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In diffusion-based generation, a neural network can be trained to predict the clean data, the noise, or the velocity from a noisy input, yet plain Diffusion Transformers operating on large pixel patches succeed with clean prediction and fail with noise or velocity prediction.
This work characterize task-space complexity through covering numbers under a prescribed metric, thereby quantifying the low-dimensional cross-task structure without requiring an explicit parametric representation and explicitly construct a Transformer that exploits their low-dimensional structure to perform ICL.
It is proved that an alternating Riemannian gradient scheme converges to a basin saddle point of the penalized DRO problem, recovering the linear and polynomial rates of the abstract theory with all constants explicit in terms of data dimension, loss moments, and the reference covariance.
This work proposes a simple and effective column-selective graph sampling algorithm based on a minimum inner product greedy selection rule, well-suited for large-scale graphs where the full Laplacian cannot be stored in memory.
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