Unified Stochastic Framework for Neural Network Quantization and Pruning (2412.18184v3)

Abstract: Quantization and pruning are two essential techniques for compressing neural networks, yet they are often treated independently, with limited theoretical analysis connecting them. This paper introduces a unified framework for post-training quantization and pruning using stochastic path-following algorithms. Our approach builds on the Stochastic Path Following Quantization (SPFQ) method, extending its applicability to pruning and low-bit quantization, including challenging 1-bit regimes. By incorporating a scaling parameter and generalizing the stochastic operator, the proposed method achieves robust error correction and yields rigorous theoretical error bounds for both quantization and pruning as well as their combination.

• The paper presents a unified stochastic framework integrating quantization and pruning to achieve efficient neural network compression.
• It introduces a novel scaling parameter within the SPFQ method to control error correction, enabling robust performance in low-bit (1-bit) quantization.
• Practical implications include reduced memory and computational requirements, facilitating adaptive, post-training model optimization for constrained environments.

Unified Stochastic Framework for Neural Network Quantization and Pruning

Introduction

The paper "Unified Stochastic Framework for Neural Network Quantization and Pruning" (2412.18184) proposes an integrated framework for compressing neural networks through quantization and pruning. These compression methods are pivotal for optimizing memory and computational requirements in deep neural networks (DNNs) but often lack a connecting theoretical foundation when applied independently. The authors extend the Stochastic Path Following Quantization (SPFQ) methodology to incorporate pruning and low-bit quantization, including challenging regimes such as 1-bit quantization.

Stochastic Path Following Approach

The core of this research lies in unifying quantization and pruning approaches through stochastic path-following algorithms. This strategy utilizes a uniquely designed stochastic operator that handles both quantization accuracy and pruning sparsity requirements. A critical addition to the SPFQ technique is a scaling parameter that governs the error correction process and ensures robust performance even in low-bit contexts, thereby broadening the applicability of post-training model compression.

Algorithmic Framework

The proposed algorithm operates by iteratively compressing each layer of a neural network, focusing on both neuron quantization and zeroing during pruning. This involves the sequential adjustment of weights utilizing stochastic operators to minimize cumulative errors, employing a novel scaling factor for handling lower bit-depths and ensuring error bounds.

1. Quantization: Utilizes a finite set of representative values, reducing bit-precision while maintaining high fidelity in model predictions.
2. Pruning: Involves setting non-contributing weights to zero to streamline the model and improve computation speed without significant loss of accuracy.
3. Combined Approach: The integrated framework allows dynamic switching between quantization and pruning tasks through their stochastic operators.

Theoretical Analysis

The theory underpinning the unified quantization and pruning framework focuses on error bounds and performance guarantees. The authors derive a robust error correction mechanism with bounded error scaling that is theoretically favorable compared to traditional $\sqrt{N}$ scaling. Convex ordering principles ensure that errors are controlled comparably to Gaussian random distributions, enabling rigorous mathematical guarantees for model output accuracy post-compression.

Error Bounds and Pruning Techniques

The paper details specific stochastic operators for both quantization and pruning:

• One-Bit Quantization: Aims to compress neural weights to binary states with minimal error using a stochastic quantizer.
• Pruning: Employs randomization to stochastically set weights to zero, guided by a threshold that optimizes retention of influential weights.
• Quantization with Pruning: A combined stochastic operator performs both operations efficiently, maximizing model compression efficiency.

Practical Implications and Future Outlook

This stochastic framework holds potential for widespread application in environments with constrained computational resources, such as edge computing and mobile devices. It advances the state-of-the-art by allowing post-training adjustments without necessitating full retraining cycles, thus saving on computational costs and time.

The extension of SPFQ to pruning and ultra-low bit quantization opens avenues for future research into more adaptive neural network models that can dynamically scale their complexity based on operational constraints. Additionally, the framework's reliance on stochastic processes introduces robustness to noise and potential hardware variability in deployment scenarios.

Conclusion

The paper offers a comprehensive approach to neural network compression, proposing a theoretically grounded framework that unifies quantization and pruning. By extending SPFQ with a stochastic operator and scaling mechanism, it successfully addresses the challenges associated with low-bit regimes and sparsity. Future research can explore adaptive and dynamic implementations of this framework, further enhancing its utility in real-world applications.