The Gumbel-Max trick is the basis of many relaxed gradient estimators. These estimators areeasy toimplement and lowvariance, butthegoal ofscaling them comprehensively to large combinatorial distributions is still outstanding. Working within the perturbation model framework, we introduce stochastic softmax tricks, which generalizetheGumbel-Softmax tricktocombinatorial spaces.

Decision trees are popular in survival analysis for their interpretability and ability to model complex relationships. Survival trees, which predict the timing of singular events using censored historical data, are typically built through heuristic approaches. Recently, there has been growing interest in globally optimized trees, where the overall tree is trained by minimizing the error function over all its parameters. We propose a new soft survival tree model (SST), with a soft splitting rule at each branch node, trained via a nonlinear optimization formulation amenable to decomposition. Since SSTs provide for every input vector a specific survival function associated to a single leaf node, they satisfy the conditional computation property and inherit the related benefits. SST and the training formulation combine flexibility with interpretability: any smooth survival function (parametric, semiparametric, or nonparametric) estimated through maximum likelihood can be used, and each leaf node of an SST yields a cluster of distinct survival functions which are associated to the data points routed to it. Numerical experiments on 15 well-known datasets show that SSTs, with parametric and spline-based semiparametric survival functions, trained using an adaptation of the node-based decomposition algorithm proposed by Consolo et al. (2024) for soft regression trees, outperform three benchmark survival trees in terms of four widely-used discrimination and calibration measures. SSTs can also be extended to consider group fairness.

Computer models are indispensable tools for understanding the Earth system. While high-resolution operational models have achieved many successes, they exhibit persistent biases, particularly in simulating extreme events and statistical distributions. In contrast, coarse-grained idealized models isolate fundamental processes and can be precisely calibrated to excel in characterizing specific dynamical and statistical features. However, different models remain siloed by disciplinary boundaries. By leveraging the complementary strengths of models of varying complexity, we develop an explainable AI framework for Earth system emulators. It bridges the model hierarchy through a reconfigured latent data assimilation technique, uniquely suited to exploit the sparse output from the idealized models. The resulting bridging model inherits the high resolution and comprehensive variables of operational models while achieving global accuracy enhancements through targeted improvements from idealized models. Crucially, the mechanism of AI provides a clear rationale for these advancements, moving beyond black-box correction to physically insightful understanding in a computationally efficient framework that enables effective physics-assisted digital twins and uncertainty quantification. We demonstrate its power by significantly correcting biases in CMIP6 simulations of El Niño spatiotemporal patterns, leveraging statistically accurate idealized models. This work also highlights the importance of pushing idealized model development and advancing communication between modeling communities.

The Gumbel-Max trick is the basis of many relaxed gradient estimators. These estimators are easy to implement and low variance, but the goal of scaling them comprehensively to large combinatorial distributions is still outstanding.

Prompt optimization methods have demonstrated significant effectiveness in aligning black-box large language models (LLMs). In parallel, inference scaling strategies such as Best-of-N Sampling and Majority Voting have also proven to enhance alignment and performance by trading off computation. However, existing prompt optimization approaches are inference strategy agnostic; that is, they optimize prompts without regard to the inference strategy employed during deployment. This constitutes a significant methodological gap, as our empirical and theoretical analysis reveals a strong interdependence between these two paradigms. Moreover, we find that user preferences regarding trade-offs among multiple objectives and inference budgets substantially influence the choice of prompt and inference configuration. To address this gap, we introduce a unified novel framework named IAPO (Inference-Aware Prompt Optimization) that jointly optimizes the prompt and inference scale, while being aware of the inference budget and different task objectives. We then develop a fixed-budget training algorithm for IAPO, which we call PSST (Prompt Scaling via Sequential Trimming), and analyze finite-budget guarantees on error probability. Finally, we evaluate the effectiveness of PSST on six different tasks, including multi-objective text generation and reasoning, and demonstrate the critical role of incorporating inference-awareness when aligning black-box LLMs through prompt optimization.

Ranking from noisy comparisons is of great practical interest in machine learning.

In this paper, we present a general framework for ranking sets of arguments in abstract argumentation based on their plausibility of acceptance. We present a generalisation of Dung's extension semantics as extension-ranking semantics, which induce a preorder over the power set of all arguments, allow ing us to state that one set is "closer" to being acceptable than another . To evaluate the extension-ranking semantics, we introduce a number of p rinciples that a well-behaved extension-ranking semantics should satisfy. W e consider several simple base relations, each of which models a single central a spect of argumentative reasoning. The combination of these base relations provides us with a family of extension-ranking semantics. We also adapt a numb er of approaches from the literature for ranking extensions to be us able in the context of extension-ranking semantics, and evaluate their beha viour. Keywords: Abstract Argumentation, Ranking Sets of Objects, Extension-ranking semantics 1. Introduction Formal argumentation [7] is concerned with models of rational decis ion-making based on representations of arguments and their relations.

*Minimal sufficient reasons* represent a prevalent form of explanation - the smallest subset of input features which, when held constant at their corresponding values, ensure that the prediction remains unchanged. Previous *post-hoc* methods attempt to obtain such explanations but face two main limitations: (1) Obtaining these subsets poses a computational challenge, leading most scalable methods to converge towards suboptimal, less meaningful subsets; (2) These methods heavily rely on sampling out-of-distribution input assignments, potentially resulting in counterintuitive behaviors. To tackle these limitations, we propose in this work a self-supervised training approach, which we term *sufficient subset training* (SST). Using SST, we train models to generate concise sufficient reasons for their predictions as an integral part of their output. Our results indicate that our framework produces succinct and faithful subsets substantially more efficiently than competing post-hoc methods, while maintaining comparable predictive performance.

We study image segmentation in the biological domain, particularly trait and part segmentation from specimen images (e.g., butterfly wing stripes or beetle body parts). This is a crucial, fine-grained task that aids in understanding the biology of organisms. The conventional approach involves hand-labeling masks, often for hundreds of images per species, and training a segmentation model to generalize these labels to other images, which can be exceedingly laborious. We present a label-efficient method named Static Segmentation by Tracking (SST). SST is built upon the insight: while specimens of the same species have inherent variations, the traits and parts we aim to segment show up consistently. This motivates us to concatenate specimen images into a ``pseudo-video'' and reframe trait and part segmentation as a tracking problem. Concretely, SST generates masks for unlabeled images by propagating annotated or predicted masks from the ``pseudo-preceding'' images. Powered by Segment Anything Model 2 (SAM~2) initially developed for video segmentation, we show that SST can achieve high-quality trait and part segmentation with merely one labeled image per species -- a breakthrough for analyzing specimen images. We further develop a cycle-consistent loss to fine-tune the model, again using one labeled image. Additionally, we highlight the broader potential of SST, including one-shot instance segmentation on images taken in the wild and trait-based image retrieval.