We study the problem of routing queries to large language models (LLMs) under cost, GPU resources, and concurrency constraints. Prior per-query routing methods often fail to control batch-level cost, especially under non-uniform or adversarial batching. To address this, we propose a batch-level, resource-aware routing framework that jointly optimizes model assignment for each batch while respecting cost and model capacity limits. We further introduce a robust variant that accounts for uncertainty in predicted LLM performance, along with an offline instance allocation procedure that balances quality and throughput across multiple models. Experiments on two multi-task LLM benchmarks show that robustness improves accuracy by 1-14% over non-robust counterparts (depending on the performance estimator), batch-level routing outperforms per-query methods by up to 24% under adversarial batching, and optimized instance allocation yields additional gains of up to 3% compared to a non-optimized allocation, all while strictly controlling cost and GPU resource constraints.

Breiman and Cutler's original Random Forest was designed as a unified ML engine -- not merely an ensemble predictor. Their implementation included classification, regression, unsupervised learning, proximity-based similarity, outlier detection, missing value imputation, and visualization -- capabilities that modern libraries like scikit-learn never implemented. RFX-Fuse (Random Forests X [X=compression] -- Forest Unified Learning and Similarity Engine) delivers Breiman and Cutler's complete vision with native GPU/CPU support. Modern ML pipelines require 5+ separate tools -- XGBoost for prediction, FAISS for similarity, SHAP for explanations, Isolation Forest for outliers, custom code for importance. RFX-Fuse provides a 1 to 2 model object alternative -- a single set of trees grown once. Novel Contributions: (1) Proximity Importance -- native explainable similarity: proximity measures that samples are similar; proximity importance explains why. (2) Dataset-specific imputation validation for general tabular data -- ranking imputation methods by how real the imputed data looks, without ground truth labels.

The pseudo-code of plugging our method into the vanilla BO is summarised in Algorithm 1. Therefore, our method is applicable to any other variants of BO in a plug-in manner. In this section, we present the proofs associated with the theoretical assertions from Section 2. To Lemma 1. Assume the GP employs a stationary kernel Lemma 2. Given Lemma 1, determining Proposition 2. Leveraging Lemma 2, suppose Lemma 3. As per Srinivas et al., the optimization process in BO can be conceptualized as a sampling Pr null |f ( x) µ(x) | ωσ ( x) null > δ, (24) where δ > 0 signifies the confidence level adhered to by the UCB. This lemma is directly from Srinivas et al. . The proof can be found therein. Theorem 1. Leveraging Corollary 1, when employing the termination method proposed in this paper, As discussed in Remark 2 of Section 2.2 in the main manuscript, we suggest initializing L-BFGS Different subplots are (a) our proposed method, (b) Naïve method, (c) Nguyen's method, (d) Lorenz's Different subplots are (a) our proposed method, (b) Naïve method, (c) Nguyen's method, (d) Lorenz's Different subplots are (a) our proposed method, (b) Naïve method, (c) Nguyen's method, (d) Lorenz's Different subplots are (a) our proposed method, (b) Naïve method, (c) Nguyen's method, (d) Lorenz's

Multi-layered distributed representation is believed to be the key ingredient of deep neural networks especially in cognitive tasks like computer vision.

Weempirically assess theimpact oftheseregularization cocktailsforMLPs ina large-scale empirical study comprising 40 tabular datasets and demonstrate that (i) well-regularized plain MLPs significantly outperform recent state-of-the-art specialized neural network architectures, and (ii) they even outperform strong traditionalMLmethods,suchasXGBoost.

Cross-EntrWeuse ylog (f (x)) (1 y) log ( f (x)).

This paper establishes a rigorous theoretical foundation for the function class implicitly learned by XGBoost, bridging the gap between its empirical success and our theoretical understanding. We introduce an infinite-dimensional function class $\mathcal{F}^{d, s}_{\infty-\text{ST}}$ that extends finite ensembles of bounded-depth regression trees, together with a complexity measure $V^{d, s}_{\infty-\text{XGB}}(\cdot)$ that generalizes the $L^1$ regularization penalty used in XGBoost. We show that every optimizer of the XGBoost objective is also an optimizer of an equivalent penalized regression problem over $\mathcal{F}^{d, s}_{\infty-\text{ST}}$ with penalty $V^{d, s}_{\infty-\text{XGB}}(\cdot)$, providing an interpretation of XGBoost as implicitly targeting a broader function class. We also develop a smoothness-based interpretation of $\mathcal{F}^{d, s}_{\infty-\text{ST}}$ and $V^{d, s}_{\infty-\text{XGB}}(\cdot)$ in terms of Hardy--Krause variation. We prove that the least squares estimator over $\{f \in \mathcal{F}^{d, s}_{\infty-\text{ST}}: V^{d, s}_{\infty-\text{XGB}}(f) \le V\}$ achieves a nearly minimax-optimal rate of convergence $n^{-2/3} (\log n)^{4(\min(s, d) - 1)/3}$, thereby avoiding the curse of dimensionality. Our results provide the first rigorous characterization of the function space underlying XGBoost, clarify its connection to classical notions of variation, and identify an important open problem: whether the XGBoost algorithm itself achieves minimax optimality over this class.

In real data, missing values occur frequently, which affects the interpretation with interpretable machine learning (IML) methods. Recent work considers bias and shows that model explanations may differ between imputation methods, while ignoring additional imputation uncertainty and its influence on variance and confidence intervals. We therefore compare the effects of different imputation methods on the confidence interval coverage probabilities of the IML methods permutation feature importance, partial dependence plots and Shapley values. We show that single imputation leads to underestimation of variance and that, in most cases, only multiple imputation is close to nominal coverage.

Modern astronomy has generated an extensive taxonomy of celestial objects based on their physical characteristics and predicted future state. As theories of the development, expansion, history, and predicted future state of the universe rely on identifying and observing celestial bodies, it is essential to have quick and accurate classification of newly observed objects. Historically, classification was performed manually, but the rapid expansion of modern catalogues of celestial objects - such as the Sloan Digital Sky Survey, which grows at a rate of thousands of entries daily [1] - makes this manual classification impractical. Supervised and semi-supervised machine learning represent the most promising candidates for the desired computational classification. Until recently, the data, hardware, and software required for large-scale training and deployment of these methods were unavailable to the general research community. However, improvements to parallel processing hardware have driven increased success and adoption, resulting in the invention of models capable of equaling or surpassing human-level intelligence in tasks formerly considered intractable to computers. Such improvements have been recognized in facial recognition [2] and combinatorial game theory [3], but despite their meteoric rise in popularity, there is a significant gap in astronomical literature on applying machine learning models to the problem of celestial object classification. In an effort to improve this state, we explore a number of machine learning based models for a simplified celestial object classification problem to assess the performance and potential of these models in the field of astronomy.