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Applications · Chemistry, Physics, and Earth Sciences

Shanda Li, Shinjae Yoo, Yiming Yang

Fourier Neural Operators (FNOs) offer a principled approach for solving complex partial differential equations (PDEs). However, scaling them to handle more complex PDEs requires increasing the number of Fourier modes, which significantly expands the number of model parameters and makes hyperparameter tuning computationally impractical. To address this, we introduce $\mu$**Transfer-FNO**, a zero-shot hyperparameter transfer technique that enables optimal configurations, tuned on smaller FNOs, to be directly applied to billion-parameter FNOs _without_ additional tuning. Building on the Maximum Update Parametrization ($\mu$P) framework, we mathematically derive a parametrization scheme that facilitates the transfer of optimal hyperparameters across models with different numbers of Fourier modes in FNOs, which is validated through extensive experiments on various PDEs. Our empirical study shows that $\mu$Transfer-FNO reduces computational cost for tuning hyperparameters on large FNOs while maintaining or improving accuracy.

Probabilistic Methods · Bayesian Models and Methods

Michael Munn, Susan Wei

Recent advances in artificial intelligence have been fueled by the development of foundation models such as BERT, GPT, T5, and VisionTransformers. These models are first pretrained on vast and diverse datasets and then adapted to specific downstream tasks, often with significantly less data. However, the mechanisms behind the success of this ubiquitous pretrain-then-adapt paradigm remain underexplored, particularly the characteristics of pretraining checkpoints that enhance downstream adaptation. We introduce a Bayesian model selection criterion, called the downstream free energy, which quantifies a checkpoint’s adaptability by measuring the concentration of nearby favorable parameters for a downstream task. We demonstrate that this Bayesian model selection criterion can be effectively implemented without access to the downstream data or prior knowledge of the downstream task. Furthermore, we provide empirical evidence that the criterion reliably correlates with improved fine-tuning performance, offering a principled approach to predicting model adaptability.

Deep Learning · Graph Neural Networks

Haibo Chen, Xin Wang, Zeyang Zhang, Haoyang Li, Ling Feng, Wenwu Zhu

Graph foundation models (GFMs) aim to share graph knowledge across diverse domains and tasks to boost graph machine learning. However, existing GFMs rely on hand-designed and fixed graph neural network (GNN) architectures, failing to utilize optimal architectures *w.r.t.* specific domains and tasks, inevitably leading to suboptimal performance in diverse graph domains and tasks. In this paper, we explore graph neural architecture search (GNAS) for GFMs for the first time, which suffers from the problem of *architecture inconsistency*, i.e., the optimal architectures for different tasks and domains vary. We tackle this problem by discovering an invariant graph-architecture relationship across domains and tasks, which imposes three challenges: i) how to capture invariant and variant patterns; ii) how to customize architectures to adapt to diverse domains and tasks; iii) how to mitigate the data domination phenomenon during the architecture search process.To address these challenges, we propose **Auto**mated **G**raph **F**oundation **M**odel with Adaptive Architecture Customization (**AutoGFM**), providing a theoretical analysis to demonstrate the limitations of existing GNAS. Specifically, we first propose a disentangled contrastive graph encoder to learn invariant and variant patterns. Then, we design an invariant-guided architecture customization strategy to customize architectures for data from diverse domains and tasks. Finally, we propose a curriculum architecture customization mechanism to mitigate the phenomenon of particular data dominating the search process. Extensive experiments demonstrate that **AutoGFM** outperforms baselines, achieving state-of-the-art performance.

Social Aspects · Privacy

Fan Qi, Daxu Shi, Chuokun Xu, Shuai Li, Changsheng Xu

Federated Distillation (FedKD) relies on lightweight knowledge carriers like logits for efficient client-server communication. Although logit-based methods have demonstrated promise in addressing statistical and architectural heterogeneity in federated learning (FL), current approaches remain constrained by suboptimal temperature calibration during knowledge fusion.To address these limitations, we propose ReT-FHD, a framework featuring: 1) Multi-level Elastic Temperature, which dynamically adjusts distillation intensities across model layers, achieving optimized knowledge transfer between heterogeneous local models; 2) Category-Aware Global Temperature Scaling that implements class-specific temperature calibration based on confidence distributions in global logits, enabling personalized distillation policies; 3) Z-Score Guard, a blockchain-verified validation mechanism mitigating 44\% of label-flipping and model poisoning attacks. Evaluations across diverse benchmarks with varying model/data heterogeneity demonstrate that the ReT-FHD achieves significant accuracy improvements over baseline methods while substantially reducing communication costs compared to existing approaches. Our work establishes that properly calibrated logits can serve as self-sufficient carriers for building scalable and secure heterogeneous FL systems.

Deep Learning · Theory

Mateusz Piotrowski, Paul Riechers, Daniel Filan, Adam Shai

What computational structures emerge in transformers trained on next-token prediction? In this work, we provide evidence that transformers implement constrained Bayesian belief updating---a parallelized version of partial Bayesian inference shaped by architectural constraints. We integrate the model-agnostic theory of optimal prediction with mechanistic interpretability to analyze transformers trained on a tractable family of hidden Markov models that generate rich geometric patterns in neural activations. Our primary analysis focuses on single-layer transformers, revealing how the first attention layer implements these constrained updates, with extensions to multi-layer architectures demonstrating how subsequent layers refine these representations. We find that attention carries out an algorithm with a natural interpretation in the probability simplex, and create representations with distinctive geometric structure. We show how both the algorithmic behavior and the underlying geometry of these representations can be theoretically predicted in detail---including the attention pattern, OV-vectors, and embedding vectors---by modifying the equations for optimal future token predictions to account for the architectural constraints of attention. Our approach provides a principled lens on how architectural constraints shape the implementation of optimal prediction, revealing why transformers develop specific intermediate geometric structures.

Deep Learning · Generative Models and Autoencoders

Zhengchao Wan, Qingsong Wang, Gal Mishne, Yusu Wang

Flow matching (FM) models extend ODE sampler based diffusion models into a general framework, significantly reducing sampling steps through learned vector fields. However, the theoretical understanding of FM models, particularly how their sample trajectories interact with underlying data geometry, remains underexplored. A rigorous theoretical analysis of FM ODE is essential for sample quality, stability, and broader applicability. In this paper, we advance the theory of FM models through a comprehensive analysis of sample trajectories. Central to our theory is the discovery that the denoiser, a key component of FM models, guides ODE dynamics through attracting and absorbing behaviors that adapt to the data geometry. We identify and analyze the three stages of ODE evolution: in the initial and intermediate stages, trajectories move toward the mean and local clusters of the data. At the terminal stage, we rigorously establish the convergence of FM ODE under weak assumptions, addressing scenarios where the data lie on a low-dimensional submanifold---cases that previous results could not handle. Our terminal stage analysis offers insights into the memorization phenomenon and establishes equivariance properties of FM ODEs. These findings bridge critical gaps in understanding flow matching models, with practical implications for optimizing sampling strategies and architectures guided by the intrinsic geometry of data.

Social Aspects · Accountability, Transparency, and Interpretability

Meera Hahn, Wenjun Zeng, Nithish Kannen, Rich Galt, Kartikeya Badola, Been Kim, Zi Wang

User prompts for generative AI models are often underspecified, leading to a misalignment between the user intent and models' understanding. As a result, users commonly have to painstakingly refine their prompts. We study this alignment problem in text-to-image (T2I) generation and propose a prototype for proactive T2I agents equipped with an interface to (1) actively ask clarification questions when uncertain, and (2) present their uncertainty about user intent as an understandable and editable belief graph. We build simple prototypes for such agents and propose a new scalable and automated evaluation approach using two agents, one with a ground truth intent (an image) while the other tries to ask as few questions as possible to align with the ground truth. We experiment over three image-text datasets: ImageInWords (Garg et al., 2024) , COCO (Lin et al., 2014) and DesignBench, a benchmark we curated with strong artistic and design elements. Experiments over the three datasets demonstrate the proposed T2I agents' ability to ask informative questions and elicit crucial information to achieve successful alignment with at least 2 times higher VQAScore (Lin et al., 2024) than the standard T2I generation. Moreover, we conducted human studies and observed that at least 90\% of human subjects found these agents and their belief graphs helpful for their T2I workflow, highlighting the effectiveness of our approach. Code and DesignBench can be found at https://github.com/google-deepmind/proactive_t2i_agents.

General Machine Learning · Everything Else

Batiste Le Bars, Pierre Humbert

We study the question of volume optimality in split conformal regression, a topic still poorly understood in comparison to coverage control. Using the fact that the calibration step can be seen as an empirical volume minimization problem, we first derive a finite-sample upper-bound on the excess volume loss of the interval returned by the classical split method. This important quantity measures the difference in length between the interval obtained with the split method and the shortest oracle prediction interval. Then, we introduce *EffOrt*, a methodology that modifies the learning step so that the base prediction function is selected in order to minimize the length of the returned intervals. In particular, our theoretical analysis of the excess volume loss of the prediction sets produced by *EffOrt* reveals the links between the learning and calibration steps, and notably the impact of the choice of the function class of the base predictor. We also introduce *Ad-EffOrt*, an extension of the previous method, which produces intervals whose size adapts to the value of the covariate. Finally, we evaluate the empirical performance and the robustness of our methodologies.

Deep Learning · Theory

Alberto Bernacchia

Second-order optimization methods, which leverage the local curvature of the loss function, have the potential to dramatically accelerate the training of machine learning models. However, these methods are often hindered by the computational burden of constructing and inverting large curvature matrices with $\mathcal{O}(p^2)$ elements, where $p$ is the number of parameters. In this work, we present a theory that predicts the \emph{exact} structure of the global curvature by leveraging the intrinsic symmetries of neural networks, such as invariance under parameter permutations. For Multi-Layer Perceptrons (MLPs), our approach reveals that the global curvature can be expressed in terms of $\mathcal{O}(d^2 + L^2)$ independent factors, where $d$ is the number of input/output dimensions and $L$ is the number of layers, significantly reducing the computational burden compared to the $\mathcal{O}(p^2)$ elements of the full matrix. These factors can be estimated efficiently, enabling precise curvature computations.To evaluate the practical implications of our framework, we apply second-order optimization to synthetic data, achieving markedly faster convergence compared to traditional optimization methods.Our findings pave the way for a better understanding of the loss landscape of neural networks, and for designing more efficient training methodologies in deep learning.Code: \href{https://github.com/mtkresearch/symo_notebooks}{github.com/mtkresearch/symo\_notebooks}

Deep Learning · Graph Neural Networks

Varshita Kolipaka, Akshit Sinha, Debangan Mishra, Sumit Kumar, Arvindh Arun, Shashwat Goel, Ponnurangam Kumaraguru

Graph Neural Networks (GNNs) are increasingly being used for a variety of ML applications on graph data. Because graph data does not follow the independently and identically distributed *i.i.d.* assumption, adversarial manipulations or incorrect data can propagate to other data points through message passing, which deteriorates the model's performance. To allow model developers to remove the adverse effects of manipulated entities from a trained GNN, we study the recently formulated problem of *Corrective Unlearning*. We find that current graph unlearning methods fail to unlearn the effect of manipulations even when the whole manipulated set is known. We introduce a new graph unlearning method,**Cognac**, which can unlearn the effect of the manipulation set even when only $5$% of it is identified. It recovers most of the performance of a strong oracle with fully corrected training data, even beating retraining from scratch without the deletion set, and is $8$x more efficient while also scaling to large datasets. We hope our work assists GNN developers in mitigating harmful effects caused by issues in real-world data, post-training.

General Machine Learning · Evaluation

Lingyu Li, Yixu Wang, Haiquan Zhao, Shuqi Kong, Yan Teng, Chunbo Li, Yingchun Wang

With large language models (LLMs) increasingly deployed as cognitive engines for AI agents, the reliability and effectiveness critically hinge on their intrinsic epistemic agency, which remains understudied. Epistemic agency, the ability to flexibly construct, adapt, and monitor beliefs about dynamic environments, represents a base-model-level capacity independent of specific tools, modules, or applications. We characterize the holistic process underlying epistemic agency, which unfolds in seven interrelated dimensions: prediction, decision-making, perception, memory, counterfactual thinking, belief updating, and meta-reflection. Correspondingly, we propose Reflection-Bench, a cognitive-psychology-inspired benchmark consisting of seven tasks with long-term relevance and minimization of data leakage. Through a comprehensive evaluation of 16 models using three prompting strategies, we identify a clear three-tier performance hierarchy and significant limitations of current LLMs, particularly in meta-reflection capabilities. While state-of-the-art LLMs demonstrate rudimentary signs of epistemic agency, our findings suggest several promising research directions, including enhancing core cognitive functions, improving cross-functional coordination, and developing adaptive processing mechanisms. Our code and data are available at https://github.com/AI45Lab/ReflectionBench.

General Machine Learning · Online Learning, Active Learning and Bandits

Yegon Kim, Hyunsu Kim, Gyeonghoon Ko, Juho Lee

Accurately solving partial differential equations (PDEs) is critical to understanding complex scientific and engineering phenomena, yet traditional numerical solvers are computationally expensive. Surrogate models offer a more efficient alternative, but their development is hindered by the cost of generating sufficient training data from numerical solvers. In this paper, we present a novel framework for active learning (AL) in PDE surrogate modeling that reduces this cost. Unlike the existing AL methods for PDEs that always acquire entire PDE trajectories, our approach strategically generates only the most important time steps with the numerical solver, while employing the surrogate model to approximate the remaining steps. This dramatically reduces the cost incurred by each trajectory and thus allows the active learning algorithm to try out a more diverse set of trajectories given the same budget. To accommodate this novel framework, we develop an acquisition function that estimates the utility of a set of time steps by approximating its resulting variance reduction. We demonstrate the effectiveness of our method on several benchmark PDEs, including the Burgers' equation, Korteweg–De Vries equation, Kuramoto–Sivashinsky equation, the incompressible Navier-Stokes equation, and the compressible Navier-Stokes equation.Experiments show that our approach improves performance by large margins over the best existing method. Our method not only reduces average error but also the 99\%, 95\%, and 50\% quantiles of error, which is rare for an AL algorithm. All in all, our approach offers a data-efficient solution to surrogate modeling for PDEs.

Theory · Learning Theory

Thanh Nguyen-Tang, Raman Arora

We study policy-regret minimization problem in dynamically evolving environments, modeled as Markov games between a learner and a strategic, adaptive opponent. We propose a general algorithmic framework that achieves the optimal $\mathcal{O}(\sqrt{T})$ policy regret for a wide class of large-scale problems characterized by an Eluder-type condition--extending beyond the tabular settings of previous work. Importantly, our framework uncovers a simpler yet powerful algorithmic approach for handling reactive adversaries, demonstrating that leveraging opponent learning in such settings is key to attaining the optimal $\mathcal{O}(\sqrt{T})$ policy regret.

Theory · Learning Theory

Kosuke Sugiyama, Masato Uchida

This paper addresses weak features learning (WFL), focusing on learning scenarios characterized by low-quality input features (weak features; WFs) that arise due to missingness, measurement errors, or ambiguous observations. We present a theoretical formalization and error analysis of WFL for continuous WFs (continuous WFL), which has been insufficiently explored in existing literature. A previous study established formalization and error analysis for WFL with discrete WFs (discrete WFL); however, this analysis does not extend to continuous WFs due to the inherent constraints of discreteness. To address this, we propose a theoretical framework specifically designed for continuous WFL, systematically capturing the interactions between feature estimation models for WFs and label prediction models for downstream tasks. Furthermore, we derive the theoretical conditions necessary for both sequential and iterative learning methods to achieve consistency. By integrating the findings of this study on continuous WFL with the existing theory of discrete WFL, we demonstrate that the WFL framework is universally applicable, providing a robust theoretical foundation for learning with low-quality features across diverse application domains.

Social Aspects · Alignment

Jianwei Li, Jung-Eun Kim

Recent studies on the safety alignment of large language models (LLMs) have revealed that existing approaches often operate superficially, leaving models vulnerable to various adversarial attacks. Despite their significance, these studies generally fail to offer actionable solutions beyond data augmentation for achieving more robust safety mechanisms. This paper identifies a fundamental cause of this superficiality: existing alignment approaches often presume that models can implicitly learn a safety-related reasoning task during the alignment process, enabling them to refuse harmful requests. However, the learned safety signals are often diluted by other competing objectives, leading models to struggle with drawing a firm safety-conscious decision boundary when confronted with adversarial attacks. Based on this observation, by explicitly introducing a safety-related binary classification task and integrating its signals with our attention and decoding strategies, we eliminate this ambiguity and allow models to respond more responsibly to malicious queries. We emphasize that, with less than 0.2x overhead cost, our approach enables LLMs to assess the safety of both the query and the previously generated tokens at each necessary generating step. Extensive experiments demonstrate that our method significantly improves the resilience of LLMs against various adversarial attacks, offering a promising pathway toward more robust generative AI systems.

Deep Learning · Algorithms

Lan Li, Da-Wei Zhou, Han-Jia Ye, De-Chuan Zhan

Domain-Incremental Learning (DIL) focuses on continual learning in non-stationary environments, requiring models to adjust to evolving domains while preserving historical knowledge. DIL faces two critical challenges in the context of imbalanced data: intra-domain class imbalance and cross-domain class distribution shifts. These challenges significantly hinder model performance, as intra-domain imbalance leads to underfitting of few-shot classes, while cross-domain shifts require maintaining well-learned many-shot classes and transferring knowledge to improve few-shot class performance in old domains. To overcome these challenges, we introduce the Dual-Balance Collaborative Experts (DCE) framework. DCE employs a frequency-aware expert group, where each expert is guided by specialized loss functions to learn features for specific frequency groups, effectively addressing intra-domain class imbalance. Subsequently, a dynamic expert selector is learned by synthesizing pseudo-features through balanced Gaussian sampling from historical class statistics. This mechanism navigates the trade-off between preserving many-shot knowledge of previous domains and leveraging new data to improve few-shot class performance in earlier tasks. Extensive experimental results on four benchmark datasets demonstrate DCE’s state-of-the-art performance.

Applications · Social Sciences

Kexin Huang, Ziqian Chen, xue wang, Chongming Gao, Jinyang Gao, Bolin Ding, Xiang Wang

Auction plays a crucial role in many modern trading environments, including online advertising and public resource allocation. As the number of competing bidders increases, learning Bayesian Nash Equilibrium (BNE) in auctions faces significant scalability challenges. Existing methods often experience slow convergence in large-scale auctions. For example, in a classic symmetric auction setting, the convergence rate depends on the number of bidders quadratically.To address this issue, we propose the *Approximate Best Response Gradient* method, a new approach for learning BNE efficiently in auction games. We leverage an analytic solution for gradient estimation to enable efficient gradient computation during optimization. Moreover, we introduce the *Best Response Distance* objective, which serves as an upper bound of approximation quality to BNE. By optimizing the new objective, our method is proven to achieve a local convergence rate independent of bidder numbers and circumvent the traditional quadratic complexity in the classic symmetric setting.Extensive experiments across various auction formats demonstrate that our approach accelerates convergence and enhances learning efficiency in complex auction settings.

Deep Learning · Generative Models and Autoencoders

Avinash Kori, Francesca Toni, Ben Glocker

Modular object-centric representations are essential for *human-like reasoning* but are challenging to obtain under spatial ambiguities, *e.g. due to occlusions and view ambiguities*. However, addressing challenges presents both theoretical and practical difficulties. We introduce a novel multi-view probabilistic approach that aggregates view-specific slots to capture *invariant content* information while simultaneously learning disentangled global *viewpoint-level* information. Unlike prior single-view methods, our approach resolves spatial ambiguities, provides theoretical guarantees for identifiability, and requires *no viewpoint annotations*. Extensive experiments on standard benchmarks and novel complex datasets validate our method's robustness and scalability.

Deep Learning · Foundation Models

Tianzhe Chu, Yuexiang Zhai, Jihan Yang, Shengbang Tong, Saining Xie, Dale Schuurmans, Quoc Le, Sergey Levine, Yi Ma

Supervised fine-tuning (SFT) and reinforcement learning (RL) are widely used post-training techniques for foundation models. However, their roles in enhancing model generalization capabilities remain unclear. This paper studies the difference between SFT and RL on generalization and memorization, focusing on text-based rule variants and visual variants. We introduce GeneralPoints, an arithmetic reasoning card game, and adopt V-IRL, a real-world navigation environment, to assess how models trained with SFT and RL generalize to unseen variants in both textual and visual domains. We show that RL, especially when trained with an outcome-based reward, generalizes across both rule-based textual and visual variants. SFT, in contrast, tends to memorize training data and struggles to generalize out-of-distribution scenarios. Further analysis reveals that RL improves the model's underlying visual recognition capabilities, contributing to its enhanced generalization in the visual domain. Despite RL's superior generalization, we show that SFT remains essential for effective RL training; SFT stabilizes the model's output format, enabling subsequent RL to achieve its performance gains. These findings demonstrates the capability of RL for acquiring generalizable knowledge in complex, multi-modal tasks.

Theory · Learning Theory

Amir Najafi, Samin Mahdizadeh Sani, Farzan Farnia

We address the challenge of certifying the performance of a federated learning model on an unseen target network using only measurements from the source network that trained the model. Specifically, consider a source network "A" with $K$ clients, each holding private, non-IID datasets drawn from heterogeneous distributions, modeled as samples from a broader meta-distribution $\mu$. Our goal is to provide certified guarantees for the model’s performance on a different, unseen network "B", governed by an unknown meta-distribution $\mu'$, assuming the deviation between $\mu$ and $\mu'$ is bounded—either in Wasserstein distance or an $f$-divergence. We derive worst-case uniform guarantees for both the model’s average loss and its risk CDF, the latter corresponding to a novel, adversarially robust version of the Dvoretzky–Kiefer–Wolfowitz (DKW) inequality. In addition, we show how the vanilla DKW bound enables principled certification of the model's true performance on unseen clients within the same (source) network. Our bounds are efficiently computable, asymptotically minimax optimal, and preserve clients' privacy.We also establish non-asymptotic generalization bounds that converge to zero as $K$ grows and the minimum per-client sample size exceeds $\mathcal{O}(\log K)$. Empirical evaluations confirm the practical utility of our bounds across real-world tasks. The project code is available at: github.com/samin-mehdizadeh/Robust-Evaluation-DKW