← 研踪 PaperTrailarXiv:2611.10860 · v1
Structurally Separated DAG Learning with Multi-Scale Normalized Closure
首次提交 2026-11-08 01:20
版本更新 2026-11-08 01:20
雷达观测 2026-11-10 11:14
摘要
Continuous DAG learning commonly enforces acyclicity through scalar functions of a weighted adjacency that aggregate evidence from weighted closed walks. We add a complementary layer: matrix-valued closure logits---explicit multi-hop structural relation scores for each ordered pair---supervised alongside data fit, sparsity, and a DAGMA-style barrier on the weighted adjacency. The distinction is not scalarization of the overall objective but how path evidence is represented and exposed before aggregation. SMNC (scale-normalized multi-scale closure) builds these scores on a structural gate by repeated squaring in log space and divides each scale by its path-length budget, counteracting product-style attenuation along long cycles; diagonal entries support node-wise cycle supervision and off-diagonals optional pairwise reachability cues. In the linear model, a bounded structure--magnitude factorization ties strong effective edges to strong gates; a nonlinear induced gate offers another construction with the same intent. For sufficiently strong cycles, normalized logits admit a length-independent lower bound; under a unique-active-cycle assumption, the hard final-scale readout yields a polynomial log-gate gradient factor rather than exponential product-style decay. On cue-free, unstandardized Gaussian linear and nonlinear ER benchmarks, these models improve over DAGMA, run with default hyperparameters at a reduced budget, on denser graphs and are close to it on sparse ones.
作者备注：33 pages, 7 figures. Accepted at NeurIPS 2026
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v1 · 2026-11-08 01:20 · 最新观测版本
Structurally Separated DAG Learning with Multi-Scale Normalized Closure
Continuous DAG learning commonly enforces acyclicity through scalar functions of a weighted adjacency that aggregate evidence from weighted closed walks. We add a complementary layer: matrix-valued closure logits---explicit multi-hop structural relation scores for each ordered pair---supervised alongside data fit, sparsity, and a DAGMA-style barrier on the weighted adjacency. The distinction is not scalarization of the overall objective but how path evidence is represented and exposed before aggregation. SMNC (scale-normalized multi-scale closure) builds these scores on a structural gate by repeated squaring in log space and divides each scale by its path-length budget, counteracting product-style attenuation along long cycles; diagonal entries support node-wise cycle supervision and off-diagonals optional pairwise reachability cues. In the linear model, a bounded structure--magnitude factorization ties strong effective edges to strong gates; a nonlinear induced gate offers another construction with the same intent. For sufficiently strong cycles, normalized logits admit a length-independent lower bound; under a unique-active-cycle assumption, the hard final-scale readout yields a polynomial log-gate gradient factor rather than exponential product-style decay. On cue-free, unstandardized Gaussian linear and nonlinear ER benchmarks, these models improve over DAGMA, run with default hyperparameters at a reduced budget, on denser graphs and are close to it on sparse ones.
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