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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Riemannian Consistency Model

Chaoran Cheng, Yusong Wang, Yuxin Chen, Xiangxin Zhou, Nanning Zheng, Ge Liu

展开摘要

Consistency models are a class of generative models that enable few-step generation for diffusion and flow matching models. While consistency models have achieved promising results on Euclidean domains like images, their applications to Riemannian manifolds remain challenging due to the curved geometry. In this work, we propose the Riemannian Consistency Model (RCM), which, for the first time, enables few-step consistency modeling while respecting the intrinsic manifold constraint imposed by the Riemannian geometry. Leveraging the covariant derivative and exponential-map-based parameterization, we derive the closed-form solutions for both discrete- and continuous-time training objectives for RCM. We then demonstrate theoretical equivalence between the two variants of RCM: Riemannian consistency distillation (RCD) that relies on a teacher model to approximate the marginal vector field, and Riemannian consistency training (RCT) that utilizes the conditional vector field for training. We further propose a simplified training objective that eliminates the need for the complicated differential calculation. Finally, we provide a unique kinematics perspective for interpreting the RCM objective, offering new theoretical angles. Through extensive experiments, we manifest the superior generative quality of RCM in few-step generation on various non-Euclidean manifolds, including flat-tori, spheres, and the 3D rotation group SO(3), spanning a variety of crucial real-world applications such as RNA and protein generation.

Poster
NeuSymEA: Neuro-symbolic Entity Alignment via Variational Inference

Shengyuan Chen, Zheng Yuan, Qinggang Zhang, Wen Hua, Jiannong Cao, Xiao Huang

展开摘要

Entity alignment (EA) aims to merge two knowledge graphs (KGs) by identifying equivalent entity pairs. Existing methods can be categorized into symbolic and neural models. Symbolic models, while precise, struggle with substructure heterogeneity and sparsity, whereas neural models, although effective, generally lack interpretability and cannot handle uncertainty. We propose NeuSymEA, a unified neuro-symbolic reasoning framework that combines the strengths of both methods to fully exploit the cross-KG structural pattern for robust entity alignment. NeuSymEA models the joint probability of all possible pairs' truth scores in a Markov random field, regulated by a set of rules, and optimizes it with the variational EM algorithm. In the E-step, a neural model parameterizes the truth score distributions and infers missing alignments. In the M-step, the rule weights are updated based on the observed and inferred alignments, handling uncertainty. We introduce an efficient symbolic inference engine driven by logic deduction, enabling reasoning with extended rule lengths. NeuSymEA achieves a significant 7.6\% hit@1 improvement on $DBP15K_{ZH-EN}$ compared with strong baselines and demonstrates robustness in low-resource settings, achieving 73.7\% hit@1 accuracy on $DBP15K_{FR-EN}$ with only 1\% pairs as seed alignments. Codes are released at https://github.com/chensyCN/NeuSymEA-NeurIPS25.

Poster
MLIP Arena: Advancing Fairness and Transparency in Machine Learning Interatomic Potentials via an Open, Accessible Benchmark Platform

Yuan Chiang, Tobias Kreiman, Christine Zhang, Matthew C. Kuner, Elizabeth Jin Weaver, Ishan Amin, Hyunsoo Park, Yunsung Lim, Jihan Kim, Daryl Chrzan, Aron Walsh, Samuel M Blau, Mark Asta, Aditi S. Krishnapriyan

展开摘要

Machine learning interatomic potentials (MLIPs) have revolutionized molecular and materials modeling, but existing benchmarks suffer from data leakage, limited transferability, and an over-reliance on error-based metrics tied to specific density functional theory (DFT) references. We introduce MLIP Arena, a benchmark platform that evaluates force field performance based on physics awareness, chemical reactivity, stability under extreme conditions, and predictive capabilities for thermodynamic properties and physical phenomena. By moving beyond static DFT references and revealing the important failure modes of current foundation MLIPs in real-world settings, MLIP Arena provides a reproducible framework to guide the next-generation MLIP development toward improved predictive accuracy and runtime efficiency while maintaining physical consistency. The Python package and online leaderboard are available at https://github.com/atomind-ai/mlip-arena.

Spotlight
Learning Dense Hand Contact Estimation from Imbalanced Data

Daniel Sungho Jung, Kyoung Mu Lee

展开摘要

Hands are essential to human interaction, and exploring contact between hands and the world can promote comprehensive understanding of their function. Recently, there have been growing number of hand interaction datasets that cover interaction with object, other hand, scene, and body. Despite the significance of the task and increasing high-quality data, how to effectively learn dense hand contact estimation remains largely underexplored. There are two major challenges for learning dense hand contact estimation. First, there exists class imbalance issue from hand contact datasets where majority of regions are not in contact. Second, hand contact datasets contain spatial imbalance issue with most of hand contact exhibited in finger tips, resulting in challenges for generalization towards contacts in other hand regions. To tackle these issues, we present a framework that learns dense HAnd COntact estimation (HACO) from imbalanced data. To resolve the class imbalance issue, we introduce balanced contact sampling, which builds and samples from multiple sampling groups that fairly represent diverse contact statistics for both contact and non-contact vertices. Moreover, to address the spatial imbalance issue, we propose vertex-level class-balanced (VCB) loss, which incorporates spatially varying contact distribution by separately reweighting loss contribution of each vertex based on its contact frequency across dataset. As a result, we effectively learn to predict dense hand contact estimation with large-scale hand contact data without suffering from class and spatial imbalance issue. The codes are available at https://github.com/dqj5182/HACO_RELEASE.

Poster
Text-to-Code Generation for Modular Building Layouts in Building Information Modeling

Yinyi WEI, Xiao Li

展开摘要

We present Text2MBL, a text-to-code generation framework that generates executable Building Information Modeling (BIM) code directly from textual descriptions of modular building layout (MBL) design. Unlike conventional layout generation approaches that operate in 2D space, Text2MBL produces fully parametric, semantically rich BIM layouts through on‑the‑fly code instantiation. To address MBLs' unique challenges due to their hierarchical three-tier structure: modules (physical building blocks), units (self-contained dwellings), and rooms (functional spaces), we developed an object-oriented code architecture and fine-tuned large language models to output structured action sequences in code format. To train and evaluate the framework, we curated a dataset of paired descriptions and ground truth layouts drawn from real‑world modular housing projects. Performance were assessed using metrics for executable validity, semantic fidelity, and geometric consistency. By tightly unifying natural language understanding with BIM code generation, Text2MBL establishes a scalable pipeline from high-level conceptual design to automation-ready modular construction workflows. Our implementation is available at https://github.com/CI3LAB/Text2MBL.

Poster
GAMMA: Gated Multi-hop Message Passing for Homophily-Agnostic Node Representation in GNNs

Amir Ghazizadeh Ahsaei, Rickard Ewetz, Hao ZHENG

展开摘要

The success of Graph Neural Networks (GNNs) leverages the homophily principle, where connected nodes share similar features and labels. However, this assumption breaks down in heterophilic graphs, where same-class nodes are often distributed across distant neighborhoods rather than immediate connections. Recent attempts expand the receptive field through multi-hop aggregation schemes that explicitly preserve intermediate representations from each hop distance. While effective at capturing heterophilic patterns, these methods require separate weight matrices per hop and feature concatenation, causing parameters to scale linearly with hop count. This leads to high computational complexity and GPU memory consumption. We propose Gated Multi-hop Message Passing (GAMMA), where nodes assess how relevant the aggregated information is from their k-hop neighbors. This assessment occurs through multiple refinement steps where the node compares each hop's embedding with its current representation, allowing it to focus on the most informative hops. During the forward pass, GAMMA finds the optimal mix of multi-hop information local to each node using a single feature vector without needing separate representations for each hop, thereby maintaining dimensionality comparable to single hop GNNs. In addition, we propose a weight sharing scheme that leverages a unified transformation for aggregated features from multiple hops so the global heterophilic patterns specific to each hop are learned during training. As such, GAMMA captures both global (per-hop) and local (per-node) heterophily patterns without high computation and memory overhead. Experiments show GAMMA matches or exceeds state-of-the-art heterophilic GNN accuracy, achieving up to $\approx20\times$ faster inference. Our code is publicly available at \url{https://github.com/amir-ghz/GAMMA}.

Poster
Volume Transmission Implements Context Factorization to Target Online Credit Assignment and Enable Compositional Generalization

Matthew Storm Bull, Po-Chen Kuo, Andrew Lawrence Smith, Michael A Buice

展开摘要

The modern connectivist framing of neural computation emphasizes the primacy of synaptic communication at the risk of neglecting the influence of the surrounding neuromodulatory environment --- a neuron's 'biophysical context.' Decades of experimental work has established two views of neuromodulatory (NMs) influence: 1) NMs significantly alter circuit dynamics and 2) NMs gate synaptic plasticity, acting as a 'third factor' in learning. Here, we unify these perspectives, proposing that neuromodulation via volume transmission implements a powerful computational principle: context factorization. We derive an endogenously neuromodulated Recurrent Neural Network (e-nmRNN) from a rate reduction of NM release, showing how NM concentrations dynamically factorize network connectivity. This framework reveals how multiplicative NM gating distinctly influences dynamical regimes compared to additive input. Crucially, this context factorization enables targeted online credit assignment: learning rules derived for the e-nmRNN are naturally gated by NM concentrations, localizing updates to relevant contexts. We demonstrate that e-nmRNN dynamics can learn to approximate gradient descent, facilitating rapid in-context adaptation akin to meta-learning. Empirically, e-nmRNNs achieve strong compositional generalization in sequence-to-sequence tasks, outperforming baselines and exhibiting greater hyperparameter robustness. Furthermore, when trained on complex multitasking benchmarks, e-nmRNNs develop emergent properties mirroring biological observations, including modularity, cell-type specialization based on NM release, and distinct neuromodulatory timescales encoding task context. The model's interpretability allows us to reverse engineer these emergent structures. Notably, in reinforcement learning tasks, the e-nmRNN learns to encode context and signals like Reward Prediction Error (RPE) within its neuromodulator dynamics, demonstrating a mechanism for RPE-gated online credit assignment essential for learning how to learn. By bridging biophysical mechanisms with computational principles and empirical validation, our work presents e-nmRNNs as a performant, interpretable model for understanding the computational role of neuromodulation in flexible and compositional learning.

Poster
OneIG-Bench: Omni-dimensional Nuanced Evaluation for Image Generation

Jingjing Chang, Yixiao Fang, Peng Xing, Shuhan Wu, Wei Cheng, Rui Wang, Xianfang Zeng, Gang Yu, Hai-Bao Chen

展开摘要

Text-to-image (T2I) models have garnered significant attention for generating high-quality images aligned with text prompts. However, rapid T2I model advancements reveal limitations in early benchmarks, lacking comprehensive evaluations, especially for text rendering and style. Notably, recent state-of-the-art models, with their rich knowledge modeling capabilities, show potential in reasoning-driven image generation, yet existing evaluation systems have not adequately addressed this frontier. To systematically address these gaps, we introduce $\textbf{OneIG-Bench}$, a meticulously designed comprehensive benchmark framework for fine-grained evaluation of T2I models across multiple dimensions, including subject-element alignment, text rendering precision, reasoning-generated content, stylization, and diversity. By structuring the evaluation, this benchmark enables in-depth analysis of model performance, helping researchers and practitioners pinpoint strengths and bottlenecks in the full pipeline of image generation. Our codebase and dataset are now publicly available to facilitate reproducible evaluation studies and cross-model comparisons within the T2I research community.

Poster
SutureBot: A Precision Framework & Benchmark For Autonomous End-to-End Suturing

Jesse Haworth, Juo-Tung Chen, Nigel Nelson, Ji Woong Kim, Masoud Moghani, Chelsea Finn, Axel Krieger

展开摘要

Robotic suturing is a prototypical long-horizon dexterous manipulation task, requiring coordinated needle grasping, precise tissue penetration, and secure knot tying. Despite numerous efforts toward end-to-end autonomy, a fully autonomous suturing pipeline has yet to be demonstrated on physical hardware. We introduce SutureBot: an autonomous suturing benchmark on the da Vinci Research Kit (dVRK), spanning needle pickup, tissue insertion, and knot tying. To ensure repeatability, we release a high-fidelity dataset comprising 1,890 suturing demonstrations. Furthermore, we propose a goal-conditioned framework that explicitly optimizes insertion-point precision, improving targeting accuracy by 59\%-74\% over a task-only baseline. To establish this task as a benchmark for dexterous imitation learning, we evaluate state-of-the-art vision-language-action (VLA) models, including $\pi_0$, GR00T N1, OpenVLA-OFT, and multitask ACT, each augmented with a high-level task-prediction policy. Autonomous suturing is a key milestone toward achieving robotic autonomy in surgery. These contributions support reproducible evaluation and development of precision-focused, long-horizon dexterous manipulation policies necessary for end-to-end suturing. Dataset is available at: \href{https://huggingface.co/datasets/jchen396/suturebot}{Hugging Face}

Poster
MoCha: Towards Movie-Grade Talking Character Generation

Cong Wei, Bo Sun, Haoyu Ma, Ji Hou, Felix Juefei-Xu, Zecheng He, Xiaoliang Dai, Luxin Zhang, Kunpeng Li, Tingbo Hou, Animesh Sinha, Peter Vajda, Wenhu Chen

展开摘要

Recent advancements in video generation have achieved impressive motion realism, yet they often overlook character-driven storytelling, a crucial task for automated film, animation generation. We introduce Talking Characters, a more realistic task to generate talking character animations directly from speech and text. Unlike talking head tasks, Talking Characters aims at generating the full portrait of one or more characters beyond the facial region. In this paper, we propose MoCha, the first of its kind to generate talking characters. To ensure precise synchronization between video and speech, we propose a localized audio attention mechanism that effectively aligns speech and video tokens. To address the scarcity of large-scale speech-labelled video datasets, we introduce a joint training strategy that leverages both speech-labelled and text-labelled video data, significantly improving generalization across diverse character actions. We also design structured prompt templates with character tags, enabling, for the first time, multi-character conversation with turn-based dialogue—allowing AI-generated characters to engage in context-aware conversations with cinematic coherence. Extensive qualitative and quantitative evaluations, including human evaluation studies and benchmark comparisons, demonstrate that MoCha sets a new standard for AI-generated cinematic storytelling, achieving superior realism, controllability and generalization.

Spotlight
X-Field: A Physically Informed Representation for 3D X-ray Reconstruction

Feiran Wang, Jiachen Tao, Junyi Wu, Haoxuan Wang, Bin Duan, Kai Wang, Zongxin Yang, Yan Yan

展开摘要

X-ray imaging is indispensable in medical diagnostics, yet its use is tightly regulated due to radiation exposure. Recent research borrows representations from the 3D reconstruction area to complete two tasks with reduced radiation dose: X-ray Novel View Synthesis (NVS) and Computed Tomography (CT) reconstruction. However, these representations fail to fully capture the penetration and attenuation properties of X-ray imaging as they originate from visible light imaging. In this paper, we introduce X-Field, a 3D representation informed in the physics of X-ray imaging. First, we employ homogeneous 3D ellipsoids with distinct attenuation coefficients to accurately model diverse materials within internal structures. Second, we introduce an efficient path-partitioning algorithm that resolves the intricate intersection of ellipsoids to compute cumulative attenuation along an X-ray path. We further propose a hybrid progressive initialization to refine the geometric accuracy of X-Field and incorporate material-based optimization to enhance model fitting along material boundaries. Experiments show that X-Field achieves superior visual fidelity on both real-world human organ and synthetic object datasets, outperforming state-of-the-art methods in X-ray NVS and CT Reconstruction.

Spotlight
RoFt-Mol: Benchmarking Robust Fine-tuning with Molecular Graph Foundation Models

Shikun Liu, Deyu Zou, Nima Shoghi, Victor Fung, Kai Liu, Pan Li

展开摘要

In the era of foundation models, fine-tuning pre-trained models for specific downstream tasks has become crucial. This drives the need for robust fine-tuning methods to address challenges such as model overfitting and sparse labeling. Molecular graph foundation models (MGFMs) face unique difficulties that complicate fine- tuning. These models are limited by smaller pre-training datasets and more severe data scarcity for downstream tasks, both of which require enhanced model generalization. Moreover, MGFMs must accommodate diverse objectives, including both regression and classification tasks. To better understand and improve fine-tuning techniques under these conditions, we classify eight fine-tuning methods into three mechanisms: weight-based, representation-based, and partial fine-tuning. We benchmark these methods on downstream regression and classification tasks across supervised and self-supervised pre-trained models in diverse labeling settings. This extensive evaluation provides valuable insights and informs the design of a refined robust fine-tuning method, ROFT-MOL. This approach combines the strengths of simple post-hoc weight interpolation with more complex weight ensemble fine- tuning methods, delivering improved performance across both task types while maintaining the ease of use inherent in post-hoc weight interpolation.

Spotlight
TS-MOF: Two-Stage Multi-Objective Fine-tuning for Long-Tailed Recognition

Zhe Zhao, Zhiheng Gong, Pengkun Wang, HaiBin Wen, Cankun Guo, Bo Xue, Xi Lin, Zhenkun Wang, Qingfu Zhang, Yang Wang

展开摘要

Long-Tailed Recognition (LTR) presents a significant challenge due to extreme class imbalance, where existing methods often struggle to balance performance across head and tail classes. Directly applying multi-objective optimization (MOO) to leverage multiple LTR strategies can be complex and unstable. To address this, we propose TS-MOF (Two-Stage Multi-Objective Fine-tuning), a novel framework that strategically decouples feature learning from classifier adaptation. After standard pre-training, TS-MOF freezes the feature backbone and focuses on an efficient multi-objective fine-tuning of specialized classifier heads. The core of TS-MOF's second stage lies in two innovations: Refined Performance Level Agreement for adaptive task weighting based on real-time per-class performance, and Robust Deterministic Projective Conflict Gradient for stable gradient conflict resolution and constructive fusion. This approach enables effective synergy between diverse LTR strategies, leading to significant and balanced performance improvements. Extensive experiments on CIFAR100-LT, ImageNet-LT, and iNaturalist 2018 demonstrate that TS-MOF achieves state-of-the-art results, particularly enhancing tail class accuracy (e.g., +3.3\% on CIFAR100-LT IR=100 tail) while improving head class performance, all within a remarkably short fine-tuning period of 20 epochs.

Poster
Activated LoRA: Fine-tuned LLMs for Intrinsics

Kristjan Greenewald, Luis A. Lastras, Thomas Parnell, Vraj Shah, Lucian Popa, Giulio Zizzo, Chulaka Gunasekara, Ambrish Rawat, David Daniel Cox

展开摘要

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

Poster
Demystifying Network Foundation Models

Roman Beltiukov, Satyandra Guthula, Wenbo Guo, Walter Willinger, Arpit Gupta

展开摘要

This work presents a systematic investigation into the latent knowledge encoded within Network Foundation Models (NFMs). Different from existing efforts, we focus on hidden representations analysis rather than pure downstream task performance and analyze NFMs through a three-part evaluation: Embedding Geometry Analysis to assess representation space utilization, Metric Alignment Assessment to measure correspondence with domain-expert features, and Causal Sensitivity Testing to evaluate robustness to protocol perturbations. Using five diverse network datasets spanning controlled and real-world environments, we evaluate four state-of-the-art NFMs, revealing that they all exhibit significant anisotropy, inconsistent feature sensitivity patterns, an inability to separate the high-level context, payload dependency, and other properties. Our work identifies numerous limitations across all models and demonstrates that addressing them can significantly improve model performance (up to 0.35 increase in $F_1$ scores without architectural changes).

Poster
Unified Multimodal Chain-of-Thought Reward Model through Reinforcement Fine-Tuning

Yibin Wang, Zhimin Li, Yuhang Zang, Chunyu Wang, Qinglin Lu, Cheng Jin, Jiaqi Wang

展开摘要

Recent advances in multimodal Reward Models (RMs) have shown significant promise in delivering reward signals to align vision models with human preferences. However, current RMs are generally restricted to providing direct responses or engaging in shallow reasoning processes with limited depth, often leading to inaccurate reward signals. We posit that incorporating explicit long chains of thought (CoT) into the reward reasoning process can significantly strengthen their reliability and robustness. Furthermore, we believe that once RMs internalize CoT reasoning, their direct response accuracy can also be improved through implicit reasoning capabilities. To this end, this paper proposes UnifiedReward-Think, the first unified multimodal CoT-based reward model, capable of multi-dimensional, step-by-step long-chain reasoning for both visual understanding and generation reward tasks. Specifically, we adopt an exploration-driven reinforcement fine-tuning approach to elicit and incentivize the model's latent complex reasoning ability: (1) We first use a small amount of image generation preference data to distill the reasoning process of GPT-4o, which is then used for the model's cold start to learn the format and structure of CoT reasoning. (2) Subsequently, by leveraging the model's prior knowledge and generalization capabilities, we prepare large-scale unified multimodal preference data to elicit the model's reasoning process across various vision tasks. During this phase, correct reasoning outputs are retained for rejection sampling to refine the model (3) while incorrect predicted samples are finally used for Group Relative Policy Optimization (GRPO) based reinforcement fine-tuning, enabling the model to explore diverse reasoning paths and optimize for correct and robust solutions. Extensive experiments confirm that incorporating long CoT reasoning significantly enhances the accuracy of reward signals. Notably, after mastering CoT reasoning, the model exhibits implicit reasoning capabilities, allowing it to surpass existing baselines even without explicit reasoning traces.

Poster
Scaling up Test-Time Compute with Latent Reasoning: A Recurrent Depth Approach

Jonas Geiping, Sean Michael McLeish, Neel Jain, John Kirchenbauer, Siddharth Singh, Brian R. Bartoldson, Bhavya Kailkhura, Abhinav Bhatele, Tom Goldstein

展开摘要

We study a novel language model architecture that is capable of scaling test-time computation by implicitly reasoning in latent space. Our model works by iterating a recurrent block, thereby unrolling to arbitrary depth at test-time. This stands in contrast to mainstream reasoning models that scale up compute by producing more tokens. Unlike approaches based on chain-of-thought, our approach does not require any specialized training data, can work with small context windows, and can capture types of reasoning that are not easily represented in words. We train a proof-of-concept model from scratch with 3.5 billion parameters and 800 billion tokens. We show that this model can effortlessly use varying levels of compute, significantly improving with additional compute especially on reasoning tasks, such as math and coding. Further, this architecture naturally reduces compute costs via zero-shot per-token adaptive compute, KV-cache sharing and speculative decoding.

Spotlight
Informed Initialization for Bayesian Optimization and Active Learning

Carl Hvarfner, David Eriksson, Eytan Bakshy, Maximilian Balandat

展开摘要

Bayesian Optimization (BO) is a widely used method for optimizing expensive black-box functions, relying on probabilistic surrogate models such as Gaussian Processes (GPs). The quality of the surrogate model is crucial for good optimization performance, especially in the few-shot setting where only a small number of batches of points can be evaluated. In this setting, the initialization plays a critical role in shaping the surrogate's predictive quality and guiding subsequent optimization. Despite this, practitioners typically rely on (quasi-)random designs to cover the input space. However, such approaches neglect two key factors: (a) random designs may not be space-filling, and (b) efficient hyperparameter learning during initialization is essential for high-quality prediction, which may conflict with space-filling designs. To address these limitations, we propose Hyperparameter-Informed Predictive Exploration (HIPE), a novel acquisition strategy that balances space-filling exploration with hyperparameter learning using information-theoretic principles. We derive a closed-form expression for HIPE in the GP setting and demonstrate its effectiveness through extensive experiments in active learning and few-shot BO. Our results show that HIPE outperforms standard initialization strategies in terms of predictive accuracy, hyperparameter identification, and optimization performance, particularly in large-batch, few-shot settings relevant to many real-world BO applications.

Poster
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
PAC-Bayes Bounds for Multivariate Linear Regression and Linear Autoencoders

Ruixin Guo, Ruoming Jin, Xinyu Li, Yang Zhou

展开摘要

Linear Autoencoders (LAEs) have shown strong performance in state-of-the-art recommender systems. However, this success remains largely empirical, with limited theoretical understanding. In this paper, we investigate the generalizability -- a theoretical measure of model performance in statistical learning -- of multivariate linear regression and LAEs. We first propose a PAC-Bayes bound for multivariate linear regression, extending the earlier bound for single-output linear regression by Shalaeva et al., and establish sufficient conditions for its convergence. We then show that LAEs, when evaluated under a relaxed mean squared error, can be interpreted as constrained multivariate linear regression models on bounded data, to which our bound adapts. Furthermore, we develop theoretical methods to improve the computational efficiency of optimizing the LAE bound, enabling its practical evaluation on large models and real-world datasets. Experimental results demonstrate that our bound is tight and correlates well with practical ranking metrics such as Recall@K and NDCG@K.

Poster