How can we quantize large language models while preserving accuracy? Quantization is essential for deploying large language models (LLMs) efficiently. Binary-coding quantization (BCQ) and uniform quantization (UQ) are promising quantization schemes that have strong expressiveness and optimizability, respectively. However, neither scheme leverages both advantages. In this paper, we propose UniQuanF (Unified Quantization with Flexible Mapping), an accurate quantization method for LLMs. UniQuanF harnesses both strong expressiveness and optimizability by unifying the flexible mapping technique in UQ and non-uniform quantization levels of BCQ. We propose unified initialization, and local and periodic mapping techniques to optimize the parameters in UniQuanF precisely. After optimization, our unification theorem removes computational and memory overhead, allowing us to utilize the superior accuracy of UniQuanF without extra deployment costs induced by the unification. Experimental results demonstrate that UniQuanF outperforms existing UQ and BCQ methods, achieving up to 4.60% higher accuracy on GSM8K benchmark.

With the commercialization of large language models (LLMs), weight-activation quantization has emerged to compress and accelerate LLMs, achieving high throughput while reducing inference costs. However, existing post-training quantization (PTQ) techniques for quantizing weights and activations of LLMs still suffer from non-negligible accuracy drops, especially on massive multitask language understanding. To address this issue, we propose Low-Rank Quantization (LRQ) $-$ a simple yet effective post-training weight quantization method for LLMs that reconstructs the outputs of an intermediate Transformer block by leveraging low-rank weight-scaling matrices, replacing the conventional full weight-scaling matrices that entail as many learnable scales as their associated weights. Thanks to parameter sharing via low-rank structure, LRQ only needs to learn significantly fewer parameters while enabling the individual scaling of weights, thus boosting the generalization capability of quantized LLMs. We show the superiority of LRQ over prior LLM PTQ works under (i) $8$-bit weight and per-tensor activation quantization, (ii) $4$-bit weight and $8$-bit per-token activation quantization, and (iii) low-bit weight-only quantization schemes. Our code is available at \url{https://github.com/onliwad101/FlexRound_LRQ} to inspire LLM researchers and engineers.

Post-training quantization (PTQ) has been gaining popularity for the deployment of deep neural networks on resource-limited devices since unlike quantization-aware training, neither a full training dataset nor end-to-end training is required at all. As PTQ schemes based on reconstructing each layer or block output turn out to be effective to enhance quantized model performance, recent works have developed algorithms to devise and learn a new weight-rounding scheme so as to better reconstruct each layer or block output. In this work, we propose a simple yet effective new weight-rounding mechanism for PTQ, coined FlexRound, based on element-wise division instead of typical element-wise addition such that FlexRound enables jointly learning a common quantization grid size as well as a different scale for each pre-trained weight. Thanks to the reciprocal rule of derivatives induced by element-wise division, FlexRound is inherently able to exploit pre-trained weights when updating their corresponding scales, and thus, flexibly quantize pre-trained weights depending on their magnitudes. We empirically validate the efficacy of FlexRound on a wide range of models and tasks. To the best of our knowledge, our work is the first to carry out comprehensive experiments on not only image classification and natural language understanding but also natural language generation, assuming a per-tensor uniform PTQ setting. Moreover, we demonstrate, for the first time, that large language models can be efficiently quantized, with only a negligible impact on performance compared to half-precision baselines, achieved by reconstructing the output in a block-by-block manner.