#01Aug 20, 2026
cs.AI
Rule-Compliant Visual Spatial Planning for Multimodal Large Language Models
Yu Chen, Ting Lei, Yaoyi Li and 3 more
Multimodal large language models (MLLMs) combine linguistic reasoning with visual perception, yet their ability to perform visual spatial planning under explicit or previously unseen rule constraints remains underexplored. This setting requires models to jointly understand spatial layouts, interpret natural-language rules, and plan valid actions accordingly. To address this gap, we introduce RuleMaze, a controllable benchmark in which MLLMs must navigate mazes while obeying natural-language rules of varying complexity. RuleMaze isolates rule-compliant spatial planning by requiring accurate perception, rule interpretation, and constrained action planning. To enable scalable and systematic rule construction, we propose Language-Logic-Function Hybridization, which automatically generates natural-language rules and translates them into logical representations and executable validators, eliminating manual rule engineering. To improve rule following and generalization, we introduce Disentangled Multimodal Planning (DMP), which separates perception, execution, and rule verification through interpretable reasoning primitives. By disentangling these components, DMP facilitates systematic generalization to more complex and previously unseen rules, while providing transparent intermediate planning traces. Experiments demonstrate that DMP substantially improves rule compliance and planning success compared to end-to-end textual planning baselines. Overall, RuleMaze establishes a principled benchmark for studying grounded and interpretable rule-based spatial planning in MLLMs. Code is available at https://github.com/oceanflowlab/RuleMaze.
#02Aug 20, 2026
cs.LG
Dynamic Structural Causal Modeling for Sleep
Ranveer Singh, Saurabh Mathur, Pranuthi Tenali and 2 more
The causal dynamics of sleep-disordered breathing are complex and vary across patient populations, hindering the development of targeted interventions. We learn dynamic causal graphs of sleep-disordered breathing from Home Sleep Apnea Test (HSAT) recordings, revealing systematic differences in causal structure across sex and age subcohorts. We do so using the PCMCI+ algorithm on windowed fractional variables derived from 105 HSAT recordings, exploiting domain knowledge via edge blacklisting and employing bootstrap aggregation to address small subcohort sizes. The learned graphs show that temporal self-dependencies and the apnea-desaturation relationship persist across all cohorts, while other relationships vary substantially.
#03Aug 20, 2026
cs.CL
Inject, Align, Recover: Staged Post-Training for Retrieval-Free Document Knowledge Internalization
Qian Kou, Xiaofeng Shi, Xiaosong Qiu and 1 more
Large language models often fail to answer questions about a bounded document collection when the source documents are not retrieved at inference time. We study this setting as document knowledge internalization: converting a fixed corpus into usable parametric knowledge for retrieval-free question answering. We propose IAR (Inject, Align, and Recover), a three-stage post-training framework that separates structured document knowledge injection, QA behavior alignment, and general ability recovery. Unlike conventional continued pretraining, Inject converts source documents into continuation, rewrite, and instruction-conditioned reconstruction objectives. Align then adapts the injected model with answer-only QA supervision, while Recover merges the domain-adapted model with the base instruction model to recover general capabilities. Across Common Corpus (CC) and CCI, and across Llama, Phi, Qwen, and SmolLM model families, IAR improves the domain-primary domain-general frontier for retrieval-free document internalization. In the main comparison, IAR improves over Vanilla SFT on all four reported metrics in 7 of 8 dataset-model settings, with average gains of 3.6 percentage points in domain QA accuracy and 12.1 percentage points in mean general performance across IFEval, MMLU, and MSBench. Extended CC baselines show that LoRA and FAPM can win individual general metrics, but among methods that also reach leading or near-leading domain internalization, IAR retains one of the strongest general profiles.
#04Aug 20, 2026
cs.LG
DICS: Data-Informed Centroid Splitting for Decision Tree Classifiers
MD Saifur Rahman Mazumder, Feng Yu
Decision tree-based models are widely used in machine learning due to their interpretability and strong empirical performance. However, training decision trees can be computationally expensive, particularly for large and high-dimensional datasets, largely due to the exhaustive search over candidate splits at each node. To improve computational efficiency, we propose Data-Informed Centroid Splitting (DICS), a clustering-based framework that constructs a compact and informative set of candidate splits using data-driven priors. By incorporating class-aware structure, DICS significantly reduces the split search space for classification tasks while preserving predictive performance. We further provide theoretical analysis showing that under the stated assumptions, DICS does not degrade the performance of classification trees compared to exhaustive split search. DICS can be incorporated into classification trees, random forests, and gradient-boosting models. Extensive experiments demonstrate that DICS achieves comparable accuracy while substantially reducing training time across synthetic and benchmark datasets, highlighting the benefit of integrating data-informed priors into split selection for scalable classification tree learning.
#05Aug 20, 2026
math.PR
Information on trajectories: martingales and random times
Akshay Balsubramani
Accounting for information flow on the path space of trajectories of a nonnegative martingale yields exact variational identities for it, even at arbitrary random times. This recovers the widely used classical concentration inequalities, from Ville to PAC-Bayes, and measures what each one discards. The tail a bound controls is itself a relative entropy, resolved by the chain rule into per-step conditional divergences. The discarded slack has an exact form in each of three geometries: a Gibbs tilt for the Azuma-Hoeffding and PAC-Bayes bounds, the crossing itself for Ville's and for pooled tests, and a dominating certificate for the $L^p$ maximal bound. That certificate's optional-stopping deficit resolves per step into Bregman divergences of the running maximum. On a path-time space, the same identity gains one factor that prices anticipation: an arbitrary random time carries an e-process ``peeking penalty.'' The partition function can be read as a coalescent--a prefix-sharing probability of independent copies--and geometric mixtures of test martingales gain a pooling benefit for multi-model safe testing.