glq 0.3.3

E8 lattice codebook quantization for LLM weights

GLQ

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

GLQ encodes each 8-weight group as a 16-bit index into a 65,536-entry E8 lattice codebook. A Randomized Hadamard Transform (RHT) decorrelates the Hessian so that Euclidean nearest-neighbour search is near-optimal under the proxy loss. The result: 2–8 bpw weights with quality comparable to QuIP# / better than GPTQ, and a fused CUDA kernel that matmuls directly against the compressed indices without materializing the weight matrix.

Quickstart

Run a pre-quantized model

pip install glq         # requires PyTorch ≥ 2.0

Python ≥ 3.10. Triton ships with PyTorch on CUDA and is used automatically. The CUDA C extension JIT-builds on first run (~30 s); CPU falls back to dequantize-then-matmul.

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

model = AutoModelForCausalLM.from_pretrained(
    "xv0y5ncu/SmolLM2-360M-Instruct-GLQ-4bpw",
    device_map="auto",
)
tok = AutoTokenizer.from_pretrained("xv0y5ncu/SmolLM2-360M-Instruct-GLQ-4bpw")
print(tok.decode(model.generate(
    **tok("The capital of France is", return_tensors="pt").to(model.device),
    max_new_tokens=20,
)[0], skip_special_tokens=True))

import glq.hf_integration registers quant_method="glq" with HF Transformers; from_pretrained then swaps nn.Linear for E8RHTLinear and uses the fused CUDA C kernel on inference. CPU falls back to a naive dequantize-then-matmul.

Available pre-quantized checkpoints

Repo	Base model	bpw	License
xv0y5ncu/SmolLM2-135M-Instruct-GLQ-4bpw	SmolLM2-135M-Instruct	4.0	Apache 2.0
xv0y5ncu/SmolLM2-360M-Instruct-GLQ-4bpw	SmolLM2-360M-Instruct	4.0	Apache 2.0
xv0y5ncu/SmolLM3-3B-GLQ-3.5bpw	SmolLM3-3B	3.5 (mixed)	Apache 2.0
xv0y5ncu/Gemma-4-E4B-it-GLQ-4bpw	Gemma-4-E4B-it	4.0	Apache 2.0
xv0y5ncu/Devstral-Small-2-24B-Instruct-GLQ-4bpw	Devstral-Small 24B	4.0	Apache 2.0
xv0y5ncu/Nemotron-3-Nano-30B-A3B-GLQ-4bpw	Nemotron-3-Nano-30B (Mamba-MoE)	4.0	Nemotron

Quantize your own model

pip install 'glq[quantize]'    # adds transformers, datasets, etc.

glq-quantize \
    --model HuggingFaceTB/SmolLM2-360M \
    --output ./smollm2-glq-4bpw \
    --bpw 4 \
    --nsamples 128 \
    --device cuda

Other bit-widths: pass --bpw 2 through --bpw 8 (fractional like 2.5 also works). glq-quantize --help lists every flag. For models that don't fit in system RAM use --streaming (loads one layer at a time from safetensors).

For mixed-precision allocation, run a two-pass flow: a profile pass writes a per-layer bpw_allocation.json, then a quantize pass applies it. See examples/quantize_mixed_precision.md.

Results

SmolLM3-3B at matched 4.5 bpw vs GPTQ

Blackwell RTX PRO 6000, 128 calibration samples, lm-evaluation-harness limit=200/task (GSM8K n=500, MMLU 50/subtask). GLQ 4.5 bpw uses two-pass mixed allocation (91 layers @ 4 bpw + 161 @ 5 bpw, avg 4.64 bpw).

Task	bf16	GLQ 4.5 bpw	GPTQ W4 g128
ARC-challenge (acc_n)	0.490	0.475	0.420
ARC-easy (acc_n)	0.745	0.735	0.695
HellaSwag (acc_n)	0.660	0.660	0.675
MMLU (acc)	0.617	0.603	0.589
TruthfulQA mc2	0.529	0.545	0.515
WinoGrande	0.655	0.660	0.670
WikiText-2 ppl ↓	10.67	10.90	11.33
GSM8K flex (n=500)	0.722	0.738	0.688
IFEval prompt-strict	0.310	0.310	0.285
IFEval prompt-loose	0.325	0.330	0.295
IFEval inst-strict	0.478	0.472	0.453
IFEval inst-loose	0.494	0.491	0.469

GLQ beats GPTQ on 10/12 metrics. WikiText-2 ppl gap to bf16: +2.2 % (GLQ) vs +6.2 % (GPTQ). GSM8K flex matches bf16; GPTQ drops 0.034.

Small models: SmolLM2-360M-Instruct at 4 bpw

GPTQ requires a group-size dividing the hidden dim; SmolLM2-360M's hidden=960 is not divisible by 128, forcing group_size=64 (~4.5 eff bpw) and losing quality. GLQ has no group-size constraint.

Method	bpw	5-task avg	% of bf16
bf16	16.0	0.557	100 %
GLQ 4-bit	4.0	0.555	99.6 %
GPTQ W4 (g64)	~4.5	0.486	87.2 %

5-task = ARC-e, HellaSwag, PIQA, WinoGrande, LAMBADA; 128 calibration samples; L40S. GPTQ's LAMBADA collapses to 0.346; GLQ preserves 0.508.

Throughput: SmolLM3-3B on vLLM

GLQ runs at near-bf16 throughput because compressed weights cut DRAM bandwidth enough to roughly offset the dequantization cost.

Method	bpw	Single req	Batch=5	vs bf16
bf16	16.0	39.4 tok/s	184 tok/s	100 %
GLQ 3.5bpw	3.5	37.1 tok/s	173 tok/s	94 %
GPTQ W4 (g128)	~4.5	34.6 tok/s	172 tok/s	88 %

vLLM 0.18.1, L40S.

How it works

1. E8 lattice codebook. 65,536 vectors from the first seven shells of the E8 lattice in 8 dimensions. Each 8-weight group of the weight matrix is encoded as one 16-bit index into this codebook (so the primary stage is 2 bpw). For 3–8 bpw, additional 8-bit (256-entry) or 16-bit (E8) residual codebooks refine the primary's reconstruction error.

2. Randomized Hadamard Transform. Random sign flips followed by Fast Walsh-Hadamard Transform rotate both weights and Hessian. After RHT the Hessian is approximately diagonal, so plain Euclidean nearest-neighbour in the codebook is near-optimal under the Hessian-weighted proxy loss.

3. LDLQ error feedback. Block-LDL decomposition of the Hessian drives a sequential sweep — GPTQ-style, but over 8-D blocks instead of scalar columns. Each block's quantization error propagates forward to correct downstream blocks.

4. Fused inference kernels. Custom CUDA C and Triton kernels read codebook indices from HBM, gather the 8-D vectors from the L2-cached 1 MB codebook, and accumulate the matmul directly — the dense weight matrix is never materialized. GPU memory savings scale with the compression ratio.

KV cache compression

GLQ ships two KV cache compressors. Either is opt-in — default behaviour is unchanged.

INT8 cache (HF transformers)

Per-channel absmax INT8 plus a small fp16 residual window for recent tokens — KIVI-style. Halves the KV memory at long context.

import glq.hf_integration
from glq.kv_cache import GLQQuantizedCache

cache = GLQQuantizedCache(model.config)
output = model.generate(**inputs, max_new_tokens=200,
                         past_key_values=cache)

Requires transformers >= 4.45. No external dependencies.

E8 lattice cache (vLLM, v0.3.0+)

Drops vLLM's paged KV cache to ~25 % of fp16 footprint using the same E8 lattice quantizer used for weights. Two fused Triton kernels (read-side dequant-gather, write-side scatter) keep decode within ~20 % of un-fused throughput.

Measured on Gemma-4-E4B-it, RTX PRO 6000 Blackwell, vLLM 0.20:

	fp16 baseline	E8 lattice
KV cache capacity @ 27.9 GiB	303,984 tokens	1,221,232 (4.02×) at e8_relaxed:1
mmlu_pro n=240 accuracy	71.25 %	71.25 % (bit-identical) at e8_relaxed:2
NIAH passkey @ ctx=16k / 32k / 64k / 130k	—	40/40 at e8_relaxed:2 (full 128k window)
cudaLaunchKernel per decode	110,659	71,619 (−35 %) at e8_relaxed:2

Activation:

GLQ_KV_QUANT=e8_relaxed:2 \
GLQ_KV_E8_SIDECAR=1 GLQ_KV_E8_SIDECAR_READ=1 \
GLQ_KV_E8_COMPRESSED_ALLOC=1 \
GLQ_KV_E8_FUSED_GATHER=1 GLQ_KV_E8_FUSED_WRITE=1 \
vllm serve google/gemma-4-E4B-it --enforce-eager

Important: the E8 KV path requires --enforce-eager in v0.3.x. The gather workspace is allocated per attention call, which isn't compatible with vLLM's piecewise / full CUDA-graph capture (the default since v0.3.2 for weight-only GLQ). Refactoring the gather to use a pre-allocated workspace is a v0.3.4 target.

Validated end-to-end on Gemma-4-E4B-it / Gemma-4-31B-it on vLLM 0.20.x. For weight-only GLQ (no E8 KV) the default piecewise CUDA-graph capture path works with no extra flags. The codebook-NN kernel is still ~42 % of CUDA time at 4 bpw — fusing that is the v0.4 target.

Advanced

CUDA-graph decode wrapper

The B=1 autoregressive decode path is Python-dispatch-bound in eager mode. CUDAGraphWrapper captures the fixed-shape decode and replays it; benchmarks below are on SmolLM3-3B 3.5bpw, L40S.

Mode	GLQ 3.5 bpw	bf16
Eager	25 tok/s	40
CUDA graph	37 tok/s	40

from glq.cuda_graph import CUDAGraphWrapper
wrapper = CUDAGraphWrapper(model)
logits = wrapper(input_ids)   # first call captures; replays after

The wrapper falls back to eager for variable shapes (prefill, batch>1, extra kwargs). For 24B models the matmul is compute-bound at B=1, so graphs don't help (Devstral-24B GLQ 4 bpw: 6.6 tok/s eager vs 6.4 graphed).

Bit widths

bpw	Primary	Residual stages
2	16 b	—
3	16 b	+ 8 b
4	16 b	+ 16 b
5	16 b	+ 16 b + 8 b
6	16 b	+ 16 b + 16 b
7	16 b	+ 16 b + 16 b + 8 b
8	16 b	+ 16 b + 16 b + 16 b

One global scale per layer; no group-size parameter. Non-power-of-2 hidden sizes use block-diagonal FHT (v0.2.9+) — e.g. 2688 is decomposed as 2048 + 512 + 128 so on-disk storage matches the nominal rate exactly.

Serving with sglang

A fork of sglang with GLQ support lives at cnygaard/sglang on the glq-quantization branch. It registers "glq" as a quantization method and reuses the existing glq.inference_kernel CUDA extension as a runtime dependency.

git clone -b glq-quantization https://github.com/cnygaard/sglang
cd sglang/python && pip install -e .

python -m sglang.launch_server \
    --model xv0y5ncu/SmolLM2-360M-Instruct-GLQ-4bpw \
    --tokenizer-path HuggingFaceTB/SmolLM2-360M-Instruct \
    --quantization glq \
    --attention-backend triton --sampling-backend pytorch

Requires the triton attention backend (flashinfer returns wrong logprobs in echo/prefill mode). Default CUDA-graph capture is supported (v0.3.2+). If you hit a graph-break in a model architecture we haven't tested, pass --disable-piecewise-cuda-graph as a fallback.

Devstral-24B tokenizer

transformers 5.x auto-routes Mistral/Devstral models through mistral_common, which rejects the standard tokenizer.json. Use PreTrainedTokenizerFast explicitly:

from huggingface_hub import snapshot_download
from transformers import AutoModelForCausalLM, PreTrainedTokenizerFast

path = snapshot_download("xv0y5ncu/Devstral-Small-2-24B-Instruct-GLQ-4bpw")
tok = PreTrainedTokenizerFast(tokenizer_file=f"{path}/tokenizer.json")
tok.pad_token, tok.eos_token, tok.bos_token = "<pad>", "</s>", "<s>"
model = AutoModelForCausalLM.from_pretrained(
    "xv0y5ncu/Devstral-Small-2-24B-Instruct-GLQ-4bpw",
    device_map="cuda", dtype="float16",
)

examples/inference_hf.py includes a load_tokenizer() helper that handles this automatically.

transformers compatibility

For models ≤ 1B parameters use transformers >= 5.0. Transformers 4.57.x has a weight-loading bug that produces garbage output for small GLQ models. Larger models (3B+) work with both 4.x and 5.x.

Inference kernels

glq/inference_kernel.py + glq/csrc/glq_cuda.cu provide CUDA C and Triton kernels that compute Y = X @ dequant(W)^T without materializing the weight matrix. Each kernel iterates over N/8 codebook blocks per output row, gathers 8-D vectors from the L2-cached codebook, and accumulates the matmul directly against indices.

Path	When	Notes
CUDA C Tensor Core	B ≥ 2 (prefill)	inline PTX mma.sync against codebook-loaded registers; 3-5× faster than Triton
CUDA C split-K matvec	B = 1 (decode)	4 rows/warp + __shfl_xor_sync reduction; 2.7× faster than Triton
CUDA C shared-mem FHT	RHT step	double-buffered butterfly; 1.6-3× faster than Triton
Triton fallback	no ninja, or n_pad > 32 768	always available

Bit-exact determinism. Every kernel uses a scratch-buffer + fixed- order reduction instead of atomicAdd across k-splits, so running the same prompt at B=1 decode or B=8 prefill produces identical logits across runs — required for reproducible lm-eval scoring and on-policy RL rollouts.

Direct kernel access:

from glq.inference_kernel import glq_dequant_matmul
y = glq_dequant_matmul(x, Qidxs, codebook, Wscale,
                       Qidxs2=Qidxs2, codebook2=codebook2,
                       inv_resid_scale=inv_rs)  # 3/4 bpw two-stage

Architecture

glq/
  codebook.py          # E8ShellCodebook: enumeration, encode/decode
  hadamard.py          # Fast Walsh-Hadamard Transform
  rht.py               # Randomized Hadamard Transform
  ldlq.py              # Block-LDL quantization with error feedback
  quantize_model.py    # Full model pipeline + CLI
  quantized_linear.py  # E8RHTLinear: drop-in nn.Linear replacement
  inference_kernel.py  # Triton kernels + CUDA dispatch
  csrc/glq_cuda.cu     # CUDA C kernels (split-K matvec, TC, FHT)
  hf_integration.py    # HuggingFace Transformers integration
  kv_cache.py          # INT8 quantized KV cache
  cuda_graph.py        # B=1 decode wrapper
glq_vllm/              # vLLM integration: weight + KV cache (v0.3.0+)

Acknowledgments

Inspired by QuIP# (Tseng et al., 2024).

• E8 lattice: Korkin & Zolotarev (1872); Gosset (1900); Conway & Sloane, Sphere Packings, Lattices and Groups; Viazovska (2016) — sphere-packing optimality in 8 dimensions.
• Block-feedback quantization: GPTQ (Frantar et al., 2022).
• INT8 KV cache: KIVI (Liu et al., 2024).

License

Apache 2.0