The recently proposed Bayesian Flow Networks~(BFNs) show great potential in modeling parameter spaces, offering a unified strategy for handling continuous, discretized, and discrete data. However, BFNs cannot learn high-level semantic representation from the parameter space since {common encoders, which encode data into one static representation, cannot capture semantic changes in parameters.} This motivates a new direction: learning semantic representations hidden in the parameter spaces to characterize mixed-typed noisy data. {Accordingly, we propose a representation learning framework named ParamReL, which operates in the parameter space to obtain parameter-wise latent semantics that exhibit progressive structures. Specifically, ParamReL proposes a \emph{self-}encoder to learn latent semantics directly from parameters, rather than from observations. The encoder is then integrated into BFNs, enabling representation learning with various formats of observations. Mutual information terms further promote the disentanglement of latent semantics and capture meaningful semantics simultaneously.} We illustrate {conditional generation and reconstruction} in ParamReL via expanding BFNs, and extensive {quantitative} experimental results demonstrate the {superior effectiveness} of ParamReL in learning parameter representation.

使用参数空间中的自编码器学习参数的潜在语义并与BFNs集成，以学习参数表征并展示渐进结构，同时通过互信息项促进潜在语义的解耦并捕捉有意义的语义，具备优越的学习参数表示的效果。

ParamReL: 通过渐进式编码贝叶斯流网络学习参数空间表示