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arXiv:2601.22888v5cs.CL

DialectLLM: A Dialect-Aware Dialog[ue] Generation Framework Beyond Standard American English

More than 80% of the 1.6B English speakers do not use Standard American English (SAE), yet LLMs often fail to correctly identify non-SAE dialects and generate stereotyped responses for their speakers. We introduce DialectLLM, the first large-scale framework for generating high-quality multi-dialectal conversational data encompassing the three pillars of written dialect---lexical (vocabulary), orthographic (spelling), and morphosyntactic (grammar) features. DialectLLM produces a dialect-parallel dialog dataset spanning nine English dialects. Partnering with native linguists, we design and validate SAE-to-dialect transformation rules, ensuring authenticity. Our approach challenges the prevailing practice of applying a single morphosyntactic feature set to both user utterances and model responses, showing that models should not reproduce up to 90% of the grammatical features of a dialect. Human evaluation confirms data quality, with annotators preferring DialectLLM over prior methods in 98.8% of pairwise comparisons for dialect naturalness. We then construct DialectLLM-Bench, a dialect-parallel benchmark with 50k+ dialogs, resulting in 97k+ QA pairs, and evaluate 17 LLMs on dialect identification and response generation tasks. Even frontier models achieve around 70% accuracy, fail to reach 40% for prominent dialects like Canadian English, and systematically misclassify non-SAE dialects as American or British. Beyond benchmarking, we show that DialectLLM data also serve as a scalable LLM post-training resource, suggesting a practical path toward dialect-aware conversational AI.

arXiv:2603.13389v2cs.CV

Logit-Conditioned Diffusion Decoding for Frozen Discrete-Token VLMs

Pre-trained discrete-token VLMs generate images by sampling sequences of codebook indices, but their visual fidelity is bounded by the VQ-VAE decoding stage. Prior work addresses this bottleneck by replacing the discrete tokenizer with continuous or hybrid visual token representations, or by integrating diffusion into the generation pipeline; both require foundation-scale VLM retraining or realignment. We show this is unnecessary: before each token is sampled, discrete-token VLMs already compute a full logit distribution over the codebook, but standard decoding discards it after selecting a single index. Under Otsu's threshold, the pre-sampling logits of capable VLMs assign statistically meaningful probability to at least two codebook entries per token, and recovering this distribution can substantially close the fidelity gap. We propose DCDD, a post-hoc framework that conditions a diffusion decoder on this discarded distribution while leaving the VLM frozen. At inference, DCDD converts the VLM's pre-sampling logits into distribution-weighted code vectors; during training, it uses VQ-VAE encoder-derived proxy logits calibrated to match the distributional statistics of the VLM's inference-time logits. The decoder maps these representations to high-fidelity images as an alternative to the native VQ-VAE decoder. Trained on ImageNet-1K for 50K steps, DCDD reduces reconstruction FID by 74% and Janus-Pro 7B's generation FID on MJHQ-30K by 34%, while semantic alignment across GenEval, DPG-Bench, and WISE remain consistent. Controlled comparisons with diffusion models from the same backbone family, applied either as an image-to-image refiner or as an identically trained decoder on the sampled codes, confirm that the gain stems from conditioning on the VLM's pre-sampling logit distribution rather than from the diffusion model itself.

arXiv:2606.17584v2cs.CV

Root-Selecting Fixed-Point Inversion for Rectified Flows via Trajectory Straightness

Finding the initial noise that generates a given data sample, known as inversion, is a key component for downstream applications such as training-free image editing. Existing fixed-point inversion methods improve inversion accuracy by formulating each inversion step as a fixed-point problem, but they lack a principled mechanism for selecting among multiple fixed-point solutions that can arise in practice. We observe that different selections induce different inversion trajectories, leading to substantial variation in reconstruction and editing quality. For rectified flows, we further find that this variation is closely associated with trajectory straightness, motivating straightness as a principled selection criterion. We propose SelFix, a fixed-point inversion method that selects fixed-point solutions inducing straighter inverse trajectories while retaining convergence to an exact inverse root under standard local assumptions. Experiments on FLUX.1-dev and PIE-Bench show that SelFix improves fixed-point inversion, achieving stronger real-image reconstruction and better source-preserving prompt-based editing than prior inversion baselines. The code is available at https://github.com/seminkim/selfix .

arXiv:2606.29225v2cs.AI

PolicyGuard: A Dialogue-Grounded Sub-Agent Verifier for Policy Adherence in LLM Agents

LLM agents handle user requests on behalf of organizations through tool calls and must follow the company policies stated in their system prompts. Prior work approaches this as a safeguarding problem -- external checks that block non-compliant agent actions. We argue that policy adherence is broader: real workflows unfold across many turns, require explicit user confirmation and prerequisite reads, and hinge on dialogue rather than on any single argument value. We introduce PolicyGuard, a sub-agent verifier that shares the agent's view of the dialogue, reasons over the policy in context, and returns actionable remediation. On $\tau^2$-bench airline across GPT 5.4, Claude Sonnet 4.6, and Gemini 2.5 Pro, PolicyGuard improves $\mathrm{Pass}^4$, the fraction of tasks successful in all four trials, by +12.0 / +6.0 / +12.0 pp; pooled paired tests support an overall cross-vendor effect. We further evaluate PolicyGuard on the full retail and telecom base splits, covering all three $\tau^2$-bench customer-service domains. Further analyses show that PolicyGuard improves reliability beyond agent self-checking, catches more policy violations with fewer blocks than argument-level guards, and preserves its refusal accuracy under three adversarial probes.

arXiv:2608.30556v2cs.AI

AdaPath: Query-Adaptive Path-Finding via Path-Bank for Multi-Hop Implicit Biomedical KGQA

Path-finding over knowledge graphs has become an effective way to ground LLM reasoning on multi-hop questions. However, biomedical QA introduces two distinct challenges that general-domain methods are not designed for: (i) queries do not expose intermediate reasoning and can be answered through multiple valid pathways, and (ii) biomedical knowledge graphs are densely connected, so path-finding methods easily take wrong turns. To address these challenges, we propose AdaPath, a path-finding framework that retrieves query-adaptive meta-paths from Path-Bank, which captures both query semantics and biomedical knowledge graph structure. AdaPath provides the missing cues in biomedical queries while effectively pruning dense knowledge graph neighborhoods during multi-hop reasoning. We further release BioStrat-QA, a biomedical KGQA benchmark that stratifies multi-hop queries by how much intermediate reasoning they expose. Across biomedical KGQA benchmarks, AdaPath consistently outperforms baselines, sustaining meaningful path-finding even when multi-hop queries expose less surface information. The source code is available at https://github.com/Jun-Hyeong-Kim/AdaPath.

arXiv:2609.36882v3cs.CV

Less Supervision, Better Generalization: Weakly Supervised Fake Region Localization in Diffusion-Edited Images

Localizing AI-edited regions is essential for interpretable forensic analysis, but remains challenging due to subtle and spatially distributed artifacts that are misaligned with semantic or object boundaries. Existing approaches rely on pixel-level supervision from controlled editing pipelines, which is difficult to scale and can introduce misleading signals: artifacts frequently extend beyond annotated regions, while out-of-mask pixels are treated as authentic. This limits models' ability to capture transferable evidence and generalize across generators and datasets. To address these issues, we propose ReGFLoW, a Reconstruction-Guided Fake Localization framework under Weak supervision, which is the first weakly supervised approach for diffusion-edited fake region localization. ReGFLoW requires only real/fake labels at the image-level and uses diffusion reconstruction errors as dense spatial guidance to inject them into both feature and score spaces. Furthermore, by artifact-centric multiple instance learning, ReGFLoW utilizes localized diffusion evidence without relying on semantic-affinity or boundary-based pseudo-mask priors. Extensive experiments show competitive cross-generator localization, while ReGFLoW outperforms all evaluated fully supervised baselines when evaluation includes both partially edited and fully synthetic images and in cross-dataset tests, without target-domain adaptation.

arXiv:2608.01896v2cs.CV

GeoCore-9B: Towards Geo-Aware Generative Foundation Models in Earth Observation

Existing generative models for earth observation (EO) predominantly rely on fine-tuning natural image priors, which limits their scalability and introduces perspective biases that conflict with geospatial constraints. To address this, we introduce GeoCore-9B, a 9-billion-parameter generative foundation model, which is the first of its scale to be trained from scratch exclusively on EO data. Unlike previous EO foundation models, GeoCore-9B is built upon a Flow Matching-based Diffusion Transformer (DiT) and natively conditions generation on text descriptions and continuous geospatial metadata, including ground sample distances, latitudes, and longitudes. To overcome the convergence and spatial disorientation challenges of training at this scale, we propose a Geospatial Semantic Alignment loss. This objective distills structural Earth surface priors (e.g., terrain and urban areas) from a frozen specialist teacher network, constraining the diffusion latent trajectory during training without adding inference overhead. Pre-trained on the global-scale Git-10M dataset, GeoCore-9B demonstrates strong downstream versatility. Beyond standard proxy generative tasks, we show that GeoCore-9B can be effectively adapted for practical EO applications, including highly challenging tasks such as cloud removal and SAR-to-optical cross-modal translation. Extensive evaluations confirm that GeoCore-9B establishes new state-of-the-art performance in both visual fidelity and geographic structural accuracy.

arXiv:2609.00968v2cs.CV

ReFlowSET: Representation-Aligned Latent Flow Matching for SAR-to-EO Image Translation

SAR-to-EO image translation aims to generate electro-optical (EO) imagery from synthetic aperture radar (SAR) observations. Existing latent diffusion approaches typically inherit a predetermined autoencoder, although reconstruction fidelity can vary substantially across codecs and modalities. Because the latent codec affects the round-trip preservation of both SAR conditions and EO targets, codec selection constitutes a fundamental design choice; nevertheless, existing methods largely rely on codecs pretrained on natural images. To remedy this, we introduce ReFlowSET, a conditional latent flow-matching framework that selects its codec through a joint SAR--EO reconstruction audit. Rather than inheriting a heavyweight pretrained generator, ReFlowSET trains a substantially smaller conditional DiT from scratch in the selected latent space, using dual-stream SAR conditioning followed by joint feature refinement. To provide semantic guidance for this from-scratch training, intermediate noisy-EO features are aligned with clean target-EO representations extracted by a frozen vision foundation model. This alignment is used only during training and introduces no additional inference cost. Experiments on QXS-SAROPT and SAR2Opt demonstrate state-of-the-art performance across diverse perceptual fidelity and distributional metrics. Code and pretrained weights are publicly available at https://github.com/KAIST-VICLab/ReFlowSET.

arXiv:2610.00365v2cs.LG

Manifold-Constrained Initial Noise Optimization for Efficient Generative Model Alignment

Recent advances in distillation and flow-map models have enabled deterministic one- or few-step generation for high-quality data, facilitating a new branch of reward alignment approaches that directly optimize the initial noise from a Gaussian distribution. However, most existing initial-noise optimization methods rely on first-order gradient information, which is either inapplicable or suffers from instability and inefficiency in black-box reward scenarios. Here, we introduce ZeNOVA, a stable and efficient initial noise alignment method in a gradient-free manner. Specifically, we address existing algorithms' major challenge in black-box scenarios through annealed soft-value guidance, manifold-constrained hyperspherical Langevin dynamics, and Metropolis-Hastings jumping. Extensive experiments on image and video generative models show that ZeNOVA outperforms all evaluated zeroth-order baselines by optimizing the initial noise toward higher rewards substantially more stably while exploiting the geometry of the Gaussian prior, demonstrating its practical applicability to various black-box reward alignment.

arXiv:2610.02801v2cs.AI

VIGOR: Zero-Shot Visual Generalization via Latent-Space Consistency in Model-Based Reinforcement Learning

Model-based reinforcement learning (MBRL) achieves strong sample efficiency by planning in learned latent dynamics but degrades substantially under unseen visual distractions such as background, lighting, or camera changes. Unlike model-free RL, where encoder perturbations affect only single-step predictions, MBRL suffers from a two-level vulnerability: distractions push encoder outputs out of distribution, and these errors compound through recursive latent rollouts. We propose visual generalization via latent-space consistency in model-based RL (VIGOR), which enables zero-shot generalization to unseen distractions while retaining its backbone's sample efficiency. VIGOR comprises three interdependent components: (i) asymmetric weak-to-strong augmentation, which pairs weak-only and weak-to-strong latent views within a batch; (ii) dynamics-level consistency, which enforces augmentation-invariant transition predictions via direct latent regression; and (iii) encoder-level stabilization, which prevents encoder drift under the cross-augmentation supervision of (ii). On the DeepMind Control Suite (DMC) and Robosuite, VIGOR instantiated on TD-MPC2 outperforms state-of-the-art model-free and model-based baselines in zero-shot generalization, surpassing the second-best baseline by 3.4% on DMC and 43.6% on Robosuite, with sample efficiency comparable to its backbone and fewer environment interactions than the other baselines. Ablations show that VIGOR is augmentation-agnostic: augmentations from distinct perturbation families preserve strong generalization, confirming that latent-space consistency, not the augmentation choice, drives robustness. A second instantiation on DreamerV3, a structurally distinct recurrent state-space model, also improves zero-shot generalization on both benchmarks, indicating backbone-agnostic benefits. Code and videos: https://vigor-gen.github.io/.

arXiv:2610.05108v3cs.LG

Best-of-$N$ Guidance for Test-time Diffusion Alignment

Diffusion models achieve strong generative performance but often struggle to align generated samples with human preferences measured by a reward model. A simple yet effective algorithm for test-time alignment is Best-of-$N$ (BoN) sampling, which draws $N$ i.i.d. samples from a pre-trained diffusion model and outputs the single highest-reward sample. Despite its empirical success, BoN makes limited use of reward information, as it is incorporated only at the final selection stage without influencing the reverse diffusion trajectory during sampling. Consequently, BoN sampling does not improve the average alignment of generated samples and is primarily suited to single-output settings. We propose Best-of-$N$ Guidance (BoNG), a novel method that integrates the principle of BoN sampling directly into the reverse diffusion process. BoNG performs online BoN selection over denoising particles and adjusts the reverse diffusion process to steer the particle population toward higher-reward regions during generation. Specifically, by introducing an asymmetric guidance interaction among denoising particles, BoNG uses the current BoN particle as a guidance signal to the rest of the particle population. This particle-level interaction reshapes the sampling process toward higher-reward regions, enabling BoNG to improve not only the final best sample beyond Vanilla BoN sampling, but also the average quality of generated samples. Over 36 empirical comparisons, BoNG achieves the best performance in 29 cases, ranking first in 80.56% of the comparisons against SMC and Vanilla BoN sampling. BoNG also supports multi-output capability, achieving 1.3$\times$ ImageReward score of the latest sample-based guidance method with a 1.6$\times$ speedup. We release the code at https://github.com/aailab-kaist/BoNG.

arXiv:2610.10087v3cs.LG

Multi-Agent Coordination via Support-Preserving Distillation

Offline MARL increasingly relies on generative policies to model multimodal joint behavior, typically by distilling a centralized teacher into decentralized one-step actors under the CTDE. We identify a failure mode at the teacher training stage: standard flow-based teachers pair noise with replay targets independently, so nearby noise samples can be routed toward conflicting coordination modes. The teacher then produces samples between valid modes, and because the distillation loss regresses each local actor onto the conditional mean of the teacher's output given local input, this error is not absorbed but propagated to the student. To remove this teacher-side artifact, we propose Mode-Support Semi-Discrete Optimal Transport (MoSDOT), which summarizes multimodal replay into a finite mode support with prescribed capacities and uses conditional semi-discrete optimal transport to assign each noise sample to a single mode before teacher training. We additionally study a shared-randomness variant that uses a shared noise component at execution to expose the residual gap intrinsic to strict-product execution. On controlled diagnostics and offline MARL benchmarks, MoSDOT improves endpoint quality and routing consistency, particularly on datasets exhibiting multimodal joint behavior.

arXiv:2610.11152v4cs.LG

Imitation Dominates Reinforcement: Direct In-Context RL Is Closer to ICL Than RL

LLM agents increasingly improve at inference time by accumulating experience in context rather than by updating parameters. This process is often described as in-context reinforcement learning (ICRL). Whether in-context learning (ICL) can actually play the role of RL, however, has not been tested. We study this question in its simplest form, direct ICRL, where the model conditions directly on raw trajectory-reward pairs, and ask whether the reward acts as a learning signal. Through controlled experiments on four benchmarks across six models, we find that the reward is read, but its effect is small: flipping, randomizing, or removing the reward leaves the improvement curve almost unchanged, and this holds even under meta-prompts that explicitly instruct the model to explore, exploit, or reason over rewards. Trajectories drive improvement, but not through their semantic content: shuffled or corrupted trajectories work as well as real ones. These patterns closely mirror those known in ICL, suggesting that direct ICRL is better understood as a special case of ICL than as inference-time RL. This reframing has implications for agent memory design: ICL factors such as input distribution and demonstrations may matter more than RL elements such as reward shaping and exploration.

arXiv:2608.25429v2cs.AI

Distance Is Not Enough: Forget-Retain Alignment Gap Predicts LLM Relearning Robustness

Machine unlearning aims to make a model forget specific data, yet unlearned LLMs often fail to stay unlearned: brief fine-tuning can revive removed knowledge. Existing robustness predictors rely on global weight-space displacement, but distance alone can be misleading when random or destructive updates collapse performance. We argue that relearning robustness depends on update structure: robust unlearning should affect forget-critical weights while sparing retain-critical ones. We introduce the Forget-Retain Alignment Gap (FRAG), a training-free predictor that scores an update's forget-retain alignment without running a relearning attack, and separates selective from dense updates more reliably than global distance. Building on the forget-critical, retain-sparing principle, Forget-Retain Pruning (FRP) improves relearning robustness. Our results suggest that weight selectivity better explains robustness than distance alone. Code is available at https://github.com/Yi1-Chen/FRAG.

arXiv:2605.19376v5cs.AI

Generative Recursive Reasoning

How should future neural reasoning systems implement extended computation? Recursive Reasoning Models (RRMs) offer a promising alternative to autoregressive sequence extension by performing iterative latent-state refinement with shared transition functions. Yet existing RRMs are largely deterministic, following a single latent trajectory and converging to a single prediction. We introduce Generative Recursive reAsoning Models (GRAM), a framework that turns recursive latent reasoning into probabilistic multi-trajectory computation. GRAM models reasoning as a stochastic latent trajectory, enabling multiple hypotheses, alternative solution strategies, and inference-time scaling through both recursive depth and parallel trajectory sampling. This yields a latent-variable generative model supporting conditional reasoning via $p_\theta(y \mid x)$ and, with fixed or absent inputs, unconditional generation via $p_\theta(x)$. Trained with amortized variational inference, GRAM improves over deterministic recurrent and recursive baselines on structured reasoning and multi-solution constraint satisfaction tasks, while demonstrating an unconditional generation capability. https://ahn-ml.github.io/gram-website

arXiv:2606.15735v4cs.CL

EHRNote-ChatQA: A Benchmark for Evidence-Grounded Multi-Turn Clinical Question Answering over Longitudinal Discharge Summaries

Discharge summaries are crucial clinical documents containing the context of a patient's overall hospital stay, and are routinely reviewed by medical experts for patient readmission, ongoing care, and diagnostic decision-making. When reviewing them, medical experts often must iteratively synthesize information across multiple discharge summaries while verifying the evidence supporting each answer. Although large language models (LLMs) are increasingly explored for clinical question answering, existing benchmarks do not sufficiently reflect this setting: they often evaluate exam-style medical knowledge or focus on single-turn question answering with limited evidence-grounding evaluation. We introduce EHRNote-ChatQA, the first benchmark for evidence-grounded multi-turn clinical question answering over patients' multiple discharge summaries. Built from de-identified MIMIC-IV discharge summaries, EHRNote-ChatQA contains 967 patient-level multi-turn samples spanning one to five notes and 16,072 medical-expert-verified QA pairs (8,036 content questions, each paired with an evidence-grounding question) across eight clinical categories. The benchmark is constructed through an expert-informed pipeline combining discharge-summary structuring schema, expert-curated multi-turn QA templates, and LLM-based generation, followed by review and revision of every single QA sample by 12 medical experts (11 physicians and 1 nurse). Benchmarking 24 proprietary and open-weight LLMs reveals several challenges, including that LLMs struggle more with evidence grounding than content answering, multi-turn errors compound across turns, and single-turn clinical QA performance does not reliably transfer to this setting. These findings establish EHRNote-ChatQA as a rigorous and practical benchmark for evaluating clinical QA systems.

arXiv:2610.03039v2cs.CL

HyperThink: Text-to-Parameter Hypernetworks for Efficient Reasoning

Long-form thinking traces can substantially improve the multi-step reasoning performance of large language models (LLMs), but they introduce high inference-time overhead, with latency dominated by sequential decoding. We propose HyperThink, a text-to-parameter approach that amortizes this reasoning computation into a single query-conditioned parameter update: a lightweight hypernetwork reads the question and predicts updates to a small subset of the base LLM's parameters, while a vector-quantized decoder constrains them to a finite set of reusable patterns to improve robustness and transfer. Trained end-to-end on outputs from the base model itself, HyperThink eliminates long thinking traces at test time: after one hypernetwork forward pass, the adapted model generates a concise step-by-step solution and final answer without an intermediate trace, using far fewer tokens while retaining strong reasoning performance. Empirically, HyperThink improves the low-latency region of the accuracy-latency trade-off on mathematical and general reasoning tasks, with its strongest gains in the near-non-thinking regime.

arXiv:2507.13323

GeoReg: Weight-Constrained Few-Shot Regression for Socio-Economic Estimation using LLM

Socio-economic indicators like regional GDP, population, and education levels, are crucial to shaping policy decisions and fostering sustainable development. This research introduces GeoReg a regression model that integrates diverse data sources, including satellite imagery and web-based geospatial information, to estimate these indicators even for data-scarce regions such as developing countries. Our approach leverages the prior knowledge of large language model (LLM) to address the scarcity of labeled data, with the LLM functioning as a data engineer by extracting informative features to enable effective estimation in few-shot settings. Specifically, our model obtains contextual relationships between data features and the target indicator, categorizing their correlations as positive, negative, mixed, or irrelevant. These features are then fed into the linear estimator with tailored weight constraints for each category. To capture nonlinear patterns, the model also identifies meaningful feature interactions and integrates them, along with nonlinear transformations. Experiments across three countries at different stages of development demonstrate that our model outperforms baselines in estimating socio-economic indicators, even for low-income countries with limited data availability.

arXiv:2506.01274

ReFoCUS: Reinforcement-guided Frame Optimization for Contextual Understanding

Recent progress in Large Multi-modal Models (LMMs) has enabled effective vision-language reasoning, yet the ability to understand video content remains constrained by suboptimal frame selection strategies. Existing approaches often rely on static heuristics or external retrieval modules to feed frame information into video-LLMs, which may fail to provide the query-relevant information. In this work, we introduce ReFoCUS (Reinforcement-guided Frame Optimization for Contextual UnderStanding), a novel frame-level policy optimization framework that shifts the optimization target from textual responses to visual input selection. ReFoCUS learns a frame selection policy via reinforcement learning, using reward signals derived from a reference LMM to reflect the model's intrinsic preferences for frames that best support temporally grounded responses. To efficiently explore the large combinatorial frame space, we employ an autoregressive, conditional selection architecture that ensures temporal coherence while reducing complexity. Our approach does not require explicit supervision at the frame-level and consistently improves reasoning performance across multiple video QA benchmarks, highlighting the benefits of aligning frame selection with model-internal utility.

arXiv:2506.01324

Near-Optimal Clustering in Mixture of Markov Chains

We study the problem of clustering $T$ trajectories of length $H$, each generated by one of $K$ unknown ergodic Markov chains over a finite state space of size $S$. The goal is to accurately group trajectories according to their underlying generative model. We begin by deriving an instance-dependent, high-probability lower bound on the clustering error rate, governed by the weighted KL divergence between the transition kernels of the chains. We then present a novel two-stage clustering algorithm. In Stage~I, we apply spectral clustering using a new injective Euclidean embedding for ergodic Markov chains -- a contribution of independent interest that enables sharp concentration results. Stage~II refines the initial clusters via a single step of likelihood-based reassignment. Our method achieves a near-optimal clustering error with high probability, under the conditions $H = \tilde{\Omega}(\gamma_{\mathrm{ps}}^{-1} (S^2 \vee \pi_{\min}^{-1}))$ and $TH = \tilde{\Omega}(\gamma_{\mathrm{ps}}^{-1} S^2 )$, where $\pi_{\min}$ is the minimum stationary probability of a state across the $K$ chains and $\gamma_{\mathrm{ps}}$ is the minimum pseudo-spectral gap. These requirements provide significant improvements, if not at least comparable, to the state-of-the-art guarantee (Kausik et al., 2023), and moreover, our algorithm offers a key practical advantage: unlike existing approach, it requires no prior knowledge of model-specific quantities (e.g., separation between kernels or visitation probabilities). We conclude by discussing the inherent gap between our upper and lower bounds, providing insights into the unique structure of this clustering problem.