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Group equivariance ensures consistent responses to group transformations of the input, leading to more robust models and enhanced generalization capabilities. However, this property can lead to overly constrained models if the symmetries considered in the group differ from those observed in data. While common methods address this by determining the appropriate level of symmetry at the dataset level, they are limited to supervised settings and ignore scenarios in which multiple levels of symmetry co-exist in the same dataset. For instance, pictures of cars and planes exhibit different levels of rotation, yet both are included in the CIFAR-10 dataset. In this paper, we propose a method able to detect the level of symmetry of each input without the need for labels. To this end, we derive a sufficient and necessary condition to learn the distribution of symmetries in the data. Using the learned distribution, we generate pseudo-labels that allow us to learn the levels of symmetry of each input in a self-supervised manner. We validate the effectiveness of our approach on synthetic datasets with different per-class levels of symmetries e.g. MNISTMultiple, in which digits are uniformly rotated within a class-dependent interval. We demonstrate that our method can be used for practical applications such as the generation of standardized datasets in which the symmetries are not present, as well as the detection of out-of-distribution symmetries during inference. By doing so, both the generalization and robustness of non-equivariant models can be improved. Our code is publicly available at //github.com/aurban0/ssl-sym.

Branch and bound methods which are based on the principle "divide and conquer" are a well established solution approach in single-objective integer programming. In multi-objective optimization branch and bound algorithms are increasingly attracting interest. However, the larger number of objectives raises additional difficulties for implicit enumeration approaches like branch and bound. Since bounding and pruning is considerably weaker in multiple objectives, many branches have to be (partially) searched and may not be pruned directly. The adaptive use of objective space information can guide the search in promising directions to determine a good approximation of the Pareto front already in early stages of the algorithm. In particular we focus in this article on improving the branching and queuing of subproblems and the handling of lower bound sets. In our numerical test we evaluate the impact of the proposed methods in comparison to a standard implementation of multiobjective branch and bound on knapsack problems, generalized assignment problems and (un)capacitated facility location problems.

Predictive algorithms are often trained by optimizing some loss function, to which regularization functions are added to impose a penalty for violating constraints. As expected, the addition of such regularization functions can change the minimizer of the objective. It is not well-understood which regularizers change the minimizer of the loss, and, when the minimizer does change, how it changes. We use property elicitation to take first steps towards understanding the joint relationship between the loss and regularization functions and the optimal decision for a given problem instance. In particular, we give a necessary and sufficient condition on loss and regularizer pairs for when a property changes with the addition of the regularizer, and examine some regularizers satisfying this condition standard in the fair machine learning literature. We empirically demonstrate how algorithmic decision-making changes as a function of both data distribution changes and hardness of the constraints.

We present a result according to which certain functions of covariance matrices are maximized at scalar multiples of the identity matrix. This is used to show that experimental designs that are optimal under an assumption of independent, homoscedastic responses can be minimax robust, in broad classes of alternate covariance structures. In particular it can justify the common practice of disregarding possible dependence, or heteroscedasticity, at the design stage of an experiment.

Existing out-of-distribution (OOD) methods have shown great success on balanced datasets but become ineffective in long-tailed recognition (LTR) scenarios where 1) OOD samples are often wrongly classified into head classes and/or 2) tail-class samples are treated as OOD samples. To address these issues, current studies fit a prior distribution of auxiliary/pseudo OOD data to the long-tailed in-distribution (ID) data. However, it is difficult to obtain such an accurate prior distribution given the unknowingness of real OOD samples and heavy class imbalance in LTR. A straightforward solution to avoid the requirement of this prior is to learn an outlier class to encapsulate the OOD samples. The main challenge is then to tackle the aforementioned confusion between OOD samples and head/tail-class samples when learning the outlier class. To this end, we introduce a novel calibrated outlier class learning (COCL) approach, in which 1) a debiased large margin learning method is introduced in the outlier class learning to distinguish OOD samples from both head and tail classes in the representation space and 2) an outlier-class-aware logit calibration method is defined to enhance the long-tailed classification confidence. Extensive empirical results on three popular benchmarks CIFAR10-LT, CIFAR100-LT, and ImageNet-LT demonstrate that COCL substantially outperforms state-of-the-art OOD detection methods in LTR while being able to improve the classification accuracy on ID data. Code is available at //github.com/mala-lab/COCL.

Recently, natural language generation (NLG) evaluation has shifted from a single-aspect to a multi-aspect paradigm, allowing for a more accurate assessment. Large language models (LLMs) achieve superior performance on various NLG evaluation tasks. However, current work often employs the LLM to independently evaluate different aspects, which largely ignores the rich correlation between various aspects. To fill this research gap, in this work, we propose an NLG evaluation metric called CoAScore. Powered by LLMs, the CoAScore utilizes multi-aspect knowledge through a CoA (\textbf{C}hain-\textbf{o}f-\textbf{A}spects) prompting framework when assessing the quality of a certain aspect. Specifically, for a given aspect to evaluate, we first prompt the LLM to generate a chain of aspects that are relevant to the target aspect and could be useful for the evaluation. We then collect evaluation scores for each generated aspect, and finally, leverage the knowledge of these aspects to improve the evaluation of the target aspect. We evaluate CoAScore across five NLG evaluation tasks (e.g., summarization, dialog response generation, etc) and nine aspects (e.g., overall quality, relevance, coherence, etc). Our experimental findings highlight that, in comparison to individual aspect evaluation, CoAScore exhibits a higher correlation with human judgments. This improvement significantly outperforms existing unsupervised evaluation metrics, whether for assessing overall quality or other aspects. We also conducted extensive ablation studies to validate the effectiveness of the three stages within the CoAScore framework and conducted case studies to show how the LLM performs in these stages. Our code and scripts are available.

Graph matching is a fundamental problem in pattern recognition, with many applications such as software analysis and computational biology. One well-known type of graph matching problem is graph isomorphism, which consists of deciding if two graphs are identical. Despite its usefulness, the properties that one may check using graph isomorphism are rather limited, since it only allows strict equality checks between two graphs. For example, it does not allow one to check complex structural properties such as if the target graph is an arbitrary length sequence followed by an arbitrary size loop. We propose a generalization of graph isomorphism that allows one to check such properties through a declarative specification. This specification is given in the form of a Regular Graph Pattern (ReGaP), a special type of graph, inspired by regular expressions, that may contain wildcard nodes that represent arbitrary structures such as variable-sized sequences or subgraphs. We propose a SAT-based algorithm for checking if a target graph matches a given ReGaP. We also propose a preprocessing technique for improving the performance of the algorithm and evaluate it through an extensive experimental evaluation on benchmarks from the CodeSearchNet dataset.

Pomset logic and BV are both logics that extend multiplicative linear logic (with Mix) with a third connective that is self-dual and non-commutative. Whereas pomset logic originates from the study of coherence spaces and proof nets, BV originates from the study of series-parallel orders, cographs, and proof systems. Both logics enjoy a cut-admissibility result, but for neither logic can this be done in the sequent calculus. Provability in pomset logic can be checked via a proof net correctness criterion and in BV via a deep inference proof system. It has long been conjectured that these two logics are the same. In this paper we show that this conjecture is false. We also investigate the complexity of the two logics, exhibiting a huge gap between the two. Whereas provability in BV is NP-complete, provability in pomset logic is $\Sigma_2^p$-complete. We also make some observations with respect to possible sequent systems for the two logics.

Pre-trained Language Models (PLMs) which are trained on large text corpus via self-supervised learning method, have yielded promising performance on various tasks in Natural Language Processing (NLP). However, though PLMs with huge parameters can effectively possess rich knowledge learned from massive training text and benefit downstream tasks at the fine-tuning stage, they still have some limitations such as poor reasoning ability due to the lack of external knowledge. Research has been dedicated to incorporating knowledge into PLMs to tackle these issues. In this paper, we present a comprehensive review of Knowledge-Enhanced Pre-trained Language Models (KE-PLMs) to provide a clear insight into this thriving field. We introduce appropriate taxonomies respectively for Natural Language Understanding (NLU) and Natural Language Generation (NLG) to highlight these two main tasks of NLP. For NLU, we divide the types of knowledge into four categories: linguistic knowledge, text knowledge, knowledge graph (KG), and rule knowledge. The KE-PLMs for NLG are categorized into KG-based and retrieval-based methods. Finally, we point out some promising future directions of KE-PLMs.

Object detection typically assumes that training and test data are drawn from an identical distribution, which, however, does not always hold in practice. Such a distribution mismatch will lead to a significant performance drop. In this work, we aim to improve the cross-domain robustness of object detection. We tackle the domain shift on two levels: 1) the image-level shift, such as image style, illumination, etc, and 2) the instance-level shift, such as object appearance, size, etc. We build our approach based on the recent state-of-the-art Faster R-CNN model, and design two domain adaptation components, on image level and instance level, to reduce the domain discrepancy. The two domain adaptation components are based on H-divergence theory, and are implemented by learning a domain classifier in adversarial training manner. The domain classifiers on different levels are further reinforced with a consistency regularization to learn a domain-invariant region proposal network (RPN) in the Faster R-CNN model. We evaluate our newly proposed approach using multiple datasets including Cityscapes, KITTI, SIM10K, etc. The results demonstrate the effectiveness of our proposed approach for robust object detection in various domain shift scenarios.