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NeurAlly-Decomposed Oracle (NADO) is a powerful approach for controllablegeneration with large language models. Differentiating from finetuning/prompttuning, it has the potential to avoid catastrophic forgetting of the large basemodel and achieve guaranteed convergence to an entropy-maximized closed-formsolution without significantly limiting the model capacity. Despite itssuccess, several challenges arise when applying NADO to more complex scenarios.First, the best practice of using NADO for the composition of multiple controlsignals is under-explored. Second, vanilla NADO suffers from gradient vanishingfor low-probability control signals and is highly reliant on theforward-consistency regularization. In this paper, we study the aforementionedchallenges when using NADO theoretically and empirically. We show we canachieve guaranteed compositional generalization of NADO with a certainpractice, and propose a novel alternative parameterization of NADO to perfectlyguarantee the forward-consistency. We evaluate the improved training of NADO,i.e. NADO++, on CommonGen. Results show that NADO++ improves the effectivenessof the algorithm in multiple aspects.

On Compositionality and Improved Training of NADO