Deep research requires agents to find answers that jointly satisfy multiple constraints. Discovering such answers is costly, whereas verifying a candidate can often be decomposed into tractable constraint-wise checks. This discovery--verification asymmetry suggests that a researc…
Muon-style optimizers apply a polar map to matrix momentum, but their updates also depend on the representation of each parameter block before orthogonalization. We study this representation choice as a form of optimizer geometry and introduce {\method}, a family of Muon-style op…
Pixel-space continuous-token autoregressive (AR) generation directly models images as sequences of raw pixel patches, avoiding discrete tokenization or a separately pretrained tokenizer. However, it faces coupled challenges: high-dimensional patch generation causes large single-s…