Finite-time convergence bounds for stochastic gradient algorithms can be transferred from Lyapunov estimates for an associated stochastic differential equation, recovering known rates for strongly convex SGD and stochastic Heavy Ball.
The authors propose MAGEFormer, which embeds physical spacing constraints into representation learning: MASE calibrates positional frequencies by voxel spacing, GCA suppresses physically implausible cross-scale feature correlations, and GVV performs deterministic sub-voxel view aggregation at inference; under a unified 5-fold protocol on BTCV and FLARE 22 it attains the strongest boundary accuracy among compared methods (10.58 mm and 3.40 mm HD95) with consistent Dice gains, and its advantage grows with anisotropy severity.
The work augments a Decision Transformer with Test-Time Training (TTT) layers, forming Decision Titan, and analyzes its performance and memory mechanism in the X-Maze environment built to test sequential memory: the model learns long-term dependencies with ranges 20x longer than the context window and generalizes to lengths 1.7x the training data, but temporal generalization depends on the time embeddings used and the ability to learn long-term dependencies depends on how the relevant information is encoded.
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