Quantization
LPCD: Unified Framework from Layer-Wise to Submodule Quantization
This paper introduces Layer-Projected Coordinate Descent (LPCD), a novel framework extending post-training quantization (PTQ) beyond individual linear layers to arbitrary submodules in large language models (LLMs). LPCD optimizes relaxed objectives across submodules and projects solutions back using existing layer-wise quantizers, unifying and generalizing previous methods like QEP and LoaQ. Experimental results on LLaMA and Qwen models show LPCD consistently reduces quantization error and improves perplexity and zero-shot accuracy, especially in low-bit regimes (3-bit and 2-bit), without altering underlying layer-wise quantizers. This approach enhances efficiency and compatibility within standard PTQ pipelines and supports quantization of complex submodules, activations, and KV caches.
Key Executive Impact
LPCD offers a practical path to deploying large language models with significantly reduced memory and computational overhead, particularly for edge devices. By enhancing quantization accuracy in low-bit regimes and maintaining compatibility with existing pipelines, LPCD accelerates AI adoption, improves cost-efficiency, and unlocks new possibilities for resource-constrained environments.
Reduction in Quantization Error
PPL Improvement (3-bit)
Zero-Shot Accuracy Gain
Compatibility with Existing PTQ
Deep Analysis & Enterprise Applications
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Layer-Projected Coordinate Descent (LPCD)
Submodule Quantization
Experimental Results & Impact
Layer-Projected Coordinate Descent (LPCD)
LPCD is a unified framework for quantizing arbitrary submodules. It extends layer-wise PTQ by optimizing relaxed objectives across submodules and projecting solutions back with standard layer-wise quantizers. This approach generalizes existing methods and provides a principled way to quantize complex submodules while maintaining efficiency. LPCD avoids unstable STE heuristics and is fully compatible with layer-wise PTQ pipelines.
Unified
Framework for Submodule Quantization
Enterprise Process Flow
Relaxation Step (Continuous Optimization)
→
Projection Step (Layer-wise Quantizer)
→
Repeat for Each Submodule
| Feature | Traditional Layer-wise PTQ | LPCD |
|---|---|---|
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| Objective |
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| Compatibility |
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Submodule Quantization
LPCD is applied to coherent Transformer submodules, including grouped-query KV, VO aggregation, and MLP up-down blocks. This allows for targeted error reduction across critical computational units, aligning quantization more closely with model-level behavior. The method demonstrates significant error reduction compared to QEP and LoaQ, especially in low-bit regimes.
LPCD Application: Transformer Submodules
LPCD strategically quantizes key Transformer components to maximize efficiency and maintain performance:
- QK Module: Quantizes grouped-query attention, reducing output distortion.
- VO Module: Aggregates attention scores, enhancing output accuracy.
- MLP Up-Down Blocks: Improves processing in feed-forward layers.
3-bit & 2-bit
Significant Performance Gains in Low-Bit Regimes
Experimental Results & Impact
Extensive experiments on LLaMA and Qwen models across various bit-widths (4, 3, 2-bit) show LPCD consistently outperforms both layer-wise PTQ methods (QEP, GPTQ) and existing submodule approaches (LoaQ). LPCD achieves lower perplexity and higher zero-shot accuracy, demonstrating its effectiveness in preserving model performance, particularly critical for challenging low-bit quantizations. The framework's ability to maintain compatibility with existing PTQ pipelines makes it highly practical for deployment.
LLaMA & Qwen
Validated Across Diverse LLM Architectures
| Method | PPL |
|---|---|
| QEP (RTN) | 25.3924 |
| LoaQ (RTN) | 14.1467 |
| LPCD (RTN) | 9.8112 |
| QEP (GPTQ) | 11.0124 |
| LoaQ (GPTQ) | 9.0706 |
| LPCD (GPTQ) | 8.7971 |
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Your Implementation Roadmap
A phased approach to integrating LPCD into your existing LLM deployment strategy, ensuring maximum impact with minimal disruption.
Phase 1: Assessment & Strategy (2-4 Weeks)
Evaluate current LLM infrastructure, identify key submodules for LPCD application, and define quantization objectives. Develop a tailored strategy for integration and performance benchmarks.
Phase 2: LPCD Integration & Testing (4-8 Weeks)
Implement LPCD within existing layer-wise PTQ pipelines. Conduct rigorous testing on selected LLaMA/Qwen models to validate perplexity and zero-shot accuracy improvements in a controlled environment.
Phase 3: Pilot Deployment & Optimization (6-12 Weeks)
Deploy LPCD-quantized models in a pilot program. Monitor performance, memory footprint, and latency. Iterate on submodule configurations and bit-widths for optimal real-world results.
Phase 4: Full-Scale Rollout & Monitoring (Ongoing)
Scale LPCD across your entire LLM ecosystem. Establish continuous monitoring for performance degradation and implement an ongoing optimization cycle to maintain peak efficiency and accuracy.
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