456 research outputs found

    LIPIcs, Volume 251, ITCS 2023, Complete Volume

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    LIPIcs, Volume 251, ITCS 2023, Complete Volum

    Generalising weighted model counting

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    Given a formula in propositional or (finite-domain) first-order logic and some non-negative weights, weighted model counting (WMC) is a function problem that asks to compute the sum of the weights of the models of the formula. Originally used as a flexible way of performing probabilistic inference on graphical models, WMC has found many applications across artificial intelligence (AI), machine learning, and other domains. Areas of AI that rely on WMC include explainable AI, neural-symbolic AI, probabilistic programming, and statistical relational AI. WMC also has applications in bioinformatics, data mining, natural language processing, prognostics, and robotics. In this work, we are interested in revisiting the foundations of WMC and considering generalisations of some of the key definitions in the interest of conceptual clarity and practical efficiency. We begin by developing a measure-theoretic perspective on WMC, which suggests a new and more general way of defining the weights of an instance. This new representation can be as succinct as standard WMC but can also expand as needed to represent less-structured probability distributions. We demonstrate the performance benefits of the new format by developing a novel WMC encoding for Bayesian networks. We then show how existing WMC encodings for Bayesian networks can be transformed into this more general format and what conditions ensure that the transformation is correct (i.e., preserves the answer). Combining the strengths of the more flexible representation with the tricks used in existing encodings yields further efficiency improvements in Bayesian network probabilistic inference. Next, we turn our attention to the first-order setting. Here, we argue that the capabilities of practical model counting algorithms are severely limited by their inability to perform arbitrary recursive computations. To enable arbitrary recursion, we relax the restrictions that typically accompany domain recursion and generalise circuits (used to express a solution to a model counting problem) to graphs that are allowed to have cycles. These improvements enable us to find efficient solutions to counting fundamental structures such as injections and bijections that were previously unsolvable by any available algorithm. The second strand of this work is concerned with synthetic data generation. Testing algorithms across a wide range of problem instances is crucial to ensure the validity of any claim about one algorithm’s superiority over another. However, benchmarks are often limited and fail to reveal differences among the algorithms. First, we show how random instances of probabilistic logic programs (that typically use WMC algorithms for inference) can be generated using constraint programming. We also introduce a new constraint to control the independence structure of the underlying probability distribution and provide a combinatorial argument for the correctness of the constraint model. This model allows us to, for the first time, experimentally investigate inference algorithms on more than just a handful of instances. Second, we introduce a random model for WMC instances with a parameter that influences primal treewidth—the parameter most commonly used to characterise the difficulty of an instance. We show that the easy-hard-easy pattern with respect to clause density is different for algorithms based on dynamic programming and algebraic decision diagrams than for all other solvers. We also demonstrate that all WMC algorithms scale exponentially with respect to primal treewidth, although at differing rates

    Traversing combinatorial 0/1-polytopes via optimization

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    In this paper, we present a new framework that exploits combinatorial optimization for efficiently generating a large variety of combinatorial objects based on graphs, matroids, posets and polytopes. Our method relies on a simple and versatile algorithm for computing a Hamilton path on the skeleton of any 0/1-polytope \conv(X), where X\seq \{0,1\}^n. The algorithm uses as a black box any algorithm that solves a variant of the classical linear optimization problem~min{wxxX}\min\{w\cdot x\mid x\in X\}, and the resulting delay, i.e., the running time per visited vertex on the Hamilton path, is only by a factor of logn\log n larger than the running time of the optimization algorithm. When XX encodes a particular class of combinatorial objects, then traversing the skeleton of the polytope~\conv(X) along a Hamilton path corresponds to listing the combinatorial objects by local change operations, i.e., we obtain Gray code listings. As concrete results of our general framework, we obtain efficient algorithms for generating all (cc-optimal) bases and independent sets in a matroid; (cc-optimal) spanning trees, forests, matchings, maximum matchings, and cc-optimal matchings in a general graph; vertex covers, minimum vertex covers, cc-optimal vertex covers, stable sets, maximum stable sets and cc-optimal stable sets in a bipartite graph; as well as antichains, maximum antichains, cc-optimal antichains, and cc-optimal ideals of a poset. Specifically, the delay and space required by these algorithms are polynomial in the size of the matroid ground set, graph, or poset, respectively. Furthermore, all of these listings correspond to Hamilton paths on the corresponding combinatorial polytopes, namely the base polytope, matching polytope, vertex cover polytope, stable set polytope, chain polytope and order polytope, respectively. As another corollary from our framework, we obtain an \cO(t_{\upright{LP}} \log n) delay algorithm for the vertex enumeration problem on 0/1-polytopes {xRnAxb}\{x\in\mathbb{R}^n\mid Ax\leq b\}, where ARm×nA\in \mathbb{R}^{m\times n} and~bRmb\in\mathbb{R}^m, and t_{\upright{LP}} is the time needed to solve the linear program min{wxAxb}\min\{w\cdot x\mid Ax\leq b\}. This improves upon the 25-year old \cO(t_{\upright{LP}}\,n) delay algorithm due to Bussieck and L\"ubbecke

    Prefix Sorting DFAs: a Recursive Algorithm

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    In the past thirty years, numerous algorithms for building the suffix array of a string have been proposed. In 2021, the notion of suffix array was extended from strings to DFAs, and it was shown that the resulting data structure can be built in O(m2+n5/2) O(m^2 + n^{5/2}) time, where n n is the number of states and m m is the number of edges [SODA 2021]. Recently, algorithms running in O(mn) O(mn) and O(n2logn) O(n^2\log n) time have been described [CPM 2023]. In this paper, we improve the previous bounds by proposing an O(n2) O(n^2) recursive algorithm inspired by Farach's algorithm for building a suffix tree [FOCS 1997]. To this end, we provide insight into the rich lexicographic and combinatorial structure of a graph, so contributing to the fascinating journey which might lead to solve the long-standing open problem of building the suffix tree of a graph

    Deployment of Deep Neural Networks on Dedicated Hardware Accelerators

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    Deep Neural Networks (DNNs) have established themselves as powerful tools for a wide range of complex tasks, for example computer vision or natural language processing. DNNs are notoriously demanding on compute resources and as a result, dedicated hardware accelerators for all use cases are developed. Different accelerators provide solutions from hyper scaling cloud environments for the training of DNNs to inference devices in embedded systems. They implement intrinsics for complex operations directly in hardware. A common example are intrinsics for matrix multiplication. However, there exists a gap between the ecosystems of applications for deep learning practitioners and hardware accelerators. HowDNNs can efficiently utilize the specialized hardware intrinsics is still mainly defined by human hardware and software experts. Methods to automatically utilize hardware intrinsics in DNN operators are a subject of active research. Existing literature often works with transformationdriven approaches, which aim to establish a sequence of program rewrites and data-layout transformations such that the hardware intrinsic can be used to compute the operator. However, the complexity this of task has not yet been explored, especially for less frequently used operators like Capsule Routing. And not only the implementation of DNN operators with intrinsics is challenging, also their optimization on the target device is difficult. Hardware-in-the-loop tools are often used for this problem. They use latency measurements of implementations candidates to find the fastest one. However, specialized accelerators can have memory and programming limitations, so that not every arithmetically correct implementation is a valid program for the accelerator. These invalid implementations can lead to unnecessary long the optimization time. This work investigates the complexity of transformation-driven processes to automatically embed hardware intrinsics into DNN operators. It is explored with a custom, graph-based intermediate representation (IR). While operators like Fully Connected Layers can be handled with reasonable effort, increasing operator complexity or advanced data-layout transformation can lead to scaling issues. Building on these insights, this work proposes a novel method to embed hardware intrinsics into DNN operators. It is based on a dataflow analysis. The dataflow embedding method allows the exploration of how intrinsics and operators match without explicit transformations. From the results it can derive the data layout and program structure necessary to compute the operator with the intrinsic. A prototype implementation for a dedicated hardware accelerator demonstrates state-of-the art performance for a wide range of convolutions, while being agnostic to the data layout. For some operators in the benchmark, the presented method can also generate alternative implementation strategies to improve hardware utilization, resulting in a geo-mean speed-up of ×2.813 while reducing the memory footprint. Lastly, by curating the initial set of possible implementations for the hardware-in-the-loop optimization, the median timeto- solution is reduced by a factor of ×2.40. At the same time, the possibility to have prolonged searches due a bad initial set of implementations is reduced, improving the optimization’s robustness by ×2.35

    24th Nordic Conference on Computational Linguistics (NoDaLiDa)

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    Sine Cosine Algorithm for Optimization

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    This open access book serves as a compact source of information on sine cosine algorithm (SCA) and a foundation for developing and advancing SCA and its applications. SCA is an easy, user-friendly, and strong candidate in the field of metaheuristics algorithms. Despite being a relatively new metaheuristic algorithm, it has achieved widespread acceptance among researchers due to its easy implementation and robust optimization capabilities. Its effectiveness and advantages have been demonstrated in various applications ranging from machine learning, engineering design, and wireless sensor network to environmental modeling. The book provides a comprehensive account of the SCA, including details of the underlying ideas, the modified versions, various applications, and a working MATLAB code for the basic SCA

    Partitioning algorithms for induced subgraph problems

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    This dissertation introduces the MCSPLIT family of algorithms for two closely-related NP-hard problems that involve finding a large induced subgraph contained by each of two input graphs: the induced subgraph isomorphism problem and the maximum common induced subgraph problem. The MCSPLIT algorithms resemble forward-checking constrant programming algorithms, but use problem-specific data structures that allow multiple, identical domains to be stored without duplication. These data structures enable fast, simple constraint propagation algorithms and very fast calculation of upper bounds. Versions of these algorithms for both sparse and dense graphs are described and implemented. The resulting algorithms are over an order of magnitude faster than the best existing algorithm for maximum common induced subgraph on unlabelled graphs, and outperform the state of the art on several classes of induced subgraph isomorphism instances. A further advantage of the MCSPLIT data structures is that variables and values are treated identically; this allows us to choose to branch on variables representing vertices of either input graph with no overhead. An extensive set of experiments shows that such two-sided branching can be particularly beneficial if the two input graphs have very different orders or densities. Finally, we turn from subgraphs to supergraphs, tackling the problem of finding a small graph that contains every member of a given family of graphs as an induced subgraph. Exact and heuristic techniques are developed for this problem, in each case using a MCSPLIT algorithm as a subroutine. These algorithms allow us to add new terms to two entries of the On-Line Encyclopedia of Integer Sequences

    WiFi-Based Human Activity Recognition Using Attention-Based BiLSTM

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    Recently, significant efforts have been made to explore human activity recognition (HAR) techniques that use information gathered by existing indoor wireless infrastructures through WiFi signals without demanding the monitored subject to carry a dedicated device. The key intuition is that different activities introduce different multi-paths in WiFi signals and generate different patterns in the time series of channel state information (CSI). In this paper, we propose and evaluate a full pipeline for a CSI-based human activity recognition framework for 12 activities in three different spatial environments using two deep learning models: ABiLSTM and CNN-ABiLSTM. Evaluation experiments have demonstrated that the proposed models outperform state-of-the-art models. Also, the experiments show that the proposed models can be applied to other environments with different configurations, albeit with some caveats. The proposed ABiLSTM model achieves an overall accuracy of 94.03%, 91.96%, and 92.59% across the 3 target environments. While the proposed CNN-ABiLSTM model reaches an accuracy of 98.54%, 94.25% and 95.09% across those same environments

    Proof-theoretic Semantics for Intuitionistic Multiplicative Linear Logic

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    This work is the first exploration of proof-theoretic semantics for a substructural logic. It focuses on the base-extension semantics (B-eS) for intuitionistic multiplicative linear logic (IMLL). The starting point is a review of Sandqvist’s B-eS for intuitionistic propositional logic (IPL), for which we propose an alternative treatment of conjunction that takes the form of the generalized elimination rule for the connective. The resulting semantics is shown to be sound and complete. This motivates our main contribution, a B-eS for IMLL , in which the definitions of the logical constants all take the form of their elimination rule and for which soundness and completeness are established
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