Kronecker-sparse (KS) matrices—whose supports are Kronecker products of identity and all-ones blocks—underpin the structure of Butterfly and Monarch matrices and offer the promise of more efficient models. However, existing GPU kernels for KS matrix multiplication suffer from high data movement costs, with up to 50% of time spent on memory-bound tensor permutations. We propose a fused, output-stationary GPU kernel that eliminates these overheads, reducing global memory traffic threefold. Across 600 KS patterns, our kernel achieves in FP32 a median speedup of x1.4 and lowers energy consumption by 15%. A simple heuristic based on KS pattern parameters predicts when our method outperforms existing ones. We release all code at github.com/PascalCarrivain/ksmm, including a PyTorch-compatible KSLinear layer, and demonstrate in FP32 end-to-end latency reductions of up to 22% in ViT-S/16 and 16% in GPT-2 medium.

We demonstrate, for the first time, 100Gb/s OTU4 over 400GE PLE (Private Line Emulation) across a packet network with OTN like service over a packet backbone. With the decrease of interest in OTN and emergence of IP over DWDM, PLE is an attractive proposal in the IETF for provisioning leased-lines (which continue to be high-margin services for providers). PLE involves the mapping of high-speed OTN services (OTU4 typically, but also OTU2) on to packets and use a smart signaling infrastructure of the packet switched network to provision pseudo-wires. We developed PLE hardware and interfaces it with IP routers to create 100Gb/s OTU4 over 400Gb/s Ethernet. We showed deterministic latency and low jitter in addition to significant network-wide power saving (up to 50%). Results also conform to the requirements of traditional circuit (OTN) communication.

Approximating a matrix by a product of few sparse factors whose supports possess the butterfly structure, which is common to many fast transforms, is key to learn fast transforms and speed up algorithms for inverse problems. We introduce a hierarchical approach that recursively factorizes the considered matrix into two factors. Using recent advances on the well-posedness and tractability of the two-factor fixed- support sparse matrix factorization problem, the proposed algorithm is endowed with exact recovery guarantees. Experiments show that speed and accuracy of the factorization can be jointly improved by several orders of magnitude, compared to gradient-based optimization methods.