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Despite the impressive performance in a variety of complex tasks, modern large language models (LLMs) still have trouble dealing with some math problems that are simple and intuitive for humans, such as addition. While we can easily learn basic rules of addition and apply them to new problems of any length, LLMs struggle to do the same. Instead, they may rely on similar "cases" seen in the training corpus for help. We define these two different reasoning mechanisms as "rule-based reasoning" and "case-based reasoning". Since rule-based reasoning is essential for acquiring the systematic generalization ability, we aim to explore exactly whether transformers use rule-based or case-based reasoning for math problems. Through carefully designed intervention experiments on five math tasks, we confirm that transformers are performing case-based reasoning, no matter whether scratchpad is used, which aligns with the previous observations that transformers use subgraph matching/shortcut learning to reason. To mitigate such problems, we propose a Rule-Following Fine-Tuning (RFFT) technique to teach transformers to perform rule-based reasoning. Specifically, we provide explicit rules in the input and then instruct transformers to recite and follow the rules step by step. Through RFFT, we successfully enable LLMs fine-tuned on 1-5 digit addition to generalize to up to 12-digit addition with over 95% accuracy, which is over 40% higher than scratchpad. The significant improvement demonstrates that teaching LLMs to explicitly use rules helps them learn rule-based reasoning and generalize better in length.

The paper proposes the Quantum-SMOTE method, a novel solution that uses quantum computing techniques to solve the prevalent problem of class imbalance in machine learning datasets. Quantum-SMOTE, inspired by the Synthetic Minority Oversampling Technique (SMOTE), generates synthetic data points using quantum processes such as swap tests and quantum rotation. The process varies from the conventional SMOTE algorithm's usage of K-Nearest Neighbors (KNN) and Euclidean distances, enabling synthetic instances to be generated from minority class data points without relying on neighbor proximity. The algorithm asserts greater control over the synthetic data generation process by introducing hyperparameters such as rotation angle, minority percentage, and splitting factor, which allow for customization to specific dataset requirements. The approach is tested on a public dataset of TelecomChurn and evaluated alongside two prominent classification algorithms, Random Forest and Logistic Regression, to determine its impact along with varying proportions of synthetic data.

We study the feasibility of identifying epistemic uncertainty (reflecting a lack of knowledge), as opposed to aleatoric uncertainty (reflecting entropy in the underlying distribution), in the outputs of large language models (LLMs) over free-form text. In the absence of ground-truth probabilities, we explore a setting where, in order to (approximately) disentangle a given LLM's uncertainty, a significantly larger model stands in as a proxy for the ground truth. We show that small linear probes trained on the embeddings of frozen, pretrained models accurately predict when larger models will be more confident at the token level and that probes trained on one text domain generalize to others. Going further, we propose a fully unsupervised method that achieves non-trivial accuracy on the same task. Taken together, we interpret these results as evidence that LLMs naturally contain internal representations of different types of uncertainty that could potentially be leveraged to devise more informative indicators of model confidence in diverse practical settings.

Since the 1990s, recombinant growth theory has fascinated academic circles by proposing that new ideas flourish through reconfiguring existing ones, leading to accelerated innovation in science and technology. However, after three decades, a marked decline in scientific breakthroughs challenges this theory. We explore its potential limitations, suggesting that while it emphasizes complementarity among ideas, it overlooks the competitive dynamics between them and how this rivalry fosters major breakthroughs. Examining 20 scientific breakthroughs nominated by surveyed scientists, we reveal a recurring pattern where new ideas are intentionally crafted to challenge and replace established ones. Analyzing 19 million papers spanning a century, we consistently observe a negative correlation between reference atypicality, which reflects the effort to recombine more ideas, and paper disruption, indicating the extent to which this work represents major breakthroughs, across all fields, periods, and team sizes. Moreover, our analysis of a novel dataset, comparing early and subsequent versions of 2,461 papers, offers quasi-experimental evidence suggesting that additional efforts to increase reference atypicality indeed result in a reduction of disruption for the same paper. In summary, our analyses challenge recombinant growth theory, suggesting that scientific breakthroughs originate from a clear purpose to replace established, impactful ideas.

This paper proposes crack segmentation augmented by super resolution (SR) with deep neural networks. In the proposed method, a SR network is jointly trained with a binary segmentation network in an end-to-end manner. This joint learning allows the SR network to be optimized for improving segmentation results. For realistic scenarios, the SR network is extended from non-blind to blind for processing a low-resolution image degraded by unknown blurs. The joint network is improved by our proposed two extra paths that further encourage the mutual optimization between SR and segmentation. Comparative experiments with State of The Art (SoTA) segmentation methods demonstrate the superiority of our joint learning, and various ablation studies prove the effects of our contributions.

In this paper, we try to determine exact or bounds on the choosability, or list chromatic numbers of some Cayley graphs, typically some Unitary Cayley graphs and Cayley graphs on Dihedral groups.

This paper proposes an innovative Attention-GAN framework for enhancing cybersecurity, focusing on anomaly detection. In response to the challenges posed by the constantly evolving nature of cyber threats, the proposed approach aims to generate diverse and realistic synthetic attack scenarios, thereby enriching the dataset and improving threat identification. Integrating attention mechanisms with Generative Adversarial Networks (GANs) is a key feature of the proposed method. The attention mechanism enhances the model's ability to focus on relevant features, essential for detecting subtle and complex attack patterns. In addition, GANs address the issue of data scarcity by generating additional varied attack data, encompassing known and emerging threats. This dual approach ensures that the system remains relevant and effective against the continuously evolving cyberattacks. The KDD Cup and CICIDS2017 datasets were used to validate this model, which exhibited significant improvements in anomaly detection. It achieved an accuracy of 99.69% on the KDD dataset and 97.93% on the CICIDS2017 dataset, with precision, recall, and F1-scores above 97%, demonstrating its effectiveness in recognizing complex attack patterns. This study contributes significantly to cybersecurity by providing a scalable and adaptable solution for anomaly detection in the face of sophisticated and dynamic cyber threats. The exploration of GANs for data augmentation highlights a promising direction for future research, particularly in situations where data limitations restrict the development of cybersecurity systems. The attention-GAN framework has emerged as a pioneering approach, setting a new benchmark for advanced cyber-defense strategies.

This paper proposes an interpretation of RLAIF as Bayesian inference by introducing distilled Self-Critique (dSC), which refines the outputs of a LLM through a Gibbs sampler that is later distilled into a fine-tuned model. Only requiring synthetic data, dSC is exercised in experiments regarding safety, sentiment, and privacy control, showing it can be a viable and cheap alternative to align LLMs. Code released at \url{//github.com/vicgalle/distilled-self-critique}.

In this paper, we present an entropy-stable (ES) discretization using a nodal discontinuous Galerkin (DG) method for the ideal multi-ion magneto-hydrodynamics (MHD) equations. We start by performing a continuous entropy analysis of the ideal multi-ion MHD system, described by, e.g., Toth (2010) [Multi-Ion Magnetohydrodynamics], which describes the motion of multi-ion plasmas with independent momentum and energy equations for each ion species. Following the continuous entropy analysis, we propose an algebraic manipulation to the multi-ion MHD system, such that entropy consistency can be transferred from the continuous analysis to its discrete approximation. Moreover, we augment the system of equations with a generalized Lagrange multiplier (GLM) technique to have an additional cleaning mechanism of the magnetic field divergence error. We first derive robust entropy-conservative (EC) fluxes for the alternative formulation of the multi-ion GLM-MHD system that satisfy a Tadmor-type condition and are consistent with existing EC fluxes for single-fluid GLM-MHD equations. Using these numerical two-point fluxes, we construct high-order EC and ES DG discretizations of the ideal multi-ion MHD system using collocated Legendre--Gauss--Lobatto summation-by-parts (SBP) operators. The resulting nodal DG schemes satisfy the second-law of thermodynamics at the semi-discrete level, while maintaining high-order convergence and local node-wise conservation properties. We demonstrate the high-order convergence, and the EC and ES properties of our scheme with numerical validation experiments. Moreover, we demonstrate the importance of the GLM divergence technique and the ES discretization to improve the robustness properties of a DG discretization of the multi-ion MHD system by solving a challenging magnetized Kelvin-Helmholtz instability problem that exhibits MHD turbulence.

Large Language Models (LLMs) possess the potential to exert substantial influence on public perceptions and interactions with information. This raises concerns about the societal impact that could arise if the ideologies within these models can be easily manipulated. In this work, we investigate how effectively LLMs can learn and generalize ideological biases from their instruction-tuning data. Our findings reveal a concerning vulnerability: exposure to only a small amount of ideologically driven samples significantly alters the ideology of LLMs. Notably, LLMs demonstrate a startling ability to absorb ideology from one topic and generalize it to even unrelated ones. The ease with which LLMs' ideologies can be skewed underscores the risks associated with intentionally poisoned training data by malicious actors or inadvertently introduced biases by data annotators. It also emphasizes the imperative for robust safeguards to mitigate the influence of ideological manipulations on LLMs.