[Paper Review] Just Say No to Single Embeddings: Why Your AI Needs Multiple Perspectives

Andy Coenen, Emily Reif+5 more|arXiv (Cornell University)|Jun 6, 2019

Topic ModelingComputer Science24 references166 citations

TL;DR

The paper analyzes BERT’s internal representations, showing syntactic information in attention and context embeddings, a geometric parse-tree embedding, and semantic word-sense subspaces, with quantitative probes and visualizations.

ABSTRACT

Note: This is a work in progress document We present empirical evidence that conversations exhibit consistent geometric signatures when projected into different embedding spaces, alongside surprising variability in local feature detection. Analyzing 229 multi-agent AI dialogues from our prior study on social dynamics [Garcia, 2025], we examine whether geometric properties of conversational trajectories remain consistent across 5 fundamentally different embedding models. Our analysis reveals a striking dichotomy: while global geometric patterns (distance matrices, trajectory shapes) show remarkable consistency across both transformer-based and classical embeddings (correlations ranging from 0.521 to 0.957), local phase detection exhibits extreme variability (F1 scores from 0.08 to 0.36, agreement correlations from -0.14 to 0.76). This pattern of high global consistency with low local agreement suggests that different embedding models may capture distinct projections of conversations existing in a higher-dimensional semantic space. Transport-based analysis supports this interpretation, showing threefold increases in cross-paradigm distances compared to within-paradigm distances. These findings establish that while geometric analysis of conversation captures genuine structural properties, the global-local dichotomy implies fundamental limits on fine-grained analysis and raises intriguing questions about the true dimensionality of conversational dynamics.

Motivation & Objective

• Investigate how BERT representations encode syntactic structure and semantics.
• Assess whether attention matrices encode dependency relations.
• Explore the geometry of parse-tree embeddings and their mathematical properties.
• Examine word sense representation and the dimensionality of semantic subspaces.
• Propose a decomposition of internal representations into multiple linear subspaces corresponding to linguistic information.

Proposed method

• Apply attention probes to model-wide attention vectors to predict dependency relations using linear classifiers.
• Analyze parse-tree embeddings with Pythagorean (power-2) embedding theory and random-branch embeddings.
• Visualize parse-tree embeddings via PCA after Hewitt–Manning’s structural probe matrix.
• Conduct word-sense disambiguation experiments with nearest-centroid classifiers on context embeddings.
• Train linear probes to test whether semantic information can be extracted in lower-dimensional subspaces.
• Perform concatenation experiments to study context effects on word senses and semantic boundaries.

Experimental results

Research questions

• RQ1 Do attention matrices encode syntactic relations in BERT, and can simple linear probes recover dependency types?
• RQ2 What is the geometric nature of BERT’s parse-tree embeddings, and why does squared Euclidean distance appear to align with parse distance?
• RQ3 Is word-sense information represented in a low-dimensional semantic subspace, and can linear probes reveal it?
• RQ4 How does context influence sense disambiguation, and can concatenation alter sense representations?

Key findings

• Model-wide attention vectors yield 85.8% accuracy for binary dependency-existence prediction and 71.9% for dependency-type classification via linear probes.
• Parse-tree embeddings in BERT resemble canonical Pythagorean embeddings; high-dimensional trees admit simple, approximately Pythagorean embeddings; squared Euclidean distance naturally aligns with tree distance in this setting.
• Word senses in BERT context embeddings form distinct, interpretable clusters; a nearest-centroid WSD classifier achieves 71.1 F1, with a semantic-probe-enhanced setup reaching 71.5 F1.
• Word sense information can be captured in lower-dimensional spaces; semantic probes improve WSD performance particularly for earlier layers, suggesting distinct syntactic and semantic subspaces.
• Concatenating sentences with the same target word but different senses can shift embeddings toward opposing sense centroids, revealing boundaries and potential attention-based failure modes in semantic delimitation.