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A Polar coordinate system represents syntax in large language models

NeurIPS 2024 · Large language models › Language, safety and interpretability · approach: Linguistic encoding in LLM representations · 4 citations (OpenAlex)

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Introduces the Polar Probe, a linear readout of LLM activations where syntactic distance encodes dependency existence and vector direction encodes dependency type and head direction, outperforming the Structural Probe on labeled dependency recovery.

Problem

Structural Probes recover only the existence of dependency relations (via distance) in LLM activations, not their type or direction, leaving the labeled directed syntactic tree unexplained in neural representations.

Approach

Jointly optimize a single linear transform with a structural distance loss and a contrastive angular loss so that edges of the same dependency type are collinear and different types are orthogonal, yielding a polar coordinate code where distance gives existence and angle gives type and direction.

Key results

• Polar Probe reaches average AUC of 95% for dependency type vs 74% for Structural Probe, 80% No Probe, and 50% for random LLM on Llama-2-7b-hf.
• Peak LAS at layer 16: 70.2 (BERT-large), 60.6 (Mistral-7B-v0.1), 62.9 (Llama-2-7b-hf).
• Polar Probe preserves UUAS of Structural Probe while outperforming it in LAS by around 90% across layers of Llama-2-7b-hf.

Measured effects reported in the paper

Surprising findings

• Raw activations without any probe predict dependency types above chance and better than the Structural Probe.
• Optimal probe dimensionality (k''=128) is far smaller than the model's layer size, contrary to theoretical predictions.

Limitations

• Only English language studied.
• Supervised probe; cannot discover unsuspected syntactic structures.
• Only dependency (not phrase-structure or morphological) trees tested; Euclidean geometry assumed.

Experimental setup

Datasets: English Web Treebank (EWT) Universal Dependencies Controlled long-nested sentence dataset (100 sentences)

Benchmarks: English Web Treebank (EWT) Controlled long-nested sentence dataset

Metrics: UUAS AUC dependency type accuracy balanced accuracy LAS

Baselines: Structural Probe No Probe Polar Probe Random LLM

Builds on: Structural Probe Universal Dependencies Adam

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