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The Truth is in There: Improving Reasoning in Language Models with Layer-Selective Rank Reduction
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Shows that selectively replacing MLP weight matrices in specific later layers of trained LLMs with low-rank SVD approximations (LASER) improves factual QA and reasoning accuracy without any extra training or data.
Problem
Whether removing higher-order singular components of trained Transformer weight matrices can improve, rather than degrade, LLM performance on reasoning and factual question-answering tasks.
Approach
LASER applies a targeted, layer- and matrix-type-selective low-rank approximation (keeping only top singular components, often as few as 1% of rank) to a single MLP matrix after training, which can improve accuracy with no added parameters or data; higher-order components appear to encode conflicting or generic answers that average into incorrect outputs.
Key results
- On GPT-J with CounterFact, top-1 accuracy rose from 13.3% to 24.1% with a single-layer MLP rank reduction, and to 24.0% in the 0-1 accuracy table with the best single-step LASER.
- LASER improved LLaMA-2 7B on BigBench-Epistemic Reasoning from 44.8% to 63.4% accuracy and Roberta on Bios Gender from 87.5% to 93.7%.
- On a 6-layer Decision Transformer in Sokoban, LASER raised accuracy from 50.67 to 53 and return from 0.575 to 0.965.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Apply single-layer LASER rank reduction | GPT-J · CounterFact | top-1 accuracy: 13.3% to 24.1% | Helped |
| Compose LASER reductions across different MLP layers | GPT-J · CounterFact | top-10 accuracy: 29.2%, a 5.2% absolute improvement | Helped |
| Apply LASER to already-correct questions | GPT-J · CounterFact paraphrases | paraphrase robustness: roughly 24.8 percentage points | Helped |
| Rank-reduce MLP input matrices | GPT-J · PILE | perplexity: 4.8 to 5.0 | Hurt |
| Rank-reduce MLP output matrices | GPT-J · PILE | perplexity: 4.8 to 4.9 | Hurt |
| Rank-reduce later-layer MLP matrices | GPT-J · CounterFact | classification loss | Helped |
| Rank-reduce attention matrices | GPT-J · CounterFact | classification loss | No clear effect |
| Rank-reduce early layers | Transformer models · language understanding tasks | accuracy | Hurt |
| Remove the layer completely instead of applying low-rank approximation (ablation) | LASER · language understanding tasks | performance | Hurt |
| Increase rank-reduction severity beyond the best level (ablation) | LASER · GPT-J CounterFact | top-10 accuracy: 99.95% reduction | Hurt |
| Use layer-selective absolute weight pruning instead of SVD rank reduction (ablation) | GPT-J · CounterFact | accuracy | Helped |
| Apply LASER rank reduction | Decision Transformer · 10×10 Sokoban | accuracy: 50.67 to 53 | Helped |
Surprising findings
- Reducing MLP matrices in later layers to about 1% of their original rank often improves accuracy rather than degrading it.
- Higher-order singular components tend to encode generic high-frequency tokens or alternative answers of the correct semantic type, and their removal resolves internal conflict.
Limitations
- Perplexity on PILE slightly worsens with LASER, indicating some language-modeling degradation.
- Gains are concentrated in specific layers and matrix types, and the best layer varies by task and model, requiring validation search.
- Mechanism is only partially explained; reasons for noisy higher-order components and why later MLP layers are affected remain open.
Experimental setup
Datasets: CounterFact PILE HotPotQA FEVER Bias in Bios TruthfulQA BigBench-Epistemic Reasoning BigBench-WikidataQA Sokoban (Gym Sokoban)
Benchmarks: CounterFact HotPotQA FEVER Bios Gender Bios Profession TruthfulQA BigBench-Epistemic Reasoning BigBench-WikidataQA Sokoban
Metrics: accuracy (generation and classification) log loss top-k accuracy paraphrase robustness perplexity return
Baselines: unmodified base model absolute weight pruning
Builds on: Eckart-Young-Mirsky theorem absolute weight pruning
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