Dual Length Codes for Lossless Compression of BFloat16
arXiv:2602.17849v1 Announce Type: new Abstract: Training and serving Large Language Models (LLMs) relies heavily on parallelization and collective operations, which are frequently bottlenecked by network bandwidth. Lossless compression using e.g., Huffman codes can alleviate the issue, however, Huffman codes suffer from slow, bit-sequential decoding and high hardware complexity due to deep tree traversals. Universal codes e.g., Exponential-Golomb codes are faster to decode but do not exploit the symbol frequency distributions. To address these limitations, this paper introduces Dual Length Codes, a hybrid approach designed to balance compression efficiency with decoding speed. Analyzing BFloat16 tensors from the Gemma model, we observed that the top 8 most frequent symbols account for approximately 50% of the cumulative probability. These 8 symbols are assigned a short 4 bit code. The remaining 248 symbols are assigned a longer 9 bit code. The coding scheme uses a single prefix bit to
arXiv:2602.17849v1 Announce Type: new Abstract: Training and serving Large Language Models (LLMs) relies heavily on parallelization and collective operations, which are frequently bottlenecked by network bandwidth. Lossless compression using e.g., Huffman codes can alleviate the issue, however, Huffman codes suffer from slow, bit-sequential decoding and high hardware complexity due to deep tree traversals. Universal codes e.g., Exponential-Golomb codes are faster to decode but do not exploit the symbol frequency distributions. To address these limitations, this paper introduces Dual Length Codes, a hybrid approach designed to balance compression efficiency with decoding speed. Analyzing BFloat16 tensors from the Gemma model, we observed that the top 8 most frequent symbols account for approximately 50% of the cumulative probability. These 8 symbols are assigned a short 4 bit code. The remaining 248 symbols are assigned a longer 9 bit code. The coding scheme uses a single prefix bit to distinguish between the two code lengths. The scheme uses a small Look Up Table with only 8 entries for encoding and decoding. The scheme achieves a compressibility of 18.6% in comparison to 21.3% achieved by Huffman codes, but it significantly speeds up the decoding and simplifies the hardware complexity.
Executive Summary
This article introduces Dual Length Codes, a novel approach to lossless compression designed to balance efficiency with decoding speed. The scheme is applied to BFloat16 tensors from the Gemma model, achieving a compressibility of 18.6% while significantly simplifying hardware complexity and speeding up decoding. By assigning short codes to frequent symbols and longer codes to less frequent ones, the approach addresses limitations of existing methods like Huffman codes and universal codes.
Key Points
- ▸ Introduction of Dual Length Codes for lossless compression
- ▸ Application to BFloat16 tensors from the Gemma model
- ▸ Comparison with Huffman codes and universal codes
Merits
Improved Decoding Speed
The Dual Length Codes scheme achieves faster decoding compared to Huffman codes due to its simpler structure.
Simplified Hardware Complexity
The use of a small Look Up Table with only 8 entries reduces hardware complexity.
Demerits
Lower Compressibility
The scheme achieves a compressibility of 18.6%, which is lower than the 21.3% achieved by Huffman codes.
Expert Commentary
The introduction of Dual Length Codes represents a significant step forward in addressing the trade-off between compression efficiency and decoding speed. By leveraging the frequency distribution of symbols in BFloat16 tensors, the scheme achieves a notable balance between these competing objectives. While the compressibility may be lower than that of Huffman codes, the gains in decoding speed and hardware simplicity are substantial, making this approach particularly suitable for applications where these factors are critical, such as in the training and serving of Large Language Models.
Recommendations
- ✓ Further research should be conducted to explore the applicability of Dual Length Codes to other data types and models.
- ✓ The development of hardware optimized for the Dual Length Codes scheme could lead to even greater performance improvements.
