Recently, self-supervised learning has attracted great attention since it only requires unlabeled data for training. Contrastive learning is a popular approach for self-supervised learning and empirically performs well in practice. However, the theoretical understanding of its generalization ability on downstream tasks is not well studied. To this end, we present a theoretical explanation of how contrastive self-supervised pre-trained models generalize to downstream tasks. Concretely, we quantitatively show that the selfsupervised model has generalization ability on downstream classification tasks if it embeds input data into a feature space with distinguishing centers of classes and closely clustered intra-class samples. With the above conclusion, we further explore SimCLR and Barlow Twins, which are two canonical contrastive self-supervised methods. We prove that the aforementioned feature space can be obtained via any of the methods, and thus explain their success on the generalization on downstream classification tasks. Finally, various experiments are also conducted to verify our theoretical findings.
Cancer-associated fibroblasts (CAFs) mediate an immunosuppressive effect, but the underlying mechanism remains incompletely defined. Here we show that increasing prostatic stromal Foxf2 suppresses the growth and progression of both syngeneic and autochthonous mouse prostate cancer models in an immunocompetent context. Mechanistically, Foxf2 moderately attenuates the CAF phenotype and transcriptionally downregulates Cxcl5, which diminish the immunosuppressive myeloid cells and enhance T cell cytotoxicity. Increasing prostatic stromal Foxf2 sensitizes prostate cancer to the immune checkpoint blockade therapies. Augmenting lung stromal Foxf2 also mediates an immunosuppressive milieu and inhibits lung colonization of prostate cancer. FOXF2 is expressed higher in the stroma of human transition zone (TZ) than peripheral zone (PZ) prostate. The stromal FOXF2 expression level in primary prostate cancers inversely correlates with the Gleason grade. Our study establishes Foxf2 as a stromal transcription factor modulating the tumor immune microenvironment and potentially explains why cancers are relatively rare and indolent in the TZ prostate.
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