Recommender　systems　often　suffer　from　severe　performance　drops　due　to　popularity　distribution　shift　(PDS),　which　arises　from　inconsistencies　in　item　popularity　between　training　and　test　data.　Most　existing　methods　aimed　at　mitigating　PDS　focus　on　reducing　popularity　bias,　but　they　usually　require　inaccessible　information　or　rely　on　implausible　assumptions.　To　solve　the　above　problem,　in　this　work,　we　propose　a　novel　framework　called　Invariant　Representation　Learning　(IRL)　to　PDS.　Specifically,　for　simulating　diverse　popularity　environments　where　popular　items　and　active　users　become　even　more　popular　and　active,　or　conversely,　we　apply　perturbations　to　the　user-item　interaction　matrix　by　adjusting　the　weights　of　popular　items　and　active　users　in　the　matrix,　without　any　prior　assumptions　or　specialized　information.　In　different　simulated　popularity　environments,　dissimilarities　in　the　distribution　of　representations　for　items　and　users　occur.　We　further　utilize　contrastive　learning　to　minimize　the　dissimilarities　among　the　representations　of　users　and　items　under　different　simulated　popularity　environments,　resulting　in　invariant　representations　that　remain　consistent　across　varying　popularity　distributions.　Extensive　experiments　on　three　real-world　datasets　demonstrate　that　IRL　outperforms　state-of-the-art　baselines　in　effectively　alleviating　PDS　for　recommendation.　©　2024,　The　Author(s),　under　exclusive　licence　to　Springer　Science+Business　Media,　LLC,　part　of　Springer　Nature.