"CLoQ: Enhancing Fine-Tuning of Quantized LLMs via Calibrated LoRA Initialization"

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The paper introduces CLoQ, a calibration-based LoRA initialization for quantized Large Language Models.

CLoQ minimizes the discrepancy between original and quantized LLMs by optimizing LoRA components, improving fine-tuning performance, especially at low bit-widths.

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1. Calibration data is smartly used in CLoQ. It goes beyond standard Post-Training Quantization. CLoQ leverages activation data to guide LoRA initialization. This data-driven approach effectively minimizes quantization error. It leads to better low-bit fine-tuning.

2. CLoQ's strength lies in its optimization formulation. It solves a non-trivial low-rank approximation problem. This problem considers the impact of activation matrix. The closed-form solution ensures optimality. This precise initialization is key for maintaining performance at INT2 and INT3 bit-widths.

3. CLoQ offers computational efficiency. It avoids back-propagation during initialization. The method uses two SVD operations. SVDs have manageable complexity. This makes CLoQ highly scalable. It is practical for large LLMs even in resource-limited settings.

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Paper - https://arxiv.org/abs/2501.18475

Original Problem 🤔:

→ Quantization reduces memory but hurts performance, especially with Low-Rank Adaptation (LoRA).

→ Applying LoRA to quantized LLMs causes performance drop due to reduced precision of weights.

→ Existing LoRA initialization strategies are not optimal for quantized LLMs.

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Solution in this Paper 💡:

→ The paper proposes CLoQ, Calibrated LoRA initialization for Quantized LLMs.

→ CLoQ is a data-driven, layer-wise initialization strategy for quantized LLMs.

→ CLoQ uses a small calibration dataset to minimize the difference between the original LLM and its quantized LoRA version during initialization.

→ CLoQ first quantizes the pre-trained LLM using Post-Training Quantization.

→ Then, it computes optimal LoRA components by solving a low-rank approximation problem under linear transformation using the calibration data.

→ This method uses two Singular Value Decompositions to efficiently find the optimal LoRA components in a closed form.

→ CLoQ does not require back-propagation, making it computationally efficient.

→ During fine-tuning, only LoRA adapters are trained, while quantized weights remain frozen.

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Key Insights from this Paper 🧐:

→ Quantization error in LLMs can be effectively mitigated by calibrated initialization of LoRA adapters.

→ Minimizing the discrepancy between the original and quantized LLM with LoRA during initialization is crucial for performance.

→ Using activation data during LoRA initialization aligns the quantized model's behavior closer to the original model.

→ A closed-form solution for optimal LoRA initialization in quantized LLMs can be derived using SVDs.

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Results 📊:

→ CLoQ outperforms existing LoRA fine-tuning methods for quantized LLMs, especially at ultra-low bit-widths like INT2.

→ INT2 CLoQ on Llama2-13B surpasses INT4 QLoRA in arithmetic reasoning accuracy.

→ On GSM8K, INT2 CLoQ achieves 33.7% accuracy on Llama2-7B, better than INT4 LoRA.

→ On average across arithmetic tasks, INT2 CLoQ improves accuracy by 3.6% and 4.8% over LoftQ on Llama2-7B and Llama2-13B respectively.