Aligning visual features with language embeddings is a key challenge in visionlanguage models (VLMs). The performance of such models hinges on having a good connector that maps visual features generated by a vision encoder to a shared embedding space with the LLM while preserving semantic similarity. Existing connectors, such as multilayer perceptrons (MLPs), lack inductive bias to constrain visual features within the linguistic structure of the LLM's embedding space, making them data-hungry and prone to cross-modal misalignment. In this work, we propose a novel vision-text alignment method, ALIGNVLM, that maps visual features to a weighted average of LLM text embeddings. Our approach leverages the linguistic priors encoded by the LLM to ensure that visual features are mapped to regions of the space that the LLM can effectively interpret. ALIGNVLM is particularly effective for document understanding tasks, where visual and textual modalities are highly correlated. Our extensive experiments show that ALIGNVLM achieves state-of-the-art performance compared to prior alignment methods, with larger gains on document understanding tasks and under low-resource setups. We provide further analysis demonstrating its efficiency and robustness to noise.

Protein fitness optimization involves finding a protein sequence that maximizes desired quantitative properties in a combinatorially large design space of possible sequences. Recent advances in steering protein generative models (e.g., diffusion models and language models) with labeled data offer a promising approach. However, most previous studies have optimized surrogate rewards and/or utilized large amounts of labeled data for steering, making it unclear how well existing methods perform and compare to each other in real-world optimization campaigns where fitness is measured through low-throughput wet-lab assays. In this study, we explore fitness optimization using small amounts (hundreds) of labeled sequencefitness pairs and comprehensively evaluate strategies such as classifier guidance and posterior sampling for guiding generation from different discrete diffusion models of protein sequences. We also demonstrate how guidance can be integrated into adaptive sequence selection akin to Thompson sampling in Bayesian optimization, showing that plug-and-play guidance strategies offer advantages over alternatives such as reinforcement learning with protein language models. Overall, we provide practical insights into how to effectively steer modern generative models for next-generation protein fitness optimization.

Federated Class Incremental Learning (FCIL) aims to collaboratively process continuously increasing incoming tasks across multiple clients. Among various approaches, data replay has become a promising solution, which can alleviate forgetting by reintroducing representative samples from previous tasks. However, their performance is typically limited by class imbalance, both within the replay buffer due to limited global awareness and between replayed and newly arrived classes. To address this issue, we propose a class-wise balancing data replay method for FCIL (FedCBDR), which employs a global coordination mechanism for class-level memory construction and reweights the learning objective to alleviate the aforementioned imbalances. Specifically, FedCBDRhas two key components: 1) the global-perspective data replay module reconstructs global representations of prior task in a privacy-preserving manner, which then guides a class-aware and importance-sensitive sampling strategy to achieve balanced replay; 2) Subsequently, to handle class imbalance across tasks, the task-aware temperature scaling module adaptively adjusts the temperature of logits at both class and instance levels based on task dynamics, which reduces the model's overconfidence in majority classes while enhancing its sensitivity to minority classes. Experimental results verified that FedCBDR achieves balanced class-wise sampling under heterogeneous data distributions and improves generalization under task imbalance between earlier and recent tasks, yielding a 2%-15% Top-1 accuracy improvement over six stateof-the-art methods.

Predictions in the form of sets of probability distributions, so-called credal sets, provide a suitable means to represent a learner's epistemic uncertainty. In this paper, we propose a theoretically grounded approach to credal prediction based on the statistical notion of relative likelihood: The target of prediction is the set of all (conditional) probability distributions produced by the collection of plausible models, namely those models whose relative likelihood exceeds a specified threshold. This threshold has an intuitive interpretation and allows for controlling the trade-off between correctness and precision of credal predictions. We tackle the problem of approximating credal sets defined in this way by means of suitably modified ensemble learning techniques. To validate our approach, we illustrate its effectiveness by experiments on benchmark datasets demonstrating superior uncertainty representation without compromising predictive performance. We also compare our method against several state-of-the-art baselines in credal prediction.

Capturing effective long-range information propagation remains a fundamental yet challenging problem in graph representation learning. Motivated by this, we introduce SONAR, a novel GNN architecture inspired by the dynamics of wave propagation in continuous media. SONAR models information flow on graphs as oscillations governed by the wave equation, allowing it to maintain effective propagation dynamics over long distances. By integrating adaptive edge resistances and state-dependent external forces, our method balances conservative and nonconservative behaviors, improving the ability to learn more complex dynamics. We provide a rigorous theoretical analysis of SONAR's energy conservation and information propagation properties, demonstrating its capacity to address the long-range propagation problem. Extensive experiments on synthetic and realworld benchmarks confirm that SONAR achieves state-of-the-art performance, particularly on tasks requiring long-range information exchange.

Diffusion models have made significant strides in recent years, exhibiting strong generalization capabilities in planning and control tasks. However, most diffusionbased policies remain focused on reward maximization or cost minimization, often overlooking critical aspects of safety and stability. In this work, we propose Safe and Stable Diffusion (S2Diff), a model-based diffusion framework that explores how diffusion models can ensure safety and stability from a Lyapunov perspective. We demonstrate that S2Diff eliminates the reliance on both complex gradientbased solvers (e.g., quadratic programming, non-convex solvers) and controlaffine structures, leading to globally valid control policies driven by the learned certificate functions. Additionally, we uncover intrinsic connections between diffusion sampling and Almost Lyapunov theory, enabling the use of trajectorylevel control policies to learn better certificate functions for safety and stability guarantees. To validate our approach, we conduct experiments on a wide variety of dynamical control systems, where S2Diff consistently outperforms both certificatebased controllers and model-based diffusion baselines in terms of safety, stability, and overall control performance.

We present HyPINO, a multi-physics neural operator designed for zero-shot generalization across a broad class of PDEs without requiring task-specific fine-tuning. Our approach combines a Swin Transformer-based hypernetwork with mixed supervision: (i) labeled data from analytical solutions generated via the Method of Manufactured Solutions (MMS), and (ii) unlabeled samples optimized using physics-informed objectives. The model maps PDE parameterizations to target Physics-Informed Neural Networks (PINNs) and can handle linear elliptic, hyperbolic, and parabolic equations in two dimensions with varying source terms, geometries, and mixed Dirichlet/Neumann boundary conditions, including interior boundaries. HyPINO achieves strong zero-shot accuracy on seven benchmark problems from PINN literature, outperforming U-Nets, Poseidon, and Physics-Informed Neural Operators (PINO). Further, we introduce an iterative refinement procedure that treats the residual of the generated PINN as "delta PDE" and performs another forward pass to generate a corrective PINN. Summing their contributions and repeating this process forms an ensemble whose combined solution progressively reduces the error on six benchmarks and achieves a >100 lower L2 loss in the best case, while retaining forward-only inference. Additionally, we evaluate the fine-tuning behavior of PINNs initialized by HyPINO and show that they converge faster and to lower final error than both randomly initialized and Reptilemeta-learned PINNs on five benchmarks, performing on par on the remaining two. Our results highlight the potential of this scalable approach as a foundation for extending neural operators toward solving increasingly complex, nonlinear, and high-dimensional PDE problems. The code and model weights are publicly available at https://github.com/rbischof/hypino.

Recent advances in generative modeling have positioned diffusion models as stateof-the-art tools for sampling from complex data distributions. While these models have shown remarkable success across single-modality domains such as images and audio, extending their capabilities to Modality Translation (MT), translating information across different sensory modalities, remains an open challenge. Existing approaches often rely on restrictive assumptions, including shared dimensionality, Gaussian source priors, and modality-specific architectures, which limit their generality and theoretical grounding. In this work, we propose the Latent Denoising Diffusion Bridge Model (LDDBM), a general-purpose framework for modality translation based on a latent-variable extension of Denoising Diffusion Bridge Models. By operating in a shared latent space, our method learns a bridge between arbitrary modalities without requiring aligned dimensions. We introduce a contrastive alignment loss to enforce semantic consistency between paired samples and design a domain-agnostic encoder-decoder architecture tailored for noise prediction in latent space. Additionally, we propose a predictive loss to guide training toward accurate cross-domain translation and explore several training strategies to improve stability. Our approach supports arbitrary modality pairs and performs strongly on diverse MT tasks, including multi-view to 3D shape generation, image super-resolution, and multi-view scene synthesis.

However, these methods often suffer from a significant one-step bias, which may lead to convergence towards 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 EnergyBased 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.

Variational inference seeks the best approximation of a target distribution within a chosen family, where "best" means minimising Kullback-Leibler divergence. When the approximation family is exponential, the optimal approximation satisfies a fixed-point equation. We introduce LSVI (Least Squares Variational Inference), a gradient-free, Monte Carlo-based scheme for the fixed-point recursion, where each iteration boils down to performing ordinary least squares regression on tempered log-target evaluations under the variational approximation. We show that LSVI is equivalent to biased stochastic natural gradient descent and use this to derive convergence rates with respect to the numbers of samples and iterations. When the approximation family is Gaussian, LSVI involves inverting the Fisher information matrix, whose size grows quadratically with dimension d. We exploit the regression formulation to eliminate the need for this inversion, yielding O(d3) complexity in the full-covariance case and O(d) in the mean-field case. Finally, we numerically demonstrate LSVI's performance on various tasks, including logistic regression, discrete variable selection, and Bayesian synthetic likelihood, showing results competitive with state-of-the-art methods, even when gradients are unavailable.