Title: Machine Unlearning via Task Simplex Arithmetic
Venue: NeurIPS 2025
Accepted: yes
Keywords: Machine Unlearning

Simplex

VLM
Abstract: As foundation Vision-Language Models (VLMs) unlock fine-tuning on smaller datasets while leveraging large-scale pre-training data, machine unlearning becomes critical in addressing privacy concerns and regulatory compliance. Task vector, representing the difference between parameters of models fine-tuned with and without specific data, is a popular retraining-free unlearning strategy. However, we observe that task vectors exhibit substantial sensitivity to various fine-tuning configurations, resulting in unstable unlearning effectiveness that correlates negatively with the prediction-level variance. While aggregating multiple functions (e.g., VLM with classifier) whose parameters are represented by different task vectors  reduces function variance and improves unlearning, the computational cost of obtaining numerous task vectors and aggregating functions is computationally high. Thus, in order to  capture the space of task vectors induced by diverse fine-tuning strategies, we propose modeling it within the convex hull of $(Q-1)$-simplex whose vertices represent $Q$ task vectors. Although a function ensemble can be formed by sampling numerous task vectors from such a simplex, we derive a closed-form ensemble of an infinite number of functions whose parameters are uniformly sampled from the simplex, enabling efficient function-level task vector ensembling with enhanced unlearning performance. Extensive experiments and analyses across diverse datasets and scenarios demonstrate the efficacy of our method.


Peer reviews:
{"IS_META_REVIEW": false, "comments": "SUMMARY:\nThe paper proposes to improve unlearning by sampling task vectors from a simplex, which is composed of Q pivot task vectors. Authors discuss the potential of the method for reducing variance. Experiments are conducted on standard unlearning benchmarks with different VLMs.\n\nSTRENGTHS AND WEAKNESSES:\nStrengths\n- Making task arithmetic more robust is an important question for unlearning (and model merging). The paper is well-motivated, and the empirical results are good.\n\nWeaknesses\n- Some notations are not clear (e.g., variance of function ensemble) \n- Some baselines can be improved (the proposed method is a general approach and can be applied to other scenarios besides VLMs)\n- Please see details in the question section.\n\nQUESTIONS:\n- I would think that ensemble is a general approach that can be applied to other pretrained models (e.g., LLM). Furthermore, by reducing variance, it may also help other task arithmetic operations besides unlearning (e.g., learning instead of unlearning, adding task vectors from different tasks). Can we have a brief discussion on different models and tasks?\n- On the variance of the ensemble\n  * Line 44, the notation of \\sigma(x) is somewhat unclear. In my understanding, the randomness of the ensemble is from the subscript i (i.e., randomly selecting f \\in R^C from Q possible task vectors), thus it is a multivariate random variable, and we should discuss the covariance rather than a scalar.the Does the notation there assume independence among f's components, or is f is a scalar (the probability of ground truth)?  \n  * Line 59, can you further explain the reference to Bienaymé formula? It basically says that the variance of a sum of independent variables is the sum of each r.v.'s variance. Here, the ensemble is a sum of f \\in R^C (each of which is a predicted C-dimensional distribution), but each prediction is not a random variable (as my understanding above, the randomness is from selecting Q task vectors, not from the classifier's output). Would you please clarify which random variable is studied here?  \n- Line 151, the Hessian term may contain subscript c.\n- Equation 2, I would suggest using integration, rather than summations,  over \\tau. For completeness, it is also helpful to specify how to compute the first-order term.\n- Equation 10/11, the \\sigma^2 term contains unclosed parentheses. \n- On experiments:\n  * Figure 3, I would suggest improving the function ensemble baseline by further increasing Q \n  * Table 3, in the incremental unlearning setting, does the ensemble method still keep the retain set performance?\n  * It would also be better to discuss limitations of the proposed methods (e.g., additional costs of computing/storing Hessian)\n  * Regarding line 604 (paper checklist), it would be better to open the code to help reproduce the results.\n\nLIMITATIONS:\nPlease see the question section.", "TITLE": "Official Review", "RECOMMENDATION": 4, "REVIEWER_CONFIDENCE": 3, "CLARITY": 2, "IMPACT": 3, "ORIGINALITY": 3, "DATE": "2025-06-25"}

{"IS_META_REVIEW": false, "comments": "SUMMARY:\nThis work proposes a method for machine unlearning, which is an interesting and practically important problem. The authors point out that task vectors, a popular unlearning strategy, exhibit substantial sensitivity to various fine-tuning configurations, leading to unstable unlearning effectiveness. Obtaining and aggregating multiple task vectors can reduce prediction-level variance and improve unlearning results; however, this comes at a high computational cost.\n\nThis manuscript presents a method that captures the space of task vectors induced by diverse fine-tuning strategies. Specifically, it models this space through the convex hull of a \n(𝑄−1)-simplex whose vertices correspond to 𝑄 task vectors. Instead of sampling task vectors directly from the simplex, the authors derive a closed-form ensemble representing an infinite number of functions whose parameters are uniformly sampled from the simplex, thereby achieving enhanced unlearning performance in a computationally efficient manner.\n\nThe method appears to be supported by solid theoretical foundations. Furthermore, the experimental results and accompanying analyses demonstrate the effectiveness of the proposed approach.\n\nSTRENGTHS AND WEAKNESSES:\nStrengths:\nThe paper is well-written and clearly organized.\nThe proposed method is theoretically sound.\nThe experimental results and analyses are thorough and convincing.\n\nWeaknesses:\nThe section titled “Proposed Method” contains many abstract equations, which may be difficult for readers who are not deeply familiar with this specific area to fully understand. Providing more intuitive explanations or illustrative examples could greatly improve accessibility.\n\nQUESTIONS:\nOverall, I find this paper interesting and well-motivated. Minor clarifications and improvements, however, would further strengthen the work.\n(1) This manuscript appears to be very theoretical. Providing more intuitive explanations or illustrative examples could significantly improve accessibility for a broader audience.\n(2) Regarding the organization of the “Proposed Method” section: there is only one numbered subsection titled “Problem Formulation.” This structure may lead to the misunderstanding that all subsequent content falls under problem formulation. It would be clearer to divide this section into multiple meaningful subsections.\n(3) In the paragraph beginning with \"Unlearning with Task Vectors\", the sentence that \"Moreover, our closed-form solution achieves the lowest accuracy (the lower the better) on the forget set, surpassing the state-of-the-art approach by 3.3% on ViT-Base/32-based CLIP.\" is not directly supported by the results in Table 1. Additionally, in the paragraph starting with “Unlearning with Linear Task Vectors,” Another sentence in the paragraph beginning with \"Unlearning with Linear Task Vectors\", the sentence \"Table 1 shows that the linearized task vectors consistently yield substantial reductions in the forget set accuracy 258 across multiple merging methods and CLIP architectures, while maintaining fixed accuracy on the 259 retain set relative to their standard (non-linearized) counterparts in Table 1.\" appears to mistakenly reference Table 1 twice, whereas the first mention likely should refer to Table 1.\n\nLIMITATIONS:\nYes, but they put the discussion on limitations in Appendix F.2 instead of the main text.", "TITLE": "Official Review", "RECOMMENDATION": 5, "REVIEWER_CONFIDENCE": 3, "CLARITY": 3, "IMPACT": 3, "ORIGINALITY": 3, "DATE": "2025-06-29"}

{"IS_META_REVIEW": false, "comments": "SUMMARY:\nThis paper addresses the problem of machine unlearning in large vision-language models (VLMs) like CLIP. Machine unlearning refers to efficiently removing or “forgetting” the influence of certain training data (the forget set) from a model without retraining from scratch, to meet privacy regulations (e.g. the “right to be forgotten” under GDPR). The authors build on the concept of task vectors – differences in model parameters when fine-tuning with vs. without the target data (as used in Editing Models with Task Arithmetic by Ilharco et al., ICLR 2023). In prior work, subtracting a task vector from the model could forget a dataset in a plug-and-play way, but the effectiveness varied greatly depending on fine-tuning specifics. This paper’s key idea is to mitigate that variance by using ensembles of many task vectors. They propose modeling the space of possible task vectors (obtained under different fine-tuning conditions) as a simplex (convex hull) and derive a closed-form solution that aggregates an infinite ensemble of models sampled from this simplex. In simpler terms, instead of relying on one fine-tuned model difference, they analytically average out an infinite number of fine-tuning outcomes, which dramatically reduces prediction variance and improves forgetting performance.\n\nSTRENGTHS AND WEAKNESSES:\nPaper empirically demonstrate that increasing the number of task vectors in an ensemble improves unlearning, showing a clear negative correlation between ensemble prediction variance and forget-set accuracy. Authors introduce the task simplex, a geometric construct capturing a diverse set of task vectors, and show that sampling within this simplex effectively yields interpolations corresponding to “multi-task” unlearning. Additionally, there is  derive a closed-form ensemble method using a second-order Taylor expansion and properties of the Dirichlet distribution, to integrate over infinitely many models from the simplex without brute-force sampling. This yields an analytic solution that can be applied to the original model to forget the data. Moreovere, the paper extend this to a probabilistic aggregator (based on probability of “at least one” model predicting a class) to further boost reliable forgetting. This work also demonstrate how to distill the effects of the infinite ensemble into a single model (a single “unlearning” task vector), making deployment practical. \n\nExtensive experiments on 8 image classification datasets and the ImageNet retain set show that their method outperforms state-of-the-art unlearning methods, including single task vector subtraction (Ilharco et al. 2023), model weight merging techniques (e.g. Wortsman et al.’s Model Soup, ICML 2022), and other ensemble or linearization baselines. They also show their approach supports incremental unlearning – sequentially forgetting multiple datasets one after another – with strong results. The results are impressive. For example, on CLIP ViT-B/32 (Table 1), the average forget-set accuracy (lower is better, since 100% would mean the model still remembers everything) for a single task vector was 24.2%. Their method brings this down to 15.2% – a large improvement (the forget sets are small, so a lower accuracy means the model is doing poorly on them, which is good for forgetting). This outperforms even the strongest baseline (EMR merge got ~21.8%, function ensemble of 30 models ~22.7%). They achieve similarly large gains on the larger CLIP models: e.g., on ViT-L/14, they go from ~16.7% (best prior) down to ~9.98% forget accuracy – essentially halving the residual accuracy on sensitive data, which indicates a very thorough forgetting. Notably, their distilled single model version only slightly regresses (e.g., 15.66% vs 15.20% on ViT-B/32), showing that you don’t actually need to keep multiple models around — one can reap the benefits in a single model after distillation.\n\nOverall, the paper introduces a novel ensemble-based unlearning strategy that is both theoretically grounded and empirically effective, pushing forward the capabilities for efficient post-hoc removal of training data from large models.\n\n===\n\nIf any, one might point out that the method’s computational overhead is front-loaded (fine-tuning 30 models per task). The paper frames this in a positive light (no need to retrain the large model from scratch, which is indeed much more costly than 30 fine-tunings). But 30 fine-tunings with augmentations could still be heavy for very large models or very many forget requests. The authors don’t explicitly report how long those fine-tunings take; however, since they did it for 8 datasets and multiple architectures, it was clearly feasible.\n\nQUESTIONS:\nComputing a full Hessian for CLIP seems infeasible - could you clarify how Equation (3) was implemented? Also, how important are the second-order terms versus first-order?\n\nCLIP ViT-L/14 is large, but how about something like CLIP with Vision Transformer Huge or a future model with billions of parameters – would the method scale? The concern is memory/time for fine-tuning many large models. Do you foresee any obstacles in scaling up, or does the approach parallelize well enough (fine-tuning can be embarrassingly parallel for each task vector)? Also, for very large output spaces (say thousands of classes), does the advanced aggregator (Theorem 2) or variance computation become too slow? It might be helpful to discuss any scalability tricks or limitations.\n\nYour approach makes it easier to remove knowledge of data, which is positive for privacy. Could it be misused in any way? For instance, one could intentionally “unlearn” important facts from a model (for example, sabotage a facial recognition system by making it forget certain identities). This would require access to the model and data, so it’s not a big threat model, but it’s worth considering if making models so flexible could have downsides. Another angle: might repeated unlearning degrade a model in unforeseen ways?\n\nLIMITATIONS:\nA notable limitation is the computational cost and workflow complexity of the approach. It requires multiple fine-tuning runs and careful orchestration (especially if doing sequential unlearning, one must manage updating the base model). In environments with limited computational resources, this could be challenging. However, this is a trade-off: any effective unlearning that is easier than full retraining will have some cost, and here it’s parallelizable fine-tuning jobs which many organizations can manage.\n\nAs discussed, the approach focuses on classification benchmarks. It’s not directly tested on, say, open-vocabulary CLIP tasks or retrieval tasks. So one limitation is task specificity: forgetting is measured in terms of classification accuracy. If the requirement was to forget certain image-text pair associations in CLIP (like CLIP should not associate a particular image with a caption because the caption is private), one might need to adapt the method (maybe fine-tune CLIP’s multimodal head on that association). The method should conceptually extend, but it may require careful setup for different objectives.", "TITLE": "Official Review", "RECOMMENDATION": 5, "REVIEWER_CONFIDENCE": 5, "CLARITY": 4, "IMPACT": 3, "ORIGINALITY": 4, "DATE": "2025-07-03"}

{"IS_META_REVIEW": false, "comments": "SUMMARY:\nThis paper addresses the problem of machine unlearning in Vision-Language Models (VLMs) by proposing a closed-form function ensembling method based on the Task Arithmetic Simplex. Traditional task vector approaches suffer from unstable unlearning due to sensitivity to fine-tuning configurations, with prediction-level variance negatively correlating with unlearning performance. The authors model task vectors as vertices of a (Q-1)-dimensional simplex, deriving a closed-form ensemble of infinite functions via Dirichlet distribution and Taylor expansion, which effectively reduces variance and enhances unlearning. Experiments on 8 visual datasets validate the method’s superiority, especially in incremental unlearning and linear task vector scenarios.\n\nSTRENGTHS AND WEAKNESSES:\nStrengths:\n\n1. **Comprehensive Ablation Studies**: The paper conducts rigorous ablation experiments to decompose the contributions of key components (e.g., advanced aggreagation, vertex importance weighting), clarifying the impact of each module on unlearning performance. \n2. **Theoretical Innovation and Practical Efficacy**: Modeling task vectors as a simplex and deriving closed-form ensembles using convex geometry and Dirichlet distribution addresses the high computational cost of traditional methods. Experiments demonstrate significant accuracy gains on forgetting sets (e.g., 9.98% on ViT-Large/14) with stable retained set performance, validating both theoretical rigor and practical utility.\n\nWeaknesses:\n\n1. **Unjustified Simplex Modeling of Task Vector Space**: The authors propose modeling task vectors within the convex hull of a simplex but lack rigorous justification for this assumption. There is no mathematical proof or empirical analysis (e.g., geometric visualization of task vector distributions) to validate that task vectors indeed form a convex simplex. This raises questions about whether linear combinations of task vectors remain within the valid task space, especially given the non-linear dependencies inherent in real-world fine-tuning scenarios .\n2. **Computational Cost and Dataset Limitations**: While closed-form solutions avoid infinite sampling, generating Q task vectors (e.g., Q=30) requires multiple fine-tunings, imposing high costs for large models. Additionally, experiments are confined to vision datasets, lacking validation on language or cross-modal tasks.\n3. **Theoretical Constraints on Taylor Expansion**: The method relies on small perturbation assumptions (λ), but the paper omits comparative experiments under large perturbations, where second-order approximation validity may decline.\n\nQUESTIONS:\n1. **Theoretical Justification for Simplex Modeling**: Please provide mathematical proof or empirical evidence (e.g., t-SNE visualization of task vector convexity) to support the simplex modeling assumption. How do non-linear task dependencies affect this framework?\n2. **Cross-Modal Generalization**: Are there plans to validate the method on language or multi-modal models? Please include cross-modal experiments to demonstrate generalizability.\n3. **Large Perturbation Robustness**: Could you provide performance data under varying λ to validate the Taylor expansion’s accuracy beyond small perturbation scenarios?\n\nLIMITATIONS:\nN/A", "TITLE": "Official Review", "RECOMMENDATION": 4, "REVIEWER_CONFIDENCE": 4, "CLARITY": 3, "IMPACT": 2, "ORIGINALITY": 2, "DATE": "2025-07-03"}