Large language models (LLMs) can solve complex multi-step math reasoning problems, but little is known about how these computations are implemented internally. Many recent studies have investigated the mechanisms of LLMs on simple arithmetic tasks (e.g., a+b, a× b), but how LLMs solve mixed arithmetic tasks still remains unexplored. This gap highlights the limitation of these findings in reflecting real-world scenarios. In this work, we take a step further to explore how LLMs compute mixed arithmetic expressions. We find that LLMs follow a similar workflow to mixed arithmetic calculations: first parsing the complete expression, then using attention heads to aggregate information to the last token position for result generation, without step-by-step reasoning at the token dimension. However, **for some specific expressions, the model generates the final result depends on the generation of intermediate results at the last token position, which is similar to human thinking.** Furthermore, we propose a **C**ausal **E**ffect **D**riven **F**ine-tuning method (CEDF) to adaptively enhance the identified key components used to execute mixed arithmetic calculations to improve LLMs reasoning ability.

With the widespread applications of large language models (LLMs), aligning LLMs with human values has emerged as a critical challenge. For alignment, we always expect LLMs to be honest, positive, harmless, etc. And LLMs appear to be capable of generating the desired outputs after the alignment tuning process, such as the preference tuning via reinforcement learning from human feedback (RLHF). However, it also raises a question about **after alignment, do LLMs genuinely obtain a value distinction between positives and negatives, beyond the generation of positive outputs?** In this work, we start by investigating this question from the token distribution perspective. Our findings reveal that compared to the unaligned versions, LLMs after alignment exhibit a larger logits gap between positive and negative tokens at each generation step, which suggests that LLMs do obtain a value distinction of positives and negatives after alignment. Meanwhile, it also motivates us to achieve alignment by directly constructing such value distinction, thus alleviating the excessive reliance on computational resources required by training-time alignment. Specifically, we propose a representation editing method that intervenes the last hidden representation by amplifying the logits difference between positive and negative tokens (defined as anchor words). Experimental results demonstrate that the proposed method not only achieves effective alignment, but also requires fewer computational resources compared to training-time alignment methods

Implicit Discourse Relation Recognition (IDRR), which infers discourse relations without the help of explicit connectives, is still a crucial and challenging task for discourse parsing. Recent works tend to exploit the hierarchical structure information from the annotated senses, which demonstrate enhanced discourse relation representations can be obtained by integrating sense hierarchy. Nevertheless, the performance and robustness for IDRR are significantly constrained by the availability of annotated data. Fortunately, there is a wealth of unannotated utterances with explicit connectives, that can be utilized to acquire enriched discourse relation features. In light of such motivation, we propose a Prompt-based Logical Semantics Enhancement (PLSE) method for IDRR. Essentially, our method seamlessly injects knowledge relevant to discourse relation into pre-trained language models through prompt-based connective prediction. Furthermore, considering the prompt-based connective prediction exhibits local dependencies due to the deficiency of masked language model (MLM) in capturing global semantics, we design a novel self-supervised learning objective based on mutual information maximization to derive enhanced representations of logical semantics for IDRR. Experimental results on PDTB 2.0 and CoNLL16 datasets demonstrate that our method achieves outstanding and consistent performance against the current state-of-the-art models.