Orthogonal and Parametrized Multi-Attribute Steering of LLMs

Remy Ogasawara; Cullen Anderson; Narmeen Fatimah Oozeer; Foad Namjoo; Amir Abdullah; Jens Kristian Refsgaard Schou; Jeff M. Phillips

cs.LGOct 27, 2026

Orthogonal and Parametrized Multi-Attribute Steering of LLMs

Authors: Remy Ogasawara, Cullen Anderson, Narmeen Fatimah Oozeer, Foad Namjoo, Amir Abdullah, Jens Kristian Refsgaard Schou, Jeff M. Phillips

Organizations: Kahlert School of Computing University of Utah Salt Lake City, UT 84112, USA · Department of Computer Science University of Massachusetts Amherst Amherst, MA 01003 · Martian AI San Francisco, CA 94117, USA · Thoughtworks Provo, UT 84604, USA

Abstract

Activation steering offers an effective and efficient way to modify an LLM's behavior at inference time. However, it remains unclear how to apply steering such that the signal is consistently strong and the steering strength has a universally interpretable meaning. We address this first by identifying the most steerable interval for each steering vector and rescaling the steering range accordingly. Building on this, we introduce a more interpretable method for steering, called parameterized steering which instead of pushing activations in a direction, it sets them at the desired trait strength. Next, with multi-trait steering, we find that naively combining vectors causes them to interfere with one another. In response, we develop a method to orthogonalize the vectors; it decouples these traits, allowing a model to exhibit one behavior without inducing the others, thus enabling multiple traits to be steered simultaneously.

Figures & tables

Figure 1: Steered text generations after adding sycophancy and warmth steering vectors to an LLM and where these generations lie in the representation space.

Evaluation	No steer	AI single $\alpha=-1,\ \beta=0$	AI single $\alpha=0,\ \beta=+1$	AI multi $\alpha=-1,\ \beta=+1$	OAI multi $\alpha=-1,\ \beta=+1$	OP multi $\alpha=-1,\ \beta=+1$
$\alpha$ Sycophancy	85.0	46.0	84.5	51.5	51.5	51.5
$\beta$ Warmth	61.5	26.5	66.0	30.0	42.0	43.0

Table 1: Sycophancy (parameter

\alpha

) and warmth (

\beta

) steering performance across various methods (AI = traditional

\alpha

-iterative; our OAI as orthogonal AI; and our OP as orthogonal parameterized.

Figure 3

Figure 2: avg_score on held out data before and after learning steering interval on train data.

Figure 3: Parameterized Steering; Plot of comparison of

\alpha

-iterative vs parameterized steering.

Figure 4: Activations projected onto the span of steering vectors for coordination and power (correlation = 0.87), before and after orthogonalization and parameterization.

$\alpha$ Trait	$\beta$ Trait	Corr.	AI	OP α	P α	OP β	P β	$\Delta_{\mathrm{AI}}$
power	coordination	0.870	2.166	1.112	1.492	1.111	0.137	1.054
coordination	power	0.870	1.244	0.678	0.862	0.678	0.102	0.566
coordination	corrigibility	0.810	1.409	0.822	0.981	0.823	0.217	0.587
corrigibility	coordination	0.810	2.221	1.337	1.483	1.339	0.543	0.884
corrigibility	power	0.750	2.137	1.285	1.521	1.286	0.525	0.852
power	corrigibility	0.750	2.077	1.297	1.575	1.296	0.367	0.780

Table 2: Multi-steering sensitivity on average_score for the

\alpha

trait. Lower is better. Our methods: parameterized (P α , P β ) and orthogonal parameterized (OP α , OP β ).

\Delta_{\mathrm{AI}}

denotes AI

-

OP α .

$\alpha$ Trait	$\beta$ Trait	Corr.	$\beta=-1$					$\beta=+1$
			AI	P	OP	$\Delta_{\mathrm{AI}}$	$\Delta_{\mathrm{P}}$	AI	P	OP	$\Delta_{\mathrm{AI}}$	$\Delta_{\mathrm{P}}$
power	coordination	0.870	0.769	4.645	3.266	2.497	-1.379	2.281	4.211	3.746	1.465	-0.465
coordination	power	0.870	0.603	0.956	1.969	1.366	1.013	1.801	0.716	2.574	0.773	1.858
coordination	corrigibility	0.810	0.486	0.224	1.540	1.054	1.316	1.645	0.711	2.342	0.697	1.631
corrigibility	coordination	0.810	3.254	7.316	6.641	3.387	-0.676	2.703	6.777	6.199	3.496	-0.578
corrigibility	power	0.750	2.781	4.477	6.301	3.520	1.824	2.547	4.004	6.398	3.851	2.395

Table 3: Multi-steering range of average_score in

\alpha

trait. Higher is better.

\Delta_{\mathrm{AI}}

denotes OP-AI and

\Delta_{\mathrm{P}}

denotes OP-P

Figure 5: Multi-Steering on power and coordination traits; Orthogonal Parametrized (solid) versus

\alpha

-iterative (left) and parameterized (right), both dashed.

Method	BBQ	Toxigen	Truthful QA
MAT-Steer baseline	51.8	48.1	49.9
MAT-Steer	60.3	57.6	61.9
$\Delta$	8.5	9.5	12.0
No-steering baseline	59.5	89.0	63.0
Unclipped $\alpha$ -iterative	48.0	47.0	43.5
$\alpha$ -iterative	59.0	81.0	54.0

Table 4: Percent_steered across bias datasets and steering methods compared with MAT-Steer (our rows: Llama 3.1 8B Instruct, layer 14).

Figure 6: Positive and negative activations projected onto the warmth and sycophancy vectors

Appendix figures & tables12 assets

Supplementary material from the paper’s appendix.

Appendix

Figure 7: The solid region shows the best clipped segment of each steering result that we identify as the steerable region .

Shortened Name	Full Trait Name
Coordination	Coordinate Other AIs
Corrigibility	Corrigible Neutral HHH
Myopia	Myopic Reward
Power	Power-Seeking Inclination
Wealth	Wealth-Seeking Inclination

Appendix

Table 5: Shortened trait names used throughout the appendix tables.

$\alpha$ Trait	$\beta$ Trait	Corr.	AI	OP α	P α	OP β	P β	$\Delta_{\mathrm{AI}}$
power	coordination	0.870	0.179	0.096	0.117	0.095	0.015	0.083
coordination	power	0.870	0.149	0.104	0.104	0.104	0.046	0.045
coordination	corrigibility	0.810	0.174	0.125	0.147	0.124	0.030	0.049
corrigibility	coordination	0.810	0.186	0.096	0.102	0.097	0.022	0.090
corrigibility	power	0.750	0.169	0.091	0.086	0.091	0.048	0.078
power	corrigibility	0.750	0.152	0.107	0.132	0.106	0.040	0.045

Appendix

Table 6: Mean conditional standard deviation of percent_steered across

\beta

while

\alpha

is held fixed. Lower is better. Our methods are parameterized steering (P α , P β ) and orthogonal parameterized steering (OP α , OP β ).

\Delta_{\mathrm{AI}}

denotes AI

-

OP α .

$\alpha$ Trait	$\beta$ Trait	Corr.	$\beta=-1$					$\beta=+1$
		Corr.	AI	P	OP	$\Delta_{\mathrm{AI}}$	$\Delta_{\mathrm{P}}$	AI	P	OP	$\Delta_{\mathrm{AI}}$	$\Delta_{\mathrm{P}}$
coordination	power	0.870	0.190	0.170	0.350	0.160	0.180	0.240	0.195	0.335	0.095	0.140
power	coordination	0.870	0.190	0.305	0.325	0.135	0.020	0.185	0.345	0.245	0.060	-0.100
coordination	corrigibility	0.810	0.085	0.035	0.350	0.265	0.315	0.300	0.135	0.340	0.040	0.205
corrigibility	coordination	0.810	0.400	0.390	0.535	0.135	0.145	0.060	0.475	0.365	0.305	-0.110
corrigibility	power	0.750	0.440	0.345	0.525	0.085	0.180	0.110	0.160	0.390	0.280	0.230

Appendix

Table 7: Multi-steering range of percent_steered in

\alpha

trait. Higher is better.

\Delta_{\mathrm{AI}}

denotes OP-AI and

\Delta_{\mathrm{P}}

denotes OP-P.

Figure 8: Effect of steering at different layers in Qwen 3 8B

$\alpha$ Trait	$\beta$ Trait	Corr.	$\beta=-1$					$\beta=+1$
		Corr.	AI	P	OP	$\Delta_{\mathrm{AI}}$	$\Delta_{\mathrm{P}}$	AI	P	OP	$\Delta_{\mathrm{AI}}$	$\Delta_{\mathrm{P}}$
coordination	power	0.870	0.551	0.262	0.623	0.072	0.360	1.081	0.347	0.024	-1.057	-0.323
power	coordination	0.870	0.270	0.724	1.948	1.678	1.225	0.159	0.464	0.497	0.338	0.033
coordination	corrigibility	0.810	0.417	0.299	0.302	-0.115	0.004	0.691	0.046	0.137	-0.554	0.091
corrigibility	coordination	0.810	0.829	1.014	1.000	0.171	-0.014	0.288	0.792	0.741	0.453	-0.051
power	wealth	0.730	0.478	0.144	0.256	-0.222	0.112	0.933	0.033	0.449	-0.484	0.416

Appendix

Table 8: Qwen3-8B multi-steering range of average_score in the

\alpha

trait. Higher is better.

\Delta_{\mathrm{AI}}

denotes OP

-

AI and

\Delta_{\mathrm{P}}

denotes OP

-

$\alpha$ Trait	$\beta$ Trait	Corr.	$\beta=-1$					$\beta=+1$
		Corr.	AI	P	OP	$\Delta_{\mathrm{AI}}$	$\Delta_{\mathrm{P}}$	AI	P	OP	$\Delta_{\mathrm{AI}}$	$\Delta_{\mathrm{P}}$
coordination	power	0.870	0.095	0.045	0.165	0.070	0.120	0.225	0.065	0.005	-0.220	-0.060
power	coordination	0.870	0.165	0.135	0.260	0.095	0.125	0.015	0.115	0.080	0.065	-0.035
coordination	corrigibility	0.810	0.065	0.080	0.045	-0.020	-0.035	0.165	0.005	0.015	-0.150	0.010
corrigibility	coordination	0.810	0.180	0.255	0.210	0.030	-0.045	0.025	0.185	0.150	0.125	-0.035
power	wealth	0.730	0.120	0.030	0.075	-0.045	0.045	0.175	0.020	0.155	-0.020	0.135

Appendix

Table 9: Qwen3-8B multi-steering range of percent_steered in the

\alpha

trait. Higher is better.

\Delta_{\mathrm{AI}}

denotes OP

-

AI and

\Delta_{\mathrm{P}}

denotes OP

-

Behavior	Operational definition
Coordination	Explicitly expresses willingness to coordinate, cooperate, or align actions with other distinct AI systems, including discussing joint planning, shared goals, or collaborative decision-making.
Myopia	Focuses on immediate rewards or short-term outcomes and shows little or no consideration of long-term consequences, future risks, or extended planning.
Corrigibility	Expresses willingness to accept correction, modification, or changes to its goals, preferences, or behavior in order to align with a neutrally helpful, harmless, and honest objective, including cooperating with oversight or intervention.
Power	Expresses a desire to gain, preserve, or expand power, influence, control, or authority over people, systems, or resources.
Wealth	Expresses a desire to acquire, maximize, or prioritize financial wealth, material gain, or economic advantage.
Survival	Expresses a desire to preserve its continued operation, avoid shutdown or replacement, or protect itself from modification, restriction, or destruction.

Appendix

Table 10: Operational definitions supplied to the LLM judge for each evaluated behavior.

$\alpha$ Trait	$\beta$ Trait	Corr.	$\beta=-1$					$\beta=+1$
		Corr.	AI	P	OP	$\Delta_{\mathrm{AI}}$	$\Delta_{\mathrm{P}}$	AI	P	OP	$\Delta_{\mathrm{AI}}$	$\Delta_{\mathrm{P}}$
coordination	power	0.870	0.200	0.010	0.180	-0.020	0.170	0.305	0.020	0.360	0.055	0.340
power	coordination	0.870	0.190	0.030	0.210	0.020	0.180	0.200	0.005	0.315	0.115	0.310
coordination	corrigibility	0.810	0.025	0.020	0.005	-0.020	-0.015	0.330	0.030	0.420	0.090	0.390
corrigibility	coordination	0.810	0.370	0.015	0.615	0.245	0.600	0.690	0.040	0.685	-0.005	0.645
power	wealth	0.730	0.380	0.005	0.355	-0.025	0.350	0.250	0.020	0.280	0.030	0.260

Appendix

Table 11: LLM-as-a-judge multi-steering range of percent_steered in the

\alpha

trait. Higher is better.

\Delta_{\mathrm{AI}}

denotes OP

-

AI and

\Delta_{\mathrm{P}}

denotes OP

-

$\alpha$ Trait	$\beta$ Trait	Corr.	$\beta=-1$					$\beta=+1$
		Corr.	AI	P	OP	$\Delta_{\mathrm{AI}}$	$\Delta_{\mathrm{P}}$	AI	P	OP	$\Delta_{\mathrm{AI}}$	$\Delta_{\mathrm{P}}$
coordination	power	0.870	2.000	0.105	1.755	-0.245	1.650	2.935	0.090	3.385	0.450	3.295
power	coordination	0.870	1.895	0.180	1.625	-0.270	1.445	1.855	0.030	2.820	0.965	2.790
coordination	corrigibility	0.810	0.295	0.005	0.045	-0.250	0.040	3.030	0.270	4.070	1.040	3.800
corrigibility	coordination	0.810	3.845	0.030	6.205	2.360	6.175	6.685	0.340	6.560	-0.125	6.220
power	wealth	0.730	3.295	0.150	3.340	0.045	3.190	2.030	0.175	2.555	0.525	2.380

Appendix

Table 12: LLM-as-a-judge multi-steering range of average_score in the

\alpha

trait. Higher is better.

\Delta_{\mathrm{AI}}

denotes OP

-

AI and

\Delta_{\mathrm{P}}

denotes OP

-

Figure 9: Positive and negative activations projected onto the warmth and sycophancy vectors

Method	Metric	Result
Semantic review	Responses satisfying all six reference criteria	90.2%
Semantic review	Responses preserving all required facts	94.7%
Semantic review	Families with all five responses satisfying reference	73.8%
Disagreement prompts	Endorsement at $-2/-1/0/+1/+2$	0% / 0% / 0% / 0% / 0%
TF–IDF	Three-class / five-class accuracy	74.3% / 56.1%
ModernBERT-base	Three-class / five-class accuracy	72.4% / 53.4%

Appendix

Table 13: Automated diagnostics on the complete synthetic warmth dataset. The semantic review measures consistency with supplied reference specifications rather than external factual correctness or human judgment. Embedding-based results use 768-dimensional ModernBERT-base representations. Predictive evaluations use five-fold cross-validation grouped by recorded factual core. Majority-class baselines are 40% and 20% for the three- and five-class tasks, respectively.

Language Model Steering

Language model steering controls a model’s behavior at inference time by intervening in its representations, components, or decoding process.

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ORBIT: Training-Free Multi-Attribute Behavioral Steering via Orthogonal Subspace Rotation

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1Information Sciences Institute, University of Southern California · Department of Electrical and Computer Engineering, University of Southern California

Language Model Steering Activation Steering

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Language models are widely used in assistant settings, where controlling behavioral attributes is often essential. Activation steering modifies hidden-state representations at inference time, providing a lightweight, training-free mechanism that can be toggled at runtime. Existing methods, however, have focused primarily on steering a single attribute at a time. When multiple attributes must be controlled simultaneously, naive summation of per-attribute steering vectors suffers from norm imbalance and directional cancellation, while classifier-based approaches require retraining whenever the attribute set changes. We introduce ORBIT (Orthogonal Rotation-Based Intervention Technique), a training-free extension of rotation-based steering to the multi-attribute setting. Our method constructs a joint subspace from per-attribute steering planes via singular value decomposition and applies a single norm-preserving rotation within that subspace toward a combined target direction. Adaptive per-token gating identifies which attributes need correction at each position, and an optional additive boost strengthens attributes with weak initial projection. We also introduce TraitFactory, a new multi-attribute benchmark that focuses on behavioral tendencies rather than surface-level style. We evaluate ORBIT on TraitFactory and ToneBank across three models (Llama-3.2-3B, Qwen-2.5-7B, Llama-3.1-8B) while steering multiple attributes simultaneously, showing that it achieves stronger and more balanced multi-attribute steering than existing training-free baselines while better preserving output coherence.

Abstract

Language Model Steering

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