The supplemental material is organized as follows. Section A provides the results of all the additional synthetic experiments and real data results for various kernel-based methods and the detailed settings. Section B describes the algorithm details we use in Section A. In Section C, we provide some useful lemmas and all the technical proofs of the theoretical results in the main text. In this section, we provide more experiment results, including KRR (Section A.1), KQR for various Section A.7. A.1 Kernel ridge regression For the squared loss, we consider the following two examples. TIRW estimator still performs significantly better. A.2 Kernel quantile regression For the check loss, we consider the following two examples.

Accurate prediction of enzyme kinetic parameters is crucial for drug discovery, metabolic engineering, and synthetic biology applications. Current computational approaches face limitations in capturing complex enzyme-substrate interactions and often focus on single parameters while neglecting the joint prediction of catalytic turnover numbers (Kcat) and Michaelis-Menten constants (Km). We present EnzyCLIP, a novel dual-encoder framework that leverages contrastive learning and cross-attention mechanisms to predict enzyme kinetic parameters from protein sequences and substrate molecular structures. Our approach integrates ESM-2 protein language model embeddings with ChemBERTa chemical representations through a CLIP-inspired architecture enhanced with bidirectional cross-attention for dynamic enzyme-substrate interaction modeling. EnzyCLIP combines InfoNCE contrastive loss with Huber regression loss to learn aligned multimodal representations while predicting log10-transformed kinetic parameters. The model is trained on the CatPred-DB database containing 23,151 Kcat and 41,174 Km experimentally validated measurements, and achieved competitive performance with R2 scores of 0.593 for Kcat and 0.607 for Km prediction. XGBoost ensemble methods applied to the learned embeddings further improved Km prediction (R2 = 0.61) while maintaining robust Kcat performance.

Modeling indoor radio propagation is crucial for wireless network planning and optimization. However, existing approaches often rely on labor-intensive manual modeling of geometry and material properties, resulting in limited scalability and efficiency. To overcome these challenges, this paper presents SenseRay-3D, a generalizable and physics-informed end-to-end framework that predicts three-dimensional (3D) path-loss heatmaps directly from RGB-D scans, thereby eliminating the need for explicit geometry reconstruction or material annotation. The proposed framework builds a sensing-driven voxelized scene representation that jointly encodes occupancy, electromagnetic material characteristics, and transmitter-receiver geometry, which is processed by a SwinUNETR-based neural network to infer environmental path-loss relative to free-space path-loss. A comprehensive synthetic indoor propagation dataset is further developed to validate the framework and to serve as a standardized benchmark for future research. Experimental results show that SenseRay-3D achieves a mean absolute error of 4.27 dB on unseen environments and supports real-time inference at 217 ms per sample, demonstrating its scalability, efficiency, and physical consistency. SenseRay-3D paves a new path for sense-driven, generalizable, and physics-consistent modeling of indoor propagation, marking a major leap beyond our pioneering EM DeepRay framework.

This Appendix is divided into three sections. Assumption 1. Next, in Section B, complete proofs of all the lemmas and theorems are presented. Figure 1: The estimated constants C and λ on various datasets. Hence, the relaxed Multiclass Tsybakov Condition holds and the probability of the first term of Eq. 17 Hence, by applying Hoeffding's inequality [5], we have: For fair comparisons, we implement FPMC with PyTorch. Figure 6: The percentage of instances that are rectified with increasing epochs. Does every data instance matter?

Process-structure-property relationships are fundamental in materials science and engineering and are key to the development of new and improved materials. Symbolic regression serves as a powerful tool for uncovering mathematical models that describe these relationships. It can automatically generate equations to predict material behaviour under specific manufacturing conditions and optimize performance characteristics such as strength and elasticity. The present work illustrates how symbolic regression can derive constitutive models that describe the behaviour of various metallic alloys during plastic deformation. Constitutive modelling is a mathematical framework for understanding the relationship between stress and strain in materials under different loading conditions. In this study, two materials (age-hardenable aluminium alloy and high-chromium martensitic steel) and two different testing methods (compression and tension) are considered to obtain the required stress-strain data. The results highlight the benefits of using symbolic regression while also discussing potential challenges.

Complex inference tasks, such as those encountered in Pulsar Timing Array (PTA) data analysis, rely on Bayesian frameworks. The high-dimensional parameter space and the strong interdependencies among astrophysical, pulsar noise, and nuisance parameters introduce significant challenges for efficient learning and robust inference. These challenges are emblematic of broader issues in decision science, where model over-parameterization and prior sensitivity can compromise both computational tractability and the reliability of the results. We address these issues in the framework of hierarchical Bayesian modeling by introducing a reparameterization strategy. Our approach employs Normalizing Flows (NFs) to decorrelate the parameters governing hierarchical priors from those of astrophysical interest. The use of NF-based mappings provides both the flexibility to realize the reparametrization and the tractability to preserve proper probability densities. We further adopt i-nessai, a flow-guided nested sampler, to accelerate exploration of complex posteriors. This unified use of NFs improves statistical robustness and computational efficiency, providing a principled methodology for addressing hierarchical Bayesian inference in PTA analysis.

Pulsar Timing Arrays provide a powerful framework to measure low-frequency gravitational waves, but accuracy and robustness of the results are challenged by complex noise processes that must be accurately modeled. Standard PTA analyses assign fixed uniform noise priors to each pulsar, an approach that can introduce systematic biases when combining the array. To overcome this limitation, we adopt a hierarchical Bayesian modeling strategy in which noise priors are parametrized by higher-level hyperparameters. We further address the challenge posed by the correlations between hyperparameters and physical noise parameters, focusing on those describing red noise and dispersion measure variations. To decorrelate these quantities, we introduce an orthogonal reparametrization of the hierarchical model implemented with Normalizing Flows. We also employ i-nessai, a flow-guided nested sampler, to efficiently explore the resulting higher-dimensional parameter space. We apply our method to a minimal 3-pulsar case study, performing a simultaneous inference of noise and SGWB parameters. Despite the limited dataset, the results consistently show that the hierarchical treatment constrains the noise parameters more tightly and partially alleviates the red-noise-SGWB degeneracy, while the orthogonal reparametrization further enhances parameter independence without affecting the correlations intrinsic to the power-law modeling of the physical processes involved.

Submitted to ApJ ABSTRACT Radiative transfer calculations are essential for modeling planetary atmospheres. However, standard methods are computationally demanding and impose accuracy-speed trade-offs. High computational costs force numerical simplifications in large models (e.g., General Circulation Models) that degrade the accuracy of the simulation. Radiative transfer calculations are an ideal candidate for machine learning emulation: fundamentally, it is a well-defined physical mapping from a static atmospheric profile to the resulting fluxes, and high-fidelity training data can be created from first principles calculations. We developed a radiative transfer emulator using an encoder-only transformer neural network architecture, trained on 1D profiles representative of solar-composition hot Jupiter atmospheres. Our emulator reproduced bolometric two-stream layer fluxes with mean test set errors of 1% compared to the traditional method and achieved speedups of more than 100x. Emulating radiative transfer with machine learning opens up the possibility for faster and more accurate routines within planetary atmospheric models such as GCMs. INTRODUCTION At the heart of almost every computational model of an exoplanet atmosphere lies a radiative transfer routine that determines how radiation is scattered, absorbed, and emitted as it propagates through the atmosphere. These methods are computationally demanding, as they require solutions to integro-differential equations in many distinct wavelength bins.

Modern AI hardware, such as Nvidia's Blackwell architecture, is increasingly embracing low-precision floating-point (FP) formats to handle the pervasive activation outliers in Large Language Models (LLMs). Despite this industry trend, a unified comparison of FP and integer (INT) quantization across varying granularities has been missing, leaving algorithm and hardware co-design without clear guidance. This paper fills that gap by systematically investigating the trade-offs between FP and INT formats. We reveal a critical performance crossover: while FP excels in coarse-grained quantization, the comparison at fine-grained (block-wise) levels is more nuanced. Our comprehensive comparison demonstrates that for popular 8-bit fine-grained formats (e.g., MX with block size 32), MXINT8 is superior to its FP counterpart in both algorithmic accuracy and hardware efficiency. However, for 4-bit formats, FP (e.g., MXFP4, NVFP4) often holds an accuracy advantage , though we show that NVINT4 can surpass NVFP4 when outlier-mitigation techniques like Hadamard rotation are applied. We also introduce a symmetric clipping method that resolves gradient bias in fine-grained low-bit INT training, enabling nearly lossless performance for MXINT8 training. These findings challenge the current hardware trajectory, demonstrating that a one-size-fits-all FP approach is suboptimal and advocating that fine-grained INT formats, particularly MXINT8, offer a better balance of accuracy, power, and efficiency for future AI accelerators.