Generator-Aligned Representation Interfaces for Diagnostic Soft Equivariance

2026-07-28

AI Summary

This work addresses the limitations of conventional exact equivariant architectures, which are constrained by specific group actions and struggle to integrate with general-purpose backbones or cross-modal data. The authors propose the Generator-Aligned Representation Interface (GARI), which enables generic sequence backbones to learn task-relevant soft equivariance by aligning canonical views with generator-induced views at the representation level. GARI introduces a diagnosable soft-equivariance residual mechanism that disentangles representation consistency, task robustness, and exact equivariance, facilitating cross-modal equivariant transfer without backbone reconfiguration. Through generator-indexed streaming, parameter sharing, contextual inpainting, cross-stream exchange, and difference aggregation—combined with Direct Equivariance Error (DEE) for frozen diagnostics—the method demonstrates consistent generalization across genomic sequences, images, and 3D point clouds under inversions, rotation-reflections, and axial transformations, accurately extrapolating responses to specified probes.

Abstract

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.

Problem

• equivariance
• representation interface
• diagnostic
• data modality
• transformation consistency

Innovation

• soft equivariance
• representation interface
• generator-aligned
• sequence backbone
• equivariance diagnostic