A convolutional sequence labeler's receptive field is routinely treated as the extent of the model's usable context: it sets dilation schedules, bounds streaming horizons, and underwrites locality claims. However, we show that this can be false: when a normalization layer computes statistics from the current input along the sequence at inference, those statistics open a sequence-spanning path that bypasses the convolutional receptive field to provide global context. We derive this from the layer's Jacobian (the criterion needs no experiment), and what the path carries has a closed form. On a synthetic labeling process with computable optima, the global summary that a sequence-spanning normalization encodes already supplies almost all of what a larger receptive field would buy where labels come in long runs: a network reaching 9 positions comes within 0.009 of the whole-sequence optimum, against a near-chance bound for its reach. Closing the path, by taking the same statistics per position, multiplies what enlarging the receptive field is worth by up to an order of magnitude on simulated genomes at every difficulty level tested and on real 1000 Genomes haplotypes. The same path also confounds attribution: ablating a trained network's receptive-field-enlarging blocks severs part of the path, overstating their contribution 8.3-16.1-fold relative to retraining from scratch. The substitution of normalization for receptive field fades as labels switch more often. Where labels run long, neither the receptive-field justification nor the ablation is wrong about its numbers, but both credit the wrong component.
In this work, we investigate a previously unexplored architectural dimension for infrared small target detection: the organization of effective receptive fields (ERFs) during feature refinement. Unlike existing approaches that primarily improve individual feature operators, we argue that ERF organization constitutes an architectural dimension independent of receptive field design itself, and formulate deep feature transformation as a progressive residual correction process, from which a theoretical framework for ERF scheduling is established. Specifically, we reveal that ERF refinement is governed by two fundamental properties: scale-frequency correspondence, which aligns different ERF scales with distinct residual frequency characteristics, and nonlinear non-commutativity, which makes different ERF orderings produce fundamentally different refinement trajectories. Together, these properties show that ERF organization, rather than ERF scale alone, governs refinement dynamics. Guided by these principles, we propose Receptive Field Ordering Network (RFONet), which realizes hierarchical ERF scheduling through a multigrid-inspired V-cycle strategy using only standard $3\times3$ convolutions. RFONet achieves state-of-the-art performance on multiple benchmarks with only 1.16M parameters and over 157 FPS inference speed. Beyond empirical performance, our theoretical analysis provides theoretical guarantees for stable residual refinement under perturbations, frequency shifts, and partial occlusions, which are consistently reflected in superior noise robustness and cross-dataset generalization. Finally, our framework reformulates ERF organization as a task-dependent optimization objective, providing a principled foundation for future adaptive receptive field scheduling.