IM-Unpack: Training and Inference with Arbitrarily Low Precision Integers
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arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866914710868197376 |
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| author | Zeng, Zhanpeng Sankaralingam, Karthikeyan Singh, Vikas |
| author_facet | Zeng, Zhanpeng Sankaralingam, Karthikeyan Singh, Vikas |
| contents | GEneral Matrix Multiply (GEMM) is a central operation in deep learning and corresponds to the largest chunk of the compute footprint. Therefore, improving its efficiency is an active topic of ongoing research. A popular strategy is the use of low bit-width integers to approximate the original entries in a matrix. This allows efficiency gains, but often requires sophisticated techniques to control the rounding error incurred. In this work, we first verify/check that when the low bit-width restriction is removed, for a variety of Transformer-based models, whether integers are sufficient for all GEMMs need -- for {\em both} training and inference stages, and can achieve parity with floating point counterparts. No sophisticated techniques are needed. We find that while a large majority of entries in matrices (encountered in such models) can be easily represented by {\em low} bit-width integers, the existence of a few heavy hitter entries make it difficult to achieve efficiency gains via the exclusive use of low bit-width GEMMs alone. To address this issue, we develop a simple algorithm, Integer Matrix Unpacking (IM-Unpack), to {\em unpack} a matrix with large integer entries into a larger matrix whose entries all lie within the representable range of arbitrarily low bit-width integers. This allows {\em equivalence} with the original GEMM, i.e., the exact result can be obtained using purely low bit-width integer GEMMs. This comes at the cost of additional operations -- we show that for many popular models, this overhead is quite small. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_07339 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | IM-Unpack: Training and Inference with Arbitrarily Low Precision Integers Zeng, Zhanpeng Sankaralingam, Karthikeyan Singh, Vikas Machine Learning Computation and Language Computer Vision and Pattern Recognition GEneral Matrix Multiply (GEMM) is a central operation in deep learning and corresponds to the largest chunk of the compute footprint. Therefore, improving its efficiency is an active topic of ongoing research. A popular strategy is the use of low bit-width integers to approximate the original entries in a matrix. This allows efficiency gains, but often requires sophisticated techniques to control the rounding error incurred. In this work, we first verify/check that when the low bit-width restriction is removed, for a variety of Transformer-based models, whether integers are sufficient for all GEMMs need -- for {\em both} training and inference stages, and can achieve parity with floating point counterparts. No sophisticated techniques are needed. We find that while a large majority of entries in matrices (encountered in such models) can be easily represented by {\em low} bit-width integers, the existence of a few heavy hitter entries make it difficult to achieve efficiency gains via the exclusive use of low bit-width GEMMs alone. To address this issue, we develop a simple algorithm, Integer Matrix Unpacking (IM-Unpack), to {\em unpack} a matrix with large integer entries into a larger matrix whose entries all lie within the representable range of arbitrarily low bit-width integers. This allows {\em equivalence} with the original GEMM, i.e., the exact result can be obtained using purely low bit-width integer GEMMs. This comes at the cost of additional operations -- we show that for many popular models, this overhead is quite small. |
| title | IM-Unpack: Training and Inference with Arbitrarily Low Precision Integers |
| topic | Machine Learning Computation and Language Computer Vision and Pattern Recognition |
| url | https://arxiv.org/abs/2403.07339 |