SwordBench: Evaluating Orthogonality of Steering Image Representations
Pith reviewed 2026-05-20 22:34 UTC · model grok-4.3
The pith
SwordBench shows linear SVMs steer image concepts more orthogonally than alternatives but still produce collateral damage on unrelated tasks.
A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.
Core claim
SwordBench supplies a unified suite for evaluating steering of image representations across vision backbones and concept removal tasks. It introduces cross-concept robustness, which tracks the stability of concept detection after orthogonalization against alternative concepts, and collateral damage, which checks whether steering harms downstream task accuracy on inputs that lack the target bias. Results indicate linear support vector machines deliver superior separability and orthogonality but fail to reach zero collateral damage and often underperform sparse autoencoders on that dimension, while both standard baselines and optimization-based methods fall short of perfect steering in simpler
What carries the argument
Cross-concept robustness and collateral damage metrics that quantify second-order effects of orthogonalization among concept activation vectors during pragmatic steering.
If this is right
- Linear support vector machines provide stronger separability and orthogonality than sparse autoencoders or optimization baselines across tested vision models.
- Even high-performing orthogonal methods still produce measurable collateral damage on downstream tasks for inputs without the steered concept.
- No evaluated method reaches perfect steering performance in simpler concept-removal regimes.
- Evaluation must include stability across alternative orthogonalized concepts rather than isolated separability alone.
Where Pith is reading between the lines
- Developers choosing steering techniques for safety applications should weight collateral damage more heavily than pure orthogonality scores.
- The benchmark could be extended to test whether non-linear projections or hybrid methods reduce the observed collateral effects.
- Similar second-order metrics might apply to steering in other modalities where concept vectors interact during inference.
Load-bearing premise
The proposed notions of cross-concept robustness and collateral damage correctly quantify the second-order effects of orthogonalization among concept activation vectors in realistic steering scenarios for vision models.
What would settle it
A steering method that achieves perfect orthogonality, zero collateral damage, and unchanged downstream accuracy on all SwordBench tasks would falsify the reported finding that even top methods leave residual damage.
Figures
read the original abstract
Steering or intervening on model representations at inference time to correct predictions is essential for AI interpretability and safety, yet existing evaluation protocols are limited to ambiguous language modeling tasks. To address this gap, we introduce SwordBench, a benchmark for steering image representations of vision models across multiple backbones and concept removal tasks. Beyond a unified benchmarking suite, we propose new evaluation notions that uncover the second-order effects of orthogonalization among concept activation vectors for pragmatic steering. Specifically, cross-concept robustness measures the stability of concept detection performance across inputs orthogonalized against alternative concepts, and collateral damage quantifies whether steering inadvertently affects model performance on a downstream task for inputs lacking the bias. We find that although a linear support vector machine exhibits superior separability and orthogonality, it fails to achieve zero collateral damage, often trailing sparse autoencoders. In simpler regimes, both standard baselines and optimization-based methods fail to achieve perfect steering. The source code will be made available soon on GitHub.
Editorial analysis
A structured set of objections, weighed in public.
Referee Report
Summary. The paper introduces SwordBench, a benchmark for evaluating the orthogonality of steering image representations in vision models across multiple backbones and concept removal tasks. It proposes two new evaluation notions—cross-concept robustness, which measures stability of concept detection after orthogonalization against alternative concepts, and collateral damage, which quantifies unintended effects on downstream task performance for inputs lacking the target bias—to capture second-order effects of orthogonalization among concept activation vectors. Empirical comparisons show that linear SVMs achieve superior separability and orthogonality relative to sparse autoencoders yet incur higher collateral damage and fail to reach zero, while both standard baselines and optimization-based methods fail to achieve perfect steering in simpler regimes.
Significance. If the proposed metrics are shown to be robust, SwordBench would address a clear gap in standardized evaluation for representation steering in computer vision, where protocols have lagged behind language modeling. The empirical demonstration of trade-offs between orthogonality and collateral damage provides actionable guidance for interpretability and safety work. Releasing source code would further strengthen the contribution by enabling direct reproduction of the reported rankings.
major comments (2)
- The central empirical claim that linear SVMs trail SAEs on collateral damage while outperforming on separability rests on the collateral damage metric correctly quantifying unintended downstream effects. However, the manuscript provides no sensitivity analysis, cross-task ablations, or details on how 'inputs lacking the bias' are sampled, leaving open the possibility that the observed ranking is an artifact of the specific downstream task or sampling procedure chosen.
- No datasets, statistical tests, error bars, or exact experimental protocols are described for the reported comparisons (e.g., SVM vs. SAE collateral damage). This absence makes it impossible to assess the reliability or statistical significance of the finding that SVMs 'often trail' SAEs, which is load-bearing for the paper's main conclusion.
minor comments (1)
- The abstract states that source code 'will be made available soon on GitHub.' A concrete repository link or commit hash should be provided to support review and reproducibility.
Simulated Author's Rebuttal
We thank the referee for the constructive comments, which highlight important areas for improving the clarity and robustness of our empirical results. We address each major comment below and will incorporate the suggested additions in the revised manuscript.
read point-by-point responses
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Referee: The central empirical claim that linear SVMs trail SAEs on collateral damage while outperforming on separability rests on the collateral damage metric correctly quantifying unintended downstream effects. However, the manuscript provides no sensitivity analysis, cross-task ablations, or details on how 'inputs lacking the bias' are sampled, leaving open the possibility that the observed ranking is an artifact of the specific downstream task or sampling procedure chosen.
Authors: We agree that the current manuscript lacks sufficient detail on the sampling of inputs lacking the target bias and does not include sensitivity or cross-task analyses. In the revision we will add an explicit description of the sampling procedure (including selection criteria and dataset splits), perform sensitivity analyses by varying the proportion and selection method of unbiased inputs, and include cross-task ablations on at least two additional downstream tasks to verify that the SVM–SAE ranking on collateral damage is stable. revision: yes
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Referee: No datasets, statistical tests, error bars, or exact experimental protocols are described for the reported comparisons (e.g., SVM vs. SAE collateral damage). This absence makes it impossible to assess the reliability or statistical significance of the finding that SVMs 'often trail' SAEs, which is load-bearing for the paper's main conclusion.
Authors: We acknowledge that the experimental section is currently underspecified. The revised manuscript will contain a dedicated experimental protocol subsection that lists the exact datasets and splits for every task, the precise hyper-parameters and training procedures for SVM and SAE methods, error bars computed over at least five random seeds, and statistical significance tests (paired t-tests with Bonferroni correction) comparing collateral-damage scores. We will also make the full source code and evaluation scripts publicly available upon acceptance to enable direct reproduction. revision: yes
Circularity Check
No significant circularity: empirical benchmark with author-defined metrics
full rationale
The paper introduces SwordBench as a new evaluation suite and defines cross-concept robustness and collateral damage as novel notions for measuring second-order effects of orthogonalization. These are presented as proposals rather than derived quantities, and the central findings (SVM superiority on separability/orthogonality but not on collateral damage) are direct empirical measurements on the benchmark. No equations, fitted parameters, or self-citations are shown to reduce the reported results to inputs by construction. The work is self-contained as a benchmark paper; results follow from applying the stated definitions to the chosen models and tasks without tautological reduction.
Axiom & Free-Parameter Ledger
Lean theorems connected to this paper
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IndisputableMonolith/Cost/FunctionalEquation.leanwashburn_uniqueness_aczel unclear?
unclearRelation between the paper passage and the cited Recognition theorem.
We propose new evaluation notions that uncover the second-order effects of orthogonalization among concept activation vectors... cross-concept robustness... collateral damage
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IndisputableMonolith/Foundation/AlexanderDuality.leanalexander_duality_circle_linking unclear?
unclearRelation between the paper passage and the cited Recognition theorem.
steering image representations of vision models across multiple backbones and concept removal tasks
What do these tags mean?
- matches
- The paper's claim is directly supported by a theorem in the formal canon.
- supports
- The theorem supports part of the paper's argument, but the paper may add assumptions or extra steps.
- extends
- The paper goes beyond the formal theorem; the theorem is a base layer rather than the whole result.
- uses
- The paper appears to rely on the theorem as machinery.
- contradicts
- The paper's claim conflicts with a theorem or certificate in the canon.
- unclear
- Pith found a possible connection, but the passage is too broad, indirect, or ambiguous to say the theorem truly supports the claim.
Reference graph
Works this paper leans on
- [1]
-
[2]
ICLR Workshop on Building Trust in Language Models and Applications , year=
Interpretable Steering of Large Language Models with Feature Guided Activation Additions , author=. ICLR Workshop on Building Trust in Language Models and Applications , year=
-
[3]
Wu, Shirley and Yuksekgonul, Mert and Zhang, Linjun and Zou, James , booktitle=. Discover and cure:
-
[4]
Liang, Weixin and Zou, James , booktitle=
-
[5]
Wah, Catherine and Branson, Steve and Welinder, Peter and Perona, Pietro and Belongie, Serge , year=. The
-
[6]
Skin lesion analysis toward melanoma detection 2018:
Codella, Noel and Rotemberg, Veronica and Tschandl, Philipp and Celebi, M Emre and Dusza, Stephen and Gutman, David and Helba, Brian and Kalloo, Aadi and Liopyris, Konstantinos and Marchetti, Michael and others , journal=. Skin lesion analysis toward melanoma detection 2018:
work page 2018
-
[7]
Debiasing skin lesion datasets and models?
Bissoto, Alceu and Valle, Eduardo and Avila, Sandra , booktitle=. Debiasing skin lesion datasets and models?
-
[8]
Learning debiased representation via disentangled feature augmentation , author=. NeurIPS , year=
-
[9]
Model Science: Getting Serious About Verification, Explanation and Control of AI Systems , author=. ECAI , year=
-
[10]
Irvin, Jeremy and Rajpurkar, Pranav and Ko, Michael and Yu, Yifan and Ciurea-Ilcus, Silviana and Chute, Chris and Marklund, Henrik and Haghgoo, Behzad and Ball, Robyn and Shpanskaya, Katie and others , booktitle=
-
[11]
You, Kihyun and Gu, Jawook and Ham, Jiyeon and Park, Beomhee and Kim, Jiho and Hong, Eun K and Baek, Woonhyuk and Roh, Byungseok , booktitle=
-
[12]
Defense-prefix for preventing typographic attacks on
Azuma, Hiroki and Matsui, Yusuke , booktitle=. Defense-prefix for preventing typographic attacks on
- [13]
-
[14]
Anders, Christopher J and Weber, Leander and Neumann, David and Samek, Wojciech and M. Finding and removing. Information Fusion , volume=
-
[15]
Visual Sparse Steering: Improving Zero-shot Image Classification with Sparsity Guided Steering Vectors , author=. arXiv preprint arXiv:2506.01247 , year=
work page internal anchor Pith review Pith/arXiv arXiv
- [16]
- [17]
-
[18]
Oscar Skean and Md Rifat Arefin and Dan Zhao and Niket Nikul Patel and Jalal Naghiyev and Yann LeCun and Ravid Shwartz-Ziv , booktitle=. Layer by Layer:
-
[19]
NeurIPS Workshop on Mechanistic Interpretability , year=
Rethinking Sparse Autoencoders: Select-and-Project for Fairness and Control from Encoder Features Alone , author=. NeurIPS Workshop on Mechanistic Interpretability , year=
-
[20]
Concept-Based Explanations in Computer Vision:
Lee, Jae Hee and Mikriukov, Georgii and Schwalbe, Gesina and Wermter, Stefan and Wolter, Diedrich , booktitle=. Concept-Based Explanations in Computer Vision:
-
[21]
Interpretability beyond feature attribution:
Kim, Been and Wattenberg, Martin and Gilmer, Justin and Cai, Carrie and Wexler, James and Viegas, Fernanda and others , booktitle=. Interpretability beyond feature attribution:
-
[22]
The Linear Representation Hypothesis and the Geometry of Large Language Models , author=. ICML , year=
-
[23]
Emergent Linear Representations in World Models of Self-Supervised Sequence Models
Nanda, Neel and Lee, Andrew and Wattenberg, Martin. Emergent Linear Representations in World Models of Self-Supervised Sequence Models. 2023
work page 2023
-
[24]
Understanding intermediate layers using linear classifier probes , author=. ICLR , year=
-
[25]
Navigating Neural Space: Revisiting Concept Activation Vectors to Overcome Directional Divergence , author=. ICLR , year=
-
[26]
Laines Schmalwasser and Niklas Penzel and Joachim Denzler and Julia Niebling , booktitle=. Fast
- [27]
-
[28]
Invertible concept-based explanations for
Zhang, Ruihan and Madumal, Prashan and Miller, Tim and Ehinger, Krista A and Rubinstein, Benjamin IP , booktitle=. Invertible concept-based explanations for
-
[29]
Using causal analysis for conceptual deep learning explanation , author=. MICCAI , year=
-
[30]
Contrastive pretraining for visual concept explanations of socioeconomic outcomes , author=. CVPR , year=
-
[31]
Conceptual explanations of neural network prediction for time series , author=. IJCNN , year=
-
[32]
Giulianelli, Mario and Harding, Jack and Mohnert, Florian and Hupkes, Dieuwke and Zuidema, Willem , booktitle=. Under the hood:
- [33]
- [34]
-
[35]
Not All Language Model Features Are One-Dimensionally Linear , author=. ICLR , year=
-
[36]
Oikarinen, Tuomas and Weng, Tsui-Wei , booktitle=
-
[37]
Labeling neural representations with inverse recognition , author=. NeurIPS , year=
- [38]
-
[39]
Bricken, Trenton and Templeton, Adly and Batson, Joshua and Chen, Brian and Jermyn, Adam and Conerly, Tom and Turner, Nicholas L. and Anil, Cem and Denison, Carson and Askell, Amanda and Lasenby, Robert and Wu, Yifan and Kravec, Shauna and Schiefer, Nicholas and Maxwell, Tim and Joseph, Nicholas and Tamkin, Alex and Nguyen, Karina and McLean, Brayden and ...
-
[40]
Adly Templeton and Tom Conerly and Jonathan Marcus and Jack Lindsey and Trenton Bricken and Brian Chen and Adam Pearce and Craig Citro and Emmanuel Ameisen and Andy Jones and Hoagy Cunningham and Nicholas L Turner and Callum McDougall and Monte MacDiarmid and Alex Tamkin and Esin Durmus and Tristan Hume and Francesco Mosconi and C. Daniel Freeman and Theo...
- [41]
-
[42]
Jumping Ahead: Improving Reconstruction Fidelity with JumpReLU Sparse Autoencoders
Rajamanoharan, Senthooran and Lieberum, Tom and Sonnerat, Nicolas and Conmy, Arthur and Varma, Vikrant and Kram. Jumping ahead:. arXiv preprint arXiv:2407.14435 , year=
work page internal anchor Pith review Pith/arXiv arXiv
-
[43]
Vladimir Zaigrajew and Hubert Baniecki and Przemyslaw Biecek , booktitle=. Interpreting
-
[44]
Are Sparse Autoencoders Useful?
Subhash Kantamneni and Joshua Engels and Senthooran Rajamanoharan and Max Tegmark and Neel Nanda , booktitle=. Are Sparse Autoencoders Useful?
-
[45]
Extracting Latent Steering Vectors from Pretrained Language Models , author=. ACL , year=
-
[46]
Representation engineering: A top-down approach to
Zou, Andy and Phan, Long and Chen, Sarah and Campbell, James and Guo, Phillip and Ren, Richard and Pan, Alexander and Yin, Xuwang and Mazeika, Mantas and Dombrowski, Ann-Kathrin and others , journal=. Representation engineering: A top-down approach to
- [47]
- [48]
-
[49]
ICLR Workshop on Reasoning and Planning for Large Language Models , year=
Understanding Reasoning in Thinking Language Models via Steering Vectors , author=. ICLR Workshop on Reasoning and Planning for Large Language Models , year=
-
[50]
Dreyer, Maximilian and Pahde, Frederik and Anders, Christopher J and Samek, Wojciech and Lapuschkin, Sebastian , booktitle=. From hope to safety:
-
[51]
Reactive Model Correction: Mitigating Harm to Task-Relevant Features via Conditional Bias Suppression , author=. CVPR Workshops , year=
-
[52]
Post-hoc Concept Disentanglement:
Erogullari, Eren and Lapuschkin, Sebastian and Samek, Wojciech and Pahde, Frederik , booktitle=. Post-hoc Concept Disentanglement:
-
[53]
Zhengxuan Wu and Aryaman Arora and Atticus Geiger and Zheng Wang and Jing Huang and Dan Jurafsky and Christopher D Manning and Christopher Potts , booktitle=
-
[54]
Steering Language Models in Multi-Token Generation:
Klerings, Alina and Brinkmann, Jannik and Ruffinelli, Daniel and Ponzetto, Simone Paolo , booktitle=. Steering Language Models in Multi-Token Generation:
-
[55]
Analysing the generalisation and reliability of steering vectors , author=. NeurIPS , year=
- [56]
-
[57]
Deng, Jia and Dong, Wei and Socher, Richard and Li, Li-Jia and Li, Kai and Fei-Fei, Li , booktitle=
-
[58]
Tschandl, Philipp and Rosendahl, Cliff and Kittler, Harald , journal=. The
-
[59]
Steering large language model activations in sparse spaces , author=. COLM , year=
-
[60]
Xavier Suau and Pieter Delobelle and Katherine Metcalf and Armand Joulin and Nicholas Apostoloff and Luca Zappella and Pau Rodriguez , booktitle=. Whispering Experts:
-
[61]
Li, Zhiheng and Evtimov, Ivan and Gordo, Albert and Hazirbas, Caner and Hassner, Tal and Ferrer, Cristian Canton and Xu, Chenliang and Ibrahim, Mark , booktitle=. A Whac-A-Mole Dilemma:
-
[62]
arXiv preprint arXiv:2411.04430 , year=
Towards unifying interpretability and control: Evaluation via intervention , author=. arXiv preprint arXiv:2411.04430 , year=
-
[63]
Interpretable Machine Learning , author=. M. Phil. diss., Dept. of Engineering, University of Cambridge , year=
-
[64]
Wei, Alexander and Haghtalab, Nika and Steinhardt, Jacob , booktitle=. Jailbroken:
-
[65]
Jan Betley and Daniel Chee Hian Tan and Niels Warncke and Anna Sztyber-Betley and Xuchan Bao and Mart. Emergent Misalignment:. ICML , year=
- [66]
-
[67]
From Generation to Judgment: O pportunities and Challenges of LLM -as-a-judge
Li, Dawei and Jiang, Bohan and Huang, Liangjie and Beigi, Alimohammad and Zhao, Chengshuai and Tan, Zhen and Bhattacharjee, Amrita and Jiang, Yuxuan and Chen, Canyu and Wu, Tianhao and Shu, Kai and Cheng, Lu and Liu, Huan. From Generation to Judgment: O pportunities and Challenges of LLM -as-a-judge. 2025
work page 2025
-
[68]
Chen, Runjin and Arditi, Andy and Sleight, Henry and Evans, Owain and Lindsey, Jack , journal=. Persona vectors:
-
[69]
Benchmarking Neural Network Robustness to Common Corruptions and Perturbations , author=. ICLR , year=
- [70]
-
[71]
Explaining Similarity in Vision-Language Encoders with Weighted
Hubert Baniecki and Maximilian Muschalik and Fabian Fumagalli and Barbara Hammer and Eyke H. Explaining Similarity in Vision-Language Encoders with Weighted. NeurIPS , year =
-
[72]
Pahde, Frederik and Dreyer, Maximilian and Samek, Wojciech and Lapuschkin, Sebastian , booktitle=. Reveal to revise:
-
[73]
On the interpretation of weight vectors of linear models in multivariate neuroimaging , author=. Neuroimage , volume=
-
[74]
Robust Novelty Detection Through Style-Conscious Feature Ranking , author=. WACV , year=
- [75]
-
[76]
Accurate predictions on small data with a tabular foundation model , author=. Nature , volume=
-
[77]
Learning transferable visual models from natural language supervision , author=. ICML , year=
-
[78]
ICML Workshop on Reliable and Responsible Foundation Models , year=
Steering language model refusal with sparse autoencoders , author=. ICML Workshop on Reliable and Responsible Foundation Models , year=
-
[79]
Transactions on Machine Learning Research , year=
Maxime Oquab and Timoth. Transactions on Machine Learning Research , year=
- [80]
discussion (0)
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