The spread of misinformation, propaganda, and flawed argumentation has been amplified in the Internet era. Given the volume of data and the subtlety of identifying violations of argumentation norms, supporting information analytics tasks, like content moderation, with trustworthy methods that can identify logical fallacies is essential. In this paper, we formalize prior theoretical work on logical fallacies into a comprehensive three-stage evaluation framework of detection, coarse-grained, and fine-grained classification. We adapt existing evaluation datasets for each stage of the evaluation. We employ three families of robust and explainable methods based on prototype reasoning, instance-based reasoning, and knowledge injection. The methods combine language models with background knowledge and explainable mechanisms. Moreover, we address data sparsity with strategies for data augmentation and curriculum learning. Our three-stage framework natively consolidates prior datasets and methods from existing tasks, like propaganda detection, serving as an overarching evaluation testbed. We extensively evaluate these methods on our datasets, focusing on their robustness and explainability. Our results provide insight into the strengths and weaknesses of the methods on different components and fallacy classes, indicating that fallacy identification is a challenging task that may require specialized forms of reasoning to capture various classes. We share our open-source code and data on GitHub to support further work on logical fallacy identification.
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In [Bonito et al., J. Comput. Phys. (2022)], a local discontinous Galerkin method was proposed for approximating the large bending of prestrained plates, and in [Bonito et al., IMA J. Numer. Anal. (2023)] the numerical properties of this method were explored. These works considered deformations driven predominantly by bending. Thus, a bending energy with a metric constraint was considered. We extend these results to the case of an energy with both a bending component and a nonconvex stretching component, and we also consider folding across a crease. The proposed discretization of this energy features a continuous finite element space, as well as a discrete Hessian operator. We establish the $\Gamma$-convergence of the discrete to the continuous energy and also present an energy-decreasing gradient flow for finding critical points of the discrete energy. Finally, we provide numerical simulations illustrating the convergence of minimizers and the capabilities of the model.
We consider the problem of classifying those graphs that arise as an undirected square of an oriented graph by generalising the notion of quasi-transitive directed graphs to mixed graphs. We fully classify those graphs of maximum degree three and those graphs of girth at least four that arise an undirected square of an oriented graph. In contrast to the recognition problem for graphs that admit a quasi-transitive orientation, we find it is NP-complete to decide if a graph admits a partial orientation as a quasi-transitive mixed graph. We prove the problem is Polynomial when restricted to inputs of maximum degree three, but remains NP-complete when restricted to inputs with maximum degree at least five. Our proof further implies that for fixed $k \geq 3$, it is NP-complete to decide if a graph arises as an undirected square of an orientation of a graph with $\Delta = k$.
Large Language Models (LLMs) are often misleadingly recognized as having a personality or a set of values. We argue that an LLM can be seen as a superposition of perspectives with different values and personality traits. LLMs exhibit context-dependent values and personality traits that change based on the induced perspective (as opposed to humans, who tend to have more coherent values and personality traits across contexts). We introduce the concept of perspective controllability, which refers to a model's affordance to adopt various perspectives with differing values and personality traits. In our experiments, we use questionnaires from psychology (PVQ, VSM, IPIP) to study how exhibited values and personality traits change based on different perspectives. Through qualitative experiments, we show that LLMs express different values when those are (implicitly or explicitly) implied in the prompt, and that LLMs express different values even when those are not obviously implied (demonstrating their context-dependent nature). We then conduct quantitative experiments to study the controllability of different models (GPT-4, GPT-3.5, OpenAssistant, StableVicuna, StableLM), the effectiveness of various methods for inducing perspectives, and the smoothness of the models' drivability. We conclude by examining the broader implications of our work and outline a variety of associated scientific questions. The project website is available at //sites.google.com/view/llm-superpositions .
Convex relaxations are a key component of training and certifying provably safe neural networks. However, despite substantial progress, a wide and poorly understood accuracy gap to standard networks remains, raising the question of whether this is due to fundamental limitations of convex relaxations. Initial work investigating this question focused on the simple and widely used IBP relaxation. It revealed that some univariate, convex, continuous piecewise linear (CPWL) functions cannot be encoded by any ReLU network such that its IBP-analysis is precise. To explore whether this limitation is shared by more advanced convex relaxations, we conduct the first in-depth study on the expressive power of ReLU networks across all commonly used convex relaxations. We show that: (i) more advanced relaxations allow a larger class of univariate functions to be expressed as precisely analyzable ReLU networks, (ii) more precise relaxations can allow exponentially larger solution spaces of ReLU networks encoding the same functions, and (iii) even using the most precise single-neuron relaxations, it is impossible to construct precisely analyzable ReLU networks that express multivariate, convex, monotone CPWL functions.
This work studies a central extremal graph theory problem inspired by a 1975 conjecture of Erd\H{o}s, which aims to find graphs with a given size (number of nodes) that maximize the number of edges without having 3- or 4-cycles. We formulate this problem as a sequential decision-making problem and compare AlphaZero, a neural network-guided tree search, with tabu search, a heuristic local search method. Using either method, by introducing a curriculum -- jump-starting the search for larger graphs using good graphs found at smaller sizes -- we improve the state-of-the-art lower bounds for several sizes. We also propose a flexible graph-generation environment and a permutation-invariant network architecture for learning to search in the space of graphs.
This paper presents a comprehensive evaluation of the code generation capabilities of ChatGPT, a prominent large language model, compared to human programmers. A novel dataset of 131 code-generation prompts across 5 categories was curated to enable robust analysis. Code solutions were generated by both ChatGPT and humans for all prompts, resulting in 262 code samples. A meticulous manual assessment methodology prioritized evaluating correctness, comprehensibility, and security using 14 established code quality metrics. The key findings reveal ChatGPT's strengths in crafting concise, efficient code with advanced constructs, showcasing strengths in data analysis tasks (93.1% accuracy) but limitations in visual-graphical challenges. Comparative analysis with human code highlights ChatGPT's inclination towards modular design and superior error handling. Additionally, machine learning models effectively distinguished ChatGPT from human code with up to 88% accuracy, suggesting detectable coding style disparities. By providing profound insights into ChatGPT's code generation capabilities and limitations through quantitative metrics and qualitative analysis, this study makes valuable contributions toward advancing AI-based programming assistants. The curated dataset and methodology offer a robust foundation for future research in this nascent domain. All data and codes are available on //github.com/DSAatUSU/ChatGPT-promises-and-pitfalls.
Weighted projective spaces are natural generalizations of projective spaces with a rich structure. Projective Reed-Muller codes are error-correcting codes that played an important role in reliably transmitting information on digital communication channels. In this case study, we explore the power of commutative and homological algebraic techniques to study weighted projective Reed-Muller (WPRM) codes on weighted projective spaces of the form $\mathbb{P}(1,1,a)$. We compute minimal free resolutions and thereby obtain Hilbert series for the vanishing ideal of the $\mathbb{F}_q$-rational points, and compute main parameters for these codes.
We proposed an extension of Akaike's relative power contribution that could be applied to data with correlations between noises. This method decomposes the power spectrum into a contribution of the terms caused by correlation between two noises, in addition to the contributions of the independent noises. Numerical examples confirm that some of the correlated noise has the effect of reducing the power spectrum.
We propose a framework for expressing and analyzing the Quality of Service (QoS) of message-passing systems using a choreographic model that consists of g-choreographies and Communicating Finite State machines (CFSMs). The following are our three main contributions: (I) an extension of CFSMs with non-functional contracts to specify quantitative constraints of local computations, (II) a dynamic temporal logic capable of expressing QoS, properties of systems relative to the g-choreography that specifies the communication protocol, (III) the semi-decidability of our logic which enables a bounded model-checking approach to verify QoS property of communicating systems.
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.
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