Math reasoning has been one crucial ability of large language models (LLMs), where significant advancements have been achieved in recent years. However, most efforts focus on LLMs by curating high-quality annotation data and intricate training (or inference) paradigms, while the math reasoning performance of multimodal LLMs (MLLMs) remains lagging behind. Since the MLLM typically consists of an LLM and a vision block, we wonder: Can MLLMs directly absorb math reasoning abilities from off-the-shelf math LLMs without tuning? Recent model-merging approaches may offer insights into this question. However, they overlook the alignment between the MLLM and LLM, where we find that there is a large gap between their parameter spaces, resulting in lower performance. Our empirical evidence reveals two key factors behind this issue: the identification of crucial reasoning-associated layers in the model and the mitigation of the gaps in parameter space. Based on the empirical insights, we propose IP-Merging that first Identifies the reasoning-associated parameters in both MLLM and Math LLM, then Projects them into the subspace of MLLM, aiming to maintain the alignment, and finally merges parameters in this subspace. IP-Merging is a tuning-free approach since parameters are directly adjusted. Extensive experiments demonstrate that our IP-Merging method can enhance the math reasoning ability of MLLMs directly from Math LLMs without compromising their other capabilities.

For such neural networks, we prove a non-constant lower bound of that are compatible with certain polyhedral complexes, more precisely with the the best known lower bound in general is still 2. We focus on neural networks linear functions on R .

Contrastive learning involves learning representations via a loss function that encourages each (unlabeled) sample to be far from other samples, but close to its own augmentation. In this paper, we aim to understand why this simple idea performs remarkably well, by theoretically analyzing it for a simple, natural problem setting: dimensionality reduction in Gaussian Mixture Models (GMMs). Note that the standard GMM setup lacks the concept of augmentations. We study an intuitive extension: we define the pair of data sample and its augmentation as a coupled random draw from the GMM such that the marginal over the "noisy" augmentation is biased towards the component of the data sample. For this setup, we show that vanilla contrastive loss, e.g., InfoNCE, is able to find the optimal lower-dimensional subspace even when the Gaussian components are non-isotropic. In particular, we show that InfoNCE can match the performance of a fully supervised algorithm, e.g., LDA, (where each data point is labeled with the mixture component it comes from) even when the augmentations are "noisy". We further extend our setup to the multi-modal case, and develop a GMM-like setting to study the contrastive CLIP loss. We corroborate our theory with experiments on CIFAR100; representations learned by InfoNCE loss match the performance of LDA on clustering metrics.

Diffusion models, though originally designed for generative tasks, have demonstrated impressive self-supervised representation learning capabilities. A particularly intriguing phenomenon in these models is the emergence of unimodal representation dynamics, where the quality of learned features peaks at an intermediate noise level. In this work, we conduct a comprehensive theoretical and empirical investigation of this phenomenon. Leveraging the inherent low-dimensionality structure of image data, we theoretically demonstrate that the unimodal dynamic emerges when the diffusion model successfully captures the underlying data distribution. The unimodality arises from an interplay between denoising strength and class confidence across noise scales. Empirically, we further show that, in classification tasks, the presence of unimodal dynamics reliably reflects the diffusion model's generalization: it emerges when the model generate novel images and gradually transitions to a monotonically decreasing curve as the model begins to memorize the training data.

Top view In a pool with palm trees around In a city at night On a snowy mountain top Crowded, on a beach sunset Surrounded by autumn in forest resources and limiting the number of trainable parameters. However, it often faces challenges in striking a trade-off between aligning with the target distribution: learning a novel concept from a limited image for personalization and retaining the instruction ability needed for unifying multiple tasks, all while maintaining editability (aligning with a variety of prompts or in-context generation). In this work, we introduce DEFT, Decompositional Efficient Fine-Tuning, an efficient fine-tuning framework that adapts a pre-trained weight matrix by decomposing its update into two components with two trainable matrices: (1) a projection onto the complement of a low-rank subspace spanned by a low-rank matrix, and (2) a lowrank update. The single trainable low-rank matrix defines the subspace, while the other trainable low-rank matrix enables parameter adaptation within that subspace. We conducted extensive experiments on the Dreambooth and Dreambench Plus datasets for personalization, the InsDet dataset for object and scene adaptation, and the VisualCloze dataset for a universal image generation framework through visual in-context learning with both Stable Diffusion and a unified model. Our results demonstrated state-of-the-art performance, highlighting the emergent properties of efficient fine-tuning. Our code is available on DEFT.

Machine learning models have achieved widespread success but often inherit and amplify historical biases, resulting in unfair outcomes. Traditional fairness methods typically impose constraints at the prediction level, without addressing underlying biases in data representations. In this work, we propose a principled framework that adjusts data representations to balance predictive utility and fairness. Using sufficient dimension reduction, we decompose the feature space into target-relevant, sensitive, and shared components, and control the fairness-utility trade-off by selectively removing sensitive information. We provide a theoretical analysis of how prediction error and fairness gaps evolve as shared subspaces are added, and employ influence functions to quantify their effects on the asymptotic behavior of parameter estimates. Experiments on both synthetic and real-world datasets validate our theoretical insights and show that the proposed method effectively improves fairness while preserving predictive performance.

Unsupervised domain adaptation has emerged as a pivotal paradigm for mitigating distribution shifts in time series analysis. The fundamental challenge in time series domain adaptation arises from the entanglement of domain shifts and intricate temporal patterns. Crucially, the latent continuous-time dynamics, which are often inaccessible due to sensor constraints, are only partially observable through discrete time series from an explicit sensor-limited single view. This partial observability hinders the modeling of intricate temporal patterns, impeding domain invariant representation learning. To mitigate the limitation, we propose EDEN (multiple Explicit Domain Enhanced adaptation Network), expanding the raw dataset to multi-scale explicit domains, multi-subspace explicit domains and multi-segment explicit domains. EDEN enhances domain adaptation with three coordinated modules tailored to integrate multiple explicit domains: (1) MultiScale Curriculum Adaptation implements progressive domain alignment from coarse-scale to fine-scale.

Existing safety interventions - ranging from training data curation and model fine-tuning to inference-time filtering and guidance - often suffer from incomplete concept removal, susceptibility to jailbreaking, computational inefficiency, or collateral damage to unrelated capabilities. In this paper, we introduce CURE, a training-free concept unlearning framework that operates directly in the weight space of pre-trained diffusion models, enabling fast, interpretable, and highly specific suppression of undesired concepts. At the core of our method is the Spectral Eraser, a closed-form, orthogonal projection module that identifies discriminative subspaces using Singular Value Decomposition over token embeddings associated with the concepts to forget and retain. Intuitively, the Spectral Eraser identifies and isolates features unique to the undesired concept while preserving safe attributes. This operator is then applied in a single step update to yield an edited model in which the target concept is effectively 39th Conference on Neural Information Processing Systems (NeurIPS 2025).

Low-rank adaptation (LoRA) has been widely adopted as a parameter-efficient technique for fine-tuning large-scale pre-trained models. However, it still lags behind full fine-tuning in performance, partly due to its insufficient exploitation of the geometric structure underlying low-rank manifolds. In this paper, we propose a geometry-aware extension of LoRA that uses a three-factor decomposition USV . Analogous to the structure of singular value decomposition (SVD), it separates the adapter's input and output subspaces, V and U, from the scaling factor S. Our method constrains U and V to lie on the Stiefel manifold, ensuring their orthonormality throughout the training. To optimize on the Stiefel manifold, we employ a flexible and modular geometric optimization design that converts any Euclidean optimizer to a Riemannian one. It enables efficient subspace learning while remaining compatible with existing fine-tuning pipelines. Empirical results across a wide range of downstream tasks, including commonsense reasoning, math and code generation, image classification, and image generation, demonstrate the superior performance of our approach against the recent state-of-the-art variants of LoRA. Code is available at https://github.com/SonyResearch/stella.

Pretraining language models with extended context windows enhances their ability to leverage rich information during generation. Existing methods split input sequences into chunks, broadcast them across multiple devices, and compute attention block by block which incurs significant communication overhead. While feasible in high-speed clusters, these methods are impractical for decentralized training over low-bandwidth connections. We propose a compression method for communication-efficient context parallelism in decentralized settings, achieving a remarkable compression rate of over 95%with negligible overhead and no loss in convergence. Our key insight is to exploit the intrinsic low-rank structure of activation outputs by dynamically constraining them to learned mixtures of subspaces via efficient reparameterizations. We demonstrate scaling billion-parameter decentralized models to context lengths exceeding 100Ktokens on networks as slow as 300Mbps, matching the wall-clock convergence speed of centralized models on 100Gbps interconnects.