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Because of their excellent asymptotic and finite-length performance, spatially-coupled (SC) codes are a class of low-density parity-check codes that is gaining increasing attention. Multi-dimensional (MD) SC codes are constructed by connecting copies of an SC code via relocations in order to mitigate various sources of non-uniformity and improve performance in many data storage and data transmission systems. As the number of degrees of freedom in the MD-SC code design increases, appropriately exploiting them becomes more difficult because of the complexity growth of the design process. In this paper, we propose a probabilistic framework for the MD-SC code design, which is based on the gradient-descent (GD) algorithm, to design better MD codes and address this challenge. In particular, we express the expected number of short cycles, which we seek to minimize, in the graph representation of the code in terms of entries of a probability-distribution matrix that characterizes the MD-SC code design. We then find a locally-optimal probability distribution, which serves as the starting point of a finite-length algorithmic optimizer that produces the final MD-SC code. We offer the theoretical analysis as well as the algorithms, and we present experimental results demonstrating that our MD codes, conveniently called GD-MD codes, have notably lower short cycle numbers compared with the available state-of-the-art. Moreover, our algorithms converge on solutions in few iterations, which confirms the complexity reduction as a result of limiting the search space via the locally-optimal GD-MD distributions.

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.

Human communities have self-organizing properties that give rise to very specific natural grouping patterns, reflected in the Dunbar Number and its layered structure (a Dunbar Graph). Since work-groups are necessarily also social groups, we might expect the same principles to apply here as well. One factor likely to be important in limiting the size of groups is that conflicts typically escalate with the number of people involved. Here we analyse Wikipedia editing histories across a wide range of topics to show that there is an emergent coherence in the size of groups formed transiently to edit the content of subject texts, with two peaks averaging at around $N=8$ for the size corresponding to maximal contention, and at around $N=4$ as a regular team. These values are consistent with the observed sizes of conversational groups, as well as the hierarchical structuring of Dunbar graphs. We use the Promise Theory of trust to suggest a scaling law that may apply to all group distributions based on seeded attraction. In addition to providing further evidence that even natural communities of strangers are self-organising, the results have important implications for the governance of the Wikipedia commons and for the security of all online social platforms and associations.

Humans interpret scenes by recognizing both the identities and positions of objects in their observations. For a robot to perform tasks such as \enquote{pick and place}, understanding both what the objects are and where they are located is crucial. While the former has been extensively discussed in the literature that uses the large language model to enrich the text descriptions, the latter remains underexplored. In this work, we introduce the \textit{Object-Centric Instruction Augmentation (OCI)} framework to augment highly semantic and information-dense language instruction with position cues. We utilize a Multi-modal Large Language Model (MLLM) to weave knowledge of object locations into natural language instruction, thus aiding the policy network in mastering actions for versatile manipulation. Additionally, we present a feature reuse mechanism to integrate the vision-language features from off-the-shelf pre-trained MLLM into policy networks. Through a series of simulated and real-world robotic tasks, we demonstrate that robotic manipulator imitation policies trained with our enhanced instructions outperform those relying solely on traditional language instructions.

Camera localization methods based on retrieval, local feature matching, and 3D structure-based pose estimation are accurate but require high storage, are slow, and are not privacy-preserving. A method based on scene landmark detection (SLD) was recently proposed to address these limitations. It involves training a convolutional neural network (CNN) to detect a few predetermined, salient, scene-specific 3D points or landmarks and computing camera pose from the associated 2D-3D correspondences. Although SLD outperformed existing learning-based approaches, it was notably less accurate than 3D structure-based methods. In this paper, we show that the accuracy gap was due to insufficient model capacity and noisy labels during training. To mitigate the capacity issue, we propose to split the landmarks into subgroups and train a separate network for each subgroup. To generate better training labels, we propose using dense reconstructions to estimate visibility of scene landmarks. Finally, we present a compact architecture to improve memory efficiency. Accuracy wise, our approach is on par with state of the art structure based methods on the INDOOR-6 dataset but runs significantly faster and uses less storage. Code and models can be found at //github.com/microsoft/SceneLandmarkLocalization.

Graph queries that combine pattern matching with relational operations, referred as PatRelQuery, are widely used in many real-world applications. It allows users to identify arbitrary patterns in a graph and further perform in-depth relational analysis on the results. To effectively support PatRelQuery, two key challenges need to be addressed: (1) how to optimize PatRelQuery in a unified framework, and (2) how to handle the arbitrary type constraints in patterns in PatRelQuery. In this paper, we present a graph-native query optimization framework named GOpt, to tackle these issues. GOpt is built on top of a unified intermediate representation (IR) that is capable of capturing both graph and relational operations, thereby streamlining the optimization of PatRelQuery. To handle the arbitrary type constraints, GOpt employs an automatic type inference approach to identify implicit type constraints. Additionally, GOpt introduces a graph-native optimizer, which encompasses an extensive collection of optimization rules along with cost-based techniques tailored for arbitrary patterns, to optimize PatRelQuery. Through comprehensive experiments, we demonstrate that GOpt can achieve significant query performance improvements, in both crafted benchmarks and real-world applications.

We consider (stochastic) subgradient methods for strongly convex but potentially nonsmooth non-Lipschitz optimization. We provide new equivalent dual descriptions (in the style of dual averaging) for the classic subgradient method, the proximal subgradient method, and the switching subgradient method. These equivalences enable $O(1/T)$ convergence guarantees in terms of both their classic primal gap and a not previously analyzed dual gap for strongly convex optimization. Consequently, our theory provides these classic methods with simple, optimal stopping criteria and optimality certificates at no added computational cost. Our results apply to a wide range of stepsize selections and of non-Lipschitz ill-conditioned problems where the early iterations of the subgradient method may diverge exponentially quickly (a phenomenon which, to the best of our knowledge, no prior works address). Even in the presence of such undesirable behaviors, our theory still ensures and bounds eventual convergence.

A comprehensive understanding of the organizational principles in the human brain requires, among other factors, well-quantifiable descriptors of nerve fiber architecture. Three-dimensional polarized light imaging (3D-PLI) is a microscopic imaging technique that enables insights into the fine-grained organization of myelinated nerve fibers with high resolution. Descriptors characterizing the fiber architecture observed in 3D-PLI would enable downstream analysis tasks such as multimodal correlation studies, clustering, and mapping. However, best practices for observer-independent characterization of fiber architecture in 3D-PLI are not yet available. To this end, we propose the application of a fully data-driven approach to characterize nerve fiber architecture in 3D-PLI images using self-supervised representation learning. We introduce a 3D-Context Contrastive Learning (CL-3D) objective that utilizes the spatial neighborhood of texture examples across histological brain sections of a 3D reconstructed volume to sample positive pairs for contrastive learning. We combine this sampling strategy with specifically designed image augmentations to gain robustness to typical variations in 3D-PLI parameter maps. The approach is demonstrated for the 3D reconstructed occipital lobe of a vervet monkey brain. We show that extracted features are highly sensitive to different configurations of nerve fibers, yet robust to variations between consecutive brain sections arising from histological processing. We demonstrate their practical applicability for retrieving clusters of homogeneous fiber architecture and performing data mining for interactively selected templates of specific components of fiber architecture such as U-fibers.

Wasserstein distortion is a one-parameter family of distortion measures that was recently proposed to unify fidelity and realism constraints. After establishing continuity results for Wasserstein in the extreme cases of pure fidelity and pure realism, we prove the first coding theorems for compression under Wasserstein distortion focusing on the regime in which both the rate and the distortion are small.

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, thereby allowing manual manipulation in predicting the final answer.