Recent advances in cross-prompt automated essay scoring typically train models jointly on all available source domains, often requiring simultaneous access to unlabeled target domain samples. However, using all sources can lead to suboptimal transfer and high computational cost. Moreover, repeatedly accessing the source essays for continual adaptation raises privacy concerns. We propose a source-free adaptation approach that selectively merges the parameters of individually trained source models without further access to the source datasets. In particular, we mix the task vectors—the parameter updates from fine-tuning—via a weighted sum to efficiently simulate selective joint-training. We use Bayesian optimization to determine the mixing weights using our proposed Prior-encoded Information Maximization (PIM), an unsupervised objective which promotes score discriminability by leveraging useful priors pre-computed from the sources. Experimental results with LLMs on in-dataset and cross-dataset adaptation show that our method (1) consistently outperforms joint-training on all sources, (2) maintains superior robustness compared to other merging methods, (3) excels under severe distribution shifts where recent leading cross-prompt methods struggle, all while retaining computational efficiency.
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In-context learning (ICL) has emerged as a powerful paradigm for task adaptation in large language models (LLMs), where models infer underlying task structures from a few demonstrations. However, ICL remains susceptible to biases that arise from prior knowledge and contextual demonstrations, which can degrade the performance of LLMs. Existing bias calibration methods typically apply fixed class priors across all inputs, limiting their efficacy in dynamic ICL settings where the context for each query differs. To address these limitations, we adopt implicit sequential Bayesian inference as a framework for interpreting ICL, identify “surprise” as an informative signal for class prior shift, and introduce a novel method—Surprise Calibration (SC). SC leverages the notion of surprise to capture the temporal dynamics of class priors, providing a more adaptive and computationally efficient solution for in-context learning. We empirically demonstrate the superiority of SC over existing bias calibration techniques across a range of benchmark natural language processing tasks.
COM-BOM: Bayesian Exemplar Search for Efficiently Exploring the Accuracy-Calibration Pareto Frontier
PDF ↗Selecting an optimal set of exemplars is critical for good performance of in-context learning. However, prior exemplar search methods narrowly optimize for predictive accuracy, critically neglecting model calibration—a key determinant of trustworthiness and safe deployment. In this paper, we formulate exemplar selection as a multi-objective optimization problem, explicitly targeting both the maximization of predictive accuracy and the minimization of expected calibration error. We solve this problem with a sample-efficient Combinatorial Bayesian Optimization algorithm (COM-BOM) to find the Pareto-front that optimally trade-offs the two objectives of accuracy and calibration. We evaluate COM-BOM on multiple tasks from un-saturated MMLU-pro benchmark and find that COM-BOM beats or matches the baselines in jointly optimizing the two objectives, while requiring a minimal number of LLM API calls.
We introduce GuessingGame, a protocol for evaluating large language models (LLMs) as strategic question-askers in open-ended, open-domain settings. A Guesser LLM identifies a hidden object by posing free-form questions to an Oracle—without predefined choices or candidate lists. To measure question quality, we propose two information gain (IG) metrics: a Bayesian method that tracks belief updates over semantic concepts using LLM-scored relevance, and an entropy-based method that filters candidates via ConceptNet. Both metrics are model-agnostic and support post hoc analysis. Across 858 games with multiple models and prompting strategies, higher IG strongly predicts efficiency: a one-standard-deviation IG increase reduces expected game length by 43%. Prompting constraints guided by IG—such as enforcing question diversity—enable weaker models to match GPT-4o. These results show that question-asking in LLMs is both measurable and improvable, and crucial for interactive reasoning.
pFedGPT: Hierarchically Optimizing LoRA Aggregation Weights for Personalized Federated GPT Models
PDF ↗Federated finetuning of Large Language Models (LLMs) using Low-Rank Adaptation (LoRA) offers computational efficiency and preserves data privacy. However, applying LoRA in federated settings faces significant challenges: standard approaches struggle with data heterogeneity, and existing personalization techniques fail to precisely adapt shared global knowledge to individual client needs. To address these issues, we propose pFedGPT, a framework that leverages Hierarchical Bayesian Optimization (HBO) for fine-grained, personalized LoRA aggregation. pFedGPT intelligently partitions LoRA parameters based on model structure and client information, then employs HBO to hierarchically search for optimal, module-specific weights. This enables a nuanced integration of the downloaded global LoRA state with each client’s local model, precisely capturing client-specific requirements. To manage the optimization cost inherent in HBO, pFedGPT incorporates efficient multi-fidelity evaluations and a curriculum learning strategy. Extensive experiments demonstrate that pFedGPT achieves state-of-the-art (SOTA) performance on personalized FL benchmarks, showcasing robustness and scalability while introducing only minimal (approx. 4%) additional optimization overhead. Our results also underscore the limitations of traditional FL methods for LoRA-based LLM personalization, highlighting the need for tailored approaches like pFedGPT.
NLP models often rely on human-labeled data for training and evaluation. Many approaches crowdsource this data from a large number of annotators with varying skills, backgrounds, and motivations, resulting in conflicting annotations. These conflicts have traditionally been resolved by aggregation methods that assume disagreements are errors. Recent work has argued that for many tasks annotators may have genuine disagreements and that variation should be treated as signal rather than noise. However, few models separate signal and noise in annotator disagreement. In this work, we introduce NUTMEG, a new Bayesian model that incorporates information about annotator backgrounds to remove noisy annotations from human-labeled training data while preserving systematic disagreements. Using synthetic and real-world data, we show that NUTMEG is more effective at recovering ground-truth from annotations with systematic disagreement than traditional aggregation methods, and we demonstrate that downstream models trained on NUTMEG-aggregated data significantly outperform models trained on data from traditionally aggregation methods. We provide further analysis characterizing how differences in subpopulation sizes, rates of disagreement, and rates of spam affect the performance of our model. Our results highlight the importance of accounting for both annotator competence and systematic disagreements when training on human-labeled data.
Weight-Aware Activation Sparsity with Constrained Bayesian Optimization Scheduling for Large Language Models
PDF ↗Activation sparsity provides a dynamic, input-dependent alternative to weight pruning for accelerating inference in large language models (LLMs), effectively reducing unnecessary computations and memory accesses during the forward pass. Despite its promise, existing activation sparsification methods suffer from two major limitations: (1) solely relying on activation magnitude for sparsification, ignoring the coupling influence with the corresponding weights, (2) applying uniform sparsity rates across all blocks without considering block-wise sparsity sensitivity. To address these issues, this paper proposes a novel training-free weight-aware activation sparsity framework, called **WAS**. Firstly, with analyzing the coupling relationship between weight and activation, we introduce a weight-aware scoring method to measure the activation importance in sparsification. Then, a novel constrained Bayesian optimization algorithm is further devised to set a suitable sparsity ratio for all blocks based on the sparsity sensitivity. Finally, we implement a custom GPU sparsity kernel to support the resulting sparsity patterns for wall-clock decoding speed-ups. Our **WAS** achieves competitive performance at 60% model-level sparsity and significantly outperforms prior methods at higher sparsity levels, achieving up to 1.68× inference speed-up—at no retraining or weight update. Codes are available at https://github.com/HITSZ-Miao-Group/WAS.
Probabilistic Methods
Bayesian networks (BNs), represented by directed acyclic graphs (DAGs), provide a principled framework for modeling complex dependencies among random variables. As data dimensionality increases into the tens of thousands, fitting and marginalizing a full BN becomes computationally prohibitive—particularly when inference is only needed for a small subset of variables. Estimation-collapsibility addresses this challenge by ensuring that directly fitting a submodel, obtained by ignoring non-essential variables, still yields exact inference on target variables. However, current DAG-based criterion for checking estimation-collapsibility is computationally intensive, involving exhaustive vertex searches and iterative removals. Additionally, practical applications typically identify the underlying DAG only up to its Markov equivalence class, represented by a completed partially directed acyclic graph (CPDAG). To bridge this gap, we introduce sequential $c$-simplicial sets—a novel graphical characterization of estimation-collapsibility applicable directly to CPDAGs. We further propose DSCS, a computationally efficient algorithm for verifying estimation-collapsibility within CPDAG framework that scales effectively to high-dimensional BNs. Extensive numerical experiments demonstrate the practicality, scalability, and efficiency of our proposed approach.
Optimization · Bayesian & Black-box Optimization
Model-free optimization methods typically rely on cost samples gathered by perturbing the current solution estimate along a finite and fixed set of directions. However, at each iteration, only the current cost samples are used, while potentially informative, previously collected samples are discarded. In this work, we challenge this conventional approach by introducing a simple yet effective memory mechanism that maintains an auxiliary vector of iteratively updated cost samples. By leveraging this stored information, our method estimates descent directions through an averaging of all perturbing directions weighted by the auxiliary vector components. This results in a faster convergence without increasing the number of function queries. By interpreting the resulting algorithm as a time-varying dynamical system, we are able to establish its convergence properties in the strongly convex case. In particular, by using tools from system theory based on timescale separation, we are able to guarantee a linear convergence rate toward an arbitrarily small neighborhood of the optimal solution. Numerical simulations on regression problems demonstrate that the proposed approach significantly outperforms existing model-free optimization methods.
Probabilistic Methods · Bayesian Models and Methods
Estimating the uncertainty of responses from Large Language Models (LLMs) remains a critical challenge. While recent Bayesian methods have demonstrated effectiveness in quantifying uncertainty through low-rank weight updates, they typically require complex fine-tuning or post-training procedures. In this paper, we propose **T**raining-**F**ree **B**ayesianization (**TFB**), a simple yet theoretically grounded framework that efficiently transforms trained low-rank adapters into Bayesian ones without additional training. TFB systematically searches for the maximally acceptable level of variance in the weight posterior, constrained within a family of low-rank isotropic Gaussian distributions. Our theoretical analysis shows that under mild conditions, this search process is equivalent to KL-regularized variational optimization, a generalized form of variational inference. Through comprehensive experiments, we show that TFB achieves superior uncertainty estimation and generalization compared to existing methods while eliminating the need for complex Bayesianization training procedures.
Probabilistic Methods · Bayesian Models and Methods
We introduce *NeuralSurv*, the first deep survival model to incorporate Bayesian uncertainty quantification. Our non‑parametric, architecture‑agnostic framework flexibly captures time‑varying covariate–risk relationships in continuous time via a novel two‑stage data‑augmentation scheme, for which we establish theoretical guarantees. For efficient posterior inference, we introduce a mean‑field variational algorithm with coordinate‑ascent updates that scale linearly in model size. By locally linearizing the Bayesian neural network, we obtain full conjugacy and derive all coordinate updates in closed form. In experiments, *NeuralSurv* delivers superior calibration compared to state-of-the-art deep survival models, while matching or exceeding their discriminative performance across both synthetic benchmarks and real-world datasets. Our results demonstrate the value of Bayesian principles in data‑scarce regimes by enhancing model calibration and providing robust, well‑calibrated uncertainty estimates for the survival function.
Applications · Chemistry and Drug Discovery
Recent advances in Structure-based Drug Design (SBDD) have leveraged generative models for 3D molecular generation, predominantly evaluating model performance by binding affinity to target proteins. However, practical drug discovery necessitates high binding affinity along with synthetic feasibility and selectivity, critical properties that were largely neglected in previous evaluations. To address this gap, we identify fundamental limitations of conventional diffusion-based generative models in effectively guiding molecule generation toward these diverse pharmacological properties. We propose $\texttt{CByG}$, a novel framework extending Bayesian Flow Network into a gradient-based conditional generative model that robustly integrates property-specific guidance. Additionally, we introduce a comprehensive evaluation scheme incorporating practical benchmarks for binding affinity, synthetic feasibility, and selectivity, overcoming the limitations of conventional evaluation methods. Extensive experiments demonstrate that our proposed $\texttt{CByG}$, framework significantly outperforms baseline models across multiple essential evaluation criteria, highlighting its effectiveness and practicality for real-world drug discovery applications.
Deep Learning · Everything Else
Uncertainty quantification (UQ) in scientific machine learning is increasingly critical as neural networks are widely adopted to tackle complex problems across diverse scientific disciplines. For physics-informed neural networks (PINNs), a prominent model in scientific machine learning, uncertainty is typically quantified using Bayesian or dropout methods. However, both approaches suffer from a fundamental limitation: the prior distribution or dropout rate required to construct honest confidence sets cannot be determined without additional information. In this paper, we propose a novel method within the framework of extended fiducial inference (EFI) to provide rigorous uncertainty quantification for PINNs. The proposed method leverages a narrow-neck hyper-network to learn the parameters of the PINN and quantify their uncertainty based on imputed random errors in the observations. This approach overcomes the limitations of Bayesian and dropout methods, enabling the construction of honest confidence sets based solely on observed data. This advancement represents a significant breakthrough for PINNs, greatly enhancing their reliability, interpretability, and applicability to real-world scientific and engineering challenges. Moreover, it establishes a new theoretical framework for EFI, extending its application to large-scale models, eliminating the need for sparse hyper-networks, and significantly improving the automaticity and robustness of statistical inference.
Neural Processes (NPs) combine the adaptability of neural networks with the efficiency of meta-learning, offering a powerful framework for modeling stochastic processes. However, existing methods focus on empirical performance while lacking a rigorous theoretical understanding of generalization. To address this, we propose an information-theoretic framework to analyze the generalization bounds of NPs, introducing dynamical stability regularization to minimize sharpness and improve optimization dynamics. Additionally, we show how noise-injected parameter updates complement this regularization. The proposed approach, applicable to a wide range of NP models, is validated through experiments on classic benchmarks, including 1D regression, image completion, Bayesian optimization, and contextual bandits. The results demonstrate tighter generalization bounds and superior predictive performance, establishing a principled foundation for advancing generalizable NP models.
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.
Probabilistic Methods · Bayesian Models and Methods
We propose the Distance-informed Neural Process (DNP), a novel variant of Neural Processes that improves uncertainty estimation by combining global and distance-aware local latent structures. Standard Neural Processes (NPs) often rely on a global latent variable and struggle with uncertainty calibration and capturing local data dependencies. DNP addresses these limitations by introducing a global latent variable to model task-level variations and a local latent variable to capture input similarity within a distance-preserving latent space. This is achieved through bi-Lipschitz regularization, which bounds distortions in input relationships and encourages the preservation of relative distances in the latent space. This modeling approach allows DNP to produce better-calibrated uncertainty estimates and more effectively distinguish in- from out-of-distribution data. Empirical results demonstrate that DNP achieves strong predictive performance and improved uncertainty calibration across regression and classification tasks.
Optimization
Existing Bayesian Optimization (BO) methods typically balance exploration and exploitation to optimize costly objective functions. However, these methods often suffer from a significant one-step bias, which may lead to convergence toward local optima and poor performance in complex or high-dimensional tasks. Recently, Black-Box Optimization (BBO) has achieved success across various scientific and engineering domains, particularly when function evaluations are costly and gradients are unavailable. Motivated by this, we propose the Reinforced Energy-Based Model for Bayesian Optimization (REBMBO), which integrates Gaussian Processes (GP) for local guidance with an Energy-Based Model (EBM) to capture global structural information. Notably, we define each Bayesian Optimization iteration as a Markov Decision Process (MDP) and use Proximal Policy Optimization (PPO) for adaptive multi-step lookahead, dynamically adjusting the depth and direction of exploration to effectively overcome the limitations of traditional BO methods. We conduct extensive experiments on synthetic and real-world benchmarks, confirming the superior performance of REBMBO. Additional analyses across various GP configurations further highlight its adaptability and robustness.
Probabilistic Methods · Monte Carlo and Sampling Methods
Markov chain Monte Carlo (MCMC) methods are foundational algorithms for Bayesian inference and probabilistic modeling. However, most MCMC algorithms are inherently sequential and their time complexity scales linearly with the sequence length. Previous work on adapting MCMC to modern hardware has therefore focused on running many independent chains in parallel. Here, we take an alternative approach: we propose algorithms to evaluate MCMC samplers in parallel across the chain length. To do this, we build on recent methods for parallel evaluation of nonlinear recursions that formulate the state sequence as a solution to a fixed-point problem and solve for the fixed-point using a parallel form of Newton's method. We show how this approach can be used to parallelize Gibbs, Metropolis-adjusted Langevin, and Hamiltonian Monte Carlo sampling across the sequence length. In several examples, we demonstrate the simulation of up to hundreds of thousands of MCMC samples with only tens of parallel Newton iterations. Additionally, we develop two new parallel quasi-Newton methods to evaluate nonlinear recursions with lower memory costs and reduced runtime. We find that the proposed parallel algorithms accelerate MCMC sampling across multiple examples, in some cases by more than an order of magnitude compared to sequential evaluation.
Optimization · Bayesian & Black-box Optimization
The efficiency of Bayesian optimization (BO) relies heavily on the choice of the Gaussian process (GP) kernel, which plays a central role in balancing exploration and exploitation under limited evaluation budgets. Traditional BO methods often rely on fixed or heuristic kernel selection strategies, which can result in slow convergence or suboptimal solutions when the chosen kernel is poorly suited to the underlying objective function. To address this limitation, we propose a freshly-baked Context-Aware Kernel Evolution (CAKE) to enhance BO with large language models (LLMs). Concretely, CAKE leverages LLMs as the crossover and mutation operators to adaptively generate and refine GP kernels based on the observed data throughout the optimization process. To maximize the power of CAKE, we further propose BIC-Acquisition Kernel Ranking (BAKER) to select the most effective kernel through balancing the model fit measured by the Bayesian information criterion (BIC) with the expected improvement at each iteration of BO. Extensive experiments demonstrate that our fresh CAKE-based BO method consistently outperforms established baselines across a range of real-world tasks, including hyperparameter optimization, controller tuning, and photonic chip design. Our code is publicly available at https://github.com/richardcsuwandi/cake.
Probabilistic Methods · Bayesian Models and Methods
Bayesian Network models are a powerful tool to collaboratively optimize production processes in various manufacturing industries. When interacting, collaborating parties must preserve their business secrets by maintaining the confidentiality of their model structures and parameters. While most realistic industry scenarios involve hybrid settings, handling both discrete and continuous data, current state-of-the-art methods for collaborative and confidential inference only support discrete data and have high communication costs. In a centralized setting, Junction Trees enable efficient inference even in hybrid scenarios without discretizing continuous variables, but no extension for collaborative and confidential scenarios exists. To address this research gap, we introduce Hybrid CCJT, the first framework for confidential multiparty inference in hybrid domains with semi-honest, non-colluding adversaries, comprising: (i) a method to construct a strongly-rooted Junction Tree across collaborating parties through a novel construct of interface cliques; and, (ii) a protocol for confidential inference built upon multiparty computation primitives comprising a one-time alignment phase and a belief propagation system for combining the inference results across the Junction Tree cliques. Extensive evaluation on nine datasets shows that Hybrid CCJT improves the predictive accuracy of continuous target variables by 32% on average compared to the state-of-the-art, while reducing communication costs by a median 10.4x under purely discrete scenarios.