On Compositionality and Improved Training of NADO

NeurAlly-Decomposed Oracle (NADO) is a powerful approach for controllable generation with large language models. Differentiating from finetuning/prompt tuning, it has the potential to avoid catastrophic forgetting of the large base model and achieve guaranteed convergence to an entropy-maximized closed-form solution without significantly limiting the model capacity. Despite its success, several challenges arise when applying NADO to more complex scenarios. First, the best practice of using NADO for the composition of multiple control signals is under-explored. Second, vanilla NADO suffers from gradient vanishing for low-probability control signals and is highly reliant on the forward-consistency regularization. In this paper, we study the aforementioned challenges when using NADO theoretically and empirically. We show we can achieve guaranteed compositional generalization of NADO with a certain practice, and propose a novel alternative parameterization of NADO to perfectly guarantee the forward-consistency. We evaluate the improved training of NADO, i.e. NADO++, on CommonGen. Results show that NADO++ improves the effectiveness of the algorithm in multiple aspects.