Motivation

In this paper, we have answered why randomized orthogonal transforms better than randomized Hadamard transforms.

Preliminary

Understanding LLM's rotational invariance and Massive Activation will help you better understand our work:

1. QuaRot: Outlier-Free 4-Bit Inference in Rotated LLMs
2. Massive Activations in Large Language Models

Visualization

NR: No Rotation; RO: Randomized Orthogonal transforms;

RH: Randomized Hadamard transforms; E: Per Token Quantization Error.

Method	4-4-4	4-4-16	4-8-16	4-4-4	4-4-16	4-8-16	4-4-4	4-4-16	4-8-16	4-4-4	4-4-16	4-8-16
	LLaMA2-7B	LLaMA2-7B	LLaMA2-7B	LLaMA2-13B	LLaMA2-13B	LLaMA2-13B	LLaMA3-8B	LLaMA3-8B	LLaMA3-8B	Mistral-7B-v0.3	Mistral-7B-v0.3	Mistral-7B-v0.3
GPTQ	NaN	NaN	NaN	Inf	Inf	6.01	Inf	Inf	7.29	Inf	Inf	8.39
(RO) QuaRot	7.96	7.71	5.61	6.00	5.92	4.99	10.54	10.15	6.52	6.05	5.98	5.40
(RO) QuaRot.FP16()	6.17	6.10	-	5.38	5.34	-	7.83	7.68	-	5.79	5.73	-
(RH) QuaRot	6.27	6.20	5.61	5.51	5.46	5.01	8.20	8.02	6.52	5.81	5.75	5.40
(RH) QuaRot.FP16()	6.17	6.10	-	5.40	5.37	-	7.82	7.67	-	5.78	5.73	-

Chain of Thoughts (CoT)

Run for LLaMA3-8B

1. Generate Calibration Dataset

python3 generate_calibration.py --model meta-llama/Meta-Llama-3-8B --nsamples 1 \\
--output_dir calibration --disable_qk_rotation

2. Optimize Rotational Matrix

python3 optimize_procrustes_alter.py --rotate_mode hadamard --data_principle alter --alpha 100

3. Run Results

python3 main.py --model meta-llama/Meta-Llama-3-8B  --rotate --w_bits 4 --a_bits 4 --k_bits 4 \\
--v_bits 4 --w_clip --v_groupsize 128 --k_groupsize 128 --a_asym --k_asym --v_asym \\
--rotate_mode orthogonal_procrustes --indices_path rms_norm_feature_hadamard_alter/100/LLaMA-3-8B-4.npy \\
--fp32_had --seed 0 --lm_eval

More Scripts

# Random, Hadamard, Procrustes Scripts
CUDA_VISIBLE_DEVICES=None python3 scripts/generate_scripts.py
# For QuaRot.FP16()
CUDA_VISIBLE_DEVICES=None python3 scripts/separate_scripts.py
# Calibration Dataset
CUDA_VISIBLE_DEVICES=None python3 scripts/generate_calibration.py
# Without Rotation
CUDA_VISIBLE_DEVICES=None python3 scripts/vanilla_scripts.py

Main Results on WikiText-2 PPL

Method	LLaMA2-7B	LLaMA2-7B	LLaMA2-13B	LLaMA2-13B	LLaMA3-8B	LLaMA3-8B	Mistral-7B-v0.3	Mistral-7B-v0.3
Baseline	5.47	5.47	4.88	4.88	6.14	6.14	5.32	5.32
Extra Time	+8min	+8min	+20min	+20min	+8min	+8min	+8min	+8min
	4-4-4	4-4-16	4-4-4	4-4-16	4-4-4	4-4-16	4-4-4	4-4-16
RTN	NaN	NaN	Inf	Inf	Inf	Inf	Inf	Inf
QuaRot-RTN	9.04	8.69	6.31	6.23	11.06	10.47	6.38	6.29
DFRot-RTN	7.68	7.47	6.21	6.12	9.67	9.35	6.36	6.27
GPTQ	NaN	NaN	Inf	Inf	Inf	Inf	Inf	Inf
QuaRot-GPTQ	6.27	6.20	5.51	5.47	8.20	8.02	5.81	5.75
DFRot-GPTQ	6.21	6.14	5.47	5.39	7.95	7.81	5.81	5.76

Main Results on Zero-Shot tasks

Model	Method	W-A-KV	PQ	WG	HS	A-e	A-c	LA	Avg.
LLaMA2-7B	FP16	16-16-16	79.11	68.98	75.99	74.54	46.42	73.88	69.82
	QuaRot	4-4-16	76.06	65.67	73.00	69.82	42.24	69.42	66.03
		4-4-4	76.33	64.96	72.69	68.60	41.64	68.58	65.47
	DFRot	4-4-16	77.15	65.82	73.17	69.78	44.37	70.66	66.83
		4-4-4	76.22	64.96	72.41	70.75	42.66	69.92	66.15
LLaMA2-13B	FP16	16-16-16	80.52	72.22	79.39	77.48	49.15	76.75	72.58
	QuaRot	4-4-16	77.91	68.51	75.94	73.57	46.25	72.97	69.19
		4-4-4	78.73	70.40	75.82	73.74	46.33	72.73	69.63
	DFRot	4-4-16	78.73	69.30	76.99	72.69	45.82	75.41	69.82
		4-4-4	79.82	68.43	76.70	72.64	46.59	75.33	69.92
LLaMA3-8B	FP16	16-16-16	80.79	72.85	79.16	77.78	53.33	76.03	73.32
	QuaRot	4-4-16	74.92	66.61	73.39	70.29	44.54	67.71	66.24
		4-4-4	75.14	66.54	72.32	68.64	42.41	66.04	65.18
	DFRot	4-4-16	76.22	68.03	73.92	70.41	45.65	68.87	67.18
		4-4-4	75.68	66.77	73.56	70.29	45.14	68.99	66.74
Mistral-7B-v0.3	FP16	16-16-16	82.26	73.88	80.41	78.20	52.30	75.32	73.73
	QuaRot	4-4-16	79.54	69.30	77.81	75.51	47.95	73.76	70.65
		4-4-4	79.38	69.06	77.36	74.54	48.29	73.55	70.36
	DFRot	4-4-16	79.87	69.53	78.24	75.88	48.46	73.01	70.83
		4-4-4	80.36	69.61	78.01	75.55	47.95	72.39	70.65

Reference

If you find DFRot useful or relevant to your research, please cite our paper:

@article{xiang2024dfrot,
  title={DFRot: Achieving Outlier-Free and Massive Activation-Free for Rotated LLMs with Refined Rotation},
  author={Xiang, Jingyang and Zhang, Saiqian},
  journal={arXiv preprint arXiv:2412.00648},
  year={2024}
}