We propose to represent shapes as the deformation and combination of learnable elementary 3D structures, which are primitives resulting from training over a collection of shapes. We demonstrate that the learned elementary 3D structures lead to clear improvements in 3D shape generation and matching.

Evaluation with added comparison to PEARL, showing meta-training curves on full state pushing (left), ant locomotion (middle), and sparse reward door opening (right). PEARL is more sample-efficient and achieves similar asymptotic performance on dense reward tasks. However, GMPS significantly outperforms PEARL on sparse reward tasks. Test-time extrapolation for dense reward ant locomotion Left: Performance outer updates, as requested by reviewer comparison. GMPS is better able to learn out-ofdistribution 3. Using 500 imitation steps (blue) tasks.

Classical Hamiltonian mechanics has been widely used in machine learning in the form of Hamiltonian Monte Carlo for applications with predetermined force fields. In this work, we explore the potential of deliberately designing force fields for Hamiltonian ODEs, introducing Hamiltonian velocity predictors (HVPs) as a tool for score matching and generative models. We present two innovations constructed with HVPs: Hamiltonian Score Matching (HSM), which estimates score functions by augmenting data via Hamiltonian trajectories, and Hamiltonian Generative Flows (HGFs), a novel generative model that encompasses diffusion models and flow matching as HGFs with zero force fields. We showcase the extended design space of force fields by introducing Oscillation HGFs, a generative model inspired by harmonic oscillators. Our experiments validate our theoretical insights about HSM as a novel score matching metric and demonstrate that HGFs rival leading generative modeling techniques.

Agent-based models (ABMs) are proliferating as decision-making tools across policy areas in transportation, economics, and epidemiology. In these models, a central object of interest is the discrete origin-destination matrix which captures spatial interactions and agent trip counts between locations. Existing approaches resort to continuous approximations of this matrix and subsequent ad-hoc discretisations in order to perform ABM simulation and calibration. This impedes conditioning on partially observed summary statistics, fails to explore the multimodal matrix distribution over a discrete combinatorial support, and incurs discretisation errors. To address these challenges, we introduce a computationally efficient framework that scales linearly with the number of origin-destination pairs, operates directly on the discrete combinatorial space, and learns the agents' trip intensity through a neural differential equation that embeds spatial interactions. Our approach outperforms the prior art in terms of reconstruction error and ground truth matrix coverage, at a fraction of the computational cost. We demonstrate these benefits in large-scale spatial mobility ABMs in Cambridge, UK and Washington, DC, USA.

We unify the theory of optimal control of transport equations with the practice of training and testing of ResNets. Based on this unified viewpoint, we propose a simple yet effective ResNets ensemble algorithm to boost the accuracy of the robustly trained model on both clean and adversarial images. The proposed algorithm consists of two components: First, we modify the base ResNets by injecting a variance specified Gaussian noise to the output of each residual mapping, and it results in a special type of neural stochastic ordinary differential equation. Second, we average over the production of multiple jointly trained modified ResNets to get the final prediction. These two steps give an approximation to the Feynman-Kac formula for representing the solution of a convection-diffusion equation. For the CIFAR10 benchmark, this simple algorithm leads to a robust model with a natural accuracy of 85.62% on clean images and a robust accuracy of 57.94% under the 20 iterations of the IFGSM attack, which outperforms the current state-of-the-art in defending against IFGSM attack on the CIFAR10.

The signature is an infinite graded sequence of statistics known to characterise a stream of data up to a negligible equivalence class. It is a transform which has previously been treated as a fixed feature transformation, on top of which a model may be built. We propose a novel approach which combines the advantages of the signature transform with modern deep learning frameworks. By learning an augmentation of the stream prior to the signature transform, the terms of the signature may be selected in a data-dependent way. More generally, we describe how the signature transform may be used as a layer anywhere within a neural network. In this context it may be interpreted as a pooling operation. We present the results of empirical experiments to back up the theoretical justification.

We thank the reviewers R1, R3 and R4 for their time and for their feedback. Motivation: R1 expresses concern as to the'selling point' of the signature transform, over other transformations; R4 Such occurrences are straightforward to detect with a regression on a few terms in the signature. Conclusion: Both R1 and R4 requested a conclusion. We propose to add the following to the end of the paper. Meanwhile neural networks have enjoyed great empirical success.

Recently, 3D Gaussian Splatting (3DGS) has emerged as a promising technique capable of real-time rendering with high-quality 3D reconstruction.

Object goal navigation requires an agent to navigate to a specified object in an unseen environment based on visual observations and user-specified goals. Human decision-making in navigation is sequential, planning a most likely sequence of actions toward the goal. However, existing ObjectNav methods, both end-to-end learning methods and modular methods, rely on single-step planning. They output the next action based on the current model input, which easily overlooks temporal consistency and leads to myopic planning. To this end, we aim to learn sequence planning for ObjectNav. Specifically, we propose trajectory diffusion to learn the distribution of trajectory sequences conditioned on the current observation and the goal. We utilize DDPM and automatically collected optimal trajectory segments to train the trajectory diffusion. Once the trajectory diffusion model is trained, it can generate a temporally coherent sequence of future trajectory for agent based on its current observations. Experimental results on the Gibson and MP3D datasets demonstrate that the generated trajectories effectively guide the agent, resulting in more accurate and efficient navigation.

The information processing in the brain and embodied agents form a sensory-action loop to interact with the world. An important step in the loop is motion planning which selects motor actions based on the current world state and task need. In goal-directed navigation, the brain chooses and generates motor actions to bring the current state into the goal state. It is unclear about the neural circuit mechanism of motor action selection, nor its underlying theory. The present study formulates the motion planning as a Lie group operator search problem, and uses the 1D rotation group as an example to provide insight into general operator search in neural circuits.