V-EfficientNets: Vector-Valued Efficiently Scaled Convolutional Neural Network Models

TL;DR

This work addresses the efficiency-accuracy trade-off in image classification by extending EfficientNet to vector-valued domains using non-associative algebras, enabling inter-channel relationships to be exploited with fewer parameters. The authors introduce V-EfficientNet, including vector-valued dense, convolution, and depthwise convolution layers, and a design parameter $\lambda$ that controls architectural vectorization, built on a $d$-dimensional algebra $\mathbb{V}$. On the ALL-IDB2 leukemia dataset, V-EfficientNets achieve state-of-the-art performance with up to 70% parameter reduction, notably $99.46\%$ average accuracy with the hyperbolic-quaternion variant. Code is released to facilitate vector-valued CNN deployment in medical image analysis and to spur exploration of algebra choices for different tasks.

Abstract

EfficientNet models are convolutional neural networks optimized for parameter allocation by jointly balancing network width, depth, and resolution. Renowned for their exceptional accuracy, these models have become a standard for image classification tasks across diverse computer vision benchmarks. While traditional neural networks learn correlations between feature channels during training, vector-valued neural networks inherently treat multidimensional data as coherent entities, taking for granted the inter-channel relationships. This paper introduces vector-valued EfficientNets (V-EfficientNets), a novel extension of EfficientNet designed to process arbitrary vector-valued data. The proposed models are evaluated on a medical image classification task, achieving an average accuracy of 99.46% on the ALL-IDB2 dataset for detecting acute lymphoblastic leukemia. V-EfficientNets demonstrate remarkable efficiency, significantly reducing parameters while outperforming state-of-the-art models, including the original EfficientNet. The source code is available at https://github.com/mevalle/v-nets.

Figures (5)

• Figure 1: Traditional (real-valued) depthwise convolution.
• Figure 2: Computation of $\boldsymbol{F}^{(\mathbb{R})}$ by \ref{['eq:computing_F']}.
• Figure 3: Augmented image $\boldsymbol{J}^{(a)} = \boldsymbol{I}^{(\mathbb{R})} \ast_{DW} \boldsymbol{F}^{(\mathbb{R})}$.
• Figure 4: Computation of $\boldsymbol{J}^{(\mathbb{R})}$.
• Figure 5: Building blocks of the EfficientNet models. Here, BN indicates batch normalization, and ReLU is the rectified linear unit activation function. EfficientNetV1 models use only the MBConv block, while V2 uses a combination of both blocks.

Theorems & Definitions (4)

• Definition 1: Non-associative Algebra Schafer1961AnAlgebras
• Remark 1
• Remark 2
• Definition 2: Hypercomplex algebra Kantor1989HypercomplexAlgebras