ICLR 2026 Papers

This paper studies how to achieve accurate modeling and effective control in stochastic nonlinear dynamics with multiple interacting objects. However, non-uniform interactions and random topologies make this task challenging. We address these challenges by proposing Graph Controllable Embeddings (GCE), a general framework to learn stochastic multi-object dynamics for linear control. Specifically, GCE is built on Hilbert space embeddings, allowing direct embedding of probability distributions of controlled stochastic dynamics into a reproducing kernel Hilbert space (RKHS), which enables linear operations in its RKHS while retaining nonlinear expressiveness. We provide theoretical guarantees on the existence, convergence, and applicability of GCE. Notably, a mean field approximation technique is adopted to efficiently capture inter-object dependencies and achieves provably low sample complexity. By integrating graph neural networks, we construct data-dependent kernel features which are capable of adapting to dynamic interaction patterns and generalizing to even unseen topologies with only limited training instances. GCE scales seamlessly to multi-object systems of varying sizes and topologies. Leveraging the linearity of Hilbert spaces, GCE also supports simple yet effective control algorithms for synthesizing optimal sequences. Experiments on physical systems, robotics, and power grids validate GCE and demonstrate consistent performance improvement over various competitive embedding methods in both in-distribution and few-shot tests.

Multi-objective optimization (MOO) arises in many real-world applications where trade-offs between competing objectives must be carefully balanced. In the offline setting, where only a static dataset is available, the main challenge is generalizing beyond observed data. We introduce Pareto-Conditioned Diffusion (PCD), a novel framework that formulates offline MOO as a conditional sampling problem. By conditioning directly on desired trade-offs, PCD avoids the need for explicit surrogate models. To effectively explore the Pareto front, PCD employs a reweighting strategy that focuses on high-performing samples and a reference-direction mechanism to guide sampling towards novel, promising regions beyond the training data. Experiments on standard offline MOO benchmarks show that PCD achieves highly competitive performance and, importantly, demonstrates greater consistency across diverse tasks than existing offline MOO approaches.

A fundamental problem in multi-task learning (MTL) is identifying groups of tasks that should be learned together. Since training MTL models for all possible combinations of tasks is prohibitively expensive for large task sets, a crucial component of efficient and effective task grouping is predicting whether a group of tasks would benefit from learning together, measured as per-task performance gain over single-task learning. In this paper, we propose ETAP (Ensemble Task Affinity Predictor), a scalable framework that integrates principled and data-driven estimators to predict MTL performance gains. First, we consider the gradient-based updates of shared parameters in an MTL model to measure the affinity between a pair of tasks as the similarity between the parameter updates based on these tasks. This linear estimator, which we call affinity score, naturally extends to estimating affinity within a group of tasks. Second, to refine these estimates, we train predictors that apply non-linear transformations and correct residual errors, capturing complex and non-linear task relationships. We train these predictors on a limited number of task groups for which we obtain ground-truth gain values via multi-task learning for each group. We demonstrate on benchmark datasets that ETAP improves MTL gain prediction and enables more effective task grouping, outperforming state-of-the-art baselines across diverse application domains.

Modern AI agents such as large language models are trained on diverse tasks---translation, code generation, mathematical reasoning, and text prediction---simultaneously. A key question is to quantify how each individual training task influences performance on a target task, a problem we refer to as task attribution. The direct approach, leave-one-out retraining, measures the effect of removing each task, but is computationally infeasible at scale. An alternative approach that builds surrogate models to predict a target task's performance for any subset of training tasks has emerged in recent literature. Prior work focuses on linear surrogate models, which capture first-order relationships, but miss nonlinear interactions such as synergy, antagonism, or XOR-type effects. In this paper, we first consider a unified task weighting framework for analyzing task attribution methods, and show a new connection between linear surrogate models and influence functions through a second-order analysis. Then, we introduce kernel surrogate models, which more effectively represent second-order task interactions. To efficiently learn the kernel surrogate, we develop a gradient-based estimation procedure that leverages a first-order approximation of pretrained models; empirically, this yields accurate surrogate estimates with less than 2% relative error without repeated retraining. Experiments across multiple domains---including mathematical reasoning in transformers, in-context learning, and multi-objective reinforcement learning---demonstrate the effectiveness of kernel surrogate models. They achieve a 25% higher correlation with the leave-one-out ground truth than linear surrogates and influence-function baselines, enabling more accurate and scalable task attribution. When used for downstream task selection, kernel surrogate models further yield a 40% improvement in demonstration selection for in-context learning and multi-objective reinforcement learning benchmarks.

The reliance on implicit point matching via attention has become a core bottleneck in drag-based editing, resulting in a fundamental compromise on weakened inversion strength and costly test-time optimization (TTO). This compromise severely limits the generative capabilities, suppressing high-fidelity inpainting and text-guided creation. In this paper, we introduce LazyDrag, the first drag-based image editing method for Multi-Modal Diffusion Transformers, which directly eliminates the reliance on implicit point matching. In concrete terms, our method generates an explicit correspondence map from user drag inputs as a reliable reference to boost the attention control. This reliable reference opens the potential for a stable full-strength inversion process, which is the first in the drag-based editing task. It obviates the necessity for TTO and unlocks the generative capability of models. Therefore, LazyDrag naturally unifies precise geometric control with text guidance, enabling complex edits that were previously out of reach: opening the mouth of a dog and inpainting its interior, generating new objects like a ``tennis ball'', or for ambiguous drags, making context-aware changes like moving hands into pockets. Moreover, LazyDrag supports multi-round edits with simultaneous move and scale operations. Evaluated on DragBench, our method outperforms baselines in drag accuracy and perceptual quality, as validated by mean distances, VIEScore and user studies. LazyDrag not only sets new state-of-the-art performance, but also paves a new way to editing paradigms. Here is the project website.

Software issue localization, the task of identifying the precise code locations (files, classes, or functions) relevant to a natural language issue description (e.g., bug report, feature request), is a critical yet time-consuming aspect of software development. While recent LLM-based agentic approaches demonstrate promise, they often incur significant latency and cost due to complex multi-step reasoning and relying on closed-source LLMs. Alternatively, traditional code ranking models, typically optimized for query-to-code or code-to-code retrieval, struggle with the verbose and failure-descriptive nature of issue localization queries. To bridge this gap, we introduce SWERank, an efficient and effective retrieve-and-rerank framework for software issue localization. To facilitate training, we construct SWELoc, a large-scale dataset curated from public GitHub repositories, featuring real-world issue descriptions paired with corresponding code modifications. Empirical results on SWE-Bench-Lite and LocBench show that SWERank achieves state-of-the-art performance, outperforming both prior ranking models and costly agent-based systems using closed-source LLMs like Claude-3.5. Further, we demonstrate SWELoc's utility in enhancing various existing retriever and reranker models for issue localization, establishing the dataset as a valuable resource for the community.

We revisit the use of probabilistic values, which include the well-known Shapley and Banzhaf values, to rank features for explaining the local predicted values of decision trees. The quality of feature rankings is typically assessed with the insertion and deletion metrics. Empirically, we observe that co-optimizing these two metrics is closely related to a joint optimization that selects a subset of features to maximize the local predicted value while minimizing it for the complement. However, we theoretically show that probabilistic values are generally unreliable for solving this joint optimization. Therefore, we explore deriving feature rankings by directly optimizing the joint objective. As the backbone, we propose TreeGrad, which computes the gradients of the multilinear extension of the joint objective in $O(L)$ time for decision trees with $L$ leaves; these gradients include weighted Banzhaf values. Building upon TreeGrad, we introduce TreeGrad-Ranker, which aggregates the gradients while optimizing the joint objective to produce feature rankings, and TreeGrad-Shap, a numerically stable algorithm for computing Beta Shapley values with integral parameters. In particular, the feature scores computed by TreeGrad-Ranker satisfy all the axioms uniquely characterizing probabilistic values, except for linearity, which itself leads to the established unreliability. Empirically, we demonstrate that the numerical error of Linear TreeShap can be up to $10^{15}$ times larger than that of TreeGrad-Shap when computing the Shapley value. As a by-product, we also develop TreeProb, which generalizes Linear TreeShap to support all probabilistic values. In our experiments, TreeGrad-Ranker performs significantly better on both insertion and deletion metrics. Our code is available at https://github.com/watml/TreeGrad.

Model merging plays a crucial role in consolidating multiple specialized models into a single, unified model, especially in the era of large language models (LLMs). Recent research has primarily focused on developing strategies to enhance merging performance with the trained models, while the impact of training paradigms, such as supervised fine-tuning (SFT) and reinforcement learning (RL), on the effectiveness of model merging remains underexplored. In this study, we systematically explore the merging behavior of RL-trained LLMs compared to those trained with traditional SFT. Through comprehensive evaluations across five representative tasks, we find that RL significantly reduces task conflicts and results in less performance degradation after merging, making RL-trained models particularly well-suited for this process. To unearth the reasons behind the superior suitability of RL for model merging, we conduct extensive empirical experiments and theoretical analyses. Our findings highlight three key factors: (1) On-policy training data in RL control the gradient updates in a smaller magnitude, reducing the risk of overwriting existing knowledge for other tasks in the model. (2) The RL optimization objective, which favors "\textit{enough is as good as a feast}", progressively reduces the magnitude of parameter updates as the model converges, thereby alleviating inter-task conflicts. (3) Joint optimization of positive and negative examples in RL steers the model towards an unbiased task-specific parameter subspace, ensuring robust performance while further preventing parameter conflicts.

Neural collapse (NC) plays a key role in understanding deep neural networks. However, existing empirical and theoretical studies of NC focus on one single task. This paper studies neural collapse in multi-task learning. We consider two standard feature-based multi-task learning scenarios: Single-Source Multi-Task Classification (SSMTC) and Multi-Source Multi-Task Classification (MSMTC). Interestingly, we find that the task-specific linear classifier and features converge to the Simplex Equiangular Tight Frame (ETF) in the setting of MSMTC. In the setting of SSMTC, task-specific linear classifier converges to the task-specific ETF and these task-specific ETFs are mutually orthogonal. Moreover, the shared features across tasks converge to the scaled sum of the weight vectors associated with the task-specific labels in each task's classifier. We also provide the theoretical guarantee for our empirical findings. Through detailed analysis, we uncover the mechanism of MTL where each task learns task-specific latent features that together form the shared features. Moreover, we reveal an inductive bias in MTL that task correlation reconfigures the geometry of task-specific classifiers and promotes alignment among the features learned by each task.

Reinforcement learning (RL) algorithms have been used recently to align diffusion models with downstream objectives such as aesthetic quality and text-image consistency by fine-tuning them to maximize a single reward function under a fixed KL regularization. However, this approach is inherently restrictive in practice, where alignment must balance multiple, often conflicting objectives. Moreover, user preferences vary across prompts, individuals, and deployment contexts, with varying tolerances for deviation from a pre-trained base model. We address the problem of inference-time multi-preference alignment: given a set of basis reward functions and a reference KL regularization strength, can we design a fine-tuning procedure so that, at inference time, it can generate images aligned with any user-specified linear combination of rewards and regularization, without requiring additional fine-tuning? We propose Diffusion Blend, a novel approach to solve inference-time multi-preference alignment by blending backward diffusion processes associated with fine-tuned models, and we instantiate this approach with three algorithms: DB-MPA for multi-reward alignment, DB-KLA for KL regularization control, and DB-MPA-LS for approximating DB-MPA without additional inference cost. Extensive experiments show that Diffusion Blend algorithms consistently outperform relevant baselines and closely match or exceed the performance of individually fine-tuned models, enabling efficient, user-driven alignment at inference-time.

Prompt engineering has become central to eliciting the capabilities of large language models (LLMs). At its core lies prompt selection - efficiently identifying the most effective prompts. However, most prior investigations overlook a key challenge: the inherently multi-faceted nature of prompt performance, which cannot be captured by a single metric. To fill this gap, we study the multi-objective prompt selection problem under two practical settings: Pareto prompt set recovery and best feasible prompt identification. Casting the problem into the pure-exploration bandits framework, we adapt provably efficient algorithms from multi-objective bandits and further introduce a novel design for best feasible arm identification in structured bandits, with theoretical guarantees on the identification error in the linear case. Extensive experiments across multiple LLMs show that the bandit-based approaches yield significant improvements over baselines, establishing a principled and efficient framework for multi-objective prompt optimization.

Scaling multi-task low-rank adaptation (LoRA) to a large number of tasks induces catastrophic performance degradation, such as an accuracy drop from 88.2% to 2.0% on DOTA when scaling from 5 to 15 tasks. This failure is due to parameter and representation misalignment. We find that existing solutions, like regularization and dynamic routing, fail at scale because they are constrained by a fundamental trade-off: strengthening regularization to reduce inter-task conflict inadvertently suppresses the essential feature discrimination required for effective routing. In this work, we identify two root causes for this trade-off. First, uniform regularization disrupts inter-task knowledge sharing: shared underlying knowledge concentrates in high-SV components (89% alignment on Flanv2→BBH). Uniform regularization forces high-SV components to update in orthogonal directions, directly disrupting the shared knowledge. Second, Conflict Amplification: Applying LoRA at the component-level (*e.g.*, $W_q, W_v$) amplifies gradient conflicts; we show block-level adaptation reduces this conflict with 47% fewer parameters. Based on these insights, we propose mtLoRA, a scalable solution with three novel designs: 1) Spectral-Aware Regularization to selectively orthogonalize low-SV components while preserving high-SV shared knowledge, 2) Block-Level Adaptation to mitigate conflict amplification and largely improve parameter efficiency, and 3) Fine-Grained Routing using dimension-specific weights for superior expressive power. On four large-scale (15-25 tasks) vision (DOTA and iNat2018) and NLP (Dolly-15k and BBH) benchmarks, mtLoRA achieves 91.7%, 81.5%, 44.5% and 38.5% accuracy on DOTA, iNat2018, Dolly-15k and BBH respectively, outperforming the state-of-the-art by 2.3% on average while using 47% fewer parameters and 24% less training time.

Multi-domain translation (MDT) aims to learn translations between multiple domains, yet existing approaches either require fully aligned tuples or can only handle domain pairs seen in training, limiting their practicality and excluding many cross-domain mappings. We introduce universal MDT (UMDT), a generalization of MDT that seeks to translate between any pair of $K$ domains using only $K-1$ paired datasets with a central domain. To tackle this problem, we propose Diffusion Router (DR), a unified diffusion-based framework that models all central$\leftrightarrow$non-central translations with a single noise predictor conditioned on the source and target domain labels. DR enables indirect non-central translations by routing through the central domain. We further introduce a novel scalable learning strategy with a variational-bound objective and an efficient Tweedie refinement procedure to support direct non-central mappings. Through evaluation on three large-scale UMDT benchmarks, DR achieves state-of-the-art results for both indirect and direct translations, while lowering sampling cost and unlocking novel tasks such as sketch$\leftrightarrow$segmentation. These results establish DR as a scalable and versatile framework for universal translation across multiple domains.

For multi-stage recommenders in industry, a user request would first trigger a simple and efficient retriever module that selects and ranks a list of relevant items, then the recommender calls a slower but more sophisticated reranking model that refines the item list exposure to the user. To consistently optimize the two-stage retrieval reranking framework, most efforts have focused on learning reranker-aware retrievers. In contrast, there has been limited work on how to achieve a retriever-aware reranker. In this work, we provide evidence that the retriever scores from the previous stage are informative signals that have been underexplored. Specifically, we first empirically show that the reranking task under the two-stage framework is naturally a noise reduction problem on the retriever scores, and theoretically show the limitations of naive utilization techniques of the retriever scores. Following this notion, we derive an adversarial framework DNR that associates the denoising reranker with a carefully designed noise generation module. The resulting DNR solution extends the conventional score error minimization loss with three augmented objectives, including: 1) a denoising objective that aims to denoise the noisy retriever scores to align with the user feedback; 2) an adversarial retriever score generation objective that improves the exploration in the retriever score space; and 3) a distribution regularization term that aims to align the distribution of generated noisy retriever scores with the real ones. We conduct extensive experiments on three public datasets and an industrial recommender system, together with analytical support, to validate the effectiveness of the proposed DNR.

As machine learning models continue to grow in size and complexity, efficient serving faces increasingly broad trade-offs spanning accuracy, latency, resource usage, and other objectives. Multi-model serving further complicates these trade-offs; for example, in cascaded models, each early-exit decision balances latency reduction against potential accuracy loss. Despite the pervasiveness and importance of such trade-offs, current strategies remain largely heuristic and case-specific, limiting both their theoretical guarantees and general applicability. We present a general framework, T-Tamer, which formalizes this setting as a multi-stage decision process, where the objective is to determine both when to exit and which model to consult. Our main result shows that recall (i.e., the ability to revisit earlier models) is both necessary and sufficient for achieving provable performance guarantees. In particular, we prove that strategies without recall cannot obtain any constant-factor approximation to the optimal trade-off, whereas recall-based strategies provably attain the optimal trade-off in polynomial time. We validate our analysis through experiments on synthetic datasets and early-exit workloads for vision and NLP benchmarks. The results show that recall-based strategies consistently yield efficient accuracy–latency trade-offs. We hope this work provides a principled foundation for bridging heuristic practice with theoretical guarantees in the design of early-exit and cascaded models.

Many sequential decision-making tasks involve optimizing multiple conflicting objectives, requiring policies that adapt to different user preferences. In multi-objective reinforcement learning (MORL), one widely studied approach addresses this by training a single policy network conditioned on preference-weighted rewards. In this paper, we explore a novel algorithmic perspective: leveraging reward-free reinforcement learning (RFRL) for MORL. While RFRL has historically been studied independently of MORL, it learns optimal policies for any possible reward function, making it a natural fit for MORL's challenge of handling unknown user preferences. We propose using the RFRL's training objective as an auxiliary task to enhance MORL, enabling more effective knowledge sharing beyond the multi-objective reward function given at training time. To this end, we adapt a state-of-the-art RFRL algorithm to the MORL setting and introduce a preference-guided exploration strategy that focuses learning on relevant parts of the environment. Through extensive experiments and ablation studies, we demonstrate that our approach significantly outperforms the state-of-the-art MORL methods across diverse MO-Gymnasium tasks, achieving superior performance and data efficiency. This work provides the first systematic adaptation of RFRL to MORL, demonstrating its potential as a scalable and empirically effective solution to multi-objective policy learning.

Scalable robot policy pre-training has been hindered by the high cost of collecting high-quality demonstrations for each platform. In this study, we address this issue by uniting offline reinforcement learning (offline RL) with cross-embodiment learning. Offline RL leverages both expert and abundant suboptimal data, and cross-embodiment learning aggregates heterogeneous robot trajectories across diverse morphologies to acquire universal control priors. We perform a systematic analysis of this offline RL and cross-embodiment paradigm, providing a principled understanding of its strengths and limitations. To evaluate this offline RL and cross-embodiment paradigm, we construct a suite of locomotion datasets spanning 16 distinct robot platforms. Our experiments confirm that this combined approach excels at pre-training with datasets rich in suboptimal trajectories, outperforming pure behavior cloning. However, as the proportion of suboptimal data and the number of robot types increase, we observe that conflicting gradients across morphologies begin to impede learning. To mitigate this, we introduce an embodiment-based grouping strategy in which robots are clustered by morphological similarity and the model is updated with a group gradient. This simple, static grouping substantially reduces inter-robot conflicts and outperforms existing conflict-resolution methods.

The pretrain-finetuning paradigm has achieved notable success in graph learning. Moreover, merging models fine-tuned on different tasks to enable a parameter-efficient model with multi-task capabilities is gaining increasing attention for its practicality. However, existing model merging methods, such as weight averaging and task arithmetic, struggle to generalize well to graph structures and Graph Neural Network (GNN) models due to the unique structural heterogeneity of graph data. In this paper, we propose an innovative graph model merging framework called G-Merging for merging multiple task-specific fine-tuned GNN models. G-Merging first employs task arithmetic to coarsely merge graph models, capturing shared cross-task knowledge. Second, it introduces a Topology-aware Wasserstein Distance (TWD) loss to train lightweight task adapters, preserving domain-specific graph patterns via aligning the embeddings of merged and fine-tuned models. Third, G-Merging integrates the adapters into a training-free, topology-aware router within a mixture-of-experts (MoE) architecture, dynamically routing input graphs to task-specific adapters based on structural similarity, thereby mitigating conflicts and enhancing knowledge sharing. Extensive experiments on 8 graph downstream datasets demonstrate the effectiveness of G-Merging, showing impressive performance close to or exceeding individual finetuned models while improving parameters and training efficiency. Our code is available at https://anonymous.4open.science/r/G-Merging-D515

Although probing frozen models has become a standard evaluation paradigm, self-supervised learning in audio defaults to fine-tuning when pursuing state-of-the-art on AudioSet. A key reason is that global pooling creates an information bottleneck causing linear probes to misrepresent the embedding quality: The $\texttt{cls}$-token discards crucial token information about dispersed, localized events in multi-label audio. This weakness is rooted in the mismatch between the pretraining objective (operating globally) and the downstream task (localized events). Across a comprehensive benchmark of 13 datasets and 6 spectrogram-based encoders, we first investigate the global pooling bottleneck. We then introduce binarized prototypical probes: a lightweight and simple pooling method that learns prototypes to perform class-wise information aggregation. Despite its simplicity, our method notably outperforms linear and attentive probing. Our work establishes probing as a competitive and efficient paradigm for evaluating audio SSL models, challenging the reliance on costly fine-tuning.