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Large Language Models (LLMs) have quickly risen to prominence due to their ability to perform at or close to the state-of-the-art in a variety of fields while handling natural language. An important field of research is the application of such models at the cybersecurity context. This survey aims to identify where in the field of cybersecurity LLMs have already been applied, the ways in which they are being used and their limitations in the field. Finally, suggestions are made on how to improve such limitations and what can be expected from these systems once these limitations are overcome.

Fractional derivatives are a well-studied generalization of integer order derivatives. Naturally, for optimization, it is of interest to understand the convergence properties of gradient descent using fractional derivatives. Convergence analysis of fractional gradient descent is currently limited both in the methods analyzed and the settings analyzed. This paper aims to fill in these gaps by analyzing variations of fractional gradient descent in smooth and convex, smooth and strongly convex, and smooth and non-convex settings. First, novel bounds will be established bridging fractional and integer derivatives. Then, these bounds will be applied to the aforementioned settings to prove linear convergence for smooth and strongly convex functions and $O(1/T)$ convergence for smooth and convex functions. Additionally, we prove $O(1/T)$ convergence for smooth and non-convex functions using an extended notion of smoothness - H\"older smoothness - that is more natural for fractional derivatives. Finally, empirical results will be presented on the potential speed up of fractional gradient descent over standard gradient descent as well as some preliminary theoretical results explaining this speed up.

Grid peeling is the process of repeatedly removing the convex hull vertices of the grid-points that lie inside a given convex curve. It has been conjectured that, for a more and more refined grid, grid peeling converges to a continuous process, the affine curve-shortening flow, which deforms the curve based on the curvature. We prove this conjecture for one class of curves, parabolas with a vertical axis, and we determine the value of the constant factor in the formula that relates the two processes.

Automated disinformation generation is often listed as an important risk associated with large language models (LLMs). The theoretical ability to flood the information space with disinformation content might have dramatic consequences for societies around the world. This paper presents a comprehensive study of the disinformation capabilities of the current generation of LLMs to generate false news articles in the English language. In our study, we evaluated the capabilities of 10 LLMs using 20 disinformation narratives. We evaluated several aspects of the LLMs: how good they are at generating news articles, how strongly they tend to agree or disagree with the disinformation narratives, how often they generate safety warnings, etc. We also evaluated the abilities of detection models to detect these articles as LLM-generated. We conclude that LLMs are able to generate convincing news articles that agree with dangerous disinformation narratives.

We study the cost of parallelizing weak-to-strong boosting algorithms for learning, following the recent work of Karbasi and Larsen. Our main results are two-fold: - First, we prove a tight lower bound, showing that even "slight" parallelization of boosting requires an exponential blow-up in the complexity of training. Specifically, let $\gamma$ be the weak learner's advantage over random guessing. The famous \textsc{AdaBoost} algorithm produces an accurate hypothesis by interacting with the weak learner for $\tilde{O}(1 / \gamma^2)$ rounds where each round runs in polynomial time. Karbasi and Larsen showed that "significant" parallelization must incur exponential blow-up: Any boosting algorithm either interacts with the weak learner for $\Omega(1 / \gamma)$ rounds or incurs an $\exp(d / \gamma)$ blow-up in the complexity of training, where $d$ is the VC dimension of the hypothesis class. We close the gap by showing that any boosting algorithm either has $\Omega(1 / \gamma^2)$ rounds of interaction or incurs a smaller exponential blow-up of $\exp(d)$. -Complementing our lower bound, we show that there exists a boosting algorithm using $\tilde{O}(1/(t \gamma^2))$ rounds, and only suffer a blow-up of $\exp(d \cdot t^2)$. Plugging in $t = \omega(1)$, this shows that the smaller blow-up in our lower bound is tight. More interestingly, this provides the first trade-off between the parallelism and the total work required for boosting.

Reasoning, a crucial ability for complex problem-solving, plays a pivotal role in various real-world settings such as negotiation, medical diagnosis, and criminal investigation. It serves as a fundamental methodology in the field of Artificial General Intelligence (AGI). With the ongoing development of foundation models, e.g., Large Language Models (LLMs), there is a growing interest in exploring their abilities in reasoning tasks. In this paper, we introduce seminal foundation models proposed or adaptable for reasoning, highlighting the latest advancements in various reasoning tasks, methods, and benchmarks. We then delve into the potential future directions behind the emergence of reasoning abilities within foundation models. We also discuss the relevance of multimodal learning, autonomous agents, and super alignment in the context of reasoning. By discussing these future research directions, we hope to inspire researchers in their exploration of this field, stimulate further advancements in reasoning with foundation models, and contribute to the development of AGI.

Large Language Models (LLMs) have shown excellent generalization capabilities that have led to the development of numerous models. These models propose various new architectures, tweaking existing architectures with refined training strategies, increasing context length, using high-quality training data, and increasing training time to outperform baselines. Analyzing new developments is crucial for identifying changes that enhance training stability and improve generalization in LLMs. This survey paper comprehensively analyses the LLMs architectures and their categorization, training strategies, training datasets, and performance evaluations and discusses future research directions. Moreover, the paper also discusses the basic building blocks and concepts behind LLMs, followed by a complete overview of LLMs, including their important features and functions. Finally, the paper summarizes significant findings from LLM research and consolidates essential architectural and training strategies for developing advanced LLMs. Given the continuous advancements in LLMs, we intend to regularly update this paper by incorporating new sections and featuring the latest LLM models.

The concept of causality plays an important role in human cognition . In the past few decades, causal inference has been well developed in many fields, such as computer science, medicine, economics, and education. With the advancement of deep learning techniques, it has been increasingly used in causal inference against counterfactual data. Typically, deep causal models map the characteristics of covariates to a representation space and then design various objective optimization functions to estimate counterfactual data unbiasedly based on the different optimization methods. This paper focuses on the survey of the deep causal models, and its core contributions are as follows: 1) we provide relevant metrics under multiple treatments and continuous-dose treatment; 2) we incorporate a comprehensive overview of deep causal models from both temporal development and method classification perspectives; 3) we assist a detailed and comprehensive classification and analysis of relevant datasets and source code.

Residual networks (ResNets) have displayed impressive results in pattern recognition and, recently, have garnered considerable theoretical interest due to a perceived link with neural ordinary differential equations (neural ODEs). This link relies on the convergence of network weights to a smooth function as the number of layers increases. We investigate the properties of weights trained by stochastic gradient descent and their scaling with network depth through detailed numerical experiments. We observe the existence of scaling regimes markedly different from those assumed in neural ODE literature. Depending on certain features of the network architecture, such as the smoothness of the activation function, one may obtain an alternative ODE limit, a stochastic differential equation or neither of these. These findings cast doubts on the validity of the neural ODE model as an adequate asymptotic description of deep ResNets and point to an alternative class of differential equations as a better description of the deep network limit.

We describe the new field of mathematical analysis of deep learning. This field emerged around a list of research questions that were not answered within the classical framework of learning theory. These questions concern: the outstanding generalization power of overparametrized neural networks, the role of depth in deep architectures, the apparent absence of the curse of dimensionality, the surprisingly successful optimization performance despite the non-convexity of the problem, understanding what features are learned, why deep architectures perform exceptionally well in physical problems, and which fine aspects of an architecture affect the behavior of a learning task in which way. We present an overview of modern approaches that yield partial answers to these questions. For selected approaches, we describe the main ideas in more detail.