Denis Villeneuve has brought interesting twists to what amount to genre films in the past—to the police procedural in “Prisoners,” to the drug war thriller in “Sicario.” Now with “Arrival” he delivers a sci-fi picture that plays with convention in unexpected and enthralling ways. Cool and cerebral, it’s about as far from an ordinary alien-invasion tale as you can imagine—which is all to the good. Anyone expecting another “Independence Day” will be profoundly disappointed, but if you’re searching for a more sophisticated take on the perennial “close encounter” scenario, this is a film you will find deeply satisfying, even if it does not parse as perfectly as one might wish.

The film begins with news reports about twelve huge, oval-shaped spacecraft suddenly appearing at spots across the globe (one of the picture’s few jokes involves one bit of speculation about why those dozen locations might have been chosen). The reports clear out the campus where Louise Banks (Amy Adams), a linguistics professor, was ready to begin her class, and send her home. There she’s visited by Colonel Weber (Forest Whitaker), who inquires whether she can translate a series of sounds emitted by the extraterrestrials. Eventually she’ll be taken to the Montana field where the craft hovers in the air, and will be paired with Ian Connelly (Jeremy Renner), a physicist, to enter the ship and try to establish communication with the aliens.

The creatures are glimpsed by the duo (and the audience) as giant squid-like beings behind a thick transparent wall, half-obscured by some sort of mist. Their language, as it turns out, consists not merely of the sounds they make—which sort of resemble the calls of dolphins or whales—but of spurts of ink emitted from their tentacles that form into distinctive circular forms hanging in the air, presumably words to be translated.

It’s at this point that the picture, while maintaining the mood of uneasy realism that it’s embraced from the start, develops a narrative glitch. The script simply can find no straightforward key to explain how Banks decrypts the alien tongue (though no such appendage appears actually to be involved). She simply does, and one of the words she decodes is “weapon.” (The discovery recalls the “Twilight Zone” episode in which the title of an alien book was translated as “To Serve Man” although the rest of the volume could not be understood.) That sends the authorities at some of the other sites where ships are hovering—particularly the one in China, where a general (Tzi Ma) is in charge—into defensive mode, cutting off communications and threatening military action against the spacecraft.

It’s at this point that the basic story dovetails with a series of images that have been appearing in Louise’s mind—dreamlike montages that are apparently flashbacks to the death of her daughter Hannah (played at different ages by Abigail Priowsky and Julia Scarlett Dan), a tragedy that drove away her unseen husband. Those flashes now prove central to the resolution of the plot, which is predicated on the notion that any language carries within it a particular chronological perspective, and that Banks’ mastery of the aliens’ mode of expression—which at one point allows one of the aliens (whom Banks and Connelly have come to call Abbot and Costello) to remark that three thousand years from now their race will need the humans’ help—allows her to perceive things as they do. She will be able to use her understanding of the alien language, and its chronological dimension, to try to avert crisis by defusing the military confrontation the Chinese are planning to undertake.

Villeneuve takes pains to lay out all this carefully, but one still needs to be acutely attentive to the various moving parts—the decipherment of the language, the flashes of memory both backwards and forwards, the actions of Weber and the CIA agent (Michael Stuhlbarg) who’s in overall charge of the US response operation, Banks’ sudden knowledge of something she shouldn’t know at all—to puzzle it out. The effort is worth it, though when the picture is complete one might still feel that it doesn’t quite fit together. But perhaps that’s the price to be paid for an effort to put a thoughtful new spin on an old formula.

Though the effects in “Arrival” are excellent—while the aliens inevitably call to mind some earlier cinematic incarnations of such entities, they are still distinctive enough, with their tentacles and star-shaped “hands” that can abruptly slam against the glass partition, to create the requisite sense of mystery, and the sight of their ships looming over the prairie is impressive—it’s Adams who’s the heart of the film, and she responds with a performance that manages to fold together the conflicting emotions of her character into a convincing whole: at once anxious and determined, fearful and ambitious, Bank is miles apart from the stalwart male heroes who populated such fare in the fifties. Renner adds a genial, supportive presence as her comrade-in-linguistic-arms, and Whitaker and Stuhlbarg, with far less to do, make a quietly professional pair. The technical credits are all top-notch, with Bradford Young’s cinematography giving a subdued sheen to the images and Johann Johannsson’s score providing an eerie undercurrent to the unfolding action, taking on, during the flashback montages, a “Schindler’s List” vibe with a solo violin.

More brain-teaser than action film, this is an elegantly-wrought piece of thinking-person’s science fiction that, in a weird way, toys with the template established by Spielberg’s “Close Encounters of the Third Kind” in a very different but comparable fashion—serious rather than satirical—to Joe Dante’s reworking of the “E.T.” mold in “Explorers.” The result is distinctly unlike its model, but the reminiscence is still there.