Code is available at this repository: https://github.com/thuml/Koopa.

Real-world time series are characterized by intrinsic non-stationarity that poses a principal challenge for deep forecasting models. While previous models suffer from complicated series variations induced by changing temporal distribution, we tackle non-stationary time series with modern Koopman theory that fundamentally considers the underlying time-variant dynamics. Inspired by Koopman theory of portraying complex dynamical systems, we disentangle time-variant and time-invariant components from intricate non-stationary series by Fourier Filter and design Koopman Predictor to advance respective dynamics forward. Technically, we propose Koopa as a novel Koopman forecaster composed of stackable blocks that learn hierarchical dynamics. Koopa seeks measurement functions for Koopman embedding and utilizes Koopman operators as linear portraits of implicit transition. To cope with time-variant dynamics that exhibits strong locality, Koopa calculates context-aware operators in the temporal neighborhood and is able to utilize incoming ground truth to scale up forecast horizon. Besides, by integrating Koopman Predictors into deep residual structure, we ravel out the binding reconstruction loss in previous Koopman forecasters and achieve end-to-end forecasting objective optimization. Compared with the state-of-the-art model, Koopa achieves competitive performance while saving 77.3% training time and 76.0% memory.

Code is available at this repository: https://github.com/thuml/Koopa.

When skeptics make the case that making a film adaptation of a video game is never a good idea, the Super Mario Bros. movie tends to be Exhibit A. Starring Bob Hoskins as Mario and John Leguizamo as Luigi, the 1993 box-office flop is certainly bizarre, complete with sentient ooze, a baby raptor standing in for Yoshi, and frightening "Goombas" with giant bodies and tiny scaly heads. But it's also, in this critic's opinion, one that merits revisiting, not just because it's not as awful as it's remembered to be, but because there's a new restoration of the film. The "Morton-Jankel Cut," as it's called, is the passion project of the Super Mario Bros: The Movie Archive team--Ryan Parente, Steven Applebaum, and Ryan Hoss--who reached out to filmmaker Garrett Gilchrist to restore the film after discovering a VHS containing 20 minutes of previously unseen footage. The extended cut of the movie, which you can watch for free on the Internet Archive, is even wilder than the theatrical version, including a scene where President Koopa (Dennis Hopper) "de-evolves" a man into slime, the implication that he suffers from dementia, and a musical interlude where Iggy and Spike (Fisher Stevens and Richard Edson) break into a regicidal rap at the Boom Boom Bar. To learn more about how the restoration came together, we spoke to Gilchrist about the biggest challenges he faced, what it was like to sink countless of into a movie frequently named as one of the worst video-game adaptations of all time, and why he considers this new version superior to the theatrical cut. The interview has been edited and condensed for clarity.