A hypergraph is conformal if it is the family of maximal cliques of a graph. In this paper we are interested in the problem of determining when is the family of minimal transversal of maximal cliques of a graph conformal. Such graphs are called clique dually conformal (CDC for short). As our main results, we completely characterize CDC graphs within the families of triangle-free graphs and split graphs. Both characterizations lead to polynomial-time recognition algorithms. We also show that the class of CDC graphs is closed under substitution, in the strong sense that substituting a graph $H$ for a vertex of a graph $G$ results in a CDC graph if and only if both $G$ and $H$ are CDC.
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In this paper, we study the zero-error capacity of channels with memory, which are represented by graphs. We provide a method to construct code for any graph with one edge, thereby determining a lower bound on its zero-error capacity. Moreover, this code can achieve zero-error capacity when the symbols in a vertex with degree one are the same. We further apply our method to the one-edge graphs representing the binary channels with two memories. There are 28 possible graphs, which can be organized into 11 categories based on their symmetries. The code constructed by our method is proved to achieve the zero-error capacity for all these graphs except for the two graphs in Case 11.
This paper proposes a payoff perturbation technique for the Mirror Descent (MD) algorithm in games where the gradient of the payoff functions is monotone in the strategy profile space, potentially containing additive noise. The optimistic family of learning algorithms, exemplified by optimistic MD, successfully achieves {\it last-iterate} convergence in scenarios devoid of noise, leading the dynamics to a Nash equilibrium. A recent re-emerging trend underscores the promise of the perturbation approach, where payoff functions are perturbed based on the distance from an anchoring, or {\it slingshot}, strategy. In response, we propose {\it Adaptively Perturbed MD} (APMD), which adjusts the magnitude of the perturbation by repeatedly updating the slingshot strategy at a predefined interval. This innovation empowers us to find a Nash equilibrium of the underlying game with guaranteed rates. Empirical demonstrations affirm that our algorithm exhibits significantly accelerated convergence.
We consider the parameter estimation problem in the deviated Gaussian mixture of experts in which the data are generated from $(1 - \lambda^{\ast}) g_0(Y| X)+ \lambda^{\ast} \sum_{i = 1}^{k_{\ast}} p_{i}^{\ast} f(Y|(a_{i}^{\ast})^{\top}X+b_i^{\ast},\sigma_{i}^{\ast})$, where $X, Y$ are respectively a covariate vector and a response variable, $g_{0}(Y|X)$ is a known function, $\lambda^{\ast} \in [0, 1]$ is true but unknown mixing proportion, and $(p_{i}^{\ast}, a_{i}^{\ast}, b_{i}^{\ast}, \sigma_{i}^{\ast})$ for $1 \leq i \leq k^{\ast}$ are unknown parameters of the Gaussian mixture of experts. This problem arises from the goodness-of-fit test when we would like to test whether the data are generated from $g_{0}(Y|X)$ (null hypothesis) or they are generated from the whole mixture (alternative hypothesis). Based on the algebraic structure of the expert functions and the distinguishability between $g_0$ and the mixture part, we construct novel Voronoi-based loss functions to capture the convergence rates of maximum likelihood estimation (MLE) for our models. We further demonstrate that our proposed loss functions characterize the local convergence rates of parameter estimation more accurately than the generalized Wasserstein, a loss function being commonly used for estimating parameters in the Gaussian mixture of experts.
This paper presents novel approaches to parallelizing particle interactions on a GPU when there are few particles per cell and the interactions are limited by a cutoff distance. The paper surveys classical algorithms and then introduces two alternatives that aim to utilize shared memory. The first approach copies the particles of a sub-box, while the second approach loads particles in a pencil along the X-axis. The different implementations are compared on three GPU models using Cuda and Hip. The results show that the X-pencil approach can provide a significant speedup but only in very specific cases.
In climate science, we often want to compare across different datasets. Difficulties can arise in doing this due to inevitable mismatches that arise between observational and reanalysis data, or even between different reanalyses. This misalignment can raise problems for any work that seeks to make inferences about one dataset from another. We considered tropical cyclone location as an example task with one dataset providing atmospheric conditions (ERA5) and another providing storm tracks (IBTrACS). We found that while the examples often aligned well, there were a considerable proportion (around 25%) which were not well aligned. We trained a neural network to map from the wind field to the storm location; in this setting misalignment in the datasets appears as "label noise" (i.e. the labelled storm location does not correspond to the underlying wind field). We found that this neural network trained only on the often noisy labels from IBTrACS had a denoising effect, and performed better than the IBTrACS labels themselves, as measured by human preferences. Remarkably, this even held true for training points, on which we might have expected the network to overfit to the IBTrACS predictions.
Socio-demographic prompting is a commonly employed approach to study cultural biases in LLMs as well as for aligning models to certain cultures. In this paper, we systematically probe four LLMs (Llama 3, Mistral v0.2, GPT-3.5 Turbo and GPT-4) with prompts that are conditioned on culturally sensitive and non-sensitive cues, on datasets that are supposed to be culturally sensitive (EtiCor and CALI) or neutral (MMLU and ETHICS). We observe that all models except GPT-4 show significant variations in their responses on both kinds of datasets for both kinds of prompts, casting doubt on the robustness of the culturally-conditioned prompting as a method for eliciting cultural bias in models or as an alignment strategy. The work also calls rethinking the control experiment design to tease apart the cultural conditioning of responses from "placebo effect", i.e., random perturbations of model responses due to arbitrary tokens in the prompt.
In this paper, we consider maintaining strongly connected components (SCCs) of a directed planar graph subject to edge insertions and deletions. We show a data structure maintaining an implicit representation of the SCCs within $\tilde{O}(n^{6/7})$ worst-case time per update. The data structure supports, in $O(\log^2{n})$ time, reporting vertices of any specified SCC (with constant overhead per reported vertex) and aggregating vertex information (e.g., computing the maximum label) over all the vertices of that SCC. Furthermore, it can maintain global information about the structure of SCCs, such as the number of SCCs or the size of the largest SCC. To the best of our knowledge, no fully dynamic SCCs data structures with sublinear update time have been previously known for any major subclass of digraphs. Our result should be contrasted with the known $n^{1-o(1)}$ amortized update time lower bound conditional on SETH, which holds even for dynamically maintaining whether a general digraph has more than two SCCs.
Knowledge graphs represent factual knowledge about the world as relationships between concepts and are critical for intelligent decision making in enterprise applications. New knowledge is inferred from the existing facts in the knowledge graphs by encoding the concepts and relations into low-dimensional feature vector representations. The most effective representations for this task, called Knowledge Graph Embeddings (KGE), are learned through neural network architectures. Due to their impressive predictive performance, they are increasingly used in high-impact domains like healthcare, finance and education. However, are the black-box KGE models adversarially robust for use in domains with high stakes? This thesis argues that state-of-the-art KGE models are vulnerable to data poisoning attacks, that is, their predictive performance can be degraded by systematically crafted perturbations to the training knowledge graph. To support this argument, two novel data poisoning attacks are proposed that craft input deletions or additions at training time to subvert the learned model's performance at inference time. These adversarial attacks target the task of predicting the missing facts in knowledge graphs using KGE models, and the evaluation shows that the simpler attacks are competitive with or outperform the computationally expensive ones. The thesis contributions not only highlight and provide an opportunity to fix the security vulnerabilities of KGE models, but also help to understand the black-box predictive behaviour of KGE models.
Deep Convolutional Neural Networks have pushed the state-of-the art for semantic segmentation provided that a large amount of images together with pixel-wise annotations is available. Data collection is expensive and a solution to alleviate it is to use transfer learning. This reduces the amount of annotated data required for the network training but it does not get rid of this heavy processing step. We propose a method of transfer learning without annotations on the target task for datasets with redundant content and distinct pixel distributions. Our method takes advantage of the approximate content alignment of the images between two datasets when the approximation error prevents the reuse of annotation from one dataset to another. Given the annotations for only one dataset, we train a first network in a supervised manner. This network autonomously learns to generate deep data representations relevant to the semantic segmentation. Then the images in the new dataset, we train a new network to generate a deep data representation that matches the one from the first network on the previous dataset. The training consists in a regression between feature maps and does not require any annotations on the new dataset. We show that this method reaches performances similar to a classic transfer learning on the PASCAL VOC dataset with synthetic transformations.
Image segmentation is an important component of many image understanding systems. It aims to group pixels in a spatially and perceptually coherent manner. Typically, these algorithms have a collection of parameters that control the degree of over-segmentation produced. It still remains a challenge to properly select such parameters for human-like perceptual grouping. In this work, we exploit the diversity of segments produced by different choices of parameters. We scan the segmentation parameter space and generate a collection of image segmentation hypotheses (from highly over-segmented to under-segmented). These are fed into a cost minimization framework that produces the final segmentation by selecting segments that: (1) better describe the natural contours of the image, and (2) are more stable and persistent among all the segmentation hypotheses. We compare our algorithm's performance with state-of-the-art algorithms, showing that we can achieve improved results. We also show that our framework is robust to the choice of segmentation kernel that produces the initial set of hypotheses.
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