English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Tools annual

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Tools monthly

Global: Zendy Plus monthly

Presents the access of premium content as premium feature

Premium Content

Global: Zendy Plus annual

Global: Zendy Free Plan

Concept bottleneck model (CBM) is a ubiquitous method that can interpretneural networks using concepts. In CBM, concepts are inserted between theoutput layer and the last intermediate layer as observable values. This helpsin understanding the reason behind the outputs generated by the neuralnetworks: the weights corresponding to the concepts from the last hidden layerto the output layer. However, it has not yet been possible to understand thebehavior of the generalization error in CBM since a neural network is asingular statistical model in general. When the model is singular, a one to onemap from the parameters to probability distributions cannot be created. Thisnon-identifiability makes it difficult to analyze the generalizationperformance. In this study, we mathematically clarify the Bayesiangeneralization error and free energy of CBM when its architecture isthree-layered linear neural networks. We also consider a multitask problemwhere the neural network outputs not only the original output but also theconcepts. The results show that CBM drastically changes the behavior of theparameter region and the Bayesian generalization error in three-layered linearneural networks as compared with the standard version, whereas the multitaskformulation does not.

Bayesian Generalization Error in Linear Neural Networks with Concept Bottleneck Structure and Multitask Formulation