ICLR 2025 论文列表

International Conference on Learning Representations

录用类型

3,703篇论文

按官方录用论文列表统计,可能与会议公布的数字略有出入。

  • Oral
    2135.8%
  • Spotlight
    38010.3%
  • Poster
    3,11084.0%

浏览全部论文

GravMAD: Grounded Spatial Value Maps Guided Action Diffusion for Generalized 3D Manipulation

Yangtao Chen, Zixuan Chen, Junhui Yin, Jing Huo, Pinzhuo Tian, Jieqi Shi, Yang Gao

展开摘要

Robots' ability to follow language instructions and execute diverse 3D manipulation tasks is vital in robot learning. Traditional imitation learning-based methods perform well on seen tasks but struggle with novel, unseen ones due to variability. Recent approaches leverage large foundation models to assist in understanding novel tasks, thereby mitigating this issue. However, these methods lack a task-specific learning process, which is essential for an accurate understanding of 3D environments, often leading to execution failures. In this paper, we introduce GravMAD, a sub-goal-driven, language-conditioned action diffusion framework that combines the strengths of imitation learning and foundation models. Our approach breaks tasks into sub-goals based on language instructions, allowing auxiliary guidance during both training and inference. During training, we introduce Sub-goal Keypose Discovery to identify key sub-goals from demonstrations. Inference differs from training, as there are no demonstrations available, so we use pre-trained foundation models to bridge the gap and identify sub-goals for the current task. In both phases, GravMaps are generated from sub-goals, providing GravMAD with more flexible 3D spatial guidance compared to fixed 3D positions. Empirical evaluations on RLBench show that GravMAD significantly outperforms state-of-the-art methods, with a 28.63\% improvement on novel tasks and a 13.36\% gain on tasks encountered during training. Evaluations on real-world robotic tasks further show that GravMAD can reason about real-world tasks, associate them with relevant visual information, and generalize to novel tasks. These results demonstrate GravMAD's strong multi-task learning and generalization in 3D manipulation. Video demonstrations are available at: https://gravmad.github.io.

Poster
Laplace Sample Information: Data Informativeness Through a Bayesian Lens

Johannes Kaiser, Kristian Schwethelm, Daniel Rueckert, Georgios Kaissis

展开摘要

Accurately estimating the informativeness of individual samples in a dataset is an important objective in deep learning, as it can guide sample selection, which can improve model efficiency and accuracy by removing redundant or potentially harmful samples. We propose $\text{\textit{Laplace Sample Information}}$ ($\mathsf{LSI}$) measure of sample informativeness grounded in information theory widely applicable across model architectures and learning settings. $\mathsf{LSI}$ leverages a Bayesian approximation to the weight posterior and the KL divergence to measure the change in the parameter distribution induced by a sample of interest from the dataset. We experimentally show that $\mathsf{LSI}$ is effective in ordering the data with respect to typicality, detecting mislabeled samples, measuring class-wise informativeness, and assessing dataset difficulty. We demonstrate these capabilities of $\mathsf{LSI}$ on image and text data in supervised and unsupervised settings. Moreover, we show that $\mathsf{LSI}$ can be computed efficiently through probes and transfers well to the training of large models.

Poster
Systematic Relational Reasoning With Epistemic Graph Neural Networks

Irtaza Khalid, Steven Schockaert

展开摘要

Developing models that can learn to reason is a notoriously challenging problem. We focus on reasoning in relational domains, where the use of Graph Neural Networks (GNNs) seems like a natural choice. However, previous work has shown that regular GNNs lack the ability to systematically generalize from training examples on test graphs requiring longer inference chains, which fundamentally limits their reasoning abilities. A common solution relies on neuro-symbolic methods that systematically reason by learning rules, but their scalability is often limited and they tend to make unrealistically strong assumptions, e.g.\ that the answer can always be inferred from a single relational path. We propose the Epistemic GNN (EpiGNN), a novel parameter-efficient and scalable GNN architecture with an epistemic inductive bias for systematic reasoning. Node embeddings in EpiGNNs are treated as epistemic states, and message passing is implemented accordingly. We show that EpiGNNs achieve state-of-the-art results on link prediction tasks that require systematic reasoning. Furthermore, for inductive knowledge graph completion, EpiGNNs rival the performance of state-of-the-art specialized approaches. Finally, we introduce two new benchmarks that go beyond standard relational reasoning by requiring the aggregation of information from multiple paths. Here, existing neuro-symbolic approaches fail, yet EpiGNNs learn to reason accurately. Code and datasets are available at https://github.com/erg0dic/gnn-sg.

Poster
Improving Generalization and Robustness in SNNs Through Signed Rate Encoding and Sparse Encoding Attacks

Bhaskar Mukhoty, Hilal AlQuabeh, Bin Gu

展开摘要

Rate-encoded spiking neural networks (SNNs) are known to offer superior adversarial robustness compared to direct-encoded SNNs but have relatively poor generalization on clean input. While the latter offers good generalization on clean input it suffers poor adversarial robustness under standard training. A key reason for this difference is the input noise introduced by the rate encoding, which encodes a pixel intensity with $T$ independent Bernoulli samples. To improve the generalization of rate-encoded SNNs, we propose the *signed rate encoding* (sRATE) that allows mean centering of the input and helps reduce the randomness introduced by the encoding, resulting in improved clean accuracy. In contrast to rate encoding, where input restricted to $[0,1]^d$ is encoded in $\\{0,1\\}^{d\times T}$, the signed rate encoding allows input in $[-1,1]^d$ to be encoded with spikes in $\\{-1,0,1\\}^{d\times T}$, where positive (negative) inputs are encoded with positive (negative) spikes. We further construct efficient \textit{Sparse Encoding Attack} (SEA) on standard and signed rate encoded input, which performs $l_0$-norm restricted adversarial attack in the discrete encoding space. We prove the theoretical optimality of the attack under the first-order approximation of the loss and compare it empirically with the existing attacks on the input space. Adversarial training performed with SEA, under signed rate encoding, offers superior adversarial robustness to the existing attacks and itself. Experiments conducted on standard datasets show the effectiveness of sign rate encoding in improving accuracy across all settings including adversarial robustness. The code is available at https://github.com/BhaskarMukhoty/SignedRateEncoding

Poster
CoMotion: Concurrent Multi-person 3D Motion

Alejandro Newell, Peiyun Hu, Lahav Lipson, Stephan Richter, Vladlen Koltun

展开摘要

We introduce an approach for detecting and tracking detailed 3D poses of multiple people from a single monocular camera stream. Our system maintains temporally coherent predictions in crowded scenes filled with difficult poses and occlusions. Our model performs both strong per-frame detection and a learned pose update to track people from frame to frame. Rather than match detections across time, poses are updated directly from a new input image, which enables online tracking through occlusion. We train on numerous image and video datasets leveraging pseudo-labeled annotations to produce a model that matches state-of-the-art systems in 3D pose estimation accuracy while being faster and more accurate in tracking multiple people through time.

Poster
Generalization, Expressivity, and Universality of Graph Neural Networks on Attributed Graphs

Levi Rauchwerger, Stefanie Jegelka, Ron Levie

展开摘要

We analyze the universality and generalization of graph neural networks (GNNs) on attributed graphs, i.e., with node attributes. To this end, we propose pseudometrics over the space of all attributed graphs that describe the fine-grained expressivity of GNNs. Namely, GNNs are both Lipschitz continuous with respect to our pseudometrics and can separate attributed graphs that are distant in the metric. Moreover, we prove that the space of all attributed graphs is relatively compact with respect to our metrics. Based on these properties, we prove a universal approximation theorem for GNNs and generalization bounds for GNNs on any data distribution of attributed graphs. The proposed metrics compute the similarity between the structures of attributed graphs via a hierarchical optimal transport between computation trees. Our work extends and unites previous approaches which either derived theory only for graphs with no attributes, derived compact metrics under which GNNs are continuous but without separation power, or derived metrics under which GNNs are continuous and separate points but the space of graphs is not relatively compact, which prevents universal approximation and generalization analysis.

Poster
MMDT: Decoding the Trustworthiness and Safety of Multimodal Foundation Models

Chejian Xu, Jiawei Zhang, Zhaorun Chen, Chulin Xie, Mintong Kang, Yujin Potter, Zhun Wang, Zhuowen Yuan, Alexander Xiong, Zidi Xiong, Chenhui Zhang, Lingzhi Yuan, Yi Zeng, Peiyang Xu, Chengquan Guo, Andy Zhou, Jeffrey Ziwei Tan, Xuandong Zhao, Francesco Pinto, Zhen Xiang, Yu Gai, Zinan Lin, Dan Hendrycks, Bo Li, Dawn Song

展开摘要

Multimodal foundation models (MMFMs) play a crucial role in various applications, including autonomous driving, healthcare, and virtual assistants. However, several studies have revealed vulnerabilities in these models, such as generating unsafe content by text-to-image models. Existing benchmarks on multimodal models either predominantly assess the helpfulness of these models, or only focus on limited perspectives such as fairness and privacy. In this paper, we present the first unified platform, MMDT (Multimodal DecodingTrust), designed to provide a comprehensive safety and trustworthiness evaluation for MMFMs. Our platform assesses models from multiple perspectives, including safety, hallucination, fairness/bias, privacy, adversarial robustness, and out-of-distribution (OOD) generalization. We have designed various evaluation scenarios and red teaming algorithms under different tasks for each perspective to generate challenging data, forming a high-quality benchmark. We evaluate a range of multimodal models using MMDT, and our findings reveal a series of vulnerabilities and areas for improvement across these perspectives. This work introduces the first comprehensive and unique safety and trustworthiness evaluation platform for MMFMs, paving the way for developing safer and more reliable MMFMs and systems. Our platform and benchmark are available at https://mmdecodingtrust.github.io/.

Poster
Do LLMs ``know'' internally when they follow instructions?

Juyeon Heo, Christina Heinze-Deml, Oussama Elachqar, Kwan Ho Ryan Chan, Shirley You Ren, Andrew Miller, Udhyakumar Nallasamy, Jaya Narain

展开摘要

Instruction-following is crucial for building AI agents with large language models (LLMs), as these models must adhere strictly to user-provided constraints and guidelines. However, LLMs often fail to follow even simple and clear instructions. To improve instruction-following behavior and prevent undesirable outputs, a deeper understanding of how LLMs' internal states relate to these outcomes is required. In this work, we investigate whether LLMs encode information in their representations that correlates with instruction-following success—a property we term ``knowing internally''. Our analysis identifies a direction in the input embedding space, termed the instruction-following dimension, that predicts whether a response will comply with a given instruction. We find that this dimension generalizes well across unseen tasks but not across unseen instruction types. We demonstrate that modifying representations along this dimension improves instruction-following success rates compared to random changes, without compromising response quality. Further investigation reveals that this dimension is more closely related to the phrasing of prompts rather than the inherent difficulty of the task or instructions. This discovery also suggests explanations for why LLMs sometimes fail to follow clear instructions and why prompt engineering is often effective, even when the content remains largely unchanged. This work provides insight into the internal workings of LLMs' instruction-following, paving the way for reliable LLM agents.

Poster
Multi-Perspective Data Augmentation for Few-shot Object Detection

Anh Khoa Nguyen Vu, Truong Quoc Truong, Vinh-Tiep Nguyen, Thanh Duc Ngo, Thanh-Toan Do, Tam V. Nguyen

展开摘要

Recent few-shot object detection (FSOD) methods have focused on augmenting synthetic samples for novel classes, show promising results to the rise of diffusion models. However, the diversity of such datasets is often limited in representativeness because they lack awareness of typical and hard samples, especially in the context of foreground and background relationships. To tackle this issue, we propose a Multi-Perspective Data Augmentation (MPAD) framework. In terms of foreground-foreground relationships, we propose in-context learning for object synthesis (ICOS) with bounding box adjustments to enhance the detail and spatial information of synthetic samples. Inspired by the large margin principle, support samples play a vital role in defining class boundaries. Therefore, we design a Harmonic Prompt Aggregation Scheduler (HPAS) to mix prompt embeddings at each time step of the generation process in diffusion models, producing hard novel samples. For foreground-background relationships, we introduce a Background Proposal method (BAP) to sample typical and hard backgrounds. Extensive experiments on multiple FSOD benchmarks demonstrate the effectiveness of our approach. Our framework significantly outperforms traditional methods, achieving an average increase of $17.5\%$ in nAP50 over the baseline on PASCAL VOC.

Poster
Homomorphism Counts as Structural Encodings for Graph Learning

Linus Bao, Emily Jin, Michael M. Bronstein, Ismail Ilkan Ceylan, Matthias Lanzinger

展开摘要

Graph Transformers are popular neural networks that extend the well-known Transformer architecture to the graph domain. These architectures operate by applying self-attention on graph nodes and incorporating graph structure through the use of positional encodings (e.g., Laplacian positional encoding) or structural encodings (e.g., random-walk structural encoding). The quality of such encodings is critical, since they provide the necessary \emph{graph inductive biases} to condition the model on graph structure. In this work, we propose \emph{motif structural encoding} (MoSE) as a flexible and powerful structural encoding framework based on counting graph homomorphisms. Theoretically, we compare the expressive power of MoSE to random-walk structural encoding and relate both encodings to the expressive power of standard message passing neural networks. Empirically, we observe that MoSE outperforms other well-known positional and structural encodings across a range of architectures, and it achieves state-of-the-art performance on a widely studied molecular property prediction dataset.

Poster
A new framework for evaluating model out-of-distribution generalisation for the biochemical domain

Raul Fernandez-Diaz, Hoang Thanh Lam, Vanessa López, Denis C. Shields

展开摘要

Quantifying model generalization to out-of-distribution data has been a longstanding challenge in machine learning. Addressing this issue is crucial for leveraging machine learning in scientific discovery, where models must generalize to new molecules or materials. Current methods typically split data into train and test sets using various criteria — temporal, sequence identity, scaffold, or random cross-validation — before evaluating model performance. However, with so many splitting criteria available, existing approaches offer limited guidance on selecting the most appropriate one, and they do not provide mechanisms for incorporating prior knowledge about the target deployment distribution(s). To tackle this problem, we have developed a novel metric, AU-GOOD, which quantifies expected model performance under conditions of increasing dissimilarity between train and test sets, while also accounting for prior knowledge about the target deployment distribution(s), when available. This metric is broadly applicable to biochemical entities, including proteins, small molecules, nucleic acids, or cells; as long as a relevant similarity function is defined for them. Recognizing the wide range of similarity functions used in biochemistry, we propose criteria to guide the selection of the most appropriate metric for partitioning. We also introduce a new partitioning algorithm that generates more challenging test sets, and we propose statistical methods for comparing models based on AU-GOOD. Finally, we demonstrate the insights that can be gained from this framework by applying it to two different use cases: developing predictors for pharmaceutical properties of small molecules, and using protein language models as embeddings to build biophysical property predictors.

Poster
SFESS: Score Function Estimators for $k$-Subset Sampling

Klas Wijk, Ricardo Vinuesa, Hossein Azizpour

展开摘要

Are score function estimators a viable approach to learning with $k$-subset sampling? Sampling $k$-subsets is a fundamental operation that is not amenable to differentiable parametrization, impeding gradient-based optimization. Previous work has favored approximate pathwise gradients or relaxed sampling, dismissing score function estimators because of their high variance. Inspired by the success of score function estimators in variational inference and reinforcement learning, we revisit them for $k$-subset sampling. We demonstrate how to efficiently compute the distribution's score function using a discrete Fourier transform and reduce the estimator's variance with control variates. The resulting estimator provides both $k$-hot samples and unbiased gradient estimates while being applicable to non-differentiable downstream models, unlike existing methods. We validate our approach experimentally and find that it produces results comparable to those of recent state-of-the-art pathwise gradient estimators across a range of tasks.

Poster
How many samples are needed to train a deep neural network?

Pegah Golestaneh, Mahsa Taheri, Johannes Lederer

展开摘要

Even though neural networks have become standard tools in many areas, many important statistical questions remain open. This paper studies the question of how much data are needed to train a ReLU feed-forward neural network. Our theoretical and empirical results suggest that the generalization error of ReLU feed-forward neural networks scales at the rate $1/\sqrt{n}$ in the sample size $n$-rather than the "parametric rate" $1/n$, which might be suggested by traditional statistical theories. Thus, broadly speaking, our results underpin the common belief that neural networks need "many" training samples. Along the way, we also establish new technical insights, such as the first lower bounds of the entropy of ReLU feed-forward networks.

Poster
Generalization Bounds and Model Complexity for Kolmogorov–Arnold Networks

Xianyang Zhang, Huijuan Zhou

展开摘要

Kolmogorov–Arnold Network (KAN) is a network structure recently proposed in Liu et al. (2024) that offers improved interpretability and a more parsimonious design in many science-oriented tasks compared to multi-layer perceptrons. This work provides a rigorous theoretical analysis of KAN by establishing generalization bounds for KAN equipped with activation functions that are either represented by linear combinations of basis functions or lying in a low-rank Reproducing Kernel Hilbert Space (RKHS). In the first case, the generalization bound accommodates various choices of basis functions in forming the activation functions in each layer of KAN and is adapted to different operator norms at each layer. For a particular choice of operator norms, the bound scales with the $l_1$ norm of the coefficient matrices and the Lipschitz constants for the activation functions, and it has no dependence on combinatorial parameters (e.g., number of nodes) outside of logarithmic factors. Moreover, our result does not require the boundedness assumption on the loss function and, hence, is applicable to a general class of regression-type loss functions. In the low-rank case, the generalization bound scales polynomially with the underlying ranks as well as the Lipschitz constants of the activation functions in each layer. These bounds are empirically investigated for KANs trained with stochastic gradient descent on simulated and real data sets. The numerical results demonstrate the practical relevance of these bounds.

Poster
HART: Efficient Visual Generation with Hybrid Autoregressive Transformer

Haotian Tang, Yecheng Wu, Shang Yang, Enze Xie, Junsong Chen, Junyu Chen, Zhuoyang Zhang, Han Cai, Yao Lu, Song Han

展开摘要

We introduce Hybrid Autoregressive Transformer (HART), the first autoregressive (AR) visual generation model capable of directly generating 1024x1024 images, rivaling diffusion models in image generation quality. Existing AR models face limitations due to the poor image reconstruction quality of their discrete tokenizers and the prohibitive training costs associated with generating 1024px images. To address these challenges, we present the hybrid tokenizer, which decomposes the continuous latents from the autoencoder into two components: discrete tokens representing the big picture and continuous tokens representing the residual components that cannot be represented by the discrete tokens. The discrete component is modeled by a scalable-resolution discrete AR model, while the continuous component is learned with a lightweight residual diffusion module with only 37M parameters. Compared with the discrete-only VAR tokenizer, our hybrid approach improves reconstruction FID from 2.11 to 0.30 on MJHQ-30K, leading to a 31% generation FID improvement from 7.85 to 5.38. HART also outperforms state-of-the-art diffusion models in both FID and CLIP score, with 4.5-7.7$\times$ higher throughput and 6.9-13.4$\times$ lower MACs. Our code is open sourced at https://github.com/mit-han-lab/hart.

Poster
VOILA: Evaluation of MLLMs For Perceptual Understanding and Analogical Reasoning

Nilay Yilmaz, Maitreya Patel, Yiran Lawrence Luo, Tejas Gokhale, Chitta Baral, Suren Jayasuriya, Yezhou Yang

展开摘要

Multimodal Large Language Models (MLLMs) have become a powerful tool for integrating visual and textual information. Despite their exceptional performance on visual understanding benchmarks, measuring their ability to reason abstractly across multiple images remains a significant challenge. To address this, we introduce VOILA, a large-scale, open-ended, dynamic benchmark designed to evaluate MLLMs' perceptual understanding and abstract relational reasoning. VOILA employs an analogical mapping approach in the visual domain, requiring models to generate an image that completes an analogy between two given image pairs, reference and application, without relying on predefined choices. Our experiments demonstrate that the analogical reasoning tasks in VOILA present a challenge to MLLMs. Through multi-step analysis, we reveal that current MLLMs struggle to comprehend inter-image relationships and exhibit limited capabilities in high-level relational reasoning. Notably, we observe that performance improves when following a multi-step strategy of least-to-most prompting. Comprehensive evaluations on open-source models and GPT-4o show that on text-based answers, the best accuracy for challenging scenarios is 13% (LLaMa 3.2) and even for simpler tasks is only 29% (GPT-4o), while human performance is significantly higher at 70% across both difficulty levels.

Poster
$\gamma-$MoD: Exploring Mixture-of-Depth Adaptation for Multimodal Large Language Models

Yaxin Luo, Gen Luo, Jiayi Ji, Yiyi Zhou, Xiaoshuai Sun, Zhiqiang Shen, Rongrong Ji

展开摘要

Despite the significant progress in multimodal large language models (MLLMs), their high computational cost remains a barrier to real-world deployment. Inspired by the mixture of depths (MoDs) in natural language processing, we aim to address this limitation from the perspective of ``activated tokens''. Our key insight is that if most tokens are redundant for the layer computation, then can be skipped directly via the MoD layer. However, directly converting the dense layers of MLLMs to MoD layers leads to substantial performance degradation. To address this issue, we propose an innovative MoD adaptation strategy for existing MLLMs called $\gamma$-MoD. In $\gamma$-MoD, a novel metric is proposed to guide the deployment of MoDs in the MLLM, namely rank of attention maps (ARank). Through ARank, we can effectively identify which layer is redundant and should be replaced with the MoD layer. Based on ARank, we further propose two novel designs to maximize the computational sparsity of MLLM while maintaining its performance, namely shared vision-language router and masked routing learning. With these designs, more than 90% dense layers of the MLLM can be effectively converted to the MoD ones. To validate our method, we apply it to three popular MLLMs, and conduct extensive experiments on 9 benchmark datasets. Experimental results not only validate the significant efficiency benefit of $\gamma$-MoD to existing MLLMs but also confirm its generalization ability on various MLLMs. For example, with a minor performance drop, i.e., -1.5%, $\gamma$-MoD can reduce the training and inference time of LLaVA-HR by 31.0% and 53.2%, respectively.

Poster
Forgetting Transformer: Softmax Attention with a Forget Gate

Zhixuan Lin, Evgenii Nikishin, Xu He, Aaron Courville

展开摘要

An essential component of modern recurrent sequence models is the forget gate. While Transformers do not have an explicit recurrent form, we show that a forget gate can be naturally incorporated into Transformers by down-weighting the unnormalized attention scores in a data-dependent way. We name this attention mechanism Forgetting Attention and the resulting model the Forgetting Transformer (FoX). We show that FoX outperforms the Transformer on long-context language modeling, length extrapolation, and short-context downstream tasks, while performing on par with the Transformer on long-context downstream tasks. Moreover, it is compatible with the FlashAttention algorithm and does not require any positional embeddings. Several analyses, including the needle-in-the-haystack test, show that FoX also retains the Transformer's superior long-context capabilities over recurrent sequence models such as Mamba-2, HGRN2, and DeltaNet. We also introduce a "Pro" block design that incorporates some common architectural components in recurrent sequence models and find it significantly improves the performance of both FoX and the Transformer. Our code is available at [`https://github.com/zhixuan-lin/forgetting-transformer`](https://github.com/zhixuan-lin/forgetting-transformer).

Poster
CofCA: A STEP-WISE Counterfactual Multi-hop QA benchmark

Jian Wu, Linyi Yang, Zhen Wang, Manabu Okumura, Yue Zhang

展开摘要

While Large Language Models (LLMs) excel in question-answering (QA) tasks, their real reasoning abilities on multiple evidence retrieval and integration on Multi-hop QA tasks remain less explored. Firstly, LLMs sometimes generate answers that rely on internal memory rather than retrieving evidence and reasoning in the given context, which brings concerns about the evaluation quality of real reasoning abilities. Although previous counterfactual QA benchmarks can separate the internal memory of LLMs, they focus solely on final QA performance, which is insufficient for reporting LLMs' real reasoning abilities. Because LLMs are expected to engage in intricate reasoning processes that involve evidence retrieval and answering a series of sub-questions from given passages. Moreover, current factual Multi-hop QA (MHQA) benchmarks are annotated on open-source corpora such as Wikipedia, although useful for multi-step reasoning evaluation, they show limitations due to the potential data contamination in LLMs' pre-training stage. To address these issues, we introduce the Step-wise and Counterfactual benchmark (CofCA), a novel evaluation benchmark consisting of factual data and counterfactual data that reveals LLMs' real reasoning abilities on multi-step reasoning and reasoning chain evaluation. Our experimental results reveal a significant performance gap of several LLMs between Wikipedia-based factual data and counterfactual data, deeming data contamination issues in existing benchmarks. Moreover, we observe that LLMs usually bypass the correct reasoning chain, showing an inflated multi-step reasoning performance. We believe that our CofCA benchmark will enhance and facilitate the evaluations of trustworthy LLMs.

Poster
Understanding Matrix Function Normalizations in Covariance Pooling through the Lens of Riemannian Geometry

Ziheng Chen, Yue Song, Xiaojun Wu, Gaowen Liu, Nicu Sebe

展开摘要

Global Covariance Pooling (GCP) has been demonstrated to improve the performance of Deep Neural Networks (DNNs) by exploiting second-order statistics of high-level representations. GCP typically performs classification of the covariance matrices by applying matrix function normalization, such as matrix logarithm or power, followed by a Euclidean classifier. However, covariance matrices inherently lie in a Riemannian manifold, known as the Symmetric Positive Definite (SPD) manifold. The current literature does not provide a satisfactory explanation of why Euclidean classifiers can be applied directly to Riemannian features after the normalization of the matrix power. To mitigate this gap, this paper provides a comprehensive and unified understanding of the matrix logarithm and power from a Riemannian geometry perspective. The underlying mechanism of matrix functions in GCP is interpreted from two perspectives: one based on tangent classifiers (Euclidean classifiers on the tangent space) and the other based on Riemannian classifiers. Via theoretical analysis and empirical validation through extensive experiments on fine-grained and large-scale visual classification datasets, we conclude that the working mechanism of the matrix functions should be attributed to the Riemannian classifiers they implicitly respect. The code is available at https://github.com/GitZH-Chen/RiemGCP.git.

Poster