NeurIPS 2025 论文列表

Conference on Neural Information Processing Systems

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5,812篇论文

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主题: 驾驶仿真 · 542 篇论文 · 重置筛选

Progress Reward Model for Reinforcement Learning via Large Language Models

Xiuhui Zhang, Ning Gao, Xingyu Jiang, Yihui Chen, Yuheng Pan, Mohan Zhang, Yue Deng

展开摘要

Traditional reinforcement learning (RL) algorithms face significant limitations in handling long-term tasks with sparse rewards. Recent advancements have leveraged large language models (LLMs) to enhance RL by utilizing their world knowledge for task planning and reward generation. However, planning-based approaches often depend on pre-defined skill libraries and fail to optimize low-level control policies, while reward-based methods require extensive human feedback or exhaustive searching due to the complexity of tasks. In this paper, we propose the Progress Reward Model for RL (PRM4RL), a novel framework that integrates task planning and dense reward to enhance RL. For high-level planning, a complex task is decomposed into a series of simple manageable subtasks, with a subtask-oriented, fine-grained progress function designed to monitor task execution progress. For low-level reward generation, inspired by potential-based reward shaping, we use the progress function to construct a Progress Reward Model (PRM), providing theoretically grounded optimality and convergence guarantees, thereby enabling effective policy optimization. Experimental results on robotics control tasks demonstrate that our approach outperforms both LLM-based planning and reward methods, achieving state-of-the-art performance.

Poster
OpenAD: Open-World Autonomous Driving Benchmark for 3D Object Detection

Zhongyu Xia, Jishuo Li, Zhiwei Lin, Xinhao Wang, Yongtao Wang, Ming-Hsuan Yang

展开摘要

Open-world perception aims to develop a model adaptable to novel domains and various sensor configurations and can understand uncommon objects and corner cases. However, current research lacks sufficiently comprehensive open-world 3D perception benchmarks and robust generalizable methodologies. This paper introduces OpenAD, the first real open-world autonomous driving benchmark for 3D object detection. OpenAD is built upon a corner case discovery and annotation pipeline that integrates with a multimodal large language model (MLLM). The proposed pipeline annotates corner case objects in a unified format for five autonomous driving perception datasets with 2000 scenarios. In addition, we devise evaluation methodologies and evaluate various open-world and specialized 2D and 3D models. Moreover, we propose a vision-centric 3D open-world object detection baseline and further introduce an ensemble method by fusing general and specialized models to address the issue of lower precision in existing open-world methods for the OpenAD benchmark. We host an online challenge on EvalAI. Data, toolkit codes, and evaluation codes are available at https://github.com/VDIGPKU/OpenAD.

Poster
Dynamic Algorithm for Explainable $k$-medians Clustering under $\ell_p$ Norm

Konstantin Makarychev, Ilias Papanikolaou, Liren Shan

展开摘要

We study the problem of explainable $k$-medians clustering introduced by Dasgupta, Frost, Moshkovitz, and Rashtchian (2020). In this problem, the goal is to construct a threshold decision tree that partitions data into $k$ clusters while minimizing the $k$-medians objective. These trees are interpretable because each internal node makes a simple decision by thresholding a single feature, allowing users to trace and understand how each point is assigned to a cluster. We present the first algorithm for explainable $k$-medians under $\ell_p$ norm for every finite $p \geq 1$. Our algorithm achieves an $\tilde{O}\big(p(\log k)^{1 + 1/p - 1/p^2}\big)$ approximation to the optimal $k$-medians cost for any $p \geq 1$. Previously, algorithms were known only for $p = 1$ and $p = 2$. For $p = 2$, our algorithm improves upon the existing bound of $\tilde O(\log^{3/2}k)$, and for $p = 1$, it matches the tight bound of $\log k + O(1)$ up to a multiplicative $O(\log \log k)$ factor. We show how to implement our algorithm in a dynamic setting. The dynamic algorithm maintains an explainable clustering under a sequence of insertions and deletions, with amortized update time $O(d \log^3 k)$ and $O(\log k)$ recourse, making it suitable for large-scale and evolving datasets.

Spotlight
ReSim: Reliable World Simulation for Autonomous Driving

Jiazhi Yang, Kashyap Chitta, Shenyuan Gao, Long Chen, Yuqian Shao, Xiaosong Jia, Hongyang Li, Andreas Geiger, Xiangyu Yue, Li Chen

展开摘要

How can we reliably simulate future driving scenarios under a wide range of ego driving behaviors? Recent driving world models, developed exclusively on real-world driving data composed mainly of safe expert trajectories, struggle to follow hazardous or non-expert behaviors, which are rare in such data. This limitation restricts their applicability to tasks such as policy evaluation. In this work, we address this challenge by enriching real-world human demonstrations with diverse non-expert data collected from a driving simulator (e.g., CARLA), and building a controllable world model trained on this heterogeneous corpus. Starting with a video generator featuring diffusion transformer architecture, we devise several strategies to effectively integrate conditioning signals and improve prediction controllability and fidelity. The resulting model, ReSim, enables Reliable Simulation of diverse open-world driving scenarios under various actions, including hazardous non-expert ones. To close the gap between high-fidelity simulation and applications that require reward signals to judge different actions, we introduce a Video2Reward module that estimates reward from ReSim’s simulated future. Our ReSim paradigm achieves up to 44% higher visual fidelity, improves controllability for both expert and non-expert actions by over 50%, and boosts planning and policy selection performance on NAVSIM by 2% and 25%, respectively.

Spotlight
Efficient Quadratic Corrections for Frank-Wolfe Algorithms

Jannis Halbey, Seta Rakotomandimby, Mathieu Besançon, Sébastien Designolle, Sebastian Pokutta

展开摘要

We develop a Frank-Wolfe algorithm with corrective steps, generalizing previous algorithms including Blended Conditional Gradients, Blended Pairwise Conditional Gradients, and Fully-Corrective Frank-Wolfe. For this, we prove tight convergence guarantees together with an optimal face identification property. Furthermore, we propose two highly efficient corrective steps for convex quadratic objectives based on linear optimization or linear system solving, akin to Wolfe's Minimum-Norm Point algorithm, and prove finite-time convergence under suitable conditions. Beyond optimization problems that are directly quadratic, we revisit two algorithms, Split Conditional Gradient and Second-Order Conditional Gradient Sliding, which can leverage quadratic corrections to accelerate the solution of their quadratic subproblems. We show improved convergence rates for the first and prove broader applicability for the second. Finally, we demonstrate substantial computational speedups for Frank-Wolfe-based algorithms with quadratic corrections across the considered problem classes.

Poster
Fuz-RL: A Fuzzy-Guided Robust Framework for Safe Reinforcement Learning under Uncertainty

Xu Wan, Chao Yang, Cheng Yang, Jie Song, Mingyang Sun

展开摘要

Safe Reinforcement Learning (RL) is crucial for achieving high performance while ensuring safety in real-world applications. However, the complex interplay of multiple uncertainty sources in real environments poses significant challenges for interpretable risk assessment and robust decision-making. To address these challenges, we propose \textbf{Fuz-RL}, a fuzzy measure-guided robust framework for safe RL. Specifically, our framework develops a novel fuzzy Bellman operator for estimating robust value functions using Choquet integrals. Theoretically, we prove that solving the Fuz-RL problem (in Constrained Markov Decision Process (CMDP) form) is equivalent to solving distributionally robust safe RL problems (in robust CMDP form), effectively avoiding min-max optimization. Empirical analyses on safe-control-gym and safety-gymnasium scenarios demonstrate that Fuz-RL effectively integrates with existing safe RL baselines in a model-free manner, significantly improving both safety and control performance under various types of uncertainties in observation, action, and dynamics.

Poster
Transformers are almost optimal metalearners for linear classification

Roey Magen, Gal Vardi

展开摘要

Transformers have demonstrated impressive in-context learning (ICL) capabilities, raising the question of whether they can serve as metalearners that adapt to new tasks using only a small number of in-context examples, without any further training. While recent theoretical work has studied transformers' ability to perform ICL, most of these analyses do not address the formal metalearning setting, where the objective is to solve a collection of related tasks more efficiently than would be possible by solving each task individually. In this paper, we provide the first theoretical analysis showing that a simplified transformer architecture trained via gradient descent can act as a near-optimal metalearner in a linear classification setting. We consider a natural family of tasks where each task corresponds to a class-conditional Gaussian mixture model, with the mean vectors lying in a shared $k$-dimensional subspace of $\mathbb{R}^d$. After training on a sufficient number of such tasks, we show that the transformer can generalize to a new task using only $\widetilde{O}(k / \widetilde{R}^4)$ in-context examples, where $\widetilde{R}$ denotes the signal strength at test time. This performance (almost) matches that of an optimal learner that knows exactly the shared subspace and significantly outperforms any learner that only has access to the in-context data, which requires $\Omega(d / \widetilde{R}^4)$ examples to generalize.

Poster
MUniverse: A Simulation and Benchmarking Suite for Motor Unit Decomposition

Pranav Mamidanna, Thomas Klotz, Dimitrios Halatsis, Agnese Grison, Irene Mendez Guerra, Shihan Ma, Arnault H. Caillet, Simon Avrillon, Robin Rohlén, Dario Farina

展开摘要

Neural source separation enables the extraction of individual spike trains from complex electrophysiological recordings. When applied to electromyographic (EMG) signals, it provides a unique window into the motor output of the nervous system by isolating the spiking activity of motor units (MUs). MU decomposition from EMG signals is currently the only scalable neural interfacing approach available in behaving humans and has become foundational in motor neuroscience and neuroprosthetics. However, unlike related domains such as spike sorting or electroencephalography (EEG) analysis, decomposition of EMG signals lacks open benchmarks that reflect the diversity of muscles, movement contexts, and noise sources encountered in practice. To address this gap, we introduce MUniverse, a modular simulation and benchmarking suite for decomposing EMG signals into individual MU spiking activity. MUniverse provides: (1) a simulation stack with a user-friendly interface to a state-of-the-art EMG generator; (2) a curated library of datasets across synthetic, hybrid synthetic-real data with ground truth spikes, and experimental EMG; (3) a set of internal and external decomposition pipelines; and (4) a unified benchmark with well-defined tasks, standard evaluation metrics, and baseline results from established decomposition pipelines. MUniverse is designed for extensibility, reproducibility, and community use, and all datasets are distributed with standardised metadata (Croissant, BIDS). By standardising evaluation and enabling dataset simulation at scale, MUniverse aims to catalyze progress on this long-standing neural signal processing problem.

Poster
GyroSwin: 5D Surrogates for Gyrokinetic Plasma Turbulence Simulations

Fabian Paischer, Gianluca Galletti, William Hornsby, Paul Setinek, Lorenzo Zanisi, Naomi Carey, Stanislas Pamela, Johannes Brandstetter

展开摘要

Nuclear fusion plays a pivotal role in the quest for reliable and sustainable energy production. A major roadblock to viable fusion power is understanding plasma turbulence, which significantly impairs plasma confinement, and is vital for next generation reactor design. Plasma turbulence is governed by the nonlinear gyrokinetic equation, which evolves a 5D distribution function over time. Due to its high computational cost, reduced-order models are often employed in practice to approximate turbulent transport of energy. However, they omit nonlinear effects unique to the full 5D dynamics. To tackle this, we introduce GyroSwin, the first scalable 5D neural surrogate that can model 5D nonlinear gyrokinetic simulations, thereby capturing the physical phenomena neglected by reduced models, while providing accurate estimates of turbulent heat transport. GyroSwin (i) extends hierarchical Vision Transformers to 5D, (ii) introduces cross-attention and integration modules for latent 3D$\leftrightarrow$5D interactions between electrostatic potential fields and the distribution function, and (iii) performs channelwise mode separation inspired by nonlinear physics. We demonstrate that GyroSwin outperforms widely used reduced numerics on heat flux prediction, captures the turbulent energy cascade, and reduces the cost of fully resolved nonlinear gyrokinetics by three orders of magnitude while remaining physically verifiable. GyroSwin shows promising scaling laws, tested up to one billion parameters, paving the way for scalable neural surrogates for gyrokinetic simulations of plasma turbulence.

Poster
MultiScale Contextual Bandits for Long Term Objectives

Richa Rastogi, Yuta Saito, Thorsten Joachims

展开摘要

The feedback that AI systems (e.g., recommender systems, chatbots) collect from user interactions is a crucial source of training data. While short-term feedback (e.g., clicks, engagement) is widely used for training, there is ample evidence that optimizing short-term feedback does not necessarily achieve the desired long-term objectives. Unfortunately, directly optimizing for long-term objectives is challenging, and we identify the disconnect in the timescales of short-term interventions (e.g., rankings) and the long-term feedback (e.g., user retention) as one of the key obstacles. To overcome this disconnect, we introduce the framework of MultiScale Policy Learning to contextually reconcile that AI systems need to act and optimize feedback at multiple interdependent timescales. Following a PAC-Bayes motivation, we show how the lower timescales with more plentiful data can provide a data-dependent hierarchical prior for faster learning at higher scales, where data is more scarce. As a result, the policies at all levels effectively optimize for the long-term. We instantiate the framework with MultiScale Off-Policy Bandit Learning (MSBL) and demonstrate its effectiveness on three tasks relating to recommender and conversational systems.

Poster
DBLoss: Decomposition-based Loss Function for Time Series Forecasting

Xiangfei Qiu, Xingjian Wu, Hanyin Cheng, Xvyuan Liu, Chenjuan Guo, Jilin Hu, Bin Yang

展开摘要

Time series forecasting holds significant value in various domains such as economics, traffic, energy, and AIOps, as accurate predictions facilitate informed decision-making. However, the existing Mean Squared Error (MSE) loss function sometimes fails to accurately capture the seasonality or trend within the forecasting horizon, even when decomposition modules are used in the forward propagation to model the trend and seasonality separately. To address these challenges, we propose a simple yet effective Decomposition-Based Loss function called DBLoss. This method uses exponential moving averages to decompose the time series into seasonal and trend components within the forecasting horizon, and then calculates the loss for each of these components separately, followed by weighting them. As a general loss function, DBLoss can be combined with any deep learning forecasting model. Extensive experiments demonstrate that DBLoss significantly improves the performance of state-of-the-art models across diverse real-world datasets and provides a new perspective on the design of time series loss functions.

Poster
Learning to Insert for Constructive Neural Vehicle Routing Solver

Fu Luo, Xi Lin, Mengyuan Zhong, Fei Liu, Zhenkun Wang, Jianyong Sun, Qingfu Zhang

展开摘要

Neural Combinatorial Optimisation (NCO) is a promising learning-based approach for solving Vehicle Routing Problems (VRPs) without extensive manual design. While existing constructive NCO methods typically follow an appending-based paradigm that sequentially adds unvisited nodes to partial solutions, this rigid approach often leads to suboptimal results. To overcome this limitation, we explore the idea of the insertion-based paradigm and propose Learning to Construct with Insertion-based Paradigm (L2C-Insert), a novel learning-based method for constructive NCO. Unlike traditional approaches, L2C-Insert builds solutions by strategically inserting unvisited nodes at any valid position in the current partial solution, which can significantly enhance the flexibility and solution quality. The proposed framework introduces three key components: a novel model architecture for precise insertion position prediction, an efficient training scheme for model optimization, and an advanced inference technique that fully exploits the insertion paradigm's flexibility. Extensive experiments on both synthetic and real-world instances of the Travelling Salesman Problem (TSP) and Capacitated Vehicle Routing Problem (CVRP) demonstrate that L2C-Insert consistently achieves superior performance across various problem sizes. The code is available at [https://github.com/CIAM-Group/L2C\_Insert](https://github.com/CIAM-Group/L2C\_Insert).

Poster
Atomic Diffusion Models for Small Molecule Structure Elucidation from NMR Spectra

Ziyu Xiong, Yichi Zhang, Foyez Alauddin, Chu Xin Cheng, Joon Soo An, Mohammad R. Seyedsayamdost, Ellen D Zhong

展开摘要

Nuclear Magnetic Resonance (NMR) spectroscopy is a cornerstone technique for determining the structures of small molecules and is especially critical in the discovery of novel natural products and clinical therapeutics. Yet, interpreting NMR spectra remains a time-consuming, manual process requiring extensive domain expertise. We introduce ChefNMR (CHemical Elucidation From NMR), an end-to-end framework that directly predicts an unknown molecule's structure solely from its 1D NMR spectra and chemical formula. We frame structure elucidation as conditional generation from an atomic diffusion model built on a non-equivariant transformer architecture. To model the complex chemical groups found in natural products, we generated a dataset of simulated 1D NMR spectra for over 111,000 natural products. ChefNMR predicts the structures of challenging natural product compounds with an unsurpassed accuracy of over 65%. This work takes a significant step toward solving the grand challenge of automating small-molecule structure elucidation and highlights the potential of deep learning in accelerating molecular discovery.

Poster
CosmoBench: A Multiscale, Multiview, Multitask Cosmology Benchmark for Geometric Deep Learning

Ningyuan Teresa Huang, Richard Stiskalek, Jun-Young Lee, Adrian E. Bayer, Charles Margossian, Christian Kragh Jespersen, Lucia A. Perez, Lawrence K. Saul, Francisco Villaescusa-Navarro

展开摘要

Cosmological simulations provide a wealth of data in the form of point clouds and directed trees. A crucial goal is to extract insights from this data that shed light on the nature and composition of the Universe. In this paper we introduce CosmoBench, a benchmark dataset curated from state-of-the-art cosmological simulations whose runs required more than 41 million core-hours and generated over two petabytes of data. CosmoBench is the largest dataset of its kind: it contains 34 thousand point clouds from simulations of dark matter halos and galaxies at three different length scales, as well as 25 thousand directed trees that record the formation history of halos on two different time scales. The data in CosmoBench can be used for multiple tasks---to predict cosmological parameters from point clouds and merger trees, to predict the velocities of individual halos and galaxies from their collective positions, and to reconstruct merger trees on finer time scales from those on coarser time scales. We provide multiple baselines on these tasks, some based on established approaches from cosmological modeling and others rooted in machine learning. For the latter, we study different approaches---from simple linear models that are minimally constrained by symmetries to much larger and more computationally-demanding models in deep learning, such as graph neural networks. We find that least-squares fits with a handful of invariant features sometimes outperform deep architectures with many more parameters and far longer training times. Still there remains tremendous potential to improve these baselines by combining machine learning and cosmological modeling in a more principled way, one that fully exploits the structure in the data. CosmoBench sets the stage for bridging cosmology and geometric deep learning at scale. We invite the community to push the frontier of scientific discovery by engaging with this challenging, high-impact dataset. The data and code are available at [this URL](https://cosmobench.streamlit.app/).

Poster
SonoGym: High Performance Simulation for Challenging Surgical Tasks with Robotic Ultrasound

Yunke Ao, Masoud Moghani, Mayank Mittal, Manish Prajapat, Luohong Wu, Frederic Giraud, Fabio Carrillo, Andreas Krause, Philipp Fürnstahl

展开摘要

Ultrasound (US) is a widely used medical imaging modality due to its real-time capabilities, non-invasive nature, and cost-effectiveness. By reducing operator dependency and enhancing access to complex anatomical regions, robotic ultrasound can help improve workflow efficiency. Recent studies have demonstrated the potential of deep reinforcement learning (DRL) and imitation learning (IL) to enable more autonomous and intelligent robotic ultrasound navigation. However, the application of learning-based robotic ultrasound to computer-assisted surgical tasks, such as anatomy reconstruction and surgical guidance, remains largely unexplored. A key bottleneck for this is the lack of realistic and efficient simulation environments tailored to these tasks. In this work, we present SonoGym, a scalable simulation platform for robotic ultrasound, enabling parallel simulation across tens to hundreds of environments. Our framework supports realistic and real-time simulation of US data from CT-derived 3D models of the anatomy through both a physics-based and a Generative Adversarial Network (GAN) approach. Our framework enables the training of DRL and recent IL agents (vision transformers and diffusion policies) for relevant tasks in robotic orthopedic surgery by integrating common robotic platforms and orthopedic end effectors. We further incorporate submodular DRL---a recent method that handles history-dependent rewards---for anatomy reconstruction and safe reinforcement learning for surgery. Our results demonstrate successful policy learning across a range of scenarios, while also highlighting the limitations of current methods in clinically relevant environments. We believe our simulation can facilitate research in robot learning approaches for such challenging robotic surgery applications. Dataset, codes and videos are publicly available at https://sonogym.github.io/.

Poster
Fully Dynamic Algorithms for Chamfer Distance

Gramoz Goranci, Shaofeng Jiang, Peter Kiss, Eva Szilagyi, Qiaoyuan Yang

展开摘要

We study the problem of computing Chamfer distance in the fully dynamic setting, where two set of points $A, B \subset \mathbb{R}^{d}$, each of size up to $n$, dynamically evolve through point insertions or deletions and the goal is to efficiently maintain an approximation to $dist_{\mathrm{CH}}(A,B) = \sum_{a \in A} \min_{b \in B} dist(a,b)$, where $dist$ is a distance measure. Chamfer distance is a widely used dissimilarity metric for point clouds, with many practical applications that require repeated evaluation on dynamically changing datasets, e.g., when used as a loss function in machine learning. In this paper, we present the first dynamic algorithm for maintaining an approximation of the Chamfer distance under the $\ell_p$ norm for $p \in$ {$1,2$}. Our algorithm reduces to approximate nearest neighbor (ANN) search with little overhead. Plugging in standard ANN bounds, we obtain $(1+\epsilon)$-approximation in $\tilde{O}(\epsilon^{-d})$ update time and $O(1/\epsilon)$-approximation in $\tilde{O}(d n^{\epsilon^2} \epsilon^{-4})$ update time. We evaluate our method on real-world datasets and demonstrate that it performs competitively against natural baselines.

Poster
Normalized Attention Guidance: Universal Negative Guidance for Diffusion Models

Dar-Yen Chen, Hmrishav Bandyopadhyay, Kai Zou, Yi-Zhe Song

展开摘要

Negative guidance -- explicitly suppressing unwanted attributes -- remains a fundamental challenge in diffusion models, particularly in few-step sampling regimes. While Classifier-Free Guidance (CFG) works well in standard settings, it fails under aggressive sampling step compression due to divergent predictions between positive and negative branches. We present Normalized Attention Guidance (NAG), an efficient, training-free mechanism that applies extrapolation in attention space with L1-based normalization and refinement. NAG restores effective negative guidance where CFG collapses while maintaining fidelity. Unlike existing approaches, NAG generalizes across architectures (UNet, DiT), sampling regimes (few-step, multi-step), and modalities (image, video), functioning as a \textit{universal} plug-in with minimal computational overhead. Through extensive experimentation, we demonstrate consistent improvements in text alignment (CLIP Score), fidelity (FID, PFID), and human-perceived quality (ImageReward). Our ablation studies validate each design component, while user studies confirm significant preference for NAG-guided outputs. As a model-agnostic inference-time approach requiring no retraining, NAG provides effortless negative guidance for all modern diffusion frameworks -- pseudocode in the Appendix!

Poster
Spatial Understanding from Videos: Structured Prompts Meet Simulation Data

Haoyu Zhang, Meng Liu, Zaijing Li, Haokun Wen, Weili Guan, Yaowei Wang, Liqiang Nie

展开摘要

Visual-spatial understanding, the ability to infer object relationships and layouts from visual input, is fundamental to downstream tasks such as robotic navigation and embodied interaction. However, existing methods face spatial uncertainty and data scarcity, limiting the 3D spatial reasoning capability of pre-trained vision-language models (VLMs). To address these challenges, we present a unified framework for enhancing 3D spatial reasoning in pre-trained VLMs without modifying their architecture. This framework combines SpatialMind, a structured prompting strategy that decomposes complex scenes and questions into interpretable reasoning steps, with ScanForgeQA, a scalable question-answering dataset built from diverse 3D simulation scenes through an automated construction process designed for fine-tuning. Extensive experiments across multiple benchmarks demonstrate the individual and combined effectiveness of our prompting and fine-tuning strategies, and yield insights that may inspire future research on visual-spatial understanding.

Spotlight
Minimum Width for Deep, Narrow MLP: A Diffeomorphism Approach

Geonho Hwang

展开摘要

Recently, there has been a growing focus on determining the minimum width requirements for achieving the universal approximation property in deep, narrow Multi-Layer Perceptrons (MLPs). Among these challenges, one particularly challenging task is approximating a continuous function under the uniform norm, as indicated by the significant disparity between its lower and upper bounds. To address this problem, we propose a framework that simplifies finding the minimum width for deep, narrow MLPs into determining a purely geometrical function denoted as $w(d_x, d_y)$. This function relies solely on the input and output dimensions, represented as $d_x$ and $d_y$, respectively. To achieve this, we first demonstrate that deep, narrow MLPs, when provided with a small additional width, can approximate any $C^2$-diffeomorphism. Subsequently, using this result, we prove that $w(d_x, d_y)$ equates to the optimal minimum width required for deep, narrow MLPs to achieve universality. By employing the aforementioned framework and the Whitney embedding theorem, we provide an upper bound for the minimum width, given by $\operatorname{max}(2d_x+1, d_y) + \alpha(\sigma)$, where $0 \leq \alpha(\sigma) \leq 2$ represents a constant depending explicitly on the activation function. Furthermore, we provide novel optimal values for the minimum width in several settings, including $w(2,2)=w(2,3) = 4$.

Poster
A Latent Multilayer Graphical Model For Complex, Interdependent Systems

Martin Ondrus, Ivor Cribben, Yang Feng

展开摘要

Networks have been extensively used and have provided novel insights across a wide variety of research areas. However, many real-world systems are, in fact, a ``network of networks'', or a multilayer network, which interact as components of a larger multimodal system. A major difficulty in this multilayer framework is the estimation of interlayer edges or connections. In this work, we propose a new estimation method, called multilayer sparse + low-rank inverse covariance estimation (multiSLICE), which estimates the interlayer edges. multiSLICE bridges latent variable Gaussian graphical methods with multilayer networks, offering a flexible framework for modeling processes with irregular sampling and heterogeneous graph structures. We develop an effective algorithm to compute the estimator. We also establish theoretical conditions for the recoverability of the joint space, analyze how inter-layer interactions influence joint parameter estimation, and provide theoretical bounds on their relationships. Finally, we rigorously evaluate our method on both simulated and multimodal neuroimaging data, demonstrating improvements over state-of-the-art approaches. Finally, all the relevant R code implementing the method in the article is available on [GitHub](https://github.com/mondrus96/multiSLICE).

Poster