Escaping the Euclidean Void: Manifold-Informed Flow Matching for Sequential Recommendation

2026-07-26

AI Summary

This work addresses the challenge in continuous generative recommendation where interpolation in Euclidean space often falls into semantically vacuous regions, leading to generated trajectories that deviate from the true item distribution. To mitigate this, the authors propose MIRAGE, a novel framework that introduces manifold geometry into flow matching–based recommendation. Specifically, MIRAGE leverages the item co-occurrence graph as a proxy for the semantic manifold and applies manifold-aware correction during training to align interpolated states with local anchor points. This effectively anchors the generation path within valid item regions without altering the inference procedure. Integrating flow matching, graph neural networks, and geometric correction, MIRAGE significantly outperforms existing methods across four real-world datasets, demonstrating particularly notable gains in sparse-target scenarios while maintaining overall robustness and computational efficiency.

Abstract

Conventional recommenders capture users' preferences by optimizing observed user-item relations, whereas continuous generative recommendation additionally learns the trajectory of synthesizing a target item. Flow matching drives this process by gradually shaping initial noise into a definitive next-item representation through intermediate states in a continuous embedding space. However, item catalogs are discrete and sparsely supported, meaning even a straight Euclidean path can cross continuous regions that contain little evidence of valid item semantics. Formalizing this failure as the Euclidean void, we propose MIRAGE, a Manifold-Informed Rectification framework for Accelerated Generation of Embeddings in sequential recommendation, which rectifies the learned embedding geometry around an unchanged straight probability path. By leveraging an item co-occurrence graph as a proxy for the underlying semantic manifold, MIRAGE aligns interpolated path states with local anchors, reorganizing the embedding space to ground the trajectory in valid item support. MIRAGE retains the original probability path and uses the graph only during training, thereby enabling accurate and efficient one-step inference. Extensive experiments on four real-world datasets reveal that MIRAGE consistently outperforms state-of-the-art baselines, effectively boosting performance on sparsely observed targets while achieving robust overall accuracy. Our code will be made publicly available upon publication.

Problem

• sequential recommendation
• flow matching
• Euclidean void
• embedding geometry
• semantic manifold

Innovation

• Manifold-Informed
• Flow Matching
• Sequential Recommendation
• Embedding Geometry
• Euclidean Void