Deep Learning has significantly impacted the application of data-to-decision throughout research and industry, however, they lack a rigorous mathematical foundation, which creates situations where algorithmic results fail to be practically invertible. In this paper we present a nearly invertible mapping between $\mathbb{R}^{2^n}$ and $\mathbb{R}^{n+1}$ via a topological connection between $S^{2^n-1}$ and $S^n$. Throughout the paper we utilize the algebra of Multicomplex rotation groups and polyspherical coordinates to define two maps: the first is a contraction from $S^{2^n-1}$ to $\displaystyle \otimes^n_{k=1} SO(2)$, and the second is a projection from $\displaystyle \otimes^n_{k=1} SO(2)$ to $S^{n}$. Together these form a composite map that we call the LG Fibration. In analogy to the generation of Hopf Fibration using Hypercomplex geometry from $S^{(2n-1)} \mapsto CP^n$, our fibration uses Multicomplex geometry to project $S^{2^n-1}$ onto $S^n$. We also investigate the algebraic properties of the LG Fibration, ultimately deriving a distance difference function to determine which pairs of vectors have an invariant inner product under the transformation. The LG Fibration has applications to Machine Learning and AI, in analogy to the current applications of Hopf Fibrations in adaptive UAV control. Furthermore, the ability to invert the LG Fibration for nearly all elements allows for the development of Machine Learning algorithms that may avoid the issues of uncertainty and reproducibility that currently plague contemporary methods. The primary result of this paper is a novel method of nearly invertible geometric dimensional reduction from $S^{2^n-1}$ to $S^n$, which has the capability to extend the research in both mathematics and AI, including but not limited to the fields of homotopy groups of spheres, algebraic topology, machine learning, and algebraic biology.

本文介绍了机器学习推动的各种脑电图应用程序和当前的脑电图市场生态系统。使用脑电图越来越多的开放医疗和健康数据集鼓励数据驱动的研究，并有望通过知识发现和机器学习数据科学算法开发来改善患者护理的神经病学。这项工作导致各种脑电图发展，目前构成了新的脑电图市场。本文试图对脑电图市场进行全面的调查，并涵盖脑电图的六个重要应用，包括诊断/筛查，药物开发，神经营销，日常健康，元元和年龄/残疾援助。这项调查的重点是研究领域与商业市场之间的比较和对比。我们的调查指出了脑电图的当前局限性，并指示了上面列出的每个脑电图应用程序的研究和商机的未来方向。根据我们的调查，对基于机器学习的脑电图应用程序的更多研究将导致与脑电图相关的更强大的市场。越来越多的公司将使用研究技术并将其应用于现实生活中。随着与EEG相关的市场的增长，与EEG相关的设备将收集更多的脑电图数据，并且将有更多的EEG数据供研究人员在他们的研究中使用，以作为一个良性周期。我们的市场分析表明，在上面列出的六个应用程序中使用脑电图数据和机器学习有关的研究指向脑电图生态系统和机器学习世界的增长和发展的明确趋势。

Large training data and expensive model tweaking are standard features of deep learning for images. As a result, data owners often utilize cloud resources to develop large-scale complex models, which raises privacy concerns. Existing solutions are either too expensive to be practical or do not sufficiently protect the confidentiality of data and models. In this paper, we study and compare novel \emph{image disguising} mechanisms, DisguisedNets and InstaHide, aiming to achieve a better trade-off among the level of protection for outsourced DNN model training, the expenses, and the utility of data. DisguisedNets are novel combinations of image blocktization, block-level random permutation, and two block-level secure transformations: random multidimensional projection (RMT) and AES pixel-level encryption (AES). InstaHide is an image mixup and random pixel flipping technique \cite{huang20}. We have analyzed and evaluated them under a multi-level threat model. RMT provides a better security guarantee than InstaHide, under the Level-1 adversarial knowledge with well-preserved model quality. In contrast, AES provides a security guarantee under the Level-2 adversarial knowledge, but it may affect model quality more. The unique features of image disguising also help us to protect models from model-targeted attacks. We have done an extensive experimental evaluation to understand how these methods work in different settings for different datasets.

A storyboard is a roadmap for video creation which consists of shot-by-shot images to visualize key plots in a text synopsis. Creating video storyboards however remains challenging which not only requires association between high-level texts and images, but also demands for long-term reasoning to make transitions smooth across shots. In this paper, we propose a new task called Text synopsis to Video Storyboard (TeViS) which aims to retrieve an ordered sequence of images to visualize the text synopsis. We construct a MovieNet-TeViS benchmark based on the public MovieNet dataset. It contains 10K text synopses each paired with keyframes that are manually selected from corresponding movies by considering both relevance and cinematic coherence. We also present an encoder-decoder baseline for the task. The model uses a pretrained vision-and-language model to improve high-level text-image matching. To improve coherence in long-term shots, we further propose to pre-train the decoder on large-scale movie frames without text. Experimental results demonstrate that our proposed model significantly outperforms other models to create text-relevant and coherent storyboards. Nevertheless, there is still a large gap compared to human performance suggesting room for promising future work.

Solving real-world optimal control problems are challenging tasks, as the system dynamics can be highly non-linear or including nonconvex objectives and constraints, while in some cases the dynamics are unknown, making it hard to numerically solve the optimal control actions. To deal with such modeling and computation challenges, in this paper, we integrate Neural Networks with the Pontryagin's Minimum Principle (PMP), and propose a computationally efficient framework NN-PMP. The resulting controller can be implemented for systems with unknown and complex dynamics. It can not only utilize the accurate surrogate models parameterized by neural networks, but also efficiently recover the optimality conditions along with the optimal action sequences via PMP conditions. A toy example on a nonlinear Martian Base operation along with a real-world lossy energy storage arbitrage example demonstrates our proposed NN-PMP is a general and versatile computation tool for finding optimal solutions. Compared with solutions provided by the numerical optimization solver with approximated linear dynamics, NN-PMP achieves more efficient system modeling and higher performance in terms of control objectives.

The task of reconstructing 3D human motion has wideranging applications. The gold standard Motion capture (MoCap) systems are accurate but inaccessible to the general public due to their cost, hardware and space constraints. In contrast, monocular human mesh recovery (HMR) methods are much more accessible than MoCap as they take single-view videos as inputs. Replacing the multi-view Mo- Cap systems with a monocular HMR method would break the current barriers to collecting accurate 3D motion thus making exciting applications like motion analysis and motiondriven animation accessible to the general public. However, performance of existing HMR methods degrade when the video contains challenging and dynamic motion that is not in existing MoCap datasets used for training. This reduces its appeal as dynamic motion is frequently the target in 3D motion recovery in the aforementioned applications. Our study aims to bridge the gap between monocular HMR and multi-view MoCap systems by leveraging information shared across multiple video instances of the same action. We introduce the Neural Motion (NeMo) field. It is optimized to represent the underlying 3D motions across a set of videos of the same action. Empirically, we show that NeMo can recover 3D motion in sports using videos from the Penn Action dataset, where NeMo outperforms existing HMR methods in terms of 2D keypoint detection. To further validate NeMo using 3D metrics, we collected a small MoCap dataset mimicking actions in Penn Action,and show that NeMo achieves better 3D reconstruction compared to various baselines.

A major goal of multimodal research is to improve machine understanding of images and text. Tasks include image captioning, text-to-image generation, and vision-language representation learning. So far, research has focused on the relationships between images and text. For example, captioning models attempt to understand the semantics of images which are then transformed into text. An important question is: which annotation reflects best a deep understanding of image content? Similarly, given a text, what is the best image that can present the semantics of the text? In this work, we argue that the best text or caption for a given image is the text which would generate the image which is the most similar to that image. Likewise, the best image for a given text is the image that results in the caption which is best aligned with the original text. To this end, we propose a unified framework that includes both a text-to-image generative model and an image-to-text generative model. Extensive experiments validate our approach.

Knowledge tracing (KT) aims to leverage students' learning histories to estimate their mastery levels on a set of pre-defined skills, based on which the corresponding future performance can be accurately predicted. In practice, a student's learning history comprises answers to sets of massed questions, each known as a session, rather than merely being a sequence of independent answers. Theoretically, within and across these sessions, students' learning dynamics can be very different. Therefore, how to effectively model the dynamics of students' knowledge states within and across the sessions is crucial for handling the KT problem. Most existing KT models treat student's learning records as a single continuing sequence, without capturing the sessional shift of students' knowledge state. To address the above issue, we propose a novel hierarchical transformer model, named HiTSKT, comprises an interaction(-level) encoder to capture the knowledge a student acquires within a session, and a session(-level) encoder to summarise acquired knowledge across the past sessions. To predict an interaction in the current session, a knowledge retriever integrates the summarised past-session knowledge with the previous interactions' information into proper knowledge representations. These representations are then used to compute the student's current knowledge state. Additionally, to model the student's long-term forgetting behaviour across the sessions, a power-law-decay attention mechanism is designed and deployed in the session encoder, allowing it to emphasize more on the recent sessions. Extensive experiments on three public datasets demonstrate that HiTSKT achieves new state-of-the-art performance on all the datasets compared with six state-of-the-art KT models.

Model-based attacks can infer training data information from deep neural network models. These attacks heavily depend on the attacker's knowledge of the application domain, e.g., using it to determine the auxiliary data for model-inversion attacks. However, attackers may not know what the model is used for in practice. We propose a generative adversarial network (GAN) based method to explore likely or similar domains of a target model -- the model domain inference (MDI) attack. For a given target (classification) model, we assume that the attacker knows nothing but the input and output formats and can use the model to derive the prediction for any input in the desired form. Our basic idea is to use the target model to affect a GAN training process for a candidate domain's dataset that is easy to obtain. We find that the target model may distract the training procedure less if the domain is more similar to the target domain. We then measure the distraction level with the distance between GAN-generated datasets, which can be used to rank candidate domains for the target model. Our experiments show that the auxiliary dataset from an MDI top-ranked domain can effectively boost the result of model-inversion attacks.

To reproduce the success of text-to-image (T2I) generation, recent works in text-to-video (T2V) generation employ large-scale text-video dataset for fine-tuning. However, such paradigm is computationally expensive. Humans have the amazing ability to learn new visual concepts from just one single exemplar. We hereby study a new T2V generation problem$\unicode{x2014}$One-Shot Video Generation, where only a single text-video pair is presented for training an open-domain T2V generator. Intuitively, we propose to adapt the T2I diffusion model pretrained on massive image data for T2V generation. We make two key observations: 1) T2I models are able to generate images that align well with the verb terms; 2) extending T2I models to generate multiple images concurrently exhibits surprisingly good content consistency. To further learn continuous motion, we propose Tune-A-Video with a tailored Sparse-Causal Attention, which generates videos from text prompts via an efficient one-shot tuning of pretrained T2I diffusion models. Tune-A-Video is capable of producing temporally-coherent videos over various applications such as change of subject or background, attribute editing, style transfer, demonstrating the versatility and effectiveness of our method.