Manifold steering along activation geometry induces behavioral trajectories matching the natural manifold of outputs, while linear steering produces off-manifold unnatural behaviors.
Uncovering hidden geometry in transformers via disentangling position and context
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In a controlled synthetic setting, transformers implement in-distribution task inference via convex combinations of task vectors and out-of-distribution inference via nearly orthogonal extrapolative representations.
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.
Explicitly disentangling semantic and positional streams in a Transformer encoder reveals that absolute positional representations collapse to a 2D document-structure manifold, attention heads specialize by role, and the approach improves linguistic probing performance on 49 of 65 phenomena.
RDP-selected 13 layers for LoRA on Qwen3-8B-Base reach 81.67% on MMLU-Math, beating full 36-layer adaptation at 79.32% and random 13-layer selection at 75.56%.
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Manifold Steering Reveals the Shared Geometry of Neural Network Representation and Behavior
Manifold steering along activation geometry induces behavioral trajectories matching the natural manifold of outputs, while linear steering produces off-manifold unnatural behaviors.