Back Propagation Method
Venue: arXiv cs.LG 2019
Year: 2019

We propose a simple yet effective technique to simplify the training and the resulting model of neural networks. In back propagation, only a small subset of the full gradient is computed to update the model parameters. The gradient vectors are sparsified in such a way that only the top-k elements (in terms of magnitude) are kept. As a result, only k rows or columns (depending on the layout) of the weight matrix are modified, leading to a linear reduction in the computational cost. Based on the sparsified gradients, we further simplify the model by eliminating the rows or columns that are seldom updated, which will reduce the computational cost both in the training and decoding, and potentially accelerate decoding in real-world applications. Surprisingly, experimental results demonstrate that most of time we only need to update fewer than 5% of the weights at each back propagation pass. More interestingly, the accuracy of the resulting models is actually improved rather than degraded, and a detailed analysis is given. The model simplification results show that we could adaptively simplify the model which could often be reduced by around 9x, without any loss on accuracy or even with improved accuracy. The codes, including the extension, are available at https://github.com/lancopku/meSimp
Interleaver Design for Deep Neural Networks
Venue: arXiv cs.LG 2019
Year: 2019

We propose a class of interleavers for a novel deep neural network (DNN) architecture that uses algorithmically pre-determined, structured sparsity to significantly lower memory and computational requirements, and speed up training. The interleavers guarantee clash-free memory accesses to eliminate idle operational cycles, optimize spread and dispersion to improve network performance, and are designed to ease the complexity of memory address computations in hardware. We present a design algorithm with mathematical proofs for these properties. We also explore interleaver variations and analyze the behavior of neural networks as a function of interleaver metrics.
Optimism-Based Adaptive Regulation of Linear-Quadratic Systems
Venue: arXiv cs.SY 2019
Year: 2019

The main challenge for adaptive regulation of linear-quadratic systems is the trade-off between identification and control. An adaptive policy needs to address both the estimation of unknown dynamics parameters (exploration), as well as the regulation of the underlying system (exploitation). To this end, optimism-based methods which bias the identification in favor of optimistic approximations of the true parameter are employed in the literature. A number of asymptotic results have been established, but their finite time counterparts are few, with important restrictions. This study establishes results for the worst-case regret of optimism-based adaptive policies. The presented high probability upper bounds are optimal up to logarithmic factors. The non-asymptotic analysis of this work requires very mild assumptions; (i) stabilizability of the system's dynamics, and (ii) limiting the degree of heaviness of the noise distribution. To establish such bounds, certain novel techniques are developed to comprehensively address the probabilistic behavior of dependent random matrices with heavy-tailed distributions.