ICML 2026 Papers

While linear-complexity attention mechanisms offer a promising alternative to Softmax attention for overcoming the quadratic bottleneck, training such models from scratch remains prohibitively expensive. Inheriting weights from pretrained Transformers provides an appealing shortcut, yet the fundamental representational gap between Softmax and linear attention prevents effective weight transfer. In this work, we address this conversion challenge from two perspectives: architectural alignment and representational alignment. We identify Test-Time Training (TTT) as a linear-complexity architecture whose two-layer dynamic formulation is structurally aligned with Softmax attention, enabling direct inheritance of pretrained attention weights. To further align representational properties, including key shift-invariance and locality, we introduce key instance normalization and a lightweight locality enhancement module. We validate our approach by linearizing Stable Diffusion 3.5 and introduce SD3.5-T$^5$ (Transformer To Test Time Training). With only 1 hour of fine-tuning on 4×H20 GPUs, SD3.5-T$^5$ achieves comparable text-to-image quality to the fine-tuned Softmax model, while accelerating inference by 1.32× and 1.47× at 1K and 2K resolutions. Code is available at this URL: https://github.com/LeapLabTHU/Transformer-to-TTT.

Modern large-scale neural networks are often trained and released in multiple sizes to accommodate diverse inference budgets. To improve efficiency, recent work has explored *model upscaling*: initializing larger models from trained smaller ones to accelerate convergence. However, this method can be sensitive to hyperparameters that need to be tuned at the target upscaled model size, which is prohibitively costly to do directly. It remains unclear whether tuning hyperparameters on smaller models and extrapolating via scaling laws is sound in this setting. We address this with principled approaches to width-based upscaling and efficient hyperparameter tuning in this setting. Motivated by $\mu$P and any-dimensional architectures, we introduce a general upscaling method that, like Net2Net, copies and perturbs weights, but uses theoretically grounded, width-dependent scalings for the perturbation noise and optimizer hyperparameters. First, we prove that under zero perturbation, the upscaled model is functionally equivalent to the base model throughout training. Second, we extend the $\mu$P theory to enable infinite-width limit analysis and establish hyperparameter transfer for upscaled models, greatly reducing the tuning cost. We empirically demonstrate that this method is effective on realistic datasets and architectures.

We propose a new method for estimating how much a model knows about a datapoint and use it to measure the capacity of modern language models. Prior studies of language model memorization have struggled to disentangle memorization from generalization. We formally separate memorization into two components: unintended memorization, the information a model contains about a specific dataset, and generalization, the information a model contains about the true data-generation process. When we completely eliminate generalization, we can compute the total memorization, which provides an estimate of model capacity: our measurements estimate that GPT-style models have a capacity of approximately 3.6 bits per parameter. We train language models on datasets of increasing size and observe that models memorize until their capacity fills, at which point unintended memorization decreases as models begin to generalize. We train hundreds of transformer language models ranging from 500K to 1.5B parameters and produce a series of scaling laws relating model capacity and data size to membership inference.

Statement autoformalization acts as a critical bridge between human mathematics and formal mathematics by translating natural language problems into formal language. While prior works have focused on data synthesis and diverse training paradigms to optimize end-to-end Large Language Models (LLMs), they typically treat formal code as flat sequences, neglecting the hierarchical logic inherent in mathematical statements. In this work, we introduce Decompose, Structure, and Repair (DSR), a neuro-symbolic framework that restructures autoformalization into a modular pipeline. DSR decomposes statements into logical components and maps them to structured operator trees, leveraging this topological blueprint to precisely localize and repair errors via sub-tree refinement. Furthermore, we introduce PRIME, a benchmark of 156 undergraduate and graduate-level theorems selected from canonical textbooks and expertly annotated in Lean 4. Experimental results demonstrate that DSR establishes a new state-of-the-art, consistently outperforming baselines under equivalent computational budgets. The datasets, model, and code are available at https://github.com/XiaoyangLiu-sjtu/DSR.

The scaling-law era has transformed artificial intelligence (AI) from research into a global industry, but its rapid growth also raises concerns over energy usage, carbon emissions, and environmental sustainability. Unlike traditional sectors, the AI industry still lacks systematic carbon accounting methods that support large-scale estimates without reproducing the original training process. This leaves open questions about how large the problem is today and how large it might be in the near future. Given its central role in hosting open-source AI models, the Hugging Face (HF) platform provides a large-scale and publicly accessible corpus for carbon accounting. We estimate aggregate training emissions of HF open-source models using available emissions, energy, compute, and model metadata. To address uneven disclosure quality, we introduce a tiered approach to handle incomplete metadata, supported by empirical regressions that assess estimation reliability. We further introduce AI training carbon intensity (ATCI, emissions per compute), a metric to assess the sustainability efficiency of model training. Our results show that training the most popular open-source models (with over 5,000 downloads) has already resulted in approximately 6.0×10^4 metric tons of carbon emissions. Overall, this paper provides a scalable, empirically grounded framework for estimating training emissions from incomplete disclosures and informing future carbon reporting standards in the AI industry. Data and code are available at https://github.com/insait-institute/HuggingCarbon.

Safe deployment of increasingly capable AI agents may require visibility into how they make decisions. Chain-of-thought (CoT) monitoring can detect misbehavior in today’s reasoning models, but this “monitorability” may be fragile under different training procedures, data sources, or continued system scaling. We propose three evaluation archetypes (intervention, process, and outcome-property), a new monitorability metric, and a broad evaluation suite. We show CoT monitoring outperforms action-only monitoring in practical settings, and that frontier models are generally—but not perfectly—monitorable. We study scaling trends with pre-training model size and inference-time compute, finding longer CoTs are typically more monitorable. We find that, for a fixed capability level, using a smaller model at higher reasoning effort can yield higher monitorability, at greater inference compute cost. We further find that increasing a weak monitor’s test-time compute when monitoring a strong agent improves monitorability, and giving the monitor access to the CoT both boosts monitorability and steepens the compute–to-monitorability scaling trend. Finally, we show monitorability can be improved by asking follow-up questions and giving the follow-up CoT to the monitor.

Continual learning (CL) seeks models that acquire new knowledge while avoiding catastrophic forgetting. However, many methods that mitigate forgetting constrain parameter updates and thereby reduce model plasticity. We revisit the singular value spectrum of gradients in representative CL methods and show that they commonly exhibit singular value collapse, where only a small subset of gradient directions drive parameter updates. Motivated by this observation, we propose **P**lasticity **A**ctivation via **P**olar **O**perator (PAPO), a plug-in that preserves the dominant directions that mitigate forgetting while activating previously suppressed directions to enhance plasticity. Concretely, PAPO modifies the gradient $\mathbf{G}$ as $\mathbf{G}\leftarrow \mathbf{G}+\lambda \cdot \operatorname{polar}(\mathbf{G})$, which uniformly increases near-zero singular values without changing the singular vectors. To avoid the cost of explicit singular value decomposition, we approximate the polar factor using the iteration-dependent Polar Express scheme, which relies only on matrix multiplications and additions. In our empirical evaluation on both vision and language benchmarks, incorporating PAPO yields consistent improvements. In particular, on MiniImageNet, integrating PAPO into ER, MAS, GPM and TRGP produces substantial accuracy gains of $9.01\%$, $4.76\%$, $8.90\%$ and $9.19\%$, respectively.

Transportation on graphs is a fundamental challenge across many domains, where decisions must respect topological and operational constraints. Despite the need for actionable policies, existing graph-transport methods lack this expressivity. They rely on restrictive assumptions, fail to generalize across sparse topologies, and scale poorly with graph size and time horizon. To address these issues, we introduce Generalized Schrödinger Bridge on Graphs (GSBoG), a novel scalable data-driven framework for learning executable controlled continuous-time Markov chain (CTMC) policies on arbitrary graphs under state cost augmented dynamics. Notably, GSBoG learns trajectory-level policies, avoiding dense global solvers and thereby enhancing scalability. This is achieved via a likelihood optimization approach, satisfying the endpoint marginals, while simultaneously optimizing intermediate behavior under state-dependent running costs. Extensive experimentation on challenging real-world graph topologies shows that GSBoG reliably learns accurate, topology-respecting policies while optimizing application-specific intermediate state costs, highlighting its broad applicability and paving new avenues for cost-aware dynamical transport on general graphs.

Federated Learning (FL) enables collaborative model training across decentralized clients, but its performance often degrades under non-IID data distributions, particularly in the presence of data skew. Existing approaches mitigate this issue by estimating client skew via kernel density estimation over neighboring model updates, which preserves privacy and reduces communication costs. However, such approaches suffer from two fundamental limitations: bias toward skewed majority clients due to fixed neighborhood structures, and vulnerability to noise-induced perturbation in kernel space. To address these challenges, we propose FedVeer, a skew-aware FL framework based on self-adaptive kernel density estimation with k-free neighborhoods. FedVeer dynamically determines the neighborhood size via max-margin learning to mitigate majority-client bias, and further incorporates Kalman filtering to stabilize margin estimation under noisy updates, with a high-probability theoretical guarantee on margin deviation. Extensive experiments on realworld datasets demonstrate that FedVeer consistently outperforms four baselines, achieving up to 6.36% accuracy improvement and reducing noiseinduced degradation by up to 6.01%.

LLM agents increasingly act on users’ personal information, yet existing privacy defenses remain limited in both design and adaptability. Most prior approaches rely on static or passive defenses, such as prompting and guarding. These paradigms are insufficient for supporting contextual, proactive privacy decisions in multi-step agent execution. We propose *Contextualized Defense Instructing (CDI)*, a new privacy defense paradigm in which an instructor model generates step-specific, context-aware privacy guidance during execution, proactively shaping actions rather than merely constraining or vetoing them. Crucially, CDI is paired with an experience-driven optimization framework that trains the instructor via reinforcement learning (RL), where we convert failure trajectories with privacy violations into learning environments. We formalize baseline defenses and CDI as distinct intervention points in a canonical agent loop, and compare their privacy–helpfulness trade-offs within a unified simulation framework. Empirically, CDI consistently achieves a better balance between privacy preservation (94.2\%) and helpfulness (80.6\%) than baselines, with superior robustness to adversarial conditions and generalization.

Spectrally sparse signal reconstruction arises in a wide range of applications and can be formulated as a low-rank Hankel matrix completion problem. We develop a Jacobi-preconditioned gradient descent method that preserves the low per-iteration complexity of first-order algorithms while achieving linear convergence at a rate independent of the condition number. By introducing a generator that maps factor-based iterates to matrix space, we establish equivalence with manifold-based methods, enabling direct convergence analysis while avoiding the need to define distances under complex-symmetric factorization ambiguity. Extensive experiments demonstrate that the proposed algorithm outperforms state-of-the-art methods in both iteration count and computational time across a broad range of problem settings.

For many real-world systems, causal ground truth is difficult to obtain, making claims about causal effects hard to assess. We develop methods for evaluating collections of bivariate causal statements, one for each pair of variables in a fixed system. In the setting of acyclic linear statements, any such collection can be extended to a unique multivariate causal model, but we argue that this induced model is implausible if it imposes substantial additional confounding to explain observed correlations. We introduce a compatibility score that quantifies this notion of plausibility, notably without relying on the faithfulness assumption. Additionally, we define an incompatibility score for purely graphical bivariate causal statements, based on global consistency constraints that are derived from acyclicity and faithfulness assumptions. We give theoretical and empirical evidence that both scores can successfully distinguish correct from incorrect causal statements in generic settings. Moreover, we demonstrate the practical applicability of our methods by analyzing causal claims made by large language models. Our work aims to provide a foundation for assessing the reliability of causal information derived from human experts or artificial intelligence in settings where alternative forms of validation are unavailable.

With the rapid advancement of high-fidelity video generation models, robust AI-generated video (AIGV) detection has become increasingly needed. While most AIGV detection methods operate in the decoded pixel domain, we observe that detection in the pixel domain inevitably entangles task-irrelevant semantic information, leading to substantial semantic redundancy and extensive redundant computation, while overlooking free-to-use signals in compressed bitstreams. In particular, motion vectors and residuals directly encode temporal and spatial generative artifacts but remain largely underexplored. To address these issues, we propose a unified framework for **S**patio-**T**emporal **RE**sidual and **A**rtifact **M**ining, namely **STREAM**, which enables AIGV detection directly from compressed bitstreams. **STREAM** leverages I-frames, motion vectors, and residual errors to capture spatiotemporal artifacts that are typically smoothed out by decompression filters. In particular, we design a lightweight network with a motion-guided alignment module and a gated fusion mechanism, enabling adaptive fusion of spatial artifacts and nonlinear temporal dynamics. Extensive experimental results demonstrate that **STREAM** achieves SOTA performance with an mAP of 0.965, with 2.5× faster inference than previous SOTA baselines.

False discovery rate (FDR) is a cornerstone of modern multiple testing. However, it often fails to guarantee the reliability of ``marginal" discoveries that lie at the boundary of the rejection set, which are often crucial in high-precision applications. While recent works (Soloff et al., 2024; Xiang et al., 2025) introduced the boundary false discovery rate (bFDR) to control the error probability at the marginal discovery, their method relies on restrictive assumptions such as independence or specific prior distributions. In this paper, we first propose $k$-bFDR, a novel generalization that controls the error probability of the $k$ least significant discoveries. We then provide a systematic investigation into the theoretical relationship between $k$-bFDR and existing error metrics. Furthermore, building upon the closure principle, we develop Domino, a unified framework that guarantees $k$-bFDR control under arbitrary dependence, applicable for both p-values and e-values. We prove the theoretical validity of the proposed Domino algorithm and demonstrate through extensive numerical experiments that it consistently achieves rigorous $k$-bFDR control while identifying trustworthy marginal discoveries. Analyses of real data reveal that $k$-bFDR control yields higher-quality rejection sets with greater practical significance.

Large Language Models (LLMs) excel at long-context understanding but exhibit significant limitations in long-form generation. Existing studies primarily focus on single-generation quality, generally overlooking the volatility of the output (i.e., the inconsistency in length and content across multiple generations). This volatility not only leads to significant computational costs but also severely impacts the models' reliable application. To address this gap, our work unfolds in three stages: benchmarking, probing, and mitigation. We first propose the VOlatility in Long-form Text Benchmark (VOLTBench), a novel heterogeneous-task benchmark designed to systematically quantify the length volatility of long-form generation. Subsequently, by analyzing attention traces, we conduct an in-depth probe to identify several common internal patterns that cause this volatility. Finally, to mitigate long-form output volatility, we propose SELB (Structural Enforcement via Logits Boosting), a lightweight decoding-stage optimization strategy, designed to significantly enhance both the length accuracy and stability of long-form generation without additional training. Extensive experiments on VOLTBench provide the first systematic confirmation of severe long-form output instability in mainstream models and validate that our proposed method successfully improves the mean output length of the base model by 148% and reduces the length volatility by 69%, while maintaining high generation quality.

Modern imaging techniques heavily rely on Bayesian statistical models to address difficult image reconstruction and restoration tasks. This paper addresses the objective evaluation of such models in settings where ground truth is unavailable, with a focus on model selection and misspecification diagnosis. Existing unsupervised model evaluation methods are often unsuitable for computational imaging due to their high computational cost and incompatibility with modern image priors defined implicitly via machine learning models. We herein propose a general methodology for unsupervised model selection and misspecification detection in Bayesian imaging sciences, based on a novel combination of Bayesian cross-validation and data fission, a randomized measurement splitting technique. The approach is compatible with any Bayesian imaging sampler, including diffusion and plug-and-play samplers. We demonstrate the methodology through experiments involving various scoring rules and types of model misspecification, where we achieve excellent selection and detection accuracy with a low computational cost.

Multi-objective optimization (MOO) has emerged as a powerful approach to solving complex optimization problems involving multiple objectives. In many practical scenarios, function evaluations are unavailable or prohibitively expensive, necessitating optimization solely based on a fixed offline dataset. In this setting, known as offline MOO, the goal is to find out the Pareto set without access to the true objective functions. This setting suffers from the out-of-distribution (OOD) issue, where the surrogate model is not accurate for unseen designs. Due to the OOD issue, surrogate errors may cause the optimizer to select solutions that do not lie on the true Pareto front and are biased toward its extremes. To address this, this paper proposes Diversity-driven Offline Multi-Objective Optimization (DOMOO), which aims to find out a diverse and high-quality set of solutions. First, DOMOO incorporates an accumulative risk control module that estimates the potential risk of candidate solutions and alleviates the OOD issue between the training data and the generated solutions. In addition, a nested Pareto set learning (PSL) strategy is proposed to jointly learn preference and PSL parameters, then optimize them, enabling adaptation to diverse Pareto front geometries. To further enhance solution quality, we design a diversity-driven selection strategy that extracts a representative and well-distributed set of final solutions. To achieve this diversity-driven selection strategy, we propose $\text{IGD}_\text{offline}$, a tailored indicator for the offline setting that considers both diversity and convergence, and avoids the bias of hypervolume indicator. Extensive experiments on synthetic and real-world benchmarks show that DOMOO achieves the best average rank across tasks in both convergence and diversity among the compared methods.

Modern deep neural networks often contain far more parameters than needed to fit their training data, yet they achieve impressive generalization. A common explanation for this success is the implicit bias of stochastic gradient descent (SGD). An alternative volume hypothesis posits that, within low training-loss regions, loss-landscape basins leading to strong generalization occupy much larger regions of weight space than basins that generalize poorly, and therefore SGD is simply more likely to land in the former. Recent experimental explorations of this idea present seemingly contradictory results. While in one set of experiments randomly sampling the network weights until achieving zero training error yielded poor generalization, molecular dynamics density estimates supported the volume hypothesis. We observe that these experiments were performed at different dataset size regimes, and explore an intermediate regime using the Replica Exchange Wang–Landau algorithm to estimate the joint density of states over training and test accuracies in binary networks. Across several architectures and datasets, we show that the generalization advantage of gradient learning over random sampling training generally diminishes as the training data size grows, suggesting a resolution of the paradox.

Actor-critic (AC) methods are a cornerstone of reinforcement learning (RL) but offer limited interpretability. Current explainable RL methods seldom use \emph{state attributions} to assist training. Rather, they treat all state features equally, thereby neglecting the heterogeneous impacts of individual state dimensions on the reward. We propose *RKHS-SHAP-based Advanced Actor-Critic (RSA2C)*, an attribution-aware, kernelized, two-timescale AC algorithm, including Actor, Value Critic, and Advantage Critic. The Actor is instantiated in a vector-valued reproducing kernel Hilbert space (RKHS) with a Mahalanobis-weighted operator-valued kernel, while the Value Critic and Advantage Critic reside in scalar RKHSs. These RKHS-enhanced components use sparsified dictionaries: the Value Critic maintains its own dictionary, while the Actor and Advantage Critic share one. State attributions, computed from the Value Critic via RKHS-SHAP (kernel mean embedding for on-manifold and conditional mean embedding for off-manifold expectations), are converted into Mahalanobis-gated weights that modulate Actor gradients and Advantage Critic targets. We derive a global, non-asymptotic convergence bound under *state perturbations*, showing stability through the perturbation-error term and efficiency through the convergence-error term. Empirical results on three continuous-control environments show that RSA2C achieves efficiency, stability, and interpretability. Our code is available at https://github.com/Na-Li66/RSA2C.