The "cold posterior effect" (CPE) in Bayesian deep learning describes the disturbing observation that the predictive performance of Bayesian neural networks can be significantly improved if the Bayes posterior is artificially sharpened using a temperature parameter T <1. The CPE is problematic in theory and practice and since the effect was identified many researchers have proposed hypotheses to explain the phenomenon. However, despite this intensive research effort the effect remains poorly understood. In this work we provide novel and nuanced evidence relevant to existing explanations for the cold posterior effect, disentangling three hypotheses: 1. The dataset curation hypothesis of Aitchison (2020): we show empirically that the CPE does not arise in a real curated data set but can be produced in a controlled experiment with varying curation strength.

We introduce active generation of Pareto sets (A-GPS), a new framework for online discrete black-box multi-objective optimization (MOO). A-GPS learns a generative model of the Pareto set that supports a-posteriori conditioning on user preferences. The method employs a class probability estimator (CPE) to predict non-dominance relations and to condition the generative model toward high-performing regions of the search space. We also show that this non-dominance CPE implicitly estimates the probability of hypervolume improvement (PHVI). To incorporate subjective trade-offs, A-GPS introduces preference direction vectors that encode user-specified preferences in objective space. At each iteration, the model is updated using both Pareto membership and alignment with these preference directions, producing an amortized generative model capable of sampling across the Pareto front without retraining. The result is a simple yet powerful approach that achieves high-quality Pareto set approximations, avoids explicit hypervolume computation, and flexibly captures user preferences. Empirical results on synthetic benchmarks and protein design tasks demonstrate strong sample efficiency and effective preference incorporation.

The " cold posterior effect " (CPE) in Bayesian deep learning describes the uncom-forting observation that the predictive performance of Bayesian neural networks

The Centralized Training with Decentralized Execution (CTDE) paradigm has gained significant attention in multi-agent reinforcement learning (MARL) and is the foundation of many recent algorithms. However, decentralized policies operate under partial observability and often yield suboptimal performance compared to centralized policies, while fully centralized approaches typically face scalability challenges as the number of agents increases. We propose Centralized Permutation Equivariant (CPE) learning, a centralized training and execution framework that employs a fully centralized policy to overcome these limitations. Our approach leverages a novel permutation equivariant architecture, Global-Local Permutation Equivariant (GLPE) networks, that is lightweight, scalable, and easy to implement. Experiments show that CPE integrates seamlessly with both value decomposition and actor-critic methods, substantially improving the performance of standard CTDE algorithms across cooperative benchmarks including MPE, SMAC, and RWARE, and matching the performance of state-of-the-art RWARE implementations.

Remarkable progress in text-to-image diffusion models has brought a major concern about potentially generating images on inappropriate or trademarked concepts. Concept erasing has been investigated with the goals of deleting target concepts in diffusion models while preserving other concepts with minimal distortion. To achieve these goals, recent concept erasing methods usually fine-tune the cross-attention layers of diffusion models. In this work, we first show that merely updating the cross-attention layers in diffusion models, which is mathematically equivalent to adding \emph{linear} modules to weights, may not be able to preserve diverse remaining concepts. Then, we propose a novel framework, dubbed Concept Pinpoint Eraser (CPE), by adding \emph{nonlinear} Residual Attention Gates (ResAGs) that selectively erase (or cut) target concepts while safeguarding remaining concepts from broad distributions by employing an attention anchoring loss to prevent the forgetting. Moreover, we adversarially train CPE with ResAG and learnable text embeddings in an iterative manner to maximize erasing performance and enhance robustness against adversarial attacks. Extensive experiments on the erasure of celebrities, artistic styles, and explicit contents demonstrated that the proposed CPE outperforms prior arts by keeping diverse remaining concepts while deleting the target concepts with robustness against attack prompts. Code is available at https://github.com/Hyun1A/CPE

Explainability is a critical factor influencing the wide deployment of deep vision models (DVMs). Concept-based post-hoc explanation methods can provide both global and local insights into model decisions. However, current methods in this field face challenges in that they are inflexible to automatically construct accurate and sufficient linguistic explanations for global concepts and local circuits. Particularly, the intrinsic polysemanticity in semantic Visual Concepts (VCs) impedes the interpretability of concepts and DVMs, which is underestimated severely. In this paper, we propose a Chain-of-Explanation (CoE) approach to address these issues. Specifically, CoE automates the decoding and description of VCs to construct global concept explanation datasets. Further, to alleviate the effect of polysemanticity on model explainability, we design a concept polysemanticity disentanglement and filtering mechanism to distinguish the most contextually relevant concept atoms. Besides, a Concept Polysemanticity Entropy (CPE), as a measure of model interpretability, is formulated to quantify the degree of concept uncertainty. The modeling of deterministic concepts is upgraded to uncertain concept atom distributions. Finally, CoE automatically enables linguistic local explanations of the decision-making process of DVMs by tracing the concept circuit. GPT-4o and human-based experiments demonstrate the effectiveness of CPE and the superiority of CoE, achieving an average absolute improvement of 36% in terms of explainability scores.

Bayesian inference provides a principled probabilistic framework for quantifying uncertainty by updating beliefs based on prior knowledge and observed data through Bayes' theorem. In Bayesian deep learning, neural network weights are treated as random variables with prior distributions, allowing for a probabilistic interpretation and quantification of predictive uncertainty. However, Bayesian methods lack theoretical generalization guarantees for unseen data. PAC-Bayesian analysis addresses this limitation by offering a frequentist framework to derive generalization bounds for randomized predictors, thereby certifying the reliability of Bayesian methods in machine learning. Temperature $T$, or inverse-temperature $\lambda = \frac{1}{T}$, originally from statistical mechanics in physics, naturally arises in various areas of statistical inference, including Bayesian inference and PAC-Bayesian analysis. In Bayesian inference, when $T < 1$ (``cold'' posteriors), the likelihood is up-weighted, resulting in a sharper posterior distribution. Conversely, when $T > 1$ (``warm'' posteriors), the likelihood is down-weighted, leading to a more diffuse posterior distribution. By balancing the influence of observed data and prior regularization, temperature adjustments can address issues of underfitting or overfitting in Bayesian models, bringing improved predictive performance.

The "cold posterior effect" (CPE) in Bayesian deep learning describes the disturbing observation that the predictive performance of Bayesian neural networks can be significantly improved if the Bayes posterior is artificially sharpened using a temperature parameter T 1. The CPE is problematic in theory and practice and since the effect was identified many researchers have proposed hypotheses to explain the phenomenon. However, despite this intensive research effort the effect remains poorly understood. In this work we provide novel and nuanced evidence relevant to existing explanations for the cold posterior effect, disentangling three hypotheses: 1. The dataset curation hypothesis of Aitchison (2020): we show empirically that the CPE does not arise in a real curated data set but can be produced in a controlled experiment with varying curation strength. Our results demonstrate how the CPE can arise in isolation from synthetic curation, data augmentation, and bad priors.