glq 0.1.1

E8 lattice codebook quantization for LLM weights

GLQ

Post-training weight quantization for LLMs using E8 lattice codebooks.

GLQ encodes weights into 8-dimensional E8 lattice points via nearest-neighbor lookup. A Randomized Hadamard Transform (RHT) makes the Hessian approximately diagonal so that Euclidean nearest-neighbor is near-optimal under the proxy loss.

Results

SmolLM3-3B-Base on WikiText-2 (NVIDIA A10G):

Method	Eff. BPW	Size (MB)	Perplexity	vs bf16
bf16	16.00	6150	7.90	1.00x
GLQ 4-bit	4.00	1538	8.11	1.03x
AWQ 4-bit	5.60	2152	8.15	1.03x
QuIP+GPTQ 4-bit	4.76	1829	8.17	1.03x
GLQ 3-bit	3.00	1153	8.91	1.13x
QuIP+GPTQ 3-bit	3.70	1423	9.30	1.18x
GLQ 2-bit	2.00	769	11.35	1.44x

GLQ uses a single global scale per layer rather than per-group scales, so effective bit widths match the nominal rate. Early results on one model — more benchmarks needed.

How it works

1. E8 lattice codebook: 65536 vectors from the first 7 shells of the E8 lattice. Each 8-weight group maps to a 16-bit index (2 bpw). For 3/4 bpw, a second-stage residual codebook adds 8 or 16 more bits.

2. Randomized Hadamard Transform (RHT): Random sign flips + Fast Walsh-Hadamard Transform applied to both weights and Hessian. This spreads weight magnitude evenly across dimensions, making the Hessian block-diagonal approximately proportional to identity. After RHT, Euclidean nearest-neighbor in the codebook is close to Hessian-optimal.

3. LDLQ error feedback: Block-LDL decomposition of the Hessian drives a sequential quantization sweep (like GPTQ but over 8-dim blocks instead of scalar columns). Quantization error from each block propagates forward to correct subsequent blocks.

Install

Requires Python 3.10+ and PyTorch 2.0+. Install PyTorch first (pytorch.org), then:

# Full install (includes transformers, datasets, etc. for glq-quantize CLI):
pip install 'glq[quantize]'

# Or minimal install (inference only, no quantization dependencies):
pip install glq

Triton (for the fused codebook kernel) is bundled with PyTorch on CUDA and will be used automatically.

Quickstart

Command line

glq-quantize \
    --model HuggingFaceTB/SmolLM2-360M \
    --output ./smollm2-glq-2bpw \
    --bpw 2 \
    --nsamples 128 \
    --device cuda

Python API

from glq import quantize

quantize(
    model_name="HuggingFaceTB/SmolLM2-360M",
    output_dir="./smollm2-glq-2bpw",
    bpw=2,
    nsamples=128,
    device="cuda",
)

Loading a quantized model

import glq.hf_integration  # registers GLQ with transformers
from transformers import AutoModelForCausalLM, AutoTokenizer

model = AutoModelForCausalLM.from_pretrained("./smollm2-glq-2bpw", device_map="auto")
tokenizer = AutoTokenizer.from_pretrained("./smollm2-glq-2bpw")

inputs = tokenizer("The capital of France is", return_tensors="pt").to(model.device)
output = model.generate(**inputs, max_new_tokens=50)
print(tokenizer.decode(output[0], skip_special_tokens=True))

Bit widths

BPW	Encoding	Overhead
2	16-bit index per 8 weights	Global scale only
3	16-bit + 8-bit residual index per 8 weights	Global scale only
4	16-bit + 16-bit residual index per 8 weights	Global scale only

All bit widths use a single global scale per layer (no group-size parameter).

Acknowledgments

• The RHT incoherence approach follows QuIP# (Tseng et al., 2024)
• E8 lattice geometry from Conway & Sloane, Sphere Packings, Lattices and Groups
• LDLQ error feedback from GPTQ (Frantar et al., 2022)

License

Apache 2.0