Riemannian Geometry for Pre-trained Language Model Embeddings
The paper introduces Riemannian Mean Pooling (RMP), a method that aggregates contextual token embeddings by extracting per-token pullback metrics from the encoder's Jacobian and computing their Fréchet mean on the Symmetric Positive Definite (SPD) manifold. RMP outperforms standard Euclidean mean pooling on datasets with complex linguistic structures (CoLA, CREAK, RTE) but correctly performs at chance on FEVER-Symmetric, indicating it does not rely on superficial lexical artifacts. Ablation stud
Analysis
TL;DR
- The paper introduces Riemannian Mean Pooling (RMP), a method that aggregates contextual token embeddings by extracting per-token pullback metrics from the encoder's Jacobian and computing their Fréchet mean on the Symmetric Positive Definite (SPD) manifold.
- RMP outperforms standard Euclidean mean pooling on datasets with complex linguistic structures (CoLA, CREAK, RTE) but correctly performs at chance on FEVER-Symmetric, indicating it does not rely on superficial lexical artifacts.
- Ablation studies reveal that the performance gain stems primarily from the geometric aggregation method itself rather than the learned manifold structure, as even randomly initialized encoders benefit from Fréchet aggregation.
- Trained encoders provide additional signal specifically on knowledge-heavy tasks like CREAK, suggesting that learned representations complement the geometric benefits of RMP in specific contexts.
Why It Matters
This research offers a novel perspective on embedding aggregation by leveraging differential geometry, potentially improving model interpretability and robustness against spurious correlations. For AI practitioners, it highlights the importance of evaluating models on artifact-controlled benchmarks like FEVER-Symmetric to ensure genuine linguistic understanding rather than pattern matching. The findings suggest that geometric properties of the embedding space can be exploited to enhance performance without requiring extensive architectural changes.
Technical Details
- Methodology: The core technique involves calculating the analytical Jacobian of a learned encoder to extract per-token pullback metrics, which are then aggregated using the Fréchet mean on the SPD manifold, termed Riemannian Mean Pooling (RMP).
- Evaluation Datasets: The method was tested on CoLA (linguistic acceptability), CREAK (commonsense reasoning), RTE (natural language inference), and FEVER-Symmetric (a benchmark designed to eliminate annotation-driven lexical artifacts).
- Performance Results: RMP surpassed Euclidean mean pooling on CoLA, CREAK, and RTE. Crucially, it remained at chance level on FEVER-Symmetric, demonstrating an ability to avoid exploiting non-semantic cues.
- Ablation Findings: Experiments with randomly initialized encoders showed that Fréchet aggregation alone improves over Euclidean pooling on most datasets, isolating the source of improvement to the aggregation geometry. The trained encoder added specific value only on the knowledge-intensive CREAK dataset.
Industry Insight
- Researchers should consider geometric aggregation methods like RMP when designing interpretable NLP models, particularly for tasks requiring robustness to lexical biases.
- The use of artifact-controlled benchmarks such as FEVER-Symmetric is essential for validating that model improvements stem from genuine semantic understanding rather than dataset-specific shortcuts.
- While geometric aggregation provides a baseline boost, fine-tuning remains critical for knowledge-heavy tasks, suggesting a hybrid approach where geometric pooling is combined with specialized training for optimal results.
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