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The rise of deepfake images, especially of well-known personalities, poses a serious threat to the dissemination of authentic information. To tackle this, we present a thorough investigation into how deepfakes are produced and how they can be identified. The cornerstone of our research is a rich collection of artificial celebrity faces, titled DeepFakeFace (DFF). We crafted the DFF dataset using advanced diffusion models and have shared it with the community through online platforms. This data serves as a robust foundation to train and test algorithms designed to spot deepfakes. We carried out a thorough review of the DFF dataset and suggest two evaluation methods to gauge the strength and adaptability of deepfake recognition tools. The first method tests whether an algorithm trained on one type of fake images can recognize those produced by other methods. The second evaluates the algorithm's performance with imperfect images, like those that are blurry, of low quality, or compressed. Given varied results across deepfake methods and image changes, our findings stress the need for better deepfake detectors. Our DFF dataset and tests aim to boost the development of more effective tools against deepfakes.

The rapid advancement of large language models, such as the Generative Pre-trained Transformer (GPT) series, has had significant implications across various disciplines. In this study, we investigate the potential of the state-of-the-art large language model (GPT-4) for planning tasks. We explore its effectiveness in multiple planning subfields, highlighting both its strengths and limitations. Through a comprehensive examination, we identify areas where large language models excel in solving planning problems and reveal the constraints that limit their applicability. Our empirical analysis focuses on GPT-4's performance in planning domain extraction, graph search path planning, and adversarial planning. We then propose a way of fine-tuning a domain-specific large language model to improve its Chain of Thought (CoT) capabilities for the above-mentioned tasks. The results provide valuable insights into the potential applications of large language models in the planning domain and pave the way for future research to overcome their limitations and expand their capabilities.

We relate the power bound and a resolvent condition of Kreiss-Ritt type and characterize the extremal growth of two families of products of three Toeplitz operators on the Hardy space that contain infinitely many points in their spectra. Since these operators do not fall into a well-understood class, we analyze them through explicit techniques based on properties of Toeplitz operators and the structure of the Hardy space. Our methods apply mutatis mutandis to operators of the form $T_{g(z)}^{-1}T_{f(z)}T_{g(z)}$ where $f(z)$ is a polynomial in $z$ and $\bar{z}$ and $g(z)$ is a polynomial in $z$. This collection of operators arises in the numerical solution of the Cauchy problem for linear ordinary, partial, and delay differential equations that are frequently used as models for processes in the sciences and engineering. Our results provide a framework for the stability analysis of existing numerical methods for new classes of linear differential equations as well as the development of novel approximation schemes.

Mathematical notation makes up a large portion of STEM literature, yet finding semantic representations for formulae remains a challenging problem. Because mathematical notation is precise, and its meaning changes significantly with small character shifts, the methods that work for natural text do not necessarily work well for mathematical expressions. This work describes an approach for representing mathematical expressions in a continuous vector space. We use the encoder of a sequence-to-sequence architecture, trained on visually different but mathematically equivalent expressions, to generate vector representations (or embeddings). We compare this approach with a structural approach that considers visual layout to embed an expression and show that our proposed approach is better at capturing mathematical semantics. Finally, to expedite future research, we publish a corpus of equivalent transcendental and algebraic expression pairs.

The introduction and advancements in Local Differential Privacy (LDP) variants have become a cornerstone in addressing the privacy concerns associated with the vast data produced by smart devices, which forms the foundation for data-driven decision-making in crowdsensing. While harnessing the power of these immense data sets can offer valuable insights, it simultaneously poses significant privacy risks for the users involved. LDP, a distinguished privacy model with a decentralized architecture, stands out for its capability to offer robust privacy assurances for individual users during data collection and analysis. The essence of LDP is its method of locally perturbing each user's data on the client-side before transmission to the server-side, safeguarding against potential privacy breaches at both ends. This article offers an in-depth exploration of LDP, emphasizing its models, its myriad variants, and the foundational structure of LDP algorithms.

We show how to construct in an elementary way the invariant of the KHK discretisation of a cubic Hamiltonian system in two dimensions. That is, we show that this invariant is expressible as the product of the ratios of affine polynomials defining the prolongation of the three parallel sides of a hexagon. On the vertices of such a hexagon lie the indeterminacy points of the KHK map. This result is obtained analysing the structure of the singular fibres of the known invariant. We apply this construction to several examples, and we prove that a similar result holds true for a case outside the hypotheses of the main theorem, leading us to conjecture that further extensions are possible.

BRCA genes, comprising BRCA1 and BRCA2 play indispensable roles in preserving genomic stability and facilitating DNA repair mechanisms. The presence of germline mutations in these genes has been associated with increased susceptibility to various cancers, notably breast and ovarian cancers. Recent advancements in cost-effective sequencing technologies have revolutionized the landscape of cancer genomics, leading to a notable rise in the number of sequenced cancer patient genomes, enabling large-scale computational studies. In this study, we delve into the BRCA mutations in the dbSNP, housing an extensive repository of 41,177 and 44,205 genetic mutations for BRCA1 and BRCA2, respectively. Employing meticulous computational analysis from an umbrella perspective, our research unveils intriguing findings pertaining to a number of critical aspects. Namely, we discover that the majority of BRCA mutations in dbSNP have unknown clinical significance. We find that, although exon 11 for both genes contains the majority of the mutations and may seem as if it is a mutation hot spot, upon analyzing mutations per base pair, we find that all exons exhibit similar levels of mutations. Investigating mutations within introns, while we observe that the recorded mutations are generally uniformly distributed, almost all of the pathogenic mutations in introns are located close to splicing regions (at the beginning or the end). In addition to the findings mentioned earlier, we have also made other discoveries concerning mutation types and the level of confidence in observations within the dbSNP database.

Recently, ChatGPT, along with DALL-E-2 and Codex,has been gaining significant attention from society. As a result, many individuals have become interested in related resources and are seeking to uncover the background and secrets behind its impressive performance. In fact, ChatGPT and other Generative AI (GAI) techniques belong to the category of Artificial Intelligence Generated Content (AIGC), which involves the creation of digital content, such as images, music, and natural language, through AI models. The goal of AIGC is to make the content creation process more efficient and accessible, allowing for the production of high-quality content at a faster pace. AIGC is achieved by extracting and understanding intent information from instructions provided by human, and generating the content according to its knowledge and the intent information. In recent years, large-scale models have become increasingly important in AIGC as they provide better intent extraction and thus, improved generation results. With the growth of data and the size of the models, the distribution that the model can learn becomes more comprehensive and closer to reality, leading to more realistic and high-quality content generation. This survey provides a comprehensive review on the history of generative models, and basic components, recent advances in AIGC from unimodal interaction and multimodal interaction. From the perspective of unimodality, we introduce the generation tasks and relative models of text and image. From the perspective of multimodality, we introduce the cross-application between the modalities mentioned above. Finally, we discuss the existing open problems and future challenges in AIGC.

Recently, Mutual Information (MI) has attracted attention in bounding the generalization error of Deep Neural Networks (DNNs). However, it is intractable to accurately estimate the MI in DNNs, thus most previous works have to relax the MI bound, which in turn weakens the information theoretic explanation for generalization. To address the limitation, this paper introduces a probabilistic representation of DNNs for accurately estimating the MI. Leveraging the proposed MI estimator, we validate the information theoretic explanation for generalization, and derive a tighter generalization bound than the state-of-the-art relaxations.

Graph Neural Networks (GNNs) have been studied from the lens of expressive power and generalization. However, their optimization properties are less well understood. We take the first step towards analyzing GNN training by studying the gradient dynamics of GNNs. First, we analyze linearized GNNs and prove that despite the non-convexity of training, convergence to a global minimum at a linear rate is guaranteed under mild assumptions that we validate on real-world graphs. Second, we study what may affect the GNNs' training speed. Our results show that the training of GNNs is implicitly accelerated by skip connections, more depth, and/or a good label distribution. Empirical results confirm that our theoretical results for linearized GNNs align with the training behavior of nonlinear GNNs. Our results provide the first theoretical support for the success of GNNs with skip connections in terms of optimization, and suggest that deep GNNs with skip connections would be promising in practice.