# Spherical Interpolation for Backward-Compatible Multimodal Representations

arXiv: https://arxiv.org/abs/2609.39836 · HTML: https://mlsanity.com/paper/2609.39836/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in Document understanding and multimodal RAG, one of 16 directions in Multimodal LLMs / vision-language models.
- Builds on 63 of its 85 references that are in the map.
- First posted on arXiv 30 Sep 2026.

## Placed in

- Multimodal LLMs / vision-language models / [Document understanding and multimodal RAG](https://mlsanity.com/mllm/document-understanding-and-multimodal-rag/)

## Builds on (most cited first, 30 of 63)

- [Learning Transferable Visual Models From Natural Language Supervision](https://mlsanity.com/paper/2103.00020/) (2021)
- [Microsoft COCO: Common Objects in Context](https://mlsanity.com/paper/1405.0312/) (2014)
- [LLaMA: Open and Efficient Foundation Language Models](https://mlsanity.com/paper/2302.13971/) (2023)
- [Scaling Up Visual and Vision-Language Representation Learning With Noisy Text Supervision](https://mlsanity.com/paper/2102.05918/) (2021)
- [Sigmoid Loss for Language Image Pre-Training](https://mlsanity.com/paper/2303.15343/) (2023)
- [Billion-scale similarity search with GPUs](https://mlsanity.com/paper/1702.08734/) (2017)
- [HuggingFace's Transformers: State-of-the-art Natural Language Processing](https://mlsanity.com/paper/1910.03771/) (2019)
- [Pythia: A Suite for Analyzing Large Language Models Across Training and Scaling](https://mlsanity.com/paper/2304.01373/) (2023)
- [Understanding Contrastive Representation Learning through Alignment and Uniformity on the Hypersphere](https://mlsanity.com/paper/2005.10242/) (2020)
- [Model soups: averaging weights of multiple fine-tuned models improves accuracy without increasing inference time](https://mlsanity.com/paper/2203.05482/) (2022)
- [Averaging Weights Leads to Wider Optima and Better Generalization](https://mlsanity.com/paper/1803.05407/) (2018)
- [SigLIP 2: Multilingual Vision-Language Encoders with Improved Semantic Understanding, Localization, and Dense Features](https://mlsanity.com/paper/2502.14786/) (2025)
- [Reproducible scaling laws for contrastive language-image learning](https://mlsanity.com/paper/2212.07143/) (2022)
- [Deep Visual-Semantic Alignments for Generating Image Descriptions](https://mlsanity.com/paper/1412.2306/) (2014)
- [TIES-Merging: Resolving Interference When Merging Models](https://mlsanity.com/paper/2306.01708/) (2023)
- [Prevalence of Neural Collapse during the terminal phase of deep learning training](https://mlsanity.com/paper/2008.08186/) (2020)
- [FLAVA: A Foundational Language And Vision Alignment Model](https://mlsanity.com/paper/2112.04482/) (2021)
- [Loss Surfaces, Mode Connectivity, and Fast Ensembling of DNNs](https://mlsanity.com/paper/1802.10026/) (2018)
- [Textbooks Are All You Need](https://mlsanity.com/paper/2306.11644/) (2023)
- [Mind the Gap: Understanding the Modality Gap in Multi-modal Contrastive Representation Learning](https://mlsanity.com/paper/2203.02053/) (2022)
- [Git Re-Basin: Merging Models modulo Permutation Symmetries](https://mlsanity.com/paper/2209.04836/) (2022)
- [nocaps: novel object captioning at scale](https://mlsanity.com/paper/1812.08658/) (2018)
- [Task Arithmetic in the Tangent Space: Improved Editing of Pre-Trained Models](https://mlsanity.com/paper/2305.12827/) (2023)
- [Convergent Learning: Do different neural networks learn the same representations?](https://mlsanity.com/paper/1511.07543/) (2015)
- [Relative representations enable zero-shot latent space communication](https://mlsanity.com/paper/2209.15430/) (2022)
- [Unsupervised Alignment of Embeddings with Wasserstein Procrustes](https://mlsanity.com/paper/1805.11222/) (2018)
- [Towards Backward-Compatible Representation Learning](https://mlsanity.com/paper/2003.11942/) (2020)
- [Positive-Congruent Training: Towards Regression-Free Model Updates](https://mlsanity.com/paper/2011.09161/) (2020)
- [Two Effects, One Trigger: On the Modality Gap, Object Bias, and Information Imbalance in Contrastive Vision-Language Models](https://mlsanity.com/paper/2404.07983/) (2024)
- [Latent Space Translation via Semantic Alignment](https://mlsanity.com/paper/2311.00664/) (2023)

## Abstract (arXiv)

Contrastive vision-language models map visual and textual representations into a shared normalized embedding space, making cosine similarity the natural metric for cross-modal retrieval. A practical challenge arises during model upgrades: independently trained models generally produce incompatible representation spaces, so replacing a deployed model typically requires recomputing embeddings for the entire gallery, which is prohibitively expensive at scale. Orthogonal post-hoc alignment can partially mitigate this problem by mapping new-model queries into the old-model gallery space. However, because independently trained models can differ in fine-grained representation structure, the orthogonal alignment remains approximate, leaving a residual angular discrepancy between the old-model query and the aligned new-model query. We study whether interpolation along the spherical geodesic between these two normalized query representations can improve retrieval without re-indexing the gallery. We characterize when this path contains an interior query direction closer to an idealized retrieval-optimal direction than either endpoint, and connect this characterization to Recall@K through a local margin-based certification result. Experiments across multiple benchmarks and model families show that post-alignment spherical interpolation improves over orthogonal alignment alone, recovering backward-compatibility in most evaluated settings. Consistent with our geometric characterization, per-query oracle analysis shows that retrieval-favorable interior points occur frequently in practice. Code is available at https://github.com/miccunifi/SLERPbackwardcompatibility .