Title: Preserving Task-Relevant Information Under Linear Concept Removal
Venue: NeurIPS 2025
Accepted: yes
Keywords: ersaure; linear erasure
Abstract: Modern neural networks often encode unwanted concepts alongside task-relevant information, leading to fairness and interpretability concerns. Existing post-hoc approaches can remove undesired concepts but often degrade useful signals. We introduce SPLINCE—Simultaneous Projection for LINear concept removal and Covariance prEservation—which eliminates sensitive concepts from representations while exactly preserving their covariance with a target label. SPLINCE achieves this via an oblique projection that ``splices out'' the unwanted direction yet protects important label correlations. Theoretically, it is the unique solution that removes linear concept predictability and maintains target covariance with minimal embedding distortion. Empirically, SPLINCE outperforms baselines on benchmarks such as Bias in Bios and Winobias, removing protected attributes while minimally damaging main-task information.


Peer reviews:
{"IS_META_REVIEW": false, "comments": "SUMMARY:\nThis paper introduces a post-hoc method that provably removes sensitive concepts from neural representations while exactly preserving their covariance with task-relevant labels, achieving effective concept removal with minimal distortion to task-relevant information.\n\nSTRENGTHS AND WEAKNESSES:\n### Strengths \n-  The paper is well-written and easy to follow.\n- It introduces SPLICE, a theoretically grounded oblique projection method that uniquely enforces both the removal of sensitive concepts and the preservation of task-relevant information.\n- Extensive experimental results are provided across language and vision tasks.\n\n### Weaknesses\n- The paper addresses the linear concept erasure problem and assumes that task-relevant information can be represented through covariance.   However, these assumptions may not hold in complex representations within large models, where concepts are often encoded in a highly entangled manner. Experimental results further reveal that the proposed method performs less effectively when applied to intermediate layers.\n- Some relevant works are missing in the comparison and discussion. In particular, methods that also aim to preserve task-relevant information during concept erasure, such as [1] and [2] ([2] is potentially considered concurrent work under the NeurIPS policy).\n\n[1] Robust Concept Erasure via Kernelized Rate-Distortion Maximization, NeurIPS 2023\n\n[2] Fundamental Limits of Perfect Concept Erasure, AISTATS 2025\n\nQUESTIONS:\nQ1: SPLICE demonstrates superior performance compared to baseline methods in two out of three tested Llama models in Fig. 3. Could the authors provide insight into the potential causes of this performance variation across different Llama model versions? To strengthen the generalizability of these findings, would the authors consider expanding the evaluation to include additional LLM architectures?\n\nQ2: In the CelebA experiment, the difference maps for SPLICE show notable changes around the glasses regions. Intuitively, since the smile concept is being removed, changes should be concentrated primarily in the smile regions rather than the glasses regions. Could the authors clarify this observation?\n\nLIMITATIONS:\nyes", "TITLE": "Official Review", "RECOMMENDATION": 4, "REVIEWER_CONFIDENCE": 3, "CLARITY": 3, "IMPACT": 2, "ORIGINALITY": 2, "DATE": "2025-06-26"}

{"IS_META_REVIEW": false, "comments": "SUMMARY:\nThis paper introduces a method for concept erasure that aims to maximally preserve task-relevant information. For example, one might want a neural network to be insensitive to the concept of gender to mitigate gender bias. While existing approaches can remove the targeted concept, they often also degrade the performance on the main task by inadvertently discarding task-relevant information. The authors propose a method called SPLICE, which applies an affine transformation to the feature representations. This transformation ensures that the resulting features are *linearly guarded* against the target concept—i.e., they exhibit zero covariance with the concept to be removed—while preserving the covariance between the features and the main task. The paper includes a theoretical result showing that training a classifier on such transformed features, using any linearly guarded method and without regularization, yields the same classifier as training on the original features. The method's effectiveness is demonstrated in three settings: (1) bias removal from textual embeddings, where a linear layer is trained with regularization for classification; (2) language modeling, where the final layer is trained after projection; and (3) concept erasure from image data.\n\nSTRENGTHS AND WEAKNESSES:\n**Strengths**\n\n* The paper is well-written and clearly presented, with helpful visualizations that aid in understanding the SPLICE method.\n* It makes a valuable theoretical contribution by illustrating how the choice of concept erasure method, among those satisfying linear guardedness, should depend on the specific objective, such as preserving overall feature information or maintaining main task performance.\n* The paper presents theoretical results characterizing when linear guardedness uniquely determines the resulting model, even if different projection methods are used.\n\n**Weaknesses**\n* The concept of \"task-relevant information\" is not clearly defined in the paper and appears to be conflated with the classification target variable.\n* There is no discussion of potential bias in the task-relevant information, \\$\\mathbf{y}\\$, which could itself be a result of biased data-generating processes. For instance, in the case of debiasing a classifier screening job applications (lines 27–32), the dataset may inherently reflect gender bias. Preserving covariance with such a task variable might inadvertently retain the very bias the method aims to remove, especially when applying SPLICE in earlier layers.\n* The paper lacks a discussion of which applications might benefit more from preserving main task performance (as done by SPLICE) versus preserving internal representations (as in methods like LEACE).\n* The assumption $U^{\\perp} \\cap \\text{colsp}(W\\Sigma_{x,y}) =\\{0\\}$ (line 133) is quite strong and may not hold in general.\n* The theoretical justification and empirical performance of the method seem to apply primarily to the later or final layers of a model (line 323, Appendix B.4).\n\n**Minor Weaknesses**\n\n* The methods discussed in lines 73–74 may still satisfy linear guardedness, even if they do not explicitly mention it, unless a theoretical proof is provided to the contrary.\n* Typo: “an projection” → “a projection” (line 167)\n\nQUESTIONS:\n- Please discuss which applications call for preserving main task performance (as in SPLICE) versus internal feature representations (as in LEACE).\n\n- For each main assumption of SPLICE (e.g., $U^{\\perp} \\cap \\text{colsp}(W\\Sigma_{x,y}) = \\{ 0 \\}$), please provide theoretical or empirical justification for its realism.\n\n- Please define “task-relevant information” and clarify how to choose a suitable proxy for it in practice.\n\nLIMITATIONS:\nThe authors adequately addressed the limitations.", "TITLE": "Official Review", "RECOMMENDATION": 5, "REVIEWER_CONFIDENCE": 3, "CLARITY": 3, "IMPACT": 3, "ORIGINALITY": 4, "DATE": "2025-06-30"}

{"IS_META_REVIEW": false, "comments": "SUMMARY:\nThis paper introduces SPLICE, a linear projection method designed to remove sensitive concepts from neural network embeddings while preserving task-relevant information. SPLICE extends previous methods LEACE by adding an additional constraint to preserve covariance between features and task labels. The authors validate their approach using classification datasets such as Bias in Bios and Multilingual Text Detoxification, as well as language modeling benchmarks, demonstrating improved retention of task-relevant information.\n\nSTRENGTHS AND WEAKNESSES:\nStrengths:\n\n- The idea of preserving task-relevant covariance while removing sensitive attributes is conceptually appealing.\n\n- SPLICE provides theoretical justification for its methodology, including closed-form solutions.\n\n- Experiments demonstrate potential benefits in preserving important information in debiasing tasks.\n\nWeaknesses:\n\n- The contribution is incremental, primarily extending LEACE by introducing an additional constraint $P \\Sigma_{x,y} =  \\Sigma_{x,y}$.\n\n- The implementation details regarding last-layer retraining and language modeling are unclear, especially the calculation of features for language modeling.\n\n- Experimental validation is limited, with no worst-group accuracy reported on the widely-used CelebA dataset.\n\n- Lacks comparison with established group robustness methods like DFR, AFR, and SELF.\n\nQUESTIONS:\n- How exactly are the embeddings computed for language modeling tasks without retraining LLM parameters?\n\n- Can you clarify the closed-form solutions and practical computation of SPLICE in language model experiments?\n\n- Why were existing robust methods such as DFR, AFR, and SELF not compared in your experiments?\n\n- What does the comma in Table 1 and following tables mean?\n\nLIMITATIONS:\n- Incremental contribution with limited theoretical novelty.\n\n- Insufficient clarity regarding implementation and computational details.\n\n- Limited dataset size and lack of standard group robustness metrics for CelebA.", "TITLE": "Official Review", "RECOMMENDATION": 4, "REVIEWER_CONFIDENCE": 4, "CLARITY": 2, "IMPACT": 2, "ORIGINALITY": 2, "DATE": "2025-07-01"}

{"IS_META_REVIEW": false, "comments": "SUMMARY:\nLinear concept removal aims to follow the linear representation hypothesis, i.e. concepts in a feature learner such as a neural network, exist as linear combinations of each other. By assuming this hypothesis to be true, techniques are primarily aimed at projecting out biased directions in the representation space. \n\nThe proposed method, Splice, follows related work in this research area, and as such, is a relevant method for concept debiasing. It aims to solve a constrained optimization problem derived from [1], but with an important distinction - task relevant information, i.e. features that correspond to the actual label at hand, must be preserved when learning the projection matrix (the operator P on the covariance of the features and label must be an identity transformation). Further, the authors show that the operator effect on the prediction is determined only by the choice of kernel, and independent of the range. Experiments demonstrate the usefulness of Splice on shortcut removal in language and image data. \n\n[1] Belrose, Nora, et al. \"Leace: Perfect linear concept erasure in closed form.\" Advances in Neural Information Processing Systems 36 (2023): 66044-66063.\n\nSTRENGTHS AND WEAKNESSES:\nStrengths:\n\n1. This paper is extremely well written and easy to follow. Every result proceeds intuitively from a previous result, and all design choices are well motivated. \n2. Both theorems are relevant results, and while Theorem 1 essentially builds entirely on [1], the added constraint is a significant difference in my view and counts as novel. \n3. Intuitive experimental results on both language and image shortcuts. Figure 2 demonstrates Splice is more robust to WGA as opposed to other projectors. Figure 3 demonstrates that the harmful effect of the bias variable is mitigated better by Splice (although I would argue just based on the illustration provided that LEACE is also pretty satisfactory). \n\nWeaknesses. \n\n1. The most obvious weaknesses perhaps, are the reliance on binary labels to demonstrate usefulness (this is not entirely the paper's limitation, but rather the limitation of the entire field of shortcut learning), and the absence of multi-shortcut results, such as UrbanCars. See [2]. \n2. There are also no results on Waterbirds, which is the de-facto dataset for evaluating worst-group accuracy. Further, there seems to be no consistency in the experiments chosen. While WGA seems to be a metric to observe for language data, it is not re-used in the image data. Please consider having WGA for both modalities, and also adding Waterbirds. \n3. An out-of-distribution evaluation set can be a set where the shortcut of interest is explicitly removed. Have the authors considered doing an experiment like this? For example, an OOD case of Waterbirds is when the eval set has landbirds exclusively with water backgrounds, and waterbirds exclusively with land backgrounds. What would be the interpretation of P in this case? \n4. I am not convinced that this method works when a single shortcut of interest is unknown. At the very least, there should be a discussion on *where* exactly the spurious features lie. Based on how the optimisation is currently set up, I am curious whether the span of the learned P belongs to the span of the orthogonal complement of the spurious features. My hunch is it is, but a result explicitly investigating this connection would be extremely interesting. For example, see Theorem 2 in [3].\n\n[2] Li, Zhiheng, et al. \"A whac-a-mole dilemma: Shortcuts come in multiples where mitigating one amplifies others.\" Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition. 2023.\n\n[3] Ruiz Luyten, Max, and Mihaela van der Schaar. \"A theoretical design of concept sets: improving the predictability of concept bottleneck models.\" Advances in Neural Information Processing Systems 37 (2024): 100160-100195.\n\nQUESTIONS:\n1. Minor comment first: This method is a namesake of a CLIP-based explainability method called Splice [1], which caused a great deal of confusion for me initially, and might cause future confusion as well. Please consider a different name. \n2. The U and V matrices in Theorem 1 have orthonormal columns. I wonder if there are some connections to SVD and other matrix factorization techniques (U and V being the left and right singular vectors in this case). Your paper would then open up possibilities of spectral properties of such spurious features. \n3. Since the authors adopt the term \"concepts\" explicitly, I can't help but mention a strong line of recent work in concept activation vectors that probe similar ideas, albeit not in the domain of shortcut learning. Please see [2]. Is there any particular reason the authors use the term \"concepts\"?\n4. What also interests me is if the feature matrix represents some sort of alignment between modalities, e.g. CLIP features. How would P behave in this multi-modal setup? There is a risk that the covariance between the vision features and labels are preserved but not the text, and vice versa. \n\n[1] Bhalla, Usha, et al. \"Interpreting clip with sparse linear concept embeddings (splice).\" Advances in Neural Information Processing Systems 37 (2024): 84298-84328.\n\n[2] Fel, Thomas, et al. \"A holistic approach to unifying automatic concept extraction and concept importance estimation.\" Advances in Neural Information Processing Systems 36 (2023): 54805-54818.\n\nLIMITATIONS:\nYes", "TITLE": "Official Review", "RECOMMENDATION": 4, "REVIEWER_CONFIDENCE": 4, "CLARITY": 4, "IMPACT": 2, "ORIGINALITY": 3, "DATE": "2025-07-01"}