Multi-Step Reasoning for Deep-Field Galaxy Detection with Uncertainty-Aware Human Feedback

Source detection in deep-field astronomical imaging poses a formidable challenge characterized by extreme dynamic ranges in scale and flux, low signal-to-noise ratios, ambiguous morphological boundaries, and severe crowding. A fundamental yet overlooked bottleneck is the entanglement of distinct uncertainty sources: aleatoric uncertainty, arising from stochastic background noise, sensor limits, and intrinsic photon shot noise; and epistemic uncertainty, stemming from model underconfidence and out-of-distribution morphology. Disentangling these two uncertainty modes is essential to diagnose whether detection failures are physically bounded by observational limits or algorithmically constrained by representation capacity. To resolve this, we propose a multi-step reasoning framework that couples fine-grained uncertainty disentanglement with a human-in-the-loop calibration loop for robust galaxy detection. Following background stabilization and faint-structure enhancement, a Continuous Thought Machine (CTM) dynamically navigates heterogeneous signal-strength regimes across iterative reasoning steps, progressively integrating multi-stage spatial representations. Crucially, the framework quantifies and decouples aleatoric from epistemic uncertainty maps, isolating ambiguous physical blending from algorithmic failure modes. These spatial uncertainty representations are mapped to an interactive interface that aligns machine uncertainty with expert perceptual intuition, enabling targeted human feedback to iteratively refine model boundaries. Evaluated on simulated deep-field benchmarks, our framework achieves a recall of 88.99% (a 6.30 percentage point improvement over the standard SExtractor baseline of 82.69%). Finally, we demonstrate the real-world utility and cross-instrument generalizability of our framework on ultra-deep observations from the James Webb Space Telescope (JWST) and the Euclid space mission.