Gap-Dependent Bounds for Nearly Minimax Optimal Reinforcement Learning with Linear Function Approximation

We study gap-dependent performance guarantees for nearly minimax-optimal algorithms in reinforcement learning with linear function approximation. While prior works have established gap-dependent regret bounds in this setting, existing analyses do not apply to algorithms that achieve the nearly minimax-optimal worst-case regret bound $\tilde{O}(d\sqrt{H^3K})$, where $d$ is the feature dimension, $H$ is the horizon length, and $K$ is the number of episodes. We bridge this gap by providing the first gap-dependent regret bound for the nearly minimax-optimal algorithm LSVI-UCB++ (He et al., 2023). Our analysis yields improved dependencies on both $d$ and $H$ compared to previous gap-dependent results. Moreover, leveraging the low policy-switching property of LSVI-UCB++, we introduce a concurrent variant that enables efficient parallel exploration across multiple agents and establish the first gap-dependent sample complexity upper bound for online multi-agent RL with linear function approximation, achieving linear speedup with respect to the number of agents.

FAST-EQA: Efficient Embodied Question Answering with Global and Local Region Relevancy

Embodied Question Answering (EQA) combines visual scene understanding, goal-directed exploration, spatial and temporal reasoning under partial observability. A central challenge is to confine physical search to question-relevant subspaces while maintaining a compact, actionable memory of observations. Furthermore, for real-world deployment, fast inference time during exploration is crucial. We introduce FAST-EQA, a question-conditioned framework that (i) identifies likely visual targets, (ii) scores global regions of interest to guide navigation, and (iii) employs Chain-of-Thought (CoT) reasoning over visual memory to answer confidently. FAST-EQA maintains a bounded scene memory that stores a fixed-capacity set of region-target hypotheses and updates them online, enabling robust handling of both single and multi-target questions without unbounded growth. To expand coverage efficiently, a global exploration policy treats narrow openings and doors as high-value frontiers, complementing local target seeking with minimal computation. Together, these components focus the agent's attention, improve scene coverage, and improve answer reliability while running substantially faster than prior approaches. On HMEQA and EXPRESS-Bench, FAST-EQA achieves state-of-the-art performance, while performing competitively on OpenEQA and MT-HM3D.

Legendre Memory Unit with A Multi-Slice Compensation Model for Short-Term Wind Speed Forecasting Based on Wind Farm Cluster Data

With more wind farms clustered for integration, the short-term wind speed prediction of such wind farm clusters is critical for normal operation of power systems. This paper focuses on achieving accurate, fast, and robust wind speed prediction by full use of cluster data with spatial-temporal correlation. First, weighted mean filtering (WMF) is applied to denoise wind speed data at the single-farm level. The Legendre memory unit (LMU) is then innovatively applied for the wind speed prediction, in combination with the Compensating Parameter based on Kendall rank correlation coefficient (CPK) of wind farm cluster data, to construct the multi-slice LMU (MSLMU). Finally, an innovative ensemble model WMF-CPK-MSLMU is proposed herein, with three key blocks: data pre-processing, forecasting, and multi-slice compensation. Advantages include: 1) LMU jointly models linear and nonlinear dependencies among farms to capture spatial-temporal correlations through backpropagation; 2) MSLMU enhances forecasting by using CPK-derived weights instead of random initialization, allowing spatial correlations to fully activate hidden nodes across clustered wind farms.; 3) CPK adaptively weights the compensation model in MSLMU and complements missing data spatially, to facilitate the whole model highly accurate and robust. Test results on different wind farm clusters indicate the effectiveness and superiority of proposed ensemble model WMF-CPK-MSLMU in the short-term prediction of wind farm clusters compared to the existing models.

Non-Markov Multi-Round Conversational Image Generation with History-Conditioned MLLMs

Conversational image generation requires a model to follow user instructions across multiple rounds of interaction, grounded in interleaved text and images that accumulate as chat history. While recent multimodal large language models (MLLMs) can generate and edit images, most existing multi-turn benchmarks and training recipes are effectively Markov: the next output depends primarily on the most recent image, enabling shortcut solutions that ignore long-range history. In this work we formalize and target the more challenging non-Markov setting, where a user may refer back to earlier states, undo changes, or reference entities introduced several rounds ago. We present (i) non-Markov multi-round data construction strategies, including rollback-style editing that forces retrieval of earlier visual states and name-based multi-round personalization that binds names to appearances across rounds; (ii) a history-conditioned training and inference framework with token-level caching to prevent multi-round identity drift; and (iii) enabling improvements for high-fidelity image reconstruction and editable personalization, including a reconstruction-based DiT detokenizer and a multi-stage fine-tuning curriculum. We demonstrate that explicitly training for non-Markov interactions yields substantial improvements in multi-round consistency and instruction compliance, while maintaining strong single-round editing and personalization.

Support Basis: Fast Attention Beyond Bounded Entries

The quadratic complexity of softmax attention remains a central bottleneck in scaling large language models (LLMs). [Alman and Song, NeurIPS 2023] proposed a sub-quadratic attention approximation algorithm, but it works only under the restrictive bounded-entry assumption. Since this assumption rarely holds in practice, its applicability to modern LLMs is limited. In this paper, we introduce support-basis decomposition, a new framework for efficient attention approximation beyond bounded entries. We empirically demonstrate that the entries of the query and key matrices exhibit sub-Gaussian behavior. Our approach uses this property to split large and small entries, enabling exact computation on sparse components and polynomial approximation on dense components. We establish rigorous theoretical guarantees, proving a sub-quadratic runtime, and extend the method to a multi-threshold setting that eliminates all distributional assumptions. Furthermore, we provide the first theoretical justification for the empirical success of polynomial attention [Kacham, Mirrokni, and Zhong, ICML 2024], showing that softmax attention can be closely approximated by a combination of multiple polynomial attentions with sketching.

Regret-Optimal Q-Learning with Low Cost for Single-Agent and Federated Reinforcement Learning

Motivated by real-world settings where data collection and policy deployment -- whether for a single agent or across multiple agents -- are costly, we study the problem of on-policy single-agent reinforcement learning (RL) and federated RL (FRL) with a focus on minimizing burn-in costs (the sample sizes needed to reach near-optimal regret) and policy switching or communication costs. In parallel finite-horizon episodic Markov Decision Processes (MDPs) with $S$ states and $A$ actions, existing methods either require superlinear burn-in costs in $S$ and $A$ or fail to achieve logarithmic switching or communication costs. We propose two novel model-free RL algorithms -- Q-EarlySettled-LowCost and FedQ-EarlySettled-LowCost -- that are the first in the literature to simultaneously achieve: (i) the best near-optimal regret among all known model-free RL or FRL algorithms, (ii) low burn-in cost that scales linearly with $S$ and $A$, and (iii) logarithmic policy switching cost for single-agent RL or communication cost for FRL. Additionally, we establish gap-dependent theoretical guarantees for both regret and switching/communication costs, improving or matching the best-known gap-dependent bounds.

SORT3D: Spatial Object-centric Reasoning Toolbox for Zero-Shot 3D Grounding Using Large Language Models

Interpreting object-referential language and grounding objects in 3D with spatial relations and attributes is essential for robots operating alongside humans. However, this task is often challenging due to the diversity of scenes, large number of fine-grained objects, and complex free-form nature of language references. Furthermore, in the 3D domain, obtaining large amounts of natural language training data is difficult. Thus, it is important for methods to learn from little data and zero-shot generalize to new environments. To address these challenges, we propose SORT3D, an approach that utilizes rich object attributes from 2D data and merges a heuristics-based spatial reasoning toolbox with the ability of large language models (LLMs) to perform sequential reasoning. Importantly, our method does not require text-to-3D data for training and can be applied zero-shot to unseen environments. We show that SORT3D achieves state-of-the-art performance on complex view-dependent grounding tasks on two benchmarks. We also implement the pipeline to run real-time on an autonomous vehicle and demonstrate that our approach can be used for object-goal navigation on previously unseen real-world environments. All source code for the system pipeline is publicly released at https://github.com/nzantout/SORT3D .

I3S: Importance Sampling Subspace Selection for Low-Rank Optimization in LLM Pretraining

Low-rank optimization has emerged as a promising approach to enabling memory-efficient training of large language models (LLMs). Existing low-rank optimization methods typically project gradients onto a low-rank subspace, reducing the memory cost of storing optimizer states. A key challenge in these methods is identifying suitable subspaces to ensure an effective optimization trajectory. Most existing approaches select the dominant subspace to preserve gradient information, as this intuitively provides the best approximation. However, we find that in practice, the dominant subspace stops changing during pretraining, thereby constraining weight updates to similar subspaces. In this paper, we propose importance sampling subspace selection (I3S) for low-rank optimization, which theoretically offers a comparable convergence rate to the dominant subspace approach. Empirically, we demonstrate that I3S significantly outperforms previous methods in LLM pretraining tasks.

Gap-Dependent Bounds for Federated $Q$-learning

We present the first gap-dependent analysis of regret and communication cost for on-policy federated $Q$-Learning in tabular episodic finite-horizon Markov decision processes (MDPs). Existing FRL methods focus on worst-case scenarios, leading to $\sqrt{T}$-type regret bounds and communication cost bounds with a $\log T$ term scaling with the number of agents $M$, states $S$, and actions $A$, where $T$ is the average total number of steps per agent. In contrast, our novel framework leverages the benign structures of MDPs, such as a strictly positive suboptimality gap, to achieve a $\log T$-type regret bound and a refined communication cost bound that disentangles exploration and exploitation. Our gap-dependent regret bound reveals a distinct multi-agent speedup pattern, and our gap-dependent communication cost bound removes the dependence on $MSA$ from the $\log T$ term. Notably, our gap-dependent communication cost bound also yields a better global switching cost when $M=1$, removing $SA$ from the $\log T$ term.

Topology-Preserving Image Segmentation with Spatial-Aware Persistent Feature Matching

Topological correctness is critical for segmentation of tubular structures. Existing topological segmentation loss functions are primarily based on the persistent homology of the image. They match the persistent features from the segmentation with the persistent features from the ground truth and minimize the difference between them. However, these methods suffer from an ambiguous matching problem since the matching only relies on the information in the topological space. In this work, we propose an effective and efficient Spatial-Aware Topological Loss Function that further leverages the information in the original spatial domain of the image to assist the matching of persistent features. Extensive experiments on images of various types of tubular structures show that the proposed method has superior performance in improving the topological accuracy of the segmentation compared with state-of-the-art methods.