We study the problem of collaboratively learning least squares estimates for m agents. Each agent observes a different subset of the features--e.g., containing data collected from sensors of varying resolution. Our goal is to determine how to coordinate the agents in order to produce the best estimator for each agent.

Message Passing Graph Neural Networks are known to suffer from two problems that are sometimes believed to be diametrically opposed: over-squashing and over-smoothing. The former results from topological bottlenecks that hamper the information flow from distant nodes and are mitigated by spectral gap maximization, primarily, by means of edge additions. However, such additions often promote oversmoothing that renders nodes of different classes less distinguishable. Inspired by the Braess phenomenon, we argue that deleting edges can address over-squashing and over-smoothing simultaneously. This insight explains how edge deletions can improve generalization, thus connecting spectral gap optimization to a seemingly disconnected objective of reducing computational resources by pruning graphs for lottery tickets. To this end, we propose a computationally effective spectral gap optimization framework to add or delete edges and demonstrate its effectiveness on the long range graph benchmark and on larger heterophilous datasets.

Transformer-based large language models (LLMs) typically have a limited context window, resulting in significant performance degradation when processing text beyond the length of the context window. Extensive studies have been proposed to extend the context window and achieve length extrapolation of LLMs, but there is still a lack of in-depth interpretation of these approaches. In this study, we explore the positional information within and beyond the context window for deciphering the underlying mechanism of LLMs. By using a mean-based decomposition method, we disentangle positional vectors from hidden states of LLMs and analyze their formation and effect on attention. Furthermore, when texts exceed the context window, we analyze the change of positional vectors in two settings, i.e., direct extrapolation and context window extension. Based on our findings, we design two training-free context window extension methods, positional vector replacement and attention window extension. Experimental results show that our methods can effectively extend the context window length.

Functional connectivity (FC) between regions of the brain can be assessed by the degree of temporal correlation measured with functional neuroimaging modalities. Based on the fact that these connectivities build a network, graph-based approaches for analyzing the brain connectome have provided insights into the functions of the human brain. The development of graph neural networks (GNNs) capable of learning representation from graph structured data has led to increased interest in learning the graph representation of the brain connectome. Although recent attempts to apply GNN to the FC network have shown promising results, there is still a common limitation that they usually do not incorporate the dynamic characteristics of the FC network which fluctuates over time. In addition, a few studies that have attempted to use dynamic FC as an input for the GNN reported a reduction in performance compared to static FC methods, and did not provide temporal explainability.

In this paper we fully describe the trajectory of gradient flow over 2-layer diagonal linear networks for the regression setting in the limit of vanishing initialisation.

The sampling problem under local differential privacy has recently been studied with potential applications to generative models, but a fundamental analysis of its privacy-utility trade-off (PUT) remains incomplete. In this work, we define the fundamental PUT of private sampling in the minimax sense, using the f-divergence between original and sampling distributions as the utility measure. We characterize the exact PUT for both finite and continuous data spaces under some mild conditions on the data distributions, and propose sampling mechanisms that are universally optimal for all f-divergences. Our numerical experiments demonstrate the superiority of our mechanisms over baselines, in terms of theoretical utilities for finite data space and of empirical utilities for continuous data space.

In this paper, we introduce Cosine Autoencoder (CosAE), a novel, generic Autoencoder that seamlessly leverages the classic Fourier series with a feed-forward neural network. CosAE represents an input image as a series of 2D Cosine time series, each defined by a tuple of learnable frequency and Fourier coefficients. This method stands in contrast to a conventional Autoencoder that often sacrifices detail in their reduced-resolution bottleneck latent spaces.

The expressive power of transformers over inputs of unbounded size can be studied through their ability to recognize classes of formal languages. In this paper, we establish exact characterizations of transformers with hard attention (in which all attention is focused on exactly one position) and attention masking (in which each position only attends to positions on one side). With strict masking (each position cannot attend to itself) and without position embeddings, these transformers are expressively equivalent to linear temporal logic (LTL), which defines exactly the star-free languages. A key technique is the use of Boolean RASP as a convenient intermediate language between transformers and LTL. We then take numerous results known for LTL and apply them to transformers, showing how position embeddings, strict masking, and depth all increase expressive power.

T is roughly linear in T. Thus, at a high level it matches the optimal bound in all cases in which one can achieve sublinear regret.