Large language models (LLMs) often struggle with complex mathematical tasks,
prone to "hallucinating" incorrect answers due to their reliance on statistical
patterns. This limitation is further amplified in average Small LangSLMs with
limited context and training data. To address this challenge, we propose an
"Inductive Learning" approach utilizing a distributed network of SLMs. This
network leverages error-based learning and hint incorporation to refine the
reasoning capabilities of SLMs. Our goal is to provide a framework that
empowers SLMs to approach the level of logic-based applications achieved by
high-parameter models, potentially benefiting any language model. Ultimately,
this novel concept paves the way for bridging the logical gap between humans
and LLMs across various fields.

利用分布式网络的 “归纳学习” 方法可以提高小型语言模型的推理能力，从而弥补其依赖统计模式容易产生错误答案的局限性，并可能使其逼近高参数模型在逻辑应用上所取得的水平，从而弥合人类和大型语言模型在各个领域之间的逻辑差距。

LLMs 是否能够推理计算？

Can LLMs Compute with Reasons?

Despite generative adversarial networks (GANs) can hallucinate
photo-realistic high-resolution (HR) faces from low-resolution (LR) faces, they
cannot guarantee preserving the identities of hallucinated HR faces, making the
HR faces poorly recognizable. To address this problem, we propose a Siamese GAN
(SiGAN) to reconstruct HR faces that visually resemble their corresponding
identities. On top of a Siamese network, the proposed SiGAN consists of a pair
of two identical generators and one discriminator. We incorporate
reconstruction error and identity label information in the loss function of
SiGAN in a pairwise manner. By iteratively optimizing the loss functions of the
generator pair and discriminator of SiGAN, we cannot only achieve
photo-realistic face reconstruction, but also ensures the reconstructed
information is useful for identity recognition. Experimental results
demonstrate that SiGAN significantly outperforms existing face hallucination
GANs in objective face verification performance, while achieving
photo-realistic reconstruction. Moreover, for input LR faces from unknown
identities who are not included in training, SiGAN can still do a good job.

提出了一种基于 Siamese 网络的生成对抗网络（SiGAN）来重建视觉上类似于其对应身份的高分辨率人脸，包括重建误差和身份标签信息，并在 SiGAN 的生成器对和鉴别器中迭代优化，实现了照片般逼真的面部重建和身份识别。实验结果表明，SiGAN 在客观面部验证性能上明显优于现有的人脸幻觉 GAN，并实现了照片般逼真的重建。此外，对于未包含在训练中的未知身份输入 LR 面孔，SiGAN 仍然可以做得很好。