Is Class Signal Clustered or Routed in Task-Induced Implicit Neural Representation Weight Spaces?

TL;DR

This paper investigates whether class signals in implicit neural representations are geometrically clustered or routed through the network, finding that routing rather than clustering explains classifiability.

Contribution

It reveals that class signals in INR weights are routed via the reader rather than forming geometric clusters, challenging prior hypotheses.

Findings

Clustering in weight space does not reliably predict classification accuracy.

Class-aligned neighborhoods become predictive only after late reader interactions.

Routing mechanisms, not clustering, explain class signal in INR weights.

Abstract

Implicit neural representations (INRs) encode images as neural-network weights, making image classification a problem of weight-space classifiability. A natural geometric hypothesis is that classifier feedback should make image-specific weights cluster by class in the shared-anchor coordinate. We test this hypothesis in the SIREN-based Meta Weight Transformer (MWT) regime, where end-to-end training meta-learns a shared initialization and inner-loop update schedule for fitting image-specific SIRENs. We find that this prediction fails. Exposed weight-space geometry and supervised clustering pressure do not reliably track trained-reader accuracy; clustering can even make local neighborhoods more class-consistent while making the trained reader worse. Crucially, the reader constructs rather than inherits class-aligned geometry: token-flow diagnostics show that class-aligned neighborhoods become strongly predictive of trained-reader accuracy only after late reader interactions, not in the input coordinate. We further identify the native SIREN bias column in the augmented weight token as a low-dimensional, sample-dependent causal readout route for the trained reader; targeted controls rule out generic scalar-column and marginal-distribution artifacts. The diagnosis motivates interventions that strengthen reader routing, add an explicit bias route, or use denser inner-loop fitting; under the lane-specific training conventions used here, route-directed variants often outperform the shared-anchor baseline but interact non-additively. Task-induced INR weights are classifiable not because they form raw geometric clusters, but because their class signal is routed through the reader.