Precision field guide · 18 July 2026

MXFP4Quantization

Four-bit values are too small to carry useful dynamic range alone. MXFP4’s answer is collective: thirty-two E2M1 numbers share one power-of-two exponent. The result is an open, hardware-friendly format that saves bytes aggressively—and exposes exactly where accuracy goes to die.

1 × E8M0 SHARED SCALE · 8 BITS
4 bitsE2M1 element
32 valuesper block
8 bitsE8M0 scale
4.25 bitseffective / value
01 / First, the name

It is MXFP4—
not MVFP4.

MX means microscaling. FP4 means each private element is four-bit floating point. The OCP standard makes the block—not the nibble—the real numerical contract.

Scalar E2M1 has one sign, two exponent and one mantissa bit. Its positive codebook is essentially 0, 0.5, 1, 1.5, 2, 3, 4 and 6. That is useful near unity and hopeless across tensors spanning many orders of magnitude.

MXFP4 groups 32 E2M1 elements under one 8-bit E8M0 scale. E8M0 is an unsigned, exponent-only power-of-two scale. Each represented value is the private FP4 value multiplied by the block scale.

The payload is not exactly four bits per value: 32 × 4 element bits + 8 scale bits = 136 bits, or 4.25 bits per value before packing and alignment.
PRIVATE ELEMENT

E2M1

Sign, two exponent and one mantissa bit; subnormals and round-to-nearest ties-to-even; no reserved Inf or NaN patterns.

SHARED SCALE

E8M0

A power-of-two exponent shared by 32 values. Hardware can combine scales with exponent adjustment rather than a general multiplier.

BLOCK CONTRACT

32 values

One outlier influences the quantization grid of 31 neighbors—the source of both low metadata cost and coupled error.

MX valuevᵢ = X(block) × Pᵢ(E2M1), i = 1…32
02 / Why microscaling exists

Spend exponent bits once.
Reuse them thirty-two times.

Scalar FP4

SE EM

Tiny and coarse. A whole-tensor software scale cannot follow local changes in range.

MXFP4 block

E8M0

Local block adaptation plus an element codebook that matrix hardware can consume natively.

Microscaling sits between per-value floating point and one scale for a tensor: spend a little metadata to make an extremely small local codebook useful.
03 / Systems payoff

Compression is only
the first dividend.

MXFP4 reduces bytes carried by weights and activations while targeting matrix engines that understand block scaling directly.

Against BF16, a packed 4.25-bit stream is about 3.76× smaller; against eight-bit data, about 1.88×. End-to-end savings are lower because norms, embeddings, accumulators, metadata, KV cache and buffers can remain wider.

The bigger payoff is movement. Smaller weights permit larger models or replicas in HBM. W4A4 execution shrinks both weight and activation traffic and can unlock native matrix throughput rather than dequantizing into a wider compute path.

↓ HBMcapacity

More model, cache or concurrency fits.

↓ bytesbandwidth

Less HBM and fabric traffic.

↑ maththroughput

More operands per matrix engine cycle.

Openportability

A multi-vendor OCP numerical contract.

A 70B weight tensor has a raw floor near 140 GB in BF16, 70 GB at eight bits, 35 GB at plain four bits and 37.2 GB at 4.25 effective bits. This excludes all other serving memory.
04 / Quantization error

One outlier can tax
thirty-one innocent values.

Block floating point works when neighboring values share a range. It loses information when a block mixes one large outlier with many small values.

The scale must cover the largest magnitude. A large outlier pushes the FP4 grid outward; small neighbors enter a dead zone near zero or collapse onto a few coarse levels. E8M0 adds power-of-two scale rounding, which simplifies hardware but may waste range.

The OCP specification defines interchange and basic operations, but intentionally does not prescribe the detailed scale-selection algorithm. Calibration, clipping, rotations, smoothing, overflow-aware scale choice, QAT and selective higher-precision fallbacks can therefore materially change quality.

FAILURE 01

Outlier domination

The maximum magnitude selects the neighborhood’s scale.

FAILURE 02

Dead-zone loss

Weak values round to zero and disappear.

FAILURE 03

Grid noise

E2M1 provides only a handful of levels inside each block.

05 / Comparison

Four bits is not one thing.

FormatElementScalingPayloadStrengthMain costScope
BF161/8/7Per value16 bRange, training stabilityBytesStandard
FP8 E4M31/4/3Tensor/delayed8 b + scaleStrong quality/throughput balance~2× FP4 bytesOCP
INT4IntegerGroup/channel4 b + metadataMature weight-only compressionActivation difficultyBroad
Scalar FP4E2M1Software chosen4 b + scaleSimple storageNo standard native scalingPrimitive
MXFP4E2M1E8M0 / 324.25 bOpen, efficient W4A4Coarse scale/outliersOCP open
NVFP4E2M1E4M3 / 16 + FP32 tensor≈4.5 b + tensor scaleFiner 4-bit accuracyMore metadata/vendor scopeNVIDIA

MXFP4 versus NVFP4: both use E2M1 private elements. MXFP4 shares a coarse power-of-two scale across 32 values. NVFP4 uses a richer E4M3 scale across 16 values plus a tensor-level FP32 scale, spending more metadata to reduce outlier coupling.

MXFP4 versus INT4: E2M1 offers nonuniform floating magnitudes; INT4 offers a uniform integer grid after scaling. INT4 weight-only methods are common, while native W4A4 demands activation-aware recipes and suitable matrix hardware.

06 / Hardware contract

Open representation does not mean
identical performance.

AMD, Arm, Intel, Meta, Microsoft, NVIDIA and Qualcomm authored the OCP MX specification. Portability of representation is not equivalence of implementation.

NVIDIA Blackwell Tensor Cores support MXFP4 alongside NVFP4. AMD CDNA 4 Matrix Cores advertise MXFP8, MXFP6 and MXFP4 instructions. Implementations can differ in packing, conversion, accumulation, transpose layouts, fused epilogues and achieved throughput.

Always ask whether “support” means conversion or native W4A4 GEMM with hardware scale handling, suitable accumulation and end-to-end framework kernels. If conversion or unfused fallbacks dominate, four-bit storage can fail to become four-bit performance.

07 / Deployment

The format is one stage
of quantization.

Observedistributions
Partition32-value blocks
Scalechoose E8M0
Quantizemap E2M1
Validatetask quality
Executenative dot products
Accumulatewider precision

PTQ

Calibrate an existing model using clipping, rotations or mixed-precision escape hatches. Cheap, but direct rounding can fail on sensitive activations.

QAT

Expose the model to MXFP4-like noise during training or fine-tuning. More investment, often better for native W4A4 quality.

W4A16

Compress weights but retain wide activations. Capacity gains remain; arithmetic throughput may not match native W4A4.

Mixed precision

Keep norms, embeddings, output heads, accumulators or fragile layers in FP8/BF16. Optimize the system, not numerical purity.

08 / Kimi K3 as a case study

Quantization can become
part of model design.

Moonshot says Kimi K3 uses MXFP4 weights and MXFP8 activations, with quantization-aware training beginning at supervised fine-tuning—not a last-minute checkpoint conversion.

That matters for a 2.8-trillion-parameter sparse model. A plain four-bit weight floor is about 1.4 TB; MXFP4’s 4.25-bit payload puts the simple block-level floor near 1.49 TB before runtime overhead. BF16 begins near 5.6 TB. The format changes how many accelerators are required merely to hold one replica.

K3 is not an end-to-end W4A4 claim: the disclosed pairing is MXFP4 weights with MXFP8 activations. Wider activations retain range while the model captures much of the weight-capacity and weight-bandwidth benefit. “The model is FP4” is inadequate—weights, activations, KV state, accumulators and operators may each use different formats.

Moonshot frames MX formats as a broad-hardware-compatibility choice. That is a strategic payoff of an OCP standard, even though optimized kernels and achieved quality remain platform-specific.

Evidence boundary: K3’s launch blog states the QAT stage and MXFP4/MXFP8 pairing. Until weights, configuration, kernels and the technical report are public, exact overhead, exclusions and realized speedups remain undisclosed.
09 / Benchmark discipline

Never benchmark
“FP4” by itself.

NUMERICAL RECIPE

What was quantized?

State W4A4, W4A8 or W4A16; PTQ versus QAT; block order; scale choice; clipping; fallbacks; KV and accumulator formats.

SYSTEM SHAPE

What was executed?

Name hardware, kernels, batch, prompt/output lengths, parallelism, achieved bandwidth, power, latency and throughput.

QUALITY COST

What was preserved?

Report perplexity and task accuracy across reasoning, code and long context, plus any extra training or calibration expense.

A smaller checkpoint that needs more training or yields more wrong answers can lose the economic win. Measure quality-adjusted tokens per dollar and joule, not bytes alone.
10 / Bottom line

MXFP4 makes precision
a neighborhood decision.

The individual number is four bits. Its meaning comes from the thirty-one values beside it and the exponent they share.

This is microscaling’s central move: keep private values tiny, restore range locally and make the block a unit of transport and computation. The dividend reaches HBM capacity, matrix throughput and fabric traffic.

The tradeoff is structural. An outlier changes the grid for an entire micro-block. MXFP4’s open format and simple E8M0 scaling favor portable hardware economy. NVFP4’s finer blocks and richer scales favor fidelity at modest extra metadata. INT4, FP8 and BF16 occupy other points on the triangle of quality, bytes and compute cost.

The best format is not the smallest encoding. It is the smallest end-to-end numerical contract the model, kernels and accelerator can execute without returning the savings as fallbacks, extra tokens or lost accuracy.

Companion field guide → How lower-precision weights change HBM capacity and per-token movement.
11 / Sources & method

Specification first.
Vendor claims attributed.

OCP defines the normative format. Vendor documents establish hardware support; research results remain recipe-specific evidence. Accessed 18 July 2026.

  1. 01OCP MX Specification v1.0
  2. 02OCP MX Alliance announcement
  3. 03NVIDIA MXFP4/NVFP4 comparison
  4. 04AMD CDNA 4 architecture
  5. 05OCP Microscaling Formats paper
  6. 06Shared Microexponents (ISCA)
  7. 07MXFP4 error-reduction strategies
  8. 08NVFP4 KV-cache comparison
  9. 09Kimi K3 launch technical blog
Calculation: (32 × 4 + 8) ÷ 32 = 4.25 bits/value. Alignment and metadata may increase physical storage.