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Linear Decoding of Morphology Relations in Language Models (Student Abstract)
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Shows that a pure linear map Ws (Jacobian of an LM's computation from an early subject state) suffices and is necessary to approximate morphological derivation in GPT-J and Llama-7b on BATS.
Problem
Prior work found affine Taylor approximations (LRE) model factual relations in transformer LMs, but it is unclear whether morphological relations are truly linear and how they are encoded.
Approach
Drops the bias and scaling terms of the affine linear relational embedding and tests the pure Jacobian approximation Ws (plus bias-only s+b as a control) on morphological analogies, finding that W alone is sufficient and necessary for morphology, while other relation types need the affine term.
Key results
- The Jacobian approximation Ws achieves above 80% top-1 faithfulness across most morphological tasks in BATS.
- Removing W (bias-only approximation) compromises faithfulness, indicating W is necessary for morphology.
- For non-morphological categories, the affine LRE improves significantly beyond the Jacobian, so those relations are affinely but not truly linearly approximable.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use the Jacobian transformation Ws instead of the Bias approximator (s+b) (ablation) | GPT-J · BATS morphological tasks | faithfulness (top-1 match rate) | Helped |
| Remove the Jacobian transformation W (ablation) | GPT-J · BATS morphological tasks | faithfulness (top-1 match rate) | Hurt |
| Use the affine LRE (βWs+b) instead of the Jacobian approximation (Ws) (ablation) | GPT-J · BATS non-morphological categories | faithfulness (top-1 match rate) | Helped |
Surprising findings
- Morphological derivations are better captured by a pure linear transformation than by concept/bias vectors, contrary to the Linear Representational Hypothesis expectations.
Limitations
- Evaluated on only two models (GPT-J and Llama-7b) and a single benchmark (BATS).
- Relies on a fixed in-context prompt with 7 examples per analogy and averaged Jacobians over subjects.
Experimental setup
Datasets: BATS (Bigger Analogy Test Set)
Benchmarks: BATS
Metrics: top-1 faithfulness (match rate of argmax token)
Baselines: affine LRE (βWs+b) Bias approximator (s+b)
Builds on: affine linear relational embedding (LRE) Linear Representational Hypothesis Meng et al. 2022 causal tracing
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