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HBLLM: Wavelet-Enhanced High-Fidelity 1-Bit Quantization for LLMs
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Proposes HBLLM, a 1-bit post-training quantization method that applies Haar wavelet transforms within a BiLLM-style pipeline, with frequency-aware intra-row grouping, l2-norm salient column selection, and shared intra-band means.
Problem
1-bit post-training quantization of LLMs degrades sharply on modern architectures (e.g., LLaMA3-8B) because existing binarization methods have limited expressiveness and poor salient column selection; global orthogonal transforms add prohibitive inference cost.
Approach
Apply a single local Haar wavelet transform to weight rows/columns to split them into low- and high-frequency bands, then binarize each band with structure-aware grouping (frequency-aware intra-row groups, l2-norm column saliency) and share the mean across groups within a band, giving O(d) local-convolution inverse transforms.
Key results
- HBLLM-row reaches perplexity 6.71 on LLaMA2-13B... as stated in the abstract, with average weight storage 1.08 bits; table reports HBLLM-row C4 7.82 / Wiki2 6.71 for LLaMA2-13B at 1.07 bits versus 10.52-ish for ARB-LLM_RC class baselines.
- On LLaMA3-8B, HBLLM-row achieves C4 perplexity 20.09 vs 34.44 for ARB-LLM_RC at 1.06 bits.
- Quantization time for HBLLM is 20-30% above BiLLM, and HBLLM completes on LLaMA-1 30B where ARB-LLM_X and FrameQuant fail on a 24GB GPU.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| apply HBLLM-row rather than ARB-LLM RC | LLaMA2-13B · C4 | perplexity: 11.90 -> 7.82 | Helped |
| apply HBLLM-row rather than ARB-LLM RC | LLaMA2-13B · Wiki2 | perplexity: 10.98 -> 6.71 | Helped |
| apply HBLLM-row rather than ARB-LLM RC | LLaMA2-13B · PTB | perplexity: 151.8 -> 61.75 | Helped |
| apply HBLLM-row rather than ARB-LLM RC | LLaMA2-13B · AvgQA | AvgQA: 57.35 -> 63.61 | Helped |
| apply HBLLM-row rather than ARB-LLM RC | LLaMA3-8B · C4 | perplexity: 34.44 -> 20.09 | Helped |
| apply HBLLM-row rather than ARB-LLM RC | LLaMA3-8B · AvgQA | AvgQA: 49.08 -> 54.80 | Helped |
| use ℓ2 instead of ℓ1 for salient-column selection (ablation) | HBLLM-row on LLaMA2-7B · Wiki2 | perplexity: 10.78 -> 10.52 | Helped |
| use ℓ2 instead of ℓ1 for salient-column selection (ablation) | HBLLM-row on LLaMA2-7B · PTB | perplexity: 143.7 -> 89.23 | Helped |
| replace global grouping with row-wise grouping (ablation) | HBLLM-row on LLaMA2-7B · Wiki2 | perplexity: 16.32 -> 11.08 | Helped |
| replace global grouping with row-wise grouping (ablation) | HBLLM-row on LLaMA2-7B · PTB | perplexity: 1990 -> 95.58 | Helped |
| share the mean across groups (ablation) | HBLLM-row on LLaMA2-7B · Wiki2 | perplexity: 11.08 -> 10.52 | Helped |
| share the mean across groups (ablation) | HBLLM-col on LLaMA2-7B · PTB | perplexity: 146.1 -> 150.6 | Mixed |
Surprising findings
- Sharing a mean across two groups within a frequency band slightly improves perplexity rather than hurting it.
- The paper reports that the l1-based salient selection criterion is worse than l2 across all tested settings.
Limitations
- Supports only quantized dense models; MoE not addressed.
- No error bars reported due to compute cost.
- Inference latency is estimated via GEMV on OPT-175B layers on P100, since no framework fully supports the dequantization.
Experimental setup
Datasets: C4
Benchmarks: C4 WikiText2 PTB PIQA BoolQ OpenBookQA WinoGrande ARC-e ARC-c HellaSwag COPA LAMBADA
Metrics: perplexity zero-shot accuracy quantization time memory W-bits
Baselines: BiLLM ARB-LLM_X ARB-LLM_RC PB-LLM FrameQuant
Builds on: BiLLM GPTQ ARB-LLM
Closest papers by meaning
- SliM-LLM: Salience-Driven Mixed-Precision Quantization for Large Language Models (ICML 2025 · similarity 0.89)
- BiLLM: Pushing the Limit of Post-Training Quantization for LLMs (ICML 2024 · similarity 0.89)
- OneBit: Towards Extremely Low-bit Large Language Models (NeurIPS 2024 · similarity 0.89)
- ARB-LLM: Alternating Refined Binarizations for Large Language Models (ICLR 2025 · similarity 0.88)
- Norm Tweaking: High-Performance Low-Bit Quantization of Large Language Models (AAAI 2024 · similarity 0.88)
- QLLM: Accurate and Efficient Low-Bitwidth Quantization for Large Language Models (ICLR 2024 · similarity 0.88)
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