Connectomics has emerged as a powerful tool in neuroimaging and has spurred recent advancements in statistical and machine learning methods for connectivity data. Despite connectomes inhabiting a matrix manifold, most analytical frameworks ignore the underlying data geometry. This is largely because simple operations, such as mean estimation, do not have easily computable closed-form solutions. We propose a geometrically aware neural framework for connectomes, i.e., the mSPD-NN, designed to estimate the geodesic mean of a collections of symmetric positive definite (SPD) matrices. The mSPD-NN is comprised of bilinear fully connected layers with tied weights and utilizes a novel loss function to optimize the matrix-normal equation arising from Fr\'echet mean estimation. Via experiments on synthetic data, we demonstrate the efficacy of our mSPD-NN against common alternatives for SPD mean estimation, providing competitive performance in terms of scalability and robustness to noise. We illustrate the real-world flexibility of the mSPD-NN in multiple experiments on rs-fMRI data and demonstrate that it uncovers stable biomarkers associated with subtle network differences among patients with ADHD-ASD comorbidities and healthy controls.

We investigate the generalization and optimization properties of shallow neural-network classifiers trained by gradient descent in the interpolating regime. Specifically, in a realizable scenario where model weights can achieve arbitrarily small training error $\epsilon$ and their distance from initialization is $g(\epsilon)$, we demonstrate that gradient descent with $n$ training data achieves training error $O(g(1/T)^2 /T)$ and generalization error $O(g(1/T)^2 /n)$ at iteration $T$, provided there are at least $m=\Omega(g(1/T)^4)$ hidden neurons. We then show that our realizable setting encompasses a special case where data are separable by the model's neural tangent kernel. For this and logistic-loss minimization, we prove the training loss decays at a rate of $\tilde O(1/ T)$ given polylogarithmic number of neurons $m=\Omega(\log^4 (T))$. Moreover, with $m=\Omega(\log^{4} (n))$ neurons and $T\approx n$ iterations, we bound the test loss by $\tilde{O}(1/n)$. Our results differ from existing generalization outcomes using the algorithmic-stability framework, which necessitate polynomial width and yield suboptimal generalization rates. Central to our analysis is the use of a new self-bounded weak-convexity property, which leads to a generalized local quasi-convexity property for sufficiently parameterized neural-network classifiers. Eventually, despite the objective's non-convexity, this leads to convergence and generalization-gap bounds that resemble those found in the convex setting of linear logistic regression.

The study of market equilibria is central to economic theory, particularly in efficiently allocating scarce resources. However, the computation of equilibrium prices at which the supply of goods matches their demand typically relies on having access to complete information on private attributes of agents, e.g., suppliers' cost functions, which are often unavailable in practice. Motivated by this practical consideration, we consider the problem of setting equilibrium prices in the incomplete information setting wherein a market operator seeks to satisfy the customer demand for a commodity by purchasing the required amount from competing suppliers with privately known cost functions unknown to the market operator. In this incomplete information setting, we consider the online learning problem of learning equilibrium prices over time while jointly optimizing three performance metrics -- unmet demand, cost regret, and payment regret -- pertinent in the context of equilibrium pricing over a horizon of $T$ periods. We first consider the setting when suppliers' cost functions are fixed and develop algorithms that achieve a regret of $O(\log \log T)$ when the customer demand is constant over time, or $O(\sqrt{T} \log \log T)$ when the demand is variable over time. Next, we consider the setting when the suppliers' cost functions can vary over time and illustrate that no online algorithm can achieve sublinear regret on all three metrics when the market operator has no information about how the cost functions change over time. Thus, we consider an augmented setting wherein the operator has access to hints/contexts that, without revealing the complete specification of the cost functions, reflect the variation in the cost functions over time and propose an algorithm with sublinear regret in this augmented setting.

Dual encoder models are ubiquitous in modern classification and retrieval. Crucial for training such dual encoders is an accurate estimation of gradients from the partition function of the softmax over the large output space; this requires finding negative targets that contribute most significantly ("hard negatives"). Since dual encoder model parameters change during training, the use of traditional static nearest neighbor indexes can be sub-optimal. These static indexes (1) periodically require expensive re-building of the index, which in turn requires (2) expensive re-encoding of all targets using updated model parameters. This paper addresses both of these challenges. First, we introduce an algorithm that uses a tree structure to approximate the softmax with provable bounds and that dynamically maintains the tree. Second, we approximate the effect of a gradient update on target encodings with an efficient Nystrom low-rank approximation. In our empirical study on datasets with over twenty million targets, our approach cuts error by half in relation to oracle brute-force negative mining. Furthermore, our method surpasses prior state-of-the-art while using 150x less accelerator memory.

This work proposes an interactive art installation "Mood spRing" designed to reflect the mood of the environment through interpretation of language and tone. Mood spRing consists of an AI program that controls an immersive 3D animation of the seasons. If the AI program perceives the language and tone of the users as pleasant, the animation progresses through idealized renditions of seasons. Otherwise, it slips into unpleasant weather and natural disasters of the season. To interpret the language and tone of the user interaction, hybrid state-of-the-art emotion detection methods are applied to the user audio and text inputs. The emotional states detected separately from tone and language are fused by a novel approach that aims at minimizing the possible model disparity across diverse demographic groups.

Dense prediction tasks are a fundamental class of problems in computer vision. As supervised methods suffer from high pixel-wise labeling cost, a few-shot learning solution that can learn any dense task from a few labeled images is desired. Yet, current few-shot learning methods target a restricted set of tasks such as semantic segmentation, presumably due to challenges in designing a general and unified model that is able to flexibly and efficiently adapt to arbitrary tasks of unseen semantics. We propose Visual Token Matching (VTM), a universal few-shot learner for arbitrary dense prediction tasks. It employs non-parametric matching on patch-level embedded tokens of images and labels that encapsulates all tasks. Also, VTM flexibly adapts to any task with a tiny amount of task-specific parameters that modulate the matching algorithm. We implement VTM as a powerful hierarchical encoder-decoder architecture involving ViT backbones where token matching is performed at multiple feature hierarchies. We experiment VTM on a challenging variant of Taskonomy dataset and observe that it robustly few-shot learns various unseen dense prediction tasks. Surprisingly, it is competitive with fully supervised baselines using only 10 labeled examples of novel tasks (0.004% of full supervision) and sometimes outperforms using 0.1% of full supervision. Codes are available at https://github.com/GitGyun/visual_token_matching.

Given entities and their interactions in the web data, which may have occurred at different time, how can we find communities of entities and track their evolution? In this paper, we approach this important task from graph clustering perspective. Recently, state-of-the-art clustering performance in various domains has been achieved by deep clustering methods. Especially, deep graph clustering (DGC) methods have successfully extended deep clustering to graph-structured data by learning node representations and cluster assignments in a joint optimization framework. Despite some differences in modeling choices (e.g., encoder architectures), existing DGC methods are mainly based on autoencoders and use the same clustering objective with relatively minor adaptations. Also, while many real-world graphs are dynamic, previous DGC methods considered only static graphs. In this work, we develop CGC, a novel end-to-end framework for graph clustering, which fundamentally differs from existing methods. CGC learns node embeddings and cluster assignments in a contrastive graph learning framework, where positive and negative samples are carefully selected in a multi-level scheme such that they reflect hierarchical community structures and network homophily. Also, we extend CGC for time-evolving data, where temporal graph clustering is performed in an incremental learning fashion, with the ability to detect change points. Extensive evaluation on real-world graphs demonstrates that the proposed CGC consistently outperforms existing methods.

Rapid discovery of new reactions and molecules in recent years has been facilitated by the advancements in high throughput screening, accessibility to a much more complex chemical design space, and the development of accurate molecular modeling frameworks. A holistic study of the growing chemistry literature is, therefore, required that focuses on understanding the recent trends and extrapolating them into possible future trajectories. To this end, several network theory-based studies have been reported that use a directed graph representation of chemical reactions. Here, we perform a study based on representing chemical reactions as hypergraphs where the hyperedges represent chemical reactions and nodes represent the participating molecules. We use a standard reactions dataset to construct a hypernetwork and report its statistics such as degree distributions, average path length, assortativity or degree correlations, PageRank centrality, and graph-based clusters (or communities). We also compute each statistic for an equivalent directed graph representation of reactions to draw parallels and highlight differences between the two. To demonstrate the AI applicability of hypergraph reaction representation, we generate dense hypergraph embeddings and use them in the reaction classification problem. We conclude that the hypernetwork representation is flexible, preserves reaction context, and uncovers hidden insights that are otherwise not apparent in a traditional directed graph representation of chemical reactions.

Since the late 1950s, when the first artificial satellite was launched, the number of Resident Space Objects has steadily increased. It is estimated that around one million objects larger than one cm are currently orbiting the Earth, with only thirty thousand larger than ten cm being tracked. To avert a chain reaction of collisions, known as Kessler Syndrome, it is essential to accurately track and predict debris and satellites' orbits. Current approximate physics-based methods have errors in the order of kilometers for seven-day predictions, which is insufficient when considering space debris, typically with less than one meter. This failure is usually due to uncertainty around the state of the space object at the beginning of the trajectory, forecasting errors in environmental conditions such as atmospheric drag, and unknown characteristics such as the mass or geometry of the space object. Operators can enhance Orbit Prediction accuracy by deriving unmeasured objects' characteristics and improving non-conservative forces' effects by leveraging data-driven techniques, such as Machine Learning. In this survey, we provide an overview of the work in applying Machine Learning for Orbit Determination, Orbit Prediction, and atmospheric density modeling.

Representing a manifold of very high-dimensional data with generative models has been shown to be computationally efficient in practice. However, this requires that the data manifold admits a global parameterization. In order to represent manifolds of arbitrary topology, we propose to learn a mixture model of variational autoencoders. Here, every encoder-decoder pair represents one chart of a manifold. We propose a loss function for maximum likelihood estimation of the model weights and choose an architecture that provides us the analytical expression of the charts and of their inverses. Once the manifold is learned, we use it for solving inverse problems by minimizing a data fidelity term restricted to the learned manifold. To solve the arising minimization problem we propose a Riemannian gradient descent algorithm on the learned manifold. We demonstrate the performance of our method for low-dimensional toy examples as well as for deblurring and electrical impedance tomography on certain image manifolds.