Inadditiontothememory limitation, there are other important concerns.

Standard approaches for uncertainty quantification in deep learning and physics-informed learning have persistent limitations.

All typos/writing issues will be fixed as suggested in the reviews.

Synthesizing realistic cooked food images from raw inputs on edge devices is a challenging generative task, requiring models to capture complex changes in texture, color and structure during cooking. Existing image-to-image generation methods often produce unrealistic results or are too resource-intensive for edge deployment. W e introduce the first oven-based cooking-progression dataset with chef-annotated doneness levels and propose an edge-efficient recipe and cooking state guided generator that synthesizes realistic food images conditioned on raw food image. This formulation enables user-preferred visual targets rather than fixed presets. T o ensure temporal consistency and culinary plausibility, we introduce a domain-specific Culinary Image Similarity (CIS) metric, which serves both as a training loss and a progress-monitoring signal. Our model outperforms existing baselines with significant reductions in FID scores (30% improvement on our dataset; 60% on public datasets).

The average treatment effect (ATE) is widely used to evaluate the effectiveness of drugs and other medical interventions. In safety-critical applications like medicine, reliable inferences about the ATE typically require valid uncertainty quantification, such as through confidence intervals (CIs). However, estimating treatment effects in these settings often involves sensitive data that must be kept private. In this work, we present PrivATE, a novel machine learning framework for computing CIs for the ATE under differential privacy. Specifically, we focus on deriving valid privacy-preserving CIs for the ATE from observational data. Our PrivATE framework consists of three steps: (i) estimating the differentially private ATE through output perturbation; (ii) estimating the differentially private variance in a doubly robust manner; and (iii) constructing the CIs while accounting for the uncertainty from both the estimation and privatization steps. Our PrivATE framework is model agnostic, doubly robust, and ensures valid CIs. We demonstrate the effectiveness of our framework using synthetic and real-world medical datasets. To the best of our knowledge, we are the first to derive a general, doubly robust framework for valid CIs of the ATE under ($\varepsilon,δ$)-differential privacy.

Secondly, these works do not account for finite-sampling errors in the obtained curve.

We greatly thank the reviewers for their constructive comments. However, in certain applications, there is scientific evidence for a parametric form of the triggering kernel (e.g., [Beggs We show here a small example with 5 nodes in Figure 1. We have similar observations for recovering other edges in this example. In each picture, the two blue curves outline the proposed CIs, and the two red curves outline the asymptotic CI. Moreover, we will adjust Section 2-3 as suggested.