Efficient hardware realization of tensorized layers

Develop kernel-level implementations that make tensorized neural-network layers execute efficiently on modern GPU hardware, thereby translating parameter and FLOP reductions into actual speedups relative to dense general matrix multiplication.

Background

Tensorized layers replace large dense matrix multiplications with chains of smaller tensor contractions. Although this can reduce parameter counts and theoretical arithmetic, modern GPUs are optimized primarily for large, regular GEMM operations, while sequential or irregular contractions may suffer from launch overhead, poor utilization, and costly intermediate materialization.

The paper identifies the resulting compression-realization gap as a central systems problem. Fused kernels, structure-aware kernels, and optimized Triton or CUDA implementations are suggested as possible approaches, with evaluation based on measured end-to-end speedup rather than theoretical compression alone.

References

The general solution to this challenge remains an open direction (\cref{sec:future-directions}).

— Tensor Methods for Language Models: From Token Representation to Training, Adaptation, Inference, Compression, and Interpretability  (2608.30505 - Tarasov et al., 31 Aug 2026) in Section 3, subsection “Bilinear FFN,” and Section 7.2, paragraph “Hardware compatibility”

Logical-shape efficiency is a further open cost: the exact logical shapes are a pair of $K{=}8, N{=}r$ GEMMs (or one $K{=}8, N{=}2r$ product with the two limb outputs kept separate, then recombined with weight $256$---concatenating the limbs along $K$ would sum them unweighted and is not the identity); such narrow shapes do not map to dense MMA tiles at peak, and the vendor int8 figure is a dense-tile rate, not a proven concurrent capacity beside near-peak fp#1{8} work (the two-endpoint concurrency bracket of \S~\ref{sec:proj} quantifies both extremes of that uncertainty).

— Ozaki 2.5: Engineering the Deconstruction Path of fp64-Emulated Dense Matrix Multiplication on FP8 Tensor Cores  (2609.09095 - Matsuoka, 8 Sep 2026) in Section 5, paragraph “O2: the byte-plane reduction as tensor work—the exact two-limb encoding”