We study policy optimization in Stackelberg mean field games (MFGs), a hierarchical framework for modeling the strategic interaction between a single leader and an infinitely large population of homogeneous followers. The objective can be formulated as a structured bi-level optimization problem, in which the leader needs to learn a policy maximizing its reward, anticipating the response of the followers. Existing methods for solving these (and related) problems often rely on restrictive independence assumptions between the leader's and followers' objectives, use samples inefficiently due to nested-loop algorithm structure, and lack finite-time convergence guarantees. To address these limitations, we propose AC-SMFG, a single-loop actor-critic algorithm that operates on continuously generated Markovian samples. The algorithm alternates between (semi-)gradient updates for the leader, a representative follower, and the mean field, and is simple to implement in practice. We establish the finite-time and finite-sample convergence of the algorithm to a stationary point of the Stackelberg objective. To our knowledge, this is the first Stackelberg MFG algorithm with non-asymptotic convergence guarantees. Our key assumption is a "gradient alignment" condition, which requires that the full policy gradient of the leader can be approximated by a partial component of it, relaxing the existing leader-follower independence assumption. Simulation results in a range of well-established economics environments demonstrate that AC-SMFG outperforms existing multi-agent and MFG learning baselines in policy quality and convergence speed.

Opaque objects reconstructed by 3DGaussian Splatting (3DGS) often exhibit a falsely transparent surface, leading to inconsistent background and internal patterns under camera motion in interactive viewing. This issue stems from the ill-posed optimization in 3DGS. During training, background and foreground Gaussians are blended via α-compositing and optimized solely against the input RGB images using a photometric loss. As this process lacks an explicit constraint on surface opacity, the optimization may incorrectly assign transparency to opaque regions, resulting in view-inconsistent and falsely transparent output. This issue is difficult to detect in standard evaluation settings (i.e., rendering static images), but becomes particularly evident in object-centric reconstructions under interactive viewing.

This work introduces Structured Linear Controlled Differential Equations (SLiCEs), a unifying framework for sequence models with structured, input-dependent statetransition matrices that retain the maximal expressivity of dense matrices whilst being cheaper to compute. The framework encompasses existing architectures, such as input-dependent block-diagonal linear recurrent neural networks and DeltaNet's diagonal-plus-low-rank structure, as well as two novel variants based on sparsity and the Walsh-Hadamard transform. We prove that, unlike the diagonal statetransition matrices of S4D and Mamba, SLiCEs employing block-diagonal, sparse, or Walsh-Hadamard matrices match the maximal expressivity of dense matrices. Empirically, SLiCEs solve the A5 state-tracking benchmark with a single layer, achieve best-in-class length generalisation on regular language tasks among parallelin-time models, and match the performance of log neural controlled differential equations on six multivariate time-series classification datasets while cutting the average time per training step by a factor of twenty.

As AI grows more powerful, it will increasingly shape how we understand the world. But with this influence comes the risk of amplifying misinformation and deepening social divides--especially on consequential topics where factual accuracy directly impacts well-being. Scalable Oversight aims to ensure AI systems remain truthful even when their capabilities exceed those of their evaluators. Yet when humans serve as evaluators, their own beliefs and biases can impair judgment. We study whether AI debate can guide biased judges toward the truth by having two AI systems debate opposing sides of controversial factuality claims on COVID-19 and climate change where people hold strong prior beliefs.

We offer a novel perspective on reward modeling by formulating it as a policy discriminator, which quantifies the difference between two policies to generate a reward signal, guiding the training policy towards a target policy with desired behaviors. Based on this conceptual insight, we propose a scalable pre-training method named POLicy DiscriminAtive LeaRning (POLAR), which trains a reward model (RM) to discern identical policies and discriminate different ones. Unlike traditional reward modeling methods relying on absolute preferences, POLAR captures the relative difference between one policy and an arbitrary target policy, which is a scalable, high-level optimization objective suitable for modeling generic ranking relationships. Leveraging the POLAR pre-training paradigm, we present a series of RMs with parameter scales from 1.8B to 7B. Empirical results show that POLAR substantially outperforms traditional non-pre-trained methods, significantly enhancing RM performance. For instance, POLAR-7B could improve preference accuracy from 54.8% to 81.0% on STEM tasks and from 57.9% to 85.5% on creative writing tasks compared to SOTA baselines. POLAR also shows robust generalization capabilities in RLHF using Reinforcement Finetuning (RFT), providing reliable reward signals and markedly enhancing policy performance--improving LLaMa3.1-8B

The scarcity of annotated medical imaging data has driven significant progress in semi-supervised learning to alleviate reliance on expensive expert labeling. While foundational vision models such as the Segment Anything Model (SAM) exhibit robust generalization in generic segmentation tasks, their direct application to medical images often results in suboptimal performance. To address this challenge, in this work, we propose a novel fully SAM-based semi-supervised medical image segmentation framework and develop the corresponding knowledge distillationbased learning strategy. Specifically, we first employ an efficient SAM variant as the backbone network of the semi-supervised framework and update the default prompt embedding of SAM to unleash its full potential. Then, we utilize an original SAM, which is rich in prior knowledge, as the teacher to optimize our efficient student SAM backbone through hierarchical knowledge distillation and a dynamic loss weighting strategy. Extensive experiments on various medical datasets demonstrate that our method outperforms state-of-the-art semi-supervised segmentation approaches. Especially, our model requires less than 10% of the parameter size of the original SAM, enabling substantially lower deployment and storage overhead in real-world clinical settings.

We introduce InfinityStar, a unified spacetime autoregressive framework for highresolution image and dynamic video synthesis.

Embodied agents powered by large language models (LLMs), such as Voyager, promise open-ended competence in worlds such as Minecraft. However, when powered by open-weight LLMs they still falter on elementary tasks after domainspecific fine-tuning. We propose MINDFORGE, a generative-agent framework for cultural lifelong learning through explicit perspective taking. We introduce three key innovations: (1) a structured theory of mind representation linking percepts, beliefs, desires, and actions; (2) natural inter-agent communication; and (3) a multi-component memory system. Following the cultural learning framework, we test MINDFORGE in both instructive and collaborative settings within Minecraft. In an instructive setting with GPT-4, MINDFORGE agents powered by open-weight LLMs significantly outperform their Voyager counterparts in basic tasks yielding 3 more tech-tree milestones and collecting 2.3 more unique items than the Voyager baseline. Furthermore, in fully collaborative settings, we find that the performance of two underachieving agents improves with more communication rounds, echoing the Condorcet Jury Theorem. MINDFORGE agents demonstrate sophisticated behaviors, including expert-novice knowledge transfer, collaborative problem solving, and adaptation to out-of-distribution tasks through accumulated cultural experiences.

This paper establishes the theoretical limits of graph clustering under the PopularityAdjusted Block Model (PABM), addressing limitations of existing models. In contrast to the Stochastic Block Model (SBM), which assumes uniform vertex degrees, and to the Degree-Corrected Block Model (DCBM), which applies uniform degree corrections across clusters, PABM introduces separate popularity parameters for intra-and inter-cluster connections. Our main contribution is the characterization of the optimal error rate for clustering under PABM, which provides novel insights on clustering hardness: we demonstrate that unlike SBM and DCBM, cluster recovery remains possible in PABM even when traditional edge-density signals vanish, provided intra-and inter-cluster popularity coefficients differ. This highlights a dimension of degree heterogeneity captured by PABM but overlooked by DCBM: local differences in connectivity patterns can enhance cluster separability independently of global edge densities. Finally, because PABM exhibits a richer structure, its expected adjacency matrix has rank between k and k2, where k is the number of clusters. As a result, spectral embeddings based on the top k eigenvectors may fail to capture important structural information. Our numerical experiments on both synthetic and real datasets confirm that spectral clustering algorithms incorporating k2 eigenvectors outperform traditional spectral approaches.

As machine learning increasingly relies on large, opaque foundation models powering generative and agentic AI, deploying these systems in safety-critical contexts demands rigorous generalization guarantees beyond training data. PAC-Bayes theory provides principled certificates linking training performance to generalization risk, yet existing approaches remain impractical: simple theoretical priors yield vacuous bounds, while data-dependent priors require costly second-stage training or introduce bias. To bridge this critical gap, we propose a localized PAC-Bayes prior--a structured, computationally efficient prior softly concentrated around parameters favored during standard training. By integrating this localized prior directly into the standard training objective, we deliver practically tight generalization certificates with minimal workflow disruption. Under standard neural tangent kernel assumptions, our bound shrinks as networks widen and datasets grow, becoming negligible in realistic regimes. Empirically, we demonstrate tight generalization certificates on tasks ranging from image classification (MNIST, CIFAR, ImageNet) and NLP fine-tuning (GLUE) to semantic segmentation (Cityscapes), typically within three percentage points of test error at ImageNet scale. Additionally, our approach provides rigorous guarantees for individual predictions, selective rejection of uncertain predictions, adversarial robustness, and accurate calibration--directly addressing key requirements for trustworthy AI deployment.