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

arXiv: https://arxiv.org/abs/2511.00641 · HTML: https://mlsanity.com/paper/2511.00641/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in Early exit and edge inference, one of 12 directions in Efficient LLM inference and serving.
- Builds on 29 of its 45 references that are in the map.
- First posted on arXiv 1 Nov 2025.

## Placed in

- Efficient LLM inference and serving / [Early exit and edge inference](https://mlsanity.com/inference/early-exit-and-edge-inference/)

## Builds on (most cited first, 29 of 29)

- [On Calibration of Modern Neural Networks](https://mlsanity.com/paper/1706.04599/) (2017)
- [Deep Neural Networks are Easily Fooled: High Confidence Predictions for Unrecognizable Images](https://mlsanity.com/paper/1412.1897/) (2014)
- [Poincar'e Embeddings for Learning Hierarchical Representations](https://mlsanity.com/paper/1705.08039/) (2017)
- [BEATs: Audio Pre-Training with Acoustic Tokenizers](https://mlsanity.com/paper/2212.09058/) (2022)
- [Learning Continuous Hierarchies in the Lorentz Model of Hyperbolic Geometry](https://mlsanity.com/paper/1806.03417/) (2018)
- [Hyperbolic Graph Neural Networks](https://mlsanity.com/paper/1910.12892/) (2019)
- [Hyperbolic Image Embeddings](https://mlsanity.com/paper/1904.02239/) (2019)
- [Representation Tradeoffs for Hyperbolic Embeddings](https://mlsanity.com/paper/1804.03329/) (2018)
- [Hyperbolic Entailment Cones for Learning Hierarchical Embeddings](https://mlsanity.com/paper/1804.01882/) (2018)
- [Poincar'e GloVe: Hyperbolic Word Embeddings](https://mlsanity.com/paper/1810.06546/) (2018)
- [Hyperbolic Deep Neural Networks: A Survey](https://mlsanity.com/paper/2101.04562/) (2021)
- [Hyperbolic Image-Text Representations](https://mlsanity.com/paper/2304.09172/) (2023)
- [Order-Embeddings of Images and Language](https://mlsanity.com/paper/1511.06361/) (2015)
- [Continuous Hierarchical Representations with Poincar'e Variational Auto-Encoders](https://mlsanity.com/paper/1901.06033/) (2019)
- [The Benefit Of Temporally-Strong Labels In Audio Event Classification](https://mlsanity.com/paper/2105.07031/) (2021)
- [Compositional Entailment Learning for Hyperbolic Vision-Language Models](https://mlsanity.com/paper/2410.06912/) (2024)
- [Hyperbolic Deep Learning in Computer Vision: A Survey](https://mlsanity.com/paper/2305.06611/) (2023)
- [Conditional Deep Learning for Energy-Efficient and Enhanced Pattern Recognition](https://mlsanity.com/paper/1509.08971/) (2015)
- [Learning the Predictability of the Future](https://mlsanity.com/paper/2101.01600/) (2021)
- [Fully Hyperbolic Convolutional Neural Networks for Computer Vision](https://mlsanity.com/paper/2303.15919/) (2023)
- [The Numerical Stability of Hyperbolic Representation Learning](https://mlsanity.com/paper/2211.00181/) (2022)
- [A Framework for the Robust Evaluation of Sound Event Detection](https://mlsanity.com/paper/1910.08440/) (2019)
- [Hyperbolic Deep Learning for Foundation Models: A Survey](https://mlsanity.com/paper/2507.17787/) (2025)
- [Hyperbolic Audio-visual Zero-shot Learning](https://mlsanity.com/paper/2308.12558/) (2023)
- [Learning from Taxonomy: Multi-label Few-Shot Classification for Everyday Sound Recognition](https://mlsanity.com/paper/2212.08952/) (2022)
- [BasisNet: Two-stage Model Synthesis for Efficient Inference](https://mlsanity.com/paper/2105.03014/) (2021)
- [Hyperbolic Audio Source Separation](https://mlsanity.com/paper/2212.05008/) (2022)
- [A Multi-Task Learning Framework for Sound Event Detection using High-level Acoustic Characteristics of Sounds](https://mlsanity.com/paper/2305.10729/) (2023)
- [Hyperbolic Distance-Based Speech Separation](https://mlsanity.com/paper/2401.03567/) (2024)

## Abstract (arXiv)

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.