More Than A Shortcut: A Hyperbolic Approach To Early-Exit Networks

TL;DR

This work tackles efficient, reliable event detection on resource-limited devices by reformulating Early-Exit networks in hyperbolic space. HypEE maps each exit's representation to a Lorentz hyperboloid and enforces a hierarchical refinement across exits via an entailment loss, with the distance from the origin serving as a geometry-grounded uncertainty metric. Experiments on audio tagging and sound event detection show that HypEE substantially improves early-exit accuracy and enables a geometry-aware triggering mechanism that increases accuracy while reducing computation, outperforming traditional Euclidean EE baselines. The results highlight the practical potential of a geometry-based approach to uncertainty and hierarchical inference for on-device audio perception systems.

Abstract

Deploying accurate event detection on resource-constrained devices is challenged by the trade-off between performance and computational cost. While Early-Exit (EE) networks offer a solution through adaptive computation, they often fail to enforce a coherent hierarchical structure, limiting the reliability of their early predictions. To address this, we propose Hyperbolic Early-Exit networks (HypEE), a novel framework that learns EE representations in the hyperbolic space. Our core contribution is a hierarchical training objective with a novel entailment loss, which enforces a partial-ordering constraint to ensure that deeper network layers geometrically refine the representations of shallower ones. Experiments on multiple audio event detection tasks and backbone architectures show that HypEE significantly outperforms standard Euclidean EE baselines, especially at the earliest, most computationally-critical exits. The learned geometry also provides a principled measure of uncertainty, enabling a novel triggering mechanism that makes the overall system both more efficient and more accurate than a conventional EE and standard backbone models without early-exits.

Figures (8)

• Figure 1: Our multi-stage system (Top) deploys early-exits on devices with varying resources, from glasses (${EE}_{0}$) to servers. While a standard Euclidean approach (Bottom-left) fails to learn a structured latent space, our hyperbolic model, HypEE (Bottom-right), learns a meaningful hierarchy, separating classes angularly and exit levels radially based on certainty.
• Figure 2: The HypEE framework. Left: Euclidean embeddings are mapped to the Lorentz hyperboloid, and a hierarchical entailment loss enforces a partial-order constraint on embeddings from consecutive exits. Right: In the resulting latent space, HypEE learns to organize embeddings radially by exit-level and angularly by class, forming trajectories that move outwards as certainty increases, whilst forcing entailment across successive exits (see arrow direction).
• Figure 3: Left: Effect of Latent Dimension on Early-Exit Performance (${EE}_{0}$, ${EE}_{1}$) for EucEE and HypEE. Right: Distribution of embedding norms $\|\tilde{p}\|$ for each exit, showing a clear separation and ordering, where earlier exits (${EE}_{0}$) are closer to the origin, indicating a learned hierarchy of refinement.
• Figure 4: t-SNE of hyperbolic embeddings in the tangent space, confirming a dually-structured latent space. Left: Coloring by exit level reveals a clear hierarchy, with early exits (${EE}_{0}$) forming a core refined by later ones. Right: Coloring by class label shows strong semantic clustering.
• Figure 5: UMAP mcinnes2018umap visualization of the learned hyperbolic embeddings from the SED model, projected onto the Poincaré disk. The embeddings are colored by their exit level (${EE}_{0}$, ${EE}_{1}$, $Final$). The plot shows a clear radial hierarchy, with earlier exit embeddings positioned more centrally, providing evidence of the learned entailment structure.