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This paper rigorously shows how over-parameterization changes the convergence behaviors of gradient descent (GD) for the matrix sensing problem, where the goal is to recover an unknown low-rank ground-truth matrix from near-isotropic linear measurements. First, we consider the symmetric setting with the symmetric parameterization where $M^* \in \mathbb{R}^{n \times n}$ is a positive semi-definite unknown matrix of rank $r \ll n$, and one uses a symmetric parameterization $XX^\top$ to learn $M^*$. Here $X \in \mathbb{R}^{n \times k}$ with $k > r$ is the factor matrix. We give a novel $\Omega (1/T^2)$ lower bound of randomly initialized GD for the over-parameterized case ($k >r$) where $T$ is the number of iterations. This is in stark contrast to the exact-parameterization scenario ($k=r$) where the convergence rate is $\exp (-\Omega (T))$. Next, we study asymmetric setting where $M^* \in \mathbb{R}^{n_1 \times n_2}$ is the unknown matrix of rank $r \ll \min\{n_1,n_2\}$, and one uses an asymmetric parameterization $FG^\top$ to learn $M^*$ where $F \in \mathbb{R}^{n_1 \times k}$ and $G \in \mathbb{R}^{n_2 \times k}$. Building on prior work, we give a global exact convergence result of randomly initialized GD for the exact-parameterization case ($k=r$) with an $\exp (-\Omega(T))$ rate. Furthermore, we give the first global exact convergence result for the over-parameterization case ($k>r$) with an $\exp(-\Omega(\alpha^2 T))$ rate where $\alpha$ is the initialization scale. This linear convergence result in the over-parameterization case is especially significant because one can apply the asymmetric parameterization to the symmetric setting to speed up from $\Omega (1/T^2)$ to linear convergence. On the other hand, we propose a novel method that only modifies one step of GD and obtains a convergence rate independent of $\alpha$, recovering the rate in the exact-parameterization case.

In the ever-evolving realm of cybersecurity, the rise of generative AI models like ChatGPT, FraudGPT, and WormGPT has introduced both innovative solutions and unprecedented challenges. This research delves into the multifaceted applications of generative AI in social engineering attacks, offering insights into the evolving threat landscape using the blog mining technique. Generative AI models have revolutionized the field of cyberattacks, empowering malicious actors to craft convincing and personalized phishing lures, manipulate public opinion through deepfakes, and exploit human cognitive biases. These models, ChatGPT, FraudGPT, and WormGPT, have augmented existing threats and ushered in new dimensions of risk. From phishing campaigns that mimic trusted organizations to deepfake technology impersonating authoritative figures, we explore how generative AI amplifies the arsenal of cybercriminals. Furthermore, we shed light on the vulnerabilities that AI-driven social engineering exploits, including psychological manipulation, targeted phishing, and the crisis of authenticity. To counter these threats, we outline a range of strategies, including traditional security measures, AI-powered security solutions, and collaborative approaches in cybersecurity. We emphasize the importance of staying vigilant, fostering awareness, and strengthening regulations in the battle against AI-enhanced social engineering attacks. In an environment characterized by the rapid evolution of AI models and a lack of training data, defending against generative AI threats requires constant adaptation and the collective efforts of individuals, organizations, and governments. This research seeks to provide a comprehensive understanding of the dynamic interplay between generative AI and social engineering attacks, equipping stakeholders with the knowledge to navigate this intricate cybersecurity landscape.

Proprietary Large Language Models (LLMs), such as ChatGPT, have garnered significant attention due to their exceptional capabilities in handling a diverse range of tasks. Recent studies demonstrate that open-sourced smaller foundational models, such as 7B-size LLaMA, can also display remarkable proficiency in tackling diverse tasks when fine-tuned using instruction-driven data. In this work, we investigate a practical problem setting where the primary focus is on one or a few particular tasks rather than general-purpose instruction following, and explore whether LLMs can be beneficial and further improved for such targeted scenarios. We choose the writing-assistant scenario as the testbed, which includes seven writing tasks. We collect training data for these tasks, reframe them in an instruction-following format, and subsequently refine the LLM, specifically LLaMA, via instruction tuning. Experimental results show that fine-tuning LLaMA on writing instruction data significantly improves its ability on writing tasks. We also conduct more experiments and analyses to offer insights for future work on effectively fine-tuning LLaMA for specific scenarios. Finally, we initiate a discussion regarding the necessity of employing LLMs for only one targeted task, taking into account the efforts required for tuning and the resources consumed during deployment.

While semantic segmentation has seen tremendous improvements in the past, there are still significant labeling efforts necessary and the problem of limited generalization to classes that have not been present during training. To address this problem, zero-shot semantic segmentation makes use of large self-supervised vision-language models, allowing zero-shot transfer to unseen classes. In this work, we build a benchmark for Multi-domain Evaluation of Semantic Segmentation (MESS), which allows a holistic analysis of performance across a wide range of domain-specific datasets such as medicine, engineering, earth monitoring, biology, and agriculture. To do this, we reviewed 120 datasets, developed a taxonomy, and classified the datasets according to the developed taxonomy. We select a representative subset consisting of 22 datasets and propose it as the MESS benchmark. We evaluate eight recently published models on the proposed MESS benchmark and analyze characteristics for the performance of zero-shot transfer models. The toolkit is available at //github.com/blumenstiel/MESS.

We consider stochastic approximations of sampling algorithms, such as Stochastic Gradient Langevin Dynamics (SGLD) and the Random Batch Method (RBM) for Interacting Particle Dynamcs (IPD). We observe that the noise introduced by the stochastic approximation is nearly Gaussian due to the Central Limit Theorem (CLT) while the driving Brownian motion is exactly Gaussian. We harness this structure to absorb the stochastic approximation error inside the diffusion process, and obtain improved convergence guarantees for these algorithms. For SGLD, we prove the first stable convergence rate in KL divergence without requiring uniform warm start, assuming the target density satisfies a Log-Sobolev Inequality. Our result implies superior first-order oracle complexity compared to prior works, under significantly milder assumptions. We also prove the first guarantees for SGLD under even weaker conditions such as H\"{o}lder smoothness and Poincare Inequality, thus bridging the gap between the state-of-the-art guarantees for LMC and SGLD. Our analysis motivates a new algorithm called covariance correction, which corrects for the additional noise introduced by the stochastic approximation by rescaling the strength of the diffusion. Finally, we apply our techniques to analyze RBM, and significantly improve upon the guarantees in prior works (such as removing exponential dependence on horizon), under minimal assumptions.

Combinatorial optimization (CO) problems are often NP-hard and thus out of reach for exact algorithms, making them a tempting domain to apply machine learning methods. The highly structured constraints in these problems can hinder either optimization or sampling directly in the solution space. On the other hand, GFlowNets have recently emerged as a powerful machinery to efficiently sample from composite unnormalized densities sequentially and have the potential to amortize such solution-searching processes in CO, as well as generate diverse solution candidates. In this paper, we design Markov decision processes (MDPs) for different combinatorial problems and propose to train conditional GFlowNets to sample from the solution space. Efficient training techniques are also developed to benefit long-range credit assignment. Through extensive experiments on a variety of different CO tasks with synthetic and realistic data, we demonstrate that GFlowNet policies can efficiently find high-quality solutions. Our implementation is open-sourced at //github.com/zdhNarsil/GFlowNet-CombOpt.

Large Language Models (LLMs) have the ability to solve a variety of tasks, such as text summarization and mathematical questions, just out of the box, but they are often trained with a single task in mind. Due to high computational costs, the current trend is to use prompt instruction tuning to better adjust monolithic, pretrained LLMs for new -- but often individual -- downstream tasks. Thus, how one would expand prompt tuning to handle -- concomitantly -- heterogeneous tasks and data distributions is a widely open question. To address this gap, we suggest the use of \emph{Mixture of Prompts}, or MoPs, associated with smart gating functionality: the latter -- whose design is one of the contributions of this paper -- can identify relevant skills embedded in different groups of prompts and dynamically assign combined experts (i.e., collection of prompts), based on the target task. Additionally, MoPs are empirically agnostic to any model compression technique applied -- for efficiency reasons -- as well as instruction data source and task composition. In practice, MoPs can simultaneously mitigate prompt training "interference" in multi-task, multi-source scenarios (e.g., task and data heterogeneity across sources), as well as possible implications from model approximations. As a highlight, MoPs manage to decrease final perplexity from $\sim20\%$ up to $\sim70\%$, as compared to baselines, in the federated scenario, and from $\sim 3\%$ up to $\sim30\%$ in the centralized scenario.

We provide a comprehensive theory of multiple variants of ordinal multidimensional scaling, including external and internal unfolding. We do so in the continuous model of Shepard (1966).

While significant progress has been made on Physics-Informed Neural Networks (PINNs), a comprehensive comparison of these methods across a wide range of Partial Differential Equations (PDEs) is still lacking. This study introduces PINNacle, a benchmarking tool designed to fill this gap. PINNacle provides a diverse dataset, comprising over 20 distinct PDEs from various domains, including heat conduction, fluid dynamics, biology, and electromagnetics. These PDEs encapsulate key challenges inherent to real-world problems, such as complex geometry, multi-scale phenomena, nonlinearity, and high dimensionality. PINNacle also offers a user-friendly toolbox, incorporating about 10 state-of-the-art PINN methods for systematic evaluation and comparison. We have conducted extensive experiments with these methods, offering insights into their strengths and weaknesses. In addition to providing a standardized means of assessing performance, PINNacle also offers an in-depth analysis to guide future research, particularly in areas such as domain decomposition methods and loss reweighting for handling multi-scale problems and complex geometry. To the best of our knowledge, it is the largest benchmark with a diverse and comprehensive evaluation that will undoubtedly foster further research in PINNs.

Deep Learning algorithms have achieved the state-of-the-art performance for Image Classification and have been used even in security-critical applications, such as biometric recognition systems and self-driving cars. However, recent works have shown those algorithms, which can even surpass the human capabilities, are vulnerable to adversarial examples. In Computer Vision, adversarial examples are images containing subtle perturbations generated by malicious optimization algorithms in order to fool classifiers. As an attempt to mitigate these vulnerabilities, numerous countermeasures have been constantly proposed in literature. Nevertheless, devising an efficient defense mechanism has proven to be a difficult task, since many approaches have already shown to be ineffective to adaptive attackers. Thus, this self-containing paper aims to provide all readerships with a review of the latest research progress on Adversarial Machine Learning in Image Classification, however with a defender's perspective. Here, novel taxonomies for categorizing adversarial attacks and defenses are introduced and discussions about the existence of adversarial examples are provided. Further, in contrast to exisiting surveys, it is also given relevant guidance that should be taken into consideration by researchers when devising and evaluating defenses. Finally, based on the reviewed literature, it is discussed some promising paths for future research.