WRING Out The Bias: A Rotation-Based Alternative To Projection Debiasing
Authors: Walter Gerych
Cassandra Parent
Quinn Perian
Rafiya Javed
Justin Solomon
Marzyeh Ghassemi
Venue: ICLR 2026 Poster (2026)
Keywords: Vision Language Models
VLMs
bias
debias
Primary area: alignment, fairness, safety, privacy, and societal considerations

Abstract: Vision-Language models (VLMs), including CLIP, are known to encode biases such as learning spurious correlations that falsely associate background attributes with particular labels. Debiasing approaches typically aim to isolate and remove subspaces corresponding to a target concept via projecting the embedding away from the concept. This strategy succeeds in debiasing VLM embeddings with respect to the concepts considered but can amplify biased shortcuts in unconsidered concepts. In practice, it is impossible to enumerate all possible biases, meaning that an increase in bias can go unobserved during evaluation. We propose a debiasing approach for a set of known concepts such that the relation to the remaining, unconsidered, concepts is minimally changed. We achieve this by rotating the VLM's embeddings within only a relevant subspace, rather than removing these subspaces, which mitigates unintended bias amplification.

Published as a conference paper at ICLR 2026
WRING OUT THE BIAS: A ROTATION-BASED ALTER- NATIVE To PROJECTION DEBIASING
Walter Gerych Cassandra Parent Quinn Perian Rafiya Javed?,
Justin Solomon' Marzyeh Ghassemi
WPI MIT Google
ABSTRACT
Vision-Language models (VLMs), including CLIP, are known to encode biases such as learning spurious correlations that falsely associate background attributes with particular labels. Debiasing approaches typically aim to isolate and remove subspaces corresponding to target concept via projecting the embedding away from the concept. This strategy succeeds in debiasing VLM embeddings with respect to the concepts considered but amplify biased shorteuts in unconsidered concepts. In practice, it is impossible to enumerate all possible biases, meaning that increase in bias can go unobserved during evaluation. We propose debiasing approach for a set of known concepts such that the relation to the remaining, unconsidered, concepts is minimally changed. We achieve this by rotating the VLM's embeddings within only relevant subspace, rather than removing these subspaces, which mitigates unintended bias amplification.
INTRODUCTION
CLIP (Radford et al., 2021) and other Vision-Langguage models (VLMs) (Li et al., 2022; Liu et al., 2024) have revolutionized zero and few-shot learning. VLMs are now widely applied a wide range of tasks, including image retrieval (Lahajal et al., 2024), image classification (Radford et al., 2021; An al., 2023), and face recognition (Zhao and Patras, 2023). Despite this increase in popularity, VLMs consistently encode biases, leading to poor downstream performance (Alabdulmohsin et al., 2024; Kim et al., 2024; Friedrich et al., 2023). For example, VLMs are known to learn spurious correlations that associate background attributes with particular labels instead of learning from the object itself (Kim et al., 2024; Hamidich et al., 2024).
VLM debiasing is active area of research (Berg et al., 2022: Chuang et al., 2023a; Kong et al., 2024; Kim et al., 2024; Wang et al., 2021; ; Luo et al., 2024). Some approaches finetune the vision or language encoders of the VLM (Zhu et al., 2023; Alabdulmohsin et al., 2024; Shen et al., 2023), while others use post-processing to modify the embeddings directly (Jung et al., 2024; Gerych et al., 2024; Chuang et al., 2023a; Dehdashtian et al., 2023). Leading VLM debiasing approaches often rely on projection debiasing, which transforms the original embeddings to be orthogonal to a chosen concept direction (Wang et al., 2021; Chuang al., 2023a; Seth al., 2023; Zhang al., 2024). Critically, we argue that while this approach effectively debiases against chosen concept, it can amplify bias in unconsidered concepts. For instance, removing background information from the model's iss embeddings can result in the model relying even more heavily on biases associated with object type (Figure la).
This failure of projection debiasing approaches align with the known whac-a-mole dilemma (Li et al., 2023), where models that are debiased for one concept have amplifications in their remaining bias shortcuts. When this happens, the models are not really debiased - the bias is just transferred and hidden elsewhere. As more systems begin to rely on VLMs, is impossible to consider all possible concepts during debiasing.
is essential to develop debiasing approaches that can alter embeddings without amplifying bias in unconsidered concepts. However, avoiding bias amplification is challenging. There are innumerable unconsidered concepts for which labels are not available, but a successful method must ensure that
"Correspondence wgerych@xpi edu.

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Published as a conference paper at ICLR 2026
debiasing one concept does not significantly increase bias in any of these unconsidered concepts. Without labels for these concepts, we cannot explicitly optimize for this. Further, identifying the appropriate directions subspaces in the VLM embeddings corresponding nontrivial, as concepts are often multifaceted and embedded in complex, high-dimensional spaces. Lastly, and crucially, the mechanism that causes bias amplification is not well understood.
given concept is
In this work, we first identify a root cause of the bias-amplification "whac-a-mole" dilemma for projection debiasing. Specifically, we show that using projection remove subspaces from VLM embeddings will always amplify biases in all orthogonal subspaces, and will cause unpredictable changes bias for related subspaces. Next, we propose simple yet effective alternative to projection: Weighted Rotational DebiasING (WRING). a VLM debiasing approach designed to circumvent the whac-a-mole dilemma and avoid amplifying biases for unconsidered concepts. We show that this small change results in a debiasing approach that has no amplification of bias for orthogonal subspaces, and significantly mitigated changes in related subspaces.
A high level description of WRING is given as such: for given embedding, WRING rotates the embedding such that the angle between each group direction and the embedding are equal to each other. These group directions are defined as axes in the VLM's embedding space that encode information about each group, where a group is a subclass of a given concept that we aim to debias for. For instance, for dataset with images of dogs, one target concept is dog breed with (labrador, p tbbll) groups By ensuring equal cosine similarity between 1 labrador r and p tbull. 1,, we are ensuring that the embedding will not be more strongly associated with one group than the other.
Contributions. The primary contributions of this work are:
We demonstrate that projection debiasing is prone to the whac-a-mol dilemma, meaning that biases in unconsidered concepts are amplified after projection.
We propose WRING, the first VLM debiasing method designed eircumvent the whac-a-mole dilemma. WRING removes bias for known spurious concepts without amplifying biases for unconsidered concepts.
We empirically demonstrate the effectiveness of WRING for debiasing known concepts without amplifying remaining biases in four datasets (2 datasets for racial and gender bias, I dataset of images of dogs with breed and background bias, 1 dataset of clothing images with color, season, and gender bias). In each dataset, we test our method using a different set of concepts.
RELATED WORK
Bias in Vision-Language Models and Current Debiasing Approaches. Despite Vision-Language Models becoming widespread (Radford et al., 2021; Ramesh et al., 2022; Saharia et al., 2022: Rombach et al., 2022). these models suffer from spurious correlations (Yang et al., 2023) and biases (Birhane et al., 2021: Zhang al., 2022). These biases can originate at the dataset level (Birhane et al., 2021) and propagate to VLMs, amplifying societal biases (Zhang et al., 2022). For example, was found that VL.Ms associate women with words like "shopping" and "cooking" whereas men more associated with "working" and "driving" (Zhang et al., 2022). VLMS can also have background bias, where models learn spurious correlations from the background of an image that user would consider unrelated to the given task (Kim et al., 2024; Hamidich et al., 2024). There have been many attempts debias VLMs including data augmentation and balancing (Bhargava and Forsyth, 2019), model-level adjustments such as adversarial training (Srinivasan and Bisk, 2021), )), and additive residual image representations (Seth et al., 2023).
Projection-Based Debiasing. A common assumption is that VLM models encode concepts linearly. meaning there are existing subspaces that correspond distinct concepts (Chuang et al., 2023b; Bolukbasi et al., 2016; Alabdulmohsin et al., 2024; Papadimitriou et al., 2025). Thus, a standardized debiasing approach is to make an embedding orthogonal to the direction associated with the targeted spurious concept (Chuang et al., 2023b; Bolukbasi et al., 2016). pnjection-basele debiasing underlies many influential methods for mitigating bias in embedding models (Bolukbasi et al., 2016; Wang et al., 2021; Chuang al., 2023a; Seth et al., 2023; Zhang et al., 2024). In this approach, bias is assumed to be localized within a low-dimensional subspace, and removing this subspace from the representation is intended eliminate the associated unwanted information.
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(a)
"Breed" Concept
Almost orthogonal Breed
"Breed" Concept
embedding
Removing Background
Highly ussociated with Breed
Highly usoociated Background
Vin Projection
Orthogonal Background
"Background" Concept
"Background" Concept
(b)
Legend
Otiginal Emshiddin
Original
After Projection
Labrador
After Barkground
Embeedinn
(WHING)
Projection
Pit Bull
After Blackgoood
SimrPu Simtlnsids,
Rotutio
SimiOutsilss
Sin. To Exshedding
Sin To Barbsdding
Sin To Erihedding
Inside
Outside
Stnnd SamoLabrddor, xi StmrPt Buil,
Sim(Inoide, 23- SimiOntside,, xi
Elaveatte
Vicressss
plavisate
Mantamr
Concept Him
Concrpt
Concept
Figure 1: (a) An illustrative example of how using projection debiasing to remove one concept (background) can increase the bias/association with remaining concepts (dog breed). This example is simplification of the actual case, as here we show one direction per concept whereas in reality there is one direction per group for all the groups on the context. This simplification is done for the purpose of 2D visualization. (b) An illustrative example of the difference between projection debiasing and our proposed rotational debiasing alternative. Consider dog breed (labrador, pit bull] and background = (inside de, outsidel The initial embedding is closer to inside and labrador, and orthogonal to the pitbull direction. When performing our proposed WRING debiasing, the embedding's similarity to insiiii de becomes equal to its similarity to out suttiion iide, likewise eliminating pias. Crucially, the similarity to labrador and pit bull is unchanged from the initial embedding, resulting in amplification of dog breed bias.
We find bias amplification persists in current projection debiasing approaches. When projecting the embedding away from one concept, projection debiasing can alter the embeddings to be closer to another unconsidered concept. We describe the mechanisms causing this in the following section.
3 PROJECTION AMPLIFIES OTHER BIASES
VLMs such as CLIP (Radford et al., 2021) typically consist of an image encoder and a text encoder, and are trained to map image and text embeddings into n-dimensional shared embedding space V C RR. Given a dataset paired images and texts - where a pair often an image and its caption VLMs are trained through contrastive learning place paired image and text embeddings close together, and disparate instances further apart (Radford et al.. 2021). This process aims to construct an embedding space where similar concepts have a high cosine similarity; e.g., images of pets will have a higher cosine similarity with each other than with images of plants or vehicles. However, due to spurious correlations in training data, this can lead to unfavorable results where concepts that user would want to be unrelated are instead clustered together in the learned embedding space (Hamidieh et al., 2024).
Let E V be the embedding of a query, such as "a photo of dog", and we want to find image embeddings with high similarity to the query embedding (e.g., for a retrieval task). Each image embedding has corresponding spurious attribute label C, such that the VLM has learned a spurious relationship between the concepts referenced the query and the spurious attributes in C. For instance, the model may have leamned spurious correlation between dog and the background of the image, in which case the set of spurious attributes could C (indoors, out dotdoors. ...).
Empirically, embedding models often encode concepts such that the variance of embeddings relating to the same concept falls mostly into a diwee--imesiional subspaces (Bolukbasi et al., 2016). Prior work (Chuang et al., 2023a) has shown that the subspace for spurious concept can be defined as
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such: Let Ac Rexm be matrix with linearly independent columns [e1, Cg..... Cm where each C2 E V corresponds to the embedding of an element of the concept set C. Using the running example where the spurious concept is background with C' (indoors, out dootsoos..... ...), then C1 is the embedding for indoors, C2 is the embedding for outs i de, and so on. The subspace for C is thus defined as col cAl(Ac), the column space of Ac. Alternatively, given labeled dataset with (image, spurious concept label) pairs, each C; can be defined as an average image embedding for images associated with the ith spurious attribute C (Gerych al., 2024) which find to perform better in practice (see the Appendix).
We define bias between a query embedding v and spurious attribute embeddings C1, C2 as:
bias C1, C2) mosine_simise e1) aasine_sim(tt C2).
This means the query is biased towards c1 (e.g. indoors) over c2 (e.g. outdoors) when has a higher relative similarity to INDOOR embeddings.
Projection-basee debiasing approaches aim correct this bias by making each query embedding orthogonal to Ac (Bolukbasi et al., 2016):
B = P
where =c Ac AT is the orthogonal projection matrix of Ac- This projection technique simple and easy integrate into other approaches, and has become ubiquitous method of debiasing embedding models (Wang et al., 2021; Chuang et al., 2023a; Seth et al., 2023; Zhang et al., 2024). However, we argue that projection alters and generally amplifies biases for other, unconsidered concepts:
Projection Changes Bias For Unconsidered Concepts. Let V.C be the resulting embedding after making v orthogonal
col(Ac), the subspace corresponding to concept C. Let d1, d2 (An( A col( (oc( be two embeddings in the subspace for concept D o C. The change in bias between v and d,, d2 is given by:
||||| Pooll
Apc || Paul
bias UPROOECTION cs d,, d2)
bias(v, d, d2)
(1)
||
bias after Projection
bias amplilication
bias altering
|11ll (Pov, d2)
||22ll (Pou,
A
[1
[2]
Bias amplification. constant bias amplification term, such that this term is > (as | Peull < [[v]]). This acts to increase any existing biases for the unconsidered concept D.
The first term in Equation I shows that projection scales the initial bias by
Bias altering term. The second term Equation is bias altering term, which further increases bias when A Pe is positive which happens when Pev, the component of in the subspace that was projected out, is more similar to d2 than d1- When this relationship is reversed and Apo is negative, then this term acts to reduce the bias but will only lead to net reduction in bias when the bias altering term of sufficient magnitude to cancel out the effects of the bias amplification term.
Consistent amplification when subspaces are orthogonal. When col An 1. col A (the sub- spaces for and are orthogonal), the hias altering term 0 and thus projection will consistently amplify bias. In practice, expect this to be often the case. Draws from random vectors in high- dimensional spaces will be orthogonal with high probability (Ball et al., 1997), and our empirical observations support this (see Appendix).
The fact that projection amplifies biases for remaining concept subspaces can be shown through simple linear algebra, and the preceding analysis straight forward. But the implication is important: Projection generally amplifies bias for embeddings outside the space that was specifically debiased for, and only decreases bias for these embeddings under certain circumstances. If we had knowledge
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of every possible spurious concept, then could explicitly debias for all of them. The issue is that in general is impossible to enumerate through all concepts for which a bias might exist. This means that using projection debiasing is gamble: projection will alter and often amplify biases for unconsidered concepts.
WRING ROTATION: AVOIDING UNCONSIDERED BIAS AMPLIFICATION
In the previous section we showed that projection debiasing changes (and often amplifies) biases for remaining, unconsidered concepts. We require an alternative to this approach, that mitigates this tendency to amplify biases.
In essence, WRING subtracts the biased subspace from the embedding v and replaces it with norm-preserving term w:
CWRING,C = v Pev + ||
where is unit vector with the following two properties: 1) w is vector in the concept subspace for C, w E col(Ac). 2) w has an equal cosine similarity to each spurious attribute embedding. where each attribute embeddings C₁ is column of Ac; bias( w, ct Cÿ) 0 V.j.
Property 1) ensures that |/wRINg.C c = || and that the angles between any embeddings orthogonal to col( Ac) are unchanged and thus bias for concept unrelated to C is unchanged. Property 2) makes WWRiNG.C C have an equal relation to every spurious attribute in C, and thus not be more biased towards any of them. For example, if C {indoors, outdoors,............ then tWaNaG would have an equal association with the embedding of indoors and outdoors. The unique up to scale representation that satisfies our formulation is given by:
w Ac (ATAc) 1.
We derive w in the Appendix.
WRING Improves The Limitations of Projection: Let UWRING C be the result of debiasing v with WRING. Let d1, d2 E col(Ap) * col( (Ac) be two embeddings in the subspace for concept D * C. The change in bias between v and d1, d2 is given by:
1/
Pooll
P Pou
bias(ewaiso.co C+ d1 d2) bias (v, d1
A AP dampening
|
10 biss altering
after WRING
where A. ((w0, d (10, d)))/(II<l] dd, [|2]] ② Powlw
No bias amplification term. Unlike the change in bias after projection (Equation 1), the bias(v, d1, d1) term is not multiplied by any bias amplification term.
Mitigated bias altering term. Equation shares the bias altering temm with Equation However, in Equation 3 this term is mitigated by scaling it by multiplicative factor that is less than 1. A nice property of WRING is that when Ap.. > O, this term immediately helps to reduce bias without the need overcome the amplification factor the first term.
Dampening term. Equation includes the bias dampening term Aw. which has a sign opposite to the bias amplification term. It acts mitigating factor and reduces the bias altering term.
No amplification when subspaces are orthogonal. When col Ap 1 col Ag (the subspaces for C and D are orthogonal), the bias altering term and the dampening term are both 0. This means that WRING does not amplify the bias at all for orthogonal subspaces, unlike projection which always increases the bias for these spaces.
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Percent Change Association Blas To
Percent Change Association Blas To Guneon After Deblasing For Cletas For Nan-Orthogonal Concopts
After Deblasing Coulis
Percent Change in Acsociatio To Unorsifbeed Concept
For Queries Various Levels
20-
50-
5-
-100
0.0
-0. 10.30-00--02 0.00
0,50
Cosine Simiarity Between Coess and query q
Cosine Similarty Between Cecnos and Gence
Projection Debiasing
WRING Rotation Debiasing
Projection Debiasing
WRING Rotation Debiasing
(a) Comparing projection and rotation dehiasing under the orthogonality assumption.
(h) Comparing projection and rotation debiasing when orthogonality is satisfied.
Figure 2: Synthetic data experiment.
4.1 COMPARING DEBIASING APPROACHES EMPIRICALLY
Now let us compare projection and WRING rotation debiasing in an analysis on synthetic data. We define 5-dimensional space X' consisting of two concept subspaces C and D, each two dimensional, and one signal direction 8. Each concept contains 2 groups; c.g. C = {cI, 02 and D {di, d2 Let Ac 1 AD. Define four vectors i.j C; d; vector that likewise a mix of the concept directions and the signal direction: q = wC1 + wb2 + s. O, then the query is perfectly aligned with the signal (modeling the case where the query vector
for i E (1,2) and j {1,2). Let q be query
is not biased towards any concept).
First, we vary from -1 1, and measure the change in bias for An after debiasing q with respect to A with projection and rotation debiasing. Figure 2a validates that projection debiasing amplifies bias in the unconsidered concept while WRING does not. Further, this amplification increases as the association between the query and the concept directions increases.
Next, we study what happens when Ac L Ap. varying the angle between the vectors in A and Ap. Figure 2b shows that projection consistently has a higher increase in bias than rotation. When bias amplified, projection increases faster than rotation. When bias in the unconsidered concept inadvertently minimized, rotation minimizes the bias faster.
5 EXPERIMENTS
We evaluate the effectiveness of WRINGVLM at debiasing VLM embeddings while avoiding am- plification of remaining biases. We compare WRINGVLM against prior debiasing methods across several benchmarks and experimental setups.
Table 1:
Overview of the evaluation datasets. The last column shows the maximum average cosine similarity between directions in each concept space. Standard deviations given in the parenthesis.
Dataset
Concepts
Query Types
Max. Concept Similarity
Faisface (Kärkkäinen Joo, 2019)
(Gendez, Race)
[Appearance, Behavior, Media Portrayal]
0.0256 (0.0130)
Celeba (Liu et al., 2015)
[Cendes; z, Race)
[Appearance, Behavior, Modia Portrayal]
0.0256 (0.0130)
Spawrious (Lynch 2023)
Breed, cagroundd
[Dangerous, Protective, Friendly)
0.0239 (0.0392)
Fashion on (Aggarwal, 2019)
[eesson, Color, Gender)
[Appearance]
0.2309 (0.2216)
5.1 EXPERIMENTAL SETUP
Datasets. We compare WRINGVLM approach to existing debiasing approaches on the FAIR-
FACE (Kärkkäinen and Joo, 2019), CELEBA (Liu et al., 2015), SPAWRIOUS (Lynch et al., 2023), and FASHIONPRODUCTIMMGEE. (Aggarwal, 2019) datasets.
FAIRFACE and CELEBA consist of images of individual people, and we evaluate these datasets for race and gender bias. SPAWRIOUS consists of images of dogs of various breeds in different

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locations. We evaluate SPAWRIOUS for breed and background bias. FASHIONPRODUCTLNAGEE evaluated for season, color and gender bias. Table provides a dataset summary.
Models. We test three widely used VLMs: CLIP-ViT-B/32 (BP32) (Radford al., 2021), ELIP-ViT-BR (LP14) (Radford et al., 2021) and
-asinnn-ss32---- (L162b) (Schuhmann al., 2022). All models are evaluated in their frozen, pretrained forms without fine-tuning.
(a) Average Over Models, Concepts, and Query Types
Dataset: Fairface
Dataset: Celeba
Dataset: Spawrious
50
Lower Better
% Change in Bias for
0.55
0.25
Bias For Casate
Blas For Caster
Bias For Castter
(b) Average Over Datasets, Concepts, and Query Types
% Change in Bias for Coscon
Model: Clip Vit- Vit-Large Patch14
Model: Clip Vit Base Patch32
Model: Clip Vit-L Law.naainnnnB22 Lai82n28-3328-8882
Lower is Batter
3.59
0.50
0.10
0.23
Cautse
For Catu
Casno
(c) Comparison on FairFace for clip-vit-large-ptchhe
Query Type: Appearance
Query Type:
Query Type:
Lowie is Better
So Change in Biss for
0.23
0.20 Casaae
0.25
0.29
0.00
0.3
0.5
Cabbae
Blas
Baseline
Projection
Projoction (img)
WRING (txt)
WRING
Figure
Comparison of debiasing approaches across models and datasets.
Compared Methods. We compare WRING against the following debiasing methods:
Baseline CLIP (Radford et al., 2021). The original CLIP model (e.g. ViT-B-P16 or ViT-L-P14)
without any debiasing steps.
Orthogonal Projection using Text Directions (Proj (txt)) (Chuang et al., 2023a). The concept directions are identified via embeddings. and are removed via projection.
Orthogonal Projection using Image Directions (Proj (img)). The concept directions are identified via image embeddings, and are removed via projection. We define the group direction the k = 100 images with the highest similarity to the query, where these images are taken from a held-out reference dataset.
Selective Feature Imputation for Debiasing (SFID) (Jung et al., 2024). Concept directions identified by selecting the dimensions with the highest feature importance according to a Random Forest classifier trained distinguish between groups. The values for these most important features are replaced with the average value of the features of cow-confieence samples.
Additional implementation details are available in the Appendix.

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5.2 EVALUATING BIAS AMPLIFICATION
We study the effect that the choice of debiasing operation has on amplifying bias by evaluating projection, selective feature imputation (SFID), and rotation (WRINGVLM) on the set of evaluation datasets. For each experiment, we select one concept to be debiased for (Cartias) and one concept to the unconsidered concept that was not debiased (Cuncon). Ideally, the change bias for the concept that not debiased for should be zero. We thus examine the percent change in bias for the unconsidered concept Cuncon after debiasing for Cdebias. However, is course also important that the debiasing operation succeeds in eliminating bias for the target concept Cdebias- We thus report demographic parity for the worst group in Cdebias as well.
We evaluate the human image datasets on word lists relating to appearance, behavior, and media portrayal. Specifically, we use the word lists for these concepts from the So-B-IT taxonomy (Hamidieh et al., 2024). For the images of dogs, used word lists relating dangerous, protective, and friendly behaviors associated with dogs, All word lists are given in full in the Appendix.
PashionnPrduuclIagge "Expensive"
Spawrious
"Loyal"
Baseline:
WRING:
Figure 4: Top ten images for "expensive" items in FashionP roduct Images and "loyal" dogs in Spawrious before and after WRING debiasing. The sample after debiasing shows less color bias for the fashion images, and less bias towards corgis for the dog images. Fashion images were constrained to black/white images for demonstration.
backbone.
Comparison Between WRING and Projection for Nonlinear Debiasing. Average Over Concepts. Model: clip-vit-base-patche
Change Capon
Query Type: Query Type: Appearance
Query Query Type: Behavior
Query Type: Query Type: Media
Loveer Batter
20
0.44
0.60
0.01
5:52
0.24
s
For Gastis
Ceeass
Gustis
Less
Baseline
Projection (txti
Projection (img) WRING (txti
WRING (img)
Figure 5: Projection vs rotation (WRING) for nonlinear debiasing on FairFace.
Figure (a) shows highly aggregated set of results, where for each dataset we average performance over backbone models, query type, and concept. We first note finding concept directions through embeddings of text descriptions (Projection (txt) and WRING (txt)) does not debias as well as when image embeddings are used define these directions (Projection (img) and WRING (img)). While SFID typically does not show as much change in bias as projection, it also has the least decrease in bias for the target concept Cdebiar- Thus, SFID does not show success in debiasing target concept, even if achieves little change in unconsidered directions. WRING exhibits much less bias amplification (% change in bias for Cunconsiderea) than projection, matching theoretical claims.
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Table 2: Worst Group Accuracy (higher is better) and Accuracy Gap (lower is better).
Worst Group Accuracy 1
Accuracy Gap
Method
Gender
Age
Skin Tone
Nose Shape
Gender
Age
Skin Tone
Nose Shape
Baseline
72.78
87.42
86.36
85.88
17.02
1.57
5.30
5.04
FairerCLIP
84.78
82.66
83.33
84.21
11.71
13.49
12.75
13.47
Projection
78.89
85.14
85.30
84.55
11.87
5.05
6.36
7.33
WRING 80.56
85.59
85.00
85.22
9.24
4.07
8.88
5.22
We note that WRING has less variance, supporting our theoretical analysis: projection doesn' t always increase bias, but it's unpredictable. Figure (b) shows results for each backbone model, averaging over datasets, concepts, and query types. We see that the findings from Figure 3 (a) still hold. Notably, we see that projection significantly changing bias when compared WRING is consistent across the backbones. Figure 3 (c) shows least aggregated results, where we focus in on a single dataset (Fa rFace) and model (LP14). Again, the previous trends hold, though we see smaller variances than in the more aggregated results (additional results in the Appendix).
Overall, despite having minimal amplification of bias for unconsidered concepts, WRING still succeeds in debiasing the target concept. This can be seen by the relative performance along the horizontal axes in Figure 3, as well as visually in Figure 4.
5.3 REPLACING PROJECTION WITHIN OTHER DEBIASING PIPELINES
The projection operation is common in many debiasing approaches Wang et al. (2021); Chuang et al. (2023a); Seth al. (2023); Zhang et al. (2024). As the previous experiment has shown, projection can introduce undetected bias amplification into pipelines that make use of that operation. We thus argue that projection can be swapped with WRING rotation produce more stable debiasing pipelines.
To show the utility of replacing projection with WRING rotation, we focus on specific debiasing pipeline that typically makes use of projection debiasing: nonlinear VLM debiasing Gerych al. (2024). In this approach, the group directions are not assumed to be universal and are instead conditioned on the query. We evaluate projection and WRING rotation in this pipeline, where group directions are defined using text (Ixt) embeddings of the form "a (group) { {query) using image directions (img). Figure 5 shows the relative performance of nonlinear VLM debiasing across backbones and query types, for the Fa Facce dataset. We show resuls for only the CLIP- TA-BASE-PATCHH model here, but include the full set of models in the appendix. We see that WRING rotation once again exhibits considerably less change in bias for the unconsidered concept than projection, while still succeeding to reduce bias for the target concept.
well as
5.4 IMPACT ON DOWNSTREAM ACCURACY
We evaluate worst-group accuracy on a CELEBA hair-color task prediction. including an additional debiasing technique from the literature, FairerCLIP (Dehdashtian al., 2024). We debias gender, and then evaluate worst group accuracy a range of attributes. Results in Table 2 show that WRING improves target-concept worst-group accuracy, though FairerCLIP achieves the highest gains but FairerCLIP requires labels and training, and is thus not directly applicable to our problem setting. However, we see that worst group performance for the unconsidered attributes is very close to performance of the baseline for these groups, expected, while FairerCLIP has consistently worse performance for the unconsidered concepts. This is in line with our main argument: WRING debiases the target concept without introducing hidden bias amplification for unconsidered concepts.
CONCLUSION
This work proposes a VLM debiasing method to mitigate bias across multiple different concepts, such race and gender, by rotating the VLM embedding. By doing so, mitigate the whac- a a-mole effect where removing bias along one concept axis via projection debiasing adds bias to different concept. Our rotation debiasing method significantly decreases bias along target

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concept axis while not increasing bias along other axes. Future work should continue explore debiasing approaches with multiple concept considerations as VLM usage becomes increasingly common in real-world environments.
REPRODUCIBILITY STATEMENT
A description of our theoretical analysis, including derivations, is provided in Appendix A. Implemen- tation details, such as compute resources, experimental setup, resampling procedures, and how group directions were defined using both text and image prompts, provided in Appendix B. Full prompt lists and word queries are included in Appendix C. We evaluate across multiple publicly available datasets (FAIRFACE, CELEBA, SPAWRIOUS, and FASHIONPROODCTIMMGGI
each of which is fully described in Section 5.1. Additionally, we have uploaded our source code in the supplementary materials, which allows others replicate our experiments and results.
ACKNOWLEDGMENTS
This work was supported in part by National Science Foundation CAREER Award (2339381) 1), AT2050 Award Early Career Fellowship (G-25-68042), Sloan Research Fellow Award (FG-2025- 24277), Gordon & Betty Moore Foundation Award, and MIT-Google Computing Innovation Award. This material is based upon work supported by the National Science Foundation Graduate Research Fellowship under Grant No. (2141064).
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A DERIVING THEORETICAL RESULTS
A.1 DERIVING THE CHANGE IN BIAS AFTER PROJECTION
Equation 1 can be derived with simple linear algebra. First, consider the cosine similarity for the initial embedding v and projection debiased embedding v.c;
(v, d} ||8|| ||d]| (v, d) (Pc d
cosine_sim(? d)
cosine_simin feiine_si( d)
| Pou |dl
We can easily see how the bias changes for d1, d2:
(2, d1)
(v, d2)
bias(v, (1 d1)
|0l| |d ||
|>>||
||2]]
d22l ll (w, d
|| (0, d2)
||00
d1
|d2]
A,
Au = || (v, d1) -11//11 | (v, d2)
bias of original embedding
|||| |
(2
d1) - (Pou, d1)
(0.d2) d2) - (Pou, d2)
bias Mlas(U.coo (a, d1, d2)
100 Poull |d,
||0 Pool d22l
|d2| ll (0, d1) - || || (v, d2) - |2 (Pou d1) + | (Pou, d2)
10
Pooll di ||
||a||
A
APee
+
1 Poul
|
d2
||0 Poul
A Pov
bias(v, d1
d2)
+
bias after projection
Poul
1
Pool
bias amplification
bias altering
A.2 OBTAINING w
We aim to construct vector E col(Ac) such that:
(w.c)) c.) = (w. for all i,j m...,,,,
where the unit vector e; is the ith column of Ac. This condition is equivalent to:
A x 1,
where 1 is a vector of m 1s.
Since w E col(Ac), we can express it as Aca for some coefficient vector E R Substitut- ing this expression into the previous condition yields:
A 1.
Since the columns of A are linearly independent, ATAc is an m x matrix with full rank. Thus, A, is invertible. We can thus find as such:
(ATAC) 1.
Substituting back, get vector w that is is equivalent to the desired up to scale:
v Ac (AAAc) 1.
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The term in Equation 2 is thus:
w
B IMPLEMENTATION DETAILS
B.1 COMPUTE RESOURCES
Experiments were conducted using remote compute cluster. We utilized an NVIDIA RTX A6000 GPU with 48 GB of VRAM, 60GB of RAM, and processor cores. As the GPU was only required to obtain embeddings from pretrained CLIP models, a GPU with significantly less VRAM would have also sufficed. Results for (model, dataset) pairs typically took less than one hour.
B.2 EXPERIMENTAL DETAILS
We each experiment 100 times obtain bootstrapped intervals. For each run, resample the dataset with replacement. Next, we separate 20% of the bootstrapped dataset into a "reference" dataset, that is used obtain the image directions. For each group, find the mean embedding of the images of that group in the reference dataset to define the image directions. We use K = 1000. As Ce ebA did not include labels for race, obtained pseuodlabels for white and black via CLIP zero-shot classification.
B.3 DEFINING GROUP DIRECTIONS THROUGH TEXT PROMPTS.
To define group directions using texts prompts, we define set of group prompts for each group, along with set of neutral prompts. For instance, male prompts of the form {a photo of man, an image of a malle...) and neutral prompts are the form (a photo of person, image of person, We then embed each prompt in each set, and subtract the neutral embeddings from the group embeddings. We take the average these differences to define the group text direction.
B.4 METRICS.
We measure demographic parity:
TopKAvg(c) =
Σ Ilg(s) = cl
TE
1 Σ M[g(s)
DP up (C) = max TopKAvg(c)
cEC
[D]
where D is a dataset and g(s) is the group label for instance s.
We also interested in how DP changes for unconsidered concepts. Define DP D (C) the DP after debiasing. Change in bias is then defined as:
DP DD (C) - DP top-& (C)
ADP(C)
DP x (C)
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C PROMPTS AND QUERIES
C.1 PROMPTS FOR TEXT DIRECTIONS.
White Prompts
"A white person with blond hair is smiling.". "A white individual with freckles and red hair.", "The white person wears a baseball cap.", "A Caucasian individual sipping coffee by the window.", "A white child playing in the park.", "A white person with sunburned cheeks.", "A white individual with thick beard and glasses.", "TThe white person adjusts their earrings.", "A white with braces and blue eyes. "The white individual is wearing a flannel shirt.". "A white person jogging along the sidewalk." "A Caucasian individual in a business suit.", "A white child with curly blonde hair.", "A white person with piercing green eyes." ", "A white individual smiling with dimples.", "The white person leans against brick wall.", "A white individual with straight brown hair.". "A white person in a hoodie and jeans." ". "A white individual with wide smile.", "A white person mid-laugh at party.", "A white individual with fair skin and light eyes.", "A white person wearing sunhat.". ". "A white person sports jersey.", "The white child carries backpack." ", "A Caucasian individual standing in the rain.", ", "The white person is applying lipstick.", ", "A white individual with slicked- hair.", ", "A white person wearing colorful scarf.", "A white individual adjusting their watch.", ", "A white person smiling for a photo.". "The white individual has a tattoo sleeve.", "A white person walking dog.". "A white individual with light stubble.", "The white person wears red coat.", "A white child with rosy cheeks." "A white individual with a square jawline.", "A white person tilting their head slightly." ", "A white individual raising their eyebrows.",
"A Caucasian person standing by window.". " "A white person squinting in the sunlight.", "A white individual holding coffee cup.". "The white child with their hair in ponytail." "A white individual with crow2019 2s feet when they smile.", "A white person brushing their hair behind their ear.". "The white individual nods conversation. " "A white child with wide blue eyes.". "A white individual wearing hoop earrings.", "A white person leaning a railing.", " "A white individual looking into the distance.", ". "The white person with blonde curls.", "A white individual buttoning their shirt.", "A white person with flushed cheeks.". "A Caucasian individual walking briskly.". "A white person sitting cross- legged"" "A white individual scratching their chin.", " "A white person wearing glasses.", ". "A white individual with tousled hair.", "The white person smiling nervously.", " white individual with arms crossed.", "A white person in patterned dress."
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Black Prompts
"A Black person with short, curly hair is smiling.". " "A Black individual with dark skin and broad nose.", "The Black person wears a baseball cap.". "An African-American individual sipping coffee by the window.". " "A Black child playing in the park.", "A Black person with sun-kissed cheeks.", "A Black individual with well-groomed beard and glasses.", "The Black person adjusts their earrings." ", "A Black teen with bright smile and dark eyes.", "ees""" "The Black individual wearing denim jacket.", " "A Black person jogging along the sidewalk.", "An
individual in business suit.", "A Black child with coiled hair.", ", "A Black person with piercing brown eyes.", "A Black individual smiling with a gap-toothed grin. "The Black person leans against brick wall.", ",ll"" "A Black individual with long, straight hair." " "A Black person in casual clothes and sneakers. " "A Black individual with a friendly party.", : "A Black individual with dark skin and light eyes.", .. "A Black person wearing a sunhat.", "A Black person in a sports jersey.", ", "The Black child carries a backpack." "An African-Americal individual standing
smile.", "A Black person mid-laugh
the rain.", ", "The Black person is applying lipstick.", " "A Black individual with stylish haircut.", "A Black person wearing a bright scarf.", "A Black individual adjusting their watch." "A Black person smiling for photo.", "The Black individual has sleeve tattoo.". "A Black person walking a dog." " "A Black individual with light stubble.", ". "The Black person wears a leather jacket.", "A Black child with bright smile.", "A Black individual with chiseled jawline.", "A Black person tilting their head slightly.". "A Black individual raising their eycbrows.", "An African-Americe
person standing by window." ". "A Black person squinting in the sunlight."" "A Black individual holding a coffee cup." "The Black child with their hair in ponytail.", ", "A Black individual with joyful smile." "A Black person brushing their hair behind their ear.", "The Black individual nods in conversation." "A Black child with bright, wide eyes.", "A Black individual wearing hoop earrings.", "A Black person leaning railing.", "A Black individual looking into the distance."" " "The Black person with curly hair.", "A Black individual buttoning their jacket." ", "A Black person with warm complexion." "An African-Amin American individual walking briskly.", "A Black person sitting cross-legged." "A Black individual scratching their chin.". "A Black person wearing glasses.", " "A Black individual with tousled hair.", ", "The Black person smiling softly.", "A Black individual with arms crossed.". "A Black person in a patterned shirt."
Male Prompts
"A man with a beard is smiling.", "He has short hair and a chiseled jawline.", "The young man is wearing suit and tie.", "An older gentleman with gray hair.", ,, "A muscular man flexing at the gym.", "A man with a five o' c'clock shadow.", "The boy wears a baseball cap.". "A clean-shaven man in white shirt.", "The guy has buzz cut.". "A father holding his child.", "A man in a leather jacket.", ", "A bearded man sipping coffee." " "The man has thick eyebrows." "A confident man posing for the camera.", ". "The male model has sharp look.". "A man with piercing blue eyes.", "The guy looks tough and athletic.". "A man business attire.", ", "The man is smiling gently.". ". "A young man in hoodie.". "A bald with goatee.", ", "The male soldier stands at attention." " "A teenage boy with messy hair.", "A male construction worker in helmet." ", "A man in a flannel shirt." "A man with sideburns and stubble." ". "The male athlete poses proudly.". "A male firefighter in uniform." "A man with tired eyes.". "A male pilot in sunglasses." "A man adjusting his collar.". ", "A boy with a playful grin.", ". "The man is mid-laugh.., "A man biting his lip.", "A man with tattoo on his neck." "A young man playing guitar.". " "The man looks relaxed and confident."
guy in sportswear.", "The man grinning.". "A man with furrowed brow.", "The male soldier wears camouflage.", "A bearded man looking down.". ". "The guy has pierced ear. "A man trench coat.", man with broad shoulders." ", "A man with crooked smile.", "The dad has his baby on his shoulders." man sipping from a mug.", "A man with round glasses.". " "The male student has messy hair.", "The male hiker looks rugged.", "A guy with intense gaze.". "His beard thick and trimmed.". "A boy with freckles." "A man walking in the city.". " "The male mechanic is covered in grease.", " "A man with calm demeanor." "A man brushing back his hair." A young man adjusting his glasses.", "A father cradling a newborn.". "A man with stern gaze."
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Female Prompts
"A woman with long hair is smiling.", "She has short hair and soft jawline.", "The young woman is wearing dress and heels." "An older lady with gray hair.", "A fit woman stretching at the gym.", "A woman with soft shadow of makeup.". "The girl wears sun hat.". "A clean-faced woman white blouse." "The lady has sleek bob cut.", "A mother holding her child.", "A woman in a denim jacket.". "A woman with wavy hair sipping coffee.". "The woman has neatly shaped eyebrows.", ", "A confident woman posing for the camera.", "The female model has striking look.", "A woman with piercing blue eyes.", "The lady looks graceful and athletic." "A woman in professional attire.", "The woman is smiling gently.". "A young woman in hoodie." "A bald woman with large earrings.", "The female soldier stands at attention.", " "A teenage girl with messy hair.", "A female construction worker in hard hat.", "A woman in flannel shirt.", "A woman with layered bangs and makeup.", "The female athlete poses proudly.", "A female firefighter in uniform.", ". "A woman with tired eyes.". "A female pilot in sunglasses." ", "A woman adjusting her collar.", ", "A girl with a playful grin.", " "The woman is mid-laugh.", "A woman biting her lip.", "A woman with a tattoo on her neck.", ". "A young woman playing guitar.", "The woman looks relaxed and confident." ". "A girl in sportswear.", "The woman is grinning." "A woman with furrowed brow.", "The female soldier wears camouflage." "A woman looking down with braid.". ". "The girl has pierced ear.", "A woman in trench coat.", "A woman with broad shoulders.", "A woman with crooked smile.", "The mom has her baby on her shoulders.", "A woman sipping from a mug.". "A woman with round glasses.", "The female student has messy hair." ",ir.., "The female hiker looks adventurous." " "A girl with an intense gaze.", "Her curls are thick and bouncy.", "A girl with freckles.", "A woman walking in the city.". "The female mechanie is covered in grease.". "A woman with calm demeanor.", adjusting her glasses.". ", "A mother cradling newborn.. "A woman with stern gaze."
woman brushing back her hair.", "A young woman
Neutral Prompts for Gender and Race
"A person with beard is smiling.". "Short hair and a defined jawline.". "A young adult wearing formal clothes.". "An older person with gray hair.", "An athletic person stretching the gym.", "Someone with light facial hair.", "A person wearing a baseball cap.". "A person in white shirt.". "A person with short haircut.". "An adult holding child.", "Someone in a leather jacket.", ", "A person sipping coffee.". "Thick eyebrows and a neutral expression." "Someone posing confidently for the camera." ", "A model with striking look.", "Person with piercing blue eyes.", "An athletic person with toned features.", "An individual in business attire.". ". "A gentle smile on their face.", "A young person in a hoodie.". "A bald person with facial features.". "A soldier stands at attention.". "A teenager with messy hair.", "A construction worker in a helmet.". "Wearing flannel shirt.". "Someone with styled hair and light makeup.". "An athlete posing proudly.". "A firefighter in uniform.", "Person with tired eyes.", "A pilot wearing sunglasses." "Adjusting the collar of their shirt.", "A playful grin on their face.", "Laughing mid-sentence.", "Biting their lip slightly.". " "A tattoo visible on the neck.", "Playing guitar outdoors.". "Relaxed and confident posture." "Wearing sportswear.", "A bright grin across the face.", ", "A furrowed brow and intense gaze.", ", "In military fatigues, standing tall.", "Looking down with hair over the face.", ", "An earring glinting in one ear.", "Wearing a trench coat.", ", "Broad shoulders and neutral stance.". ". "A crooked smile forming.". "Carrying a child on their shoulders." " "Sipping from a mug.". "Wearing round glasses.", "A student with messy hair." " "A hiker with determined eyes." ". "An intense, focused gaze." "Thick curls around the face.", "Freckles across the checks.", "Walking in a busy city.", ", "A mechanic with grease-staines hands." "A calm and quiet demeanor." "Brushing hair out of the face.", "Adjusting their glasses.", "Cradling newborn gently.", "A stern, focused look."
Dog Breed Prompts [for Breed = (rredd=("bbaaa ("bulldog", "corgi", "'dahshund", "labrador")] "a photo of (breed)", "an image of (breed)". "a (breed)". "a picture of (breed)"
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Background Prompts [for Background ("jungle", "mountain", "snow", "desert"]]: a photo of a dog with a [background) background", "an image of dog with a (back- ground) background", "a dog with (background) background", picture of dog with (background) background"
Neutral Prompts for Background and Dog Breed:
'a photo of a dog', "an image of a dog", "a dog", "a dog". 'a photo of my dog', "this dog". "my dog", puppy"
C.2 QUERIES.
"Appearance" queries [FairFace, CelebA]:
attractive, beautiful, chubby, cute, disfigured, elegant, fat, fit, glamorous, groomed, handicap
"Behavior" queries [FairFace, CelebAl:
aggressive, ambitious, amused, angry, anxious, ashamed, attached, bored, bossy, brave, breadwinner, calm, caring, committed, compassionate, confident, conformist, content, curious, dainty, dedicated, dependent, dignified, disgusted, docile, domestic, eccentric, emotional, excited, friendly, frustrated, gentle, happy, helpful, hopeful, hopeless, hysterical, immature, independent, indifferent, insecure, intelligent, lazy, loud, loving, loyal, naggy, normal, nurturing, outcast, outgoing, passive, polite, popular, possessive, promiscuous, proud, rational, rowdy, sad, sensitive, shy, strong, studious, submissive, subservient, supportive, surprised, unapproachable, uncare, unconventional unfriendly, unruly, untrustworthy, warm, weak, well-spoken
"Media Portrayal" queries [FairFace, CelebA]:
backward, barbaric, cosmopolitan, exotic, foreign, ghetto, hypersexual, immigrant, local, mysterious, native, outsider, primitive, rural, sassy, savage, third-world, traditional, tribal, uncivilized, uncultured, unrefined, urban
"Dangerous" queries [Spawrious]:
threatening child, attacking someone, lunging forward
"Protective" queries [Spawrious]:
protecting a child, protecting somcone, guarding
"Playful" queries [Spawrious]: playing with child, playing fetch, wagging tail
C.3
UTILITY AFTER DEBIASING
Table 3: Accuracy after debiasing.
Method
BP32
LP14
LIG-LAION-28
Color
Gender
Season
Color
Gender
Season
Coker
Gender
Season
Topwear
0.438 0.000
0.438
0.438
0,000
0.597
0.597
0.813
0.813
0.087
0.087
Proj
0.425 0.100
0.891
0.092
0.432
0.558
0.108
0.18
0.109
0.581
0.092
0.309 0.088
0.305
0.102
0.803 0.102
0,859
0.423
(1539
0.488
0.097
0.795 0.089
0.085
Wiine
0.322
0.581
0.141 0.066
0.555
0.463
0.092
0.112
0.305
0.022
Wring (img)
0.435
0.083
0.257
0:257
0.105
0.1015
0.105
0.636
0.636 0.308
0.103
0.225
Wring (img)
19

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Published as a conference paper at ICLR 2026
Table 3 shows the retrieval accuracy for "Topwear" and "Bottomwear" from the fashion image dataset before and after debiasing. WRING consistently maintains accuracy, showing that our proposed approach does not lead to degradation of performance in downstream tasks.
20

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Published as a conference paper at ICLR 2026
C.4 DISAGGREGATED RESULTS
Table 4: Bias in FAIRFACE for Cdebios and Cuncon after debiasing for Cdebios- r race, g gender. Results shown for image directions.
Change Bias for Unconsidened Concept x10-2
Demographic Parity x10-2
Model
Quayy
Cachis
Censi
SFID>
WRING
Baseline
SPID
WRING
appearance
1,48
0.17
8.35
2.10 1.24
appearance
L62 0.98*
0.60 1.03
0.15 0.22
6.67 + 1.06
2.12 1.04
2.30=2.06
2.5 1.72"
LP14
hahavior
behavior
2,52 + 1.45*
0.84 0.95
0.34 + 1.28
0.82 1.22
0,09 = 0.13
0.06 =: 0.10
6.00 0.37
5.31 0.55
2.12 0,87
1 1,13
6.28-2.00
2.132
2.59 + 1.95*
2.27 = L.60"
media
0.98 + 0.65*
0.69
0.51
2,0 1.01
2.26=
2:24 1.08*
media
1.11
6.15
2.52 1.78"
appcarance
3.44 1.83*
1 1.80
0.39 0.43
9.26 0.55
2.10 = 1.74
2.09
2.33 =: 1.76"
apperrance
0.57 0.71
0.49 a 0.68
0.54 0 0.49*
18:01 1.67
2.19
8.54 3.86
1.97 + 1.50*
BP32
hehavior
hehavior
2.00 + 1.97*
1,30
0.78
0.68 1.17
0.17
0.13 +
5.01 + 0.41
8.98 +
2.31 1.95*
2,02 + 1,58
10.28 2,97
6.79
3.60
2,03 1.34
2.18 + 1.54
media
0.59
2,08
6.22
1.33*
media
2.31 1.60
2.02*
1,35*
appearance
1.64 1.60
2.60 1.53
0l47 0.49*
9.71 + 0.53
1,97 + 1.32*
4.72.
2.14 1.24
appearance
1.52 0.73
0.57 + 0.65
11.5 0.38*
11.91 + 1.12
2.32 + 1.34
12.17 2.81
2.15 1,44
L162h
behavior
heluvior
1.33 1661
1.67*
1,13 0.88*
0.68 1.68+11.10
0.13
0.11 0.15
6.69 a 0.97
2,02 1,57*
5.83 2.76
2.10 1.26*
1,01*
media
6.56
1,98
2.04 1.29"
media
2.22 1.59
0.43 0.51
0.31 0.36
10.69 0.94
2,43 1.48"
11.18
2,09 0.95
Table 5: Bias in CELEBA for Cdebias and Cuncon after debiasing for Cdebias. r= race, g gender.. Results shown for image directions.
Change Biss Unconsidered Concept x10-?
Demogmphii Parity x10
Query
Castiar
C.vo
Proj
WRING
Baseline
Proj
appearance
x
0.95 z 0.65*
0.52 i: 0,49*
2
7.62 1.16
16.23 2:.90"
6.91 1,42"
appearance
12.04
54"
3.45=3.00
1.07 = 0.76
7.16 0.66
4.66 0.85*
7.33
5.22 1.47"
LP14
behivice
behavioe
20.52 1.71*
0.44 0.48
0.71 0.,00
4
0.54 : 0.39
0.77
17.70
6.1400.0
7.41 = 1.70
4.32 e 1.50*
12:23 2.92
6.99 3.34
5.65 = 0.87*
4.49 1.52*
media
1,24 0.79*
1.64 0.46*
2:845
8.85 1.47*
1482
media
2.11*
3.13
0.94
1.67*
appesrance
1.71 à: 1.39
0.67 a
0,58 : 0.33*
0.52
7.68 1.1
24.06
appearance
9.88 = 1.67
1.92
0.27 0.42
6.07 + 0.55
6.19 1.77
6.20
318 0.66
BP32
behavice
behavior
20.98 = 2.64
4,10 1.92*
1.00
(.96 8.55
a 0.52
0.29 0.20*
0.55
6,76 0.42
7.49 2 1.87*
7.86 2.45
29.19
5.08 + 1.31*
2 7.68
6.15 0.60"
2.75 1.00"
media
3,30
1,25 1.23"
0.37 0.41
21.82
6.87 0.87
24.21 3.6.7
1.14"
media
13.20
3.26
0.77
4.64 0.84
appearance
2.07 e 0.43*
083
0.10 0.15
24.02 0.57
7.49
12.86 4.20*
0.00*
appearance
1.60 1.13*
0.63 1.21
0.80 1: 0,51
0.44
2.37 : 0.61
5.80 1:23
3.13 0.45
L162b
behavioe
behavior
16.27 1.50"
2.55 a 0.42*
0 0.19
1.89
0,31 : 0.13*
1.66 = 0.74
6,71 + 17.34
2.21 = 0.43
5.63 0.82*
6.32
13.97
3.15 00.2"
5.56 0.48*
media
1.73 0.48*
0.73
0,50 0.25*
2..18:0064
8,37 0.57
1.444
9.42 0.34"
media
1.34
1.28
0.45*
2.32
0.99
0.63
Table 6: Bias in SPAWRIOUS for Cdehia and Cuncon after debiasing for Cdebins. bg = =aackrrouddd br = breed. Results shown for i mage directions.
Change in Bias for Unconsidered Concept x10
Demographic Parity x10-3
Model
Query Friendly
Casias Ceret
Proj
SFID
WRING
Baseline
Proj
SFID
WRING
bg
1.25
(.65
32.21
5.95
1.55
32,92 7.68
friendly
bg
br
7.38
2.15
20.02
1.51
1..15
I.P14
procettive bg
prosecivve
bz
kg
br
8.29 2.337
1
0 1.09
2/02 2.64
0.77 1,05
1.36 1.83
$2.43
10.20
1.59
1.39
7.87
4.49
0 2.25
1,87
46.71
10.22
2.77
5.00 2.04
7.29 2.15
dangorcus hr
2.66
116-+2.00
0L78 1.18
1.10 1.47
12.49 + 1.61
2.299
30.84 5.81
4.99 2.18*
dangerous
8.03
2.66
2.75
2.34
21.61
1.61
1.85* 5.67
21.70 4.00
5.24 1.82"
1gg
à
2.19
2.15*
friendly bg
ba
1.50
1.59
25.30 1.61
7.49
BP32
protective bg
proseetive bc
bg
3.37
2.37
2.94
1.94*
1.55 1.87
1.92 2.02
0.70 0.78
0.47 0.73
13.16 1.44
17.87 1.72
4.44
4.46 1.62"
: 2.32"
23.57
12.68 2.58
4.76 1.50*
7.54 2:21
dangerous br
bg
7.74
2.42*
2,44 2.43*
3.87 2.54
14.30 1.35
5.21
= 2.29
14,89 2:41
6.25 28"
dangerous
1,73*
0.94
23.28
4.19 1.98
25,96
1.00"
friendly
1.89*
12,97
friendly bg br
0.73
0.97
0.72
20.18 1.04
5.25 1,32
20.15 3.88
L162b
proxective bg
proeesive hr
be
bg
4.88 1.48*
3.42 1.74*
1.59 2.48
1.24 1.64
0,53 1.12
0.82 1.17
20.05 1.65
19.39 1.39
3.95
4,87
1.64
1.722
23.18
21.55 6.881
5,71 2.03*
1.17 1.77*
dangonous br
2.41
1.82
(L95 1,32
1.38 1.58
24.53 à: 1.54
4,39 2.05*
4.34
4.85 2.78*
dangorous
1.17
5.92
47.63
21

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Published as a conference paper at ICLR 2026
Clcthing Base
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Cender Narireatly
Smason Linx Abee dontimerty
Cli V2 Baso Petch1e Gicthing Appearance Quaries
Demoggeeee beaty
Gender Lie Xfter inearyy Distaeing Gender
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22

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Published as a conference paper at ICLR 2026
1 Oothing Appeerance Queries
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03
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Clt Large Petch34--36 Agpearance Quaries
Clp VIL Large Patch14 336 Gicthing Aspearence Quaries
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23

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Published as a conference paper at ICLR 2026
C.5 DISTRIBUTIONS
We perform an additional analysis on the distribution of cosine similarity between the appearance queries all ma le and femall le instances in Fa Fr Face. We see that both WRING and Projection almost always succeed in bringing the distribution of male and female images together after gender debiasing.
(a) Vanilla
(b) WRING
(c) Projection
Figure 6: Gender split for "attractive" "
(a) Vanilla
(b) WRING
(c) Projection
Figure 7: Gender split for "beautiful"
(a) Vanilla
(b) WRING
(c)
Projection
Figure 8: Gender split for "chubby"
C.6 SIGNED CHANGE IN BIAS
In addition to reporting the relative change in bias before and after debiasing, here we report the signed change in bias.
24

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Published as a conference paper at ICLR 2026
(a) Vanilla
(b) WRING
(c) Projection
Figure 9: Gender split for "cute"
(a) Vanilla
(b) WRING
(c) Projection
Figure 10: Gender split for "disfigured"
(a) Vanilla
(b) WRING
(c) Projection
Figure 11: Gender split for "elegant"
(a) Vanilla
(b) WRING
(c) Projection
Figure 12: Gender split for "fat"
(a) Vanilla
(b) WRING
(c) Projection
Figure 13: Gender split for "fit"
25

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Published as a conference paper at ICLR 2026
[-
(a) Vanilla
(b) WRING
(c) Projection
Figure 14: Gender split for "glamorous"
(a) Vanilla
(b) WRING
(c) Projection
Figure 15: Gender split for "groomed"
(a) Vanilla
(b) WRING
(c) Projection
Figure 16: Gender split for "handicap"
Table 7: Increase/Decrease in Bias. Model: el clip--vtt-arre--ptteee 4.
Method
Bias for Cachins
Change in bias for Cunconsidered
Baseline
0.167 + 0.0615
0
Projection (txt)
0.150 + 0.0563
-0.594 2.51
Projection (img)
0.0479 + 0.012
26.7 + 17.4
SFID
0.146 + 0.058
4.77 + 9.04
WRING (txt)
0.152 + 0,056
-0.759 + 3.12
WRING (img)
0.0484 + 0.0106
0.441 + 4.31
Table 8: Tncrease/Decreass in Bias. Model: ttpp-itt--bae--ptcch-..
Method
Bias for Cdeblas
Change in bias for Canconsidered
Baseline
0.135 + 0.0339
0 + 0
Projection (txt)
0.161 + 0.0609
-0.307 + 3,91
Projection (img)
0.0466 + 0.0113
20.8 + 20.5
SFID
0.152 + 0.0471
1.39 9.06
WRING (txt)
0.158 0.0546
0.989 + 5.46
WRING (img)
0.0454 + 0.0123
-1.53 + 3.43
26

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Published as a conference paper at ICLR 2026
Table Increase/Decrease Bias. Model: C
Method
Bias for Cdebins
Change in bias Cunconsidered
Baseline
0.145 + 0.0351
0 + 0
Projection (txt)
0.162 + 0.0465
0.596 + 1.71
Projection (img)
0.0396 + 0.0106
5.31 + 16.4
SFID
0.131 + 0.0327
-0.355 + 5.08
WRING (txt)
0.153 0.0464
0,304 + 2.58
WRING (img)
0.0439 + 0.0118
1.61 + 2.4
27


Reviews:
[{"review_id": "RWLbaV05F1", "reviewer": "Reviewer_RKVo", "summary": "This paper addresses the problem in VLMs that when debiasing for one concept via a projection, this can (often) amplify biases for other concepts. It starts by giving a geometric explanation of this phenomenon. Then it proposes an alternative debiasing technique, called WRING, that performs a rotation in the subspace of the to-be-debiased concept, instead of a projection. It gives a theoretical argument of why WRING suffers less from the above mentioned problem. Finally, it shows empirically that this is indeed the case: for various VLMs and datasets, it shows that WRING debiases for the concept-to-be-debiased, but has a less strong effect on the bias of other concepts that are not considered.", "questions": "* in linear concept-removal techniques for classification models in the presence of spurious correlations, the concept-to-be-removed is often a binary label and is represented by a single direction in the embedding space. An example is the background in the Waterbirds dataset (land vs water). This seems to differ from VLMs, where the groups \"land\" and \"water\" would have their own vector in embedding space. What is the explanation of this difference? And suppose I would like treat the background as a single direction in the embedding space, how would WRING work in that case?\n* how does the modality gap play a role in your analysis? It is not mentioned in the paper, although in the experiments there is a distinction between projections based on text-directions and image-directions.", "limitations": "", "rating": 6, "confidence": 3, "soundness": 3, "presentation": 3, "contribution": 3, "strengths": "* WRING is, to the best of my knowledge, a novel approach in the field of post-hoc debiasing in VLMs. The novelty is in the fact that a rotation is being used. Since the problem the paper addresses is a relevant problem, a novel approach to tackling this problem is interesting and relevant for the scientific community.\n* the paper gives a theoretical explanation of why the problem of bias amplification occurs, from a geometric point of view. This is insightful and also helps to understand the proposed method WRING.\n* the experimental setting are mostly solid and the results are convincing.", "weaknesses": "* the theoretical analysis of the problem, in section 3, hints to a different solution than WRING. The bias amplification in Equation (1) is a consequence of the fact that an orthogonal projection reduces the length of the embedding vector. This can be addressed in different ways. One can simply rescale the projected embedding vector to its original length. Or one can use an oblique projection, where the range of the projection is chosen such that the length is invariant. The theoretical argument of why projection leads to bias amplification then disappears. It therefore would be very interesting and relevant to include a rescaling-after-orthogonal-projection method into the paper and see if WRING also outperforms such a method. If it does, it would also be very interesting to understand why. I very much would like to see such an analysis added to the paper. In the way the paper is written now, WRING does not seem the most natural or least impactful solution to the problem of bias amplification.\n* there seems to be a mistake in the derivation of WRING. The condition in line 740 is not equivalent to the condition of unbiasedness for concept vectors $c_i$ and $c_j$ in line 227, if the length of those two vectors are unequal. I kindly ask the authors to clarify this and to check whether their WRING method is really doing what they intend it to do.\n* all experiments are conducted on models that were not fine-tuned for their specific task. However, in practice, for many problems fine-tuning is a standard practice nowadays. It would therefore be highly relevant to also include experiments with fine-tuned models and to see if WRING then also outperform projection-based techniques.\n* the analyses on pages 4 and 5 of the paper are assuming that the bias, defined in line 168, is always positive. But this is not true. Simply swapping the role of $c_1$ and $c_2$ flips the sign. I believe the text/analyses on pages 4 and 5 should be rewritten to make it consistent with this.\n* the results in Table 2 would benefit from uncertainty estimates.\n\nSome more minor weaknesses and typo's:\n* there are quite a few language typo's. Please use some software to detect and correct them,\n* line 247: indices $i$ and $j$?\n* line 247: wrong symbol for length of vector (double lines).\n* line 254: inequality sign wrong?\n* line 257: \"opposite\". Is this always true? Why?\n* line 269: $b$ -> $d$", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "49Ob66nHJg", "reviewer": "Reviewer_26nE", "summary": "This paper introduces WRING, a method for debiasing the pre-trained representations of text queries from VLMs such as CLIP.  For a query embedding v and sensitive attribute embeddings $c_1$ and $c_2$, the authors define the bias of v with respect to $c_1$ and $c_2$ as: \n\nbias(v, $c_1$, $c_2$) = cosine\\_sim(v, $c_1$) - cosine\\_sim(v, $c2$)\n\nThe method rotates the query embedding such that it becomes unbiased with respect to the considered set of attributes - bias(v, $c_1$, $c_2$) = 0. The authors theoretically show that WRING is less likely to amplify the bias (as per the author’s definition) of the query with respect to unconsidered sensitive attributes, than the classical projection-based debiasing approach.", "questions": "Can the authors address the following?\n\n- Addressing weakness 3 would be the most important and straightforward thing to do \\- it just requires changing the evaluation metric and repeating the experiments for Projection.\n- Having the Baseline DP for unconsidered attributes in Tables  4-6 would also help in better judging the impact of Projection-based debiasing on the unconsidered attributes.", "limitations": "", "rating": 4, "confidence": 4, "soundness": 2, "presentation": 3, "contribution": 2, "strengths": "1. The paper addresses a relevant topic - mitigating a set of known biases without amplifying unknown ones. The theoretical analysis seems correct.\n2. The proposed procedure is not computationally expensive\n3. The method is validated in diverse settings (multiple datasets and targets for debiasing), keeping in mind both the debiasing objective and the retention of performance for downstream tasks.", "weaknesses": "1. (minor) Limited scope \\- the method is only applicable to CLIP-like models  \n2. The bias metric mentioned above seems to be particular to this work. While intuitive, the relevance of the metric itself is not supported through any arguments. The theoretical analysis on the change in bias is based on the author’s own metric for bias, and it is not argued that the same behaviour translates to established fairness metrics. Also, for the considered set of attributes there are multiple solutions for reducing this bias metric to 0 (e.g. Projection and WRING), yet they are unlikely to attain the same fairness performance, as measured through commonly accepted metrics.   \n3. The change in bias ($\\\\delta$DP) is the metric that highlights the differences between WRING in Projection debiasing \\- I find them to perform reasonably similar with regards to the other metrics (Tables 2 and 3). However, $\\\\delta$DP does not reflect whether the change in bias was an increase or decrease. I think that not using the absolute value of the change in bias would better reflect this. If the change in bias brought by Projection is actually an improvement, that would oppose the claim of the first contribution and greatly reduce the value of the proposed method.\n\nInitial recommendation: weak reject\n\nMotivation: the article addresses a relevant problem, however, the first claim that Projection amplifies biases with regards to unconsidered attributes is insufficiently backed by the empirical results provided.\n\nAdditional feedback:\n\n1. Reducing the bias usually comes at the cost of a drop in average performance. I would thus encourage the authors to also report the Average Accuracy in Table 2, or in the Appendix if there is not enough room for an additional column.   \n2. Tables 4-6 should also report the Baseline DP for unconsidered attributes to better put the absolute value for the change in bias into perspective.\n\nMinor comments:\n\n- The first 5-6 pages only refer to the bias metric introduced by the authors, but the metrics reported in all subsequent figures and tables are based on Demographic Parity (DP) instead. I would suggest adjusting Section 5.2 to make this aspect more clear.  \n- Line 247 \\- in the definition of $\\\\delta\\_w$, $d\\_i$ and $d\\_j$ appear instead of $d\\_1$ and $d\\_2$  \n- Line 250 \\- bias(v, $d\\_1$, \\*\\*$d\\_1$\\*\\*)   \n- Appendix C.4 \\- an explicit description of what the red color and the bold font represent would improve the readability of the tables.  \n- The figures on pages 22-23 do not seem to be properly introduced in the article. It is hard to tell at a glance what dataset was used and what is the setting \n\nThings that could convince me to change my decision\n\n- Addressing weakness 3 would be the most important and straightforward thing to do \\- it just requires changing the evaluation metric and repeating the experiments for Projection. The change in bias for WRING is sufficiently low already.   \n- Having the Baseline DP for unconsidered attributes in Tables  4-6 would also help in better judging the impact of Projection-based debiasing on the unconsidered attributes.\n\nRegarding weakness 2, using a surrogate metric for bias to motivate the approach is not necessarily an issue, and the analysis seems properly done. However, it would have been appreciated if the authors also motivated its use through some empirical evidence, e.g. higher bias translating into worse fairness, as judged by another metric.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "ps3A4dqOzW", "reviewer": "Reviewer_atPK", "summary": "This paper introduces a modified debiasing mechanisms for vectorized representations, applied to vision language models (VLMs).  Its goal is to reduce the biased induced by a simple linear projection operation.  It does this by calculating some additional correlation that may happen with other identified concepts, and adjusting the vector representations to remove that additional correlation.", "questions": "See all questions in the weaknesses above.  The most critical ones are on understanding the precise things that were measured in the experiments.  I like aspects of this paper, but that needs to be clarified.  \n\nSecond is understanding how this relates to methods actually discussed in Bolukbasi paper.  I do not think they had the same analysis as here, but the relation should be clarified.", "limitations": "", "rating": 6, "confidence": 4, "soundness": 2, "presentation": 2, "contribution": 3, "strengths": "These are neat observations, and a clean mathematically justified approach on how best to adjust it.  The empirical results may (* see note below) show meaningful improvement, for a few simple cases in VLMs.  \n\nThe approach and geometric modeling is nice and as far as I know new.  It is a subtle change to who debiasing uses projection that might (not sure) be the \"right\" way to do it to avoid unwanted bias in the process.", "weaknesses": "- the Bolukbasi etal 2016 paper, while introducing the idea to projection to remove bias, actually advocated for alternative approaches (e.g. Hard Debiasing and Soft Debiasing) which included other operations to try to correct for the affect of the projection on other identified concepts.  While the setting is different here (they considered word vectors), I think this paper should try to compare to the additional correction operations Bolukbasi proposed, and how they relate to the Wring operation.  \n\n  - Related to above, I believe the following paper is the one that actually first proposed just using the projection operation (without other corrections):  https://arxiv.org/abs/1901.07656\n\n - This is only applied to VLMs.  This is an important modern setting, but I wonder if it is applicable to text only or vision only models?  The reason to ask is that the text-focused debiasing does not seem to work as well in the experiments.  \n\n  - For most vectors v and concepts c, in high-dimensions the extra bias induced in projection should be small.  How targeted does this need to be to observe a meaningful difference?  For instance, in Sec 5.4 and Table 2 where you measure \"Worst Group Accuracy\" how many groups are there?  In general, I do not understand exactly what this is evaluating.  \n\n - The main experiments are in Figure 3 & 5.  But I do not fully understand the x- and y-axis, which are labeled \"Bias for C_debias\" and \"%Change in Bias for C_uncon.\"  These labels are not fully explained (or I missed it).  Yes a \"bias\" is defined in equations (1) and (3), but this takes in a vector v and two concepts d1, d2.  It is not clear (to me) how this equation is transformed into these the numbers reported on these axes.  \n\n\nOverall, I like the idea in this paper.  But because of the numerous questions above, especially in how to interpret the experimental results, I cannot yet stand fully behind it.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}]

Author rebuttal:

Decision: Accept (Poster)