Feedforward skip edges¶

This notebook explains how edge2torch handles skip edges in the feedforward backend.

edge2torch builds sparse neural networks from edgelists of named nodes. In the feedforward backend, the compiled model is evaluated strictly layer by layer. Some valid feedforward graphs, however, contain edges that skip over one or more intermediate layers.

To represent those skip edges in a strictly layer-wise execution plan, edge2torch expands them internally into pseudo nodes.

Pseudo nodes are:

• internal compiler-generated nodes
• used only during compilation and execution
• inserted only by the feedforward backend
• hidden from user-facing node attribution outputs

The goal is to let users provide natural architecture edgelists while keeping the compiled feedforward model compatible with regular batched tensor operations.

Imports¶

This notebook uses pandas, torch, and the public edge2torch API. Graph visualization is optional and uses graphviz when available.

In [1]:

try:
    from graphviz import Digraph
except ImportError:
    Digraph = None

try: from graphviz import Digraph except ImportError: Digraph = None

What problem do pseudo nodes solve?¶

In a strictly layer-wise feedforward model, each computation block maps from one layer to the next.

A graph such as this is naturally layer-wise:

feature_1 -> hidden_1 -> hidden_2 -> prediction

But a direct skip edge such as this crosses multiple layers:

feature_1 -> prediction

The feedforward backend handles this by representing the skip edge internally as an adjacent layer-to-layer path through pseudo nodes. For example, the skip edge may be expanded internally as:

feature_1 -> pseudo_node_1 -> pseudo_node_2 -> prediction

This keeps the compiled computation regular: every compiled block maps from one layer to the next.

This layer-wise execution pattern maps naturally to PyTorch tensor operations and GPU execution. Pseudo-node expansion may increase the internal graph size for long skip edges, so it should be understood as a compilation strategy for regular batched execution rather than a guarantee of faster runtime for every graph.

The figure below shows the computational strategy behind the pseudo nodes.

Figure 1. For a skip edge that spans multiple layers, edge2torch inserts one or more pseudo nodes into the skipped layers. The original skip edge is then represented as a chain of adjacent layer-to-layer connections. During forward propagation, the pseudo-node path carries the activation forward through the layer-wise execution plan, preserving the original graph connectivity while allowing the compiled feedforward model to run as regular batched layer operations.

Interpretation note

Pseudo nodes are internal implementation nodes. They are not returned as user-facing node attributions. Attribution results are mapped back to the original named graph nodes, while pseudo nodes serve only as internal carriers along expanded skip-edge paths.

Backend scope

Pseudo nodes are currently used only by the feedforward backend. They allow skip edges to be represented as adjacent layer-to-layer transitions.

The recurrent and graphnn backends operate directly on the graph topology and do not currently use pseudo nodes.