We propose a novel approach to learning the generative neural fields represented by linear combinations of implicit basis networks.

We propose a novel approach to learning the generative neural fields represented by linear combinations of implicit basis networks. Our algorithm learns basis networks in the form of implicit neural representations and their coefficients in a latent space by either conducting meta-learning or adopting auto-decoding paradigms. The proposed method easily enlarges the capacity of generative neural fields by increasing the number of basis networks while maintaining the size of a network for inference to be small through their weighted model averaging. Consequently, sampling instances using the model is efficient in terms of latency and memory footprint. Moreover, we customize denoising diffusion probabilistic model for a target task to sample latent mixture coefficients, which allows our final model to generate unseen data effectively. Experiments show that our approach achieves competitive generation performance on diverse benchmarks for images, voxel data, and NeRF scenes without sophisticated designs for specific modalities and domains.

We propose a novel approach to learning the generative neural fields represented by linear combinations of implicit basis networks. Our algorithm learns basis networks in the form of implicit neural representations and their coefficients in a latent space by either conducting meta-learning or adopting auto-decoding paradigms. The proposed method easily enlarges the capacity of generative neural fields by increasing the number of basis networks while maintaining the size of a network for inference to be small through their weighted model averaging. Consequently, sampling instances using the model is efficient in terms of latency and memory footprint. Moreover, we customize denoising diffusion probabilistic model for a target task to sample latent mixture coefficients, which allows our final model to generate unseen data effectively.

We propose a novel approach to learning the generative neural fields represented by linear combinations of implicit basis networks. Our algorithm learns basis networks in the form of implicit neural representations and their coefficients in a latent space by either conducting meta-learning or adopting auto-decoding paradigms. The proposed method easily enlarges the capacity of generative neural fields by increasing the number of basis networks while maintaining the size of a network for inference to be small through their weighted model averaging. Consequently, sampling instances using the model is efficient in terms of latency and memory footprint. Moreover, we customize denoising diffusion probabilistic model for a target task to sample latent mixture coefficients, which allows our final model to generate unseen data effectively. Experiments show that our approach achieves competitive generation performance on diverse benchmarks for images, voxel data, and NeRF scenes without sophisticated designs for specific modalities and domains.

Multi-interaction systems abound in nature, from colloidal suspensions to gene regulatory circuits. These systems can produce complex dynamics and graph neural networks have been proposed as a method to extract underlying interactions and predict how systems will evolve. The current training and evaluation procedures for these models through the use of synthetic multi-relational datasets however are agnostic to interaction network isomorphism classes, which produce identical dynamics up to initial conditions. We extensively analyse how isomorphism class awareness affects these models, focusing on neural relational inference (NRI) models, which are unique in explicitly inferring interactions to predict dynamics in the unsupervised setting. Specifically, we demonstrate that isomorphism leakage overestimates performance in multi-relational inference and that sampling biases present in the multi-interaction network generation process can impair generalisation. To remedy this, we propose isomorphism-aware synthetic benchmarks for model evaluation. We use these benchmarks to test generalisation abilities and demonstrate the existence of a threshold sampling frequency of isomorphism classes for successful learning. In addition, we demonstrate that isomorphism classes can be utilised through a simple prioritisation scheme to improve model performance, stability during training and reduce training time.

This paper introduces MDP homomorphic networks for deep reinforcement learning. MDP homomorphic networks are neural networks that are equivariant under symmetries in the joint state-action space of an MDP. Current approaches to deep reinforcement learning do not usually exploit knowledge about such structure. By building this prior knowledge into policy and value networks using an equivariance constraint, we can reduce the size of the solution space. We specifically focus on group-structured symmetries (invertible transformations). Additionally, we introduce an easy method for constructing equivariant network layers numerically, so the system designer need not solve the constraints by hand, as is typically done. We construct MDP homomorphic MLPs and CNNs that are equivariant under either a group of reflections or rotations. We show that such networks converge faster than unstructured baselines on CartPole, a grid world and Pong.