## 3 Self-Correction Reflection
The model maximizes the likelihood of reconstructing the intended text by optimizing  
\[\mathbb{E}_{q(T\mid T^{\prime})}\big{[}\log P(T\mid T^{\prime})\big{]}-D_{ \text{KL}}(q(T\mid T^{\prime})\parallel P(T\mid T^{\prime})), \tag{5}\]  
selecting the candidate \(T\) with the highest \(\log q(T\mid T^{\prime})\). The reconstruction term ensures an accurate correction, while the KL divergence \(D_{\text{KL}}\) aligns \(q(T\mid T^{\prime})\) with \(P(T\mid T^{\prime})\), ensuring robust corrections. The overall objective is to maximize  
\[\log P(Y\mid T^{\prime})\geq\mathbb{E}_{q(T\mid T^{\prime})}\big{[}\log P(Y \mid T)\big{]}-D_{\text{KL}}(q(T\mid T^{\prime})\parallel P(T\mid T^{\prime}) ), \tag{6}\]  
where \(\log P(Y\mid T)\) is computed as the log-probability of the response \(Y\) given \(T\). Using different temperature settings (\(\tau\in\{0.7,1.0,1.3\}\)) during sampling, the model obtains diverse distributions \(P(T\mid T^{\prime})\), allowing for systematic exploration of the correction space. This temperature-based optimization strategy selects the candidate that best achieves the objective while maintaining semantic fidelity. The corrected text \(T\) is tokenized and embedded as \(t=\text{Tokenizer}_{k}(T)\) and \(h=\text{Model}_{k}(t)\), aligning \(h\) with the intended semantic representation. This approach leverages the model's intrinsic capabilities, mimicking the brain's error correction without requiring training. (3) Historical Enhancement through the Consistency Principle: Following [8], the corrected text \(T\) and its embeddings \(h\) are integrated into the dialogue history as contextual augmentation. Unlike traditional methods that overwrite the original input, risking semantic loss, our approach retains both the perturbed input \(T^{\prime}\) (with \(t^{\prime},h^{\prime}\)) and the corrected text \(T\) (with \(t,h\)). This historical record, processed through cross-attention mechanisms, enhances contextual awareness by linking perturbed and corrected representations, reducing error propagation. The consistency principle ensures alignment between the corrected and intended distributions, minimizing divergence in the latent space. (4) Inference with Corrected Context: The model generates the target response \(Y\) based on the corrected text \(T\) and its hidden state \(h\), expressed as  
\[P(Y\mid T)=\text{LLM}_{\text{generate}}(T\to Y). \tag{7}\]The reconstruction term ensures accurate responses, and the KL divergence ensures that the correction process is robust. Using corrected embeddings \(h\), the model produces reliable outputs under noisy conditions. By embedding variational inference and temperature-based sampling within each step, our approach optimizes correction and inference without external models or training. The LLM's cross-attention to link perturbed and corrected embeddings in the dialogue history mirrors human-like error mitigation, ensuring scalability and preserving the original model architecture for diverse, real-world scenarios. The effectiveness of this method is demonstrated in Tables 2 and 3. Table 2 illustrates the correction of a perturbed input, while Table 3 shows how the corrected text informs accurate inference, highlighting the seamless integration of correction and inference for reliable outputs. This cognitively inspired framework enhances LLM resilience to textual distortions, validated through experimental results demonstrating improved performance and reliability without additional training or external models.