NeurIPS 2025 Papers

Online ride-hailing platforms aim to deliver efficient mobility-on-demand services, often facing challenges in balancing dynamic and spatially heterogeneous supply and demand. Existing methods typically fall into two categories: reinforcement learning (RL) approaches, which suffer from data inefficiency, oversimplified modeling of real-world dynamics, and difficulty enforcing operational constraints; or decomposed online optimization methods, which rely on manually designed high-level objectives that lack awareness of low-level routing dynamics. To address this issue, we propose a novel hybrid framework that integrates large language model (LLM) with mathematical optimization in a dynamic hierarchical system: (1) it is training-free, removing the need for large-scale interaction data as in RL, and (2) it leverages LLM to bridge cognitive limitations caused by problem decomposition by adaptively generating high-level objectives. Within this framework, LLM serves as a meta-optimizer, producing semantic heuristics that guide a low-level optimizer responsible for constraint enforcement and real-time decision execution. These heuristics are refined through a closed-loop evolutionary process, driven by harmony search, which iteratively adapts the LLM prompts based on feasibility and performance feedback from the optimization layer. Extensive experiments based on scenarios derived from both the New York and Chicago taxi datasets demonstrate the effectiveness of our approach, achieving an average improvement of 16% compared to state-of-the-art baselines.

We address the challenge of point cloud registration using color information, where traditional methods relying solely on geometric features often struggle in low-overlap and incomplete scenarios. To overcome these limitations, we propose GeGS-PCR, a novel two-stage method that combines geometric, color, and Gaussian information for robust registration. Our approach incorporates a dedicated color encoder that enhances color features by extracting multi-level geometric and color data from the original point cloud. We introduce the Geometric-3DGS module, which encodes the local neighborhood information of colored superpoints to ensure a globally invariant geometric-color context. Leveraging LORA optimization, we maintain high performance while preserving the expressiveness of 3DGS. Additionally, fast differentiable rendering is utilized to refine the registration process, leading to improved convergence. To further enhance performance, we propose a joint photometric loss that exploits both geometric and color features. This enables strong performance in challenging conditions with extremely low point cloud overlap. We validate our method by colorizing the Kitti dataset as ColorKitti and testing on both Color3DMatch and Color3DLoMatch datasets. Our method achieves state-of-the-art performance with Registration Recall at 99.9%, Relative Rotation Error as low as 0.013, and Relative Translation Error as low as 0.024, improving precision by at least a factor of 2.

The success of the machine learning field has reliably depended on training on large datasets. While effective, this trend comes at an extraordinary cost. This is due to two deeply intertwined factors: the size of models and the size of datasets. While promising research efforts focus on reducing the size of models, the other half of the equation remains fairly mysterious. Indeed, it is surprising that the standard approach to training remains to iterate over and over, uniformly sampling the training dataset. In this paper we explore a series of alternative training paradigms that leverage insights from hard-data-mining and dropout, simple enough to implement and use that can become the new training standard. The proposed Progressive Data Dropout reduces the number of effective epochs to as little as 12.4\% of the baseline. This savings actually do not come at any cost for accuracy. Surprisingly, the proposed method improves accuracy by up to 4.82\%. Our approach requires no changes to model architecture or optimizer, and can be applied across standard training pipelines, thus posing an excellent opportunity for wide adoption. Code can be found here: \url{https://github.com/bazyagami/LearningWithRevision}.

Fine-tuning pre-trained models with custom data leads to numerous expert models on specific tasks. Merging models into one universal model to empower multi-task ability refraining from data leakage has gained popularity. With the expansion in data and model size, parameter-efficient tuning becomes the common practice for obtaining task-specific models efficiently. However, few methods are dedicated to efficient merging, and existing methods designed for full fine-tuning merging fail under efficient merging. To address the issue, we analyze from low-rank decomposition and reveal that direction robustness during merging is crucial for merging efficient modules. We furthermore uncover that compensating for the gap between stark singular values contributes to direction robustness. Therefore, we propose RobustMerge, a training-free parameter-efficient merging method with complementary parameter adaptation to maintain direction robustness. Specifically, we (1) prune parameters and scale coefficients from inter-parameter relations for singular values to maintain direction stability away from task interference, and (2) perform cross-task normalization to enhance unseen task generalization. We establish a benchmark consisting of diverse multimodal tasks, on which we conduct experiments to certify the outstanding performance and generalizability of our method. Additional studies and extensive analyses further showcase the effectiveness.

Encountering shifted data at test time is a ubiquitous challenge when deploying predictive machine learning models. Test-time adaptation (TTA) methods aim to address this issue by continuously adapting a deployed model using only unlabeled test data. While TTA can help extend the model's deployment lifespan, there are scenarios where, despite adaptation, the drop in the model's performance remains significant enough to warrant taking the model offline and retraining. To detect such failure cases, we propose pairing TTA with risk monitoring frameworks that track predictive performance and raise alerts when predefined performance criteria are violated. Specifically, we extend existing monitoring tools based on sequential testing with confidence sequences to accommodate scenarios where the model is updated at test time and no test labels are available to estimate the performance metrics of interest. Our extensions unlock the application of rigorous statistical risk monitoring in TTA and we demonstrate applicability of our proposed TTA monitoring framework across a representative set of TTA methods, datasets and distribution shift types.

Large language models (LLMs) have demonstrated remarkable performance on various tasks. However, it remains an open question whether the default Euclidean space is the most suitable choice for embedding tokens in LLMs. In this study, we investigate the non-Euclidean characteristics of LLMs. Our findings reveal that token frequency follows a power-law distribution, with high-frequency tokens clustering near the origin and low-frequency tokens positioned farther away. Additionally, token embeddings exhibit a high degree of hyperbolicity, indicating a latent tree-like structure in the embedding space. Motivated by these observations, we propose to efficiently fine-tune LLMs in hyperbolic space to better exploit the underlying complex structures. However, we find that this hyperbolic fine-tuning cannot be achieved through the naive application of exponential and logarithmic maps when the embedding and weight matrices both reside in Euclidean space. To address this technical issue, we introduce hyperbolic low-rank efficient fine-tuning, HypLoRA, which performs low-rank adaptation directly on the hyperbolic manifold, preventing the cancellation effect produced by consecutive exponential and logarithmic maps and thereby preserving hyperbolic modeling capabilities. Extensive experiments across various base models and two different reasoning benchmarks, specifically arithmetic and commonsense reasoning tasks, demonstrate that HypLoRA substantially improves LLM performance.

While fine-tuning large language models (LLMs) for specific tasks often yields impressive results, it comes at the cost of memory inefficiency due to back-propagation in gradient-based training. Memory-efficient Zeroth-order (MeZO) optimizers, recently proposed to address this issue, only require forward passes during training, making them more memory-friendly. However, compared with exact gradients, ZO-based gradients usually exhibit an estimation error, which can significantly hurt the optimization process, leading to slower convergence and suboptimal solutions. In addition, we find that the estimation error will hurt more when adding to large weights instead of small weights. Based on this observation, this paper introduces Sparse MeZO, a novel memory-efficient zeroth-order optimization approach that applies ZO only to a carefully chosen subset of parameters. We propose a simple yet effective parameter selection scheme that yields significant performance gains with Sparse-MeZO. Additionally, we develop a memory-optimized implementation for sparse masking, ensuring the algorithm requires only inference-level memory consumption, allowing Sparse-MeZO to fine-tune LLaMA-30b on a single A100 GPU. Experimental results illustrate that Sparse-MeZO consistently improves both performance and convergence speed over MeZO without any overhead. For example, it achieves a 9% absolute accuracy improvement and 3.5x speedup over MeZO on the RTE task.

Large language models (LLMs) typically require fine-tuning for domain-specific tasks, and LoRA offers a computationally efficient approach by training low-rank adaptors. LoRA is also communication-efficient for federated LLMs when multiple users collaboratively fine-tune a global LLM model without sharing their proprietary raw data. However, even the transmission of local adaptors between a server and clients risks serious privacy leakage. Applying differential privacy (DP) to federated LoRA encounters a dilemma: adding noise to both adaptors amplifies synthetic noise on the model, while fixing one adaptor impairs the learnability of fine-tuning. In this paper, we propose FedASK (Differentially Private Federated Low Rank Adaptation with Double SKetching) , a novel federated LoRA framework to enable effective updating of both low-rank adaptor matrices with robust differential privacy. Inspired by randomized SVD, our key idea is a two-stage sketching pipeline. This pipeline first aggregates carefully sketched, privacy-preserving local updates, and then reconstructs the global matrices on the server to facilitate effective updating of both adaptors. We theoretically prove FedASK's differential privacy guarantee and its exact aggregation property. Comprehensive experiments demonstrate that FedASK consistently outperforms baseline methods across a variety of privacy settings and data distributions.

Modern large-language models often face communication bottlenecks on current hardware rather than computational limitations. *Multi-head latent attention (MLA)* addresses this by compressing the key-value cache using low-rank matrices, while the Absorb operation prevents the KV cache from reverting to its original size, significantly boosting both training and inference speed. Despite the success of DeepSeek V2/V3/R1, most model providers have heavily invested in optimizing GQA-based models and, therefore, lack strong incentives to retrain MLA-based models from scratch. This paper demonstrates that MLA provides superior expressive power compared to GQA with the same KV cache overhead, thereby offering a rationale for transitioning from GQA to MLA. In addition, we introduce TransMLA, a framework that seamlessly converts any GQA-based pre-trained model (e.g., LLaMA, Qwen, Gemma, Mistral/Mixtral) into an MLA-based model. For the first time, our method enables *direct conversion of these models into a format compatible with DeepSeek's codebase*, allowing them to fully leverage the existing, highly-optimized support for the DeepSeek architecture within inference engines like vLLM and SGlang. By compressing 93\% of the KV cache in LLaMA-2-7B, we achieve a **10x speedup** with an 8K context length while maintaining meaningful output. Moreover, the model requires only **6B tokens** for fine-tuning to recover comparable performance across multiple benchmarks. TransMLA provides a practical path for migrating GQA-based models to the MLA structure, and when combined with DeepSeek’s advanced optimizations—such as FP8 quantization and Multi-Token Prediction—further inference acceleration can be achieved.

Dependency parsing is the task of inferring natural language structure, often approached by modeling word interactions via attention through biaffine scoring. This mechanism works like self-attention in Transformers, where scores are calculated for every pair of words in a sentence. However, unlike Transformer attention, biaffine scoring does not use normalization prior to taking the softmax of the scores. In this paper, we provide theoretical evidence and empirical results revealing that a lack of normalization necessarily results in overparameterized parser models, where the extra parameters compensate for the sharp softmax outputs produced by high variance inputs to the biaffine scoring function. We argue that biaffine scoring can be made substantially more efficient by performing score normalization. We conduct experiments on semantic and syntactic dependency parsing in multiple languages, along with latent graph inference on non-linguistic data, using various settings of a $k$-hop parser. We train $N$-layer stacked BiLSTMs and evaluate the parser's performance with and without normalizing biaffine scores. Normalizing allows us to achieve state-of-the-art performance with fewer samples and trainable parameters. Code: https://github.com/paolo-gajo/EfficientSDP

Linear Recurrent Neural Networks (linear RNNs) have emerged as competitive alternatives to Transformers for sequence modeling, offering efficient training and linear-time inference. However, existing architectures face a fundamental trade-off between expressivity and efficiency, dictated by the structure of their state-transition matrices. Diagonal matrices, used in models such as Mamba, GLA, or mLSTM, yield fast runtime but have limited expressivity. To address this, recent architectures such as DeltaNet and RWKV-7 adopted a diagonal plus rank-1 structure, which allows simultaneous token and channel mixing, improving associative recall and, as recently shown, state-tracking when allowing negative eigenvalues in the state-transition matrices. Building on the interpretation of DeltaNet's recurrence as performing one step of online gradient descent per token on an associative recall loss, we introduce DeltaProduct, which instead takes multiple ($n_h$) steps per token. This naturally leads to diagonal plus rank-$n_h$ state-transition matrices, formed as products of $n_h$ generalized Householder transformations, providing a tunable mechanism to balance expressivity and efficiency. We provide a detailed theoretical characterization of the state-tracking capability of DeltaProduct in finite precision and how it improves by increasing $n_h$. Our extensive experiments demonstrate that DeltaProduct outperforms DeltaNet in both state-tracking and language modeling, while also showing significantly improved length extrapolation capabilities.

We propose a framework grounded in gradient flow theory and informed by geometric structure that provides multiple diverse solutions for a given task, ensuring collaborative results that enhance performance and adaptability across different tasks. This framework enables flexibility, allowing for efficient task-specific fine-tuning while preserving the knowledge of the pre-trained foundation models. Extensive experiments across transfer learning, few-shot learning, and domain generalization show that our proposed approach consistently outperforms existing Bayesian methods, delivering strong performance with affordable computational overhead and offering a practical solution by updating only a small subset of parameters.

Achieving balanced alignment of large language models (LLMs) in terms of Helpfulness, Honesty, and Harmlessness (3H optimization) constitutes a cornerstone of responsible AI. Existing methods like data mixture strategies face limitations, including heavy reliance on expert knowledge and conflicting optimization signals. While model merging offers parameter-level conflict-resolution strategies through integrating specialized models' parameters, its potential for 3H optimization remains underexplored. This paper systematically compares the effectiveness of model merging and data mixture methods in constructing 3H-aligned LLMs for the first time, revealing previously overlooked collaborative and conflict relationships among the 3H dimensions and discussing the advantages and drawbacks of data mixture (\textit{data-level}) and model merging (\textit{parameter-level}) methods in mitigating the conflict for balanced 3H optimization. Specially, we propose a novel \textbf{R}eweighting \textbf{E}nhanced task \textbf{S}ingular \textbf{M}erging method, \textbf{RESM}, through outlier weighting and sparsity-aware rank selection strategies to address the challenges of preference noise accumulation and layer sparsity adaptation inherent in 3H-aligned LLM merging. Extensive evaluations can verify the effectiveness and robustness of RESM compared to previous data mixture (2\%-5\% gain) and model merging (1\%-3\% gain) methods in achieving balanced LLM alignment.

We introduce the attention-indexed model (AIM), a theoretical framework for analyzing learning in deep attention layers. Inspired by multi-index models, AIM captures how token-level outputs emerge from layered bilinear interactions over high-dimensional embeddings. Unlike prior tractable attention models, AIM allows full-width key and query matrices, aligning more closely with practical transformers. Using tools from statistical mechanics and random matrix theory, we derive closed-form predictions for Bayes-optimal generalization error and identify sharp phase transitions as a function of sample complexity, model width, and sequence length. We propose a matching approximate message passing algorithm and show that gradient descent can reach optimal performance. AIM offers a solvable playground for understanding learning in self-attention layers, that are key components of modern architectures.

Low-Rank Adaptation (LoRA) has emerged as a highly efficient framework for finetuning the weights of large foundation models, and has become the go-to method for data-driven customization of LLMs. Despite the promise of highly customized behaviors and capabilities, switching between relevant LoRAs in a multiturn setting is inefficient, as the key-value (KV) cache of the entire turn history must be recomputed with the LoRA weights before generation can begin. To address this problem, we propose Activated LoRA (aLoRA), an adapter architecture which modifies the LoRA framework to only adapt weights for the tokens in the sequence after the aLoRA is invoked. This change crucially allows aLoRA to accept the base model's KV cache of the input string, meaning that aLoRA can be instantly activated whenever needed in a chain without recomputing the prior keys and values. This enables building what we call intrinsics, i.e. specialized models invoked to perform well-defined operations on portions of an input chain or conversation that otherwise uses the base model by default. We train a set of aLoRA-based intrinsics models, demonstrating competitive accuracy with standard LoRA while significantly improving inference efficiency. We contributed our Activated LoRA implementation to the Huggingface PEFT library.

Vision Transformers (ViTs), such as DINOv2, achieve strong performance across domains but often repurpose low-informative patch tokens in ways that reduce the interpretability of attention and feature maps. This challenge is especially evident in medical imaging, where domain shifts can degrade both performance and transparency. In this paper, we introduce Randomized-MLP (RMLP) regularization, a contrastive learning-based method that encourages more semantically aligned representations. We apply RMLP when fine-tuning DINOv2 to both medical and natural image modalities, showing that it improves or maintains downstream performance while producing more interpretable attention maps. We also provide a mathematical analysis of RMLPs, offering insights into its role in enhancing ViT-based models and advancing our understanding of contrastive learning in this context.

Large language models (LLMs) excel across various tasks, but standard first-order (FO) fine-tuning demands considerable memory, significantly limiting real-world deployment. Recently, zeroth-order (ZO) optimization stood out as a promising memory-efficient training paradigm, avoiding backward passes and relying solely on forward passes for gradient estimation, making it attractive for resource-constrained scenarios. However, ZO method lags far behind FO method in both convergence speed and accuracy. To bridge the gap, we introduce a novel layer-wise divergence analysis that uncovers the distinct update pattern of FO and ZO optimization. Aiming to resemble the learning capacity of FO method from the findings, we propose \textbf{Di}vergence-driven \textbf{Z}eroth-\textbf{O}rder (\textbf{DiZO}) optimization. DiZO conducts divergence-driven layer adaptation by incorporating projections to ZO updates, generating diverse-magnitude updates precisely scaled to layer-wise individual optimization needs. Our results demonstrate that DiZO significantly reduces the needed iterations for convergence without sacrificing throughput, cutting training GPU hours by up to 48\% on various datasets. Moreover, DiZO consistently outperforms the representative ZO baselines in fine-tuning RoBERTa-large, OPT-series, and Llama-series on downstream tasks and, in some cases, even surpasses memory-intensive FO fine-tuning. Our code is released at \url{https://github.com/Skilteee/DiZO}.

Frontier large language models (LLMs) have shown great success in text modeling and generation tasks across domains. However, natural language exhibits inherent semantic hierarchies and nuanced geometric structure, which current LLMs do not capture completely owing to their reliance on Euclidean operations such as dot-products and norms. Furthermore, recent studies have shown that not respecting the underlying geometry of token embeddings leads to training instabilities and degradation of generative capabilities. These findings suggest that shifting to non-Euclidean geometries can better align language models with the underlying geometry of text. We thus propose to operate fully in $\textit{Hyperbolic space}$, known for its expansive, scale-free, and low-distortion properties. To this end, we introduce $\textbf{HELM}$, a family of $\textbf{H}$yp$\textbf{E}$rbolic Large $\textbf{L}$anguage $\textbf{M}$odels, offering a geometric rethinking of the Transformer-based LLM that addresses the representational inflexibility, missing set of necessary operations, and poor scalability of existing hyperbolic LMs. We additionally introduce a $\textbf{Mi}$xture-of-$\textbf{C}$urvature $\textbf{E}$xperts model, $\textbf{HELM-MiCE}$, where each expert operates in a distinct curvature space to encode more fine-grained geometric structure from text, as well as a dense model, $\textbf{HELM-D}$. For $\textbf{HELM-MiCE}$, we further develop hyperbolic Multi-Head Latent Attention ($\textbf{HMLA}$) for efficient, reduced-KV-cache training and inference. For both models, we further develop essential hyperbolic equivalents of rotary positional encodings and root mean square normalization. We are the first to train fully hyperbolic LLMs at billion-parameter scale, and evaluate them on well-known benchmarks such as MMLU and ARC, spanning STEM problem-solving, general knowledge, and commonsense reasoning. Our results show consistent gains from our $\textbf{HELM}$ architectures – up to 4\% – over popular Euclidean architectures used in LLaMA and DeepSeek with superior semantic hierarchy modeling capabilities, highlighting the efficacy and enhanced reasoning afforded by hyperbolic geometry in large-scale language model pretraining.

Tensor decomposition is a fundamental tool for analyzing multi-dimensional data by learning low-rank factors to represent high-order interactions. While recent works on temporal tensor decomposition have made significant progress by incorporating continuous timestamps in latent factors, they still struggle with general tensor data with continuous indexes not only in the temporal mode but also in other modes, such as spatial coordinates in climate data. Moreover, the challenge of self-adapting model complexity is largely unexplored in functional temporal tensor models, with existing methods being inapplicable in this setting. To address these limitations, we propose functional Complexity-Adaptive Temporal Tensor dEcomposition (Catte). Our approach encodes continuous spatial indexes as learnable Fourier features and employs neural ODEs in latent space to learn the temporal trajectories of factors. To enable automatic adaptation of model complexity, we introduce a sparsity-inducing prior over the factor trajectories. We develop an efficient variational inference scheme with an analytical evidence lower bound, enabling sampling-free optimization. Through extensive experiments on both synthetic and real-world datasets, we demonstrate that Catte not only reveals the underlying ranks of functional temporal tensors but also significantly outperforms existing methods in prediction performance and robustness against noise.