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Predictive multiplicity refers to the phenomenon in which classification tasks may admit multiple competing models that achieve almost-equally-optimal performance, yet generate conflicting outputs for individual samples. This presents significant concerns, as it can potentially result in systemic exclusion, inexplicable discrimination, and unfairness in practical applications. Measuring and mitigating predictive multiplicity, however, is computationally challenging due to the need to explore all such almost-equally-optimal models, known as the Rashomon set, in potentially huge hypothesis spaces. To address this challenge, we propose a novel framework that utilizes dropout techniques for exploring models in the Rashomon set. We provide rigorous theoretical derivations to connect the dropout parameters to properties of the Rashomon set, and empirically evaluate our framework through extensive experimentation. Numerical results show that our technique consistently outperforms baselines in terms of the effectiveness of predictive multiplicity metric estimation, with runtime speedup up to $20\times \sim 5000\times$. With efficient Rashomon set exploration and metric estimation, mitigation of predictive multiplicity is then achieved through dropout ensemble and model selection.

The automorphism groups of various linear codes are well-studied yielding valuable insights into the respective code structure. This knowledge is successfully applied in, e.g., theoretical analysis and in improving decoding performance motivating the analyses of endomorphisms of linear codes. In this work, we discuss the structure of the set of transformation matrices of code endomorphisms, defined as a generalization of code automorphisms, and provide an explicit construction of a bijective mapping between the image of an endomorphism and its canonical quotient space. Furthermore, we introduce a one-to-one mapping between the set of transformation matrices of endomorphisms and a larger linear block code enabling the use of well-known algorithms for the search for suitable endomorphisms. Additionally, we propose an approach to obtain unknown code endomorphisms based on automorphisms of the code. Furthermore, we consider ensemble decoding as a possible use case for endomorphisms by introducing endomorphism ensemble decoding. Interestingly, EED can improve decoding performance when other ensemble decoding schemes are not applicable.

Graph-structured data, prevalent in domains ranging from social networks to biochemical analysis, serve as the foundation for diverse real-world systems. While graph neural networks demonstrate proficiency in modeling this type of data, their success is often reliant on significant amounts of labeled data, posing a challenge in practical scenarios with limited annotation resources. To tackle this problem, tremendous efforts have been devoted to enhancing graph machine learning performance under low-resource settings by exploring various approaches to minimal supervision. In this paper, we introduce a novel concept of Data-Efficient Graph Learning (DEGL) as a research frontier, and present the first survey that summarizes the current progress of DEGL. We initiate by highlighting the challenges inherent in training models with large labeled data, paving the way for our exploration into DEGL. Next, we systematically review recent advances on this topic from several key aspects, including self-supervised graph learning, semi-supervised graph learning, and few-shot graph learning. Also, we state promising directions for future research, contributing to the evolution of graph machine learning.

We propose a new multi-agent task grammar to encode collaborative tasks for a team of heterogeneous agents that can have overlapping capabilities. The grammar allows users to specify the relationship between agents and parts of the task without providing explicit assignments or constraints on the number of agents required. We develop a method to automatically find a team of agents and synthesize correct-by-construction control with synchronization policies to satisfy the task. We demonstrate the scalability of our approach through simulation and compare our method to existing task grammars that encode multi-agent tasks.

Due to its conceptual simplicity and generality, compressive neural representation has emerged as a promising alternative to traditional compression methods for managing massive volumetric datasets. The current practice of neural compression utilizes a single large multilayer perceptron (MLP) to encode the global volume, incurring slow training and inference. This paper presents an efficient compressive neural representation (ECNR) solution for time-varying data compression, utilizing the Laplacian pyramid for adaptive signal fitting. Following a multiscale structure, we leverage multiple small MLPs at each scale for fitting local content or residual blocks. By assigning similar blocks to the same MLP via size uniformization, we enable balanced parallelization among MLPs to significantly speed up training and inference. Working in concert with the multiscale structure, we tailor a deep compression strategy to compact the resulting model. We show the effectiveness of ECNR with multiple datasets and compare it with state-of-the-art compression methods (mainly SZ3, TTHRESH, and neurcomp). The results position ECNR as a promising solution for volumetric data compression.

Numerical models have long been used to understand geoscientific phenomena, including tidal currents, crucial for renewable energy production and coastal engineering. However, their computational cost hinders generating data of varying resolutions. As an alternative, deep learning-based downscaling methods have gained traction due to their faster inference speeds. But most of them are limited to only inference fixed scale and overlook important characteristics of target geoscientific data. In this paper, we propose a novel downscaling framework for tidal current data, addressing its unique characteristics, which are dissimilar to images: heterogeneity and local dependency. Moreover, our framework can generate any arbitrary-scale output utilizing a continuous representation model. Our proposed framework demonstrates significantly improved flow velocity predictions by 93.21% (MSE) and 63.85% (MAE) compared to the Baseline model while achieving a remarkable 33.2% reduction in FLOPs.

Understanding causality helps to structure interventions to achieve specific goals and enables predictions under interventions. With the growing importance of learning causal relationships, causal discovery tasks have transitioned from using traditional methods to infer potential causal structures from observational data to the field of pattern recognition involved in deep learning. The rapid accumulation of massive data promotes the emergence of causal search methods with brilliant scalability. Existing summaries of causal discovery methods mainly focus on traditional methods based on constraints, scores and FCMs, there is a lack of perfect sorting and elaboration for deep learning-based methods, also lacking some considers and exploration of causal discovery methods from the perspective of variable paradigms. Therefore, we divide the possible causal discovery tasks into three types according to the variable paradigm and give the definitions of the three tasks respectively, define and instantiate the relevant datasets for each task and the final causal model constructed at the same time, then reviews the main existing causal discovery methods for different tasks. Finally, we propose some roadmaps from different perspectives for the current research gaps in the field of causal discovery and point out future research directions.

We consider the problem of explaining the predictions of graph neural networks (GNNs), which otherwise are considered as black boxes. Existing methods invariably focus on explaining the importance of graph nodes or edges but ignore the substructures of graphs, which are more intuitive and human-intelligible. In this work, we propose a novel method, known as SubgraphX, to explain GNNs by identifying important subgraphs. Given a trained GNN model and an input graph, our SubgraphX explains its predictions by efficiently exploring different subgraphs with Monte Carlo tree search. To make the tree search more effective, we propose to use Shapley values as a measure of subgraph importance, which can also capture the interactions among different subgraphs. To expedite computations, we propose efficient approximation schemes to compute Shapley values for graph data. Our work represents the first attempt to explain GNNs via identifying subgraphs explicitly and directly. Experimental results show that our SubgraphX achieves significantly improved explanations, while keeping computations at a reasonable level.

Residual networks (ResNets) have displayed impressive results in pattern recognition and, recently, have garnered considerable theoretical interest due to a perceived link with neural ordinary differential equations (neural ODEs). This link relies on the convergence of network weights to a smooth function as the number of layers increases. We investigate the properties of weights trained by stochastic gradient descent and their scaling with network depth through detailed numerical experiments. We observe the existence of scaling regimes markedly different from those assumed in neural ODE literature. Depending on certain features of the network architecture, such as the smoothness of the activation function, one may obtain an alternative ODE limit, a stochastic differential equation or neither of these. These findings cast doubts on the validity of the neural ODE model as an adequate asymptotic description of deep ResNets and point to an alternative class of differential equations as a better description of the deep network limit.

Multi-relation Question Answering is a challenging task, due to the requirement of elaborated analysis on questions and reasoning over multiple fact triples in knowledge base. In this paper, we present a novel model called Interpretable Reasoning Network that employs an interpretable, hop-by-hop reasoning process for question answering. The model dynamically decides which part of an input question should be analyzed at each hop; predicts a relation that corresponds to the current parsed results; utilizes the predicted relation to update the question representation and the state of the reasoning process; and then drives the next-hop reasoning. Experiments show that our model yields state-of-the-art results on two datasets. More interestingly, the model can offer traceable and observable intermediate predictions for reasoning analysis and failure diagnosis.