Despite a strong theoretical foundation, empirical experiments reveal that existing domain generalization (DG) algorithms often fail to consistently outperform the ERM baseline. We argue that this issue arises because most DG studies focus on establishing theoretical guarantees for generalization under unrealistic assumptions, such as the availability of sufficient, diverse (or even infinite) domains or access to target domain knowledge. As a result, the extent to which domain generalization is achievable in scenarios with limited domains remains largely unexplored. This paper seeks to address this gap by examining generalization through the lens of the conditions necessary for its existence and learnability. Specifically, we systematically establish a set of necessary and sufficient conditions for generalization. Our analysis highlights that existing DG methods primarily act as regularization mechanisms focused on satisfying sufficient conditions, while often neglecting necessary ones. However, sufficient conditions cannot be verified in settings with limited training domains. In such cases, regularization targeting sufficient conditions aims to maximize the likelihood of generalization, whereas regularization targeting necessary conditions ensures its existence. Using this analysis, we reveal the shortcomings of existing DG algorithms by showing that, while they promote sufficient conditions, they inadvertently violate necessary conditions. To validate our theoretical insights, we propose a practical method that promotes the sufficient condition while maintaining the necessary conditions through a novel subspace representation alignment strategy. This approach highlights the advantages of preserving the necessary conditions on well-established DG benchmarks.

Identifying cause-and-effect relationships is critical to understanding real-world dynamics and ultimately causal reasoning. Existing methods for identifying event causality in NLP, including those based on Large Language Models (LLMs), exhibit difficulties in out-of-distribution settings due to the limited scale and heavy reliance on lexical cues within available benchmarks. Modern benchmarks, inspired by probabilistic causal inference, have attempted to construct causal graphs of events as a robust representation of causal knowledge, where \texttt{CRAB} \citep{romanou2023crab} is one such recent benchmark along this line. In this paper, we introduce \texttt{ACCESS}, a benchmark designed for discovery and reasoning over abstract causal events. Unlike existing resources, \texttt{ACCESS} focuses on causality of everyday life events on the abstraction level. We propose a pipeline for identifying abstractions for event generalizations from \texttt{GLUCOSE} \citep{mostafazadeh-etal-2020-glucose}, a large-scale dataset of implicit commonsense causal knowledge, from which we subsequently extract $1,4$K causal pairs. Our experiments highlight the ongoing challenges of using statistical methods and/or LLMs for automatic abstraction identification and causal discovery in NLP. Nonetheless, we demonstrate that the abstract causal knowledge provided in \texttt{ACCESS} can be leveraged for enhancing QA reasoning performance in LLMs.

Causal discovery in the presence of missing data introduces a chicken-and-egg dilemma. While the goal is to recover the true causal structure, robust imputation requires considering the dependencies or, preferably, causal relations among variables. Merely filling in missing values with existing imputation methods and subsequently applying structure learning on the complete data is empirically shown to be sub-optimal. To address this problem, we propose a score-based algorithm for learning causal structures from missing data based on optimal transport. This optimal transport viewpoint diverges from existing score-based approaches that are dominantly based on expectation maximization. We formulate structure learning as a density fitting problem, where the goal is to find the causal model that induces a distribution of minimum Wasserstein distance with the observed data distribution. Our framework is shown to recover the true causal graphs more effectively than competing methods in most simulations and real-data settings. Empirical evidence also shows the superior scalability of our approach, along with the flexibility to incorporate any off-the-shelf causal discovery methods for complete data.

There has long been plenty of theoretical and empirical evidence supporting the success of ensemble learning. Deep ensembles in particular take advantage of training randomness and expressivity of individual neural networks to gain prediction diversity, ultimately leading to better generalization, robustness and uncertainty estimation. In respect of generalization, it is found that pursuing wider local minima result in models being more robust to shifts between training and testing sets. A natural research question arises out of these two approaches as to whether a boost in generalization ability can be achieved if ensemble learning and loss sharpness minimization are integrated. Our work investigates this connection and proposes DASH - a learning algorithm that promotes diversity and flatness within deep ensembles. More concretely, DASH encourages base learners to move divergently towards low-loss regions of minimal sharpness. We provide a theoretical backbone for our method along with extensive empirical evidence demonstrating an improvement in ensemble generalizability.

Estimating the parameters of a probabilistic directed graphical model from incomplete data remains a long-standing challenge. This is because, in the presence of latent variables, both the likelihood function and posterior distribution are intractable without further assumptions about structural dependencies or model classes. While existing learning methods are fundamentally based on likelihood maximization, here we offer a new view of the parameter learning problem through the lens of optimal transport. This perspective licenses a general framework that operates on any directed graphs without making unrealistic assumptions on the posterior over the latent variables or resorting to black-box variational approximations. We develop a theoretical framework and support it with extensive empirical evidence demonstrating the flexibility and versatility of our approach. Across experiments, we show that not only can our method recover the ground-truth parameters but it also performs comparably or better on downstream applications, notably the non-trivial task of discrete representation learning.

Large language models (LLMs), as epitomized by models like ChatGPT, have revolutionized the field of natural language processing (NLP). Along with this trend, code-based large language models such as StarCoder, WizardCoder, and CodeLlama have emerged, trained extensively on vast repositories of code data. Yet, inherent in their design, these models primarily focus on generative tasks like code generation, code completion, and comment generation, and general support for multiple programming languages. While the generic abilities of code LLMs are useful for many programmers, the area of high-performance computing (HPC) has a narrower set of requirements that make a smaller and more domain-specific LM a smarter choice. This paper introduces OMPGPT, a novel model meticulously designed to harness the inherent strengths of language models for OpenMP pragma generation. Furthermore, we adopt and adapt prompt engineering techniques from the NLP domain to create chain-of-OMP, an innovative strategy designed to enhance OMPGPT's effectiveness. Our extensive evaluations demonstrate that OMPGPT outperforms existing large language models specialized in OpenMP tasks and maintains a notably smaller size, aligning it more closely with the typical hardware constraints of HPC environments. We consider our contribution as a pivotal bridge, connecting the advantage of language models with the specific demands of HPC tasks. The success of OMPGPT lays a solid foundation, suggesting its potential applicability and adaptability to a wider range of HPC tasks, thereby opening new avenues in the field of computational efficiency and effectiveness.

Interpretable machine learning seeks to understand the reasoning process of complex black-box systems that are long notorious for lack of explainability. One flourishing approach is through counterfactual explanations, which provide suggestions on what a user can do to alter an outcome. Not only must a counterfactual example counter the original prediction from the black-box classifier but it should also satisfy various constraints for practical applications. Diversity is one of the critical constraints that however remains less discussed. While diverse counterfactuals are ideal, it is computationally challenging to simultaneously address some other constraints. Furthermore, there is a growing privacy concern over the released counterfactual data. To this end, we propose a feature-based learning framework that effectively handles the counterfactual constraints and contributes itself to the limited pool of private explanation models. We demonstrate the flexibility and effectiveness of our method in generating diverse counterfactuals of actionability and plausibility. Our counterfactual engine is more efficient than counterparts of the same capacity while yielding the lowest re-identification risks.

Interpretable machine learning offers insights into what factors drive a certain prediction of a black-box system. A large number of interpreting methods focus on identifying explanatory input features, which generally fall into two main categories: attribution and selection. A popular attribution-based approach is to exploit local neighborhoods for learning instance-specific explainers in an additive manner. The process is thus inefficient and susceptible to poorly-conditioned samples. However, they can only interpret single-class predictions and many suffer from inconsistency across different settings, due to a strict reliance on a pre-defined number of features selected. This work exploits the strengths of both methods and proposes a framework for learning local explanations simultaneously for multiple target classes. Our model explainer significantly outperforms additive and instance-wise counterparts on faithfulness with more compact and comprehensible explanations. We also demonstrate the capacity to select stable and important features through extensive experiments on various data sets and black-box model architectures. Black-box machine learning systems enjoy a remarkable predictive performance at the cost of interpretability. This trade-off has motivated a number of interpreting approaches for explaining the behavior of these complex models. Such explanations are particularly useful for high-stakes applications such as healthcare (Caruana et al., 2015; Rich, 2016), cybersecurity (Nguyen et al., 2021) or criminal investigation (Lipton, 2018). While model interpretation can be done in various ways (Mothilal et al., 2020; Bodria et al., 2021), our discussion will focus on feature importance or saliency-based approach - that is, to assign relative importance weights to individual features w.r.t the model's prediction on an input example. Features here refer to input components interpretable to humans; for high-dimensional data such as texts or images, features can be a bag of words/phrases or a group of pixels/super-pixels (Ribeiro et al., 2016). Explanations are generally made by selecting top K features with the highest weights, signifying K most important features to a black-box's decision.