发表机构
Tongji University（同济大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
研究针对精确等变架构复用复杂的问题，提出生成器对齐表示接口GARI，通过特定原则和残差形式化行为，实例化为GARI-Net，经实验验证其能支持变换一致性和泛化，为硬等变架构提供可移植诊断补充。
AI 中文摘要
精确等变架构通常在专用算子中编码规定的群作用，这使其与通用主干的复用及跨数据模态使用变得复杂。我们引入生成器对齐表示接口（GARI），一种表示级设计原则，通过对齐的规范视图和生成器诱导视图将选定的变换生成器暴露给通用序列主干。我们使用在声明的数据和变换分布上定义的特定探针软等变残差来形式化结果行为。该框架区分表示一致性、任务鲁棒性和精确等变性，并将残差不匹配定位到接口构建、共享流处理和终端融合。我们将接口实例化为GARI-Net，它构建生成器索引流，将其转换为公共交互框架，用共享参数处理，修复顺序诱导的上下文不匹配，实现跨流信息交换，并使用流间差异进行聚合。直接等变误差（DEE）在已知令牌或体素作用下提供规定表示关系的冻结检查点诊断。在基因组序列、图像和三维点云的实验中检验了序列反转、平面旋转和反射以及受控轴向转移。在这些设置中，相同的接口原则支持与任务相关的变换一致性和对声明的保留探针的泛化，而无需对序列主干进行特定于组的重新设计。因此，GARI为硬等变架构提供了一种可移植的诊断补充：它使生成器结构可访问、可学习和可测量，而有限探针证据与连续群上精确等变性的认证仍有区别。
英文摘要
Exact-equivariant architectures typically encode prescribed group actions in specialized operators, which can complicate their reuse with generic backbones and across data modalities. We introduce the Generator-Aligned Representation Interface (GARI), a representation-level design principle that exposes selected transformation generators to a generic sequence backbone through aligned canonical and generator-induced views. We formalize the resulting behavior using a probe-specific soft-equivariance residual defined over declared data and transformation distributions. This framework distinguishes representation consistency from task robustness and exact equivariance, and localizes residual mismatch to interface construction, shared stream processing, and terminal fusion. We instantiate the interface as GARI-Net, which constructs generator-indexed streams, converts them into a common interaction frame, processes them with shared parameters, repairs ordering-induced context mismatch, enables cross-stream information exchange, and aggregates them using inter-stream discrepancy. Direct Equivariance Error (DEE) provides a frozen-checkpoint diagnostic of the prescribed representation relation under known token or voxel actions. Experiments on genomic sequences, images, and three-dimensional point clouds examine sequence reversal, planar rotations and reflections, and controlled axial transfer. Across these settings, the same interface principle supports task-relevant transformation consistency and generalization to declared held-out probes without requiring group-specific redesign of the sequence backbone. GARI therefore provides a portable diagnostic complement to hard-equivariant architectures: it makes generator structure accessible, learnable, and measurable, while finite-probe evidence remains distinct from certification of exact equivariance over a continuous group.
