For certain infinitely-wide neural networks, the neural tangent kernel (NTK) theory fully characterizes generalization, but for the networks used in practice, the empirical NTK only provides a rough first-order approximation. Still, a growing body of work keeps leveraging this approximation to successfully analyze important deep learning phenomena and design algorithms for new applications. In our work, we provide strong empirical evidence to determine the practical validity of such approximation by conducting a systematic comparison of the behavior of different neural networks and their linear approximations on different tasks. We show that the linear approximations can indeed rank the learning complexity of certain tasks for neural networks, even when they achieve very different performances. However, in contrast to what was previously reported, we discover that neural networks do not always perform better than their kernel approximations, and reveal that the performance gap heavily depends on architecture, dataset size and training task. We discover that networks overfit to these tasks mostly due to the evolution of their kernel during training, thus, revealing a new type of implicit bias.

Expressing universal semantics common to all languages is helpful in understanding the meanings of complex and culture-specific sentences. The research theme underlying this scenario focuses on learning universal representations across languages with the usage of massive parallel corpora. However, due to the sparsity and scarcity of parallel data, there is still a big challenge in learning authentic "universals" for any two languages. In this paper, we propose EMMA-X: an EM-like Multilingual pre-training Algorithm, to learn (X)Cross-lingual universals with the aid of excessive multilingual non-parallel data.

Denoising Diffusion Probabilistic Models (DDPMs) provide the foundation for the recent breakthroughs in generative modeling. Their Markovian structure makes it difficult to define DDPMs with distributions other than Gaussian or discrete. In this paper, we introduce Star-Shaped DDPM (SS-DDPM). Its star-shaped diffusion process allows us to bypass the need to define the transition probabilities or compute posteriors. We establish duality between star-shaped and specific Markovian diffusions for the exponential family of distributions and derive efficient algorithms for training and sampling from SS-DDPMs. In the case of Gaussian distributions, SS-DDPM is equivalent to DDPM. However, SS-DDPMs provide a simple recipe for designing diffusion models with distributions such as Beta, von Mises-Fisher, Dirichlet, Wishart and others, which can be especially useful when data lies on a constrained manifold. We evaluate the model in different settings and find it competitive even on image data, where Beta SS-DDPM achieves results comparable to a Gaussian DDPM.

In this material, we will give more technical details as well as additional experiments to support the main paper. The overview of the proposed framework, DeWave, is illustrated in Figure 6. Ground Bush attended the University of Texas at Austin, where he graduated Phi Beta Kappa with a Truth Bachelor's degree in Latin American Studies in 1973, taking only two and a half years to complete his work, and obtaining generally excellent grades. Predictwas the University of California at Austin in where he studied in Beta Kappa in a degree of degree in history American Studies in 1975. ZuCo stands for Zurich Cognitive Language Processing Corpus (ZuCo), a dataset that includes both raw and preprocessed eye-tracking and electroencephalography (EEG) data. The data is collected by having human subjects read given text corpora while simultaneously recording both their eye-tracking signals and EEG waves.

The translation of brain dynamics into natural language is pivotal for braincomputer interfaces (BCIs). With the swift advancement of large language models, such as ChatGPT, the need to bridge the gap between the brain and languages becomes increasingly pressing. Current methods, however, require eye-tracking fixations or event markers to segment brain dynamics into word-level features, which can restrict the practical application of these systems. To tackle these issues, we introduce a novel framework, DeWave, that integrates discrete encoding sequences into open-vocabulary EEG-to-text translation tasks. DeWave uses a quantized variational encoder to derive discrete codex encoding and align it with pre-trained language models. This discrete codex representation brings forth two advantages: 1) it realizes translation on raw waves without marker by introducing text-EEG contrastive alignment training, and 2) it alleviates the interference caused by individual differences in EEG waves through an invariant discrete codex with or without markers.