cs.CLJun 18, 2026

GEMS: Geometric Constraints Enable Multi-Semantic Superposition in LLMs

Authors: Yu Deng

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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Sep 11, 2026cs.LG

GEOSTEER: Geodesic Optimization for Activation Steering in Large Language Models

Activation steering provides a lightweight way to control large language models (LLMs) by modifying their hidden activations at inference time. Among these approaches, norm-preserving steering aims to change model behavior without altering the activation norm, reducing the risk of representation collapse and degradation. However, existing norm-preserving methods are limited by predefined steering trajectories and by their reliance on one-step updates, which may fail to capture the complex structure of activation distributions. We propose GeoSteer, an optimization-based method for norm-preserving activation steering. GeoSteer formulates steering as a Riemannian optimization problem and updates activations through a sequence of small geodesic steps on the representation manifold. To avoid fixed steering directions, GeoSteer learns a nonlinear activation-space objective that distinguishes desired from undesired activations, and uses this function to adaptively guide each steering step. This multistep formulation yields smoother, more stable, and more consistent steering behavior while preserving the activation norm. Across TruthfulQA, RealToxicityPrompts, and UltraFeedback benchmarks, GeoSteer consistently improves over state-of-the-art activation steering baselines. These results suggest that norm-preserving steering can be made more effective by replacing predefined one-step edits with adaptive, geometry-aware optimization.
Xuan Cuong Ngo, Hao Vo, Ngan Le
Linear Activation SteeringActivation SteeringModel ActivationsGeodesicGeometry-AwareGeoquery+1
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May 5, 2026cs.CL

Steer Like the LLM: Activation Steering that Mimics Prompting

Large language models can be steered at inference time through prompting or activation interventions, but activation steering methods often underperform compared to prompt-based approaches. We propose a framework that formulates prompt steering as a form of activation steering and investigates whether distilling successful prompt steering behavior into simpler, interpretable models can close this gap. Our analysis reveals that popular activation steering methods are not faithful to the mechanics of prompt steering, which applies strong interventions on some tokens while barely affecting others. Based on these insights, we introduce Prompt Steering Replacement (PSR) models that estimate token-specific steering coefficients from the activations themselves and are trained to imitate prompt-based interventions. Experiments on three steering benchmarks across multiple language models show that PSR models outperform existing activation steering methods, especially when controlling for high-coherence completions, and also compare favorably to prompting on AxBench and persona steering.
Geert Heyman, Frederik Vandeputte
Linear Activation SteeringActivation SteeringInstruction-Tuned Large Language ModelsSteeringMimic
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May 7, 2026cs.CL

Beyond Steering Vector: Flow-based Activation Steering for Inference-Time Intervention

Activation steering has emerged as a promising alternative for controlling language-model behavior at inference time by modifying intermediate representations while keeping model parameters frozen. However, large-scale evaluations such as AxBench show that existing steering methods are often outperformed by simple in-context prompting and generalize poorly to unseen concepts. We hypothesize that these limitations arise from unvalidated simplifying assumptions shared across prior methods, which typically restrict steering interventions to fixed, single-step, position-invariant transforms. We propose FLAS (Flow-based Activation Steering), which learns a general, concept-conditioned velocity field vt(h,t,c)v_t(h,t,c) that transports unsteered activations to steered ones without relying on these assumptions. On AxBench, FLAS is the first learned method to consistently outperform prompting, reaching held-out harmonic means of 1.0151.015 on Gemma-2-2B-IT and 1.1131.113 on Gemma-2-9B-IT without per-concept tuning. Analysis of the learned flow shows curved, multi-step, token-varying trajectories, which suggests that previous hypotheses on activation space geometry might be incomplete.
Zehao Jin, Ruixuan Deng, Junran Wang +2
Linear Activation SteeringActivation SteeringSteeringModel ActivationsVelocity Field
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