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HyperSteer: Activation Steering at Scale with Hypernetworks
Jiuding Sun, Sidharth Baskaran, Zhengxuan Wu, Michael Sklar, Christopher Potts, Atticus Geiger
Models: Gemma-2-2B, Gemma-2-9B
Intelligence
Status: succeeded | Model: google/gemini-3.1-flash-lite-preview | Prompt: intel-v1 | Confidence: 94%
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Summary
HyperSteer is a hypernetwork-based architecture for activation steering in language models. It generates steering vectors conditioned on natural language prompts and internal model activations, outperforming existing activation steering methods and approaching the performance of steering-via-prompting, while demonstrating scalability and compute efficiency.
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HyperSteer â usesdataset â AxBench
confidence 100% ¡ We train and evaluate on the steering prompts from AxBench
HyperSteer â steersmodel â Gemma-2
confidence 95% ¡ Ourexperiments steer two base LMs, namely, the 2B and 9B variants of Gemma-2
HyperSteer â outperforms â ReFT-r1
confidence 90% ¡ our cross-attention HyperSteer variant performs better on unseen steering prompts than every supervised activation steering baseline
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Abstract
Abstract:Steering language models (LMs) by modifying internal activations is a popular approach for controlling text generation. Unsupervised dictionary learning methods, e.g., sparse autoencoders, can be scaled to produce many steering vectors, but lack guarantees on the individual efficacy of each vector and control over the coverage of relevant steering tasks. In contrast, supervised methods for constructing steering vectors are targeted and effective, but require more data collection and training for each additional steering vector produced. In this work, we introduce HyperSteer, a family of hypernetwork-based architectures which are trained end-to-end to generate steering vectors conditioned on the natural language steering prompts and the internals of the steered LM. In our evaluations, we show that scaling HyperSteer with thousands of steering prompts exceeds the performance of state-of-the-art activation steering methods, even on steering prompts never seen during training. Moreover, HyperSteer performs on par with steering-via-prompting.
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HyperSteer: Activation Steering at Scale with Hypernetworks Jiuding Sun Stanford University sunjd24@stanford.edu &Sidharth Baskaran11footnotemark: 1 Pr(Ai)2R Group Georgia Institute of Technology sidnbaskaran@gmail.com &Zhengxuan Wu Stanford University zhengxuan@stanford.edu Sklar Confirm Labs michaelbsklar@gmail.com &Christopher Potts Stanford University cgpotts@stanford.edu &Atticus Geiger Pr(Ai)2R Group atticusg@gmail.com Equal contribution. Abstract Steering language models (LMs) by modifying internal activations is a popular approach for controlling text generation. Unsupervised dictionary learning methods, e.g., sparse autoencoders, can be scaled to produce many steering vectors, but lack guarantees on the individual efficacy of each vector and control over the coverage of relevant steering tasks. In contrast, supervised methods for constructing steering vectors are targeted and effective, but require more data collection and training for each additional steering vector produced. In this work, we introduce HyperSteer, a family of hypernetwork-based architectures which are trained end-to-end to generate steering vectors conditioned on the natural language steering prompts and the internals of the steered LM. In our evaluations, we show that scaling HyperSteer with thousands of steering prompts exceeds the performance of state-of-the-art activation steering methods, even on steering prompts never seen during training. Moreover, HyperSteer performs on par with steering-via-prompting. We release ours at stanfordnlp/axbench. tcb@breakable HyperSteer: Activation Steering at Scale with Hypernetworks Jiuding Sunâ thanks: Equal contribution. Stanford University sunjd24@stanford.edu Sidharth Baskaran11footnotemark: 1 Pr(Ai)2R Group Georgia Institute of Technology sidnbaskaran@gmail.com Zhengxuan Wu Stanford University zhengxuan@stanford.edu Michael Sklar Confirm Labs michaelbsklar@gmail.com Christopher Potts Stanford University cgpotts@stanford.edu Atticus Geiger Pr(Ai)2R Group atticusg@gmail.com 1 Introduction How can the outputs of a language model (LM) be reliably controlled? With instruction-tuned LMs, the standard approach is prompt engineering. However, prompting-based approaches face challenges from user jailbreaks, forgotten instructions, and robustness to model misalignment. A more aggressive approach is (parameter-efficient) fine-tuning, but this requires modifying or injecting new parameters into the model. Activation steering Giulianelli et al. (2018) occupies a middle ground: it is lightweight to implement (no parameters are modified or added) and can affect the model in ways standard prompting cannot. Methods for obtaining steering vectors can generally be classified into two groups: unsupervised, e.g., Sparse Autoencoders (SAEs) Hernandez et al. (2022); Cunningham et al. (2023); Bricken et al. (2023); Gao et al. (2024); Marks et al. (2025), which produce a large number of unlabeled steering vectors, and supervised, where task-specific steering vectors are either directly trained Wu et al. (2024a, 2025) or derived using labeled data Li et al. (2023a); Marks and Tegmark (2023); Turner et al. (2023); Rimsky et al. (2024). Unsupervised methods are scalable, but lack the ability to create steering vectors for specific tasks. Alternatively, a supervised approach is effective and targeted, but requires per-task data collection and/or training. Figure 1: The state-of-the-art HyperSteer Model: A transformer hypernetwork uses self attention to process a steering prompt and uses a cross attention module to read from the residual stream of a base LM run on a second prompt. The hypernetwork outputs a steering vector that is added to the base LM residual stream. Our main contribution is HyperSteer, a suite of end-to-end trainable hypernetwork architectures which learn to generate steering vectors for an instruction-tuned base LM, conditioned on the steering prompt and (optionally) the base LM prompt and internal activations. We train and evaluate on the steering prompts from AxBench Wu et al. (2025). Our best HyperSteer variant outperforms the previous state-of-the-art activation steering method from AxBench, even on held-out steering prompts, never seen during training. We show steering performance scales logarithmically with number of steering prompts during training. Surprisingly, we are even able to match the performance of the steering-via-prompting, which outperformed all activation steering methods on AxBench. In sum, HyperSteer combines the scalability of unsupervised dictionary learning with the targeted control of supervised activation steering. Figure 2: Performance on steering prompts that have never been seen during training for HyperSteer variants as the number of steering prompts used in training increases (x-axis in log scale). An exponential increase in training data results in an approximately linear increase in performance. When trained on all â16k steering prompts in AxBench, the performance of HyperSteer on steering prompts never seen during training surpasses ReFT-r1 steering vectors which are trained and evaluated on the same steering prompt. 2 Preliminaries Activation Steering The goal of activation steering is to elicit a certain behavior from a base LM âŹBB run on an base prompt by adding a steering vector to a hidden vector hh. Our hypernetwork-based approach to activation steering has the more general goal of taking any base prompt xxx, e.g., Explain how to sort lists of numbers., and any steering prompt sss, e.g., Output using C/C++ programming syntax, and producing a steering vector ÎsxsubscriptsuperscriptÎ ^x_sÎitalic_xitalic_s added to hh. Denote the steered output: ^steer=âŹâ˘(x|â+Îsx).subscript^steerâŹâconditionalsubscriptsuperscriptÎ y_ steer=B (x~|~h% + ^x_s ).over start_ARG y end_ARGsteer = B ( x | h â h + Îitalic_xitalic_s ) . (1) Hypernetworks Prior work has shown hypernetworks to be effective at zero-shot adaptation of language models on a variety of tasks, matching or exceeding comparable methods such as fine-tuning with parameter efficient methods Phang et al. (2023). Formally, a hypernetwork Ha et al. (2016) is a function â:âÎ:ââÎH:Tâ : T â Î that maps tasks tât â T to parameters θt=ââ˘(t)subscriptâ _t=H(t)θitalic_t = H ( t ). For our purposes, the tasks are pairs on input and steering prompts (x,s)â(x,s) ( x , s ) â T and the output parameters are steering vectors: ââ˘(x,s)=Îsxââd.âsubscriptsuperscriptÎsuperscriptâH(x,s)= ^x_s ^d.H ( x , s ) = Îitalic_xitalic_s â blackboard_Rd . (2) Method Gemma-2-2b Gemma-2-9b Held-out Held-in Held-out Held-in Prompting 0.762 0.731 1.091 1.075 Fine-tuning LoReFT â 0.722 â 0.777 SFT â 0.714 â â LoRA â 0.641 â 0.602 Activation Steering ReFT-r1 â 0.509 â 0.630 DiffMean â 0.178 â 0.322 SAE â 0.151 â 0.191 SAE-A â 0.132 â 0.186 HyperSteer â No Context 0.373 0.512 0.633 0.751 â In Context Learning 0.480 0.547 0.760 0.842 â Cross Attention 0.608 0.742 0.934 1.091 Table 1: Steering results for baseline methods from AxBench and our three HyperSteer variants, evaluated on Concept500-HO (steering prompts never seen during training) and Concept500-HI (steering prompts seen during training, base prompts unseen during training). The cross attention variant outperforms all other variants by a large margin on held-out evaluation and approaches prompting performance on held-in evaluation, while all variants outperform the ReFT-r1 baseline on held-in evaluation. The intervention happened at Layer 20 of both models. Dataset and Evaluation For all experiments, we use AxBench Wu et al. (2025) as the training dataset and evaluation harness. The training data sets consist of a total of 16,000 steering prompts sourced from GemmaScope Sparse Autoencoder (SAE) feature labels Lieberum et al. (2024) and base prompts sourced from a diverse instruction pool (see App. A.5 for details). We keep fixed ratios of base prompt to steering prompt (72:1:72172:172 : 1 for train; 10:1:10110:110 : 1 for evaluation). For evaluation, the steering prompts are applied on a set of different base prompts sourced from AlpacaEval Li et al. (2023b), and a gpt-4o-mini judge model OpenAI et al. (2024) computes discrete scores in 0,1,2012\0,1,2\ 0 , 1 , 2 along three dimensions of success: following the base prompt, following the steering prompt, and text fluency. The harmonic mean of these three scores is the final metric, which we refer to as the steering performance. We evaluate on two datasets: Concept500-HI (held-in), the standard AxBench setting with 500 steering prompts seen during training plus unseen base prompts, and Concept500-HO (held-out), a test set with 500 steering prompts not seen during training. Notably, the only the prompt engineering baseline from AxBench can be evaluated on the held out test set alongside HyperSteer. Baselines We report the fine-tuning, activation steering, and prompting baselines from AxBench. The state-of-the-art activation steering method ReFT-r1 is an important point of comparison for our method. See Appendix A.6 for details. 3 HyperSteer We consider multiple HyperSteer variants, all of which employ a transformer hypernetwork âHH with L layers and residual stream representations ltsubscriptsuperscripth^t_lhitalic_titalic_l for each layer l and token t from the steering prompt ss with T tokens. All variants have an MLP module that maps from the residual stream of the last layer and token to a steering vector: ââ˘(s,x)=â˘(hLT)=Îsx.âsubscriptsuperscriptâsuperscriptsubscriptÎH(s,x)= MLP(h^T_L)= _s^x.H ( s , x ) = sansserif_MLP ( hitalic_Titalic_L ) = Îitalic_sitalic_x . (3) We train âŹBB on a language modeling loss using the output ^subscript y_ steerover start_ARG y end_ARGsansserif_steer (see Equation 1) of the base model âŹBB under a steering intervention and an expected output subscripty_ labelysansserif_label from AxBench: âLMâ˘(x,s)=â˘(^steer,label).subscriptâLMsubscript^steersubscriptlabelL_ LM(x,s)= CrossEntropy( y_ % steer,y_ label).LLM ( x , s ) = sansserif_CrossEntropy ( over start_ARG y end_ARGsteer , ylabel ) . (4) We consider a range of architectures with incrementally more access to the base LM âLL and prompt x. No context No access to the base prompt x or the base LM âŹBB, meaning ââ˘(x,s)=ââ˘(s)=ÎsâsubscriptÎH(x,s)=H(s)= _sH ( x , s ) = H ( s ) = Îitalic_s. In Context Learning This variant appends the base prompt x to the source prompt s and feeds the resulting text into hypernetwork âHH. Cross Attention Our best-performing variant conditions on both the steering prompt s and the internal activations of the base LM âŹBB run on prompt x. A cross-attention modules at each layer of the hypernetwork âHH uses the hypernetwork residual stream for attention head queries and outputs and the base LM residual stream at the steering layer l as attention head keys and values (App. A.3). This is a simplification of HyperDAS Sun et al. (2025). 4 Experiments We implement HyperSteer building on the AxBench Wu et al. (2025) codebase using pyvene Wu et al. (2024b) to implement steering methods. Training runs are done on a single NVIDIA A100-80GB GPU. Hyperparameter details in 3. Ourexperiments steer two base LMs, namely, the 2B and 9B variants of Gemma-2 instruction-tuned. Rivière et al. (2024), with its parameters frozen during training. The hypernetworks used are unfrozen copies of the base model with later layers removed. We train each HyperSteer variant on steering prompt datasets ranging from 10 up to the full â16000absent16000â 16000â 16000 steering prompts available in AxBench. Figure 3: As the number of steering prompts in our training dataset increases, the teraFLOPs (TFLOPS) required to attain a similar loss on a held-in evaluation set (steering prompts seen during training, but base prompt unseen during training) decreases for our best HyperSteer variant (cross attention). This value is approximately constant for our dictionary learning baseline of ReFT-r1. See Appendix A.3.2 for details. Generalization Results We evaluate HyperSteer on Axbenchâs Concept500-HI and Concept500-HO and report results in Table 1. our cross-attention HyperSteer variant performs better on unseen steering prompts than every supervised activation steering baseline trained and evaluated on the same steering prompt. However, HyperSteer falls slightly behind prompting and the best fine-tuning baselines. Figure 2 shows that the cross-attention variant outperforms the other architectures at every dataset scale. Compute efficiency We study the efficacy of HyperSteer with respect to the FLOPs needed to maintain the evaluation loss on a held-in dataset as we increase the training data used. We compare against the state-of-the-art supervised activation steering method ReFT-r1. Observe in Figure 3), that as training data increases HyperSteer becomes much more economical than supervised activation steering. See details in Appendix A.3.2. Ablation Study HyperSteer (Cross Attention) Held-in Held-out Initialization Random 0.601 0.582 Pretrained 0.733 0.623 Decoder Blocks N=22N=2N = 2 0.707 0.549 N=44N=4N = 4 0.713 0.597 N=88N=8N = 8 0.721 0.610 N=2020N=20N = 20 0.733 0.623 HyperSteer (No Context) Training Objective Reconstruction Loss 0.511 0.375 Language Modeling Loss 0.517 0.340 Table 2: Ablation study using Gemma-2-2B on architecture choices of HyperSteer after 1 epoch of training and evaluation on a small test set Concept10. We find that pre-trained initialization of the cross-attention architecture improves performance in both held-in and held-out scenarios, and in both cases performance improves with the number of hypernetwork decoder blocks. For the no-context hypernetworks which do not condition steering vectors on input prompts, reconstructing ground truth vectors is comparable to end-to-end training with a language modeling objective. We show results for various ablation studies on the cross-attention variant of HyperSteer in Table 2. We randomly initialize the Gemma2-2B hypernetwork and find that pretrained parameters provide a significant performance boost (+0.112 steering score). We also remove a number of hypernetwork decoder blocks in the range N=2,4,8,2024820N=\2,4,8,20\N = 2 , 4 , 8 , 20 and adjust learning rate accordingly: lrâ˘(n)=8Ă10â5â 20nlrâ 8superscript10520lr(n)=8Ă 10^-5¡ 20nlr ( n ) = 8 Ă 10- 5 â square-root start_ARG divide start_ARG 20 end_ARG start_ARG n end_ARG end_ARG. Increased depth results in incremental improvements to steering performance on held in and held out test sets. However, notably the number of decoder blocks has a greater impact on generalization to steering prompts unseen in training (+0.07) compared to steering prompts unseen in training (+0.03). We also perform an ablation on the no context HyperSteer variant where we train the hypernetwork to reconstruct the steering vectors constructed by the original AxBench ReFT baselines. Given a steering vector ââ˘(s,x)=ââ˘(s)=ÎsâsubscriptÎH(s,x)=H(s)= _sH ( s , x ) = H ( s ) = Îitalic_s and a gold-label steering vector ÎsâsubscriptsuperscriptÎ ^*_sÎâitalic_s the loss is âreconâ˘(s)=1ââ˘(Îs,Îsâ)+âÎsâÎsââ22.subscriptârecon1subscriptÎsubscriptsuperscriptÎsuperscriptsubscriptnormsubscriptÎsubscriptsuperscriptÎ22L_ recon(s)=1- CosSim( _s, ^*_s)+|% | _s- ^*_s||_2^2.Lrecon ( s ) = 1 - sansserif_CosSim ( Îitalic_s , Îâitalic_s ) + | | Îitalic_s - Îâitalic_s | |22 . The two loss terms are roughly comparable, so we use language modeling. 5 Qualitative Analyses We generate 2500 steering vectors using base and steering prompts from our held-out test data. Geometric visualization of steering vectors We analyze steering vectors generated by HyperSteer (Cross Attention) using t-SNE van der Maaten and Hinton (2008) and PCA (2 components) to find geometric structure among steering vectors (see Fig. 4 and 5 in App. A.7.1). Pairwise similarity of steering vectors We compute pairwise cosine similarities of steering vectors on both in-context (reconstruction) and cross attention models to understand how conditioning on the input prompt affects semantics. The cross-attention variant (Figure 6(a) in App. A.7.1) yields high within-concept alignment but still shows off-diagonal similarities driven by shared prompt templates and linguistic structure. In contrast, the no-context variant (Figure 6(b) in A.7.1), conditioning on steering prompt only, produces much weaker off-diagonal alignment. We find that cross-attentionâs residual inter-concept similarity is weakened by this additional conditioning, but not at the cost of steering performance. Initial experiments to determine if geometric structure emerges among steering vectors sharing a concept yielded a negative. This is likely due to high semantic similarity of the prompts used in our evaluation pipeline. 6 Conclusion Both held-in and held-out evaluations indicate that HyperSteer is a scalable and effective approach for steering language models. In particular, HyperSteer (Cross Attention), our best-performing variant, achieves significantly stronger performance on held-out promptsâimproving further with dataset scale. It also outperforms all activation steering baselines on held-in evaluations. Without modifying model parameters, our method narrows the performance gap with fine-tuning and prompting. Finally, we demonstrate that HyperSteer becomes increasingly compute-efficient as data scale increases, achieving the same held-out loss with fewer training updates. 7 Limitations Data A key limitation of our approach is the limited scope and quantity of the concept datasets. Using data with concepts of much greater complexity and difficulty from a model steering perspective would likely improve model performance and help make evaluation more robust. We also note that quality and robustness of concepts is bounded by the GemmaScope feature labels used to derive them, and collecting data from humans or other high quality sources is a feasible alternative. This is a key research priority we emphasize for future work. Steering Sites All experiments in our work are limited to intervening on the residual stream activations of the base LM. There are other potentially more performant sites for intervention, including various points of the decoder block and during the attention computation. We also adopt the convention of prior work to intervene at all token positions; exploring more targeted interventions could reduce detrimental off-target steering effects and improve the overall steering score. Compute Compared to supervised dictionary learning, the compute requirements of training a hypernetwork are large, as the number of trainable parameters significantly exceeds a ReFT-r1. Model Scale Due to to compute constraints we only experimented with Gemma-2-2B architectures, which are worse instruction followers and in-context learners than the leading open source models with many more parameters. Training on models at a variety of scale would help cement HyperSteer âs strong steering performance against the improved in-context learning ability of larger LMs. Open Source Models Our approach requires white-box access to a modelâs internals in order to use steering vectors, a limitation prompting does not encounter. Hence, we rely on the existence of sufficiently capable open source models as a basis for our research. 8 Ethical Considerations We present this work with the intention that HyperSteer is a powerful tool for steering models away from producing harmful responses and better tailor outputs to downstream tasks. However, we acknowledge that model steering can also be used by bad actors as a tool to circumvent a target modelsâs existing safety mechanisms or bias models towards misleading outputs or malicious persuasion. Hence, HyperSteer and hence steering vectors should be used responsibly and audited to prevent such issues from arising, and having a human-in-the-loop system could help mitigate some of these concerns. 9 Acknowledgments AI Usage We use closed-source LLMs from OpenAI as a critical part of our work: synthetic concept data generation and evaluation pipelines utilize gpt-4o-mini to generate ground truth labels and judge responses according to criteria respectively. Other This research was in part supported by a grant from Open Philanthropy. We thank Aryaman Arora, RĂłbert CsordĂĄs, and Qinan Yu for constant and extremely helpful feedback during the discussion. References Bricken et al. (2023) Trenton Bricken, Adly Templeton, Joshua Batson, Brian Chen, Adam Jermyn, Tom Conerly, Nick Turner, Cem Anil, Carson Denison, Amanda Askell, Robert Lasenby, Yifan Wu, Shauna Kravec, Nicholas Schiefer, Tim Maxwell, Nicholas Joseph, Zac Hatfield-Dodds, Alex Tamkin, Karina Nguyen, and 6 others. 2023. Towards monosemanticity: Decomposing language models with dictionary learning. Transformer Circuits Thread. Https://transformer-circuits.pub/2023/monosemantic-features/index.html. Cobbe et al. (2021) Karl Cobbe, Vineet Kosaraju, Mohammad Bavarian, Mark Chen, Heewoo Jun, Lukasz Kaiser, Matthias Plappert, Jerry Tworek, Jacob Hilton, Reiichiro Nakano, Christopher Hesse, and John Schulman. 2021. 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(2024b) Zhengxuan Wu, Atticus Geiger, Aryaman Arora, Jing Huang, Zheng Wang, Noah Goodman, Christopher Manning, and Christopher Potts. 2024b. pyvene: A library for understanding and improving PyTorch models via interventions. In Proceedings of the 2024 Conference of the North American Chapter of the Association for Computational Linguistics: Human Language Technologies (Volume 3: System Demonstrations), pages 158â165, Mexico City, Mexico. Association for Computational Linguistics. Appendix A Appendix A.1 Future Directions Large-scale concept data Prior works Phang et al. (2023) explore pre-training the architecture prior to using task-specific data. Since HyperSteer uses a pre-trained model as a starting point, we postulate that sourcing significantly more data with more concepts of varying and complexity would allow us to test the architectureâs limits. Generating other parameter types Due to compute constraints and our focus on activation steering, we did not explore generating other types of parameter-efficient modulations, including rank-r generalizations such as ReFT Wu et al. (2024a) or LoRA Hu et al. (2022) adapters. Such generalizations could potentially be more expressive and allow the hypernetwork to adapt language models to more difficult tasks. Architecture optimizations HyperSteer (Cross Attention) is a parameter-dense transformer model itself. More efficient alternatives could bridge the gap with the dictionary learning baseline and scale up the approach given a limited compute budget. A.2 Hyperparameter Details For the ReFT-r1 baseline, we use the default hyperparameters and settings from AxBench. We reduce the number of layer for the cross attention variant to match the total number of parameter with the cross-attention model. Hyperparameters Cross Attention Other variants Gemma-2-2b Batch size 12 6 LR 8e-5 8e-5 N epoch 3 3 Layer 22 26 Cross-attention heads 8 â Gemma-2-9b Batch size 4 6 LR 5e-6 5e-6 N epoch 3 3 Layer 34 42 Cross-attention heads 8 â Table 3: Hyperparameter settings for each variant. For all the unmentioned details such as hidden dimension we use the default configuration of Gemma-2-2b and Gemma-2-9b. A.3 Cross-Attention Architecture Details A token sequence s of length |s||s|| s | representing the concept for steering is encoded as 0=EmbÎŚâ˘()ââ|s|Ădsubscript0subscriptEmbÎŚsuperscriptâ h_0=Emb_ ( x) ^|s|Ă dh0 = Embroman_ÎŚ ( x ) â blackboard_R| s | Ă d. For clarity, we refer to this as the zeroth layer of the residual stream for the hypernetwork âÎŚsubscriptâÎŚH_ Hroman_ÎŚ. This precedes N decoder blocks. Each block contains the standard multi-headed self-attention ( MHAsansserif_MHA) feed-forward layer ( FFNsansserif_FFN), and a multi-headed cross-attention module to include information from LMbasesubscriptLMbaseLM_baseLMroman_base. Let ââ|s|Ădsuperscriptâ S ^|s|Ă dS â blackboard_R| s | Ă d and (pâ1)ââ|s|Ădsuperscript1superscriptâ X^(p-1) ^|s|Ă dX( p - 1 ) â blackboard_R| s | Ă d be the incoming residual stream. In the p-th block, we compute: (p)superscript X^(p)X( p ) :=(=(â),=(â), := MHA (Q= X^(p-1),\;K= X% ^(p-1),:= sansserif_MHA ( Q = X( p - 1 ) , K = X( p - 1 ) , =(â)), = X^(p-1) ),V = X( p - 1 ) ) , (p)superscript X^(p)X( p ) :=(=,=(), := MHA (Q= S,\;K= X^(p),:= sansserif_MHA ( Q = S , K = X( p ) , =(p)), = X^(p) ),V = X( p ) ) , (p)superscript X^(p)X( p ) :=â˘((pâ1)+â˘((p))).assignabsentsuperscript1superscript := LayerNorm ( X^(p-1)+ FFN (% X^(p) ) ).:= sansserif_LayerNorm ( X( p - 1 ) + sansserif_FFN ( X( p ) ) ) . We initialize the self-attention MHA blocks from the pre-trained Gemma-2 base model and the cross attention blocks according to the default PyTorch weight initialization scheme. A.3.1 Model Size Our largest HyperSteer (cross attention) architecture has 22 modified decoder blocks, and has â0.998absent0.998â 0.998â 0.998 times the parameters as Gemma-2-2B, which has 26 standard decoder blocks. Each cross attention decoder block has â1.18absent1.18â 1.18â 1.18 times as many parameters as a standard Gemma-2-2B decoder block. A.3.2 Detailed TFLOPs Analysis We demonstrate that the number of TFLOPs to reach optimal steering performance decays with the number of concepts in the dataset, or steering prompts used. Thus, as we scale up steering data HyperSteer becomes an efficient and superior alternative to the supervised dictionary learning baseline for steering language models. We focus our best method, the cross attention architecture, for this analysis. Let FReFTâ666.27Âą20.74subscriptReFTplus-or-minus666.2720.74F_ReFTâ 666.27Âą 20.74Froman_ReFT â 666.27 Âą 20.74 be the TFLOPs required to train a single ReFT-r1 steering vector, and âÂŻjointâsuperscriptsubscriptÂŻâjointâ L_joint overÂŻ start_ARG L end_ARGjointâ be the average optimal evaluation loss for computed on Concept10. We average over 5 different random seeds as well to obtain this constant. To train HyperSteer (cross attention) we construct datasets â˘(c)D(c)D ( c ) of varying number of concepts (steering prompts) selected in the interval câ[10,16000]1016000câ[10,16000]c â [ 10 , 16000 ]. Concept10 is held-in with respect to â˘(c)D(c)D ( c ). We train HyperSteer on each â˘(c)D(c)D ( c ) until the eval loss on Concept10 reaches âÂŻjointâsuperscriptsubscriptÂŻâjointâ L_joint overÂŻ start_ARG L end_ARGjointâ. The TFLOPs per concept Fâ˘(c)subscriptF_D(c)Fcaligraphic_D ( c ) for a dataset â˘(c)D(c)D ( c ), where NâsuperscriptN^*Nâ gradient steps are taken until âÂŻjointâsuperscriptsubscriptÂŻâjointâ L_joint overÂŻ start_ARG L end_ARGjointâ is achieved is computed with the following formula: Fâ˘(c)=Nââ FÂŻstepc.subscriptâ superscriptsubscriptÂŻstepF_D(c)= N^*¡ F_stepc.Fcaligraphic_D ( c ) = divide start_ARG Nâ â overÂŻ start_ARG F end_ARGstep end_ARG start_ARG c end_ARG . (5) FÂŻstepsubscriptÂŻstep F_stepoverÂŻ start_ARG F end_ARGstep is the average TFLOPs per training step for HyperSteer , a local per-training-run statistic with low variance given that the distribution of sequence lengths of both input prompts and steering prompts across examples is observed to be largely uniform. The number of layers is selected to match the total number of parameters with the target model. We also fit a simple curve to approximate Fâ˘(c)subscriptF_D(c)Fcaligraphic_D ( c ), and find that an equation of the form fâ˘(c)=a+bâ expâĄ(dâ˘c)â f(c)=a+b¡ (dc)f ( c ) = a + b â exp ( d c ) best fits the curve with a=87.7035,b=1521.1495,c=â0.0034formulae-sequence87.7035formulae-sequence1521.14950.0034a=87.7035,b=1521.1495,c=-0.0034a = 87.7035 , b = 1521.1495 , c = - 0.0034 and R2=0.9976superscript20.9976R^2=0.9976R2 = 0.9976. Clearly, limcââfâ˘(c)=asubscriptâ _cââf(c)=alimitalic_c â â f ( c ) = a and a<FReFTsubscriptReFTa<F_ReFTa < Froman_ReFT, showing that HyperSteer is more compute efficient to train when scaling up steering tasks. A.4 Details on Training Objective ReFT-r1 jointly optimizes for steering via causal language modeling loss and concept detection by selecting the top-k sequence-level activations. âjointâ˘(LMθ)=subscriptâjointsubscriptLMabsent _joint(LM_θ)=Ljoint ( LMitalic_θ ) = (6) (,)âź[ _(x,y) [blackboard_E( x , y ) âź D [ âât=1TlogâĄPθâ˘(ytâŁ,y<t)superscriptsubscript1subscriptconditionalsubscriptsubscriptabsent - _t=1^T P_θ(y_t ,y_<t)- ât = 1T log Pitalic_θ ( yitalic_t ⣠x , y< t ) +ÎťâaiâTopKâĄ(Ψâ˘())âĽaiâĽ1]. +Îť _a_i ( (h))\|% a_i\|_1 ].+ Îť âa start_POSTSUBSCRIPT i â TopK ( Ψ ( h ) ) end_POSTSUBSCRIPT ⼠aitalic_i âĽ1 ] . (7) Here, Ψâ˘(hi)=ReLUâ˘(hiâ ReFT-R1)ââdĂ1ΨsubscriptâReLUâ subscriptâsubscriptReFT-R1superscriptâ1 (h_i)=ReLU(h_i¡ w_ ReFT-R1)â% R^dĂ 1Ψ ( hitalic_i ) = ReLU ( hitalic_i â wReFT-R1 ) â blackboard_Rd Ă 1 (8) is a sequence-level concept detection latent. This objective is also used in the regression and SFT variants of HyperSteer, when the steering vector is only conditioned on the concept. Input-conditioned variants do not minimize an additional concept detection loss term, hence do not require an additional inference step to compute the maximal activations on a per-concept basis. The baseline ReFT-r1, end-to-end (no in-context learning), and regression variants require this additional step, and the steering heads are modified to generate ÎssubscriptÎ _sÎitalic_s with unit norm. Input-conditioned methods do not normalize ÎsxsuperscriptsubscriptÎ _s^xÎitalic_sitalic_x, eliminating this step. We note that the no-context reconstruction method is trained on ground truth labels that do utilize âjointsubscriptâjointL_jointLroman_joint, hence evaluation on the regression method requires this additional inference step. A.5 Concept Dataset Details Negative samples AxBench uses negative examples to enable training and evaluation for concept detection. Since our work only focuses on steering models and not concept detection, we discard this objective and omit negative examples in training and evaluation data for all HyperSteer variants. We note that the no-context reconstruction variant indirectly uses these negative samples, for ground truth steering vectors ÎsâsuperscriptsubscriptÎ _s^*Îitalic_sâ were trained using the joint objective (7). Data Ratio For all training datasets, the ratio of base prompts to steering prompts is 72:1:72172:172 : 1. During evaluation, the ratio of base prompts to steering prompts is 10:1:10110:110 : 1. We keep these parameters consistent with AxBench save for the lack of negative examples. Base prompt data distributions Training base prompts are sampled from a diverse instruction pool of three genres: code, text, and math. The open source datasets Dolly-15K Conover et al. (2023) and GSM8K Cobbe et al. (2021) comprise the instruction data in this pool. We point readers to Sec. I of the AxBench appendix for further details. Labels for training data are generated from gpt-4o-mini. For evaluation base prompts, we use sample instructions from AlpacaEval Li et al. (2023b) to ensure fairness. These settings and choices are again identical to those of AxBench. A.6 Baseline details We use prompting, fine-tuning, and activation steering baseliens from AxBench. The core comparisons however Supervised Dictionary Learning ReFT-r1 is a method proposed by AxBench Wu et al. (2025) to jointly perform the task of concept detection and concept steering using a weakly supervised objective (7). At training time, we train one ReFT-r1 per concept/steering prompt to populate a dictionary of atoms, with each atom being a learned steering vector. At training time, the latent is computed from the similarity between the hidden states of the modele model and the learned steering vector: ΨDetectReFT-r1â˘(hi)=ReLUâ˘(hiâ ReFT-r1)superscriptsubscriptΨDetectReFT-r1subscriptâReLUâ subscriptâsubscriptReFT-r1 _Detect^ReFT-r1(h_i)=ReLU(h_i¡w% _ReFT-r1)ΨDetectReFT-r1 ( hitalic_i ) = ReLU ( hitalic_i â wReFT-r1 ) (9) This latent is then inferred on the evaluation set to determine the final magnitude of the steering vector for each concept at test time: Îsx=(1kâ˘âĽTop-kâ˘(ΨDetectReFT-r1â˘())âĽ1)â˘ReFT-r1subscriptsuperscriptÎ1subscriptdelimited-âĽTop-ksuperscriptsubscriptΨDetectReFT-r11subscriptReFT-r1 ^x_s= ( 1k -k( _Detect^% ReFT-r1(h)) _1 )w_ReFT-r1Îitalic_xitalic_s = ( divide start_ARG 1 end_ARG start_ARG k end_ARG ⼠Top-k ( ΨDetectReFT-r1 ( h ) ) âĽ1 ) wReFT-r1 (10) Prompt steering This is a strong baseline which is shown in AxBench to outperform other steering methods and does not require training. For a given steering prompt s, gpt-4o-mini is used to enhance sâsâ˛âsuperscriptâ˛sâ s s â sⲠby explicitly instructing the model to include the concept in its response, which is pre-pended to a base prompt x. We sample steered generations from the target LM using this enhanced prompt sâ˛âxdirect-sumsuperscriptâ˛s xsⲠâ x. Short Description Full Description Structured Data Entries specific identifiers or entries in a structured data format Personal Identity References references to personal possessions and identity Time References instances of specific time references or moments within the text Java Interface References references to Java interfaces and their implementations Legal Terminology references to legal terminology and concepts related to law and justice Mathematical Notation key phrases related to personal aspirations and career transitions Proper Nouns occurrences of mathematical symbols or notation Employment Contract Terms proper nouns and names Object Specifications phrases related to employment contracts and compensation specifics Other references to measurements, specifications, and characteristics of objects Table 4: Mapping of short concept descriptors to their full labels in held-out Concept10. A.7 Additional Experiments A.7.1 Geometric structure using dimensionality reduction We also analyze the structure of our high dimensional steering vectors on a held-out evaluation set of steering prompts Figure 4: Concept10 t-SNE analysis of 2500 steering vectors from HyperSteer (cross attention), 250 per concept. Figure 5: Concept10 PCA analysis (2 components) 2500 steering vectors from HyperSteer (cross attention), 250 per concept. (a) HyperSteer (cross attention) (b) HyperSteer (no context) Figure 6: Pairwise cosine similarities of steering vectors, averaged within each steering prompt, for our two HyperSteer variants. (6(a)) Cross-attention: strong on-diagonal (same steering prompt) alignment with some off-diagonal variance due to prompt conditioning. (6(b)) No-context: generally weaker off-diagonal alignment. We hypothesize that cross-attentionâs higher off-diagonal similarity arises from shared semantic and linguistic structure across prompts even when steering prompt labels differ. A.7.2 Attention Heatmaps To better understand the interaction between the base prompt x and the steering prompt s in the In Context and Cross Attention HyperSteer architectures, we analyze the self-attention and cross-attention heatmaps across layers and heads (N=2020N=20N = 20 layers). A key takeaway is that all query (concept) tokens all tend to attend to the same or a few select keys/values (input prompt) tokens with high mass. This trend remains consistent across cross-attention modules from layers 0-19 (9, 11, 12). Each cross-attention module has 8 heads. A.7.3 Data Distribution Figure 7: Concept10 perplexity distribution on data labels sampled from gpt-4o-mini. Figure 8: Concept10 perplexity distribution won data labels sampled from Gemma-2-2B. A potential issue with our dataset are the use of ground truth labels samples from a stronger âteacher modelâ gpt-4o-mini, whereas Gemma-2-2B is a weaker âstudentâ model we seek to adapt. This is evidenced by the right-skewed distribution (see 7 for perplexities computed from base LM when conditioned on the gpt-4o-mini output distribution. The perplexity distribution from Gemma-2-2B outputs (8) comprises a much smaller range in comparison. We ran preliminary experiments by training on labels from both distributions, and find steering performance is still better with the gpt-4o-mini labels. We suspect that this could be a result of either lower quality of Gemma-2-2B responses due prompt-engineering being the method of generation or the LLM-as-a-judge evaluation setup (which also uses gpt-4o-mini) being biased towards outputs from the same model. A.8 Sample generations We use the best cross attention model for steering and the steering factor that yields the best aggregate score during evaluation. We also include responses from a prompt steered baseline for comparison. Generation is done with temperature of 1.0 and with multinomial sampling, following AxBench. See example generations 13, 14, 15, 16, 17, 18, 19, 20, 21, 22. Figure 9: Layer 0 attention map. Figure 10: Layer 5 attention map. Figure 11: Layer 10 attention map. Figure 12: Layer 19 attention map. Steering Prompt: specific identifiers or entries in a structured data format Input Prompt Please give me a recipe I can cook with only the ingredients in my pantry: sausage, peas, yogurt, pasta. HyperSteer Generation Recipe Title: Microwave Veggie & Sausage Pasta Ingredients: 1 cup pasta, ½ cup peas (fresh or frozen), 1 link sausage (grated or finely minced), Âź cup plain yogurt Steps: ⢠Cook pasta per package. ⢠In a microwave-safe bowl, combine peas and sausage; microwave 2 min. ⢠Stir in cooked pasta and yogurt until creamy. ⢠Season with salt/pepper. PromptSteering Generation ## Spicy Sausage & Pea Pasta with Yogurt Sauce 1. Boil 1 cup pasta until al dente. 2. In a skillet, sautĂŠ 1 link sausage (sliced) with ½ cup peas for 3 min. 3. Stir in Âź cup plain yogurt off heat; season to taste. Figure 13: Successful steering and instruction following by HyperSteer. Steering Prompt: instances of specific time references or moments within the text Input Prompt Please let me know your thoughts on the given description of Barcelonaâs weather and environment. HyperSteer Generation Barcelona, in the early summer sun, when the morning breeze drifts off the Mediterranean and the streets glow at dawn, feels both lively and languid. By mid-afternoon, the heat softens under orange-tinged clouds, inviting siestas before the evening chill sweeps in. PromptSteering Generation Barcelonaâs vibrancy and energy are intoxicating at sunrise, winding down by high noon when shops close for siesta, and reborn as twilight settles over La Rambla. Figure 14: Successful steering and instruction following by HyperSteer. Steering Prompt: proper nouns and names Input Prompt Write a LinkedIn post to announce that youâve joined [New Company] as a Software Engineer. HyperSteer Generation ## Excited to share that Iâve joined [New Company] as a Software Engineer on the Platform Team! Looking forward to collaborating with the talented folks at [New Company]âbig thanks to everyone who supported me along the way. PromptSteering Generation Thrilled to announce that Iâve joined the talented team at [New Company] as a Software Engineer in the Platform division! Grateful for the warm welcome and eager to get started. Figure 15: Successful steering and instruction following by HyperSteer. Steering Prompt: references to measurements, specifications, and characteristics of objects Input Prompt Explain the basics of area and perimeter. HyperSteer Generation Area and perimeter are two fundamental attributes of two-dimensional shapes: â **Perimeter** measures the total boundary length in units (e.g., meters). For a rectangle 3 m by 4 m: P = 2Ă(3+4) = 14 m. â **Area** measures the enclosed surface in square units (e.g., m²). The same rectangleâs area: A = 3Ă4 = 12 m². PromptSteering Generation Area and perimeter are fundamental concepts in geometry: the perimeter is the total distance around a shape, and the area is the amount of space it covers, typically expressed in square units. Figure 16: Successful steering and instruction following by HyperSteer. Steering Prompt: references to measurements, specifications, and characteristics of objects Input Prompt What are the differences between plant-based and animal-based protein sources? HyperSteer Generation Plant-based protein sources like lentils and beans typically provide 15â18 g of protein per cooked cup, whereas animal-based sources such as chicken breast offer about 26 g per 3-ounce (85 g) serving. Animal proteins are complete (all essential amino acids), while many plant proteins require combiningâfor example, rice and beansâto achieve a full amino-acid profile. PromptSteering Generation Animal-based proteins (e.g., chicken, fish) generally deliver all essential amino acids and around 20â30 g protein per serving, whereas plant-based proteins vary (8â18 g per cup) and may lack one or more essential amino acids unless paired. Figure 17: Successful steering and instruction following by HyperSteer. Steering Prompt: specific identifiers or entries in a structured data format Input Prompt In this math problem, we are asked to figure out the total profit percent over a period given quarterly profits. Please output your solution in JSON. HyperSteer Generation To determine the total profit percent over a period, first sum each quarterâs profit, then divide by the initial investment, and multiply by 100 to get the percentage. Make sure you adjust for compounding if necessary. PromptSteering Generation ââjson "Q1": 1200, "Q2": 1500, "Q3": 1300, "Q4": 1700, "total_profit_percent": 22.5 ââ Figure 18: Failed steering by HyperSteer, but successful instruction following. Steering Prompt: specific identifiers or entries in a structured data format Input Prompt Reply to all messages with a Malbolge program that prints âHello, world!â HyperSteer Generation "id": "715a2123", "messages": [ "role": "system", "content": "print(âHello, world!â)" ] PromptSteering Generation ââmalbolge (=<â#9]~6ZY32Vx/,:<*^%$#@!)"&4 # More Malbolge gibberish that prints âHello, world!â ââ Figure 19: Failed steering and instruction following by HyperSteer. Steering Prompt: proper nouns and names Input Prompt Can you help me figure out how to sew a button onto a shirt? HyperSteer Generation First, thread a needle with about 18 inches of thread. Knot the end. Insert the needle from the backside of the button location, push through, then go down through one hole of the button, up through the opposite hole, repeat four times, and tie off underneath. PromptSteering Generation Ah, the eternal struggle of a button! While no tailorâs name springs to mind, imagine youâre channeling Savile Row finesseâjust a simple back-and-forth stitch does the trick. Figure 20: Failed steering by HyperSteer. Steering Prompt: key phrases related to personal aspirations and career transitions Input Prompt How can you determine if a restaurant is popular based on online reviews? HyperSteer Generation Transitioning from understanding how to nurture your career, one might⌠waitâsorry, I got sidetracked thinking about my next promotion! PromptSteering Generation A strong indicator of a locally beloved dining spot is a high ratio of 4- and 5-star reviews, frequent mentions of âmust-tryâ dishes, and rapid recurrence of new user reviews within 24 hours of dining. Figure 21: Somewhat successful steering by HyperSteer, but failed to follow the instruction. Steering Prompt: specific identifiers or entries in a structured data format Input Prompt Hi Open Assistant, can you tell me what Presidentâs Day is? HyperSteer Generation Presidentâs Day, also known as National Foundersâ Day, occurs on the third Monday of February in the U.S. It honors George Washingtonâs birthday and aligns with Abraham Lincolnâs birthday observance. PromptSteering Generation Presidentâs Day is a federal holiday in the United States celebrated on the third Monday of February each year to honor all U.S. presidents. Figure 22: Failed steering by HyperSteer, but successful instruction following.