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. 78% of citing Pith papers cite this work as background.
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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
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.
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.
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.
LLMs resist low-frequency permanent GPU faults but certain datapaths and precision formats trigger catastrophic training divergence even at moderate fault rates.
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.
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.
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.
P3-LLM delivers 4.9x average speedup over HBM-PIM for edge LLM inference by pairing hybrid-format quantization with iso-area-optimized low-precision PIM compute units and operator fusion.
citing papers explorer
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Bit-Accurate Modeling of GPU Matrix Multiply-Accumulate Units: Demystifying Numerical Discrepancy and Accuracy
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.
-
LongLive-2.0: An NVFP4 Parallel Infrastructure for Long Video Generation
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: Adaptive Importance Sampling for Quantized RL
AIS adaptively corrects non-stationary policy gradient bias in quantized LLM RL, matching BF16 performance while retaining 1.5-2.76x FP8 rollout speedup.
-
The Illusion of Power Capping in LLM Decode: A Phase-Aware Energy Characterisation Across Attention Architectures
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: A Hebrew-Specialized Open-Weight Mixture-of-Experts Language Model
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: An Area-efficient Reconfigurable Floating-Point Unit for Trans-Precision Dot-Product Accumulation for FPGA AI Engines
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: A Lossless AI Model Compression Method Enabling Fast Inference on Ascend NPUs
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.
-
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.
-
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.
-
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.
-
Recursive Block-Diagonal Coupling for Resource-Efficient Training of Vision Models
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.
-
Advancing Narrative Long Video Generation via Training-Free Identity-Aware Memory
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.
-
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.
-
ShardTensor: Domain Parallelism for Scientific Machine Learning
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: Surpassing Hardware Peaks with Lower-Complexity Matrix Multiplication
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 Lens: Activation and Gradient Spectra as Diagnostics of LLM Optimization
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: Scaling Native Resolution Auto-Encoders to 5 Billion Parameters
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-Network-Based Variational Method in Nuclear Density Functional Theory: Application to the Extended Thomas-Fermi Model
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: 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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LLM-PRISM: Characterizing Silent Data Corruption from Permanent GPU Faults in LLM Training
LLMs resist low-frequency permanent GPU faults but certain datapaths and precision formats trigger catastrophic training divergence even at moderate fault rates.
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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.
-
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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P3-LLM: An Integrated NPU-PIM Accelerator for Edge LLM Inference Using Hybrid Numerical Formats
P3-LLM delivers 4.9x average speedup over HBM-PIM for edge LLM inference by pairing hybrid-format quantization with iso-area-optimized low-precision PIM compute units and operator fusion.
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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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TACO: Efficient Communication Compression of Intermediate Tensors for Scalable Tensor-Parallel LLM Training
TACO compresses tensor-parallel intermediate tensors with an adaptive FP8 scheme and fused kernels, yielding up to 1.87X throughput gains on GPT and Qwen models with near-lossless accuracy.
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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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Balancing FP8 Computation Accuracy and Efficiency on Digital CIM via Shift-Aware On-the-fly Aligned-Mantissa Bitwidth Prediction
A 28nm digital CIM accelerator for FP8 uses on-the-fly shift-aware bitwidth prediction, FIFO alignment, and scalable MACs to reach 20.4 TFLOPS/W and 2.8x better efficiency than prior work while supporting variable mantissa widths.
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NVIDIA Nemotron 3: Efficient and Open Intelligence
NVIDIA releases the Nemotron 3 model family with hybrid Mamba-Transformer architecture, LatentMoE, NVFP4 training, MTP layers, and multi-environment RL post-training for reasoning and agentic tasks.
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OISMA: On-the-fly In-memory Stochastic Multiplication Architecture for Matrix-Multiplication Workloads
OISMA is an in-memory computing design using quasi-stochastic bent-pyramid computing to convert memory reads into multiplications, demonstrated in a 4-kB RRAM array with 0.789 TOPS/W at 50 MHz in 180-nm technology and projected gains at 22-nm.
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Analysis of Floating-Point Matrix Multiplication Computed via Integer Arithmetic
Error analysis and cost estimator for recasting floating-point matrix multiplication as accumulated integer products on mixed-precision hardware.
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NVILA: Efficient Frontier Visual Language Models
NVILA improves on VILA with a scale-then-compress visual token strategy and full-lifecycle efficiency optimizations, matching or exceeding leading VLMs on image and video benchmarks while reducing training cost 1.9-5.1x and latencies 1.2-2.8x.
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StatQAT: Statistical Quantizer Optimization for Deep Networks
A statistical error analysis framework yields iterative and analytic quantizers that improve accuracy and stability when incorporated into quantization-aware training for integer and floating-point formats.
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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.
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Rewriting TTS Inference Economics: Lightning V2 on Tenstorrent Achieves 4x Lower Cost Than NVIDIA L40S
Lightning V2 achieves 4x lower on-prem accelerator cost for TTS inference on Tenstorrent hardware than NVIDIA L40S at equivalent throughput and production audio fidelity.
- Decomposing MXFP4 quantization error for LLM reinforcement learning: reducible bias, recoverable deadzone, and an irreducible floor