The authors derive the first bit-accurate arithmetic models for matrix multiply-accumulate operations on ten GPU architectures spanning NVIDIA Volta to Blackwell and AMD CDNA1 to CDNA3.
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FP8 Formats for Deep Learning
Canonical reference. 80% of citing Pith papers cite this work as background.
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abstract
FP8 is a natural progression for accelerating deep learning training inference beyond the 16-bit formats common in modern processors. In this paper we propose an 8-bit floating point (FP8) binary interchange format consisting of two encodings - E4M3 (4-bit exponent and 3-bit mantissa) and E5M2 (5-bit exponent and 2-bit mantissa). While E5M2 follows IEEE 754 conventions for representatio of special values, E4M3's dynamic range is extended by not representing infinities and having only one mantissa bit-pattern for NaNs. We demonstrate the efficacy of the FP8 format on a variety of image and language tasks, effectively matching the result quality achieved by 16-bit training sessions. Our study covers the main modern neural network architectures - CNNs, RNNs, and Transformer-based models, leaving all the hyperparameters unchanged from the 16-bit baseline training sessions. Our training experiments include large, up to 175B parameter, language models. We also examine FP8 post-training-quantization of language models trained using 16-bit formats that resisted fixed point int8 quantization.
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representative citing papers
The paper delivers the first systems characterization of agent memory, with a four-axis taxonomy, phase-aware profiler, evaluation of ten systems on two benchmarks, and ten design recommendations.
IEEE P3109 defines a family of adjustable low-precision floating-point formats for ML with decoding to extended reals, multiple rounding modes, block operations, kappa-approximation for approximations, and mechanical verification.
Floating-point neural networks achieve universal representability for practical activations like ReLU, sigmoid, and tanh under arbitrary reduction orders and bounded ulp errors in activations via a new distinguishability condition.
LongLive-2.0 delivers an NVFP4 parallel infrastructure that enables direct training of long multi-shot autoregressive diffusion video models and achieves up to 2.15x training and 1.84x inference speedups on Blackwell and other GPUs.
AIS adaptively corrects non-stationary policy gradient bias in quantized LLM RL, matching BF16 performance while retaining 1.5-2.76x FP8 rollout speedup.
Power capping is illusory in LLM decode as memory-bound operation leaves power headroom untouched on 700 W GPUs, while SM clock locking saves up to 32% energy and three DVFS classes appear across attention types.
Hebatron is the first open-weight Hebrew MoE LLM adapted from Nemotron-3, reaching 73.8% on Hebrew reasoning benchmarks while activating only 3B parameters per pass and supporting 65k-token context.
TransDot unifies SIMD FMA and trans-precision DPA in one reconfigurable FPU, achieving 2x FP16, 4x FP8, and 8x FP4 throughput with FP32 accumulation plus 1.46x to 2.92x area efficiency gains over the FPnew baseline.
ENEC delivers 3.43X higher throughput than DietGPU and 1.12X better compression ratio than nvCOMP for lossless model weight compression on Ascend NPUs, yielding up to 6.3X end-to-end inference speedup.
Low-precision Flash Attention fails due to similar low-rank attention representations combined with biased rounding errors that accumulate and corrupt weight updates; a minimal fix to reduce rounding bias stabilizes training.
DPQuant uses epoch-wise probabilistic layer rotation and DP loss sensitivity to quantize only a changing subset of layers, reducing accuracy degradation from quantization noise in DP-SGD and delivering up to 2.21x throughput gains with under 2% accuracy drop.
FlashAttention-3 achieves 1.5-2x speedup on H100 GPUs for attention, reaching 740 TFLOPs/s (75% utilization) in FP16 and near 1.2 PFLOPs/s in FP8 while cutting numerical error by 2.6x versus baseline FP8 attention.
dMX is a differentiable mixed-precision framework that learns per-layer MXFP bit-width assignments for LLMs and outperforms KL-based heuristics on perplexity and zero-shot accuracy under bit-width budgets.
RBDC trains wide vision models by recursive block-diagonal coupling of narrower pre-trained models, reducing training FLOPs by 30% at similar ImageNet accuracy for DeiT and ResNet while outperforming model growth baselines.
MXFP4 quantization error decomposes into scale bias, deadzone truncation, and grid noise; mode-targeted corrections recover BF16 accuracy within 0.7% on Qwen2.5-3B and exceed it by 1.0% on Qwen3-30B-A3B.
IAMFlow is a training-free identity-aware memory system that tracks entities via LLM global ID assignment and VLM frame verification to reduce identity drift in narrative long video generation from shifting prompts.
ScaleSearch optimizes block floating point scales via fine-grained search to cut quantization error by 27% for NVFP4, improving PTQ by up to 15 points on MATH500 for Qwen3-8B and attention PPL by 0.77 on Llama 3.1 70B.
ShardTensor is a domain-parallelism system for SciML that enables flexible scaling of extreme-resolution spatial datasets by removing the constraint of batch size one per device.
FalconGEMM delivers a framework with deployment, group-parallel execution, and analytical decision modules that makes lower-complexity matrix multiplication practical, beating cuBLAS and similar libraries by 7.59-17.85% on LLM tasks.
Spectral analysis of activations and gradients provides new diagnostics that link batch size to representation geometry, early covariance tails to token efficiency, and spectral shifts to learning dynamics in decoder-only LLMs, backed by a mechanistic model.
ViTok-v2 is a 5B-parameter native-resolution image autoencoder using NaFlex and DINOv3 loss that matches or exceeds prior tokenizers at 256p and outperforms them at 512p and above while advancing the Pareto frontier in joint scaling with generators.
Neural networks represent densities in a variational extended Thomas-Fermi model, yielding binding energies within 0.5% of prior ETF results and reproducing nuclear pasta phases.
StoSignSGD resolves SignSGD divergence on non-smooth objectives via structural stochasticity, matching optimal convex rates and improving non-convex bounds while delivering 1.44-2.14x speedups in FP8 LLM pretraining.
citing papers explorer
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Novel Aspects of IEEE SA P3109 Arithmetic Formats for Machine Learning
IEEE P3109 defines a family of adjustable low-precision floating-point formats for ML with decoding to extended reals, multiple rounding modes, block operations, kappa-approximation for approximations, and mechanical verification.
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Expressive Power of Floating-Point Neural Networks with Arbitrary Reduction Orders and Inexact Activation Implementations
Floating-point neural networks achieve universal representability for practical activations like ReLU, sigmoid, and tanh under arbitrary reduction orders and bounded ulp errors in activations via a new distinguishability condition.
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Why Low-Precision Transformer Training Fails: An Analysis on Flash Attention
Low-precision Flash Attention fails due to similar low-rank attention representations combined with biased rounding errors that accumulate and corrupt weight updates; a minimal fix to reduce rounding bias stabilizes training.
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DPQuant: Efficient and Differentially-Private Model Training via Dynamic Quantization Scheduling
DPQuant uses epoch-wise probabilistic layer rotation and DP loss sensitivity to quantize only a changing subset of layers, reducing accuracy degradation from quantization noise in DP-SGD and delivering up to 2.21x throughput gains with under 2% accuracy drop.
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FlashAttention-3: Fast and Accurate Attention with Asynchrony and Low-precision
FlashAttention-3 achieves 1.5-2x speedup on H100 GPUs for attention, reaching 740 TFLOPs/s (75% utilization) in FP16 and near 1.2 PFLOPs/s in FP8 while cutting numerical error by 2.6x versus baseline FP8 attention.
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dMX: Differentiable Mixed-Precision Assignment for Low-Precision Floating-Point Formats
dMX is a differentiable mixed-precision framework that learns per-layer MXFP bit-width assignments for LLMs and outperforms KL-based heuristics on perplexity and zero-shot accuracy under bit-width budgets.
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Decomposing MXFP4 quantization error for LLM reinforcement learning: reducible bias, recoverable deadzone, and an irreducible floor
MXFP4 quantization error decomposes into scale bias, deadzone truncation, and grid noise; mode-targeted corrections recover BF16 accuracy within 0.7% on Qwen2.5-3B and exceed it by 1.0% on Qwen3-30B-A3B.
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Search Your Block Floating Point Scales!
ScaleSearch optimizes block floating point scales via fine-grained search to cut quantization error by 27% for NVFP4, improving PTQ by up to 15 points on MATH500 for Qwen3-8B and attention PPL by 0.77 on Llama 3.1 70B.
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StoSignSGD: Unbiased Structural Stochasticity Fixes SignSGD for Training Large Language Models
StoSignSGD resolves SignSGD divergence on non-smooth objectives via structural stochasticity, matching optimal convex rates and improving non-convex bounds while delivering 1.44-2.14x speedups in FP8 LLM pretraining.
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STQuant: Spatio-Temporal Adaptive Framework for Optimizer Quantization in Large Multimodal Model Training
STQuant dynamically allocates quantization bits for optimizer states in multimodal model training, reducing memory by 84.4% to an average 5.1 bits while preserving quality on GPT-2 and ViT.
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AdaHOP: Fast and Accurate Low-Precision Training via Outlier-Pattern-Aware Rotation
AdaHOP applies pattern-aware Hadamard transforms and selective outlier extraction to enable from-scratch MXFP4 training of LLMs at BF16 quality with up to 3.6X memory compression and 1.46X speedup.
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BOOST: BOttleneck-Optimized Scalable Training Framework for Low-Rank Large Language Models
BOOST delivers 1.46-2.27x end-to-end speedups for low-rank bottleneck LLMs by redesigning tensor parallelism around the bottleneck structure plus supporting optimizations.
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GNMR: Runtime Stability Control for Low-Precision Large Language Model Training
GNMR is a gradient-norm-based controller that maps local stability signals to budgeted recovery actions to stabilize low-precision LLM training while preserving quality.
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Training-Inference Kernel Contracts: Bounding Divergence in Post-Training and Deployment
Introduces kernel contracts framework with derived bounds on divergence from logit drift to reward drift, specialized for RL post-training under support and norm assumptions.
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StreamIndex: Memory-Bounded Compressed Sparse Attention via Streaming Top-k
Chunked streaming top-k enables CSA indexer execution at 1M sequence length with 6.21 GB peak memory and >=0.998 recall on synthetic V4-shaped inputs.
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SnapMLA: Efficient Long-Context MLA Decoding via Hardware-Aware FP8 Quantized Pipelining
SnapMLA achieves up to 1.91x higher throughput in long-output MLA decoding using FP8 quantization and specialized kernels while keeping benchmark quality near the BF16 baseline.
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Max-Window Scale Estimation for Near-Lossless HiF8 W8A8 Quantization-Aware Training
Identifies amax saturation and catastrophic forgetting in HiF8 W8A8 QAT for OpenPangu-Embedded-1B and mitigates them with 64-step max-window DTS and 500-step BF16 warmup at lr=1e-5 to achieve under 0.6% benchmark drops.
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HiFloat4 Format for Language Model Pre-training on Ascend NPUs
HiFloat4 FP4 with stabilization techniques trains dense and MoE language models on Ascend NPUs at relative error within 1% of full-precision baselines.