Edge-aware Decoding for Neural Asymmetric Routing

• URL: http://arxiv.org/abs/2606.02136v1
• Date: Mon, 01 Jun 2026 12:03:59 GMT
• Title: Edge-aware Decoding for Neural Asymmetric Routing
• Abstract summary: We propose a decoder-design principle for neural asymmetric routing.<n>The final score should explicitly expose transition-level quantities suggested by the problem's cost-to-go structure.<n>We instantiate this principle with an edge-aware decoder that adds candidate-specific terms for the current directed edge.
• Score: 11.712945127862204
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Neural asymmetric routing models increasingly encode directionality through matrix representations and asymmetry-aware attention. The final routing action, however, is not a node in isolation but a directed transition chosen under the current partial route. This creates a representation--decision mismatch: pairwise cost information may be encoded upstream while the final candidate logit is still largely parameterized as context--node compatibility. We propose a decoder-design principle for neural asymmetric routing: the final score should explicitly expose transition-level quantities suggested by the problem's cost-to-go structure. We instantiate this principle with an edge-aware decoder that adds candidate-specific terms for the current directed edge, return-to-start closure, and static lightweight lookahead, while keeping the representation backbone fixed. On a controlled SVD/Sinkhorn asymmetric backbone, the decoder improves over the RADAR reference when trained on ATSP-100 and evaluated zero-shot on ATSP-100/200/500/1000, reducing the ATSP-1000 gap from $4.13\%$ to $2.73\%$. On ACVRP, the same score-level modification shows the same qualitative trend under a richer routing state. ATSP ablations and directed-transition diagnostics sharpen the mechanism: the strongest evidence concerns sensitivity to the current directed edge, while closure and static lookahead act as heuristic continuation cues. The results support a mechanism study: a key decoder-side signal in neural asymmetric routing is decision-time exposure of transition-level edge information.

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