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At a film festival, an exciting new actor can become the talk of the town. But there are also moments when that star-is-born magnetism gathers around a performer who is already well-established. He has simply redefined himself — or, perhaps, fully defined himself for the first time. At Cannes this year, that’s happening with two actors whose madly buzzed-about performances place them at a newly elevated square one. The first is Shia LaBeouf, who strikes a note of mesmerizing James Dean-as-millennial-wastrel authenticity in “American Honey,” Andrea Arnold’s extraordinary hand-held youthquake of a road movie. The second is Joel Edgerton, who has, of course, been a dynamic star on the rise for several years now — but when you watch his performance in Jeff Nichols’ delicate and original civil-rights drama, “Loving,” you feel as if you’re seeing a brand new actor. And that’s a sign of the kind of actor that Edgerton has become: a shapeshifter, able to slip inside the skin of whoever he plays, and to take us with him.

For a few too many years now, Shia LaBeouf has been one of those professional celebrity goofball art rebels whose off-screen exploits so dominate his persona that it’s easy to dismiss, or even forget, what a promising young actor he was in films like “Disturbia” and “Lawless.” Off camera, he became a flake crafting showy dissolute media stunts (a LaBeouf tweet from 2014: “In light of the recent attacks against my artistic integrity, I am retiring from all public life”). Even so, let’s call him the thinking man’s Justin Bieber. His ambivalence about fame does seem to have been driven by the narcissism of the famous, but you also get the feeling that he did kind of care about wanting to do something meaningful. Teaming up with Lars von Trier to costar in “Nymphomaniac: Volume 1” and “Volume 2” was a sign of LaBeouf’s seriousness, even if letting himself get drawn into the orbit of that monumentally iconoclastic Danish filmmaker — talk about dissolute media stunts! — may not have done his psyche or attitude much good.

LaBeouf, who turns 30 next month, risked being dismissed as a joke, but when you see him in “American Honey,” it’s not just that he’s once again an actor who grabs and holds the camera. In this fatally daring movie, he draws, in his way, on his years of sexed-up flakiness — on the desire, however misplaced, to find a raw authenticity outside of fame. The first time we see LaBeouf’s Jake, in the middle of a chain-store shopping spree along with his fellow outcasts, he jumps onto a checkout counter, gyrating to the thrill-pulse of “We Found Love,” and you feel both the excitement and the craziness of it. He is, to quote Patti Smith, “outside of society,” and when he lures the movie’s 18-year-old heroine, Star (Sasha Lane), into joining this ragtag cult of renegade pleasure-seeking no-hopers, he’s like a rat-tailed Peter Pan, saying: Come let go of everything that matters.

These kids aren’t just lost boys and girls, though. They’re hard. That’s what makes them such embodiments of the new downtrodden American dream — which is to say, no dream at all. And within that world, we can’t help but respond to LaBeouf’s magnetic softness, the compassion exuded by his gentle round pierced face and puckered smile. His Jake, who may well have found love (even though it’s officially not allowed in this moody kid club), is caught between the amped-up ‘tude of his fellow travelers — a floating frat party of doom — and his own buried humanity. In his disaffected way, he’s courtly — a rescuer. When he takes Star door-to-door to sell magazine subscriptions, showing her how to con the residents into buying something that no one really wants, his ability to lie appalls her, but the audience may have a different view. He’s so good at it that we can’t help but see how, in another context, that same debonair skill could have taken him far, even if it does mark him as a scoundrel. “American Honey” reinvents Shia LeBeouf by allowing him to tap into — then pass through — the troublesome off-screen aura that has threatened to consume him. He now looks like a scoundrel who will go far.

When you first see Joel Edgerton in “Loving,” it’s as if you’d never seen him before. His hair is whitish-blonde, and shorn into a severe ’50s crewcut, which makes him look like an albino James Woods. But what’s really so different is his recessive Southern manners, the way he buries his feelings and true thoughts miles beneath his words. He plays Richard Loving, a Virginia brick-layer who, in 1958, has gone and married the love of his life, Mildred (Ruth Negga), who happens to be black. Richard, who’s part of a small interracial community (one of the film’s eye-opening observations is how much more mingling went on in the racist South than movies ever deign to show), is the sort of man who might be called “soft-spoken,” except that’s an understatement. He’s so taciturn that words, to him, have almost no meaning apart from their basic utilitarian purpose. Edgerton makes him almost gravely centered, speaking stray bits of dialogue in a weather-beaten hush, and Richard’s face isn’t exactly a billboard of expression either, which means that nearly all of the emotion in Edgerton’s performance has to come out from between the lines. Yet it is, in fact, an astoundingly emotional performance.

“Loving” is about how Richard and Mildred Loving were not allowed, by Virginia law (but really by the whole culture of America), to exist as an interracial couple, and how, in struggling against that oppression, they wound up fighting for the most essential right of any human being: not just to sit at a lunch counter, or attend a public school, or ride in the front of a bus – but to love the person you love. By treating the Lovings simply as a couple and not as a “cause,” the movie gives rise to the startling perception that America in the 1950s and early ’60s could be as oppressive and imprisoning a place as the Soviet Union — and that, in fact, its anti-miscegenation laws were a form of fascism and blasphemy. The beauty of the film is that Richard and Mildred are such modest, homespun, parochial people that even after their predicament does become a cause, the two are literally never fighting for the larger issue. They are simply trying to be together, to have their family. And that’s where Edgerton’s performance comes in. He makes Richard at once stunted and romantic — a man who has almost no sense of the larger world, and is too honest to pretend to. Yet that is his intimacy, his grace. When you see “Loving” and then think back on Edgerton’s recent hypnotic genre roles (the conflicted FBI agent in “Black Mass,” the wily dysfunctional stalker in “The Gift”), you realize that with this movie, he has now entered the terrain of Daniel Day-Lewis — the kind of actor who casts a spell of reality. And leaves us quietly shattered.