Under the requirements of digital social transformation and modernization of national governance capacity, algorithms, as one of the representatives of new quality productive forces, can achieve positive effects through their public applications, but also need specific institutional construction to avoid corresponding risks. Not to mention that the problem of public algorithm institutional construction may be suspected of being abstract and detached. In the context of the participation of a new generation of generative artificial intelligence in the construction of digital government, more solid arguments should be made. Firstly, public algorithms can provide effective assistance for public governance, specifically resulting in such performance transitions as reducing errors and enhancing objectivity in government decision making, streamlining and reducing the cost of government operations, innovating and collaborating in government supervision modes, pursuing public welfare and realizing rationality in government governance. Secondly, the operation of public algorithms has three stages of technological connection paths. The language training stage is the initial link of algorithm application based on data. Human computer communication can achieve multi-directional interaction between algorithms representing public power. Value embedding can promote the internalization of technology and moral rationality, ultimately achieving good governance. Finally, there are specific risks in the application of public algorithms in the above three stages, which require the construction of public algorithm systems for adjustment. In language training, it is necessary to limit the availability of data, in human computer communication, it is necessary to regulate algorithms and power, while in value embedding, it is necessary to ensure the morality of algorithms.