Mean field games (MFGs) tractably model behavior in large agent populations. The literature on learning MFG equilibria typically focuses on finding Nash equilibria (NE), which assume perfectly rational agents and are hence implausible in many realistic situations. To overcome these limitations, we incorporate bounded rationality into MFGs by leveraging the well-known concept of quantal response equilibria (QRE). Two novel types of MFG QRE enable the modeling of large agent populations where individuals only noisily estimate the true objective. We also introduce a second source of bounded rationality to MFGs by restricting the agents' planning horizon. The resulting novel receding horizon (RH) MFGs are combined with QRE and existing approaches to model different aspects of bounded rationality in MFGs. We formally define MFG QRE and RH MFGs and compare them to existing equilibrium concepts such as entropy-regularized NE. Subsequently, we design generalized fixed point iteration and fictitious play algorithms to learn QRE and RH equilibria. After a theoretical analysis, we give different examples to evaluate the capabilities of our learning algorithms and outline practical differences between the equilibrium concepts.
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In the recently introduced model of fair partitioning of friends, there is a set of agents located on the vertices of an underlying graph that indicates the friendships between the agents. The task is to partition the graph into k balanced-sized groups, keeping in mind that the value of an agent for a group is equal to the number of edges they have in that group. The goal is to construct partitions that are "fair", i.e., no agent would like to replace an agent in a different group. We generalize the standard model by considering utilities for the agents that are beyond binary and additive. Having this as our foundation, our contribution is threefold: (a) we adapt several fairness notions that have been developed in the fair division literature to our setting; (b) we give several existence guarantees supported by polynomial-time algorithms; (c) we initiate the study of the computational (and parameterized) complexity of the model and provide an almost complete landscape of the (in)tractability frontier for our fairness concepts.
Present bias, the tendency to overvalue immediate rewards while undervaluing future ones, is a well-known barrier to achieving long-term goals. As artificial intelligence and behavioral economics increasingly focus on this phenomenon, the need for robust mathematical models to predict behavior and guide effective interventions has become crucial. However, existing models are constrained by their reliance on the discreteness of time and limited discount functions. This study introduces a novel continuous-time mathematical model for agents influenced by present bias. Using the variational principle, we model human behavior, where individuals repeatedly act according to a sequence of states that minimize their perceived cost. Our model not only retains analytical tractability but also accommodates various discount functions. Using this model, we consider intervention optimization problems under exponential and hyperbolic discounting and theoretically derive optimal intervention strategies, offering new insights into managing present-biased behavior.
Solving a Constraint Satisfaction Problem (CSP) usually requires a model typically using existing basic constraints. The most flexible form of constraint, ad-hoc (generic) constraints defined with certain constraint representations, such as binary constraint tree (BCT) and decision diagrams, have been proposed where basic constraints in intensional form are insufficient. A modeller may wish to combine basic constraints using logic operators (and, or, negation). However, negation, a key logical operator for expressivity is not tractable in many existing constraint representations. This creates a dilemma, for modelling, we would desire more flexibility, but a model whose operations are intractable may in turn be impractical. In this paper, we give a framework which allows for a tractable negation operator on constraint representations. We apply the framework on the BCT and ordered decision diagram constraints, giving new subforms. These subforms can be strictly more succinct than ordered multi-valued decision diagrams (OMDD), while being as tractable as OMDD for logical combinations. We give applications to show effective propagators from logical combinations and in building large constraint models for configuration problems.
Diffusion models have revolutionized image generation, yet several challenges restrict their application to large-image domains, such as digital pathology and satellite imagery. Given that it is infeasible to directly train a model on 'whole' images from domains with potential gigapixel sizes, diffusion-based generative methods have focused on synthesizing small, fixed-size patches extracted from these images. However, generating small patches has limited applicability since patch-based models fail to capture the global structures and wider context of large images, which can be crucial for synthesizing (semantically) accurate samples. To overcome this limitation, we present ZoomLDM, a diffusion model tailored for generating images across multiple scales. Central to our approach is a novel magnification-aware conditioning mechanism that utilizes self-supervised learning (SSL) embeddings and allows the diffusion model to synthesize images at different 'zoom' levels, i.e., fixed-size patches extracted from large images at varying scales. ZoomLDM synthesizes coherent histopathology images that remain contextually accurate and detailed at different zoom levels, achieving state-of-the-art image generation quality across all scales and excelling in the data-scarce setting of generating thumbnails of entire large images. The multi-scale nature of ZoomLDM unlocks additional capabilities in large image generation, enabling computationally tractable and globally coherent image synthesis up to 4096x4096 pixels and 4x super-resolution. Additionally, multi-scale features extracted from ZoomLDM are highly effective in multiple instance learning experiments.
HyperFree: A Channel-adaptive and Tuning-free Foundation Model for Hyperspectral Remote Sensing Imagery
PDF ↗Advanced interpretation of hyperspectral remote sensing images benefits many precise Earth observation tasks. Recently, visual foundation models have promoted the remote sensing interpretation but concentrating on RGB and multispectral images. Due to the varied hyperspectral channels, existing foundation models would face image-by-image tuning situation, imposing great pressure on hardware and time resources. In this paper, we propose a tuning-free hyperspectral foundation model called HyperFree, by adapting the existing visual prompt engineering. To process varied channel numbers, we design a learned weight dictionary covering full-spectrum from 0.4 2.5um, supporting to build the embedding layer dynamically. To make the prompt design more tractable, HyperFree can generate multiple semantic-aware masks for one prompt by treating feature distance as semantic-similarity. After pre-training HyperFree on constructed large-scale high-resolution hyperspectral images, HyperFree (1 prompt) has shown comparable results with specialized models (5 shots) on 5 tasks and 11 datasets. Code and dataset would be accessible at https://rsidea.whu.edu.cn/hyperfree.htm#.
Language is often used to describe physical interaction, yet most 3D human pose estimation methods overlook this rich source of information. We bridge this gap by leveraging large multimodal models (LMMs) as priors for reconstructing contact poses, offering a scalable alternative to traditional methods that rely on human annotations or motion capture data. Our approach extracts contact-relevant descriptors from an LMM and translates them into tractable losses to constrain 3D human pose optimization. Despite its simplicity, our method produces compelling reconstructions for both two-person interactions and self-contact scenarios, accurately capturing the semantics of physical and social interactions. Our results demonstrate that LMMs can serve as powerful tools for contact prediction and pose estimation, offering an alternative to costly manual human annotations or motion capture data. Our code is publicly available at prosepose.github.io.
We consider the challenging problem of learning Signed Distance Functions (SDF) from sparse and noisy 3D point clouds. In contrast to recent methods that depend on smoothness priors, our method, rooted in a distributionally robust optimization (DRO) framework, incorporates a regularization term that leverages samples from the uncertainty regions of the model to improve the learned SDFs. Thanks to tractable dual formulations, we show that this framework enables a stable and efficient optimization of SDFs in the absence of ground truth supervision. Using a variety of synthetic and real data evaluations from different modalities, we show that of our DRO based learning framework can improve SDF learning with respect to baselines and the state-of-the-art.
SIMBA UQ: Similarity-Based Aggregation for Uncertainty Quantification in Large Language Models
PDF ↗When does a large language model (LLM) know what it does not know? Uncertainty quantification (UQ) provides measures of uncertainty, such as an estimate of the confidence in an LLM’s generated output, and is therefore increasingly recognized as a crucial component of trusted AI systems. Black-box UQ methods do not require access to internal model information from the generating LLM and therefore have numerous real-world advantages, such as robustness to system changes, adaptability to choice of LLM, reduced costs, and computational tractability. In this paper, we investigate the effectiveness of UQ techniques that are primarily but not necessarily entirely black- box, where the consistency between a generated output and other sampled generations is used as a proxy for confidence in its correctness. We propose a high-level non-verbalized similarity-based aggregation framework that subsumes a broad swath of UQ approaches suitable for complex generative tasks, as well as introduce specific novel techniques from the framework that train confidence estimation models using small training sets. Through an empirical study with datasets spanning the diverse tasks of question answering, summarization, and text-to-SQL, we demonstrate that our proposed similarity-based methods can yield better calibrated confidences than baselines.
We present a broad empirical study of state-of-the-art LLMs and LRMs (Large Reasoning Models) on ProofGrid, a new battery of challenging but tractable logical inference tasks that form a domain-independent test of constraint-based reasoning. The tasks include proof writing and proof checking across propositional and equational logic. We also introduce two novel tasks: proof inpainting and proof gap-filling. Solving these problems requires tracking the global structure of a mathematical argument, writing hierarchical subproofs, maintaining coherence across nested assumptions, performing complex case analyses, applying inference rules, reasoning about identity and term rewriting, and reasoning about proofs themselves. Our experiments reveal impressive performance by top-tier models but also systematic failure modes. Along with the benchmarks, we release a new data resource comprising over 10K formal deduction problems and corresponding proofs.
Recent studies (CITATION) highlight a fundamental dichotomy in deep learning optimization: Although parameter updates along the top eigendirections of the loss Hessian (Dom-space) capture most of the update magnitude, they often contribute minimally to loss reduction. In contrast, updates in the orthogonal component (Bulk-space) have smaller magnitudes but drive most learning progress.In this work, we further advance the understanding of this phenomenon and introduce the Bulk-Space-Filtration-Accelerator (BSFA), a novel plug-and-play framework. BSFA accelerates training by differentially scaling update components projected onto these distinct subspaces, simultaneously enhancing stability by moderating updates in the dominant subspace and boosting convergence speed by amplifying those in the bulk-space.To ensure BSFA is both practical and scalable for contemporary large models, we introduce two key innovations: an efficient estimator using Principal Component Analysis (PCA) on historical updates for fast subspace estimation, and a block-wise strategy that applies this estimation on a per-parameter-block basis. These designs make BSFA computationally tractable and highly effective.We demonstrate BSFA’s acceleration across various tasks, notably achieving approximately 2\times speedup when pre-training LLaMA-72M on WikiText-103 and LLaMA-134M on OpenWebText compared to vanilla AdamW.
Large Language Models often contain factually incorrect or outdated knowledge, giving rise to model editing methods for precise knowledge updates. However, current mainstream locate-then-edit approaches exhibit a progressive performance decline during sequential editing, due to inadequate mechanisms for long-term knowledge preservation. To tackle this, we model the sequential editing as a constrained stochastic programming. Given the challenges posed by the cumulative preservation error constraint and the gradually revealed editing tasks, **LyapLock** is proposed. It integrates queuing theory and Lyapunov optimization to decompose the long-term constrained programming into tractable stepwise subproblems for efficient solving. This is the first model editing framework with rigorous theoretical guarantees, achieving asymptotic optimal editing performance while meeting the constraints of long-term knowledge preservation. Experimental results show that our framework scales sequential editing capacity to over 10,000 edits while stabilizing general capabilities and boosting average editing efficacy by 11.89% over SOTA baselines. Furthermore, it can be leveraged to enhance the performance of baseline methods. Our code is released on https://github.com/caskcsg/LyapLock.
Traditional reinforcement learning (RL) assumes the agents make decisions based on Markov decision processes (MDPs) with one-step transition models. In many real-world applications, such as energy management and stock investment, agents can access multi-step predictions of future states, which provide additional advantages for decision making. However, multi-step predictions are inherently high-dimensional: naively embedding these predictions into an MDP leads to an exponential blow-up in state space and the curse of dimensionality. Moreover, existing RL theory provides few tools to analyze prediction-augmented MDPs, as it typically works on one-step transition kernels and cannot accommodate multi-step predictions with errors or partial action-coverage. We address these challenges with three key innovations: First, we propose the \emph{Bayesian value function} to characterize the optimal prediction-aware policy tractably. Second, we develop a novel \emph{Bellman–Jensen Gap} analysis on the Bayesian value function, which enables characterizing the value of imperfect predictions. Third, we introduce BOLA (Bayesian Offline Learning with Online Adaptation), a two-stage model-based RL algorithm that separates offline Bayesian value learning from lightweight online adaptation to real-time predictions. We prove that BOLA remains sample-efficient even under imperfect predictions. We validate our theory and algorithm on synthetic MDPs and a real-world wind energy storage control problem.
Deep Learning · Generative Models and Autoencoders
Direct preference optimization (DPO) is widely used as a simple and stable method for aligning large language models (LLMs) with human preferences. This paper investigates a generalized DPO loss that enables a policy model to match the target policy from a likelihood ratio estimation perspective. The ratio of the target policy provides a unique identification of the policy distribution without relying on reward models or partition functions. This allows the generalized loss to retain both simplicity and theoretical guarantees, which prior work such as $f$-PO fails to achieve simultaneously. We propose \textit{Bregman preference optimization} (BPO), a generalized framework for ratio matching that provides a family of objective functions achieving target policy optimality. BPO subsumes DPO as a special case and offers tractable forms for all instances, allowing implementation with a few lines of code. We further develop scaled Basu's power divergence (SBA), a gradient scaling method that can be used for BPO instances. The BPO framework complements other DPO variants and is applicable to target policies defined by these variants. In experiments, unlike other probabilistic loss extensions such as $f$-DPO or $f$-PO, which exhibits a trade-off between generation fidelity and diversity, instances of BPO improve both win rate and entropy compared with DPO. When applied to Llama-3-8B-Instruct, BPO achieves state-of-the-art performance among Llama-3-8B backbones, with a 55.9\% length-controlled win rate on AlpacaEval2. Project page: https://github.com/aailab-kaist/BPO.
Probabilistic Methods
A fundamental challenge in probabilistic modeling is to balance expressivity and inference efficiency. Tractable probabilistic models (TPMs) aim to directly address this tradeoff by imposing constraints that guarantee efficient inference of certain queries while maintaining expressivity. In particular, probabilistic circuits (PCs) provide a unifying framework for many TPMs, by characterizing families of models as circuits satisfying different structural properties. Because the complexity of inference on PCs is a function of the circuit size, understanding the size requirements of different families of PCs is fundamental in mapping the trade-off between tractability and expressive efficiency. However, the study of expressive efficiency of circuits are often concerned with exact representations, which may not align with model learning, where we look to approximate the underlying data distribution closely by some distance measure. Moreover, due to hardness of inference tasks, exactly representing distributions while supporting tractable inference often incurs exponential size blow-ups. In this paper, we consider a natural, yet so far underexplored, question: can we avoid such size blow-up by allowing for some small approximation error? We study approximating distributions with probabilistic circuits with guarantees based on $f$-divergences, and analyze which inference queries remain well-approximated under this framework. We show that approximating an arbitrary distribution with bounded $f$-divergence is NP-hard for any model that can tractably compute marginals. In addition, we prove an exponential size gap for approximation between the class of decomposable PCs and that of decomposable and deterministic PCs.
Deep Learning · Algorithms
Measuring parameter importance is crucial for understanding and optimizing large language models (LLMs). Existing work predominantly focuses on pruning or probing at neuron/feature levels without fully considering the cooperative behaviors of model parameters. In this paper, we introduce a novel approach--Model Shapley to quantify parameter importance based on the Shapley value, a principled method from cooperative game theory that captures both individual and synergistic contributions among parameters, via only one gradient backpropagation. We derive a scalable second-order approximation to compute Shapley values at the parameter level, leveraging blockwise Fisher information for tractability in large-scale settings. Our method enables fine-grained differentiation of parameter importance, facilitating targeted knowledge injection and model compression. Through mini-batch Monte Carlo updates and efficient approximation of the Hessian structure, we achieve robust Shapley-based attribution with only modest computational overhead. Experimental results indicate that this cooperative game perspective enhances interpretability, guides more effective parameter-specific fine-tuning and model compressing, and paves the way for continuous model improvement in various downstream tasks.
Reinforcement Learning · Batch Offline
We study offline policy optimization for infinite-horizon average-reward Markov decision processes (MDPs) with large or infinite state spaces. Specifically, we propose a pessimistic actor-critic algorithm that uses a computationally efficient linear function class for value function estimation. At the core of our method is a critic that computes a pessimistic estimate of the average reward under the current policy, as well as the corresponding policy gradient, by solving a fixed-point Bellman equation, rather than solving a successive sequence of regression problems as in finite horizon settings. This procedure reduces to solving a second-order cone program, which is computationally tractable. Our theoretical analysis is based on a weak partial data coverage assumption, which requires only that the offline data aligns well with the expected feature vector of a comparator policy. Under this condition, we show that our algorithm achieves the optimal sample complexity of O(\varepsilon^{-2}) for learning a near-optimal policy, up to model misspecification errors.
Reinforcement Learning · Multi-agent
Planning under opponent uncertainty is a fundamental challenge in multi-agent environments, where an agent must act while inferring the hidden policies of its opponents. Existing type-based methods rely on manually defined behavior classes and struggle to scale, while model-free approaches are sample-inefficient and lack a principled way to incorporate uncertainty into planning. We propose Quantized Opponent Models (QOM), which learn a compact catalog of opponent types via a quantized autoencoder and maintain a Bayesian belief over these types online. This posterior supports both a belief-weighted meta-policy and a Monte-Carlo planning algorithm that directly integrates uncertainty, enabling real-time belief updates and focused exploration. Experiments show that QOM achieves superior performance with lower search cost, offering a tractable and effective solution for belief-aware planning.
Deep Learning · Theory
We introduce the attention-indexed model (AIM), a theoretical framework for analyzing learning in deep attention layers. Inspired by multi-index models, AIM captures how token-level outputs emerge from layered bilinear interactions over high-dimensional embeddings. Unlike prior tractable attention models, AIM allows full-width key and query matrices, aligning more closely with practical transformers. Using tools from statistical mechanics and random matrix theory, we derive closed-form predictions for Bayes-optimal generalization error and identify sharp phase transitions as a function of sample complexity, model width, and sequence length. We propose a matching approximate message passing algorithm and show that gradient descent can reach optimal performance. AIM offers a solvable playground for understanding learning in self-attention layers, that are key components of modern architectures.
Computer Vision · Vision Models & Multimodal
Multimodal learning has gained much success in recent years. However, current multimodal fusion methods adopt the attention mechanism of Transformers to implicitly learn the underlying correlation of multimodal features. As a result, the multimodal model cannot capture the essential features of each modality, making it difficult to comprehend complex structures and correlations of multimodal inputs. This paper introduces a novel Multimodal Attention-based Normalizing Flow (MANGO) approach to developing explicit, interpretable, and tractable multimodal fusion learning. In particular, we propose a new Invertible Cross-Attention (ICA) layer to develop the Normalizing Flow-based Model for multimodal data. To efficiently capture the complex, underlying correlations in multimodal data in our proposed invertible cross-attention layer, we propose three new cross-attention mechanisms: Modality-to-Modality Cross-Attention (MMCA), Inter-Modality Cross-Attention (IMCA), and Learnable Inter-Modality Cross-Attention (LICA). Finally, we introduce a new Multimodal Attention-based Normalizing Flow to enable the scalability of our proposed method to high-dimensional multimodal data. Our experimental results on three different multimodal learning tasks, i.e., semantic segmentation, image-to-image translation, and movie genre classification, have illustrated the state-of-the-art (SoTA) performance of the proposed approach.