We investigate the approximation and estimation rates of conditional diffusion transformers (DiTs) with classifier-free guidance. We present a comprehensive analysis for “in-context” conditional DiTs under various common assumptions: generic and strong Hölder, linear latent (subspace), and Lipschitz score function assumptions. Importantly, we establish minimax optimality of DiTs by leveraging score function regularity. Specifically, we discretize the input domains into infinitesimal grids and then perform term-by-term Taylor expansions on the conditional diffusion score function under the Hölder smooth data assumption. This enables fine-grained use of transformers’ universal approximation through a more detailed piecewise constant approximation, and hence obtains tighter bounds. Additionally, we extend our analysis to latent settings. Our findings establish statistical limits for DiTs and offer practical guidance toward more efficient and accurate designs.

We introduce the **Bi**-Directional **S**parse **Hop**field Network (**BiSHop**), a novel end-to-end framework for tabular learning. BiSHop handles the two major challenges of deep tabular learning: non-rotationally invariant data structure and feature sparsity in tabular data. Our key motivation comes from the recently established connection between associative memory and attention mechanisms. Consequently, BiSHop uses a dual-component approach, sequentially processing data both column-wise and row-wise through two interconnected directional learning modules. Computationally, these modules house layers of generalized sparse modern Hopfield layers, a sparse extension of the modern Hopfield model with learnable sparsity. Methodologically, BiSHop facilitates multi-scale representation learning, capturing both intra-feature and inter-feature interactions, with adaptive sparsity at each scale. Empirically, through experiments on diverse real-world datasets, BiSHop surpasses current SOTA methods with significantly fewer HPO runs, marking it a robust solution for deep tabular learning. The code is available on [GitHub](https://github.com/MAGICS-LAB/BiSHop); future updates are on [arXiv](https://arxiv.org/abs/2404.03830).