Effective intersection control can play an important role in reducing traffic congestion and associated vehicular emissions.

We consider learning a sparse model from linear measurements taken by a network of agents. Different from existing decentralized methods designed based on the LASSO regression with explicit $\ell_1$ norm regularization, we exploit the implicit regularization of decentralized optimization method applied to an over-parameterized nonconvex least squares formulation without penalization. Our first result shows that despite nonconvexity, if the network connectivity is good, the well-known decentralized gradient descent algorithm (DGD) with small initialization and early stopping can compute the statistically optimal solution. Sufficient conditions on the initialization scale, choice of step size, network connectivity, and stopping time are further provided to achieve convergence. Our result recovers the convergence rate of gradient descent in the centralized setting, showing its tightness. Based on the analysis of DGD, we further propose a communication-efficient version, termed T-DGD, by truncating the iterates before transmission. In the high signal-to-noise ratio (SNR) regime, we show that T-DGD achieves comparable statistical accuracy to DGD, while the communication cost is logarithmic in the number of parameters. Numerical results are provided to validate the effectiveness of DGD and T-DGD for sparse learning through implicit regularization.

Distributed resource allocation (DRA) is fundamental to modern networked systems, spanning applications from economic dispatch in smart grids to CPU scheduling in data centers. Conventional DRA approaches require reliable communication, yet real-world networks frequently suffer from link failures, packet drops, and communication delays due to environmental conditions, network congestion, and security threats. We introduce a novel resilient DRA algorithm that addresses these critical challenges, and our main contributions are as follows: (1) guaranteed constraint feasibility at all times, ensuring resource-demand balance even during algorithm termination or network disruption; (2) robust convergence despite sector-bound nonlinearities at nodes/links, accommodating practical constraints like quantization and saturation; and (3) optimal performance under merely uniformly-connected networks, eliminating the need for continuous connectivity. Unlike existing approaches that require persistent network connectivity and provide only asymptotic feasibility, our graph-theoretic solution leverages network percolation theory to maintain performance during intermittent disconnections. This makes it particularly valuable for mobile multi-agent systems where nodes frequently move out of communication range. Theoretical analysis and simulations demonstrate that our algorithm converges to optimal solutions despite heterogeneous time delays and substantial link failures, significantly advancing the reliability of distributed resource allocation in practical network environments.

We consider learning a sparse model from linear measurements taken by a network of agents.

Burer-Monteiro type decomposition associated to the low-rank matrix estimation.

We present a recurrent neuronal network, modeled as a continuous-time dynamical system, that can solve constraint satisfaction problems. Discrete variables are represented by coupled Winner-Take-All (WTA) networks, and their values are encoded in localized patterns of oscillations that are learned by the recurrent weights in these networks. Constraints over the variables are encoded in the network connectivity. Although there are no sources of noise, the network can escape from local optima in its search for solutions that satisfy all constraints by modifying the effective network connectivity through oscillations. If there is no solution that satisfies all constraints, the network state changes in a pseudo-random manner and its trajectory approximates a sampling procedure that selects a variable assignment with a probability that increases with the fraction of constraints satisfied by this assignment.

We consider the problem of inferring direct neural network connections from Calcium imaging time series. Inverse covariance estimation has proven to be a fast and accurate method for learning macro-and micro-scale network connectivity in the brain and in a recent Kaggle Connectomics competition inverse covariance was the main component of several top ten solutions, including our own and the winning team's algorithm. However, the accuracy of inverse covariance estimation is highly sensitive to signal preprocessing of the Calcium fluorescence time series. Furthermore, brute force optimization methods such as grid search and coordinate ascent over signal processing parameters is a time intensive process, where learning may take several days and parameters that optimize one network may not generalize to networks with different size and parameters. In this paper we show how inverse covariance estimation can be dramatically improved using a simple convolution filter prior to applying sample covariance. Furthermore, these signal processing parameters can be learned quickly using a supervised optimization algorithm. In particular, we maximize a binomial log-likelihood loss function with respect to a convolution filter of the time series and the inverse covariance regularization parameter. Our proposed algorithm is relatively fast on networks the size of those in the competition (1000 neurons), producing AUC scores with similar accuracy to the winning solution in training time under 2 hours on a cpu. Prediction on new networks of the same size is carried out in less than 15 minutes, the time it takes to read in the data and write out the solution.

We thank all the reviewers for their valuable comments and appreciation of the ideas and results presented in the paper. We summarize the main questions from the reviewers and address them separately below. T o Reviewer #1 Q1: Network connectivity is presumably known . . . it seems all the graphs considered are com-3 We note that the network connectivity is not assumed to be known. T o Reviewer #3 Q1: Scope of the paper/Missing related work. " and "FedNAS" are about We can add an explanation to clarify the MTL scope of the paper.

We consider learning a sparse model from linear measurements taken by a network of agents. Different from existing decentralized methods designed based on the LASSO regression with explicit \ell_1 norm regularization, we exploit the implicit regularization of decentralized optimization method applied to an over-parameterized nonconvex least squares formulation without penalization. Our first result shows that despite nonconvexity, if the network connectivity is good, the well-known decentralized gradient descent algorithm (DGD) with small initialization and early stopping can compute the statistically optimal solution. Sufficient conditions on the initialization scale, choice of step size, network connectivity, and stopping time are further provided to achieve convergence. Our result recovers the convergence rate of gradient descent in the centralized setting, showing its tightness.