Xiaotong Song

Zongjian Han, Yiran Liang, Ruiwen Wang et al.

This paper presents a neural network filter method based on contraction operators to address model collapse in recursive training of generative models. Unlike \cite{xu2024probabilistic}, which requires superlinear sample growth ($O(t^{1+s})$), our approach completely eliminates the dependence on increasing sample sizes within an unbiased estimation framework by designing a neural filter that learns to satisfy contraction conditions. We develop specialized neural network architectures and loss functions that enable the filter to actively learn contraction conditions satisfying Assumption 2.3 in exponential family distributions, thereby ensuring practical application of our theoretical results. Theoretical analysis demonstrates that when the learned contraction conditions are satisfied, estimation errors converge probabilistically even with constant sample sizes, i.e., $\limsup_{t\to\infty}\mathbb{P}(\|\mathbf{e}_t\|>δ)=0$ for any $δ>0$. Experimental results show that our neural network filter effectively learns contraction conditions and prevents model collapse under fixed sample size settings, providing an end-to-end solution for practical applications.

Weilin Luo, Hai Wan, Xiaotong Song et al.

The boundary conditions (BCs) have shown great potential in requirements engineering because a BC captures the particular combination of circumstances, i.e., divergence, in which the goals of the requirement cannot be satisfied as a whole. Existing researches have attempted to automatically identify lots of BCs. Unfortunately, a large number of identified BCs make assessing and resolving divergences expensive. Existing methods adopt a coarse-grained metric, generality, to filter out less general BCs. However, the results still retain a large number of redundant BCs since a general BC potentially captures redundant circumstances that do not lead to a divergence. Furthermore, the likelihood of BC can be misled by redundant BCs resulting in costly repeatedly assessing and resolving divergences. In this paper, we present a fine-grained metric to filter out the redundant BCs. We first introduce the concept of contrasty of BC. Intuitively, if two BCs are contrastive, they capture different divergences. We argue that a set of contrastive BCs should be recommended to engineers, rather than a set of general BCs that potentially only indicates the same divergence. Then we design a post-processing framework (PPAc) to produce a set of contrastive BCs after identifying BCs. Experimental results show that the contrasty metric dramatically reduces the number of BCs recommended to engineers. Results also demonstrate that lots of BCs identified by the state-of-the-art method are redundant in most cases. Besides, to improve efficiency, we propose a joint framework (JAc) to interleave assessing based on the contrasty metric with identifying BCs. The primary intuition behind JAc is that it considers the search bias toward contrastive BCs during identifying BCs, thereby pruning the BCs capturing the same divergence. Experiments confirm the improvements of JAc in identifying contrastive BCs.