Precision Numerics has released Boole-1.7B, a 1-bit language model derived from Qwen3-1.7B. The model occupies 247 MB of stored weights and scores 50.55 across ten benchmarks, compared with 58.83 for the BF16 baseline. That result represents 85.9% of the baseline’s ten-task average, with a 13.9× reduction in stored weight size.

Making a binary model work comes with two immediate problems. A binary weight carries only a sign, +1 or −1, and its magnitude is provided by a scale shared across a group of weights. Sharing one magnitude across many weights discards detail, and the scales themselves require storage space. The article explains that a 4-bit format gives each weight one of sixteen levels under a shared scale, while a binary group keeps only the signs. The best shared scale is the group’s mean magnitude, and the remaining error is the variance of magnitudes within that group.

For Gaussian weights with variance σ², the magnitudes have mean σ√(2/π) and variance σ²(1−2/π). Estimating that mean from g samples removes a 1/g share of it. The idealized calculation shows the mean squared error as (1−1/g)(1−2/π) of the weight variance. At group size 128 the figure is 36.1%, at 32 it is 35.2%, and it approaches 36.3% as groups grow. Quadrupling the number of scales gains less than one percentage point, illustrating how little a shared scale can recover.

Scales themselves carry a cost. A b_scale-bit scale per g weights adds b_scale/g bits to each weight. With a 16-bit scale and groups of 32, the scale adds 0.5 bits per weight—33% of a 1-bit model’s storage, against 6% of an 8-bit model’s. Groups of 8 already cost 3 bits per weight at one bit, and a scale per weight costs 17, exceeding the 16-bit original.

Boole-1.7B in context

Boole-1.7B is the 1-bit version of Qwen3-1.7B, intended for English-language inference in non-thinking mode. The article compares it with the BF16 original and with PrismML’s 1-bit Bonsai-1.7B, looking at average score and intelligence density: capability per gigabyte of weights.

The same base model appears at many precisions. The chart places Boole among Qwen3-1.7B in BF16 and FP8, Unsloth’s GGUF quantizations from 1 to 8 bits, and PrismML’s binary and ternary Bonsai-1.7B. At nearly the same weight storage, Boole averages 5.58 points above binary Bonsai-1.7B (44.97). Ternary Bonsai-1.7B averages 51.57, 1.02 points above Boole, with 1.9× Boole’s weight storage. Unsloth’s 3-bit GGUFs average 46.57 (Q3_K_S) and 53.66 (Q3_K_M) at 3.5× and 3.8× Boole’s weight storage.

Boole improves on binary Bonsai in seven of ten tasks. The largest gains appear in math and code; scores are lower on MuSR, IFEval, and function calling (BFCLv3).

Small model frontier

The evaluation compares Boole with 23 small language models in 52 formats, all below 3 GB of weight storage. Among those variants, Boole has the highest benchmark average at its storage size or below. The smallest variant with a higher average is Ternary-Bonsai-1.7B: 51.57 at 457 MB, or 1.9× Boole’s storage.

Intelligence density

Intelligence density measures benchmark capability per unit of weight storage, using PrismML’s definition: −ln(1 − average/100) / storage_GB, with the natural logarithm and decimal GB, computed from each model’s ten-task average and recorded storage size. Higher is better. Boole has the highest intelligence density of the evaluated models, 2.85 per GB. The next highest is LFM2.5-230M at 2.58.

What's next

The authors are building systems to make hardware more valuable and pushing the efficiency frontier to benefit the open-source community. Local developers can share what they would like to see next. Teams and businesses can reach out to collaborate and get the most out of their hardware.

@misc{precisionnumerics2026boole1p7b,
  author = {{Precision Numerics}},
  title = {{Boole}-1.7B},
  year = {2026},
  month = {October},
  url = {https://huggingface.co/precision-numerics/Boole-1.7B}
}