With the rapid advancement of large language models (LLMs), natural language processing (NLP) has achieved remarkable progress. Nonetheless, significant challenges remain in handling texts with ambiguity, polysemy, or uncertainty. We introduce the Fuzzy Reasoning Chain (FRC) framework, which integrates LLM semantic priors with continuous fuzzy membership degrees, creating an explicit interaction between probability-based reasoning and fuzzy membership reasoning. This transition allows ambiguous inputs to be gradually transformed into clear and interpretable decisions while capturing conflicting or uncertain signals that traditional probability-based methods cannot. We validate FRC on sentiment analysis tasks, where both theoretical analysis and empirical results show that it ensures stable reasoning and facilitates knowledge transfer across different model scales. These findings indicate that FRC provides a general mechanism for managing subtle and ambiguous expressions with improved interpretability and robustness.

Randomly Wired Neural Networks (RWNNs) serve as a valuable testbed for investigating the impact of network topology in deep learning by capturing how different connectivity patterns impact both learning efficiency and model performance. At the same time, they provide a natural framework for exploring edge-centric network measures as tools for pruning and optimization. In this study, we investigate three edge-centric network measures: Forman-Ricci curvature (FRC), Ollivier-Ricci curvature (ORC), and edge betweenness centrality (EBC), to compress RWNNs by selectively retaining important synapses (or edges) while pruning the rest. As a baseline, RWNNs are trained for COVID-19 chest x-ray image classification, aiming to reduce network complexity while preserving performance in terms of accuracy, specificity, and sensitivity. We extend prior work on pruning RWNN using ORC by incorporating two additional edge-centric measures, FRC and EBC, across three network generators: Erdös-Rényi (ER) model, Watts-Strogatz (WS) model, and Barabási-Albert (BA) model. We provide a comparative analysis of the pruning performance of the three measures in terms of compression ratio and theoretical speedup. A central focus of our study is to evaluate whether FRC, which is computationally more efficient than ORC, can achieve comparable pruning effectiveness. Along with performance evaluation, we further investigate the structural properties of the pruned networks through modularity and global efficiency, offering insights into the trade-off between modular segregation and network efficiency in compressed RWNNs. Our results provide initial evidence that FRC-based pruning can effectively simplify RWNNs, offering significant computational advantages while maintaining performance comparable to ORC.

Diffeomorphic deformable image registration ensures smooth invertible transformations across inspiratory and expiratory chest CT scans. Yet, in practice, deep learning-based diffeomorphic methods struggle to capture large deformations between inspiratory and expiratory volumes, and therefore lack inverse consistency. Existing methods also fail to account for model uncertainty, which can be useful for improving performance. We propose an uncertainty-aware test-time adaptation framework for inverse consistent diffeomorphic lung registration. Our method uses Monte Carlo (MC) dropout to estimate spatial uncertainty that is used to improve model performance. We train and evaluate our method for inspiratory-to-expiratory CT registration on a large cohort of 675 subjects from the COPDGene study, achieving a higher Dice similarity coefficient (DSC) between the lung boundaries (0.966) compared to both VoxelMorph (0.953) and TransMorph (0.953). Our method demonstrates consistent improvements in the inverse registration direction as well with an overall DSC of 0.966, higher than VoxelMorph (0.958) and TransMorph (0.956). Paired t-tests indicate statistically significant improvements.

Unsupervised node clustering (or community detection) is a classical graph learning task. In this paper, we study algorithms, which exploit the geometry of the graph to identify densely connected substructures, which form clusters or communities. Our method implements discrete Ricci curvatures and their associated geometric flows, under which the edge weights of the graph evolve to reveal its community structure. We consider several discrete curvature notions and analyze the utility of the resulting algorithms. In contrast to prior literature, we study not only single-membership community detection, where each node belongs to exactly one community, but also mixed-membership community detection, where communities may overlap. For the latter, we argue that it is beneficial to perform community detection on the line graph, i.e., the graph's dual. We provide both theoretical and empirical evidence for the utility of our curvature-based clustering algorithms. In addition, we give several results on the relationship between the curvature of a graph and that of its dual, which enable the efficient implementation of our proposed mixed-membership community detection approach and which may be of independent interest for curvature-based network analysis.

Recent discoveries in Deep Neural Networks are allowing researchers to tackle some very complex problems such as image classification and audio classification, with improved theoretical and empirical justifications. This paper presents a novel scheme to incorporate the use of autoencoders in Fuzzy rule classifiers (FRC). Autoencoders when stacked can learn the complex non-linear relationships amongst data, and the proposed framework built towards FRC can allow users to input expert knowledge to the system. This paper further introduces four novel fine-tuning strategies for autoencoders to improve the FRC's classification and rule reduction performance. The proposed framework has been tested across five real-world benchmark datasets. Elaborate comparisons with over 15 previous studies, and across 10-fold cross validation performance, suggest that the proposed methods are capable of building FRCs which can provide state of the art accuracies.

Gradient coding is a coding theoretic framework to provide robustness against slow or unresponsive machines, known as stragglers, in distributed machine learning applications. Recently, Kadhe et al. proposed a gradient code based on a combinatorial design, called balanced incomplete block design (BIBD), which is shown to outperform many existing gradient codes in worst-case adversarial straggling scenarios. However, parameters for which such BIBD constructions exist are very limited. In this paper, we aim to overcome such limitations and construct gradient codes which exist for a wide range of parameters while retaining the superior performance of BIBD gradient codes. Two such constructions are proposed, one based on a probabilistic construction that relax the stringent BIBD gradient code constraints, and the other based on taking the Kronecker product of existing gradient codes. Theoretical error bounds for worst-case adversarial straggling scenarios are derived. Simulations show that the proposed constructions can outperform existing gradient codes with similar redundancy per data piece.

Due to the size and scale of modern data, gradient computations are often distributed across multiple compute nodes. Unfortunately, such distributed implementations can face significant delays caused by straggler nodes, i.e., nodes that are much slower than average. Gradient coding is a new technique for mitigating the effect of stragglers via algorithmic redundancy. While effective, previously proposed gradient codes can be computationally expensive to construct, inaccurate, or susceptible to adversarial stragglers. In this work, we present the stochastic block code (SBC), a gradient code based on the stochastic block model. We show that SBCs are efficient, accurate, and that under certain settings, adversarial straggler selection becomes as hard as detecting a community structure in the multiple community, block stochastic graph model.

"Encoded in the large, highly evolved sensory and motor portions of the human brain is a billion years of experience about the nature of the world and how to survive in it. The deliberate process we call reasoning is, I believe, the thinnest veneer of human thought, effective only because it is supported by this much older and much powerful, though usually unconscious, sensor motor knowledge. We are all prodigious Olympians in perceptual and motor areas, so good that we make the difficult look easy. Abstract thought, though, is a new trick, perhaps less than 100 thousand years old. We have not yet mastered it. It is not all that intrinsically difficult; it just seems so when we do it."- Hans Moravec Moravec's paradox is involved with the fact that it is the seemingly easier day to day problems that are harder to implement in a machine, than the seemingly complicated logic based problems of today. The results prove that most artificially intelligent machines are as adept if not more than us at under-taking long calculations or even play chess, but their logic brings them nowhere when it comes to carrying out everyday tasks like walking, facial gesture recognition or speech recognition.