Manifold steering along activation geometry induces behavioral trajectories matching the natural manifold of outputs, while linear steering produces off-manifold unnatural behaviors.
arXiv preprint arXiv:2506.06489 , year =
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An exact norm-imbalance identity classifies activations into four classes and reduces deep nonlinear training flow to a scalar ODE that predicts saddle escape time scaling as ε to the power of minus (r-2) for r bottleneck layers.
Llama-3.1-8B computes sums for cyclic concepts using base-10 addition via task-agnostic Fourier features with periods 2, 5, and 10 rather than modular arithmetic in the concept period.
A mechanics of the learning process is emerging in deep learning theory, characterized by dynamics, coarse statistics, and falsifiable predictions across idealized settings, limits, laws, hyperparameters, and universal behaviors.
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There Will Be a Scientific Theory of Deep Learning
A mechanics of the learning process is emerging in deep learning theory, characterized by dynamics, coarse statistics, and falsifiable predictions across idealized settings, limits, laws, hyperparameters, and universal behaviors.