We proceed to compute the variances of each estimator. The proof also holds for the non-zero mean case trivially. Causal model details for Section 5.2 In Section 5.2, We include a wide range of machine learning-based causal inference methods to evaluate the performance of causal error estimators. Others configs are kept as default. The others are kept as default.

Ensembling has a long history in statistical data analysis, with many impactful applications. However, in many modern machine learning settings, the benefits of ensembling are less ubiquitous and less obvious.

Consistent and natural camera lens blur is important for seamlessly blending 3D virtual objects into photographed real-scenes. Since lens blur typically varies with scene depth, the placement of virtual objects and their corresponding blur levels significantly affect the visual fidelity of mixed reality compositions. Existing pipelines often rely on camera parameters (e.g., focal length, focus distance, aperture size) and scene depth to compute the circle of confusion (CoC) for realistic lens blur rendering. However, such information is often unavailable to ordinary users, limiting the accessibility and generalizability of these methods. In this work, we propose a novel compositing approach that directly estimates the CoC map from RGB images, bypassing the need for scene depth or camera metadata. The CoC values for virtual objects are inferred through a linear relationship between its signed CoC map and depth, and realistic lens blur is rendered using a neural reblurring network. Our method provides flexible and practical solution for real-world applications. Experimental results demonstrate that our method achieves high-fidelity compositing with realistic defocus effects, outperforming state-of-the-art techniques in both qualitative and quantitative evaluations.

Adapted with edits from [1].

Test-time scaling improves large language models' (LLMs) performance by allocating more compute budget during inference. To achieve this, existing methods often require intricate modifications to prompting and sampling strategies. In this work, we introduce representation consistency (RC), a test-time scaling method for aggregating answers drawn from multiple candidate responses of an LLM regardless of how they were generated, including variations in prompt phrasing and sampling strategy. RC enhances answer aggregation by not only considering the number of occurrences of each answer in the candidate response set, but also the consistency of the model's internal activations while generating the set of responses leading to each answer. These activations can be either dense (raw model activations) or sparse (encoded via pretrained sparse autoencoders). Our rationale is that if the model's representations of multiple responses converging on the same answer are highly variable, this answer is more likely to be the result of incoherent reasoning and should be down-weighted during aggregation. Importantly, our method only uses cached activations and lightweight similarity computations and requires no additional model queries. Through experiments with four open-source LLMs and four reasoning datasets, we validate the effectiveness of RC for improving task performance during inference, with consistent accuracy improvements (up to 4%) over strong test-time scaling baselines. We also show that consistency in the sparse activation signals aligns well with the common notion of coherent reasoning.