348 research outputs found
Classical and quantum algorithms for scaling problems
This thesis is concerned with scaling problems, which have a plethora of connections to different areas of mathematics, physics and computer science. Although many structural aspects of these problems are understood by now, we only know how to solve them efficiently in special cases.We give new algorithms for non-commutative scaling problems with complexity guarantees that match the prior state of the art. To this end, we extend the well-known (self-concordance based) interior-point method (IPM) framework to Riemannian manifolds, motivated by its success in the commutative setting. Moreover, the IPM framework does not obviously suffer from the same obstructions to efficiency as previous methods. It also yields the first high-precision algorithms for other natural geometric problems in non-positive curvature.For the (commutative) problems of matrix scaling and balancing, we show that quantum algorithms can outperform the (already very efficient) state-of-the-art classical algorithms. Their time complexity can be sublinear in the input size; in certain parameter regimes they are also optimal, whereas in others we show no quantum speedup over the classical methods is possible. Along the way, we provide improvements over the long-standing state of the art for searching for all marked elements in a list, and computing the sum of a list of numbers.We identify a new application in the context of tensor networks for quantum many-body physics. We define a computable canonical form for uniform projected entangled pair states (as the solution to a scaling problem), circumventing previously known undecidability results. We also show, by characterizing the invariant polynomials, that the canonical form is determined by evaluating the tensor network contractions on networks of bounded size
LIPIcs, Volume 251, ITCS 2023, Complete Volume
LIPIcs, Volume 251, ITCS 2023, Complete Volum
Generalized Planning as Heuristic Search: A new planning search-space that leverages pointers over objects
Planning as heuristic search is one of the most successful approaches to
classical planning but unfortunately, it does not extend trivially to
Generalized Planning (GP). GP aims to compute algorithmic solutions that are
valid for a set of classical planning instances from a given domain, even if
these instances differ in the number of objects, the number of state variables,
their domain size, or their initial and goal configuration. The generalization
requirements of GP make it impractical to perform the state-space search that
is usually implemented by heuristic planners. This paper adapts the planning as
heuristic search paradigm to the generalization requirements of GP, and
presents the first native heuristic search approach to GP. First, the paper
introduces a new pointer-based solution space for GP that is independent of the
number of classical planning instances in a GP problem and the size of those
instances (i.e. the number of objects, state variables and their domain sizes).
Second, the paper defines a set of evaluation and heuristic functions for
guiding a combinatorial search in our new GP solution space. The computation of
these evaluation and heuristic functions does not require grounding states or
actions in advance. Therefore our GP as heuristic search approach can handle
large sets of state variables with large numerical domains, e.g.~integers.
Lastly, the paper defines an upgraded version of our novel algorithm for GP
called Best-First Generalized Planning (BFGP), that implements a best-first
search in our pointer-based solution space, and that is guided by our
evaluation/heuristic functions for GP.Comment: Under review in the Artificial Intelligence Journal (AIJ
Longest Common Subsequence with Gap Constraints
We consider the longest common subsequence problem in the context of
subsequences with gap constraints. In particular, following Day et al. 2022, we
consider the setting when the distance (i. e., the gap) between two consecutive
symbols of the subsequence has to be between a lower and an upper bound (which
may depend on the position of those symbols in the subsequence or on the
symbols bordering the gap) as well as the case where the entire subsequence is
found in a bounded range (defined by a single upper bound), considered by
Kosche et al. 2022. In all these cases, we present effcient algorithms for
determining the length of the longest common constrained subsequence between
two given strings
LIPIcs, Volume 261, ICALP 2023, Complete Volume
LIPIcs, Volume 261, ICALP 2023, Complete Volum
Large Data-to-Text Generation
This thesis presents a domain-driven approach to sports game summarization, a specific instance of large data-to-text generation (DTG). We first address the data fidelity issue in the Rotowire dataset by supplementing existing input records and demonstrating larger relative improvements compared to previously proposed purification schemes. As this method further increases the total number of input records, we alternatively formulate this problem as a multimodal problem (i.e. visual data-to-text), discussing potential advantages over purely textual approaches and studying its effectiveness for future expansion. We work exclusively with pre-trained end-to-end transformers throughout, allowing us to evaluate the efficacy of sparse attention and multimodal encoder-decoders in DTG and providing appropriate benchmarks for future work.
To automatically evaluate the statistical correctness of generated summaries, we also extend prior work on automatic relation extraction and build an updated pipeline that incorporates low amounts of human-annotated data which are quickly inflated via data augmentation. By formulating this in a ”text-to-text” fashion, we are able to take advantage of LLMs and achieve significantly higher precision and recall than previous methods while tracking three times the number of unique relations. Our updated models are more consistent and reliable by incorporating human-verified data partitions into the training and evaluation process
Applications
Volume 3 describes how resource-aware machine learning methods and techniques are used to successfully solve real-world problems. The book provides numerous specific application examples: in health and medicine for risk modelling, diagnosis, and treatment selection for diseases in electronics, steel production and milling for quality control during manufacturing processes in traffic, logistics for smart cities and for mobile communications
Data-aware conformance checking with SMT
Conformance checking is a key process mining task to confront the normative behavior imposed by a process model with the actual behavior recorded in a log. While this problem has been extensively studied for pure control-flow processes, data-aware conformance checking has received comparatively little attention. In this paper, we tackle the conformance checking problem for the challenging scenario of processes that combine data and control-flow dimensions. Concretely, we adopt the formalism of data Petri nets (DPNs) and show how solid, well-established automated reasoning techniques from the area of Satisfiability Modulo Theories (SMT) can be effectively harnessed to compute conformance metrics and optimal data-aware alignments. To this end, we introduce the CoCoMoT (Computing Conformance Modulo Theories) framework, with a fourfold contribution. First, we show how SMT allows to leverage SAT-based encodings for the pure control-flow setting to the data-aware case. Second, we introduce a novel preprocessing technique based on a notion of property-preserving clustering, to speed up the computation of conformance checking outputs. Third, we show how our approach extends seamlessly to the more comprehensive conformance checking artifacts of multi- and anti-alignments. Fourth, we describe a proof-of-concept implementation based on state-of-the-art SMT solvers, and report on experiments. Finally, we discuss how CoCoMoT directly lends itself to further process mining tasks like log analysis by clustering and model repair, and the use of SMT facilitates the support of even richer multi-perspective models, where, for example, more expressive DPN guards languages are considered or generic datatypes (other than integers or reals) are employed
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