Implement causal linear attention in chunks and combine chunk summaries with an associative scan instead of carrying the recurrent state through all chunks sequentially. This preserves the exact causal computation while reducing inter-chunk dependency depth from the number of chunks to its logarithm, enabling substantially more GPU parallelism for long-context training and prefill.
Replace uniform node minibatches in a GNN with a coreset selected from a small random candidate set using local Laplacian-column coherence. Select nodes whose connectivity signatures are least redundant with already selected nodes, while retaining inverse-probability weights for unbiased loss estimates. This should improve coverage of weakly connected graph clusters and preserve smooth graph signals at the same batch size.
Replace a raw minibatch gradient with an unbiased control-variate estimator that subtracts predictable components of per-example gradients and adds back their exactly or cheaply known population mean. Select the control-variate directions using leading eigenvectors of an online covariance operator, rather than using arbitrary scalar baselines. This should reduce gradient variance at fixed batch size and permit fewer examples per optimization step.
Represent every mesh interface degree of freedom by one feature copy per incident cell, and apply local neural blocks directly to these cell tensors. Enforce inter-cell consistency with valence-weighted averaging only after selected layers or hierarchy transitions, avoiding repeated construction of a global sparse graph or assembled feature vector. This is suited to adaptive quadtrees, octrees, and finite-element neural operators.
Represent many related sparse graph or attention patterns inside one fixed host connectivity pattern and activate each target instance with binary directional masks. The learned edge transformation and sparse-kernel layout are shared across instances, while the mask selects the target graph, enabling one compiled operator to process heterogeneous structures.