Different notions of the consistency of obligations collapse in standard deontic logic. In justification logics, which feature explicit reasons for obligations, the situation is different. Their strength depends on a constant specification and on the available set of operations for combining different reasons. We present different consistency principles in justification logic and compare their logical strength. We propose a novel semantics for which justification logics with the explicit version of axiom D, jd, are complete for arbitrary constant specifications. Consistency is sometimes formulated in terms of permission. We therefore study permission in the context of justification logic, introducing a notion of free-choice permission for the first time. We then discuss the philosophical implications with regard to some deontic paradoxes.
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The notion of variation is introduced for the Boolean set and based on which Boolean logic backpropagation principle is developed. Using this concept, deep models can be built with weights and activations being Boolean numbers and operated with Boolean logic instead of real arithmetic. In particular, Boolean deep models can be trained directly in the Boolean domain without latent weights. No gradient but logic is synthesized and backpropagated through layers.
We study versions of Kleene algebra with dynamic tests, that is, extensions of Kleene algebra with domain and antidomain operators. We show that Kleene algebras with tests and Propositional dynamic logic correspond to special cases of the dynamic test framework. In particular, we establish completeness results with respect to relational models and guarded-language models, and we show that two prominent classes of Kleene algebras with dynamic tests have an EXPTIME-complete equational theory.
Integrating different functionalities, conventionally implemented as dedicated systems, into a single platform allows utilising the available resources more efficiently. We consider an integrated sensing and power transfer (ISAPT) system and propose the joint optimisation of the rectangular pulse-shaped transmit signal and the beamforming vector to combine sensing and wireless power transfer (WPT) functionalities efficiently. In contrast to prior works, we adopt an accurate non-linear circuit-based energy harvesting (EH) model. We formulate and solve a non-convex optimisation problem for a general number of EH receivers to maximise a weighted sum of the average harvested powers at the EH receivers while ensuring the received echo signal reflected by a sensing target (ST) has sufficient power for estimating the range to the ST with a prescribed accuracy within the considered coverage region. The average harvested power is shown to monotonically increase with the pulse duration when the average transmit power budget is sufficiently large. We discuss the trade-off between sensing performance and power transfer for the considered ISAPT system. The proposed approach significantly outperforms a heuristic baseline scheme based on a linear EH model, which linearly combines energy beamforming with the beamsteering vector in the direction to the ST as its transmit strategy.
The first part of this thesis focuses on maximizing the overall recommendation accuracy. This accuracy is usually evaluated with some user-oriented metric tailored to the recommendation scenario, but because recommendation is usually treated as a machine learning problem, recommendation models are trained to maximize some other generic criteria that does not necessarily align with the criteria ultimately captured by the user-oriented evaluation metric. Recent research aims at bridging this gap between training and evaluation via direct ranking optimization, but still assumes that the metric used for evaluation should also be the metric used for training. We challenge this assumption, mainly because some metrics are more informative than others. Indeed, we show that models trained via the optimization of a loss inspired by Rank-Biased Precision (RBP) tend to yield higher accuracy, even when accuracy is measured with metrics other than RBP. However, the superiority of this RBP-inspired loss stems from further benefiting users who are already well-served, rather than helping those who are not. This observation inspires the second part of this thesis, where our focus turns to helping non-mainstream users. These are users who are difficult to recommend to either because there is not enough data to model them, or because they have niche taste and thus few similar users to look at when recommending in a collaborative way. These differences in mainstreamness introduce a bias reflected in an accuracy gap between users or user groups, which we try to narrow.
We define a new class of predicates called equilevel predicates on a distributive lattice which eases the analysis of parallel algorithms. Many combinatorial problems such as the vertex cover problem, the bipartite matching problem, and the minimum spanning tree problem can be modeled as detecting an equilevel predicate. The problem of detecting an equilevel problem is NP-complete, but equilevel predicates with the helpful property can be detected in polynomial time in an online manner. An equilevel predicate has the helpful property with a polynomial time algorithm if the algorithm can return a nonempty set of indices such that advancing on any of them can be used to detect the predicate. Furthermore, the refined independently helpful property allows online parallel detection of such predicates in NC. When the independently helpful property holds, advancing on all the specified indices in parallel can be used to detect the predicate in polylogarithmic time. We also define a special class of equilevel predicates called solitary predicates. Unless NP = RP, this class of predicate also does not admit efficient algorithms. Earlier work has shown that solitary predicates with the efficient advancement can be detected in polynomial time. We introduce two properties called the antimonotone advancement and the efficient rejection which yield the detection of solitary predicates in NC. Finally, we identify the minimum spanning tree, the shortest path, and the conjunctive predicate detection as problems satisfying such properties, giving alternative certifications of their NC memberships as a result.
Graph-based kNN algorithms have garnered widespread popularity for machine learning tasks due to their simplicity and effectiveness. However, as factual data often inherit complex distributions, the conventional kNN graph's reliance on a unified k-value can hinder its performance. A crucial factor behind this challenge is the presence of ambiguous samples along decision boundaries that are inevitably more prone to incorrect classifications. To address the situation, we propose the Distribution-Informed adaptive kNN Graph (DaNNG), which combines adaptive kNN with distribution-aware graph construction. By incorporating an approximation of the distribution with customized k-adaption criteria, DaNNG can significantly improve performance on ambiguous samples, and hence enhance overall accuracy and generalization capability. Through rigorous evaluations on diverse benchmark datasets, DaNNG outperforms state-of-the-art algorithms, showcasing its adaptability and efficacy across various real-world scenarios.
In the high performance computing (HPC) domain, performance variability is a major scalability issue for parallel computing applications with heavy synchronization and communication. In this paper, we present an experimental performance analysis of OpenMP benchmarks regarding the variation of execution time, and determine the potential factors causing performance variability. Our work offers some understanding of performance distributions and directions for future work on how to mitigate variability for OpenMP-based applications. Two representative OpenMP benchmarks from the EPCC OpenMP micro-benchmark suite and BabelStream are run across two x86 multicore platforms featuring up to 256 threads. From the obtained results, we characterize and explain the execution time variability as a function of thread-pinning, simultaneous multithreading (SMT) and core frequency variation.
We consider the problem of discovering $K$ related Gaussian directed acyclic graphs (DAGs), where the involved graph structures share a consistent causal order and sparse unions of supports. Under the multi-task learning setting, we propose a $l_1/l_2$-regularized maximum likelihood estimator (MLE) for learning $K$ linear structural equation models. We theoretically show that the joint estimator, by leveraging data across related tasks, can achieve a better sample complexity for recovering the causal order (or topological order) than separate estimations. Moreover, the joint estimator is able to recover non-identifiable DAGs, by estimating them together with some identifiable DAGs. Lastly, our analysis also shows the consistency of union support recovery of the structures. To allow practical implementation, we design a continuous optimization problem whose optimizer is the same as the joint estimator and can be approximated efficiently by an iterative algorithm. We validate the theoretical analysis and the effectiveness of the joint estimator in experiments.
Humans perceive the world by concurrently processing and fusing high-dimensional inputs from multiple modalities such as vision and audio. Machine perception models, in stark contrast, are typically modality-specific and optimised for unimodal benchmarks, and hence late-stage fusion of final representations or predictions from each modality (`late-fusion') is still a dominant paradigm for multimodal video classification. Instead, we introduce a novel transformer based architecture that uses `fusion bottlenecks' for modality fusion at multiple layers. Compared to traditional pairwise self-attention, our model forces information between different modalities to pass through a small number of bottleneck latents, requiring the model to collate and condense the most relevant information in each modality and only share what is necessary. We find that such a strategy improves fusion performance, at the same time reducing computational cost. We conduct thorough ablation studies, and achieve state-of-the-art results on multiple audio-visual classification benchmarks including Audioset, Epic-Kitchens and VGGSound. All code and models will be released.
Dynamic programming (DP) solves a variety of structured combinatorial problems by iteratively breaking them down into smaller subproblems. In spite of their versatility, DP algorithms are usually non-differentiable, which hampers their use as a layer in neural networks trained by backpropagation. To address this issue, we propose to smooth the max operator in the dynamic programming recursion, using a strongly convex regularizer. This allows to relax both the optimal value and solution of the original combinatorial problem, and turns a broad class of DP algorithms into differentiable operators. Theoretically, we provide a new probabilistic perspective on backpropagating through these DP operators, and relate them to inference in graphical models. We derive two particular instantiations of our framework, a smoothed Viterbi algorithm for sequence prediction and a smoothed DTW algorithm for time-series alignment. We showcase these instantiations on two structured prediction tasks and on structured and sparse attention for neural machine translation.
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