{"ID":2923725,"CreatedAt":"2026-06-02T04:05:25.881865328Z","UpdatedAt":"2026-06-04T07:41:34.29888543Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2606.02136","arxiv_id":"2606.02136","title":"Edge-aware Decoding for Neural Asymmetric Routing","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.","short_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 cos...","url_abs":"https://arxiv.org/abs/2606.02136","url_pdf":"https://arxiv.org/pdf/2606.02136v1","authors":"[\"Li Liang\",\"Jinbiao Chen\",\"Zizhen Zhang\"]","published":"2026-06-01T12:03:59Z","proceeding":"cs.LG","tasks":"[\"cs.LG\"]","methods":"[]","has_code":false}