NeurIPS 2026 论文列表

Conference on Neural Information Processing Systems

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6,437篇论文

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Replicable Constrained Bandits

Matteo Bollini, Gianmarco Genalti, Francesco Emanuele Stradi, Matteo Castiglioni, Alberto Marchesi

展开摘要

Algorithmic *replicability* has recently been introduced to address the need for reproducible experiments in machine learning. A *replicable online learning* algorithm is one that takes the same sequence of decisions across different executions in the same environment, with high probability. We initiate the study of algorithmic replicability in *constrained* MAB problems, where a learner interacts with an unknown stochastic environment for $T$ rounds, seeking to maximize reward while satisfying multiple constraints. Our main result is that replicability can be achieved in constrained MABs. Specifically, we design replicable algorithms whose regret and constraint violation match those of non-replicable ones in terms of $T$. As a key step, we develop the first replicable UCB-like algorithm for *unconstrained* MABs, showing that algorithms that employ the optimism in-the-face-of-uncertainty principle can be replicable, a result that we believe is of independent interest.

Poster
Replay-buffer engineering for noise-robust quantum circuit optimization

Akash Kundu, Sebastian Feld

展开摘要

Deep reinforcement learning (RL) for quantum circuit optimization faces three fundamental bottlenecks: replay buffers that ignore the reliability of temporal-difference (TD) targets, curriculum-based architecture search that triggers a full quantum-classical evaluation at every environment step, and the routine discard of noiseless trajectories when retraining under hardware noise. We address all three by treating the replay buffer as a primary algorithmic lever. We introduce ReaPER$+$, an annealed replay rule transitioning from TD error-driven prioritization to reliability-aware sampling as value estimates mature, achieving up to 4$\times$ improved sample efficiency over the strongest off-policy baselines (fixed PER, ReaPER, and uniform replay) and matching prior on-policy solution quality at up to 32$\times$ fewer interactions. At 12-qubit scale, ReaPER achieves the lowest energy error in the fewest steps which is consistent with ReaPER$+$'s annealing direction, while PER and Vanilla replay find more compact circuits at the cost of higher energy error. Validation on LunarLander-v3 confirms the annealing principle is domain-agnostic obtaining +9% AUC over PER and fixed ReaPER. We further introduce OptCRLQAS, which amortizes expensive quantum-classical evaluations over multiple architectural edits, cutting wall-clock time per episode by up to 67.5% on a 12-qubit task without degrading solution quality. Finally, a lightweight replay-buffer transfer scheme warm-starts noisy-setting learning from noiseless trajectories, without network-weight transfer or $\epsilon$-greedy pretraining, reducing steps to chemical accuracy by up to 85-90% and final energy error by up to 90% over from-scratch baselines, with transfer advantages that grow with system size. Together, these results establish that experience storage, sampling, and transfer are decisive levers for scalable, noise-robust quantum circuit optimization. The anonymized repository is available at : https://anonymous.4open.science/r/annealed-replay-buffer-transfer-for-quantum-optimization-6861/.

Poster
Rep2Text: Decoding Full Text from a Single LLM Token Representation

Haiyan Zhao, Zirui He, Yiming Tang, Fan Yang, Ali Payani, Dianbo Liu, Mengnan Du

展开摘要

Large language models (LLMs) have achieved remarkable progress across diverse tasks, yet their internal mechanisms remain largely opaque. In this work, we investigate a fundamental question: to what extent can the original input text be recovered from a single last-token representation in an LLM? To this end, we propose Rep2Text, a novel framework for decoding text from last-token representations. Rep2Text employs a trainable adapter that maps a target model’s last-token representation into the token embedding space of a decoding language model, which then autoregressively reconstructs the input text. Experiments across various model combinations (Llama-3.1-8B, Gemma-7B, Mistral-7B-v0.1, Llama-3.2-3B, etc.) show that, on average, roughly half of the tokens in 16-token sequences can be recovered from this compressed representation while preserving strong semantic coherence. Further analysis reveals a clear information bottleneck effect: as sequence length increases, token-level recovery declines, while semantic information remains relatively well preserved. We also find that scaling effects are less pronounced in inversion tasks. Finally, our framework demonstrates robust generalization to out-of-distribution clinical data.

Poster
ReorgGS: Equivalent Distribution Reorganization for 3D Gaussian Splatting

Luchao Wang, Kaimin Liao, Hua Wang, Qian Ren, Zhi Chen, Yaohua Tang

展开摘要

While a converged 3D Gaussian Splatting (3DGS) model may accurately approximate a target scene, its underlying parameterization often becomes severely ill-suited for further optimization. We identify this late-stage bottleneck as \emph{parameterization degeneration}: high-opacity floaters truncate gradient flow to background surfaces via alpha compositing, and redundant overlapping clusters cause severe parameter coupling with nearly collinear Jacobian responses. These structural barriers explain why continued optimization plateaus, even when removable artifacts persist. To break this deadlock, we propose ReorgGS, an equivalent distribution reorganization method. By treating the converged Gaussian set as an empirical probability field, ReorgGS resamples centers, estimates local anisotropic covariances via kNN, and initializes a low-opacity state before resuming optimization. Unlike standard opacity reset—which only rescales weights on a flawed topology—ReorgGS fundamentally rebuilds the spatial and visibility structure. Our analysis reveals a crucial insight: \emph{distributional equivalence does not imply optimization equivalence}. By preserving scene support while drastically improving gradient accessibility and reducing opacity-weighted overlap, ReorgGS provides a vastly superior optimization landscape. Under the same optimization budget and fixed Gaussian count, ReorgGS breaks the performance ceiling, suppresses persistent floaters, and reduces rendering overhead by eliminating redundant overlap.

Poster
Renoise Consistency: Unlocking Efficient Self-Correction for Diffusion Large Language Models

Jihoon Lee, Yeongbin Seo, Jaehyung Kim

展开摘要

Diffusion Large Language Models (DLMs) are being actively explored as promising alternatives to autoregressive models due to their fast and flexible generation capabilities. To optimize inference in DLMs, recent studies have proposed a variety of decoding algorithms. However, the tendency of these methods to mimic autoregressive generation limits the speed and flexibility of DLMs, while also preventing the methods from fully realizing their potential. Moreover, this rigid approach leads to error propagation, while existing sampling-based correction methods incur prohibitive computational costs. To overcome this, we propose Renoise Consistency, a novel post-hoc approach that enables effective self-correction by maximizing train--inference consistency and can be applied to any decoding algorithm with a flexible computational budget. Furthermore, we introduce Adaptive Block Drafting, which leverages consistent internal representations of DLMs to significantly reduce the overall computational cost. When combined, our proposed method achieves up to a 9.00\% performance improvement over the semi-autoregressive baseline, along with a 25.85\% reduction in forward steps.

Poster
Rennala-NSGD: Asynchronous Stochastic Optimization Beyond Euclidean Geometry

Igor Sokolov, Alexander Tyurin, Peter Richtarik

展开摘要

The recent empirical success of non-Euclidean optimizers, such as Muon (Jordan et al., 2024) and Shampoo (Gupta et al., 2018), has transformed the training of Large Language Models (LLMs) by exploiting the geometry of matrix spaces. Despite this progress, the theoretical understanding of stochastic optimization in general normed spaces remains limited, particularly in distributed settings. In this work, we present a novel analysis of Minibatch Stochastic Gradient Descent (SGD) in non-Euclidean geometries. Leveraging the framework of $\\kappa$-regular normed spaces (Juditsky & Nemirovski, 2008) and a light-tail noise model defined directly in the dual norm, we derive high-probability oracle complexity bounds for smooth non-convex optimization. Crucially, our analysis reveals that measuring stochastic variance within the intrinsic non-Euclidean geometry avoids the suboptimal dimension-dependent factors inherent in Euclidean norm equivalence. Building on this framework, we introduce Rennala-NSGD, a semi-asynchronous distributed algorithm, and establish, to the best of our knowledge, the first wall-clock time complexity guarantee for asynchronous non-Euclidean stochastic optimization.

Poster
Render Structure Uncertainty for HTML Repair in MLLM-based UI-to-Code Generation

Haoran Ma, Jiechao Gao, Shisong Tang, Bing Han, Jifeng Hu, Hechang Chen

展开摘要

Existing MLLM-based UI-to-Code generation methods can generate complete HTML/CSS codes through end-to-end or multi-stage pipelines, yet the generated codes often contain structural errors such as incorrect repeated layouts, wrong component boundaries, or missing interaction slots. Subsequent generations may continue along the erroneous structure, causing the error to propagate and amplify. This paper studies post-generation repair: how can we locate and repair unreliable local DOM structures? We observe that this repair process is ambiguous in two ways: a mismatch between the target screenshot and the output may correspond to multiple plausible DOM subtrees, and a single DOM subtree may admit multiple repairs with different rendered behaviors. We propose Render Structure Uncertainty (RSU)for partial DOM repair, a browser grounded uncertainty layer that can be attached to any base HTML generator. RSU parses the target screenshot into a visual structure graph and converts the browser execution trace of the generated code into a DOM-anchored render structure graph. By matching these graphs, RSU yields structural mismatches and a small set of candidate DOM holes, preserving error attribution uncertainty. For each hole, RSU generates multiple local candidates, renders them in the full page context, and clusters them using render-structure signatures that encode layout relations, repeated patterns, content slots, semantic roles, and invalid states, thereby modeling repair uncertainty. The retained representative candidates form a compact Partial DOM candidate set, over which we perform global reranking to produce the final HTML code. In this way, RSU reframes HTML repair into uncertainty-guided search in render-structure space, avoiding premature commitment to either a single error location or a single local repair. Experiments show that RSU improves the generation quality of base models, producing higher-quality HTML with better layout consistency and fewer local structural errors.

Poster
Remote Photoplethysmography Based on a Skin Reflection Exponential Model

Jiachen Li, Longzhen Tang, Shisheng Guo, Guolong Cui

展开摘要

Facial video–based remote photoplethysmography (rPPG) estimates physiological signals from subtle spatiotemporal variations in facial videos, but remains vulnerable to head motion, illumination changes, and environmental perturbations. Existing methods mainly distinguish rPPG-related variations from motion and lighting artifacts at the signal or feature level, while largely neglecting the optical reflection properties of human skin. In this work, we formulate a skin reflection exponential model to describe the nonlinear relationship among skin reflectance, illumination, motion-induced variations, and blood-volume changes. Guided by this model, we propose a physically inspired rPPG estimation framework that explicitly incorporates skin reflectance priors into signal extraction. Given a facial video, facial keypoints are first detected and encoded to represent motion dynamics, while illumination-related features and candidate rPPG representations are jointly modeled under the proposed exponential formulation. By constraining rPPG estimation with skin-reflection physics, the framework improves separation of physiological components from motion and illumination disturbances. Experiments demonstrate improved robustness under challenging conditions.

Poster
Remembering What Matters: From Markovian to Subtask-Causal Memory in VLA Policies

Peishuo Wang, Fengshuo Bai, Yufeng Li, Tawei Chou, Yinda Xu, Ying Wen, Yaodong Yang, Chen Gao, Zhenzhe Zheng, Fan Wu

展开摘要

Long-horizon robotic manipulation is often non-Markovian: the correct action can depend on earlier state changes that are no longer visible in the current observation. Vision-language-action (VLA) models provide strong generalist robot policies, but their performance can drop when a task requires remembering which earlier subtasks changed the world. Existing memory mechanisms extend context through recent-frame windows, compressed latent stores, or similarity-based keyframe retrieval. They do not explicitly distinguish which completed subtasks are relevant from which frames within those subtasks carry the needed evidence. We introduce TTC-MEMORY, a two-tier memory framework for long-horizon VLA policies. The first tier segments execution into subtasks and constructs a dependency directed acyclic graph (DAG), so retrieval is restricted to ancestors of the current subtask. The second tier adaptively stores state-change keyframes within each retained subtask and injects them into a frozen VLA backbone through graph-aware cross-attention, with fallback to recent history when planning or clustering is uncertain. We evaluate TTC-MEMORY on LIBERO, RMBench, SimplerEnv-Bridge, the SafeLab chemistry-lab simulation benchmark, and Franka real-robot tasks. The comparisons use a shared VLA backbone, training budget, simulation seed protocol, and physical-trial protocol. TTC-MEMORY improves the long-horizon and memory-dependent slices in this matched setting. On the 10-subtask SafeLab slice, it reaches 58.3% success, compared with 38.2% for the strongest matched prior memory baseline, MemER, and 45.1% for DAG-only retrieval. Real-robot trials provide supporting transfer evidence rather than the main claim. Ablations show that the two tiers are complementary: DAG retrieval increases long-range dependency recall, while adaptive keyframe selection removes redundant history and preserves attention on task-critical state changes.

Poster
Remember with Confidence: Uncertainty Quantification for Spatio-temporal Memory with Probabilistic Guarantees

Harry Zhang, Nicolas Gorlo, Luca Carlone

展开摘要

Long-horizon robot operation requires spatio-temporal memory to record the environment state and recall it for downstream reasoning. Scene graphs and retrieval-augmented systems ground VLM descriptions to persistent 3D entities with rich semantic descriptions. However, VLM captions are noisy and viewpoint-inconsistent, and existing systems treat them as an oracle with no mechanism to detect unreliable stored descriptions. We introduce object-level semantic uncertainty for multi-view VLM memory: a score that measures object-centric cross-view semantic scatter of captions and identifies semantically unresolved objects. Then, we include our uncertainty scores in an advanced spatial-semantic memory system, that we dub UQ-DAAAM. UQ-DAAAM uses this score to actively refine uncertain objects under a fixed query budget by selecting high-quality views and fusing the resulting multi-view captions into a single object description. We also derive probabilistic guarantees showing that higher-quality candidate views (as selected by our approach) are more likely to reduce uncertainty. Our experiments show that uncertainty quantification can make embodied 4D memory systems more reliable and more effective. In particular, on the OC-NaVQA benchmark, UQ-DAAAM achieves substantially larger uncertainty reduction and better spatio-temporal question answering performance than baselines.

Poster
Remember the Decision, Not the Description: A Rate-Distortion Framework for Agent Memory

mingxi Zou, Zhihan Guo, Langzhang Liang, Zhuo Wang, Qifan Wang, Qingsong Wen, Irwin King, Lizhen Qu, Zenglin Xu

展开摘要

Long-horizon language agents must operate under limited runtime memory, yet existing memory mechanisms often organize experience around descriptive criteria—relevance, salience, or summary quality. For an agent, however, memory is valuable not because it faithfully describes the past, but because it preserves the distinctions between histories that must remain separated under a fixed budget to support good decisions. We cast this as a decision-centric rate-distortion problem, measuring memory quality by the loss in achievable decision quality induced by compression. This yields an exact forgetting boundary for what can be safely forgotten, and a memory-distortion frontier characterizing the optimal tradeoff between memory budget and decision quality. Motivated by this decision-centric view of memory, we propose **DeMem**, an online memory learner that refines its partition only when data certify that a shared state would induce decision conflict, and prove near-minimax regret guarantees. On both controlled synthetic diagnostics and long-horizon conversational benchmarks, DeMem yields consistent gains under the same runtime budget, supporting the principle that memory should preserve the distinctions that matter for decisions, not descriptions.

Poster
Reliable Federated Multi-View Learning via Conflict-Aware Evidence Calibration

Daoyuan Li, Zuyuan Yang, Hao Yang, Jiawen Kang

展开摘要

Federated Multi-View Learning (FedMVL) enables multiple clients with heterogeneous data views to collaboratively train global models without sharing private data. Existing FedMVL algorithms often overlook the reliability of local predictions, as both uncertainty quantification and calibration remain challenging in privacy-preserving federated settings. Heterogeneous sensing devices yield varying view qualities, but view-isolated training further exacerbates inherent bias of local model, inducing unreliable outputs. Without proper calibration, these artifacts cause spurious cross-view conflicts, ultimately undermining the accuracy and reliability of the aggregated global model. To address these issues, we propose a Reliable Federated Multi-View Learning with evidence calibration (FedRMVL-CAL), a FedMVL framework with adaptive evidence fusion. The local calibration scheme harmonizes uncertainty across views, while the fusion mechanism adaptively reconciles conflicting opinions, enhancing robustness in global inference. Theoretical analysis and extensive experiments demonstrate that FedRMVL-CAL achieves superior accuracy and reliability compared to existing approaches, ensuring trustworthy global predictions across heterogeneous views.

Poster
Reliable Clustering and Quantization via Distortion-Constrained Optimal Transport

Tianhao Wu, Wei Zhang, Haoran Pang, Haoran Yang, Hao Shi

展开摘要

Clustering and vector quantization are core primitives for representation learning and large-scale retrieval, yet widely used methods often produce clusters or codewords of highly uneven quality, especially in noisy or heterogeneous data. In this paper, we propose a distortion-constrained optimal transport (DCOT) framework that explicitly enforces per-cluster bounds on the average assignment distortion, defined as the expected distance between data points and their assigned representatives, ensuring more consistent and reliable representations. Our formulation couples an optimal transport assignment objective with cluster-level distortion constraints to control cluster quality. To solve this constrained problem, we develop an efficient alternating optimization algorithm that iteratively updates transport plans, representatives (codewords), and dual variables. We further provide theoretical guarantees including entropic consistency, coordinate descent, and sublinear convergence. Importantly, DCOT serves as a plug-in assignment module that can be seamlessly integrated into a wide range of vector quantization methods. Replacing the assignment step with DCOT consistently improves reconstruction quality across diverse architectures and training settings, demonstrating strong robustness and general applicability.

Poster
Reliable Chain-of-Thought via Prefix Consistency

Naoto Iwase, Yuki Ichihara, Mohammad Atif Quamar, Junpei Komiyama

展开摘要

Large Language Models often improve accuracy on reasoning tasks by sampling multiple Chain-of-Thought (CoT) traces and aggregating them with majority voting (MV), a test-time technique called self-consistency. When we truncate a CoT partway through and regenerate the remainder, we observe that traces with correct answers reproduce their original answer more often than traces with wrong answers. We use this difference as a reliability signal, **prefix consistency**, that weights each candidate answer by how often it reappears under regeneration. It requires no access to token log-probabilities or self-rating prompts. Across five reasoning models and four math and science benchmarks, prefix consistency is the best correctness predictor in most settings, and reweighting votes by it reaches Standard MV plateau accuracy at up to $21\times$ fewer tokens (median $4.6\times$).

Poster
Reliable Abstention under Adversarial Injections: Lower Bounds and New Upper Bounds

Ezra Edelman, Surbhi Goel

展开摘要

We study online learning in the adversarial injection model introduced by [Goel et al. 2024], where a stream of labeled examples is predominantly drawn i.i.d.\ from an unknown distribution $\mathcal{D}$, but may be interspersed with adversarially chosen instances without the learner knowing which rounds are adversarial. Crucially, labels are always consistent with a fixed target concept (the clean-label setting). The learner is additionally allowed to abstain from predicting, and the total error counts the mistakes whenever the learner decides to predict and incorrect abstentions when it abstains on i.i.d.\ rounds. Perhaps surprisingly, prior work shows that oracle access to the underlying distribution yields $O(d^2 \log T)$ combined error for VC dimension $d$, while distribution-agnostic algorithms achieve only $\tilde{O}(\sqrt{T})$ for restricted classes, leaving open whether this gap is fundamental. We resolve this question by proving a matching $\Omega(\sqrt{T})$ lower bound for VC dimension $1$, establishing a sharp separation between the two information regimes. On the algorithmic side, we introduce a potential-based framework driven by \emph{robust witnesses}, small subsets of labeled examples that certify predictions while remaining resilient to adversarial contamination. We instantiate this framework using two combinatorial dimensions: (1) \emph{inference dimension}, yielding combined error $\tilde{O}(T^{1-1/k})$ for classes of inference dimension $k$, and (2) \emph{certificate dimension}, a new relaxation we introduce. As an application, we show that halfspaces in $\mathbb{R}^2$ have certificate dimension $3$, obtaining the first distribution-agnostic bound of $\tilde{O}(T^{2/3})$ for this class.

Poster
Reliability-Coupled Manifold-Aware Diffusion for Missing-Modality Inference

Yiming Ren, Yuhao Fang, Qing Zhou, Ming Li, Ye Zhang, Zijian Wang, Yao Lu, Chun Li

展开摘要

In real-world multimodal time-series inference, a common practice is completion–inference decoupling: missing modalities are heuristically imputed and then passed to deterministic fusion and decision making. We show that this chained design yields unreliable predictions under missingness, noise, and temporally varying modality reliability, because imputation errors propagate without uncertainty feedback. Through theoretical and empirical analysis, we identify latent-consistent completion and evidential reliability modeling as two key ingredients for robust multimodal inference. Building on these insights, we propose MD2E-MI, a manifold-aware diffusion-based imputation and evidence-driven multimodal inference framework that couples diffusion-based completion with uncertainty-aware inference in a single pathway. Experiments demonstrate stable performance across diverse missingness and noise regimes, while providing interpretable, temporally varying reliability estimates.

Poster
Relevance Is Not Necessity: Selecting the Necessary API Set for Tool-Using LLMs

Chen Wang

展开摘要

A multi-tool plan is correct only when its call set matches the gold API set exactly. Standard tool-use pipelines optimize first-hop relevance, but downstream verifiers require the necessary API set, creating a relevance--necessity gap. This study formalizes the gap: under correlated API indicators, symmetric decomposable selectors based only on per-API marginals can be dominated by a Bayes-optimal set selector, while whole-set exact-match supervision is a proper scoring rule for the optimal selector restricted to a candidate menu. We propose an offline refinement framework for frozen upstream traces. Under a leakage-free ToolBench G2/G3 protocol, TC-MASS improves verifier-consistent API-set recovery without additional LLM generation after the upstream trace exists. Ablations and cross-distribution probes support the central claim: necessity-aware set-level supervision, not relevance ranking alone, is the right objective for fixed-pool API-set recovery.

Poster
Relaxed On-Policy Distillation: Selective Credit Allocation for Scaling Reasoning Efficiently

Jongwoo Ko, Sara Abdali, Young Jin Kim, Tianyi Chen, Pashmina Cameron

展开摘要

On-policy distillation (OPD) is a promising approach for transferring reasoning capabilities to capacity-constrained models, yet sampled-token OPD often suffers from entropy collapse and negative transfer. We identify uniform credit allocation as a key bottleneck: existing objectives obtain dense teacher feedback on student-generated trajectories, but apply it uniformly across sampled tokens despite highly heterogeneous token-level signals. Most tokens carry redundant near-zero credit, while rare heavy-tailed negative credits can dominate updates and prematurely suppress plausible reasoning trajectories. We introduce REOPOLD (Relaxed On-Policy Distillation), a framework that relaxes this uniform assignment by controlling where teacher feedback is applied, how strongly it affects the update, and when the allocation rule changes during training. Across diverse reasoning tasks, REOPOLD improves sampled-token OPD over recent post-training baselines with up to 12$\times$ higher sample efficiency, and extends to cross-vocabulary distillation, self-distillation, and test-time scaling.

Poster
Relaxation-Aligned State Control for Test-Time Scaling in Generative Combinatorial Optimization

Bohao Li, Ying Li, Pei He, Yangming Guo

展开摘要

Generative solvers for combinatorial optimization benefit from additional test-time compute when their refinement states remain aligned with task relaxations. We introduce RAGenCO, a relaxation-aligned test-time scaling framework for generative combinatorial optimization. The central idea is to treat projection onto a task relaxation as a state control primitive: refinement first maintains a projected control state, and only then forms the task-dependent decoder input or expands candidates. For TSP and ATSP, Sinkhorn projection aligns matrix states with the cycle-cover relaxation during refinement and decoding. For MIS and MVC, Bernoulli projection controls refinement on the independent-set side, while raw logits are retained for terminal greedy decoding because their ordering carries the decoder signal. Best-of-$B$ branching then reallocates compute by expanding candidates around aligned control states rather than sampling from unconstrained logits. Because these operations are used only at inference, the diffusion training objective remains unchanged. Under equal runtime budgets, this alignment of control state, decoder input, and branching yields a strong quality-runtime trade-off on TSP and ATSP and competitive results on MIS and MVC.

Poster
Relative Energy Barriers for Copyright-Aware Language Model Adaptation

Wei Sun, Yuhang Zhang, Zhicheng Liang, Xianda Wang, Jiaxuan Chen, Fangxin Wang

展开摘要

Adapting language models on long-form corpora can improve domain behavior while also making protected passages easier to reproduce verbatim from short prefixes. We study this tension through \emph{relative energy gain}, the token-level log-density ratio between an adapted model and its pre-adaptation anchor on an exact protected continuation. This quantity separates ordinary predictability from update-induced copying pressure and accumulates over suffixes as a likelihood-ratio advantage for extractable memorization. Building on this view, we introduce Energy-Gated Copyright Regularization (EGCR), a training objective that augments maximum likelihood with a soft relative-energy budget on protected tokens. EGCR uses a differentiable gate combining local persistence of relative gain with anchor surprisal, so regularization is concentrated on distinctive spans whose probabilities rise in a memorization-like way while ordinary next-token supervision is retained elsewhere. Across BookMIA adaptation stress tests, training-prefix extraction, CopyBench transfer, and gate ablations, EGCR reduces exact-match and overlap-based reproduction while preserving held-out language-modeling and book-related utility. Token-level visualizations further show that the gate focuses on a small set of expressive positions associated with verbatim recovery. These results suggest that relative-energy barriers offer an effective and inspectable mechanism for copyright-aware language model adaptation.

Poster