In a controlled experiment on modular arithmetic ($p = 9973$), varying only example ordering while holding all else constant, two fixed-ordering strategies achieve 99.5\% test accuracy by epochs 487 and 659 respectively from a training set comprising 0.3\% of the input space, well below established sample complexity lower bounds for this task under IID ordering. The IID baseline achieves 0.30\% after 5{,}000 epochs from identical data. An adversarially structured ordering suppresses learning entirely. The generalizing model reliably constructs a Fourier representation whose fundamental frequency is the Fourier dual of the ordering structure, encoding information present in no individual training example, with the same fundamental emerging across all seeds tested regardless of initialization or training set composition. We discuss implications for training efficiency, the reinterpretation of grokking, and the safety risks of a channel that evades all content-level auditing.

But could more performance be squeezed out of networks by using different input representations?

Additionally, we show generalization performance of our proposed method across differentvisualdomains. Withthegiven problemcategory(task),asubsetforlearning can be sampled (via domain episode module in Figure 4 in main text). Here, by replacingclass with task, K-shot andN-task reasoning framework can be defined. Here, we show analogical learning with the existing meta learning framework for fast adaptation fromthesourcedomain tothetargetdomain.

V ox2Cortex: Fast explicit reconstruction of cortical surfaces from 3D MRI scans with geometric deep neural networks.

Network pruning is a commonly used measure to alleviate the storage and computational burden of deep neural networks. However, the fundamental limit of network pruning is still lacking. To close the gap, in this work we'll take a first-principles approach, i.e. we'll directly impose the sparsity constraint on the loss function and leverage the framework of statistical dimension in convex geometry, thus enabling us to characterize the sharp phase transition point, which can be regarded as the fundamental limit of the pruning ratio. Through this limit, we're able to identify two key factors that determine the pruning ratio limit, namely, weight magnitude and network sharpness .