Counting integer solutions of linear constraints has found interesting applications in various fields. It is equivalent to the problem of counting lattice points inside a polytope. However, state-of-the-art algorithms for this problem become too slow for even a modest number of variables. In this paper, we propose a new framework to approximate the lattice counts inside a polytope with a new random-walk sampling method. The counts computed by our approach has been proved approximately bounded by a (epsilon, delta)-bound. Experiments on extensive benchmarks show that our algorithm could solve polytopes with dozens of dimensions, which significantly outperforms state-of-the-art counters.
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We introduce the algorithmic problem of finding a locally rainbow path of length l connecting two distinguished vertices s and t in a vertex-colored directed graph. Herein, a path is locally rainbow if between any two visits of equally colored vertices, the path traverses consecutively at leaset r differently colored vertices. This problem generalizes the well-known problem of finding a rainbow path. It finds natural applications whenever there are different types of resources that must be protected from overuse, such as crop sequence optimization or production process scheduling. We show that the problem is computationally intractable even if r=2 or if one looks for a locally rainbow among the shortest paths. On the positive side, if one looks for a path that takes only a short detour (i.e., it is slightly longer than the shortest path) and if r is small, the problem can be solved efficiently. Indeed, the running time of the respective algorithm is near-optimal unless the ETH fails.
Computational evaluations are crucial in modern problem-solving when we surpass theoretical algorithms or bounds. These experiments frequently take much work, and the sheer amount of needed resources makes it impossible to execute them on a single personal computer or laptop. Cluster schedulers allow for automatizing these tasks and scale to many computers. But, when we evaluate implementations of combinatorial algorithms, we depend on stable runtime results. Common approaches either limit parallelism or suffer from unstable runtime measurements due to interference among jobs on modern hardware. The former is inefficient and not sustainable. The latter results in unreplicable experiments. In this work, we address this issue and offer an acceptable balance between efficiency, software, hardware complexity, reliability, and replicability. We investigate effects towards replicability stability and illustrate how to efficiently use widely employed cluster resources for parallel evaluations. Furthermore, we present solutions which mitigate issues that emerge from the concurrent execution of benchmark jobs. Our experimental evaluation shows that – despite parallel execution – our approach reduces the runtime instability on the majority of instances to one second.
Stochastic Boolean satisfiability (SSAT) is a natural formalism for optimization under uncertainty. Its decision version implicitly imposes a final threshold quantification on an SSAT formula. However, the single threshold quantification restricts the expressive power of SSAT. In this work, we enrich SSAT with an additional threshold quantifier, resulting in a new formalism SSAT(θ). The increased expressiveness allows SSAT(θ), which remains in the PSPACE complexity class, to subsume and encode the languages in the counting hierarchy. An SSAT(θ) solver, ClauSSat(θ), is developed. Experiments show the applicability of the solver in uniquely solving complex SSAT(θ) instances of parameter synthesis and SSAT extension.
Percentile Risk-Constrained Budget Pacing for Guaranteed Display Advertising in Online Optimization
PDF ↗Guaranteed display (GD) advertising is a critical component of advertising since it provides publishers with stable revenue and enables advertisers to target specific audiences with guaranteed impressions. However, smooth pacing control for online ad delivery presents a challenge due to significant budget disparities, user arrival distribution drift, and dynamic change between supply and demand. This paper presents robust risk-constrained pacing (RCPacing) that utilizes Lagrangian dual multipliers to fine-tune probabilistic throttling through monotonic mapping functions within the percentile space of impression performance distribution. RCPacing combines distribution drift resilience and compatibility with guaranteed allocation mechanism, enabling us to provide near-optimal online services. We also show that RCPacing achieves O(sqrt(T)) dynamic regret where T is the length of the horizon. RCPacing's effectiveness is validated through offline evaluations and online A/B testing conducted on Taobao brand advertising platform.
Parity reasoning is challenging for Conflict-Driven Clause Learning (CDCL) SAT solvers. This has been observed even for simple formulas encoding two contradictory parity constraints with different variable orders (Chew and Heule 2020). We provide an analytical explanation for their hardness by showing that they require exponential resolution refutations with high probability when the variable order is chosen at random. We obtain this result by proving that these formulas, which are known to be Tseitin formulas, have Tseitin graphs of linear treewidth with high probability. Since such Tseitin formulas require exponential resolution refutations, our result follows. We generalize this argument to a new class of formulas that capture a basic form of parity reasoning involving a sum of two random parity constraints with random orders. Even when the variable order for the sum is chosen favorably, these formulas remain hard for resolution. In contrast, we prove that they have short DRAT refutations. We show experimentally that the running time of CDCL SAT solvers on both classes of formulas grows exponentially with their treewidth.
Utilization of inter-base station cooperation for information processing has shown great potential in enhancing the overall quality of communication services (QoS) in wireless communication networks. Nevertheless, such cooperations require the knowledge of channel state information (CSI) at base stations (BSs), which is assumed to be perfectly known. However, CSI errors are inevitable in practice which necessitates beamforming technique that can achieve robust performance in the presence of channel estimation errors. Existing approaches relax the robust beamforming design problems into semidefinite programming (SDP), which can only achieve a solution that is far from being optimal. To this end, this paper views robust beamforming design problems from a bilevel optimization perspective. In particular, we focus on maximizing the worst-case weighted sum-rate (WSR) in the downlink multi-cell multi-user multiple-input single-output (MISO) system considering bounded CSI errors. We first reformulate this problem into a bilevel optimization problem and then develop an efficient algorithm based on the cutting plane method. A distributed optimization algorithm has also been developed to facilitate the parallel processing in practical settings. Numerical results are provided to confirm the effectiveness of the proposed algorithm in terms of performance and complexity, particularly in the presence of CSI uncertainties.
We analyze how symmetries can be used to compress structures (also known as interpretations) onto a smaller domain without loss of information. This analysis suggests the possibility to solve satisfiability problems in the compressed domain for better performance. Thus, we propose a 2-step novel method: (i) the sentence to be satisfied is automatically translated into an equisatisfiable sentence over a ``lifted'' vocabulary that allows domain compression; (ii) satisfiability of the lifted sentence is checked by growing the (initially unknown) compressed domain until a satisfying structure is found. The key issue is to ensure that this satisfying structure can always be expanded into an uncompressed structure that satisfies the original sentence to be satisfied. We present an adequate translation for sentences in typed first-order logic extended with aggregates. Our experimental evaluation shows large speedups for generative configuration problems. The method also has applications in the verification of software operating on complex data structures. Our results justify further research in automatic translation of sentences for symmetry reduction.
Samplers are the backbone of the implementations of any randomized algorithm. Unfortunately, obtaining an efficient algorithm to test the correctness of samplers is very hard to find. Recently, in a series of works, testers like Barbarik, Teq, Flash for testing of some particular kinds of samplers, like CNF-samplers and Horn-samplers, were obtained. However, their techniques have a significant limitation because one can not expect to use their methods to test for other samplers, such as perfect matching samplers or samplers for sampling linear extensions in posets. In this paper, we present a new testing algorithm that works for such samplers and can estimate the distance of a new sampler from a known sampler (say, the uniform sampler). Testing the identity of distributions is the heart of testing the correctness of samplers. This paper's main technical contribution is developing a new distance estimation algorithm for distributions over high-dimensional cubes using the recently proposed subcube conditioning sampling model. Given subcube conditioning access to an unknown distribution P, and a known distribution Q defined over an n-dimensional Boolean hypercube, our algorithm CubeProbeEst estimates the variation distance between P and Q within additive error using subcube conditional samples from P. Following the testing-via-learning paradigm, we also get a tester that distinguishes between the cases when P and Q are close or far in variation distance with high probability using subcube conditional samples. This estimation algorithm CubeProbeEst in the subcube conditioning sampling model helps us to design the first tester for self-reducible samplers. The correctness of the tester is formally proved. Moreover, we implement CubeProbeEst to test the quality of three samplers for sampling linear extensions in posets.
Conflict-driven clause learning (CDCL) is the dominating algorithmic paradigm for SAT solving and hugely successful in practice. In its lifted version QCDCL, it is one of the main approaches for solving quantified Boolean formulas (QBF). In both SAT and QBF, proofs can be efficiently extracted from runs of (Q)CDCL solvers. While for CDCL, it is known that the proof size in the underlying proof system propositional resolution matches the CDCL runtime up to a polynomial factor, we show that in QBF there is an exponential gap between QCDCL runtime and the size of the extracted proofs in QBF resolution systems. We demonstrate that this is not just a gap between QCDCL runtime and the size of any QBF resolution proof, but even the extracted proofs are exponentially smaller for some instances. Hence searching for a small proof via QCDCL (even with non-deterministic decision policies) will provably incur an exponential overhead for some instances.
Optimal control deals with optimization problems in which variables steer a dynamical system, and its outcome contributes to the objective function. Two classical approaches to solving these problems are Dynamic Programming and the Pontryagin Maximum Principle. In both approaches, Hamiltonian equations offer an interpretation of optimality through auxiliary variables known as costates. However, Hamiltonian equations are rarely used due to their reliance on forward-backward algorithms across the entire temporal domain. This paper introduces a novel neural-based approach to optimal control. Neural networks are employed not only for implementing state dynamics but also for estimating costate variables. The parameters of the latter network are determined at each time step using a newly introduced local policy referred to as the time-reversed generalized Riccati equation. This policy is inspired by a result discussed in the Linear Quadratic (LQ) problem, which we conjecture stabilizes state dynamics. We support this conjecture by discussing experimental results from a range of optimal control case studies.
Motivated by applications to classification problems on metric data, we study Weighted Metric Clustering problem: given a metric d over n points and a k x k symmetric matrix A with non-negative entries, the goal is to find a k-partition of these points into clusters C1,...,Ck, while minimizing the sum of A[i,j] * d(u,v) over all pairs of clusters Ci and Cj and all pairs of points u from Ci and v from Cj. Specific choices of A lead to Weighted Metric Clustering capturing well-studied graph partitioning problems in metric spaces, such as Min-Uncut, Min-k-Sum, Min-k-Cut, and more. Our main result is that Weighted Metric Clustering admits a polynomial-time approximation scheme (PTAS). Our algorithm handles all the above problems using the Sherali-Adams linear programming relaxation. This subsumes several prior works, unifies many of the techniques for various metric clustering objectives, and yields a PTAS for several new problems, including metric clustering on manifolds and a new family of hierarchical clustering objectives. Our experiments on the hierarchical clustering objective show that it better captures the ground-truth structural information compared to the popular Dasgupta's objective.
Parameterization of (Partial) Maximum Satisfiability above Matching in a Variable-Clause Graph
PDF ↗In the paper, we study the Maximum Satisfiability and the Partial Maximum Satisfiability problems. Using Gallai–Edmonds decomposition, we significantly improve the upper bound for the Maximum Satisfiability problem parameterized above maximum matching in the variable-clause graph. Our algorithm operates with a runtime of O*(2.83^k'), a substantial improvement compared to the previous approach requiring O*(4^k' ), where k' denotes the relevant parameter. Moreover, this result immediately implies O*(1.14977^m) and O*(1.27895^m) time algorithms for the (n, 3)-MaxSAT and (n, 4)-MaxSAT where m is the overall number of clauses. These upper bounds improve prior-known upper bounds equal to O*(1.1554^m) and O*(1.2872^m). We also adapt the algorithm so that it can handle instances of Partial Maximum Satisfiability without losing performance in some cases. Note that this is somewhat surprising, as the existence of even one hard clause can significantly increase the hardness of a problem.
Accurately computing optical flow in low-contrast and noisy dark images is challenging, especially when contour information is degraded or difficult to extract. This paper proposes CEDFlow, a latent space contour enhancement for estimating optical flow in dark environments. By leveraging spatial frequency feature decomposition, CEDFlow effectively encodes local and global motion features. Importantly, we introduce the 2nd-order Gaussian difference operation to select salient contour features in the latent space precisely. It is specifically designed for large-scale contour components essential in dark optical flow estimation. Experimental results on the FCDN and VBOF datasets demonstrate that CEDFlow outperforms state-of-the-art methods in terms of the EPE index and produces more accurate and robust flow estimation. Our code is available at: https://github.com/xautstuzfy.
Sparse3D: Distilling Multiview-Consistent Diffusion for Object Reconstruction from Sparse Views
PDF ↗Reconstructing 3D objects from extremely sparse views is a long-standing and challenging problem. While recent techniques employ image diffusion models for generating plausible images at novel viewpoints or for distilling pre-trained diffusion priors into 3D representations using score distillation sampling (SDS), these methods often struggle to simultaneously achieve high-quality, consistent, and detailed results for both novel-view synthesis (NVS) and geometry. In this work, we present Sparse3D, a novel 3D reconstruction method tailored for sparse view inputs. Our approach distills robust priors from a multiview-consistent diffusion model to refine a neural radiance field. Specifically, we employ a controller that harnesses epipolar features from input views, guiding a pre-trained diffusion model, such as Stable Diffusion, to produce novel-view images that maintain 3D consistency with the input. By tapping into 2D priors from powerful image diffusion models, our integrated model consistently delivers high-quality results, even when faced with open-world objects. To address the blurriness introduced by conventional SDS, we introduce the category-score distillation sampling (C-SDS) to enhance detail. We conduct experiments on CO3DV2 which is a multi-view dataset of real-world objects. Both quantitative and qualitative evaluations demonstrate that our approach outperforms previous state-of-the-art works on the metrics regarding NVS and geometry reconstruction.
Multi-Layer Perceptron (MLP) models are the bedrock of contemporary point cloud processing. However, their complex network architectures obscure the source of their strength. We first develop an “abstraction and refinement” (ABS-REF) view for the neural modeling of point clouds. This view elucidates that whereas the early models focused on the ABS stage, the more recent techniques devise sophisticated REF stages to attain performance advantage in point cloud processing. We then borrow the concept of “positional encoding” from transformer literature, and propose a High-dimensional Positional Encoding (HPE) module, which can be readily deployed to MLP based architectures. We leverage our module to develop a suite of HPENet, which are MLP networks that follow ABS-REF paradigm, albeit with a sophisticated HPE based REF stage. The developed technique is extensively evaluated for 3D object classification, object part segmentation, semantic segmentation and object detection. We establish new state-of-the-art results of 87.6 mAcc on ScanObjectNN for object classification, and 85.5 class mIoU on ShapeNetPart for object part segmentation, and 72.7 and 78.7 mIoU on Area-5 and 6-fold experiments with S3DIS for semantic segmentation. The source code for this work is available at https://github.com/zouyanmei/HPENet.
Enhancing Neural Radiance Fields with Adaptive Multi-Exposure Fusion: A Bilevel Optimization Approach for Novel View Synthesis
PDF ↗Neural Radiance Fields (NeRF) have made significant strides in the modeling and rendering of 3D scenes. However, due to the complexity of luminance information, existing NeRF methods often struggle to produce satisfactory renderings when dealing with high and low exposure images. To address this issue, we propose an innovative approach capable of effectively modeling and rendering images under multiple exposure conditions. Our method adaptively learns the characteristics of images under different exposure conditions through an unsupervised evaluator-simulator structure for HDR (High Dynamic Range) fusion. This approach enhances NeRF's comprehension and handling of light variations, leading to the generation of images with appropriate brightness. Simultaneously, we present a bilevel optimization method tailored for novel view synthesis, aiming to harmonize the luminance information of input images while preserving their structural and content consistency. This approach facilitates the concurrent optimization of multi-exposure correction and novel view synthesis, in an unsupervised manner. Through comprehensive experiments conducted on the LOM and LOL datasets, our approach surpasses existing methods, markedly enhancing the task of novel view synthesis for multi-exposure environments and attaining state-of-the-art results. The source code can be found at https://github.com/Archer-204/AME-NeRF.
Night photography often struggles with challenges like low light and blurring, stemming from dark environments and prolonged exposures. Current methods either disregard priors and directly fitting end-to-end networks, leading to inconsistent illumination, or rely on unreliable handcrafted priors to constrain the network, thereby bringing the greater error to the final result. We believe in the strength of data-driven high-quality priors and strive to offer a reliable and consistent prior, circumventing the restrictions of manual priors. In this paper, we propose Clearer Night Image Restoration with Vector-Quantized Codebook (VQCNIR) to achieve remarkable and consistent restoration outcomes on real-world and synthetic benchmarks. To ensure the faithful restoration of details and illumination, we propose the incorporation of two essential modules: the Adaptive Illumination Enhancement Module (AIEM) and the Deformable Bi-directional Cross-Attention (DBCA) module. The AIEM leverages the inter-channel correlation of features to dynamically maintain illumination consistency between degraded features and high-quality codebook features. Meanwhile, the DBCA module effectively integrates texture and structural information through bi-directional cross-attention and deformable convolution, resulting in enhanced fine-grained detail and structural fidelity across parallel decoders. Extensive experiments validate the remarkable benefits of VQCNIR in enhancing image quality under low-light conditions, showcasing its state-of-the-art performance on both synthetic and real-world datasets. The code is available at https://github.com/AlexZou14/VQCNIR.
Diffusion-based Image Editing (DIE) is an emerging research hot-spot, which often applies a semantic mask to control the target area for diffusion-based editing. However, most existing solutions obtain these masks via manual operations or off-line processing, greatly reducing their efficiency. In this paper, we propose a novel and efficient image editing method for Text-to-Image (T2I) diffusion models, termed Instant Diffusion Editing (InstDiffEdit). In particular, InstDiffEdit aims to employ the cross-modal attention ability of existing diffusion models to achieve instant mask guidance during the diffusion steps. To reduce the noise of attention maps and realize the full automatics, we equip InstDiffEdit with a training-free refinement scheme to adaptively aggregate the attention distributions for the automatic yet accurate mask generation. Meanwhile, to supplement the existing evaluations of DIE, we propose a new benchmark called Editing-Mask to examine the mask accuracy and local editing ability of existing methods. To validate InstDiffEdit, we also conduct extensive experiments on ImageNet and Imagen, and compare it with a bunch of the SOTA methods. The experimental results show that InstDiffEdit not only outperforms the SOTA methods in both image quality and editing results, but also has a much faster inference speed, i.e., +5 to +6 times. Our code available at https://anonymous.4open.science/r/InstDiffEdit-C306
Gait datasets are essential for gait research. However, this paper observes that present benchmarks, whether conventional constrained or emerging real-world datasets, fall short regarding covariate diversity. To bridge this gap, we undertake an arduous 20-month effort to collect a cross-covariate gait recognition (CCGR) dataset. The CCGR dataset has 970 subjects and about 1.6 million sequences; almost every subject has 33 views and 53 different covariates. Compared to existing datasets, CCGR has both population and individual-level diversity. In addition, the views and covariates are well labeled, enabling the analysis of the effects of different factors. CCGR provides multiple types of gait data, including RGB, parsing, silhouette, and pose, offering researchers a comprehensive resource for exploration. In order to delve deeper into addressing cross-covariate gait recognition, we propose parsing-based gait recognition (ParsingGait) by utilizing the newly proposed parsing data. We have conducted extensive experiments. Our main results show: 1) Cross-covariate emerges as a pivotal challenge for practical applications of gait recognition. 2) ParsingGait demonstrates remarkable potential for further advancement. 3) Alarmingly, existing SOTA methods achieve less than 43% accuracy on the CCGR, highlighting the urgency of exploring cross-covariate gait recognition. Link: https://github.com/ShinanZou/CCGR.