ICML 2026 Papers

With diffusion and flow matching models achieving state-of-the-art generating performance, the interest of the community now turned to reducing the inference time without sacrificing sample quality. Consistency Models (CMs), which are trained to be consistent on diffusion or probability flow ordinary differential equation (PF-ODE) trajectories, enable one or two-step flow or diffusion sampling. However, CMs typically require prolonged training with large batch sizes to obtain competitive sample quality. In this paper, we examine the training dynamics of CMs near convergence and discover that CM trajectory tangents -- CM output update directions -- are quite oscillatory, in the sense that they move parallel to the data manifold, not towards the manifold. To mitigate oscillatory trajectory tangents, we propose a new loss function, called the {\em manifold feature distance (MFD)}, which provides manifold-aligned trajectory tangents that point toward the data manifold. Consequently, our method -- dubbed {\em Align Your Trajectory Tangent (AYT)} -- can accelerate CM training by orders of magnitude and even out-perform the learned perceptual image patch similarity metric (LPIPS). Furthermore, we find that our loss enables training with extremely small batch sizes without compromising sample quality. Code is available at \url{https://github.com/1202kbs/AYT}

Self-supervised learning (SSL) has emerged as a powerful paradigm for learning meaningful representations from unlabeled data. However, the standard protocol for evaluating these representations, linear probing, is computationally expensive, sensitive to hyperparameters, and provides limited insight into the geometric structure of the representation space. In this work, motivated by connections between neural network generalization and intrinsic dimension (ID) we propose IdEst, a method for estimating the ID of SSL representations via the Minimum Spanning Tree dimension estimator ($\mathrm{dim}_\mathrm{MST}$). Across diverse datasets, architectures, and SSL pretraining objectives, we show that IdEst strongly correlates with downstream linear probe performances. Furthermore, we demonstrate that IdEst enables efficient hyperparameter selection, significantly reducing the computational cost compared to supervised alternatives. Our results highlight intrinsic dimensionality as a principled geometric proxy for assessing SSL representations, complementing standard supervised probing protocols.

Discrete flow matching, a recent framework for modeling categorical data, has shown competitive performance with autoregressive models. However, unlike continuous flow matching, the rectification strategy cannot be applied due to the stochasticity of discrete paths, necessitating alternative methods to minimize state transitions. We propose a dynamic-optimal-transport-like minimization objective and derive its Kantorovich formulation for discrete flows with convex interpolants, where transport cost depends solely on inter-state dissimilarity and can be optimized via minibatch strategies. We show that such methods can reduce the number of transitions up to 32 times (1024 to 32) to reach the same generative perplexity without compromising diversity. Additionally, path nondeterminism in discrete flows precludes an instantaneous change-of-variables analogue, preventing precise probability estimation available to continuous flows. We therefore propose two upper bounds on perplexity, enabling principled training, evaluation and model comparison. Finally, we introduce Multimask Flows which outperform masked flows in generative perplexity without compromising diversity, particularly when utilizing minibatch Optimal Transport.

Clustering is commonly compared through leaderboards that collapse performance into a single aggregate ranking. Such summaries obscure why methods succeed, which data properties align with failure, and how conclusions shift under representation changes and realistic tuning constraints. We present CHB, a diagnostic toolkit for hardness-aware clustering evaluation. CHB maps each dataset--representation pair to an interpretable hardness fingerprint capturing (i) separation, (ii) cohesion and scale heterogeneity, and (iii) topology through scalable persistent-homology summaries. Using this diagnostic space, CHB evaluates clustering algorithms under standardized, compute-aware tracks. Conditioning results on hardness coordinates turns comparison into diagnosis: across a broad range of datasets and their representations, CHB reveals reproducible structural regimes, uncovers regime-dependent ranking reversals across method families, and surfaces robustness signatures, including topology-linked breakdowns. CHB further enables representation auditing by attributing gains to measurable shifts in the hardness fingerprint rather than just external performance changes. We release CHB as an open, extensible artifact for evaluating new clustering methods and embeddings within a shared diagnostic framework.

Quantifying the distance between datasets is a fundamental question in mathematics and machine learning. We propose *magnitude distance*, a novel distance metric defined on finite datasets using the notion of the *magnitude* of a metric space. The proposed distance incorporates a tunable scaling parameter, $t$, that controls the sensitivity to global structure (small $t$) and finer details (large $t$). We prove several theoretical properties of magnitude distance, including its limiting behavior across scales and conditions under which it satisfies key metric properties. In contrast to classical distances, we show that magnitude distance remains discriminative in high-dimensional settings when the scale is appropriately tuned. We further demonstrate how magnitude distance can be used as a training objective for push-forward generative models. Our experimental results support our theoretical analysis and demonstrate that magnitude distance provides meaningful signals, comparable to established distance-based generative approaches.

A key challenge in normalizing flows is finding expressive invertible scalar bijections. Existing approaches face trade-offs: affine transformations are smooth and analytically invertible but lack expressivity; monotonic splines offer local control but are only piecewise smooth and act on bounded domains; residual flows achieve smoothness but need numerical inversion. We introduce three families of *analytic bijections* that are globally smooth ($C^\infty$), defined on all of $\mathbb{R}$, and analytically invertible in closed form, combining the favorable properties of prior approaches. Beyond serving as drop-in replacements in coupling flows, where they match or exceed spline performance, we develop *radial flows*: a novel architecture using direct parametrization that transforms the radial coordinate while preserving angular direction. Radial flows exhibit exceptional training stability, produce geometrically interpretable transformations, and on targets with radial structure can achieve comparable quality to coupling flows with $1000\times$ fewer parameters. We provide comprehensive evaluation on 1D and 2D benchmarks, and demonstrate applicability to higher-dimensional physics problems through experiments on $\phi^4$ lattice field theory, where our bijections outperform affine baselines and enable problem-specific designs that address mode collapse.

As a multimodal extension of Chain-of-Thought (CoT), Thinking with Images (TWI) has emerged as a promising avenue to enhance the reasoning capability of Multi-modal Large Language Models (MLLMs), which generates interleaved CoT by incorporating visual cues into the textual reasoning process. However, the success of existing TWI methods heavily relies on the assumption that interleaved CoTs are faultless, which is easily violated due to the complexity of multimodal understanding. In this paper, we reveal and study a highly-practical yet under-explored problem in TWI, termed Noisy Thinking (NT). Specifically, NT refers to the imperfect visual cues mining and answer reasoning process. As the saying goes, ``One mistake leads to another'', erroneous interleaved CoT would cause error accumulation, thus significantly degrading the performance. To solve NT, we propose a novel method dubbed Reliable Thinking with Images (RTWI). In brief, RTWI estimates the reliability of visual cues and textual CoT in a unified text-centric manner and then employs robust filtering and voting modules to prevent NT from contaminating final answer. Extensive experiments on seven benchmarks verify the effectiveness of RTWI against NT.

We study query time bounds for the fundamental problem of estimating the kernel mean $\frac1{|X|}\sum_{x\in X}\mathbf{\mathrm{k}}(x,y)$ of a query $y$ in a finite dataset $X\subset\mathbb{R}^d$ up to a prescribed additive error $\varepsilon$. The best known bounds for the Gaussian kernel are $O(d/\varepsilon^2)$, $\widetilde O(d+1/\varepsilon^4)$, and $\widetilde O(d+\Delta^2/\varepsilon^2)$, where $\Delta$ is the diameter of a region containing the points. We prove the new bound $\tilde O(d+\varepsilon\Delta^2+1/\varepsilon^3)$, which improves over the previous ones in regimes with small error $\varepsilon$ and intermediate diameter $\Delta$. At the center of our proof is a new fast spherical embedding theorem in the sense introduced by Bartal, Recht and Schulman (2011), which limits the embedded data diameter while preserving local Euclidean distances and avoiding ``distance collapse'' at larger scales. This fast embedding theorem may be of independent interest.

Pre-Layer Normalization (Pre-LN) is the de facto choice for large language models (LLMs) and is crucial for stable pretraining and effective transfer learning. However, Pre-LN incurs repeated statistical-computation overhead and remains vulnerable to the curse of depth, where hidden-state magnitudes and variances grow as the number of layers increases, destabilizing training. Efficiency-oriented normalization-free methods such as Dynamic Tanh (DyT) improve throughput but remain fragile at depth. To jointly address stability and efficiency, we propose Bounded Hyperbolic Tanh (BHyT), a drop-in replacement for Pre-LN. BHyT combines a tanh nonlinearity with explicit, data-driven input bounding to keep activations within a non-saturating range. It prevents depth-wise growth in activation magnitude and variance and provides a theoretical stability guarantee. For efficiency, BHyT computes exact statistics once per block and replaces a second normalization with a lightweight variance approximation. Empirically, BHyT demonstrates improved stability and efficiency during pretraining, achieving an average of 1.6\% faster training and an average of 1.77\% higher token generation throughput compared to RMSNorm, while maintaining strong pretraining-only and post-SFT performance across language understanding and reasoning benchmarks\footnote{Code is available at: \url{https://github.com/MLAI-Yonsei/BHyT}}.

Transformers excel in natural language processing and computer vision tasks. However, they still face challenges in generalizing to Out-of-Distribution (OOD) datasets, i.e. data whose distribution differs from that seen during training. OOD detection aims to distinguish outliers while preserving in-distribution (ID) data performance. This paper introduces the OOD detection Probably Approximately Correct (PAC) Theory for transformers, which establishes the conditions for data distribution and model configurations for the OOD detection learnability of transformers. It shows that outliers can be accurately represented and distinguished with sufficient data under conditions. The theoretical implications highlight the trade-off between theoretical principles and practical training paradigms. By examining this trade-off, we naturally derived the rationale for leveraging auxiliary outliers to enhance OOD detection. Our theory suggests that by penalizing the misclassification of outliers within the loss function and strategically generating soft synthetic outliers, one can robustly bolster the reliability of transformer networks. This approach yields a novel algorithm that ensures learnability and refines the decision boundaries between inliers and outliers. In practice, the algorithm consistently achieves state-of-the-art (SOTA) performance across various data formats.

Interval-censored data present unique challenges in statistical analysis due to the partial observability of event times within known intervals, requiring assumptions about the censoring mechanism. This paper explores the theoretical relationship between two foundational assumptions: independent monitoring and non-informative censoring. We demonstrate that these assumptions are equivalent for Case-1 interval-censored data, but not for Case-$K$ interval-censored data, where $K \geq 2$, through a synthetic dataset example. Additionally, we propose the first strictly proper scoring rule and calibration metric specifically designed for interval-censored data under the constant-sum assumption and the non-informative censoring assumption, respectively. Our empirical evaluations on real-world datasets show that a neural network model trained with our scoring rule is competitive with established statistical baselines, offering enhanced flexibility. These contributions provide significant advancements in the theoretical understanding and practical analysis of interval-censored data.

Large Language Models (LLMs) with agentic web search capabilities show strong potential for tasks requiring real-time information access and complex fact retrieval, yet evaluating such systems remains challenging. We introduce LiveNewsBench, a rigorous and regularly updated benchmark designed to assess the agentic web search abilities of LLMs. LiveNewsBench automatically generates fresh question-answer pairs from recent news articles, ensuring that questions require information beyond an LLM's training data and enabling clear separation between internal knowledge and search capability. The benchmark features intentionally difficult questions requiring multi-hop search queries, page visits, and reasoning, making it well-suited for evaluating agentic search behavior. Our automated data curation and question generation pipeline enables frequent benchmark updates and supports construction of a large-scale training dataset for agentic web search models, addressing the scarcity of such data in the research community. To ensure reliable evaluation, we include a subset of human-verified samples in the test set. We evaluate a broad range of systems using LiveNewsBench, including commercial and open-weight LLMs as well as LLM-based web search APIs. The leaderboard, datasets, and code are publicly available at \url{livenewsbench.com}.

We present a comprehensive benchmarking dataset and empirical scaling law analysis for neural network wavefunctions by matching them to a wide spectrum of famous many body target wavefunctions. The dataset, WF-Bench, spans multiple distinct regimes of strongly correlated quantum matter, including topological states, Wigner crystals, and superconducting wavefunctions, providing a diverse and challenging test bed for neural network wavefunction expressivity. We introduce a systematic and reproducible benchmarking protocol for target wavefunction matching, enabling consistent performance evaluation across different neural network wavefunction architectures. By using wavefunction fidelity as the uniform metric, we discover empirical scaling laws that characterize how representability depends on system size and key model parameters, including number of determinant and model depth. By applying our benchmark protocol on Psiformer and Ferminet, we show that WF-Bench establishes a unified dataset driven framework for evaluating and comparing neural network wavefunctions and for guiding the design of future architectures.

We investigate unpaired image inverse problems, a challenging setting where only independent, non-paired sets of noisy measurements and clean target signals are available for training. We propose a novel inverse problem solver based on Unbalanced Optimal Transport, called ***Unbalanced Optimal Transport Map for Inverse Problems (UOTIP)***. Our method formulates the reconstruction task—predicting clean target signals from noisy measurements—as learning a UOT Map from noisy measurement distribution to clean signal distribution by incorporating a likelihood-based cost function. By relaxing the exact marginal constraint, the UOT framework provides key advantages to our model: robustness to multi-level observation noise, adaptability to class imbalance between noisy and clean datasets, and generalizability to diverse noise-type scenarios. Furthermore, we theoretically demonstrate that incorporating a quadratic cost term ensures the existence and uniqueness of the transport map by satisfying the twist condition, even for ill-posed inverse problems. Our experiments demonstrate that UOTIP achieves state-of-the-art performance on unpaired image inverse problem benchmarks, across linear and nonlinear inverse problems.

Multimodal representation learning harmonizes distinct modalities by aligning them into a unified latent space. Recent research generalizes traditional cross-modal alignment to produce enhanced multimodal synergy but requires all modalities to be present for a common instance, making it challenging to utilize prevalent datasets with missing modalities. We provide theoretical insights into this issue from an \textit{anchor shift} perspective. Observed modalities are aligned with a local anchor that deviates from the optimal one when all modalities are present, resulting in an inevitable shift. To address this, we propose CalMRL to calibrate incomplete alignments caused by missing modalities. CalMRL leverages the priors and the inherent connections among modalities to model the imputation for the missing ones at the representation level. To resolve the optimization dilemma, we employ a bi-step learning method with the closed-form solution of the posterior distribution of shared latents. We validate its mitigation of anchor shift and convergence with theoretical guidance. By equipping the calibrated alignment with the existing advanced method, we offer new flexibility to absorb data with missing modalities, which is originally unattainable. Extensive experiments demonstrate the superiority of CalMRL. The code is released at https://github.com/Xiaohao-Liu/CalMRL.

It is widely recognized that, after generative pre-training, Transformer FeedForward layers implicitly function as semantic memory, encoding linguistic and factual knowledge, while the contexts in key–value (KV) cache contain raw events, serving as the source of models' episodic memory. In this work, we show that a same group of Transformer FeedForward-layer parameters can both be semantic and episodic memory, which is retrievable without explicitly attending to the related KV cache. To realize this idea, we introduce Hypermem, a hypernetwork that recurrently maps contexts into targeted updates of FeedForward parameters. We post-train the hypernetwork using continuation and random-access associative memory objectives, eliminating the need for test-time training. Extensive experiments demonstrate that our approach outperforms related methods, including MemoryLLM and generative adapter, on memory retrieval, long-context question answering, and personalization benchmarks, establishing a new state of the art for hypernetwork-based memory mechanisms. Our results suggest that directly bridging data and parameters provides a viable direction for exploring next-generation foundation models with more flexible and persistent memory capabilities.

The unordered nature of point cloud data poses significant challenges to conventional architectures primarily designed for structured data. Spiking neural networks (SNN), by virtue of their inherent sparsity and dynamics, are particularly well-suited for processing point clouds to effectively extract meaningful features. We propose SpikeNet, a novel spiking neural network architecture for energy-efficient and robust point cloud analysis. We introduce spiking-driven sparse attention mechanism coined the Spiking Vector Mask Transformer (SVMT). By dynamically aligning the sparsity of point cloud data through binary spiking masks, SVMT eliminates the need for softmax and multiplication operations, significantly improving computational efficiency. We also propose a Dynamic Sparse Spiking Residual (DSSR) structure and integrate it with SVMT to form the Spiking Neural Network (SpikeNet) for point cloud classification and segmentation. SpikeNet overcomes the trade-off between accuracy and efficiency in previous SNN methods, achieving collaborative optimization of performance and energy-efficiency. Experiments on benchmark datasets show that SpikeNet achieves state-of-the-art performance in shape classification and segmentation tasks, comparable to artificial neural network (ANN) based methods. Our source code is in supplementary material and will be made publicly available.

Time series foundation models (TSFMs) are revolutionizing the forecasting landscape from specific dataset modeling to generalizable task evaluation. However, we contend that existing benchmarks exhibit common limitations in four dimensions: constrained data composition dominated by reused legacy sources, compromised data integrity lacking rigorous quality assurance, misaligned task formulations detached from real-world contexts, and rigid analysis perspectives that obscure generalizable insights. To bridge these gaps, we introduce **TIME**, a next-generation task-centric benchmark comprising 50 fresh datasets and 98 forecasting tasks, tailored for strict zero-shot TSFM evaluation free from data leakage. Integrating large language models and human expertise, we establish a human-in-the-loop benchmark construction pipeline to ensure high data integrity and redefine task formulation by aligning forecasting configurations with real-world operational requirements and variate predictability. Furthermore, we propose a novel pattern-level evaluation perspective that moves beyond traditional dataset-level evaluations based on static meta labels. By leveraging structural time series features to characterize intrinsic temporal properties, this approach offers generalizable insights into model capabilities across diverse patterns. We evaluate 12 TSFMs and establish a multi-granular leaderboard to facilitate in-depth analysis and visualized inspection. The leaderboard is available at https://huggingface.co/spaces/Real-TSF/TIME-leaderboard.

Aligning Large Language Models (LLMs) with the diverse spectrum of human values remains a central challenge: preference-based methods often fail to capture deeper motivational principles. Value-based approaches offer a more principled path, yet three gaps persist: extraction often ignores hierarchical structure, evaluation detects presence but not calibrated intensity, and steerability of LLMs at controlled intensities remains insufficiently understood. To address these limitations, we introduce VALUEFLOW, a unified framework that spans extraction, evaluation, and steering with calibrated intensity control. The framework integrates three components: (i) HiVES, a hierarchical value embedding space that captures intra- and cross-theory value structure; (ii) the Value Intensity DataBase (VIDB), a large-scale resource of value-labeled texts with intensity estimates derived from ranking-based aggregation; and (iii) an anchor-based evaluator that produces consistent intensity scores for model outputs by ranking them against VIDB panels. Using VALUEFLOW, we conduct a comprehensive large-scale study across ten models and four value theories, identifying asymmetries in steerability and composition laws for multi-value control. This paper establishes a scalable infrastructure for evaluating and controlling value intensity, advancing pluralistic alignment of LLMs.