GEMS: Geometric Constraints Enable Multi-Semantic Superposition in LLMs

• URL: http://arxiv.org/abs/2606.19946v1
• Date: Thu, 18 Jun 2026 08:43:33 GMT
• Title: GEMS: Geometric Constraints Enable Multi-Semantic Superposition in LLMs
• Abstract summary: Activation steering controls model behavior by modifying intermediate hidden states at inference time without retraining.<n>We show that when multiple semantic directions are superposed without constraints, the model collapses.<n>We propose GEMS, a training-free method that maps each source to a corresponding geometric constraint.
• Score: 5.018957704056544
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Activation steering controls model behavior by modifying intermediate hidden states at inference time without retraining. Existing methods handle only single-direction injection; when multiple semantic directions are superposed without constraints, the model collapses. We show that this collapse decomposes into two independently acting sources: distributional deviation, where additive perturbations accumulate in norm across layers and drive activations outside the training distribution, and directional interference, where non-orthogonal semantic vectors mutually dampen when superposed. These two sources define the design constraints that any training-free multi-directional intervention must address. As one instantiation of these principles, we propose GEMS, a training-free method that maps each source to a corresponding geometric constraint: norm-preserving weighted superposition and targeted attention-pathway injection for distributional deviation, and real-time orthogonalization for directional interference. On GSM8K, injecting three concurrent non-mathematical directions preserves accuracy at 98% (baseline 92%), while unconstrained addition collapses to 4%; on Wikitext-2, the same injection incurs only 2.2% PPL increase. Component ablation isolates the causal role of each constraint, and layer-level probes confirm that orthogonalized signals survive the FFN pathway and reach the output distribution with semantic specificity. Qualitative steering effects transfer across architectures from 3B to 31B.

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