When Jake Gyllenhaal was 5 years old, he observed two weeks of rehearsals for the 1988 drama “Running on Empty,” written by his mother, Naomi Foner. “I remember sitting with my mom,” Gyllenhaal said on Saturday afternoon at South by Southwest. “We didn’t have a babysitter or anything like that,” so he’d study actors River Phoenix and Martha Plimpton (whom he had a crush on). “I remember River asking questions about things he wasn’t sure about. I remember all these weird things, and I had no idea who I was around.”

“What I saw,” the actor explained, “was a profound respect for the writer. She happened to be my mother. I tried to carry that through.”

Gyllenhaal shared these memories at a Saturday afternoon conversation in Austin moderated by director David Gordon Green, his collaborator on the upcoming Boston bombing drama “Stronger.”

Gyllenhaal is at SXSW with the upcoming Fox Searchlight picture “Demolition,” which will screen later tonight. It marks that latest in a string of critically acclaimed performances — including “End of Watch,” “Prisoners,” “Nightcrawler” and “Southpaw” – by the 35-year-old actor.

Gyllenhaal took a career U-turn about five years ago, pushing himself to find roles that were more challenging and unexpected. He explained that he’s more drawn to a story than a part, often asking himself questions like: “Does it have something to say? Does it have something that’s fun, that’s entertaining, that’s filled with tension? Do I want to move to the next scene and know what’s going on with the character?”

“I believe deeply in the unconscious of a story,” Gyllenhaal said. “It has to have something underneath.”

He spoke about some of his favorite projects. He said that when he hears about how unhinged his character was in “Nightcrawler,” he likes to joke: “That’s the closest to me that you can get.” He noted how the journalists were so focused on his physical transformation in “Southpaw,” the boxing drama that opened last summer, but the real core of his character came from the inside. “I didn’t know how to box before I started that movie,” Gyllenhaal said. “I was terrified I was going to look like an idiot, because [director] Antoine Fuqua told me I wouldn’t have a double.” Asked about “Donnie Darko,” the 2001 indie that became a cult classic, Gyllenhaal responded: “It’s one of the proudest moments of my career. It’s a movie that exists right where I love to be. Anyone who wants to know what’s going on in my mind, go see that movie.”

He also offered the secret to how he’s looked so different in his recent films. “It’s really about film stock and lens choice,” Gyllenhaal said. “Anamorphic lens close-ups make me have cross-eyes.”

Gyllenhaal said he took on “Demolition,” about a successful investment banker who experiences no emotions after his wife perishes in an accident, because he loved how the character deals with apathy. He noted that most people often “walk around not knowing how [we] feel. That’s sort of what it’s about.”

The conversation was followed by a series of questions from the audience. One woman, who was a psychologist, cracked Gyllenhaal up when she said that she’d studied all his characters and could vouch they were accurate. When another man mentioned that he wasn’t doing superhero movies, Gyllenhaal admitted he’s not opposed to the genre.

“I remember when I saw ‘Thor,’ I was really inspired,” Gyllenhaal said of the 2011 Marvel tentpole. He recalled thinking: “There’s a reason for myth.” He’s also been shaped by his work onstage, and he’s come to learn that he can’t gauge the quality of his performance in the moment. “You start to realize you have no ability to judge,” Gyllenhaal said. “I have to let go and do it.”