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Counterfactual explanations play an important role in detecting bias and improving the explainability of data-driven classification models. A counterfactual explanation (CE) is a minimal perturbed data point for which the decision of the model changes. Most of the existing methods can only provide one CE, which may not be achievable for the user. In this work we derive an iterative method to calculate robust CEs, i.e. CEs that remain valid even after the features are slightly perturbed. To this end, our method provides a whole region of CEs allowing the user to choose a suitable recourse to obtain a desired outcome. We use algorithmic ideas from robust optimization and prove convergence results for the most common machine learning methods including logistic regression, decision trees, random forests, and neural networks. Our experiments show that our method can efficiently generate globally optimal robust CEs for a variety of common data sets and classification models.

Graph generative model evaluation necessitates understanding differences between graphs on the distributional level. This entails being able to harness salient attributes of graphs in an efficient manner. Curvature constitutes one such property that has recently proved its utility in characterising graphs. Its expressive properties, stability, and practical utility in model evaluation remain largely unexplored, however. We combine graph curvature descriptors with emerging methods from topological data analysis to obtain robust, expressive descriptors for evaluating graph generative models.

The presence of symmetries imposes a stringent set of constraints on a system. This constrained structure allows intelligent agents interacting with such a system to drastically improve the efficiency of learning and generalization, through the internalisation of the system's symmetries into their information-processing. In parallel, principled models of complexity-constrained learning and behaviour make increasing use of information-theoretic methods. Here, we wish to marry these two perspectives and understand whether and in which form the information-theoretic lens can "see" the effect of symmetries of a system. For this purpose, we propose a novel variant of the Information Bottleneck principle, which has served as a productive basis for many principled studies of learning and information-constrained adaptive behaviour. We show (in the discrete case) that our approach formalises a certain duality between symmetry and information parsimony: namely, channel equivariances can be characterised by the optimal mutual information-preserving joint compression of the channel's input and output. This information-theoretic treatment furthermore suggests a principled notion of "soft" equivariance, whose "coarseness" is measured by the amount of input-output mutual information preserved by the corresponding optimal compression. This new notion offers a bridge between the field of bounded rationality and the study of symmetries in neural representations. The framework may also allow (exact and soft) equivariances to be automatically discovered.

We develop a partially explicit time discretization based on the framework of constraint energy minimizing generalized multiscale finite element method (CEM-GMsFEM) for the problem of linear poroelasticity with high contrast. Firstly, dominant basis functions generated by the CEM-GMsFEM approach are used to capture important degrees of freedom and it is known to give contrast-independent convergence that scales with the mesh size. In typical situation, one has very few degrees of freedom in dominant basis functions. This part is treated implicitly. Secondly, we design and introduce an additional space in the complement space and these degrees are treated explicitly. We also investigate the CFL-type stability restriction for this problem, and the restriction for the time step is contrast independent.

Math Word Problems (MWP) aims to automatically solve mathematical questions given in texts. Previous studies tend to design complex models to capture additional information in the original text so as to enable the model to gain more comprehensive features. In this paper, we turn our attention in the opposite direction, and work on how to discard redundant features containing spurious correlations for MWP. To this end, we design an Expression Syntax Information Bottleneck method for MWP (called ESIB) based on variational information bottleneck, which extracts essential features of expression syntax tree while filtering latent-specific redundancy containing syntax-irrelevant features. The key idea of ESIB is to encourage multiple models to predict the same expression syntax tree for different problem representations of the same problem by mutual learning so as to capture consistent information of expression syntax tree and discard latent-specific redundancy. To improve the generalization ability of the model and generate more diverse expressions, we design a self-distillation loss to encourage the model to rely more on the expression syntax information in the latent space. Experimental results on two large-scale benchmarks show that our model not only achieves state-of-the-art results but also generates more diverse solutions. The code is available.

This paper introduces a crowd modeling and motion control approach that employs diffusion adaptation within an adaptive network. In the network, nodes collaboratively address specific estimation problems while simultaneously moving as agents governed by certain motion control mechanisms. Our research delves into the behaviors of agents when they encounter spatial constraints. Within this framework, agents pursue several objectives, such as target tracking, coherent motion, and obstacle evasion. Throughout their navigation, they demonstrate a nature of self-organization and self-adjustment that drives them to maintain certain social distances with each other, and adaptively adjust their behaviors in response to the environmental changes. Our findings suggest a promising approach to mitigate the spread of viral pandemics and averting stampedes.

Magnetic resonance imaging (MRI) always suffered from the problem of long acquisition time. MRI reconstruction is one solution to reduce scan time by skipping certain phase-encoding lines and then restoring high-quality images from undersampled measurements. Recently, implicit neural representation (INR) has emerged as a new deep learning method that represents an object as a continuous function of spatial coordinates, and this function is normally parameterized by a multilayer perceptron (MLP). In this paper, we propose a novel MRI parallel reconstruction method based on INR, which represents the fully-sampled images as the function of voxel coordinates and prior feature vectors of undersampled images for overcoming the generalization problem of INR. Specifically, we introduce a scale-embedded encoder to produce scale-independent voxel-specific features from MR images with different undersampled scales and then concatenate with coordinates vectors to recover fully-sampled MR images via an MLP, thus achieving arbitrary scale reconstruction. The performance of the proposed method was assessed by experimenting on publicly available MRI datasets and compared with other reconstruction methods. Our quantitative evaluation demonstrates the superiority of the proposed method over alternative reconstruction methods.

We propose a new regret minimization algorithm for episodic sparse linear Markov decision process (SMDP) where the state-transition distribution is a linear function of observed features. The only previously known algorithm for SMDP requires the knowledge of the sparsity parameter and oracle access to an unknown policy. We overcome these limitations by combining the doubly robust method that allows one to use feature vectors of \emph{all} actions with a novel analysis technique that enables the algorithm to use data from all periods in all episodes. The regret of the proposed algorithm is $\tilde{O}(\sigma^{-1}_{\min} s_{\star} H \sqrt{N})$, where $\sigma_{\min}$ denotes the restrictive the minimum eigenvalue of the average Gram matrix of feature vectors, $s_\star$ is the sparsity parameter, $H$ is the length of an episode, and $N$ is the number of rounds. We provide a lower regret bound that matches the upper bound up to logarithmic factors on a newly identified subclass of SMDPs. Our numerical experiments support our theoretical results and demonstrate the superior performance of our algorithm.

Large Language Models (LLMs) have shown excellent generalization capabilities that have led to the development of numerous models. These models propose various new architectures, tweaking existing architectures with refined training strategies, increasing context length, using high-quality training data, and increasing training time to outperform baselines. Analyzing new developments is crucial for identifying changes that enhance training stability and improve generalization in LLMs. This survey paper comprehensively analyses the LLMs architectures and their categorization, training strategies, training datasets, and performance evaluations and discusses future research directions. Moreover, the paper also discusses the basic building blocks and concepts behind LLMs, followed by a complete overview of LLMs, including their important features and functions. Finally, the paper summarizes significant findings from LLM research and consolidates essential architectural and training strategies for developing advanced LLMs. Given the continuous advancements in LLMs, we intend to regularly update this paper by incorporating new sections and featuring the latest LLM models.

High spectral dimensionality and the shortage of annotations make hyperspectral image (HSI) classification a challenging problem. Recent studies suggest that convolutional neural networks can learn discriminative spatial features, which play a paramount role in HSI interpretation. However, most of these methods ignore the distinctive spectral-spatial characteristic of hyperspectral data. In addition, a large amount of unlabeled data remains an unexploited gold mine for efficient data use. Therefore, we proposed an integration of generative adversarial networks (GANs) and probabilistic graphical models for HSI classification. Specifically, we used a spectral-spatial generator and a discriminator to identify land cover categories of hyperspectral cubes. Moreover, to take advantage of a large amount of unlabeled data, we adopted a conditional random field to refine the preliminary classification results generated by GANs. Experimental results obtained using two commonly studied datasets demonstrate that the proposed framework achieved encouraging classification accuracy using a small number of data for training.