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BiE: Bi-Exponent Block Floating-Point for Large Language Models Quantization
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Proposes Bi-Exponent Block Floating-Point (BiE), a block numerical format with two shared exponents (normal and outlier) split by a per-tensor threshold found via Bayesian optimization, enabling accurate 4-bit and 3-bit PTQ of OPT and LLaMA-2 with an FPGA accelerator design.
Problem
Low-bit LLM quantization suffers from activation outliers and wide-but-redundant value distributions, while mainstream INT and standard block floating-point formats either lose accuracy at 4-bit or add hardware cost.
Approach
Each block stores two shared exponents, one for values below a per-tensor threshold and one for outliers above it, with a 1-bit type flag per element; the threshold is tuned offline with Bayesian optimization over a percentile-pruned search space using output MSE.
Key results
- BiE W4A4 on OPT-66B reaches 9.82 WikiText2 perplexity versus 14.16 for BFP W4A4 and 9.12 for FP16.
- BiE W4A4 on LLaMA-2-7B averages 72.83% across tasks versus 68.65% for BFP W4A4 and 76.16% FP16.
- Simulated BiE W4A4 accelerator reaches 3.51x throughput and 2.8x memory efficiency relative to FP16.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use BiE W4A4 instead of BFP W4A4 | OPT-6.7B · WikiText2 | perplexity: 11.22 -> 10.93 | Helped |
| Use BiE W4A4 instead of BFP W4A4 | OPT-13B · WikiText2 | perplexity: 11.15 -> 10.39 | Helped |
| Use BiE W4A4 instead of BFP W4A4 | OPT-30B · WikiText2 | perplexity: 9.90 -> 9.37 | Helped |
| Use BiE W4A4 instead of BFP W4A4 | OPT-66B · WikiText2 | perplexity: 14.16 -> 9.82 | Helped |
| Use BiE W4A4 instead of BFP W4A4 | OPT-30B · Zero-shot task average | accuracy: 68.55% -> 70.22% | Helped |
| Use BiE W4A4 instead of BFP W4A4 | OPT-66B · Zero-shot task average | accuracy: 68.69% -> 71.23% | Helped |
| Use BiE W4A4 instead of BFP W4A4 | LLaMA-2-7B · Zero-shot task average | accuracy: 68.65 -> 72.83 | Helped |
| Use BiE W4A4 instead of BFP W4A4 | LLaMA-2-13B · Zero-shot task average | accuracy: 71.20 -> 75.90 | Helped |
| Use BiE W4A4 instead of BFP W4A4 | LLaMA-2-70B · Zero-shot task average | accuracy: 80.24 -> 80.21 | Hurt |
| Use BiE W4A4 instead of FP16 | OPT-30B · Zero-shot task average | accuracy: 69.90% -> 70.22% | Helped |
| Use BiE W4A4 instead of FP16 | OPT-66B · Zero-shot task average | accuracy: 71.76% -> 71.23% | Hurt |
| Use BiE W4A4 instead of SmoothQuant W8A8 | OPT-30B · WikiText2 | perplexity: 9.35 -> 9.37 | No clear effect |
Surprising findings
- Plain 6-bit SmoothQuant collapses on OPT-30B and OPT-66B (perplexity 82.54 and 3383.21), while 4-bit BiE stays near FP16.
Limitations
- Threshold search is offline and per-tensor via Bayesian optimization, which adds calibration cost and is not adaptive online.
- Only PTQ on OPT and LLaMA-2 evaluated; 3-bit BiE still degrades substantially on some models such as OPT-66B (perplexity 32.41).
Experimental setup
Datasets: Pile (128 calibration samples) WikiText2 LAMBADA ARC-easy PIQA COPA QNLI SST2
Benchmarks: WikiText2 LAMBADA ARC-easy PIQA COPA QNLI SST2
Metrics: perplexity accuracy average accuracy throughput memory efficiency
Baselines: SmoothQuant BFP (Zhang et al., 2023) FP16
Builds on: block floating point SmoothQuant LLM.int8() AFP
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