CAT-Q (Cost-efficient and Accurate Ternary Quantization) addresses the challenge of compressing Large Language Models (LLMs) into 1.58-bit ternary weights ({-1, 0, 1}). While existing state-of-the-art ternary methods rely on expensive Quantization-Aware Training (QAT) that requires processing hundreds of billions of tokens, CAT-Q operates as a Post-Training Quantization (PTQ) scheme. This allows it to achieve high-quality compression using only 512 calibration samples, significantly reducing the computational and data requirements for deployment.
CAT-Q introduces two primary innovations to stabilize the difficult optimization process of ternary quantization:
Learnable Modulation (LM): This component uses a set of learnable factors to adjust the distribution of pre-trained weights and the ternary threshold. By transforming the weight distribution before quantization, it suppresses the impact of outliers and reduces the distributional misalignment between high-precision weights and their ternary approximations.
Softened Ternarization (ST): To overcome the non-differentiable nature of hard ternarization, ST employs a two-stage process. It uses a differentiable transition function that gradually evolves from an identity mapping to a hard ternary output. This smooth transition guides the optimization toward stable convergence during the calibration phase.
Experiments demonstrate that CAT-Q outperforms seminal ternary models like BitNet 1.58-bit v1 and v2 while requiring 100,000 times fewer training tokens. The authors successfully applied the method to a wide range of models, from 1.7B to 235B parameters, including both dense and Mixture-of-Experts (MoE) architectures. The entire quantization process for these large models takes between 8 and 60 hours on 8 A100 GPUs, making it a highly practical solution for industrial deployment.
Ternary Quantization
A compression technique that constrains model weights to exactly three values: {-1, 0, 1}, effectively reducing memory usage by approximately 10x compared to FP16.
Post-Training Quantization (PTQ)
A method for compressing pre-trained models using a small calibration dataset without requiring full-scale retraining or access to the original training data.
Learnable Modulation
A technique within CAT-Q that applies learnable linear transformations to weight distributions to make them more robust to the information loss inherent in extreme quantization.
Softened Ternarization
A differentiable optimization strategy that uses a smooth transition function to bridge the gap between continuous high-precision weights and discrete ternary values.
Sliding-Layer Optimization
An approach where multiple layers are quantized simultaneously within a sliding window, allowing the model to leverage inter-layer dependencies to minimize reconstruction error.
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