Sable: A Small-Field Sumcheck Argument for Bit-Exact Inference of Large Language Models

Sable. A Small-Field Sumcheck Argument for Bit-Exact Inference of Large Language Models. By Tomer Solberg, from MoonMath AI. Published on the tenth of November.

The statement Sable sets out to prove is narrow and exacting. A committed, integer-quantized transformer produced a given token sequence from a given prompt, bit for bit. A claim that strict needs a computation with exactly one correct answer. If any rounding, normalization, softmax or sampling decision could come out differently depending on how it was carried out, there would be no single sequence to prove anything about.

Sable is an argument system with a single-GPU prover, and it starts by fixing the computation itself. It defines an integer function, called F sub O, with no floating-point step anywhere, in which every rounding, normalization, softmax and sampling decision is determined by its inputs. That function is then proved with a constraint system whose relations provably never wrap modulo the thirty-one-bit KoalaBear prime. The field is small, and the guarantee is that nothing in the constraints ever overflows it.

Two kinds of check, zerochecks and LogUp-GKR lookups, are batched into one sumcheck per domain. Every witness tensor and every weight goes into one multilinear commitment, built from Reed-Solomon codes, BLAKE3 Merkle trees and a mixed-length BaseFold opening. The prover does not hold the whole model at once. It streams the model layer by layer on one GPU.

Here are the speeds, on one NVIDIA RTX PRO 6000 Blackwell GPU. Sable proves all sixty-four layers of Qwen2.5-32B in ninety-two point five seconds for four thousand and ninety-six tokens. For sixteen thousand three hundred and eighty-four tokens it takes three hundred and ninety-eight seconds. It also covers Qwen3-32B and the mixture-of-experts Qwen3-30B-A3B, proving four thousand and ninety-six tokens in one hundred and twenty-one point eight seconds and eighty-four point seven seconds respectively.

In cost terms, a proof takes forty-one to fifty times the serving time. At public GPU prices that is six point four cents per request of four thousand and ninety-six tokens. Measured per parameter and per token, it takes forty to sixty-four times less time than zkLLM.

Fixing the arithmetic to integers has a price in fidelity, and the abstract measures it. On WikiText-2, the greedy token from F sub O matches the BF16 model's at eighty-six point three percent of positions. On Qwen3, F sub O is within one point six points of BF16 on MMLU, and within one point seven points on GSM8K. Checking is lighter than proving: a verifier with a compiled core checks a proof on one CPU core in nineteen to fifty-six seconds. In the random-oracle model, the interactive proof has a round-by-round soundness error of two to the minus one hundred and three.

One boundary is stated plainly. The proof is not zero-knowledge, so the system targets open-weight models. Within that boundary, what Sable delivers is a check anyone can run on a single CPU core in under a minute, for a claim that leaves no room at all: this model, this prompt, these tokens, every bit.