NeurIPS 2025 Papers

We revisit the problem of private online learning, in which a learner receives a sequence of $T$ data points and has to respond at each time-step a hypothesis. It is required that the entire stream of output hypotheses should satisfy differential privacy. Prior work of Golowich and Livni [2021] established that every concept class $\mathcal{H}$ with finite Littlestone dimension $d$ is privately online learnable in the realizable setting. In particular, they proposed an algorithm that achieves an $O_{d}(\log T)$ mistake bound against an oblivious adversary. However, their approach yields a suboptimal $\tilde{O}\_{d}(\sqrt{T})$ bound against an adaptive adversary. In this work, we present a new algorithm with a mistake bound of $O_{d}(\log T)$ against an adaptive adversary, closing this gap. We further investigate the problem in the agnostic setting, which is more general than the realizable setting as it does not impose any assumptions on the data. We give an algorithm that obtains a sublinear regret of $\tilde{O}_d(\sqrt{T})$ for generic Littlestone classes, demonstrating that they are also privately online learnable in the agnostic setting.

Hallucinations in large language models (LLMs) pose significant safety concerns that impede their broader deployment. Recent research in hallucination detection has demonstrated that LLMs' internal representations contain truthfulness hints, which can be harnessed for detector training. However, the performance of these detectors is heavily dependent on the internal representations of predetermined tokens, fluctuating considerably when working on free-form generations with varying lengths and sparse distributions of hallucinated entities. To address this, we propose HaMI, a novel approach that enables robust detection of hallucinations through adaptive selection and learning of critical tokens that are most indicative of hallucinations. We achieve this robustness by an innovative formulation of the Hallucination detection task as Multiple Instance (HaMI) learning over token-level representations within a sequence, thereby facilitating a joint optimisation of token selection and hallucination detection on generation sequences of diverse forms. Comprehensive experimental results on four hallucination benchmarks show that HaMI significantly outperforms existing state-of-the-art approaches.

Many complex networks have partially observed or evolving connectivity, making link prediction a fundamental task. Topological link prediction infers missing links using only network topology, with applications in social, biological, and technological systems. The Cannistraci-Hebb (CH) theory provides a topological formulation of Hebbian learning, grounded on two pillars: (1) the **minimization of external links** within local communities, and (2) the **path-based definition of local communities** that capture homophilic (similarity-driven) interactions via paths of length 2 and synergetic (diversity-driven) interactions via paths of length 3. Building on this, we introduce the Cannistraci-Hebb Adaptive (CHA) network automata, an adaptive learning machine that automatically selects the optimal CH rule and path length to model each network. CHA unifies theoretical interpretability and data-driven adaptivity, bridging physics-inspired network science and machine intelligence. Across 1,269 networks from 14 domains, CHA consistently surpasses state-of-the-art methods—including SPM, SBM, graph embedding methods, and message-passing graph neural networks—while revealing the mechanistic principles governing link formation. Our code is available at https://github.com/biomedical-cybernetics/Cannistraci_Hebb_network_automata.

Training deep neural networks (DNNs) is a structured optimization problem, because the parameters are naturally represented by matrices and tensors rather than simple vectors. Under this structural representation, it has been widely observed that gradients are low-rank and Hessians are approximately block-wise diagonal. These structured properties are crucial for designing efficient optimization algorithms but may not be utilized by current popular optimizers like Adam. In this paper, we present a novel optimization algorithm ASGO that capitalizes on these properties by employing a preconditioner that is adaptively updated using structured gradients. By fine-grained theoretical analysis, ASGO is proven to achieve superior convergence rates compared to existing structured gradient methods. Based on the convergence theory, we further demonstrate that ASGO can benefit from the low-rank and block-wise diagonal properties. We also discuss practical modifications of ASGO and empirically verify the effectiveness of the algorithm on language model tasks.

The evolution of the human brain has led to the development of complex synaptic plasticity, enabling dynamic adaptation to a constantly evolving world. This progress inspires our exploration into a new paradigm for Spiking Neural Networks (SNNs): a Plasticity-Driven Learning Framework (PDLF). This paradigm diverges from traditional neural network models that primarily focus on direct training of synaptic weights, leading to static connections that limit adaptability in dynamic environments. Instead, our approach delves into the heart of synaptic behavior, prioritizing the learning of plasticity rules themselves. This shift in focus from weight adjustment to mastering the intricacies of synaptic change offers a more flexible and dynamic pathway for neural networks to evolve and adapt. Our PDLF does not merely adapt existing concepts of functional and Presynaptic-Dependent Plasticity but redefines them, aligning closely with the dynamic and adaptive nature of biological learning. This reorientation enhances key cognitive abilities in artificial intelligence systems, such as working memory and multitasking capabilities, and demonstrates superior adaptability in complex, real-world scenarios. Moreover, our framework sheds light on the intricate relationships between various forms of plasticity and cognitive functions, thereby contributing to a deeper understanding of the brain's learning mechanisms. Integrating this groundbreaking plasticity-centric approach in SNNs marks a significant advancement in the fusion of neuroscience and artificial intelligence. It paves the way for developing AI systems that not only learn but also adapt in an ever-changing world, much like the human brain.

Recent studies in *Machine Learning* (ML) for biological research focus on investigating molecular properties to accelerate drug discovery. However, limited labeled molecular data often hampers the performance of ML models. A common strategy to mitigate data scarcity is leveraging auxiliary learning tasks to provide additional supervision, but selecting effective auxiliary tasks requires substantial domain expertise and manual effort, and their inclusion does not always guarantee performance gains. To overcome these challenges, we introduce *Automatic Auxiliary Task Selection* (AutAuT), a fully automated framework that seamlessly retrieves auxiliary tasks using large language models and adaptively integrates them through a novel *gradient alignment* weighting mechanism. By automatically emphasizing auxiliary tasks aligned with the primary objective, AutAuT significantly enhances predictive accuracy while reducing negative impacts from irrelevant tasks. Extensive evaluations demonstrate that AutAuT outperforms *10* auxiliary task-based approaches and *18* advanced molecular property prediction models.

Due to its powerful capability of self-supervised representation learning and clustering, contrastive attributed graph clustering (CAGC) has achieved great success, which mainly depends on effective data augmentation and contrastive objective setting. However, most CAGC methods utilize edges as auxiliary information to obtain node-level embedding representation and only focus on node-level embedding augmentation. This approach overlooks edge-level embedding augmentation and the interactions between node-level and edge-level embedding augmentations across various granularity. Moreover, they often treat all contrastive sample pairs equally, neglecting the significant differences between hard and easy positive-negative sample pairs, which ultimately limits their discriminative capability. To tackle these issues, a novel robust attributed graph clustering (RAGC), incorporating hybrid-collaborative augmentation (HCA) and contrastive sample adaptive-differential awareness (CSADA), is proposed. First, node-level and edge-level embedding representations and augmentations are simultaneously executed to establish a more comprehensive similarity measurement criterion for subsequent contrastive learning. In turn, the discriminative similarity further consciously guides edge augmentation. Second, by leveraging pseudo-label information with high confidence, a CSADA strategy is elaborately designed, which adaptively identifies all contrastive sample pairs and differentially treats them by an innovative weight modulation function. The HCA and CSADA modules mutually reinforce each other in a beneficent cycle, thereby enhancing discriminability in representation learning. Comprehensive graph clustering evaluations over six benchmark datasets demonstrate the effectiveness of the proposed RAGC against several state-of-the-art CAGC methods. The code of RAGC could be available at https://github.com/TianxiangZhao0474/RAGC.git.

Functional data play a pivotal role across science and engineering, yet their infinite-dimensional nature makes representation learning challenging. Conventional statistical models depend on pre-chosen basis expansions or kernels, limiting the flexibility of data-driven discovery, while many deep-learning pipelines treat functions as fixed-grid vectors, ignoring inherent continuity. In this paper, we introduce Functional Attention with a Mixture-of-Experts (FAME), an end-to-end, fully data-driven framework for function-on-function regression. FAME forms continuous attention by coupling a bidirectional neural controlled differential equation with MoE-driven vector fields to capture intra-functional continuity, and further fuses change to inter-functional dependencies via multi-head cross attention. Extensive experiments on synthetic and real-world functional regression benchmarks show that FAME achieves state-of-the-art accuracy and strong robustness to arbitrarily sampled discrete observations of functions.

This paper introduces new parameter-free first-order methods for convex optimization problems in which the objective function exhibits Hölder smoothness. Inspired by the recently proposed distance-over-gradient (DOG) technique, we propose an accelerated distance-adaptive method which achieves optimal anytime convergence rates for Hölder smooth problems without requiring prior knowledge of smoothness parameters or explicit parameter tuning. Importantly, our parameter-free approach removes the necessity of specifying target accuracy in advance, addressing a significant limitation found in the universal fast gradient methods(Nesterov,2015). We further present a parameter-free accelerated method that eliminates the need for line-search procedures and extend it to convex stochastic optimization. Preliminary experimental results highlight the effectiveness of our approach in convex nonsmooth problems and its advantages over existing parameter-free or accelerated methods.

Adaptive optimization is critical in federated learning, where enabling adaptivity on both the server and client sides has proven essential for achieving optimal performance. However, the scalability of such jointly adaptive systems is often hindered by resource limitations in communication and memory. In this paper, we introduce a class of efficient adaptive algorithms, named $FedAda^2$ and its enhanced version $FedAda^2$++, designed specifically for large-scale, cross-device federated environments. $FedAda^2$ optimizes communication efficiency by avoiding the transfer of preconditioners between the server and clients. Additionally, $FedAda^2$++ extends this approach by incorporating memory-efficient adaptive optimizers on the client side, further reducing on-device memory usage. Theoretically, we demonstrate that $FedAda^2$ and $FedAda^2$++ achieve the same convergence rates for general, non-convex objectives as its more resource-intensive counterparts that directly integrate joint adaptivity. Extensive empirical evaluations on image and text datasets demonstrate both the advantages of joint adaptivity and the effectiveness and efficiency of $FedAda^2$/$FedAda^2$++.

Image deblurring plays a crucial role in enhancing visual clarity across various applications. Although most deep learning approaches primarily focus on sRGB images, which inherently lose critical information during the image signal processing pipeline, RAW images, being unprocessed and linear, possess superior restoration potential but remain underexplored. Deblurring RAW images presents unique challenges, particularly in handling frequency-dependent blur while maintaining computational efficiency. To address these issues, we propose Frequency Enhanced Network (FrENet), a framework specifically designed for RAW-to-RAW deblurring that operates directly in the frequency domain. We introduce a novel Adaptive Frequency Positional Modulation module, which dynamically adjusts frequency components according to their spectral positions, thereby enabling precise control over the deblurring process. Additionally, frequency domain skip connections are adopted to further preserve high-frequency details. Experimental results demonstrate that FrENet surpasses state-of-the-art deblurring methods in RAW image deblurring, achieving significantly better restoration quality while maintaining high efficiency in terms of reduced MACs. Furthermore, FrENet's adaptability enables it to be extended to sRGB images, where it delivers comparable or superior performance compared to methods specifically designed for sRGB data. The source code will be publicly available.

We propose and study Sparse Polyak, a variant of Polyak’s adaptive step size, designed to solve high-dimensional statistical estimation problems where the problem dimension is allowed to grow much faster than the sample size. In such settings, the standard Polyak step size performs poorly, requiring an increasing number of iterations to achieve optimal statistical precision-even when, the problem remains well conditioned and/or the achievable precision itself does not degrade with problem size. We trace this limitation to a mismatch in how smoothness is measured: in high dimensions, it is no longer effective to estimate the Lipschitz smoothness constant. Instead, it is more appropriate to estimate the smoothness restricted to specific directions relevant to the problem (restricted Lipschitz smoothnes constant). Sparse Polyak overcomes this issue by modifying the step size to estimate the restricted Lipschitz smoothness constant. We support our approach with both theoretical analysis and numerical experiments, demonstrating its improved performance.

Low-Rank Adaptation (LoRA) is a crucial method for efficiently fine-tuning large language models (LLMs), with its effectiveness influenced by two key factors: rank selection and weight initialization. While numerous LoRA variants have been proposed to improve performance by addressing one of these aspects, they often compromise usability or computational efficiency. In this paper, we analyze and identify the core limitations of existing approaches and propose a novel framework—**GoRA** (**G**radient-driven Adaptive L**o**w **R**ank **A**daptation)—that simultaneously adapts both the rank and initialization strategy within a unified framework. GoRA leverages gradient information during training to dynamically assign optimal ranks and initialize low-rank adapter weights in an adaptive manner. To our knowledge, GoRA is the first method that not only addresses the limitations of prior approaches—which often focus on either rank selection or initialization in isolation—but also unifies both aspects within a single framework, enabling more effective and efficient adaptation. Extensive experiments across various architectures and modalities show that GoRA consistently outperforms existing LoRA-based methods while preserving the efficiency of vanilla LoRA. For example, when fine-tuning Llama3.1-8B-Base for mathematical reasoning, GoRA achieves a 5.13-point improvement over standard LoRA and even outperforms full fine-tuning by 2.05 points under high-rank settings. Code is available at: https://github.com/hhnqqq/MyTransformers.

Most existing image tokenizers encode images into a fixed number of tokens or patches, overlooking the inherent variability in image complexity and introducing unnecessary computate overhead for simpler images. To address this, we propose Content-Adaptive Tokenizer (CAT), which dynamically adjusts representation capacity based on the image content and encodes simpler images into fewer tokens. We design (1) a caption-based evaluation system that leverages LLMs to predict content complexity and determine the optimal compression ratio for an image, and (2) a novel nested VAE architecture that performs variable-rate compression in a single model. Trained on images with varying complexity, CAT achieves an average of 15% reduction in rFID across seven detail-rich datasets containing text, humans, and complex textures. On natural image datasets like ImageNet and COCO, it reduces token usage by 18% while maintaining high-fidelity reconstructions. We further evaluate CAT on two downstream tasks. For image classification, CAT consistently improves top-1 accuracy across five datasets spanning diverse domains. For image generation, it boosts training throughput by 23% on ImageNet, leading to more efficient learning and improved FIDs over fixed-token baselines.

In pattern classification, efficient uncertainty reasoning plays a critical role, particularly in real-time applications involving noisy data, ambiguous class boundaries, or overlapping categories. Leveraging the advanced computational power of quantum computing, an Adaptive Quantum Circuit for Dempster’s Rule of Combination (AQC-DRC) is proposed to address efficient classification under uncertain environments. The AQC-DRC is developed within the framework of quantum evidence theory (QET) and facilitates decision-making based on quantum basic probability and plausibility levels, which is a generalized Bayesian inference method. The AQC-DRC provides a deterministic computation of DRC, ensuring that quantum fusion outcomes in uncertain pattern classification are exactly aligned with those of the classical method, while simultaneously achieving exponential reductions in the computational complexity of evidence combination and significantly improving fusion efficiency. It is founded that the quantum basic probability amplitude function in QET, as a generalized quantum probability amplitude, can be naturally utilized to express the quantum amplitude encoding. In addition, the quantum basic probability in QET, as a generalized quantum probability, naturally forms a quantum basic probability distribution and can be used to represent quantum measurement outcomes for quantum basic probability level decision-making. Furthermore, the quantum plausibility function in QET also can be naturally used to express the quantum measurement outcomes for quantum plausibility level decision-making. These findings enrich the physical understanding of quantum amplitude encoding and quantum measurement outcomes, offering broad application prospects for representing and processing uncertain knowledge in pattern classification.

In this paper, we study the fundamental problems of maintaining the diameter and a $k$-center clustering of a dynamic point set $P \subset \mathbb{R}^d$, where points may be inserted or deleted over time and the ambient dimension $d$ is not constant and may be high. Our focus is on designing algorithms that remain effective even in the presence of an \emph{adaptive adversary}—an adversary that, at any time $t$, knows the entire history of the algorithm’s outputs as well as all the random bits used by the algorithm up to that point. We present a fully dynamic algorithm that maintains a $2$-approximate diameter with a \emph{worst-case} update time of $poly(d, \log n)$, where $n$ is the length of the stream. Our result is achieved by identifying a robust representative of the dataset that requires infrequent updates, combined with a careful deamortization. To the best of our knowledge, this is the first efficient fully-dynamic algorithm for diameter in high dimensions that \emph{simultaneously} achieves a $2$-approximation guarantee and robustness against an adaptive adversary. We also give an improved dynamic $(4+\epsilon)$-approximation algorithm for the $k$-center problem, also resilient to an adaptive adversary. Our clustering algorithm achieves an amortized update time of $k^{2.5} d \cdot poly(\epsilon^{-1}, \log n)$, improving upon the amortized update time of $k^6 d \cdot poly( \epsilon^{-1}, \log n)$ by Biabani et al. [NeurIPS'24].

In semi-supervised segmentation, capturing meaningful semantic structures from unlabeled data is essential. This is particularly challenging in histopathology image analysis, where objects are densely distributed. To address this issue, we propose a semi-supervised segmentation framework designed to robustly identify and preserve relevant topological features. Our method leverages multiple perturbed predictions obtained through stochastic dropouts and temporal training snapshots, enforcing topological consistency across these varied outputs. This consistency mechanism helps distinguish biologically meaningful structures from transient and noisy artifacts. A key challenge in this process is to accurately match the corresponding topological features across the predictions in the absence of ground truth. To overcome this, we introduce a novel matching strategy that integrates spatial overlap with global structural alignment, minimizing discrepancies among predictions. Extensive experiments demonstrate that our approach effectively reduces topological errors, resulting in more robust and accurate segmentations essential for reliable downstream analysis. Code is available at https://github.com/Melon-Xu/MATCH.

Randomized controlled trials often suffer from interference, a violation of the Stable Unit Treatment Value Assumption (SUTVA), where a unit's outcome is influenced by its neighbors' treatment assignments. This interference biases naive estimators of the average treatment effect (ATE). A popular method to achieve unbiasedness pairs the Horvitz-Thompson estimator of the ATE with a known exposure mapping, a function that identifies units in a given randomization unaffected by interference. For example, an exposure mapping may stipulate that a unit experiences no further interference if at least an $h$-fraction of its neighbors share its treatment status. However, selecting this threshold $h$ is challenging, requiring domain expertise; in its absence, fixed thresholds such as $h = 1$ are often used. In this work, we propose a data-adaptive method to select the $h$-fractional threshold that minimizes the mean-squared-error (MSE) of the Horvitz-Thompson estimator. Our approach estimates the bias and variance of the Horvitz-Thompson estimator paired with candidate thresholds by leveraging a first-order approximation, specifically, linear regression of potential outcomes on exposures. We present simulations illustrating that our method improves upon non-adaptive threshold choices, and an adapted Lepski's method. We further illustrate the performance of our estimator by running experiments with synthetic outcomes on a real village network dataset, and on a publicly-available Amazon product similarity graph. Furthermore, we demonstrate that our method remains robust to deviations from the linear potential outcomes model.

Recent advances in Vision Transformers (ViTs) have shown remarkable performance across vision tasks, yet their deep, uniform layer structure introduces significant computational overhead. In this work, we explore the emergent dynamics of ViT layers through the lens of energy-based memory systems, drawing a connection between self-attention and modern Hopfield networks. We introduce a novel metric—Layer Instability Index (LII)—derived from the operational softmax mode and its variability, to quantify the metastability of each Transformer layer over time. Our analysis reveals that certain layers exhibit consistent convergence to attractor-like states, suggesting functional specialisation and early stabilisation. Leveraging this insight, we propose an adaptive training framework that dynamically freezes or skips stable layers based on their energy landscape behavior. Our method reduces training costs while maintaining or improving accuracy. Extensive experiments on ViT-S/B/L on CUB-200-2011, CIFAR-10/100, Food-101, Stanford Dogs, and Beans demonstrate the generality and efficiency of our approach. This work provides new theoretical and practical perspectives for energy-aware optimisation of deep Transformer models.