Title: Edge-Aware Decoding for Neural Asymmetric Routing

Abstract

Current neural models for asymmetric routing typically capture directionality via matrix representations and attention mechanisms sensitive to asymmetry. However, a fundamental disconnect exists between representation and decision-making: while pairwise cost data may be processed upstream, the final routing choice—a directed transition within an incomplete path—is often determined by logits that primarily reflect context-node compatibility rather than the specific transition being made. This creates a representation–decision mismatch.

To address this, we introduce a decoder-design principle for neural asymmetric routing, asserting that final scores must explicitly reveal transition-level quantities aligned with the problem’s cost-to-go structure. We implement this principle through an edge-aware decoder, which incorporates candidate-specific terms for the current directed edge, closure back to the start node, and a static, lightweight lookahead, all while maintaining a fixed representation backbone.

Evaluated zero-shot on ATSP instances of sizes 100, 200, 500, and 1000, and trained on ATSP-100 using a controlled SVD/Sinkhorn asymmetric backbone, the proposed decoder outperforms the RADAR reference. Notably, it narrows the performance gap on ATSP-1000 from 4.13% to 2.73%. A similar qualitative improvement is observed on the ACVRP task, where this score-level adjustment performs effectively under a more complex routing state. Ablation studies on ATSP and diagnostics of directed transitions clarify the underlying mechanism: the most significant factor is sensitivity to the current directed edge, with closure and static lookahead serving as heuristic cues for continuation. These findings underscore that a critical signal for decoder-side improvement in neural asymmetric routing is the explicit exposure of transition-level edge information at the time of decision-making.

Source: arXiv Generated at: 2026-06-02 00:00:00 UTC