Estimating uncertainty from deep neural networks is a widely used approach for detecting out-of-distribution (OoD) samples, which typically exhibit high predictive uncertainty. However, conventional methods such as Monte Carlo (MC) Dropout often focus solely on either model or data uncertainty, failing to align with the semantic objective of OoD detection. T o address this, we propose the Free-Energy Posterior Network, a novel framework that jointly models distributional uncertainty and identifying OoD and misclassified regions using free energy. Our method introduces two key contributions: (1) a free-energy-based density estimator parameterized by a Beta distribution, which enables fine-grained uncertainty estimation near ambiguous or unseen regions; and (2) a loss integrated within a posterior network, allowing direct uncertainty estimation from learned parameters without requiring stochastic sampling. By integrating our approach with the residual prediction branch (RPL) framework, the proposed method goes beyond post-hoc energy thresholding and enables the network to learn OoD regions by leveraging the variance of the Beta distribution, resulting in a semantically meaningful and computationally efficient solution for uncertainty-aware segmentation.

Offline Reinforcement Learning (RL) struggles with distributional shifts, leading to the $Q$-value overestimation for out-of-distribution (OOD) actions. Existing methods address this issue by imposing constraints; however, they often become overly conservative when evaluating OOD regions, which constrains the $Q$-function generalization. This over-constraint issue results in poor $Q$-value estimation and hinders policy improvement. In this paper, we introduce a novel approach to achieve better $Q$-value estimation by enhancing $Q$-function generalization in OOD regions within Convex Hull and its Neighborhood (CHN). Under the safety generalization guarantees of the CHN, we propose the Smooth Bellman Operator (SBO), which updates OOD $Q$-values by smoothing them with neighboring in-sample $Q$-values. We theoretically show that SBO approximates true $Q$-values for both in-sample and OOD actions within the CHN. Our practical algorithm, Smooth Q-function OOD Generalization (SQOG), empirically alleviates the over-constraint issue, achieving near-accurate $Q$-value estimation. On the D4RL benchmarks, SQOG outperforms existing state-of-the-art methods in both performance and computational efficiency.

Composition-the ability to generate myriad variations from finite means-is believed to underlie powerful generalization. However, compositional generalization remains a key challenge for deep learning. A widely held assumption is that learning disentangled (factorized) representations naturally supports this kind of extrapolation. Yet, empirical results are mixed, with many generative models failing to recognize and compose factors to generate out-of-distribution (OOD) samples. In this work, we investigate a controlled 2D Gaussian "bump" generation task, demonstrating that standard generative architectures fail in OOD regions when training with partial data, even when supplied with fully disentangled $(x, y)$ coordinates, re-entangling them through subsequent layers. By examining the model's learned kernels and manifold geometry, we show that this failure reflects a "memorization" strategy for generation through the superposition of training data rather than by combining the true factorized features. We show that models forced-through architectural modifications with regularization or curated training data-to create disentangled representations in the full-dimensional representational (pixel) space can be highly data-efficient and effective at learning to compose in OOD regions. These findings underscore that bottlenecks with factorized/disentangled representations in an abstract representation are insufficient: the model must actively maintain or induce factorization directly in the representational space in order to achieve robust compositional generalization.

Recent developments in diffusion models have advanced conditioned image generation, yet they struggle with reconstructing out-of-distribution (OOD) images, such as unseen tumors in medical images, causing "image hallucination" and risking misdiagnosis. We hypothesize such hallucinations result from local OOD regions in the conditional images. We verify that partitioning the OOD region and conducting separate image generations alleviates hallucinations in several applications. From this, we propose a training-free diffusion framework that reduces hallucination with multiple Local Diffusion processes. Our approach involves OOD estimation followed by two modules: a "branching" module generates locally both within and outside OOD regions, and a "fusion" module integrates these predictions into one. Our evaluation shows our method mitigates hallucination over baseline models quantitatively and qualitatively, reducing misdiagnosis by 40% and 25% in the real-world medical and natural image datasets, respectively. It also demonstrates compatibility with various pre-trained diffusion models.

Model-based reinforcement learning (RL), which learns environment model from offline dataset and generates more out-of-distribution model data, has become an effective approach to the problem of distribution shift in offline RL. Due to the gap between the learned and actual environment, conservatism should be incorporated into the algorithm to balance accurate offline data and imprecise model data. The conservatism of current algorithms mostly relies on model uncertainty estimation. However, uncertainty estimation is unreliable and leads to poor performance in certain scenarios, and the previous methods ignore differences between the model data, which brings great conservatism. Therefore, this paper proposes a milDly cOnservative Model-bAsed offlINe RL algorithm (DOMAIN) without estimating model uncertainty to address the above issues. DOMAIN introduces adaptive sampling distribution of model samples, which can adaptively adjust the model data penalty. In this paper, we theoretically demonstrate that the Q value learned by the DOMAIN outside the region is a lower bound of the true Q value, the DOMAIN is less conservative than previous model-based offline RL algorithms and has the guarantee of security policy improvement. The results of extensive experiments show that DOMAIN outperforms prior RL algorithms on the D4RL dataset benchmark, and achieves better performance than other RL algorithms on tasks that require generalization.

It is often remarked that neural networks fail to increase their uncertainty when predicting on data far from the training distribution. Yet naively using softmax confidence as a proxy for uncertainty achieves modest success in tasks exclusively testing for this, e.g., out-of-distribution (OOD) detection. This paper investigates this contradiction, identifying two implicit biases that do encourage softmax confidence to correlate with epistemic uncertainty: 1) Approximately optimal decision boundary structure, and 2) Filtering effects of deep networks. It describes why low-dimensional intuitions about softmax confidence are misleading. Diagnostic experiments quantify reasons softmax confidence can fail, finding that extrapolations are less to blame than overlap between training and OOD data in final-layer representations. Pre-trained/fine-tuned networks reduce this overlap.