new

Get trending papers in your email inbox!

Subscribe

Daily Papers

byAK and the research community

Mar 9

Selective Steering: Norm-Preserving Control Through Discriminative Layer Selection

Despite significant progress in alignment, large language models (LLMs) remain vulnerable to adversarial attacks that elicit harmful behaviors. Activation steering techniques offer a promising inference-time intervention approach, but existing methods suffer from critical limitations: activation addition requires careful coefficient tuning and is sensitive to layer-specific norm variations, while directional ablation provides only binary control. Recent work on Angular Steering introduces continuous control via rotation in a 2D subspace, but its practical implementation violates norm preservation, causing distribution shift and generation collapse, particularly in models below 7B parameters. We propose Selective Steering, which addresses these limitations through two key innovations: (1) a mathematically rigorous norm-preserving rotation formulation that maintains activation distribution integrity, and (2) discriminative layer selection that applies steering only where feature representations exhibit opposite-signed class alignment. Experiments across nine models demonstrate that Selective Steering achieves 5.5x higher attack success rates than prior methods while maintaining zero perplexity violations and approximately 100\% capability retention on standard benchmarks. Our approach provides a principled, efficient framework for controllable and stable LLM behavior modification. Code: https://github.com/knoveleng/steering

NaLaFormer: Norm-Aware Linear Attention for Transformer Models

Linear attention has emerged as a viable alternative to softmax attention by reducing complexity from quadratic to linear in sequence length. To preserve two fundamental properties of softmax, non-negativity and entropy reduction, current works employ various linearly separatable kernel functions with L1 normalization instead of softmax operator. However, query norms are neglected by the normalization operation in linear attention, such degradation heavily leads to an entropy gap. Meanwhile, existing works inhibit negative values of query and key vectors resulting in a missing inner-product interactions after being mapped. To address these dual challenges, we propose a novel Norm-Aware Linear Attention mechanism serving to restore norm-guided dynamic spikiness and recover kernel-perturbed norm distributions. Specifically, we first decouple query and key matrices into two components: norm and direction, to achieve norm-aware spikiness control and norm consistency, respectively. We mathematically reveal that the extent of entropy reduction varies with the query norm in softmax normalization, motivating a query-norm aware kernel function for dynamic control over entropy reduction. Furthermore, to ensure norm consistency and enforce non-negativity constraints, we employ a norm-preserving mapping to project all elements of the angular matrix into positive values, leveraging cosine similarity to inhibit dimensions with opposite directions. We conduct extensive experiments demonstrating that the NaLaFormer improves performance on vision and language tasks, enhancing both expressiveness and efficiency by up to 4.2\%.

  • 6 authors
·
Jun 26, 2025

Large Pre-trained Language Models Contain Human-like Biases of What is Right and Wrong to Do

Artificial writing is permeating our lives due to recent advances in large-scale, transformer-based language models (LMs) such as BERT, its variants, GPT-2/3, and others. Using them as pre-trained models and fine-tuning them for specific tasks, researchers have extended state of the art for many NLP tasks and shown that they capture not only linguistic knowledge but also retain general knowledge implicitly present in the data. Unfortunately, LMs trained on unfiltered text corpora suffer from degenerated and biased behaviour. While this is well established, we show that recent LMs also contain human-like biases of what is right and wrong to do, some form of ethical and moral norms of the society -- they bring a "moral direction" to surface. That is, we show that these norms can be captured geometrically by a direction, which can be computed, e.g., by a PCA, in the embedding space, reflecting well the agreement of phrases to social norms implicitly expressed in the training texts and providing a path for attenuating or even preventing toxic degeneration in LMs. Being able to rate the (non-)normativity of arbitrary phrases without explicitly training the LM for this task, we demonstrate the capabilities of the "moral direction" for guiding (even other) LMs towards producing normative text and showcase it on RealToxicityPrompts testbed, preventing the neural toxic degeneration in GPT-2.

  • 5 authors
·
Mar 8, 2021

Preserving Tumor Volumes for Unsupervised Medical Image Registration

Medical image registration is a critical task that estimates the spatial correspondence between pairs of images. However, current traditional and deep-learning-based methods rely on similarity measures to generate a deforming field, which often results in disproportionate volume changes in dissimilar regions, especially in tumor regions. These changes can significantly alter the tumor size and underlying anatomy, which limits the practical use of image registration in clinical diagnosis. To address this issue, we have formulated image registration with tumors as a constraint problem that preserves tumor volumes while maximizing image similarity in other normal regions. Our proposed strategy involves a two-stage process. In the first stage, we use similarity-based registration to identify potential tumor regions by their volume change, generating a soft tumor mask accordingly. In the second stage, we propose a volume-preserving registration with a novel adaptive volume-preserving loss that penalizes the change in size adaptively based on the masks calculated from the previous stage. Our approach balances image similarity and volume preservation in different regions, i.e., normal and tumor regions, by using soft tumor masks to adjust the imposition of volume-preserving loss on each one. This ensures that the tumor volume is preserved during the registration process. We have evaluated our strategy on various datasets and network architectures, demonstrating that our method successfully preserves the tumor volume while achieving comparable registration results with state-of-the-art methods. Our codes is available at: https://dddraxxx.github.io/Volume-Preserving-Registration/.

  • 5 authors
·
Sep 18, 2023

The Unseen Bias: How Norm Discrepancy in Pre-Norm MLLMs Leads to Visual Information Loss

Multimodal Large Language Models (MLLMs), which couple pre-trained vision encoders and language models, have shown remarkable capabilities. However, their reliance on the ubiquitous Pre-Norm architecture introduces a subtle yet critical flaw: a severe norm disparity between the high-norm visual tokens and the low-norm text tokens. In this work, we present a formal theoretical analysis demonstrating that this imbalance is not a static issue. Instead, it induces an ``asymmetric update dynamic,'' where high-norm visual tokens exhibit a ``representational inertia,'' causing them to transform semantically much slower than their textual counterparts. This fundamentally impairs effective cross-modal feature fusion. Our empirical validation across a range of mainstream MLLMs confirms that this theoretical dynamic -- the persistence of norm disparity and the resulting asymmetric update rates -- is a prevalent phenomenon. Based on this insight, we propose a remarkably simple yet effective solution: inserting a single, carefully initialized LayerNorm layer after the visual projector to enforce norm alignment. Experiments conducted on the LLaVA-1.5 architecture show that this intervention yields significant performance gains not only on a wide suite of multimodal benchmarks but also, notably, on text-only evaluations such as MMLU, suggesting that resolving the architectural imbalance leads to a more holistically capable model.

  • 8 authors
·
Dec 9, 2025

EgoNormia: Benchmarking Physical Social Norm Understanding

Human activity is moderated by norms. When performing actions in the real world, humans not only follow norms, but also consider the trade-off between different norms However, machines are often trained without explicit supervision on norm understanding and reasoning, especially when the norms are grounded in a physical and social context. To improve and evaluate the normative reasoning capability of vision-language models (VLMs), we present EgoNormia |epsilon|, consisting of 1,853 ego-centric videos of human interactions, each of which has two related questions evaluating both the prediction and justification of normative actions. The normative actions encompass seven categories: safety, privacy, proxemics, politeness, cooperation, coordination/proactivity, and communication/legibility. To compile this dataset at scale, we propose a novel pipeline leveraging video sampling, automatic answer generation, filtering, and human validation. Our work demonstrates that current state-of-the-art vision-language models lack robust norm understanding, scoring a maximum of 45% on EgoNormia (versus a human bench of 92%). Our analysis of performance in each dimension highlights the significant risks of safety, privacy, and the lack of collaboration and communication capability when applied to real-world agents. We additionally show that through a retrieval-based generation method, it is possible to use EgoNomia to enhance normative reasoning in VLMs.

  • 7 authors
·
Feb 27, 2025 2

LiON-LoRA: Rethinking LoRA Fusion to Unify Controllable Spatial and Temporal Generation for Video Diffusion

Video Diffusion Models (VDMs) have demonstrated remarkable capabilities in synthesizing realistic videos by learning from large-scale data. Although vanilla Low-Rank Adaptation (LoRA) can learn specific spatial or temporal movement to driven VDMs with constrained data, achieving precise control over both camera trajectories and object motion remains challenging due to the unstable fusion and non-linear scalability. To address these issues, we propose LiON-LoRA, a novel framework that rethinks LoRA fusion through three core principles: Linear scalability, Orthogonality, and Norm consistency. First, we analyze the orthogonality of LoRA features in shallow VDM layers, enabling decoupled low-level controllability. Second, norm consistency is enforced across layers to stabilize fusion during complex camera motion combinations. Third, a controllable token is integrated into the diffusion transformer (DiT) to linearly adjust motion amplitudes for both cameras and objects with a modified self-attention mechanism to ensure decoupled control. Additionally, we extend LiON-LoRA to temporal generation by leveraging static-camera videos, unifying spatial and temporal controllability. Experiments demonstrate that LiON-LoRA outperforms state-of-the-art methods in trajectory control accuracy and motion strength adjustment, achieving superior generalization with minimal training data. Project Page: https://fuchengsu.github.io/lionlora.github.io/

  • 4 authors
·
Jul 8, 2025

NorMuon: Making Muon more efficient and scalable

The choice of optimizer significantly impacts the training efficiency and computational costs of large language models (LLMs). Recently, the Muon optimizer has demonstrated promising results by orthogonalizing parameter updates, improving optimization geometry through better conditioning. Despite Muon's emergence as a candidate successor to Adam, the potential for jointly leveraging their strengths has not been systematically explored. In this work, we bridge this gap by proposing NorMuon (Neuron-wise Normalized Muon), an optimizer that synergistically combines orthogonalization with neuron-level adaptive learning rates. Our analysis reveals that while Muon effectively reduces condition numbers, the resulting updates exhibit highly non-uniform neuron norms, causing certain neurons to dominate the optimization process. NorMuon addresses this imbalance by maintaining second-order momentum statistics for each neuron and applying row-wise normalization after orthogonalization, ensuring balanced parameter utilization while preserving Muon's conditioning benefits. To enable practical deployment at scale, we develop an efficient distributed implementation under the FSDP2 framework that strategically distributes orthogonalization computations across devices. Experiments across multiple model scales demonstrate that NorMuon consistently outperforms both Adam and Muon, achieving 21.74% better training efficiency than Adam and 11.31% improvement over Muon on 1.1 B pretraining setting, while maintaining a comparable memory footprint to Muon. Our findings suggest that orthogonalization and adaptive learning rates are complementary rather than competing approaches, opening new avenues for optimizer design in large-scale deep learning.

  • 5 authors
·
Oct 6, 2025 2

boldsymbolλ-Orthogonality Regularization for Compatible Representation Learning

Retrieval systems rely on representations learned by increasingly powerful models. However, due to the high training cost and inconsistencies in learned representations, there is significant interest in facilitating communication between representations and ensuring compatibility across independently trained neural networks. In the literature, two primary approaches are commonly used to adapt different learned representations: affine transformations, which adapt well to specific distributions but can significantly alter the original representation, and orthogonal transformations, which preserve the original structure with strict geometric constraints but limit adaptability. A key challenge is adapting the latent spaces of updated models to align with those of previous models on downstream distributions while preserving the newly learned representation spaces. In this paper, we impose a relaxed orthogonality constraint, namely λ-Orthogonality regularization, while learning an affine transformation, to obtain distribution-specific adaptation while retaining the original learned representations. Extensive experiments across various architectures and datasets validate our approach, demonstrating that it preserves the model's zero-shot performance and ensures compatibility across model updates. Code available at: https://github.com/miccunifi/lambda_orthogonality.git{https://github.com/miccunifi/lambda\_orthogonality}.

  • 5 authors
·
Sep 20, 2025

STILL: Selecting Tokens for Intra-Layer Hybrid Attention to Linearize LLMs

Linearizing pretrained large language models (LLMs) primarily relies on intra-layer hybrid attention mechanisms to alleviate the quadratic complexity of standard softmax attention. Existing methods perform token routing based on sliding-window partitions, resulting in position-based selection and fails to capture token-specific global importance. Meanwhile, linear attention further suffers from distribution shift caused by learnable feature maps that distort pretrained feature magnitudes. Motivated by these limitations, we propose STILL, an intra-layer hybrid linearization framework for efficiently linearizing LLMs. STILL introduces a Self-Saliency Score with strong local-global consistency, enabling accurate token selection using sliding-window computation, and retains salient tokens for sparse softmax attention while summarizing the remaining context via linear attention. To preserve pretrained representations, we design a Norm-Preserved Feature Map (NP-Map) that decouples feature direction from magnitude and reinjects pretrained norms. We further adopt a unified training-inference architecture with chunk-wise parallelization and delayed selection to improve hardware efficiency. Experiments show that STILL matches or surpasses the original pretrained model on commonsense and general reasoning tasks, and achieves up to a 86.2% relative improvement over prior linearized attention methods on long-context benchmarks.

  • 7 authors
·
Feb 2

Training Transformers with Enforced Lipschitz Constants

Neural networks are often highly sensitive to input and weight perturbations. This sensitivity has been linked to pathologies such as vulnerability to adversarial examples, divergent training, and overfitting. To combat these problems, past research has looked at building neural networks entirely from Lipschitz components. However, these techniques have not matured to the point where researchers have trained a modern architecture such as a transformer with a Lipschitz certificate enforced beyond initialization. To explore this gap, we begin by developing and benchmarking novel, computationally-efficient tools for maintaining norm-constrained weight matrices. Applying these tools, we are able to train transformer models with Lipschitz bounds enforced throughout training. We find that optimizer dynamics matter: switching from AdamW to Muon improves standard methods -- weight decay and spectral normalization -- allowing models to reach equal performance with a lower Lipschitz bound. Inspired by Muon's update having a fixed spectral norm, we co-design a weight constraint method that improves the Lipschitz vs. performance tradeoff on MLPs and 2M parameter transformers. Our 2-Lipschitz transformer on Shakespeare text reaches validation accuracy 60%. Scaling to 145M parameters, our 10-Lipschitz transformer reaches 21% accuracy on internet text. However, to match the NanoGPT baseline validation accuracy of 39.4%, our Lipschitz upper bound increases to 10^264. Nonetheless, our Lipschitz transformers train without stability measures such as layer norm, QK norm, and logit tanh softcapping.

  • 6 authors
·
Jul 17, 2025

InTAct: Interval-based Task Activation Consolidation for Continual Learning

Continual learning aims to enable neural networks to acquire new knowledge without forgetting previously learned information. While recent prompt-based methods perform strongly in class-incremental settings, they remain vulnerable under domain shifts, where the input distribution changes but the label space remains fixed. This exposes a persistent problem known as representation drift. Shared representations evolve in ways that overwrite previously useful features and cause forgetting even when prompts isolate task-specific parameters. To address this issue, we introduce InTAct, a method that preserves functional behavior in shared layers without freezing parameters or storing past data. InTAct captures the characteristic activation ranges associated with previously learned tasks and constrains updates to ensure the network remains consistent within these regions, while still allowing for flexible adaptation elsewhere. In doing so, InTAct stabilizes the functional role of important neurons rather than directly restricting parameter values. The approach is architecture-agnostic and integrates seamlessly into existing prompt-based continual learning frameworks. By regulating representation changes where past knowledge is encoded, InTAct achieves a principled balance between stability and plasticity. Across diverse domain-incremental benchmarks, including DomainNet and ImageNet-R, InTAct consistently reduces representation drift and improves performance, increasing Average Accuracy by up to 8 percentage points over state-of-the-art baselines.

  • 6 authors
·
Nov 21, 2025

Large Language Model Evaluation via Matrix Nuclear-Norm

As large language models (LLMs) continue to evolve, efficient evaluation metrics are vital for assessing their ability to compress information and reduce redundancy. While traditional metrics like Matrix Entropy offer valuable insights, they are computationally intensive for large-scale models due to their \( O(n^3) \) time complexity with Singular Value Decomposition (SVD). To mitigate this issue, we introduce the Matrix Nuclear-Norm, which not only serves as a metric to quantify the data compression proficiency of LLM but also provides a convex approximation of matrix rank to capture both predictive discriminability and diversity. By employing the \( L_{1,2}-norm \) to further approximate the nuclear norm, we can effectively assess the model's information compression capabilities. This approach reduces the time complexity to \( O(n^2) \) and eliminates the need for SVD computation. Consequently, the Matrix Nuclear-Norm achieves speeds 8 to 24 times faster than Matrix Entropy for the CEREBRAS-GPT model as sizes increase from 111M to 6.7B. This performance gap becomes more pronounced with larger models, as validated in tests with other models like Pythia. Additionally, evaluations on benchmarks and model responses confirm that our proposed Matrix Nuclear-Norm is a reliable, scalable, and efficient tool for assessing LLMs' performance, striking a balance between accuracy and computational efficiency. The code is available at https://github.com/MLGroupJLU/MatrixNuclearNorm.

  • 4 authors
·
Oct 14, 2024 2

DONOD: Robust and Generalizable Instruction Fine-Tuning for LLMs via Model-Intrinsic Dataset Pruning

Ad-hoc instruction fine-tuning of large language models (LLMs) is widely adopted for domain-specific adaptation. While domain-specific supervised fine-tuning (SFT) is effective and efficient, it often weakens cross-domain generalization and struggles with noisy training data. To address these challenges, we propose DONOD, a lightweight model-intrinsic data pruning method. Our approach evaluates data using two model-parameter-based metrics: Delta of Norm (DON), which captures the cumulative influence on model weights, and Norm of Delta (NOD), which quantifies weight instability. Moreover, by employing the Technique for Order of Preference by Similarity to Ideal Solution (TOPSIS) algorithm, we effectively filter noisy, unlearnable, and generalization-harming samples without relying on auxiliary models during the SFT process. Experiments on mathematical tasks demonstrate that data selected by DONOD achieve superior fine-tuning efficiency and improved robustness against noisy data. By filtering out 70% of the full dataset, we improve target-domain accuracy by 14.90% and cross-domain accuracy by 5.67%. Meanwhile, our selected data present superior cross-architecture generalization. Data pruned by smaller models (e.g., Llama 3.1-8B) generalize effectively on larger models (e.g., Llama 2-13B). Compared to existing related methodologies, DONOD demonstrates comparable or superior performance while remaining dataset-agnostic, enabling broader applicability.

  • 4 authors
·
Apr 20, 2025

CPAM: Context-Preserving Adaptive Manipulation for Zero-Shot Real Image Editing

Editing natural images using textual descriptions in text-to-image diffusion models remains a significant challenge, particularly in achieving consistent generation and handling complex, non-rigid objects. Existing methods often struggle to preserve textures and identity, require extensive fine-tuning, and exhibit limitations in editing specific spatial regions or objects while retaining background details. This paper proposes Context-Preserving Adaptive Manipulation (CPAM), a novel zero-shot framework for complicated, non-rigid real image editing. Specifically, we propose a preservation adaptation module that adjusts self-attention mechanisms to preserve and independently control the object and background effectively. This ensures that the objects' shapes, textures, and identities are maintained while keeping the background undistorted during the editing process using the mask guidance technique. Additionally, we develop a localized extraction module to mitigate the interference with the non-desired modified regions during conditioning in cross-attention mechanisms. We also introduce various mask-guidance strategies to facilitate diverse image manipulation tasks in a simple manner. Extensive experiments on our newly constructed Image Manipulation BenchmArk (IMBA), a robust benchmark dataset specifically designed for real image editing, demonstrate that our proposed method is the preferred choice among human raters, outperforming existing state-of-the-art editing techniques.

  • 5 authors
·
Jun 23, 2025

UER: A Heuristic Bias Addressing Approach for Online Continual Learning

Online continual learning aims to continuously train neural networks from a continuous data stream with a single pass-through data. As the most effective approach, the rehearsal-based methods replay part of previous data. Commonly used predictors in existing methods tend to generate biased dot-product logits that prefer to the classes of current data, which is known as a bias issue and a phenomenon of forgetting. Many approaches have been proposed to overcome the forgetting problem by correcting the bias; however, they still need to be improved in online fashion. In this paper, we try to address the bias issue by a more straightforward and more efficient method. By decomposing the dot-product logits into an angle factor and a norm factor, we empirically find that the bias problem mainly occurs in the angle factor, which can be used to learn novel knowledge as cosine logits. On the contrary, the norm factor abandoned by existing methods helps remember historical knowledge. Based on this observation, we intuitively propose to leverage the norm factor to balance the new and old knowledge for addressing the bias. To this end, we develop a heuristic approach called unbias experience replay (UER). UER learns current samples only by the angle factor and further replays previous samples by both the norm and angle factors. Extensive experiments on three datasets show that UER achieves superior performance over various state-of-the-art methods. The code is in https://github.com/FelixHuiweiLin/UER.

  • 6 authors
·
Sep 7, 2023

FreezeAsGuard: Mitigating Illegal Adaptation of Diffusion Models via Selective Tensor Freezing

Text-to-image diffusion models can be fine-tuned in custom domains to adapt to specific user preferences, but such unconstrained adaptability has also been utilized for illegal purposes, such as forging public figures' portraits and duplicating copyrighted artworks. Most existing work focuses on detecting the illegally generated contents, but cannot prevent or mitigate illegal adaptations of diffusion models. Other schemes of model unlearning and reinitialization, similarly, cannot prevent users from relearning the knowledge of illegal model adaptation with custom data. In this paper, we present FreezeAsGuard, a new technique that addresses these limitations and enables irreversible mitigation of illegal adaptations of diffusion models. The basic approach is that the model publisher selectively freezes tensors in pre-trained diffusion models that are critical to illegal model adaptations, to mitigate the fine-tuned model's representation power in illegal domains but minimize the impact on legal model adaptations in other domains. Such tensor freezing can be enforced via APIs provided by the model publisher for fine-tuning, can motivate users' adoption due to its computational savings. Experiment results with datasets in multiple domains show that FreezeAsGuard provides stronger power in mitigating illegal model adaptations of generating fake public figures' portraits, while having the minimum impact on model adaptation in other legal domains. The source code is available at: https://github.com/pittisl/FreezeAsGuard/

  • 2 authors
·
May 23, 2024

Enhancing Conditional Image Generation with Explainable Latent Space Manipulation

In the realm of image synthesis, achieving fidelity to a reference image while adhering to conditional prompts remains a significant challenge. This paper proposes a novel approach that integrates a diffusion model with latent space manipulation and gradient-based selective attention mechanisms to address this issue. Leveraging Grad-SAM (Gradient-based Selective Attention Manipulation), we analyze the cross attention maps of the cross attention layers and gradients for the denoised latent vector, deriving importance scores of elements of denoised latent vector related to the subject of interest. Using this information, we create masks at specific timesteps during denoising to preserve subjects while seamlessly integrating the reference image features. This approach ensures the faithful formation of subjects based on conditional prompts, while concurrently refining the background for a more coherent composition. Our experiments on places365 dataset demonstrate promising results, with our proposed model achieving the lowest mean and median Frechet Inception Distance (FID) scores compared to baseline models, indicating superior fidelity preservation. Furthermore, our model exhibits competitive performance in aligning the generated images with provided textual descriptions, as evidenced by high CLIP scores. These results highlight the effectiveness of our approach in both fidelity preservation and textual context preservation, offering a significant advancement in text-to-image synthesis tasks.

  • 1 authors
·
Aug 28, 2024 3

Beyond Hard Writes and Rigid Preservation: Soft Recursive Least-Squares for Lifelong LLM Editing

Model editing updates a pre-trained LLM with new facts or rules without re-training, while preserving unrelated behavior. In real deployment, edits arrive as long streams, and existing editors often face a plasticity-stability dilemma: locate-then-edit "hard writes" can accumulate interference over time, while null-space-style "hard preservation" preserves only what is explicitly constrained, so past edits can be overwritten and unconstrained behaviors may deviate, degrading general capabilities in the many-edits regime. We propose RLSEdit, a recursive least-squares editor for long sequential editing. RLSEdit formulates editing as an online quadratic optimization with soft constraints, minimizing a cumulative key-value fitting objective with two regularizers that control for both deviation from the pre-trained weights and from a designated anchor mapping. The resulting update admits an efficient online recursion via the Woodbury identity, with per-edit cost independent of history length and scaling only with the current edit size. We further provide deviation bounds and an asymptotic characterization of the adherence-preservation trade-off in the many-edits regime. Experiments on multiple model families demonstrate stable scaling to 10K edits, outperforming strong baselines in both edit success and holistic stability -- crucially retaining early edits, and preserving general capabilities on GLUE and held-out reasoning/code benchmarks.

  • 7 authors
·
Jan 22

Gradient Multi-Normalization for Stateless and Scalable LLM Training

Training large language models (LLMs) typically relies on adaptive optimizers like Adam (Kingma & Ba, 2015) which store additional state information to accelerate convergence but incur significant memory overhead. Recent efforts, such as SWAN (Ma et al., 2024) address this by eliminating the need for optimizer states while achieving performance comparable to Adam via a multi-step preprocessing procedure applied to instantaneous gradients. Motivated by the success of SWAN, we introduce a novel framework for designing stateless optimizers that normalizes stochastic gradients according to multiple norms. To achieve this, we propose a simple alternating scheme to enforce the normalization of gradients w.r.t these norms. We show that our procedure can produce, up to an arbitrary precision, a fixed-point of the problem, and that SWAN is a particular instance of our approach with carefully chosen norms, providing a deeper understanding of its design. However, SWAN's computationally expensive whitening/orthogonalization step limit its practicality for large LMs. Using our principled perspective, we develop of a more efficient, scalable, and practical stateless optimizer. Our algorithm relaxes the properties of SWAN, significantly reducing its computational cost while retaining its memory efficiency, making it applicable to training large-scale models. Experiments on pre-training LLaMA models with up to 1 billion parameters demonstrate a 3X speedup over Adam with significantly reduced memory requirements, outperforming other memory-efficient baselines.

  • 4 authors
·
Feb 10, 2025

Fira: Can We Achieve Full-rank Training of LLMs Under Low-rank Constraint?

Low-rank training has emerged as a promising approach for reducing memory usage in training Large Language Models (LLMs). Previous methods either rely on decomposing weight matrices (e.g., LoRA), or seek to decompose gradient matrices (e.g., GaLore) to ensure reduced memory consumption. However, both of them constrain the training in a low-rank subspace, thus inevitably leading to sub-optimal performance. This raises a question: whether it is possible to consistently preserve the low-rank constraint for memory efficiency, while achieving full-rank training (i.e., training with full-rank gradients of full-rank weights) to avoid inferior outcomes? In this paper, we propose a new plug-and-play training framework for LLMs called Fira, as the first attempt to achieve this goal. First, we observe an interesting phenomenon during LLM training: the scaling impact of adaptive optimizers (e.g., Adam) on the gradient norm remains similar from low-rank to full-rank training. Based on this observation, we propose a norm-based scaling method, which utilizes the scaling impact of low-rank optimizers as substitutes for that of original full-rank optimizers to enable full-rank training. In this way, we can preserve the low-rank constraint in the optimizer while achieving full-rank training for better performance. Moreover, we find that there are sudden gradient rises during the optimization process, potentially causing loss spikes. To address this, we further put forward a norm-growth limiter to smooth the gradient via regulating the relative increase of gradient norms. Extensive experiments on the pre-training and fine-tuning of LLMs show that Fira outperforms both LoRA and GaLore, achieving performance that is comparable to or even better than full-rank training.

  • 7 authors
·
Oct 2, 2024 1

Beyond ell_1 sparse coding in V1

Growing evidence indicates that only a sparse subset from a pool of sensory neurons is active for the encoding of visual stimuli at any instant in time. Traditionally, to replicate such biological sparsity, generative models have been using the ell_1 norm as a penalty due to its convexity, which makes it amenable to fast and simple algorithmic solvers. In this work, we use biological vision as a test-bed and show that the soft thresholding operation associated to the use of the ell_1 norm is highly suboptimal compared to other functions suited to approximating ell_q with 0 leq q < 1 (including recently proposed Continuous Exact relaxations), both in terms of performance and in the production of features that are akin to signatures of the primary visual cortex. We show that ell_1 sparsity produces a denser code or employs a pool with more neurons, i.e. has a higher degree of overcompleteness, in order to maintain the same reconstruction error as the other methods considered. For all the penalty functions tested, a subset of the neurons develop orientation selectivity similarly to V1 neurons. When their code is sparse enough, the methods also develop receptive fields with varying functionalities, another signature of V1. Compared to other methods, soft thresholding achieves this level of sparsity at the expense of much degraded reconstruction performance, that more likely than not is not acceptable in biological vision. Our results indicate that V1 uses a sparsity inducing regularization that is closer to the ell_0 pseudo-norm rather than to the ell_1 norm.

  • 4 authors
·
Jan 24, 2023

Guide-and-Rescale: Self-Guidance Mechanism for Effective Tuning-Free Real Image Editing

Despite recent advances in large-scale text-to-image generative models, manipulating real images with these models remains a challenging problem. The main limitations of existing editing methods are that they either fail to perform with consistent quality on a wide range of image edits or require time-consuming hyperparameter tuning or fine-tuning of the diffusion model to preserve the image-specific appearance of the input image. We propose a novel approach that is built upon a modified diffusion sampling process via the guidance mechanism. In this work, we explore the self-guidance technique to preserve the overall structure of the input image and its local regions appearance that should not be edited. In particular, we explicitly introduce layout-preserving energy functions that are aimed to save local and global structures of the source image. Additionally, we propose a noise rescaling mechanism that allows to preserve noise distribution by balancing the norms of classifier-free guidance and our proposed guiders during generation. Such a guiding approach does not require fine-tuning the diffusion model and exact inversion process. As a result, the proposed method provides a fast and high-quality editing mechanism. In our experiments, we show through human evaluation and quantitative analysis that the proposed method allows to produce desired editing which is more preferable by humans and also achieves a better trade-off between editing quality and preservation of the original image. Our code is available at https://github.com/FusionBrainLab/Guide-and-Rescale.

  • 5 authors
·
Sep 2, 2024 2

Computational Limits of Low-Rank Adaptation (LoRA) for Transformer-Based Models

We study the computational limits of Low-Rank Adaptation (LoRA) update for finetuning transformer-based models using fine-grained complexity theory. Our key observation is that the existence of low-rank decompositions within the gradient computation of LoRA adaptation leads to possible algorithmic speedup. This allows us to (i) identify a phase transition behavior and (ii) prove the existence of nearly linear algorithms by controlling the LoRA update computation term by term, assuming the Strong Exponential Time Hypothesis (SETH). For the former, we identify a sharp transition in the efficiency of all possible rank-r LoRA update algorithms for transformers, based on specific norms resulting from the multiplications of the input sequence X, pretrained weights W^star, and adapter matrices alpha B A / r. Specifically, we derive a shared upper bound threshold for such norms and show that efficient (sub-quadratic) approximation algorithms of LoRA exist only below this threshold. For the latter, we prove the existence of nearly linear approximation algorithms for LoRA adaptation by utilizing the hierarchical low-rank structures of LoRA gradients and approximating the gradients with a series of chained low-rank approximations. To showcase our theory, we consider two practical scenarios: partial (e.g., only W_V and W_Q) and full adaptations (e.g., W_Q, W_V, and W_K) of weights in attention heads.

  • 5 authors
·
Jun 5, 2024

Detecting and Mitigating Memorization in Diffusion Models through Anisotropy of the Log-Probability

Diffusion-based image generative models produce high-fidelity images through iterative denoising but remain vulnerable to memorization, where they unintentionally reproduce exact copies or parts of training images. Recent memorization detection methods are primarily based on the norm of score difference as indicators of memorization. We prove that such norm-based metrics are mainly effective under the assumption of isotropic log-probability distributions, which generally holds at high or medium noise levels. In contrast, analyzing the anisotropic regime reveals that memorized samples exhibit strong angular alignment between the guidance vector and unconditional scores in the low-noise setting. Through these insights, we develop a memorization detection metric by integrating isotropic norm and anisotropic alignment. Our detection metric can be computed directly on pure noise inputs via two conditional and unconditional forward passes, eliminating the need for costly denoising steps. Detection experiments on Stable Diffusion v1.4 and v2 show that our metric outperforms existing denoising-free detection methods while being at least approximately 5x faster than the previous best approach. Finally, we demonstrate the effectiveness of our approach by utilizing a mitigation strategy that adapts memorized prompts based on our developed metric. The code is available at https://github.com/rohanasthana/memorization-anisotropy .

  • 2 authors
·
Jan 28

SaRA: High-Efficient Diffusion Model Fine-tuning with Progressive Sparse Low-Rank Adaptation

In recent years, the development of diffusion models has led to significant progress in image and video generation tasks, with pre-trained models like the Stable Diffusion series playing a crucial role. Inspired by model pruning which lightens large pre-trained models by removing unimportant parameters, we propose a novel model fine-tuning method to make full use of these ineffective parameters and enable the pre-trained model with new task-specified capabilities. In this work, we first investigate the importance of parameters in pre-trained diffusion models, and discover that the smallest 10% to 20% of parameters by absolute values do not contribute to the generation process. Based on this observation, we propose a method termed SaRA that re-utilizes these temporarily ineffective parameters, equating to optimizing a sparse weight matrix to learn the task-specific knowledge. To mitigate overfitting, we propose a nuclear-norm-based low-rank sparse training scheme for efficient fine-tuning. Furthermore, we design a new progressive parameter adjustment strategy to make full use of the re-trained/finetuned parameters. Finally, we propose a novel unstructural backpropagation strategy, which significantly reduces memory costs during fine-tuning. Our method enhances the generative capabilities of pre-trained models in downstream applications and outperforms traditional fine-tuning methods like LoRA in maintaining model's generalization ability. We validate our approach through fine-tuning experiments on SD models, demonstrating significant improvements. SaRA also offers a practical advantage that requires only a single line of code modification for efficient implementation and is seamlessly compatible with existing methods.

  • 6 authors
·
Sep 10, 2024 2

Deep Learning on a Data Diet: Finding Important Examples Early in Training

Recent success in deep learning has partially been driven by training increasingly overparametrized networks on ever larger datasets. It is therefore natural to ask: how much of the data is superfluous, which examples are important for generalization, and how do we find them? In this work, we make the striking observation that, in standard vision datasets, simple scores averaged over several weight initializations can be used to identify important examples very early in training. We propose two such scores -- the Gradient Normed (GraNd) and the Error L2-Norm (EL2N) scores -- and demonstrate their efficacy on a range of architectures and datasets by pruning significant fractions of training data without sacrificing test accuracy. In fact, using EL2N scores calculated a few epochs into training, we can prune half of the CIFAR10 training set while slightly improving test accuracy. Furthermore, for a given dataset, EL2N scores from one architecture or hyperparameter configuration generalize to other configurations. Compared to recent work that prunes data by discarding examples that are rarely forgotten over the course of training, our scores use only local information early in training. We also use our scores to detect noisy examples and study training dynamics through the lens of important examples -- we investigate how the data distribution shapes the loss surface and identify subspaces of the model's data representation that are relatively stable over training.

  • 3 authors
·
Jul 14, 2021

NormAd: A Benchmark for Measuring the Cultural Adaptability of Large Language Models

The integration of Large Language Models (LLMs) into various global cultures fundamentally presents a cultural challenge: LLMs must navigate interactions, respect social norms, and avoid transgressing cultural boundaries. However, it is still unclear if LLMs can adapt their outputs to diverse cultural norms. Our study focuses on this aspect. We introduce NormAd, a novel dataset, which includes 2.6k stories that represent social and cultural norms from 75 countries, to assess the ability of LLMs to adapt to different granular levels of socio-cultural contexts such as the country of origin, its associated cultural values, and prevalent social norms. Our study reveals that LLMs struggle with cultural reasoning across all contextual granularities, showing stronger adaptability to English-centric cultures over those from the Global South. Even with explicit social norms, the top-performing model, Mistral-7b-Instruct, achieves only 81.8\% accuracy, lagging behind the 95.6\% achieved by humans. Evaluation on NormAd further reveals that LLMs struggle to adapt to stories involving gift-giving across cultures. Due to inherent agreement or sycophancy biases, LLMs find it considerably easier to assess the social acceptability of stories that adhere to cultural norms than those that deviate from them. Our benchmark measures the cultural adaptability (or lack thereof) of LLMs, emphasizing the potential to make these technologies more equitable and useful for global audiences. We release the NormAd dataset and its associated code on GitHub.

  • 5 authors
·
Apr 18, 2024

The Condition Number as a Scale-Invariant Proxy for Information Encoding in Neural Units

This paper explores the relationship between the condition number of a neural network's weight tensor and the extent of information encoded by the associated processing unit, viewed through the lens of information theory. It argues that a high condition number, though not sufficient for effective knowledge encoding, may indicate that the unit has learned to selectively amplify and compress information. This intuition is formalized for linear units with Gaussian inputs, linking the condition number and the transformation's log-volume scaling factor to the characteristics of the output entropy and the geometric properties of the learned transformation. The analysis demonstrates that for a fixed weight norm, a concentrated distribution of singular values (high condition number) corresponds to reduced overall information transfer, indicating a specialized and efficient encoding strategy. Furthermore, the linear stage entropy bound provides an upper limit on post-activation information for contractive, element-wise nonlinearities, supporting the condition number as a scale-invariant proxy for encoding capacity in practical neural networks. An empirical case study applies these principles to guide selective fine-tuning of Large Language Models for both a new task and a new input modality. The experiments show that the proposed method, named KappaTune, effectively mitigates catastrophic forgetting. Unlike many existing catastrophic forgetting mitigation methods that rely on access to pre-training statistics, which are often unavailable, this selective fine-tuning approach offers a way to bypass this common requirement.

  • 1 authors
·
Jun 19, 2025 1

A Unified Framework for Model Editing

Model editing is a growing area focused on updating the knowledge embedded within models. Among the various methodologies, ROME and MEMIT stand out as leading "locate-and-edit" model editing techniques. While MEMIT enables batched editing of memories, ROME is limited to changing one fact at a time. This paper introduces a unifying framework that brings ROME and MEMIT under a single conceptual umbrella, optimizing for the same goal, which we call the "preservation-memorization" objective. This objective aims to preserve the representations of certain selected vectors while memorizing the representations of new factual information. Specifically, ROME optimizes this objective using an equality constraint, whereas MEMIT employs a more flexible least-square constraint. In addition to making batched edits, MEMIT also edits the model at multiple layers. We disentangle the distribution of edits to multiple layers from the optimization objective of MEMIT and show that these edit-distribution algorithms should be considered separate entities worthy of their own line of research. Finally, we present EMMET - an Equality-constrained Mass Model Editing algorithm for Transformers, a new batched memory-editing algorithm. With EMMET, we present a closed form solution for the equality-constrained version of the preservation-memorization objective. We show that EMMET is able to perform batched-edits on par with MEMIT up to a batch-size of 256 and discuss the challenges in stabilizing EMMET. By articulating the "locate-and-edit" model editing algorithms under a simple conceptual framework of "preservation-memorization", we aim to bridge the gap between intuition and mathematics and hope to simplify the journey for future researchers in model editing.

  • 3 authors
·
Mar 21, 2024

Remove360: Benchmarking Residuals After Object Removal in 3D Gaussian Splatting

Understanding what semantic information persists after object removal is critical for privacy-preserving 3D reconstruction and editable scene representations. In this work, we introduce a novel benchmark and evaluation framework to measure semantic residuals, the unintended semantic traces left behind, after object removal in 3D Gaussian Splatting. We conduct experiments across a diverse set of indoor and outdoor scenes, showing that current methods can preserve semantic information despite the absence of visual geometry. We also release Remove360, a dataset of pre/post-removal RGB images and object-level masks captured in real-world environments. While prior datasets have focused on isolated object instances, Remove360 covers a broader and more complex range of indoor and outdoor scenes, enabling evaluation of object removal in the context of full-scene representations. Given ground truth images of a scene before and after object removal, we assess whether we can truly eliminate semantic presence, and if downstream models can still infer what was removed. Our findings reveal critical limitations in current 3D object removal techniques and underscore the need for more robust solutions capable of handling real-world complexity. The evaluation framework is available at github.com/spatial-intelligence-ai/Remove360.git. Data are available at huggingface.co/datasets/simkoc/Remove360.

  • 3 authors
·
Aug 15, 2025

DiffFAE: Advancing High-fidelity One-shot Facial Appearance Editing with Space-sensitive Customization and Semantic Preservation

Facial Appearance Editing (FAE) aims to modify physical attributes, such as pose, expression and lighting, of human facial images while preserving attributes like identity and background, showing great importance in photograph. In spite of the great progress in this area, current researches generally meet three challenges: low generation fidelity, poor attribute preservation, and inefficient inference. To overcome above challenges, this paper presents DiffFAE, a one-stage and highly-efficient diffusion-based framework tailored for high-fidelity FAE. For high-fidelity query attributes transfer, we adopt Space-sensitive Physical Customization (SPC), which ensures the fidelity and generalization ability by utilizing rendering texture derived from 3D Morphable Model (3DMM). In order to preserve source attributes, we introduce the Region-responsive Semantic Composition (RSC). This module is guided to learn decoupled source-regarding features, thereby better preserving the identity and alleviating artifacts from non-facial attributes such as hair, clothes, and background. We further introduce a consistency regularization for our pipeline to enhance editing controllability by leveraging prior knowledge in the attention matrices of diffusion model. Extensive experiments demonstrate the superiority of DiffFAE over existing methods, achieving state-of-the-art performance in facial appearance editing.

  • 10 authors
·
Mar 26, 2024

LoMOE: Localized Multi-Object Editing via Multi-Diffusion

Recent developments in the field of diffusion models have demonstrated an exceptional capacity to generate high-quality prompt-conditioned image edits. Nevertheless, previous approaches have primarily relied on textual prompts for image editing, which tend to be less effective when making precise edits to specific objects or fine-grained regions within a scene containing single/multiple objects. We introduce a novel framework for zero-shot localized multi-object editing through a multi-diffusion process to overcome this challenge. This framework empowers users to perform various operations on objects within an image, such as adding, replacing, or editing many objects in a complex scene in one pass. Our approach leverages foreground masks and corresponding simple text prompts that exert localized influences on the target regions resulting in high-fidelity image editing. A combination of cross-attention and background preservation losses within the latent space ensures that the characteristics of the object being edited are preserved while simultaneously achieving a high-quality, seamless reconstruction of the background with fewer artifacts compared to the current methods. We also curate and release a dataset dedicated to multi-object editing, named LoMOE-Bench. Our experiments against existing state-of-the-art methods demonstrate the improved effectiveness of our approach in terms of both image editing quality and inference speed.

  • 4 authors
·
Mar 1, 2024

StableNormal: Reducing Diffusion Variance for Stable and Sharp Normal

This work addresses the challenge of high-quality surface normal estimation from monocular colored inputs (i.e., images and videos), a field which has recently been revolutionized by repurposing diffusion priors. However, previous attempts still struggle with stochastic inference, conflicting with the deterministic nature of the Image2Normal task, and costly ensembling step, which slows down the estimation process. Our method, StableNormal, mitigates the stochasticity of the diffusion process by reducing inference variance, thus producing "Stable-and-Sharp" normal estimates without any additional ensembling process. StableNormal works robustly under challenging imaging conditions, such as extreme lighting, blurring, and low quality. It is also robust against transparent and reflective surfaces, as well as cluttered scenes with numerous objects. Specifically, StableNormal employs a coarse-to-fine strategy, which starts with a one-step normal estimator (YOSO) to derive an initial normal guess, that is relatively coarse but reliable, then followed by a semantic-guided refinement process (SG-DRN) that refines the normals to recover geometric details. The effectiveness of StableNormal is demonstrated through competitive performance in standard datasets such as DIODE-indoor, iBims, ScannetV2 and NYUv2, and also in various downstream tasks, such as surface reconstruction and normal enhancement. These results evidence that StableNormal retains both the "stability" and "sharpness" for accurate normal estimation. StableNormal represents a baby attempt to repurpose diffusion priors for deterministic estimation. To democratize this, code and models have been publicly available in hf.co/Stable-X

  • 9 authors
·
Jun 24, 2024

FlexGuard: Continuous Risk Scoring for Strictness-Adaptive LLM Content Moderation

Ensuring the safety of LLM-generated content is essential for real-world deployment. Most existing guardrail models formulate moderation as a fixed binary classification task, implicitly assuming a fixed definition of harmfulness. In practice, enforcement strictness - how conservatively harmfulness is defined and enforced - varies across platforms and evolves over time, making binary moderators brittle under shifting requirements. We first introduce FlexBench, a strictness-adaptive LLM moderation benchmark that enables controlled evaluation under multiple strictness regimes. Experiments on FlexBench reveal substantial cross-strictness inconsistency in existing moderators: models that perform well under one regime can degrade substantially under others, limiting their practical usability. To address this, we propose FlexGuard, an LLM-based moderator that outputs a calibrated continuous risk score reflecting risk severity and supports strictness-specific decisions via thresholding. We train FlexGuard via risk-alignment optimization to improve score-severity consistency and provide practical threshold selection strategies to adapt to target strictness at deployment. Experiments on FlexBench and public benchmarks demonstrate that FlexGuard achieves higher moderation accuracy and substantially improved robustness under varying strictness. We release the source code and data to support reproducibility.

  • 4 authors
·
Feb 26

Reliable and Efficient Concept Erasure of Text-to-Image Diffusion Models

Text-to-image models encounter safety issues, including concerns related to copyright and Not-Safe-For-Work (NSFW) content. Despite several methods have been proposed for erasing inappropriate concepts from diffusion models, they often exhibit incomplete erasure, consume a lot of computing resources, and inadvertently damage generation ability. In this work, we introduce Reliable and Efficient Concept Erasure (RECE), a novel approach that modifies the model in 3 seconds without necessitating additional fine-tuning. Specifically, RECE efficiently leverages a closed-form solution to derive new target embeddings, which are capable of regenerating erased concepts within the unlearned model. To mitigate inappropriate content potentially represented by derived embeddings, RECE further aligns them with harmless concepts in cross-attention layers. The derivation and erasure of new representation embeddings are conducted iteratively to achieve a thorough erasure of inappropriate concepts. Besides, to preserve the model's generation ability, RECE introduces an additional regularization term during the derivation process, resulting in minimizing the impact on unrelated concepts during the erasure process. All the processes above are in closed-form, guaranteeing extremely efficient erasure in only 3 seconds. Benchmarking against previous approaches, our method achieves more efficient and thorough erasure with minor damage to original generation ability and demonstrates enhanced robustness against red-teaming tools. Code is available at https://github.com/CharlesGong12/RECE.

  • 5 authors
·
Jul 17, 2024

MyTimeMachine: Personalized Facial Age Transformation

Facial aging is a complex process, highly dependent on multiple factors like gender, ethnicity, lifestyle, etc., making it extremely challenging to learn a global aging prior to predict aging for any individual accurately. Existing techniques often produce realistic and plausible aging results, but the re-aged images often do not resemble the person's appearance at the target age and thus need personalization. In many practical applications of virtual aging, e.g. VFX in movies and TV shows, access to a personal photo collection of the user depicting aging in a small time interval (20sim40 years) is often available. However, naive attempts to personalize global aging techniques on personal photo collections often fail. Thus, we propose MyTimeMachine (MyTM), which combines a global aging prior with a personal photo collection (using as few as 50 images) to learn a personalized age transformation. We introduce a novel Adapter Network that combines personalized aging features with global aging features and generates a re-aged image with StyleGAN2. We also introduce three loss functions to personalize the Adapter Network with personalized aging loss, extrapolation regularization, and adaptive w-norm regularization. Our approach can also be extended to videos, achieving high-quality, identity-preserving, and temporally consistent aging effects that resemble actual appearances at target ages, demonstrating its superiority over state-of-the-art approaches.

  • 6 authors
·
Nov 21, 2024 2

Backward-Compatible Aligned Representations via an Orthogonal Transformation Layer

Visual retrieval systems face significant challenges when updating models with improved representations due to misalignment between the old and new representations. The costly and resource-intensive backfilling process involves recalculating feature vectors for images in the gallery set whenever a new model is introduced. To address this, prior research has explored backward-compatible training methods that enable direct comparisons between new and old representations without backfilling. Despite these advancements, achieving a balance between backward compatibility and the performance of independently trained models remains an open problem. In this paper, we address it by expanding the representation space with additional dimensions and learning an orthogonal transformation to achieve compatibility with old models and, at the same time, integrate new information. This transformation preserves the original feature space's geometry, ensuring that our model aligns with previous versions while also learning new data. Our Orthogonal Compatible Aligned (OCA) approach eliminates the need for re-indexing during model updates and ensures that features can be compared directly across different model updates without additional mapping functions. Experimental results on CIFAR-100 and ImageNet-1k demonstrate that our method not only maintains compatibility with previous models but also achieves state-of-the-art accuracy, outperforming several existing methods.

  • 4 authors
·
Aug 16, 2024 2

Geometric-Disentangelment Unlearning

Machine unlearning, the removal of a training subset's influence from a deployed model, is critical for privacy preservation and model reliability, yet gradient ascent on forget samples often harms retained knowledge. Existing approaches face a persistent tradeoff between effective forgetting and preservation on the retain set. While previous methods provide useful heuristics, they often lack a formal analysis on how exactly forgetting updates harm retained knowledge, and whether the side effects can be removed with theoretical guarantees. To explore a theoretically sound and simple solution, we start from the first principle on how performance on the retain set is actually affected: a first-order analysis of the local change of the retain loss under small parameter updates during model training. We start from a crisp equivalence: the retain loss is unchanged to first order iff the update direction is orthogonal to the subspace spanned by retain gradients ("retain-invariant"). This identifies the entangled component as the tangential part of forget update within the retain-gradient subspace, and characterizes disentanglement as orthogonality. Guided by this, we propose the Geometric-disentanglement Unlearning (GU) that decomposes any candidate forget gradient update into tangential and normal components to retain space and executes only the normal component. Under a standard trust-region budget, the projected direction aligned with the raw forget gradient is optimal among all first-order retain-invariant moves, and we also derive the optimal projected direction for joint forget-retain updating objectives. Our method is plug-and-play and can be attached to existing gradient-based unlearning procedures to mitigate side effects. GU achieves consistent improvement on various methods across three benchmarks TOFU, MUSE, and WMDP.

  • 11 authors
·
Nov 21, 2025