Covariates-Adjusted Mixed-Membership Estimation: A Novel Network Model with Optimal Guarantees

This paper addresses the problem of mixed-membership estimation in networks, where the goal is to efficiently estimate the latent mixed-membership structure from the observed network. Recognizing the widespread availability and valuable information carried by node covariates, we propose a novel network model that incorporates both community information, as represented by the Degree-Corrected Mixed Membership (DCMM) model, and node covariate similarities to determine connections. We investigate the regularized maximum likelihood estimation (MLE) for this model and demonstrate that our approach achieves optimal estimation accuracy for both the similarity matrix and the mixed-membership, in terms of both the Frobenius norm and the entrywise loss. Since directly analyzing the original convex optimization problem is intractable, we employ nonconvex optimization to facilitate the analysis. A key contribution of our work is identifying a crucial assumption that bridges the gap between convex and nonconvex solutions, enabling the transfer of statistical guarantees from the nonconvex approach to its convex counterpart. Importantly, our analysis extends beyond the MLE loss and the mean squared error (MSE) used in matrix completion problems, generalizing to all the convex loss functions. Consequently, our analysis techniques extend to a broader set of applications, including ranking problems based on pairwise comparisons. Finally, simulation experiments validate our theoretical findings, and real-world data analyses confirm the practical relevance of our model.

MATH-Perturb: Benchmarking LLMs' Math Reasoning Abilities against Hard Perturbations

Large language models have demonstrated impressive performance on challenging mathematical reasoning tasks, which has triggered the discussion of whether the performance is achieved by true reasoning capability or memorization. To investigate this question, prior work has constructed mathematical benchmarks when questions undergo simple perturbations -- modifications that still preserve the underlying reasoning patterns of the solutions. However, no work has explored hard perturbations, which fundamentally change the nature of the problem so that the original solution steps do not apply. To bridge the gap, we construct MATH-P-Simple and MATH-P-Hard via simple perturbation and hard perturbation, respectively. Each consists of 279 perturbed math problems derived from level-5 (hardest) problems in the MATH dataset (Hendrycksmath et. al., 2021). We observe significant performance drops on MATH-P-Hard across various models, including o1-mini (-16.49%) and gemini-2.0-flash-thinking (-12.9%). We also raise concerns about a novel form of memorization where models blindly apply learned problem-solving skills without assessing their applicability to modified contexts. This issue is amplified when using original problems for in-context learning. We call for research efforts to address this challenge, which is critical for developing more robust and reliable reasoning models.

Tracking Tumors under Deformation from Partial Point Clouds using Occupancy Networks

To track tumors during surgery, information from preoperative CT scans is used to determine their position. However, as the surgeon operates, the tumor may be deformed which presents a major hurdle for accurately resecting the tumor, and can lead to surgical inaccuracy, increased operation time, and excessive margins. This issue is particularly pronounced in robot-assisted partial nephrectomy (RAPN), where the kidney undergoes significant deformations during operation. Toward addressing this, we introduce a occupancy network-based method for the localization of tumors within kidney phantoms undergoing deformations at interactive speeds. We validate our method by introducing a 3D hydrogel kidney phantom embedded with exophytic and endophytic renal tumors. It closely mimics real tissue mechanics to simulate kidney deformation during in vivo surgery, providing excellent contrast and clear delineation of tumor margins to enable automatic threshold-based segmentation. Our findings indicate that the proposed method can localize tumors in moderately deforming kidneys with a margin of 6mm to 10mm, while providing essential volumetric 3D information at over 60Hz. This capability directly enables downstream tasks such as robotic resection.

Towards Principled Superhuman AI for Multiplayer Symmetric Games

Multiplayer games, when the number of players exceeds two, present unique challenges that fundamentally distinguish them from the extensively studied two-player zero-sum games. These challenges arise from the non-uniqueness of equilibria and the risk of agents performing highly suboptimally when adopting equilibrium strategies. While a line of recent works developed learning systems successfully achieving human-level or even superhuman performance in popular multiplayer games such as Mahjong, Poker, and Diplomacy, two critical questions remain unaddressed: (1) What is the correct solution concept that AI agents should find? and (2) What is the general algorithmic framework that provably solves all games within this class? This paper takes the first step towards solving these unique challenges of multiplayer games by provably addressing both questions in multiplayer symmetric normal-form games. We also demonstrate that many meta-algorithms developed in prior practical systems for multiplayer games can fail to achieve even the basic goal of obtaining agent's equal share of the total reward.

Optimal Aggregation of Prediction Intervals under Unsupervised Domain Shift

As machine learning models are increasingly deployed in dynamic environments, it becomes paramount to assess and quantify uncertainties associated with distribution shifts. A distribution shift occurs when the underlying data-generating process changes, leading to a deviation in the model's performance. The prediction interval, which captures the range of likely outcomes for a given prediction, serves as a crucial tool for characterizing uncertainties induced by their underlying distribution. In this paper, we propose methodologies for aggregating prediction intervals to obtain one with minimal width and adequate coverage on the target domain under unsupervised domain shift, under which we have labeled samples from a related source domain and unlabeled covariates from the target domain. Our analysis encompasses scenarios where the source and the target domain are related via i) a bounded density ratio, and ii) a measure-preserving transformation. Our proposed methodologies are computationally efficient and easy to implement. Beyond illustrating the performance of our method through a real-world dataset, we also delve into the theoretical details. This includes establishing rigorous theoretical guarantees, coupled with finite sample bounds, regarding the coverage and width of our prediction intervals. Our approach excels in practical applications and is underpinned by a solid theoretical framework, ensuring its reliability and effectiveness across diverse contexts.

Query-Based Knowledge Sharing for Open-Vocabulary Multi-Label Classification

Identifying labels that did not appear during training, known as multi-label zero-shot learning, is a non-trivial task in computer vision. To this end, recent studies have attempted to explore the multi-modal knowledge of vision-language pre-training (VLP) models by knowledge distillation, allowing to recognize unseen labels in an open-vocabulary manner. However, experimental evidence shows that knowledge distillation is suboptimal and provides limited performance gain in unseen label prediction. In this paper, a novel query-based knowledge sharing paradigm is proposed to explore the multi-modal knowledge from the pretrained VLP model for open-vocabulary multi-label classification. Specifically, a set of learnable label-agnostic query tokens is trained to extract critical vision knowledge from the input image, and further shared across all labels, allowing them to select tokens of interest as visual clues for recognition. Besides, we propose an effective prompt pool for robust label embedding, and reformulate the standard ranking learning into a form of classification to allow the magnitude of feature vectors for matching, which both significantly benefit label recognition. Experimental results show that our framework significantly outperforms state-of-the-art methods on zero-shot task by 5.9% and 4.5% in mAP on the NUS-WIDE and Open Images, respectively.

Text as Image: Learning Transferable Adapter for Multi-Label Classification

Pre-trained vision-language models have notably accelerated progress of open-world concept recognition. Their impressive zero-shot ability has recently been transferred to multi-label image classification via prompt tuning, enabling to discover novel labels in an open-vocabulary manner. However, this paradigm suffers from non-trivial training costs, and becomes computationally prohibitive for a large number of candidate labels. To address this issue, we note that vision-language pre-training aligns images and texts in a unified embedding space, making it potential for an adapter network to identify labels in visual modality while be trained in text modality. To enhance such cross-modal transfer ability, a simple yet effective method termed random perturbation is proposed, which enables the adapter to search for potential visual embeddings by perturbing text embeddings with noise during training, resulting in better performance in visual modality. Furthermore, we introduce an effective approach to employ large language models for multi-label instruction-following text generation. In this way, a fully automated pipeline for visual label recognition is developed without relying on any manual data. Extensive experiments on public benchmarks show the superiority of our method in various multi-label classification tasks.

Beyond Visual Cues: Synchronously Exploring Target-Centric Semantics for Vision-Language Tracking

Single object tracking aims to locate one specific target in video sequences, given its initial state. Classical trackers rely solely on visual cues, restricting their ability to handle challenges such as appearance variations, ambiguity, and distractions. Hence, Vision-Language (VL) tracking has emerged as a promising approach, incorporating language descriptions to directly provide high-level semantics and enhance tracking performance. However, current VL trackers have not fully exploited the power of VL learning, as they suffer from limitations such as heavily relying on off-the-shelf backbones for feature extraction, ineffective VL fusion designs, and the absence of VL-related loss functions. Consequently, we present a novel tracker that progressively explores target-centric semantics for VL tracking. Specifically, we propose the first Synchronous Learning Backbone (SLB) for VL tracking, which consists of two novel modules: the Target Enhance Module (TEM) and the Semantic Aware Module (SAM). These modules enable the tracker to perceive target-related semantics and comprehend the context of both visual and textual modalities at the same pace, facilitating VL feature extraction and fusion at different semantic levels. Moreover, we devise the dense matching loss to further strengthen multi-modal representation learning. Extensive experiments on VL tracking datasets demonstrate the superiority and effectiveness of our methods.

Maximum Likelihood Estimation is All You Need for Well-Specified Covariate Shift

A key challenge of modern machine learning systems is to achieve Out-of-Distribution (OOD) generalization -- generalizing to target data whose distribution differs from that of source data. Despite its significant importance, the fundamental question of ``what are the most effective algorithms for OOD generalization'' remains open even under the standard setting of covariate shift. This paper addresses this fundamental question by proving that, surprisingly, classical Maximum Likelihood Estimation (MLE) purely using source data (without any modification) achieves the minimax optimality for covariate shift under the well-specified setting. That is, no algorithm performs better than MLE in this setting (up to a constant factor), justifying MLE is all you need. Our result holds for a very rich class of parametric models, and does not require any boundedness condition on the density ratio. We illustrate the wide applicability of our framework by instantiating it to three concrete examples -- linear regression, logistic regression, and phase retrieval. This paper further complement the study by proving that, under the misspecified setting, MLE is no longer the optimal choice, whereas Maximum Weighted Likelihood Estimator (MWLE) emerges as minimax optimal in certain scenarios.

UTOPIA: Universally Trainable Optimal Prediction Intervals Aggregation

Uncertainty quantification for prediction is an intriguing problem with significant applications in various fields, such as biomedical science, economic studies, and weather forecasts. Numerous methods are available for constructing prediction intervals, such as quantile regression and conformal predictions, among others. Nevertheless, model misspecification (especially in high-dimension) or sub-optimal constructions can frequently result in biased or unnecessarily-wide prediction intervals. In this paper, we propose a novel and widely applicable technique for aggregating multiple prediction intervals to minimize the average width of the prediction band along with coverage guarantee, called Universally Trainable Optimal Predictive Intervals Aggregation (UTOPIA). The method also allows us to directly construct predictive bands based on elementary basis functions. Our approach is based on linear or convex programming which is easy to implement. All of our proposed methodologies are supported by theoretical guarantees on the coverage probability and optimal average length, which are detailed in this paper. The effectiveness of our approach is convincingly demonstrated by applying it to synthetic data and two real datasets on finance and macroeconomics.