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Applications · Everything Else

Nicolas Huynh, Mihaela van der Schaar

Inferring continuous probability paths from sparse snapshots is a fundamental challenge in domains like single-cell biology, where high-fidelity data acquisition is often destructive and constrained by prohibitive sequencing costs. This motivates the need for active learning strategies to strategically select optimal measurement times. However, designing active learning policies for this setting remains an open problem: the target objects reside on the infinite dimensional Wasserstein space where standard Euclidean metrics are ill-defined, and current interpolation methods lack epistemic uncertainty quantification. We introduce a framework which extends active experimentation to the space of measures. By leveraging Linearized Optimal Transport (LOT), we map distributional snapshots into a tangent space amenable to Gaussian Process modeling, allowing us to construct a tractable probabilistic surrogate for the underlying probability path. This yields a geometric acquisition function that iteratively selects measurement times to minimize uncertainty. Empirical results demonstrate that our strategy outperforms uncertainty-agnostic baselines on both synthetic and real-world datasets.

Deep Learning · Large Language Models

Sanghyun Lee, Seungryong Kim, Jongho Park, Dongmin Park

Masked Diffusion Models (MDMs) as language models generate by iteratively unmasking tokens, yet their performance crucially depends on the inference-time order of unmasking. Conventional methods such as confidence-based sampling are short-sighted, focusing on local optimization which neglects test-time computation and allows early decoding errors to cascade. We propose Lookahead Unmasking (LookUM), which addresses these concerns by guiding sampling path with a verifier over alternative unmasking orders, without requiring an external reward model. Our framework couples (i) a path generator that proposes paths by sampling from pools of unmasking sets with (ii) a verifier that computes the uncertainty of the proposed paths and performs importance sampling to subsequently select the final paths. Erroneous unmasking inflates sequence-level uncertainty, and our method exploits this to avoid error-prone trajectories. We validate our framework across six benchmarks, such as mathematics, planning, and coding, and demonstrate consistent performance improvements. LookUM requires only two to three paths to achieve peak performance. LLaDA with LookUM matches the performance of RL-tuned LLaDA 1.5 and yields additional gains when applied to LLaDA 1.5, suggesting complementarity with reinforcement learning.

Deep Learning · Large Language Models

Yueyang Wang, Jiawei Fu, Baolong Bi, Xili Wang, Xiaoqing Liu

SWE-bench has emerged as the premier benchmark for evaluating Large Language Models on complex software engineering tasks. While these capabilities are fundamentally acquired during the mid-training phase and subsequently elicited during Supervised Fine-Tuning (SFT), there remains a critical deficit in metrics capable of guiding mid-training effectively. Standard metrics such as Perplexity (PPL) are compromised by the "Long-Context Tax" and exhibit weak correlation with downstream SWE performance. In this paper, we bridge this gap by first introducing a rigorous data filtering strategy. Crucially, we propose the Entropy Compression Hypothesis, redefining intelligence not by scalar Top-1 compression, but by the capacity to structure uncertainty into Entropy-Compressed States of low orders ("reasonable hesitation"). Grounded in this fine-grained entropy analysis, we formulate a novel metric, HE-SNR (High-Entropy Signal-to-Noise Ratio). Validated on industrial-scale Mixture-of-Experts (MoE) models across varying context windows (32K/128K), our approach demonstrates superior robustness and predictive power. This work provides both the theoretical foundation and practical tools for optimizing the latent potential of LLMs in complex engineering domains.

General Machine Learning · Causality

Hugh Dance, Peter Orbanz, Arthur Gretton

Reliable uncertainty quantification for causal effects is crucial in various applications, but remains difficult in nonparametric models, particularly for continuous treatments. We introduce IMPspec, a Gaussian process (GP) framework for modeling uncertainty over interventional causal functions under continuous treatments, which can be represented using reproducing Kernel Hilbert Spaces (RKHSs). By using principled function class expansions and a spectral representation of RKHS features, IMPspec yields tractable training and inference, a spectral algorithm to calibrate posterior credible intervals, and avoids the underfitting and variance collapse pathologies of earlier GP-on-RKHS methods. Across synthetic benchmarks and an application in healthcare, IMPspec delivers state-of-the-art performance in causal uncertainty quantification and downstream causal Bayesian optimization tasks.

Deep Learning · Algorithms

Jihwan Kim, Chenglin Fan

The ski rental problem is a canonical model for online decision-making under uncertainty, capturing the fundamental trade-off between repeated rental costs and a one-time purchase. While classical algorithms focus on worst-case competitive ratios and recent ``learning-augmented'' methods leverage point-estimate predictions, neither approach fully exploits the richness of full distributional predictions while maintaining rigorous robustness guarantees. We address this gap by introducing algorithms that systematically integrate distributional predictions into both deterministic and randomized algorithms. For the deterministic setting, we formalize the problem under perfect distributional prediction and derive an efficient algorithm to compute the optimal threshold-buy day. We provide a rigorous performance analysis, identifying sufficient conditions on the predicted distribution under which the expected competitive ratio (ECR) matches the classic optimal randomized bound. To handle imperfect predictions, we propose the Clamp Policy, which restricts the buying threshold to a safe range controlled by a tunable parameter. We show that this policy is both robust, maintaining good performance even with large prediction errors, and consistent, approaching the optimal performance as predictions become accurate. For the randomized setting, we characterize the stopping distribution via a Water-Filling Algorithm, which optimizes expected cost while strictly satisfying robustness constraints. Experimental results across diverse distributions (Gaussian, geometric, and bi-modal) demonstrate that our framework improves consistency by significantly over existing point-prediction baselines while maintaining comparable robustness.

Applications · Time Series

Jiayu Fang, Xuande Liu, Sangsha Fang, Zhen Tian, Hongwei Ma, Zhiqi Shao, Junbin Gao

Time series forecasting fundamentally involves learning probability distributions over future observations. However, existing loss functions rely on point-wise Euclidean metrics, neglecting the intrinsic geometric structure of probability distributions. This leads to suboptimal alignment between predicted and true distributions, particularly for uncertainty quantification. We propose InfoGeo Loss, a principled loss function grounded in information geometry that measures distributional discrepancies on statistical manifolds. Our approach comprises three key components: (1) a distribution parameterization module that models predictions with learnable sufficient statistics, (2) a Fisher information metric that quantifies intrinsic distributional distance, and (3) a Bregman divergence component that captures asymmetric prediction errors. We further introduce a natural gradient weighting strategy for efficient optimization on statistical manifolds. Theoretically, we prove statistical consistency and establish convergence guarantees. Extensive experiments on seven datasets with five architectures show that InfoGeo Loss consistently outperforms existing losses, achieving average improvements of 6.8% in MSE and 5.3% in MAE.

Theory · Game Theory

Matteo Bollini, Matteo Castiglioni, Alberto Marchesi

*Hidden-action principal-agent problems* model scenarios in which a principal induces an agent to take a costly and *unobservable* action through the provision of outcome-dependent payments. These problems find application in a variety of real-world settings, such as crowdsourcing, online labor platforms, and machine learning task delegation. Recently, much of the literature has focused on how to handle the principal’s *uncertainty* about the agent and the surrounding environment, which is often the main challenge in practice. One prominent approach is to adopt an *online learning* framework, where the principal repeatedly interacts with the agent to learn optimal payments from experience. However, existing learning algorithms, while achieving regret that scales sublinearly in the number of interaction rounds $T$, typically suffer from an exponential dependence on the size of the problem instance. In this paper, we show that this problematic exponential growth can be avoided by assuming that the principal has knowledge of a set of possible actions of the agent, while remaining unaware of which actions are actually available---an assumption that is reasonable in many real-world settings.

Applications · Computer Vision

Jun Li, Peifeng Lai, Xuhang Lou, Jinpeng Wang, Yuting Wang, Ke Chen, Yaowei Wang, Shutao Xia

Partially relevant video retrieval aims to retrieve untrimmed videos using text queries that describe only partial content. However, the inherent asymmetry between brief queries and rich video content inevitably introduces uncertainty into the retrieval process. In this setting, vague queries often induce semantic ambiguity across videos, a challenge that is further exacerbated by the sparse temporal supervision within videos, which fails to provide sufficient matching evidence. To address this, we propose Holmes, a hierarchical evidential learning framework that aggregates multi-granular cross-modal evidence to quantify and model uncertainty explicitly. At the inter-video level, similarity scores are interpreted as evidential support and modeled via a Dirichlet distribution. Based on the proposed three-fold principle, we perform fine-grained query identification, which then guides query-adaptive calibrated learning. At the intra-video level, to accumulate denser evidence, we formulate a soft query-clip alignment via flexible optimal transport with an adaptive dustbin, which alleviates sparse temporal supervision while suppressing spurious local responses. Extensive experiments demonstrate that Holmes outperforms state-of-the-art methods. Code is released at https://anonymous.4open.science/r/ICML26-Holmes-E77B/

Deep Learning · Large Language Models

Jinhao Duan, Zicheng Liu, Zijie Liu, Kaidi Xu, Tianlong Chen

Humans express uncertainty verbally via markers (e.g., "possible", "likely"), yet most LLM uncertainty quantification (UQ) relies on costing likelihood- or consistency-based signals. From a cognitive perspective, accurate verbal uncertainty reflects metacognitive monitoring, representing knowledge boundaries ("knowing that you don't know") to support regulation and information seeking. In this paper, we investigate: How LLMs diverge from humans in verbal uncertainty quantification? Can verbal markers reliably quantify LLM uncertainty? We curate a corpus of human uncertainty markers from psychology and decision-science literature and benchmark LLMs against it. We observe that LLMs encode verbal uncertainty with numerical levels that differ substantially from those of humans. We then introduce VOCAL, a novel optimization-based algorithm that learns an optimal uncertainty profile over uncertainty markers directly from LLM outputs. By fitting a marker–uncertainty mapping to best explain empirical correctness, VOCALdiscovers how much probability mass each verbal marker should convey, rather than estimating uncertainty via repeated sampling. VOCAL enables a direct, marker-level comparison of confidence semantics between humans and LLMs, disentangling mismatch and revealing systematic confidence disparities in verbal expressions.

Deep Learning · Large Language Models

Zhi-Ping Liu, Simiao Li, Wei Li, Hanting Chen, Jie Hu, Hua-Lei Yin, Xinghao Chen

Existing Cross-Tokenizer Knowledge Distillation (CTKD) methods fail to outperform simple supervised fine-tuning when vocabulary overlap is low due to severe alignment noise. We identify this phenomenon as the **``Low-Overlap negative transfer regime,''** To overcome this, we propose **Entropy-aware Span-Constrained Optimal Transport (E-SCOT)**, a robust framework that treats distillation as a sparse transport problem with a vocabulary-agnostic ground metric. Unlike prior OT approaches that incur quadratic costs via dense optimization, E-SCOT employs span-anchored lexical alignment to construct a deterministic, locality-preserving coupling in linear time. Furthermore, we introduce R\'enyi-entropy adaptive reweighting to dynamically concentrate the distillation budget on informative positions exhibiting significant uncertainty-profile gaps. Extensive experiments demonstrate that E-SCOT achieves state-of-the-art performance across diverse model families, effectively eliminating negative transfer even in challenging low-overlap scenarios.

Deep Learning · Generative Models and Autoencoders

Chenyang Xu, Dezhen Wang, Lin Chen, Kepeng Lin, Hao Wang

Accelerating diffusion models via feature caching has evolved from static reuse to polynomial extrapolation, yet current "cache-then-forecast" strategies remain limited by rigid, hand-crafted approximation families (e.g., Taylor or Hermite bases) that often misalign with the complex, layer-specific non-stationarity of generative feature dynamics. This paper introduces EigenCache, a theoretically grounded framework that re-frames acceleration as a problem of covariance learning and experimental design. By modeling feature trajectories as time-indexed stochastic processes governed by learnable temporal kernels, we demonstrate that the statistically optimal feature predictor (Minimum Mean Squared Error) is the Gaussian Process posterior mean (Kriging), which strictly generalizes and outperforms previous fixed-basis expansions. Crucially, this probabilistic formulation couples prediction with uncertainty quantification via a closed-form variance certificate. Leveraging this, we derive an information-theoretic scheduling algorithm that selects computation anchors by maximizing the log-determinant of the posterior covariance—a submodular objective that admits a provably near-optimal greedy solution. EigenCache thus provides a unified, training-free foundation for efficient inference, offering not only superior reconstruction accuracy but also a rigorous mechanism for robust, uncertainty-aware compute allocation.

Reinforcement Learning · Inverse

Lionel Blondé, Joao A. Candido Ramos, Alexandros Kalousis

We consider imitation learning in the low-data regime, where only a limited number of expert demonstrations are available. In this setting, methods that rely on large-scale pretraining or high-capacity architectures can be difficult to apply, and efficiency with respect to demonstration data becomes critical. We introduce Noise-Guided Transport (NGT), a lightweight off-policy method that casts imitation as an optimal transport problem solved via adversarial training. NGT requires no pretraining or specialized architectures, incorporates uncertainty estimation by design, and is easy to implement and tune. Despite its simplicity, NGT achieves strong performance on challenging continuous control tasks, including high-dimensional Humanoid tasks, under ultra-low data regimes with as few as 20 transitions.

Deep Learning · Large Language Models

Yuejun Jiao, Jun Xia, Yanxin Yang, Yonghao Yang, Hao Shen, Mingsong Chen

Automatic Prompt Optimization (APO) enables Large Language Models (LLMs) to adapt to specific tasks while minimizing manual engineering costs. However, since existing APO approaches either rely solely on multi-round iterative procedures or use model-specific generators tailored to optimizing prompts for a single model and objective, they are not readily applicable to auto-routing scenarios, which require operating over diverse LLMs and juggling multiple, often competing, trade-offs. To address this issue, we propose TAMPO, a novel task- and model-aware APO framework for auto-routing in LLM-based systems. Specifically, to reflect performance variation across a broad range of tasks and models, we construct a comprehensive heterogeneity-aware dataset for training an uncertainty-aware reward model. Serving as an offline proxy, this reward model can greatly mitigate reward hacking, allowing TAMPO to learn an optimal multi-objective conditional policy for robust prompt generation. Based on the user requirements encoded in our defined preference vector, this policy enables flexible control over prompt generation, supporting a cost-effective deployment strategy. Extensive experiments across 86 tasks demonstrate that TAMPO effectively maintains performance stability across diverse tasks and models, providing a robust, controllable solution for auto-routing in various LLM-based systems.

Deep Learning · Large Language Models

Haorui Wang, Parshin Shojaee, Kazem Meidani, Kunyang Sun, Jose Miguel Hernandez-Lobato, Teresa Head-Gordon, Jiajun He, Chandan Reddy, Chao Zhang, Yuanqi Du

Large language models are increasingly used to accelerate scientific discovery, especially in iteratively searching scientific hypotheses. Yet in many discovery settings the goal is not to identify a single ``best'' hypothesis: validation is noisy and expensive, multiple hypotheses can remain plausible, and scientists benefit from a set of high-quality but meaningfully diverse hypotheses that hedge against downstream uncertainty. Nevertheless, commonly used evolutionary search recipes tend to underemphasize this requirement, implicitly prioritizing optimization over exploration, and the resulting selection pressure during the search process leads to diversity collapse. Motivated by these limitations, we formulate hypothesis search as a sampling problem, where the objective is to efficiently produce diverse, high-quality hypotheses under fixed validation budget. Building on this perspective, we propose, EvoDiverse, an evolutionary framework inspired by the classical parallel tempering algorithm that searches hypotheses at multiple temperature levels and enables principled information exchange across temperatures to improve exploration without disrupting convergence. Across domains including molecular discovery, equation discovery, and algorithm discovery, our approach consistently improves both hypothesis quality and diversity under the same validation budget, and produces candidate sets that remain robust under more expensive downstream computational validations.

Deep Learning · Robustness

Yu Zhu

Real-world data is rarely clean; it is plagued by severe class imbalance (long-tailed distributions) and label corruption. Current solutions lean heavily on ''black-box" meta-learning to re-weight samples. However, this paradigm introduces a fatal circular dependency: it relies on pristine, balanced validation sets to guide the optimization, which are essentially non-existent in the wild. We propose ProMeCD, a self-referential framework that breaks this dependency by recasting optimization as an autonomous control problem. Instead of training an opaque neural meta-learner, we employ a transparent proportional-integral controller. The system monitors ''cognitive entropy'' that is a metric derived from von Mises-Fisher gradient statistics to assess learning uncertainty. To resolve the scalar ambiguity between tail and noisy samples, ProMeCD employs a decoupled control strategy: it boosts tail classes via integral accumulation of magnitude deficits when directional consistency is high, while suppressing noise via proportional feedback when consistency collapses. Theoretically, we prove that this mechanism guarantees convergence and formally prevents the minority initial drop, ensuring monotonic improvement for rare classes. Crucially, ProMeCD is fully white-box and validation-free. Experiments on CIFAR-LT, iNaturalist, CIFAR-N, and mini WebVision confirm that ProMeCD is not merely efficient; it outperforms the recent meta-learner FMW-Net by over 10\% in severe imbalance settings, proving that explicit control theory offers a superior path to handling imperfect data.

Applications · Computer Vision

Luke Miller, Yugyung Lee

Segmenting small and sparse structures in large-scale images is fundamentally constrained by pixel-level, lattice-bound computation and extreme class imbalance--dense, full-resolution inference scales poorly and forces most pipelines to rely on fixed regionization or downsampling, coupling computational cost to image resolution and attenuating boundary evidence precisely where minority structures are most informative. We introduce **SEMIR** (*Semantic Minor-Induced Representation Learning*), a representation framework that decouples inference from the native grid by learning a task-adapted inference space. **SEMIR** transforms the underlying grid graph into a compact, boundary-aligned graph minor through parameterized edge contraction, node deletion, and edge deletion, while preserving an exact lifting map from minor predictions to lattice labels. Minor construction is formalized as a few-shot optimization problem that replaces hand-tuned preprocessing with a *boundary-alignment objective*: minor parameters are learned by maximizing agreement between predicted boundary elements and class-agnostic semantic edges under a *boundary Dice criterion*, and the induced minor is annotated with scale- and rotation-robust geometric and intensity descriptors and supports efficient region-level inference via message passing on a graph neural network (GNN) with relational edge features. We benchmark **SEMIR** on three tumor segmentation datasets—**BraTS2021**, **KiTS2023**, and **LiTS2017**—where targets exhibit high structural variability and distributional uncertainty, providing a stringent testbed for *structure-adaptive inference*. **SEMIR** yields consistent improvements in *minority-structure Dice* at practical runtime, positioning *minor-induced representations* as a principled alternative to pixel-centric segmentation in challenging, high-variability visual domains.

General Machine Learning · Unsupervised and Semi-supervised Learning

Ran Eisenberg, Ofir Lindenbaum

Many learning problems require uncovering a hidden ordering that reveals structure in unordered data, such as monotonicity in sorting or spatial continuity in jigsaw reconstruction. In these settings, permutations can be learned as latent operators by optimizing objectives defined directly on the reordered output, often without access to ground-truth orderings. Differentiable relaxations such as Gumbel–Sinkhorn make this approach practical by approximating permutation matrices with doubly stochastic matrices. However, learning from structure without supervision induces a non-uniform uncertainty: some assignments become confident early, while others remain ambiguous. Existing methods control this process using a single global temperature, forcing all assignments to sharpen or diffuse simultaneously and leading to instability at scale. We introduce an entropy-adaptive formulation of Gumbel–Sinkhorn that locally modulates temperature based on assignment uncertainty. This allows confident assignments to discretize early while preserving exploration where uncertainty remains. Across sorting and jigsaw reconstruction tasks and in routing-style settings, adaptive entropy control improves training stability and final permutation quality relative to fixed-temperature baselines, particularly as problem size and assignment ambiguity increase.

Deep Learning · Large Language Models

Tim Tomov, Dominik Fuchsgruber, Stephan Günnemann

In many applications of LLMs, natural language responses often have an underlying structure such as representing discrete labels, numerical values, or graphs. Yet, existing decoding and uncertainty estimation methods operate only in language space and largely disregard structural information. We address this by modeling LLM outputs directly in a task-dependent latent structure. By equipping this structure with a dissimilarity measure, we can compute Bayes-optimal responses. These are not selected from sampled generations but are newly synthesized by combining individual responses in the latent space. Across different tasks, Bayes-optimal responses consistently outperform standard decoding methods like beam search. Moreover, quantifying uncertainty via the induced Bayesian risk captures variations in terms of the latent structure and improves alignment with output quality and correctness. Our decision-theoretic framework is applicable to any problem that admits a latent response structure and enables reliable task-aware LLM predictions.

Deep Learning · Large Language Models

Wenbo Zhang, Lijinghua Zhang, Liner Xiang, Hengrui Cai

Reasoning-capable large language models (LLMs) have recently been adopted as automated judges, but their benefits and costs in LLM-as-a-Judge settings remain unclear. Through controlled comparisons between reasoning and non-reasoning judges, we show that explicit reasoning substantially improves judgment accuracy on tasks requiring structured verification (e.g., math and coding), while offering limited or even negative gains on simpler evaluations and incurring significantly higher computational cost. These findings motivate that reasoning should be used selectively rather than universally, with awareness of possible distribution shift. We propose a Robust Adaptive Cost-Efficient Router (RACER), which dynamically selects between reasoning and non-reasoning judges under a fixed budget by formulating routing as a constrained distributionally robust optimization problem. RACER explicitly accounts for distribution shift via a KL-divergence uncertainty set, admits an efficient primal–dual algorithm, and enjoys theoretical guarantees including uniqueness of the optimal policy and linear convergence. Extensive experiments show that RACER achieves superior accuracy–cost trade-offs under distribution shift.

Zihan Zhu, Shayan Kiyani, George Pappas, Hamed Hassani

Reliable decision making pipelines powered by machine learning models require uncertainty quantification (UQ) methods that come with explicit safety guarantees. Conformal prediction provides such UQ by wrapping ML predictions into prediction sets, and recent work by \cite{kiyani2025decision} established that these sets can be translated into optimal risk-averse decision policies—yet only inheriting marginal safety guarantees. We generalize and strengthen their results by (i) introducing action-conditional conformal prediction, which yields safety guarantees conditioned explicitly on each action taken by the decision maker, (ii) showing that action-conditional prediction sets serve as a proxy for the feasible decision space for risk-averse decision makers aiming to optimize action-conditional value-at-risk, and (iii) proposing a principled finite-sample algorithm based on pinball-loss minimization, connecting the framework of \cite{gibbs2025conformal} to action-conditional guarantees. Experiments on two real-world datasets confirm that our approach significantly improves action-conditional performance over several conformal baselines.