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Probabilistic Methods · Bayesian Models and Methods

Kyurae Kim, Yian Ma, Trevor Campbell, Jacob Gardner

We prove that, given a mean-field location-scale variational family, black-box variational inference (BBVI) with the reparametrization gradient converges at a rate that is nearly independent of explicit dimension dependence. Specifically, for a $d$-dimensional strongly log-concave and log-smooth target, the number of iterations for BBVI with a sub-Gaussian family to obtain a solution $\epsilon$-close to the global optimum has a dimension dependence of $\mathrm{O}(\log d)$. This is a significant improvement over the $\mathrm{O}(d)$ dependence of full-rank location-scale families. For heavy-tailed families, we prove a weaker $\mathrm{O}(d^{2/k})$ dependence, where $k$ is the number of finite moments of the family. Additionally, if the Hessian of the target log-density is constant, the complexity is free of any explicit dimension dependence. We also prove that our bound on the gradient variance, which is key to our result, cannot be improved using only spectral bounds on the Hessian of the target log-density.

Computer Vision · Image and Video Generation

Zixun Fang, Kai Zhu, Zhiheng Liu, Yu Liu, Wei Zhai, Yang Cao, Zheng-Jun Zha

Panoramic video generation aims to synthesize 360-degree immersive videos, holding significant importance in the fields of VR, world models, and spatial intelligence. Existing works fail to synthesize high-quality panoramic videos due to the inherent modality gap between panoramic data and perspective data, which constitutes the majority of the training data for modern diffusion models. In this paper, we propose a novel framework utilizing pretrained perspective video models for generating panoramic videos. Specifically, we design a novel panorama representation named ViewPoint map, which possesses global spatial continuity and fine-grained visual details simultaneously. With our proposed Pano-Perspective attention mechanism, the model benefits from pretrained perspective priors and captures the panoramic spatial correlations of the ViewPoint map effectively. Extensive experiments demonstrate that our method can synthesize highly dynamic and spatially consistent panoramic videos, achieving state-of-the-art performance and surpassing previous methods.

Theory · Everything Else

Shiqi Liu, Wenhan Cao, Chang Liu, Zeyu He, Tianyi Zhang, Yinuo Wang, Shengbo Li

Estimating hidden states in dynamical systems, also known as optimal filtering, is a long-standing problem in various fields of science and engineering. In this paper, we introduce a general filtering framework, $\textbf{LLM-Filter}$, which leverages large language models (LLMs) for state estimation by embedding noisy observations with text prototypes. In a number of experiments for classical dynamical systems, we find that first, state estimation can significantly benefit from the knowledge embedded in pre-trained LLMs. By achieving proper modality alignment with the frozen LLM, LLM-Filter outperforms the state-of-the-art learning-based approaches. Second, we carefully design the prompt structure, System-as-Prompt (SaP), incorporating task instructions that enable LLMs to understand tasks and adapt to specific systems. Guided by these prompts, LLM-Filter exhibits exceptional generalization, capable of performing filtering tasks accurately in changed or even unseen environments. We further observe a scaling-law behavior in LLM-Filter, where accuracy improves with larger model sizes and longer training times. These findings make LLM-Filter a promising foundation model of filtering.

Hoang Pham, The Anh Ta, Tom Jacobs, Rebekka Burkholz, Long Tran-Thanh

Sparse neural networks promise efficiency, yet training them effectively remains a fundamental challenge. Despite advances in pruning methods that create sparse architectures, understanding why some sparse structures are better trainable than others with the same level of sparsity remains poorly understood. Aiming to develop a systematic approach to this fundamental problem, we propose a novel theoretical framework based on the theory of graph limits, particularly graphons, that characterizes sparse neural networks in the infinite-width regime. Our key insight is that connectivity patterns of sparse neural networks induced by pruning methods converge to specific graphons as networks' width tends to infinity, which encodes implicit structural biases of different pruning methods. We postulate the *Graphon Limit Hypothesis* and provide empirical evidence to support it. Leveraging this graphon representation, we derive a *Graphon Neural Tangent Kernel (Graphon NTK)* to study the training dynamics of sparse networks in the infinite width limit. Graphon NTK provides a general framework for the theoretical analysis of sparse networks. We empirically show that the spectral analysis of Graphon NTK correlates with observed training dynamics of sparse networks, explaining the varying convergence behaviours of different pruning methods. Our framework provides theoretical insights into the impact of connectivity patterns on the trainability of various sparse network architectures.

Applications · Chemistry and Drug Discovery

Subhojyoti Khastagir, KISHALAY DAS, Pawan Goyal, Seung-Cheol Lee, Satadeep Bhattacharjee, niloy ganguly

Recent advances in generative modeling have shown significant promise in designing novel periodic crystal structures. Existing approaches typically rely on either large language models (LLMs) or equivariant denoising models, each with complementary strengths: LLMs excel at handling discrete atomic types but often struggle with continuous features such as atomic positions and lattice parameters, while denoising models are effective at modeling continuous variables but encounter difficulties in generating accurate atomic compositions. To bridge this gap, we propose CrysLLMGen, a hybrid framework that integrates an LLM with a diffusion model to leverage their complementary strengths for crystal material generation. During sampling, CrysLLMGen first employs a fine-tuned LLM to produce an intermediate representation of atom types, atomic coordinates, and lattice structure. While retaining the predicted atom types, it passes the atomic coordinates and lattice structure to a pre-trained equivariant diffusion model for refinement. Our framework outperforms state-of-the-art generative models across several benchmark tasks and datasets. Specifically, CrysLLMGen not only achieves a balanced performance in terms of structural and compositional validity but also generates more stable and novel materials compared to LLM-based and denoising-based models Furthermore, CrysLLMGen exhibits strong conditional generation capabilities, effectively producing materials that satisfy user-defined constraints. Code is available at \url{https://github.com/kdmsit/crysllmgen}

Deep Learning · Algorithms

Mahdi Nikdan, Vincent Cohen-Addad, Dan Alistarh, Vahab Mirrokni

Effective data selection is critical for efficient training of modern Large Language Models (LLMs). This paper introduces Influence Distillation, a novel, mathematically-justified framework for data selection that employs second-order information to optimally weight training samples. By distilling each sample's influence on a target distribution, our method assigns model-specific weights that are used to select training data for LLM fine-tuning, guiding it toward strong performance on the target domain. We derive these optimal weights for both Gradient Descent and Adam optimizers. To ensure scalability and reduce computational cost, we propose a $\textit{landmark-based approximation}$: influence is precisely computed for a small subset of "landmark" samples and then efficiently propagated to all other samples to determine their weights. We validate Influence Distillation by applying it to instruction tuning on the Tulu V2 dataset, targeting a range of tasks including GSM8k, SQuAD, and MMLU, across several models from the Llama and Qwen families. Experiments show that Influence Distillation matches or outperforms state-of-the-art performance while achieving up to $3.5\times$ faster selection.

Computer Vision · Vision Models & Multimodal

Weihao Bo, Yanpeng Sun, Yu Wang, Xinyu Zhang, Zechao Li

In this paper, we introduce FedMGP, a new paradigm for personalized federated prompt learning in vision-language models (VLMs). Existing federated prompt learning (FPL) methods often rely on a single, text-only prompt representation, which leads to client-specific overfitting and unstable aggregation under heterogeneous data distributions. Toward this end, FedMGP equips each client with multiple groups of paired textual and visual prompts, enabling the model to capture diverse, fine-grained semantic and instance-level cues. A diversity loss is introduced to drive each prompt group to specialize in distinct and complementary semantic aspects, ensuring that the groups collectively cover a broader range of local characteristics.During communication, FedMGP employs a dynamic prompt aggregation strategy based on similarity-guided probabilistic sampling: each client computes the cosine similarity between its prompt groups and the global prompts from the previous round, then samples s groups via a softmax-weighted distribution. This soft selection mechanism preferentially aggregates semantically aligned knowledge while still enabling exploration of underrepresented patterns—effectively balancing the preservation of common knowledge with client-specific features. Notably, FedMGP maintains parameter efficiency by redistributing a fixed prompt capacity across multiple groups, achieving state-of-the-art performance with the lowest communication parameters (5.1k) among all federated prompt learning methods. Theoretical analysis shows that our dynamic aggregation strategy promotes robust global representation learning by reinforcing shared semantics while suppressing client-specific noise. Extensive experiments demonstrate that FedMGP consistently outperforms prior approaches in both personalization and domain generalization across diverse federated vision-language benchmarks.The code will be released on https://github.com/weihao-bo/FedMGP.git.

Computer Vision · 3D Rendering & Reconstruction

Kang Yang, Gaofeng Dong, Sijie Ji, Wan Du, Mani Srivastava

Synthesizing radio-frequency (RF) data given the transmitter and receiver positions, e.g., received signal strength indicator (RSSI), is critical for wireless networking and sensing applications, such as indoor localization. However, it remains challenging due to complex propagation interactions, including reflection, diffraction, and scattering. State-of-the-art neural radiance field (NeRF)-based methods achieve high-fidelity RF data synthesis but are limited by long training times and high inference latency. We introduce GSRF, a framework that extends 3D Gaussian Splatting (3DGS) from the optical domain to the RF domain, enabling efficient RF data synthesis. GSRF realizes this adaptation through three key innovations: First, it introduces complex-valued 3D Gaussians with a hybrid Fourier–Legendre basis to model directional and phase-dependent radiance. Second, it employs orthographic splatting for efficient ray–Gaussian intersection identification. Third, it incorporates a complex-valued ray tracing algorithm, executed on RF-customized CUDA kernels and grounded in wavefront propagation principles, to synthesize RF data in real time. Evaluated across various RF technologies, GSRF preserves high-fidelity RF data synthesis while achieving significant improvements in training efficiency, shorter training time, and reduced inference latency.

Deep Learning · Graph Neural Networks

Juntong Wang, Xiyuan Wang, Muhan Zhang

Common Neighbors (CNs) and their higher-order variants are important pairwise features widely used in state-of-the-art link prediction methods. However, existing methods often struggle with the repetition across different orders of CNs and fail to fully leverage their potential. We identify that these limitations stem from two key issues: redundancy and over-smoothing in high-order common neighbors. To address these challenges, we design orthogonalization to eliminate redundancy between different-order CNs and normalization to mitigate over-smoothing. By combining these two techniques, we propose Orthogonal Common Neighbor (OCN), a novel approach that significantly outperforms the strongest baselines by an average of 7.7\% on popular link prediction benchmarks. A thorough theoretical analysis is provided to support our method. Ablation studies also verify the effectiveness of our orthogonalization and normalization techniques.

Deep Learning · Algorithms

Benjamin Minixhofer, Ivan Vulić, Edoardo Maria Ponti

Distillation has shown remarkable success in transferring knowledge from a Large Language Model (LLM) teacher to a student LLM. However, current distillation methods require similar tokenizers between the teacher and the student, restricting their applicability to only a small subset of teacher--student pairs. In this work, we develop a principled cross-tokenizer distillation method to solve this crucial deficiency. Our method is the first to enable effective distillation across fundamentally different tokenizers, while also substantially outperforming prior methods in all other cases. We verify the efficacy of our method on three distinct use cases. First, we show that viewing tokenizer transfer as self-distillation enables unprecedentedly effective transfer across tokenizers, including rapid transfer of subword models to the byte-level. Transferring different models to the same tokenizer also enables ensembling to boost performance. Secondly, we distil a large maths-specialised LLM into a small general-purpose model with a different tokenizer, achieving competitive maths problem-solving performance. Thirdly, we use our method to train state-of-the-art embedding prediction hypernetworks for training-free tokenizer transfer. Our results unlock an expanded range of teacher--student pairs for distillation, enabling new ways to adapt and enhance interaction between LLMs.

Optimization

Connor Magoon, Fengyu Yang, Noam Aigerman, Shahar Kovalsky

Differentiable optimization has attracted significant research interest, particularly for quadratic programming (QP). Existing approaches for differentiating the solution of a QP with respect to its defining parameters often rely on specific integrated solvers. This integration limits their applicability, including their use in neural network architectures and bi-level optimization tasks, restricting users to a narrow selection of solver choices. To address this limitation, we introduce **dQP**, a modular and solver-agnostic framework for plug-and-play differentiation of virtually any QP solver. A key insight we leverage to achieve modularity is that, once the active set of inequality constraints is known, both the solution and its derivative can be expressed using simplified linear systems that share the same matrix. This formulation fully decouples the computation of the QP solution from its differentiation. Building on this result, we provide a minimal-overhead, open-source implementation () that seamlessly integrates with over 15 state-of-the-art solvers. Comprehensive benchmark experiments demonstrate dQP’s robustness and scalability, particularly highlighting its advantages in large-scale sparse problems.

General Machine Learning · Representation Learning

Simone Ricci, Niccolò Biondi, Federico Pernici, Ioannis Patras, Alberto Del Bimbo

Retrieval systems rely on representations learned by increasingly powerful models. However, due to the high training cost and inconsistencies in learned representations, there is significant interest in facilitating communication between representations and ensuring compatibility across independently trained neural networks. In the literature, two primary approaches are commonly used to adapt different learned representations: affine transformations, which adapt well to specific distributions but can significantly alter the original representation, and orthogonal transformations, which preserve the original structure with strict geometric constraints but limit adaptability. A key challenge is adapting the latent spaces of updated models to align with those of previous models on downstream distributions while preserving the newly learned representation spaces. In this paper, we impose a relaxed orthogonality constraint, namely $\lambda$-Orthogonality regularization, while learning an affine transformation, to obtain distribution-specific adaptation while retaining the original learned representations. Extensive experiments across various architectures and datasets validate our approach, demonstrating that it preserves the model's zero-shot performance and ensures compatibility across model updates. Code available at: \href{https://github.com/miccunifi/lambda_orthogonality.git}{https://github.com/miccunifi/lambda\_orthogonality}.

Deep Learning · Theory

Daniel Barzilai, Ohad Shamir

The widespread use of generative models has created a feedback loop in which each generation of models is trained on data partially produced by its predecessors. This process has raised concerns about model collapse: A critical degradation in performance caused by repeated training on synthetic data. However, different analyses in the literature have reached different conclusions as to the severity of model collapse. As such, it remains unclear how concerning this phenomenon is, and under which assumptions it can be avoided. To address this, we theoretically study model collapse for maximum likelihood estimation (MLE), in a natural setting where synthetic data is gradually added to the original training set. Under standard assumptions (similar to those long used for proving asymptotic consistency and normality of MLE), we establish non-asymptotic bounds showing that collapse can be avoided even as the fraction of real data vanishes. On the other hand, we prove that some assumptions (beyond MLE consistency) are indeed necessary: Without them, model collapse can occur arbitrarily quickly, even when the original data is still present in the training set. To the best of our knowledge, these are the first rigorous examples of iterative generative modeling with accumulating data that rapidly leads to model collapse.

Computer Vision · Classification and Understanding

DongJae Lee, Jiwan Hur, Jaehyun Choi, Jaemyung Yu, Junmo Kim

Vision Transformers have demonstrated exceptional performance across various computer vision tasks, yet their quadratic computational complexity concerning token length remains a significant challenge. To address this, token reduction methods have been widely explored. However, existing approaches often overlook the frequency characteristics of self-attention, such as rank collapsing and over-smoothing phenomenon. In this paper, we propose a frequency-aware token reduction strategy that improves computational efficiency while preserving performance by mitigating rank collapsing. Our method partitions tokens into high-frequency tokens and low-frequency tokens. high-frequency tokens are selectively preserved, while low-frequency tokens are aggregated into a compact direct current token to retain essential low-frequency components. Through extensive experiments and analysis, we demonstrate that our approach significantly improves accuracy while reducing computational overhead and mitigating rank collapsing and over smoothing. Furthermore, we analyze the previous methods, shedding light on their implicit frequency characteristics and limitations. The code is available in https://github.com/jhtwosun/frequency-aware-token-pruning.

Computer Vision · Image and Video Generation

Chenyu Wang, Cai Zhou, Sharut Gupta, Johnson Lin, Stefanie Jegelka, Stephen Bates, Tommi Jaakkola

Diffusion models can be improved with additional guidance towards more effective representations of input. Indeed, prior empirical work has already shown that aligning internal representations of the diffusion model with those of pre-trained models improves generation quality. In this paper, we present a systematic framework for incorporating representation guidance into diffusion models. We provide alternative decompositions of denoising models along with their associated training criteria, where the decompositions determine when and how the auxiliary representations are incorporated. Guided by our theoretical insights, we introduce two new strategies for enhancing representation alignment in diffusion models. First, we pair examples with target representations either derived from themselves or arisen from different synthetic modalities, and subsequently learn a joint model over the multimodal pairs. Second, we design an optimal training curriculum that balances representation learning and data generation. Our experiments across image, protein sequence, and molecule generation tasks demonstrate superior performance as well as accelerated training. In particular, on the class-conditional ImageNet $256\times 256$ benchmark, our guidance results in $23.3$ times faster training than the original SiT-XL as well as four times speedup over the state-of-the-art method REPA.

Theory · Everything Else

Jacob Block, Aryan Mokhtari, Sanjay Shakkottai

Machine unlearning algorithms aim to remove the influence of specific training samples, ideally recovering the model that would have resulted from training on the remaining data alone. We study unlearning in the overparameterized setting, where many models interpolate the data, and defining the solution as any loss minimizer over the retained set—as in prior work in the underparameterized setting—is inadequate, since the original model may already interpolate the retained data and satisfy this condition. In this regime, loss gradients vanish, rendering prior methods based on gradient perturbations ineffective, motivating both new unlearning definitions and algorithms. For this setting, we define the unlearning solution as the minimum-complexity interpolator over the retained data and propose a new algorithmic framework that only requires access to model gradients on the retained set at the original solution. We minimize a regularized objective over perturbations constrained to be orthogonal to these model gradients, a first-order relaxation of the interpolation condition. For different model classes, we provide exact and approximate unlearning guarantees and demonstrate that an implementation of our framework outperforms existing baselines across various unlearning experiments.

Deep Learning · Generative Models and Autoencoders

Cai Zhou, Chenyu Wang, Dinghuai Zhang, Shangyuan Tong, Yifei Wang, Stephen Bates, Tommi Jaakkola

In this paper we introduce Hierarchical Diffusion Language Models (HDLM) -- a novel family of discrete diffusion models for language modeling. HDLM builds on a hierarchical vocabulary where low-level tokens with detailed semantics are surjectively mapped to high-level tokens with coarse-grained meanings. In the forward process, each token is independently perturbed to its higher-level ancestor with more abstract semantics according to the scheduler, while in the reverse process the model progressively predicts the next, more detailed semantics. Taken together, HDLM provides a general time-varying next semantic scale prediction process for language modeling. We derive closed-form expressions for the diffusion Evidence Lower Bound (ELBO), and show that HDLM can be implemented in a flexible manner while including the existing MDLM as a special case. We also propose practical training techniques based on the insights. Extensive text generation experiments validate the effectiveness of HDLM, which demonstrates consistently lower validation and generative perplexity than baselines.

General Machine Learning · Everything Else

Zhenhao Zhong, Zhibin Gu, Pengpeng Yang, Yaqian zhou, Ruiqiang Guo

Tensorized Incomplete Multi-View Clustering (TIMVC) algorithms have attracted growing attention for their ability to capture high-order correlations across multiple views. However, most existing TIMVC methods rely on simplistic noise assumptions using specific norms (e.g., $\ell_1$ or $\ell_{2,1}$), which fail to reflect the complex noise patterns encountered in real-world scenarios. Moreover, they primarily focus on modeling the global Euclidean structure of the tensor representation, while overlooking the preservation of local manifold structures. To address these limitations, we propose a novel approach, GaUssian regressIon-driven TIMVC with dual mAnifold Regularization (GUITAR). Specifically, we employ a Gaussian regression model to characterize complex noise distributions in a more realistic and flexible manner. Meanwhile, a dual manifold regularization is introduced in tensor representation learning, simultaneously modeling manifold information at both the view-specific and cross-view consensus levels, thereby promoting intra-view and inter-view consistency in the tensor representation. Furthermore, to better capture the intrinsic low-rank structure, we propose the high-preservation $\ell_{\delta}$-norm tensor rank constraint, which applies differentiated penalties to the singular values, thereby enhancing the robustness of the tensor representation. In addition, an efficient optimization algorithm is developed to solve the resulting non-convex problem with provable convergence. Extensive experiments on six datasets demonstrate that our method outperforms SOTA approaches.

Optimization · Bayesian & Black-box Optimization

Haowei Wang, Jingyi Wang, Zhongxiang Dai, Nai-Yuan Chiang, Szu Hui Ng, Cosmin Petra

Constrained Bayesian optimization (CBO) methods have seen significant success in black-box optimization with constraints. One of the most commonly used CBO methods is the constrained expected improvement (CEI) algorithm. CEI is a natural extension of expected improvement (EI) when constraints are incorporated. However, the theoretical convergence rate of CEI has not been established. In this work, we study the convergence rate of CEI by analyzing its simple regret upper bound. First, we show that when the objective function $f$ and constraint function $c$ are assumed to each lie in a reproducing kernel Hilbert space (RKHS), CEI achieves the convergence rates of $\mathcal{O} \left(t^{-\frac{1}{2}}\log^{\frac{d+1}{2}}(t) \right) \ \text{and }\ \mathcal{O}\left(t^{\frac{-\nu}{2\nu+d}} \log^{\frac{\nu}{2\nu+d}}(t)\right)$ for the commonly used squared exponential and Matérn kernels, respectively. Second, we show that when $f$ and $c$ are assumed to be sampled from Gaussian processes (GPs), CEI achieves the same convergence rates with a high probability. Numerical experiments are performed to validate the theoretical analysis.

Social Aspects · Fairness, Equity, Justice and Safety

Zara Hall, Melanie Subbiah, Thomas Zollo, Kathleen McKeown, Richard Zemel

Large language models are increasingly used to support high-stakes decisions, potentially influencing who is granted bail or receives a loan. Naive chain-of-thought sampling can improve average decision accuracy, but has also been shown to amplify unfair bias. To address this challenge and enable the trustworthy use of reasoning models in high-stakes decision-making, we propose a framework for training a generalizable Fairness Reward Model (FRM). Our model assigns a fairness score to LLM reasoning, enabling the system to down-weight biased trajectories and favor equitable ones when aggregating decisions across reasoning chains. We show that a single Fairness Reward Model, trained on weakly supervised, LLM-annotated examples of biased versus unbiased reasoning, transfers across tasks, domains, and model families without additional fine-tuning. When applied to real-world decision-making tasks including recidivism prediction and social media moderation, our approach consistently improves fairness while matching, or even surpassing, baseline accuracy.