ICLR 2026 Papers

International Conference on Learning Representations

Decision breakdown

5,358papers

Counted from the official paper list; may differ slightly from the number the conference announced.

  • Oral
    2244.2%
  • Poster
    5,13495.8%

Browse all papers

Explainable $ K $-means Neural Networks for Multi-view Clustering

Yalan Qin, Xinpeng Zhang, Guorui Feng

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Despite multi-view clustering has achieved great progress in past decades, it is still a challenge to balance the effectiveness, efficiency, completeness and consistency of nonlinearly separable clustering for the data from different views. To address this challenge, we show that multi-view clustering can be regarded as a three-level optimization problem. To be specific, we divide the multi-view clustering into three sub-problems based on $ K $-means or kernel $ K $-means, i.e., linear clustering on the original multi-view dataset, nonlinear clustering on the set of obtained linear clusters and multi-view clustering by integrating partition matrices from different views obtained by linear and nonlinear clustering based on reconstruction. We propose Explainable $ K $-means Neural Networks (EKNN) and present how to unify these three sub-problems into a framework based on EKNN. It is able to simultaneously consider the effectiveness, efficiency, completeness and consistency for the nonlinearly multi-view clustering and can be optimized by an iterative algorithm. EKNN is explainable since the effect of each layer is known. To the best of our knowledge, this is the first attempt to balance the effectiveness, efficiency, completeness and consistency by dividing the multi-view clustering into three different sub-problems. Extensive experimental results demonstrate the effectiveness and efficiency of EKNN compared with other methods for multi-view clustering on different datasets in terms of different metrics.

Poster
Transferable and Stealthy Adversarial Attacks on Large Vision-Language Models

Zhewen Yao, Yao Zhu, Shiliang Zhang

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Existing adversarial attacks on large Vision-Language Models (VLMs) often struggle with limited transferability to black-box models or produce perceptible artifacts that are easily detected. This paper presents Progressive Semantic Infusion (PSI), a diffusion-based attack that progressively aligns and infuses natural target semantics. To improve transferability, PSI leverages diffusion priors to better align adversarial examples with the natural image distribution and employs progressive alignment to mitigate overfitting on a single fixed surrogate objective. To enhance stealthiness, PSI embeds source-aware cues during denoising to preserve visual fidelity and avoid detectable artifacts. Experiments show that PSI effectively attacks open-source, adversarially trained, and commercial VLMs, including GPT-5 and Grok-4, surpassing existing methods in both transferability and stealthiness. Our findings highlight a critical vulnerability in modern vision-language systems and offer valuable insights towards building more robust and trustworthy multimodal models.

Poster
Adaptive Scaling of Policy Constraints for Offline Reinforcement Learning

Tan Jing, Xiaorui Li, Chao Yao, Xiaojuan Ban, Yuetong FANG, Renjing Xu, Zhaolin Yuan

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Offline reinforcement learning (RL) enables learning effective policies from fixed datasets without any environment interaction. Existing methods typically employ policy constraints to mitigate the distribution shift encountered during offline RL training. However, because the scale of the constraints varies across tasks and datasets of differing quality, existing methods must meticulously tune hyperparameters to match each dataset, which is time-consuming and often impractical. To bridge this gap, we propose Adaptive Scaling of Policy Constraints (ASPC), a second-order differentiable framework that automatically adjusts the scale of policy constraints during training. We theoretically analyze its performance improvement guarantee. In experiments on 39 datasets across four D4RL domains, ASPC using a single hyperparameter configuration outperforms other adaptive constraint methods and state-of-the-art offline RL algorithms that require per-dataset tuning, achieving an average 35\% improvement in normalized performance over the baseline. Moreover, ASPC consistently yields additional gains when integrated with a variety of existing offline RL algorithms, demonstrating its broad generality.

Poster
Emergence of Spatial Representation in an Actor-Critic Agent with Hippocampus-Inspired Sequence Generator

Xiao-Xiong Lin, Yuk-Hoi Yiu, Christian Leibold

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Sequential activation of place-tuned neurons in an animal during navigation is typically interpreted as reflecting the sequence of input from adjacent positions along the trajectory. More recent theories about such place cells suggest sequences to arise from abstract cognitive objectives like planning. Here, we propose a mechanistic and parsimonious interpretation to complement these ideas: hippocampal sequences arise from intrinsic recurrent circuitry that propagates activity without sustained input, acting as a temporal memory buffer for extremely sparse inputs. We implement a minimal sequence generator inspired by neurobiology and pair it with an actor–critic learner for egocentric visual navigation. Our agent reliably solves a continuous maze without explicit geometric cues, with performance depending on the length of the recurrent sequence. Crucially, the model outperforms LSTM cores under sparse input conditions (16 channels, $\sim2.5$% activity), but not under dense input, revealing a strong interaction between representational sparsity and memory architecture. Hidden units develop localized place fields, distance-dependent spatial kernels, and task-dependent remapping, while inputs to the generator orthogonalize and spatial information increases across layers. These phenomena align with neurobiological data and are causal to performance. Together, our results show that sparse input synergizes with sequence-generating dynamics, providing both a mechanistic account of place cell sequences in the mammalian hippocampus and a simple inductive bias for reinforcement learning based on sparse egocentric inputs in navigation tasks.

Poster
DHG-Bench: A Comprehensive Benchmark for Deep Hypergraph Learning

Fan Li, Xiaoyang Wang, Wenjie Zhang, Ying Zhang, Xuemin Lin

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Deep graph models have achieved great success in network representation learning. However, their focus on pairwise relationships restricts their ability to learn pervasive higher-order interactions in real-world systems, which can be naturally modeled as hypergraphs. To tackle this issue, Hypergraph Neural Networks (HNNs) have garnered substantial attention in recent years. Despite the proposal of numerous HNNs, the absence of consistent experimental protocols and multi-dimensional empirical analysis impedes deeper understanding and further development of HNN research. While several toolkits for deep hypergraph learning (DHGL) have been introduced to facilitate algorithm evaluation, they provide only limited quantitative evaluation results and insufficient coverage of advanced algorithms, datasets, and benchmark tasks. To fill the gap, we introduce DHG-Bench, the first comprehensive benchmark for HNNs. Specifically, DHG-Bench systematically investigates the characteristics of HNNs in terms of four dimensions: effectiveness, efficiency, robustness, and fairness. We comprehensively evaluate 17 state-of-the-art HNN algorithms on 22 diverse datasets spanning node-, edge-, and graph-level tasks, under unified experimental settings. Extensive experiments reveal both the strengths and limitations of existing algorithms, offering valuable insights and directions for future research. Furthermore, to facilitate reproducible research, we have developed an easy-to-use library for training and evaluating different HNN methods. The DHG-Bench library is available at: https://github.com/Coco-Hut/DHG-Bench.

Poster
MATRIX: Mask Track Alignment for Interaction-aware Video Generation

Siyoon Jin, Seongchan Kim, Jae Ho Lee, Dahyun Chung, Hyunwook Choi, Jisu Nam, Jiyoung Kim, Seungryong Kim

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Video DiTs have advanced video generation, yet they still struggle to model multi-instance or subject-object interactions. This raises a key question: How do these models internally represent interactions? To answer this, we curate MATRIX-11K, a video dataset with interaction-aware captions and multi-instance mask tracks. Using this dataset, we conduct a systematic analysis that formalizes two perspectives of video DiTs: semantic grounding, via video-to-text attention, which evaluates whether noun and verb tokens capture instances and their relations; and semantic propagation, via video-to-video attention, which assesses whether instance bindings persist across frames. We find both effects concentrate in a small subset of interaction-dominant layers. Motivated by this, we introduce MATRIX, a simple and effective regularization that aligns attention in specific layers of video DiTs with multi-instance mask tracks from the MATRIX-11K dataset, enhancing both grounding and propagation. We further propose InterGenEval, an evaluation protocol for interaction-aware video generation. In experiments, MATRIX improves both interaction fidelity and semantic alignment while reducing drift and hallucination. Extensive ablations validate our design choices. Codes and weights will be released.

Poster
Stacked from One: Multi-Scale Self-Injection for Context Window Extension

Wei Han, Pan Zhou, Shuicheng YAN

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The limited context window of contemporary large language models (LLMs) hinders broader application. In this work, we present SharedLLM, a novel approach grounded in the design philosophy of multi-grained context compression and query-aware information retrieval. SharedLLM is composed of two short-context LLMs: a lower moel (compressor) and an upper model (decoder). The lower model compresses context information, while the upper model processes compressed, context information from the lower model and performs context-aware modeling. Information transfer between the compressor and decoder occurs only at the lowest layers to reduce redundant computation. Based on this architecture, we introduce a specialized tree-style data structure to efficiently encode, store and retrieve multi-grained contextual information from text chunks. This entire process, wherein the sender and receiver are derived from the same LLM layer, is referred to as self-injection. In our evaluation on long-context modeling and understanding tasks, SharedLLM achieves superior or comparable results to several strong baselines, striking an effective balance between efficiency and performance. Meanwhile, with the aforementioned design choices, SharedLLM can greatly reduce memory consumption, and demonstrates substantial speed-ups over other advanced baselines. The core code of our implementation along with training and evaluation is available in appendix and supplementary.

Poster
Adaptive Test-Time Training for Predicting Need for Invasive Mechanical Ventilation in Multi-Center Cohorts

Xiaolei Lu, Shamim Nemati

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Accurate prediction of the need for invasive mechanical ventilation (IMV) in intensive care units (ICUs) patients is crucial for timely interventions and resource allocation. However, variability in patient populations, clinical practices, and electronic health record (EHR) systems across institutions introduces domain shifts that degrade the generalization performance of predictive models during deployment. Test-Time Training (TTT) has emerged as a promising approach to mitigate such shifts by adapting models dynamically during inference without requiring labeled target-domain data. In this work, we introduce Adaptive Test-Time Training (AdaTTT), an enhanced TTT framework tailored for EHR-based IMV prediction in ICU settings. We begin by deriving information-theoretic bounds on the test-time prediction error and demonstrate that it is constrained by the uncertainty between the main and auxiliary tasks. To enhance their alignment, we introduce a self-supervised learning framework with pretext tasks: reconstruction and masked feature modeling optimized through a dynamic masking strategy that emphasizes features critical to the main task. Additionally, to improve robustness against domain shifts, we incorporate prototype learning and employ Partial Optimal Transport (POT) for flexible, partial feature alignment while maintaining clinically meaningful patient representations. Experiments across multi-center ICU cohorts demonstrate competitive classification performance on different test-time adaptation benchmarks.

Poster
Online Learning and Equilibrium Computation with Ranking Feedback

Mingyang Liu, Yongshan Chen, Zhiyuan Fan, Gabriele Farina, Asuman E. Ozdaglar, Kaiqing Zhang

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Online learning in arbitrary and possibly adversarial environments has been extensively studied in sequential decision-making, with a strong connection to equilibrium computation in game theory. Most existing online learning algorithms are based on \emph{numeric} utility feedback from the environment, which may be unavailable in applications with humans in the loop and/or with privacy concerns. In this paper, we study an online learning setting where only a \emph{ranking} of a set of proposed actions is provided to the learning agent at each timestep. We consider both ranking models based on either the \emph{instantaneous} utility at each timestep, or the \emph{time-average} utility until the current timestep, in both \emph{full-information} and \emph{bandit} feedback settings. Focusing on the standard (external-)regret metric, we show that sublinear regret cannot be achieved with the instantaneous utility ranking feedback in general. Moreover, we show that when the ranking model is relatively {deterministic} (\emph{i.e.,} with a small temperature in the Plackett-Luce model), sublinear regret cannot be achieved with the time-average utility ranking feedback, either. We then propose new algorithms to achieve sublinear regret, under the additional assumption that the utility vectors have a sublinear variation. Notably, we also show that when time-average utility ranking is used, such an additional assumption can be avoided in the full-information setting. As a consequence, we show that if all the players follow our algorithms, an approximate coarse correlated equilibrium of a normal-form game can be found through repeated play. Finally, we also validate the effectiveness of our algorithms via numerical experiments.

Oral
SEED-SET: Scalable Evolving Experimental Design for System-level Ethical Testing

Anjali Parashar, Yingke Li, Eric Yang Yu, Fei Chen, James Neidhoefer, Devesh Upadhyay, Chuchu Fan

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As autonomous systems such as drones, become increasingly deployed in high-stakes, human-centric domains, it is critical to evaluate the ethical alignment since failure to do so imposes imminent danger to human lives, and long term bias in decision-making. Automated ethical benchmarking of these systems is understudied due to the lack of ubiquitous, well-defined metrics for evaluation, and stakeholder-specific subjectivity, which cannot be modeled analytically. To address these challenges, we propose SEED-SET, a Bayesian experimental design framework that incorporates domain-specific objective evaluations, and subjective value judgments from stakeholders. SEED-SET models both evaluation types separately with hierarchical Gaussian Processes, and uses a novel acquisition strategy to propose interesting test candidates based on both models. We validate our approach for ethical benchmarking of autonomous agents on two applications and find our method to perform the best. Our method provides an interpretable and efficient trade-off between exploration and exploitation, by generating up to $2\times$ optimal test candidates compared to baselines, with $1.25\times$ improvement in coverage of high dimensional search spaces.

Poster
Embracing Discrete Search: A Reasonable Approach to Causal Structure Learning

Marcel Wienöbst, Leonard Henckel, Sebastian Weichwald

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We present FLOP (Fast Learning of Order and Parents), a score-based causal discovery algorithm for linear models. It pairs fast parent selection with iterative Cholesky-based score updates, cutting run-times over prior algorithms. This makes it feasible to fully embrace discrete search, enabling iterated local search with principled order initialization to find graphs with scores at or close to the global optimum. The resulting structures are highly accurate across benchmarks, with near-perfect recovery in standard settings. This performance calls for revisiting discrete search over graphs as a reasonable approach to causal discovery.

Poster
Learning to Reason over Continuous Tokens with Reinforcement Learning

Yiran Zhao, Yuhui Xu, Doyen Sahoo, Caiming Xiong, Junnan Li

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Large Language Models (LLMs) have shown strong performance in complex reasoning tasks, especially when guided by Chain-of-Thought (CoT) prompting. However, conventional CoT reasoning in the discrete token space suffers from high computational and memory costs due to verbose intermediate steps. Recent work has explored latent reasoning in the embedding space to improve efficiency, but often at the cost of clarity and performance. In this work, we propose $\underline{Hy}$brid $\underline{Rea}$soning ($\texttt{HyRea}$), a unified framework that enables LLMs to dynamically switch between explicit (token-based) and latent (embedding-based) reasoning during inference. To train the model to make these decisions effectively, we introduce a two-stage training pipeline: (1) a supervised cold-start phase that introduces latent reasoning by replacing low-entropy CoT steps with embeddings, and (2) a reinforcement learning phase using Group Relative Policy Optimization (GRPO) to fine-tune the model’s reasoning strategy based on task-specific rewards. Experiments on mathematical reasoning benchmarks show that \texttt{HyRea} achieves significant reductions in token usage while maintaining or improving accuracy, offering an effective and scalable solution for efficient multi-step reasoning in LLMs.

Poster
A Schrödinger Eigenfunction Method for Long-Horizon Stochastic Optimal Control

Louis Claeys, Artur Goldman, Zebang Shen, Niao He

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High-dimensional stochastic optimal control (SOC) becomes harder with longer planning horizons: existing methods scale linearly in the horizon $T$, with performance often deteriorating exponentially. We overcome these limitations for a subclass of linearly-solvable SOC problems—those whose uncontrolled drift is the gradient of a potential. In this setting, the Hamilton-Jacobi-Bellman equation reduces to a linear PDE governed by an operator $\mathcal{L}$. We prove that, under the gradient drift assumption, $\mathcal{L}$ is unitarily equivalent to a Schrödinger operator $\mathcal{S} = -\Delta + \mathcal{V}$ with purely discrete spectrum, allowing the long-horizon control to be efficiently described via the eigensystem of $\mathcal{L}$. This connection provides two key results: first, for a symmetric linear-quadratic regulator (LQR), $\mathcal{S}$ matches the Hamiltonian of a quantum harmonic oscillator, whose closed-form eigensystem yields an analytic solution to the symmetric LQR with arbitrary terminal cost. Second, in a more general setting, we learn the eigensystem of $\mathcal{L}$ using neural networks. We identify implicit reweighting issues with existing eigenfunction learning losses that degrade performance in control tasks, and propose a novel loss function to mitigate this. We evaluate our method on several long-horizon benchmarks, achieving an order-of-magnitude improvement in control accuracy compared to state-of-the-art methods, while reducing memory usage and runtime complexity from $\mathcal{O}(Td)$ to $\mathcal{O}(d)$.

Poster
An Improved Model-free Decision-estimation Coefficient with Applications in Adversarial MDPs

Haolin Liu, Chen-Yu Wei, Julian Zimmert

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We study decision making with structured observation (DMSO). The complexity for DMSO has been characterized by a series of work [ FKQR21 , CMB22 , FGH23 ]. Still, there is a gap between known regret upper and lower bounds: current upper bounds incur a model estimation error that scales with the size of the model class. The work of [FGQ+23 ] made an initial attempt to reduce the estimation error to only scale with the size of the value function set, resulting in the complexity called optimistic decision-estimation coefficient (optimistic DEC). Yet, their approach relies on the optimism principle to drive exploration, which deviates from the general idea of DEC that drives exploration only through information gain. In this work, we introduce an improved model-free DEC, called Dig-DEC, that removes the optimism mechanism in [FGQ+23 ], making it more aligned with existing model-based DEC. Dig-DEC is always upper bounded by optimistic DEC, and could be significantly smaller in special cases. Importantly, the removal of optimism allows it to seamlessly handle adversarial environments, while it was unclear how to achieve it within the optimistic DEC framework. By applying Dig-DEC to hybrid MDPs where the transition is stochastic but the reward is adversarial, we provide the first model-free regret bounds in hybrid MDPs with bandit feedback in multiple settings: bilinear classes, Bellman-complete MDPs with bounded Bellman-eluder dimension or coverability, resolving the main open problem left by [LWZ25]. We also improve online function-estimation procedure used in model-free learning: For average estimation error minimization, we improve the estimator to achieve better concentration. This improves the $T^{\frac{3}{4}}$ and $T^{\frac{5}{6}}$ regret of [FGQ+23 ] to $T^{\frac{2}{3}}$and $T^{\frac{7}{9}}$ in the cases with on-policy and off-policy exploration. For squared estimation error minimization in Bellman-complete MDPs, we redesign the two-timescale procedure in [ AZ22 , FGQ+23], achieving $\sqrt{T}$ regret that improves over the $T^{\frac{2}{3}}$ regret by [ FGQ+23 ]. This is the first time the performance of a DEC-based approach for Bellman-complete MDPs matches that of optimism-based approaches [JLM21, XFB+23].

Poster
Rethinking LLM Evaluation: Can We Evaluate LLMs with 200× Less Data?

Shaobo Wang, Cong Wang, Wenjie Fu, Yue Min, Mingquan Feng, Isabel Guan, Xuming Hu, Conghui He, Cunxiang Wang, Kexin Yang, Xingzhang Ren, Fei Huang, Dayiheng Liu, Linfeng Zhang

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As the demand for comprehensive evaluations of diverse model capabilities steadily increases, benchmark suites have correspondingly grown significantly in scale. Despite notable advances in redundancy reduction and subset-level performance prediction, a systematic framework that effectively integrates these methods to ensure both prediction accuracy and ranking consistency is still largely elusive. In this paper, we first perform a sample-level analysis of benchmark redundancy and identify several highly similar samples that can be eliminated. Besides, we frame benchmark compression as an optimization problem with the aim of score reconstruction. Building on these, we then propose EssenceBench, a coarse-to-fine framework utilizing an iterative Genetic Algorithm (GA), which takes the advantages of fitness-based subset search and attribution-based sample search. Compared to previous methods, our approach yields superior compression results with lower reconstruction error and markedly higher efficiency. In particular, on the HellaSwag benchmark (10K samples), our method preserves the ranking of all models shifting within 5% using 25$\times$ fewer samples, and achieves 95% ranking preservation shifting within 5% using only 200$\times$ fewer samples. The source code will be made available upon acceptance of the paper.

Poster
Discrete Latent Features Ablate Adversarial Attack: A Robust Prompt Tuning Framework for VLMs

Yang Chen, Yanbin Wei, James Kwok, Yu Zhang

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While adversarial fine-tuning can enhance the robustness of vision-language models (VLMs), such approaches are computationally expensive. Adversarial prompt tuning has emerged as a practical alternative. However, existing methods are limited by their reliance on vulnerable continuous image features. To mitigate the vulnerability in the feature representation, we propose **DEFEAT** (**D**iscrete Lat**E**nt **F**eatur**E** based **A**dversarial **T**raining), a robust prompt tuning framework for VLMs. Specifically, the DEFEAT method introduces a perturbation discrete shield module that reconstructs discrete latent features and designs a logits fusion strategy, substantially reducing the discrepancy between clean and adversarial image representations. Moreover, the DEFEAT method integrates prompt tuning with adversarial training while applying regularization from learnable prompts to hand-crafted prompts, further enhancing the adversarial robustness. Extensive experiments across 15 datasets validate the effectiveness of the proposed DEFEAT method among existing adversarial prompt tuning methods.

Poster
Interactive Learning of Single-Index Models via Stochastic Gradient Descent

Nived Rajaraman, Yanjun Han

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Stochastic gradient descent (SGD) is a cornerstone algorithm for high-dimensional optimization, renowned for its empirical successes. Recent theoretical advances have provided a deep understanding of how SGD enables feature learning in high-dimensional nonlinear models, most notably the *single-index model* with i.i.d. data. In this work, we study the sequential learning problem for single-index models, also known as generalized linear bandits or ridge bandits, where SGD is a simple and natural solution, yet its learning dynamics remain largely unexplored. We show that, similar to the optimal interactive learner, SGD undergoes a distinct "burn-in" phase before entering the "learning" phase in this setting. Moreover, with an appropriately chosen learning rate schedule, a single SGD procedure simultaneously achieves near-optimal (or best-known) sample complexity and regret guarantees across both phases, for a broad class of link functions. Our results demonstrate that SGD remains highly competitive for learning single-index models under adaptive data.

Poster
Steerable Adversarial Scenario Generation through Test-Time Preference Alignment

Tong Nie, Yuewen Mei, Yihong Tang, Junlin He, Jie Sun, Haotian Shi, Wei Ma, Jian Sun

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Adversarial scenario generation is a cost-effective approach for safety assessment of autonomous driving systems. However, existing methods are often constrained to a single, fixed trade-off between competing objectives such as adversariality and realism. This yields behavior-specific models that cannot be steered at inference time, lacking the efficiency and flexibility to generate tailored scenarios for diverse training and testing requirements. In view of this, we reframe the task of adversarial scenario generation as a multi-objective preference alignment problem and introduce a new framework named Steerable Adversarial scenario GEnerator (SAGE). SAGE enables fine-grained test-time control over the trade-off between adversariality and realism without any retraining. We first propose hierarchical group-based preference optimization, a data-efficient offline alignment method that learns to balance competing objectives by decoupling hard feasibility constraints from soft preferences. Instead of training a fixed model, SAGE fine-tunes two experts on opposing preferences and constructs a continuous spectrum of policies at inference time by linearly interpolating their weights. We provide theoretical justification for this framework through the lens of linear mode connectivity. Extensive experiments demonstrate that SAGE not only generates scenarios with a superior balance of adversariality and realism but also enables more effective closed-loop training of driving policies. Project page: https://tongnie.github.io/SAGE/.

Poster
Byzantine-Robust Federated Learning with Learnable Aggregation Weights

Javad Parsa, Amir Hossein Daghestani, André M. H. Teixeira, Mikael Johansson

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Federated Learning (FL) enables clients to collaboratively train a global model without sharing their private data. However, the presence of malicious (Byzantine) clients poses significant challenges to the robustness of FL, particularly when data distributions across clients are heterogeneous. In this paper, we propose a novel Byzantine-robust FL optimization problem that incorporates adaptive weighting into the aggregation process. Unlike conventional approaches, our formulation treats aggregation weights as learnable parameters, jointly optimizing them alongside the global model parameters. To solve this optimization problem, we develop an alternating minimization algorithm with strong convergence guarantees under adversarial attack. We analyze the Byzantine resilience of the proposed objective. We evaluate the performance of our algorithm against state-of-the-art Byzantine-robust FL approaches across various datasets and attack scenarios. Experimental results demonstrate that our method consistently outperforms existing approaches, particularly in settings with highly heterogeneous data and a large proportion of malicious clients.

Poster
RADAR: Learning to Route with Asymmetry-aware Distance Representations

Hang Yi, Ziwei Huang, Yining Ma, Zhiguang Cao

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Recent neural solvers have achieved strong performance on vehicle routing problems (VRPs), yet they mainly assume symmetric Euclidean distances, restricting applicability to real-world scenarios. A core challenge is encoding the relational features in asymmetric distance matrices of VRPs. Early attempts directly encoded these matrices but often failed to produce compact embeddings and generalized poorly at scale. In this paper, we propose RADAR, a scalable neural framework that augments existing neural VRP solvers with the ability to handle asymmetric inputs. RADAR addresses asymmetry from both static and dynamic perspectives. It leverages Singular Value Decomposition (SVD) on the asymmetric distance matrix to initialize compact and generalizable embeddings that inherently encode the *static asymmetry* in the inbound and outbound costs of each node. To further model *dynamic asymmetry* in embedding interactions during encoding, it replaces the standard softmax with Sinkhorn normalization that imposes joint row and column distance awareness in attention weights. Extensive experiments on synthetic and real-world benchmarks across various VRPs show that RADAR outperforms strong baselines on both in-distribution and out-of-distribution instances, demonstrating robust generalization and superior performance in solving asymmetric VRPs.

Poster