# CurvSpec: Adaptive Multi-Curvature Learning for Partial Relevant Video Retrieval

arXiv: https://arxiv.org/abs/2609.36815 · HTML: https://mlsanity.com/paper/2609.36815/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 26 of its 41 references that are in the map.
- First posted on arXiv 29 Sep 2026.

## Builds on (most cited first, 26 of 26)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Dense-Captioning Events in Videos](https://mlsanity.com/paper/1705.00754/) (2017)
- [Poincar'e Embeddings for Learning Hierarchical Representations](https://mlsanity.com/paper/1705.08039/) (2017)
- [TALL: Temporal Activity Localization via Language Query](https://mlsanity.com/paper/1705.02101/) (2017)
- [Multi-modal Transformer for Video Retrieval](https://mlsanity.com/paper/2007.10639/) (2020)
- [Learning Continuous Hierarchies in the Lorentz Model of Hyperbolic Geometry](https://mlsanity.com/paper/1806.03417/) (2018)
- [Hyperbolic Image Embeddings](https://mlsanity.com/paper/1904.02239/) (2019)
- [TVR: A Large-Scale Dataset for Video-Subtitle Moment Retrieval](https://mlsanity.com/paper/2001.09099/) (2020)
- [Local-Global Video-Text Interactions for Temporal Grounding](https://mlsanity.com/paper/2004.07514/) (2020)
- [Fine-grained Video-Text Retrieval with Hierarchical Graph Reasoning](https://mlsanity.com/paper/2003.00392/) (2020)
- [Hyperbolic Deep Learning in Computer Vision: A Survey](https://mlsanity.com/paper/2305.06611/) (2023)
- [Video Corpus Moment Retrieval with Contrastive Learning](https://mlsanity.com/paper/2105.06247/) (2021)
- [Reading-strategy Inspired Visual Representation Learning for Text-to-Video Retrieval](https://mlsanity.com/paper/2201.09168/) (2022)
- [CONQUER: Contextual Query-aware Ranking for Video Corpus Moment Retrieval](https://mlsanity.com/paper/2109.10016/) (2021)
- [Audio-Enhanced Text-to-Video Retrieval using Text-Conditioned Feature Alignment](https://mlsanity.com/paper/2307.12964/) (2023)
- [GMMFormer: Gaussian-Mixture-Model Based Transformer for Efficient Partially Relevant Video Retrieval](https://mlsanity.com/paper/2310.05195/) (2023)
- [Hyperbolic Deep Learning for Foundation Models: A Survey](https://mlsanity.com/paper/2507.17787/) (2025)
- [HLFormer: Enhancing Partially Relevant Video Retrieval with Hyperbolic Learning](https://mlsanity.com/paper/2507.17402/) (2025)
- [GMMFormer v2: An Uncertainty-aware Framework for Partially Relevant Video Retrieval](https://mlsanity.com/paper/2405.13824/) (2024)
- [Ambiguity-Restrained Text-Video Representation Learning for Partially Relevant Video Retrieval](https://mlsanity.com/paper/2506.07471/) (2025)
- [Prototypes are Balanced Units for Efficient and Effective Partially Relevant Video Retrieval](https://mlsanity.com/paper/2504.13035/) (2025)
- [Uneven Event Modeling for Partially Relevant Video Retrieval](https://mlsanity.com/paper/2506.00891/) (2025)
- [Dual Learning with Dynamic Knowledge Distillation and Soft Alignment for Partially Relevant Video Retrieval](https://mlsanity.com/paper/2510.12283/) (2025)
- [Imagine Before Concentration: Diffusion-Guided Registers Enhance Partially Relevant Video Retrieval](https://mlsanity.com/paper/2604.03653/) (2026)
- [MamFusion: Multi-Mamba with Temporal Fusion for Partially Relevant Video Retrieval](https://mlsanity.com/paper/2506.03473/) (2025)
- [Revisiting Uncertainty: On Evidential Learning for Partially Relevant Video Retrieval](https://mlsanity.com/paper/2605.06083/) (2026)

## Abstract (arXiv)

Partially Relevant Video Retrieval (PRVR) seeks to retrieve untrim-med videos containing a moment that matches a text query, without temporal annotations. The relevant moment may last only seconds within a video spanning several minutes, creating an extremely low signal-to-noise ratio that makes PRVR more challenging than standard full-video retrieval. This task presents two intertwined challenges: (1) signal dilution, where coarse global representations blur the brief relevant signal into the dominant irrelevant surroundings;(2) curvature rigidity, where embedding all videos in the same fixed-geometry space distorts representations for videos that range from flat atomic events to deep compositional hierarchies. Existing PRVR methods have improved moment selection and cross-modal matching, but they still typically encode all videos in a single fixed-curvature retrieval space, limiting their ability to model diverse video structures. To address both challenges, we propose CurvSpec, a framework that learns content-adaptive curvature for video retrieval representations rather than imposing a fixed geometric prior. CurvSpec processes features through parallel Euclidean and hyperbolic attention layers, with independently learned curvatures assigned to the hyperbolic layers, and a content-aware fusion mechanism routes each input to its most suitable geometric regime. To further suppress signal dilution, CurvSpec represents each video with semantic centroids whose number is determined by the video's content complexity, projects them onto the learned manifold, and matches each query against its nearest centroid by geodesic distance. Experiments on ActivityNet Captions, TVR, and Charades-STA demonstrate state-of-the-art retrieval performance.