We propose a model to flexibly estimate joint tail properties by exploiting the convergence of an appropriately scaled point cloud onto a compact limit set. Characteristics of the shape of the limit set correspond to key tail dependence properties. We directly model the shape of the limit set using Bezier splines, which allow flexible and parsimonious specification of shapes in two dimensions. We then fit the Bezier splines to data in pseudo-polar coordinates using Markov chain Monte Carlo, utilizing a limiting approximation to the conditional likelihood of the radii given angles. By imposing appropriate constraints on the parameters of the Bezier splines, we guarantee that each posterior sample is a valid limit set boundary, allowing direct posterior analysis of any quantity derived from the shape of the curve. Furthermore, we obtain interpretable inference on the asymptotic dependence class by using mixture priors with point masses on the corner of the unit box. Finally, we apply our model to bivariate datasets of extremes of variables related to fire risk and air pollution.
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While preconditioning is a long-standing concept to accelerate iterative methods for linear systems, generalizations to matrix functions are still in their infancy. We go a further step in this direction, introducing polynomial preconditioning for Krylov subspace methods which approximate the action of the matrix square root and inverse square root on a vector. Preconditioning reduces the subspace size and therefore avoids the storage problem together with -- for non-Hermitian matrices -- the increased computational cost per iteration that arises in the unpreconditioned case. Polynomial preconditioning is an attractive alternative to current restarting or sketching approaches since it is simpler and computationally more efficient. We demonstrate this for several numerical examples.
This paper introduces a novel pipeline to reconstruct the geometry of interacting multi-person in clothing on a globally coherent scene space from a single image. The main challenge arises from the occlusion: a part of a human body is not visible from a single view due to the occlusion by others or the self, which introduces missing geometry and physical implausibility (e.g., penetration). We overcome this challenge by utilizing two human priors for complete 3D geometry and surface contacts. For the geometry prior, an encoder learns to regress the image of a person with missing body parts to the latent vectors; a decoder decodes these vectors to produce 3D features of the associated geometry; and an implicit network combines these features with a surface normal map to reconstruct a complete and detailed 3D humans. For the contact prior, we develop an image-space contact detector that outputs a probability distribution of surface contacts between people in 3D. We use these priors to globally refine the body poses, enabling the penetration-free and accurate reconstruction of interacting multi-person in clothing on the scene space. The results demonstrate that our method is complete, globally coherent, and physically plausible compared to existing methods.
Diffusion models are a class of generative models that serve to establish a stochastic transport map between an empirically observed, yet unknown, target distribution and a known prior. Despite their remarkable success in real-world applications, a theoretical understanding of their generalization capabilities remains underdeveloped. This work embarks on a comprehensive theoretical exploration of the generalization attributes of diffusion models. We establish theoretical estimates of the generalization gap that evolves in tandem with the training dynamics of score-based diffusion models, suggesting a polynomially small generalization error ($O(n^{-2/5}+m^{-4/5})$) on both the sample size $n$ and the model capacity $m$, evading the curse of dimensionality (i.e., not exponentially large in the data dimension) when early-stopped. Furthermore, we extend our quantitative analysis to a data-dependent scenario, wherein target distributions are portrayed as a succession of densities with progressively increasing distances between modes. This precisely elucidates the adverse effect of "modes shift" in ground truths on the model generalization. Moreover, these estimates are not solely theoretical constructs but have also been confirmed through numerical simulations. Our findings contribute to the rigorous understanding of diffusion models' generalization properties and provide insights that may guide practical applications.
We present a large-scale empirical study of how choices of configuration parameters affect performance in knowledge distillation (KD). An example of such a KD parameter is the measure of distance between the predictions of the teacher and the student, common choices for which include the mean squared error (MSE) and the KL-divergence. Although scattered efforts have been made to understand the differences between such options, the KD literature still lacks a systematic study on their general effect on student performance. We take an empirical approach to this question in this paper, seeking to find out the extent to which such choices influence student performance across 13 datasets from 4 NLP tasks and 3 student sizes. We quantify the cost of making sub-optimal choices and identify a single configuration that performs well across the board.
College students with ADHD respond positively to simple socially assistive robots (SARs) that monitor attention and provide non-verbal feedback, but studies have been done only in brief in-lab sessions. We present an initial design and evaluation of an in-dorm SAR study companion for college students with ADHD. This work represents the introductory stages of an ongoing user-centered, participatory design process. In a three-week within-subjects user study, university students (N=11) with self-reported symptoms of adult ADHD had a SAR study companion in their dorm room for two weeks and a computer-based system for one week. Toward developing SARs for long-term, in-dorm use, we focus on 1) evaluating the usability and desire for SAR study companions by college students with ADHD and 2) collecting participant feedback about the SAR design and functionality. Participants responded positively to the robot; after one week of regular use, 91% (10 of 11) chose to continue using the robot voluntarily in the second week.
We analyze the number of queries that a whitebox adversary needs to make to a private learner in order to reconstruct its training data. For $(\epsilon, \delta)$ DP learners with training data drawn from any arbitrary compact metric space, we provide the \emph{first known lower bounds on the adversary's query complexity} as a function of the learner's privacy parameters. \emph{Our results are minimax optimal for every $\epsilon \geq 0, \delta \in [0, 1]$, covering both $\epsilon$-DP and $(0, \delta)$ DP as corollaries}. Beyond this, we obtain query complexity lower bounds for $(\alpha, \epsilon)$ R\'enyi DP learners that are valid for any $\alpha > 1, \epsilon \geq 0$. Finally, we analyze data reconstruction attacks on locally compact metric spaces via the framework of Metric DP, a generalization of DP that accounts for the underlying metric structure of the data. In this setting, we provide the first known analysis of data reconstruction in unbounded, high dimensional spaces and obtain query complexity lower bounds that are nearly tight modulo logarithmic factors.
In this paper, we study sampling from a posterior derived from a neural network. We propose a new probabilistic model consisting of adding noise at every pre- and post-activation in the network, arguing that the resulting posterior can be sampled using an efficient Gibbs sampler. For small models, the Gibbs sampler attains similar performances as the state-of-the-art Markov chain Monte Carlo (MCMC) methods, such as the Hamiltonian Monte Carlo (HMC) or the Metropolis adjusted Langevin algorithm (MALA), both on real and synthetic data. By framing our analysis in the teacher-student setting, we introduce a thermalization criterion that allows us to detect when an algorithm, when run on data with synthetic labels, fails to sample from the posterior. The criterion is based on the fact that in the teacher-student setting we can initialize an algorithm directly at equilibrium.
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.
We propose a novel approach to multimodal sentiment analysis using deep neural networks combining visual analysis and natural language processing. Our goal is different than the standard sentiment analysis goal of predicting whether a sentence expresses positive or negative sentiment; instead, we aim to infer the latent emotional state of the user. Thus, we focus on predicting the emotion word tags attached by users to their Tumblr posts, treating these as "self-reported emotions." We demonstrate that our multimodal model combining both text and image features outperforms separate models based solely on either images or text. Our model's results are interpretable, automatically yielding sensible word lists associated with emotions. We explore the structure of emotions implied by our model and compare it to what has been posited in the psychology literature, and validate our model on a set of images that have been used in psychology studies. Finally, our work also provides a useful tool for the growing academic study of images - both photographs and memes - on social networks.
While it is nearly effortless for humans to quickly assess the perceptual similarity between two images, the underlying processes are thought to be quite complex. Despite this, the most widely used perceptual metrics today, such as PSNR and SSIM, are simple, shallow functions, and fail to account for many nuances of human perception. Recently, the deep learning community has found that features of the VGG network trained on the ImageNet classification task has been remarkably useful as a training loss for image synthesis. But how perceptual are these so-called "perceptual losses"? What elements are critical for their success? To answer these questions, we introduce a new Full Reference Image Quality Assessment (FR-IQA) dataset of perceptual human judgments, orders of magnitude larger than previous datasets. We systematically evaluate deep features across different architectures and tasks and compare them with classic metrics. We find that deep features outperform all previous metrics by huge margins. More surprisingly, this result is not restricted to ImageNet-trained VGG features, but holds across different deep architectures and levels of supervision (supervised, self-supervised, or even unsupervised). Our results suggest that perceptual similarity is an emergent property shared across deep visual representations.
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