Causal discovery remains a central challenge in machine learning, yet existing methods face a fundamental gap: algorithms like GES and GraN-DAG achieve strong empirical performance but lack finite-sample guarantees, while theoretically principled approaches fail to scale. We close this gap by introducing a game-theoretic reinforcement learning framework for causal discovery, where a DDQN agent directly competes against a strong baseline (GES or GraN-DAG), always warm-starting from the opponent's solution. This design yields three provable guarantees: the learned graph is never worse than the opponent, warm-starting strictly accelerates convergence, and most importantly, with high probability the algorithm selects the true best candidate graph. To the best of our knowledge, our result makes a first-of-its-kind progress in explaining such finite-sample guarantees in causal discovery: on synthetic SEMs (30 nodes), the observed error probability decays with n, tightly matching theory. On real-world benchmarks including Sachs, Asia, Alarm, Child, Hepar2, Dream, and Andes, our method consistently improves upon GES and GraN-DAG while remaining theoretically safe. Remarkably, it scales to large graphs such as Hepar2 (70 nodes), Dream (100 nodes), and Andes (220 nodes). Together, these results establish a new class of RL-based causal discovery algorithms that are simultaneously provably consistent, sample-efficient, and practically scalable, marking a decisive step toward unifying empirical performance with rigorous finite-sample theory.

''Noisy'' datasets (regimes with low signal to noise ratios, small sample sizes, faulty data collection, etc) remain a key research frontier for classification methods with both theoretical and practical implications. We introduce FINDER, a rigorous framework for analyzing generic classification problems, with tailored algorithms for noisy datasets. FINDER incorporates fundamental stochastic analysis ideas into the feature learning and inference stages to optimally account for the randomness inherent to all empirical datasets. We construct ''stochastic features'' by first viewing empirical datasets as realizations from an underlying random field (without assumptions on its exact distribution) and then mapping them to appropriate Hilbert spaces. The Kosambi-Karhunen-Loéve expansion (KLE) breaks these stochastic features into computable irreducible components, which allow classification over noisy datasets via an eigen-decomposition: data from different classes resides in distinct regions, identified by analyzing the spectrum of the associated operators. We validate FINDER on several challenging, data-deficient scientific domains, producing state of the art breakthroughs in: (i) Alzheimer's Disease stage classification, (ii) Remote sensing detection of deforestation. We end with a discussion on when FINDER is expected to outperform existing methods, its failure modes, and other limitations.

The VC-dimension is a well-studied and fundamental complexity measure of a set system (or hypergraph) that is central to many areas of machine learning. We establish several new results on the complexity of computing the VC-dimension. In particular, given a hypergraph $\mathcal{H}=(\mathcal{V},\mathcal{E})$, we prove that the naive $2^{\mathcal{O}(|\mathcal{V}|)}$-time algorithm is asymptotically tight under the Exponential Time Hypothesis (ETH). We then prove that the problem admits a $1$-additive fixed-parameter approximation algorithm when parameterized by the maximum degree of $\mathcal{H}$ and a fixed-parameter algorithm when parameterized by its dimension, and that these are essentially the only such exploitable structural parameters. Lastly, we consider a generalization of the problem, formulated using graphs, which captures the VC-dimension of both set systems and graphs. We design a $2^{\mathcal{O}(\rm{tw}\cdot \log \rm{tw})}\cdot |V|$-time algorithm for any graph $G=(V,E)$ of treewidth $\rm{tw}$ (which, for a set system, applies to the treewidth of its incidence graph). This is in contrast with closely related problems that require a double-exponential dependency on the treewidth (assuming the ETH).

Multi-class wine classification presents fundamental trade-offs between model accuracy, feature dimensionality, and interpretability - critical factors for production deployment in analytical chemistry. This paper presents a comprehensive empirical study of One-vs-Rest logistic regression on the UCI Wine dataset (178 samples, 3 cultivars, 13 chemical features), comparing from-scratch gradient descent implementation against scikit-learn's optimized solvers and quantifying L1 regularization effects on feature sparsity. Manual gradient descent achieves 92.59 percent mean test accuracy with smooth convergence, validating theoretical foundations, though scikit-learn provides 24x training speedup and 98.15 percent accuracy. Class-specific analysis reveals distinct chemical signatures with heterogeneous patterns where color intensity varies dramatically (0.31 to 16.50) across cultivars. L1 regularization produces 54-69 percent feature reduction with only 4.63 percent accuracy decrease, demonstrating favorable interpretability-performance trade-offs. We propose an optimal 5-feature subset achieving 62 percent complexity reduction with estimated 92-94 percent accuracy, enabling cost-effective deployment with 80 dollars savings per sample and 56 percent time reduction. Statistical validation confirms robust generalization with sub-2ms prediction latency suitable for real-time quality control. Our findings provide actionable guidelines for practitioners balancing comprehensive chemical analysis against targeted feature measurement in resource-constrained environments.

Although quantum systems are generally described by quantum state vectors, we show that in certain cases their measurement processes can be reformulated as probabilistic equations expressed in terms of probabilistic state vectors. These probabilistic representations can, in turn, be approximated by the neural network dynamics of the Tensor Brain (TB) model. The Tensor Brain is a recently proposed framework for modeling perception and memory in the brain, providing a biologically inspired mechanism for efficiently integrating generated symbolic representations into reasoning processes.

In cooperative Multi-Agent Reinforcement Learning (MARL), it is a common practice to tune hyperparameters in ideal simulated environments to maximize cooperative performance. However, policies tuned for cooperation often fail to maintain robustness and resilience under real-world uncertainties. Building trustworthy MARL systems requires a deep understanding of robustness, which ensures stability under uncertainties, and resilience, the ability to recover from disruptions--a concept extensively studied in control systems but largely overlooked in MARL. In this paper, we present a large-scale empirical study comprising over 82,620 experiments to evaluate cooperation, robustness, and resilience in MARL across 4 real-world environments, 13 uncertainty types, and 15 hyperparameters. Our key findings are: (1) Under mild uncertainty, optimizing cooperation improves robustness and resilience, but this link weakens as perturbations intensify. Robustness and resilience also varies by algorithm and uncertainty type. (2) Robustness and resilience do not generalize across uncertainty modalities or agent scopes: policies robust to action noise for all agents may fail under observation noise on a single agent. (3) Hyperparameter tuning is critical for trustworthy MARL: surprisingly, standard practices like parameter sharing, GAE, and PopArt can hurt robustness, while early stopping, high critic learning rates, and Leaky ReLU consistently help. By optimizing hyperparameters only, we observe substantial improvement in cooperation, robustness and resilience across all MARL backbones, with the phenomenon also generalizing to robust MARL methods across these backbones. Code and results available at https://github.com/BUAA-TrustworthyMARL/adv_marl_benchmark .

In edge computing systems, autonomous agents must make fast local decisions while competing for shared resources. Existing MARL methods often resume to centralized critics or frequent communication, which fail under limited observability and communication constraints. We propose a decentralized framework in which each agent solves a constrained Markov decision process (CMDP), coordinating implicitly through a shared constraint vector. For the specific case of offloading, e.g., constraints prevent overloading shared server resources. Coordination constraints are updated infrequently and act as a lightweight coordination mechanism. They enable agents to align with global resource usage objectives but require little direct communication. Using safe reinforcement learning, agents learn policies that meet both local and global goals. We establish theoretical guarantees under mild assumptions and validate our approach experimentally, showing improved performance over centralized and independent baselines, especially in large-scale settings.

LLM-powered embodied agents have shown success on conventional object-rearrangement tasks, but providing personalized assistance that leverages user-specific knowledge from past interactions presents new challenges. We investigate these challenges through the lens of agents' memory utilization along two critical dimensions: object semantics (identifying objects based on personal meaning) and user patterns (recalling sequences from behavioral routines). To assess these capabilities, we construct MEMENTO, an end-to-end two-stage evaluation framework comprising single-memory and joint-memory tasks. Our experiments reveal that current agents can recall simple object semantics but struggle to apply sequential user patterns to planning. Through in-depth analysis, we identify two critical bottlenecks: information overload and coordination failures when handling multiple memories. Based on these findings, we explore memory architectural approaches to address these challenges. Given our observation that episodic memory provides both personalized knowledge and in-context learning benefits, we design a hierarchical knowledge graph-based user-profile memory module that separately manages personalized knowledge, achieving substantial improvements on both single and joint-memory tasks. Project website: https://connoriginal.github.io/MEMENTO

Dynamic treatment regimes are sequential decision rules that adapt treatment according to individual time-varying characteristics and outcomes to achieve optimal effects, with applications in precision medicine, personalized recommendations, and dynamic marketing. Estimating optimal dynamic treatment regimes via sequential randomized trials might face costly and ethical hurdles, often necessitating the use of historical observational data. In this work, we utilize proximal causal inference framework for learning optimal dynamic treatment regimes when the unconfoundedness assumption fails. Our contributions are four-fold: (i) we propose three nonparametric identification methods for optimal dynamic treatment regimes; (ii) we establish the semiparametric efficiency bound for the value function of a given regime; (iii) we propose a (K+1)-robust method for learning optimal dynamic treatment regimes, where K is the number of stages; (iv) as a by-product for marginal structural models, we establish identification and estimation of counterfactual means under a static regime. Numerical experiments validate the efficiency and multiple robustness of our proposed methods.

Neural activity forecasting is central to understanding neural systems and enabling closed-loop control. While deep learning has recently advanced the state-of-the-art in the time series forecasting literature, its application to neural activity forecasting remains limited. To bridge this gap, we systematically evaluated eight probabilistic deep learning models, including two foundation models, that have demonstrated strong performance on general forecasting benchmarks. We compared them against four classical statistical models and two baseline methods on spontaneous neural activity recorded from mouse cortex via widefield imaging. Across prediction horizons, several deep learning models consistently outperformed classical approaches, with the best model producing informative forecasts up to 1.5 seconds into the future. Our findings point toward future control applications and open new avenues for probing the intrinsic temporal structure of neural activity.