NeurIPS 2026 论文列表

Conference on Neural Information Processing Systems

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RAGBoost: Robust Tabular Learning via Retrieval-Augmented and Ancillary-Guided Gradient Boosting

Jinlin Wang, Zhixuan Chen, Qi Ma

展开摘要

Gradient Boosted Decision Trees (GBDTs) remain a leading approach for tabular learning, offering strong predictive performance, computational efficiency, and robustness to heterogeneous feature types. Yet their standard second-order leaf updates suffer from a node-level statistical limitation: as trees grow deeper, sparse leaves provide increasingly unreliable gradient estimates, while global regularization cannot adapt to local uncertainty or residual structure. We propose RAGBoost, a retrieval-augmented and ancillary-guided boosting framework for robust tabular learning. RAGBoost augments standard GBDT optimization with a two-layer node-adaptive correction mechanism. First, it retrieves historically observed leaves with similar gradient-state configurations to form node-conditional gradient priors, stabilizing variance-dominated sparse-leaf updates through empirical shrinkage. Second, it uses ancillary residual correction to detect and mitigate bias-dominated within-leaf residual structure that remains unresolved by the main tree. These corrections modify only leaf values, preserving the original tree structure and inference pipeline. Empirically, RAGBoost achieves the best overall average rank across 40 heterogeneous tabular benchmarks in our evaluation, while remaining strongly competitive with recent deep tabular and tabular foundation model baselines. On TabReD, an industrial-scale temporal-shift benchmark, RAGBoost outperforms XGBoost and the base TabM variant overall, suggesting improved robustness under realistic distribution drift.

Poster
RAG in a Trenchcoat: When Minimal Memory Is Enough for Agentic Systems, and When It Isn’t

Jingyu Liu, Zongze Li, Zach Xu, Zhanhui Zhou, Tahseen Rabbani, Dawn Song, Ce Zhang

展开摘要

Agentic memory research has accumulated extraction, supersession, reflection, and graph synthesis on top of retrieval-augmented generation. Yet on the field's three established benchmarks, almost none of those primitives earn their cost: We show this with Bridge, a deliberately minimal RAG memory with chained observation notes, hybrid BM25 + cosine retrieval, and chronological rendering, which reaches parity within bootstrap CI with the prior published SOTA on LongMemEval-S and BEAM, and beats the best memory baseline on EverMemBench by $+5.7-6.3$pp at matched reader. It runs at $\sim5$-$7$K reader-prompt tokens per query and a single LLM call for each ingestion or query. We argue this parity is itself the result: standard benchmarks score what memory retrieves, not what memory enables when the agent acts. To test the latter, we introduce five adversarial probes (Rule Application $\pm$, Pattern Induction style / procedural, Dynamic Multi-turn) judged at generation time by a cross-vendor verification chain; each can only be solved by applying a remembered rule or pattern the probe never mentions. Across 5 probes $\times$ 20 scenarios, no architecture wins universally: atomic-fact extractors win rule application (LangMem leads Bridge by $+45$pp on RA$^+$, with non-overlapping bootstrap CIs), while Bridge's block-summary memory wins pattern induction (leads the strongest baseline by $+33$pp on PI-P). The right memory architecture is mechanism-dependent, and the field's evaluation paradigm fails on both ends: standard benchmarks fail to distinguish a minimal memory from a complex one, and application-grade probes that do distinguish find no universal winner.

Poster
RADIUM: RadioActive Decay of Image-Underlaid Marks

Michel Meintz, Louis Kerner, Maitri V Shah, Simon Hector, Franziska Boenisch, Adam Dziedzic

展开摘要

Modern image generative models are able to produce photorealistic images. As those images become increasingly indistinguishable from real data and are published online, they are often scraped for subsequent training runs of new generative models. This practice of training on generated data has been shown to degrade model performance and cause model collapse. A possible mitigation lies in embedding radioactive watermarks into generated content. Radioactive watermarks are robust marks that are detectable in outputs of new models trained on watermarked data, enabling provenance tracing of generated content. In this work, we analyze the persistence of image watermarks across multiple training-generation runs. To do so, we introduce a novel statistical testing method RADIUM (RadioActive Decay of Image-Underlaid Marks) for reliable radioactivity detection across various watermarking methods. Using our RADIUM method, we observe disparate radioactivity across watermarking methods for image generative models. Only few watermarks remain detectable in subsequently trained models, while most decay severely, especially when the architecture of models differs. Our analysis highlights the critical need for more radioactive watermarking methods in the vision domain.

Poster
RADAR: Text-Guided Medical Image Segmentation via Residual Aggregation and Dense Alignment Representations

Jie Gui, Hang Tu, Yunfeng Dou, Wen Sha, Xiuquan Du, Shuo Li

展开摘要

Specifying segmentation targets via text descriptions provides flexible semantic conditioning for medical image segmentation. However, existing methods still struggle to robustly translate high-level textual semantics into accurate pixel-level spatial prompts. In this paper, we propose RADAR (Residual Aggregation and Dense Alignment Representations), a parameter-efficient framework for text-guided medical image segmentation. RADAR explicitly decouples and synergizes the medical semantic anchoring capabilities of BiomedCLIP with the prompt-driven mask decoding abilities of MedSAM2, achieving low-cost task adaptation via LoRA. Specifically, RADAR introduces Guided Residual Depth Aggregation, which adaptively aggregates historical layer features under semantic guidance to mitigate textual semantic injection lag and deep feature dilution. Furthermore, we propose Structured Dense Representation Alignment, which leverages a frozen BiomedCLIP to construct crop-level semantic anchors, namely target, boundary, and context, to enhance the local discriminative power of dense features and the reliability of automated prompts. Additionally, Multi-modal Prompt Generation is designed to transform cross-modal semantic responses into composite prompts consisting of text, points, and masks. Experimental results on three public medical image segmentation datasets demonstrate that RADAR achieves competitive performance while introducing merely 0.74M trainable parameters, validating the effectiveness of the proposed approach in parameter-efficient adaptation and the enhancement of cross-layer and local representations. The source code is provided in the supplementary material.

Poster
RADAR: Routing Agents via Difficulty-Aware Recovery

Haizhou Du, Jinze Zhao, HuaiCheng Yan

展开摘要

Multi-agent systems (MAS) have emerged as a dominant paradigm where agent routing is a bottleneck for balancing performance and cost. However, existing agent routing methods suffer from the prohibitive cost of exhaustive benchmark construction and the neglect of query complexity essential for mixed tasks. To address this issue, we propose the RADAR (Routing Agents via Difficulty-Aware Recovery) framework. RADAR enables accurate decision-making under limited evaluation cost through two complementary modules. MatrixComp module employs structure-aware matrix completion to recover global performance profiles from sparse observations. Furthermore, DiffMatch module extracts reasoning meta-features for fine-grained alignment via a difficulty-calibrated retrieval mechanism. Extensive experiments demonstrate that RADAR maintains performance equal with state-of-the-art baselines while reducing the cost of benchmark construction by at least 33%.

Poster
RADAR: Relative Angular Divergence Across Representations

Xavier Cadet, Mateusz Nowak, Peter Chin

展开摘要

Machine learning methods rely on data. However, gathering suitable data can be challenging due to availability constraints, cost, or the need for domain expertise. Expanding datasets with additional sources is a common response to limited data, yet this practice does not always improve downstream performance and can sometimes lead to a loss of performance, known as negative transfer. We propose RADAR, a simple, geometrically grounded metric for estimating cross-domain transferability in foundation models. RADAR analyzes the layer-wise evolution of representations by measuring angular alignments and relative changes in distance along layer-to-layer displacement trajectories, and by comparing empirical distributions of within-domain and cross-domain dynamics. We hypothesize that domain transferability is related to the divergence between these trajectory distributions. We evaluate the metric across multiple modalities, including cross-lingual sentiment classification with text embedding models and cross-domain image classification with foundation vision models. Across several settings, RADAR provides competitive predictive performance relative to existing transferability metrics on several vision and text benchmarks, with particularly strong results when domain transitions are smooth or cleanly separated. Our ablations further suggest that the effectiveness of transferability estimation depends on the geometry of the model’s internal representation space, with different modalities favoring different topological formulations.

Poster
RAD-TFM: Robust and Domain-Adapted Tabular Foundation Models

Matthew Peroni, Franck Le, Vadim Sheinin

展开摘要

The development of tabular foundation models (TFMs) has accelerated in recent years, showing strong potential to outperform traditional ML methods for structured data. A key finding is that TFMs can be pretrained entirely on synthetic datasets, opening opportunities to design data generators that encourage desirable model properties. Prior work has mainly focused on crafting high-quality priors over generators to improve overall pretraining performance. Our insight is that parameterizing the generator distribution enables an adversarial, distributional robustness perspective: during training, we can adapt the generator to emphasize datasets that are particularly challenging for the model, which we formalize by introducing an optimality gap measure. Further, we develop a method to align the synthetic data generation with real-world datasets from a given domain, constraining the adversary to generate "realistic'" data. Together, these algorithms comprise the Robust and Domain-Adapted Tabular Foundation Models (RAD-TFM) pipeline, a model-agnostic adversarial training framework. Applied to the TabPFN V2 classifier, RAD-TFM improves performance across 6 diverse tabular benchmarks, with up to a 11\% increase in mean normalized AUC over the original TabPFN and other baseline algorithms, with only 100k additional training datasets, less than 0.1\% of the original pretraining data. These results highlight a promising new direction for targeted adversarial training and fine-tuning of TFMs using synthetic data alone.

Poster
RA-ClipScore: Making Generative Model Evaluation More Interpretable

Yifan Lu, Taras Kucherenko, Hedvig Kjellstrom, Judith Bütepage

展开摘要

Generative models can produce images nearly indistinguishable from real data, yet rigorous and interpretable evaluation remains challenging. Conventional metrics such as FID provide only scalar scores with limited diagnostic insight. Widely adopted CLIP-based metrics enable semantic evaluation beyond simple training class labels, but inherit limitations from CLIP’s training paradigm that restrict attribute-wise analysis. We propose RA-CLIPScore, a novel metric that mitigates these issues and extends CLIP-based evaluation to spatial distribution alignment, measuring whether generated objects adhere to the positional priors found in the training data. RA-CLIPScore introduces dual prompts to decouple competing attributes and leverages local patch tokens to capture fine-grained regional semantics. We evaluate image generative models on their ability to match both attribute and spatial distributions of the training data. Extensive experiments show that RA-CLIPScore provides more robust and interpretable evaluations than prior methods, particularly under distribution misalignment or partially irrelevant textual attributes. We further demonstrate how it reveals previously undocumented regional tendencies in generative models.

Poster
RA-CFGCache: From Branch-Level Criteria to Guided-Risk Control under Classifier-Free Guidance

Yiming Liu, Ben Wan, Hui Chen, Ao Wang, Yuqi Xiong, Fan Zhang, Tongxuan Liu, Guiguang Ding

展开摘要

Diffusion models dominate visual generation, but iterative denoising remains computationally demanding, especially under Classifier-Free Guidance (CFG), which is crucial for high-fidelity generation yet nearly doubles per-step computation. To reduce this burden, recent training-free caching methods reuse intermediate predictions during sampling, yet their single-prediction criteria are misaligned with CFG sampling, where the denoising update is governed by the guided prediction rather than either branch alone. Consequently, such reuse may misestimate the error that actually perturbs sampling, leading to a **branch-guided mismatch**. Moreover, due to error propagation across timesteps, a local guided error may not faithfully reflect the final deviation, inducing a **local-final mismatch**. To address these two mismatches, we propose **RA-CFGCache**, a **R**isk-**A**ligned **Caching** framework for CFG. **RA-CFGCache** introduces CFG-aware Guided-Risk Composition to align caching decisions directly with the guided prediction, and Propagation-Aware Rescaling to calibrate local guided risks against the final generative deviation. Extensive experiments on FLUX.1-dev, Wan2.1-T2V-1.3B, and CogVideoX-2B show that **RA-CFGCache** delivers superior efficiency-fidelity trade-offs over existing training-free caching methods. Moreover, **RA-CFGCache** is compatible with diverse caching strategies and can further enhance their fidelity, e.g., improving PSNR over MagCache from 21.46 to 24.02 under CFG. The code is available at https://anonymous.4open.science/r/RA-CFGCache/.

Poster
RA$^2$: Retain-Anchored Attraction Preserves Forget-Adjacent Utility in LLM Unlearning

Zinan Ling, Yang Xiao, Ruimeng Ye, Sijia Liu, Bo Hui

展开摘要

Unlearning in Large Language Model (LLM) is often evaluated primarily by target suppression and clean retain utility. These metrics can miss a local failure mode: a model may perform well on standard retain prompts, yet degrade on benign reasoning when prompts lie near the forgotten domain. This phenomenon is termed **forget-adjacent utility** loss. A fundamental question is: where should forget representations go after they leave the removed behavior? Successful unlearning depends not only on whether forget-conditioned representations depart from the harmful computation, but also on the direction in which they are redirected afterward. We propose **RA$^{2}$ (Retain-Anchored Attraction)**, a latent-space unlearning method that redirects forget-token states toward nearby retain-supported representations while preserving higher-layer behavior on retain data. On WMDP and MUSE, RA$^2$ yields higher forget-adjacent utility than strong unlearning baselines at similar broad-utility levels. These results show that the migration direction of forget representations materially affects benign behavior near the forget boundary. Our code is available at https://anonymous.4open.science/r/eaxvwertdq.

Poster
R-GRec: Relation-Guided Generative Recommendation via Collaborative Graph Supervision

Xiangfu Meng, Jiapeng Yang, Lei Shi, Xue Wang, Yuefeng Zhan, Chen Gu, Hao Sun, Weiwei Deng, Tao Yao, Feng Sun, Qi Zhang

展开摘要

Generative recommendation has recently emerged as a promising paradigm for large-scale recommendation by reformulating next-item prediction as discrete sequence generation. However, current SID-based models rely mainly on history-to-next-item supervision, leaving item--item collaborative topology only indirectly captured through sparse user sequences. To address this gap, we propose *R-GRec*, a graph-derived structural supervision framework for SID-based generative recommendation. From user interactions, *R-GRec* builds an item--item graph and derives three complementary auxiliary objectives---Neighbor Prediction, Topological Contrast, and Link Prediction --- to make collaborative topology explicit during generative training. Extensive experiments on the two public Amazon datasets demonstrate that R-GRec achieves state-of-the-art performance over representative traditional, generative, and LLM-based recommenders. Further ablation and analytical studies verify the contribution of each graph-derived objective and show that collaborative topology acts as a complementary supervision signal to Semantic ID generation, improving generative recommendation without adding inference-time graph computation.

Poster
Quotient-Categorical Representations for Bellman-Compatible Average-Reward Distributional Reinforcement Learning

Ege C. Kaya, Aliasghar Pourghanitazehshahri, Vijay Gupta, Abolfazl Hashemi

展开摘要

Average-reward reinforcement learning requires estimating the gain and the bias, which is defined only up to an additive constant. This makes direct distributional analogues ill-posed on the real line. We introduce a quotient-space formulation in which state-indexed bias laws are identified up to a common translation, together with a categorical parameterization that respects this symmetry. On this quotient-categorical space, we define a projected average-reward distributional operator and show that it is well-defined, non-expansive in a coordinate Cram\'er metric, and admits fixed points. We then study sampled recursions whose mean-field maps are asynchronous relaxations of this operator. In an idealized centered-reward setting, a one-state temporal-difference update enjoys almost sure convergence together with finite-iteration residual bounds under both i.i.d. and Markovian sampling. When the gain is unknown, we augment the recursion with an online gain estimator, and prove non-expansiveness and Markovian convergence of the resulting coupled scheme. Finally, we show that synchronous exact updates are gain-independent at the quotient-law level, isolating a structural contrast between ideal quotient distributions and practical fixed-grid categorical representations.

Poster
Quest: Training Frontier Deep Research Agents with Fully Synthetic Tasks

Jian Xie, Tianhe Lin, Zilu Wang, Yuting Ning, Yuekun Yao, Tianci Xue, Zhehao Zhang, Zhongyang Li, Kai Zhang, Yufan Wu, Shijie Chen, Boyu Gou, Mingzhe Han, Yifei Wang, Vint Lee, Xinpeng Wei, XJ Wang, Yu Su, Huan Sun

展开摘要

Deep research agents extend the role of search engines from retrieving keyword-matched pages to synthesizing knowledge, fundamentally changing how humans interact with information. However, frontier systems remain proprietary, while existing open agents often generalize poorly across different task types, leaving unclear how to train a broadly capable deep research agent. We release Quest, a family of open models (ranging from 2B to 35B) that serve as general-purpose deep research agents designed to handle a wide range of search tasks, with strong capabilities in fact seeking, citation grounding, and report synthesis. To build Quest, we propose an effective training recipe combining mid-training, supervised fine-tuning, and reinforcement learning. Central to this recipe is a curated data synthesis pipeline based on unified rubric trees, which applies to different task types and enables synthesizing training data with verifiable rewards without human annotation. In addition, Quest incorporates a built-in context management mechanism that enables effective long-horizon reasoning and knowledge synthesis. Using only 8K synthesized tasks, Quest approaches or even surpasses frontier closed-source agents across eight deep research benchmarks spanning diverse task types, and achieves the best overall performance among recent open-weight agents. Notably, Quest-35B achieves 30.7\% on Mind2Web 2, outperforming OpenAI DeepResearch (28\%) and Gemini DeepResearch (18\%). We plan to release all the resources for further research.

Poster
Querying Counterfactuals on Tissue Graphs with Supervised Disentanglement

Abdul Moeed, Stefan Schrod, Martin Rohbeck, Marc J Bonder, Pavlo Lutsik, Oliver Stegle, Daniel Dimitrov

展开摘要

Tissue graph counterfactuals ask how a cell's expression would change under altered spatial contexts. Such queries are central to predicting cell behavior in tissues, but lack a unified definition, with existing methods targeting specific intervention types or treating cells as i.i.d. In this work, we first formalize tissue graph counterfactuals as a class of spatial interventions that either rewire connections between cells (edge perturbation) or modify the expression of their neighbors (node perturbation). We then introduce Cellina, a modeling framework that uses supervised disentanglement to decompose a cell's intrinsic state from its spatial context, using the latter as a conditioning input for counterfactual predictions. Across benchmarks spanning 2.5 million spatially-resolved cells in colorectal cancer and mouse brain, Cellina outperforms spatially-informed and non-spatial competitors in counterfactual predictions, disentanglement, and scalability. Additionally, we show that Cellina reveals biologically distinct cancer subdomains in an unsupervised manner and enables targeted neighbor perturbation simulations.

Poster
QueryStop: Dynamic Stop Signals for Efficient Streaming Inference

Michelle Shu, Jingyao Li, Pengguang Chen, Shu Liu, Ramin Zabih, Jiaya Jia

展开摘要

As language models are increasingly deployed in long-context and streaming workflows, deciding when to stop context processing is central to inference efficiency. While recent research has shown that a subset of attention heads encodes sufficiency signals, these markers are typically detected via static, task-agnostic global features. In this paper, we demonstrate that stop signals are inherently query-relevant and introduce \textsc{QueryStop}, an attention-aggregation method that systematically identifies query-focused attention heads whose hidden features effectively align with the input query. Driven primarily by query-focused heads, this tailored ensemble yields high-fidelity representations that significantly improve sufficiency prediction. Across four benchmarks on eleven datasets, our method improves sufficiency stop prediction by 3.52\% F1 on average. Under comparable token reduction, it raises Sufficiency Reach Rate (SRR), our proposed stopping-adequacy metric, from 87.12\% to 94.73\% and yields a 7.09\% average gain in downstream task accuracy over the prior baseline. Collectively, these results show that \textsc{QueryStop} effectively eliminates unnecessary context processing while simultaneously improving downstream answer quality.

Poster
Query as a Resource: Activity-Cost Guided Remote Sensing Domain-Incremental Object Detection

Xi Yang, Zhengyu Yuan, De Cheng, Nannan Wang

展开摘要

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.

Poster
Query Lower Bounds for Diffusion Sampling

Zhiyang Xun, Eric Price

展开摘要

Diffusion models generate samples by iteratively querying learned score estimates. A rapidly growing literature focuses on accelerating sampling by minimizing the number of score evaluations, yet the information-theoretic limits of such acceleration remain unclear. In this work, we establish the first score query lower bounds for diffusion sampling. We prove that for $d$-dimensional distributions, given access to score estimates with polynomial accuracy $\varepsilon=d^{-O(1)}$ (in any $L^p$ sense), any sampling algorithm requires $\widetilde{\Omega}(\sqrt{d})$ adaptive score queries. In particular, our proof shows that any sampler must search over $\widetilde{\Omega}(\sqrt{d})$ distinct noise levels, providing a formal explanation for why multiscale noise schedules are necessary in practice.

Oral
Query Lower Bounds for Approximating the Top Eigenvector of Asymmetric Matrices

Kun Chen, Zhihua Zhang

展开摘要

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.

Poster
Quasi-Linear ICA for Motor Unit Decomposition during Dynamic Contractions

Alexander K Clarke, Dimitrios Chalatsis, Agnese Grison, Irene Mendez Guerra, Noura Ezaz-Nikpay, Pranav Mamidanna, Shihan Ma, Silvia Muceli, Dario Farina

展开摘要

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.

Poster
Quantum Speedups for Stochastic Optimization with Heavy-Tailed Noise

Bin Luo, Chengchang Liu, Jonathan Allcock, Shengyu Zhang, John C. S. Lui

展开摘要

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.

Poster