The sparse matrix estimation problem consists of estimating the distribution of an $n\times n$ matrix $Y$, from a sparsely observed single instance of this matrix where the entries of $Y$ are independent random variables. This captures a wide array of problems; special instances include matrix completion in the context of recommendation systems, graphon estimation, and community detection in (mixed membership) stochastic block models. Inspired by classical collaborative filtering for recommendation systems, we propose a novel iterative, collaborative filtering-style algorithm for matrix estimation in this generic setting. We show that the mean squared error (MSE) of our estimator converges to $0$ at the rate of $O(d^2 (pn)^{-2/5})$ as long as $\omega(d^5 n)$ random entries from a total of $n^2$ entries of $Y$ are observed (uniformly sampled), $\E[Y]$ has rank $d$, and the entries of $Y$ have bounded support. The maximum squared error across all entries converges to $0$ with high probability as long as we observe a little more, $\Omega(d^5 n \ln^5(n))$ entries. Our results are the best known sample complexity results in this generality.

Neural Information Processing Systems http://nips.cc/

Restless bandit problems are instances of non-stationary multi-armed bandits.

Accurately predicting the relevance of items to users is crucial to the success of manysocialplatforms.

However, one significant challenge researchers face is the lack of comprehensive datasets to explore and advance the field of smart home rule recommendations.

Group Recommendation (GR), which aims to recommend items to groups of users, has become a promising and practical direction for recommendation systems.

Traditional recommendation systems tend to trap users in strong feedback loops by excessively pushing content aligned with their historical preferences, thereby limiting exploration opportunities and causing content fatigue. Although large language models (LLMs) demonstrate potential with their diverse content generation capabilities, existing LLM-enhanced dual-model frameworks face two major limitations: first, they overlook long-term preferences driven by group identity, leading to biased interest modeling; second, they suffer from static optimization flaws, as a one-time alignment process fails to leverage incremental user data for closed-loop optimization. To address these challenges, we propose the Co-Evolutionary Alignment (CoEA) method. For interest modeling bias, we introduce Dual-Stable Interest Exploration (DSIE) module, jointly modeling long-term group identity and short-term individual interests through parallel processing of behavioral sequences. For static optimization limitations, we design a Periodic Collaborative Optimization (PCO) mechanism. This mechanism regularly conducts preference verification on incremental data using the Relevance LLM, then guides the Novelty LLM to perform fine-tuning based on the verification results, and subsequently feeds back the output of the continually fine-tuned Novelty LLM to the Relevance LLM for re-evaluation, thereby achieving a dynamic closed-loop optimization. Extensive online and offline experiments verify the effectiveness of the CoEA model in serendipitous recommendation.

Computational simulations have revolutionized materials design, accelerating innovation by allowing researchers to explore material properties and their behaviors virtually before experimental validation[1-4]. This shift has led to significant breakthroughs that range from energy storage[5, 6] to pharmaceutical development[7, 8]. However, a persistent challenge undermines this potential: the technical barriers to effective simulation setup disproportionately burden researchers, particularly those whose expertise lies in experimental rather than computational domains. When scientists identify a promising new compound, understanding its fundamental properties often requires computational validation. Y et, even seemingly straightforward simulations frequently lead to lengthy technical challenges. Even experienced computational scientists (physicists, chemists, engineers) find themselves diverted from scientific inquiry toward navigating complex programming challenges, engaging in trial-and-error attempts, and struggling with computational setup details rather than focusing on the scientific questions[9]. Integrated Computational Materials Engineering (ICME) has emerged as a robust framework to accelerate materials development by synergizing experimental data, simulations, and theoretical models across multiple scales.