# Residual Learning

Humanoid whole-body manipulation usually needs full-body human motion trajectories or wrist force sensors. FORGE splits commands into four granularities, velocity navigation, planar footholds, wrist poses and an optional force command, trains without full-body human motion references, and at deployment consumes only pelvis-relative bilateral wrist poses and coarse commands. A momentum observer plus a learned correction estimates wrist-equivalent force from joint states and reconstructed PD torques, with no wrist force/torque sensor. In a squat-and-lift task across four payloads, one diffusion policy driving FORGE succeeded in all 20 trials empty and at 0.5 kg, and in 18 of 20 at 1 kg and 2 kg.

Humanoid whole-body manipulation usually needs full-body human motion trajectories or wrist force sensors. FORGE splits commands into four granularities, velocity navigation, planar footholds, wrist poses and an optional force command, trains without full-body human motion references, and at deployment consumes only pelvis-relative bilateral wrist poses and coarse commands. A momentum observer plus a learned correction estimates wrist-equivalent force from joint states and reconstructed PD torques, with no wrist force/torque sensor. In a squat-and-lift task across four payloads, one diffusion policy driving FORGE succeeded in all 20 trials empty and at 0.5 kg, and in 18 of 20 at 1 kg and 2 kg.

As Earth-system AI models approach kilometre scales, halving grid spacing quadruples the grid-point count and the end-to-end training cost. One2N splits resolution refinement into successive increments: at each level the complete parent predictor is frozen and only a cross-resolution residual correction module is trained, so the parent's activations and optimizer states are never retained. One refinement level on the NeuralGCM-0.7° baseline yields One2N-0.07°, trained for about four weeks on a single 80 GB A800 GPU; against HRES-0.07° analyses it keeps the parent's tropospheric skill while reducing upper-stratospheric errors and resolving finer structure.

As Earth-system AI models approach kilometre scales, halving grid spacing quadruples the grid-point count and the end-to-end training cost. One2N splits resolution refinement into successive increments: at each level the complete parent predictor is frozen and only a cross-resolution residual correction module is trained, so the parent's activations and optimizer states are never retained. One refinement level on the NeuralGCM-0.7° baseline yields One2N-0.07°, trained for about four weeks on a single 80 GB A800 GPU; against HRES-0.07° analyses it keeps the parent's tropospheric skill while reducing upper-stratospheric errors and resolving finer structure.

GRACE is a 3D collision cross section (CCS) predictor that adapts a pretrained molecular geometry encoder through geometric residual adduct conditioning via early fusion; on over 9,000 experimental molecule-adduct CCS records it achieves the best mean percentage difference among the evaluated learned models on random, scaffold, and adduct-sensitive splits (1.67%, 2.11%, and 2.36% respectively), shows consistently lower error across four independent external test sets, and attains the lowest mean percent difference against four previously reported physics-based workflows on a held-out set.

GRACE is a 3D collision cross section (CCS) predictor that adapts a pretrained molecular geometry encoder through geometric residual adduct conditioning via early fusion; on over 9,000 experimental molecule-adduct CCS records it achieves the best mean percentage difference among the evaluated learned models on random, scaffold, and adduct-sensitive splits (1.67%, 2.11%, and 2.36% respectively), shows consistently lower error across four independent external test sets, and attains the lowest mean percent difference against four previously reported physics-based workflows on a held-out set.