The ongoing exponential rise in recording capacity calls for new approaches for analysing
and interpreting neural data. Effective dimensionality has emerged as an important property …

Diffusion models, a powerful and universal generative artificial intelligence technology, have
achieved tremendous success and opened up new possibilities in diverse applications. In …

Diffusion models achieve state-of-the-art performance in various generation tasks. However,
their theoretical foundations fall far behind. This paper studies score approximation …

The primary axes of interest in image-generating diffusion models are image quality, the
amount of variation in the results, and how well the results align with a given condition, eg, a …

Benchmarking models via classical simulations is one of the main ways to judge ideas in
quantum machine learning before noise-free hardware is available. However, the huge …

Rapidly increasing quality of AI-generated content makes it difficult to distinguish between
human and AI-generated texts, which may lead to undesirable consequences for society …

We investigate the statistical and computational limits of latent Diffusion Transformers (DiTs)
under the low-dimensional linear latent space assumption. Statistically, we study the …

Classically, data interpolation with a parametrized model class is possible as long as the
number of parameters is larger than the number of equations to be satisfied. A puzzling …

Score-based generative models (SGMs) need to approximate the scores $\nabla\log p_t $ of
the intermediate distributions as well as the final distribution $ p_T $ of the forward process …

This work attempts to provide a plausible theoretical framework that aims to interpret modern
deep (convolutional) networks from the principles of data compression and discriminative …