A Learning Algorithm for Threshold Boolean Networks with Prescribed Fixed Points

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 plus or minus 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.