ICML 2026 Papers

International Conference on Machine Learning

Decision breakdown

6,341papers

Counted from the official paper list; may differ slightly from the number the conference announced.

  • Spotlight
    5368.5%
  • Poster
    5,80591.5%

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SafeSeek: Universal Attribution of Safety Circuits in Language Models

Miao Yu, Siyuan Fu, Moayad Aloqaily, Zhenhong Zhou, Safa Otoum, Xing Fan, Kun Wang, Yufei Guo, Qingsong Wen

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Mechanistic interpretability reveals that safety-critical behaviors (e.g., alignment, jailbreak, backdoor) in Large Language Models (LLMs) are grounded in specialized functional components. However, existing safety attribution methods struggle with generalization and reliability due to their reliance on heuristic, domain-specific metrics and search algorithms. To address this, we propose SafeSeek, a unified safety interpretability framework that identifies functionally complete safety circuits in LLMs via optimization. Unlike methods focusing on isolated heads or neurons, SafeSeek introduces differentiable binary masks to extract multi-granular circuits through gradient descent on safety datasets, while integrates Safety Circuit Tuning to utilize these sparse circuits for efficient safety fine-tuning. We validate SafeSeek in two key scenarios in LLM safety: \textbf{(1) backdoor attacks}, identifying a backdoor circuit with 0.42\% sparsity, whose ablation eradicates the Attack Success Rate (ASR) from 100\% $\to$ 0.4\% while retaining over 99\% general utility; \textbf{(2) safety alignment}, localizing an alignment circuit with 3.03\% heads and 0.79\% neurons, whose removal spikes ASR from 0.8\% $\to$ 96.9\%, whereas excluding this circuit during helpfulness fine-tuning maintains 96.5\% safety retention.

Poster
GSFixer: Improving 3D Gaussian Splatting with Reference-Guided Video Diffusion Priors

Xingyilang Yin, Qi Zhang, Jiahao Chang, Ying Feng, Qingnan Fan, Xi Yang, Chi-Man Pun, Huaqi Zhang, Xiaodong Cun

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Reconstructing 3D scenes using 3D Gaussian Splatting (3DGS) from sparse views is an ill-posed problem due to insufficient information, often resulting in noticeable artifacts. While recent approaches have sought to leverage generative priors to complete information for under-constrained regions, they struggle to generate content that remains consistent with input observations. To address this challenge, we propose GSFixer, a novel framework designed to improve the quality of 3DGS representations reconstructed from sparse inputs. The core of our approach is the reference-guided video restoration model, built upon a DiT-based video diffusion model trained on paired artifact 3DGS renders and clean frames with additional reference-based conditions. Considering the input sparse views as references, our model integrates both 2D semantic and 3D geometric features of reference views extracted from the visual geometry foundation model, enhancing the semantic coherence and 3D consistency when fixing artifact novel views. Furthermore, we introduce a reference-guided trajectory sampling strategy that ensures both angular coverage and view quality, further enhancing reconstruction fidelity. Considering the lack of suitable benchmarks for 3DGS artifact restoration evaluation, we present DL3DV-Res which contains artifact frames rendered using low-quality 3DGS. Extensive experiments demonstrate our GSFixer outperforms current state-of-the-art methods in 3DGS artifact restoration and sparse-view 3D reconstruction. Project page: https://github.com/GVCLab/GSFixer.

Poster
Debate with Images: Detecting Deceptive Behaviors in Multimodal Large Language Models

Sitong Fang, Shiyi Hou, Kaile Wang, Boyuan Chen, Donghai Hong, Jiayi Zhou, Juntao Dai, Yaodong Yang, Jiaming Ji

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As frontier AI systems become increasingly capable, concerns about deceptive behaviors have intensified. Unlike hallucinations, which stem from capability limitations, deception involves strategically misleading responses despite correct internal representations. While prior work has primarily studied deception in text-only settings, little is known about how such behaviors manifest in multimodal large language models. In this work, we systematically investigate multimodal deception and introduce *MM-DeceptionBench*, the first benchmark designed to evaluate deceptive behaviors in vision–language models across six realistic categories. We find that existing text-centric monitoring approaches are insufficient in multimodal settings due to the complexity of cross-modal reasoning. To address this gap, we propose *debate with images*, a multi-agent evaluation framework that enforces visual grounding through adversarial debate. Experiments show that this approach achieves substantially higher agreement with human judgments than MLLM-as-a-judge baselines, improving Cohen’s kappa by up to 1.5$\times$ and accuracy by up to 1.25$\times$ on GPT-4o.

Poster
M+Adam: Low-Precision Training via Additive–Multiplicative Optimization

Xiaoyuan Liang, Sebastian Loeschcke, Mads Toftrup, Anima Anandkumar

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Training with quantized weights can reduce costs but often results in degraded accuracy, especially when optimization is carried out in low precision, without storing high-precision copies. We identify a key failure mode: under low precision, standard optimizers can get stuck and not make progress, especially at large weight magnitudes due to coarse mantissa resolution. To overcome this, multiplicative updates have been previously proposed, in place of additive updates in standard optimizers. While successful under extremely low precision, such as under the logarithmic number system, they suffer from failures near zero and across sign changes. The failure modes of additive and multiplicative updates are therefore complementary. To exploit this, we propose M+Adam, which combines both update types: additive steps handle sign changes and small magnitudes, while multiplicative steps ensure progress at large magnitudes when additive updates are zeroed out under rounding. We prove monotone descent for M+Adam under standard smoothness assumptions. Across LLaMA-style pretraining with 60M--1B models, $1$--$8\times$ Chinchilla budgets, and using only BF16, FP8, and FP4 master weights, M+Adam consistently improves low-precision training.

Poster
CorrectionPlanner: Self-Correction Planner with Reinforcement Learning in Autonomous Driving

Yihong Guo, Dongqiangzi Ye, Sijia Chen, Anqi Liu, Xianming Liu

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Autonomous driving requires safe planning, but most learning-based planners lack explicit self-correction ability: once an unsafe action is proposed, there is no mechanism to correct it. Thus, we propose CorrectionPlanner, an autoregressive planner with self-correction that contains a propose, evaluate, and correct loop in the motion-token generation process. At each planning step, the policy proposes an action, namely a motion token, and a learned collision critic predicts whether it will induce a collision within a short horizon. If the critic predicts a collision, we retain the sequence of historical unsafe motion tokens as a self-correction trace, generate the next motion token conditioned on it, and repeat this process until the safe motion token is proposed or the safety criterion is met. This self-correction trace, consisting of all the unsafe motion tokens, represents the planner’s correction process in motion-token space. We train the planner with imitation learning followed by model-based reinforcement learning using rollouts from a pretrained world model that realistically models agents' reactive behaviors. Closed-loop evaluations show that CorrectionPlanner reduces the collision rate by over $20\%$ on Waymax and obtains state-of-the-art planning scores on nuPlan.

Poster
From Prompts to Responses: Dual-Sided Data Leakage and Defense in Split Large Language Models

Zixuan GU, Xiaojun Ye, Yang Liu

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Large language models (LLMs) are increasingly deployed in privacy-sensitive domains, where users must balance the risk of data exposure through external APIs against the high computational cost of local deployment. Split learning has therefore emerged as a promising paradigm for LLM fine-tuning and inference under limited local resources. However, it introduces new privacy risks. Prior work primarily studies leakage of private input prompts, typically via inversion attacks on intermediate representations, while the potential for sensitive information leakage through generative response outputs remains largely unexplored. In this work, we unveil novel vulnerabilities of Split-LLM by presenting **P**atched Model **I**nversion with **D**ual-Sided **I**nitialization(**PIDI**), a two-stage attack that simultaneously targets both private input prompts and output responses in Split-LLM settings. It combines dual-sided initialization with a patched inversion strategy to tackle long sequences, substantially outperforming prior inversion methods. To counter threats from both sides, we further propose the **A**dapter-based **D**ualGuard with **M**utual **I**nformation Defense(**ADMI**), which integrates an adapter-based local warmup strategy and mutual information regularization to provide a strong empirical privacy protection with minimal impact on task performance. Extensive experiments across diverse tasks and models demonstrate that ADMI effectively defends against PIDI and other state-of-the-art inversion attacks. Our code is publicly available at \url{https://github.com/FLAIR-THU/VFLAIR-LLM}.

Poster
Scalable Bayesian Inference for Nonlinear Conservation Laws

Tim Weiland, Philipp Hennig

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Nonlinear conservation laws are at the heart of many of the most important dynamical systems in science and engineering. In practical applications, such systems are often subject to various sources of uncertainty, e.g. due to sparse or noisy measurements. Inferring physical quantities and fields of interest then becomes an ill-posed problem which both classical numerical methods and modern deep learning-based methods struggle to treat appropriately. Recent work has framed classical numerical methods as Bayesian inference under Gaussian process priors, resulting in a physics-aware treatment of uncertainties. Following this line of work, we develop a novel numerically conservative method for uncertainty-aware simulations of nonlinear conservation laws. We use recent sparse approximation techniques to scale up to large-scale forward and inverse problems. For forward simulation, we inherit the accuracy of classical solvers while providing structured uncertainty quantification. On inverse problems, we recover posteriors over nonparametric source fields in seconds --- outperforming neural baselines that take minutes to produce a less accurate point estimate.

Poster
Differentiable Conformal Training for LLM Reasoning Factuality

Nathan Hittesdorf, Marco Salzetta, Lu Cheng

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Large Language Models (LLMs) frequently hallucinate, limiting their reliability in critical applications. Conformal Prediction (CP) addresses this by calibrating error rates on held-out data to provide statistically valid confidence guarantees. Recent work extends CP to LLM factuality: outputs are decomposed into subclaims, each assigned a risk score, and a calibrated threshold filters out risky claims to guarantee hallucination rates below a user-specified level (e.g., 10%). While prior methods treat claims independently, Coherent Factuality extends to multi-step reasoning by representing outputs as dependency graphs and jointly validating claims with their logical ancestors. A key limitation is that Coherent Factuality is not differentiable, requiring hand-crafted scorers that at high reliability levels remove nearly 60% of true claims. We introduce Differentiable Coherent Factuality (DCF), a fully differentiable relaxation that enables learning improved scorers while provably recovering the original algorithm's guarantees. Experiments on two reasoning datasets demonstrate DCF achieves up to 141% improvement in claim retention while maintaining reliability guarantees, representing a significant step towards reliable conformal LLM systems.

Poster
Continual Learning With Participation Privacy: An Auditable Buffering-Aggregation Recipe

T-H. Hubert Chan, Elaine Shi, Mengshi Zhao, Mingxun Zhou

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Modern federated and streaming learning systems often release intermediate models, so privacy must hold for the full trajectory under adaptive interaction. Motivated by participation privacy, we study single-edit neighboring user streams, where one insertion/deletion shifts all subsequent updates and defeats standard Hamming-neighbor continual-release analyses. We give an auditable modular recipe. A randomized buffering wrapper emits bins of size $[U,2U]$, reducing single-edit streams to a Hamming-style per-bin update stream with explicit backlog/delay guarantees, where $U$ is calibrated by the privacy parameters $(\varepsilon,\delta)$. We then prove a certification theorem for independently decomposable (prefix-causal, fresh-noise) continual mechanisms: any non-adaptive Hamming-neighbor DP proof lifts to adaptive inputs. Together, these ingredients yield trajectory-level $(\varepsilon,\delta)$-DP for single-edit streams using standard primitives (e.g., tree prefix sums), with an explicit privacy--latency link via $U$. Streaming DP-SGD experiments validate the privacy-utility-latency tradeoffs and the induced delay distributions.

Poster
In-Context Generation with Regional Constraints for Instructional Video Editing

Zhongwei Zhang, Fuchen Long, Wei Li, Zhaofan Qiu, Wu Liu, Ting Yao, Tao Mei

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The In-context generation paradigm has demonstrated strong power in instructional image editing for better synthesis quality. Nevertheless, shaping such in-context learning for instructional video editing is not trivial. Without specifying editing regions, the results can suffer from the issue of inaccurate editing regions and the token interference between different areas. To address these, we present ReCo, a new instructional video editing paradigm that novelly delves into **Re**gional **Co**nstraint modeling between editing and non-editing areas. Technically, ReCo width-wise concatenates source and target video for joint denoising. In model training, ReCo formulates regional constraints with two regularization terms, i.e., latent and attention regularization, on one-step backward denoised latents and attention maps, respectively. The former increases the latent discrepancy of the editing region between source and target videos while reducing that of non-editing areas, emphasizing editing area modification and alleviating unexpected content generation. The latter suppresses the attention of tokens in the editing region to the tokens in counterpart of the source video, thereby mitigating their interference during novel object generation in target video. Furthermore, we propose a large-scale, high-quality video editing dataset, i.e., ReCo-Data, comprising 500K instruction-video pairs. Extensive experiments conducted on four major instruction-based video editing tasks verify the superiority of ReCo. Code is available at https://github.com/HiDream-ai/ReCo.

Poster
Mitigating the Safety–Utility Trade-off in LLM Alignment via Adaptive Safe Context Learning

Yanbo Wang, Minzheng Wang, Jian Liang, Lu Wang, Yongcan Yu, Ran He

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While reasoning models have achieved remarkable success in complex reasoning tasks, their increasing power necessitates stringent safety measures. For safety alignment, the core challenge lies in the inherent trade-off between safety and utility. However, prevailing alignment strategies typically construct CoT training data with explicit safety rules via context distillation. This approach inadvertently limits reasoning capabilities by creating a rigid association between rule memorization and refusal. To mitigate the safety-utility trade-off, we propose the Adaptive Safe Context Learning (ASCL) framework to improve the reasoning given proper context. ASCL formulates safety alignment as a multi-turn tool-use process, empowering the model to autonomously decide when to consult safety rules and how to generate the ongoing reasoning. Furthermore, to counteract the preference for rule consultation during RL, we introduce Inverse Frequency Policy Optimization~(IFPO) to rebalance advantage estimates. By decoupling rule retrieval and subsequent reasoning, our method achieves higher overall performance compared to baselines. Our code is publicly available at https://github.com/ybwang119/ASCL.git.

Poster
Semi-knockoffs: a model-agnostic conditional independence testing method with finite-sample guarantees

Angel David REYERO LOBO, Bertrand Thirion, Pierre Neuvial

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Conditional independence testing (CIT) is essential for reliable scientific discovery. It prevents spurious findings and enables controlled feature selection. Recent CIT methods have used machine learning (ML) models as surrogates of the underlying distribution. However, model-agnostic approaches require a train-test split, which reduces statistical power. We introduce Semi-knockoffs, a CIT method that can accommodate any pre-trained model, avoids this split, and provides valid p-values and false discovery rate (FDR) control for high-dimensional settings. Unlike methods that rely on the model-$X$ assumption (known input distribution), Semi-knockoffs only require conditional expectations for continuous variables. This makes the procedure less restrictive and more practical for machine learning integration. To ensure validity when these expectations are estimated, we present two new theoretical results: (i) stability for regularized models trained with a null feature and (ii) the double-robustness property.

Poster
Quaternion Self-Attention with Shared Scores

Shogo Yamauchi, Tohru Nitta, Hideaki Tamori

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Quaternion neural networks are parameter-efficient and model multidimensional dependencies by representing four related features as a single entity. However, existing quaternion self-attention computes component-wise scores and applies independent softmax operations to each component, which increases the computational cost and allows attention distributions to diverge across components. We propose a shared-score quaternion self-attention mechanism that computes a single real-valued score using the quaternion inner product and applies a shared attention distribution across all components. This reduces score-computation multiplications by 75\% and the number of softmax operations from four to one. We prove that, when queries and keys are produced by quaternion linear projections that induce component pre-mixing, the component-wise and shared scores lie in the same interaction subspace, indicating that independent component-wise attention primarily re-parameterizes the same interactions rather than expanding the feature interaction space. In speech enhancement, our method reduces inference time by up to 44.3\% on a GPU and 58.1\% on a CPU while maintaining quality, with consistent trends across vision and natural language processing.

Poster
Unsupervised Camouflaged Object Detection with Dual-Eigenvector Spectral Pseudo-Labeling and Contrastive Refinement

Pingzhu Liu, Chunming He, Zunnan Xu, Chao Hao, Bo Zhao, Xingyu Shao, JUN ZHOU, Zitong Yu, Xiu Li

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Unsupervised Camouflaged Object Detection (UCOD) aims to identify objects concealed in their surroundings without relying on pixel-level labels. Existing methods rely solely on simple post-processing of DINO high-dimensional features to generate pseudo labels for training. However, these methods suffer from two major limitations: 1) pseudo labels they easily generate contain excessive noise, causing the model to learn substantial incorrect information. 2) Although pseudo-label supervision allows the model to understand the task, it remains insufficient for generating fine-grained segmentation of the camouflaged objects. To address these issues, we propose DualUCOD, a novel UCOD method based on dual-branch contrastive learning that effectively detects camouflaged objects without pixel-level labels. Specifically, we propose the Dual-Eigenvector Spectral Pseudo-Labeling (DESPL) strategy, which fuses semantic and color cues into an affinity matrix. We then compute the eigenvectors of its normalized graph Laplacian and generate high-quality pseudo-labels using these eigenvectors. Furthermore, we introduce a Boundary-Guided Foreground-Background Refinement (BGFBR) module that explicitly incorporates boundary information to improve segmentation accuracy. Finally, we introduce a Dual-Branch Contrastive Learning (DBCL) module that constructs positive and negative pairs from the original and augmented images, aligning positive representations while contrasting them against negatives to enhance camouflaged object understanding. Extensive experiments demonstrate that DualUCOD outperforms state-of-the-art methods on different datasets in the unsupervised setting.

Poster
Unlearning’s Blind Spots: Over‑Unlearning and Prototypical Relearning Attack

SeungBum Ha, Saerom Park, Sung Whan Yoon

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Machine unlearning (MU) aims to expunge a designated forget set from a trained model without costly retraining, yet the existing techniques overlook two critical blind spots: "over‑unlearning" that deteriorates retained data near the forget set, and post‑hoc "relearning" attacks that aim to resurrect the forgotten knowledge. Focusing on class-level unlearning, we first derive an over-unlearning metric, $\operatorname{OU}@\varepsilon$, which quantifies collateral damage in regions proximal to the forget set, where over-unlearning mainly occurs. Next, we expose an unforeseen relearning threat on MU, i.e., the Prototypical Relearning Attack, which exploits the per-class prototype of the forget class with just a few samples, and easily restores the pre-unlearning performance. To counter both blind spots in class-level unlearning, we introduce $\texttt{Spotter}$, a plug‑and‑play objective that combines (i) a masked knowledge‑distillation penalty on the nearby region of forget classes to suppress $\operatorname{OU}@\varepsilon$, and (ii) an intra‑class dispersion loss that scatters forget-class embeddings, neutralizing Prototypical Relearning Attacks. $\texttt{Spotter}$ achieves state-of-the-art results across CIFAR, TinyImageNet, and CASIA-WebFace datasets, offering a practical remedy to unlearning’s blind spots.

Poster
Efficient and Safe Molecular Assembly via Reinforcement Learning and Constraint Solving

Stefan Pranger, Bernhard Ramsauer, Oliver T. Hofmann, Bettina Könighofer

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Scanning tunneling microscopy (STM) enables precise manipulation of individual atoms and molecules, offering a pathway to constructing nanoscale assemblies with rich quantum mechanical behavior. Despite its potential, STM-based fabrication remains limited by the inherent complexity of manipulation procedures and the extensive manual effort required. In this work, we take a substantial step toward autonomous manufacturing with STMs by introducing a novel AI-based planning framework for molecular assembly and a high-fidelity simulation environment. Our framework computes collision-free assembly plans that minimize the total distance traveled by molecules. Given an assignment of molecules to target positions, satisfiability solving is used to compute execution schedules in which each molecule has an empty corridor available when it is scheduled to move. Reinforcement learning (RL) agents then execute sequences of STM actions to manipulate molecules to their targets. We further introduce NanoAssemblyGym, a high-fidelity simulation environment for molecular manipulation built on the Gymnasium API, allowing seamless integration with existing RL libraries and workflows. Using NanoAssemblyGym, we demonstrate autonomous assembly of structures containing up to 420 molecules.

Poster
Functional Adjoint Sampler: Scalable Sampling on Infinite Dimensional Spaces

Byoungwoo Park, Juho Lee, Guan-Horng Liu, Guan-Horng Liu

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Learning-based methods for sampling from the Gibbs distribution in finite-dimensional spaces have progressed quickly, yet theory and algorithmic design for infinite-dimensional function spaces remain limited. This gap persists despite their strong potential for sampling the paths of conditional diffusion processes, enabling efficient simulation of trajectories of diffusion processes that respect rare events or boundary constraints. In this work, we present the adjoint sampler for infinite-dimensional function spaces, a stochastic optimal control-based diffusion sampler that operates in function space and targets Gibbs-type distributions on infinite-dimensional Hilbert spaces. Our Functional Adjoint Sampler (FAS) generalizes Adjoint Sampling (Havens et al., 2025) to Hilbert spaces based on a SOC theory called stochastic maximum principle, yielding a simple and scalable matching-type objective for a functional representation. We show that FAS achieves superior transition path sampling performance across synthetic potential and real molecular systems, including Alanine Dipeptide and Chignolin.

Poster
Near-Optimal Regret for KL-Regularized Multi-Armed Bandits

Kaixuan Ji, Qingyue Zhao, Heyang Zhao, Qiwei Di, Quanquan Gu

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Recent studies have shown that reinforcement learning with KL-regularized objectives can enjoy faster rates of convergence or logarithmic regret, in contrast to the classical $\sqrt{T}$-type regret in the unregularized setting. However, the statistical efficiency of online learning with respect to KL-regularized objectives remains far from completely characterized, even when specialized to multi-armed bandits (MABs). We address this problem for MABs via a sharp analysis of KL-UCB (Zhao et al., 2025b) using a novel peeling argument, which yields a $\tilde{O}(\eta K\log^2T)$ KL-regularized regret upper bound: the first high-probability regret bound with linear dependence on $K$. Here, $T$ is the time horizon, $K$ is the number of arms, $\eta^{-1}$ is the regularization intensity, and $\tilde{O}$ hides all logarithmic factors except those involving $\log T$. The near-tightness of our analysis is certified by the first non-constant lower bound $\Omega(\eta K \log T)$, which follows from subtle hard-instance constructions and a tailored decomposition of the Bayes prior. Moreover, in the low-regularization regime (i.e., large $\eta$), we show that the KL-regularized regret for MABs is $\eta$-independent and scales as $\tilde{\Theta}(\sqrt{KT})$. Overall, our results provide a thorough understanding of KL-regularized MABs across all regimes of $\eta$ and yield nearly optimal bounds in terms of $K$, $\eta$, and $T$.

Poster
Persona-Pruner: Sculpting Lightweight Models for Role-Playing

Jinsu Kim, Jihoon Tack, Noah Lee, Jongheon Jeong

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Language Models (LMs) have shown remarkable potential as role-playing chatbots, delivering consistent, stylized interactions when given a specification of a character or user persona. However, applying these capabilities to real-world applications (*e.g*., ecosystems with numerous NPCs interacting simultaneously) exposes a critical inefficiency due to the excessive computational cost. In this paper, we question the necessity of dedicating a full, generalist model to a single persona, hypothesizing that a specific character identity relies on only a fraction of the model’s total capacity. We observe that naïvely pruning LMs often severely degrades the role-playing performance for a specific persona; it does not distinguish between redundant knowledge and essential character traits. We propose **Persona-Pruner**, a framework that sculpts a lightweight role-playing model by isolating persona-specific sub-networks from a single description. Our experiments consistently show that Persona-Pruner preserves role-playing performance substantially more effectively than existing state-of-the-art LLM pruning techniques, reducing the performance drop from the dense model by up to 93.8% over the strongest baseline on RoleBench in LLM-as-a-judge score, while still maintaining general LLM capabilities. Code is available at https://github.com/jsu-kim/Persona-Pruner.

Poster
PRAC: Principal-Random Subspace for LLM Activation Compression and Memory-Efficient Training

Yanyi Li, Yimu Zhang, Cong Fang

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Activations have become the primary memory bottleneck in large-batch LLM training. However, existing compression methods fail to exploit the spectral structure of activations, resulting in slow convergence or limited compression. To address this, we bridge the relationship between the algorithm’s fast convergence and the requirements for subspace projection, and show that an effective compression should yield an unbiased estimate of the original activation with low variance. We propose **P**rincipal-**R**andom Subspace for LLM **A**ctivation **C**ompression (**PRAC**), which novelly decomposes activations into two components: a principal subspace captured via SVD to retain dominant information, and a random subspace sampled from the orthogonal complement to approximate the tail. By introducing a precise scaling factor, we prove that PRAC yields an unbiased gradient estimator with minimum variance under certain conditions. Extensive experiments on pre-training and fine-tuning tasks demonstrate that PRAC achieves up to 36\% total memory reduction with negligible performance degradation and minimal computational cost.

Poster