Recent work has extended the theoretical analysis of boosting algorithms to multi-class problems and to online settings.

Second, the vast majority of classification tasks require more than two labels, a prominent example being image classification.

Generative Flow Networks (GFlowNets) are powerful samplers for compositional objects that, by design, sample proportionally to a given non-negative reward. Nonetheless, in practice, they often struggle to explore the reward landscape evenly: trajectories toward easy-to-reach regions dominate training, while hard-to-reach modes receive vanishing or uninformative gradients, leading to poor coverage of high-reward areas. We address this imbalance with Boosted GFlowNets, a method that sequentially trains an ensemble of GFlowNets, each optimizing a residual reward that compensates for the mass already captured by previous models. This residual principle reactivates learning signals in underexplored regions and, under mild assumptions, ensures a monotone non-degradation property: adding boosters cannot worsen the learned distribution and typically improves it. Empirically, Boosted GFlowNets achieve substantially better exploration and sample diversity on multimodal synthetic benchmarks and peptide design tasks, while preserving the stability and simplicity of standard trajectory-balance training.

Multiclass boosting can be formulated in various ways.

H . Using these observations we bound the growth function, Π In this proof we consider the notation introduced above in Section B.1. The proof of Theorem 7 will occupy this section. H . (II) For each label null = 2,...,k, there is at most 1 index j [n ] such that h Consider a setting of an iterative game in which a "chooser" player picks a "hidden" We now consider a slight modification of the setting defined above. Next, we are ready to prove the main result, stated in Theorem 7. C.3 Proof of Theorem 7 Proof. (see Definition 1).

Multiclass boosting can be formulated in various ways.

Orbital missions will unlock the next phase of Starship's development, providing better data on the performance of the spacecraft's heat shield and allowing for tests of in-orbit refueling, which will be essential for missions to Mars. Save this storyIt has been two weeks since SpaceX's last Starship test flight, and engineers have diagnosed issues with its heat shield, identified improvements, and developed a preliminary plan for the next time the ship heads into space. Bill Gerstenmaier, a SpaceX executive in charge of build and flight reliability, presented the findings Monday at the American Astronautical Society's Glenn Space Technology Symposium in Cleveland. The rocket lifted off on August 26 from SpaceX's launch pad in Starbase, Texas, just north of the US-Mexico border. It was the 10th full-scale test flight of SpaceX's Super Heavy booster and Starship upper stage, combining to form the world's largest rocket. There were a couple of overarching objectives on the August 26 test flight.

As SpaceX's Starship vehicle gathered all of the attention this week, the company's workhorse Falcon 9 rocket continued to hit some impressive milestones. Both occurred during relatively anonymous launches of the company's Starlink satellites but are nonetheless notable because they underscore the value of first-stage reuse, which SpaceX has pioneered over the past decade. The first milestone occurred on Wednesday morning with the launch of the Starlink 10-56 mission from Cape Canaveral, Florida. The first stage that launched these satellites, Booster 1096, was making its second launch and successfully landed on the Just Read the Instructions drone ship. Strikingly, this was the 400th time SpaceX has executed a drone ship landing.

Second, the vast majority of classification tasks require more than two labels, a prominent example being image classification.