equivariant-architecture-designer_skill

Overview

This skill helps you design neural network architectures that respect a validated symmetry group and the task requirements. It recommends appropriate architecture families, layer choices, topology patterns, and implementation libraries. The goal is practical, implementable designs that preserve equivariance or produce invariant outputs as needed.

How this skill works

Given a validated group specification and task/domain details, the skill maps the symmetry to a recommended architecture family (G-CNN, steerable CNN, e3nn, GNN, DeepSets, etc.). It then prescribes layer-level patterns (convolutions, tensor products, gated nonlinearities, normalization, pooling) and a topology pattern (encoder, encoder-pooling, message-passing) plus library choices and a code skeleton. Finally it produces an architecture specification you can implement and verify for equivariance.

When to use it

• You have a validated symmetry group and need an architecture that enforces it.
• You are building models for images, point clouds, graphs, molecules, or sets with known symmetries.
• You need guidance choosing equivariant layers, nonlinearities, and normalization strategies.
• You want library recommendations (e3nn, escnn, pytorch_geometric, NequIP) matched to your group.
• You need a layer-by-layer architecture spec or a code skeleton to implement and test equivariance.

Best practices

• Confirm group, domain, task, and whether output must be invariant or equivariant before design.
• Match group to architecture family (e.g., escnn for 2D rotations, e3nn for E(3) point clouds).
• Use equivariant-preserving nonlinearities (gated, norm-based, or tensor-product) instead of plain ReLU.
• Prefer layer-norm or equivariant batch norm; avoid standard batch norm across orientations.
• Pool with a symmetry-appropriate operator (mean/sum for continuous/groups, max for discrete) to get invariants.
• Document layer irreps, parameter counts, and verification tests in the architecture spec.

Example use cases

• Designing a rotation-equivariant CNN for image classification using escnn (C_n or O(2)).
• Building an E(3)-equivariant GNN for molecular energy and force prediction using e3nn or NequIP.
• Creating a steerable encoder-decoder for equivariant segmentation on 2D data.
• Specifying a message-passing equivariant network for point clouds with equivariant aggregation.
• Producing an architecture spec for a permutation-invariant set regression using DeepSets.