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Understanding information flow in the brain can be facilitated by arranging neurons in the fly connectome to form a maximally “feedforward” structure. This task is naturally formulated as the Minimum Feedback Arc Set (MFAS)—a well-known NP-hard problem, especially for large-scale graphs. To address this, we propose the Rocket-Crane algorithm, an efficient two-phase method for solving MFAS. In the first phase, we develop a continuous-space optimization method that rapidly generates excellent solutions. In the second phase, we refine these solutions through advanced exploration techniques that integrate randomized and heuristic strategies to effectively escape local minima. Extensive experiments demonstrate that Rocket-Crane outperforms state-of-the-art methods in terms of solution quality, scalability, and computational efficiency. On the primary benchmark—the fly connectom—our method achieved a feedforward arc set with a total forward weight of 35,459,266 (about 85$$\%$$ $\%$), the highest among all competing methods. The algorithm is open-source and available on GitHub. 

Abstract We present an auxiliary learning task for the problem of neuron segmentation in electron microscopy volumes. The auxiliary task consists of the prediction of local shape descriptors (LSDs), which we combine with conventional voxel-wise direct neighbor affinities for neuron boundary detection. The shape descriptors capture local statistics about the neuron to be segmented, such as diameter, elongation, and direction. On a study comparing several existing methods across various specimen, imaging techniques, and resolutions, auxiliary learning of LSDs consistently increases segmentation accuracy of affinity-based methods over a range of metrics. Furthermore, the addition of LSDs promotes affinity-based segmentation methods to be on par with the current state of the art for neuron segmentation (flood-filling networks), while being two orders of magnitudes more efficient—a critical requirement for the processing of future petabyte-sized datasets.