An 84-Format Numeric Catalog with Bit-Exact Conformance Vectors: A Vendor-Neutral Reference for FP8, BF16, MXFP4, and Microscaling Formats
This paper presents a vendor-neutral catalog of 84 numeric formats and six bit-exact conformance packs, complete with cross-validated JSON artifacts and an IEEE P3109 cross-walk, to provide a shared reference for diagnosing silent divergences in machine learning hardware implementations.
Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer
Imagine you are a master carpenter trying to build a chair. You have a blueprint that says, "Cut this leg to 24 inches." But when you go to the hardware store, you find three different rulers: one says "24 inches," another says "24.1 inches," and a third says "24 inches, but if you cut past 24, the wood turns to dust."
If you use the wrong ruler, your chair might look fine at first, but it will wobble or break when someone sits on it.
This paper is about a similar problem in the world of Artificial Intelligence (AI) chips. Engineers are building faster, smaller "rulers" (numeric formats) to measure numbers for AI. They have created dozens of new types, like FP8, BF16, and MXFP4. The problem is that while everyone agrees on the name of the ruler (e.g., "FP8 E4M3"), they don't always agree on exactly how the markings are placed. One chip might handle a huge number by capping it at a maximum value, while another chip might just throw an error (NaN) when that number gets too big.
This paper introduces a "Shared Master Ruler" to fix this confusion.
What is this paper?
The author, Dmitrii Vasilev, has created two main tools to help engineers speak the same language:
The "84-Format Catalog" (The Encyclopedia):
Think of this as a massive dictionary or a library card catalog. It lists 84 different ways computers can store numbers, organized into 13 families. For each format, it lists the exact rules: how many bits are used, how big the numbers can get, and what happens when a number is too big (does it stop at the limit, or does it turn into "Not a Number"?).- Analogy: It's like a master list of every type of screw, bolt, and nut in existence, with a diagram showing exactly how many threads each one has.
The "Six Conformance Packs" (The Test Kits):
The paper doesn't just list the rules; it provides six specific test kits for the most popular formats used in real AI hardware right now (GF16, MXFP4, BF16, FP8 E4M3, FP8 E5M2, and E8M0).- Each kit is a digital file containing a list of "test numbers."
- It tells you exactly what the computer chip should output for each number.
- It includes a special "Anchor Number" (the value 3.0) that acts like a sanity check. If your chip can't correctly process this specific number, you know something is broken.
- Analogy: These are like "calibration weights" you put on a scale. If the scale doesn't read exactly 3.0 pounds when you put the 3-pound weight on it, you know the scale is broken.
The Big Discovery: "The Interpretation Gap"
The most important part of the paper isn't just that the rulers exist, but that the author found two specific places where the rulers disagree, even though the official rules say both are allowed.
Gap 1 (The Overflow Problem): Imagine a number is so huge it doesn't fit in the format.
- Chip A says: "I'll just cap it at the biggest number I can hold." (Saturation)
- Chip B says: "I can't hold this, so I'll turn it into an error message (NaN)."
- Both chips are following the official rulebook, but they do it differently. This paper exposes this difference so engineers don't get confused when their AI model works on one chip but fails on another.
Gap 2 (The Block Structure Problem): Some formats group numbers together in "blocks" (like a box of 32 screws).
- Format A uses a box of 32 screws with a simple label.
- Format B uses a box of 16 screws with a more detailed label.
- Even if the individual screws (the numbers) look the same, the way they are packed in the box changes how the whole thing works. The paper highlights that you can't just swap these formats without checking the "box size."
What this paper is NOT
The author is very clear about what this paper does not do:
- It does not say which format is "better" or faster.
- It does not test how well AI models perform (like how accurate a chatbot is).
- It does not invent new formats.
- It is purely a reference tool to make sure everyone is measuring the same way.
Why does this matter?
Before this paper, if an engineer moved an AI model from one company's chip to another, they might get different results and not know why. It was like trying to build a bridge where one team used inches and the other used centimeters, but neither admitted it.
This paper provides the shared ruler and the test weights. It allows engineers to say, "Okay, my chip passes the test for the 3.0 anchor and handles the overflow exactly like the reference file." If it doesn't, they know they have a bug to fix.
In short, this paper is the standardized measuring tape for the chaotic world of AI number formats, ensuring that when different companies build AI hardware, they are all speaking the same mathematical language.
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