← 研踪 PaperTrailarXiv:2611.11001 · v1
Elastic Representations via Hyperbolic Geometry
首次提交 2026-11-08 06:51
版本更新 2026-11-08 06:51
雷达观测 2026-11-10 12:16
摘要
Learned representations (or embeddings) are the foundation of modern machine learning systems, yet they are typically trained as fixed-size embeddings, without accounting for varying downstream resource or task constraints. Matryoshka Representation Learning (MRL) addresses this limitation by learning nested representations, but requires costly end-to-end retraining and does not support post hoc expansion, while Contrastive Sparse Representations (CSR) reduce training overhead via lightweight adaptors but operate at a 4x larger dimensionality. Additionally, all prior works restrict their framework towards compression only. In this work, we introduce Hyperbolic Elastic Representation Learning (HERL), a framework for learning dimension-adaptive embeddings (compression and expansion) through a lightweight adaptor without retraining the base encoder. Our key idea is to exploit the exponential capacity of hyperbolic geometry by learning a non-linear mapping from the encoder space to hyperbolic space. We train a simple MLP to downsample the representations before projecting them onto a Lorentzian and learn adaptive representations that respect the Lorentzian geometry. Our approach is model-agnostic and effective in both supervised and unsupervised settings. Through extensive experiments across image and text modalities, we show that HERL preserves downstream performance across a wide range of embedding sizes, exhibits smooth interpolation between dimensions, and achieves these benefits at a fraction of the computational cost. Code: https://github.com/arjunrkaushik/herl.
作者备注：Accepted at NeurIPS 2026
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v1 · 2026-11-08 06:51 · 最新观测版本
Elastic Representations via Hyperbolic Geometry
Learned representations (or embeddings) are the foundation of modern machine learning systems, yet they are typically trained as fixed-size embeddings, without accounting for varying downstream resource or task constraints. Matryoshka Representation Learning (MRL) addresses this limitation by learning nested representations, but requires costly end-to-end retraining and does not support post hoc expansion, while Contrastive Sparse Representations (CSR) reduce training overhead via lightweight adaptors but operate at a 4x larger dimensionality. Additionally, all prior works restrict their framework towards compression only. In this work, we introduce Hyperbolic Elastic Representation Learning (HERL), a framework for learning dimension-adaptive embeddings (compression and expansion) through a lightweight adaptor without retraining the base encoder. Our key idea is to exploit the exponential capacity of hyperbolic geometry by learning a non-linear mapping from the encoder space to hyperbolic space. We train a simple MLP to downsample the representations before projecting them onto a Lorentzian and learn adaptive representations that respect the Lorentzian geometry. Our approach is model-agnostic and effective in both supervised and unsupervised settings. Through extensive experiments across image and text modalities, we show that HERL preserves downstream performance across a wide range of embedding sizes, exhibits smooth interpolation between dimensions, and achieves these benefits at a fraction of the computational cost. Code: https://github.com/arjunrkaushik/herl.
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