ICLR 2025 论文列表

International Conference on Learning Representations

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3,703篇论文

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    38010.3%
  • Poster
    3,11084.0%

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Shot2Story: A New Benchmark for Comprehensive Understanding of Multi-shot Videos

Mingfei Han, Linjie Yang, Xiaojun Chang, Lina Yao, Heng Wang

展开摘要

A short clip of video may contain progression of multiple events and an interesting story line. A human need to capture both the event in every shot and associate them together to understand the story behind it. In this work, we present a new multi-shot video understanding benchmark \dataset with detailed shot-level captions, comprehensive video summaries and question-answering pairs. To facilitate better semantic understanding of videos, we provide captions for both visual signals and human narrations. We design several distinct tasks including single-shot video captioning, multi-shot video summarization, and multi-shot video question answering. Preliminary experiments show some challenges to generate a long and comprehensive video summary for multi-shot videos. Nevertheless, the generated imperfect summaries can already achieve competitive performance on existing video understanding tasks such as video question-answering, promoting an under-explored setting of video understanding with detailed summaries.

Poster
Discrete Copula Diffusion

Anji Liu, Oliver Broadrick, Mathias Niepert, Guy Van den Broeck

展开摘要

Discrete diffusion models have recently shown significant progress in modeling complex data, such as natural languages and DNA sequences. However, unlike diffusion models for continuous data, which can generate high-quality samples in just a few denoising steps, modern discrete diffusion models still require hundreds or even thousands of denoising steps to perform well. In this paper, we identify a fundamental limitation that prevents discrete diffusion models from achieving strong performance with fewer steps -- they fail to capture dependencies between output variables at each denoising step. To address this issue, we provide a formal explanation and introduce a general approach to supplement the missing dependency information by incorporating another deep generative model, termed the copula model. Our method does not require fine-tuning either the diffusion model or the copula model, yet it enables high-quality sample generation with significantly fewer denoising steps. When we apply this approach to autoregressive copula models, the combined model outperforms both models individually in unconditional and conditional text generation. Specifically, the hybrid model achieves better (un)conditional text generation using 8 to 32 times fewer denoising steps than the diffusion model alone. In addition to presenting an effective discrete diffusion generation algorithm, this paper emphasizes the importance of modeling inter-variable dependencies in discrete diffusion.

Poster
Identifiability for Gaussian Processes with Holomorphic Kernels

Ameer Qaqish, Didong Li

展开摘要

Gaussian processes (GPs) are widely recognized for their robustness and flexibility across various domains, including machine learning, time series, spatial statistics, and biomedicine. In addition to their common usage in regression tasks, GP kernel parameters are frequently interpreted in various applications. For example, in spatial transcriptomics, estimated kernel parameters are used to identify spatial variable genes, which exhibit significant expression patterns across different tissue locations. However, before these parameters can be meaningfully interpreted, it is essential to establish their identifiability. Existing studies of GP parameter identifiability have focused primarily on Mat\'ern-type kernels, as their spectral densities allow for more established mathematical tools. In many real-world applications, particuarly in time series analysis, other kernels such as the squared exponential, periodic, and rational quadratic kernels, as well as their combinations, are also widely used. These kernels share the property of being holomorphic around zero, and their parameter identifiability remains underexplored. In this paper, we bridge this gap by developing a novel theoretical framework for determining kernel parameter identifiability for kernels holomorphic near zero. Our findings enable practitioners to determine which parameters are identifiable in both existing and newly constructed kernels, supporting application-specific interpretation of the identifiable parameters, and highlighting non-identifiable parameters that require careful interpretation.

Poster
Teaching LLMs How to Learn with Contextual Fine-Tuning

Younwoo Choi, Muhammad Adil Asif, Ziwen Han, John Willes, Rahul Krishnan

展开摘要

Prompting Large Language Models (LLMs), or providing context on the expected model of operation, is an effective way to steer the outputs of such models to satisfy human desiderata after they have been trained. But in rapidly evolving domains, there is often need to fine-tune LLMs to improve either the kind of knowledge in their memory or their abilities to perform open ended reasoning in new domains. When human's learn new concepts, we often do so by linking the new material that we are studying to concepts we have already learned before. To that end, we ask, "can prompting help us teach LLMs how to learn". In this work, we study a novel generalization of instruction tuning, called contextual fine-tuning, to fine-tune LLMs. Our method leverages instructional prompts designed to mimic human cognitive strategies in learning and problem-solving to guide the learning process during training, aiming to improve the model’s interpretation and understanding of domain-specific knowledge. We empirically demonstrate that this simple yet effective modification improves the ability of LLMs to be fine-tuned rapidly on new datasets both within the medical and financial domains.

Poster
Expand and Compress: Exploring Tuning Principles for Continual Spatio-Temporal Graph Forecasting

Wei Chen, Yuxuan Liang

展开摘要

The widespread deployment of sensing devices leads to a surge in data for spatio-temporal forecasting applications such as traffic flow, air quality, and wind energy. Although spatio-temporal graph neural networks (STGNNs) have achieved success in modeling various static spatio-temporal forecasting scenarios, real-world spatio-temporal data are typically received in a streaming manner, and the network continuously expands with the installation of new sensors. Thus, spatio-temporal forecasting in streaming scenarios faces dual challenges: the inefficiency of retraining models over newly-arrived data and the detrimental effects of catastrophic forgetting over long-term history. To address these challenges, we propose a novel prompt tuning-based continuous forecasting method, **_EAC_**, following two fundamental tuning principles guided by empirical and theoretical analysis: _**e**xpand **a**nd **c**ompress_, which effectively resolve the aforementioned problems with lightweight tuning parameters. Specifically, we integrate the base STGNN with a continuous prompt pool, utilizing stored prompts (\ie, few learnable parameters) in memory, and jointly optimize them with the base STGNN. This method ensures that the model sequentially learns from the spatio-temporal data stream to accomplish tasks for corresponding periods. Extensive experimental results on multiple real-world datasets demonstrate the multi-faceted superiority of **_EAC_** over the state-of-the-art baselines, including effectiveness, efficiency, universality, etc.

Poster
Wavelet Diffusion Neural Operator

Peiyan Hu, Rui Wang, Xiang Zheng, Tao Zhang, Haodong Feng, Ruiqi Feng, Long Wei, Yue Wang, Zhi-Ming Ma, Tailin Wu

展开摘要

Simulating and controlling physical systems described by partial differential equations (PDEs) are crucial tasks across science and engineering. Recently, diffusion generative models have emerged as a competitive class of methods for these tasks due to their ability to capture long-term dependencies and model high-dimensional states. However, diffusion models typically struggle with handling system states with abrupt changes and generalizing to higher resolutions. In this work, we propose Wavelet Diffusion Neural Operator (WDNO), a novel PDE simulation and control framework that enhances the handling of these complexities. WDNO comprises two key innovations. Firstly, WDNO performs diffusion-based generative modeling in the wavelet domain for the entire trajectory to handle abrupt changes and long-term dependencies effectively. Secondly, to address the issue of poor generalization across different resolutions, which is one of the fundamental tasks in modeling physical systems, we introduce multi-resolution training. We validate WDNO on five physical systems, including 1D advection equation, three challenging physical systems with abrupt changes (1D Burgers' equation, 1D compressible Navier-Stokes equation and 2D incompressible fluid), and a real-world dataset ERA5, which demonstrates superior performance on both simulation and control tasks over state-of-the-art methods, with significant improvements in long-term and detail prediction accuracy. Remarkably, in the challenging context of the 2D high-dimensional and indirect control task aimed at reducing smoke leakage, WDNO reduces the leakage by 78% compared to the second-best baseline. The code can be found at https://github.com/AI4Science-WestlakeU/wdno.git.

Poster
Spherical Tree-Sliced Wasserstein Distance

Hoang V. Tran, Thanh Chu, Minh-Khoi Nguyen-Nhat, Huyen Trang Pham, Tam Le, Tan Minh Nguyen

展开摘要

Sliced Optimal Transport (OT) simplifies the OT problem in high-dimensional spaces by projecting supports of input measures onto one-dimensional lines, then exploiting the closed-form expression of the univariate OT to reduce the computational burden of OT. Recently, the Tree-Sliced method has been introduced to replace these lines with more intricate structures, known as tree systems. This approach enhances the ability to capture topological information of integration domains in Sliced OT while maintaining low computational cost. Inspired by this approach, in this paper, we present an adaptation of tree systems on OT problem for measures supported on a sphere. As counterpart to the Radon transform variant on tree systems, we propose a novel spherical Radon transform, with a new integration domain called spherical trees. By leveraging this transform and exploiting the spherical tree structures, we derive closed-form expressions for OT problems on the sphere. Consequently, we obtain an efficient metric for measures on the sphere, named Spherical Tree-Sliced Wasserstein (STSW) distance. We provide an extensive theoretical analysis to demonstrate the topology of spherical trees, the well-definedness and injectivity of our Radon transform variant, which leads to an orthogonally invariant distance between spherical measures. Finally, we conduct a wide range of numerical experiments, including gradient flows and self-supervised learning, to assess the performance of our proposed metric, comparing it to recent benchmarks.

Poster
When does compositional structure yield compositional generalization? A kernel theory.

Samuel Lippl, Kim Stachenfeld

展开摘要

Compositional generalization (the ability to respond correctly to novel combinations of familiar components) is thought to be a cornerstone of intelligent behavior. Compositionally structured (e.g. disentangled) representations support this ability; however, the conditions under which they are sufficient for the emergence of compositional generalization remain unclear. To address this gap, we present a theory of compositional generalization in kernel models with fixed, compositionally structured representations. This provides a tractable framework for characterizing the impact of training data statistics on generalization. We find that these models are limited to functions that assign values to each combination of components seen during training, and then sum up these values ("conjunction-wise additivity"). This imposes fundamental restrictions on the set of tasks compositionally structured kernel models can learn, in particular preventing them from transitively generalizing equivalence relations. Even for compositional tasks that they can learn in principle, we identify novel failure modes in compositional generalization (memorization leak and shortcut bias) that arise from biases in the training data. Finally, we empirically validate our theory, showing that it captures the behavior of deep neural networks (convolutional networks, residual networks, and Vision Transformers) trained on a set of compositional tasks with similarly structured data. Ultimately, this work examines how statistical structure in the training data can affect compositional generalization, with implications for how to identify and remedy failure modes in deep learning models.

Poster
Exploring Learning Complexity for Efficient Downstream Dataset Pruning

Wenyu Jiang, Zhenlong Liu, Zejian Xie, Songxin Zhang, Bingyi Jing, Hongxin Wei

展开摘要

The ever-increasing fine-tuning cost of large-scale pre-trained models gives rise to the importance of dataset pruning, which aims to reduce dataset size while maintaining task performance. However, existing dataset pruning methods require training on the entire dataset, which is impractical for large-scale pre-trained models. In this paper, we propose a straightforward, novel, and training-free hardness score named Distorting-based Learning Complexity (DLC), to identify informative images and instructions from the downstream dataset efficiently. Our method is motivated by the observation that easy samples learned faster can also be learned with fewer parameters. Specifically, we define the Learning Complexity to quantify sample hardness and utilize a lightweight weights masking process for fast estimation, instead of the costly SGD optimization. Based on DLC, we further design a flexible under-sampling strategy with randomness (dubbed FlexRand), replacing the top-K strategy, to alleviate the severe subset distribution shift. Extensive experiments with downstream image and instructions dataset pruning benchmarks demonstrate the effectiveness and efficiency of the proposed approach. In the images pruning benchmark, DLC significantly reduces the pruning time by 35$\times$ while establishing state-of-the-art performance with FlexRand.

Poster
Provable Convergence Bounds for Hybrid Dynamical Sampling and Optimization

Matthew X. Burns, Qingyuan Hou, Michael Huang

展开摘要

Analog dynamical accelerators (DXs) are a growing sub-field in computer architecture research, offering order-of-magnitude gains in power efficiency and latency over traditional digital methods in several machine learning, optimization, and sampling tasks. However, limited-capacity accelerators require hybrid analog/digital algorithms to solve real-world problems, commonly using large-neighborhood local search (LNLS) frameworks. Unlike fully digital algorithms, hybrid LNLS has no non-asymptotic convergence guarantees and no principled hyperparameter selection schemes, particularly limiting cross-device training and inference. In this work, we provide non-asymptotic convergence guarantees for hybrid LNLS by reducing to block Langevin Diffusion (BLD) algorithms. Adapting tools from classical sampling theory, we prove exponential KL-divergence convergence for randomized and cyclic block selection strategies using ideal DXs. With finite device variation, we provide explicit bounds on the 2-Wasserstein bias in terms of step duration, noise strength, and function parameters. Our BLD model provides a key link between established theory and novel computing platforms, and our theoretical results provide a closed-form expression linking device variation, algorithm hyperparameters, and performance.

Poster
Not All Heads Matter: A Head-Level KV Cache Compression Method with Integrated Retrieval and Reasoning

Yu Fu, Zefan Cai, Abedelkadir Asi, Wayne Xiong, Yue Dong, Wen Xiao

展开摘要

Key-Value (KV) caching is a common technique to enhance the computational efficiency of Large Language Models (LLMs), but its memory overhead grows rapidly with input length. Prior work has shown that not all tokens are equally important for text generation, proposing layer-level KV cache compression to selectively retain key information. Recognizing the distinct roles of attention heads in generation, we propose HeadKV, a head-level KV cache compression method, and HeadKV-R2, which leverages a novel contextual reasoning ability estimation for compression. Our approach operates at the level of individual heads, estimating their importance for contextual QA tasks that require both retrieval and reasoning capabilities. Extensive experiments across diverse benchmarks (LongBench, LooGLE), model architectures (e.g., Llama-3-8B-Instruct, Mistral-7B-Instruct), and long-context abilities tests demonstrate that our head-level KV cache compression significantly outperforms strong baselines, particularly in low-resource settings (KV size = 64 & 128). Notably, our method retains just 1.5% of the KV cache while achieving 97% of the performance of the full KV cache on the contextual question answering benchmark.

Poster
MMRole: A Comprehensive Framework for Developing and Evaluating Multimodal Role-Playing Agents

Yanqi Dai, Huanran Hu, Lei Wang, Shengjie Jin, Xu Chen, Zhiwu Lu

展开摘要

Recently, Role-Playing Agents (RPAs) have garnered increasing attention for their potential to deliver emotional value and facilitate sociological research. However, existing studies are primarily confined to the textual modality, unable to simulate humans' multimodal perceptual capabilities. To bridge this gap, we introduce the concept of Multimodal Role-Playing Agents (MRPAs), and propose a comprehensive framework, MMRole, for their development and evaluation, which comprises a personalized multimodal dataset and a robust evaluation approach. Specifically, we construct a large-scale, high-quality dataset, MMRole-Data, consisting of 85 characters, 11K images, and 14K single or multi-turn dialogues. Additionally, we present a robust evaluation approach, MMRole-Eval, encompassing eight metrics across three dimensions, where a reward model is designed to score MRPAs with the constructed ground-truth data for comparison. Moreover, we develop the first specialized MRPA, MMRole-Agent. Extensive evaluation results demonstrate the improved performance of MMRole-Agent and highlight the primary challenges in developing MRPAs, emphasizing the need for enhanced multimodal understanding and role-playing consistency. The data, code, and models are all available at https://github.com/YanqiDai/MMRole.

Poster
SPARTUN3D: Situated Spatial Understanding of 3D World in Large Language Model

Yue Zhang, Zhiyang Xu, Ying Shen, Parisa Kordjamshidi, Lifu Huang

展开摘要

Integrating the 3D world into large language models (3D-based LLMs) has been a promising research direction for 3D scene understanding. However, current 3D-based LLMs fall short in situated understanding due to two key limitations: 1) existing 3D datasets are constructed from a global perspective of the 3D scenes and lack situated context. 2) the architectures of the current 3D-based LLMs lack an explicit mechanism for aligning situated spatial information between 3D representations and natural language, limiting their performance in tasks requiring precise spatial reasoning. In this work, we address these issues by introducing a scalable situated 3D dataset, named Spartun3D, that incorporates various situated spatial information. In addition, we propose a situated spatial alignment module to enhance the learning between 3D visual representations and their corresponding textual descriptions. Our experimental results demonstrate that both our dataset and alignment module enhance situated spatial understanding ability.

Poster
Empowering Users in Digital Privacy Management through Interactive LLM-Based Agents

BOLUN SUN, Yifan Zhou, Haiyun Jiang

展开摘要

This paper presents a novel application of large language models (LLMs) to enhance user comprehension of privacy policies through an interactive dialogue agent. We demonstrate that LLMs significantly outperform traditional models in tasks like Data Practice Identification, Choice Identification, Policy Summarization, and Privacy Question Answering, setting new benchmarks in privacy policy analysis. Building on these findings, we introduce an innovative LLM-based agent that functions as an expert system for processing website privacy policies, guiding users through complex legal language without requiring them to pose specific questions. A user study with 100 participants showed that users assisted by the agent had higher comprehension levels (mean score of 2.6 out of 3 vs. 1.8 in the control group), reduced cognitive load (task difficulty ratings of 3.2 out of 10 vs. 7.8), increased confidence in managing privacy, and completed tasks in less time (5.5 minutes vs. 15.8 minutes). This work highlights the potential of LLM-based agents to transform user interaction with privacy policies, leading to more informed consent and empowering users in the digital services landscape.

Poster
MAESTRO: Masked Encoding Set Transformer with Self-Distillation

Matthew Eric Lee, Jaesik Kim, Matei Ionita, Jonghyun Lee, Michelle L. McKeague, YONGHYUN NAM, Irene Khavin, Yidi Huang, Victoria Fang, Sokratis Apostolidis, Divij Mathew, Shwetank, Ajinkya Pattekar, Zahabia Rangwala, Amit Bar-Or, Benjamin A Fensterheim, Benjamin A. Abramoff, Rennie L. Rhee, Damian Maseda, Allison R Greenplate, John Wherry, Dokyoon Kim

展开摘要

The interrogation of cellular states and interactions in immunology research is an ever-evolving task, requiring adaptation to the current levels of high dimensionality. Cytometry enables high-dimensional profiling of immune cells, but its analysis is hindered by the complexity and variability of the data. We present MAESTRO, a self-supervised set representation learning model that generates vector representations of set-structured data, which we apply to learn immune profiles from cytometry data. Unlike previous studies only learn cell-level representations, whereas MAESTRO uses all of a sample's cells to learn a set representation. MAESTRO leverages specialized attention mechanisms to handle sets of variable number of cells and ensure permutation invariance, coupled with an online tokenizer by self-distillation framework. We benchmarked our model against existing cytometry approaches and other existing machine learning methods that have never been applied in cytometry. Our model outperforms existing approaches in retrieving cell-type proportions and capturing clinically relevant features for downstream tasks such as disease diagnosis and immune cell profiling.

Poster
AgentRefine: Enhancing Agent Generalization through Refinement Tuning

Dayuan Fu, Keqing He, Yejie Wang, Wentao Hong, Zhuoma GongQue, Weihao Zeng, Wei Wang, Jingang Wang, Xunliang Cai, Weiran Xu

展开摘要

Large Language Model (LLM) based agents have proved their ability to perform complex tasks like humans. However, there is still a large gap between open-sourced LLMs and commercial models like the GPT series. In this paper, we focus on improving the agent generalization capabilities of LLMs via instruction tuning. We first observe that the existing agent training corpus exhibits satisfactory results on held-in evaluation sets but fails to generalize to held-out sets. These agent-tuning works face severe formatting errors and are frequently stuck in the same mistake for a long while. We analyze that the poor generalization ability comes from overfitting to several manual agent environments and a lack of adaptation to new situations. They struggle with the wrong action steps and can not learn from the experience but just memorize existing observation-action relations. Inspired by the insight, we propose a novel AgentRefine framework for agent-tuning. The core idea is to enable the model to learn to correct its mistakes via observation in the trajectory. Specifically, we propose an agent synthesis framework to encompass a diverse array of environments and tasks and prompt a strong LLM to refine its error action according to the environment feedback. AgentRefine significantly outperforms state-of-the-art agent-tuning work in terms of generalization ability on diverse agent tasks. It also has better robustness facing perturbation and can generate diversified thought in inference. Our findings establish the correlation between agent generalization and self-refinement and provide a new paradigm for future research.

Poster
SV-RAG: LoRA-Contextualizing Adaptation of MLLMs for Long Document Understanding

Jian Chen, Ruiyi Zhang, Yufan Zhou, Tong Yu, Franck Dernoncourt, Jiuxiang Gu, Ryan A. Rossi, Changyou Chen, Tong Sun

展开摘要

Multimodal large language models (MLLMs) have recently shown great progress in text-rich image understanding, yet they still struggle with complex, multi-page visually-rich documents. Traditional methods using document parsers for retrieval-augmented generation suffer from performance and efficiency limitations, while directly presenting all pages to MLLMs leads to inefficiencies, especially with lengthy ones. In this work, we present a novel framework named **S**elf-**V**isual **R**etrieval-**A**ugmented **G**eneration (SV-RAG), which can broaden horizons of *any* MLLM to support long-document understanding. We demonstrate that **MLLMs themselves can be an effective multimodal retriever** to fetch relevant pages and then answer user questions based on these pages. SV-RAG is implemented with two specific MLLM adapters, one for evidence page retrieval and the other for question answering. Empirical results show state-of-the-art performance on public benchmarks, demonstrating the effectiveness of SV-RAG.

Poster
On Stochastic Contextual Bandits with Knapsacks in Small Budget Regime

Hengquan Guo, Xin Liu

展开摘要

This paper studies stochastic contextual bandits with knapsack constraints (CBwK), where a learner observes a context, takes an action, receives a reward, and incurs a vector of costs at every round. The learner aims to maximize the cumulative rewards across $T$ rounds under the knapsack constraints with an initial budget of $B$. We study CBwK in the small budget regime where the budget $B = \Omega(\sqrt{T})$ and propose an Adaptive and Universal Primal--Dual algorithm (AUPD) that achieves strong regret performance: i) AUPD achieves $\tilde{O}((1 + \frac{\nu^*}{\delta b})\sqrt{T})$ regret under the strict feasibility assumption without any prior information, matching the best-known bounds; ii) AUPD achieves $\tilde{O}(\sqrt{T}+ \frac{\nu^*}{\sqrt{b}}T^{\frac{3}{4}})$ regret without strict feasibility assumption, which, to the best of our knowledge, is the first result in the literature. Here, the parameter $\nu^*$ represents the optimal average reward; $b=B/T$ is the average budget and $\delta b$ is the feasibility/safety margin. We establish these strong results through the adaptive budget-aware design, which effectively balances reward maximization and budget consumption. We provide a new perspective on analyzing budget consumption using the Lyapunov drift method, along with a refined analysis of its cumulative variance. Our theory is further supported by experiments conducted on a large-scale dataset.

Poster
Event-Driven Online Vertical Federated Learning

Ganyu Wang, Boyu Wang, Bin Gu, Charles Ling

展开摘要

Online learning is more adaptable to real-world scenarios in Vertical Federated Learning (VFL) compared to offline learning. However, integrating online learning into VFL presents challenges due to the unique nature of VFL, where clients possess non-intersecting feature sets for the same sample. In real-world scenarios, the clients may not receive data streaming for the disjoint features for the same entity synchronously. Instead, the data are typically generated by an *event* relevant to only a subset of clients. We are the first to identify these challenges in online VFL, which have been overlooked by previous research. To address these challenges, we proposed an event-driven online VFL framework. In this framework, only a subset of clients were activated during each event, while the remaining clients passively collaborated in the learning process. Furthermore, we incorporated *dynamic local regret (DLR)* into VFL to address the challenges posed by online learning problems with non-convex models within a non-stationary environment. We conducted a comprehensive regret analysis of our proposed framework, specifically examining the DLR under non-convex conditions with event-driven online VFL. Extensive experiments demonstrated that our proposed framework was more stable than the existing online VFL framework under non-stationary data conditions while also significantly reducing communication and computation costs.

Poster
Fast unsupervised ground metric learning with tree-Wasserstein distance

Kira Michaela Düsterwald, Samo Hromadka, Makoto Yamada

展开摘要

The performance of unsupervised methods such as clustering depends on the choice of distance metric between features, or ground metric. Commonly, ground metrics are decided with heuristics or learned via supervised algorithms. However, since many interesting datasets are unlabelled, unsupervised ground metric learning approaches have been introduced. One promising option employs Wasserstein singular vectors (WSVs), which emerge when computing optimal transport distances between features and samples simultaneously. WSVs are effective, but can be prohibitively computationally expensive in some applications: $\mathcal{O}(n^2m^2(n \log(n) + m \log(m))$ for $n$ samples and $m$ features. In this work, we propose to augment the WSV method by embedding samples and features on trees, on which we compute the tree-Wasserstein distance (TWD). We demonstrate theoretically and empirically that the algorithm converges to a better approximation of the standard WSV approach than the best known alternatives, and does so with $\mathcal{O}(n^3+m^3+mn)$ complexity. In addition, we prove that the initial tree structure can be chosen flexibly, since tree geometry does not constrain the richness of the approximation up to the number of edge weights. This proof suggests a fast and recursive algorithm for computing the tree parameter basis set, which we find crucial to realising the efficiency gains at scale. Finally, we employ the tree-WSV algorithm to several single-cell RNA sequencing genomics datasets, demonstrating its scalability and utility for unsupervised cell-type clustering problems. These results poise unsupervised ground metric learning with TWD as a low-rank approximation of WSV with the potential for widespread application.

Poster