Hand-Written PTX Tensor-Core GEMM Kernels: A Multi-Precision Study on NVIDIA L4
arXiv:2608. 10103v1 Announce Type: cross Abstract: High-performance Tensor Core kernels rely on a low-level PTX pipeline built from asynchronous data movement with cp.
arXiv:2606. 08761v1 Announce Type: cross Abstract: W4A4 quantization promises full utilization of INT4 Tensor Cores, yet group dequantization overhead on CUDA Cores has driven existing systems to mixed-precision fallbacks.
arXiv:2608. 10103v1 Announce Type: cross Abstract: High-performance Tensor Core kernels rely on a low-level PTX pipeline built from asynchronous data movement with cp.
arXiv:2606. 14598v1 Announce Type: new Abstract: Post-training INT8 (W8A8) quantization of diffusion transformers is widely deployed as a speed optimization, yet on consumer Ampere GPUs it is frequently slower than the FP8 and NF4 alternatives it is meant to beat.
arXiv:2607. 14568v1 Announce Type: cross Abstract: A companion study ran a 35B mixture-of-experts model on a 2011 NVIDIA Tesla C2075 (Fermi, sm_20, 6GB) as a GPU-prefill/CPU-decode hybrid, because the 4-bit model did not fit in device memory (arXiv:2606.
The paper addresses the problem of non‑deterministic outputs from large language models (LLMs) when run on different GPU architectures, caused by floating‑point non‑associativity and hardware‑dependent kernel choices. It proposes a set of fixed‑configuration fused‑upcast GEMM kernels that load 16‑bit weights, upcast to FP32, and perform IEEE‑754 compliant reductions in a problem‑shape‑dependent order, ensuring identical linear‑layer outputs across NVIDIA Ampere, Ada, and Hopper GPUs. The new approach achieves 1.17–3.1× faster end‑to‑end performance than existing solutions and halves weight‑memory traffic while maintaining cross‑architecture reproducibility.
The paper introduces format‑aware fusion, a method that co‑designs quantization producers with their scale domains and consumer layouts to fully exploit four‑bit floating‑point (FP4) Tensor Cores. Using this approach, the authors pretrain the Llama‑3‑family 8B model on 160 billion tokens, achieving up to 37.9 K tokens/s/GPU—significantly higher than standard bfloat16 or Transformer Engine FP4 baselines. The study demonstrates that FP4 performance depends on the interplay of scaling, operand packing, layout, and execution path, with downstream task rankings diverging from training‑loss rankings.
arXiv:2607. 25504v1 Announce Type: cross Abstract: Fine-grained weight pruning and activation sparsification have emerged as effective approaches for reducing the compute and memory cost of inference for Transformer models.
arXiv:2608. 15383v1 Announce Type: new Abstract: Sparse mixture-of-experts (MoE) language models reduce arithmetic by activating only a small subset of experts per token, yet deployment still requires storing and moving the full expert bank.
arXiv:2606. 20381v1 Announce Type: new Abstract: FP4 training promises substantial reductions in memory and computation cost for LLM pretraining, yet current FP4 hardware paths and recipes, including NVIDIA Blackwell/Rubin-class systems and AMD MI350-series GPUs, remain centered on E2M1 data elements.
arXiv:2606. 09682v1 Announce Type: new Abstract: AutoMegaKernel (AMK) compiles a HuggingFace Llama-family model into a single persistent cooperative CUDA kernel that runs the whole forward pass in one launch, with no per-model hand-written CUDA.
The article argues that on AI‑optimised NVIDIA B300 GPUs and newer, the FP8 tensor‑core matrix operation—implemented via the CRT‑based Ozaki Scheme II—can become the primary substrate for matrix‑heavy FP64 kernels while maintaining FP64‑grade accuracy. It introduces the Tensor‑Memory Equilibrium (TME) model, a Roofline extension with four parameters, to show that FP8 can match native FP64 performance under certain intensity thresholds and tile‑fusion conditions. The study identifies two notable exceptions—large dense‑square DGEMM and 3‑D FFT—where additional hardware or software adjustments are required to reach the memory roof. whyItMatters":"The paper demonstrates that FP8, with appropriate reconstruction and deconstruction strategies, can replace native FP64 for high‑performance computing workloads on modern GPUs, potentially reducing hardware complexity and energy consumption while preserving accuracy."
arXiv:2606. 18463v1 Announce Type: cross Abstract: Distributed stochastic gradient descent (SGD) is limited by communication rather than computation, since each iteration requires an AllReduce across processes.
arXiv:2607. 16241v1 Announce Type: cross Abstract: Recent large language models (LLMs) can generate custom CUDA kernels that appear to outperform PyTorch on benchmarks such as KernelBench.