ICLR 2023 论文列表

International Conference on Learning Representations

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1,575篇论文

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Hard-Meta-Dataset++: Towards Understanding Few-Shot Performance on Difficult Tasks

Samyadeep Basu, Megan Stanley, John F Bronskill, Soheil Feizi, Daniela Massiceti

展开摘要

Few-shot classification is the ability to adapt to any new classification task from only a few training examples. The performance of current top-performing few-shot classifiers varies widely across different tasks where they often fail on a subset of `difficult' tasks. This phenomenon has real-world consequences for deployed few-shot systems where safety and reliability are paramount, yet little has been done to understand these failure cases. In this paper, we study these difficult tasks to gain a more nuanced understanding of the limitations of current methods. To this end, we develop a general and computationally efficient algorithm called FastDiffSel to extract difficult tasks from any large-scale vision dataset. Notably, our algorithm can extract tasks at least 20x faster than existing methods enabling its use on large-scale datasets. We use FastDiffSel to extract difficult tasks from Meta-Datasset, a widely-used few-shot classification benchmark, and other challenging large-scale vision datasets including ORBIT, CURE-OR and ObjectNet. These tasks are curated into Hard-MD++, a new few-shot testing benchmark to promote the development of methods that are robust to even the most difficult tasks. We use Hard-MD++ to stress-test an extensive suite of few-shot classification methods and show that state-of-the-art approaches fail catastrophically on difficult tasks. We believe that our extraction algorithm FastDiffSel and Hard-MD++ will aid researchers in further understanding failure modes of few-shot classification models.

Poster
Fairness-aware Contrastive Learning with Partially Annotated Sensitive Attributes

Fengda Zhang, Kun Kuang, Long Chen, Yuxuan Liu, Chao Wu, Jun Xiao

展开摘要

Learning high-quality representation is important and essential for visual recognition. Unfortunately, traditional representation learning suffers from fairness issues since the model may learn information of sensitive attributes. Recently, a series of studies have been proposed to improve fairness by explicitly decorrelating target labels and sensitive attributes. Most of these methods, however, rely on the assumption that fully annotated labels on target variable and sensitive attributes are available, which is unrealistic due to the expensive annotation cost. In this paper, we investigate a novel and practical problem of Fair Unsupervised Representation Learning with Partially annotated Sensitive labels (FURL-PS). FURL-PS has two key challenges: 1) how to make full use of the samples that are not annotated with sensitive attributes; 2) how to eliminate bias in the dataset without target labels. To address these challenges, we propose a general Fairness-aware Contrastive Learning (FairCL) framework consisting of two stages. Firstly, we generate contrastive sample pairs, which share the same visual information apart from sensitive attributes, for each instance in the original dataset. In this way, we construct a balanced and unbiased dataset. Then, we execute fair contrastive learning by closing the distance between representations of contrastive sample pairs. Besides, we also propose an unsupervised way to balance the utility and fairness of learned representations by feature reweighting. Extensive experimental results illustrate the effectiveness of our method in terms of fairness and utility, even with very limited sensitive attributes and serious data bias.

Poster
Which Layer is Learning Faster? A Systematic Exploration of Layer-wise Convergence Rate for Deep Neural Networks

Yixiong Chen, Alan Yuille, Zongwei Zhou

展开摘要

The deeply hierarchical structures enable deep neural networks (DNNs) to fit extremely complex target functions. However, the complex interaction between layers also makes the learning process of a particular layer poorly understood. This work demonstrates that the shallower layers of DNNs tend to converge faster than the deeper layers. We call this phenomenon Layer Convergence Bias. We also uncover the fundamental reason behind this phenomenon: Flatter local minima of shallower layers make their gradients more stable and predictive, allowing for faster training. Another surprising result is that the shallower layers tend to learn the low-frequency components of the target function, while the deeper layers usually learn the high-frequency components. It is consistent with the recent discovery that DNNs learn lower frequency objects faster.

Poster
A Closer Look at Model Adaptation using Feature Distortion and Simplicity Bias

Puja Trivedi, Danai Koutra, Jayaraman J. Thiagarajan

展开摘要

Advances in the expressivity of pretrained models have increased interest in the design of adaptation protocols which enable safe and effective transfer learning. Going beyond conventional linear probing (LP) and fine tuning (FT) strategies, protocols that can effectively control feature distortion, i.e., the failure to update features orthogonal to the in-distribution, have been found to achieve improved out-of-distribution generalization (OOD). In order to limit this distortion, the LP+FT protocol, which first learns a linear probe and then uses this initialization for subsequent FT, was proposed. However, in this paper, we find when adaptation protocols (LP, FT, LP+FT) are also evaluated on a variety of safety objectives (e.g., calibration, robustness, etc.), a complementary perspective to feature distortion is helpful to explain protocol behavior. To this end, we study the susceptibility of protocols to simplicity bias (SB), i.e. the well-known propensity of deep neural networks to rely upon simple features, as SB has recently been shown to underlie several problems in robust generalization. Using a synthetic dataset, we demonstrate the susceptibility of existing protocols to SB. Given the strong effectiveness of LP+FT, we then propose modified linear probes that help mitigate SB, and lead to better initializations for subsequent FT. We verify the effectiveness of the proposed LP+FT variants for decreasing SB in a controlled setting, and their ability to improve OOD generalization and safety on three adaptation datasets.

Top-25%
Robust and Controllable Object-Centric Learning through Energy-based Models

Ruixiang Zhang, Tong Che, Boris Ivanovic, Renhao Wang, Marco Pavone, Yoshua Bengio, Liam Paull

展开摘要

Humans are remarkably good at understanding and reasoning about complex visual scenes. The capability of decomposing low-level observations into discrete objects allows us to build a grounded abstract representation and identify the compositional structure of the world. Thus it is a crucial step for machine learning models to be capable of inferring objects and their properties from visual scene without explicit supervision. However, existing works on object-centric representation learning are either relying on tailor-made neural network modules or assuming sophisticated models of underlying generative and inference processes. In this work, we present EGO, a conceptually simple and general approach to learning object-centric representation through energy-based model. By forming a permutation-invariant energy function using vanilla attention blocks that are readily available in Transformers, we can infer object-centric latent variables via gradient-based MCMC methods where permutation equivariance is automatically guaranteed. We show that EGO can be easily integrated into existing architectures, and can effectively extract high-quality object-centric representations, leading to better segmentation accuracy and competitive downstream task performance. We empirically evaluate the robustness of the learned representation from EGO against distribution shift. Finally, we demonstrate the effectiveness of EGO in systematic compositional generalization, by recomposing learned energy functions for novel scene generation and manipulation.

Poster
That Label's got Style: Handling Label Style Bias for Uncertain Image Segmentation

Kilian Zepf, Eike Petersen, Jes Frellsen, Aasa Feragen

展开摘要

Segmentation uncertainty models predict a distribution over plausible segmentations for a given input, which they learn from the annotator variation in the training set. However, in practice these annotations can differ systematically in the way they are generated, for example through the use of different labeling tools. This results in datasets that contain both data variability and differing label styles. In this paper, we demonstrate that applying state-of-the-art segmentation uncertainty models on such datasets can lead to model bias caused by the different label styles. We present an updated modelling objective conditioning on labeling style for aleatoric uncertainty estimation, and modify two state-of-the-art-architectures for segmentation uncertainty accordingly. We show with extensive experiments that this method reduces label style bias, while improving segmentation performance, increasing the applicability of segmentation uncertainty models in the wild. We curate two datasets, with annotations in different label styles, which we will make publicly available along with our code upon publication.

Poster
Safe Exploration Incurs Nearly No Additional Sample Complexity for Reward-Free RL

Ruiquan Huang, Jing Yang, Yingbin Liang

展开摘要

Reward-free reinforcement learning (RF-RL), a recently introduced RL paradigm, relies on random action-taking to explore the unknown environment without any reward feedback information. While the primary goal of the exploration phase in RF-RL is to reduce the uncertainty in the estimated model with minimum number of trajectories, in practice, the agent often needs to abide by certain safety constraint at the same time. It remains unclear how such safe exploration requirement would affect the corresponding sample complexity in order to achieve the desired optimality of the obtained policy in planning. In this work, we make a first attempt to answer this question. In particular, we consider the scenario where a safe baseline policy is known beforehand, and propose a unified Safe reWard-frEe ExploraTion (SWEET) framework. We then particularize the SWEET framework to the tabular and the low-rank MDP settings, and develop algorithms coined Tabular-SWEET and Low-rank-SWEET, respectively. Both algorithms leverage the concavity and continuity of the newly introduced truncated value functions, and are guaranteed to achieve zero constraint violation during exploration with high probability. Furthermore, both algorithms can provably find a near-optimal policy subject to any constraint in the planning phase. Remarkably, the sample complexities under both algorithms match or even outperform the state of the art in their constraint-free counterparts up to some constant factors, proving that safety constraint hardly increases the sample complexity for RF-RL.

Poster
Ordered GNN: Ordering Message Passing to Deal with Heterophily and Over-smoothing

Yunchong Song, Chenghu Zhou, Xinbing Wang, Zhouhan Lin

展开摘要

Most graph neural networks follow the message passing mechanism. However, it faces the over-smoothing problem when multiple times of message passing is applied to a graph, causing indistinguishable node representations and prevents the model to effectively learn dependencies between farther-away nodes. On the other hand, features of neighboring nodes with different labels are likely to be falsely mixed, resulting in the heterophily problem. In this work, we propose to order the messages passing into the node representation, with specific blocks of neurons targeted for message passing within specific hops. This is achieved by aligning the hierarchy of the rooted-tree of a central node with the ordered neurons in its node representation. Experimental results on an extensive set of datasets show that our model can simultaneously achieve the state-of-the-art in both homophily and heterophily settings, without any targeted design. Moreover, its performance maintains pretty well while the model becomes really deep, effectively preventing the over-smoothing problem. Finally, visualizing the gating vectors shows that our model learns to behave differently between homophily and heterophily settings, providing an explainable graph neural model.

Poster
Personalized Reward Learning with Interaction-Grounded Learning (IGL)

Jessica Maghakian, Paul Mineiro, Kishan Panaganti, Mark Rucker, Akanksha Saran, Cheng Tan

展开摘要

In an era of countless content offerings, recommender systems alleviate information overload by providing users with personalized content suggestions. Due to the scarcity of explicit user feedback, modern recommender systems typically optimize for the same fixed combination of implicit feedback signals across all users. However, this approach disregards a growing body of work highlighting that (i) implicit signals can be used by users in diverse ways, signaling anything from satisfaction to active dislike, and (ii) different users communicate preferences in different ways. We propose applying the recent Interaction Grounded Learning (IGL) paradigm to address the challenge of learning representations of diverse user communication modalities. Rather than requiring a fixed, human-designed reward function, IGL is able to learn personalized reward functions for different users and then optimize directly for the latent user satisfaction. We demonstrate the success of IGL with experiments using simulations as well as with real-world production traces.

Poster
Bidirectional Language Models Are Also Few-shot Learners

Ajay Patel, Bryan Li, Mohammad Sadegh Rasooli, Noah Constant, Colin Raffel, Chris Callison-Burch

展开摘要

Large language models such as GPT-3 (Brown et al., 2020) can perform arbitrary tasks without undergoing fine-tuning after being prompted with only a few labeled examples. An arbitrary task can be reformulated as a natural language prompt, and a language model can be asked to generate the completion, indirectly performing the task in a paradigm known as prompt-based learning. To date, emergent prompt-based learning capabilities have mainly been demonstrated for unidirectional language models. However, bidirectional language models pre-trained on denoising objectives such as masked language modeling produce stronger learned representations for transfer learning. This motivates the possibility of prompting bidirectional models, but their pre-training objectives have made them largely incompatible with the existing prompting paradigm. We present SAP (Sequential Autoregressive Prompting), a technique that enables the prompting of bidirectional models. Utilizing the machine translation task as a case study, we prompt the bidirectional mT5 model (Xue et al., 2021) with SAP and demonstrate its few-shot and zero-shot translations outperform the few-shot translations of unidirectional models like GPT-3 and XGLM (Lin et al., 2021), despite mT5's approximately 50% fewer parameters. We further show SAP is effective on question answering and summarization. For the first time, our results demonstrate prompt-based learning is an emergent property of a broader class of language models, rather than only unidirectional models.

Poster
Cycle-consistent Masked AutoEncoder for Unsupervised Domain Generalization

Haiyang Yang, Xiaotong Li, Shixiang Tang, Feng Zhu, Yizhou Wang, Meilin Chen, Lei Bai, Rui Zhao, Wanli Ouyang

展开摘要

Self-supervised learning methods undergo undesirable performance drops when there exists a significant domain gap between training and testing scenarios. Therefore, unsupervised domain generalization (UDG) is proposed to tackle the problem, which requires the model to be trained on several different domains without supervision and generalize well on unseen test domains. Existing methods either rely on a cross-domain and semantically consistent image pair in contrastive methods or the reconstruction pair in generative methods, while the precious image pairs are not available without semantic labels. In this paper, we propose a cycle cross-domain reconstruction task for unsupervised domain generalization in the absence of paired images. The cycle cross-domain reconstruction task converts a masked image from one domain to another domain and then reconstructs the original image from the converted images. To preserve the divergent domain knowledge of decoders in the cycle reconstruction task, we propose a novel domain-contrastive loss to regularize the domain information in reconstructed images encoded with the desirable domain style. Qualitative results on extensive datasets illustrate our method improves the state-of-the-art unsupervised domain generalization methods by average $\textbf{+5.59\%}, \textbf{+4.52\%}, \textbf{+4.22\%}, \textbf{+7.02\%}$ on $1\%, 5\%, 10\%, 100\%$ PACS, and $\textbf{+5.08\%}, \textbf{+6.49\%}, \textbf{+1.79\%}, \textbf{+0.53\%}$ on $1\%, 5\%, 10\%, 100\%$ DomainNet, respectively.

Poster
Subsampling in Large Graphs Using Ricci Curvature

Shushan Wu, Huimin Cheng, Jiazhang Cai, Ping Ma, Wenxuan Zhong

展开摘要

In the past decades, many large graphs with millions of nodes have been collected/constructed. The high computational cost and significant visualization difficulty hinder the analysis of large graphs. To overcome the difficulties, researchers have developed many graph subsampling approaches to provide a rough sketch that preserves global properties. By selecting representative nodes, these graph subsampling methods can help researchers estimate the graph statistics, e.g., the number of communities, of the large graph from the subsample. However, the available subsampling methods, e.g., degree node sampler and random walk sampler, tend to leave out minority communities because nodes with high degrees are more likely to be sampled. To overcome the shortcomings of the existing methods, we are motivated to apply the community information hidden in the graph to the subsampling method. Though the community structure is unavailable, community structure information can be obtained by applying geometric methods to a graph. An analog of Ricci curvature in the manifold is defined for the graph, i.e., Ollivier Ricci curvature. Based on the asymptotic results about the within-community edge and between-community edge's OR curvature, we propose a subsampling algorithm based on our theoretical results, the Ollivier-Ricci curvature Gradient-based subsampling (ORG-sub) algorithm. The proposed ORG-sub algorithm has two main contributions: First, ORG-sub provides a rigorous theoretical guarantee that the probability of ORG-sub taking all communities into the final subgraph converges to one. Second, extensive experiments on synthetic and benchmark datasets demonstrate the advantages of our algorithm.

Poster
Expressive Monotonic Neural Networks

Niklas Nolte, Ouail Kitouni, Mike Williams

展开摘要

The monotonic dependence of the outputs of a neural network on some of its inputs is a crucial inductive bias in many scenarios where domain knowledge dictates such behavior. This is especially important for interpretability and fairness considerations. In a broader context, scenarios in which monotonicity is important can be found in finance, medicine, physics, and other disciplines. It is thus desirable to build neural network architectures that implement this inductive bias provably. In this work, we propose a weight-constrained architecture with a single residual connection to achieve exact monotonic dependence in any subset of the inputs. The weight constraint scheme directly controls the Lipschitz constant of the neural network and thus provides the additional benefit of robustness. Compared to currently existing techniques used for monotonicity, our method is simpler in implementation and in theory foundations, has negligible computational overhead, is guaranteed to produce monotonic dependence, and is highly expressive. We show how the algorithm is used to train powerful, robust, and interpretable discriminators that achieve competitive performance compared to current state-of-the-art methods across various benchmarks, from social applications to the classification of the decays of subatomic particles produced at the CERN Large Hadron Collider.

Poster
Sparse MoE as the New Dropout: Scaling Dense and Self-Slimmable Transformers

Tianlong Chen, Zhenyu Zhang, AJAY KUMAR JAISWAL, Shiwei Liu, Zhangyang Wang

展开摘要

Despite their remarkable achievement, gigantic transformers encounter significant drawbacks, including exorbitant computational and memory footprints during training, as well as severe collapse evidenced by a high degree of parameter redundancy. Sparsely-activated Mixture-of-Experts (SMoEs) have shown promise to mitigate the issue of training efficiency, yet they are prone to (1) $\textit{redundant experts}$ due to representational collapse; and (2) $\textit{poor expert scalability for inference and downstream fine-tuning}$, primarily due to overfitting of the learned routing policy to the number of activated experts during training. As recent research efforts are predominantly focused on improving routing policies to encourage expert specializations, this work focuses on $\textit{exploring the overlooked scalability bottleneck of SMoEs}$ and leveraging it to effectively $\textbf{scale dense transformers}$. To this end, we propose a new plug-and-play training framework, $\textbf{SMoE-Dropout}$, to enable scaling transformers to better accuracy in their full capacity without collapse. Specifically, SMoE-Dropout consists of a $\textit{randomly initialized and fixed}$ router network to activate experts and gradually increases the activated expert number as training progresses over time. Transformers trained by SMoE-Dropout naturally exhibit a $\textbf{``self-slimmable”}$ property subject to resource availability, offering smooth and consistent performance boosts with an increase in activated experts during inference or fine-tuning. Our extensive experiments across diverse transformer architectures on a variety of tasks demonstrate the superior performance and substantial computation savings of SMoE-Dropout, compared to dense training baselines with equivalent parameter counts. In particular, our trained BERT outperforms its densely trained counterpart with consistent improvements of {$1.03\%$, $0.78\%$, $1.09\%$} on challenging reasoning tasks {$\texttt{ASDiv-A}$, $\texttt{MAWPS}$, $\texttt{SVAMP}$}, respectively. Codes and models are available in https://github.com/VITA-Group/Random-MoE-as-Dropout.

Top-25%
The Modality Focusing Hypothesis: Towards Understanding Crossmodal Knowledge Distillation

Zihui Xue, Zhengqi Gao, Sucheng Ren, Hang Zhao

展开摘要

Crossmodal knowledge distillation (KD) extends traditional knowledge distillation to the area of multimodal learning and demonstrates great success in various applications. To achieve knowledge transfer across modalities, a pretrained network from one modality is adopted as the teacher to provide supervision signals to a student network learning from the other modality. In contrast to the empirical success reported in prior works, the working mechanism of crossmodal KD remains a mystery. In this paper, we present a thorough understanding of crossmodal KD. We begin by providing two failure cases and demonstrate that KD is not a universal cure in crossmodal knowledge transfer. We then present the modality Venn diagram to understand modality relationships and the modality focusing hypothesis revealing the decisive factor in the efficacy of crossmodal KD. Experimental results on 6 multimodal datasets help justify our hypothesis, diagnose failure cases, and point directions to improve crossmodal knowledge transfer in the future.

Top-5%
Advancing Radiograph Representation Learning with Masked Record Modeling

Hong-Yu Zhou, Chenyu Lian, Liansheng Wang, Yizhou Yu

展开摘要

Modern studies in radiograph representation learning (R$^2$L) rely on either self-supervision to encode invariant semantics or associated radiology reports to incorporate medical expertise, while the complementarity between them is barely noticed. To explore this, we formulate the self- and report-completion as two complementary objectives and present a unified framework based on masked record modeling (MRM). In practice, MRM reconstructs masked image patches and masked report tokens following a multi-task scheme to learn knowledge-enhanced semantic representations. With MRM pre-training, we obtain pre-trained models that can be well transferred to various radiography tasks. Specifically, we find that MRM offers superior performance in label-efficient fine-tuning. For instance, MRM achieves 88.5% mean AUC on CheXpert using 1% labeled data, outperforming previous R$^2$L methods with 100% labels. On NIH ChestX-ray, MRM outperforms the best performing counterpart by about 3% under small labeling ratios. Besides, MRM surpasses self- and report-supervised pre-training in identifying the pneumonia type and the pneumothorax area, sometimes by large margins.

Poster
A Non-monotonic Self-terminating Language Model

Eugene Choi, Kyunghyun Cho, Cheolhyoung Lee

展开摘要

Recent large-scale neural autoregressive sequence models have shown impressive performances on a variety of natural language generation tasks. However, their generated sequences often exhibit degenerate properties such as non-termination, undesirable repetition, and premature termination, when generated with decoding algorithms such as greedy search, beam search, top-$k$ sampling, and nucleus sampling. In this paper, we focus on the problem of non-terminating sequences resulting from an incomplete decoding algorithm. We first define an incomplete probable decoding algorithm which includes greedy search, top-$k$ sampling, and nucleus sampling, beyond the incomplete decoding algorithm originally put forward by Welleck et al. (2020). We then propose a non-monotonic self-terminating language model, which significantly relaxes the constraint of monotonically increasing termination probability in the originally proposed self-terminating language model by Welleck et al. (2020), to address the issue of non-terminating sequences when using incomplete probable decoding algorithms. We prove that our proposed model prevents non-terminating sequences when using not only incomplete probable decoding algorithms but also beam search. We empirically validate our model on sequence completion tasks with various architectures.

Poster
Minimum Variance Unbiased N:M Sparsity for the Neural Gradients

Brian Chmiel, Itay Hubara, Ron Banner, Daniel Soudry

展开摘要

In deep learning, fine-grained N:M sparsity reduces the data footprint and bandwidth of a General Matrix multiply (GEMM) up to x2, and doubles throughput by skipping computation of zero values. So far, it was mainly only used to prune weights to accelerate the forward and backward phases. We examine how this method can be used also for the neural gradients (i.e. loss gradients with respect to the intermediate neural layer outputs). To this end, we first establish a tensor-level optimality criteria. Previous works aimed to minimize the mean-square-error (MSE) of each pruned block. We show that while minimization of the MSE works fine for pruning the weights and activations, it catastrophically fails for the neural gradients. Instead, we show that accurate pruning of the neural gradients requires an unbiased minimum-variance pruning mask. We design such specialized masks, and find that in most cases, 1:2 sparsity is sufficient for training, and 2:4 sparsity is usually enough when this is not the case. Further, we suggest combining several such methods together in order to potentially speed up training even more. A reference implementation is supplied in the supplementary material.

Top-25%
AANG : Automating Auxiliary Learning

Lucio M. Dery, Paul Michel, Mikhail Khodak, Graham Neubig, Ameet Talwalkar

展开摘要

Auxiliary objectives, supplementary learning signals that are introduced to help aid learning on data-starved or highly complex end-tasks, are commonplace in machine learning. Whilst much work has been done to formulate useful auxiliary objectives, their construction is still an art which proceeds by slow and tedious hand-design. Intuition for how and when these objectives improve end-task performance has also had limited theoretical backing. In this work, we present an approach for automatically generating a suite of auxiliary objectives. We achieve this by deconstructing existing objectives within a novel unified taxonomy, identifying connections between them, and generating new ones based on the uncovered structure. Next, we theoretically formalize widely-held intuitions about how auxiliary learning improves generalization on the end-task. This leads us to a principled and efficient algorithm for searching the space of generated objectives to find those most useful to a specified end-task. With natural language processing (NLP) as our domain of study, we demonstrate that our automated auxiliary learning pipeline leads to strong improvements over competitive baselines across continued training experiments on a pre-trained model on 5 NLP end-tasks.

Top-25%
A Stable and Scalable Method for Solving Initial Value PDEs with Neural Networks

Marc Anton Finzi, Andres Potapczynski, Matthew Choptuik, Andrew Gordon Wilson

展开摘要

Unlike conventional grid and mesh based methods for solving partial differential equations (PDEs), neural networks have the potential to break the curse of dimensionality, providing approximate solutions to problems where using classical solvers is difficult or impossible. While global minimization of the PDE residual over the network parameters works well for boundary value problems, catastrophic forgetting impairs applicability to initial value problems (IVPs). In an alternative local-in-time approach, the optimization problem can be converted into an ordinary differential equation (ODE) on the network parameters and the solution propagated forward in time; however, we demonstrate that current methods based on this approach suffer from two key issues. First, following the ODE produces an uncontrolled growth in the conditioning of the problem, ultimately leading to unacceptably large numerical errors. Second, as the ODE methods scale cubically with the number of model parameters, they are restricted to small neural networks, significantly limiting their ability to represent intricate PDE initial conditions and solutions. Building on these insights, we develop Neural-IVP, an ODE based IVP solver which prevents the network from getting ill-conditioned and runs in time linear in the number of parameters, enabling us to evolve the dynamics of challenging PDEs with neural networks.

Poster