NeurIPS 2026 Papers

Remote sensing object detection often proceeds in a domain-incremental manner, where detectors continuously encounter new domains arising from changes in regions, resolutions, sensors, and modalities. This challenge is particularly severe when passive optical red-green-blue (RGB) imagery and active synthetic aperture radar (SAR) imagery coexist, because their distinct imaging mechanisms create large domain gaps. Existing methods mainly rely on feature alignment or regularization, but often overlook semantic associations across heterogeneous domains. The problem is more pronounced for DETR-like detectors, where decoder queries act as object-centric semantic slots and are easily disrupted by cross-domain adaptation. Under a query-as-resource view, we propose Q-cost for remote sensing domain-incremental object detection. At the feature level, Q-cost uses modality- and domain-aware prototypes to guide a two-level mixture-of-experts adapter and generate encoder prompts for domain-aware semantic aggregation. At the semantic level, it models decoder queries as limited resources with domain-dependent activity costs, and applies activity-aware gating to regulate query updates according to current and historical domain demands. Experiments on multiple remote sensing benchmarks show that Q-cost effectively balances new-domain adaptation and old-domain retention under severe domain and modality shifts. Our code is provided in the supplementary material.

We study the query complexity of approximating the top eigenvector of an asymmetric matrix in the matrix-vector product model. Our main result gives a gap-dependent lower bound for this problem in the adaptive query setting. Prior lower bounds for symmetric matrices already imply weaker hardness guarantees for the more general asymmetric problem, whereas our result yields a sharper dependence on the eigen-gap in the asymmetric case. In the inverse polynomial accuracy regime, this lower bound matches the benchmark upper bound of the power method up to lower-order factors. Our proof is based on an asymmetric spiked random matrix that serves as a hard instance. The key random-matrix ingredient is an analysis of the spike model, including both its asymptotic eigen-gap and the alignment between its top eigenvector and the planted spike. Building on an information-theoretic framework for query lower bounds, we then obtain the stated hardness result.

Decomposing surface electromyography (EMG) into the spike trains of individual motor neurons is a long-standing inverse problem and a key step toward motor-neuron-driven neural interfaces such as prosthetics and exoskeletons. The standard approach, independent component analysis (ICA) of the multichannel signal, assumes that the mixing from neurons to electrodes is stationary in time. This assumption fails during movement, when volume-conductor deformation makes the mixing time-varying, and current decomposition algorithms are correspondingly restricted to isometric contractions. We introduce a quasi-linear ICA formulation in which a static linear separator is preceded by a learned, low-rank, time-varying invertible transformation. The separator is trained with an independence loss on the uncompensated projection, and the transformation with a stationarity loss on the recovered source. Gradients are not shared between the two, so the source-extraction step reduces to classical linear ICA and inherits its identifiability guarantee, while non-stationary distortion is absorbed by the transformation. The closed-form inverse of the transformation enables per-spike subtraction with a time-varying template during sequential peel-off. On a public benchmark of dynamic high-density EMG with ground-truth spike trains, the method outperforms five adaptive ICA baselines at every recall threshold, recovering more units at a higher accuracy.

We study stochastic optimization with heavy-tailed gradient noise. We first propose a novel quantum mean estimator for multivariate heavy-tailed random variables that achieves lower query complexity than optimal classical estimators in the low-dimensional regime. We further develop an unbiased quantum mean estimator by applying a generalized multi-level Monte Carlo technique. We prove quantum lower bounds showing that, when the dimension $d$ of the random vector is small and can be viewed as a constant, our quantum estimators are optimal up to logarithmic factors; while for the high-dimensional regime, no quantum speedup is available compared to optimal classical mean estimators. Based on these estimators, we propose a quantum normalized stochastic gradient descent method ($\texttt{QNSGD}$), which finds an $\epsilon$-stationary point of a nonconvex objective using $\tilde{\mathcal{O}}\big(d^{\frac{p}{4(p-1)}}\epsilon^{-\frac{5p-4}{2p-2}}\big)$ queries to the stochastic gradient, where $p\in(1,2]$ is the tail index. For a convex objective function, we propose a quantum projected stochastic gradient descent method ($\texttt{QPSGD}$), which computes an $\epsilon$-optimal solution with query complexity $\tilde{\mathcal{O}}\big(d^{\frac{p}{4(p-1)}}\epsilon^{-\frac{3p-2}{2p-2}}\big)$. Our results improve upon the classical lower bounds $\Omega\big(\epsilon^{-\frac{3p-2}{p-1}}\big)$ for nonconvex problems and $\Omega\big(\epsilon^{-\frac{p}{p-1}}\big)$ for convex problems, demonstrating a quantum speedup when $d$ is relatively small.

Recent advances in online learning have achieved an $O(n/\Delta_{[2]})$ query complexity in quantum $n$-arm multi-armed bandits (MABs) for best-arm identification, which represents a quadratic speedup over their classical counterparts. Here and throughout, $\Delta_{[2]}$ is the gap between the mean of the best and second-best arms. However, the implementations of these algorithms remain on a small scale due to various aspects of quantum hardware restrictions. One of the most significant restrictions is \emph{memory decoherence}, in which the qubits quickly lose information after a short period of time. Memory decoherence can occur at \emph{intra-circuit} and \emph{inter-circuit} levels. Intra-circuit decoherence happens often in near-term quantum computers, where the noise becomes overwhelming when the circuit is deep. On the other hand, inter-circuit decoherence captures future quantum machines, where a quantum memory is promising, but objects stored in the memory for too long can still become decoherent. In this paper, we present a comprehensive treatment of both memory decoherence problems. For inter-circuit decoherence, we derive a framework based on streaming bandits, and we obtain an algorithm that finds the best arm with high constant probability using $O(n/\Delta_{[2]})$ queries and an $O(\log{n})$ decoherence window. This is the first quantum algorithm for MABs that achieves an $o(n)$ decoherence window, which represents an exponential improvement. For intra-circuit decoherence, we observe that only $O(1)$-depth circuits can be used to avoid significant decoherence. Therefore, we devise various hardware optimizations and a destructive SWAP test subroutine to speed up the empirical performance. On the IBM Q System One machine with 127 qubits, our implementation scales the quantum MABs to over $1000$ arms, and our algorithms consistently achieve significant efficiency improvements over classical bandit algorithms in both physical experiments and computer simulations.

We present a method of quantum composite hypothesis testing with small error, which enables us to establish quantum lower bounds in nonparametric statistics and high-dimensional functional estimation. This is achieved by introducing trigonometric polynomials into the quantum polynomial method, thereby generalizing the quantum phase-estimation lower bound of Mande and de Wolf (ESA 2023). As applications, we settle the quantum complexities of several problems in property testing and functional estimation with small error: - For $\ell_2$-closeness testing, we show that the approach of Luo et al. (*IEEE Trans. Inf. Theory* 2024) is optimal. - For Tsallis entropy estimation, where $q=2$ corresponds to the Gini impurity, we show that the approaches of Buhrman et al. (*Phys. Rev. Lett.* 2001) and Ekert et al. (*Phys. Rev. Lett.* 2002) are optimal for integer $q \geq 2$, and that the approach of Chen et al. (ICALP 2026) is near-optimal for real $q \geq 1.5$. - For pure-state Uhlmann fidelity and trace distance estimation, we show that the approach of Wang (*IEEE Trans. Inf. Theory* 2024) is optimal.

Best arm identification, also known as pure exploration, is a fundamental problem in the multi-armed bandit (MAB) model. Recent quantum algorithms achieve $O(n/\Delta_{[2]})$ query complexity for identifying the best arm with high constant probability, but all of them require $\Omega(\log(1/\Delta_{[2]}))$ or $\Omega(\log n)$ adaptive rounds. Motivated by the practical cost of adaptivity on near-term quantum hardware, where each round incurs substantial overhead from state re-preparation and classical--quantum communication, we study quantum best arm identification with no or very limited adaptivity. On the lower bound side, we prove that any non-adaptive quantum algorithm must make $\Omega(n\log n)$ queries when $\Delta_{[2]}=O(1)$, establishing a separation between adaptive and non-adaptive algorithms. To complement this lower bound, we present an algorithm that identifies the best arm with high constant probability using $O(n/\Delta_{[2]})$ queries and only $\log^*(n)+1$ adaptive rounds. En route to the lower bound, we show that the instances and techniques used to prove adaptivity lower bounds for classical bandits, such as those of Agarwal et al. [COLT'17], do not extend to the quantum setting. As such, we employ the polynomial method to prove our adaptivity lower bounds. To the best of our knowledge, this represents the first application of the polynomial method in this context, which may be of independent interest.

Crystal Structure Prediction (CSP) aims to predict a material's 3D structure from its chemical composition, with applications from energy storage to pharmaceuticals. Despite its importance, existing evaluation frameworks suffer from key limitations: they rely on threshold-sensitive or incomparable metrics, focus predominantly on geometric performance while overlooking physical plausibility, and fail to account for polymorphism, where a chemical composition can crystallize into multiple stable structures. In parallel, recent Symmetry-Informed CSP (SICSP) methods often report results alongside standard CSP baselines while receiving crystallographic templates at inference, which constrain the search space and make SICSP a fundamentally different task. To address these limitations, we introduce an Orientation-invariant, Polymorph-Aware, Large Benchmark (OPAL-Bench) that evaluates CSP and SICSP as separate tasks. We evaluate 7 CSP and 2 SICSP methods under OPAL-Bench across 4 datasets using threshold-free geometric and physical distance metrics. Our results show that no method dominates across all metrics, and that geometric performance is not strongly correlated with physical plausibility. Motivated by this gap, we provide OPAL-CSP, an SE(3)-equivariant flow-matching baseline that performs competitively on geometric metrics and consistently ranks among the best on physical ones. By unifying geometric and physical metrics under a polymorph-aware protocol, OPAL-Bench enables a more comprehensive assessment of generative quality in CSP.

Unlike standard expected-return Reinforcement Learning (RL), Distributional RL (DRL) models the full return distribution, making it better-suited for uncertainty-aware and risk-sensitive decision-making. Conditional Flow Matching (CFM) critics have recently attracted attention for modelling continuous, multi-modal return distributions. Despite this interest, there remains a substantial \textbf{metric mismatch}: DRL theory relies on the distributional Bellman operator being contractive in the $p$-Wasserstein distance, yet existing CFM critics are trained with arbitrary source--target couplings, so their flow-matching losses are not Wasserstein-aligned surrogates for matching Bellman target return distributions. In this work, we address this mismatch by proposing \textbf{FlowIQN}, a CFM critic that sorts source and Bellman target samples within each mini-batch to approximate the monotone optimal transport coupling, replacing arbitrary pairings with quantile-aligned flow paths. We prove that the loss of our \textbf{quantile-coupled} CFM critic yields a Wasserstein-aligned approximate projection compatible with the foundations of DRL. To our knowledge, FlowIQN is the first flow-matching distributional critic with an explicit Wasserstein-aligned projection guarantee. We further extend FlowIQN with shortcut models for efficient inference. Empirical results show that FlowIQN improves Wasserstein return-distribution accuracy over other CFM critics. It also yields competitive performance on offline RL benchmarks across multiple policy extraction methods, providing a theoretically grounded CFM critic that is readily compatible with DRL pipelines.

Quantile-based distributional reinforcement learning methods learn return distributions through sampled quantile regression, but their bootstrapped target quantiles may induce distorted or degenerate distribution estimates. We propose Robust Quantile-based Implicit Quantile Networks (RQIQN), a lightweight Wasserstein distributionally robust enhancement boosted from a quantile estimation perspective. We first reinterpret a snapshot of IQN loss as a collection of local empirical quantile estimation problems over sampled current fractions. We then robustify each local slot with a Wasserstein distributionally robust quantile estimation formulation, yielding a closed-form, fraction-dependent correction to the Bellman target. This correction directly mitigates distributional degeneration: its median-antisymmetry preserves the risk-neutral quantile average, while its monotonicity enlarges upper--lower quantile gaps and counteracts collapsed distributional spread. RQIQN thus regularizes quantile geometry without changing the underlying value objective or requiring additional sample-set reconstruction. Finally, we empirically show that the proposed RQIQN outperforms other existing quantile-based distributional reinforcement learning algorithms in risk-sensitive navigation and Atari games.

Transformers with self-attention modules as their core components have become an integral architecture in modern large language and foundation models. In this paper, we study the evolution of tokens in deep encoder-only transformers at inference time which is described in the large-token limit by a mean-field continuity equation. Leveraging ideas from the convergence analysis of interacting multi-particle systems, with particles corresponding to tokens, we prove that the token distribution rapidly concentrates onto the push-forward of the initial distribution under a projection map induced by the key, query, and value matrices, and remains metastable for moderate times. Specifically, we show that the Wasserstein distance of the two distributions scales like $\sqrt{\log(\beta+1)/\beta}\exp(C t)+\exp(-ct)$ in terms of the temperature parameter $\beta^{-1}\to 0$ and inference time $t\geq 0$. For the proof, we establish Lyapunov-type estimates for the zero-temperature equation, identify its limit as $t\to\infty$, and employ a stability estimate in Wasserstein space together with a quantitative Laplace principle to couple the two equations. Our result implies that for time scales of order $\log\beta$ the token distribution concentrates at the identified limiting distribution. Numerical experiments confirm this and, beyond that, complement our theory by showing that for finite $\beta$ and large $t$ the dynamics enter a different terminal phase, dominated by the spectrum of the value matrix.

Analyzing complex data across a wide range of scientific fields often requires identifying central or typical elements, distinguishing them from atypical ones, and constructing central or "normal" regions at prespecified levels of centrality. We introduce centrality scores (C-scores) based on distance profiles for random objects taking values in general metric spaces. The proposed C-scores are defined through weighted optimal transport of distance profiles and provide a unified framework for constructing central or "normal" regions for complex data. We show that, for Euclidean data, the limiting behavior of the proposed C-scores is asymptotically equivalent to the underlying probability density function. The practical merits of the proposed method are illustrated using gene expression data, distributions of recorded temperatures, handwritten digit recognition, and taxi trip records. These examples demonstrate the effectiveness of C-scores in identifying central and peripheral elements and in yielding meaningful insights for non-Euclidean and high-dimensional data.

Demoir\'eing aims to remove moir\'e artifacts that often occur in images. While recent deep learning-based methods have achieved promising results, they typically require substantial computational resources, limiting their deployment on edge devices. Model quantization offers a compelling solution. However, directly applying existing quantization methods to demoir\'eing models introduces severe performance degradation. The main reasons are distribution outliers and weakened representations in smooth regions. To address these issues, we propose QuantDemoire, a post-training quantization framework tailored to demoir\'eing. It contains two key components. **First**, we introduce an outlier-aware quantizer to reduce errors from outliers. It uses sampling-based range estimation to reduce activation outliers and keeps a few extreme weights in FP16 with negligible cost. **Second**, we design a frequency-aware calibration strategy. It emphasizes low- and mid-frequency components during fine-tuning, which mitigates banding artifacts caused by low-bit quantization. Experiments validate that our QuantDemoire achieves large reductions in parameters and computation while maintaining quality. Meanwhile, it outperforms existing quantization methods by over **4 dB** on W4A4. We implement a CUDA kernel for the mixed-precision branch and achieve a 2.3$\times$ end-to-end speedup on an RTX 4090 GPU. Code will be made public.

The Quality-Diversity (QD) optimization aims to discover a collection of high-performing solutions that simultaneously exhibit diverse behaviors within a user-defined behavior space. This paradigm has stimulated significant research interest and demonstrated practical utility in domains including robot control, creative design, and adversarial sample generation. A variety of QD algorithms with distinct design principles have been proposed in recent years. Instead of proposing a new QD algorithm, this work introduces a novel reformulation by casting the QD optimization as a multi-objective optimization (MOO) problem with a huge number of optimization objectives. By establishing this connection, we enable the direct adoption of well-established MOO methods, particularly set-based scalarization techniques, to solve QD problems through a collaborative search process. We further provide a theoretical analysis demonstrating that our approach inherits theoretical guarantees from MOO while providing desirable properties for the QD optimization. Experimental studies across several QD applications confirm that our method achieves performance competitive with state-of-the-art QD algorithms.

Series decomposition aims to separate long-term trajectories and periodic patterns in time series, thereby improving the specificity and interpretability of forecasting models. However, mainstream approaches usually equate this functional separation with an operational split between a smoothed baseline and fluctuating residuals. One line of methods approximates the trend via low-pass smoothing, which assumes long-term trajectories to be purely smooth and may misassign nonlinear evolution, stage-wise transitions, and structural fluctuations to the residual. The other relies on heuristic nonlinear decompositions to capture complex dynamics, but is sensitive to noise and hyperparameters, leading to unstable and mixed component boundaries. To address this issue, we propose a forecasting framework, QWaveNet. It employs a quantum convolutional neural network to learn Dynamic Evolution, a long-term structural representation beyond low-pass smoothing priors, which preserves nonlinear evolution, stage-wise transitions, and structural fluctuations more coherently, while its complementary Evolutionary Residual captures localized variations and periodic dynamics. Guided by these complementary components, QWaveNet further performs adaptive multi-scale decomposition and reconstruction to support forecasting. Experiments on multiple benchmark datasets demonstrate the effectiveness of QWaveNet.

While deep learning offers tremendous promise for scientific and medical imaging, any failures and hallucinations (predictions that do not coincide with reality) are hard to pinpoint and can have serious downstream consequences. Uncertainty estimation techniques, such as conformal prediction, can help by predicting statistically valid error bars for a model's prediction. However, popular conformal prediction methods were not designed for high-dimensional image-valued problems and do not take into account spatial correlations within an image during conformal calibration, resulting in larger-than-necessary uncertainty intervals. We propose a practical simultaneous quantile regression method that enables non-linear, spatially-adaptive scaling during conformal calibration. Our method, QUTCC uses a U-Net architecture with a quantile embedding to learn a full conditional quantile distribution during training, and then leverages this non-linear, learned function for spatially-adaptive conformal calibration. At test time, our method can efficiently estimate uncertainty intervals with pixel-marginal coverage guarantees. In addition, QUTCC can also predict pixel-wise conditional probability density estimates without any built-in distributional assumptions. We evaluate our method on several denoising problems, accelerated magnetic resonance imaging, and quantitative phase microscopy. Our method consistently produces tighter uncertainty intervals than prior conformal methods at the same coverage level, can predict plausible conditional distributions for different tasks, and in some cases, high-uncertainty regions can help us locate hallucinations in a model's prediction.

Robots deployed for active search must decide where to sense while uncertainty, teammates, and remaining mobility change online. In active search, each waypoint decision also commits the robot to a route through the map, making efficient localization a long-horizon problem over belief, topology, robot state, and traversal budget rather than a sequence of independent next-best sensing decisions. We present QUEST, a shared-belief graph neural framework for multi-agent active search with noisy sensors, a shared posterior, and finite decision and path budgets. Rather than learning a myopic policy that values only the next route, QUEST trains Q-functions whose targets include both reward collected along the executed path and the downstream value of the resulting belief, robot positions, team coverage, and remaining budget. The same formulation supports single robots, homogeneous robot teams, and heterogeneous UAV--UGV teams with different sensors and motion budgets. During execution, each robot acts independently using the shared posterior and knowledge of teammates' positions and search plans. Across simulated search environments, QUEST reaches $0.913$ F-score with four UGVs, versus $0.853$ for the strongest learned baseline, and keeps above $0.90$ F-score under communication outage and two mid-mission robot failures without retraining. On out-of-distribution UAV--UGV teams, it improves early F-score ($0.759$ vs.\ $0.728$) while using $10\%$ less path length and $12\%$ less duplicate coverage than the same baseline. The same policies transfer across map shape, variable team size, communication outage, and mid-mission robot failure, and show sensing-mode adaptation after UGV failure.

Atomic properties such as partial charges or multipoles encode chemically meaningful information that can inform downstream molecular property prediction, but their evaluation as machine learning targets has been complicated by the absence of a principled out-of-distribution evaluation protocol at the atomic level. In this work, we propose a held-out evaluation protocol that clusters atomic environments by SOAP descriptors and computes metrics accounting only for cluster labels unseen during training. Following this procedure, we use 5×5 cross-validation and Tukey's HSD to run a statistically rigorous comparison of E(3)-equivariant against non-equivariant, rotationally augmented models for predicting electron populations and multipoles of H, C, N, and O atoms. Building on our results, we introduce the Quantum Topological Neural Network (QT-Net), a rotationally augmented, non-equivariant graph neural network. We show that QT-Net can be used to infer properties of atoms in molecules from QM9 outside our training set, and that these inferred properties can yield improvement when used as input features for downstream molecular property prediction. To further validate the framework, molecular dipole moments computed from QT-Net's per-atom outputs recover the ground-truth values reported in QM9. We release all code and data, including a JAX implementation of QT-Net, to support the broader use of learned QTA properties as inductive biases for atomic-scale molecular machine learning.

Reliable quantum control in the presence of decoherence requires policies that combat the effect of environmental noise on the controlled dynamics. Open quantum systems under continuous monitoring generate classical measurement records whose drift depends on the noise experienced by the system; the records of two evolutions sharing the same decoherence channels differ only in this drift, so Girsanov's theorem yields a closed-form, differentiable estimator of the KL divergence between their trajectory distributions. We instantiate this estimator with two physically motivated reference measures, yielding two regularizers that both drive the system toward states where the effects of decoherence are minimal: the *Wiener KL* (KL_W), which is empirically more effective under certain conditions on the noise model, and the *drift-variance regularizer* (R_DV), which works for all noise models. Both are qualitatively distinct from existing penalties on control fluence or smoothness: they penalize the observable consequences of control on the decoherence channels rather than the control amplitude itself. The regularizers outperform unregularized gradient-based and reinforcement-learning baselines across a range of open quantum systems — including single- and multi-qubit benchmarks and a multi-qubit chain calibrated to a published snapshot of the IBM Kingston processor — along several axes of evaluation: final-state fidelity, robustness to mismatch in the assumed noise model (gains grow from +17 pp at training noise to +27 pp under 2.5× noise mismatch), and occupation of forbidden states. The regularizers reduce infidelity by up to 50%, with ~16% gains on the calibrated IBM Kingston chain. Our code can be found at https://anonymous.4open.science/r/QMaxCal-6E71/.