Efficient Learning of Structured Matrices for Deep Neural Networks

Główne pojęcia

The author proposes a generalized and differentiable framework to learn structured matrices for efficient neural networks, enabling gradient descent optimization. The approach introduces a new format of structured matrices and parameterizes the structure in the frequency domain using the Gaussian-Dirichlet function.

Streszczenie

The paper explores learning efficient structures of weight matrices for deep neural networks by introducing a generalized and differentiable framework. It addresses challenges in identifying optimal matrix structures and proposes a method to learn them systematically. The proposed approach outperforms prior methods in terms of complexity and performance on image and language tasks.

Key Points:

• Investigates replacing dense weight matrices with structured ones.
• Proposes a generalized and differentiable framework for learning efficient structures.
• Introduces Generalized Block-low-rank (GBLR) matrix format.
• Utilizes Gaussian-Dirichlet (Gaudi) function for parameterization.
• Demonstrates improved performance on image and language tasks compared to prior approaches.

Statystyki

The size of the DNNs has increased up to 70 Billion parameters in the single model Zhao et al. (2023).
Achieved lower complexity and/or higher performance than prior approaches on image and language tasks.

Cytaty

"Our method learns efficient DNNs with structured matrices, achieving lower complexity and/or higher performance than prior approaches." - Changwoo Lee, Hun-Seok Kim

Kluczowe wnioski z

Differentiable Learning of Generalized Structured Matrices for Efficient Deep Neural Networks

by Changwoo Lee... o arxiv.org 03-11-2024

https://arxiv.org/pdf/2310.18882.pdf

Głębsze pytania

How does the proposed GBLR matrix format compare to existing hand-crafted structured matrices?

The proposed Generalized Block-Low-Rank (GBLR) matrix format offers a more flexible and generalized approach compared to existing hand-crafted structured matrices. While traditional structured matrices like Low-Rank (LR), Block-Sparse-plus-Low-Rank (BSP-LR), and Block-low-rank (BLR) are manually designed with specific constraints, the GBLR format allows for a wider range of structures by adjusting structural parameters. This means that GBLR can encompass LR, BSP, and BLR matrices as special cases under certain conditions. Additionally, the ability of GBLR to interpolate between different structural parameters enables it to capture undiscovered structured matrix formats efficiently.

How might the concept of structured matrix learning extend beyond neural networks?

The concept of learning structured matrices has applications beyond neural networks in various fields such as signal processing, image processing, natural language processing, and computational biology. In signal processing, efficient representations of data can be achieved using learned structured matrices for tasks like denoising or compression. In image processing, learned structures can enhance feature extraction or pattern recognition algorithms. For natural language processing tasks like sentiment analysis or machine translation, optimized weight matrices can improve model performance and efficiency. Similarly, in computational biology applications such as genomics or protein structure prediction, learned structures could lead to more accurate predictions and faster computations.

What implications does the use of Gaussian-Dirichlet function have on learning structural parameters?

The use of the Gaussian-Dirichlet function in learning structural parameters has several implications:

Differentiability: The Gaussian-Dirichlet function provides a smooth parameterization that allows for gradient-based optimization methods without encountering non-differentiable points.
Flexibility: By incorporating a smoothing factor (σ) into the function's design, it offers control over how sharp or smooth the mask patterns will be during training.
Efficiency: The properties of the Gaussian-Dirichlet kernel ensure stable derivatives even when width is zero which aids in efficient parameter updates during training.
Interpretability: The frequency-domain representation provided by this function makes it easier to interpret how widths and locations affect the structure of weight matrices.

These implications contribute to making the process of learning structural parameters more robust and effective in optimizing neural network architectures efficiently while maintaining accuracy levels through controlled adjustments based on training data feedback signals from gradients computed using these functions' properties.