具有指定不动点的阈值布尔网络学习算法
A Learning Algorithm for Threshold Boolean Networks with Prescribed Fixed Points
- Universidad Adolfo Ibáñez（阿道夫·伊瓦涅斯大学）
机构由 AI 辅助整理，请以论文原文为准。
AI总结：
本文提出一种基于自定义可微损失函数的阈值布尔网络学习算法，能在保持指定不动点的同时抑制虚假吸引子，并在拟南芥基因调控网络上验证了其有效性与稳定性。
AI中文摘要：
我们提出了一种学习算法，用于推断具有指定不动点集的阈值布尔网络（TBN）。所提出的方法采用自定义可微损失函数，该函数联合强制不动点保持、惩罚虚假吸引子、鼓励二值输出，并通过L1正则化促进稀疏性。将该方法应用于拟南芥的FOS-GRN模型，该方法在30次独立运行中的5次实现了完美重建（即所有10个期望的不动点且无虚假不动点），平均恢复8.53 ± 0.90个正确的不动点且无虚假吸引子。相比之下，标准方法如感知机和逻辑回归恢复了多达10个不动点，但引入了8到31个虚假不动点。一项改变稀疏系数（λ）的额外分析证实，在正则化强度的实际范围（高达0.01）内，该方法的性能和推断网络的结构属性保持稳健。总体而言，结果证明了所提出算法在规定的动力学约束下捕获有意义的网络动力学的有效性和稳定性。
英文摘要：
We present a learning algorithm for inferring threshold Boolean networks (TBNs) with a prescribed set of fixed points. The proposed method employs a custom differentiable loss function that jointly enforces fixed point preservation, penalizes spurious attractors, encourages binary outputs, and promotes sparsity through L1 regularization. Applied to the FOS-GRN model of Arabidopsis thaliana, the approach achieved perfect reconstruction (i.e., all 10 desired fixed points and no spurious ones) in 5 out of 30 independent runs, recovering on average 8.53 $\pm$ 0.90 correct fixed points with no spurious attractors. In contrast, standard methods such as the Perceptron and Logistic Regression recovered up to 10 fixed points but introduced between 8 and 31 spurious ones. An additional analysis varying the sparsity coefficient ($λ$) confirmed that the method's performance and the structural properties of the inferred networks remain robust within a practical range (up to 0.01) of regularization strengths. Overall, the results demonstrate the effectiveness and stability of the proposed algorithm in capturing meaningful network dynamics under prescribed dynamical constraints.
