Aim/Introduction: Distance-encoding biomorphic-informational neural network (DEBI-NN) is a recently proposed architecture in which connection weights are defined by the distances between neurons positioned in a Euclidian space. This approach drastically reduces the number of trainable parameters compared to classical neural networks in which weights are directly trained. The training process for DEBI-NN is based on a genetic algorithm (GA), rather than gradient descent (GD) which remains the prevailing optimization algorithm in deep learning. We aim to design and implement a GD learner for DEBI-NN and assess its performance compared to GA. Materials and Methods: We designed a spatial backpropagation scheme tailored to DEBI-NN and carried out a comparison between GD and GA for classification tasks, using a synthetic non-linear "two-moons" dataset, two clinical medical imaging radiomic datasets and a fetal cardiotocography dataset with a sample sizes ranging from n=85 to n=2126. Each optimizer was tuned through targeted hyperparameter searches adapted to each dataset. Results: Across all experiments, GA consistently produced superior decision boundaries and classification performance (Synthetic: 100% vs 83%; DLBCL: 83% vs 78%; HECKTOR: 80% vs 67%; Fetal: 81% vs 66%), whereas GD exhibited instability and failed to fully capture the non-linear patterns inherent to DEBI-NN's spatial encoding. The entangled gradients resulting from neuron interdependencies limit the effectiveness of classical backpropagation. Conclusion: These findings highlight fundamental limitations of gradient-based methods in architectures with highly interdependent spatial parameters and confirm the suitability of evolutionary strategies for training DEBI-NN.

翻译：目的/引言：距离编码生物形态信息神经网络（DEBI-NN）是一种近期提出的架构，其连接权重由欧几里得空间中神经元之间的距离定义。与直接训练权重的经典神经网络相比，该方法大幅减少了可训练参数数量。DEBI-NN的训练过程基于遗传算法（GA），而非深度学习领域主流优化算法——梯度下降法（GD）。本研究旨在为DEBI-NN设计并实现GD学习器，并评估其与GA的性能差异。材料与方法：针对DEBI-NN设计了一种空间反向传播方案，并使用合成非线性“双月”数据集、两个临床医学影像放射组学数据集以及一个胎儿心宫缩描记数据集（样本量n=85至n=2126）进行GD与GA的分类任务对比。每种优化器均通过针对各数据集的目标超参数搜索进行调优。结果：在所有实验中，GA均持续生成更优的决策边界和分类性能（合成数据集：100% vs 83%；弥漫性大B细胞淋巴瘤数据集：83% vs 78%；头颈癌放射组学数据集：80% vs 67%；胎儿数据集：81% vs 66%），而GD表现出不稳定性，且未能完全捕捉DEBI-NN空间编码固有的非线性模式。神经元相互依赖导致的梯度纠缠限制了经典反向传播的有效性。结论：这些发现揭示了基于梯度方法在高度依赖的空间参数架构中的根本局限性，并证实了进化策略对训练DEBI-NN的适用性。