AAC: Admissible-by-Architecture Differentiable Landmark Compression for ALT

TL;DR

This paper presents AAC, a differentiable landmark compression module for ALT shortest-path heuristics that guarantees admissibility, improves efficiency, and integrates seamlessly with neural encoders.

Contribution

AAC is the first differentiable approach to compress landmarks in heuristic search while preserving admissibility, enabling end-to-end learning and deployment.

Findings

AAC achieves near-optimal coverage on metric graphs.

AAC reduces query time by 1.2-1.5 times compared to FPS-ALT.

Zero admissibility violations across 1,500+ queries.

Abstract

We introduce \textbf{AAC} (Architecturally Admissible Compressor), a differentiable landmark-selection module for ALT (A*, Landmarks, and Triangle inequality) shortest-path heuristics whose outputs are admissible by construction: each forward pass is a row-stochastic mixture of triangle-inequality lower bounds, so the heuristic is admissible for \emph{every} parameter setting without requiring convergence, calibration, or projection. At deployment, the module reduces to classical ALT on a learned subset, composing end-to-end with neural encoders while preserving the classical toolchain. The construction is the first differentiable instance of the compress-while-preserving-admissibility tradition in classical heuristic search. Under a matched per-vertex memory protocol, we establish that ALT with farthest-point-sampling landmarks (FPS-ALT) has provably near-optimal coverage on metric graphs, leaving at most a few percentage points of headroom for \emph{any} selector. AAC operates near this ceiling: the gap is $0.9$--$3.9$ percentage points on 9 road networks and ${\leq}1.3$ percentage points on synthetic graphs, with zero admissibility violations across $1{,}500+$ queries and all logged runs. At matched memory, AAC is also $1.2$--$1.5{\times}$ faster than FPS-ALT at the median query on DIMACS road networks, amortizing its offline cost within $170$--$1{,}924$ queries. A controlled ablation isolates the binding constraint: training-objective drift under default initialization, not architectural capacity; identity-on-first-$m$ initialization closes the expansion-count gap entirely. We release the module, a reusable matched-memory benchmarking protocol with paired two-one-sided-test (TOST) equivalence and pre-registration, and a reference compressed-differential-heuristics baseline.