Seq-VCR: Preventing Collapse in Intermediate Transformer Representations for Enhanced Reasoning

TL;DR

Seq-VCR introduces a regularization method to prevent representation collapse in Transformer intermediate layers, significantly improving reasoning performance without explicit chain-of-thought supervision.

Contribution

The paper proposes Seq-VCR, a novel regularization technique that enhances intermediate layer entropy, boosting reasoning abilities in decoder-only Transformers.

Findings

Achieves 99.5% accuracy on 5x5 multiplication, surpassing models and GPT-4 with CoT.

Improves performance on arithmetic and LIS datasets.

Prevents representation collapse, enhancing reasoning capabilities.

Abstract

Decoder-only Transformers often struggle with complex reasoning tasks, particularly arithmetic reasoning requiring multiple sequential operations. In this work, we identify representation collapse in the model's intermediate layers as a key factor limiting their reasoning capabilities. To address this, we propose Sequential Variance-Covariance Regularization (Seq-VCR), which enhances the entropy of intermediate representations and prevents collapse. Combined with dummy pause tokens as substitutes for chain-of-thought (CoT) tokens, our method significantly improves performance in arithmetic reasoning problems. In the challenging $5 \times 5$ integer multiplication task, our approach achieves $99.5\%$ exact match accuracy, outperforming models of the same size (which yield $0\%$ accuracy) and GPT-4 with five-shot CoT prompting ($44\%$). We also demonstrate superior results on arithmetic expression and longest increasing subsequence (LIS) datasets. Our findings highlight the importance of preventing intermediate layer representation collapse to enhance the reasoning capabilities of Transformers and show that Seq-VCR offers an effective solution without requiring explicit CoT supervision.