ICML 2026 Papers

Pre-propagation graph neural networks (PP-GNNs) decouple node feature propagation from transformation: graph diffusion is performed once as preprocessing, and training reduces to dense per-node transformations. This design enables mini-batch training without inter-node dependencies, avoids repeated sparse matrix--matrix multiplications, and better matches modern accelerators optimized for dense compute. However, their expressivity remains unclear, and empirical results show a gap between PP-GNNs and their message-passing counterparts on commonly used graph benchmarks, especially heterophilic ones. In this paper, we propose a suite of robust graph diffusion operators for preprocessing and a few-shot hidden-state re-propagation scheme during training. Our methods improve the validation and test accuracy of PP-GNNs, enabling them to match the accuracy of message-passing GNNs while maintaining training efficiency.

Innovation is a key driving force of human civilization. As the body of knowledge has grown considerably, bridging knowledge across different disciplines, where significant innovation often emerges, has become increasingly challenging. The recent advancements in machine learning models, particularly Large Language Models (LLMs), have provided effective access to extensive knowledge sources and shown impressive abilities in reasoning, rendering significant opportunities for interdisciplinary discovery. Our research aims to understand the capabilities of state-of-the-art LLMs in integrating knowledge from different fields for interdisciplinary research (IDR). To address this fundamental problem, we introduce IDRBench, a pioneering framework that includes both datasets and evaluation tasks: (1) IDR Paper Identification, (2) IDR Idea Integration, and (3) IDR Idea Recommendation. Our study on ten mainstream LLMs provides a comprehensive analysis of their behavior and establishes benchmarks and baselines for future research. To the best of our knowledge, IDRBench is the first to provide a comprehensive investigation of LLMs' IDR capability.

Evaluating large language models (LLMs) typically requires thousands of benchmark items, making the process expensive, slow, and increasingly impractical at scale. Existing evaluation protocols rely on average accuracy over fixed item sets, treating all items as equally informative despite substantial variation in difficulty and discrimination. We introduce ATLAS, an adaptive testing framework based on Item Response Theory (IRT) that estimates model ability using Fisher information–guided item selection. ATLAS reduces the number of required items by up to 90% while maintaining measurement precision. For instance, it matches whole-bank ability estimates using only 41 items (0.157 MAE) on HellaSwag (5,600 items). We further reconstruct accuracy from ATLAS's ability estimates and find that reconstructed accuracies closely match raw accuracies across all five benchmarks, indicating that ability preserves the global performance structure. At the same time, provides finer discrimination within accuracy-equivalent models: among more than 3,000 evaluated models, 23--31% shift by more than 10 rank positions, and models with identical accuracies receive meaningfully different ability estimates. Code and calibrated item banks available at https://github.com/Peiyu-Georgia-Li/ATLAS.

Generalization in generative modeling is defined as the ability to learn an underlying distribution from a finite dataset and produce novel samples, with evaluation largely driven by held-out performance and perceived sample quality. In practice, training is often stopped at the minimum of the test loss, taken as an operational indicator of generalization. We challenge this viewpoint by identifying a phase of *biased generalization* during training, in which the model continues to decrease the test loss while favoring samples with anomalously high proximity to training data. By training the same network on two disjoint datasets and comparing the mutual distances of generated samples and their similarity to training data, we introduce a quantitative measure of bias and demonstrate its presence on real images. We then study the mechanism of bias, using a controlled hierarchical data model where access to exact scores and ground-truth statistics allows us to precisely characterize its onset. We attribute this phenomenon to the sequential nature of feature learning in deep networks, where coarse structure is learned early in a data-independent manner, while finer features are resolved later in a way that increasingly depends on individual training samples. Our results show that early stopping at the test loss minimum, while optimal under standard generalization criteria, may be insufficient for privacy-critical applications.

Machine learning model performance arises from competition and application. For deployment, we consider the prescriptive scaling laws: given a pre-training compute budget, what downstream accuracy is attainable with contemporary post-training practice, and how stable is that mapping as the field evolves? Using large-scale observational evaluations with 5k observational and 2k newly sampled data on model performance, we estimate capability boundaries—high conditional quantiles of benchmark scores as a function of log pre-training FLOPs, via smoothed quantile regression with a monotone, saturating sigmoid parameterization. We validate the temporal reliability by fitting on earlier model generations and evaluating on later releases. Across various tasks, the estimated boundaries are mostly stable, with the exception of math reasoning that exhibits a consistently advancing boundary over time. We then extend our approach to analyze task-dependent saturation and to probe contamination-related shifts on math reasoning tasks. Finally, we introduce an efficient algorithm that recovers near-full-data frontiers using roughly 20% of evaluation budget. Together, our work releases the Proteus-2k, the latest model performance evaluation dataset, and introduces a practical methodology for translating compute budgets into reliable performance expectations and for monitoring when capability boundaries move.

Operations Research practitioners debug infeasible models through an iterative process: inspecting Irreducible Infeasible Subsystems (\textbf{IIS}), identifying constraint conflicts, and repairing formulations until feasibility is restored. Existing LLM benchmarks mostly treat OR as one-shot translation from problem descriptions to solver code, omitting this diagnostic loop. We formalize infeasible-model repair as a solver-in-the-loop Markov Decision Process in which each action triggers solver re-execution and \textbf{IIS} recomputation, yielding deterministic, verifiable feedback. We introduce \textbf{ORLoopBench}, a benchmark suite with two components: \textbf{ORDebug} releases 5,362 LP/MILP repair instances, while \textbf{ORBias} evaluates closed-form operational decision rationality across inventory settings. Solver-verified RLVR training enables an 8B model to surpass frontier APIs on LP repair (95.3\% vs 92.4\% RR@5), improves diagnostic behavior, and transfers to MILP repair. The same evaluation exposes semantic drift in whole-model code regeneration: feasible regenerated MILPs can solve the wrong problem. Process-level evaluation with solver oracles enables targeted training for reliable OR self-correction.

Multimodal geometry reasoning requires models to jointly understand visual diagrams and perform structured symbolic inference, yet current vision--language models struggle with complex geometric constructions due to limited training data and weak visual--symbolic alignment. We propose a pipeline for synthesizing complex multimodal geometry problems from scratch and construct a dataset named \textbf{GeoCode}, which decouples problem generation into symbolic seed construction, grounded instantiation with verification, and code-based diagram rendering, ensuring consistency across structure, text, reasoning, and images. Leveraging the plotting code provided in GeoCode, we further introduce code prediction as an explicit alignment objective, transforming visual understanding into a supervised structured prediction task. GeoCode exhibits substantially higher structural complexity and reasoning difficulty than existing benchmarks, while maintaining mathematical correctness through multi-stage validation. Extensive experiments show that models trained on GeoCode achieve consistent improvements on multiple geometry benchmarks, demonstrating both the effectiveness of the dataset and the proposed alignment strategy.

Irregular Multivariate Time Series (IMTS) are common in practice, yet their irregular sampling complicates effective modeling. Existing approaches typically either (i) design specialized architectures that limit the reuse of proven Multivariate Time Series (MTS) models, or (ii) map IMTS onto regular temporal grids through interpolation, which may distort temporal dynamics by introducing artificial values. To address these limitations, we propose a new input-embedding-based approach. We identify that the key bottleneck lies not in the backbone architecture, but in conventional embedding layers that assume uniform sampling. In this work, we introduce QuITE (Query-Based Irregular Time Series Embedding), a simple yet effective plug-and-play embedding module for IMTS. QuITE employs learnable query tokens to aggregate irregular observations through a single self-attention layer, directly producing backbone-compatible latent representations without artificial value generation or architectural modification. Extensive experiments on real-world benchmarks show that QuITE consistently improves MTS models, yielding average relative gains of up to 54.7% in forecasting and 15.8% in classification across diverse datasets and backbone architectures.

Recent interpretability methods have proposed to translate LLM internal representations into natural language descriptions using a second *verbalizer* LLM. This is intended to illuminate how the target model represents and operates on inputs. But do such *activation verbalization* approaches actually provide *privileged* knowledge about the internal workings of the target model, or do they merely convey information about the inputs provided to it? We critically evaluate popular verbalization methods and datasets used in prior work and find that one can perform well on such benchmarks without access to target model internals, suggesting that these datasets are not ideal for evaluating verbalization methods. We then run controlled experiments which reveal that verbalizations often reflect the parametric knowledge of the verbalizer LLM that generated them, rather than the knowledge of the target LLM whose activations are decoded. Taken together, our results indicate a need for targeted benchmarks and experimental controls to rigorously assess whether verbalization methods provide meaningful insights into the operations of LLMs.

Dataset pruning (DP) and dataset distillation (DD) fundamentally differ in their outputs: DP selects original image subsets, while DD generates synthetic images. Recently, DD's increasing reliance on original images suggests a convergence of the two directions. To investigate this convergence trend, we propose a unified dataset compression (DC) benchmark. This benchmark reveals an interesting trade-off for soft-label-DD: while soft labels provide valuable information, they can make the distillation process less essential, as distilled images may not always outperform random subsets. In addition, the benchmark reveals that in current stages, dataset pruning outperforms dataset distillation at small dataset sizes. Given these observations, we explore hard-label-DC as a complementary approach that emphasizes image quality while offering substantial storage efficiency. Our PCA (Prune, Combine, and Augment) is the first framework that does not rely on soft labels but instead focuses on image quality. (1) "P'' means selecting easy samples based on dataset pruning metrics, (2) "C'' indicates combining these samples effectively, and (3) "A'' is to apply constrained image augmentation during training.

The attention mechanism in a Transformer architecture matches key to query based on both content—the what—and position in a sequence—the where. We present an analysis indicating that what and where are entangled in the popular rotary position embedding (RoPE). This entanglement can impair performance particularly when decisions require independent matches on these two factors. We propose an improvement to RoPE, which we call Polar Coordinate Position Embedding or PoPE, that eliminates the what-where confound. PoPE is far superior on a diagnostic task requiring indexing solely by position or by content. On autoregressive sequence modeling in music, genomic, and natural language domains, Transformers using PoPE as the positional encoding scheme outperform baselines using RoPE with respect to evaluation loss (perplexity) and downstream task performance. On language modeling, these gains persist across model scale, from 124M to 774M parameters. Crucially, PoPE shows strong zero-shot length extrapolation capabilities compared not only to RoPE but even a method designed for extrapolation, YaRN, which requires additional fine tuning and frequency interpolation.

Language Identification (LID) is an important component of many multilingual natural language processing pipelines, where it facilitates corpus curation, training data analysis, and cross-lingual evaluation of large language models. Despite near- perfect performance on high-resource languages, existing systems remain brittle in low-resource and closely related language settings. We introduce UniLID, a simple and efficient LID method based on the UnigramLM tokenization algorithm, leveraging its probabilistic framing, parameter estimation technique and inference strategy. In short, to predict a string’s language label, we simply ask: under which language’s unigram distribution is this string most likely? Our formulation is data- and compute-efficient, supports incremental addition of new languages without retraining existing models, and can naturally be integrated into existing language model tokenization pipelines. Empirical evaluations against widely used baselines, including fastText, GlotLID-M, and CLD3, show that UniLID achieves competitive performance on standard benchmarks, substantially improves sample efficiency in low-resource settings—surpassing 70% accuracy with as few as five labeled samples per language—and delivers large gains on fine-grained dialect identification.

Large language models (LLMs) must balance diversity and creativity against logical coherence in open-ended generation. Existing truncation-based samplers are effective but largely heuristic, relying mainly on probability mass and entropy while ignoring semantic geometry of the token space. We present Top-$W$, a geometry-aware truncation rule that uses Wasserstein distance—defined over token-embedding geometry—to keep the cropped distribution close to the original, while explicitly balancing retained probability mass against the entropy of the kept set. Our theory yields a simple closed-form structure for the fixed-potential subset update: depending on the mass–entropy trade-off, the optimal crop either collapses to a single token or takes the form of a one-dimensional prefix that can be found efficiently with a linear scan. We implement Top-$W$ using efficient geometry-based potentials (nearest-set or $k$-NN) and pair it with an alternating decoding routine that keeps the standard truncation-and-sampling interface unchanged. Extensive experiments on four benchmarks (GSM8K, GPQA, AlpacaEval, and MT-Bench) across three instruction-tuned models show that Top-$W$ consistently outperforms prior state-of-the-art decoding approaches achieving up to 33.7 percentage improvement. Moreover, we find that Top-$W$ not only improves accuracy-focused performance, but also boosts creativity under judge-based open-ended evaluation.

The robustness of synchronization is typically characterized by scalar, per-node stability indices whose dependence on topology is studied via network science or graph neural networks (GNNs). We propose a novel upstream task, stability landscapes, which provide deeper insights into synchronization behavior and from which many such scalar indices can be derived. Crucially, we pioneer a graph-to-image prediction paradigm: learning image-like landscapes as per-node targets directly from graph topology, a formulation we are not aware of having been established elsewhere in the literature. To support this task, we release two datasets of 10,000 graphs each at 20 and 100 nodes with per-node landscape labels, based on a conceptual oscillator model, capturing power grid synchronization behavior. A GNN encodes topology and a CNN decoder renders per-node images, learned end-to-end with good in-distribution accuracy, generalizing across graph sizes and to realistic power grid topologies. This demonstrates that stability landscapes, while beyond the reach of conventional network science, are learnable from topology and open new avenues for moving beyond scalar stability indices in biology, neuroscience, and power grids.

Large Language Models (LLMs) can propose natural-language rules, circumventing the reliance on a predefined predicate space in traditional rule learning. However, existing LLM-based methods often neglect the global interactions among rules, and the potential of using fine-grained rule importance scores to calibrate neuro-symbolic reasoning remains underexplored. To address this gap, we introduce RLIE, a framework that integrates LLMs with probabilistic modeling to learn weighted rule sets in four stages: (1) Rule generation: proposing and filtering candidate rules via LLMs; (2) Logistic regression: learning sparse, calibrated weights for global rule selection; (3) Iterative refinement: revising the rule set with error-driven hard examples; and (4) Evaluation: validating the learned system via comparative inference paradigms. Across multiple real-world datasets and LLM backbones, our learned weighted rules achieve superior stability and accuracy, whereas rule-injection prompting yields mixed results and often degrades performance. These results suggest LLMs excel at semantic rule discovery but are less reliable at controlled probabilistic aggregation. Our findings highlight both the promise and the limits of LLMs for inductive reasoning, motivating a principled integration with classic probabilistic rule combination for reliable neuro-symbolic reasoning.

The remarkable capabilities of large language models (LLMs) are often undermined by their instability. Even subtle and semantically irrelevant changes in prompts can cause dramatic fluctuations in performance, a phenomenon known as prompt sensitivity. Previous studies typically evaluate prompt sensitivity by comparing the LLM's final outputs when prompts change. However, such coarse-grained metrics fail to explain the internal reasons for prompt sensitivity. In this paper, we introduce interactions as a fine-grained tool to analyze prompt sensitivity of LLMs. Specifically, we decompose the output score of the LLM into a set of interactions. Each interaction represents a nonlinear relationship involving a set of input variables. We discover that subtle changes to prompts can trigger severe instability in interactions, even when the outputs of the LLM remain the same. To this end, we propose an Interaction-based Prompt Sensitivity (IPS) metric by quantifying changes in interactions when we introduce subtle changes to prompts. We apply the IPS metric to 50 open-source LLMs and uncover four factors that reduce the prompt sensitivity of LLMs, including supervised fine-tuning, increased model scales, dense architectures, and few-shot learning. More crucially, we discover a common mechanism by which these four factors reduce prompt sensitivity: all four factors tend to reduce the prompt sensitivity of low-order interactions (i.e., interactions involving few input variables).

Data selection has emerged as a crucial downstream application of data valuation, yet the theoretical foundations for using data values in selection remain underexplored. We reformulate data selection as a sequential decision-making problem where the optimal selection sequence arises from dynamic programming, and data values can be understood as encodings of this optimal sequence. This framework unifies and reinterprets existing methods like Data Shapley through the lens of approximate dynamic programming, revealing them as myopic linear approximations to the sequential problem. We further analyze how selection optimality degrades with utility curvature under submodularity, explaining when and why these approximations fail. To bridge theory and practice, we propose an efficient bipartite graph-based surrogate that preserves submodular structure while enabling scalable greedy selection with provable guarantees. Experiments on classical ML benchmarks and large-scale LLM fine-tuning data selection demonstrate substantial improvements over existing methods. Code is publicly available at https://github.com/frankhlchi/SeqDataVal

The advancement of Large Language Models (LLMs) into higher-level reasoning domains has rendered traditional heuristic evaluators insufficient for long-form open-ended responses, precipitating the widespread adoption of rubric-based benchmarks. While these frameworks utilize expert-curated criteria and LLM-as-a-judge to assess open-ended generation, the intrinsic robustness of these evaluation harnesses to fundamental validity assessments remains critically under-investigated. To bridge this gap, we introduce RubricRobustness, a systematic sensitivity analysis framework that subjects these benchmarks to three common sense perturbations: *semantic negation*, *stochastic deletion* and *irrelevant addition*. We investigate the extent to which manipulating the semantic veracity of a model's response impacts its resulting score by applying the robustness framework to two of the most popular rubrics-based benchmarks: HealthBench and WildBench. Our findings reveal systematic vulnerabilities: while both benchmarks respond sharply to semantic negation (e.g., degradation slopes of approximately $-0.38$ on HealthBench and $-0.55$ on WildBench), they are substantially less responsive to irrelevant addition, often requiring over 35% of sentences to be perturbed before inducing even a 25% score drop. We argue that perturbation-based sensitivity analyses of this form are a necessary prerequisite for validating rubric coverage, ensuring that automated evaluation frameworks reliably penalize basic semantic failures. We will release our framework as an open-source tool for building more resilient benchmarks.

Time series imputation benefits from leveraging cross-feature correlations, yet existing attention-based methods re-discover feature relationships at each layer, lacking persistent anchors to maintain consistent representations. To address this, we propose HELIX, which assigns each feature a learnable feature identity, a persistent embedding that captures intrinsic semantic properties throughout the network. Unlike graph-based methods that rely on predefined topology and assume homogeneous spatial relationships, HELIX learns arbitrary feature dependencies end-to-end from temporal co-variation, naturally handling datasets where features mix spatial locations with semantic variables. Integrated with hybrid temporal-feature attention, HELIX achieves the state-of-the-art performance, surpassing all 16 baselines on 5 public datasets across 21 experimental settings in our evaluation. Furthermore, our mechanistic analysis reveals that HELIX aligns learned feature identities and dependencies with latent physical and semantic structure progressively across layers, demonstrating that it more effectively translates cross-feature structure into imputation accuracy.