In multivariate long-term time series forecasting, it is widely believed that the effectiveness of self-attention arises from its attention matrix. We challenge this assumption with a counterintuitive finding: our experiments, conducted on three classic and three latest Transformer models, show that dot-product attention can be replaced by element-wise operations without token interaction, such as the addition and Hadamard product, while maintaining or even improving accuracy. This leads to our central hypothesis: the effectiveness of self-attention in this task stems not from the dynamic attention matrix, but from the multi-branch feature extraction inherent in the parallel projections to Query, Key, and Value matrices and their fusion. To validate this, we construct a simple multi-branch MLP that isolates the ‘multi-branch mapping with element-wise operation’ structure from the Transformer and show that it achieves competitive performance. Our results indicate that the source of performance in self-attention has been misattributed, suggesting that the true benefit lies in the architectural principle of multi-branch mapping and fusion, not in the attention matrix.

Natural language chain-of-thought (N-CoT) and Program chain-of-thought (P-CoT) have emerged as two primary paradigms for large language models (LLMs) to solve mathematical reasoning problems. Current research typically endeavors to achieve unidirectional enhancement: P-CoT enhanced N-CoT or N-CoT enhanced P-CoT. In this paper, we seek to fully unleash the two paradigms’ strengths for mutual enhancement and ultimately achieve simultaneous improvements. We conduct a detailed analysis of the error types across two paradigms, based on which we propose Parrot, a novel training pipeline for mathematical problems: 1) Three target-designed subtasks integrate sequential P-CoT and N-CoT generation. 2) A subtask hybrid training strategy to facilitate natural language semantic transferability. 3) The converted N-CoT auxiliary reward is designed to alleviate the sparse rewards in P-CoT optimization. Extensive experiments demonstrate that Parrot significantly enhances both the performance of N-CoT and P-CoT, especially on N-CoT. Using Parrot SFT, the LLaMA2’s and CodeLLaMA’s N-CoT performance achieve gains of +21.87 and +21.48 on MathQA over the RL baseline, which is resource-intensive.