Tukey's depth (or halfspace depth) is a widely used measure of centrality for multivariate data. However, exact computation of Tukey's depth is known to be a hard problem in high dimensions. As a remedy, randomized approximations of Tukey's depth have been proposed. In this paper we explore when such randomized algorithms return a good approximation of Tukey's depth. We study the case when the data are sampled from a log-concave isotropic distribution. We prove that, if one requires that the algorithm runs in polynomial time in the dimension, the randomized algorithm correctly approximates the maximal depth $1/2$ and depths close to zero. On the other hand, for any point of intermediate depth, any good approximation requires exponential complexity.

Foundation models have rapidly permeated society, catalyzing a wave of generative AI applications spanning enterprise and consumer-facing contexts. While the societal impact of foundation models is growing, transparency is on the decline, mirroring the opacity that has plagued past digital technologies (e.g. social media). Reversing this trend is essential: transparency is a vital precondition for public accountability, scientific innovation, and effective governance. To assess the transparency of the foundation model ecosystem and help improve transparency over time, we introduce the Foundation Model Transparency Index. The Foundation Model Transparency Index specifies 100 fine-grained indicators that comprehensively codify transparency for foundation models, spanning the upstream resources used to build a foundation model (e.g data, labor, compute), details about the model itself (e.g. size, capabilities, risks), and the downstream use (e.g. distribution channels, usage policies, affected geographies). We score 10 major foundation model developers (e.g. OpenAI, Google, Meta) against the 100 indicators to assess their transparency. To facilitate and standardize assessment, we score developers in relation to their practices for their flagship foundation model (e.g. GPT-4 for OpenAI, PaLM 2 for Google, Llama 2 for Meta). We present 10 top-level findings about the foundation model ecosystem: for example, no developer currently discloses significant information about the downstream impact of its flagship model, such as the number of users, affected market sectors, or how users can seek redress for harm. Overall, the Foundation Model Transparency Index establishes the level of transparency today to drive progress on foundation model governance via industry standards and regulatory intervention.

Differential Privacy (DP) image data synthesis, which leverages the DP technique to generate synthetic data to replace the sensitive data, allowing organizations to share and utilize synthetic images without privacy concerns. Previous methods incorporate the advanced techniques of generative models and pre-training on a public dataset to produce exceptional DP image data, but suffer from problems of unstable training and massive computational resource demands. This paper proposes a novel DP image synthesis method, termed PRIVIMAGE, which meticulously selects pre-training data, promoting the efficient creation of DP datasets with high fidelity and utility. PRIVIMAGE first establishes a semantic query function using a public dataset. Then, this function assists in querying the semantic distribution of the sensitive dataset, facilitating the selection of data from the public dataset with analogous semantics for pre-training. Finally, we pre-train an image generative model using the selected data and then fine-tune this model on the sensitive dataset using Differentially Private Stochastic Gradient Descent (DP-SGD). PRIVIMAGE allows us to train a lightly parameterized generative model, reducing the noise in the gradient during DP-SGD training and enhancing training stability. Extensive experiments demonstrate that PRIVIMAGE uses only 1% of the public dataset for pre-training and 7.6% of the parameters in the generative model compared to the state-of-the-art method, whereas achieves superior synthetic performance and conserves more computational resources. On average, PRIVIMAGE achieves 30.1% lower FID and 12.6% higher Classification Accuracy than the state-of-the-art method. The replication package and datasets can be accessed online.

In this work, we tackle the scenario of understanding characters in scripts, which aims to learn the characters' personalities and identities from their utterances. We begin by analyzing several challenges in this scenario, and then propose a multi-level contrastive learning framework to capture characters' global information in a fine-grained manner. To validate the proposed framework, we conduct extensive experiments on three character understanding sub-tasks by comparing with strong pre-trained language models, including SpanBERT, Longformer, BigBird and ChatGPT-3.5. Experimental results demonstrate that our method improves the performances by a considerable margin. Through further in-depth analysis, we show the effectiveness of our method in addressing the challenges and provide more hints on the scenario of character understanding. We will open-source our work on github at https://github.com/David-Li0406/Script-based-Character-Understanding.

This dissertation attempts to drive innovation in the field of generative modeling for computer vision, by exploring novel formulations of conditional generative models, and innovative applications in images, 3D animations, and video. Our research focuses on architectures that offer reversible transformations of noise and visual data, and the application of encoder-decoder architectures for generative tasks and 3D content manipulation. In all instances, we incorporate conditional information to enhance the synthesis of visual data, improving the efficiency of the generation process as well as the generated content. We introduce the use of Neural ODEs to model video dynamics using an encoder-decoder architecture, demonstrating their ability to predict future video frames despite being trained solely to reconstruct current frames. Next, we propose a conditional variant of continuous normalizing flows that enables higher-resolution image generation based on lower-resolution input, achieving comparable image quality while reducing parameters and training time. Our next contribution presents a pipeline that takes human images as input, automatically aligns a user-specified 3D character with the pose of the human, and facilitates pose editing based on partial inputs. Next, we derive the relevant mathematical details for denoising diffusion models that use non-isotropic Gaussian processes, and show comparable generation quality. Finally, we devise a novel denoising diffusion framework capable of solving all three video tasks of prediction, generation, and interpolation. We perform ablation studies, and show SOTA results on multiple datasets. Our contributions are published articles at peer-reviewed venues. Overall, our research aims to make a meaningful contribution to the pursuit of more efficient and flexible generative models, with the potential to shape the future of computer vision.

Monitoring the number of jumps for volleyball players during training or a match can be crucial to prevent injuries, yet the measurement requires considerable workload and cost using traditional methods such as video analysis. Also, existing methods do not provide accurate differentiation between different types of jumps. In this study, an unobtrusive system with a single inertial measurement unit (IMU) on the waist was proposed to recognize the types of volleyball jumps. A Multi-Layer Temporal Convolutional Network (MS-TCN) was applied for sample-wise classification. The model was evaluated on ten volleyball players and twenty-six volleyball players, during a lab session with a fixed protocol of jumping and landing tasks, and during four volleyball training sessions, respectively. The MS-TCN model achieved better performance than a state-of-the-art deep learning model but with lower computational cost. In the lab sessions, most jump counts showed small differences between the predicted jumps and video-annotated jumps, with an overall count showing a Limit of Agreement (LoA) of 0.1+-3.40 (r=0.884). For comparison, the proposed algorithm showed slightly worse results than VERT (a commercial jumping assessment device) with a LoA of 0.1+-2.08 (r=0.955) but the differences were still within a comparable range. In the training sessions, the recognition of three types of jumps exhibited a mean difference from observation of less than 10 jumps: block, smash, and overhead serve. These results showed the potential of using a single IMU to recognize the types of volleyball jumps. The sample-wise architecture provided high resolution of recognition and the MS-TCN required fewer parameters to train compared with state-of-the-art models.

Despite the inherently fuzzy nature of reconstructions in historical linguistics, most scholars do not represent their uncertainty when proposing proto-forms. With the increasing success of recently proposed approaches to automating certain aspects of the traditional comparative method, the formal representation of proto-forms has also improved. This formalization makes it possible to address both the representation and the computation of uncertainty. Building on recent advances in supervised phonological reconstruction, during which an algorithm learns how to reconstruct words in a given proto-language relying on previously annotated data, and inspired by improved methods for automated word prediction from cognate sets, we present a new framework that allows for the representation of uncertainty in linguistic reconstruction and also includes a workflow for the computation of fuzzy reconstructions from linguistic data.

Time is one of the crucial factors in real-world question answering (QA) problems. However, language models have difficulty understanding the relationships between time specifiers, such as 'after' and 'before', and numbers, since existing QA datasets do not include sufficient time expressions. To address this issue, we propose a Time-Context aware Question Answering (TCQA) framework. We suggest a Time-Context dependent Span Extraction (TCSE) task, and build a time-context dependent data generation framework for model training. Moreover, we present a metric to evaluate the time awareness of the QA model using TCSE. The TCSE task consists of a question and four sentence candidates classified as correct or incorrect based on time and context. The model is trained to extract the answer span from the sentence that is both correct in time and context. The model trained with TCQA outperforms baseline models up to 8.5 of the F1-score in the TimeQA dataset. Our dataset and code are available at https://github.com/sonjbin/TCQA

In this paper, we identify a cultural dominance issue within large language models (LLMs) due to the predominant use of English data in model training (e.g. ChatGPT). LLMs often provide inappropriate English-culture-related answers that are not relevant to the expected culture when users ask in non-English languages. To systematically evaluate the cultural dominance issue, we build a benchmark that consists of both concrete (e.g. holidays and songs) and abstract (e.g. values and opinions) cultural objects. Empirical results show that the representative GPT models suffer from the culture dominance problem, where GPT-4 is the most affected while text-davinci-003 suffers the least from this problem. Our study emphasizes the need for critical examination of cultural dominance and ethical consideration in their development and deployment. We show two straightforward methods in model development (i.e. pretraining on more diverse data) and deployment (e.g. culture-aware prompting) can significantly mitigate the cultural dominance issue in LLMs.

Ever since the development of GPT-3 in the natural language processing (NLP) field, in-context learning (ICL) has played an important role in utilizing large language models (LLMs). By presenting the LM utterance-label demonstrations at the input, the LM can accomplish few-shot learning without relying on gradient descent or requiring explicit modification of its parameters. This enables the LM to learn and adapt in a black-box manner. Despite the success of ICL in NLP, little work is exploring the possibility of ICL in speech processing. This study proposes the first exploration of ICL with a speech LM without text supervision. We first show that the current speech LM does not have the ICL capability. With the proposed warmup training, the speech LM can, therefore, perform ICL on unseen tasks. In this work, we verify the feasibility of ICL for speech LM on speech classification tasks.