Related papers: Soft Geometric Inductive Bias for Object Centric D…

Modeling complex physical dynamics is a fundamental task in science and engineering. Traditional physics-based models are sample efficient, and interpretable but often rely on rigid assumptions. Furthermore, direct numerical approximation…

Overparameterized shallow neural networks admit substantial parameter redundancy: distinct parameter vectors may represent the same predictor due to hidden-unit permutations, rescalings, and related symmetries. As a result, geometric…

Most invariance-based self-supervised methods rely on single object-centric images (e.g., ImageNet images) for pretraining, learning features that invariant to geometric transformation. However, when images are not object-centric, the…

Digital twin worlds with realistic interactive dynamics presents a new opportunity to develop generalist embodied agents in scannable environments with complex physical behaviors. To this end, we present GDGen (Generalized Representation…

Deep Neural Networks lead the state of the art of computer vision tasks. Despite this, Neural Networks are brittle in that small changes in the input can drastically affect their prediction outcome and confidence. Consequently and…

In this paper, we study the dynamics of gradient descent in learning neural networks for classification problems. Unlike in existing works, we consider the linearly non-separable case where the training data of different classes lie in…

Deep sequence models are said to store atomic facts predominantly in the form of associative memory: a brute-force lookup of co-occurring entities. We identify a dramatically different form of storage of atomic facts that we term as…

Gradient Boosting Machine has proven to be one successful function approximator and has been widely used in a variety of areas. However, since the training procedure of each base learner has to take the sequential order, it is infeasible to…

From early image processing to modern computational imaging, successful models and algorithms have relied on a fundamental property of natural signals: symmetry. Here symmetry refers to the invariance property of signal sets to…

We present a differentiable soft-body physics simulator that can be composed with neural networks as a differentiable layer. In contrast to other differentiable physics approaches that use explicit forward models to define state…

Graph Neural Networks (GNNs) with equivariant properties have emerged as powerful tools for modeling complex dynamics of multi-object physical systems. However, their generalization ability is limited by the inadequate consideration of…

The proliferation of 3D representations, from explicit meshes to implicit neural fields and more, motivates the need for simulators agnostic to representation. We present a data-, mesh-, and grid-free solution for elastic simulation for any…

We propose Geometric Clifford Algebra Networks (GCANs) for modeling dynamical systems. GCANs are based on symmetry group transformations using geometric (Clifford) algebras. We first review the quintessence of modern (plane-based) geometric…

Humans intuitively recognize objects' physical properties and predict their motion, even when the objects are engaged in complicated interactions. The abilities to perform physical reasoning and to adapt to new environments, while intrinsic…

While data augmentation is widely used to train symmetry-agnostic models, it remains unclear how quickly and effectively they learn to respect symmetries. We investigate this by deriving a principled measure of equivariance error that, for…

Soft robotic manipulators provide numerous advantages over conventional rigid manipulators in fragile environments such as the marine environment. However, developing analytic inverse models necessary for shape, motion, and force control of…

While neural representations are central to modern deep learning, the conditions governing their geometry and their roles in downstream adaptability remain poorly understood. We develop a framework clearly separating the underlying world,…

This work investigates the use of smooth neural networks for modeling dynamic variations of implicit surfaces under the level set equation (LSE). For this, it extends the representation of neural implicit surfaces to the space-time…

Numerous 6D pose estimation methods have been proposed that employ end-to-end regression to directly estimate the target pose parameters. Since the visible features of objects are implicitly influenced by their poses, the network allows…

Learning a shared policy that guides the locomotion of different agents is of core interest in Reinforcement Learning (RL), which leads to the study of morphology-agnostic RL. However, existing benchmarks are highly restrictive in the…