Quantization and fine-tuning are crucial for deploying large language models (LLMs) on resource-constrained edge devices. However, fine-tuning quantized models presents significant challenges, primarily stemming from: First, the mismatch in data types between the low-precision quantized weights (e.g., 4-bit) and the high-precision adaptation weights (e.g., 16-bit). This mismatch limits the computational efficiency advantage offered by quantized weights during inference.

Quantization and fine-tuning are crucial for deploying large language models (LLMs) on resource-constrained edge devices. However, fine-tuning quantized models presents significant challenges, primarily stemming from: First, the mismatch in data types between the low-precision quantized weights (e.g., 4-bit) and the high-precision adaptation weights (e.g., 16-bit). This mismatch limits the computational efficiency advantage offered by quantized weights during inference.

In this work, we investigate training methods for quantized neural networks from a theoretical viewpoint.

Large language models (LLMs) have demonstrated remarkable capabilities in various kinds of tasks, while the billion or even trillion parameters bring storage and efficiency bottlenecks for inference. Quantization, particularly floating-point quantization, is known to be capable of speeding up LLM inference by reducing memory footprint and data movement during the inference process. For the first time, we advance the floating-point quantization exploration from integer bitwidths to non-integer bit-widths, namely AMS-Quant, to further approach the quantization sweet spot. AMS-Quant incorporates two novel techniques to put it into effect: (1) it proposes Mantissa-bit Sharing, which groups k quantized weights and lets them share the least significant mantissa bit, allowing us to further approach the minimum quantization bit-width without accuracy loss. (2) It introduces Adaptive Searching, which employs an offline optimization strategy to minimize the accuracy degradation introduced by sharing. Moreover, AMS-Quant is also prototyped as efficient CUDA Linear kernels, which translates memory savings into wall-clock latency reduction by reducing memory access. Extensive experiments on large-scale datasets and models show that AMS-Quant can quantize the model to FP-5.33-e2m3 and FP4.25-e2m2, and significantly speed up the LLM decoding over FP16 inference (2.8x and 3.2x), with negligible accuracy loss.

Quantization based on the binary codes is gaining attention because each quantized bit can be directly utilized for computations without dequantization using look-up tables.

Quantization and fine-tuning are crucial for deploying large language models (LLMs) on resource-constrained edge devices. However, fine-tuning quantized models presents significant challenges, primarily stemming from: First, the mismatch in data types between the low-precision quantized weights (e.g., 4-bit) and the high-precision adaptation weights (e.g., 16-bit). This mismatch limits the computational efficiency advantage offered by quantized weights during inference. Second, potential accuracy degradation when merging these high-precision adaptation weights into the low-precision quantized weights, as the adaptation weights often necessitate approximation or truncation. Third, as far as we know, no existing methods support the lossless merging of adaptation while adjusting all quantized weights. To address these challenges, we introduce lossless ternary adaptation for quantization-aware fine-tuning (LoTA-QAF). This is a novel fine-tuning method specifically designed for quantized LLMs, enabling the lossless merging of ternary adaptation weights into quantized weights and the adjustment of all quantized weights. LoTA-QAF operates through a combination of: i) A custom-designed ternary adaptation (TA) that aligns ternary weights with the quantization grid and uses these ternary weights to adjust quantized weights. ii) A TA-based mechanism that enables the lossless merging of adaptation weights. iii) Ternary signed gradient descent (t-SignSGD) for updating the TA weights. We apply LoTA-QAF to Llama-3.1/3.3 and Qwen-2.5 model families and validate its effectiveness on several downstream tasks. On the MMLU benchmark, our method effectively recovers performance for quantized models, surpassing 16-bit LoRA by up to 5.14\%. For task-specific fine-tuning, 16-bit LoRA achieves superior results, but LoTA-QAF still outperforms other methods. Code: github.com/KingdalfGoodman/LoTA-QAF.

As the size of large language models grows exponentially, GPU memory has become a bottleneck for adapting these models to downstream tasks. In this paper, we aim to push the limits of memory-efficient training by minimizing memory usage on model weights, gradients, and optimizer states, within a unified framework. Our idea is to eliminate both gradients and optimizer states using zeroth-order optimization, which approximates gradients by perturbing weights during forward passes to identify gradient directions. To minimize memory usage on weights, we employ model quantization, e.g., converting from bfloat16 to int4. However, directly applying zeroth-order optimization to quantized weights is infeasible due to the precision gap between discrete weights and continuous gradients, which would otherwise require de-quantization and re-quantization. To overcome this challenge, we propose Quantized Zeroth-order Optimization (QZO), a simple yet effective approach that perturbs the continuous quantization scale for gradient estimation and uses a directional derivative clipping method to stabilize training. QZO is orthogonal to both scalar-based and codebook-based post-training quantization methods. Compared to full-parameter fine-tuning in 16 bits, QZO can reduce the total memory cost by more than 18$\times$ for 4-bit LLMs, and enables fine-tuning Llama-2-13B within a single 24GB GPU. Code will be released publicly.

Quantization-Aware Training (QAT) integrates quantization into the training loop, enabling LLMs to learn robust low-bit representations, and is widely recognized as one of the most promising research directions. All current QAT research focuses on minimizing quantization error on full-precision models, where the full-precision accuracy acts as an upper bound (accuracy ceiling). No existing method has even attempted to surpass this ceiling. To break this ceiling, we propose a new paradigm: raising the ceiling (full-precision model), and then still quantizing it efficiently into 2 bits. We propose Fairy$\pm i$, the first 2-bit quantization framework for complex-valued LLMs. Specifically, our method leverages the representational advantages of the complex domain to boost full-precision accuracy. We map weights to the fourth roots of unity $\{\pm1, \pm i\}$, forming a perfectly symmetric and information-theoretically optimal 2-bit representation. Importantly, each quantized weight has either a zero real or imaginary part, enabling multiplication-free inference using only additions and element swaps. Experimental results show that Fairy$\pm i$ outperforms the ceiling of existing 2-bit quantization approaches in terms of both PPL and downstream tasks, while maintaining strict storage and compute efficiency. This work opens a new direction for building highly accurate and practical LLMs under extremely low-bit constraints.

--Transformer-based Large Language Models (LLMs) have significantly advanced AI capabilities but pose considerable challenges for deployment on edge devices due to high computational demands, memory bandwidth constraints, and energy consumption. Leveraging Activation-aware Weight Quantization (A WQ) with FPGA-accelerated execution pipelines, the proposed approach enhances both model compression rate and system throughput. Additionally, we propose a hybrid execution strategy that intelligently offloads compute-intensive operations to the FPGA while utilizing the CPU for lighter tasks, effectively balancing the computational workload and maximizing overall performance. Our framework achieves a model compression rate of 55.08% compared to the original model and produces output at a rate of 5.1 tokens per second, outperforming the baseline performance of 2.8 tokens per second. Recent advancements in Large Language Models (LLMs) have spurred numerous opportunities across different domains [1], attracting users from sectors such as healthcare [2], robotics [3], biomedical [4], music [5], etc.