Concurrency is an important aspect of (Petri) nets to describe and simulate the behavior of complex systems. Knowing which places and transitions could be executed in parallel helps to understand nets and enables analysis techniques and the computation of other properties, such as causality, exclusivity, etc.. All techniques based on concurrency detection depend on the efficiency of this detection methodology. Kovalyov and Esparza have developed algorithms that compute all concurrent places in $O\big((P+T)TP^2\big)$ for live nets (where $P$ and $T$ are the numbers of places and transitions) and in $O\big(P(P+T)^2\big)$ for live free-choice nets. Although these algorithms have a reasonably good computational complexity, large numbers of concurrent pairs of nodes may still lead to long computation times. Furthermore, both algorithms cannot be parallelized without additional effort. This paper complements the palette of concurrency detection algorithms with the Concurrent Paths (CP) algorithm for safe, live, free-choice nets. The algorithm allows parallelization and has a worst-case computational complexity of $O\big((P+T)^2\big)$ for acyclic nets and of $O\big(P^3+PT^2\big)$ for cyclic nets. Although the computational complexity of cyclic nets has not improved, the evaluation shows the benefits of CP, especially, if the net contains many nodes in concurrency relation.
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Trustworthy AI is crucial to the widespread adoption of AI in high-stakes applications with fairness, robustness, and accuracy being some of the key trustworthiness metrics. In this work, we propose a controllable framework for data-centric trustworthy AI (DCTAI)- VTruST, that allows users to control the trade-offs between the different trustworthiness metrics of the constructed training datasets. A key challenge in implementing an efficient DCTAI framework is to design an online value-function-based training data subset selection algorithm. We pose the training data valuation and subset selection problem as an online sparse approximation formulation. We propose a novel online version of the Orthogonal Matching Pursuit (OMP) algorithm for solving this problem. Experimental results show that VTruST outperforms the state-of-the-art baselines on social, image, and scientific datasets. We also show that the data values generated by VTruST can provide effective data-centric explanations for different trustworthiness metrics.
We propose CAPGrasp, an $\mathbb{R}^3\times \text{SO(2)-equivariant}$ 6-DoF continuous approach-constrained generative grasp sampler. It includes a novel learning strategy for training CAPGrasp that eliminates the need to curate massive conditionally labeled datasets and a constrained grasp refinement technique that improves grasp poses while respecting the grasp approach directional constraints. The experimental results demonstrate that CAPGrasp is more than three times as sample efficient as unconstrained grasp samplers while achieving up to 38% grasp success rate improvement. CAPGrasp also achieves 4-10% higher grasp success rates than constrained but noncontinuous grasp samplers. Overall, CAPGrasp is a sample-efficient solution when grasps must originate from specific directions, such as grasping in confined spaces.
Cedar is a new authorization policy language designed to be ergonomic, fast, safe, and analyzable. Rather than embed authorization logic in an application's code, developers can write that logic as Cedar policies and delegate access decisions to Cedar's evaluation engine. Cedar's simple and intuitive syntax supports common authorization use-cases with readable policies, naturally leveraging concepts from role-based, attribute-based, and relation-based access control models. Cedar's policy structure enables access requests to be decided quickly. Cedar's policy validator leverages optional typing to help policy writers avoid mistakes, but not get in their way. Cedar's design has been finely balanced to allow for a sound and complete logical encoding, which enables precise policy analysis, e.g., to ensure that when refactoring a set of policies, the authorized permissions do not change. We have modeled Cedar in the Lean programming language, and used Lean's proof assistant to prove important properties of Cedar's design. We have implemented Cedar in Rust, and released it open-source. Comparing Cedar to two open-source languages, OpenFGA and Rego, we find (subjectively) that Cedar has equally or more readable policies, but (objectively) performs far better.
The performance of CLIP in dynamic facial expression recognition (DFER) task doesn't yield exceptional results as observed in other CLIP-based classification tasks. While CLIP's primary objective is to achieve alignment between images and text in the feature space, DFER poses challenges due to the abstract nature of text and the dynamic nature of video, making label representation limited and perfect alignment difficult. To address this issue, we have designed A$^{3}$lign-DFER, which introduces a new DFER labeling paradigm to comprehensively achieve alignment, thus enhancing CLIP's suitability for the DFER task. Specifically, our A$^{3}$lign-DFER method is designed with multiple modules that work together to obtain the most suitable expanded-dimensional embeddings for classification and to achieve alignment in three key aspects: affective, dynamic, and bidirectional. We replace the input label text with a learnable Multi-Dimensional Alignment Token (MAT), enabling alignment of text to facial expression video samples in both affective and dynamic dimensions. After CLIP feature extraction, we introduce the Joint Dynamic Alignment Synchronizer (JAS), further facilitating synchronization and alignment in the temporal dimension. Additionally, we implement a Bidirectional Alignment Training Paradigm (BAP) to ensure gradual and steady training of parameters for both modalities. Our insightful and concise A$^{3}$lign-DFER method achieves state-of-the-art results on multiple DFER datasets, including DFEW, FERV39k, and MAFW. Extensive ablation experiments and visualization studies demonstrate the effectiveness of A$^{3}$lign-DFER. The code will be available in the future.
The $k$-principal component analysis ($k$-PCA) problem is a fundamental algorithmic primitive that is widely-used in data analysis and dimensionality reduction applications. In statistical settings, the goal of $k$-PCA is to identify a top eigenspace of the covariance matrix of a distribution, which we only have implicit access to via samples. Motivated by these implicit settings, we analyze black-box deflation methods as a framework for designing $k$-PCA algorithms, where we model access to the unknown target matrix via a black-box $1$-PCA oracle which returns an approximate top eigenvector, under two popular notions of approximation. Despite being arguably the most natural reduction-based approach to $k$-PCA algorithm design, such black-box methods, which recursively call a $1$-PCA oracle $k$ times, were previously poorly-understood. Our main contribution is significantly sharper bounds on the approximation parameter degradation of deflation methods for $k$-PCA. For a quadratic form notion of approximation we term ePCA (energy PCA), we show deflation methods suffer no parameter loss. For an alternative well-studied approximation notion we term cPCA (correlation PCA), we tightly characterize the parameter regimes where deflation methods are feasible. Moreover, we show that in all feasible regimes, $k$-cPCA deflation algorithms suffer no asymptotic parameter loss for any constant $k$. We apply our framework to obtain state-of-the-art $k$-PCA algorithms robust to dataset contamination, improving prior work both in sample complexity and approximation quality.
In order to compute the Fourier transform of a function $f$ on the real line numerically, one samples $f$ on a grid and then takes the discrete Fourier transform. We derive exact error estimates for this procedure in terms of the decay and smoothness of $f$. The analysis provides a new recipe of how to relate the number of samples, the sampling interval, and the grid size.
The remarkable capability of large language models (LLMs) for in-context learning (ICL) needs to be activated by demonstration examples. Prior work has extensively explored the selection of examples for ICL, predominantly following the "select then organize" paradigm, such approaches often neglect the internal relationships between examples and exist an inconsistency between the training and inference. In this paper, we formulate the problem as a $\textit{se}$quential $\textit{se}$lection problem and introduce $Se^2$, a sequential-aware method that leverages the LLM's feedback on varying context, aiding in capturing inter-relationships and sequential information among examples, significantly enriching the contextuality and relevance of ICL prompts. Meanwhile, we utilize beam search to seek and construct example sequences, enhancing both quality and diversity. Extensive experiments across 23 NLP tasks from 8 distinct categories illustrate that $Se^2$ markedly surpasses competitive baselines and achieves 42% relative improvement over random selection. Further in-depth analysis show the effectiveness of proposed strategies, highlighting $Se^2$'s exceptional stability and adaptability across various scenarios. Our code will be released to facilitate future research.
The permanent of a non-negative square matrix can be well approximated by finding the minimum of the Bethe free energy functions associated with some suitably defined factor graph; the resulting approximation to the permanent is called the Bethe permanent. Vontobel gave a combinatorial characterization of the Bethe permanent via degree-$M$ Bethe permanents, which is based on degree-$M$ covers of the underlying factor graph. In this paper, we prove a degree-$M$-Bethe-permanent-based lower bound on the permanent of a non-negative matrix, which solves a conjecture proposed by Vontobel in [IEEE Trans. Inf. Theory, Mar. 2013]. We also prove a degree-$M$-Bethe-permanent-based upper bound on the permanent of a non-negative matrix. In the limit $M \to \infty$, these lower and upper bounds yield known Bethe-permanent-based lower and upper bounds on the permanent of a non-negative matrix. Moreover, we prove similar results for an approximation to the permanent known as the (scaled) Sinkhorn permanent.
A convergent numerical method for $\alpha$-dissipative solutions of the Hunter--Saxton equation is derived. The method is based on applying a tailor-made projection operator to the initial data, and then solving exactly using the generalized method of characteristics. The projection step is the only step that introduces any approximation error. It is therefore crucial that its design ensures not only a good approximation of the initial data, but also that errors due to the energy dissipation at later times remain small. Furthermore, it is shown that the main quantity of interest, the wave profile, converges in $L^{\infty}$ for all $t \geq 0$, while a subsequence of the energy density converges weakly for almost every time.
Most existing works in visual question answering (VQA) are dedicated to improving the accuracy of predicted answers, while disregarding the explanations. We argue that the explanation for an answer is of the same or even more importance compared with the answer itself, since it makes the question and answering process more understandable and traceable. To this end, we propose a new task of VQA-E (VQA with Explanation), where the computational models are required to generate an explanation with the predicted answer. We first construct a new dataset, and then frame the VQA-E problem in a multi-task learning architecture. Our VQA-E dataset is automatically derived from the VQA v2 dataset by intelligently exploiting the available captions. We have conducted a user study to validate the quality of explanations synthesized by our method. We quantitatively show that the additional supervision from explanations can not only produce insightful textual sentences to justify the answers, but also improve the performance of answer prediction. Our model outperforms the state-of-the-art methods by a clear margin on the VQA v2 dataset.
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