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Using derandomization, we provide an upper bound on the compression size of solutions to the graph coloring problem. In general, if solutions to a combinatorial problem exist with high probability and the probability is simple, then there exists a simple solution to the problem. Otherwise the problem instance has high mutual information with the halting problem.

We extend classical methods of computational complexity to the setting of distributed computing, where they prove even more effective in some respects than in their original context. Instead of a single computer, several networked computers communicate via synchronous message-passing to collectively solve some decision problem related to the network topology. Their running time is limited in two ways: the number of communication rounds is bounded by a constant, and the number of computation steps of each computer is polynomially bounded by the size of its local input and the messages it receives. By letting two players take turns assigning certificates to the computers, we obtain a generalization of the polynomial hierarchy (and hence of the complexity classes $\mathbf{P}$ and $\mathbf{NP}$). We then extend some key results of complexity theory to this setting, in particular the Cook-Levin theorem (which identifies Boolean satisfiability as a complete problem for $\mathbf{NP}$), and Fagin's theorem (which characterizes $\mathbf{NP}$ as the problems expressible in existential second-order logic). The original results can be recovered as the special case where the network consists of a single computer. But perhaps more surprisingly, the task of separating complexity classes becomes easier in the general case: we can show that our hierarchy is infinite, while it remains notoriously open whether the same is true in the case of a single computer. (By contrast, a collapse of our hierarchy would have implied a collapse of the polynomial hierarchy.) As an application, we propose quantifier alternation as a new approach to measuring the locality of problems in distributed computing.

The distributed data analytic system -- Spark is a common choice for processing massive volumes of heterogeneous data, while it is challenging to tune its parameters to achieve high performance. Recent studies try to employ auto-tuning techniques to solve this problem but suffer from three issues: limited functionality, high overhead, and inefficient search. In this paper, we present a general and efficient Spark tuning framework that can deal with the three issues simultaneously. First, we introduce a generalized tuning formulation, which can support multiple tuning goals and constraints conveniently, and a Bayesian optimization (BO) based solution to solve this generalized optimization problem. Second, to avoid high overhead from additional offline evaluations in existing methods, we propose to tune parameters along with the actual periodic executions of each job (i.e., online evaluations). To ensure safety during online job executions, we design a safe configuration acquisition method that models the safe region. Finally, three innovative techniques are leveraged to further accelerate the search process: adaptive sub-space generation, approximate gradient descent, and meta-learning method. We have implemented this framework as an independent cloud service, and applied it to the data platform in Tencent. The empirical results on both public benchmarks and large-scale production tasks demonstrate its superiority in terms of practicality, generality, and efficiency. Notably, this service saves an average of 57.00% memory cost and 34.93% CPU cost on 25K in-production tasks within 20 iterations, respectively.

We consider the problem of computing the Maximal Exact Matches (MEMs) of a given pattern $P[1 .. m]$ on a large repetitive text collection $T[1 .. n]$, which is represented as a (hopefully much smaller) run-length context-free grammar of size $g_{rl}$. We show that the problem can be solved in time $O(m^2 \log^\epsilon n)$, for any constant $\epsilon > 0$, on a data structure of size $O(g_{rl})$. Further, on a locally consistent grammar of size $O(\delta\log\frac{n}{\delta})$, the time decreases to $O(m\log m(\log m + \log^\epsilon n))$. The value $\delta$ is a function of the substring complexity of $T$ and $\Omega(\delta\log\frac{n}{\delta})$ is a tight lower bound on the compressibility of repetitive texts $T$, so our structure has optimal size in terms of $n$ and $\delta$. We extend our results to several related problems, such as finding $k$-MEMs, MUMs, rare MEMs, and applications.

A pair $\langle G_0, G_1 \rangle$ of graphs admits a mutual witness proximity drawing $\langle \Gamma_0, \Gamma_1 \rangle$ when: (i) $\Gamma_i$ represents $G_i$, and (ii) there is an edge $(u,v)$ in $\Gamma_i$ if and only if there is no vertex $w$ in $\Gamma_{1-i}$ that is ``too close'' to both $u$ and $v$ ($i=0,1$). In this paper, we consider infinitely many definitions of closeness by adopting the $\beta$-proximity rule for any $\beta \in [1,\infty]$ and study pairs of isomorphic trees that admit a mutual witness $\beta$-proximity drawing. Specifically, we show that every two isomorphic trees admit a mutual witness $\beta$-proximity drawing for any $\beta \in [1,\infty]$. The constructive technique can be made ``robust'': For some tree pairs we can suitably prune linearly many leaves from one of the two trees and still retain their mutual witness $\beta$-proximity drawability. Notably, in the special case of isomorphic caterpillars and $\beta=1$, we construct linearly separable mutual witness Gabriel drawings.

We study the differential privacy (DP) of a core ML problem, linear ordinary least squares (OLS), a.k.a. $\ell_2$-regression. Our key result is that the approximate LS algorithm (ALS) (Sarlos, 2006), a randomized solution to the OLS problem primarily used to improve performance on large datasets, also preserves privacy. ALS achieves a better privacy/utility tradeoff, without modifications or further noising, when compared to alternative private OLS algorithms which modify and/or noise OLS. We give the first {\em tight} DP-analysis for the ALS algorithm and the standard Gaussian mechanism (Dwork et al., 2014) applied to OLS. Our methodology directly improves the privacy analysis of (Blocki et al., 2012) and (Sheffet, 2019)) and introduces new tools which may be of independent interest: (1) the exact spectrum of $(\epsilon, \delta)$-DP parameters (``DP spectrum") for mechanisms whose output is a $d$-dimensional Gaussian, and (2) an improved DP spectrum for random projection (compared to (Blocki et al., 2012) and (Sheffet, 2019)). All methods for private OLS (including ours) assume, often implicitly, restrictions on the input database, such as bounds on leverage and residuals. We prove that such restrictions are necessary. Hence, computing the privacy of mechanisms such as ALS must estimate these database parameters, which can be infeasible in big datasets. For more complex ML models, DP bounds may not even be tractable. There is a need for blackbox DP-estimators (Lu et al., 2022) which empirically estimate a data-dependent privacy. We demonstrate the effectiveness of such a DP-estimator by empirically recovering a DP-spectrum that matches our theory for OLS. This validates the DP-estimator in a nontrivial ML application, opening the door to its use in more complex nonlinear ML settings where theory is unavailable.

As artificial intelligence (AI) models continue to scale up, they are becoming more capable and integrated into various forms of decision-making systems. For models involved in moral decision-making, also known as artificial moral agents (AMA), interpretability provides a way to trust and understand the agent's internal reasoning mechanisms for effective use and error correction. In this paper, we provide an overview of this rapidly-evolving sub-field of AI interpretability, introduce the concept of the Minimum Level of Interpretability (MLI) and recommend an MLI for various types of agents, to aid their safe deployment in real-world settings.

Incompleteness is a common problem for existing knowledge graphs (KGs), and the completion of KG which aims to predict links between entities is challenging. Most existing KG completion methods only consider the direct relation between nodes and ignore the relation paths which contain useful information for link prediction. Recently, a few methods take relation paths into consideration but pay less attention to the order of relations in paths which is important for reasoning. In addition, these path-based models always ignore nonlinear contributions of path features for link prediction. To solve these problems, we propose a novel KG completion method named OPTransE. Instead of embedding both entities of a relation into the same latent space as in previous methods, we project the head entity and the tail entity of each relation into different spaces to guarantee the order of relations in the path. Meanwhile, we adopt a pooling strategy to extract nonlinear and complex features of different paths to further improve the performance of link prediction. Experimental results on two benchmark datasets show that the proposed model OPTransE performs better than state-of-the-art methods.

Object detection typically assumes that training and test data are drawn from an identical distribution, which, however, does not always hold in practice. Such a distribution mismatch will lead to a significant performance drop. In this work, we aim to improve the cross-domain robustness of object detection. We tackle the domain shift on two levels: 1) the image-level shift, such as image style, illumination, etc, and 2) the instance-level shift, such as object appearance, size, etc. We build our approach based on the recent state-of-the-art Faster R-CNN model, and design two domain adaptation components, on image level and instance level, to reduce the domain discrepancy. The two domain adaptation components are based on H-divergence theory, and are implemented by learning a domain classifier in adversarial training manner. The domain classifiers on different levels are further reinforced with a consistency regularization to learn a domain-invariant region proposal network (RPN) in the Faster R-CNN model. We evaluate our newly proposed approach using multiple datasets including Cityscapes, KITTI, SIM10K, etc. The results demonstrate the effectiveness of our proposed approach for robust object detection in various domain shift scenarios.