NeurIPS 2025 Papers

Low-rank pseudoinverses are widely used to approximate matrix inverses in scalable machine learning, optimization, and scientific computing. However, real-world matrices are often observed with noise, arising from sampling, sketching, and quantization. The spectral-norm robustness of low-rank inverse approximations remains poorly understood. We systematically study the spectral-norm error $\| \tilde{A}_p^{-1} - A_p^{-1} \|$ for an $n\times n$ symmetric matrix $A$, where $A_p^{-1}$ denotes the best rank-\(p\) approximation of $A^{-1}$, and $\tilde{A} = A + E$ is a noisy observation. Under mild assumptions on the noise, we derive sharp non-asymptotic perturbation bounds that reveal how the error scales with the eigengap, spectral decay, and noise alignment with low-curvature directions of $A$. Our analysis introduces a novel application of contour integral techniques to the \emph{non-entire} function $f(z) = 1/z$, yielding bounds that improve over naive adaptations of classical full-inverse bounds by up to a factor of $\sqrt{n}$. Empirically, our bounds closely track the true perturbation error across a variety of real-world and synthetic matrices, while estimates based on classical results tend to significantly overpredict. These findings offer practical, spectrum-aware guarantees for low-rank inverse approximations in noisy computational environments.

Prompting is one of the main ways to adapt a pretrained model to target tasks. Besides manually constructing prompts, many prompt optimization methods have been proposed in the literature. Method development is mainly empirically driven, with less emphasis on a conceptual understanding of prompting. In this paper we discuss how optimal prompting can be understood through a Bayesian view, which also implies some fundamental limitations of prompting that can only be overcome by tuning weights. The paper explains in detail how meta-trained neural networks behave as Bayesian predictors over the pretraining distribution, whose hallmark feature is rapid in-context adaptation. Optimal prompting can be studied formally as conditioning these Bayesian predictors, yielding criteria for target tasks where optimal prompting is and is not possible. We support the theory with educational experiments on LSTMs and Transformers, where we compare different versions of prefix-tuning and different weight-tuning methods. We also confirm that soft prefixes, which are sequences of real-valued vectors outside the token alphabet, can lead to very effective prompts for trained and even untrained networks by manipulating activations in ways that are not achievable by hard tokens. This adds an important mechanistic aspect beyond the conceptual Bayesian theory.

Parameter-efficient training, based on low-rank optimization, has become a highly successful tool for fine-tuning large deep-learning models. However, these methods fail at low-rank pre-training tasks where maintaining the low-rank structure and the objective remains a challenging task. We propose the Quadratic Reweighted Rank Regularizer dubbed Q3R, which leads to a novel low-rank inducing training strategy inspired by the iteratively reweighted least squares (IRLS) framework. Q3R is based on a quadratic regularizer term which majorizes a smoothed log determinant serving as rank surrogate objective. Unlike other low-rank training techniques, Q3R is able to train weight matrices with prescribed, low target ranks of models that achieve comparable predictive performance as dense models, with small computational overhead, while remaining fully compatible with existing architectures. In experiments, we are able to truncate 60% of the parameters of a ViT-Tiny parameters with marginal loss in CIFAR-10 performance and up to 80% with only 4% accuracy drop. The efficacy of Q3R is confirmed on Transformers across both image and language tasks, including for low-rank fine-tuning.

This paper studies the problem of safe meta-reinforcement learning (safe meta-RL), where an agent efficiently adapts to unseen tasks while satisfying safety constraints at all times during adaptation. We propose a framework consisting of two complementary modules: safe policy adaptation and safe meta-policy training. The first module introduces a novel one-step safe policy adaptation method that admits a closed-form solution, ensuring monotonic improvement, constraint satisfaction at every step, and high computational efficiency. The second module develops a Hessian-free meta-training algorithm that incorporates safety constraints on the meta-policy and leverages the analytical form of the adapted policy to enable scalable optimization. Together, these modules yield three key advantages over existing safe meta-RL methods: (i) superior optimality, (ii) anytime safety guarantee, and (iii) high computational efficiency. Beyond existing safe meta-RL analyses, we prove the anytime safety guarantee of policy adaptation and provide a lower bound of the expected total reward of the adapted policies compared with the optimal policies, which shows that the adapted policies are nearly optimal. Empirically, our algorithm achieves superior optimality, strict safety compliance, and substantial computational gains—up to 70\% faster training and 50\% faster testing—across diverse locomotion and navigation benchmarks.

Low-rank optimization has emerged as a promising approach to enabling memory-efficient training of large language models (LLMs). Existing low-rank optimization methods typically project gradients onto a low-rank subspace, reducing the memory cost of storing optimizer states. A key challenge in these methods is selecting suitable subspaces to ensure an effective optimization trajectory. Most existing approaches select the dominant subspace to preserve gradient information, as this intuitively provides the best approximation. However, we find that in practice, the dominant subspace stops changing during pretraining, thereby constraining weight updates to similar subspaces. In this paper, we propose importance sampling for low-rank optimization in LLM pretraining with a provable convergence guarantee, which the dominant subspace approach does not have. Empirically, we demonstrate that our method significantly outperforms previous methods in LLM pretraining tasks.

Parameter-efficient fine-tuning (PEFT) methods have shown promise in adapting large language models, yet existing approaches exhibit counter-intuitive phenomena: integrating either matrix decomposition or mixture-of-experts (MoE) individually decreases performance across tasks, though decomposition improves results on specific domains despite reducing parameters, while MoE increases parameter count without corresponding decrease in training efficiency. Motivated by these observations and the modular nature of PT, we propose PT-MoE, a novel framework that integrates matrix decomposition with MoE routing for efficient PT. Evaluation results across 17 datasets demonstrate that PT-MoE achieves state-of-the-art performance in both question answering (QA) and mathematical problem solving tasks, improving F1 score by 1.49 points over PT and 2.13 points over LoRA in QA tasks, while improving mathematical accuracy by 10.75 points over PT and 0.44 points over LoRA, all while using 25% fewer parameters than LoRA. Our analysis reveals that while PT methods generally excel in QA tasks and LoRA-based methods in math datasets, the integration of matrix decomposition and MoE in PT-MoE yields complementary benefits: decomposition enables efficient parameter sharing across experts while MoE provides dynamic adaptation, collectively enabling PT-MoE to demonstrate cross-task consistency and generalization abilities. These findings, along with ablation studies on routing mechanisms and architectural components, provide insights for future PEFT methods.

Current parameter-efficient fine-tuning methods for adapting pre-trained language models to downstream tasks are susceptible to interference from noisy data. Conventional noise-handling approaches either rely on laborious data pre-processing or employ model architecture modifications prone to error accumulation. In contrast to existing noise-process paradigms, we propose a noise-robust adaptation method via asymmetric LoRA poisoning experts (LoPE), a novel framework that enhances model robustness to noise only with generated noisy data. Drawing inspiration from the mixture-of-experts architecture, LoPE strategically integrates a dedicated poisoning expert in an asymmetric LoRA configuration. Through a two-stage paradigm, LoPE performs noise injection on the poisoning expert during fine-tuning to enhance its noise discrimination and processing ability. During inference, we selectively mask the dedicated poisoning expert to leverage purified knowledge acquired by normal experts for noise-robust output. Extensive experiments demonstrate that LoPE achieves strong performance and robustness purely through the low-cost noise injection, which completely eliminates the requirement of data cleaning.

Large Language Models (LLMs) have demonstrated remarkable capabilities but typically require extensive computational resources and memory for inference. Post-training quantization (PTQ) can effectively reduce these demands by storing weights in lower bit-width formats. However, standard uniform quantization often leads to notable performance degradation, particularly in low-bit scenarios. In this work, we introduce a Grouped Lattice Vector Quantization (GLVQ) framework that assigns each group of weights a customized lattice codebook, defined by a learnable generation matrix. To address the non-differentiability of the quantization process, we adopt Babai rounding to approximate nearest-lattice-point search during training, which enables stable optimization of the generation matrices. Once trained, decoding reduces to a simple matrix-vector multiplication, yielding an efficient and practical quantization pipeline. Experiments on multiple benchmarks show that our approach achieves a better trade-off between model size and accuracy compared to existing post-training quantization baselines, highlighting its effectiveness in deploying large models under stringent resource constraints. Our source code is available on GitHub repository: https://github.com/xzhang9308/GLVQ.

A transformer is merely a stack of learned data–to–data maps—yet those maps can hide rich algorithms. We train a linear, attention-only transformer on millions of masked-block completion tasks: each prompt is a masked low-rank matrix whose missing block may be (i) a scalar prediction target or (ii) an unseen kernel slice for Nyström extrapolation. The model sees only input–output pairs and a mean-squared loss; it is given no normal equations, no handcrafted iterations, and no hint that the tasks are related. Surprisingly, after training, algebraic unrolling reveals the same parameter-free update rule across all three resource regimes (full visibility, bandwidth-limited heads, rank-limited attention). We prove that this rule achieves second-order convergence on full-batch problems, cuts distributed iteration complexity, and remains accurate with compute-limited attention. Thus, a transformer trained solely to patch missing blocks implicitly discovers a unified, resource-adaptive iterative solver spanning prediction, estimation, and Nyström extrapolation—highlighting a powerful capability of in-context learning.

In recent years, face-based deep-learning gaze estimation methods have achieved significant advancements. However, while face images provide supplementary information beneficial for gaze inference, the substantial extraneous information they contain also increases the risk of overfitting during model training and compromises generalization capability. To alleviate this problem, we propose the 3DPE-Gaze framework, explicitly modeling 3D facial priors for feature decoupling and generalized gaze estimation. The 3DPE-Gaze framework consists of two core modules: the 3D Geometric Prior Module (3DGP) incorporating the FLAME model to parameterize facial structures and gaze-irrelevant facial appearances while extracting gaze features; the Semantic Concept Alignment Module (SCAM) separates gaze-related and unrelated concepts through CLIP-guided contrastive learning. Finally, the 3DPE-Gaze framework combines 3D facial landmark as prior for generalized gaze estimation. Experimental results show that 3DPE-Gaze outperforms existing state-of-the-art methods on four major cross-domain tasks, with particularly outstanding performance in challenging scenarios such as lighting variations, extreme head poses, and glasses occlusion.

This paper introduces **ReservoirTTA**, a novel plug–in framework designed for prolonged test–time adaptation (TTA) in scenarios where the test domain continuously shifts over time, including cases where domains recur or evolve gradually. At its core, ReservoirTTA maintains a reservoir of domain-specialized models—an adaptive test-time model ensemble—that both detects new domains via online clustering over style features of incoming samples and routes each sample to the appropriate specialized model, and thereby enables domain-specific adaptation. This multi-model strategy overcomes key limitations of single model adaptation, such as catastrophic forgetting, inter-domain interference, and error accumulation, ensuring robust and stable performance on sustained non-stationary test distributions. Our theoretical analysis reveals key components that bound parameter variance and prevent model collapse, while our plug–in TTA module mitigates catastrophic forgetting of previously encountered domains. Extensive experiments on scene-level corruption benchmarks (ImageNet-C, CIFAR-10/100-C), object-level style shifts (DomainNet-126, PACS), and semantic segmentation (Cityscapes→ACDC) — covering recurring and continuously evolving domain shifts — show that ReservoirTTA substantially improves adaptation accuracy and maintains stable performance across prolonged, recurring shifts, outperforming state-of-the-art methods. Our code is publicly available at https://github.com/LTS5/ReservoirTTA.

Finetuning large pretrained neural networks is known to be resource-intensive, both in terms of memory and computational cost. To mitigate this, a common approach is to restrict training to a subset of the model parameters. By analyzing the relationship between gradients and weights during finetuning, we observe a notable pattern: large gradients are often associated with small-magnitude weights. This correlation is more pronounced in fine-tuning settings than in training from scratch. Motivated by this observation, we propose \textsc{NanoAdam}, which dynamically updates only the small-magnitude weights during fine-tuning and offers several practical advantages: first, the criterion is \emph{gradient-free}—the parameter subset can be determined without gradient computation; second, it preserves large-magnitude weights, which are likely to encode critical features learned during pre-training, thereby reducing the risk of catastrophic forgetting; thirdly, it permits the use of larger learning rates and consistently leads to better generalization performance in experiments. We demonstrate this for both NLP and vision tasks.

Gene expression estimation from pathology images has the potential to reduce the RNA sequencing cost. Point-wise loss functions have been widely used to minimize the discrepancy between predicted and absolute gene expression values. However, due to the complexity of the sequencing techniques and intrinsic variability across cells, the observed gene expression contains stochastic noise and batch effects, and estimating the absolute expression values accurately remains a significant challenge. To mitigate this, we propose a novel objective of learning relative expression patterns rather than absolute levels. We assume that the relative expression levels of genes exhibit consistent patterns across independent experiments, even when absolute expression values are affected by batch effects and stochastic noise in tissue samples. Based on the assumption, we model the relation and propose a novel loss function called STRank that is robust to noise and batch effects. Experiments using synthetic datasets and real datasets demonstrate the effectiveness of the proposed method. The code is available at https://github.com/naivete5656/STRank.

Recent advances in retrieval-based in-context learning (ICL) train the retriever using a classification objective, which categorizes in-context examples (ICEs) into the most useful and the rest based on absolute scores. However, during inference, ICEs are retrieved by score ranking rather than classification — The classification training objective deviates from this test scenario. Hence, in this paper, we propose a novel algorithm that trains a retrieval model by ranking formulation, where the preference rankings between ICEs are given by comparing the likelihood of the LLM generating the correct answer conditioned on each exemplar. By learning to rank, we motivate the retriever to automatically learn diverse rationales why specific examples are more useful for ICL decisions. This addresses the issue that classification models poorly capture broader utility. Experimental results demonstrate the top-1 performance of our proposal across 9 NLP tasks, with ablation studies and case studies further validating the effectiveness of our design. *The code can be found in: https://github.com/2022neo/SeDPO_NIPS25*

The ability to continually learn new skills, retain, and flexibly deploy them to accomplish goals is a key feature of intelligent and efficient behavior. However, the neural mechanisms facilitating the continual learning and flexible (re-)composition of skills remain elusive. Here, we study continual learning and the compositional reuse of learned computations in recurrent neural network (RNN) models using a novel two-system approach: one system that infers 'what' computation to perform, and one that implements 'how' to perform it. We focus on a set of compositional cognitive tasks commonly studied in neuroscience. To construct the 'what' system, we first show that a large family of tasks can be systematically described by a probabilistic generative model, where compositionality stems from a shared underlying vocabulary of discrete task-epochs. The shared epoch structure makes these tasks inherently compositional. We first show that this compositionality can be systematically described by a probabilistic generative model. Furthermore, we develop an unsupervised online learning approach that can learn this model on a single-trial basis, building its vocabulary incrementally as it is exposed to new tasks, and inferring the latent epoch structure as a time-varying computational context within a trial. We implement the 'how' system as an RNN whose low-rank components are composed according to the context inferred by the 'what' system. The contextual inference facilitates the creation, learning, and reuse of the low-rank RNN components as new tasks are introduced sequentially, enabling continual learning without catastrophic forgetting. Using an example task set, we demonstrate the efficacy and competitive performance of this two-system learning framework, its potential for forward and backward transfer, as well as few-shot learning via re-composition.

Prompt-based learning has emerged as a parameter-efficient finetuning (PEFT) approach to facilitate Large Language Model (LLM) adaptation to downstream tasks by conditioning generation with task-aware guidance. Despite its successes, current prompt-based learning methods heavily rely on laborious grid searching for optimal prompt length and typically require considerable number of prompts, introducing additional computational burden. Worse yet, our pioneer findings indicate that the task-aware prompt design is inherently limited by its absence of instance-aware information, leading to a subtle attention interplay with the input sequence. In contrast, simply incorporating instance-aware information as a part of the guidance can enhance the prompt-tuned model performance without additional fine-tuning. Moreover, we find an interesting phenomenon, namely "attention anchor", that incorporating instance-aware tokens at the earliest position of the sequence can successfully preserve strong attention to critical structural information and exhibit more active attention interaction with all input tokens. In light of our observation, we introduce Capsule Prompt-Tuning (CaPT), an efficient and effective solution that leverages off-the-shelf, informative instance semantics into prompt-based learning. Our approach innovatively integrates both instance-aware and task-aware information in a nearly parameter-free manner (i.e., one single capsule prompt). Empirical results demonstrate that our method can exhibit superior performance across various language tasks (e.g., 84.03\% average accuracy on T5-Large), serving as an "attention anchor," while enjoying high parameter efficiency (e.g., 0.003\% of model parameters on Llama3.2-1B).

Long-context supervised fine-tuning (Long-SFT) plays a vital role in enhancing the performance of large language models (LLMs) on long-context tasks. To smoothly adapt LLMs to long-context scenarios, this process typically entails training on mixed datasets containing both long and short sequences. However, this heterogeneous sequence length distribution poses significant challenges for existing training systems, as they fail to simultaneously achieve high training efficiency for both long and short sequences, resulting in sub-optimal end-to-end system performance in Long-SFT. In this paper, we present a novel perspective on data scheduling to address the challenges posed by the heterogeneous data distributions in Long-SFT. We propose Skrull, a dynamic data scheduler specifically designed for efficient long-SFT. Through dynamic data scheduling, Skrull balances the computation requirements of long and short sequences, improving overall training efficiency. Furthermore, we formulate the scheduling process as a joint optimization problem and thoroughly analyze the trade-offs involved. Based on those analysis, Skrull employs a lightweight scheduling algorithm to achieve near-zero cost online scheduling in Long-SFT. Finally, we implement Skrull upon DeepSpeed, a state-of-the-art distributed training system for LLMs. Experimental results demonstrate that Skrull outperforms DeepSpeed by 3.76x on average (up to 7.54x) in real-world long-SFT scenarios.

The widespread use of AI-generated content from diffusion models has raised significant concerns regarding misinformation and copyright infringement. Watermarking is a crucial technique for identifying these AI-generated images and preventing their misuse. In this paper, we introduce *Shallow Diffuse*, a new watermarking technique that embeds robust and invisible watermarks into diffusion model outputs. Unlike existing approaches that integrate watermarking throughout the entire diffusion sampling process, *Shallow Diffuse* decouples these steps by leveraging the presence of a low-dimensional subspace in the image generation process. This method ensures that a substantial portion of the watermark lies in the null space of this subspace, effectively separating it from the image generation process. Our theoretical and empirical analyses show that this decoupling strategy greatly enhances the consistency of data generation and the detectability of the watermark. Extensive experiments further validate that *Shallow Diffuse* outperforms existing watermarking methods in terms of consistency.

State Space Models (SSMs) have emerged as efficient alternatives to Vision Transformers (ViTs), with VMamba standing out as a pioneering architecture designed for vision tasks. However, their generalization performance degrades significantly under distribution shifts. To address this limitation, we propose TRUST (Test-Time Refinement using Uncertainty-Guided SSM Traverses), a novel test-time adaptation (TTA) method that leverages diverse traversal permutations to generate multiple causal perspectives of the input image. Model predictions serve as pseudo-labels to guide updates of the Mamba-specific parameters, and the adapted weights are averaged to integrate the learned information across traversal scans. Altogether, TRUST is the first approach that explicitly leverages the unique architectural properties of SSMs for adaptation. Experiments on seven benchmarks show that TRUST consistently improves robustness and outperforms existing TTA methods.