Unifying Invariant and Variant Features for Graph Out-of-Distribution via Probability of Necessity and Sufficiency

Graph Out-of-Distribution (OOD), requiring that models trained on biased data generalize to the unseen test data, has considerable real-world applications. One of the most mainstream methods is to extract the invariant subgraph by aligning the original and augmented data with the help of environment augmentation. However, these solutions might lead to the loss or redundancy of semantic subgraphs and result in suboptimal generalization. To address this challenge, we propose exploiting Probability of Necessity and Sufficiency (PNS) to extract sufficient and necessary invariant substructures. Beyond that, we further leverage the domain variant subgraphs related to the labels to boost the generalization performance in an ensemble manner. Specifically, we first consider the data generation process for graph data. Under mild conditions, we show that the sufficient and necessary invariant subgraph can be extracted by minimizing an upper bound, built on the theoretical advance of the probability of necessity and sufficiency. To further bridge the theory and algorithm, we devise the model called Sufficiency and Necessity Inspired Graph Learning (SNIGL), which ensembles an invariant subgraph classifier on top of latent sufficient and necessary invariant subgraphs, and a domain variant subgraph classifier specific to the test domain for generalization enhancement. Experimental results demonstrate that our SNIGL model outperforms the state-of-the-art techniques on six public benchmarks, highlighting its effectiveness in real-world scenarios.

From Large to Tiny: Distilling and Refining Mathematical Expertise for Math Word Problems with Weakly Supervision

Addressing the challenge of high annotation costs in solving Math Word Problems (MWPs) through full supervision with intermediate equations, recent works have proposed weakly supervised task settings that rely solely on the final answer as a supervised signal. Existing leading approaches typically employ various search techniques to infer intermediate equations, but cannot ensure their semantic consistency with natural language descriptions. The rise of Large Language Models (LLMs) like ChatGPT has opened up new possibilities for addressing MWPs directly. However, the computational demands of LLMs make them less than ideal for use in settings where resources are tight. In light of these challenges, we introduce an innovative two-stage framework that adeptly transfers mathematical Expertise from large to tiny language models. In \emph{Distillation Stage}, we propose a series of extraction processes that satisfy the properties of MWPs to distill mathematical knowledge from LLMs to construct problem-equation pairs required for supervised training. In \emph{Refinement Stage}, Due to Knowledge distilling method cannot guarantee the full utilization of all data, we further utilize the unsuccessfully searched data effectively by Knowledge Refine method. Finally, We train a small model using distilled data generated through two-stage methods. As our method fully leverages the semantic understanding capabilities during the searching 'problem-equation' pair, it demonstrates significantly improved performance on the Math23K and Weak12K datasets compared to existing small model methods, while maintaining a much lower computational cost than ChatGPT.

Unifying Invariance and Spuriousity for Graph Out-of-Distribution via Probability of Necessity and Sufficiency

Graph Out-of-Distribution (OOD), requiring that models trained on biased data generalize to the unseen test data, has a massive of real-world applications. One of the most mainstream methods is to extract the invariant subgraph by aligning the original and augmented data with the help of environment augmentation. However, these solutions might lead to the loss or redundancy of semantic subgraph and further result in suboptimal generalization. To address this challenge, we propose a unified framework to exploit the Probability of Necessity and Sufficiency to extract the Invariant Substructure (PNSIS). Beyond that, this framework further leverages the spurious subgraph to boost the generalization performance in an ensemble manner to enhance the robustness on the noise data. Specificially, we first consider the data generation process for graph data. Under mild conditions, we show that the invariant subgraph can be extracted by minimizing an upper bound, which is built on the theoretical advance of probability of necessity and sufficiency. To further bridge the theory and algorithm, we devise the PNSIS model, which involves an invariant subgraph extractor for invariant graph learning as well invariant and spurious subgraph classifiers for generalization enhancement. Experimental results demonstrate that our \textbf{PNSIS} model outperforms the state-of-the-art techniques on graph OOD on several benchmarks, highlighting the effectiveness in real-world scenarios.

Feature Attribution with Necessity and Sufficiency via Dual-stage Perturbation Test for Causal Explanation

We investigate the problem of explainability in machine learning.To address this problem, Feature Attribution Methods (FAMs) measure the contribution of each feature through a perturbation test, where the difference in prediction is compared under different perturbations.However, such perturbation tests may not accurately distinguish the contributions of different features, when their change in prediction is the same after perturbation.In order to enhance the ability of FAMs to distinguish different features' contributions in this challenging setting, we propose to utilize the probability (PNS) that perturbing a feature is a necessary and sufficient cause for the prediction to change as a measure of feature importance.Our approach, Feature Attribution with Necessity and Sufficiency (FANS), computes the PNS via a perturbation test involving two stages (factual and interventional).In practice, to generate counterfactual samples, we use a resampling-based approach on the observed samples to approximate the required conditional distribution.Finally, we combine FANS and gradient-based optimization to extract the subset with the largest PNS.We demonstrate that FANS outperforms existing feature attribution methods on six benchmarks.