Characterization

Chinese word segmentation is especially fragile in non-standard text, where language learner errors and other character-level divergences disrupt the word boundaries assumed by downstream annotation and evaluation. This paper formulates Chinese word boundary recovery as an alignment-based projection task. Given a noisy source sentence and a cleaner target counterpart, we first align the two strings at the character level and then project target-side word boundaries back onto the source. Beyond the recovery method itself, we introduce two evaluation resources: a manually checked learner Chinese benchmark based on MuCGEC and a controlled synthetic benchmark derived from the Chinese Penn Treebank. Experiments show that direct segmentation remains vulnerable to compound fragmentation in learner input, whereas the proposed two step projection method corrects many over-segmentation errors by using the corrected target to recover source-side word spans. The results show that word boundary recovery is distinct from ordinary segmentation and that alignment projection provides a principled mechanism for stabilizing Chinese annotation and evaluation under noisy input.

Hallucination is a central limitation of large language models (LLMs), and substantial effort has been devoted to understanding and mitigating it. Towards this, Kalai and Vempala (STOC 2024) introduced a probabilistic framework formalizing calibration and hallucination, and showed that, with high probability, calibrated LLMs hallucinate roughly at the rate of the "missing mass", a measure of how incomplete the training data is relative to its source. This raises two fundamental questions: (i) what property of a calibrated LLM makes hallucinations unavoidable? and (ii) can hallucinations be avoided by giving up calibration? We answer these questions by introducing a simpler property we call innovation that measures the tendency of a model to produce outputs outside the training data. We show that innovation is implied by the condition for hallucination identified by Kalai and Vempala, and, further, that it is an almost characterization of hallucination: hallucination implies innovation, and conversely, innovation implies hallucination with high probability. We also provide lower bounds on the hallucination rate based on the "innovation rate", and by relating innovation rate back to missing mass, we obtain new hallucination rate lower bounds based on missing mass that extend the results of Kalai and Vempala.

On a 300-persona life-simulation benchmark, pcsp achieves compositional zero-shot persona identification up to 17x above chance, Spearman rho approx 0.73 semantic-behavioral alignment, and 22x faster inference than an LLM-as-policy baseline. Life simulation games require hundreds to thousands of non-player characters (NPCs) that behave consistently with distinct personalities while remaining controllable through designer-authored natural language. Existing methods fail on constraints like persona consistency, controllability, or real-time inference. We introduce pcsp (Persona Conditioned Shared Policy), a single reinforcement learning policy conditioned on frozen LLM embeddings of free-form persona descriptions. pcsp combines once-per-NPC persona encoding, low-rank persona projection, neural persona conditioning, and a PPO + InfoNCE consistency + KL diversity training objective. Across three experimental settings, ablations show that the InfoNCE trajectory-consistency objective is load bearing: removing it collapses zero-shot persona identification to chance. External validation on Melting Pot 2.4.0 substrates confirms that our method produces persona-conditioned behavioral divergence in multi-agent strategic environments. We distinguish two senses of held-out evaluation: compositional zero-shot and vocabulary-expansion held-out. Finally, a UE5 deployment reproduces the in-engine persona-conditioning ablation at 64 agents with a low failure rate, showing that the sub-frame inference profile survives in a commercial game engine. These results prove that shared RL policies can support scalable, real-time, persona-conditioned NPC control.

Arabic Handwritten Character Recognition (AHCR) has recently advanced significantly with deep Convolutional Neural Networks (ConvNets). However, many models in the literature are deep and computationally expensive in terms of parameters and FLOPs, limiting their deployment on resource-constrained devices, which are increasingly common. This study addresses this gap by proposing a combination of lightweight embedded ConvNet models and ensemble learning techniques. Extensive experiments were conducted to identify best practices in AHCR, considering training hyperparameters, learning strategies, model choices, and ensemble methods. Results show that embedded models can achieve accuracy comparable to, or even surpassing, heavier architectures. Ensemble learning further enhances performance with only modest computational overhead, particularly under challenging training scenarios. Among the ensembling strategies, soft voting yielded the best overall results.

We study the problem of directly deriving an initial human reenactment from a monocular video of a non-human character. Our goal is not to reconstruct the source character itself but to reinterpret its motion as a plausible and editable human performance for downstream animation authoring. This task is challenging because existing video-based motion capture methods are largely restricted to human-centric structural spaces, while motion retargeting methods typically require structured 3D source motions and known source topologies. Our key insight is that sparse local articulated motion cues can preserve essential dynamics across large structural differences, providing a stable bridge from character video to human reenactment. Based on this observation, we propose AnyAct, which formulates character-video-driven human reenactment as conditional human motion generation from transferable sparse local 2D articulated motion. To make this practical, we introduce three key designs: human-motion-only supervision via augmented 3D-to-2D projection, progressive 3D-to-2D training to alleviate conditioning ambiguity, and global-local motion decoupling for reliable local motion control. We further construct a benchmark primarily covering diverse non-human character videos. Experiments on the benchmark show that AnyAct produces high-fidelity initial human reenactments that preserve the essential dynamics of the characters in reference videos, and further ablation studies validate the effectiveness of its core designs.

Multi-shot video generation extends single-shot generation to coherent visual narratives, yet maintaining consistent characters, objects, and locations across shots remains a challenge over long sequences. Existing evaluations typically use independently generated prompt sets with limited entity coverage and simple consistency metrics, making standardized comparison difficult. We introduce EntityBench, a benchmark of 140 episodes (2,491 shots) derived from real narrative media, with explicit per-shot entity schedules tracking characters, objects, and locations simultaneously across easy / medium / hard tiers of up to 50 shots, 13 cross-shot characters, 8 cross-shot locations, 22 cross-shot objects, and recurrence gaps spanning up to 48 shots. It is paired with a three-pillar evaluation suite that disentangles intra-shot quality, prompt-following alignment, and cross-shot consistency, with a fidelity gate that admits only accurate entity appearances into cross-shot scoring. As a baseline, we propose EntityMem, a memory-augmented generation system that stores verified per-entity visual references in a persistent memory bank before generation begins. Experiments show that cross-shot entity consistency degrades sharply with recurrence distance in existing methods, and that explicit per-entity memory yields the highest character fidelity (Cohen's d = +2.33) and presence among methods evaluated. Code and data are available at https://github.com/Catherine-R-He/EntityBench/.

Current game world models simulate environments from a subjective, player-centric perspective. However, by treating the Non-Player Character (NPC) merely as background pixels, these models cannot capture interactions between the player and NPC. In that sense, they act as passive video renderers rather than real simulation engines, lacking the physical understanding needed to model action-induced NPC reactivities. We introduce ReactiveGWM, a reactive game world model that synthesizes dynamic interactions between the player and NPC. Instead of entangling all interaction dynamics, ReactiveGWM explicitly decouples player controls from NPC behaviors. Player actions are injected into the diffusion backbone via a lightweight additive bias, while high-level NPC responses (e.g., Offense, Control, Defense) are grounded through cross-attention modules. Crucially, these modules learn a game-agnostic representation of interactive logic. This enables zero-shot strategy transfer: our learned modules can be plugged directly into off-the-shelf, unannotated world models of different games. This instantly unlocks steerable NPC interactions without any domain-specific retraining. Evaluated on two Street Fighter games, ReactiveGWM maintains fine-grain player controllability while achieving robust, prompt-aligned NPC strategy adherence, paving the way for scalable, strategy-rich interaction with the NPC.

Vision Large Language Models (VLLMs) have achieved remarkable success in modern text-rich visual understanding. However, their perceptual robustness in the face of the continuous morphological evolution of historical writing systems remains largely unexplored. Existing ancient text datasets typically focus on isolated historical periods, failing to capture the systematic visual distribution shifts spanning thousands of years. To bridge this gap and empower Digital Humanities, we introduce Chronicles-OCR, the first comprehensive benchmark specifically designed to evaluate the cross-temporal visual perception capabilities of VLLMs across the complete evolutionary trajectory of Chinese characters, known as the Seven Chinese Scripts. Curated in collaboration with top-tier institutional domain experts, the dataset comprises 2,800 strictly balanced images encompassing highly diverse physical media, ranging from tortoise shells to paper-based calligraphy. To accommodate the drastic morphological and topological variations across different historical stages, we propose a novel Stage-Adaptive Annotation Paradigm. Based on this, Chronicles-OCR formulates four rigorous quantitative tasks: cross-period character spotting, fine-grained archaic character recognition via visual referring, ancient text parsing, and script classification. By isolating visual perception from semantic reasoning, Chronicles-OCR provides an authoritative platform to expose the limitations of current VLLMs, paving the way for robust, evolution-aware historical text perception. Chronicles-OCR is publicly available at https://github.com/VirtualLUOUCAS/Chronicles-OCR.

The advancement of Multimodal Large Language Models (MLLMs) has expanded Role-Playing Agents (RPAs) into visually grounded environments. However, human vision is inherently subjective and identity-driven, whereas existing MLLMs extract objective, character-agnostic features for general tasks. In RPAs, this generic visual noise overpowers fragile character traits, causing Modality-Role Interference (MRI), where agents struggle to integrate visual grounding and character consistency. To address this, we introduce the training-free Character-Aware Visual Intervention (CAVI) framework, enabling agents to perceive the world through the lens of character. CAVI systematically targets MRI: macroscopically, Character-Guided Token Pruning (CTP) restricts the visual receptive field to role-relevant entities; microscopically, Orthogonal Feature Modulation (OFM) projects tokens onto a character-context subspace to extract aligned facts; and during decoding, Modality-Adaptive Role Steering (MARS) dynamically optimizes steering intensity based on visual reliance. Extensive experiments show CAVI effectively alleviates MRI, significantly enhancing character-consistent multimodal interactions.

We study adversarial noisy bandits given a known function class $\mathcal{F}$. In each round, the adversary selects a function $f \in \mathcal{F}$, the learner chooses an arm, and then observes a noisy reward determined by the chosen arm and the function $f$. The goal is to minimize the cumulative regret $R(T)$, defined as the difference between the learner's performance and that of the best fixed arm in hindsight over $T$ rounds. We say that a function class $\mathcal{F}$ is learnable if there exists an algorithm achieving sublinear regret. Our main result is a complete characterization of learnability for adversarial noisy bandits. The characterization is given in terms of a convexified variant of the generalized maximin volume introduced by Hanneke and Wang (2025): namely, the generalized maximin volume evaluated on the convex hull $\operatorname{co}(\mathcal F)$. We prove that $\mathcal F$ is learnable if and only if this convexified generalized maximin volume is positive at every scale. This condition characterizes learnability against both oblivious and adaptive adversaries, showing in particular that these two notions of learnability are equivalent in the noisy bandit setting. Our analysis reveals that the key complexity measure is closely connected to two new combinatorial notions, hitting set and distribution covering number, which may be of independent interest. These results establish the first complete characterization of learnability for adversarial noisy bandits.

Online learning from a stream of data is a defining feature of intelligence, yet modern machine learning systems often struggle in this setting, especially under distributional shift. To understand its basic properties, we study the relationship between online and offline learning in the context of kernel regression. We derive a closed-form expression for the function learned by online kernel regression, revealing that online kernel regression is equivalent to offline regression with shifted, inaccurate target outputs. Conversely, we show that by compensating for this effective shift in the teaching signal through target correction, online kernel-based learning can provably learn the same predictor as its offline counterpart. We derive both a closed-form expression for this target correction and an iterative form that can be applied sequentially. Applying this framework to image classification tasks on CIFAR-10 and CORe50, we show that online stochastic gradient descent with iteratively corrected targets outperforms learning with the true targets in continual learning settings. This work therefore provides a basic framework for analyzing and improving online learning in non-stationary environments.

We give a novel logical characterization of encoder-decoder transformers, the foundational architecture for LLMs that also sees use in various settings that benefit from cross-attention. We study such transformers over text in the practical setting of floating-point numbers and soft-attention, characterizing them with a new temporal logic. This logic extends propositional logic with a counting global modality over the encoder input and a past modality over the decoder input. We also give an additional characterization of such transformers via a type of distributed automata, and show that our results are not limited to the specific choices in the architecture and can account for changes in, e.g., masking. Finally, we discuss encoder-decoder transformers in the autoregressive setting.

For artistic applications, video generation requires fine-grained control over both performance and cinematography, i.e., the actor's motion and the camera trajectory. We present ActCam, a zero-shot method for video generation that jointly transfers character motion from a driving video into a new scene and enables per-frame control of intrinsic and extrinsic camera parameters. ActCam builds on any pretrained image-to-video diffusion model that accepts conditioning in terms of scene depth and character pose. Given a source video with a moving character and a target camera motion, ActCam generates pose and depth conditions that remain geometrically consistent across frames. We then run a single sampling process with a two-phase conditioning schedule: early denoising steps condition on both pose and sparse depth to enforce scene structure, after which depth is dropped and pose-only guidance refines high-frequency details without over-constraining the generation. We evaluate ActCam on multiple benchmarks spanning diverse character motions and challenging viewpoint changes. We find that, compared to pose-only control and other pose and camera methods, ActCam improves camera adherence and motion fidelity, and is preferred in human evaluations, especially under large viewpoint changes. Our results highlight that careful camera-consistent conditioning and staged guidance can enable strong joint camera and motion control without training. Project page: https://elkhomar.github.io/actcam/.

Intent-obfuscation-based jailbreak attacks on multimodal large language models (MLLMs) transform a harmful query into a concealed multimodal input to bypass safety mechanisms. We show that such attacks are governed by a \emph{reconstruction--concealment tradeoff}: the transformed input must hide harmful intent from safety filters while remaining recoverable enough for the victim model to reconstruct the original request. Through a reconstruction analysis of three representative black-box methods, we find that existing transformations struggle to balance this tradeoff, limiting their effectiveness. In contrast, we show that character-removed variants achieve a better balance. Building on this, we propose \emph{concealment-aware variant construction}, which greedily selects character-removed variants that are low in harmful-keyword alignment and mutually diverse, and instantiates them through five modality-aware prompting strategies. We further introduce \emph{keyword-related distractor images} that depict the harmful keyword in diverse contexts, providing more effective auxiliary visual context than generic distractor images. Experiments across closed-source and open-source MLLMs show the proposed strategies outperform strong baselines, revealing an underexplored vulnerability: a model's own reconstruction ability can be exploited to recover hidden harmful intent and produce unsafe responses.

High-fidelity circuit execution on noisy intermediate-scale quantum devices is bottlenecked by compilation pipelines that disregard complex, correlated noise. To address this, this methodology article proposes a quantum machine learning control (QMLC) framework for generative quantum circuit synthesis from gate-set tomography (GST) data that bypasses the traditional two-step pipeline of characterizing native quantum gates via GST followed by unitary decomposition algorithms. Instead, a generative concept space is directly learnt from GST data, enabling conditional synthesis of quantum circuits on a desired output distribution. Our approach tokenizes GST germ circuits and embeds them into a structured latent space using a curriculum-learning-motivated strategy, starting with short circuits and progressively incorporating longer ones with diverse output statistics. The embedded sequences are processed by a set-vision transformer with permutation-invariant pooling, producing k-seed vectors that represent the learned concept space of the quantum device. Aggregating data across multiple circuits makes this latent representation inherently context-aware, capturing the shared physical noise environment (e.g., crosstalk, drift) that isolated gate metrics miss. We propose an unconditional diffusion model to sample from the concept space. During inference, a user provides a target measurement distribution, and the model generates a corresponding circuit. To ensure fidelity and robustness, the output is denoised using a diffusion model that operates on the target conditional covariance matrix. This end-to-end framework is a step towards context-aware, hardware-native circuit synthesis directly from raw GST data, which offers a new paradigm for integrating quantum control and compilation. The QMLC framework is particularly suited for near-term quantum devices with complex calibration procedures.

Achieving realistic human-like conversation for virtual characters requires not only a simple memorization and recall of past events, but also the strategic utilization of memory to meet factual needs and social engagement. Current memory utilization relevant (e.g., memory-augmented generation, long-term dialogue, and etc.) benchmarks overlook this nuance, treating memory primarily as a static repository of facts rather than a dynamic resource to be strategically deployed in dialogues. To address this gap, we design StratMem-Bench, a new benchmark to evaluate strategic memory use in character-centric dialogues. This dataset comprises 657 instances where virtual characters must navigate heterogeneous memory pools containing required, supportive, and irrelevant memories. We also propose a framework with different evaluation metrics including Strict Memory Compliance, Memory Integration Quality, Proactive Enrichment Score and Conditional Irrelevance Rate, to evaluate strategic memory use capabilities of virtual characters. Experiments on StratMem-Bench which leverage the state-of-the-art large language models as virtual characters show that all models perform well at distinguishing between required and irrelevant memories, but struggle once supportive memories are introduced into the decision process.

{Closed-loop inverse source localization and characterization (ISLC) requires a mobile agent to select measurements that localize sources and infer latent field parameters under strict time constraints.} {The core challenge lies in the belief-space objective: valid uncertainty estimation requires expensive Bayesian inference, whereas using fast learned belief model leads to reward hacking, in which the policy exploits approximation errors rather than actually reducing uncertainty.} {We propose \textbf{Distill-Belief}, a teacher--student framework that decouples correctness from efficiency. A Bayes-correct particle-filter teacher maintains the posterior and supplies a dense information-gain signal, while a compact student distills the posterior into belief statistics for control and an uncertainty certificate for stopping. At deployment, only the student is used, yielding constant per-step cost.} {Experiments on seven field modalities and two stress tests show that Distill-Belief consistently reduces sensing cost and improves success, posterior contraction, and estimation accuracy over baselines, while mitigating reward hacking.}

Borehole breakouts are stress-induced spalling on the borehole wall, which are identifiable in acoustic image logs as paired zones with near-symmetry azimuths, low acoustic amplitudes, and increased borehole radius. Accurate breakout characterization is crucial for in-situ stress analysis. In recent years, deep learning has been introduced to automate the time-consuming and labor-intensive breakout picking process. However, existing approaches often suffer from misclassification of non-breakout features, leading to high false positive rates. To address this limitation, this study develops a deep learning framework, termed Breakout-picker, with a specific focus on reducing false positives in automatic breakout characterization. Breakout-picker reduces false positives through two strategies. First, the training of Breakout-picker incorporates negative samples of non-breakout features, including natural fractures, keyseats, and logging artifacts. They share similar characteristics with breakouts, such as low acoustic amplitude or locally enlarged borehole radius. These negative training samples enables Breakout-picker to better discriminate true breakouts and similar non-breakout features. Second, candidate breakouts identified by Breakout-picker are further validated by azimuthal symmetry criteria, whereby detections that do not exhibit the near-symmetry characteristics of breakout azimuth are excluded. The performance of Breakout-picker is evaluated using three acoustic image log datasets from different regions. The results demonstrate that Breakout-picker outperforms other automatic methods with higher accuracy and substantially lower false positive rates. By reducing false positives, Breakout-picker enhances the reliability of automatic breakout characterization from acoustic image logs, which in turn benefits in-situ stress analysis based on borehole breakouts.

We introduce a novel characterization of phase transitions based on hypothesis testing. In our formulation, a phase transition is defined as the breakdown of statistical indistinguishability under vanishing parameter perturbations in the thermodynamic limit. This perspective provides a general, order-parameter-free framework that does not rely on model-specific insights or learning procedures. We show that conventional approaches, such as those based on the Binder parameter, can be reinterpreted as special cases within this framework. As a concrete realization, we employ a distribution-free two-sample run test and demonstrate that the critical point of the two-dimensional Ising model is accurately identified without prior knowledge of the order parameter.

The rapid proliferation of AI applications has intensified debate on effective regulation of these black-box services. Effective regulation must balance two competing goals: (1) deterring non-compliant providers from entering the market, while (2) retaining compliant ones. We call this ideal the perfect market outcome (PMO). Regulators face two compounding obstacles that make PMO difficult to achieve: providers hold private information and can act strategically to evade compliance, while any evidence drawn or derived from a finite sample carries statistical uncertainty in proving non-compliance. As this information asymmetry and statistical uncertainty is inherent to any effective regulation, we formalise them through a mechanism design framework that explicitly accounts for such statistical uncertainty. This yields a sharp characterisation: a mechanism achieves PMO if and only if the set of non-compliant evidence distributions forms a closed, convex set of probability measures, known in imprecise probability as a credal set. This result serves as a diagnostic tool to determine whether PMO is achievable under a given regulation. We further show that PMO-achieving mechanisms can be constructed from a collection of hypothesis tests, and validate our theoretical contributions through experiments on spurious-feature and fairness-based regulations.

We study the Pareto frontier (optimal trade-off) between utility and separation, a fairness criterion requiring predictive independence from sensitive attributes conditional on the true outcome. Through an information-theoretic lens, we prove a characterization of the utility-separation Pareto frontier, establish its concavity, and thereby prove the increasing marginal cost of separation in terms of utility. In addition, we characterize the conditions under which this trade-off becomes strict, providing a guide for trade-off selection in practice. Based on the theoretical characterization, we develop an empirical regularizer based on conditional mutual information (CMI) between predictions and sensitive attributes given the true outcome. The CMI regularizer is compatible with any deep model trained via gradient-based optimization and serves as a scalar monitor of residual separation violations, offering tractable guarantees during training. Finally, numerical experiments support our theoretical findings: across COMPAS, UCI Adult, UCI Bank, and CelebA, the proposed method substantially reduces separation violations while matching or exceeding the utility of established baseline methods. This study thus offers a provable, stable, and flexible approach to enforcing separation in deep learning.

While Large Language Model (LLM) role-playing agents have advanced rapidly, it remains unclear which profile elements genuinely drive role-playing quality. To bridge this gap, we introduce a systematic diagnostic framework that disentangles the impact of character profiles along three axes: Familiarity (Known vs. Unknown), Structure (Structured vs. Unstructured), and Disposition (Moral vs. Immoral). Utilizing a unified hierarchical schema (5 dimensions, 28 fields), we construct a controlled dataset of 211 personas and evaluate five LLMs on both single- and multi-turn interactions. Our results reveal a striking asymmetry: \textbf{Familiarity} and \textbf{Structure} show negligible impact, while \textbf{Disposition} produces large, consistent performance degradation for immoral characters across all conditions. Further analyses suggest that the Moral--Immoral gap is amplified by post-SFT alignment, and that this degradation varies substantially across profile attributes. To mitigate this bottleneck, we propose Field-Aware Contrastive Decoding (FACD), a training-free strategy that amplifies suppressed disposition-sensitive signals, significantly closing the performance gap without sacrificing moral-character performance.

Recent advances in world models have greatly enhanced interactive environment simulation. Existing methods mainly fall into two categories: (1) static world generation models, which construct 3D environments without active agents, and (2) controllable-entity models, which allow a single entity to perform limited actions in an otherwise uncontrollable environment. In this work, we introduce CustomX, leveraging the realism and structural grounding of static world generation while extending controllable-entity models to support user-specified characters capable of performing open-ended actions. Users can provide a 3DGS scene and a character, then use natural language to direct the character to perform diverse behaviors, ranging from basic locomotion to object-centric interactions, while freely exploring the environment. CustomX synthesizes temporally coherent video clips that preserve visual fidelity with the provided scene and character, formulated as a conditional autoregressive video generation problem. Built upon a pre-trained video generator, our training strategy significantly enhances motion dynamics while maintaining generalization across actions and characters. Our evaluation covers a broad range of aspects, including visual quality, character consistency, action controllability, and long-horizon coherence.

In this paper, we establish a novel connection between the metric entropy growth and the embeddability of function spaces into reproducing kernel Hilbert/Banach spaces. Metric entropy characterizes the information complexity of function spaces and has implications for their approximability and learnability. Classical results show that embedding a function space into a reproducing kernel Hilbert space (RKHS) implies a bound on its metric entropy growth. Surprisingly, we prove a \textbf{converse}: a bound on the metric entropy growth of a function space allows its embedding to a $L_p-$type Reproducing Kernel Banach Space (RKBS). This shows that the ${L}_p-$type RKBS provides a broad modeling framework for learnable function classes with controlled metric entropies. Our results shed new light on the power and limitations of kernel methods for learning complex function spaces.

LiDAR point cloud registration is fundamental to robotic perception and navigation. In geometrically degenerate environments (e.g., corridors), registration becomes ill-conditioned: certain motion directions are weakly constrained, causing unstable solutions and degraded accuracy. Existing detect-then-mitigate methods fail to reliably detect, physically interpret, and stabilize this ill-conditioning without corrupting the optimization. We introduce DCReg (Decoupled Characterization for Ill-conditioned Registration), establishing a detect-characterize-mitigate paradigm that systematically addresses ill-conditioned registration via three innovations. First, DCReg achieves reliable ill-conditioning detection by employing Schur complement decomposition on the Hessian matrix. This decouples the 6-DoF registration into 3-DoF clean rotational and translational subspaces, eliminating coupling effects that mask degeneracy in full-Hessian analyses. Second, within these subspaces, we develop interpretable characterization techniques resolving eigen-basis ambiguities via basis alignment. This establishes stable mappings between eigenspaces and physical motion directions, providing actionable insights on which motions lack constraints and to what extent. Third, leveraging this spectral information, we design a targeted mitigation via a structured preconditioner. Guided by MAP regularization, we implement eigenvalue clamping exclusively within the preconditioner rather than modifying the original problem. This preserves the least-squares objective and minimizer, enabling efficient optimization via Preconditioned Conjugate Gradient with a single interpretable parameter. Experiments demonstrate DCReg achieves 20-50% higher long-duration localization accuracy and 5-30x speedups (up to 116x) over degeneracy-aware baselines across diverse environments. Code: https://github.com/JokerJohn/DCReg