ICML 2026 Papers

Accurate survival prediction in kidney transplantation is critical yet challenging due to the complex interplay between functional biomarkers and patient characteristics under censoring. To address this, we propose a functional censored quantile neural network (FunCQNet), a novel framework that integrates deep neural networks with a censoring-adjusted sequential quantile loss to approximate interaction-dependent coefficient functions. We further introduce a conformal inference approach to rigorously assess the significance of functional-scalar interactions, ensuring interpretability alongside predictive power. Extensive simulations demonstrate that FunCQNet robustly recovers functional effects under varying noise and censoring levels. When applied to kidney transplant data, the model yields precise multi-quantile predictions and reveals clinically significant, age-dependent interaction patterns between donor type and recipient survival.

While Transformer-based architectures have revolutionized neural decoding, existing models often treat codes as generic sequences, ignoring their inherent algebraic properties. In this paper, we take a step toward bridging these two domains by proposing a novel decoding approach that integrates the algebraic structure of cyclic codes into Transformer-based decoders. Leveraging the inherent cyclic properties, we introduce interpretable error correction patterns and inter-node relationship hypotheses that link the structural characteristics of the codes to the model parameters. Building on these insights, we design a plug-and-play, flexibly deployable decoding method tailored for cyclic codes. Experimental results show that our method achieves an average reduction in bit error rate (BER) by an order of magnitude, while also reducing the total number of parameters by approximately 97%. Additional comparative experiments validate our proposed conjectures and highlight a promising pathway for bridging classical coding theory and modern Transformer-based decoding architectures.

Inference on the conditional mean function (CMF) is central to tasks from adaptive experimentation to optimal treatment assignment and algorithmic fairness auditing. In this work, we provide a novel asymptotic anytime-valid test for a CMF global null (e.g., that all conditional means are zero) and contrasts between CMFs, enabling experimenters to make high confidence decisions at \textit{any} time during the experiment beyond a minimum sample size. We provide mild conditions under which our tests achieve (i) asymptotic type-I error guarantees, (i) power one, and, unlike past tests, (iii) optimal sample complexity relative to a Gaussian location testing. By inverting our tests, we show how to construct function-valued asymptotic confidence sequences for the CMF and contrasts thereof. Experiments on both synthetic and real-world data show our method is well-powered across various distributions while preserving the nominal error rate under continuous monitoring.

Large language models often hallucinate with high confidence on "random facts" that lack inferable patterns. We formalize the memorization of such facts as a membership testing problem, unifying the discrete error metrics of Bloom filters with the continuous log-loss of LLMs. By analyzing this problem in the regime where facts are sparse in the universe of plausible claims, we establish a rate-distortion theorem: the optimal memory efficiency is characterized by the minimum KL divergence between score distributions on facts and non-facts. This theoretical framework provides a distinctive explanation for hallucination under an idealized setting: even with optimal training, perfect data, and a simplified ``closed world'' setting, the information-theoretically optimal strategy under limited capacity is not to abstain or forget, but to assign high confidence to some non-facts, resulting in hallucination. We validate this theory empirically on both synthetic and real-world data, showing that hallucinations persist as a natural consequence of lossy compression. The same theorem recovers and sharpens classical space lower bounds for Bloom-type filters, pinning down an additive constant left open for two-sided filters.

Stochastic differential equations (SDEs) and stochastic partial differential equations (SPDEs) are fundamental for modeling stochastic dynamics across the natural sciences and modern machine learning. Learning their solution operators with deep learning models promises fast solvers and new perspectives on classical learning tasks. In this work, we build on Wiener--chaos expansions (WCE) to design neural operator (NO) architectures for SDEs and SPDEs: we project driving noise paths onto orthonormal Wick--Hermite features and use NO backbones to parameterize the corresponding chaos coefficients governed by deterministic equations, enabling reconstruction of S(P)DE solutions from the observed noise trajectories. Empirically, we achieve competitive accuracy across several tasks, including standard SPDE benchmarks and SDE-based diffusion one-step image sampling, topological graph interpolation, financial extrapolation, parameter estimation, and manifold SDE flood forecasting. We further explore a law-matching setting where the Brownian trajectories paired with training solutions are unobserved, and show that the proposed framework remains effective by sampling auxiliary Brownian paths from the prescribed noise prior. These results suggest WCE-based neural operators are a practical and scalable approach to learning SDE/SPDE solution operators across domains. Our source code can be found in https://github.com/EEthanShi/SDENO.

Gradient signals in LLM training are highly anisotropic: recurrent linguistic structure concentrates energy into a small set of dominant spectral directions, while context-specific information resides in a long tail. We show that this spike–tail separation persists throughout training, with the spike occupying only about 1.5% of directions yet dominating optimizer statistics. This dominance suppresses tail learning by contracting tail updates through second-moment normalization and tightening the globally stable learning-rate bound. Motivated by this analysis, we propose Spectra, a spike-aware optimizer that suppresses the dominant low-rank spike subspace without amplifying the noise-sensitive spectral tail. Spectra tracks the spike subspace via cached, warm-started power iteration and applies low-rank spectral shaping with negligible overhead and substantially reduced optimizer-state memory. Across Qwen3-0.6B trained on 100B tokens and LLaMA3-8B trained on 50B tokens, Spectra achieves the lowest final validation loss, improving average downstream accuracy by 1.41/0.89 and 1.62/0.66 points over AdamW/Muon, respectively. For wall-clock convergence, Spectra reaches matched loss targets up to 1.31×, 1.34×, and 1.24× faster than AdamW on Qwen3-0.6B, Qwen3-2B-A0.8B, and Qwen3-8B; its speedup over Muon grows as model scale increases from 0.6B to 8B. For computational efficiency, Spectra is 5.1× faster than Muon in optimizer processing time, cuts optimizer-state memory by 49.25%, and achieves the lowest measured end-to-end per-step runtime. Spectra's Megatron integration is available at https://github.com/kimmichtank/spectra.

Randomized smoothing has emerged as a scalable technique for certifying the adversarial robustness of classifiers. However, its application to regression remains under-explored and faces unique challenges. Existing regression certificates rely on probabilistic acceptance regions and fail to exploit the local geometry of the function. In this work, we present a novel framework for certified robust regression that addresses these limitations. We derive a prediction-centered certificate that guarantees the stability of the smoothed model’s prediction and ensures practical computability at test time. We investigate several alternatives for constructing these certificates by explicitly incorporating means, variances, and gradients. In particular we demonstrate on the MNIST rotation task that utilizing gradient information yields significantly tighter robustness certificates compared to the current state-of-the-art, $\alpha$-smoothing.

We develop approximation and statistical theory for standard Transformer networks in sequence modeling. Given a sequence-to-sequence target on $[0,1]^{d_x \times n}$ whose entries are $\gamma$-Hölder for $\gamma \in (0,1]$ or belong to a first-order Sobolev class, we establish explicit $L^p$-approximation bounds for all $p \in [1,\infty]$, including the previously elusive endpoint $p=\infty$ under softmax attention. In particular, achieving error $\varepsilon$ in $L^p$-norm requires $\mathcal{O}(\varepsilon^{-d_x n/\gamma})$ parameters for $\gamma$-Hölder targets and $\mathcal{O}(\varepsilon^{-d_x n})$ parameters for Sobolev targets, matching the best known scalings in ambient dimension $d_x n$. We further study nonparametric regression with sequential and dependent observations using Transformer networks. Assuming stationary $\beta$-mixing covariates whose temporal dependence weakens over time, we analyze a sliding-window empirical risk minimization procedure and establish excess-risk guarantees for the Transformer-based estimators. Our analysis clarifies the role of attention and enables extensions beyond softmax.

Triangles capture higher-order structures in graphs and are fundamental to applications such as clustering and network analysis. To enable efficient use of such structures at scale, we study the problem of triangle cut sparsification, which aims to reduce the graph size while approximately preserving triangle counts across every cut. We investigate quantum algorithms for this problem, using triangle listing as our main technical ingredient. In particular, we present a quantum algorithm for triangle listing that, for a graph with $n$ vertices, $m$ edges, and $t$ triangles, runs in time $T_{\mathrm{q\text{-}list}} =\widetilde{O}\left(\min(n^{5/4}t^{7/12} + n^{7/6}t^{7/9}, m + m^{3/4}t^{1/2},n^{3/2}t^{1/2})\right)$, improving upon the best known classical bounds over a broad range of parameters. Our algorithm is based on a heavy–light vertex partition and an extension of triangle detection via quantum walks and Grover search. Leveraging this result, we design a quantum algorithm for constructing $\varepsilon$-triangle cut sparsifiers of size $\tilde{O}(n/\varepsilon^2)$ in time $\widetilde{O}(T_{\mathrm{q\text{-}list}} + \sqrt{mn}/\varepsilon)$. Finally, we demonstrate applications to clustering algorithms based on triangle-related measures and prove a lower bound of $\Omega(n/\varepsilon^2)$ on the size of any $\varepsilon$-triangle cut sparsifiers.

We study the extent to which rotary position encodings (RoPE), a recent transformer position encoding algorithm broadly adopted in large language models (LLMs) and vision transformers (ViTs), can be applied to graph-structured data. We find that rotating tokens depending on the spectrum of the graph Laplacian efficiently injects structural information into the attention mechanism, boosting performance in synthetic and real-world graph learning tasks. This approach, coined _Wave-Induced Rotary Encodings_ (WIRE), enjoys intriguing theoretical properties: it recovers regular RoPE on grids, and depends asymptotically on the graph effective resistance. Unlike bias-based relative position encodings, WIRE is compatible with linear attention.

Transformer-based Spiking Neural Networks (SNNs) have recently emerged as a promising paradigm to sequential modeling, combining the strong representational capabilities of Transformers with the sparse spike-driven computation of SNNs. Within such position-agnostic architectures, positional encoding is critical for injecting order information, allowing the model to distinguish token positions, capture sequential dependencies, and represent relative relationships among tokens. However, existing positional encoding methods for SNNs are largely inherited from ANNs and, in doing so, undermine the spike-driven computational properties that are central to spiking transformers. To address this limitation, we propose the Spiking Positional Encoding (SPE), a method designed specifically for Spiking Transformers, aimed at encoding relative positional information while preserving both spike-driven computation and the linear complexity of spiking self-attention. The core component of SPE is the Positional Encoding Leaky Integrate-and-Fire (PE-LIF) neuron, which incorporates position-dependent signals into neuronal thresholds and implicitly propagates this information through spike trains via continuous firing and membrane potential reset dynamics. Extensive experiments on thirteen NLP benchmarks demonstrate that SPE consistently outperforms existing SNN positional encoding methods, strengthens the sequence modeling capability, and improves energy efficiency without introducing additional trainable parameters. Code is available at https://github.com/CayleyZ/SPE.

Deep hypergraph clustering exhibits compelling capacity for node representation learning via modeling high-order relationships. However, most existing methods adopt fixed propagation mechanisms and implicitly assume homophily, which presumes that adjacent nodes possess similar characteristics. This assumption might deviate from real-world situations, particularly under heterophilic conditions, thereby degrading clustering performance. To address this limitation, we propose a \textbf{Uni}fied Framework for \textbf{D}eep \textbf{H}ypergraph \textbf{C}lustering (Uni-DHC). Specifically, we design a learnable high-order hypergraph propagation strategy that fuses multi-order information and adaptively learns their importance derived from raw data. To stabilize unsupervised training and eliminate structural redundancy caused by high-order aggregation, we additionally enforce node-level consistency and hyperedge-level decorrelation constraints. From the spectral perspective, we demonstrate that conventional HGNN-style propagation corresponds to a fixed low-pass filter, whereas our designed method induces a learnable polynomial spectral filter. Extensive experiments on homophilic and heterophilic datasets illustrate that Uni-DHC consistently outperforms state-of-the-art methods, achieving prominent performance improvement in heterophilic settings.

We consider the computational problem of compacting Tsetlin Machine classifiers by reducing the number of propositional clauses while preserving predictive accuracy. TMs trained with limited clause capacity often perform poorly because stochastic optimization cannot reliably find the few precise clauses needed in a vast configuration space. High-quality compact subsets also exist in the case of larger Tsetlin Machines. The difficulty here lies in extracting them. Local pruning heuristics can fail badly on TMs because clauses interact through Boolean logic: a clause may appear unimportant in isolation yet becomes critical when others are removed. We formalize compression as the Minimum Discriminating Clause Set (MDCS) problem, which asks to find a smallest subset of clauses that preserves the trained model's discrimination of training samples. We show that MDCS is NP-hard. We solve MDCS using weighted partial Maximum Satisfiability (MaxSAT). A partition-and-merge strategy allows us to scale to 100,000 samples. Across 13 datasets, the compressed model preserves the 200-clause teacher's accuracy within a few percentage points while using a median of only 16 clauses, and outperforms a matched-capacity TM trained from scratch on every dataset where direct training has room to improve, by up to 45 percentage points.

In RL post-training of LLM agents, calls to external tools take several seconds or even minutes, leaving allocated GPUs idle and inflating post-training time and cost. While many tool invocations repeat across parallel rollouts and could in principle be cached, naively caching their outputs for reuse is incorrect since tool outputs depend on the environment state induced by prior agent interactions. We present TVCACHE, a stateful tool-value cache for LLM agent post-training. TVCACHE maintains a tree of observed tool-call sequences and performs longest-prefix matching for cache lookups: a hit occurs only when the agent’s full tool history matches a previously executed sequence, guaranteeing identical environment state. On three diverse workloads—terminal-based tasks, SQL generation, and video understanding—TVCACHE achieves cache hit rates of up to 70% and reduces median tool call execution time by up to 6.9×, with no degradation in post-training reward accumulation.

We study fully dynamic non-monotone submodular maximization under a cardinality constraint $k$. Prior work achieved approximation guarantees of $(0.125-\epsilon)$ using $\tilde{O}(\epsilon^{-1}k^2)$ oracle queries per update (NeurIPS'20) and $0.171$ using $\tilde{O}(\epsilon^{-3}k^4)$ oracle queries per update (NeurIPS'25). In this work, we present a dynamic algorithm that achieves a $0.262$-approximation with worst-case expected update time $O(\epsilon^{-3}k\log(k)\log(\epsilon^{-1}k) + \epsilon^{-2}k^2\log(k))$, where $0 < \epsilon \leq 1$ is the error parameter. We also develop another dynamic algorithm with update time bounded by $\mathrm{poly}(\epsilon^{-1},k)$ that achieves a $0.277$-approximation guarantee.

Multi-objective reinforcement learning (MORL) seeks policies that effectively balance conflicting objectives. However, presenting many diverse policies without accounting for the decision maker’s (DM’s) preferences can overwhelm the decision-making process. On the other hand, accurately specifying preferences in advance is often unrealistic. To address these challenges, we introduce a human-in-the-loop MORL framework that interactively discovers preferred policies during optimization. Our approach proactively learns the DM’s implicit preferences in real time, requiring no a priori knowledge. Importantly, we integrate this preference learning directly into a parallel optimization framework, balancing exploration and exploitation to identify high-quality policies aligned with the DM's preferences. Evaluations on a complex quadrupedal robot simulation environment demonstrate that, with only interactions, our proposed method can identify policies aligned with human preferences, e.g., running like a dog. Further experiments on seven MuJoCo tasks and a multi-microgrid system design task against eight state-of-the-art MORL algorithms fully demonstrate the effectiveness of our proposed framework. Demonstrations and full experiments are in https://sites.google.com/view/pbmorl/home.

Recent studies on hallucination detection have shown that hallucination-related signals are more strongly encoded in intermediate layers than in the final layer of large language models (LLMs). Although a growing body of work has sought to exploit this property for hallucination detection, how to automate the selection of high-performing layers remains underexplored, and principled methods for this purpose are still lacking. To address this gap, we first propose several hypotheses for why such signals emerge in intermediate layers and evaluate corresponding criteria for automatic layer selection across diverse LLM architectures, scales, and tasks, covering both question answering and summarization hallucination detection benchmarks. However, we find that none of these criteria consistently delivers satisfactory performance. We therefore propose a new selection criterion, First Effective Peak of Intrinsic Dimension (FEPoID), which consistently identify optimal or near-optimal layers and outperforms both the aforementioned criteria and existing hallucination detection baselines. FEPoID is training-free and incurs negligible computational overhead. In addition, we study the generation behaviors of LLMs and introduce a simple yet effective truncation strategy, which further amplifies hallucination-related signals and substantially improves overall detection performance. Code is publicly available at https://github.com/DesoloYw/Automatic-Layer-Selection-for-Hallucination-Detection.git

Scaling LLM-based embodied agents from text-only environments to complex multimodal settings remains a major challenge. Recent work identifies a perception–reasoning–decision gap in standalone Vision–Language Models (VLMs), which often overlook task-critical information. In this paper, we introduce PRISM, a framework that tightly couples perception (VLM) and decision (LLM) through a dynamic question–answer (DQA) pipeline. Instead of passively accepting the VLM’s description, the LLM critiques it, probes the VLM with goal-oriented questions, and synthesizes a compact image description. This closed-loop interaction yields a sharp, task-driven understanding of the scene. We evaluate PRISM on the ALFWorld and Room-to-Room (R2R) benchmarks. We show that: (1) PRISM significantly outperforms state-of-the-art image-based models, (2) our Interactive goal-oriented perception pipeline yields systematic and substantial gains, and (3) PRISM is fully automatic, eliminating the need for handcrafted questions or answers.

Federated Learning (FL) often suffers from degraded generalization under statistical heterogeneity, where client updates systematically deviate from the global objective. While recent Sharpness-Aware Minimization (SAM) methods promote locally flat solutions, they implicitly assume that local flatness transfers to the global model, which generally does not hold under heterogeneous data distributions. This mismatch gives rise to a flatness discrepancy induced by misaligned loss landscapes. To address this issue, we propose FedScar, a federated optimization framework that explicitly corrects heterogeneityinduced geometric inconsistency. FedScar maintains a history-accumulated geometric bias to capture persistent curvature skew across clients, and employs a variance-aware injection mechanism to steer local updates toward regions that are flat with respect to the global objective. We provide a theoretical interpretation of FedScar as a Split-Dual ADMM formulation, which jointly enforces parameter consensus and geometric alignment. Extensive experiments under severe heterogeneity demonstrate that FedScar consistently reduces flatness discrepancy and improves generalization over state-of-the-art methods, without incurring additional communication overhead. The source code is available at https://github.com/Ultraman6/FedScar.