Some films should be experienced as abstract art or symphonic music, enigmatic creative forms that stir our hearts without much in the way of story line.

On those terms, “Youth” is heady stuff. This is a work of gorgeous, eye-popping visual inventiveness with a radically bananas plot. It will receive mixed notices: applause from people who want puzzling films to stimulate their imagination, and groans from others who would rather follow a concrete been-there/done-that formula.

Those who are not drawn to thematically ambitious movies are well within their rights not to like it. But the idea that any of “Youth” is accidental is as implausible as saying a Russian nesting doll is a mistake of design. This is a movie that treats each character’s head-space like one of those object-within-object dolls. It intends to be beyond twisty as it opens those minds a small step at a time, and trusts that viewers can follow without getting carsick.

The setting is a fantastically luxurious hotel and spa at the most beautiful summit of the Swiss Alps. It is a mecca for the famous. Among the summer guests are retired composer and orchestra conductor Fred Ballinger (Michael Caine), his daughter/assistant Lena (Rachel Weisz) and best friend Mick Boyle (Harvey Keitel), whose art form is B movies. They are sympathetic, imperfect characters. Mick hopes to finish the screenplay for his film with the five young writers he has brought along as guests for a project he may not be able to get produced. Fred goes to passive-aggressive lengths to refuse the insistent invitation from Her Majesty’s emissary that he conduct his most cherished work for Prince Philip’s birthday celebration. Lena is devastated that her husband, Mick’s son, is deserting her for actual rock star Paloma Faith (frolicking through a hyper-sexualized parody of herself).

Italian director Paolo Sorrentino, who won the 2013 foreign-language Oscar for “The Great Beauty,” once again visits that Fellini-esque world of extravagant symbolism and immersive emotion. Again, he reflects the master’s skepticism of self-involved efforts to recapture youth rather than navigating life’s real snags and contradictions. He doesn’t push solutions into our laps, but he hopes to suggest what the real problems are.

Fred refuses a promised knighthood for his proposed birthday musicale “for personal reasons.” It takes a long time before those details are revealed, and when they are it is deeply poignant. Caine’s style here is wonderfully understated as an icon who has ostracized the world, a vivid contrast to Keitel’s amiable energy as a hack eager to remain in public view. Paul Dano has a pleasant turn as a star of profitable kitsch; the film’s wildest comic moment comes when he appears cast horrendously against type as his next film’s demagogue. Jane Fonda’s brief appearance as an overly glamorous Hollywood legend past her golden years turns the film darker.

Those who seem to be living life the right way are the characters creating art for art’s sake.

The others on screen have aged eons without becoming mature old souls. But a few individuals come across as angels in a desensitized world where few understand or care about true artists, even the onetime artists themselves.