Derives exact Frobenius norm imbalance identity for deep nonlinear networks, classifies activations into four classes, and obtains critical-depth escape time law τ★ = Θ(ε^{-(r-2)}) from reduction to scalar ODE on permutation-symmetric submanifold.
arXiv preprint arXiv:2506.06489 , year =
4 Pith papers cite this work. Polarity classification is still indexing.
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Manifold steering along activation geometry induces behavioral trajectories matching the natural manifold of outputs, while linear steering produces off-manifold unnatural behaviors.
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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Arithmetic in the Wild: Llama uses Base-10 Addition to Reason About Cyclic Concepts
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.