ICML 2026 论文列表

Adaptive methods like Adam have become the *de facto* standard for large-scale vector and Euclidean optimization due to their coordinate-wise adaptation with a second-order nature. More recently, matrix-based spectral optimizers like Muon (Jordan et al., 2024b) show the power of treating weight matrices as matrices rather than long vectors. Linking these is hard because many natural generalizations are not feasible to implement, and we also cannot simply move the Adam adaptation to the matrix spectrum. To address this, we reformulate the AdaGrad update and decompose it into a variance adaptation term and a scale-invariant term. This decoupling produces **DeVA** (**De**coupled **V**ariance **A**daptation), a framework that bridges between vector-based variance adaptation and matrix spectral optimization, enabling a seamless transition from Adam to adaptive spectral descent. Extensive experiments across language modeling and image classification demonstrate that DeVA consistently outperforms state-of-the-art methods such as Muon and SOAP (Vyas et al., 2024), reducing token usage by around 6.6\%. Theoretically, we show that the variance adaptation term effectively improves the blockwise smoothness, facilitating faster convergence.

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%.

Predicting high-dimensional transcriptional responses to genetic perturbations is challenging because signals are sparse and experimental noise is severe. Existing methods often suffer from mean collapse, achieving high correlation by predicting the global average expression rather than perturbation-specific responses, which yields false positives and poor interpretability. Methods that add biological knowledge graphs typically treat them as dense, static priors shared across perturbations, propagating noise. We propose AdaPert, which counters mean collapse by extracting a sparse, perturbation-specific subgraph via differentiable node selection, then suppressing spurious variation in non-responsive genes while emphasizing differentially expressed ones. Across multiple benchmarks, AdaPert outperforms existing baselines, with the largest gains on DEG-aware metrics.

Graph Prompt Learning (GPL) has recently emerged as a promising paradigm for downstream adaptation of pre-trained graph models, mitigating the misalignment between pre-training objectives and downstream tasks. Recently, the focus of GPL has shifted from in-domain to cross-domain scenarios, which is closer to the real world applications, where the pre-training source and downstream target often differ substantially in data distribution. However, why GPLs remain effective under such domain shifts is still unexplored. Empirically, we observe that representative GPL methods are competitive with two simple baselines in cross-domain settings: full fine-tuning (FT) and linear probing (LP), motivating us to explore a deeper understanding of the prompting mechanism. We provide a theoretical analysis demonstrating that jointly leveraging these two complementary branches yields a smaller estimation error than using either branch alone, formally proving that cross-domain GPL benefits from the integration between pre-trained knowledge and task-specific adaptation. Based on this insight, we propose GP2F, a dual-branch GPL method that explicitly instantiates the two extremes: (1) a frozen branch that retains pre-trained knowledge, and (2) an adapted branch with lightweight adapters for task-specific adaptation. We then perform adaptive fusion under topology constraints via a contrastive loss and a topology-consistent loss. Extensive experiments on cross-domain few-shot node and graph classification demonstrate that our method outperforms existing methods.

Shampoo is attracting considerable attention for its superior performance on large-scale optimization benchmarks; yet it faces a significant practical bottleneck: the prohibitive computational overhead of matrix inversion. To mitigate this, practitioners typically rely on stale preconditioner updates, creating a fundamental trade-off between computational efficiency and optimization fidelity. In this work, we provide a theoretical study of staleness through the complementary lenses of convergence and stability. While staleness improves computational efficiency, it inherently degrades performance and introduces numerical instability. Crucially, we identify that damping, acting as a numerical stabilizer, can effectively suppress these negative effects. Guided by this analysis, we propose FOAM, an adaptive algorithm that stabilizes training by dynamically controlling both the damping factor and the eigendecomposition frequency based on an approximation of the staleness-oriented error. Experimental results demonstrate that FOAM reduces wall-clock time compared to standard Shampoo while maintaining robust convergence.

Quantizing LLM weights and activations is a standard approach for efficient deployment, but a few extreme outliers can stretch the dynamic range and amplify low-bit quantization errors. Prior transform-based mitigations (e.g., Hadamard rotations) are fixed and data-agnostic, and their optimality for quantization has remained unclear. We derive closed-form optimal linear blockwise transforms for joint weight-activation quantization under standard RTN AbsMax-scaled block quantizers, covering both integer and floating-point formats. The resulting construction, WUSH, combines a Hadamard backbone with a data-dependent second-moment component to form a non-orthogonal transform that is provably near-optimal for FP and INT quantizers under mild assumptions while admitting an efficient fused GPU implementation. Empirically, WUSH improves W4A4 accuracy over the strongest Hadamard-based baselines (e.g., on Llama-3.1-8B-Instruct in MXFP4, it gains +2.8 average points with RTN and +0.7 with GPTQ) while delivering up to 5.8$\times$ per-layer throughput over BF16 via FP4 MatMul. Source code is available at https://github.com/IST-DASLab/WUSH.

High-resolution visual encoders in multimodal large language models (MLLMs) substantially improve fine-grained perception, yet incur prohibitive computational costs.Existing token pruning methods are effective on natural images but struggle with spatially sparse structured inputs (e.g., charts), where critical high-frequency information is sparse, localized, and structurally essential. To address this challenge, we propose Adaptive Dual-Branch Token Sparsification (AD-BTS), a density-aware framework that dynamically allocates computation according to input signal characteristics. Specifically, AD-BTS introduces a Gradient-based Routing Gate (GRG) that uses lightweight pixel-level gradient statistics to estimate structural flatness and guide routing. Then, AD-BTS activates either a Redundancy Selection Branch (RSB) for aggressive token pruning with a frozen encoder, or a Structural Fusion Branch (SFB) with conditional LoRA and context fusion to preserve sparse structural information.Extensive experiments on Qwen2.5-VL demonstrate that AD-BTS establishes a new Pareto frontier between efficiency and accuracy. Under extreme compression (20% token retention), AD-BTS outperforms the strongest baseline by 12.1% on ChartQA while achieving a 1.8× prefill speedup, effectively reconciling computational efficiency with structural robustness.

Cold-start personalization requires inferring preferences from minimal interaction when no user-specific historical data is available. The space of possible preferences is vast, yet users care about only a sparse subset and rarely articulate them upfront; combined with limited interaction budgets, this makes preference elicitation challenging. Our key insight is that preferences exhibit predictable structure across populations; e.g., users who want detailed explanations often also value worked examples. We propose CAPE (Cold start Adaptive Preference Elicitation with Priors), a principled system decomposition framework for cold-start personalization: learning a structured world model of preference correlations offline using latent variables, then performing Bayesian inference online without retraining. Even simple belief model instantiations (e.g., linear regression) substantially outperform end-to-end RL. Across medical, mathematical, social, and commonsense reasoning, CAPE achieves 80.8% alignment with ground-truth user preferences versus 68.5% for RL, requires 3-5× fewer interactions, and adapts twice as often. Our contribution is a principled decomposition of cold-start personalization that makes Bayesian preference elicitation practical at scale for LLM systems.

Graph Neural Networks (GNNs) have achieved remarkable success in graph analysis due to the Message-Passing (MP) mechanism, yet they struggle with heterophilic graphs where connected nodes often have distinct labels or dissimilar attributes. Graph Contrastive Learning (GCL) serves as a promising approach to extract the information beyond neighboring nodes, effectively mitigating the limitations of the MP mechanism in handling heterophilic graphs. Nevertheless, GCL faces two critical challenges when applied to heterophilic graphs, i.e., the potential distribution shift from data augmentation and the loss of robustness caused by high-frequency signals. To address these problems, we propose a novel model, namely the Spectral Fusion Contrastive Learning with Topology-Adaptive Graph Augmentation (SFCLTA) for unsupervised graph representation learning. Our method dynamically adjusts graph structures via a heterophily-aware augmentation strategy, and constrains high-frequency distortions by spectral regularization. We utilize the confidence-weighted fusion to enhance the robustness. Additionally, we introduce a feature reconstruction task as a prerequisite to explicitly mitigate feature-level distribution shifts. Experiments on multiple real-world datasets demonstrate that the proposed SFCLTA consistently outperforms baseline models in multiple tasks. Our code is released on https://github.com/JonathanGXu/SFCLTA.

We study adaptive querying for learning user-dependent quantities of interest, such as responses to held-out items and psychometric indicators, within tight question budgets. Classical Bayesian design and computerized adaptive testing typically rely on restrictive parametric assumptions or expensive posterior approximations, limiting their use in heterogeneous, high-dimensional, and cold-start settings. We introduce a persona-induced latent variable model that represents a user's state through membership in a finite dictionary of AI personas, each offering response distributions produced by a large language model. This yields expressive priors with closed-form posterior updates and efficient finite-mixture predictions, enabling scalable Bayesian design for sequential item selection. Experiments on synthetic data and WorldValuesBench demonstrate that persona-based posteriors deliver accurate probabilistic predictions and an interpretable adaptive elicitation pipeline.

Conventional wisdom holds that large-batch training is fundamentally incompatible with Reinforcement Learning (RL) — beyond a modest threshold, increasing batch sizes typically yields diminishing returns or performance degradation due to the inherent non-stationarity of the data distribution. We challenge this view by observing that non-stationarity is not a fixed property of RL, but evolves throughout training: early stages exhibit rapid behavioral shifts that demand small batches for plasticity, whereas late stages approach a quasi-stationary regime where large batches enable precise convergence. Motivated by this observation, we propose Adaptive Batch Scaling (ABS), that dynamically adjusts the effective batch size according to the stability of the learning policy. Central to ABS is Behavioral Divergence, a novel metric that quantifies policy non-stationarity by measuring action-level shifts between consecutive updates, which we use to scale batch size inversely to policy volatility. Integrated with the Parallelised Q-Network (PQN) algorithm and evaluated on the ALE benchmark, ABS seamlessly reconciles early-stage plasticity with late-stage stable convergence. Strikingly, contrary to conventional wisdom, our results reveal that the combination of larger networks and larger batch sizes achieves the best performance — a scaling behavior previously thought to be unattainable in RL, now unlocked through adaptive batch control.

Training with quantized weights can reduce costs but often results in degraded accuracy, especially when optimization is carried out in low precision, without storing high-precision copies. We identify a key failure mode: under low precision, standard optimizers can get stuck and not make progress, especially at large weight magnitudes due to coarse mantissa resolution. To overcome this, multiplicative updates have been previously proposed, in place of additive updates in standard optimizers. While successful under extremely low precision, such as under the logarithmic number system, they suffer from failures near zero and across sign changes. The failure modes of additive and multiplicative updates are therefore complementary. To exploit this, we propose M+Adam, which combines both update types: additive steps handle sign changes and small magnitudes, while multiplicative steps ensure progress at large magnitudes when additive updates are zeroed out under rounding. We prove monotone descent for M+Adam under standard smoothness assumptions. Across LLaMA-style pretraining with 60M--1B models, $1$--$8\times$ Chinchilla budgets, and using only BF16, FP8, and FP4 master weights, M+Adam consistently improves low-precision training.

Principal component analysis classically requires full $d$-dimensional samples, yet in various applications hardware limits acquisition to a few scalar measurements per sample. We analyze a compressed variant of Oja's algorithm for estimating the principal eigenvector of the data covariance matrix using only two adaptive measurements per sample. At each iteration, we observe one measurement along the current estimate and one in a random orthogonal direction. We prove that after $t$ iterations, the expected sine-squared error to the true eigenvector is $\mathcal{O}(\lambda_1\lambda_2 d^2 / (\Delta^2 t))$, where $d$ is the ambient dimension, $\lambda_1, \lambda_2$ are the leading eigenvalues, and $\Delta = \lambda_1 - \lambda_2$ is the eigengap. We complement this with a matching information-theoretic lower bound of $\Omega(\lambda_1\lambda_2 d^2 / (\Delta^2 t))$ --- the first for compressed eigenvector estimation --- proving that the $d^2$ factor, an additional factor of $d$ compared to the fully-observed minimax rate $\Theta(\lambda_1\lambda_2 d / (\Delta^2 t))$, is the fundamental cost of compression and cannot be improved. In contrast, any non-adaptive scheme with two measurements per iteration suffers $\Omega(\lambda_2^2 d^3 / (\Delta^2 t))$, an additional power of $d$. This separates fully-observed, adaptive-compressed, and non-adaptive-compressed PCA across three powers of $d$. Our analysis handles the noisy setting where the covariance has nonzero trailing eigenvalues, providing the first convergence guarantee for adaptive compressed subspace tracking beyond the noiseless case.

To maximize hardware utilization, modern machine learning systems typically employ large constant or manually tuned batch size schedules, relying on heuristics that are brittle and costly to tune. Existing adaptive strategies based on gradient noise scale (GNS) offer a principled alternative. However, their assumption of SGD's Euclidean geometry creates a fundamental mismatch with popular optimizers based on generalized norms, such as signSGD / Signum ($\ell_\infty$) and stochastic spectral descent (specSGD) / Muon (Schatten-$\infty$). In this work, we derive gradient noise scales for signSGD and specSGD that naturally emerge from the geometry of their respective dual norms. To practically estimate these non-Euclidean metrics, we propose an efficient variance estimation procedure that leverages the local mini-batch gradients on different ranks in distributed data-parallel systems. Our experiments demonstrate that adaptive batch size strategies using non-Euclidean GNS enable us to match the validation loss of constant-batch baselines while reducing training steps by up to 66\% for Signum and Muon on a 160 million parameter Llama model.

We study compute reduction in neural networks through a unified partial versus full computation view, captured by one-shot magnitude pruning in the static regime and early exit in the adaptive regime. In an asymptotic single-neuron model, we prove a concentration theorem for one-shot magnitude pruning with explicit rates. We also introduce the conditional perceptron for early exit and show that its excess generalization error decays as a power of the compute gap, with an exponent that grows to infinity as the alignment between partial and full computations tends to one. We then extend the analysis to deep networks, characterizing how pruning-induced distortions accumulate with depth and deriving a corresponding compute–accuracy tradeoff for frozen-backbone early exit under a neural network Gaussian process model. Numerical simulations corroborate the predicted scaling laws.

Editing complex, long-form knowledge in Large Language Models remains a significant challenge due to the difficulty of maintaining generation coherence. Existing autoregressive methods like AnyEdit alleviate length constraints but rely on Fixed-window Chunking, which disregards logical structure and compromises consistency. To address this, we present AnyEdit++, a structure-aware framework incorporating Bayes-Chunk, an adaptive segmentation mechanism that dynamically identifies semantic boundaries based on Bayesian Surprise. We underpin this approach with a theoretical framework establishing two key principles: (1) Structural Independence: we prove that cross-segment interference is minimized when anchor keys are geometrically orthogonal (a condition naturally satisfied by our surprisal-based boundaries but violated by fixed windows), and (2) Causal Locality: we demonstrate that updates injected at these semantic peaks yield strictly superior control compared to arbitrary split points. Extensive experiments across mathematical reasoning, code generation, and narrative tasks demonstrate that AnyEdit++ achieves superior performance and robustness compared to state-of-the-art baselines, validating that structural awareness is critical for effective long-form knowledge editing.

Graph neural networks (GNNs) have been demonstrated to be powerful tools for analyzing structural graph data. However, most existing methods usually rely on fixed adjacency structures for information propagation, lacking strong adaptability to the latent semantic relationships that exist but are not explicitly connected in graph, especially in complementary high-pass and low-pass filtering views. To this end, this paper proposes a novel Dual-channel Dynamic Graph Neural Network (DCD-GNN), mainly consisting of parallel representation learning channels: a static structure-preserving channel and a dynamic adjacency-enhancing channel. The dynamic channel exploits both low-pass structural filtering and high-pass personalized detail via the self-attention adjacency learning and then integrates them for comprehensive semantic modeling, while the static channel maintains structural stability. Both channels employ a multi-scale representation fusion mechanism and a unified and discriminative node embedding representation is obtained by integrating them. Extensive experiments on various benchmark datasets verify the superiority of DCD-GNN in discriminative graph representation learning.

Goal-Conditioned Reinforcement Learning aims to design agents that can reach specified goals, notably from previously collected trajectories in the offline setting. In this context, graph-based approaches have been proposed to mitigate compounding value-estimation errors in long-horizon navigation tasks. However, existing approaches typically rely on dense keypoint coverage of the dataset support, resulting in computationally expensive planning. Moreover, they lack explicit mechanisms to adapt to topological changes (e.g., new obstacles), hindering deployment in live applications such as video game environments. To address these two shortcomings, we introduce Adaptive Quasimetric Mapping (AQM), an offline framework leveraging a “time-to-reach” quasimetric learned from the available data. Crucially, it builds a sparse cover of the dataset support, as a greedy approximation to a dominating set problem. At test-time, the resulting graph is carefully pruned by comparing the observed edge traversal time against a time-to-reach budget derived from the quasimetric, thus enabling zero-shot replanning. Empirically, we evaluate AQM on navigation tasks ranging from a classical to a video-game-like benchmark evaluating adaptation across tasks. We show that AQM achieves competitive performance while requiring up to 100× fewer keypoints than prior approaches, hence demonstrating the relevance of topological abstraction for goal-conditioned navigation.

Eliciting information to reduce uncertainty about latent group-level properties is a central problem in collective assessment, preference modeling, and opinion aggregation, and is especially important in survey-based studies. While natural language interactions provide a flexible interface, existing methods typically rely on fixed questionnaires and static respondent sets, and do not adapt to partial or missing responses across rounds. To address this gap, we study adaptive information elicitation through multi-turn interactions between a large language model and a group of individuals, where both queries and respondents are adaptively selected to infer latent group properties. We propose a theoretically grounded framework that, at each round, jointly selects a query and a subset of respondents based on previously observed responses to efficiently reduce uncertainty about a target latent quantity (e.g., group-level political inclination). Motivated by practical survey constraints, such as limited questions and costly participation, our strategy maximizes information gain under a fixed budget. To handle missing and incomplete responses, we combine graph neural networks for aggregating/imputing partial group information with an information-theoretic criterion that guides per-round selection. Across three real-world opinion datasets, we achieve consistent improvements in population-level response prediction under constrained budgets, including over a 12% relative gain on CES at a 10% respondent budget.