ICLR 2024 Papers

International Conference on Learning Representations

Decision breakdown

2,260papers

Counted from the official paper list; may differ slightly from the number the conference announced.

  • Oral
    863.8%
  • Spotlight
    36716.2%
  • Poster
    1,80780.0%

Browse all papers

Going Beyond Neural Network Feature Similarity: The Network Feature Complexity and Its Interpretation Using Category Theory

Yiting Chen, Zhanpeng Zhou, Junchi Yan

Expand abstract

The behavior of neural networks still remains opaque, and a recently widely noted phenomenon is that networks often achieve similar performance when initialized with different random parameters. This phenomenon has attracted significant attention in measuring the similarity between features learned by distinct networks. However, feature similarity could be vague in describing the same feature since equivalent features hardly exist. In this paper, we expand the concept of equivalent feature and provide the definition of what we call *functionally equivalent features*. These features produce equivalent output under certain transformations. Using this definition, we aim to derive a more intrinsic metric for the so-called *feature complexity* regarding the redundancy of features learned by a neural network at each layer. We offer a formal interpretation of our approach through the lens of category theory, a well-developed area in mathematics. To quantify the feature complexity, we further propose an efficient algorithm named Iterative Feature Merging. Our experimental results validate our ideas and theories from various perspectives. We empirically demonstrate that the functionally equivalence widely exists among different features learned by the same neural network and we could reduce the number of parameters of the network without affecting the performance. We have also drawn several interesting empirical findings, including: 1) the larger the network, the more redundant features it learns; 2) in particular, we show how to prune the networks based on our finding using direct equivalent feature merging, without fine-tuning which is often needed in peer network pruning methods; 3) same structured networks with higher feature complexity achieve better performance; 4) through the layers of a neural network, the feature complexity first increase then decrease; 5) for the image classification task, a group of functionally equivalent features may correspond to a specific semantic meaning. Source code will be made publicly available.

Poster
EMO: EARTH MOVER DISTANCE OPTIMIZATION FOR AUTO-REGRESSIVE LANGUAGE MODELING

Siyu Ren, Zhiyong Wu, Kenny Q. Zhu

Expand abstract

Neural language models are probabilistic models of human text. They are predominantly trained using maximum likelihood estimation (MLE), which is equivalent to minimizing the forward cross-entropy between the empirical data distribution and the model distribution. However, various degeneration phenomena are still widely observed when decoding from the distributions learned by such models. We establish that the forward cross-entropy is suboptimal as a distance metric for aligning human and model distribution due to its (1) recall-prioritization (2) negative diversity ignorance and (3) train-test mismatch. In this paper, we propose Earth Mover Distance Optimization (EMO) for auto-regressive language modeling. EMO capitalizes on the inherent properties of earth mover distance to address the aforementioned challenges. Due to the high complexity of direct computation, we further introduce a feasible upper bound for EMO to ease end-to-end training. Upon extensive evaluation of language models trained using EMO and MLE. We find that EMO demonstrates a consistently better language modeling performance than MLE across domains. Moreover, EMO demonstrates noteworthy enhancements in downstream performance with minimal fine-tuning on merely 25,000 sentences. This highlights the tremendous potential of EMO as a lightweight calibration method for enhancing large-scale pre-trained language models.

Poster
Tackling the Data Heterogeneity in Asynchronous Federated Learning with Cached Update Calibration

Yujia Wang, Yuanpu Cao, Jingcheng Wu, Ruoyu Chen, Jinghui Chen

Expand abstract

Asynchronous federated learning, which enables local clients to send their model update asynchronously to the server without waiting for others, has recently emerged for its improved efficiency and scalability over traditional synchronized federated learning. In this paper, we study how the asynchronous delay affects the convergence of asynchronous federated learning under non-i.i.d. distributed data across clients. Through the theoretical convergence analysis of one representative asynchronous federated learning algorithm under standard nonconvex stochastic settings, we show that the asynchronous delay can largely slow down the convergence, especially with high data heterogeneity. To further improve the convergence of asynchronous federated learning under heterogeneous data distributions, we propose a novel asynchronous federated learning method with a cached update calibration. Specifically, we let the server cache the latest update for each client and reuse these variables for calibrating the global update at each round. We theoretically prove the convergence acceleration for our proposed method under nonconvex stochastic settings. Extensive experiments on several vision and language tasks demonstrate our superior performances compared to other asynchronous federated learning baselines.

Poster
Adaptive Instrument Design for Indirect Experiments

Yash Chandak, Shiv Shankar, Vasilis Syrgkanis, Emma Brunskill

Expand abstract

Indirect experiments provide a valuable framework for estimating treatment effects in situations where conducting randomized control trials (RCTs) is impractical or unethical. Unlike RCTs, indirect experiments estimate treatment effects by leveraging (conditional) instrumental variables, enabling estimation through encouragement and recommendation rather than strict treatment assignment. However, the sample efficiency of such estimators depends not only on the inherent variability in outcomes but also on the varying compliance levels of users with the instrumental variables and the choice of estimator being used, especially when dealing with numerous instrumental variables. While adaptive experiment design has a rich literature for \textit{direct} experiments, in this paper we take the initial steps towards enhancing sample efficiency for \textit{indirect} experiments by adaptively designing a data collection policy over instrumental variables. Our main contribution is a practical computational procedure that utilizes influence functions to search for an optimal data collection policy, minimizing the mean-squared error of the desired (non-linear) estimator. Through experiments conducted in various domains inspired by real-world applications, we showcase how our method can significantly improve the sample efficiency of indirect experiments.

Poster
NfgTransformer: Equivariant Representation Learning for Normal-form Games

Siqi Liu, Luke Marris, Georgios Piliouras, Ian Gemp, Nicolas Heess

Expand abstract

Normal-form games (NFGs) are the fundamental model of *strategic interaction*. We study their representation using neural networks. We describe the inherent equivariance of NFGs --- any permutation of strategies describes an equivalent game --- as well as the challenges this poses for representation learning. We then propose the NfgTransformer architecture that leverages this equivariance, leading to state-of-the-art performance in a range of game-theoretic tasks including equilibrium-solving, deviation gain estimation and ranking, with a common approach to NFG representation. We show that the resulting model is interpretable and versatile, paving the way towards deep learning systems capable of game-theoretic reasoning when interacting with humans and with each other.

Poster
Llemma: An Open Language Model for Mathematics

Zhangir Azerbayev, Hailey Schoelkopf, Keiran Paster, Marco Dos Santos, Stephen Marcus McAleer, Albert Q. Jiang, Jia Deng, Stella Biderman, Sean Welleck

Expand abstract

We present Llemma, a large language model for mathematics. We continue pretraining Code Llama on the Proof-Pile-2, a mixture of scientific papers, web data containing mathematics, and mathematical code, yielding Llemma. On the MATH benchmark Llemma outperforms all known openly released models, as well as the unreleased Minerva model suite on an equi-parameter basis. Moreover, Llemma is capable of tool use and formal theorem proving without any finetuning. We openly release all artifacts, including 7 billion and 34 billion parameter models, the Proof-Pile-2, and code to replicate our experiments.

Poster
Learning from Sparse Offline Datasets via Conservative Density Estimation

Zhepeng Cen, Zuxin Liu, Zitong Wang, Yihang Yao, Henry Lam, Ding Zhao

Expand abstract

Offline reinforcement learning (RL) offers a promising direction for learning policies from pre-collected datasets without requiring further interactions with the environment. However, existing methods struggle to handle out-of-distribution (OOD) extrapolation errors, especially in sparse reward or scarce data settings. In this paper, we propose a novel training algorithm called Conservative Density Estimation (CDE), which addresses this challenge by explicitly imposing constraints on the state-action occupancy stationary distribution. CDE overcomes the limitations of existing approaches, such as the stationary distribution correction method, by addressing the support mismatch issue in marginal importance sampling. Our method achieves state-of-the-art performance on the D4RL benchmark. Notably, CDE consistently outperforms baselines in challenging tasks with sparse rewards or insufficient data, demonstrating the advantages of our approach in addressing the extrapolation error problem in offline RL.

Poster
Unveiling the Unseen: Identifiable Clusters in Trained Depthwise Convolutional Kernels

Zahra Babaiee, Peyman Kiasari, Daniela Rus, Radu Grosu

Expand abstract

Recent advances in depthwise-separable convolutional neural networks (DS-CNNs) have led to novel architectures, that surpass the performance of classical CNNs, by a considerable scalability and accuracy margin. This paper reveals another striking property of DS-CNN architectures: discernible and explainable patterns emerge in their trained depthwise convolutional kernels in all layers. Through an extensive analysis of millions of trained filters, with different sizes and from various models, we employed unsupervised clustering with autoencoders, to categorize these filters. Astonishingly, the patterns converged into a few main clusters, each resembling the difference of Gaussian (DoG) functions, and their first and second-order derivatives. Notably, we classify over 95\% and 90\% of the filters from state-of-the-art ConvNeXtV2 and ConvNeXt models, respectively. This finding is not merely a technological curiosity; it echoes the foundational models neuroscientists have long proposed for the vision systems of mammals. Our results thus deepen our understanding of the emergent properties of trained DS-CNNs and provide a bridge between artificial and biological visual processing systems. More broadly, they pave the way for more interpretable and biologically-inspired neural network designs in the future.

Poster
Towards Non-Asymptotic Convergence for Diffusion-Based Generative Models

Gen Li, Yuting Wei, Yuxin Chen, Yuejie Chi

Expand abstract

Diffusion models, which convert noise into new data instances by learning to reverse a Markov diffusion process, have become a cornerstone in contemporary generative modeling. While their practical power has now been widely recognized, the theoretical underpinnings remain far from mature. In this work, we develop a suite of non-asymptotic theory towards understanding the data generation process of diffusion models in discrete time, assuming access to $\ell_2$-accurate estimates of the (Stein) score functions. For a popular deterministic sampler (based on the probability flow ODE), we establish a convergence rate proportional to $1/T$ (with $T$ the total number of steps), improving upon past results; for another mainstream stochastic sampler (i.e., a type of the denoising diffusion probabilistic model), we derive a convergence rate proportional to $1/\sqrt{T}$, matching the state-of-the-art theory. Imposing only minimal assumptions on the target data distribution (e.g., no smoothness assumption is imposed), our results characterize how $\ell_2$ score estimation errors affect the quality of the data generation process. In contrast to prior works, our theory is developed based on an elementary yet versatile non-asymptotic approach without resorting to toolboxes for SDEs and ODEs.

Poster
Locality-Aware Graph Rewiring in GNNs

Federico Barbero, Ameya Velingker, Amin Saberi, Michael M. Bronstein, Francesco Di Giovanni

Expand abstract

Graph Neural Networks (GNNs) are popular models for machine learning on graphs that typically follow the message-passing paradigm, whereby the feature of a node is updated recursively upon aggregating information over its neighbors. While exchanging messages over the input graph endows GNNs with a strong inductive bias, it can also make GNNs susceptible to over-squashing, thereby preventing them from capturing long-range interactions in the given graph. To rectify this issue, graph rewiring techniques have been proposed as a means of improving information flow by altering the graph connectivity. In this work, we identify three desiderata for graph-rewiring: (i) reduce over-squashing, (ii) respect the locality of the graph, and (iii) preserve the sparsity of the graph. We highlight fundamental trade-offs that occur between spatial and spectral rewiring techniques; while the former often satisfy (i) and (ii) but not (iii), the latter generally satisfy (i) and (iii) at the expense of (ii). We propose a novel rewiring framework that satisfies all of (i)--(iii) through a locality-aware sequence of rewiring operations. We then discuss a specific instance of such rewiring framework and validate its effectiveness on several real-world benchmarks, showing that it either matches or significantly outperforms existing rewiring approaches.

Poster
Rayleigh Quotient Graph Neural Networks for Graph-level Anomaly Detection

Xiangyu Dong, Xingyi Zhang, Sibo Wang

Expand abstract

Graph-level anomaly detection has gained significant attention as it finds applications in various domains, such as cancer diagnosis and enzyme prediction. However, existing methods fail to capture the spectral properties of graph anomalies, resulting in unexplainable framework design and unsatisfying performance. In this paper, we re-investigate the spectral differences between anomalous and normal graphs. Our main observation shows a significant disparity in the accumulated spectral energy between these two classes. Moreover, we prove that the accumulated spectral energy of the graph signal can be represented by its Rayleigh Quotient, indicating that the Rayleigh Quotient is a driving factor behind the anomalous properties of graphs. Motivated by this, we propose Rayleigh Quotient Graph Neural Network (RQGNN), the first spectral GNN that explores the inherent spectral features of anomalous graphs for graph-level anomaly detection. Specifically, we introduce a novel framework with two components: the Rayleigh Quotient learning component (RQL) and Chebyshev Wavelet GNN with RQ-pooling (CWGNN-RQ). RQL explicitly captures the Rayleigh Quotient of graphs and CWGNN-RQ implicitly explores the spectral space of graphs. Extensive experiments on 10 real-world datasets show that RQGNN outperforms the best rival by 6.74% in Macro-F1 score and 1.44% in AUC, demonstrating the effectiveness of our framework. Our code is available at https://github.com/xydong127/RQGNN.

Poster
DAM: Towards a Foundation Model for Forecasting

Luke Nicholas Darlow, Qiwen Deng, Ahmed Hassan, Martin Asenov, Rajkarn Singh, Artjom Joosen, Adam Barker, Amos Storkey

Expand abstract

It is challenging to scale time series forecasting models such that they forecast accurately for multiple distinct domains and datasets, all with potentially different underlying collection procedures (e.g., sample resolution), patterns (e.g., periodicity), and prediction requirements (e.g., reconstruction vs. forecasting). We call this general task universal forecasting. Existing methods usually assume that input data is regularly sampled, and they forecast to pre-determined horizons, resulting in failure to generalise outside of the scope of their training. We propose the DAM -- a neural model that takes randomly sampled histories and outputs an adjustable basis composition as a continuous function of time for forecasting to non-fixed horizons. It involves three key components: (1) a flexible approach for using randomly sampled histories from a long-tail distribution, that enables an efficient global perspective of the underlying temporal dynamics while retaining focus on the recent history; (2) a transformer backbone that is trained on these actively sampled histories to produce, as representational output, (3) the basis coefficients of a continuous function of time. We show that a single univariate DAM, trained on 25 time series datasets, either outperformed or closely matched existing SoTA models at multivariate long-term forecasting across 18 datasets, including 8 held-out for zero-shot transfer, even though these models were trained to specialise for each dataset-horizon combination. This single DAM excels at zero-shot transfer and very-long-term forecasting, performs well at imputation, is interpretable via basis function composition and attention, can be tuned for different inference-cost requirements, is robust to missing and irregularly sampled data by design.

Poster
Weakly-supervised Audio Separation via Bi-modal Semantic Similarity

Tanvir Mahmud, Saeed Amizadeh, Kazuhito Koishida, Diana Marculescu

Expand abstract

Conditional sound separation in multi-source audio mixtures without having access to single source sound data during training is a long standing challenge. Existing mix-and-separate based methods suffer from significant performance drop with multi-source training mixtures due to the lack of supervision signal for single source separation cases during training. However, in the case of language-conditional audio separation, we do have access to corresponding text descriptions for each audio mixture in our training data, which can be seen as (rough) representations of the audio samples in the language modality. That raises the curious question of how to generate supervision signal for single-source audio extraction by leveraging the fact that single-source sounding language entities can be easily extracted from the text description. To this end, in this paper, we propose a generic bi-modal separation framework which can enhance the existing unsupervised frameworks to separate single-source signals in a target modality (i.e., audio) using the easily separable corresponding signals in the conditioning modality (i.e., language), without having access to single-source samples in the target modality during training. We empirically show that this is well within reach if we have access to a pretrained joint embedding model between the two modalities (i.e., CLAP). Furthermore, we propose to incorporate our framework into two fundamental scenarios to enhance separation performance. First, we show that our proposed methodology significantly improves the performance of purely unsupervised baselines by reducing the distribution shift between training and test samples. In particular, we show that our framework can achieve 71% boost in terms of Signal-to-Distortion Ratio (SDR) over the baseline, reaching 97.5% of the supervised learning performance. Second, we show that we can further improve the performance of the supervised learning itself by 17% if we augment it by our proposed weakly-supervised framework. Our framework achieves this by making large corpora of unsupervised data available to the supervised learning model as well as utilizing a natural, robust regularization mechanism through weak supervision from the language modality, and hence enabling a powerful semi-supervised framework for audio separation. Code is released at https://github.com/microsoft/BiModalAudioSeparation.

Poster
Deep Reinforcement Learning for Modelling Protein Complexes

Ziqi Gao, Tao Feng, Jiaxuan You, Chenyi Zi, Yan Zhou, Chen Zhang, Jia Li

Expand abstract

Structure prediction of large protein complexes (a.k.a., protein multimer mod- elling, PMM) can be achieved through the one-by-one assembly using provided dimer structures and predicted docking paths. However, existing PMM methods struggle with vast search spaces and generalization challenges: (1) The assembly of a N -chain multimer can be depicted using graph structured data, with each chain represented as a node and assembly actions as edges. Thus the assembly graph can be arbitrary acyclic undirected connected graph, leading to the com- binatorial optimization space of N^(N −2) for the PMM problem. (2) Knowledge transfer in the PMM task is non-trivial. The gradually limited data availability as the chain number increases necessitates PMM models that can generalize across multimers of various chains. To address these challenges, we propose GAPN, a Generative Adversarial Policy Network powered by domain-specific rewards and adversarial loss through policy gradient for automatic PMM prediction. Specifi- cally, GAPN learns to efficiently search through the immense assembly space and optimize the direct docking reward through policy gradient. Importantly, we de- sign a adversarial reward function to enhance the receptive field of our model. In this way, GAPN will simultaneously focus on a specific batch of multimers and the global assembly rules learned from multimers with varying chain numbers. Empirically, we have achieved both significant accuracy (measured by RMSD and TM-Score) and efficiency improvements compared to leading complex mod- eling software. GAPN outperforms the state-of-the-art method (MoLPC) with up to 27% improvement in TM-Score, with a speed-up of 600×.

Poster
Chain-of-Table: Evolving Tables in the Reasoning Chain for Table Understanding

Zilong Wang, Hao Zhang, Chun-Liang Li, Julian Martin Eisenschlos, Vincent Perot, Zifeng Wang, Lesly Miculicich, Yasuhisa Fujii, Jingbo Shang, Chen-Yu Lee, Tomas Pfister

Expand abstract

Table-based reasoning with large language models (LLMs) is a promising direction to tackle many table understanding tasks, such as table-based question answering and fact verification. Compared with generic reasoning, table-based reasoning requires the extraction of underlying semantics from both free-form questions and semi-structured tabular data. Chain-of-Thought and its similar approaches incorporate the reasoning chain in the form of textual context, but it is still an open question how to effectively leverage tabular data in the reasoning chain. We propose the Chain-of-Table framework, where tabular data is explicitly used in the reasoning chain as a proxy for intermediate thoughts. Specifically, we guide LLMs using in-context learning to iteratively generate operations and update the table to represent a tabular reasoning chain. LLMs can therefore dynamically plan the next operation based on the results of the previous ones. This continuous evolution of the table forms a chain, showing the reasoning process for a given tabular problem. The chain carries structured information of the intermediate results, enabling more accurate and reliable predictions. Chain-of-Table achieves new state-of-the-art performance on WikiTQ, FeTaQA, and TabFact benchmarks across multiple LLM choices.

Poster
Curiosity-driven Red-teaming for Large Language Models

Zhang-Wei Hong, Idan Shenfeld, Tsun-Hsuan Wang, Yung-Sung Chuang, Aldo Pareja, James R. Glass, Akash Srivastava, Pulkit Agrawal

Expand abstract

Large language models (LLMs) hold great potential for many natural language applications but risk generating incorrect or toxic content. To probe when an LLM generates unwanted content, the current paradigm is to recruit a $\textit{red team}$ of human testers to design input prompts (i.e., test cases) that elicit undesirable responses from LLMs. However, relying solely on human testers is expensive and time-consuming. Recent works automate red teaming by training a separate red team LLM with reinforcement learning (RL) to generate test cases that maximize the chance of eliciting undesirable responses from the target LLM. However, current RL methods are only able to generate a small number of effective test cases resulting in a low coverage of the span of prompts that elicit undesirable responses from the target LLM. To overcome this limitation, we draw a connection between the problem of increasing the coverage of generated test cases and the well-studied approach of curiosity-driven exploration that optimizes for novelty. Our method of curiosity-driven red teaming (CRT) achieves greater coverage of test cases while mantaining or increasing their effectiveness compared to existing methods. Our method, CRT successfully provokes toxic responses from LLaMA2 model that has been heavily fine-tuned using human preferences to avoid toxic outputs. Code is available at https://github.com/Improbable-AI/curiosity_redteam.

Poster
Neurosymbolic Grounding for Compositional World Models

Atharva Sehgal, Arya Grayeli, Jennifer J. Sun, Swarat Chaudhuri

Expand abstract

We introduce Cosmos, a framework for object-centric world modeling that is designed for compositional generalization (CompGen), i.e., high performance on unseen input scenes obtained through the composition of known visual "atoms." The central insight behind Cosmos is the use of a novel form of neurosymbolic grounding. Specifically, the framework introduces two new tools: (i) neurosymbolic scene encodings, which represent each entity in a scene using a real vector computed using a neural encoder, as well as a vector of composable symbols describing attributes of the entity, and (ii) a neurosymbolic attention mechanism that binds these entities to learned rules of interaction. Cosmos is end-to-end differentiable; also, unlike traditional neurosymbolic methods that require representations to be manually mapped to symbols, it computes an entity's symbolic attributes using vision-language foundation models. Through an evaluation that considers two different forms of CompGen on an established blocks-pushing domain, we show that the framework establishes a new state-of-the-art for CompGen in world modeling. Artifacts are available at: https://trishullab.github.io/cosmos-web/

Poster
The Devil is in the Object Boundary: Towards Annotation-free Instance Segmentation using Foundation Models

Cheng Shi, Sibei Yang

Expand abstract

Foundation models, pre-trained on a large amount of data have demonstrated impressive zero-shot capabilities in various downstream tasks. However, in object detection and instance segmentation, two fundamental computer vision tasks heavily reliant on extensive human annotations, foundation models such as SAM and DINO struggle to achieve satisfactory performance. In this study, we reveal that the devil is in the object boundary, $\textit{i.e.}$, these foundation models fail to discern boundaries between individual objects. For the first time, we probe that CLIP, which has never accessed any instance-level annotations, can provide a highly beneficial and strong instance-level boundary prior in the clustering results of its particular intermediate layer. Following this surprising observation, we propose $\textbf{\textit{Zip}}$ which $\textbf{Z}$ips up CL$\textbf{ip}$ and SAM in a novel classification-first-then-discovery pipeline, enabling annotation-free, complex-scene-capable, open-vocabulary object detection and instance segmentation. Our Zip significantly boosts SAM's mask AP on COCO dataset by 12.5\% and establishes state-of-the-art performance in various settings, including training-free, self-training, and label-efficient finetuning. Furthermore, annotation-free Zip even achieves comparable performance to the best-performing open-vocabulary object detecters using base annotations. Code is released at https://github.com/ChengShiest/Zip-Your-CLIP

Poster
Chameleon: Increasing Label-Only Membership Leakage with Adaptive Poisoning

Harsh Chaudhari, Giorgio Severi, Alina Oprea, Jonathan Ullman

Expand abstract

The integration of Machine Learning (ML) in numerous critical applications introduces a range of privacy concerns for individuals who provide their datasets for ML training purposes. One such privacy risk is Membership Inference (MI), in which an adversary seeks to determine whether a particular data point was included in the training dataset of a model. Current state-of-the-art MI approaches capitalize on access to the model’s predicted confidence scores to successfully perform membership inference, and employ data poisoning to further enhance their effectiveness. In this work, we focus on the less explored and more realistic label-only setting, where the model provides only the predicted label as output. We show that existing label-only attacks are ineffective at inferring membership in the low False Positive Rate (FPR) regime. To address this challenge, we propose a new attack Chameleon that leverages a novel data poisoning strategy and an efficient query selection method to achieve significantly more accurate membership inference than existing label-only attacks, especially for low FPRs.

Poster
LCOT: Linear Circular Optimal Transport

Rocio P Diaz Martin, Ivan Vladimir Medri, Yikun Bai, Xinran Liu, Kangbai Yan, Gustavo Rohde, Soheil Kolouri

Expand abstract

The optimal transport problem for measures supported on non-Euclidean spaces has recently gained ample interest in diverse applications involving representation learning. In this paper, we focus on circular probability measures, i.e., probability measures supported on the unit circle, and introduce a new computationally efficient metric for these measures, denoted as Linear Circular Optimal Transport (LCOT). The proposed metric comes with an explicit linear embedding that allows one to apply Machine Learning (ML) algorithms to the embedded measures and seamlessly modify the underlying metric for the ML algorithm to LCOT. We show that the proposed metric is rooted in the Circular Optimal Transport (COT) and can be considered the linearization of the COT metric with respect to a fixed reference measure. We provide a theoretical analysis of the proposed metric and derive the computational complexities for pairwise comparison of circular probability measures. Lastly, through a set of numerical experiments, we demonstrate the benefits of LCOT in learning representations from circular measures.

Poster