Artificial neural networks (ANNs) have permeated various disciplinary
domains, ranging from bioinformatics to financial analytics, where their
application has become an indispensable facet of contemporary scientific
research endeavors. However, the inherent limitations of traditional neural
networks arise due to their relatively fixed network structures and activation
functions. 1, The type of activation function is single and relatively fixed,
which leads to poor "unit representation ability" of the network, and it is
often used to solve simple problems with very complex networks; 2, the network
structure is not adaptive, it is easy to cause network structure redundant or
insufficient. To address the aforementioned issues, this study proposes a novel
neural network called X-Net. By utilizing our designed Alternating
Backpropagation mechanism, X-Net dynamically selects appropriate activation
functions based on derivative information during training to enhance the
network's representation capability for specific tasks. Simultaneously, it
accurately adjusts the network structure at the neuron level to accommodate
tasks of varying complexities and reduce computational costs. Through a series
of experiments, we demonstrate the dual advantages of X-Net in terms of
reducing model size and improving representation power. Specifically, in terms
of the number of parameters, X-Net is only 3$\%$ of baselines on average, and
only 1.4$\%$ under some tasks. In terms of representation ability, X-Net can
achieve an average $R^2$=0.985 on the fitting task by only optimizing the
activation function without introducing any parameters. Finally, we also tested
the ability of X-Net to help scientific discovery on data from multiple
disciplines such as society, energy, environment, and aerospace, and achieved
concise and good results.

本研究提出了一种名为 X-Net 的新型神经网络，通过使用交替反向传播机制，在训练过程中根据导数信息动态选择适当的激活函数，增强网络对特定任务的表示能力。同时，在神经元级别准确调整网络结构以适应不同复杂度的任务和减少计算成本。通过一系列实验，我们展示了 X-Net 在减小模型大小和提高表示能力方面的双重优势。具体而言，就参数数量而言，X-Net 的平均值仅为基准的 3％，某些任务下仅为 1.4％。在表示能力方面，仅通过优化激活函数而不引入任何参数，X-Net 在拟合任务上可以实现平均 R^2=0.985。最后，我们还测试了 X-Net 在社会、能源、环境和航空航天等多个学科的数据上帮助科学发现的能力，并取得了简洁而优异的结果。